Finite Group Databasebeta

← #36312864

Subgroups — #36312864

Order 21248.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921560C211yesmaximal, characteristic, complemented
2#24921554C211yesmaximal, characteristic, complemented
3#24921515C213yesmaximal, complemented
4#24921511C213yesmaximal, complemented
5#24921471C212yesmaximal, complemented
6#24921437C216yesmaximal, complemented
7#24921373C213yesmaximal, complemented
8#24921343C213yesmaximal, complemented
9#24921280C211yesmaximal, characteristic, complemented
10#24921247C211yesmaximal, characteristic, complemented
11#24921214C216yesmaximal, complemented
12#24921142C212yesmaximal, complemented
13#24921085C213yesmaximal, complemented
14#24921085C211yesmaximal, characteristic, complemented
15#24921081C213yesmaximal, complemented
16Q8×#13050590C212yesmaximal, complemented
17#24921019C216yesmaximal, complemented
18#24920888C216yesmaximal, complemented
19#24920756C213yesmaximal, complemented
20#533×D83C213yesmaximal, complemented
21C4×#14581840C212yesmaximal, complemented
22C4×#41×D83C211yesmaximal, characteristic, complemented
23C83×#3482C211yesmaximal, characteristic, complemented
24C2×#14581840C2212yes—
25C2×#41×D83C2211yescharacteristic
26Q8×Dic166C2212yescomplemented
27#19128430C2211yescharacteristic, complemented
28#19128430C2213yescomplemented
29#19128429C2216yescomplemented
30#19128426C2213yescomplemented
31#19128425C2213yescomplemented
32#19128422C2216yescomplemented
33#19128421C2213yescomplemented
34#19128421C2216yescomplemented
35#19128421C2213yescomplemented
36#19128420C2216yescomplemented
37#19128415C2216yescomplemented
38#19128411C2216yes—
39#19128407C2216yescomplemented
40#19128406C2216yes—
41#19128406C2216yescomplemented
42#19128396C22112yescomplemented
43#19128390C2216yescomplemented
44#19128390C22112yescomplemented
45#19128390C2216yescomplemented
46#19128389C2216yes—
47#19128387C22112yescomplemented
48#19128385C2216yes—
49#19128385C2216yescomplemented
50#19128383C22112yescomplemented
51#19128379C22112yes—
52#19128376C22112yes—
53Q8×D332C2212yes—
54Q8×D332C2211yescharacteristic, complemented
55Q8×D332C2213yescomplemented
56#19128366C2213yescomplemented
57Q8×C22⋊D83C2212yes—
58Q8×C22⋊D83C2212yescomplemented
59#19128361C2216yescomplemented
60#19128358C2212yes—
61#19128358C2216yescomplemented
62#19128356C2216yes—
63#19128356C2213yescomplemented
64#19128356C2213yescomplemented
65#19128354C2213yescomplemented
66#19128353C2216yes—
67#19128353C2216yescomplemented
68#19128348C2216yes—
69#19128344C2216yes—
70#19128331C2216yescomplemented
71#19128320C2216yescomplemented
72#19128319C22112yescomplemented
73#19128318C2216yescomplemented
74#19128314C2216yescomplemented
75#19128311C2216yescomplemented
76#19128308C22112yescomplemented
77#19128294C22112yescomplemented
78#19128292C22112yescomplemented
79#19128280C2216yes—
80#19128274C2216yescomplemented
81#19128271C2216yes—
82#19128258C2216yescomplemented
83#19128258C2213yescomplemented
84#19128257C2216yes—
85#19128256C2213yes—
86#19128256C2213yes—
87#19128255C2213yes—
88#19128255C2216yes—
89#19128255C2216yescomplemented
90#19128255C2213yescomplemented
91#19128254C2216yescomplemented
92#19128254C2213yescomplemented
93#19128253C2216yescomplemented
94#19128253C2216yescomplemented
95#19128248C2211yescharacteristic
96#19128248C2213yescomplemented
97#19128247C2213yescomplemented
98C4⋊Q8×D83C2213yescomplemented
99C4⋊Q8×D83C2213yescomplemented
100#19128238C2213yes—
101#19128238C2213yescomplemented
102#19128233C2213yes—
103#19128233C2216yescomplemented
104#19128233C22112yescomplemented
105#19128233C2213yescomplemented
106#19128231C2216yescomplemented
107#19128231C2216yescomplemented
108#19128229C2216yes—
109#19128229C22112yescomplemented
110#19128229C2216yescomplemented
111#125×D83C2216yescomplemented
112#19128213C2213yes—
113#19128210C2216yes—
114#19128210C2216yes—
115#19128208C2213yes—
116C22⋊Q8×D83C2216yes—
117C22⋊Q8×D83C2216yes—
118#19128183C2212yes—
119#19128183C2216yescomplemented
120#19128182C2216yescomplemented
121#19128182C2216yescomplemented
