Finite Group Databasebeta

← #36312630

Subgroups — #36312630

Order 21248.

7094 conjugacy classes of subgroups.

The subgroup lattice has 1344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921560C211yesmaximal, characteristic, complemented
2#24921558C213yesmaximal, complemented
3#24921545C213yesmaximal, complemented
4#24921543C211yesmaximal, characteristic, complemented
5#24921447C216yesmaximal, complemented
6#24921445C212yesmaximal, complemented
7#24921320C213yesmaximal, complemented
8#24921318C213yesmaximal, complemented
9#24921267C211yesmaximal, characteristic, complemented
10#24921228C211yesmaximal, characteristic, complemented
11#24921167C216yesmaximal, complemented
12#24921109C212yesmaximal, complemented
13#24921085C212yesmaximal, complemented
14#24921076C216yesmaximal, complemented
15#24921060C213yesmaximal, complemented
16Q8×#13050590C211yesmaximal, characteristic, complemented
17#41×Dic166C213yesmaximal, complemented
18#24920888C216yesmaximal, complemented
19#24920758C213yesmaximal, complemented
20#24920756C213yesmaximal, complemented
21C4×#14581839C212yesmaximal, complemented
22C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
23C83×#3480C211yesmaximal, characteristic, complemented
24C2×#14581839C2212yes—
25C22×Q8×D83C2211yescharacteristic
26#19128437C2213yescomplemented
27#19128433C2216yescomplemented
28Q8×Dic166C2211yescharacteristic, complemented
29Q8×Dic166C2213yescomplemented
30#19128430C2212yescomplemented
31#19128430C2213yescomplemented
32#19128429C2213yescomplemented
33#19128428C2216yescomplemented
34#19128427C2216yescomplemented
35#19128426C2213yescomplemented
36#19128425C2213yescomplemented
37#19128421C2216yescomplemented
38#19128420C2216yescomplemented
39#19128420C2216yescomplemented
40#19128418C22112yescomplemented
41#19128411C2213yescomplemented
42#19128410C22112yes—
43#19128410C2216yescomplemented
44#19128408C2216yes—
45#19128408C2213yescomplemented
46#19128406C2216yes—
47#19128403C2216yes—
48#19128394C22112yes—
49#19128393C2216yescomplemented
50#19128390C2216yes—
51#19128390C2216yescomplemented
52#19128389C2216yes—
53#19128388C22112yescomplemented
54#19128387C22112yes—
55#19128371C2213yescomplemented
56Q8×D332C2212yes—
57Q8×D332C2211yescharacteristic, complemented
58D4×Dic166C2216yes—
59D4×Dic166C2213yescomplemented
60Q8×C22⋊D83C2212yes—
61#19128364C2216yes—
62#19128359C2216yes—
63#19128358C2212yes—
64#19128358C2212yescomplemented
65#19128357C2216yes—
66#19128357C2216yescomplemented
67#19128356C2216yes—
68#19128351C2216yes—
69#19128349C22112yes—
70#19128331C2216yes—
71#19128320C2216yescomplemented
72#19128319C22112yescomplemented
73#19128318C2216yescomplemented
74#19128314C2216yescomplemented
75#19128311C2216yescomplemented
76#19128308C22112yescomplemented
77#19128294C22112yes—
78#19128292C22112yes—
79#19128280C2216yes—
80#19128274C2216yes—
81#19128271C2216yes—
82#19128258C2213yes—
83#19128258C2216yescomplemented
84#19128256C2213yes—
85#19128256C2213yes—
86#19128255C2213yes—
87#19128255C2213yes—
88#19128255C2216yescomplemented
89#19128254C2213yes—
90#19128254C22112yescomplemented
91#19128249C2213yes—
92#19128249C2213yes—
93#19128248C2213yes—
94#19128248C2213yes—
95#19128247C2213yes—
96#19128238C2213yes—
97#19128238C2213yes—
98#19128233C2216yes—
99#19128233C2213yes—
100#19128233C2213yes—
101#19128233C2216yes—
102#19128233C2216yescomplemented
103#19128232C2216yes—
104#19128232C2216yes—
105#19128231C2216yes—
106#19128231C2216yes—
107#19128231C22112yescomplemented
108#19128230C2216yes—
109#19128230C2216yes—
110#19128229C2216yes—
111#19128229C2216yes—
112#19128213C2211yescharacteristic
113#19128211C2216yes—
114#19128211C2216yes—
115#19128210C2216yes—
116#19128210C2216yes—
117#19128208C2213yes—
118#19128184C2212yescomplemented
119#19128181C2216yes—
120#19128180C2216yes—
121#19128180C2216yescomplemented
122#19128178C2216yescomplemented
123#19128177C2212yes—
