Finite Group Databasebeta

← #36312635

Subgroups — #36312635

Order 21248.

7094 conjugacy classes of subgroups.

The subgroup lattice has 944 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921553C214yesmaximal, complemented
2#24921542C214yesmaximal, complemented
3#24921458C214yesmaximal, complemented
4#24921448C214yesmaximal, complemented
5#24921321C216yesmaximal, complemented
6#24921269C211yesmaximal, characteristic, complemented
7#24921230C211yesmaximal, characteristic, complemented
8#24921166C216yesmaximal, complemented
9#24921115C211yesmaximal, characteristic, complemented
10#24921111C211yesmaximal, characteristic, complemented
11#24921085C214yesmaximal, complemented
12#24921080C214yesmaximal, complemented
13#24921061C214yesmaximal, complemented
14Q8×#13050590C214yesmaximal, complemented
15#24920890C216yesmaximal, complemented
16#24920756C216yesmaximal, complemented
17C4×#14581840C211yesmaximal, characteristic, complemented
18C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
19C4×2−1+4×C83C211yesmaximal, characteristic, complemented
20C2×#14581840C2211yescharacteristic
21C22×Q8×D83C2211yescharacteristic
22#19128434C22112yescomplemented
23Q8×Dic166C2214yescomplemented
24#19128430C2214yescomplemented
25#19128429C22112yescomplemented
26#19128427C2214yescomplemented
27#19128427C2214yescomplemented
28#19128423C22112yescomplemented
29#19128421C22112yescomplemented
30#19128419C22112yescomplemented
31#19128411C22112yes—
32#19128406C22112yes—
33#19128406C22112yescomplemented
34#19128401C22112yes—
35#19128395C22112yes—
36#19128392C22112yes—
37#19128390C22112yes—
38#19128390C22112yescomplemented
39#19128386C22112yescomplemented
40#19128370C2214yescomplemented
41Q8×D332C2214yes—
42Q8×D332C2214yes—
43Q8×C22⋊D83C2214yes—
44Q8×C22⋊D83C2214yes—
45Q8×C22⋊D83C2214yescomplemented
46#19128363C2214yes—
47#19128363C2214yes—
48#19128362C2214yescomplemented
49#19128358C2214yes—
50#19128358C2214yes—
51#19128358C2214yescomplemented
52#19128356C22112yes—
53#19128352C22112yes—
54#19128329C2216yes—
55#19128322C22112yescomplemented
56#19128316C22112yescomplemented
57#19128313C22112yescomplemented
58#19128309C22112yescomplemented
59#19128293C22124yes—
60#19128279C2216yes—
61#19128277C2216yes—
62#19128272C2216yes—
63#19128258C22112yescomplemented
64#19128255C2216yes—
65#19128255C2216yes—
66#19128255C22112yescomplemented
67#19128254C2216yes—
68#19128248C2216yes—
69#19128248C2216yes—
70#19128247C2216yes—
71#19128238C2216yes—
72#19128238C2216yes—
73#19128235C22112yescomplemented
74#19128233C2216yes—
75#19128233C2216yes—
76#19128233C22112yescomplemented
77#19128231C22112yes—
78#19128231C22112yes—
79#19128229C22112yes—
80#19128229C22112yes—
81#19128213C2216yes—
82#19128210C22112yes—
83#19128210C2214yes—
