Finite Group Databasebeta

← #36312637

Subgroups — #36312637

Order 21248.

7094 conjugacy classes of subgroups.

The subgroup lattice has 2028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921552C213yesmaximal, complemented
2#24921550C211yesmaximal, characteristic, complemented
3#24921541C213yesmaximal, complemented
4#24921539C211yesmaximal, characteristic, complemented
5#24921459C211yesmaximal, characteristic, complemented
6#24921455C213yesmaximal, complemented
7#24921451C213yesmaximal, complemented
8#24921449C211yesmaximal, characteristic, complemented
9#24921324C213yesmaximal, complemented
10#24921322C213yesmaximal, complemented
11#24921270C211yesmaximal, characteristic, complemented
12#24921231C211yesmaximal, characteristic, complemented
13#24921165C213yesmaximal, complemented
14#24921163C213yesmaximal, complemented
15#24921113C211yesmaximal, characteristic, complemented
16#24921109C211yesmaximal, characteristic, complemented
17#24921080C211yesmaximal, characteristic, complemented
18#24921078C213yesmaximal, complemented
19#24921076C213yesmaximal, complemented
20#24921061C211yesmaximal, characteristic, complemented
21#24921054C213yesmaximal, complemented
22Q8×#13050590C211yesmaximal, characteristic, complemented
23#24921041C213yesmaximal, complemented
24#24920894C213yesmaximal, complemented
25#24920888C213yesmaximal, complemented
26#24920757C213yesmaximal, complemented
27#24920756C213yesmaximal, complemented
28C4×#14581840C211yesmaximal, characteristic, complemented
29C4×#14581839C211yesmaximal, characteristic, complemented
30C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
31C83×#3482C211yesmaximal, characteristic, complemented
32C2×#14581840C2211yescharacteristic
33C2×#14581839C2211yescharacteristic
34C22×Q8×D83C2211yescharacteristic
35#19128435C2216yescomplemented
36#19128434C2213yescomplemented
37#19128433C2213yescomplemented
38Q8×Dic166C2211yescharacteristic, complemented
39#19128431C2213yescomplemented
40#19128429C2213yescomplemented
41#19128429C2213yescomplemented
42#19128428C2213yescomplemented
43#19128428C2213yescomplemented
44#19128428C2216yescomplemented
45#19128427C2211yescharacteristic, complemented
46#19128427C2211yescharacteristic, complemented
47#19128426C2213yescomplemented
48#19128424C2213yescomplemented
49#19128423C2213yescomplemented
50#19128422C2213yescomplemented
51#19128420C2213yescomplemented
52#19128419C2216yescomplemented
53#19128419C2213yescomplemented
54#19128418C2216yescomplemented
55#19128418C2216yescomplemented
56#19128412C2213yes—
57#19128411C2213yes—
58#19128409C2213yes—
59#19128409C2213yescomplemented
60#19128407C2216yes—
61#19128406C2213yes—
62#19128406C2213yescomplemented
63#19128405C2216yes—
64#19128405C2216yescomplemented
65#19128404C2213yes—
66#19128402C2216yes—
67#19128401C2213yes—
68#19128398C2213yes—
69#19128396C2216yes—
70#19128395C2213yes—
71#19128393C2213yes—
72#19128392C2213yescomplemented
73#19128391C2213yes—
74#19128391C2213yescomplemented
75#19128389C2213yescomplemented
76#19128388C2216yes—
77#19128387C2216yescomplemented
78#19128386C2213yes—
79#19128384C2216yes—
80#19128384C2216yescomplemented
81#19128370C2211yescharacteristic, complemented
82#19128369C2213yescomplemented
83Q8×D332C2211yescharacteristic
84D4×Dic166C2213yes—
85#19128366C2213yes—
86Q8×C22⋊D83C2211yescharacteristic
87Q8×C22⋊D83C2211yescharacteristic
88Q8×C22⋊D83C2211yescharacteristic, complemented
89#19128364C2213yes—
90#19128364C2213yes—
91#19128364C2213yescomplemented
92#19128363C2211yescharacteristic
93#19128363C2211yescharacteristic, complemented
94#19128362C2211yescharacteristic
95#19128361C2213yes—
96#19128360C2213yes—
97#19128360C2213yescomplemented
98#19128359C2213yes—
99#19128359C2213yescomplemented
100#19128358C2211yescharacteristic
101#19128357C2213yes—
102#19128355C2213yes—
103#19128352C2213yes—
104#19128351C2213yes—
105#19128350C2216yes—
106#19128349C2216yes—
107#19128331C2213yes—
108#19128328C2213yes—
109#19128325C2213yescomplemented
110#19128324C2213yescomplemented
111#19128321C2216yescomplemented
112#19128320C2213yescomplemented
113#19128319C2216yescomplemented
114#19128318C2213yescomplemented
115#19128314C2213yescomplemented
116#19128312C2213yescomplemented
117#19128311C2213yescomplemented
118#19128311C2213yescomplemented
119#19128310C2216yescomplemented
120#19128308C2216yescomplemented
121#19128299C2216yes—
122#19128297C2216yes—
123#19128294C2216yes—
124#19128292C2216yes—
125#19128281C2213yes—
126#19128280C2213yes—
127#19128276C2213yes—
128#19128274C2213yes—
129#19128274C2213yes—
130#19128271C2213yes—
131#19128258C2213yescomplemented
132#19128257C2213yes—
133#19128255C2213yes—
134#19128255C2213yes—
135#19128255C2213yes—
136#19128255C2213yescomplemented
137#19128255C2216yescomplemented
138#19128255C2213yescomplemented
139#19128254C2213yes—
140#19128254C2216yescomplemented
141#19128253C2213yes—
142#19128250C2213yes—
143#19128248C2213yes—
144#19128248C2213yes—
145#19128248C2213yes—
146#19128247C2213yes—
147#19128246C2213yes—
148#19128238C2213yes—
149#19128238C2213yes—
150#19128238C2213yescomplemented
151#19128236C2213yes—
152#19128235C2213yes—
153#19128235C2213yescomplemented
154#19128234C2216yes—
155#19128234C2216yes—
156#19128233C2213yes—
157#19128233C2213yes—
158#19128233C2213yescomplemented
159#19128231C2213yes—
160#19128231C2213yes—
161#19128231C2213yes—
162#19128231C2213yes—
163#19128231C2216yescomplemented
164#19128230C2213yes—
165#19128229C2216yes—
166#19128229C2213yes—
167#19128229C2213yes—
168#19128229C2213yes—
169#19128229C2213yes—
170#19128229C2216yescomplemented
171#19128228C2216yes—
172#19128214C2213yes—
173#19128213C2213yes—
174#19128211C2213yes—
175#19128210C2213yes—
176#19128210C2213yes—
177#19128210C2211yescharacteristic
178#19128210C2213yes—
179#19128209C2216yes—
180#19128208C2213yes—
181#19128184C2211yescharacteristic, complemented
182#19128183C2213yes—
183#19128183C2211yescharacteristic, complemented
184#19128182C2213yes—
185#19128182C2213yescomplemented
