Finite Group Databasebeta

← #11906308

Subgroups — #11906308

Order 1152.

2031 conjugacy classes of subgroups.

The subgroup lattice has 1103 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596094C211yesmaximal, characteristic
2C3×#5623C211yesmaximal, characteristic
3C3×#5622C211yesmaximal, characteristic
4#10595421C212yesmaximal, complemented
5#10595420C212yesmaximal, complemented
6#10594813C211yesmaximal, characteristic
7#10594812C211yesmaximal, characteristic
8#10594808C211yesmaximal, characteristic
9C2×#63837C211yesmaximal, characteristic
10#10594596C212yesmaximal, complemented
11#10594596C212yesmaximal, complemented
12#10594315C212yesmaximal, complemented
13#10594314C212yesmaximal, complemented
14#10594314C212yesmaximal, complemented
15#10594312C212yesmaximal, complemented
16#10594245C212yesmaximal
17#10594035C212yesmaximal
18#10594030C212yesmaximal
19#10594029C212yesmaximal
20#86585—31nomaximal
21#86258—31nomaximal
22C22×#627C2211yescharacteristic
23C32×C22⋊Q8C2211yescharacteristic
24#64153C2212yes—
25#64133C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64098C2212yes—
28#64098C2212yes—
29#64097C2212yes—
30#64087C2212yes—
31#64086C2212yes—
32C3×Q8×Dic3C2211yescharacteristic
33C3×#944C2212yes—
34C3×#944C2211yescharacteristic
35C3×#924C2211yescharacteristic
36C3×#924C2211yescharacteristic
37C2×C3×Dic3⋊C4C2211yescharacteristic
38C2×C3×C4×Dic3C2211yescharacteristic
39C3×#889C2212yes—
40C3×#889C2212yes—
41C3×#889C2212yes—
42C3×#888C2212yes—
43C3×#888C2211yescharacteristic
44C3×#887C2212yes—
45C3×#887C2211yescharacteristic
46C3×#878C2212yes—
47C3×#878C2212yes—
48C3×#877C2212yes—
49C3×#877C2212yes—
50#63982C2212yes—
51C2×Dic3⋊Dic3C2211yescharacteristic
52#63964C2212yes—
53#63964C2212yes—
54#63957C2212yes—
55#63955C2212yes—
56#63955C2212yes—
57C2×Dic32C2211yescharacteristic
58C2×Dic32C2211yescharacteristic
59#63918C2212yes—
60#63918C2211yescharacteristic
61C4×#627C2212yes—
62C4×#627C2212yes—
63#63867C2212yes—
64#63867C2212yes—
65#63867C2212yes—
66#63866C2211yescharacteristic
67#63866C2212yes—
68#63847C2212yes—
69#63847C2212yes—
70#63847C2212yes—
71#63847C2212yes—
72#63846C2212yes—
73#63846C2212yes—
74#63846C2212yes—
75#63845C2212yes—
76#63845C2212yes—
77#63845C2212yes—
78#63844C2211yescharacteristic
79#63844C2212yes—
80#63843C2212yes—
81#63843C2212yes—
82Dic3×Dic6C2212yes—
83Dic3×Dic6C2211yescharacteristic
84#63840C2212yes—
85#63840C2212yes—
86#63840C2212yes—
87#63839C2212yes—
88#63839C2212yes—
89#63839C2212yes—
90#63839C2212yes—
91#63839C2212yes—
92#63839C2212yes—
93#63839C2212yes—
94#63838C2212yes—
95#63838C2212yes—
96#63838C2212yes—
97#63838C2212yes—
98#63837C2212yes—
99#63837C2212yes—
100#63837C2212yes—
101#63837C2212yes—
102#63837C2212yes—
103#63837C2212yes—
104#63837C2212yes—