84#19128208C2216yes—
85#19128183C2214yescomplemented
86#19128182C2216yes—
87#19128179C2211yescharacteristic
88#19128177C2214yescomplemented
89C4×#13050591C2214yescomplemented
90C4×#13050590C2216yes—
91C4×#13050590C22112yes—
92C4×#13050590C22112yes—
93C2×Q8×Dic83C2211yescharacteristic
94C2×C4×Dic166C2213yes—
95C2×#14581757C2213yes—
96C4×Q8×D83C2214yes—
97C4×Q8×D83C2214yes—
98C4×Q8×D83C2214yes—
99C4×Q8×D83C2214yes—
100C4×Q8×D83C2214yescomplemented
101C2×C4⋊C4×D83C2213yes—
102C2×C42×D83C2213yes—
103C2×2−1+4×C83C2211yescharacteristic
104#520×C83C2216yes—
105#520×C83C2214yescomplemented
106#519×C83C2211yescharacteristic
107#519×C83C2214yescomplemented
108C4×#41×C83C2216yes—
109C4×#41×C83C2214yescomplemented
110C2×C4×Q8×C83C2211yescharacteristic
111C2×C4×Q8×C83C2214yescomplemented
112#14581840—28no—
113C2×#13050591C2314yes—
114C2×#13050590C2314yes—
115C2×#13050590C2316yes—
116C2×#13050590C23112yes—
117C22×Dic166C2313yes—
118C2×Q8×D83—28no—
119C2×Q8×D83C2314yes—
120C2×Q8×D83C2314yes—
121C2×Q8×D83C2314yes—
122C22×C4×D83C2311yescharacteristic
123C22×C4×D83C2313yes—
124C22×C4×D83C2313yes—
125#14581792C23112yes—
126#14581792C23112yes—
127#14581791C23112yes—
128#14581791C2316yes—
129#14581791C2316yes—
130#14581790C23112yes—
131#14581790C2316yes—
132#14581788C2316yes—
133#14581787C23112yes—
134#14581787C23112yes—
135#14581786C23124yes—
136#14581785C23124yes—
137#14581785C23112yes—
138#14581785C23112yes—
139#14581784C23112yes—
140#14581784C23124yes—
141#14581783C23112yes—
142#14581783C2316yes—
143#14581783C2316yes—
144#14581782C23124yes—
145#14581782C23112yes—
146#14581782C23112yes—
147#14581781C2316yes—
148#14581780C23112yes—
149#14581779C23112yes—
150#14581779C2316yes—
151#14581778C23112yes—
152#14581778C23112yes—
153#14581777C23112yes—
154#14581777C2314yes—
155#14581776C23112yes—
156#14581775C23124yes—
157#14581774C23124yes—
158#14581774C23112yes—
159#14581774C2314yes—
160#14581773C23112yes—
161#14581772C23112yes—
162#14581772C23112yes—
163#14581772C2316yes—
164#14581772C2316yes—
165#14581771C23112yes—
166#14581771C23124yes—
167#14581771C23112yes—
168#14581771C23112yes—
169#14581770C23124yes—
170#14581770C23112yes—
171#14581770C2314yes—
172#14581769C23112yes—
173#14581769C2314yes—
174#14581768C23112yes—
175#14581768C2316yes—
176#14581768C2316yes—
177#14581767C2316yes—
178#14581767C2316yes—
179#14581766C23112yes—
180#14581765C23112yes—
181#14581765C2314yes—
182#14581764C2314yes—
183#14581764C23112yes—
184#14581763C2316yes—
185#14581763C23112yes—
186#14581763C2316yes—
187#14581762C2314yes—
188#14581760C2314yes—
189Q8×Dic83C2314yes—
190Q8×Dic83C2314yes—
191Q8×Dic83C2314yes—
192Q8×Dic83C2314yes—
193C4×Dic166C23112yes—
194C4×Dic166C23112yes—
195C4×Dic166C23112yes—
196C4×Dic166C2316yes—
197C4×Dic166C23112yes—