124#19128177C2212yescomplemented
125#41×Dic83C2216yes—
126C4×#13050590C2216yes—
127C4×#13050590C2213yes—
128C4×#13050590C2216yes—
129C4×#13050589C2216yes—
130C4×#13050589C2216yes—
131C4×#13050589C2216yescomplemented
132C2×Q8×Dic83C2211yescharacteristic
133C2×C4×Dic166C2213yes—
134C2×C4×Dic166C2216yescomplemented
135C2×#14581757C2213yes—
136C4×Q8×D83C2213yes—
137C4×Q8×D83C2211yescharacteristic
138C4×Q8×D83C2211yescharacteristic
139C4×Q8×D83C2211yescharacteristic
140C4×Q8×D83C2213yes—
141C4×Q8×D83C2213yes—
142C4×Q8×D83C2213yes—
143C4×Q8×D83C2211yescharacteristic
144C4×Q8×D83C2212yescomplemented
145C2×C4⋊C4×D83C2213yes—
146C2×C42×D83C2213yes—
147#559×C83C2213yescomplemented
148#557×C83C2211yescharacteristic, complemented
149#556×C83C2213yescomplemented
150#553×C83C2216yes—
151#550×C83C2211yescharacteristic, complemented
152#548×C83C2212yes—
153#532×C83C2213yes—
154#529×C83C2216yescomplemented
155C4×#41×C83C2213yes—
156C4×#41×C83C2212yescomplemented
157C2×C4×Q8×C83C2211yescharacteristic
158#14581839—216no—
159C2×#13050590C2311yescharacteristic
160C2×#13050590C2316yes—
161C2×#13050590C2316yes—
162C2×#13050589C2316yes—
163C2×#13050589C2316yes—
164C2×#13050589C2316yes—
165C22×Dic166C2313yes—
166C22×Dic166C2316yes—
167C2×Q8×D83—28no—
168C2×Q8×D83C2311yescharacteristic
169C2×Q8×D83C2312yes—
170C2×Q8×D83C2313yes—
171C2×Q8×D83C2313yes—
172C2×Q8×D83C2311yescharacteristic
173C22×C4×D83C2311yescharacteristic
174C22×C4×D83C2313yes—
175C22×C4×D83C2313yes—
176#14581792C2316yes—
177#14581792C2316yes—
178#14581792C2313yes—
179#14581792C2313yes—
180#14581791C23112yes—
181#14581791C2316yes—
182#14581791C23112yes—
183#14581791C2313yes—
184#14581791C2313yes—
185#14581790C2316yes—
186#14581790C2313yes—
187#14581788C2313yes—
188#14581787C23112yes—
189#14581787C2316yes—
190#14581787C2316yes—
191#14581785C23112yes—
192#14581785C23112yes—
193#14581785C2316yes—
194#14581785C23112yes—
195#14581785C23112yes—
196#14581785C2316yes—
197#14581784C23112yes—
198#14581784C2316yes—
199#14581783C2316yes—
200#14581783C23112yes—
201#14581783C23112yes—
202#14581783C2316yes—
203#14581783C2313yes—
204#14581783C2313yes—
205#14581783C2316yes—
206#14581782C23112yes—
207#14581782C23112yes—
208#14581782C2316yes—
209#14581782C2316yes—
210#14581781C2313yes—
211#14581779C2316yes—
212#14581779C2316yes—
213#14581779C2313yes—
214#14581779C2316yes—
215#14581778C2316yes—
216#14581778C23112yes—
217#14581778C2316yes—
218#14581777C2316yes—
219#14581777C2316yes—
220#14581776C23112yes—
221#14581776C2312yes—
222#14581774C23112yes—
223#14581774C2316yes—
224#14581774C23112yes—
225#14581774C2316yes—
226#14581774C23112yes—
227#14581773C23112yes—
228#14581773C2316yes—
229#14581772C2316yes—
230#14581772C2316yes—
231#14581772C2316yes—
232#14581772C2316yes—
233#14581772C2311yescharacteristic
234#14581772C2311yescharacteristic
235#14581771C23112yes—
236#14581771C2316yes—
237#14581771C2316yes—
238#14581771C2316yes—
239#14581771C2316yes—
240#14581770C2316yes—
241#14581770C23112yes—
242#14581770C2316yes—
243#14581769C23112yes—
244#14581769C23112yes—
245#14581769C23112yes—
246#14581769C23112yes—
247#14581769C23112yes—
248#14581769C2316yes—
249#14581769C2316yes—
250#14581768C2316yes—
251#14581768C2313yes—
252#14581768C2313yes—
253#14581767C2311yescharacteristic
254#14581767C2311yescharacteristic
255#14581765C2316yes—
256#14581765C2316yes—
257#14581764C23112yes—
258#14581764C2316yes—
259#14581764C2316yes—
260#14581763C2316yes—
261#14581763C2316yes—
262#14581763C2313yes—
263#14581763C2313yes—
264#14581763C2316yes—
265#14581762C2312yes—
266#14581760C2316yes—
267Q8×Dic83C2313yes—
268Q8×Dic83C2312yes—
269Q8×Dic83C2311yescharacteristic
270Q8×Dic83C2313yes—
271Q8×Dic83C2311yescharacteristic
272Q8×Dic83C2316yes—
273Q8×Dic83C2316yes—
274C4×Dic166C2316yes—
275C4×Dic166C2313yes—
276C4×Dic166C23112yes—
277C4×Dic166C2316yes—
278C4×Dic166C2313yes—
279C4×Dic166C2316yes—
280C4×Dic166C2313yes—
