Finite Group Databasebeta

← #11904225

Subgroups — #11904225

Order 1152.

2288 conjugacy classes of subgroups.

The subgroup lattice has 933 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5584C211yesmaximal, characteristic, complemented
3C3×C4×#239C211yesmaximal, characteristic, complemented
4#10595367C212yesmaximal, complemented
5#10595357C212yesmaximal, complemented
6#10594581C212yesmaximal, complemented
7#10594409C214yesmaximal, complemented
8#10594405C214yesmaximal, complemented
9#10594358C212yesmaximal, complemented
10#10593921C212yesmaximal, complemented
11#10593917C212yesmaximal, complemented
12#10593905C212yesmaximal, complemented
13#10593904C211yesmaximal, characteristic, complemented
14#10593895C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic, complemented
16C4×D3×Dic6C212yesmaximal, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#86981—31nomaximal
19#85826—31nomaximal
20C2×C3×#239C2211yescharacteristic
21C2×#3795C2212yes—
22C2×#3795C2211yescharacteristic
23C2×D3×Dic6C2212yes—
24C32×C4×Q8C2211yescharacteristic
25#64153C2212yes—
26#64098C2214yes—
27#64096C2212yes—
28#64079C2212yes—
29#64078C2211yescharacteristic
30C4×#634C2212yes—
31C4×#634C2211yescharacteristic
32C3×#946C2212yes—
33C3×Q8×Dic3C2211yescharacteristic
34C3×#898C2214yes—
35C3×#893C2211yescharacteristic
36C3×#893C2212yes—
37C3×#892C2211yescharacteristic
38C3×#892C2212yes—
39C3×#892C2212yes—
40C3×#875C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C4×D12C2212yes—
43C3×C4×D12C2211yescharacteristic
44C3×C42×D3C2211yescharacteristic
45C3×C42×D3C2212yes—
46C3×#869C2211yescharacteristic
47C3×C4×Dic6C2212yes—
48#63919C2212yes—
49C4×#627C2214yes—
50#63915C2214yes—
51#63908C2212yes—
52#63905C2214yes—
53#63902C2214yes—
54C4×#625C2212yes—
55#63899C2214yes—
56#63899C2214yes—
57#63898C2212yes—
58Dic3×D12C2211yescharacteristic
59#63891C2214yes—
60D3×C4⋊Dic3C2212yes—
61#63885C2214yes—
62#63884C2214yes—
63#63879C2214yes—
64#63879C2212yes—
65#63877C2214yes—
66#63877C2214yes—
67#63877C2212yes—
68D3×Dic3⋊C4C2214yes—
69C4×D3×Dic3C2212yes—
70C4×D3×Dic3C2214yes—
71#63869C2212yes—
72#63859C2214yes—
73#63859C2214yes—
74#63857C2212yes—
75#63857C2212yes—
76#63856C2212yes—
77#63856C2212yes—
78#63847C2214yes—
79#63844C2212yes—
80#63844C2211yescharacteristic
81Dic3×Dic6C2212yes—
82#63841C2212yes—
83#63841C2211yescharacteristic
84#63837C2214yes—
85C3×#556—31no—
86C3×C4×#41—31no—
87#5824—32no—
88#5728—31no—
89#5727—31no—
90#5708—34no—
91#5706—34no—
92#5680—32no—
93#5677—32no—
94#5631—32no—
95#5622—32no—
96#5584D311yescharacteristic, complemented
97#5581—32no—
98#5578—32no—
99C4×#239D311yescharacteristic, complemented
100C4×D3×Q8—32no—
101#5567—31no—
102#5567—31no—