198C4×Dic166C23112yes—
199C4×Dic166C2316yes—
200C4×Dic166C23112yes—
201#14581757C23112yes—
202#14581757C23112yes—
203#14581757C23112yes—
204C4×D332C2316yes—
205C4×D332C23112yes—
206C4×D332C23112yes—
207C4×D332C23112yes—
208C4×D332C2314yes—
209C4×D332C2316yes—
210#14581754C23112yes—
211C4×C22⋊D83C23112yes—
212C4×C22⋊D83C23112yes—
213C4×C22⋊D83C23112yes—
214C4×C22⋊D83C23112yes—
215C4×C22⋊D83C23112yes—
216C4×C22⋊D83C23112yes—
217C4×C22⋊D83C2314yes—
218C4×C22⋊D83C2314yes—
219C4×C22⋊D83C23112yes—
220C4×C22⋊D83C23112yes—
221#14581751C2316yes—
222#14581751C23112yes—
223#14581751C23112yes—
224#14581750C23112yes—
225#14581749C23112yes—
226#14581749C23112yes—
227#14581749C2314yes—
228#14581749C23112yes—
229#14581749C23112yes—
230C2×C4⋊Dic83C2313yes—
231C2×Dic83⋊C4C2316yes—
232C4⋊C4×D83C23112yes—
233C4⋊C4×D83C23112yes—
234C4⋊C4×D83C23112yes—
235C2×C4×Dic83C2313yes—
236C2×C4×Dic83C2313yes—
237C2×C4×Dic83C2313yes—
238C42×D83C2316yes—
239C42×D83C2316yes—
240C42×D83C2316yes—
241C42×D83C2316yes—
242C42×D83C23112yes—
2432−1+4×C83—28no—
244C2×#41×C83C2314yes—
245C2×#41×C83C2316yes—
246C22×Q8×C83C2314yes—
247C22×Q8×C83C2311yescharacteristic
248C4×Q8×C83C2314yes—
249C4×Q8×C83C2314yes—
250C4×Q8×C83C2314yes—
251C4×Q8×C83C2314yes—
252C4×Q8×C83C2316yes—
253C4×Q8×C83C23112yes—
254C4×Q8×C83C2316yes—
255C4×D4×C83C23112yes—
256C4×D4×C83C2314yes—
257C4×D4×C83C2316yes—
258C4×D4×C83C23112yes—
259C4×D4×C83C2316yes—
260#117×C83C23112yes—
261#117×C83C2316yes—
262#117×C83C23112yes—
263C2×C4⋊C4×C83C23112yes—
264C2×C4⋊C4×C83C2313yes—
265C2×C42×C83C2313yes—
266C2×C42×C83C23112yes—
267C23×D83C2411yescharacteristic
268#13050591—216no—
269#13050590—224no—
270#13050590—216no—
271#13050590—424no—
272C2×Dic166—212no—
273C2×Dic166C2414yes—
274C2×Dic166C24112yes—
275C2×Dic166C2416yes—
276C2×Dic166C24112yes—
277Q8×D83—216no—
278Q8×D83—216no—
279Q8×D83—216no—
280C2×D332C2414yes—
281C2×D332C2414yes—
282C2×D332C2416yes—
283C2×C22⋊D83C2414yes—
284C2×C22⋊D83C2414yes—
285C2×C22⋊D83C2414yes—
286C2×C22⋊D83C2414yes—
287C2×C22⋊D83C24112yes—
288C22×Dic83C2411yescharacteristic
289C22×Dic83C2413yes—
290C22×Dic83C2413yes—
291C2×C4×D83—212no—
292C2×C4×D83—24no—
293C2×C4×D83—46no—
294C2×C4×D83C2416yes—
295C2×C4×D83C2416yes—
296C2×C4×D83C24112yes—
297C2×C4×D83C2411yescharacteristic
298C2×C4×D83C2411yescharacteristic
299C2×C4×D83C2416yes—
300C2×C4×D83C2411yescharacteristic
301C2×C4×D83C2414yes—
302C2×C4×D83C2416yes—
303C2×C4×D83C24112yes—
304C2×C4×D83C2411yescharacteristic
305C4⋊Dic83C24112yes—
306C4⋊Dic83C2416yes—
307C4⋊Dic83C2416yes—
308C4⋊Dic83C24112yes—
309C4⋊Dic83C2414yes—
310C4⋊Dic83C24112yes—
311C4⋊Dic83C24112yes—
312Dic83⋊C4C24112yes—
313Dic83⋊C4C2414yes—
314Dic83⋊C4C2414yes—
315Dic83⋊C4C24112yes—
316Dic83⋊C4C24112yes—
317Dic83⋊C4C24112yes—