281C4×Dic166C2316yes—
282C4×Dic166C2313yes—
283C4×Dic166C2316yes—
284C4×Dic166C2313yes—
285C4×Dic166C2316yes—
286C4×Dic166C2316yes—
287C4×Dic166C2316yes—
288C4×Dic166C2313yes—
289C4×Dic166C2316yes—
290C4×Dic166C2316yes—
291#14581757C2316yes—
292#14581757C2313yes—
293#14581757C2316yes—
294#14581757C2316yes—
295#14581757C2313yes—
296#14581757C2316yes—
297#14581757C2313yes—
298#14581757C2316yes—
299#14581757C2313yes—
300#14581757C2316yes—
301C4×D332C2316yes—
302C4×D332C2313yes—
303C4×D332C2313yes—
304C4×D332C2312yes—
305C4×D332C2312yes—
306C4×D332C2316yes—
307D4×Dic83C2316yes—
308D4×Dic83C2316yes—
309D4×Dic83C23112yes—
310D4×Dic83C2316yes—
311D4×Dic83C2316yes—
312D4×Dic83C23112yes—
313D4×Dic83C2316yes—
314C4×C22⋊D83C2316yes—
315C4×C22⋊D83C2316yes—
316C4×C22⋊D83C2316yes—
317C4×C22⋊D83C2316yes—
318C4×C22⋊D83C2316yes—
319C4×C22⋊D83C2316yes—
320C4×C22⋊D83C2316yes—
321C4×C22⋊D83C2316yes—
322C4×C22⋊D83C2316yes—
323C4×C22⋊D83C2316yes—
324(C22⋊D83)⋊C4C23112yes—
325(C22⋊D83)⋊C4C23112yes—
326(C22⋊D83)⋊C4C23112yes—
327#14581751C2316yes—
328#14581751C2313yes—
329#14581751C2316yes—
330#14581751C23112yes—
331#14581750C2316yes—
332#14581750C2316yes—
333#14581750C2316yes—
334#14581749C2316yes—
335#14581749C2316yes—
336#14581749C2316yes—
337#14581749C2316yes—
338#14581749C2316yes—
339#14581748C23112yes—
340#14581748C23112yes—
341#14581748C23112yes—
342C2×C4⋊Dic83C2316yes—
343C2×C4⋊Dic83C2313yes—
344C2×Dic83⋊C4C23112yes—
345C2×Dic83⋊C4C2316yes—
346C4⋊C4×D83C2313yes—
347C4⋊C4×D83C2316yes—
348C4⋊C4×D83C2313yes—
349C4⋊C4×D83C2313yes—
350C4⋊C4×D83C2316yes—
351C4⋊C4×D83C2313yes—
352C4⋊C4×D83C2316yes—
353C2×C4×Dic83C2313yes—
354C2×C4×Dic83C2313yes—
355C2×C4×Dic83C2313yes—
356C2×C4×Dic83C23112yes—
357C42×D83C2313yes—
358C42×D83C2313yes—
359C42×D83C2313yes—
360C42×D83C2313yes—
361C42×D83C2313yes—
362C42×D83C2313yes—
363C42×D83C2313yes—
364C42×D83C2313yes—
365C42×D83C2316yes—
366C2×#41×C83C2312yes—
367C2×#41×C83C2313yes—
368C22×Q8×C83C2311yescharacteristic
369C4⋊Q8×C83C2313yes—
370#127×C83C2313yes—
371#126×C83C23112yes—
372#125×C83C2316yes—
373#124×C83C2316yes—
374#124×C83C2316yes—
375#123×C83C23112yes—
376C22⋊Q8×C83C2316yes—
377#121×C83C2316yes—
378#121×C83C2316yes—
379#121×C83C2316yes—
380C4×Q8×C83C2312yes—
381C4×Q8×C83C2311yescharacteristic
382C4×Q8×C83C2311yescharacteristic
383C4×Q8×C83C2313yes—
384C4×Q8×C83C2313yes—
385C4×Q8×C83C2313yes—
386C4×Q8×C83C2313yes—
387C4×D4×C83C2316yes—
388C4×D4×C83C2316yes—
389C4×D4×C83C2313yes—
390C4×D4×C83C2316yes—
391C4×D4×C83C2313yes—
392C4×D4×C83C2316yes—
393C4×D4×C83C2316yes—
394#117×C83C2311yescharacteristic
395#117×C83C2316yes—
396#117×C83C2316yes—
397C2×C4⋊C4×C83C2313yes—
398C2×C42×C83C2313yes—
399C2×C42×C83C2316yes—
400C23×D83C2411yescharacteristic
401#13050590—24no—
402#13050590—224no—
403#13050590—412no—
404#13050589—224no—
405#13050589—224no—
406#13050589—412no—
407C2×Dic166—212no—
408C2×Dic166—224no—
409C2×Dic166C2416yes—
410C2×Dic166C2416yes—
411C2×Dic166C2413yes—
412C2×Dic166C2416yes—
413C2×Dic166C2411yescharacteristic
414C2×Dic166C2416yes—
415C2×Dic166C2416yes—
416C2×Dic166C2413yes—
417Q8×D83—24no—
418Q8×D83—28no—
419Q8×D83—212no—
420Q8×D83—212no—
421Q8×D83#4118yescomplemented
422C2×D332C2412yes—
423C2×D332C2412yes—
424C2×D332C2411yescharacteristic
425C2×C22⋊D83C2416yes—
426C2×C22⋊D83C2416yes—
427C2×C22⋊D83C2412yes—
428C2×C22⋊D83C2416yes—
429C2×C22⋊D83C2416yes—
430C22×Dic83C2413yes—
431C22×Dic83C24112yes—
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2413yes—
434C22×Dic83C24112yes—
435C2×C4×D83—24no—
436C2×C4×D83—212no—
437C2×C4×D83—46no—
438C2×C4×D83C2411yescharacteristic
439C2×C4×D83C2411yescharacteristic
440C2×C4×D83C2413yes—
441C2×C4×D83C2416yes—
442C2×C4×D83C2413yes—
443C2×C4×D83C2413yes—
444C2×C4×D83C2413yes—
445C2×C4×D83C2413yes—
446C2×C4×D83C2411yescharacteristic
447C2×C4×D83C2411yescharacteristic
448C2×C4×D83C2412yes—
449C2×C4×D83C2413yes—
450C2×C4×D83C2416yes—