122#19128179C2212yescomplemented
123#19128177C2216yescomplemented
124#19128177C2212yescomplemented
125#41×Dic83C2211yescharacteristic
126C4×#13050591C2211yescharacteristic
127C4×#13050591C2211yescharacteristic
128C4×#13050591C2216yescomplemented
129C4×#13050590C2213yes—
130C4×#13050590C2216yes—
131C4×#13050590C2216yescomplemented
132C4×#13050590C2216yescomplemented
133C4×#13050590C2213yescomplemented
134#19128169C2213yes—
135C4×#13050589C2213yes—
136C4×#13050589C2213yes—
137C4×Q8×D83C2211yescharacteristic
138C4×Q8×D83C2211yescharacteristic
139C4×Q8×D83C2216yescomplemented
140C4×Q8×D83C2212yescomplemented
141C4×Q8×D83C2216yescomplemented
142C4×D4×D83C2213yes—
143C4×D4×D83C2213yes—
144#117×D83C2213yes—
145#117×D83C2216yes—
146C2×C42×D83C2213yes—
147#557×C83C2211yescharacteristic, complemented
148#556×C83C2213yescomplemented
149#552×C83C2216yescomplemented
150D4×Q8×C83C2211yescharacteristic, complemented
151#548×C83C2212yes—
152#547×C83C2213yescomplemented
153#533×C83C2213yescomplemented
154#529×C83C2216yescomplemented
155C4×#41×C83C2211yescharacteristic
156C4×#41×C83C2213yescomplemented
157C2×C4×Q8×C83C2212yescomplemented
158#14581840—216no—
159C2×#13050591C2316yes—
160C2×#13050591C2311yescharacteristic
161C2×#13050590C2316yes—
162C2×#13050590C2313yes—
163C2×#13050590C2312yes—
164C2×#13050590C2316yes—
165C2×#13050590C2313yes—
166C2×#13050589C2313yes—
167#41×D83—28no—
168C2×Q8×D83C2312yes—
169C2×Q8×D83C2311yescharacteristic
170C2×Q8×D83C2316yes—
171C2×Q8×D83C2316yes—
172C2×D4×D83C2313yes—
173C22×C4×D83C2313yes—
174C22×C4×D83C2313yes—
175C22×C4×D83C2313yes—
176#14581792C2316yes—
177#14581792C2316yes—
178#14581792C2313yes—
179#14581792C2313yes—
180#14581791C2316yes—
181#14581791C2316yes—
182#14581791C2316yes—
183#14581791C2313yes—
184#14581791C2316yes—
185#14581791C2311yescharacteristic
186#14581790C2316yes—
187#14581790C2316yes—
188#14581790C2313yes—
189#14581788C2311yescharacteristic
190#14581787C2316yes—
191#14581787C23112yes—
192#14581787C2316yes—
193#14581785C23112yes—
194#14581785C23112yes—
195#14581785C23112yes—
196#14581785C23112yes—
197#14581785C2316yes—
198#14581785C2316yes—
199#14581784C2316yes—
200#14581784C23112yes—
201#14581783C2316yes—
202#14581783C2313yes—
203#14581783C23112yes—
204#14581783C2313yes—
205#14581783C2316yes—
206#14581783C2316yes—
207#14581782C2316yes—
208#14581782C23112yes—
209#14581782C23112yes—
210#14581782C23112yes—
211#14581782C2316yes—
212#14581781C2313yes—
213#14581779C2316yes—
214#14581779C2313yes—
215#14581779C23112yes—
216#14581778C23112yes—
217#14581778C2316yes—
218#14581778C2312yes—
219#14581777C2316yes—
220#14581777C23112yes—
221#14581777C2316yes—
222#14581776C2316yes—
223#14581774C23112yes—
224#14581774C23112yes—
225#14581774C23112yes—
226#14581774C2316yes—
227#14581774C23112yes—
228#14581774C2316yes—
229#14581773C2316yes—
230#14581772C23112yes—
231#14581772C2316yes—
232#14581772C2316yes—
233#14581772C2316yes—
234#14581772C2313yes—
235#14581772C2313yes—
236#14581771C2316yes—
237#14581771C2316yes—
238#14581771C2316yes—
239#14581771C2316yes—
240#14581771C23112yes—
241#14581770C23112yes—
242#14581770C23112yes—
243#14581770C23112yes—
244#14581770C2316yes—
245#14581770C2316yes—
246#14581769C23112yes—
247#14581769C2316yes—
248#14581769C23112yes—
249#14581769C2316yes—
250#14581768C2316yes—
251#14581768C2316yes—
252#14581768C2313yes—
253#14581768C2313yes—
254#14581767C2313yes—
255#14581767C2311yescharacteristic
256#14581765C23112yes—
257#14581765C2316yes—
258#14581765C2312yes—
259#14581764C2316yes—
260#14581764C2316yes—
261#14581763C2316yes—
262#14581763C23112yes—
263#14581763C2313yes—
264#14581763C2311yescharacteristic
265#14581762C2316yes—
266#14581760C2316yes—
267Q8×Dic83C2316yes—
268Q8×Dic83C2312yes—
269Q8×Dic83C2316yes—
270Q8×Dic83C2311yescharacteristic
271Q8×Dic83C2316yes—
272Q8×Dic83C2311yescharacteristic
273C4×Dic166C2313yes—
274C4×Dic166C2316yes—
275C4×Dic166C2316yes—
276C4×Dic166C2316yes—
277C4×Dic166C2313yes—
278C4×Dic166C2313yes—
279C4×Dic166C2316yes—
280C4×Dic166C2316yes—
281C4×Dic166C2313yes—
282C4×Dic166C23112yes—