186#19128181C2213yes—
187#19128180C2213yes—
188#19128180C2213yescomplemented
189#19128179C2211yescharacteristic, complemented
190#19128178C2213yescomplemented
191#19128177C2211yescharacteristic
192#19128177C2211yescharacteristic
193#19128177C2211yescharacteristic, complemented
194#19128177C2213yescomplemented
195C4×#13050591C2213yes—
196C4×#13050591C2211yescharacteristic, complemented
197C4×#13050590C2213yes—
198C4×#13050590C2213yes—
199C4×#13050590C2213yes—
200C4×#13050590C2213yes—
201C4×#13050590C2213yes—
202C4×#13050590C2213yescomplemented
203#19128169C2216yes—
204C4×#13050589C2213yes—
205C4×#13050589C2216yes—
206C4×#13050589C2213yescomplemented
207C2×Q8×Dic83C2211yescharacteristic
208C2×C4×Dic166C2213yes—
209C2×C4×Dic166C2213yescomplemented
210C2×#14581757C2213yes—
211C4×Q8×D83C2213yes—
212C4×Q8×D83C2211yescharacteristic
213C4×Q8×D83C2211yescharacteristic
214C4×Q8×D83C2213yes—
215C4×Q8×D83C2211yescharacteristic
216C4×Q8×D83C2213yes—
217C4×Q8×D83C2211yescharacteristic
218C4×Q8×D83C2213yes—
219C4×Q8×D83C2211yescharacteristic, complemented
220C4×Q8×D83C2213yescomplemented
221C2×C4⋊C4×D83C2213yes—
222C2×C42×D83C2213yes—
223#557×C83C2211yescharacteristic, complemented
224#556×C83C2213yescomplemented
225#552×C83C2213yes—
226#552×C83C2213yescomplemented
227D4×Q8×C83C2211yescharacteristic
228#548×C83C2211yescharacteristic
229#548×C83C2211yescharacteristic, complemented
230#547×C83C2213yes—
231#533×C83C2213yescomplemented
232#529×C83C2213yes—
233#529×C83C2213yescomplemented
234C4×#41×C83C2213yes—
235C4×#41×C83C2211yescharacteristic, complemented
236C2×C4×Q8×C83C2211yescharacteristic
237C2×C4×Q8×C83C2211yescharacteristic, complemented
238#14581840—28no—
239#14581839—28no—
240C2×#13050591C2311yescharacteristic
241C2×#13050591C2313yes—
242C2×#13050590C2313yes—
243C2×#13050590C2313yes—
244C2×#13050590C2311yescharacteristic
245C2×#13050590C2313yes—
246C2×#13050590C2313yes—
247C2×#13050590C2313yes—
248C2×#13050589C2313yes—
249C2×#13050589C2313yes—
250C2×#13050589C2316yes—
251C22×Dic166C2313yes—
252C22×Dic166C2313yes—
253C2×Q8×D83—28no—
254C2×Q8×D83C2311yescharacteristic
255C2×Q8×D83C2313yes—
256C2×Q8×D83C2313yes—
257C2×Q8×D83C2311yescharacteristic
258C2×Q8×D83C2313yes—
259C2×Q8×D83C2311yescharacteristic
260C22×C4×D83C2311yescharacteristic
261C22×C4×D83C2313yes—
262C22×C4×D83C2313yes—
263#14581792C2313yes—
264#14581792C2313yes—
265#14581791C2313yes—
266#14581791C2316yes—
267#14581791C2313yes—
268#14581791C2316yes—
269#14581791C2316yes—
270#14581791C2313yes—
271#14581791C2313yes—
272#14581791C2313yes—
273#14581791C2313yes—
274#14581790C2316yes—
275#14581790C2313yes—
276#14581790C2313yes—
277#14581790C2313yes—
278#14581790C2313yes—
279#14581788C2313yes—
280#14581788C2313yes—
281#14581787C2313yes—
282#14581787C2313yes—
283#14581787C2316yes—
284#14581787C2316yes—
285#14581787C2313yes—
286#14581787C2316yes—
287#14581787C2313yes—
288#14581787C2316yes—
289#14581786C2316yes—
290#14581786C2316yes—
291#14581785C2313yes—
292#14581785C2316yes—
293#14581785C2313yes—
294#14581785C2316yes—
295#14581785C2316yes—
296#14581785C2316yes—
297#14581785C2313yes—
298#14581785C2313yes—
299#14581784C2313yes—
300#14581784C2316yes—
301#14581784C2313yes—
302#14581783C2313yes—
303#14581783C2313yes—
304#14581783C2316yes—
305#14581783C2316yes—
306#14581783C2313yes—
307#14581783C2313yes—
308#14581782C2316yes—
309#14581782C2316yes—
310#14581782C2316yes—
311#14581782C2313yes—
312#14581782C2316yes—
313#14581782C2316yes—
314#14581782C2313yes—
315#14581782C2316yes—
316#14581782C2313yes—
317#14581782C2316yes—
318#14581782C2313yes—
319#14581782C2316yes—
320#14581781C2313yes—
321#14581781C2313yes—
322#14581780C2313yes—
323#14581780C2313yes—
324#14581779C2313yes—
325#14581779C2313yes—
326#14581778C2316yes—
327#14581778C2316yes—
328#14581778C2313yes—
329#14581778C2316yes—
330#14581778C2313yes—
331#14581778C2313yes—
332#14581778C2316yes—
333#14581778C2313yes—
334#14581777C2316yes—
335#14581777C2316yes—
336#14581777C2311yescharacteristic
337#14581777C2313yes—
338#14581777C2313yes—
339#14581777C2313yes—
340#14581777C2316yes—
341#14581776C2316yes—
342#14581776C2313yes—
343#14581776C2313yes—
344#14581775C2316yes—
345#14581775C2316yes—
346#14581774C2316yes—
347#14581774C2316yes—
348#14581774C2311yescharacteristic
349#14581774C2313yes—
350#14581774C2313yes—
351#14581774C2313yes—
352#14581774C2316yes—
353#14581773C2313yes—
354#14581773C2316yes—
355#14581773C2313yes—
356#14581772C2316yes—
357#14581772C2313yes—
358#14581772C2313yes—
359#14581772C2313yes—
360#14581772C2313yes—
361#14581772C2313yes—
362#14581772C2313yes—
363#14581771C2316yes—
364#14581771C2313yes—
365#14581771C2313yes—
366#14581771C2313yes—
367#14581771C2313yes—
368#14581770C2316yes—
369#14581770C2316yes—
370#14581770C2316yes—
371#14581770C2316yes—
372#14581770C2316yes—
373#14581770C2316yes—
374#14581770C2313yes—
375#14581770C2313yes—
376#14581770C2316yes—
377#14581770C2311yescharacteristic
378#14581770C2313yes—
379#14581769C2316yes—
380#14581769C2316yes—
381#14581769C2316yes—
382#14581769C2316yes—
383#14581769C2316yes—
384#14581769C2313yes—
385#14581769C2313yes—
386#14581769C2313yes—
387#14581769C2311yescharacteristic
388#14581768C2313yes—
389#14581768C2316yes—
390#14581768C2313yes—
391#14581768C2313yes—
392#14581768C2313yes—
393#14581768C2313yes—
394#14581768C2313yes—
395#14581767C2313yes—
396#14581767C2313yes—
397#14581767C2313yes—
398#14581767C2313yes—
399#14581766C2313yes—
400#14581766C2313yes—
401#14581765C2316yes—
402#14581765C2313yes—
403#14581765C2313yes—
404#14581765C2316yes—
405#14581765C2316yes—
406#14581765C2311yescharacteristic
407#14581765C2313yes—
408#14581764C2313yes—
409#14581764C2313yes—
410#14581764C2316yes—
411#14581764C2313yes—
412#14581764C2311yescharacteristic
413#14581763C2313yes—
414#14581763C2313yes—
415#14581763C2313yes—
416#14581763C2313yes—
417#14581762C2313yes—
418#14581762C2311yescharacteristic
419#14581760C2311yescharacteristic
420#14581760C2313yes—
421Q8×Dic83C2313yes—
