Finite Group Databasebeta

← #36312641

Subgroups — #36312641

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#24921551C213yesmaximal, complemented
2#24921548C211yesmaximal, characteristic, complemented
3#24921546C213yesmaximal, complemented
4#24921458C212yesmaximal, complemented
5#24921454C216yesmaximal, complemented
6#24921329C213yesmaximal, complemented
7#24921318C213yesmaximal, complemented
8#24921267C211yesmaximal, characteristic, complemented
9#24921233C211yesmaximal, characteristic, complemented
10#24921163C216yesmaximal, complemented
11#24921113C212yesmaximal, complemented
12#24921084C212yesmaximal, complemented
13#24921077C216yesmaximal, complemented
14#24921063C211yesmaximal, characteristic, complemented
15#24921055C213yesmaximal, complemented
16#24921045C213yesmaximal, complemented
17Q8×#13050589C211yesmaximal, characteristic, complemented
18#24920895C216yesmaximal, complemented
19#24920760C213yesmaximal, complemented
20#24920757C213yesmaximal, complemented
21#24920672C212yesmaximal, complemented
22C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
23C83×#3523C211yesmaximal, characteristic, complemented
24C2×#14581840C2212yes—
25C22×Q8×D83C2211yescharacteristic
26#19128436C2213yescomplemented
27#19128436C2213yescomplemented
28#19128433C2216yescomplemented
29Q8×Dic166C2213yescomplemented
30Q8×Dic166C2211yescharacteristic, complemented
31#19128430C2212yescomplemented
32#19128428C2216yescomplemented
33#19128427C2216yescomplemented
34#19128426C2213yescomplemented
35#19128426C2213yescomplemented
36#19128425C2216yescomplemented
37#19128425C2213yescomplemented
38#19128423C2216yescomplemented
39#19128423C2216yescomplemented
40#19128418C22112yescomplemented
41#19128411C2216yes—
42#19128411C2213yescomplemented
43#19128409C2216yes—
44#19128408C2213yescomplemented
45#19128407C22112yes—
46#19128407C2216yescomplemented
47#19128404C2216yes—
48#19128402C22112yes—
49#19128395C2216yes—
50#19128393C2216yes—
51#19128393C2216yescomplemented
52#19128390C2216yescomplemented
53#19128384C22112yes—
54#19128383C22112yescomplemented
55#19128373C2211yescharacteristic, complemented
56#19128372C2213yescomplemented
57#19128366C2216yes—
58#19128366C2213yescomplemented
59Q8×C22⋊D83C2212yes—
60#19128364C2216yes—
61#19128363C2212yes—
62#19128362C2212yes—
63#19128362C2212yescomplemented
64#19128361C2216yes—
65#19128361C2216yescomplemented
66#19128360C2216yes—
67#19128355C2216yes—
68#19128352C2216yes—
69#19128349C22112yes—
70#19128331C2216yes—
71#19128323C2216yescomplemented
72#19128322C2216yescomplemented
73#19128317C22112yescomplemented
74#19128310C22112yescomplemented
75#19128309C2216yescomplemented
76#19128299C22112yes—
77#19128292C22112yes—
78#19128281C2216yes—
79#19128276C2216yes—
80#19128274C2216yes—
81#19128257C2213yes—
82#19128257C22112yescomplemented
83#19128256C2213yes—
84#19128256C2213yes—
85#19128256C2216yescomplemented
86#19128255C2213yes—
87#19128253C2213yes—
88#19128253C2216yescomplemented
89#19128252C2213yes—
90#19128252C2213yes—
91#19128251C2213yes—
92#19128250C2213yes—
93#19128248C2213yes—
94#19128246C2213yes—
95#19128238C2216yes—
96#19128238C2216yes—
97#19128237C2216yes—
98#19128237C2216yes—
99#19128237C2216yescomplemented
100#19128236C2216yes—
101#19128236C2216yes—
102#19128236C2213yes—
103#19128236C2216yescomplemented
104#19128235C2213yes—
105#19128234C2216yes—
106#19128234C2216yes—
107#19128234C22112yescomplemented
108#19128230C2213yes—
109#19128229C2216yes—
110#19128228C2216yes—
111#19128214C2216yes—
112#19128214C2213yes—
113#19128213C2216yes—
114#19128211C2211yescharacteristic
115#19128210C2216yes—
116#19128209C2216yes—
117#19128183C2216yes—
118#19128183C2212yescomplemented
119#19128181C2216yes—
120#19128181C2216yescomplemented
121#19128177C2212yes—
122#19128177C2216yescomplemented
123C4×#13050591C2216yes—