318Dic83⋊C4C24112yes—
319Dic83⋊C4C2414yes—
320Dic83⋊C4C24112yes—
321Dic83⋊C4C24124yes—
322Dic83⋊C4C2414yes—
323C22⋊Dic83C2414yes—
324C22⋊Dic83C24112yes—
325C22⋊Dic83C24112yes—
326C22⋊Dic83C24112yes—
327C22⋊Dic83C2414yes—
328(C2×D83)⋊C4C2414yes—
329(C2×D83)⋊C4C2414yes—
330(C2×D83)⋊C4C2414yes—
331(C2×D83)⋊C4C2414yes—
332(C2×D83)⋊C4C24112yes—
333(C2×D83)⋊C4C2414yes—
334(C2×D83)⋊C4C24112yes—
335(C2×D83)⋊C4C2414yes—
336(C2×D83)⋊C4C24112yes—
337(C2×D83)⋊C4C24112yes—
338C4×Dic83C2416yes—
339C4×Dic83C2416yes—
340C4×Dic83C2416yes—
341C4×Dic83C24112yes—
342C4×Dic83C24112yes—
343C4×Dic83C2416yes—
344C4×Dic83C2416yes—
345C4×Dic83C2414yes—
346C4×Dic83C2416yes—
347#41×C83—216no—
348#41×C83—224no—
349C2×Q8×C83—216no—
350C2×Q8×C83#4118yescomplemented
351C2×Q8×C83C2416yes—
352C2×Q8×C83C2414yes—
353C2×D4×C83C2414yes—
354C2×D4×C83C2416yes—
355C22×C4×C83C24112yes—
356C22×C4×C83C2411yescharacteristic
357C22×C4×C83C2414yes—
358C22×C4×C83C24112yes—
359C22×C4×C83C2413yes—
360C22×C4×C83C2413yes—
361C4⋊C4×C83C2416yes—
362C4⋊C4×C83C2416yes—
363C4⋊C4×C83C24112yes—
364C4⋊C4×C83C2414yes—
365C4⋊C4×C83C24112yes—
366C22⋊C4×C83C2414yes—
367C22⋊C4×C83C24112yes—
368C22⋊C4×C83C2414yes—
369C42×C83C24112yes—
370C42×C83C24112yes—
371C42×C83C2416yes—
372C42×C83C2414yes—
373C42×C83C2416yes—
374C23×C83C2514yes—
375C23×C83C2511yescharacteristic
376C22×D83—22no—
377C22×D83—22no—
378C22×D83—22no—
379C22×D83C2514yes—
380C22×D83C2511yescharacteristic
381C22×D83C2511yescharacteristic
382Q8×C83—212no—
383Q8×C83C2×#41116yes—
384D4×C83—28no—
385D4×C83—212no—
386C2×C4×C83—224no—
387C2×C4×C83—22no—
388C2×C4×C83—28no—
389C2×C4×C83—43no—
390C2×C4×C83—412no—
391C2×C4×C83C2×#41112yes—
392C2×C4×C83C2511yescharacteristic
393C2×C4×C83C2514yes—
394C2×C4×C83C2516yes—
395C2×C4×C83C2514yes—
396C2×C4×C83C2514yes—
397C2×C4×C83C2516yes—
398C2×C4×C83C2511yescharacteristic
399C22⋊D83—28no—
400C22⋊D83—28no—
401C22⋊D83—28no—
402C22⋊D83—28no—
403C22⋊D83—412no—
404C2×Dic83—26no—
405C2×Dic83—22no—
406C2×Dic83—43no—
407C2×Dic83C2511yescharacteristic
408C2×Dic83C2514yes—
409C2×Dic83C2516yes—
410C2×Dic83C2514yes—
411C2×Dic83C2514yes—
412C2×Dic83C2516yes—
413C2×Dic83C2511yescharacteristic
414D332—28no—
415D332—28no—
416D332—212no—
417C4×D83—22no—
418C4×D83—212no—
419C4×D83—212no—
420C4×D83—212no—
421C4×D83—224no—
422C4×D83—22no—
423C4×D83—28no—
424C4×D83—22no—
425C4×D83—46no—
426C4×D83—412no—
427C4×D832−1+414yescomplemented
428Dic166—224no—
429Dic166—212no—
430Dic166—28no—
431Dic166—412no—
432C22×C83—21no—
433C22×C83—21no—
434C22×C83—24no—
435C22×C83—24no—
436C22×C83—24no—
437C22×C83C22×#4112yes—
438C22×C83C2611yescharacteristic
439C2×D83—28no—
440C2×D83—21no—
441C2×D83—21no—
442C2×D83—21no—
443C2×D83—21no—
444C2×D83—24no—
445C2×D83—24no—
446C2×D83—24no—
447C2×D83C2×2−1+412yes—