422Q8×Dic83C2311yescharacteristic
423Q8×Dic83C2311yescharacteristic
424Q8×Dic83C2311yescharacteristic
425Q8×Dic83C2313yes—
426Q8×Dic83C2313yes—
427Q8×Dic83C2311yescharacteristic
428Q8×Dic83C2313yes—
429C4×Dic166C2313yes—
430C4×Dic166C2313yes—
431C4×Dic166C2313yes—
432C4×Dic166C2316yes—
433C4×Dic166C2316yes—
434C4×Dic166C2313yes—
435C4×Dic166C2313yes—
436C4×Dic166C2313yes—
437C4×Dic166C2313yes—
438C4×Dic166C2313yes—
439C4×Dic166C2316yes—
440C4×Dic166C2313yes—
441C4×Dic166C2313yes—
442C4×Dic166C2313yes—
443C4×Dic166C2313yes—
444C4×Dic166C2313yes—
445C4×Dic166C2316yes—
446C4×Dic166C2313yes—
447C4×Dic166C2313yes—
448C4×Dic166C2313yes—
449C4×Dic166C2313yes—
450C4×Dic166C2313yes—
451#14581757C2316yes—
452#14581757C2313yes—
453#14581757C2313yes—
454#14581757C2313yes—
455#14581757C2313yes—
456#14581757C2313yes—
457#14581757C2316yes—
458#14581757C2316yes—
459#14581757C2313yes—
460#14581757C2316yes—
461#14581757C2316yes—
462#14581757C2313yes—
463#14581757C2313yes—
464#14581757C2316yes—
465C4×D332C2313yes—
466C4×D332C2313yes—
467C4×D332C2313yes—
468C4×D332C2313yes—
469C4×D332C2313yes—
470C4×D332C2313yes—
471C4×D332C2311yescharacteristic
472C4×D332C2313yes—
473C4×D332C2313yes—
474C4×D332C2313yes—
475C4×D332C2313yes—
476C4×D332C2313yes—
477D4×Dic83C2313yes—
478D4×Dic83C2316yes—
479D4×Dic83C2313yes—
480#14581754C2313yes—
481#14581754C2313yes—
482#14581754C2316yes—
483#14581754C2316yes—
484#14581754C2316yes—
485C4×C22⋊D83C2313yes—
486C4×C22⋊D83C2316yes—
487C4×C22⋊D83C2313yes—
488C4×C22⋊D83C2313yes—
489C4×C22⋊D83C2313yes—
490C4×C22⋊D83C2313yes—
491C4×C22⋊D83C2313yes—
492C4×C22⋊D83C2313yes—
493C4×C22⋊D83C2313yes—
494C4×C22⋊D83C2313yes—
495C4×C22⋊D83C2313yes—
496C4×C22⋊D83C2313yes—
497C4×C22⋊D83C2313yes—
498C4×C22⋊D83C2313yes—
499C4×C22⋊D83C2316yes—
500C4×C22⋊D83C2313yes—
501C4×C22⋊D83C2311yescharacteristic
502C4×C22⋊D83C2311yescharacteristic
503C4×C22⋊D83C2313yes—
504C4×C22⋊D83C2313yes—
505C4×C22⋊D83C2313yes—
506C4×C22⋊D83C2313yes—
507(C22⋊D83)⋊C4C2316yes—
508(C22⋊D83)⋊C4C2316yes—
509(C22⋊D83)⋊C4C2316yes—
510(C22⋊D83)⋊C4C2316yes—
511(C22⋊D83)⋊C4C2316yes—
512(C22⋊D83)⋊C4C2316yes—
513(C22⋊D83)⋊C4C2316yes—
514(C22⋊D83)⋊C4C2316yes—
515#14581751C2313yes—
516#14581751C2313yes—
517#14581751C2313yes—
518#14581751C2313yes—
519#14581751C2313yes—
520#14581751C2313yes—
521#14581750C2316yes—
522#14581750C2313yes—
523#14581750C2313yes—
524#14581750C2313yes—
525#14581750C2316yes—
526#14581750C2313yes—
527#14581749C2313yes—
528#14581749C2313yes—
529#14581749C2313yes—
530#14581749C2313yes—
531#14581749C2316yes—
532#14581749C2313yes—
533#14581749C2313yes—
534#14581749C2313yes—
535#14581749C2316yes—
536#14581749C2311yescharacteristic
537#14581749C2313yes—
538#14581749C2313yes—
539#14581748C2316yes—
540#14581748C2316yes—
541#14581748C2316yes—
542#14581748C2316yes—
543C2×C4⋊Dic83C2313yes—
544C2×C4⋊Dic83C2313yes—
545C2×Dic83⋊C4C2316yes—
546C2×Dic83⋊C4C2316yes—
547C4⋊C4×D83C2313yes—
548C4⋊C4×D83C2316yes—
549C4⋊C4×D83C2313yes—
550C4⋊C4×D83C2313yes—
551C4⋊C4×D83C2313yes—
552C4⋊C4×D83C2316yes—
553C4⋊C4×D83C2313yes—
554C4⋊C4×D83C2313yes—
555C4⋊C4×D83C2316yes—
556C2×C4×Dic83C2313yes—
557C2×C4×Dic83C2313yes—
558C2×C4×Dic83C2313yes—
559C2×C4×Dic83C2316yes—
560C42×D83C2313yes—
561C42×D83C2313yes—
562C42×D83C2313yes—
563C42×D83C2313yes—
564C42×D83C2313yes—
565C42×D83C2313yes—
566C42×D83C2313yes—
567C42×D83C2313yes—
568C42×D83C2316yes—
569C42×D83C2313yes—
570C42×D83C2313yes—
571C2×#41×C83C2311yescharacteristic
572C2×#41×C83C2313yes—
573C22×Q8×C83C2311yescharacteristic
574C22×Q8×C83C2311yescharacteristic
575C4⋊Q8×C83C2313yes—
576C4⋊Q8×C83C2313yes—
577#126×C83C2316yes—
578#126×C83C2316yes—
579#125×C83C2313yes—
580#125×C83C2313yes—
581#125×C83C2316yes—
582#124×C83C2313yes—
583#124×C83C2313yes—
584#123×C83C2316yes—
585#123×C83C2316yes—
586C22⋊Q8×C83C2316yes—
587C22⋊Q8×C83C2313yes—
588C22⋊Q8×C83C2313yes—
589C22⋊Q8×C83C2313yes—
590C22⋊Q8×C83C2313yes—
591#121×C83C2313yes—
592#121×C83C2313yes—
593C4×Q8×C83C2311yescharacteristic
594C4×Q8×C83C2311yescharacteristic
595C4×Q8×C83C2311yescharacteristic
596C4×Q8×C83C2311yescharacteristic
597C4×Q8×C83C2313yes—
598C4×Q8×C83C2313yes—
599C4×Q8×C83C2313yes—
600C4×Q8×C83C2313yes—
601C4×Q8×C83C2313yes—
602C4×Q8×C83C2313yes—
603C4×D4×C83C2313yes—
604C4×D4×C83C2313yes—
605C4×D4×C83C2313yes—
606C4×D4×C83C2311yescharacteristic
607C4×D4×C83C2313yes—
608C4×D4×C83C2313yes—
609C4×D4×C83C2313yes—
610C4×D4×C83C2313yes—
611#117×C83C2313yes—
612#117×C83C2313yes—
613#117×C83C2313yes—
614#117×C83C2313yes—
615#117×C83C2316yes—
616C2×C4⋊C4×C83C2313yes—
617C2×C4⋊C4×C83C2313yes—
618C2×C42×C83C2313yes—
619C2×C42×C83C2313yes—
620C2×C42×C83C2313yes—
621C23×D83C2411yescharacteristic
622#13050591—24no—
623#13050591—212no—
624#13050590—212no—
625#13050590—212no—
626#13050590—212no—
627#13050590—24no—
628#13050590—212no—
629#13050590—46no—
630#13050589—212no—
631#13050589—212no—
632#13050589—412no—
633C2×Dic166—212no—
634C2×Dic166—212no—
635C2×Dic166C2413yes—
636C2×Dic166C2416yes—
637C2×Dic166C2413yes—
638C2×Dic166C2413yes—
639C2×Dic166C2411yescharacteristic
640C2×Dic166C2413yes—
641C2×Dic166C2413yes—
642C2×Dic166C2413yes—
643C2×Dic166C2416yes—
644C2×Dic166C2413yes—
645Q8×D83—24no—
646Q8×D83—24no—
647Q8×D83—212no—
648Q8×D83—212no—
649Q8×D83—212no—
650Q8×D83#4118yescomplemented
651C2×D332C2413yes—
652C2×D332C2411yescharacteristic
653C2×D332C2413yes—
654C2×D332C2411yescharacteristic
655C2×D332C2413yes—
656C2×D332C2413yes—
657C2×C22⋊D83C2413yes—
658C2×C22⋊D83C2411yescharacteristic
659C2×C22⋊D83C2411yescharacteristic
660C2×C22⋊D83C2413yes—
661C2×C22⋊D83C2411yescharacteristic
662C2×C22⋊D83C2413yes—
663C2×C22⋊D83C2413yes—
664C2×C22⋊D83C2413yes—
665C2×C22⋊D83C2413yes—
666C2×C22⋊D83C2411yescharacteristic
667C2×C22⋊D83C2416yes—
668C22×Dic83C2411yescharacteristic
669C22×Dic83C2413yes—
670C22×Dic83C2416yes—
671C22×Dic83C2413yes—
672C22×Dic83C2416yes—
673C2×C4×D83—212no—
674C2×C4×D83—24no—
675C2×C4×D83—46no—
676C2×C4×D83C2413yes—
677C2×C4×D83C2413yes—
678C2×C4×D83C2411yescharacteristic