124C4×#13050591C2213yes—
125C4×#13050591C2216yes—
126C4×#13050591C2212yescomplemented
127#19128169C2216yes—
128#19128169C2216yes—
129#19128169C2216yescomplemented
130C4×#13050589C2213yes—
131C4×#13050589C2216yes—
132C2×Q8×Dic83C2211yescharacteristic
133C2×Q8×Dic83C2212yescomplemented
134C2×C4×Dic166C2213yes—
135C2×#14581757C2213yes—
136C4×Q8×D83C2213yes—
137C4×Q8×D83C2211yescharacteristic
138C4×Q8×D83C2213yes—
139C4×Q8×D83C2211yescharacteristic
140C4×Q8×D83C2211yescharacteristic
141C4×Q8×D83C2211yescharacteristic
142C4×Q8×D83C2213yes—
143C4×Q8×D83C2213yes—
144C4×Q8×D83C2216yescomplemented
145C2×C4⋊C4×D83C2213yes—
146C2×C42×D83C2213yes—
147#557×C83C2211yescharacteristic, complemented
148#557×C83C2213yescomplemented
149#556×C83C2213yescomplemented
150#552×C83C2216yes—
151D4×Q8×C83C2212yes—
152D4×Q8×C83C2211yescharacteristic, complemented
153#541×C83C2216yescomplemented
154#533×C83C2213yes—
155#529×C83C2213yes—
156#519×C83C2212yescomplemented
157C2×C4×Q8×C83C2211yescharacteristic
158#14581840—216no—
159C2×#13050591C2312yes—
160C2×#13050591C2313yes—
161C2×#13050591C2316yes—
162C2×#13050590C2316yes—
163C2×#13050590C2316yes—
164C2×#13050590C2316yes—
165C2×#13050589C2311yescharacteristic
166C2×#13050589C2316yes—
167C22×Dic166C2313yes—
168C2×Q8×D83—28no—
169C2×Q8×D83C2313yes—
170C2×Q8×D83C2316yes—
171C2×Q8×D83C2311yescharacteristic
172C2×Q8×D83C2313yes—
173C2×Q8×D83C2311yescharacteristic
174C22×C4×D83C2311yescharacteristic
175C22×C4×D83C2313yes—
176C22×C4×D83C2313yes—
177#14581792C2316yes—
178#14581792C2313yes—
179#14581791C2316yes—
180#14581791C23112yes—
181#14581791C23112yes—
182#14581791C2313yes—
183#14581791C2313yes—
184#14581790C2316yes—
185#14581790C2313yes—
186#14581789C2313yes—
187#14581788C2313yes—
188#14581787C23112yes—
189#14581787C2316yes—
190#14581787C23112yes—
191#14581787C23112yes—
192#14581787C23112yes—
193#14581786C2316yes—
194#14581786C23112yes—
195#14581785C2316yes—
196#14581784C23112yes—
197#14581784C2313yes—
198#14581783C2316yes—
199#14581783C2316yes—
200#14581783C23112yes—
201#14581783C2316yes—
202#14581782C23112yes—
203#14581782C2316yes—
204#14581782C23112yes—
205#14581782C2316yes—
206#14581781C2316yes—
207#14581781C2316yes—
208#14581781C2316yes—
209#14581780C2316yes—
210#14581780C2316yes—
211#14581780C2313yes—
212#14581778C2316yes—
213#14581778C23112yes—
214#14581778C2316yes—
215#14581777C23112yes—
216#14581777C23112yes—
217#14581777C2316yes—
218#14581777C2316yes—
219#14581777C23112yes—
220#14581776C23112yes—
221#14581776C23112yes—
222#14581775C2316yes—
223#14581774C23112yes—
224#14581774C2316yes—
225#14581774C2312yes—
226#14581772C2316yes—
227#14581772C23112yes—
228#14581772C2316yes—
229#14581772C2316yes—
230#14581772C2311yescharacteristic
231#14581771C2316yes—
232#14581771C2311yescharacteristic
233#14581770C23112yes—
234#14581770C23112yes—
235#14581770C2316yes—
236#14581770C23112yes—
237#14581770C23112yes—
238#14581770C23112yes—
239#14581770C2316yes—
240#14581770C2316yes—
241#14581769C23112yes—
242#14581769C2316yes—
243#14581768C2316yes—
244#14581768C2316yes—
245#14581768C2316yes—
246#14581768C2313yes—
247#14581767C2316yes—
248#14581767C2316yes—
249#14581767C2316yes—
250#14581767C2316yes—
251#14581767C2313yes—
252#14581766C2316yes—
253#14581766C2316yes—
254#14581766C2313yes—
255#14581765C23112yes—
256#14581765C2316yes—
257#14581765C2316yes—
258#14581765C2316yes—
259#14581764C2316yes—
260#14581763C2311yescharacteristic
261#14581762C2316yes—
262#14581760C2312yes—
263Q8×Dic83C2312yes—
264Q8×Dic83C2311yescharacteristic
265Q8×Dic83C2316yes—
266Q8×Dic83C2313yes—
267Q8×Dic83C2311yescharacteristic
268Q8×Dic83C2313yes—
269Q8×Dic83C2316yes—
270Q8×Dic83C2313yes—
271Q8×Dic83C2316yes—
272C4×Dic166C2313yes—
273C4×Dic166C2316yes—
274C4×Dic166C2313yes—
275C4×Dic166C23112yes—
276C4×Dic166C2316yes—