103#5567—61no—
104#5555—31no—
105#5552—32no—
106#5551—31no—
107#5541—32no—
108#5538—34no—
109D4×Dic6—31no—
110C4×#237—32no—
111C4×#237—31no—
112#5533—32no—
113#5533—32no—
114#5531—34no—
115#5522—32no—
116#5479—32no—
117C4×#235—31no—
118#5470—31no—
119C2×C4×Dic6—32no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C3×#239—24no—
124C2×C3×D12C2312yes—
125C2×C3×D12C2311yescharacteristic
126C2×C3×D12C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2312yes—
130C2×C3×C4×D3C2311yescharacteristic
131C2×C3×C4×D3C2312yes—
132C2×C3×C4×D3C2312yes—
133C2×C3×C4×D3C2311yescharacteristic
134C2×C3×Dic6C2312yes—
135C2×#627C2314yes—
136C2×#625C2312yes—
137C2×#625C2314yes—
138C2×D3×Dic3C2314yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141C2×D3×Dic3C2312yes—
142#3795—24no—
143#3795—28no—
144D3×Dic6—28no—
145C32×C4⋊C4C2311yescharacteristic
146C32×C4⋊C4C2312yes—
147C32×C42C2311yescharacteristic
148C32×C42C2312yes—
149C4⋊(C3⋊Dic3)C2312yes—
150C4⋊(C3⋊Dic3)C2311yescharacteristic
151C4⋊(C3⋊Dic3)C2312yes—
152#3750C2314yes—
153#3750C2312yes—
154#3750C2314yes—
155#3750C2314yes—
156C4×C3⋊Dic3C2314yes—
157C4×C3⋊Dic3C2312yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×(C2×D3)⋊C4C2312yes—
160C3×(C2×D3)⋊C4C2312yes—
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2312yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×C4⋊Dic3C2312yes—
165C3×C4⋊Dic3C2311yescharacteristic
166C3×C4⋊Dic3C2312yes—
167C3×C4⋊Dic3C2312yes—
168C3×C4⋊Dic3C2311yescharacteristic
169C3×Dic3⋊C4C2314yes—
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2311yescharacteristic
172C3×C4×Dic3C2314yes—
173C3×C4×Dic3C2312yes—
174C3×C4×Dic3C2311yescharacteristic
175C3×C4×Dic3C2311yescharacteristic
176#3724C2314yes—
177#3724C2312yes—
178#3724C2314yes—
179Dic3⋊Dic3C2314yes—
180Dic3⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2314yes—
184(C2×D3)⋊Dic3C2314yes—
185(C2×D3)⋊Dic3C2312yes—
186Dic32C2312yes—
187Dic32C2314yes—
188Dic32C2312yes—
189#3482—91noSylow
190C2×C3×#41—31no—
191C2×#239C2×D311yescharacteristic
192C2×D3×Q8—32no—
193C2×#237—31no—
194C2×#237—32no—
195C2×#235—31no—
196C2×#235—32no—
197C22×Dic6—32no—
198C3×C4⋊Q8—31no—
199C3×#126—34no—
200C3×#124—32no—
201C3×C22⋊Q8—32no—
202C3×C4×Q8—21no—
203C3×C4×Q8—31no—
204C3×C4×Q8—32no—
205C3×C4×Q8C2×D311yescharacteristic
206C3×C4×Q8C2×D311yescharacteristic
207C3×C4×D4—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×C4×D4—31no—
211C3×C4×D4—32no—
212C3×#117—32no—
213C3×#117—32no—
214C3×#117—31no—
215C2×C3×C42—32no—
216C2×C3×C42—31no—
217#946—32no—
218#946—32no—
219#946C2×D312yes—
220Q8×Dic3—32no—
221Q8×Dic3C2×D311yescharacteristic
222#944—32no—
223#944—32no—
224#944—62no—
225#939—34no—
226#938—32no—
227#935—34no—