451C2×C4×D83C2413yes—
452C2×C4×D83C2413yes—
453C4⋊Dic83C2413yes—
454C4⋊Dic83C2416yes—
455C4⋊Dic83C2413yes—
456C4⋊Dic83C2413yes—
457C4⋊Dic83C2416yes—
458C4⋊Dic83C2416yes—
459C4⋊Dic83C2416yes—
460C4⋊Dic83C2416yes—
461C4⋊Dic83C24112yes—
462C4⋊Dic83C24112yes—
463C4⋊Dic83C2412yes—
464C4⋊Dic83C2412yes—
465C4⋊Dic83C2413yes—
466Dic83⋊C4C2416yes—
467Dic83⋊C4C2416yes—
468Dic83⋊C4C2416yes—
469Dic83⋊C4C2416yes—
470Dic83⋊C4C2416yes—
471Dic83⋊C4C24112yes—
472Dic83⋊C4C2416yes—
473Dic83⋊C4C2416yes—
474Dic83⋊C4C2416yes—
475Dic83⋊C4C2416yes—
476Dic83⋊C4C2416yes—
477Dic83⋊C4C2416yes—
478Dic83⋊C4C24112yes—
479Dic83⋊C4C2416yes—
480Dic83⋊C4C2416yes—
481Dic83⋊C4C2416yes—
482C22⋊Dic83C2416yes—
483C22⋊Dic83C24112yes—
484C22⋊Dic83C24112yes—
485C22⋊Dic83C2416yes—
486C22⋊Dic83C2416yes—
487C22⋊Dic83C2416yes—
488C22⋊Dic83C2416yes—
489(C2×D83)⋊C4C2416yes—
490(C2×D83)⋊C4C2416yes—
491(C2×D83)⋊C4C2412yes—
492(C2×D83)⋊C4C2412yes—
493(C2×D83)⋊C4C2416yes—
494(C2×D83)⋊C4C2416yes—
495(C2×D83)⋊C4C2416yes—
496(C2×D83)⋊C4C2416yes—
497(C2×D83)⋊C4C2412yes—
498(C2×D83)⋊C4C2412yes—
499C4×Dic83C2413yes—
500C4×Dic83C2413yes—
501C4×Dic83C24112yes—
502C4×Dic83C2413yes—
503C4×Dic83C2413yes—
504C4×Dic83C2413yes—
505C4×Dic83C2416yes—
506C4×Dic83C2416yes—
507C4×Dic83C24112yes—
508C4×Dic83C2413yes—
509C4×Dic83C2413yes—
510C4×Dic83C2413yes—
511C4×Dic83C2413yes—
512C4×Dic83C2413yes—
513C4×Dic83C2413yes—
514C4×Dic83C2413yes—
515C4×Dic83C2416yes—
516#41×C83—28no—
517#41×C83—212no—
518C2×Q8×C83—24no—
519C2×Q8×C83C2413yes—
520C2×Q8×C83C2413yes—
521C2×Q8×C83C2411yescharacteristic
522C2×D4×C83C2416yes—
523C2×D4×C83C2416yes—
524C2×D4×C83C2413yes—
525C2×D4×C83C2416yes—
526C22×C4×C83C2413yes—
527C22×C4×C83C2416yes—
528C22×C4×C83C2416yes—
529C22×C4×C83C2413yes—
530C22×C4×C83C2416yes—
531C22×C4×C83C2411yescharacteristic
532C4⋊C4×C83C2411yescharacteristic
533C4⋊C4×C83C2411yescharacteristic
534C4⋊C4×C83C2416yes—
535C4⋊C4×C83C2416yes—
536C4⋊C4×C83C2416yes—
537C4⋊C4×C83C2416yes—
538C4⋊C4×C83C2413yes—
539C4⋊C4×C83C2416yes—
540C4⋊C4×C83C2413yes—
541C22⋊C4×C83C2412yes—
542C22⋊C4×C83C2416yes—
543C22⋊C4×C83C2416yes—
544C22⋊C4×C83C24112yes—
545C22⋊C4×C83C24112yes—
546C42×C83C2416yes—
547C42×C83C2413yes—
548C42×C83C2416yes—
549C42×C83C2413yes—
550C42×C83C2412yes—
551C42×C83C2413yes—
552C42×C83C2413yes—
553C23×C83C2516yes—
554C23×C83C2511yescharacteristic
555C22×D83—22no—
556C22×D83—22no—
557C22×D83—22no—
558C22×D83C2512yes—
559C22×D83C2511yescharacteristic
560C22×D83C2511yescharacteristic
561Q8×C83—26no—
562Q8×C83—26no—
563Q8×C83C2×#4114yes—
564D4×C83—212no—
565D4×C83—212no—
566D4×C83—26no—
567D4×C83—46no—
568C2×C4×C83—26no—
569C2×C4×C83—212no—
570C2×C4×C83—212no—
571C2×C4×C83—43no—
572C2×C4×C83—46no—
573C2×C4×C832−1+414yescomplemented
574C2×C4×C83C2513yes—
575C2×C4×C83C2512yes—
576C2×C4×C83C2512yes—
577C2×C4×C83C2513yes—
578C2×C4×C83C2516yes—
579C2×C4×C83C2513yes—
580C2×C4×C83C2513yes—
581C2×C4×C83C2511yescharacteristic
582C2×C4×C83C2511yescharacteristic
583C22⋊D83—24no—
584C22⋊D83—212no—
585C22⋊D83—212no—
586C22⋊D83—212no—
587C22⋊D83—46no—
588C2×Dic83—22no—
589C2×Dic83—26no—
590C2×Dic83—224no—
591C2×Dic83—43no—
592C2×Dic83—412no—
593C2×Dic83C2511yescharacteristic
594C2×Dic83C2511yescharacteristic
595C2×Dic83C2513yes—
596C2×Dic83C2512yes—
597C2×Dic83C2513yes—
598C2×Dic83C2516yes—
599C2×Dic83C2516yes—
600C2×Dic83C2513yes—
601C2×Dic83C2513yes—
602D332—24no—
603D332—24no—
604D332—22no—
605C4×D83—26no—
606C4×D83—26no—
607C4×D83—26no—
608C4×D83—26no—
609C4×D83—212no—
610C4×D83—22no—
611C4×D83—22no—
612C4×D83—22no—
613C4×D83—22no—
614C4×D83—24no—
615C4×D83—26no—
616C4×D83—43no—
617C4×D83—43no—
618C4×D83—46no—
619C4×D83C2×#41112yes—
620Dic166—26no—
621Dic166—212no—
622Dic166—22no—
623Dic166—212no—
624Dic166—212no—
625Dic166—46no—
626Dic166—46no—
627Dic166C2×#41112yes—
628C22×C83—21no—
629C22×C83—21no—
630C22×C83—26no—
631C22×C83—26no—
632C22×C83—26no—
633C22×C83C2×2−1+412yes—