679C2×C4×D83C2413yes—
680C2×C4×D83C2416yes—
681C2×C4×D83C2413yes—
682C2×C4×D83C2413yes—
683C2×C4×D83C2411yescharacteristic
684C2×C4×D83C2411yescharacteristic
685C2×C4×D83C2413yes—
686C2×C4×D83C2411yescharacteristic
687C2×C4×D83C2413yes—
688C2×C4×D83C2413yes—
689C2×C4×D83C2413yes—
690C2×C4×D83C2416yes—
691C2×C4×D83C2413yes—
692C2×C4×D83C2413yes—
693C2×C4×D83C2413yes—
694C2×C4×D83C2413yes—
695C2×C4×D83C2411yescharacteristic
696C4⋊Dic83C2413yes—
697C4⋊Dic83C2413yes—
698C4⋊Dic83C2413yes—
699C4⋊Dic83C2413yes—
700C4⋊Dic83C2413yes—
701C4⋊Dic83C2416yes—
702C4⋊Dic83C2413yes—
703C4⋊Dic83C2413yes—
704C4⋊Dic83C2413yes—
705C4⋊Dic83C2416yes—
706C4⋊Dic83C2413yes—
707C4⋊Dic83C2411yescharacteristic
708C4⋊Dic83C2413yes—
709C4⋊Dic83C2413yes—
710C4⋊Dic83C2413yes—
711C4⋊Dic83C2413yes—
712Dic83⋊C4C2416yes—
713Dic83⋊C4C2413yes—
714Dic83⋊C4C2413yes—
715Dic83⋊C4C2411yescharacteristic
716Dic83⋊C4C2413yes—
717Dic83⋊C4C2416yes—
718Dic83⋊C4C2413yes—
719Dic83⋊C4C2413yes—
720Dic83⋊C4C2413yes—
721Dic83⋊C4C2411yescharacteristic
722Dic83⋊C4C2416yes—
723Dic83⋊C4C2413yes—
724Dic83⋊C4C2413yes—
725Dic83⋊C4C2413yes—
726Dic83⋊C4C2416yes—
727Dic83⋊C4C2416yes—
728Dic83⋊C4C2416yes—
729Dic83⋊C4C2413yes—
730Dic83⋊C4C2413yes—
731Dic83⋊C4C2413yes—
732Dic83⋊C4C2413yes—
733Dic83⋊C4C2413yes—
734Dic83⋊C4C2413yes—
735Dic83⋊C4C2411yescharacteristic
736Dic83⋊C4C2416yes—
737Dic83⋊C4C2416yes—
738Dic83⋊C4C2416yes—
739Dic83⋊C4C2411yescharacteristic
740Dic83⋊C4C2413yes—
741Dic83⋊C4C2416yes—
742C22⋊Dic83C2411yescharacteristic
743C22⋊Dic83C2413yes—
744C22⋊Dic83C2413yes—
745C22⋊Dic83C2413yes—
746C22⋊Dic83C2416yes—
747C22⋊Dic83C2413yes—
748C22⋊Dic83C2413yes—
749C22⋊Dic83C2413yes—
750C22⋊Dic83C2413yes—
751C22⋊Dic83C2413yes—
752C22⋊Dic83C2411yescharacteristic
753(C2×D83)⋊C4C2411yescharacteristic
754(C2×D83)⋊C4C2411yescharacteristic
755(C2×D83)⋊C4C2413yes—
756(C2×D83)⋊C4C2413yes—
757(C2×D83)⋊C4C2413yes—
758(C2×D83)⋊C4C2411yescharacteristic
759(C2×D83)⋊C4C2413yes—
760(C2×D83)⋊C4C2411yescharacteristic
761(C2×D83)⋊C4C2416yes—
762(C2×D83)⋊C4C2413yes—
763(C2×D83)⋊C4C2413yes—
764(C2×D83)⋊C4C2413yes—
765(C2×D83)⋊C4C2411yescharacteristic
766(C2×D83)⋊C4C2413yes—
767(C2×D83)⋊C4C2413yes—
768(C2×D83)⋊C4C2413yes—
769(C2×D83)⋊C4C2416yes—
770(C2×D83)⋊C4C2411yescharacteristic
771(C2×D83)⋊C4C2413yes—
772(C2×D83)⋊C4C2413yes—
773(C2×D83)⋊C4C2416yes—
774(C2×D83)⋊C4C2416yes—
775(C2×D83)⋊C4C2413yes—
776(C2×D83)⋊C4C2413yes—
777C4×Dic83C2413yes—
778C4×Dic83C2413yes—
779C4×Dic83C2413yes—
780C4×Dic83C2413yes—
781C4×Dic83C2416yes—
782C4×Dic83C2416yes—
783C4×Dic83C2413yes—
784C4×Dic83C2413yes—
785C4×Dic83C2413yes—
786C4×Dic83C2413yes—
787C4×Dic83C2416yes—
788C4×Dic83C2413yes—
789C4×Dic83C2416yes—
790C4×Dic83C2413yes—
791C4×Dic83C2413yes—
792C4×Dic83C2413yes—
793C4×Dic83C2413yes—
794C4×Dic83C2411yescharacteristic
795C4×Dic83C2413yes—
796C4×Dic83C2413yes—
797C4×Dic83C2413yes—
798C4×Dic83C2413yes—
799#41×C83—24no—
800#41×C83—46no—
801C2×Q8×C83—24no—
802C2×Q8×C83—24no—
803C2×Q8×C83C2413yes—
804C2×Q8×C83C2413yes—
805C2×Q8×C83C2413yes—
806C2×Q8×C83C2411yescharacteristic
807C2×D4×C83C2411yescharacteristic
808C2×D4×C83C2413yes—
809C2×D4×C83C2413yes—
810C2×D4×C83C2413yes—
811C22×C4×C83C2413yes—
812C22×C4×C83C2413yes—
813C22×C4×C83C2413yes—
814C22×C4×C83C2413yes—
815C22×C4×C83C2411yescharacteristic
816C22×C4×C83C2411yescharacteristic
817C22×C4×C83C2413yes—
818C22×C4×C83C2413yes—
819C22×C4×C83C2413yes—
820C4⋊C4×C83C2413yes—
821C4⋊C4×C83C2413yes—
822C4⋊C4×C83C2413yes—
823C4⋊C4×C83C2413yes—
824C4⋊C4×C83C2413yes—
825C4⋊C4×C83C2416yes—
826C4⋊C4×C83C2413yes—
827C4⋊C4×C83C2411yescharacteristic
828C4⋊C4×C83C2416yes—
829C4⋊C4×C83C2416yes—
830C4⋊C4×C83C2416yes—
831C4⋊C4×C83C2413yes—
832C4⋊C4×C83C2413yes—
833C4⋊C4×C83C2413yes—
834C22⋊C4×C83C2411yescharacteristic
835C22⋊C4×C83C2413yes—
836C22⋊C4×C83C2416yes—
837C22⋊C4×C83C2413yes—
838C22⋊C4×C83C2411yescharacteristic
839C22⋊C4×C83C2413yes—
840C22⋊C4×C83C2416yes—
841C22⋊C4×C83C2413yes—
842C22⋊C4×C83C2416yes—
843C42×C83C2413yes—
844C42×C83C2413yes—
845C42×C83C2413yes—
846C42×C83C2413yes—
847C42×C83C2413yes—
848C42×C83C2413yes—
849C42×C83C2413yes—
850C42×C83C2411yescharacteristic
851C42×C83C2413yes—
852C42×C83C2413yes—
853C23×C83C2513yes—
854C23×C83C2511yescharacteristic
855C23×C83C2511yescharacteristic
856C22×D83—22no—
857C22×D83—22no—
858C22×D83—22no—
859C22×D83C2513yes—
860C22×D83C2511yescharacteristic
861C22×D83C2511yescharacteristic
862C22×D83C2511yescharacteristic
863Q8×C83—26no—
864Q8×C83—26no—
865Q8×C83—43no—
866Q8×C83C2×#4114yes—
867D4×C83—22no—
868D4×C83—26no—
869D4×C83—26no—
870D4×C83—43no—
871C2×C4×C83—26no—
872C2×C4×C83—26no—
873C2×C4×C83—26no—
874C2×C4×C83—26no—
875C2×C4×C83—22no—
876C2×C4×C83—22no—
877C2×C4×C83—26no—
878C2×C4×C83—43no—
879C2×C4×C83—43no—
880C2×C4×C83C2511yescharacteristic
881C2×C4×C83C2511yescharacteristic
882C2×C4×C83C2513yes—
883C2×C4×C83C2511yescharacteristic
884C2×C4×C83C2511yescharacteristic
885C2×C4×C83C2513yes—
886C2×C4×C83C2513yes—
887C2×C4×C83C2513yes—
888C2×C4×C83C2513yes—
889C2×C4×C83C2513yes—
890C2×C4×C83C2513yes—
891C2×C4×C83C2511yescharacteristic
892C22⋊D83—26no—
893C22⋊D83—22no—
894C22⋊D83—26no—
895C22⋊D83—22no—
896C22⋊D83—26no—
897C22⋊D83—22no—
898C22⋊D83—26no—
899C22⋊D83—26no—
900C22⋊D83—26no—
901C22⋊D83—22no—
902C22⋊D83—46no—
903C2×Dic83—26no—
904C2×Dic83—26no—
905C2×Dic83—212no—
906C2×Dic83—22no—
907C2×Dic83—46no—
908C2×Dic83C2511yescharacteristic
909C2×Dic83C2513yes—
910C2×Dic83C2513yes—
911C2×Dic83C2511yescharacteristic
912C2×Dic83C2513yes—
913C2×Dic83C2513yes—
914C2×Dic83C2513yes—
915C2×Dic83C2511yescharacteristic
916C2×Dic83C2511yescharacteristic
917C2×Dic83C2513yes—
918C2×Dic83C2513yes—
919C2×Dic83C2511yescharacteristic
920D332—22no—
921D332—26no—
922D332—26no—
923D332—22no—
924D332—26no—
925D332—43no—
926C4×D83—26no—
927C4×D83—22no—
928C4×D83—26no—
929C4×D83—26no—
930C4×D83—26no—
931C4×D83—22no—
932C4×D83—26no—
933C4×D83—22no—
934C4×D83—26no—
935C4×D83—212no—
936C4×D83—22no—
937C4×D83—43no—
938C4×D83—43no—