228D4×Dic3—32no—
229D4×Dic3—31no—
230#930—32no—
231#929—34no—
232C4×#67—32no—
233C4×#67—32no—
234C4×#67—32no—
235C4×#67—34no—
236#926—32no—
237#926—31no—
238C2×C4⋊Dic3—32no—
239#924—32no—
240#924—32no—
241#924—32no—
242#924—32no—
243C2×Dic3⋊C4—34no—
244C2×C4×Dic3—34no—
245C2×C4×Dic3—32no—
246#898C2×D314yes—
247#897—32no—
248#897—32no—
249#896—34no—
250#896—34no—
251#894—34no—
252#893—32no—
253#893C2×D312yes—
254#893C2×D311yescharacteristic
255#892—32no—
256#892—31no—
257#892C2×D312yes—
258#892C2×D311yescharacteristic
259#892C2×D312yes—
260D3×C4⋊C4—34no—
261D3×C4⋊C4—32no—
262#890—32no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—34no—
267#889—64no—
268#888—32no—
269#888—32no—
270#887—32no—
271#887—32no—
272#887—34no—
273#887—32no—
274#887—31no—
275#887—62no—
276#886—34no—
277#885—34no—
278#885—34no—
279#884—34no—
280#883—34no—
281#883—34no—
282#67⋊C4—34no—
283#67⋊C4—32no—
284#67⋊C4—34no—
285#67⋊C4—34no—
286#879—34no—
287#879—34no—
288#878—34no—
289#878—34no—
290#877—34no—
291#877—32no—
292#877—34no—
293#876—34no—
294#876—34no—
295#875C2×D312yes—
296C4×D12—31no—
297C4×D12C2×D312yes—
298C4×D12C2×D311yescharacteristic
299C4×D12C2×D311yescharacteristic
300#872—34no—
301#872—32no—
302#872—34no—
303C42×D3—34no—
304C42×D3—32no—
305C42×D3C2×D312yes—
306C42×D3C2×D311yescharacteristic
307#870—32no—
308#870—32no—
309#870—32no—
310#870—62no—
311#869—31no—
312#869—31no—
313#869—61no—
314#869C2×D311yescharacteristic
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—32no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—31no—
321C4×Dic6—32no—
322C4×Dic6—34no—
323C4×Dic6—34no—
324C4×Dic6—34no—
325C4×Dic6—62no—
326C4×Dic6—61no—
327C4×Dic6C2×D312yes—
328C22×C3×D3C2411yescharacteristic
329C22×C3×D3C2412yes—
330C22×C3×D3C2412yes—
331C32×Q8—22no—
332C2×C32×C4C2412yes—
333C2×C32×C4C2412yes—
334C2×C32×C4C2411yescharacteristic
335C2×C32×C4C2411yescharacteristic
336C2×C32×C4C2411yescharacteristic
337C2×C3⋊Dic3C2412yes—
338C2×C3⋊Dic3C2414yes—
339C2×C3⋊Dic3C2412yes—
340#634—24no—
341#634#4114yescomplemented
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2411yescharacteristic
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2411yescharacteristic
348C3×D12—24no—
349C3×D12—22no—
350C3×D12#4114yescomplemented
351C3×C4×D3—24no—
352C3×C4×D3—24no—
353C3×C4×D3—24no—
354C3×C4×D3—22no—
355C3×C4×D3—22no—
356C3×C4×D3—24no—
357C3×C4×D3—22no—
358C3×Dic6—24no—
359#627—28no—
360#625—28no—
361#625—24no—
362D3×Dic3—28no—
363D3×Dic3—28no—
364D3×Dic3—24no—
365D3×Dic3—24no—
366#557—91no—
367#556—31no—
368#556—92no—
369#552—94no—
370#552—92no—
371D4×Q8—91no—
372#548—92no—
373#547—91no—
374#547—92no—
375#533—91no—
376#533—92no—
377#529—92no—
378#529—94no—
379C4×#41—31no—