634C22×C83C2611yescharacteristic
635C2×D83—28no—
636C2×D83—21no—
637C2×D83—21no—
638C2×D83—21no—
639C2×D83—21no—
640C2×D83—22no—
641C2×D83—22no—
642C2×D83—22no—
643C2×D83C22×#4112yes—
644C2×D83#58512yes—
645C4×C83—22no—
646C4×C83—23no—
647C4×C83—26no—
648C4×C83—22no—
649C4×C83—23no—
650C4×C83—23no—
651C4×C83C22×#4116yes—
652C4×C83C2×2−1+412yes—
653C4×C83C2×2−1+412yes—
654Dic83—23no—
655Dic83—26no—
656Dic83—22no—
657Dic83—21no—
658Dic83—21no—
659Dic83—26no—
660Dic83—23no—
661Dic83—23no—
662Dic83C22×#4116yes—
663#62788—831nomaximal, Sylow
664C2×C83—22no—
665C2×C83—46no—
666C2×C83C23×#4111yescharacteristic
667C2×C83C22×2−1+411yescharacteristic
668C2×C83C2×#58511yescharacteristic
669D83—22no—
670D83—22no—
671D83—42no—
672#3523—831no—
673#3523—833no—
674#3522—833no—
675#3522—831no—
676#3516—836no—
677#3516—832no—
678#3507—833no—
679#3507—833no—
680#3502—831no—
681#3497—831no—
682#3492—836no—
683#3486—832no—
684#3482—836no—
685#3482—832no—
686#3480—833no—
687#3480D8311yescharacteristic, complemented
688Q8×#41—833no—
689Q8×#41—831no—
690#3461—836no—
691#3444—833no—
692#3444—833no—
693C4×2−1+4—832no—
694C22×C4×Q8—831no—
695C83#6278811yescharacteristic, complemented, Sylow
696C2×2−1+4—832no—
697C23×Q8—831no—
698#559—833no—
699#559—836no—
700#559C2×D8313yescomplemented
701Q82—831no—
702Q82—833no—
703#557—833no—
704#557—836no—
705#557—836no—
706#557—833no—
707#557—833no—
708#557—832no—
709#557C2×D8311yescharacteristic, complemented
710#556—833no—
711#556—8312no—
712#556—836no—
713#556—836no—
714#556—836no—
715#556C2×D8313yescomplemented
716#554—833no—
717#554—836no—
718#554—833no—
719#554—8312no—
720#554—836no—
721#554—836no—
722#553—8312no—
723#553—836no—
724#553C2×D8316yes—
725#552—8312no—
726#552—836no—
727#552—8312no—
728#552—836no—
729#552—836no—
730#552—836no—
731#550—833no—
732#550C2×D8311yescharacteristic, complemented
733D4×Q8—832no—
734D4×Q8—836no—
735D4×Q8—832no—
736D4×Q8—831no—
737D4×Q8—836no—
738D4×Q8—833no—
739#548—832no—
740#548—832no—
741#548—836no—
742#548—836no—
743#548—836no—
744#548C2×D8312yes—
745#547—8312no—
746#547—836no—
747#547—836no—
748#544—836no—
749#542—836no—
750#542—8312no—
751#542—836no—
752#541—8312no—
753#541—836no—
754#541—836no—
755#539—8312no—
756#539—8312no—
757#537—836no—
758#536—836no—
759#536—836no—
760#533—833no—
761#533—833no—
762#533—833no—
763#533—833no—
764#533—836no—
765#533—833no—
766#533—8312no—
767#533—833no—
768#533—836no—
769#532—833no—
770#532—833no—
771#532—833no—
772#532—833no—
773#532—833no—
774#532C2×D8313yes—
775#529—836no—
776#529—836no—
777#529—836no—
778#529—836no—
779#529—833no—
780#529—833no—
781#529—836no—
782#529—836no—
783#529—836no—
784#529—836no—
785#529—833no—
786#529—833no—
787#529—8312no—
788#529—836no—
789#529—836no—
790#529—836no—
791#529C2×D8316yescomplemented
792#525—833no—
793#525—836no—
794#525—836no—
795#525—836no—
796#525—836no—
797#525—831no—
798#520—832no—
799#520—836no—
800#520—836no—
801#520—836no—
802#519—832no—
803#519—832no—
804#519—836no—
805C4×#41—836no—
806C4×#41—836no—
807C4×#41—836no—
808C4×#41—836no—
809C4×#41—836no—
810C4×#41—833no—
811C4×#41—836no—
812C4×#41C2×D8313yes—
813C4×#41C2×D8312yescomplemented
814C2×C4×Q8—831no—
815C2×C4×Q8—831no—
816C2×C4×Q8—833no—
817C2×C4×Q8—831no—
818C2×C4×Q8—833no—
819C2×C4×Q8—831no—
820C2×C4×Q8—833no—
821C2×C4×Q8—831no—
822C2×C4×Q8—833no—
823C2×C4×Q8—832no—
824C2×C4×Q8—833no—
825C2×C4×Q8—833no—
826C2×C4×Q8—836no—
827C2×C4×Q8C2×D8311yescharacteristic
828C22×C4⋊C4—833no—
829C22×C42—833no—
8302−1+4—16616no—
831C2×#41—836no—
832C2×#41—836no—
833C2×#41—836no—
834C2×#41—836no—
835C2×#41—831no—
836C2×#41—836no—
837C2×#41C22×D8313yes—
838C2×#41C22×D8312yes—
839C22×Q8—831no—
840C22×Q8—833no—
841C22×Q8—833no—
842C22×Q8—831no—
843C22×Q8—832no—
844C22×Q8—833no—
845C22×Q8—836no—
846C22×Q8—1668no—
847C22×Q8C22×D8311yescharacteristic
848C23×C4—833no—
849C23×C4—833no—
850C23×C4—831no—
851C4⋊Q8—833no—