283C4×Dic166C2316yes—
284#14581757C2316yes—
285#14581757C23112yes—
286#14581757C2316yes—
287#14581757C2313yes—
288#14581757C2313yes—
289#14581757C2316yes—
290#14581757C23112yes—
291C4×D332C2316yes—
292C4×D332C2316yes—
293C4×D332C2313yes—
294C4×D332C2313yes—
295C4×D332C2316yes—
296C4×D332C2313yes—
297C4×D332C2311yescharacteristic
298C4×D332C2316yes—
299C4×D332C2316yes—
300D4×Dic83C2313yes—
301D4×Dic83C2313yes—
302#14581754C2316yes—
303#14581754C2313yes—
304#14581754C23112yes—
305#14581754C2313yes—
306C4×C22⋊D83C2316yes—
307C4×C22⋊D83C2316yes—
308C4×C22⋊D83C2316yes—
309C4×C22⋊D83C2316yes—
310C4×C22⋊D83C23112yes—
311C4×C22⋊D83C2316yes—
312C4×C22⋊D83C2316yes—
313C4×C22⋊D83C2316yes—
314C4×C22⋊D83C2316yes—
315C4×C22⋊D83C2312yes—
316C4×C22⋊D83C2316yes—
317C4×C22⋊D83C2316yes—
318C4×C22⋊D83C2316yes—
319(C22⋊D83)⋊C4C2316yes—
320(C22⋊D83)⋊C4C2316yes—
321#14581751C2316yes—
322#14581751C2313yes—
323#14581751C2313yes—
324#14581751C2316yes—
325#14581751C2316yes—
326#14581751C2316yes—
327#14581750C2313yes—
328#14581750C2316yes—
329#14581750C2316yes—
330#14581750C23112yes—
331#14581750C2316yes—
332#14581750C2313yes—
333#14581749C2316yes—
334#14581749C2316yes—
335#14581749C23112yes—
336#14581749C2316yes—
337#14581749C2316yes—
338#14581749C2316yes—
339#14581749C2316yes—
340#14581748C23112yes—
341#14581748C2316yes—
342C4⋊C4×D83C2316yes—
343C4⋊C4×D83C23112yes—
344C4⋊C4×D83C2316yes—
345C4⋊C4×D83C2316yes—
346C4⋊C4×D83C2316yes—
347C4⋊C4×D83C2313yes—
348C4⋊C4×D83C2316yes—
349C4⋊C4×D83C2313yes—
350C4⋊C4×D83C23112yes—
351C22⋊C4×D83C23112yes—
352C22⋊C4×D83C2316yes—
353C2×C4×Dic83C2313yes—
354C2×C4×Dic83C2313yes—
355C2×C4×Dic83C2313yes—
356C42×D83C2311yescharacteristic
357C42×D83C2313yes—
358C42×D83C2313yes—
359C42×D83C2313yes—
360C42×D83C2313yes—
361C42×D83C2313yes—
362C42×D83C2313yes—
363C42×D83C2313yes—
364C42×D83C23112yes—
365C42×D83C2316yes—
366C2×#41×C83C2311yescharacteristic
367C2×#41×C83C2313yes—
368C22×Q8×C83C2312yes—
369C4⋊Q8×C83C2313yes—
370C4⋊Q8×C83C2313yes—
371#126×C83C23112yes—
372#125×C83C2316yes—
373#125×C83C2316yes—
374#124×C83C2316yes—
375#123×C83C23112yes—
376C22⋊Q8×C83C2316yes—
377C22⋊Q8×C83C2316yes—
378C22⋊Q8×C83C2316yes—
379#121×C83C2316yes—
380C4×Q8×C83C2312yes—
381C4×Q8×C83C2311yescharacteristic
382C4×Q8×C83C2313yes—
383C4×Q8×C83C2311yescharacteristic
384C4×Q8×C83C2316yes—
385C4×Q8×C83C2316yes—
386C4×Q8×C83C2313yes—
387C4×D4×C83C2316yes—
388C4×D4×C83C2313yes—
389C4×D4×C83C2313yes—
390C4×D4×C83C2313yes—
391C4×D4×C83C2311yescharacteristic
392C4×D4×C83C2316yes—
393#117×C83C2313yes—
394#117×C83C2316yes—
395#117×C83C2313yes—
396#117×C83C2316yes—
397C2×C4⋊C4×C83C2316yes—
398C2×C42×C83C2316yes—
399C2×C42×C83C2313yes—
400C23×D83C2413yes—
401#13050591—224no—
402#13050591#4118yescomplemented
403#13050590—212no—
404#13050590—224no—
405#13050590—224no—
406#13050590—28no—
407#13050590—46no—
408#13050589—212no—
409C2×Dic166C2412yes—
410C2×Dic166C2416yes—
411C2×Dic166C2416yes—
412C2×Dic166C2413yes—
413C2×Dic166C2413yes—
414C2×Dic166C24112yes—
415Q8×D83—24no—
416Q8×D83—28no—
417Q8×D83—224no—
418Q8×D83—412no—
419C2×D332C2412yes—
420C2×D332C2416yes—
421C2×D332C2411yescharacteristic
422C2×D332C2413yes—
423C2×C22⋊D83C2412yes—
424C2×C22⋊D83C2416yes—
425C2×C22⋊D83C2416yes—
426C2×C22⋊D83C2412yes—
427C2×C22⋊D83C2412yes—
428C2×C22⋊D83C2416yes—
429D4×D83—212no—
430C22×Dic83C2413yes—
431C22×Dic83C2413yes—
432C22×Dic83C2413yes—
433C2×C4×D83—212no—
434C2×C4×D83—212no—
435C2×C4×D83—46no—
436C2×C4×D83C2411yescharacteristic
437C2×C4×D83C2413yes—
438C2×C4×D83C2416yes—
439C2×C4×D83C2411yescharacteristic
440C2×C4×D83C2413yes—
441C2×C4×D83C2413yes—
442C2×C4×D83C24112yes—
443C2×C4×D83C2413yes—
444C2×C4×D83C2413yes—
445C2×C4×D83C2413yes—
446C2×C4×D83C2412yes—
447C2×C4×D83C24112yes—
448C2×C4×D83C2413yes—
449C2×C4×D83C2416yes—
450C2×C4×D83C2413yes—
451C2×C4×D83C2413yes—
452C2×C4×D83C2411yescharacteristic
453C4⋊Dic83C2411yescharacteristic
454C4⋊Dic83C2416yes—
455C4⋊Dic83C2413yes—
456C4⋊Dic83C24112yes—
457C4⋊Dic83C2413yes—
458C4⋊Dic83C2416yes—
459C4⋊Dic83C2416yes—
460C4⋊Dic83C2416yes—
461C4⋊Dic83C2416yes—