939C4×D83—43no—
940C4×D83—43no—
941C4×D83—46no—
942C4×D83—43no—
943C4×D83—43no—
944C4×D83C2×#41112yes—
945C4×D832−1+414yescomplemented
946Dic166—26no—
947Dic166—26no—
948Dic166—212no—
949Dic166—26no—
950Dic166—26no—
951Dic166—26no—
952Dic166—22no—
953Dic166—46no—
954Dic166—43no—
955Dic166C2×#41112yes—
956C22×C83—21no—
957C22×C83—21no—
958C22×C83—23no—
959C22×C83—21no—
960C22×C83—23no—
961C22×C83—21no—
962C22×C83—23no—
963C22×C83—21no—
964C22×C83#58512yes—
965C22×C83C2611yescharacteristic
966C2×D83—28no—
967C2×D83—21no—
968C2×D83—21no—
969C2×D83—21no—
970C2×D83—21no—
971C2×D83—23no—
972C2×D83—21no—
973C2×D83—23no—
974C2×D83—21no—
975C2×D83—21no—
976C2×D83—23no—
977C2×D83C22×#4112yes—
978C2×D83C2×2−1+412yes—
979C4×C83—21no—
980C4×C83—23no—
981C4×C83—23no—
982C4×C83—21no—
983C4×C83—23no—
984C4×C83—21no—
985C4×C83—23no—
986C4×C83—23no—
987C4×C83—23no—
988C4×C83—21no—
989C4×C83C22×#4116yes—
990C4×C83C2×2−1+412yes—
991Dic83—23no—
992Dic83—21no—
993Dic83—23no—
994Dic83—23no—
995Dic83—21no—
996Dic83—21no—
997Dic83—21no—
998Dic83—23no—
999Dic83—23no—
1000Dic83—23no—
1001Dic83C22×#4116yes—
1002Dic83C2×2−1+412yes—
1003#62788—831nomaximal, Sylow
1004C2×C83—22no—
1005C2×C83—43no—
1006C2×C83—41no—
1007C2×C83C23×#4111yescharacteristic
1008C2×C83C22×2−1+411yescharacteristic
1009C2×C83C2×#58511yescharacteristic
1010D83—22no—
1011D83—22no—
1012D83—43no—
1013D83—41no—
1014#3523—833no—
1015#3523—831no—
1016#3522—831no—
1017#3522—833no—
1018#3516—831no—
1019#3516—833no—
1020#3516—833no—
1021#3516—831no—
1022#3507—833no—
1023#3507—833no—
1024#3502—831no—
1025#3497—831no—
1026#3492—833no—
1027#3492—833no—
1028#3486—831no—
1029#3486—831no—
1030#3482—833no—
1031#3482—833no—
1032#3482—831no—
1033#3482D8311yescharacteristic, complemented
1034#3480—833no—
1035#3480—831no—
1036Q8×#41—833no—
1037Q8×#41—831no—
1038#3461—833no—
1039#3461—833no—
1040#3444—833no—
1041#3444—833no—
1042C4×2−1+4—831no—
1043C4×2−1+4—831no—
1044C22×C4×Q8—831no—
1045C83#6278811yescharacteristic, complemented, Sylow
1046C2×2−1+4—831no—
1047C2×2−1+4—831no—
1048C23×Q8—831no—
1049#559—833no—
1050#559—836no—
1051#559—833no—
1052Q82—833no—
1053Q82—831no—
1054#557—833no—
1055#557—836no—
1056#557—833no—
1057#557—833no—
1058#557—831no—
1059#557—831no—
1060#557—833no—
1061#557—833no—
1062#557C2×D8311yescharacteristic, complemented
1063#556—836no—
1064#556—836no—
1065#556—833no—
1066#556—833no—
1067#556—833no—
1068#556—833no—
1069#556—833no—
1070#556—836no—
1071#556C2×D8313yescomplemented
1072#554—833no—
1073#554—836no—
1074#554—836no—
1075#554—836no—
1076#554—833no—
1077#554—833no—
1078#554—833no—
1079#554—833no—
1080#554—833no—
1081#553—836no—
1082#553—833no—
1083#553—836no—
1084#553—833no—
1085#553—833no—
1086#553—833no—
1087#552—836no—
1088#552—833no—
1089#552—836no—
1090#552—833no—
1091#552—833no—
1092#552—833no—
1093#552—833no—
1094#552—836no—
1095#552—836no—
1096#552—833no—
1097#552C2×D8313yes—
1098#552C2×D8313yescomplemented
1099#550—831no—
1100#550—833no—
1101D4×Q8—831no—
1102D4×Q8—831no—
1103D4×Q8—831no—
1104D4×Q8—833no—
1105D4×Q8—833no—
1106D4×Q8—833no—
1107D4×Q8—833no—
1108D4×Q8—831no—
1109D4×Q8—833no—
1110D4×Q8C2×D8311yescharacteristic
1111#548—831no—
1112#548—831no—
1113#548—833no—
1114#548—833no—
1115#548—833no—
1116#548—833no—
1117#548—831no—
1118#548—831no—
1119#548—833no—
1120#548—833no—
1121#548C2×D8311yescharacteristic
1122#548C2×D8311yescharacteristic, complemented
1123#547—836no—
1124#547—836no—
1125#547—833no—
1126#547—833no—
1127#547—833no—
1128#547C2×D8313yes—
1129#544—833no—
1130#544—833no—
1131#542—833no—
1132#542—833no—
1133#542—836no—
1134#542—836no—
1135#542—833no—
1136#542—833no—
1137#541—833no—
1138#541—836no—
1139#541—836no—
1140#541—833no—
1141#541—833no—
1142#541—833no—
1143#539—836no—
1144#539—836no—
1145#539—836no—
1146#539—836no—
1147#537—833no—
1148#537—833no—
1149#536—833no—
1150#536—833no—
1151#536—833no—
1152#536—833no—
1153#533—833no—
1154#533—833no—
1155#533—833no—
1156#533—833no—
1157#533—833no—
1158#533—836no—
1159#533—833no—
1160#533—833no—
1161#533—833no—
1162#533—836no—
1163#533—833no—
1164#533C2×D8313yescomplemented
1165#532—833no—
1166#532—833no—
1167#532—833no—
1168#532—833no—
1169#532—833no—
1170#532—833no—
1171#529—836no—
1172#529—836no—
1173#529—833no—
1174#529—833no—
1175#529—836no—
1176#529—833no—
1177#529—833no—
1178#529—833no—
1179#529—833no—
1180#529—833no—
1181#529—833no—
1182#529—833no—
1183#529—833no—
1184#529—833no—
1185#529—836no—
1186#529—833no—
1187#529—836no—
1188#529—833no—
1189#529—833no—
1190#529—833no—
1191#529—833no—
1192#529—836no—
1193#529—833no—
1194#529—833no—
1195#529C2×D8313yes—
1196#529C2×D8313yescomplemented
1197#525—833no—
1198#525—836no—
1199#525—833no—
1200#525—833no—
1201#525—833no—
1202#525—831no—
1203#525—833no—
1204#525—833no—
1205#525—833no—
1206#520—831no—
1207#520—833no—
1208#520—831no—
1209#520—833no—
1210#520—833no—
1211#520—833no—
1212#520—833no—
1213#520—833no—
1214#519—831no—
1215#519—831no—
1216#519—831no—
1217#519—833no—
1218#519—831no—
1219#519—833no—
1220C4×#41—833no—
1221C4×#41—831no—
1222C4×#41—833no—
1223C4×#41—833no—
1224C4×#41—836no—
1225C4×#41—836no—
1226C4×#41—833no—
1227C4×#41—833no—
1228C4×#41—833no—
1229C4×#41—833no—
1230C4×#41—833no—
1231C4×#41—833no—
1232C4×#41C2×D8313yes—
1233C4×#41C2×D8311yescharacteristic, complemented
1234C2×C4×Q8—831no—
1235C2×C4×Q8—831no—
1236C2×C4×Q8—833no—
1237C2×C4×Q8—831no—
1238C2×C4×Q8—833no—
1239C2×C4×Q8—831no—
1240C2×C4×Q8—833no—
1241C2×C4×Q8—831no—
1242C2×C4×Q8—833no—
1243C2×C4×Q8—831no—
1244C2×C4×Q8—833no—
1245C2×C4×Q8—833no—
1246C2×C4×Q8—833no—
1247C2×C4×Q8—833no—
1248C2×C4×Q8C2×D8311yescharacteristic
1249C2×C4×Q8C2×D8311yescharacteristic, complemented
1250C22×C4⋊C4—833no—
1251C22×C42—833no—
12522−1+4—1668no—
12532−1+4—1668no—
1254C2×#41—833no—
1255C2×#41—831no—
1256C2×#41—836no—
1257C2×#41—833no—
1258C2×#41—833no—
1259C2×#41—833no—
1260C2×#41—833no—
1261C2×#41—831no—
1262C2×#41—833no—
1263C2×#41—833no—
1264C2×#41—833no—
1265C2×#41C22×D8311yescharacteristic