105#63837C2212yes—
106#63837C2212yes—
107#63837C2212yes—
108#63837C2212yes—
109C3×#544—31no—
110C3×#533—31no—
111#5722—32no—
112#5722—32no—
113#5722—32no—
114#5721—32no—
115#5721—32no—
116#5721—32no—
117#5685—32no—
118#5685—32no—
119#5685—32no—
120#5685—32no—
121#5685—32no—
122#5685—32no—
123#5623—31no—
124#5623—31no—
125#5623—31no—
126#5623—31no—
127#5623—31no—
128#5623—32no—
129#5623—61no—
130#5623D311yescharacteristic
131#5622—31no—
132#5622—32no—
133#5622—32no—
134#5622—32no—
135#5622D311yescharacteristic
136#5567—32no—
137#5567—32no—
138#5567—32no—
139Q8×Dic6—32no—
140#5519—32no—
141#5517—32no—
142#5516—32no—
143#5516—32no—
144#5500—31no—
145C2×#887—31no—
146#5470—31no—
147C2×C4×Dic6—31no—
148C2×C32×Q8C2311yescharacteristic
149C22×C32×C4C2311yescharacteristic
150C22×C3⋊Dic3C2311yescharacteristic
151C22×C3⋊Dic3C2311yescharacteristic
152C2×#634C2312yes—
153C2×#634C2311yescharacteristic
154C22×C3×Dic3C2311yescharacteristic
155C22×C3×Dic3C2311yescharacteristic
156C22×C3×Dic3C2311yescharacteristic
157C22×C3×Dic3C2311yescharacteristic
158C2×C3×Dic6C2312yes—
159C2×C3×Dic6C2312yes—
160C2×C3×Dic6C2311yescharacteristic
161C2×C3×Dic6C2311yescharacteristic
162C2×#627Q818yescomplemented
163C2×#627C2312yes—
164C2×#627C2312yes—
165C2×#627C2312yes—
166C2×#627C2312yes—
167C2×#627C2312yes—
168C32×C4⋊C4C2312yes—
169C32×C4⋊C4C2311yescharacteristic
170C32×C22⋊C4C2312yes—
171#3757C2312yes—
172C4⋊(C3⋊Dic3)C2312yes—
173C4⋊(C3⋊Dic3)C2311yescharacteristic
174#3750C2312yes—
175#3750C2312yes—
176#3750C2312yes—
177#3750C2312yes—
178#3750C2312yes—
179#3750C2312yes—
180#3750C2312yes—
181C4×C3⋊Dic3C2312yes—
182C4×C3⋊Dic3C2312yes—
183C3×#217C2312yes—
184C3×#217C2312yes—
185C3×C4⋊Dic3C2312yes—
186C3×C4⋊Dic3C2312yes—
187C3×C4⋊Dic3C2311yescharacteristic
188C3×C4⋊Dic3C2311yescharacteristic
189C3×Dic3⋊C4C2312yes—
190C3×Dic3⋊C4C2312yes—
191C3×Dic3⋊C4C2312yes—
192C3×Dic3⋊C4C2312yes—
193C3×Dic3⋊C4C2312yes—
194C3×Dic3⋊C4C2312yes—
195C3×Dic3⋊C4C2312yes—
196C3×Dic3⋊C4C2312yes—
197C3×Dic3⋊C4C2312yes—
198C3×Dic3⋊C4C2312yes—
199C3×Dic3⋊C4C2312yes—
200C3×Dic3⋊C4C2312yes—
201C3×C4×Dic3C2312yes—
202C3×C4×Dic3C2312yes—
203C3×C4×Dic3C2312yes—
204C3×C4×Dic3C2312yes—
205C3×C4×Dic3C2311yescharacteristic
206C3×C4×Dic3C2311yescharacteristic
207C3×C4×Dic3C2311yescharacteristic
208C3×C4×Dic3C2311yescharacteristic
209#3724C2312yes—
210#3724C2312yes—
211#3724C2312yes—
212#3724C2312yes—
213#3724C2312yes—
214Dic3⋊Dic3C2312yes—
215Dic3⋊Dic3C2312yes—
216Dic3⋊Dic3C2312yes—
217Dic3⋊Dic3C2312yes—
218Dic3⋊Dic3C2312yes—
219Dic3⋊Dic3C2312yes—
220Dic3⋊Dic3C2312yes—
221Dic3⋊Dic3C2312yes—
222Dic3⋊Dic3C2312yes—
223Dic3⋊Dic3C2312yes—
224Dic3⋊Dic3C2312yes—
225Dic3⋊Dic3C2312yes—
226Dic32C2312yes—
227Dic32C2312yes—
228Dic32C2312yes—
229Dic32C2312yes—