448C2×D83#58512yes—
449C4×C83—24no—
450C4×C83—24no—
451C4×C83—21no—
452C4×C83—24no—
453C4×C83—26no—
454C4×C83C22×#41112yes—
455C4×C83C2×2−1+412yes—
456Dic83—26no—
457Dic83—24no—
458Dic83—24no—
459Dic83—21no—
460Dic83—24no—
461Dic83—26no—
462Dic83C2×2−1+412yes—
463#62788—831nomaximal, Sylow
464C2×C83—22no—
465C2×C83—44no—
466C2×C83C23×#4111yescharacteristic
467C2×C83C22×2−1+411yescharacteristic
468C2×C83C2×#58511yescharacteristic
469D83—22no—
470D83—22no—
471D83—44no—
472#3523—834no—
473#3522—834no—
474#3516—834no—
475#3516—834no—
476#3507—836no—
477#3502—831no—
478#3497—831no—
479#3492—836no—
480#3486—831no—
481#3486—831no—
482#3482—834no—
483#3482—834no—
484#3480—834no—
485Q8×#41—834no—
486#3461—836no—
487#3444—836no—
488C4×2−1+4—831no—
489C4×2−1+4D8311yescharacteristic, complemented
490C22×C4×Q8—831no—
491C83#6278811yescharacteristic, complemented, Sylow
492C2×2−1+4—831no—
493C2×2−1+4C2×D8311yescharacteristic
494C23×Q8—831no—
495#559—8312no—
496Q82—834no—
497#557—834no—
498#557—834no—
499#557—8312no—
500#557—834no—
501#556—8312no—
502#556—8312no—
503#556—8312no—
504#554—8312no—
505#554—8312no—
506#554—8312no—
507#553—8312no—
508#553—8312no—
509#552—8312no—
510#552—8312no—
511#552—8312no—
512#552—8312no—
513#550—834no—
514D4×Q8—834no—
515D4×Q8—834no—
516D4×Q8—834no—
517D4×Q8—834no—
518D4×Q8—834no—
519#548—834no—
520#548—834no—
521#548—834no—
522#548—834no—
523#548—834no—
524#548—834no—
525#547—8312no—
526#547—8312no—
527#544—836no—
528#542—8312no—
529#542—8312no—
530#541—8312no—
531#541—8312no—
532#539—8324no—
533#537—836no—
534#536—836no—
535#536—836no—
536#533—836no—
537#533—836no—
538#533—8312no—
539#533—836no—
540#533—8312no—
541#532—836no—
542#532—836no—
543#532—836no—
544#529—836no—
545#529—836no—
546#529—8312no—
547#529—836no—
548#529—8312no—
549#529—836no—
550#529—8312no—
551#529—8312no—
552#529—8312no—
553#529—8312no—
554#525—836no—
555#525—834no—
556#525—8312no—
557#525—836no—
558#520—834no—
559#520—836no—
560#520C2×D8316yes—
561#520C2×D8314yescomplemented
562#519—831no—
563#519—834no—
564#519C2×D8311yescharacteristic
565#519C2×D8314yescomplemented
566C4×#41—834no—
567C4×#41—836no—
568C4×#41—8312no—
569C4×#41—8312no—
570C4×#41C2×D8316yes—
571C4×#41C2×D8314yescomplemented
572C2×C4×Q8—831no—
573C2×C4×Q8—834no—
574C2×C4×Q8—834no—
575C2×C4×Q8—834no—
576C2×C4×Q8—834no—
577C2×C4×Q8—834no—
578C2×C4×Q8—833no—
579C2×C4×Q8—833no—
580C2×C4×Q8C2×D8311yescharacteristic
581C2×C4×Q8C2×D8314yescomplemented
582C22×C4⋊C4—833no—
583C22×C42—833no—
5842−1+4—28no—
5852−1+4—1668no—
586C2×#41—834no—
587C2×#41—8312no—
588C2×#41—834no—
589C2×#41—836no—
590C2×#41C22×D8316yes—
591C2×#41C22×D8314yes—
592C22×Q8—834no—
593C22×Q8—834no—
594C22×Q8—834no—
595C22×Q8—833no—
596C22×Q8—1668no—
597C22×Q8C22×D8314yes—