852C4⋊Q8—836no—
853C4⋊Q8—833no—
854C4⋊Q8—833no—
855C4⋊Q8—8312no—
856C4⋊Q8—8312no—
857C4⋊Q8—836no—
858C4⋊Q8—833no—
859C4⋊Q8—833no—
860C4⋊Q8—836no—
861C4⋊Q8—836no—
862C4⋊Q8C22×D8313yes—
863#127—833no—
864#127C22×D8313yes—
865#126—836no—
866#126—836no—
867#126—8312no—
868#126—8312no—
869#126—836no—
870#126—836no—
871#126—8312no—
872#126—8312no—
873#126—8312no—
874#126C22×D83112yes—
875#125—836no—
876#125—836no—
877#125—836no—
878#125—836no—
879#125—833no—
880#125—833no—
881#125—8312no—
882#125—836no—
883#125—8312no—
884#125—8312no—
885#125—8312no—
886#125—836no—
887#125—8312no—
888#125C22×D8316yes—
889#124—833no—
890#124—836no—
891#124—836no—
892#124—833no—
893#124—836no—
894#124—836no—
895#124—836no—
896#124—8312no—
897#124C22×D8316yes—
898#124C22×D8316yes—
899#123—836no—
900#123—8312no—
901#123—836no—
902#123—836no—
903#123—8312no—
904#123—836no—
905#123—836no—
906#123—8312no—
907#123—832no—
908#123—8312no—
909#123—8312no—
910#123C22×D83112yes—
911C22⋊Q8—833no—
912C22⋊Q8—833no—
913C22⋊Q8—836no—
914C22⋊Q8—836no—
915C22⋊Q8—836no—
916C22⋊Q8—836no—
917C22⋊Q8—836no—
918C22⋊Q8—8312no—
919C22⋊Q8—836no—
920C22⋊Q8—836no—
921C22⋊Q8—8312no—
922C22⋊Q8—831no—
923C22⋊Q8—831no—
924C22⋊Q8—836no—
925C22⋊Q8—836no—
926C22⋊Q8—836no—
927C22⋊Q8—836no—
928C22⋊Q8—836no—
929C22⋊Q8—836no—
930C22⋊Q8—8312no—
931C22⋊Q8—8312no—
932C22⋊Q8—8312no—
933C22⋊Q8—8312no—
934C22⋊Q8—8312no—
935C22⋊Q8C22×D8316yes—
936#121—833no—
937#121—833no—
938#121—836no—
939#121—836no—
940#121—836no—
941#121—836no—
942#121—836no—
943#121—8312no—
944#121—831no—
945#121—831no—
946#121—836no—
947#121—836no—
948#121C22×D8316yes—
949#121C22×D8316yes—
950#121C22×D8316yes—
951#120—836no—
952#120—832no—
953C4×Q8—831no—
954C4×Q8—833no—
955C4×Q8—831no—
956C4×Q8—833no—
957C4×Q8—832no—
958C4×Q8—836no—
959C4×Q8—836no—
960C4×Q8—833no—
961C4×Q8—836no—
962C4×Q8—833no—
963C4×Q8—833no—
964C4×Q8—836no—
965C4×Q8—833no—
966C4×Q8—836no—
967C4×Q8—836no—
968C4×Q8—836no—
969C4×Q8—836no—
970C4×Q8—833no—
971C4×Q8—836no—
972C4×Q8—833no—
973C4×Q8—833no—
974C4×Q8—833no—
975C4×Q8—836no—
976C4×Q8—836no—
977C4×Q8—836no—
978C4×Q8—836no—
979C4×Q8—836no—
980C4×Q8—8312no—
981C4×Q8—836no—
982C4×Q8—836no—
983C4×Q8—836no—
984C4×Q8—836no—
985C4×Q8—833no—
986C4×Q8—833no—
987C4×Q8C22×D8311yescharacteristic
988C4×Q8C22×D8313yes—
989C4×Q8C22×D8311yescharacteristic
990C4×Q8C22×D8313yes—
991C4×Q8C22×D8313yes—
992C4×Q8C22×D8313yes—
993C4×Q8C22×D8312yes—
994C4×D4—836no—
995C4×D4—836no—
996C4×D4—8312no—
997C4×D4—8312no—
998C4×D4—836no—
999C4×D4—836no—
1000C4×D4—836no—
1001C4×D4—836no—
1002C4×D4—836no—
1003C4×D4—836no—
1004C4×D4—836no—
1005C4×D4—836no—
1006C4×D4—836no—
1007C4×D4—836no—
1008C4×D4—836no—
1009C4×D4—836no—
1010C4×D4—836no—
1011C4×D4—8312no—
1012C4×D4—8312no—
1013C4×D4—8312no—
1014C4×D4—832no—
1015C4×D4—832no—
1016C4×D4—836no—
1017C4×D4—836no—
1018C4×D4—833no—
1019C4×D4—833no—
1020C4×D4C22×D8316yes—
1021C4×D4C22×D8316yes—
1022C4×D4C22×D8316yes—
1023C4×D4C22×D8316yes—
1024C4×D4C22×D8313yes—
1025C4×D4C22×D8313yes—
1026C4×D4C22×D8316yes—
1027#117—833no—
1028#117—836no—
1029#117—8312no—
1030#117—836no—
1031#117—836no—
1032#117—836no—
1033#117—836no—
1034#117—8312no—
1035#117—8312no—
1036#117—8312no—
1037#117—836no—
1038#117—836no—
1039#117—836no—
1040#117—836no—
1041#117—836no—
1042#117C22×D8311yescharacteristic
1043#117C22×D8316yes—
1044#117C22×D8316yes—
1045C2×C4⋊C4—836no—
1046C2×C4⋊C4—833no—
1047C2×C4⋊C4—8312no—
1048C2×C4⋊C4—836no—
1049C2×C4⋊C4—833no—
1050C2×C4⋊C4—833no—
1051C2×C4⋊C4—836no—
1052C2×C4⋊C4—836no—
1053C2×C4⋊C4—833no—
1054C2×C4⋊C4—833no—
1055C2×C4⋊C4—836no—
1056C2×C4⋊C4C22×D8313yes—
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—833no—
1066C2×C42—833no—
1067C2×C42—833no—
1068C2×C42—833no—
1069C2×C42—836no—
1070C2×C42C22×D8313yes—
1071C2×C42C22×D8316yes—
1072C24—831no—
1073#41—28no—
1074#41—212no—
1075#41—33212no—
1076#41—33212no—
1077#41—16624no—
1078#41—16624no—
1079#41—16624no—