462C4⋊Dic83C2416yes—
463C4⋊Dic83C2416yes—
464C4⋊Dic83C2413yes—
465Dic83⋊C4C2416yes—
466Dic83⋊C4C2416yes—
467Dic83⋊C4C24112yes—
468Dic83⋊C4C2412yes—
469Dic83⋊C4C2416yes—
470Dic83⋊C4C2416yes—
471Dic83⋊C4C24112yes—
472Dic83⋊C4C2416yes—
473Dic83⋊C4C2416yes—
474Dic83⋊C4C2416yes—
475Dic83⋊C4C2416yes—
476Dic83⋊C4C2416yes—
477Dic83⋊C4C24112yes—
478Dic83⋊C4C2416yes—
479Dic83⋊C4C2416yes—
480C22⋊Dic83C2416yes—
481C22⋊Dic83C2416yes—
482C22⋊Dic83C24112yes—
483C22⋊Dic83C2416yes—
484C22⋊Dic83C2412yes—
485C22⋊Dic83C2416yes—
486C22⋊Dic83C2416yes—
487(C2×D83)⋊C4C2416yes—
488(C2×D83)⋊C4C2416yes—
489(C2×D83)⋊C4C2416yes—
490(C2×D83)⋊C4C2416yes—
491(C2×D83)⋊C4C2416yes—
492(C2×D83)⋊C4C2416yes—
493(C2×D83)⋊C4C2416yes—
494(C2×D83)⋊C4C2412yes—
495(C2×D83)⋊C4C2416yes—
496(C2×D83)⋊C4C2412yes—
497(C2×D83)⋊C4C2416yes—
498(C2×D83)⋊C4C2416yes—
499C4×Dic83C2411yescharacteristic
500C4×Dic83C2413yes—
501C4×Dic83C24112yes—
502C4×Dic83C2413yes—
503C4×Dic83C24112yes—
504C4×Dic83C2416yes—
505C4×Dic83C2413yes—
506C4×Dic83C2416yes—
507C4×Dic83C2413yes—
508C4×Dic83C2413yes—
509C4×Dic83C2411yescharacteristic
510C4×Dic83C2413yes—
511C4×Dic83C2411yescharacteristic
512C4×Dic83C2416yes—
513C4×Dic83C2413yes—
514C4×Dic83C2413yes—
515C4×Dic83C2413yes—
516#41×C83—24no—
517#41×C83—46no—
518C2×Q8×C83—28no—
519C2×Q8×C83C2413yes—
520C2×Q8×C83C2416yes—
521C2×Q8×C83C2411yescharacteristic
522C2×D4×C83C2411yescharacteristic
523C2×D4×C83C2413yes—
524C2×D4×C83C2416yes—
525C22×C4×C83C2413yes—
526C22×C4×C83C2413yes—
527C22×C4×C83C2416yes—
528C22×C4×C83C2413yes—
529C22×C4×C83C2412yes—
530C22×C4×C83C2416yes—
531C4⋊C4×C83C2411yescharacteristic
532C4⋊C4×C83C2413yes—
533C4⋊C4×C83C24112yes—
534C4⋊C4×C83C2416yes—
535C4⋊C4×C83C2416yes—
536C4⋊C4×C83C2416yes—
537C4⋊C4×C83C2413yes—
538C4⋊C4×C83C2416yes—
539C4⋊C4×C83C2416yes—
540C4⋊C4×C83C2413yes—
541C22⋊C4×C83C2416yes—
542C22⋊C4×C83C24112yes—
543C22⋊C4×C83C2412yes—
544C22⋊C4×C83C2416yes—
545C22⋊C4×C83C2416yes—
546C42×C83C2413yes—
547C42×C83C2416yes—
548C42×C83C2413yes—
549C42×C83C2416yes—
550C42×C83C2413yes—
551C42×C83C2411yescharacteristic
552C42×C83C2416yes—
553C23×C83C2513yes—
554C23×C83C2512yes—
555C22×D83—26no—
556C22×D83—26no—
557C22×D83—43no—
558C22×D83C2512yes—
559C22×D83C2513yes—
560C22×D83C2511yescharacteristic
561Q8×C83—212no—
562Q8×C83—26no—
563Q8×C83C2×#4114yes—
564D4×C83—26no—
565D4×C83—22no—
566D4×C83—46no—
567C2×C4×C83—212no—
568C2×C4×C83—26no—
569C2×C4×C83—26no—
570C2×C4×C83—24no—
571C2×C4×C83—26no—
572C2×C4×C83—46no—
573C2×C4×C83C2512yes—
574C2×C4×C83C2511yescharacteristic
575C2×C4×C83C2513yes—
576C2×C4×C83C2513yes—
577C2×C4×C83C2516yes—
578C2×C4×C83C2516yes—
579C2×C4×C83C2513yes—
580C2×C4×C83C2511yescharacteristic
581C2×C4×C83C2511yescharacteristic
582C22⋊D83—212no—
583C22⋊D83—212no—
584C22⋊D83—24no—
585C22⋊D83—24no—
586C22⋊D83—24no—
587C22⋊D83—46no—
588C2×Dic83—26no—
589C2×Dic83—26no—
590C2×Dic83—43no—
591C2×Dic83C2513yes—
592C2×Dic83C2511yescharacteristic
593C2×Dic83C2512yes—
594C2×Dic83C2513yes—
595C2×Dic83C2516yes—
596C2×Dic83C2516yes—
597C2×Dic83C2513yes—
598C2×Dic83C2511yescharacteristic
599C2×Dic83C2511yescharacteristic
600D332—212no—
601D332—24no—
602D332—22no—
603D332C2×#41112yes—
604C4×D83—26no—
605C4×D83—224no—
606C4×D83—26no—
607C4×D83—26no—
608C4×D83—212no—
609C4×D83—26no—
610C4×D83—24no—
611C4×D83—22no—
612C4×D83—26no—
613C4×D83—22no—
614C4×D83—26no—
615C4×D83—43no—
616C4×D83—43no—
617C4×D83—412no—
618C4×D83—46no—
619C4×D83C2×#41112yes—
620C4×D832−1+414yescomplemented
621Dic166—212no—
622Dic166—26no—
623Dic166—26no—
624Dic166—212no—
625Dic166—24no—
626Dic166—412no—
627C22×C83—23no—
628C22×C83—22no—
629C22×C83—23no—
630C22×C83—22no—
631C22×C83—23no—
632C22×C83—22no—
633C22×C83C2611yescharacteristic
634C2×D83—21no—
635C2×D83—23no—
636C2×D83—23no—
637C2×D83—21no—
638C2×D83—22no—
639C2×D83—22no—
640C2×D83—22no—
641C2×D83—412no—
642C2×D83C22×#4116yes—
643C2×D83C2×2−1+412yes—
644C4×C83—26no—
645C4×C83—21no—
646C4×C83—22no—
647C4×C83—23no—
648C4×C83—26no—
649C4×C83—23no—
650C4×C83C22×#4116yes—
651C4×C83C2×2−1+412yes—
652C4×C83#58512yes—
653Dic83—26no—