598C22×Q8C22×D8311yescharacteristic
599C23×C4—833no—
600C23×C4—833no—
601C23×C4—831no—
602C4⋊Q8—836no—
603C4⋊Q8—8312no—
604C4⋊Q8—836no—
605C4⋊Q8—836no—
606C4⋊Q8—8312no—
607C4⋊Q8—8312no—
608C4⋊Q8—8312no—
609#127—836no—
610#126—8312no—
611#126—8312no—
612#126—8312no—
613#126—8312no—
614#126—8324no—
615#126—8324no—
616#125—8312no—
617#125—8312no—
618#125—836no—
619#125—836no—
620#125—8312no—
621#125—8324no—
622#125—8312no—
623#125—8324no—
624#124—836no—
625#124—836no—
626#124—8312no—
627#124—8312no—
628#124—8312no—
629#124—8312no—
630#123—8312no—
631#123—8324no—
632#123—834no—
633#123—8312no—
634#123—834no—
635#123—8312no—
636#123—8312no—
637#123—8324no—
638C22⋊Q8—836no—
639C22⋊Q8—836no—
640C22⋊Q8—8312no—
641C22⋊Q8—8312no—
642C22⋊Q8—8312no—
643C22⋊Q8—8312no—
644C22⋊Q8—8324no—
645C22⋊Q8—834no—
646C22⋊Q8—8312no—
647C22⋊Q8—8324no—
648C22⋊Q8—836no—
649C22⋊Q8—836no—
650C22⋊Q8—8312no—
651C22⋊Q8—8312no—
652C22⋊Q8—834no—
653C22⋊Q8—8312no—
654#121—836no—
655#121—836no—
656#121—8312no—
657#121—834no—
658#121—8312no—
659#121—8312no—
660#121—836no—
661#121—836no—
662#121—834no—
663#121—8312no—
664#120—834no—
665#120—834no—
666C4×Q8—834no—
667C4×Q8—834no—
668C4×Q8—834no—
669C4×Q8—834no—
670C4×Q8—8312no—
671C4×Q8—8312no—
672C4×Q8—8312no—
673C4×Q8—8312no—
674C4×Q8—8312no—
675C4×Q8—836no—
676C4×Q8—836no—
677C4×Q8—8312no—
678C4×Q8—8312no—
679C4×Q8—8312no—
680C4×Q8—8312no—
681C4×Q8C22×D8314yes—
682C4×Q8C22×D8314yes—
683C4×Q8C22×D8316yes—
684C4×Q8C22×D8314yes—
685C4×Q8C22×D83112yes—
686C4×Q8C22×D8316yes—
687C4×Q8C22×D8314yes—
688C4×D4—834no—
689C4×D4—834no—
690C4×D4—8312no—
691C4×D4—8312no—
692C4×D4—8312no—
693C4×D4—8312no—
694C4×D4—8312no—
695C4×D4—8312no—
696C4×D4—8312no—
697C4×D4—8312no—
698C4×D4—8312no—
699C4×D4—834no—
700C4×D4—836no—
701C4×D4—836no—
702C4×D4—8312no—
703C4×D4—8312no—
704C4×D4—8312no—
705C4×D4C22×D8314yes—
706C4×D4C22×D8316yes—
707C4×D4C22×D83112yes—
708C4×D4C22×D8316yes—
709C4×D4C22×D83112yes—
710#117—836no—
711#117—8312no—
712#117—8312no—
713#117—8312no—
714#117—834no—
715#117—8312no—
716#117—8312no—
717#117—8312no—
718#117—8312no—
719#117C22×D8316yes—
720#117C22×D83112yes—
721#117C22×D83112yes—
722C2×C4⋊C4—833no—
723C2×C4⋊C4—836no—
724C2×C4⋊C4—8312no—
725C2×C4⋊C4—8312no—
726C2×C4⋊C4—8312no—
727C2×C4⋊C4C22×D8313yes—
728C2×C4⋊C4C22×D83112yes—
729C2×C42—833no—
730C2×C42—833no—
731C2×C42—833no—
732C2×C42—836no—
733C2×C42—836no—
734C2×C42—836no—
735C2×C42—836no—
736C2×C42—8312no—
737C2×C42C22×D8313yes—
738C2×C42C22×D83112yes—
739C24—831no—
740#41—216no—
741#41—224no—
742#41—33224no—
743#41—16616no—
744#41—16616no—
745#41—16624no—
746C2×Q8—216no—
747C2×Q8—8312no—
748C2×Q8—834no—
749C2×Q8—8312no—
750C2×Q8—836no—
751C2×Q8—16616no—
752C2×Q8—16616no—
753C2×Q8—16616no—
754C2×Q8—16612no—