1080#41—1664no—
1081C2×Q8—24no—
1082C2×Q8—838no—
1083C2×Q8—836no—
1084C2×Q8—836no—
1085C2×Q8—833no—
1086C2×Q8—831no—
1087C2×Q8—836no—
1088C2×Q8—833no—
1089C2×Q8—836no—
1090C2×Q8—836no—
1091C2×Q8—16612no—
1092C2×Q8—16624no—
1093C2×Q8—16612no—
1094C2×Q8—16612no—
1095C2×Q8—1664no—
1096C2×Q8—1668no—
1097C2×Q8C23×D8313yes—
1098C2×Q8C23×D8313yes—
1099C2×Q8C23×D8311yescharacteristic
1100C2×D4—836no—
1101C2×D4—832no—
1102C2×D4—836no—
1103C2×D4—836no—
1104C2×D4—836no—
1105C2×D4—831no—
1106C2×D4—832no—
1107C2×D4—832no—
1108C2×D4C23×D8316yes—
1109C2×D4C23×D8313yes—
1110C2×D4C23×D8316yes—
1111C2×D4C23×D8316yes—
1112C22×C4—3326no—
1113C22×C4—833no—
1114C22×C4—8312no—
1115C22×C4—833no—
1116C22×C4—833no—
1117C22×C4—836no—
1118C22×C4—833no—
1119C22×C4—831no—
1120C22×C4—833no—
1121C22×C4—8312no—
1122C22×C4—831no—
1123C22×C4—831no—
1124C22×C4—833no—
1125C22×C4—833no—
1126C22×C4—833no—
1127C22×C4—833no—
1128C22×C4—833no—
1129C22×C4—836no—
1130C22×C4—831no—
1131C22×C4—831no—
1132C22×C4—832no—
1133C22×C4—16612no—
1134C22×C4—1664no—
1135C22×C4C23×D8313yes—
1136C22×C4C23×D8316yes—
1137C22×C4C23×D8316yes—
1138C22×C4C23×D8313yes—
1139C22×C4C23×D8316yes—
1140C22×C4C23×D8311yescharacteristic
1141C4⋊C4—836no—
1142C4⋊C4—833no—
1143C4⋊C4—836no—
1144C4⋊C4—833no—
1145C4⋊C4—836no—
1146C4⋊C4—836no—
1147C4⋊C4—836no—
1148C4⋊C4—836no—
1149C4⋊C4—836no—
1150C4⋊C4—836no—
1151C4⋊C4—8312no—
1152C4⋊C4—836no—
1153C4⋊C4—836no—
1154C4⋊C4—836no—
1155C4⋊C4—836no—
1156C4⋊C4—832no—
1157C4⋊C4—832no—
1158C4⋊C4—833no—
1159C4⋊C4—833no—
1160C4⋊C4—836no—
1161C4⋊C4—836no—
1162C4⋊C4—836no—
1163C4⋊C4—836no—
1164C4⋊C4—8312no—
1165C4⋊C4—836no—
1166C4⋊C4—836no—
1167C4⋊C4—8312no—
1168C4⋊C4—836no—
1169C4⋊C4—8312no—
1170C4⋊C4C23×D8313yes—
1171C4⋊C4C23×D8313yes—
1172C4⋊C4C23×D8316yes—
1173C4⋊C4C23×D8316yes—
1174C4⋊C4C23×D8316yes—
1175C4⋊C4C23×D8311yescharacteristic
1176C4⋊C4C23×D8311yescharacteristic
1177C4⋊C4C23×D8316yes—
1178C4⋊C4C23×D8316yes—
1179C22⋊C4—836no—
1180C22⋊C4—836no—
1181C22⋊C4—836no—
1182C22⋊C4—836no—
1183C22⋊C4—8312no—
1184C22⋊C4—8312no—
1185C22⋊C4—836no—
1186C22⋊C4—832no—
1187C22⋊C4—832no—
1188C22⋊C4—836no—
1189C22⋊C4—836no—
1190C22⋊C4—836no—
1191C22⋊C4—832no—
1192C22⋊C4—832no—
1193C22⋊C4—836no—
1194C22⋊C4—836no—
1195C22⋊C4—836no—
1196C22⋊C4C23×D83112yes—
1197C22⋊C4C23×D83112yes—
1198C22⋊C4C23×D8312yes—
1199C22⋊C4C23×D8316yes—
1200C22⋊C4C23×D8316yes—
1201C42—833no—
1202C42—833no—
1203C42—833no—
1204C42—833no—
1205C42—833no—
1206C42—833no—
1207C42—833no—
1208C42—833no—
1209C42—833no—
1210C42—833no—
1211C42—8312no—
1212C42—836no—
1213C42—8312no—
1214C42—836no—
1215C42—833no—
1216C42—833no—
1217C42—836no—
1218C42C23×D8313yes—
1219C42C23×D8313yes—
1220C42C23×D8316yes—
1221C42C23×D8316yes—
1222C42C23×D8313yes—
1223C42C23×D8313yes—
1224C42C23×D8312yes—
1225C23—831no—
1226C23—831no—
1227C23—832no—
1228C23—1662no—
1229C23—1662no—
1230C23—1662no—
1231C23C24×D8316yes—
1232C23C24×D8311yescharacteristic
1233Q8—26no—
1234Q8—26no—
1235Q8—3326no—
1236Q8—3326no—
1237Q8—8312no—
1238Q8—16612no—
1239Q8—16612no—
1240Q8—1666no—
1241Q8—16612no—
1242Q8—1662no—
1243Q8#41×D8314yes—
1244D4—212no—
1245D4—212no—
1246D4—26no—
1247D4—46no—
1248D4—3326no—
1249D4—1664no—
1250D4—1664no—
1251D4—16612no—
1252D4—16612no—
1253D4—16612no—
1254D4—1664no—
1255D4—1662no—
1256C2×C4—26no—
1257C2×C4—212no—
1258C2×C4—212no—
1259C2×C4—43no—
1260C2×C4—46no—
1261C2×C4—3323no—
1262C2×C4—3323no—
1263C2×C4—3326no—
1264C2×C4—3323no—
1265C2×C4—33212no—
1266C2×C4—833no—
1267C2×C4—8312no—
1268C2×C4—831no—
1269C2×C4—831no—
1270C2×C4—833no—
1271C2×C4—832no—
1272C2×C4—833no—
1273C2×C4—836no—
1274C2×C4—836no—
1275C2×C4—833no—
1276C2×C4—1666no—
1277C2×C4—1666no—
1278C2×C4—1666no—
1279C2×C4—1666no—
1280C2×C4—1666no—
1281C2×C4—16624no—
1282C2×C4—1662no—
1283C2×C4—1666no—
1284C2×C4—16612no—
1285C2×C4—1662no—
1286C2×C4—1662no—
1287C2×C4—1662no—
1288C2×C4—1662no—
1289C2×C4—1664no—
1290C2×C4#1458183914yescomplemented