230Dic32C2312yes—
231Dic32C2312yes—
232Dic32C2312yes—
233Dic32C2312yes—
234Dic32C2312yes—
235Dic32C2312yes—
236#3502—91noSylow
237C22×Dic6—31no—
238C22×Dic6—31no—
239C3×C4⋊Q8—32no—
240C3×C4⋊Q8—31no—
241C3×C4⋊Q8—31no—
242C3×C4⋊Q8—32no—
243C3×#125—32no—
244C3×#125—32no—
245C3×#125—32no—
246C3×C22⋊Q8—21no—
247C3×C22⋊Q8—31no—
248C3×C22⋊Q8—31no—
249C3×C22⋊Q8—32no—
250C3×C22⋊Q8—32no—
251C3×C22⋊Q8C2×D311yescharacteristic
252C3×C22⋊Q8C2×D311yescharacteristic
253C3×C4×Q8—31no—
254C3×C4×Q8—32no—
255C3×C4×Q8—31no—
256C3×#117—32no—
257C3×#117—32no—
258C2×C3×C4⋊C4—31no—
259C2×C3×C42—31no—
260Q8×Dic3—32no—
261Q8×Dic3—32no—
262Q8×Dic3—31no—
263Q8×Dic3—32no—
264Q8×Dic3C2×D311yescharacteristic
265#944—32no—
266#944—32no—
267#944—32no—
268#944—32no—
269#944—32no—
270#944—32no—
271#944—32no—
272#944—32no—
273#944—32no—
274#944—32no—
275#944—31no—
276#944—62no—
277#944C2×D311yescharacteristic
278#944C2×D312yes—
279#926—32no—
280#926—32no—
281C2×C4⋊Dic3—31no—
282#924—31no—
283#924—31no—
284#924—32no—
285#924—32no—
286#924—61no—
287#924C2×D311yescharacteristic
288#924C2×D311yescharacteristic
289C2×Dic3⋊C4—31no—
290C2×Dic3⋊C4—31no—
291C2×Dic3⋊C4—31no—
292C2×Dic3⋊C4—61no—
293C2×Dic3⋊C4C2×D311yescharacteristic
294C2×C4×Dic3—31no—
295C2×C4×Dic3—31no—
296C2×C4×Dic3—31no—
297C2×C4×Dic3—31no—
298C2×C4×Dic3C2×D311yescharacteristic
299#890—32no—
300#890—32no—
301#890—32no—
302#890—32no—
303#890—32no—
304#890—32no—
305#889—32no—
306#889—32no—
307#889—32no—
308#889—32no—
309#889—32no—
310#889—32no—
311#889—32no—
312#889—32no—
313#889—32no—
314#889—32no—
315#889—32no—
316#889—32no—
317#889—32no—
318#889—32no—
319#889—32no—
320#889—32no—
321#889—32no—
322#889—32no—
323#889—32no—
324#889—32no—
325#889—32no—
326#889—62no—
327#889—62no—
328#889C2×D312yes—
329#889C2×D312yes—
330#889C2×D312yes—
331#888—32no—
332#888—32no—
333#888—32no—
334#888—32no—
335#888—32no—
336#888—32no—
337#888—32no—
338#888—32no—
339#888—32no—
340#888—32no—
341#888—32no—
342#888—32no—
343#888—32no—
344#888—32no—
345#888—32no—
346#888—31no—
347#888—32no—
348#888—62no—
349#888C2×D311yescharacteristic
350#888C2×D312yes—
351#887—32no—
352#887—32no—
353#887—32no—
354#887—32no—
355#887—32no—
356#887—32no—
357#887—32no—
358#887—32no—
359#887—32no—
360#887—32no—
361#887—32no—
362#887—31no—
363#887—32no—
364#887—32no—
365#887—32no—
366#887—32no—
367#887—32no—
368#887—32no—
369#887—32no—
370#887—32no—
371#887—32no—
372#887—32no—
373#887—32no—
374#887C2×D311yescharacteristic
375#887C2×D312yes—
376#878—32no—
377#878—32no—
378#878—32no—
379#878—32no—
380#878—32no—
381#878—32no—
382#878—62no—
383#878C2×D312yes—
384#878C2×D312yes—
385#877—32no—
386#877—32no—
387#877—32no—
388#877—32no—
389#877—32no—
390#877—32no—
391#877—62no—
392#877C2×D312yes—
393#877C2×D312yes—