755C2×Q8#1305059018yescomplemented
756C2×Q8C23×D8316yes—
757C2×Q8C23×D8314yes—
758C2×D4—8312no—
759C2×D4—834no—
760C2×D4—834no—
761C2×D4—834no—
762C2×D4—834no—
763C2×D4—834no—
764C2×D4—834no—
765C2×D4—836no—
766C2×D4C23×D8314yes—
767C2×D4C23×D8316yes—
768C22×C4—3326no—
769C22×C4—833no—
770C22×C4—836no—
771C22×C4—8312no—
772C22×C4—831no—
773C22×C4—831no—
774C22×C4—833no—
775C22×C4—831no—
776C22×C4—831no—
777C22×C4—836no—
778C22×C4—836no—
779C22×C4—836no—
780C22×C4—8312no—
781C22×C4—831no—
782C22×C4—834no—
783C22×C4—1664no—
784C22×C4—16612no—
785C22×C4C23×D83112yes—
786C22×C4C23×D8311yescharacteristic
787C22×C4C23×D8314yes—
788C22×C4C23×D8313yes—
789C22×C4C23×D83112yes—
790C22×C4C23×D8313yes—
791C4⋊C4—8312no—
792C4⋊C4—8324no—
793C4⋊C4—836no—
794C4⋊C4—8312no—
795C4⋊C4—836no—
796C4⋊C4—834no—
797C4⋊C4—834no—
798C4⋊C4—834no—
799C4⋊C4—834no—
800C4⋊C4—834no—
801C4⋊C4—8312no—
802C4⋊C4—8312no—
803C4⋊C4—8312no—
804C4⋊C4—8312no—
805C4⋊C4—8312no—
806C4⋊C4—8312no—
807C4⋊C4—8312no—
808C4⋊C4—8312no—
809C4⋊C4C23×D83112yes—
810C4⋊C4C23×D8316yes—
811C4⋊C4C23×D83112yes—
812C4⋊C4C23×D8316yes—
813C4⋊C4C23×D8314yes—
814C22⋊C4—834no—
815C22⋊C4—834no—
816C22⋊C4—8312no—
817C22⋊C4—8312no—
818C22⋊C4—8312no—
819C22⋊C4—834no—
820C22⋊C4—834no—
821C22⋊C4—8312no—
822C22⋊C4—834no—
823C22⋊C4—834no—
824C22⋊C4—834no—
825C22⋊C4—834no—
826C22⋊C4—8312no—
827C22⋊C4—8312no—
828C22⋊C4—8312no—
829C22⋊C4C23×D8314yes—
830C22⋊C4C23×D83112yes—
831C22⋊C4C23×D8314yes—
832C42—836no—
833C42—836no—
834C42—836no—
835C42—836no—
836C42—836no—
837C42—8312no—
838C42—8312no—
839C42—836no—
840C42—834no—
841C42C23×D8316yes—
842C42C23×D83112yes—
843C42C23×D83112yes—
844C42C23×D8316yes—
845C42C23×D8314yes—
846C23—831no—
847C23—831no—
848C23—834no—
849C23—1662no—
850C23—1662no—
851C23—1662no—
852C23C24×D8314yes—
853C23C24×D8311yescharacteristic
854Q8—212no—
855Q8—33212no—
856Q8—1668no—
857Q8—16624no—
858Q8—16612no—
859Q8C2×#13050590116yes—
860D4—28no—
861D4—212no—
862D4—33212no—
863D4—1668no—
864D4—1668no—
865D4—1668no—
866D4—1668no—
867D4—1668no—
868D4—1668no—
869D4—16612no—
870C2×C4—224no—
871C2×C4—22no—
872C2×C4—28no—
873C2×C4—43no—
874C2×C4—412no—
875C2×C4—3326no—
876C2×C4—33212no—
877C2×C4—3323no—
878C2×C4—831no—
879C2×C4—834no—
880C2×C4—831no—
881C2×C4—834no—
882C2×C4—836no—
883C2×C4—834no—
884C2×C4—834no—
885C2×C4—836no—
886C2×C4—1662no—
887C2×C4—16612no—
888C2×C4—1662no—
889C2×C4—1662no—
890C2×C4—1666no—
891C2×C4—16612no—
892C2×C4—16612no—
893C2×C4—16624no—
894C2×C4—1662no—
895C2×C4—1668no—
896C2×C4C2×#13050590112yes—
897C2×C4C24×D8311yescharacteristic
898C2×C4C24×D8316yes—
899C2×C4C24×D8314yes—
900C2×C4C24×D8314yes—
901C2×C4C24×D8314yes—
902C2×C4C24×D8316yes—
903C2×C4C24×D8311yescharacteristic
904C22—21no—
905C22—21no—
906C22—24no—
907C22—24no—