654Dic83—23no—
655Dic83—22no—
656Dic83—23no—
657Dic83—26no—
658Dic83—23no—
659Dic83—21no—
660Dic83C22×#4112yes—
661Dic83C2×2−1+412yes—
662#62805—831nomaximal, Sylow
663C2×C83—43no—
664C2×C83—42no—
665C2×C83C23×#4111yescharacteristic
666C2×C83C22×2−1+411yescharacteristic
667C2×C83C2×#58511yescharacteristic
668D83—22no—
669D83—26no—
670D83—42no—
671#3523—831no—
672#3523—831no—
673#3520—833no—
674#3520—833no—
675#3518—832no—
676#3515—836no—
677#3511—833no—
678#3509—833no—
679#3503—831no—
680#3499—831no—
681#3495—836no—
682#3489—832no—
683#3482—833no—
684#3482—831no—
685#3482—833no—
686#3482D8311yescharacteristic, complemented
687Q8×#41—832no—
688#3475—836no—
689#3461—836no—
690#3444—833no—
691C2×#533—833no—
692C4×2−1+4—832no—
693C2×C4×#41—831no—
694C83#6280511yescharacteristic, complemented, Sylow
695C2×2−1+4—832no—
696C22×#41—831no—
697Q82—832no—
698#557—833no—
699#557—836no—
700#557—831no—
701#557—833no—
702#557C2×D8311yescharacteristic, complemented
703#556—833no—
704#556—836no—
705#556—836no—
706#556—836no—
707#556—833no—
708#556—833no—
709#556C2×D8313yescomplemented
710#555—836no—
711#554—836no—
712#554—836no—
713#554—836no—
714#554—836no—
715#553—8312no—
716#552—8312no—
717#552—8312no—
718#552—836no—
719#552—836no—
720#552—836no—
721#552—836no—
722#552—8312no—
723#552—836no—
724#552C2×D8316yescomplemented
725#551—8312no—
726#551—8312no—
727D4×Q8—832no—
728D4×Q8—832no—
729D4×Q8—833no—
730D4×Q8—832no—
731D4×Q8—831no—
732D4×Q8—833no—
733D4×Q8C2×D8311yescharacteristic, complemented
734#548—832no—
735#548—836no—
736#548—836no—
737#548C2×D8312yes—
738#547—833no—
739#547—836no—
740#547—836no—
741#547—836no—
742#547—833no—
743#547—833no—
744#547C2×D8313yescomplemented
745#546—836no—
746#546—836no—
747#544—836no—
748#542—836no—
749#542—8312no—
750#542—836no—
751#541—8312no—
752#541—836no—
753#541—836no—
754#539—8312no—
755#539—8312no—
756#537—836no—
757#536—836no—
758#536—836no—
759#533—833no—
760#533—833no—
761#533—836no—
762#533—836no—
763#533—836no—
764#533—833no—
765#533—836no—
766#533—833no—
767#533—836no—
768#533—836no—
769#533—833no—
770#533—833no—
771#533—836no—
772#533C2×D8313yescomplemented
773#532—833no—
774#532—831no—
775#532—833no—
776C2×C4⋊Q8—833no—
777C2×C4⋊Q8—833no—
778#529—833no—
779#529—833no—
780#529—836no—
781#529—833no—
782#529—836no—
783#529—833no—
784#529—8312no—
785#529—836no—
786#529—836no—
787#529—836no—
788#529—8312no—
789#529C2×D8316yescomplemented
790C2×#125—836no—
791#525—833no—
792#525—836no—
793#525—836no—
794#525—833no—
795C2×C22⋊Q8—836no—
796C2×C22⋊Q8—836no—
797#520—832no—
798#520—836no—
799#520—836no—
800#520—836no—
801#519—832no—
802#519—836no—
803#519—832no—
804C4×#41—831no—
805C4×#41—831no—
806C4×#41—831no—
807C4×#41—836no—
808C4×#41—833no—
809C4×#41—833no—
810C4×#41—833no—
811C4×#41—833no—
812C4×#41—836no—
813C4×#41—836no—
814C4×#41—836no—
815C4×#41—833no—
816C4×#41C2×D8311yescharacteristic
817C4×#41C2×D8313yescomplemented
818C2×C4×Q8—831no—
819C2×C4×Q8—831no—
820C2×C4×Q8—836no—
821C2×C4×Q8—832no—
822C2×C4×Q8—836no—
823C2×C4×Q8C2×D8312yescomplemented
824C2×C4×D4—833no—
825C2×C4×D4—833no—
826C2×#117—833no—
827C2×#117—836no—
828C22×C42—833no—
8292−1+4—16616no—
830C2×#41—831no—
831C2×#41—836no—
832C2×#41—833no—
833C2×#41—833no—
834C2×#41—832no—
835C2×#41—833no—
836C2×#41—836no—
837C2×#41—836no—
838C2×#41—1668no—
839C2×#41C22×D8311yescharacteristic
840C2×#41C22×D8313yes—
841C22×Q8—836no—
842C22×Q8—831no—
843C22×Q8—836no—
844C22×Q8—832no—
845C22×Q8C22×D8312yes—
846C22×D4—833no—
847C23×C4—833no—
848C23×C4—833no—
849C23×C4—833no—
850C4⋊Q8—833no—
851C4⋊Q8—836no—
852C4⋊Q8—836no—
853C4⋊Q8—833no—
854C4⋊Q8—836no—
855C4⋊Q8—836no—
856C4⋊Q8—836no—
857C4⋊Q8—831no—
858C4⋊Q8—836no—
859C4⋊Q8—833no—
860C4⋊Q8—833no—
861C4⋊Q8—836no—
862C4⋊Q8—836no—
863C4⋊Q8C22×D8313yes—
864C4⋊Q8C22×D8313yes—
865#127—831no—
866#126—836no—
867#126—836no—
868#126—8312no—
869#126—836no—
870#126—836no—
871#126—8312no—
872#126—8312no—
873#126—8312no—
874#126—8312no—
875#126C22×D83112yes—
876#125—836no—
877#125—8312no—
878#125—836no—
879#125—836no—
880#125—836no—