394#870—32no—
395#870—32no—
396#870—32no—
397#869—31no—
398#869—32no—
399#869—31no—
400#869—32no—
401C4×Dic6—31no—
402C4×Dic6—32no—
403C4×Dic6—31no—
404C4×Dic6—32no—
405C4×Dic6—32no—
406C4×Dic6—32no—
407C4×Dic6—32no—
408C4×Dic6—32no—
409C4×Dic6—32no—
410C4×Dic6—32no—
411C4×Dic6—32no—
412C4×Dic6—32no—
413C4×Dic6—32no—
414C4×Dic6—32no—
415C4×Dic6—32no—
416C4×Dic6—32no—
417C4×Dic6—32no—
418C4×Dic6—32no—
419C4×Dic6—32no—
420C23×C32C2411yescharacteristic
421C32×Q8—41no—
422C2×C32×C4—41no—
423C2×C32×C4C2412yes—
424C2×C32×C4C2412yes—
425C2×C32×C4C2411yescharacteristic
426C2×C32×C4C2411yescharacteristic
427C2×C3⋊Dic3—41no—
428C2×C3⋊Dic3C2×Q814yes—
429C2×C3⋊Dic3C2412yes—
430C2×C3⋊Dic3C2412yes—
431C2×C3⋊Dic3C2412yes—
432C2×C3⋊Dic3C2412yes—
433#634—41no—
434#634—42no—
435C2×C3×Dic3—22no—
436C2×C3×Dic3—41no—
437C2×C3×Dic3C2×Q814yes—
438C2×C3×Dic3C2×Q814yes—
439C2×C3×Dic3C2411yescharacteristic
440C2×C3×Dic3C2412yes—
441C2×C3×Dic3C2412yes—
442C2×C3×Dic3C2412yes—
443C2×C3×Dic3C2412yes—
444C2×C3×Dic3C2412yes—
445C2×C3×Dic3C2412yes—
446C2×C3×Dic3C2411yescharacteristic
447C2×C3×Dic3C2411yescharacteristic
448C2×C3×Dic3C2411yescharacteristic
449C3×Dic6—24no—
450C3×Dic6—41no—
451C3×Dic6—41no—
452C3×Dic6—42no—
453#627—24no—
454#627—42no—
455#627—42no—
456#627C2×Q818yes—
457#627C2×Q818yes—
458Q82—92no—
459Q82—92no—
460#557—92no—
461#557—92no—
462#557—92no—
463#557—92no—
464#557—92no—
465#557—92no—
466#544—31no—
467#544—91no—
468#544—92no—
469#544—91no—
470#544—91no—
471#533—31no—
472#533—91no—
473#533—92no—
474#533—92no—
475#519—92no—
476C2×C4×Q8—91no—
477C2×C3×Q8—21no—
478C2×C3×Q8—32no—
479C2×C3×Q8—31no—
480C2×C3×Q8—31no—
481C2×C3×Q8—32no—
482C2×C3×Q8C22×D311yescharacteristic
483C2×C3×Q8C22×D311yescharacteristic
484C22×C3×C4—21no—
485C22×C3×C4—31no—
486C22×C3×C4—31no—
487C22×C3×C4—31no—
488C22×C3×C4—31no—
489C22×C3×C4C22×D311yescharacteristic
490C22×C3×C4C22×D311yescharacteristic
491C22×Dic3—31no—
492C22×Dic3—31no—
493C22×Dic3—31no—
494C22×Dic3—31no—
495C22×Dic3—61no—
496C22×Dic3—61no—
497C22×Dic3C22×D311yescharacteristic
498C22×Dic3C22×D311yescharacteristic
499C22×Dic3C22×D311yescharacteristic
500C22×Dic3C22×D311yescharacteristic
501C2×Dic6—38no—
502C2×Dic6—38no—
503C2×Dic6—32no—
504C2×Dic6—32no—
505C2×Dic6—32no—
506C2×Dic6—32no—
507C2×Dic6—32no—
508C2×Dic6—32no—
509C2×Dic6—31no—
510C2×Dic6—32no—
511C2×Dic6—32no—
512C2×Dic6—31no—
513C2×Dic6—32no—
514C2×Dic6—32no—
515C2×Dic6—32no—
516C2×Dic6—32no—
517C2×Dic6—62no—
518C2×Dic6—61no—
519C2×Dic6C22×D312yes—
520C2×Dic6C22×D311yescharacteristic
521C2×Dic6C22×D312yes—
522C2×Dic6C22×D311yescharacteristic
523C3×C4⋊C4—22no—
524C3×C4⋊C4—21no—
525C3×C4⋊C4—32no—
526C3×C4⋊C4—32no—
527C3×C4⋊C4—32no—
528C3×C4⋊C4—32no—
529C3×C4⋊C4—32no—
530C3×C4⋊C4—32no—
531C3×C4⋊C4—32no—