1266C2×#41C22×D8313yes—
1267C22×Q8—831no—
1268C22×Q8—833no—
1269C22×Q8—833no—
1270C22×Q8—831no—
1271C22×Q8—833no—
1272C22×Q8—831no—
1273C22×Q8—833no—
1274C22×Q8—833no—
1275C22×Q8—1668no—
1276C22×Q8C22×D8311yescharacteristic
1277C22×Q8C22×D8311yescharacteristic
1278C23×C4—833no—
1279C23×C4—833no—
1280C23×C4—831no—
1281C4⋊Q8—833no—
1282C4⋊Q8—833no—
1283C4⋊Q8—833no—
1284C4⋊Q8—833no—
1285C4⋊Q8—836no—
1286C4⋊Q8—833no—
1287C4⋊Q8—833no—
1288C4⋊Q8—833no—
1289C4⋊Q8—833no—
1290C4⋊Q8—836no—
1291C4⋊Q8—836no—
1292C4⋊Q8—836no—
1293C4⋊Q8—833no—
1294C4⋊Q8—833no—
1295C4⋊Q8—833no—
1296C4⋊Q8—833no—
1297C4⋊Q8C22×D8313yes—
1298C4⋊Q8C22×D8313yes—
1299#127—833no—
1300#127—833no—
1301#126—836no—
1302#126—833no—
1303#126—833no—
1304#126—833no—
1305#126—833no—
1306#126—836no—
1307#126—836no—
1308#126—836no—
1309#126—833no—
1310#126—833no—
1311#126—836no—
1312#126—833no—
1313#126—833no—
1314#126—836no—
1315#126—836no—
1316#126—836no—
1317#126—836no—
1318#126—836no—
1319#126C22×D8316yes—
1320#126C22×D8316yes—
1321#125—836no—
1322#125—833no—
1323#125—833no—
1324#125—833no—
1325#125—833no—
1326#125—836no—
1327#125—833no—
1328#125—833no—
1329#125—836no—
1330#125—836no—
1331#125—833no—
1332#125—833no—
1333#125—836no—
1334#125—836no—
1335#125—836no—
1336#125—836no—
1337#125—836no—
1338#125—836no—
1339#125—833no—
1340#125—833no—
1341#125—836no—
1342#125C22×D8313yes—
1343#125C22×D8313yes—
1344#125C22×D8316yes—
1345#124—833no—
1346#124—833no—
1347#124—833no—
1348#124—833no—
1349#124—836no—
1350#124—833no—
1351#124—833no—
1352#124—833no—
1353#124—833no—
1354#124—836no—
1355#124—836no—
1356#124—836no—
1357#124—833no—
1358#124—833no—
1359#124C22×D8313yes—
1360#124C22×D8313yes—
1361#123—833no—
1362#123—833no—
1363#123—836no—
1364#123—836no—
1365#123—836no—
1366#123—833no—
1367#123—831no—
1368#123—836no—
1369#123—833no—
1370#123—833no—
1371#123—836no—
1372#123—836no—
1373#123—833no—
1374#123—831no—
1375#123—833no—
1376#123—833no—
1377#123—836no—
1378#123—833no—
1379#123—833no—
1380#123—836no—
1381#123—836no—
1382#123—836no—
1383#123C22×D8316yes—
1384#123C22×D8316yes—
1385C22⋊Q8—833no—
1386C22⋊Q8—833no—
1387C22⋊Q8—833no—
1388C22⋊Q8—833no—
1389C22⋊Q8—833no—
1390C22⋊Q8—833no—
1391C22⋊Q8—836no—
1392C22⋊Q8—833no—
1393C22⋊Q8—833no—
1394C22⋊Q8—833no—
1395C22⋊Q8—833no—
1396C22⋊Q8—836no—
1397C22⋊Q8—833no—
1398C22⋊Q8—831no—
1399C22⋊Q8—836no—
1400C22⋊Q8—833no—
1401C22⋊Q8—833no—
1402C22⋊Q8—836no—
1403C22⋊Q8—836no—
1404C22⋊Q8—836no—
1405C22⋊Q8—836no—
1406C22⋊Q8—836no—
1407C22⋊Q8—836no—
1408C22⋊Q8—833no—
1409C22⋊Q8—833no—
1410C22⋊Q8—833no—
1411C22⋊Q8—833no—
1412C22⋊Q8—833no—
1413C22⋊Q8—833no—
1414C22⋊Q8—836no—
1415C22⋊Q8—833no—
1416C22⋊Q8—831no—
1417C22⋊Q8—833no—
1418C22⋊Q8—833no—
1419C22⋊Q8—836no—
1420C22⋊Q8—836no—
1421C22⋊Q8—836no—
1422C22⋊Q8—836no—
1423C22⋊Q8—836no—
1424C22⋊Q8C22×D8313yes—
1425C22⋊Q8C22×D8313yes—
1426C22⋊Q8C22×D8313yes—
1427C22⋊Q8C22×D8313yes—
1428C22⋊Q8C22×D8316yes—
1429#121—833no—
1430#121—833no—
1431#121—833no—
1432#121—833no—
1433#121—833no—
1434#121—831no—
1435#121—833no—
1436#121—833no—
1437#121—836no—
1438#121—833no—
1439#121—833no—
1440#121—833no—
1441#121—833no—
1442#121—833no—
1443#121—833no—
1444#121—833no—
1445#121—831no—
1446#121—836no—
1447#121—833no—
1448#121—833no—
1449#121—836no—
1450#121—836no—
1451#121C22×D8313yes—
1452#121C22×D8313yes—
1453#120—833no—
1454#120—831no—
1455#120—833no—
1456#120—831no—
1457C4×Q8—831no—
1458C4×Q8—833no—
1459C4×Q8—831no—
1460C4×Q8—833no—
1461C4×Q8—831no—
1462C4×Q8—833no—
1463C4×Q8—833no—
1464C4×Q8—831no—
1465C4×Q8—833no—
1466C4×Q8—836no—
1467C4×Q8—833no—
1468C4×Q8—833no—
1469C4×Q8—836no—
1470C4×Q8—833no—
1471C4×Q8—833no—
1472C4×Q8—836no—
1473C4×Q8—833no—
1474C4×Q8—833no—
1475C4×Q8—833no—
1476C4×Q8—836no—
1477C4×Q8—836no—
1478C4×Q8—836no—
1479C4×Q8—833no—
1480C4×Q8—836no—
1481C4×Q8—833no—
1482C4×Q8—833no—
1483C4×Q8—833no—
1484C4×Q8—836no—
1485C4×Q8—833no—
1486C4×Q8—833no—
1487C4×Q8—833no—
1488C4×Q8—833no—
1489C4×Q8—833no—
1490C4×Q8—836no—
1491C4×Q8—833no—
1492C4×Q8—833no—
1493C4×Q8—833no—
1494C4×Q8—836no—
1495C4×Q8—833no—
1496C4×Q8—833no—
1497C4×Q8—833no—
1498C4×Q8—833no—
1499C4×Q8—833no—
1500C4×Q8—833no—
1501C4×Q8C22×D8311yescharacteristic
1502C4×Q8C22×D8313yes—
1503C4×Q8C22×D8311yescharacteristic
1504C4×Q8C22×D8313yes—
1505C4×Q8C22×D8313yes—
1506C4×Q8C22×D8311yescharacteristic
1507C4×Q8C22×D8313yes—
1508C4×Q8C22×D8313yes—
1509C4×Q8C22×D8313yes—
1510C4×Q8C22×D8311yescharacteristic
1511C4×D4—833no—
1512C4×D4—833no—
1513C4×D4—836no—
1514C4×D4—833no—
1515C4×D4—831no—
1516C4×D4—833no—
1517C4×D4—831no—
1518C4×D4—833no—
1519C4×D4—833no—
1520C4×D4—833no—
1521C4×D4—833no—
1522C4×D4—833no—
1523C4×D4—833no—
1524C4×D4—836no—
1525C4×D4—833no—
1526C4×D4—833no—
1527C4×D4—833no—
1528C4×D4—833no—
1529C4×D4—833no—
1530C4×D4—833no—
1531C4×D4—836no—
1532C4×D4—833no—
1533C4×D4—833no—
1534C4×D4—833no—
1535C4×D4—833no—
1536C4×D4—836no—
1537C4×D4—833no—
1538C4×D4—833no—
1539C4×D4—836no—
1540C4×D4—836no—
1541C4×D4—836no—
1542C4×D4—836no—
1543C4×D4—836no—
1544C4×D4—836no—
1545C4×D4—836no—
1546C4×D4—836no—
1547C4×D4—836no—
1548C4×D4—836no—
1549C4×D4—833no—
1550C4×D4—831no—
1551C4×D4—833no—
1552C4×D4—833no—
1553C4×D4—833no—
1554C4×D4—833no—
1555C4×D4—833no—
1556C4×D4—833no—
1557C4×D4—833no—
1558C4×D4—833no—
1559C4×D4—833no—
1560C4×D4—833no—
1561C4×D4C22×D8313yes—
1562C4×D4C22×D8313yes—
1563C4×D4C22×D8311yescharacteristic
1564C4×D4C22×D8313yes—
1565C4×D4C22×D8313yes—
1566C4×D4C22×D8313yes—
1567C4×D4C22×D8313yes—
1568C4×D4C22×D8313yes—
1569#117—833no—
1570#117—833no—
1571#117—833no—
1572#117—833no—
1573#117—833no—
1574#117—833no—
1575#117—833no—
1576#117—833no—
1577#117—836no—
1578#117—833no—
1579#117—833no—
1580#117—836no—
1581#117—836no—
1582#117—836no—
1583#117—836no—
1584#117—836no—
1585#117—833no—
1586#117—831no—
1587#117—833no—
1588#117—833no—
1589#117—833no—
1590#117—833no—
1591#117—836no—
1592#117—836no—
1593#117—833no—
1594#117—833no—
1595#117—833no—
1596#117—833no—
1597#117C22×D8316yes—
1598#117C22×D8313yes—