881#125—833no—
882#125—833no—
883#125—8312no—
884#125—8312no—
885#125—836no—
886#125—8312no—
887#125—836no—
888#125—8312no—
889#125C22×D8316yes—
890#125C22×D8316yes—
891#124—833no—
892#124—833no—
893#124—836no—
894#124—8312no—
895#124—832no—
896#124—836no—
897#124—8312no—
898#124C22×D8316yes—
899#123—836no—
900#123—836no—
901#123—836no—
902#123—8312no—
903#123—836no—
904#123—836no—
905#123—836no—
906#123—8312no—
907#123—8312no—
908#123—8312no—
909#123—8312no—
910#123C22×D83112yes—
911C22⋊Q8—833no—
912C22⋊Q8—836no—
913C22⋊Q8—833no—
914C22⋊Q8—836no—
915C22⋊Q8—836no—
916C22⋊Q8—836no—
917C22⋊Q8—836no—
918C22⋊Q8—836no—
919C22⋊Q8—8312no—
920C22⋊Q8—836no—
921C22⋊Q8—8312no—
922C22⋊Q8—836no—
923C22⋊Q8—8312no—
924C22⋊Q8—8312no—
925C22⋊Q8—833no—
926C22⋊Q8—836no—
927C22⋊Q8—833no—
928C22⋊Q8—836no—
929C22⋊Q8—8312no—
930C22⋊Q8—836no—
931C22⋊Q8—8312no—
932C22⋊Q8—8312no—
933C22⋊Q8—836no—
934C22⋊Q8—836no—
935C22⋊Q8C22×D8316yes—
936C22⋊Q8C22×D8316yes—
937C22⋊Q8C22×D8316yes—
938#121—831no—
939#121—833no—
940#121—8312no—
941#121—836no—
942#121—836no—
943#121—836no—
944#121—831no—
945#121—833no—
946#121—832no—
947#121—836no—
948#121—8312no—
949#121C22×D8316yes—
950#120—836no—
951#120—836no—
952C4×Q8—831no—
953C4×Q8—831no—
954C4×Q8—836no—
955C4×Q8—832no—
956C4×Q8—836no—
957C4×Q8—836no—
958C4×Q8—833no—
959C4×Q8—833no—
960C4×Q8—8312no—
961C4×Q8—836no—
962C4×Q8—836no—
963C4×Q8—836no—
964C4×Q8—8312no—
965C4×Q8—836no—
966C4×Q8—836no—
967C4×Q8—833no—
968C4×Q8—833no—
969C4×Q8—833no—
970C4×Q8—8312no—
971C4×Q8—836no—
972C4×Q8—836no—
973C4×Q8—833no—
974C4×Q8—836no—
975C4×Q8—836no—
976C4×Q8C22×D8311yescharacteristic
977C4×Q8C22×D8313yes—
978C4×Q8C22×D8316yes—
979C4×Q8C22×D8311yescharacteristic
980C4×Q8C22×D8312yes—
981C4×Q8C22×D8316yes—
982C4×Q8C22×D8313yes—
983C4×D4—833no—
984C4×D4—833no—
985C4×D4—836no—
986C4×D4—836no—
987C4×D4—836no—
988C4×D4—832no—
989C4×D4—836no—
990C4×D4—836no—
991C4×D4—8312no—
992C4×D4—836no—
993C4×D4—836no—
994C4×D4—836no—
995C4×D4—836no—
996C4×D4—836no—
997C4×D4—836no—
998C4×D4—833no—
999C4×D4—833no—
1000C4×D4—836no—
1001C4×D4—8312no—
1002C4×D4—836no—
1003C4×D4—836no—
1004C4×D4—833no—
1005C4×D4—833no—
1006C4×D4—836no—
1007C4×D4—831no—
1008C4×D4—836no—
1009C4×D4—836no—
1010C4×D4—836no—
1011C4×D4—836no—
1012C4×D4—833no—
1013C4×D4C22×D8313yes—
1014C4×D4C22×D8313yes—
1015C4×D4C22×D8311yescharacteristic
1016C4×D4C22×D8316yes—
1017C4×D4C22×D8316yes—
1018C4×D4C22×D8313yes—
1019#117—833no—
1020#117—836no—
1021#117—836no—
1022#117—836no—
1023#117—833no—
1024#117—836no—
1025#117—833no—
1026#117—833no—
1027#117—836no—
1028#117—836no—
1029#117—8312no—
1030#117—836no—
1031#117—836no—
1032#117—8312no—
1033#117—836no—
1034#117—836no—
1035#117—836no—
1036#117—836no—
1037#117—8312no—
1038#117—836no—
1039#117—836no—
1040#117C22×D8313yes—
1041#117C22×D8316yes—
1042#117C22×D8313yes—
1043#117C22×D8316yes—
1044C2×C4⋊C4—833no—
1045C2×C4⋊C4—833no—
1046C2×C4⋊C4—836no—
1047C2×C4⋊C4—836no—
1048C2×C4⋊C4—8312no—
1049C2×C4⋊C4—836no—
1050C2×C4⋊C4—836no—
1051C2×C4⋊C4—8312no—
1052C2×C4⋊C4—836no—
1053C2×C4⋊C4C22×D8316yes—
1054C2×C22⋊C4—836no—
1055C2×C22⋊C4—8312no—
1056C2×C42—833no—
1057C2×C42—833no—
1058C2×C42—833no—
1059C2×C42—833no—
1060C2×C42—8312no—
1061C2×C42—833no—
1062C2×C42—833no—
1063C2×C42—833no—
1064C2×C42—833no—
1065C2×C42—836no—
1066C2×C42—833no—
1067C2×C42—833no—
1068C2×C42—831no—
1069C2×C42C22×D8316yes—
1070C2×C42C22×D8313yes—
1071C24—833no—
1072#41—24no—
1073#41—46no—
1074#41—3326no—
1075#41—838no—
1076#41—16624no—
1077#41—1668no—
1078#41—16612no—
1079#41—16624no—
1080#41—16612no—
1081#41—16624no—
1082C2×Q8—28no—
1083C2×Q8—33212no—
1084C2×Q8—8312no—
1085C2×Q8—832no—
1086C2×Q8—836no—
1087C2×Q8—836no—
1088C2×Q8—833no—
1089C2×Q8—833no—
1090C2×Q8—16624no—
1091C2×Q8—1664no—
1092C2×Q8—1668no—
1093C2×Q8C23×D8313yes—
1094C2×Q8C23×D8316yes—
1095C2×Q8C23×D8311yescharacteristic
1096C2×D4—836no—
1097C2×D4—832no—
1098C2×D4—832no—
1099C2×D4—836no—
1100C2×D4—836no—
1101C2×D4—832no—
1102C2×D4—833no—
1103C2×D4—832no—
1104C2×D4—836no—
1105C2×D4—831no—
1106C2×D4—16612no—
1107C2×D4C23×D8313yes—