532C3×C4⋊C4—32no—
533C3×C4⋊C4—32no—
534C3×C4⋊C4—32no—
535C3×C4⋊C4—32no—
536C3×C4⋊C4—32no—
537C3×C4⋊C4—31no—
538C3×C4⋊C4—32no—
539C3×C4⋊C4—32no—
540C3×C4⋊C4—31no—
541C3×C4⋊C4C22×D312yes—
542C3×C4⋊C4C22×D311yescharacteristic
543C3×C4⋊C4C22×D312yes—
544C3×C4⋊C4C22×D311yescharacteristic
545C3×C22⋊C4—22no—
546C3×C22⋊C4—32no—
547C3×C22⋊C4—32no—
548C3×C22⋊C4C22×D312yes—
549C3×C22⋊C4C22×D312yes—
550C3×C42—31no—
551C3×C42—31no—
552C3×C42—32no—
553C3×C42—32no—
554C3×C42—31no—
555C3×C42—32no—
556C3×C42—32no—
557C3×C42—31no—
558#217—32no—
559#217—32no—
560#217—62no—
561#217C22×D312yes—
562#217C22×D312yes—
563C4⋊Dic3—31no—
564C4⋊Dic3—32no—
565C4⋊Dic3—32no—
566C4⋊Dic3—31no—
567C4⋊Dic3—32no—
568C4⋊Dic3—32no—
569C4⋊Dic3—32no—
570C4⋊Dic3—32no—
571C4⋊Dic3—32no—
572C4⋊Dic3—32no—
573C4⋊Dic3—32no—
574C4⋊Dic3—32no—
575C4⋊Dic3—32no—
576C4⋊Dic3—32no—
577C4⋊Dic3—32no—
578C4⋊Dic3—32no—
579C4⋊Dic3—62no—
580C4⋊Dic3—61no—
581C4⋊Dic3C22×D311yescharacteristic
582C4⋊Dic3C22×D312yes—
583C4⋊Dic3C22×D312yes—
584C4⋊Dic3C22×D311yescharacteristic
585Dic3⋊C4—32no—
586Dic3⋊C4—32no—
587Dic3⋊C4—32no—
588Dic3⋊C4—32no—
589Dic3⋊C4—32no—
590Dic3⋊C4—32no—
591Dic3⋊C4—32no—
592Dic3⋊C4—32no—
593Dic3⋊C4—32no—
594Dic3⋊C4—32no—
595Dic3⋊C4—32no—
596Dic3⋊C4—32no—
597Dic3⋊C4—32no—
598Dic3⋊C4—32no—
599Dic3⋊C4—32no—
600Dic3⋊C4—32no—
601Dic3⋊C4—32no—
602Dic3⋊C4—32no—
603Dic3⋊C4—32no—
604Dic3⋊C4—32no—
605Dic3⋊C4—32no—
606Dic3⋊C4—32no—
607Dic3⋊C4—32no—
608Dic3⋊C4—32no—
609Dic3⋊C4—32no—
610Dic3⋊C4—32no—
611Dic3⋊C4—32no—
612Dic3⋊C4—32no—
613Dic3⋊C4—32no—
614Dic3⋊C4—32no—
615Dic3⋊C4—32no—
616Dic3⋊C4—32no—
617Dic3⋊C4—32no—
618Dic3⋊C4—32no—
619Dic3⋊C4—32no—
620Dic3⋊C4—32no—
621Dic3⋊C4—62no—
622Dic3⋊C4—62no—
623Dic3⋊C4—62no—
624Dic3⋊C4—62no—
625Dic3⋊C4—62no—
626Dic3⋊C4—62no—
627Dic3⋊C4—62no—
628Dic3⋊C4C22×D312yes—
629Dic3⋊C4C22×D312yes—
630Dic3⋊C4C22×D312yes—
631Dic3⋊C4C22×D312yes—
632Dic3⋊C4C22×D312yes—
633Dic3⋊C4C22×D312yes—
634Dic3⋊C4C22×D312yes—
635Dic3⋊C4C22×D312yes—
636Dic3⋊C4C22×D312yes—
637Dic3⋊C4C22×D312yes—
638Dic3⋊C4C22×D312yes—
639Dic3⋊C4C22×D312yes—
640C4×Dic3—32no—
641C4×Dic3—32no—
642C4×Dic3—32no—
643C4×Dic3—32no—
644C4×Dic3—32no—
645C4×Dic3—32no—
646C4×Dic3—32no—
647C4×Dic3—32no—
648C4×Dic3—32no—
649C4×Dic3—32no—
650C4×Dic3—32no—
651C4×Dic3—32no—
652C4×Dic3—32no—
653C4×Dic3—32no—
654C4×Dic3—32no—
655C4×Dic3—32no—
656C4×Dic3—32no—
657C4×Dic3—32no—
658C4×Dic3—32no—
659C4×Dic3—32no—
660C4×Dic3—32no—
661C4×Dic3—32no—
662C4×Dic3—32no—
663C4×Dic3—32no—
664C4×Dic3—62no—
665C4×Dic3—62no—
666C4×Dic3C22×D312yes—
667C4×Dic3C22×D312yes—
668C4×Dic3C22×D312yes—
669C4×Dic3C22×D312yes—
670C4×Dic3C22×D311yescharacteristic
671C4×Dic3C22×D311yescharacteristic
672C4×Dic3C22×D311yescharacteristic
673C4×Dic3C22×D311yescharacteristic
674C22×C32—21no—