277C4×Dic166C2313yes—
278C4×Dic166C2313yes—
279C4×Dic166C2316yes—
280C4×Dic166C2316yes—
281C4×Dic166C2313yes—
282#14581757C2316yes—
283#14581757C2313yes—
284#14581757C2316yes—
285#14581757C2313yes—
286#14581757C2316yes—
287#14581757C2313yes—
288#14581757C2316yes—
289#14581757C2313yes—
290#14581757C2316yes—
291#14581757C2313yes—
292#14581757C2316yes—
293#14581757C2316yes—
294#14581757C2316yes—
295C4×D332C2316yes—
296C4×D332C2316yes—
297C4×D332C2316yes—
298C4×D332C2313yes—
299C4×D332C23112yes—
300C4×D332C2316yes—
301C4×D332C23112yes—
302D4×Dic83C2313yes—
303D4×Dic83C2312yes—
304#14581754C2316yes—
305#14581754C23112yes—
306#14581754C2316yes—
307#14581754C2316yes—
308#14581754C2316yes—
309#14581754C2313yes—
310#14581754C2316yes—
311#14581754C2316yes—
312#14581754C2316yes—
313#14581754C2316yes—
314C4×C22⋊D83C2316yes—
315C4×C22⋊D83C2316yes—
316C4×C22⋊D83C2316yes—
317(C22⋊D83)⋊C4C23112yes—
318(C22⋊D83)⋊C4C23112yes—
319(C22⋊D83)⋊C4C2316yes—
320(C22⋊D83)⋊C4C2316yes—
321(C22⋊D83)⋊C4C2316yes—
322(C22⋊D83)⋊C4C2312yes—
323(C22⋊D83)⋊C4C2316yes—
324(C22⋊D83)⋊C4C2316yes—
325(C22⋊D83)⋊C4C2316yes—
326#14581750C2316yes—
327#14581750C2316yes—
328#14581750C2316yes—
329#14581750C2313yes—
330#14581750C2311yescharacteristic
331#14581750C23112yes—
332#14581750C2316yes—
333#14581750C23112yes—
334#14581749C2316yes—
335#14581749C2316yes—
336#14581749C23112yes—
337#14581749C23112yes—
338#14581748C2316yes—
339#14581748C2316yes—
340#14581748C2316yes—
341C2×C4⋊Dic83C2313yes—
342C2×C4⋊Dic83C2316yes—
343C2×Dic83⋊C4C2316yes—
344C4⋊C4×D83C2313yes—
345C4⋊C4×D83C23112yes—
346C4⋊C4×D83C2316yes—
347C4⋊C4×D83C2313yes—
348C4⋊C4×D83C2316yes—
349C4⋊C4×D83C2313yes—
350C4⋊C4×D83C2313yes—
351C4⋊C4×D83C2316yes—
352C2×C4×Dic83C2313yes—
353C2×C4×Dic83C2313yes—
354C2×C4×Dic83C2313yes—
355C2×C4×Dic83C2316yes—
356C42×D83C2313yes—
357C42×D83C2313yes—
358C42×D83C2313yes—
359C42×D83C2313yes—
360C42×D83C2313yes—
361C42×D83C2313yes—
362C42×D83C2313yes—
363C42×D83C2313yes—
364C42×D83C2316yes—
365C42×D83C23112yes—
366C22×Q8×C83C2311yescharacteristic
367C22×Q8×C83C2312yes—
368C4⋊Q8×C83C2316yes—
369C4⋊Q8×C83C2313yes—
370C4⋊Q8×C83C2313yes—
371#126×C83C2316yes—
372#126×C83C23112yes—
373#125×C83C2316yes—
374#125×C83C23112yes—
375#125×C83C2313yes—
376#125×C83C2316yes—
377#124×C83C2313yes—
378#123×C83C2316yes—
379C22⋊Q8×C83C2316yes—
380C22⋊Q8×C83C2316yes—
381C22⋊Q8×C83C2316yes—
382C22⋊Q8×C83C2313yes—
383#121×C83C2311yescharacteristic
384C4×Q8×C83C2313yes—
385C4×Q8×C83C2312yes—
386C4×Q8×C83C2311yescharacteristic
387C4×Q8×C83C2311yescharacteristic
388C4×Q8×C83C2313yes—
389C4×Q8×C83C2316yes—
390C4×Q8×C83C2316yes—
391C4×Q8×C83C2313yes—
392C4×Q8×C83C2316yes—
393C4×D4×C83C2316yes—
394C4×D4×C83C2313yes—
395#117×C83C2316yes—
396#117×C83C2316yes—
397#117×C83C2316yes—
398C2×C4⋊C4×C83C2313yes—
399C2×C42×C83C2313yes—
400C23×D83C2411yescharacteristic
401#13050591—28no—
402#13050591—224no—
403#13050591—212no—
404#13050590—224no—
405#13050590—224no—
406#13050590—412no—
407#13050589—24no—
408#13050589—412no—
409C2×Dic166—212no—
410C2×Dic166C2416yes—
411C2×Dic166C2416yes—
412C2×Dic166C2413yes—
413C2×Dic166C2411yescharacteristic
414C2×Dic166C2416yes—
415C2×Dic166C2416yes—
416C2×Dic166C2413yes—
417Q8×D83—24no—
418Q8×D83—212no—
419Q8×D83—212no—
420Q8×D83—224no—
421Q8×D83#4118yescomplemented
422C2×D332C2416yes—
423C2×D332C2416yes—
424C2×D332C2416yes—
425C2×D332C2413yes—
426C2×D332C2416yes—
427C2×C22⋊D83C2412yes—
428C2×C22⋊D83C2412yes—
429C2×C22⋊D83C2416yes—
430C2×C22⋊D83C2416yes—
431C2×C22⋊D83C2416yes—
432C22×Dic83C2413yes—
433C22×Dic83C2413yes—
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2412yes—
436C22×Dic83C2416yes—
437C2×C4×D83—212no—
438C2×C4×D83—24no—
439C2×C4×D83—46no—
440C2×C4×D83C2411yescharacteristic
441C2×C4×D83C2413yes—
442C2×C4×D83C24112yes—
443C2×C4×D83C2413yes—