1108C2×D4C23×D8311yescharacteristic
1109C2×D4C23×D8316yes—
1110C22×C4—3326no—
1111C22×C4—833no—
1112C22×C4—833no—
1113C22×C4—833no—
1114C22×C4—8312no—
1115C22×C4—836no—
1116C22×C4—833no—
1117C22×C4—831no—
1118C22×C4—833no—
1119C22×C4—833no—
1120C22×C4—831no—
1121C22×C4—831no—
1122C22×C4—833no—
1123C22×C4—833no—
1124C22×C4—833no—
1125C22×C4—833no—
1126C22×C4—833no—
1127C22×C4—8312no—
1128C22×C4—836no—
1129C22×C4—833no—
1130C22×C4—832no—
1131C22×C4—16612no—
1132C22×C4—16612no—
1133C22×C4C23×D8313yes—
1134C22×C4C23×D8313yes—
1135C22×C4C23×D8316yes—
1136C22×C4C23×D8313yes—
1137C22×C4C23×D8312yes—
1138C22×C4C23×D8316yes—
1139C4⋊C4—836no—
1140C4⋊C4—836no—
1141C4⋊C4—836no—
1142C4⋊C4—836no—
1143C4⋊C4—833no—
1144C4⋊C4—836no—
1145C4⋊C4—8312no—
1146C4⋊C4—836no—
1147C4⋊C4—836no—
1148C4⋊C4—833no—
1149C4⋊C4—836no—
1150C4⋊C4—833no—
1151C4⋊C4—836no—
1152C4⋊C4—836no—
1153C4⋊C4—836no—
1154C4⋊C4—8312no—
1155C4⋊C4—8312no—
1156C4⋊C4—8312no—
1157C4⋊C4—832no—
1158C4⋊C4—831no—
1159C4⋊C4—836no—
1160C4⋊C4—836no—
1161C4⋊C4—836no—
1162C4⋊C4—836no—
1163C4⋊C4—836no—
1164C4⋊C4—836no—
1165C4⋊C4—836no—
1166C4⋊C4C23×D8313yes—
1167C4⋊C4C23×D8313yes—
1168C4⋊C4C23×D8316yes—
1169C4⋊C4C23×D8316yes—
1170C4⋊C4C23×D83112yes—
1171C4⋊C4C23×D8313yes—
1172C4⋊C4C23×D8316yes—
1173C4⋊C4C23×D8316yes—
1174C4⋊C4C23×D8311yescharacteristic
1175C4⋊C4C23×D8316yes—
1176C22⋊C4—836no—
1177C22⋊C4—8312no—
1178C22⋊C4—832no—
1179C22⋊C4—836no—
1180C22⋊C4—836no—
1181C22⋊C4—836no—
1182C22⋊C4—836no—
1183C22⋊C4—836no—
1184C22⋊C4—836no—
1185C22⋊C4—836no—
1186C22⋊C4—836no—
1187C22⋊C4—836no—
1188C22⋊C4—836no—
1189C22⋊C4—832no—
1190C22⋊C4—832no—
1191C22⋊C4—836no—
1192C22⋊C4—836no—
1193C22⋊C4—836no—
1194C22⋊C4—836no—
1195C22⋊C4C23×D8316yes—
1196C22⋊C4C23×D83112yes—
1197C22⋊C4C23×D8312yes—
1198C22⋊C4C23×D8316yes—
1199C22⋊C4C23×D8316yes—
1200C42—831no—
1201C42—831no—
1202C42—833no—
1203C42—833no—
1204C42—833no—
1205C42—833no—
1206C42—833no—
1207C42—833no—
1208C42—833no—
1209C42—833no—
1210C42—836no—
1211C42—8312no—
1212C42—8312no—
1213C42—836no—
1214C42—831no—
1215C42—833no—
1216C42—836no—
1217C42C23×D8313yes—
1218C42C23×D8313yes—
1219C42C23×D8316yes—
1220C42C23×D8316yes—
1221C42C23×D8313yes—
1222C42C23×D8311yescharacteristic
1223C42C23×D8316yes—
1224C23—3323no—
1225C23—831no—
1226C23—833no—
1227C23—832no—
1228C23—1666no—
1229C23—1666no—
1230C23C24×D8312yes—
1231C23C24×D8313yes—
1232Q8—212no—
1233Q8—26no—
1234Q8—33212no—
1235Q8—16612no—
1236Q8—1664no—
1237Q8—16612no—
1238Q8—1666no—
1239Q8—1666no—
1240Q8#41×D8314yes—
1241D4—26no—
1242D4—22no—
1243D4—46no—
1244D4—3326no—
1245D4—8312no—
1246D4—16612no—
1247D4—1664no—
1248D4—1664no—
1249D4—1664no—
1250D4—16612no—
1251D4—16612no—
1252D4—1664no—
1253D4—1662no—
1254C2×C4—26no—
1255C2×C4—212no—
1256C2×C4—26no—
1257C2×C4—24no—
1258C2×C4—26no—
1259C2×C4—46no—
1260C2×C4—3323no—
1261C2×C4—3323no—
1262C2×C4—33212no—
1263C2×C4—3326no—
1264C2×C4—3323no—
1265C2×C4—831no—
1266C2×C4—831no—
1267C2×C4—8312no—
1268C2×C4—834no—
1269C2×C4—833no—
1270C2×C4—831no—
1271C2×C4—832no—
1272C2×C4—833no—
1273C2×C4—836no—
1274C2×C4—836no—
1275C2×C4—833no—
1276C2×C4—1662no—
1277C2×C4—1666no—
1278C2×C4—1666no—
1279C2×C4—1666no—
1280C2×C4—16624no—
1281C2×C4—1666no—
1282C2×C4—1666no—
1283C2×C4—1666no—
1284C2×C4—16612no—
1285C2×C4—1666no—
1286C2×C4—1664no—
1287C2×C4—1662no—
1288C2×C4—1666no—
1289C2×C4C24×D8311yescharacteristic
1290C2×C4C24×D8313yes—
1291C2×C4C24×D8313yes—
1292C2×C4C24×D8316yes—
1293C2×C4C24×D8316yes—
1294C2×C4C24×D8312yes—
1295C2×C4C24×D8313yes—
1296C2×C4C24×D8311yescharacteristic
1297C2×C4C24×D8311yescharacteristic
1298C22—22no—
1299C22—23no—
1300C22—23no—
1301C22—22no—
1302C22—23no—
1303C22—22no—
1304C22—33212no—
1305C22—836no—
1306C22—832no—
1307C22—1662no—
1308C22—1662no—
1309C22—1662no—
1310C22—1661no—
1311C22—1663no—
1312C22—1663no—
1313C22—1661no—
1314C22C25×D8311yescharacteristic
1315C4—21no—
1316C4—26no—
1317C4—23no—
1318C4—22no—
1319C4—23no—
1320C4—26no—
1321C4—832no—
1322C4—832no—
1323C4—1663no—
1324C4—1666no—
1325C4—1663no—
1326C4—1662no—
1327C4—1661no—
1328C4—1666no—
1329C4—1663no—