1291C2×C4C24×D8313yes—
1292C2×C4C24×D8316yes—
1293C2×C4C24×D8313yes—
1294C2×C4C24×D8313yes—
1295C2×C4C24×D8312yes—
1296C2×C4C24×D8312yes—
1297C2×C4C24×D8313yes—
1298C2×C4C24×D8311yescharacteristic
1299C2×C4C24×D8311yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—26no—
1303C22—26no—
1304C22—26no—
1305C22—832no—
1306C22—832no—
1307C22—1668no—
1308C22—1662no—
1309C22—1662no—
1310C22—1662no—
1311C22—1661no—
1312C22—1661no—
1313C22—1661no—
1314C22—1661no—
1315C22C2×#1458183912yes—
1316C22C25×D8311yescharacteristic
1317C4—22no—
1318C4—23no—
1319C4—26no—
1320C4—23no—
1321C4—22no—
1322C4—23no—
1323C4—836no—
1324C4—1666no—
1325C4—1663no—
1326C4—1661no—
1327C4—1661no—
1328C4—1662no—
1329C4—1663no—
1330C4—1666no—
1331C4—1663no—
1332C4C2×#41×D8316yes—
1333C4C2×#1458183912yes—
1334C4C2×#1458183912yes—
1335C2—22no—
1336C2—46no—
1337C2—3322no—
1338C2—1662no—
1339C2—1662no—
1340C2C22×#41×D8311yescharacteristic
1341C2C22×#1458183911yescharacteristic
1342C2#585×D8311yescharacteristic
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC83×#3480C2
hypercenter#3480D83
hypocenterC83#62788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ #3480

Complements

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

NH ≅ G/Ntype
1. #24921560C2semidirect
2. #24921558C2semidirect
3. #24921545C2semidirect
4. #24921543C2semidirect
5. #24921447C2semidirect
6. #24921445C2semidirect
7. #24921320C2semidirect
8. #24921318C2semidirect
9. #24921267C2semidirect
10. #24921228C2semidirect
11. #24921167C2semidirect
12. #24921109C2semidirect
13. #24921085C2semidirect
14. #24921076C2semidirect
15. #24921060C2semidirect
16. Q8×#13050590C2semidirect
17. #41×Dic166C2semidirect
18. #24920888C2semidirect
19. #24920758C2semidirect
20. #24920756C2semidirect
21. C4×#14581839C2semidirect
22. C2×C4×Q8×D83C2semidirect
23. C83×#3480C2semidirect
26. #19128437C22semidirect
27. #19128433C22semidirect
28. Q8×Dic166C22semidirect
29. Q8×Dic166C22semidirect
30. #19128430C22semidirect
31. #19128430C22semidirect
32. #19128429C22semidirect
33. #19128428C22semidirect
34. #19128427C22semidirect
35. #19128426C22semidirect
36. #19128425C22semidirect
37. #19128421C22semidirect
38. #19128420C22semidirect
39. #19128420C22semidirect
40. #19128418C22semidirect
41. #19128411C22semidirect
43. #19128410C22semidirect
45. #19128408C22semidirect
49. #19128393C22semidirect
51. #19128390C22semidirect
53. #19128388C22semidirect
55. #19128371C22semidirect
57. Q8×D332C22semidirect
59. D4×Dic166C22semidirect
64. #19128358C22semidirect
66. #19128357C22semidirect
71. #19128320C22semidirect
72. #19128319C22semidirect
73. #19128318C22semidirect
74. #19128314C22semidirect
75. #19128311C22semidirect
76. #19128308C22semidirect
83. #19128258C22semidirect
88. #19128255C22semidirect
90. #19128254C22semidirect
102. #19128233C22semidirect
107. #19128231C22semidirect
118. #19128184C22semidirect
121. #19128180C22semidirect
122. #19128178C22semidirect
124. #19128177C22semidirect
131. C4×#13050589C22semidirect
134. C2×C4×Dic166C22semidirect
144. C4×Q8×D83C22semidirect
147. #559×C83C22semidirect
148. #557×C83C22semidirect
149. #556×C83C22semidirect
151. #550×C83C22semidirect
154. #529×C83C22semidirect
156. C4×#41×C83C22semidirect
421. Q8×D83#41semidirect
573. C2×C4×C832−1+4semidirect
687. #3480D83semidirect
695. C83#62788semidirect
700. #559C2×D83semidirect
709. #557C2×D83semidirect
715. #556C2×D83semidirect
732. #550C2×D83semidirect
791. #529C2×D83semidirect
813. C4×#41C2×D83semidirect
1290. C2×C4#14581839semidirect

Maximal subgroups

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

subgroupindex
#249215602
#249215582
#249215452
#249215432
#249214472
#249214452
#249213202
#249213182
#249212672
#249212282
#249211672
#249211092
#249210852
#249210762
#249210602
Q8×#130505902
#41×Dic1662
#249208882
#249207582
#249207562
C4×#145818392
C2×C4×Q8×D832
C83×#34802
#6278883