444C2×C4×D83C2416yes—
445C2×C4×D83C2413yes—
446C2×C4×D83C2411yescharacteristic
447C2×C4×D83C2411yescharacteristic
448C2×C4×D83C2416yes—
449C2×C4×D83C2413yes—
450C2×C4×D83C2413yes—
451C2×C4×D83C2413yes—
452C2×C4×D83C24112yes—
453C2×C4×D83C2416yes—
454C2×C4×D83C2413yes—
455C2×C4×D83C2413yes—
456C2×C4×D83C2411yescharacteristic
457C4⋊Dic83C2411yescharacteristic
458C4⋊Dic83C2413yes—
459C4⋊Dic83C2416yes—
460C4⋊Dic83C2413yes—
461C4⋊Dic83C2416yes—
462C4⋊Dic83C24112yes—
463C4⋊Dic83C2416yes—
464C4⋊Dic83C24112yes—
465C4⋊Dic83C2412yes—
466C4⋊Dic83C2413yes—
467Dic83⋊C4C2416yes—
468Dic83⋊C4C2416yes—
469Dic83⋊C4C2416yes—
470Dic83⋊C4C2416yes—
471Dic83⋊C4C2416yes—
472Dic83⋊C4C2416yes—
473Dic83⋊C4C24112yes—
474Dic83⋊C4C2416yes—
475Dic83⋊C4C2416yes—
476Dic83⋊C4C2416yes—
477Dic83⋊C4C2416yes—
478Dic83⋊C4C2416yes—
479Dic83⋊C4C2416yes—
480Dic83⋊C4C2412yes—
481Dic83⋊C4C2416yes—
482C22⋊Dic83C2412yes—
483C22⋊Dic83C2412yes—
484C22⋊Dic83C2416yes—
485(C2×D83)⋊C4C2412yes—
486(C2×D83)⋊C4C2412yes—
487(C2×D83)⋊C4C2416yes—
488(C2×D83)⋊C4C2416yes—
489(C2×D83)⋊C4C2416yes—
490(C2×D83)⋊C4C24112yes—
491(C2×D83)⋊C4C2416yes—
492(C2×D83)⋊C4C2416yes—
493(C2×D83)⋊C4C2416yes—
494(C2×D83)⋊C4C24112yes—
495(C2×D83)⋊C4C2416yes—
496(C2×D83)⋊C4C24112yes—
497(C2×D83)⋊C4C24112yes—
498(C2×D83)⋊C4C2416yes—
499C4×Dic83C2413yes—
500C4×Dic83C2413yes—
501C4×Dic83C24112yes—
502C4×Dic83C2413yes—
503C4×Dic83C2413yes—
504C4×Dic83C2416yes—
505C4×Dic83C2416yes—
506C4×Dic83C2416yes—
507C4×Dic83C2413yes—
508C4×Dic83C2413yes—
509C4×Dic83C2413yes—
510C4×Dic83C2413yes—
511C4×Dic83C2413yes—
512C4×Dic83C2412yes—
513C4×Dic83C2413yes—
514C4×Dic83C2416yes—
515C4×Dic83C2413yes—
516C4×Dic83C2413yes—
517C2×Q8×C83—24no—
518C2×Q8×C83—28no—
519C2×Q8×C83C2413yes—
520C2×Q8×C83C2416yes—
521C2×Q8×C83C2413yes—
522C2×Q8×C83C2411yescharacteristic
523C2×D4×C83C2412yes—
524C2×D4×C83C2411yescharacteristic
525C22×C4×C83C2411yescharacteristic
526C22×C4×C83C2413yes—
527C22×C4×C83C2416yes—
528C22×C4×C83C2413yes—
529C4⋊C4×C83C2413yes—
530C4⋊C4×C83C2416yes—
531C4⋊C4×C83C2416yes—
532C4⋊C4×C83C2416yes—
533C4⋊C4×C83C2413yes—
534C4⋊C4×C83C2416yes—
535C4⋊C4×C83C2416yes—
536C4⋊C4×C83C2416yes—
537C4⋊C4×C83C2416yes—
538C4⋊C4×C83C24112yes—
539C4⋊C4×C83C2411yescharacteristic
540C4⋊C4×C83C2416yes—
541C4⋊C4×C83C2413yes—
542C22⋊C4×C83C2416yes—
543C22⋊C4×C83C2416yes—
544C22⋊C4×C83C2416yes—
545C22⋊C4×C83C2416yes—
546C22⋊C4×C83C2412yes—
547C42×C83C2413yes—
548C42×C83C2413yes—
549C42×C83C2416yes—
550C42×C83C24112yes—
551C42×C83C2413yes—
552C42×C83C2413yes—
553C23×C83C2512yes—
554C23×C83C2511yescharacteristic
555C22×D83—22no—
556C22×D83—22no—
557C22×D83—22no—
558C22×D83C2516yes—
559C22×D83C2511yescharacteristic
560C22×D83C2511yescharacteristic
561Q8×C83—26no—
562Q8×C83—212no—
563Q8×C83—26no—
564Q8×C83C2×#4114yes—
565D4×C83—24no—
566D4×C83—22no—
567C2×C4×C83—26no—
568C2×C4×C83—26no—
569C2×C4×C83—212no—
570C2×C4×C83—22no—
571C2×C4×C83C2511yescharacteristic
572C2×C4×C83C2513yes—
573C2×C4×C83C2516yes—
574C2×C4×C83C2512yes—
575C2×C4×C83C2513yes—
576C2×C4×C83C2513yes—
577C2×C4×C83C2516yes—
578C2×C4×C83C2513yes—
579C2×C4×C83C2511yescharacteristic
580C22⋊D83—212no—
581C22⋊D83—24no—
582C22⋊D83—24no—
583C22⋊D83—212no—
584C22⋊D83—46no—
585C2×Dic83—26no—
586C2×Dic83—26no—
587C2×Dic83—22no—
588C2×Dic83—24no—
589C2×Dic83—46no—
590C2×Dic83C2511yescharacteristic
591C2×Dic83C2513yes—
592C2×Dic83C2512yes—
593C2×Dic83C2513yes—
594C2×Dic83C2516yes—
595C2×Dic83C2512yes—
596C2×Dic83C2513yes—
597C2×Dic83C2513yes—
598C2×Dic83C2511yescharacteristic
599D332—212no—
600D332—212no—
601D332—212no—
602D332—26no—
603D332—46no—
604C4×D83—26no—
605C4×D83—22no—
606C4×D83—26no—
607C4×D83—212no—
608C4×D83—22no—
609C4×D83—26no—
610C4×D83—224no—
611C4×D83—22no—
612C4×D83—212no—
613C4×D83—43no—
614C4×D83—43no—
615C4×D83—43no—
616C4×D83—43no—
617C4×D83—46no—