1330C4C2×#41×D8316yes—
1331C42−1+4×D8312yes—
1332C4#1912853712yes—
1333C2—43no—
1334C2—42no—
1335C2—3322no—
1336C2—1662no—
1337C2—1666no—
1338C2C22×#41×D8311yescharacteristic
1339C2C2×2−1+4×D8311yescharacteristic
1340C2C2×#1912853711yescharacteristic
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC83×#3482C2
hypercenter#3482D83
hypocenterC83#62805
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #3482

Complements

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

NH ≅ G/Ntype
1. #24921560C2semidirect
2. #24921554C2semidirect
3. #24921515C2semidirect
4. #24921511C2semidirect
5. #24921471C2semidirect
6. #24921437C2semidirect
7. #24921373C2semidirect
8. #24921343C2semidirect
9. #24921280C2semidirect
10. #24921247C2semidirect
11. #24921214C2semidirect
12. #24921142C2semidirect
13. #24921085C2semidirect
14. #24921085C2semidirect
15. #24921081C2semidirect
16. Q8×#13050590C2semidirect
17. #24921019C2semidirect
18. #24920888C2semidirect
19. #24920756C2semidirect
20. #533×D83C2semidirect
21. C4×#14581840C2semidirect
22. C4×#41×D83C2semidirect
23. C83×#3482C2semidirect
26. Q8×Dic166C22semidirect
27. #19128430C22semidirect
28. #19128430C22semidirect
29. #19128429C22semidirect
30. #19128426C22semidirect
31. #19128425C22semidirect
32. #19128422C22semidirect
33. #19128421C22semidirect
34. #19128421C22semidirect
35. #19128421C22semidirect
36. #19128420C22semidirect
37. #19128415C22semidirect
39. #19128407C22semidirect
41. #19128406C22semidirect
42. #19128396C22semidirect
43. #19128390C22semidirect
44. #19128390C22semidirect
45. #19128390C22semidirect
47. #19128387C22semidirect
49. #19128385C22semidirect
50. #19128383C22semidirect
54. Q8×D332C22semidirect
55. Q8×D332C22semidirect
56. #19128366C22semidirect
58. Q8×C22⋊D83C22semidirect
59. #19128361C22semidirect
61. #19128358C22semidirect
63. #19128356C22semidirect
64. #19128356C22semidirect
65. #19128354C22semidirect
67. #19128353C22semidirect
70. #19128331C22semidirect
71. #19128320C22semidirect
72. #19128319C22semidirect
73. #19128318C22semidirect
74. #19128314C22semidirect
75. #19128311C22semidirect
76. #19128308C22semidirect
77. #19128294C22semidirect
78. #19128292C22semidirect
80. #19128274C22semidirect
82. #19128258C22semidirect
83. #19128258C22semidirect
89. #19128255C22semidirect
90. #19128255C22semidirect
91. #19128254C22semidirect
92. #19128254C22semidirect
93. #19128253C22semidirect
94. #19128253C22semidirect
96. #19128248C22semidirect
97. #19128247C22semidirect
98. C4⋊Q8×D83C22semidirect
99. C4⋊Q8×D83C22semidirect
101. #19128238C22semidirect
103. #19128233C22semidirect
104. #19128233C22semidirect
105. #19128233C22semidirect
106. #19128231C22semidirect
107. #19128231C22semidirect
109. #19128229C22semidirect
110. #19128229C22semidirect
111. #125×D83C22semidirect
119. #19128183C22semidirect
120. #19128182C22semidirect
121. #19128182C22semidirect
122. #19128179C22semidirect
123. #19128177C22semidirect
124. #19128177C22semidirect
128. C4×#13050591C22semidirect
131. C4×#13050590C22semidirect
132. C4×#13050590C22semidirect
133. C4×#13050590C22semidirect
139. C4×Q8×D83C22semidirect
140. C4×Q8×D83C22semidirect
141. C4×Q8×D83C22semidirect
147. #557×C83C22semidirect
148. #556×C83C22semidirect
149. #552×C83C22semidirect
150. D4×Q8×C83C22semidirect
152. #547×C83C22semidirect
153. #533×C83C22semidirect
154. #529×C83C22semidirect
156. C4×#41×C83C22semidirect
157. C2×C4×Q8×C83C22semidirect
402. #13050591#41semidirect
620. C4×D832−1+4semidirect
686. #3482D83semidirect
694. C83#62805semidirect
702. #557C2×D83semidirect
709. #556C2×D83semidirect
724. #552C2×D83semidirect
733. D4×Q8C2×D83semidirect
744. #547C2×D83semidirect
772. #533C2×D83semidirect
789. #529C2×D83semidirect
817. C4×#41C2×D83semidirect
823. C2×C4×Q8C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249215602
#249215542
#249215152
#249215112
#249214712
#249214372
#249213732
#249213432
#249212802
#249212472
#249212142
#249211422
#249210852
#249210812
Q8×#130505902
#249210192
#249208882
#249207562
#533×D832
C4×#145818402
C4×#41×D832
C83×#34822
#6280583