908C22—24no—
909C22—832no—
910C22—832no—
911C22—1668no—
912C22—1664no—
913C22—1664no—
914C22—1664no—
915C22—1661no—
916C22—1661no—
917C22—1661no—
918C22—1661no—
919C22C22×#1305059012yes—
920C22C25×D8311yescharacteristic
921C4—24no—
922C4—21no—
923C4—24no—
924C4—26no—
925C4—24no—
926C4—832no—
927C4—1664no—
928C4—1666no—
929C4—1661no—
930C4—1664no—
931C4—1664no—
932C4—1666no—
933C4C22×#13050590112yes—
934C42−1+4×D8312yes—
935C2—22no—
936C2—44no—
937C2—3324no—
938C2—1662no—
939C2—1662no—
940C2C23×#1305059011yescharacteristic
941C2C2×2−1+4×D8311yescharacteristic
942C2#585×D8311yescharacteristic
subgroupG/H
centerC2×C4C24×D83
commutator, socle, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC4×2−1+4×C83C2
hypercenterC4×2−1+4D83
hypocenterC83#62788
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #24921553C2semidirect
2. #24921542C2semidirect
3. #24921458C2semidirect
4. #24921448C2semidirect
5. #24921321C2semidirect
6. #24921269C2semidirect
7. #24921230C2semidirect
8. #24921166C2semidirect
9. #24921115C2semidirect
10. #24921111C2semidirect
11. #24921085C2semidirect
12. #24921080C2semidirect
13. #24921061C2semidirect
14. Q8×#13050590C2semidirect
15. #24920890C2semidirect
16. #24920756C2semidirect
17. C4×#14581840C2semidirect
18. C2×C4×Q8×D83C2semidirect
19. C4×2−1+4×C83C2semidirect
22. #19128434C22semidirect
23. Q8×Dic166C22semidirect
24. #19128430C22semidirect
25. #19128429C22semidirect
26. #19128427C22semidirect
27. #19128427C22semidirect
28. #19128423C22semidirect
29. #19128421C22semidirect
30. #19128419C22semidirect
33. #19128406C22semidirect
38. #19128390C22semidirect
39. #19128386C22semidirect
40. #19128370C22semidirect
45. Q8×C22⋊D83C22semidirect
48. #19128362C22semidirect
51. #19128358C22semidirect
55. #19128322C22semidirect
56. #19128316C22semidirect
57. #19128313C22semidirect
58. #19128309C22semidirect
63. #19128258C22semidirect
66. #19128255C22semidirect
73. #19128235C22semidirect
76. #19128233C22semidirect
85. #19128183C22semidirect
88. #19128177C22semidirect
89. C4×#13050591C22semidirect
100. C4×Q8×D83C22semidirect
105. #520×C83C22semidirect
107. #519×C83C22semidirect
109. C4×#41×C83C22semidirect
111. C2×C4×Q8×C83C22semidirect
350. C2×Q8×C83#41semidirect
427. C4×D832−1+4semidirect
489. C4×2−1+4D83semidirect
491. C83#62788semidirect
561. #520C2×D83semidirect
565. #519C2×D83semidirect
571. C4×#41C2×D83semidirect
581. C2×C4×Q8C2×D83semidirect
755. C2×Q8#13050590semidirect

Maximal subgroups

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

subgroupindex
#249215532
#249215422
#249214582
#249214482
#249213212
#249212692
#249212302
#249211662
#249211152
#249211112
#249210852
#249210802
#249210612
Q8×#130505902
#249208902
#249207562
C4×#145818402
C2×C4×Q8×D832
C4×2−1+4×C832
#6278883