618C4×D83—412no—
619C4×D83C2×#41112yes—
620C4×D832−1+414yescomplemented
621Dic166—26no—
622Dic166—22no—
623Dic166—212no—
624Dic166—212no—
625Dic166—46no—
626Dic166—46no—
627Dic166C2×#41112yes—
628C22×C83—21no—
629C22×C83—21no—
630C22×C83—22no—
631C22×C83—22no—
632C22×C83—22no—
633C22×C83#58512yes—
634C22×C83C2611yescharacteristic
635C2×D83—28no—
636C2×D83—21no—
637C2×D83—21no—
638C2×D83—21no—
639C2×D83—21no—
640C2×D83—26no—
641C2×D83—26no—
642C2×D83—26no—
643C2×D83C22×#4112yes—
644C2×D83C2×2−1+412yes—
645C4×C83—23no—
646C4×C83—26no—
647C4×C83—21no—
648C4×C83—26no—
649C4×C83—22no—
650C4×C83—23no—
651C4×C83—23no—
652C4×C83C22×#4116yes—
653C4×C83C2×2−1+412yes—
654Dic83—23no—
655Dic83—22no—
656Dic83—22no—
657Dic83—21no—
658Dic83—26no—
659Dic83—23no—
660Dic83—23no—
661Dic83C22×#4116yes—
662Dic83C2×2−1+412yes—
663#62788—831nomaximal, Sylow
664C2×C83—22no—
665C2×C83—42no—
666C2×C83C23×#4111yescharacteristic
667C2×C83C22×2−1+411yescharacteristic
668C2×C83C2×#58511yescharacteristic
669D83—22no—
670D83—22no—
671D83—46no—
672#3523—833no—
673#3523D8311yescharacteristic, complemented
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—831no—
687#3480—833no—
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—836no—
699#559—833no—
700#559—833no—
701Q82—831no—
702Q82—833no—
703#557—833no—
704#557—833no—
705#557—836no—
706#557—836no—
707#557—832no—
708#557C2×D8313yescomplemented
709#557C2×D8311yescharacteristic, complemented
710#556—833no—
711#556—836no—
712#556—8312no—
713#556—836no—
714#556—836no—
715#556C2×D8313yescomplemented
716#554—8312no—
717#554—836no—
718#554—836no—
719#554—836no—
720#554—833no—
721#554—833no—
722#553—8312no—
723#553—836no—
724#553—836no—
725#552—8312no—
726#552—836no—
727#552—836no—
728#552—8312no—
729#552—836no—
730#552C2×D8316yes—
731#550—831no—
732#550—833no—
733D4×Q8—832no—
734D4×Q8—836no—
735D4×Q8—833no—
736D4×Q8—836no—
737D4×Q8C2×D8312yes—
738D4×Q8C2×D8311yescharacteristic, complemented
739#548—832no—
740#548—832no—
741#548—836no—
742#548—836no—
743#548—832no—
744#548—836no—
745#547—8312no—
746#547—836no—
747#547—836no—
748#544—836no—
749#542—8312no—
750#542—836no—
751#542—836no—
752#541—8312no—
753#541—836no—
754#541C2×D8316yescomplemented
755#539—8312no—
756#539—8312no—
757#537—836no—
758#536—836no—
759#536—836no—
760#533—833no—
761#533—833no—
762#533—836no—
763#533—833no—
764#533—8312no—
765#533—833no—
766#533—836no—
767#533—833no—
768#533C2×D8313yes—
769#532—833no—
770#532—833no—
771#532—833no—
772#532—833no—
773#532—833no—
774#532—833no—
775#529—836no—
776#529—836no—
777#529—8312no—
778#529—836no—
779#529—833no—
780#529—836no—
781#529—836no—
782#529—833no—
783#529—836no—
784#529—836no—
785#529—836no—
786#529—836no—
787#529—836no—
788#529—836no—
789#529—836no—
790#529—833no—
791#529C2×D8313yes—
792#525—836no—
793#525—833no—
794#525—836no—
795#525—831no—
796#525—836no—
797#525—836no—
798#520—836no—
799#520—832no—
800#520—836no—
801#520—836no—
802#519—832no—
803#519—836no—
804#519C2×D8312yescomplemented
805C4×#41—836no—
806C4×#41—832no—
807C4×#41—836no—
808C4×#41—833no—
809C4×#41—833no—
810C4×#41—836no—
811C4×#41—836no—
812C4×#41—836no—
813C4×#41—836no—
814C2×C4×Q8—831no—
815C2×C4×Q8—832no—
816C2×C4×Q8—831no—
817C2×C4×Q8—833no—
818C2×C4×Q8—831no—
819C2×C4×Q8—833no—
820C2×C4×Q8—831no—
821C2×C4×Q8—833no—
822C2×C4×Q8—831no—
823C2×C4×Q8—833no—
824C2×C4×Q8—836no—
825C2×C4×Q8—833no—
826C2×C4×Q8—833no—
827C2×C4×Q8C2×D8311yescharacteristic
828C22×C4⋊C4—833no—
829C22×C42—833no—
8302−1+4—16616no—
831C2×#41—833no—
832C2×#41—836no—
833C2×#41—832no—
834C2×#41—836no—
835C2×#41—831no—
836C2×#41—836no—
837C2×#41—836no—
838C2×#41—836no—
839C22×Q8—831no—
840C22×Q8—833no—
841C22×Q8—833no—
842C22×Q8—831no—
843C22×Q8—836no—
844C22×Q8—833no—
845C22×Q8—1668no—
846C22×Q8C22×D8311yescharacteristic
847C22×Q8C22×D8312yes—