380C4×#41—91no—
381C4×#41—92no—
382C2×C4×Q8—92no—
383C3×#41—64no—
384C2×C3×Q8—21no—
385C2×C3×Q8—32no—
386C2×C3×Q8C22×D311yescharacteristic
387C2×C3×Q8C22×D311yescharacteristic
388C2×C3×D4—31no—
389C2×C3×D4—31no—
390C2×C3×D4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—32no—
393C22×C3×C4—32no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—32no—
397C22×C3×C4—31no—
398C2×#67—34no—
399C2×#67—32no—
400C2×#67—34no—
401C2×#67—32no—
402C22×Dic3—32no—
403C22×Dic3—32no—
404C22×Dic3—34no—
405C22×Dic3—34no—
406#239—24no—
407D3×Q8—68no—
408#237—64no—
409#237—68no—
410#235—64no—
411#235—68no—
412C2×D12C22×D311yescharacteristic
413C2×D12C22×D312yes—
414C2×D12C22×D311yescharacteristic
415C2×C4×D3—32no—
416C2×C4×D3—32no—
417C2×C4×D3—34no—
418C2×C4×D3—34no—
419C2×C4×D3C22×D312yes—
420C2×C4×D3C22×D312yes—
421C2×C4×D3C22×D312yes—
422C2×C4×D3C22×D311yescharacteristic
423C2×C4×D3C22×D311yescharacteristic
424C2×C4×D3C22×D312yes—
425C2×C4×D3C22×D311yescharacteristic
426C2×Dic6—31no—
427C2×Dic6—31no—
428C2×Dic6—32no—
429C2×Dic6—32no—
430C2×Dic6—34no—
431C2×Dic6—34no—
432C2×Dic6—61no—
433C2×Dic6—62no—
434C2×Dic6—68no—
435C2×Dic6C22×D312yes—
436C3×C4⋊C4—21no—
437C3×C4⋊C4—22no—
438C3×C4⋊C4—32no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4—31no—
441C3×C4⋊C4—31no—
442C3×C4⋊C4—32no—
443C3×C4⋊C4—32no—
444C3×C4⋊C4C22×D311yescharacteristic
445C3×C4⋊C4C22×D311yescharacteristic
446C3×C4⋊C4C22×D312yes—
447C3×C4⋊C4C22×D312yes—
448C3×C22⋊C4—32no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—32no—
451C3×C22⋊C4—32no—
452C3×C22⋊C4—32no—
453C3×C22⋊C4—34no—
454C3×C42—21no—
455C3×C42—22no—
456C3×C42—31no—
457C3×C42—31no—
458C3×C42—32no—
459C3×C42—32no—
460C3×C42—34no—
461C3×C42—31no—
462C3×C42C22×D312yes—
463C3×C42C22×D311yescharacteristic
464C3×C42C22×D311yescharacteristic
465C3×C42C22×D312yes—
466#217—34no—
467#217—34no—
468#217—32no—
469#217—32no—
470#217—34no—
471(C2×D3)⋊C4—32no—
472(C2×D3)⋊C4—34no—
473(C2×D3)⋊C4—34no—
474(C2×D3)⋊C4—32no—
475(C2×D3)⋊C4—34no—
476(C2×D3)⋊C4C22×D312yes—
477(C2×D3)⋊C4C22×D312yes—
478(C2×D3)⋊C4C22×D314yes—
479(C2×D3)⋊C4C22×D312yes—
480(C2×D3)⋊C4C22×D312yes—
481(C2×D3)⋊C4C22×D314yes—
482C4⋊Dic3—32no—
483C4⋊Dic3—32no—
484C4⋊Dic3—31no—
485C4⋊Dic3—31no—
486C4⋊Dic3—32no—
487C4⋊Dic3—32no—
488C4⋊Dic3—34no—
489C4⋊Dic3—34no—
490C4⋊Dic3—62no—
491C4⋊Dic3—61no—
492C4⋊Dic3—62no—
493C4⋊Dic3C22×D311yescharacteristic
494C4⋊Dic3C22×D312yes—
495C4⋊Dic3C22×D312yes—
496C4⋊Dic3C22×D312yes—
497C4⋊Dic3C22×D311yescharacteristic
498Dic3⋊C4—34no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—32no—
507Dic3⋊C4—34no—
508Dic3⋊C4—32no—
509Dic3⋊C4—34no—
510Dic3⋊C4—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—62no—
515Dic3⋊C4—64no—