675C22×C32—21no—
676C22×C32C22×Q812yes—
677C22×C32C2511yescharacteristic
678C32×C4—22no—
679C32×C4—21no—
680C32×C4—22no—
681C32×C4—21no—
682C3⋊Dic3—22no—
683C3⋊Dic3—22no—
684C3⋊Dic3—22no—
685C3⋊Dic3C22×Q814yes—
686C3×Dic3—22no—
687C3×Dic3—22no—
688C3×Dic3—21no—
689C3×Dic3—22no—
690C3×Dic3—22no—
691C3×Dic3—22no—
692C3×Dic3C22×Q814yes—
693C3×Dic3C22×Q812yes—
694C3×Dic3C22×Q812yes—
695C3×Dic32−1+412yes—
696C22×Q8—91no—
697C4⋊Q8—31no—
698C4⋊Q8—32no—
699C4⋊Q8—31no—
700C4⋊Q8—32no—
701C4⋊Q8—91no—
702C4⋊Q8—92no—
703C4⋊Q8—91no—
704C4⋊Q8—92no—
705C4⋊Q8—92no—
706C4⋊Q8—92no—
707C4⋊Q8—92no—
708C4⋊Q8—92no—
709C4⋊Q8—92no—
710C4⋊Q8—92no—
711C4⋊Q8—92no—
712C4⋊Q8—92no—
713C4⋊Q8—92no—
714C4⋊Q8—92no—
715C4⋊Q8—92no—
716C4⋊Q8—92no—
717#125—32no—
718#125—32no—
719#125—32no—
720#125—92no—
721#125—92no—
722#125—92no—
723#125—92no—
724#125—92no—
725#125—92no—
726#125—92no—
727#125—92no—
728#125—92no—
729#125—92no—
730#125—92no—
731#125—92no—
732#125—92no—
733#125—92no—
734#125—92no—
735C22⋊Q8—31no—
736C22⋊Q8—31no—
737C22⋊Q8—32no—
738C22⋊Q8—32no—
739C22⋊Q8—92no—
740C22⋊Q8—92no—
741C22⋊Q8—92no—
742C22⋊Q8—91no—
743C22⋊Q8—92no—
744C22⋊Q8D3211yescharacteristic
745C4×Q8—31no—
746C4×Q8—31no—
747C4×Q8—32no—
748C4×Q8—92no—
749C4×Q8—92no—
750C4×Q8—92no—
751C4×Q8—92no—
752C4×Q8—92no—
753C4×Q8—92no—
754C4×Q8—92no—
755C4×Q8—92no—
756C4×Q8—92no—
757C4×Q8—92no—
758C4×Q8—91no—
759C4×Q8—92no—
760C4×Q8—92no—
761C4×Q8—92no—
762C4×Q8—92no—
763C4×Q8—91no—
764C4×Q8—92no—
765C4×Q8—92no—
766C4×Q8—92no—
767C4×Q8—92no—
768C4×Q8—92no—
769C4×Q8—92no—
770C4×Q8—92no—
771#117—32no—
772#117—32no—
773#117—92no—
774#117—92no—
775#117—92no—
776#117—92no—
777C2×C4⋊C4—31no—
778C2×C4⋊C4—91no—
779C2×C4⋊C4—91no—
780C2×C42—31no—
781C2×C42—91no—
782C2×C42—91no—
783C23×C3—21no—
784C23×C3C23×D311yescharacteristic
785C23×C3C23×D311yescharacteristic
786C3×Q8—41no—
787C3×Q8—41no—
788C3×Q8—64no—
789C3×Q8—81no—
790C3×Q8—121no—
791C3×Q8—122no—
792C3×Q8—121no—
793C2×C3×C4—22no—
794C2×C3×C4—22no—
795C2×C3×C4—21no—
796C2×C3×C4—21no—
797C2×C3×C4—34no—
798C2×C3×C4—34no—
799C2×C3×C4—32no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—31no—
804C2×C3×C4—32no—
805C2×C3×C4—32no—
806C2×C3×C4—32no—
807C2×C3×C4—32no—
808C2×C3×C4—32no—
809C2×C3×C4—41no—
810C2×C3×C4—41no—
811C2×C3×C4—62no—
812C2×C3×C4—81no—
813C2×C3×C4—121no—
814C2×C3×C4C23×D312yes—
815C2×C3×C4C23×D312yes—
816C2×C3×C4C23×D312yes—
817C2×C3×C4C23×D312yes—
818C2×C3×C4C23×D311yescharacteristic
819C2×C3×C4C23×D311yescharacteristic
820C2×C3×C4C23×D311yescharacteristic
821C2×C3×C4C23×D311yescharacteristic
822C2×Dic3—22no—
823C2×Dic3—34no—
824C2×Dic3—34no—
825C2×Dic3—32no—
826C2×Dic3—32no—
827C2×Dic3—32no—
828C2×Dic3—32no—
829C2×Dic3—32no—
830C2×Dic3—32no—
831C2×Dic3—32no—
832C2×Dic3—32no—
833C2×Dic3—41no—