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—836no—
860C4⋊Q8C22×D8313yes—
861C4⋊Q8C22×D8313yes—
862C4⋊Q8C22×D8316yes—
863#127—833no—
864#127—833no—
865#126—8312no—
866#126—8312no—
867#126—836no—
868#126—8312no—
869#126—8312no—
870#126—836no—
871#126—836no—
872#126—8312no—
873#126C22×D8316yes—
874#126C22×D83112yes—
875#125—836no—
876#125—836no—
877#125—836no—
878#125—836no—
879#125—8312no—
880#125—836no—
881#125—8312no—
882#125—8312no—
883#125—833no—
884#125—8312no—
885#125C22×D8316yes—
886#125C22×D8313yes—
887#125C22×D8316yes—
888#125C22×D83112yes—
889#124—836no—
890#124—836no—
891#124—836no—
892#124—836no—
893#124—836no—
894#124—8312no—
895#124—836no—
896#124—833no—
897#124—836no—
898#124C22×D8313yes—
899#123—836no—
900#123—836no—
901#123—8312no—
902#123—836no—
903#123—8312no—
904#123—8312no—
905#123—832no—
906#123—836no—
907#123—8312no—
908#123—8312no—
909#123—8312no—
910#123C22×D8316yes—
911C22⋊Q8—833no—
912C22⋊Q8—836no—
913C22⋊Q8—836no—
914C22⋊Q8—836no—
915C22⋊Q8—831no—
916C22⋊Q8—836no—
917C22⋊Q8—836no—
918C22⋊Q8—836no—
919C22⋊Q8—836no—
920C22⋊Q8—8312no—
921C22⋊Q8—8312no—
922C22⋊Q8—8312no—
923C22⋊Q8—8312no—
924C22⋊Q8—8312no—
925C22⋊Q8—831no—
926C22⋊Q8—836no—
927C22⋊Q8—836no—
928C22⋊Q8—836no—
929C22⋊Q8—8312no—
930C22⋊Q8—836no—
931C22⋊Q8—8312no—
932C22⋊Q8C22×D8313yes—
933C22⋊Q8C22×D8316yes—
934C22⋊Q8C22×D8316yes—
935C22⋊Q8C22×D8316yes—
936#121—831no—
937#121—836no—
938#121—833no—
939#121—836no—
940#121—836no—
941#121—833no—
942#121—836no—
943#121—836no—
944#121—836no—
945#121—836no—
946#121—836no—
947#121—836no—
948#121—836no—
949#121—8312no—
950#121C22×D8311yescharacteristic
951#120—832no—
952#120—836no—
953C4×Q8—831no—
954C4×Q8—833no—
955C4×Q8—831no—
956C4×Q8—833no—
957C4×Q8—836no—
958C4×Q8—832no—
959C4×Q8—836no—
960C4×Q8—833no—
961C4×Q8—836no—
962C4×Q8—833no—
963C4×Q8—836no—
964C4×Q8—833no—
965C4×Q8—833no—
966C4×Q8—836no—
967C4×Q8—833no—
968C4×Q8—836no—
969C4×Q8—836no—
970C4×Q8—836no—
971C4×Q8—836no—
972C4×Q8—836no—
973C4×Q8—833no—
974C4×Q8—836no—
975C4×Q8—833no—
976C4×Q8—836no—
977C4×Q8—833no—
978C4×Q8—833no—
979C4×Q8—833no—
980C4×Q8—836no—
981C4×Q8—836no—
982C4×Q8—8312no—
983C4×Q8—836no—
984C4×Q8—833no—
985C4×Q8C22×D8311yescharacteristic
986C4×Q8C22×D8313yes—
987C4×Q8C22×D8311yescharacteristic
988C4×Q8C22×D8313yes—
989C4×Q8C22×D8316yes—
990C4×Q8C22×D8316yes—
991C4×Q8C22×D8312yes—
992C4×Q8C22×D8316yes—
993C4×Q8C22×D8313yes—
994C4×D4—832no—
995C4×D4—833no—
996C4×D4—836no—
997C4×D4—836no—
998C4×D4—836no—
999C4×D4—836no—
1000C4×D4—836no—
1001C4×D4—836no—
1002C4×D4—836no—
1003C4×D4—8312no—
1004C4×D4—836no—
1005C4×D4—836no—
1006C4×D4—836no—
1007C4×D4—836no—
1008C4×D4—833no—
1009C4×D4—832no—
1010C4×D4—836no—
1011C4×D4—836no—
1012C4×D4—836no—
1013C4×D4—836no—
1014C4×D4—8312no—
1015C4×D4—8312no—
1016C4×D4—836no—
1017C4×D4—836no—
1018C4×D4—8312no—
1019C4×D4—836no—
1020C4×D4—836no—
1021C4×D4—836no—
1022C4×D4—8312no—
1023C4×D4—833no—
1024C4×D4—836no—
1025C4×D4C22×D8316yes—
1026C4×D4C22×D8313yes—
1027#117—831no—
1028#117—833no—
1029#117—836no—
1030#117—8312no—
1031#117—836no—
1032#117—836no—
1033#117—8312no—
1034#117—836no—
1035#117—836no—
1036#117—836no—
1037#117—836no—
1038#117—836no—
1039#117—836no—
1040#117—8312no—
1041#117—8312no—
1042#117C22×D8316yes—
1043#117C22×D8316yes—
1044#117C22×D8316yes—
1045C2×C4⋊C4—836no—
1046C2×C4⋊C4—833no—
1047C2×C4⋊C4—836no—
1048C2×C4⋊C4—833no—
1049C2×C4⋊C4—833no—
1050C2×C4⋊C4—836no—
1051C2×C4⋊C4—836no—
1052C2×C4⋊C4—833no—
1053C2×C4⋊C4—833no—
1054C2×C4⋊C4—8312no—
1055C2×C4⋊C4—836no—
1056C2×C4⋊C4C22×D8313yes—
1057C2×C42—833no—
1058C2×C42—833no—
1059C2×C42—833no—
1060C2×C42—836no—
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×C42—8312no—
1071C2×C42C22×D8313yes—
1072C24—831no—
1073#41—33212no—
1074#41—33212no—
1075#41—16624no—
1076#41—16624no—
1077#41—1664no—