1599#117C22×D8313yes—
1600#117C22×D8313yes—
1601#117C22×D8313yes—
1602C2×C4⋊C4—836no—
1603C2×C4⋊C4—833no—
1604C2×C4⋊C4—836no—
1605C2×C4⋊C4—833no—
1606C2×C4⋊C4—833no—
1607C2×C4⋊C4—833no—
1608C2×C4⋊C4—836no—
1609C2×C4⋊C4—836no—
1610C2×C4⋊C4—833no—
1611C2×C4⋊C4—833no—
1612C2×C4⋊C4—836no—
1613C2×C4⋊C4—833no—
1614C2×C4⋊C4—833no—
1615C2×C4⋊C4C22×D8313yes—
1616C2×C4⋊C4C22×D8313yes—
1617C2×C42—833no—
1618C2×C42—833no—
1619C2×C42—833no—
1620C2×C42—836no—
1621C2×C42—833no—
1622C2×C42—833no—
1623C2×C42—833no—
1624C2×C42—833no—
1625C2×C42—833no—
1626C2×C42—833no—
1627C2×C42—833no—
1628C2×C42—833no—
1629C2×C42—836no—
1630C2×C42—833no—
1631C2×C42—833no—
1632C2×C42C22×D8313yes—
1633C2×C42C22×D8313yes—
1634C2×C42C22×D8313yes—
1635C24—831no—
1636#41—24no—
1637#41—46no—
1638#41—3326no—
1639#41—33212no—
1640#41—16612no—
1641#41—16612no—
1642#41—16612no—
1643#41—1664no—
1644#41—16612no—
1645#41—16612no—
1646#41—16612no—
1647#41—16612no—
1648#41—1664no—
1649C2×Q8—24no—
1650C2×Q8—24no—
1651C2×Q8—838no—
1652C2×Q8—833no—
1653C2×Q8—836no—
1654C2×Q8—833no—
1655C2×Q8—833no—
1656C2×Q8—831no—
1657C2×Q8—836no—
1658C2×Q8—833no—
1659C2×Q8—833no—
1660C2×Q8—833no—
1661C2×Q8—833no—
1662C2×Q8—16612no—
1663C2×Q8—16612no—
1664C2×Q8—16612no—
1665C2×Q8—16612no—
1666C2×Q8—16612no—
1667C2×Q8—1664no—
1668C2×Q8—1664no—
1669C2×Q8C23×D8313yes—
1670C2×Q8C23×D8313yes—
1671C2×Q8C23×D8313yes—
1672C2×Q8C23×D8311yescharacteristic
1673C2×D4—836no—
1674C2×D4—831no—
1675C2×D4—833no—
1676C2×D4—831no—
1677C2×D4—833no—
1678C2×D4—831no—
1679C2×D4—833no—
1680C2×D4—831no—
1681C2×D4—833no—
1682C2×D4—833no—
1683C2×D4—833no—
1684C2×D4—833no—
1685C2×D4—833no—
1686C2×D4—831no—
1687C2×D4—833no—
1688C2×D4—831no—
1689C2×D4—833no—
1690C2×D4C23×D8313yes—
1691C2×D4C23×D8313yes—
1692C2×D4C23×D8311yescharacteristic
1693C2×D4C23×D8313yes—
1694C22×C4—3326no—
1695C22×C4—836no—
1696C22×C4—833no—
1697C22×C4—833no—
1698C22×C4—833no—
1699C22×C4—833no—
1700C22×C4—836no—
1701C22×C4—833no—
1702C22×C4—833no—
1703C22×C4—833no—
1704C22×C4—831no—
1705C22×C4—831no—
1706C22×C4—833no—
1707C22×C4—833no—
1708C22×C4—836no—
1709C22×C4—831no—
1710C22×C4—831no—
1711C22×C4—833no—
1712C22×C4—833no—
1713C22×C4—833no—
1714C22×C4—836no—
1715C22×C4—833no—
1716C22×C4—833no—
1717C22×C4—831no—
1718C22×C4—831no—
1719C22×C4—833no—
1720C22×C4—16612no—
1721C22×C4—1664no—
1722C22×C4C23×D8313yes—
1723C22×C4C23×D8313yes—
1724C22×C4C23×D8313yes—
1725C22×C4C23×D8313yes—
1726C22×C4C23×D8311yescharacteristic
1727C22×C4C23×D8313yes—
1728C22×C4C23×D8311yescharacteristic
1729C22×C4C23×D8313yes—
1730C22×C4C23×D8313yes—
1731C4⋊C4—836no—
1732C4⋊C4—833no—
1733C4⋊C4—836no—
1734C4⋊C4—833no—
1735C4⋊C4—836no—
1736C4⋊C4—836no—
1737C4⋊C4—836no—
1738C4⋊C4—833no—
1739C4⋊C4—833no—
1740C4⋊C4—833no—
1741C4⋊C4—833no—
1742C4⋊C4—833no—
1743C4⋊C4—836no—
1744C4⋊C4—833no—
1745C4⋊C4—833no—
1746C4⋊C4—833no—
1747C4⋊C4—833no—
1748C4⋊C4—833no—
1749C4⋊C4—833no—
1750C4⋊C4—831no—
1751C4⋊C4—833no—
1752C4⋊C4—831no—
1753C4⋊C4—833no—
1754C4⋊C4—831no—
1755C4⋊C4—833no—
1756C4⋊C4—833no—
1757C4⋊C4—831no—
1758C4⋊C4—831no—
1759C4⋊C4—836no—
1760C4⋊C4—833no—
1761C4⋊C4—836no—
1762C4⋊C4—833no—
1763C4⋊C4—836no—
1764C4⋊C4—833no—
1765C4⋊C4—833no—
1766C4⋊C4—836no—
1767C4⋊C4—833no—
1768C4⋊C4—833no—
1769C4⋊C4—836no—
1770C4⋊C4—833no—
1771C4⋊C4—833no—
1772C4⋊C4—836no—
1773C4⋊C4—833no—
1774C4⋊C4—833no—
1775C4⋊C4—833no—
1776C4⋊C4—833no—
1777C4⋊C4C23×D8313yes—
1778C4⋊C4C23×D8313yes—
1779C4⋊C4C23×D8316yes—
1780C4⋊C4C23×D8313yes—
1781C4⋊C4C23×D8316yes—
1782C4⋊C4C23×D8313yes—
1783C4⋊C4C23×D8313yes—
1784C4⋊C4C23×D8311yescharacteristic
1785C4⋊C4C23×D8316yes—
1786C4⋊C4C23×D8316yes—
1787C4⋊C4C23×D8313yes—
1788C4⋊C4C23×D8313yes—
1789C4⋊C4C23×D8313yes—
1790C4⋊C4C23×D8313yes—
1791C22⋊C4—831no—
1792C22⋊C4—833no—
1793C22⋊C4—833no—
1794C22⋊C4—833no—
1795C22⋊C4—831no—
1796C22⋊C4—833no—
1797C22⋊C4—833no—
1798C22⋊C4—833no—
1799C22⋊C4—833no—
1800C22⋊C4—833no—
1801C22⋊C4—836no—
1802C22⋊C4—833no—
1803C22⋊C4—831no—
1804C22⋊C4—833no—
1805C22⋊C4—831no—
1806C22⋊C4—833no—
1807C22⋊C4—833no—
1808C22⋊C4—836no—
1809C22⋊C4—833no—
1810C22⋊C4—831no—
1811C22⋊C4—833no—
1812C22⋊C4—831no—
1813C22⋊C4—833no—
1814C22⋊C4—833no—
1815C22⋊C4—831no—
1816C22⋊C4—831no—
1817C22⋊C4—836no—
1818C22⋊C4—833no—
1819C22⋊C4—833no—
1820C22⋊C4—833no—
1821C22⋊C4—833no—
1822C22⋊C4—836no—
1823C22⋊C4—833no—
1824C22⋊C4—833no—
1825C22⋊C4—836no—
1826C22⋊C4C23×D8313yes—
1827C22⋊C4C23×D8316yes—
1828C22⋊C4C23×D8313yes—
1829C22⋊C4C23×D8311yescharacteristic
1830C22⋊C4C23×D8311yescharacteristic
1831C22⋊C4C23×D8316yes—
1832C22⋊C4C23×D8316yes—
1833C22⋊C4C23×D8313yes—
1834C22⋊C4C23×D8313yes—
1835C42—833no—
1836C42—833no—
1837C42—833no—
1838C42—833no—
1839C42—833no—
1840C42—833no—
1841C42—833no—
1842C42—833no—
1843C42—833no—
1844C42—833no—
1845C42—836no—
1846C42—836no—
1847C42—833no—
1848C42—833no—
1849C42—836no—
1850C42—836no—
1851C42—833no—
1852C42—833no—
1853C42—833no—
1854C42—833no—
1855C42—833no—
1856C42—831no—
1857C42C23×D8313yes—
1858C42C23×D8313yes—
1859C42C23×D8313yes—
1860C42C23×D8313yes—
1861C42C23×D8313yes—
1862C42C23×D8313yes—
1863C42C23×D8313yes—
1864C42C23×D8313yes—
1865C42C23×D8313yes—
1866C42C23×D8311yescharacteristic
1867C23—831no—
1868C23—831no—
1869C23—833no—
1870C23—831no—
1871C23—1662no—
1872C23—1662no—
1873C23—1662no—
1874C23C24×D8311yescharacteristic
1875C23C24×D8313yes—
1876C23C24×D8311yescharacteristic
1877Q8—26no—
1878Q8—26no—
1879Q8—43no—
1880Q8—3323no—
1881Q8—3326no—
1882Q8—8312no—
1883Q8—16612no—
1884Q8—1666no—
1885Q8—1666no—
1886Q8—1666no—
1887Q8—1662no—
1888Q8—1666no—
1889Q8—1666no—
1890Q8#41×D8314yes—
1891D4—22no—
1892D4—26no—
1893D4—26no—
1894D4—43no—
1895D4—3323no—
1896D4—3326no—
1897D4—1662no—
1898D4—1666no—
1899D4—1666no—
1900D4—1662no—
1901D4—1666no—
1902D4—1666no—
1903D4—1662no—
1904D4—1666no—
1905D4—1662no—
1906D4—1666no—
1907D4—1662no—
1908D4—1666no—
1909D4—1662no—
1910D4—1666no—
1911D4—1666no—
1912C2×C4—26no—
1913C2×C4—26no—
1914C2×C4—26no—
1915C2×C4—26no—
1916C2×C4—22no—
1917C2×C4—26no—
1918C2×C4—22no—