516Dic3⋊C4—64no—
517Dic3⋊C4—64no—
518Dic3⋊C4C22×D314yes—
519C4×Dic3—34no—
520C4×Dic3—34no—
521C4×Dic3—32no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—34no—
525C4×Dic3—32no—
526C4×Dic3—32no—
527C4×Dic3—34no—
528C4×Dic3—32no—
529C4×Dic3—64no—
530C4×Dic3—62no—
531C4×Dic3C22×D312yes—
532C4×Dic3C22×D314yes—
533C4×Dic3C22×D311yescharacteristic
534C4×Dic3C22×D312yes—
535C4×Dic3C22×D311yescharacteristic
536C4×Dic3C22×D311yescharacteristic
537C22×C32C2511yescharacteristic
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—21no—
543C2×C3×D3—21no—
544C2×C3×D3—22no—
545C2×C3×D3—21no—
546C2×C3×D3C2×#4114yes—
547C32×C4—22no—
548C32×C4—22no—
549C32×C4—21no—
550C32×C4C2×#4112yes—
551C32×C4C2×#4112yes—
552C3⋊Dic3—24no—
553C3⋊Dic3—22no—
554C3⋊Dic3C2×#4114yes—
555C3×Dic3—22no—
556C3×Dic3—21no—
557C3×Dic3—24no—
558C3×Dic3—22no—
559C3×Dic3—21no—
560C3×Dic32−1+412yes—
561C2×#41—31no—
562C2×#41—92no—
563C2×#41—91no—
564C22×Q8—92no—
565C4⋊Q8—31no—
566C4⋊Q8—92no—
567C4⋊Q8—92no—
568C4⋊Q8—91no—
569#126—34no—
570#126—94no—
571#126—94no—
572#125—92no—
573#125—94no—
574#125—94no—
575#125—92no—
576#124—32no—
577#124—94no—
578#123—94no—
579#123—94no—
580#123—94no—
581C22⋊Q8—32no—
582C22⋊Q8—94no—
583C22⋊Q8—94no—
584C22⋊Q8—92no—
585C22⋊Q8—92no—
586C22⋊Q8—92no—
587C22⋊Q8—92no—
588#121—94no—
589#121—92no—
590C4×Q8—31no—
591C4×Q8—32no—
592C4×Q8—94no—
593C4×Q8—91no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×Q8D3211yescharacteristic
601C4×D4—31no—
602C4×D4—32no—
603C4×D4—31no—
604C4×D4—32no—
605C4×D4—31no—
606C4×D4—91no—
607C4×D4—94no—
608C4×D4—92no—
609C4×D4—94no—
610C4×D4—92no—
611C4×D4—92no—
612#117—32no—
613#117—31no—
614#117—32no—
615#117—92no—
616#117—94no—
617#117—94no—
618#117—91no—
619#117—92no—
620C2×C4⋊C4—94no—
621C2×C4⋊C4—92no—
622C2×C42—32no—
623C2×C42—31no—
624C2×C42—94no—
625C2×C42—92no—
626C23×C3—32no—
627C23×C3—31no—
628C23×C3—32no—
629C22×D3C23×D311yescharacteristic
630C22×D3C23×D312yes—
631C22×D3C23×D312yes—
632C3×Q8—22no—
633C3×Q8—22no—
634C3×Q8—42no—
635C3×Q8—64no—
636C3×D4—34no—
637C3×D4—64no—
638C3×D4—62no—
639C2×C3×C4—21no—
640C2×C3×C4—21no—
641C2×C3×C4—22no—
642C2×C3×C4—22no—
643C2×C3×C4—21no—
644C2×C3×C4—31no—
645C2×C3×C4—31no—
646C2×C3×C4—32no—
647C2×C3×C4—34no—
648C2×C3×C4—31no—
649C2×C3×C4—32no—
650C2×C3×C4—64no—
651C2×C3×C4—62no—
652C2×C3×C4—64no—
653C2×C3×C4—64no—
654C2×C3×C4—64no—
655C2×C3×C4—62no—
656C2×C3×C4—62no—
657C2×C3×C4C23×D312yes—
658C2×C3×C4C23×D312yes—
659C2×C3×C4C23×D312yes—
660C2×C3×C4C23×D311yescharacteristic
661C2×C3×C4C23×D312yes—
662C2×C3×C4C23×D311yescharacteristic
663C2×C3×C4C23×D311yescharacteristic
664C2×C3×C4C23×D311yescharacteristic
665C2×C3×C4C23×D311yescharacteristic
666C2×C3×C4C23×D311yescharacteristic