1078#41—16624no—
1079#41—16612no—
1080#41—1668no—
1081C2×Q8—24no—
1082C2×Q8—28no—
1083C2×Q8—838no—
1084C2×Q8—836no—
1085C2×Q8—836no—
1086C2×Q8—833no—
1087C2×Q8—831no—
1088C2×Q8—836no—
1089C2×Q8—833no—
1090C2×Q8—836no—
1091C2×Q8—16612no—
1092C2×Q8—16612no—
1093C2×Q8—16612no—
1094C2×Q8—16624no—
1095C2×Q8—1664no—
1096C2×Q8C23×D8313yes—
1097C2×Q8C23×D8313yes—
1098C2×Q8C23×D8316yes—
1099C2×Q8C23×D8311yescharacteristic
1100C2×D4—836no—
1101C2×D4—832no—
1102C2×D4—832no—
1103C2×D4—836no—
1104C2×D4—836no—
1105C2×D4—836no—
1106C2×D4—836no—
1107C2×D4—833no—
1108C2×D4—836no—
1109C2×D4—836no—
1110C2×D4C23×D8311yescharacteristic
1111C2×D4C23×D8312yes—
1112C22×C4—3326no—
1113C22×C4—836no—
1114C22×C4—833no—
1115C22×C4—833no—
1116C22×C4—833no—
1117C22×C4—833no—
1118C22×C4—836no—
1119C22×C4—8312no—
1120C22×C4—831no—
1121C22×C4—833no—
1122C22×C4—831no—
1123C22×C4—832no—
1124C22×C4—833no—
1125C22×C4—833no—
1126C22×C4—831no—
1127C22×C4—831no—
1128C22×C4—831no—
1129C22×C4—836no—
1130C22×C4—833no—
1131C22×C4—833no—
1132C22×C4—833no—
1133C22×C4—8312no—
1134C22×C4—836no—
1135C22×C4—16612no—
1136C22×C4—1664no—
1137C22×C4C23×D8311yescharacteristic
1138C22×C4C23×D8313yes—
1139C22×C4C23×D8313yes—
1140C22×C4C23×D8316yes—
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—832no—
1155C4⋊C4—832no—
1156C4⋊C4—833no—
1157C4⋊C4—831no—
1158C4⋊C4—836no—
1159C4⋊C4—836no—
1160C4⋊C4—8312no—
1161C4⋊C4—836no—
1162C4⋊C4—836no—
1163C4⋊C4—836no—
1164C4⋊C4—836no—
1165C4⋊C4—8312no—
1166C4⋊C4C23×D8313yes—
1167C4⋊C4C23×D8313yes—
1168C4⋊C4C23×D8316yes—
1169C4⋊C4C23×D8316yes—
1170C4⋊C4C23×D8316yes—
1171C4⋊C4C23×D8316yes—
1172C4⋊C4C23×D8311yescharacteristic
1173C4⋊C4C23×D8313yes—
1174C4⋊C4C23×D83112yes—
1175C4⋊C4C23×D8316yes—
1176C4⋊C4C23×D8316yes—
1177C4⋊C4C23×D8316yes—
1178C4⋊C4C23×D8316yes—
1179C22⋊C4—832no—
1180C22⋊C4—832no—
1181C22⋊C4—836no—
1182C22⋊C4—832no—
1183C22⋊C4—836no—
1184C22⋊C4—8312no—
1185C22⋊C4—836no—
1186C22⋊C4—836no—
1187C22⋊C4—836no—
1188C22⋊C4—836no—
1189C22⋊C4—832no—
1190C22⋊C4—836no—
1191C22⋊C4—8312no—
1192C22⋊C4—836no—
1193C22⋊C4—8312no—
1194C22⋊C4—836no—
1195C22⋊C4—8312no—
1196C22⋊C4C23×D8316yes—
1197C22⋊C4C23×D8316yes—
1198C22⋊C4C23×D8316yes—
1199C22⋊C4C23×D8316yes—
1200C22⋊C4C23×D8312yes—
1201C42—833no—
1202C42—833no—
1203C42—833no—
1204C42—836no—
1205C42—832no—
1206C42—833no—
1207C42—833no—
1208C42—833no—
1209C42—833no—
1210C42—833no—
1211C42—833no—
1212C42—833no—
1213C42—833no—
1214C42—833no—
1215C42—836no—
1216C42—836no—
1217C42—8312no—
1218C42—836no—
1219C42C23×D8313yes—
1220C42C23×D8313yes—
1221C42C23×D8313yes—
1222C42C23×D8313yes—
1223C42C23×D83112yes—
1224C42C23×D8316yes—
1225C23—831no—
1226C23—831no—
1227C23—836no—
1228C23—1662no—
1229C23—1662no—
1230C23—1662no—
1231C23C24×D8312yes—
1232C23C24×D8311yescharacteristic
1233Q8—26no—
1234Q8—212no—
1235Q8—26no—
1236Q8—3326no—
1237Q8—3326no—
1238Q8—8312no—
1239Q8—16612no—
1240Q8—16612no—
1241Q8—1666no—
1242Q8—1662no—
1243Q8#41×D8314yes—
1244D4—24no—
1245D4—22no—
1246D4—3326no—
1247D4—3326no—
1248D4—16612no—
1249D4—16612no—
1250D4—16612no—
1251D4—1664no—
1252D4—1664no—
1253D4—16612no—
1254D4—16612no—
1255D4—1666no—
1256C2×C4—26no—
1257C2×C4—26no—
1258C2×C4—212no—
1259C2×C4—22no—
1260C2×C4—3323no—
1261C2×C4—3323no—
1262C2×C4—3323no—
1263C2×C4—3323no—
1264C2×C4—33212no—
1265C2×C4—3326no—
1266C2×C4—3326no—
1267C2×C4—831no—
1268C2×C4—833no—
1269C2×C4—8312no—
1270C2×C4—834no—
1271C2×C4—831no—
1272C2×C4—833no—
1273C2×C4—832no—
1274C2×C4—833no—
1275C2×C4—832no—
1276C2×C4—836no—
1277C2×C4—833no—
1278C2×C4—1666no—
1279C2×C4—1662no—
1280C2×C4—16624no—
1281C2×C4—16612no—
1282C2×C4—1666no—
1283C2×C4—1662no—
1284C2×C4—1666no—
1285C2×C4—1662no—
1286C2×C4—1664no—
1287C2×C4—1666no—
1288C2×C4—1666no—
1289C2×C4—16612no—
1290C2×C4—1662no—
1291C2×C4C24×D8311yescharacteristic
1292C2×C4C24×D8316yes—