1919C2×C4—43no—
1920C2×C4—43no—
1921C2×C4—3323no—
1922C2×C4—3323no—
1923C2×C4—3323no—
1924C2×C4—3323no—
1925C2×C4—3323no—
1926C2×C4—3323no—
1927C2×C4—3326no—
1928C2×C4—3326no—
1929C2×C4—831no—
1930C2×C4—833no—
1931C2×C4—8312no—
1932C2×C4—834no—
1933C2×C4—831no—
1934C2×C4—833no—
1935C2×C4—831no—
1936C2×C4—833no—
1937C2×C4—833no—
1938C2×C4—831no—
1939C2×C4—833no—
1940C2×C4—831no—
1941C2×C4—833no—
1942C2×C4—833no—
1943C2×C4—1666no—
1944C2×C4—1662no—
1945C2×C4—16612no—
1946C2×C4—1666no—
1947C2×C4—1662no—
1948C2×C4—1666no—
1949C2×C4—1662no—
1950C2×C4—16612no—
1951C2×C4—1666no—
1952C2×C4—1666no—
1953C2×C4—1666no—
1954C2×C4—1666no—
1955C2×C4—1662no—
1956C2×C4—1662no—
1957C2×C4—1666no—
1958C2×C4C24×D8311yescharacteristic
1959C2×C4C24×D8313yes—
1960C2×C4C24×D8313yes—
1961C2×C4C24×D8313yes—
1962C2×C4C24×D8313yes—
1963C2×C4C24×D8313yes—
1964C2×C4C24×D8313yes—
1965C2×C4C24×D8311yescharacteristic
1966C2×C4C24×D8311yescharacteristic
1967C2×C4C24×D8311yescharacteristic
1968C2×C4C24×D8313yes—
1969C2×C4C24×D8311yescharacteristic
1970C22—21no—
1971C22—21no—
1972C22—21no—
1973C22—23no—
1974C22—21no—
1975C22—23no—
1976C22—21no—
1977C22—23no—
1978C22—832no—
1979C22—832no—
1980C22—1668no—
1981C22—1663no—
1982C22—1661no—
1983C22—1663no—
1984C22—1661no—
1985C22—1661no—
1986C22—1663no—
1987C22—1661no—
1988C22—1661no—
1989C22—1661no—
1990C22—1661no—
1991C22#1912853712yes—
1992C22C25×D8311yescharacteristic
1993C4—21no—
1994C4—23no—
1995C4—23no—
1996C4—21no—
1997C4—23no—
1998C4—21no—
1999C4—23no—
2000C4—23no—
2001C4—21no—
2002C4—23no—
2003C4—836no—
2004C4—832no—
2005C4—1663no—
2006C4—1661no—
2007C4—1663no—
2008C4—1661no—
2009C4—1661no—
2010C4—1663no—
2011C4—1663no—
2012C4—1661no—
2013C4—1663no—
2014C4—1663no—
2015C4C2×#41×D8316yes—
2016C42−1+4×D8312yes—
2017C2—22no—
2018C2—41no—
2019C2—43no—
2020C2—3323no—
2021C2—3321no—
2022C2—1662no—
2023C2—1662no—
2024C2C22×#41×D8311yescharacteristic
2025C2C2×2−1+4×D8311yescharacteristic
2026C2C2×#1912853711yescharacteristic
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC83×#3482C2
hypercenter#3482D83
hypocenterC83#62788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #3482

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #24921552C2semidirect
2. #24921550C2semidirect
3. #24921541C2semidirect
4. #24921539C2semidirect
5. #24921459C2semidirect
6. #24921455C2semidirect
7. #24921451C2semidirect
8. #24921449C2semidirect
9. #24921324C2semidirect
10. #24921322C2semidirect
11. #24921270C2semidirect
12. #24921231C2semidirect
13. #24921165C2semidirect
14. #24921163C2semidirect
15. #24921113C2semidirect
16. #24921109C2semidirect
17. #24921080C2semidirect
18. #24921078C2semidirect
19. #24921076C2semidirect
20. #24921061C2semidirect
21. #24921054C2semidirect
22. Q8×#13050590C2semidirect
23. #24921041C2semidirect
24. #24920894C2semidirect
25. #24920888C2semidirect
26. #24920757C2semidirect
27. #24920756C2semidirect
28. C4×#14581840C2semidirect
29. C4×#14581839C2semidirect
30. C2×C4×Q8×D83C2semidirect
31. C83×#3482C2semidirect
35. #19128435C22semidirect
36. #19128434C22semidirect
37. #19128433C22semidirect
38. Q8×Dic166C22semidirect
39. #19128431C22semidirect
40. #19128429C22semidirect
41. #19128429C22semidirect
42. #19128428C22semidirect
43. #19128428C22semidirect
44. #19128428C22semidirect
45. #19128427C22semidirect
46. #19128427C22semidirect
47. #19128426C22semidirect
48. #19128424C22semidirect
49. #19128423C22semidirect
50. #19128422C22semidirect
51. #19128420C22semidirect
52. #19128419C22semidirect
53. #19128419C22semidirect
54. #19128418C22semidirect
55. #19128418C22semidirect
59. #19128409C22semidirect
62. #19128406C22semidirect
64. #19128405C22semidirect
72. #19128392C22semidirect
74. #19128391C22semidirect
75. #19128389C22semidirect
77. #19128387C22semidirect
80. #19128384C22semidirect
81. #19128370C22semidirect
82. #19128369C22semidirect
88. Q8×C22⋊D83C22semidirect
91. #19128364C22semidirect
93. #19128363C22semidirect
97. #19128360C22semidirect
99. #19128359C22semidirect
109. #19128325C22semidirect
110. #19128324C22semidirect
111. #19128321C22semidirect
112. #19128320C22semidirect
113. #19128319C22semidirect
114. #19128318C22semidirect
115. #19128314C22semidirect
116. #19128312C22semidirect
117. #19128311C22semidirect
118. #19128311C22semidirect
119. #19128310C22semidirect
120. #19128308C22semidirect
131. #19128258C22semidirect
136. #19128255C22semidirect
137. #19128255C22semidirect
138. #19128255C22semidirect
140. #19128254C22semidirect
150. #19128238C22semidirect
153. #19128235C22semidirect
158. #19128233C22semidirect
163. #19128231C22semidirect
170. #19128229C22semidirect
181. #19128184C22semidirect
183. #19128183C22semidirect
185. #19128182C22semidirect
188. #19128180C22semidirect
189. #19128179C22semidirect
190. #19128178C22semidirect
193. #19128177C22semidirect
194. #19128177C22semidirect
196. C4×#13050591C22semidirect
202. C4×#13050590C22semidirect
206. C4×#13050589C22semidirect
209. C2×C4×Dic166C22semidirect
219. C4×Q8×D83C22semidirect
220. C4×Q8×D83C22semidirect
223. #557×C83C22semidirect
224. #556×C83C22semidirect
226. #552×C83C22semidirect
229. #548×C83C22semidirect
231. #533×C83C22semidirect
233. #529×C83C22semidirect
235. C4×#41×C83C22semidirect
237. C2×C4×Q8×C83C22semidirect
650. Q8×D83#41semidirect
945. C4×D832−1+4semidirect
1033. #3482D83semidirect
1045. C83#62788semidirect
1062. #557C2×D83semidirect
1071. #556C2×D83semidirect
1098. #552C2×D83semidirect
1122. #548C2×D83semidirect
1164. #533C2×D83semidirect
1196. #529C2×D83semidirect
1233. C4×#41C2×D83semidirect
1249. C2×C4×Q8C2×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#249215522
#249215502
#249215412
#249215392
#249214592
#249214552
#249214512
#249214492
#249213242
#249213222
#249212702
#249212312
#249211652
#249211632
#249211132
#249211092
#249210802
#249210782
#249210762
#249210612
#249210542
Q8×#130505902
#249210412
#249208942
#249208882
#249207572
#249207562
C4×#145818402
C4×#145818392
C2×C4×Q8×D832
C83×#34822
#6278883