834C2×Dic3—64no—
835C2×Dic3—62no—
836C2×Dic3—62no—
837C2×Dic3—62no—
838C2×Dic3—62no—
839C2×Dic3—121no—
840C2×Dic3—121no—
841C2×Dic3—241no—
842C2×Dic3D3×Q814yes—
843C2×Dic3D3×Q814yes—
844C2×Dic3C23×D311yescharacteristic
845C2×Dic3C23×D312yes—
846C2×Dic3C23×D312yes—
847C2×Dic3C23×D312yes—
848C2×Dic3C23×D312yes—
849C2×Dic3C23×D312yes—
850C2×Dic3C23×D311yescharacteristic
851C2×Dic3C23×D312yes—
852C2×Dic3C23×D311yescharacteristic
853C2×Dic3C23×D311yescharacteristic
854Dic6—24no—
855Dic6—38no—
856Dic6—38no—
857Dic6—38no—
858Dic6—38no—
859Dic6—41no—
860Dic6—41no—
861Dic6—42no—
862Dic6—64no—
863Dic6—64no—
864Dic6—122no—
865Dic6—122no—
866Dic6—122no—
867Dic6—122no—
868Dic6—121no—
869Dic6—122no—
870Dic6—121no—
871Dic6—122no—
872Dic6—241no—
873Dic6—242no—
874C2×C32—22no—
875C2×C32C23×Q811yescharacteristic
876C2×C32C2×2−1+411yescharacteristic
877C2×C32#58511yescharacteristic
878C2×Q8—32no—
879C2×Q8—31no—
880C2×Q8—31no—
881C2×Q8—32no—
882C2×Q8—92no—
883C2×Q8—92no—
884C2×Q8—98no—
885C2×Q8—92no—
886C2×Q8—92no—
887C2×Q8—92no—
888C2×Q8—91no—
889C2×Q8—92no—
890C2×Q8C2×D3211yescharacteristic
891C22×C4—31no—
892C22×C4—31no—
893C22×C4—31no—
894C22×C4—31no—
895C22×C4—91no—
896C22×C4—91no—
897C22×C4C2×D3211yescharacteristic
898C4⋊C4—32no—
899C4⋊C4—32no—
900C4⋊C4—32no—
901C4⋊C4—32no—
902C4⋊C4—32no—
903C4⋊C4—32no—
904C4⋊C4—32no—
905C4⋊C4—32no—
906C4⋊C4—32no—
907C4⋊C4—32no—
908C4⋊C4—31no—
909C4⋊C4—32no—
910C4⋊C4—31no—
911C4⋊C4—32no—
912C4⋊C4—32no—
913C4⋊C4—32no—
914C4⋊C4—92no—
915C4⋊C4—92no—
916C4⋊C4—92no—
917C4⋊C4—92no—
918C4⋊C4—92no—
919C4⋊C4—92no—
920C4⋊C4—92no—
921C4⋊C4—92no—
922C4⋊C4—92no—
923C4⋊C4—92no—
924C4⋊C4—92no—
925C4⋊C4—92no—
926C4⋊C4—92no—
927C4⋊C4—92no—
928C4⋊C4—92no—
929C4⋊C4—92no—
930C4⋊C4—92no—
931C4⋊C4—92no—
932C4⋊C4—92no—
933C4⋊C4—92no—
934C4⋊C4—92no—
935C4⋊C4—92no—
936C4⋊C4—91no—
937C4⋊C4—92no—
938C4⋊C4—92no—
939C4⋊C4—92no—
940C4⋊C4C2×D3211yescharacteristic
941C4⋊C4C2×D3212yes—
942C22⋊C4—32no—
943C22⋊C4—32no—
944C22⋊C4—92no—
945C22⋊C4C2×D3212yes—
946C42—31no—
947C42—31no—
948C42—31no—
949C42—31no—
950C42—32no—
951C42—32no—
952C42—32no—
953C42—32no—
954C42—92no—
955C42—92no—
956C42—92no—
957C42—92no—
958C42—92no—
959C42—92no—
960C42—92no—
961C42—92no—
962C42—92no—
963C42—92no—
964C42—92no—
965C42—92no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—22no—
971C22×C3—21no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3C2×D3×Q812yes—
975C22×C3C2×D3×Q812yes—
976C22×C3C24×D311yescharacteristic
977C22×C3C24×D311yescharacteristic
978C3×C4—22no—
979C3×C4—21no—
980C3×C4—21no—
981C3×C4—22no—
982C3×C4—21no—
983C3×C4—22no—
984C3×C4—21no—
985C3×C4—22no—
986C3×C4—32no—
987C3×C4—32no—
988C3×C4—34no—
989C3×C4—32no—
990C3×C4—41no—
991C3×C4—42no—
992C3×C4—41no—
993C3×C4—42no—
994C3×C4—62no—
995C3×C4—62no—