1293C2×C4C24×D8313yes—
1294C2×C4C24×D8313yes—
1295C2×C4C24×D8316yes—
1296C2×C4C24×D8313yes—
1297C2×C4C24×D8312yes—
1298C2×C4C24×D8313yes—
1299C2×C4C24×D8311yescharacteristic
1300C22—21no—
1301C22—21no—
1302C22—22no—
1303C22—22no—
1304C22—22no—
1305C22—832no—
1306C22—832no—
1307C22—1668no—
1308C22—1666no—
1309C22—1666no—
1310C22—1666no—
1311C22—1661no—
1312C22—1661no—
1313C22—1661no—
1314C22—1661no—
1315C22#1912853812yes—
1316C22C25×D8311yescharacteristic
1317C4—26no—
1318C4—23no—
1319C4—21no—
1320C4—26no—
1321C4—23no—
1322C4—23no—
1323C4—22no—
1324C4—836no—
1325C4—832no—
1326C4—1662no—
1327C4—1663no—
1328C4—1661no—
1329C4—1662no—
1330C4—1663no—
1331C4—1666no—
1332C4—1663no—
1333C4C2×#41×D8316yes—
1334C42−1+4×D8312yes—
1335C2—22no—
1336C2—42no—
1337C2—3326no—
1338C2—1662no—
1339C2—1662no—
1340C2C22×#41×D8311yescharacteristic
1341C2C2×2−1+4×D8311yescharacteristic
1342C2C2×#1912853811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D83
commutator, socle, cosocleC22×C83C26
FittingC83×#3523C2
hypercenter#3523D83
hypocenterC83#62788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C22 ◁ #3523

Complements

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

NH ≅ G/Ntype
1. #24921551C2semidirect
2. #24921548C2semidirect
3. #24921546C2semidirect
4. #24921458C2semidirect
5. #24921454C2semidirect
6. #24921329C2semidirect
7. #24921318C2semidirect
8. #24921267C2semidirect
9. #24921233C2semidirect
10. #24921163C2semidirect
11. #24921113C2semidirect
12. #24921084C2semidirect
13. #24921077C2semidirect
14. #24921063C2semidirect
15. #24921055C2semidirect
16. #24921045C2semidirect
17. Q8×#13050589C2semidirect
18. #24920895C2semidirect
19. #24920760C2semidirect
20. #24920757C2semidirect
21. #24920672C2semidirect
22. C2×C4×Q8×D83C2semidirect
23. C83×#3523C2semidirect
26. #19128436C22semidirect
27. #19128436C22semidirect
28. #19128433C22semidirect
29. Q8×Dic166C22semidirect
30. Q8×Dic166C22semidirect
31. #19128430C22semidirect
32. #19128428C22semidirect
33. #19128427C22semidirect
34. #19128426C22semidirect
35. #19128426C22semidirect
36. #19128425C22semidirect
37. #19128425C22semidirect
38. #19128423C22semidirect
39. #19128423C22semidirect
40. #19128418C22semidirect
42. #19128411C22semidirect
44. #19128408C22semidirect
46. #19128407C22semidirect
51. #19128393C22semidirect
52. #19128390C22semidirect
54. #19128383C22semidirect
55. #19128373C22semidirect
56. #19128372C22semidirect
58. #19128366C22semidirect
63. #19128362C22semidirect
65. #19128361C22semidirect
71. #19128323C22semidirect
72. #19128322C22semidirect
73. #19128317C22semidirect
74. #19128310C22semidirect
75. #19128309C22semidirect
82. #19128257C22semidirect
85. #19128256C22semidirect
88. #19128253C22semidirect
99. #19128237C22semidirect
103. #19128236C22semidirect
107. #19128234C22semidirect
118. #19128183C22semidirect
120. #19128181C22semidirect
122. #19128177C22semidirect
126. C4×#13050591C22semidirect
129. #19128169C22semidirect
133. C2×Q8×Dic83C22semidirect
144. C4×Q8×D83C22semidirect
147. #557×C83C22semidirect
148. #557×C83C22semidirect
149. #556×C83C22semidirect
152. D4×Q8×C83C22semidirect
153. #541×C83C22semidirect
156. #519×C83C22semidirect
421. Q8×D83#41semidirect
620. C4×D832−1+4semidirect
673. #3523D83semidirect
695. C83#62788semidirect
708. #557C2×D83semidirect
709. #557C2×D83semidirect
715. #556C2×D83semidirect
738. D4×Q8C2×D83semidirect
754. #541C2×D83semidirect
804. #519C2×D83semidirect

Maximal subgroups

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

subgroupindex
#249215512
#249215482
#249215462
#249214582
#249214542
#249213292
#249213182
#249212672
#249212332
#249211632
#249211132
#249210842
#249210772
#249210632
#249210552
#249210452
Q8×#130505892
#249208952
#249207602
#249207572
#249206722
C2×C4×Q8×D832
C83×#35232
#6278883