996C3×C4—62no—
997C3×C4—62no—
998C3×C4—61no—
999C3×C4—62no—
1000Dic3—22no—
1001Dic3—21no—
1002Dic3—22no—
1003Dic3—22no—
1004Dic3—22no—
1005Dic3—22no—
1006Dic3—34no—
1007Dic3—34no—
1008Dic3—64no—
1009Dic3—62no—
1010Dic3—62no—
1011Dic3—62no—
1012Dic3—62no—
1013Dic3—62no—
1014Dic3—62no—
1015Dic3—122no—
1016Dic3—122no—
1017Dic3—122no—
1018Dic3C2×D3×Q814yes—
1019Dic3C2×D3×Q812yes—
1020Dic3C2×D3×Q812yes—
1021Dic3#101012yes—
1022C32#350211yescharacteristic, complemented, Sylow
1023C23C22×D3211yescharacteristic
1024Q8—41no—
1025Q8—64no—
1026Q8—98no—
1027Q8—98no—
1028Q8—121no—
1029Q8—121no—
1030Q8—122no—
1031Q8—184no—
1032Q8—361no—
1033Q8—362no—
1034Q8—362no—
1035Q8—362no—
1036C2×C4—34no—
1037C2×C4—34no—
1038C2×C4—31no—
1039C2×C4—31no—
1040C2×C4—32no—
1041C2×C4—31no—
1042C2×C4—31no—
1043C2×C4—32no—
1044C2×C4—32no—
1045C2×C4—32no—
1046C2×C4—32no—
1047C2×C4—32no—
1048C2×C4—41no—
1049C2×C4—62no—
1050C2×C4—94no—
1051C2×C4—92no—
1052C2×C4—92no—
1053C2×C4—92no—
1054C2×C4—92no—
1055C2×C4—121no—
1056C2×C4—361no—
1057C2×C4C22×D3212yes—
1058C2×C4C22×D3212yes—
1059C2×C4C22×D3211yescharacteristic
1060C2×C4C22×D3211yescharacteristic
1061C2×C3—22no—
1062C2×C3—22no—
1063C2×C3—21no—
1064C2×C3—21no—
1065C2×C3—21no—
1066C2×C3—42no—
1067C2×C3C22×D3×Q811yescharacteristic
1068C2×C3C22×D3×Q811yescharacteristic
1069C2×C3C2×#101011yescharacteristic
1070C2×C3#596411yescharacteristic
1071C2×C3#596611yescharacteristic
1072C2×C3D3×2−1+411yescharacteristic
1073C22—21no—
1074C22—21no—
1075C22D32×Q812yes—
1076C22C23×D3211yescharacteristic
1077C4—21no—
1078C4—21no—
1079C4—22no—
1080C4—22no—
1081C4—32no—
1082C4—32no—
1083C4—34no—
1084C4—32no—
1085C4—62no—
1086C4—62no—
1087C4—62no—
1088C4—61no—
1089C4—62no—
1090C4—62no—
1091C4—94no—
1092C4—182no—
1093C4—182no—
1094C4—182no—
1095C3—21no—
1096C3#8625811yescharacteristic, complemented
1097C3#8658511yescharacteristic, complemented
1098C2—22no—
1099C2#1059667811yescharacteristic
1100C2C2×D32×Q811yescharacteristic
1101C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C22⋊Q8C22
prime radicalC23×C32C24
hypercenterC22⋊Q8D32
hypocenterC32#3502
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
4. #10595421C2semidirect
5. #10595420C2semidirect
10. #10594596C2semidirect
11. #10594596C2semidirect
12. #10594315C2semidirect
13. #10594314C2semidirect
14. #10594314C2semidirect
15. #10594312C2semidirect
162. C2×#627Q8semidirect
1022. C32#3502semidirect
1096. C3#86258semidirect
1097. C3#86585semidirect

Maximal subgroups

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

subgroupindex
#105960942
C3×#56232
C3×#56222
#105954212
#105954202
#105948132
#105948122
#105948082
C2×#638372
#105945962
#105943152
#105943142
#105943122
#105942452
#105940352
#105940302
#105940292
#865853
#862583