667#67—64no—
668#67—64no—
669#67—68no—
670#67—68no—
671C2×Dic3—32no—
672C2×Dic3—32no—
673C2×Dic3—32no—
674C2×Dic3—32no—
675C2×Dic3—34no—
676C2×Dic3—34no—
677C2×Dic3—62no—
678C2×Dic3—62no—
679C2×Dic3—64no—
680C2×Dic3—68no—
681C2×Dic3—64no—
682C2×Dic3—68no—
683C2×Dic3—64no—
684C2×Dic3C23×D311yescharacteristic
685C2×Dic3C23×D312yes—
686C2×Dic3C23×D314yes—
687C2×Dic3C23×D311yescharacteristic
688C2×Dic3C23×D312yes—
689C2×Dic3C23×D311yescharacteristic
690D12—24no—
691D12—22no—
692D12#23514yescomplemented
693C4×D3—24no—
694C4×D3—22no—
695C4×D3—24no—
696C4×D3—22no—
697C4×D3—24no—
698C4×D3—24no—
699C4×D3—22no—
700C4×D3—64no—
701C4×D3—68no—
702C4×D3—64no—
703C4×D3—68no—
704Dic6—24no—
705Dic6—34no—
706Dic6—34no—
707Dic6—64no—
708Dic6—68no—
709Dic6—68no—
710Dic6—64no—
711Dic6—64no—
712Dic6—124no—
713C2×C32C22×#4111yescharacteristic
714C2×C32C22×#4111yescharacteristic
715C2×C32C2×2−1+411yescharacteristic
716C3×D3—24no—
717C3×D3—41no—
718C3×D3—42no—
719#41—64no—
720#41—188no—
721#41—184no—
722C2×Q8—32no—
723C2×Q8—94no—
724C2×Q8—91no—
725C2×Q8—92no—
726C2×Q8—188no—
727C2×Q8C2×D3211yescharacteristic
728C2×D4—31no—
729C2×D4—32no—
730C2×D4—31no—
731C2×D4—94no—
732C2×D4—92no—
733C22×C4—32no—
734C22×C4—32no—
735C22×C4—32no—
736C22×C4—31no—
737C22×C4—31no—
738C22×C4—31no—
739C22×C4—32no—
740C22×C4—94no—
741C22×C4—94no—
742C22×C4—92no—
743C22×C4—92no—
744C4⋊C4—31no—
745C4⋊C4—34no—
746C4⋊C4—32no—
747C4⋊C4—31no—
748C4⋊C4—32no—
749C4⋊C4—32no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—94no—
754C4⋊C4—94no—
755C4⋊C4—94no—
756C4⋊C4—92no—
757C4⋊C4—92no—
758C4⋊C4—91no—
759C4⋊C4—94no—
760C4⋊C4—94no—
761C4⋊C4—92no—
762C4⋊C4C2×D3211yescharacteristic
763C4⋊C4C2×D3212yes—
764C22⋊C4—32no—
765C22⋊C4—32no—
766C22⋊C4—32no—
767C22⋊C4—34no—
768C22⋊C4—32no—
769C22⋊C4—34no—
770C22⋊C4—94no—
771C22⋊C4—92no—
772C22⋊C4—92no—
773C22⋊C4—94no—
774C22⋊C4—94no—
775C42—31no—
776C42—31no—
777C42—31no—
778C42—32no—
779C42—32no—
780C42—34no—
781C42—92no—
782C42—92no—
783C42—94no—
784C42—92no—
785C42—94no—
786C42C2×D3211yescharacteristic
787C42C2×D3212yes—
788C22×C3—21no—
789C22×C3—34no—
790C22×C3—62no—
791C22×C3—62no—
792C22×C3—62no—
793C22×C3—62no—
794C22×C3—61no—
795C22×C3—61no—
796C22×C3—62no—
797C22×C3—61no—
798C22×C3C24×D311yescharacteristic
799C22×C3C24×D311yescharacteristic
800C2×D3—22no—
801C2×D3—22no—
802C2×D3—21no—
803C2×D3—22no—
804C2×D3—21no—
805C2×D3—22no—
806C2×D3—21no—
807C2×D3—22no—
808C2×D3C2×#23514yes—
809C3×C4—22no—
810C3×C4—22no—
811C3×C4—22no—
812C3×C4—21no—
813C3×C4—22no—
814C3×C4—21no—
815C3×C4—22no—
816C3×C4—22no—
817C3×C4—32no—
818C3×C4—42no—
819C3×C4—42no—
820C3×C4—41no—
821C3×C4—62no—
822C3×C4—62no—
823C3×C4—64no—
824C3×C4—61no—
825C3×C4—61no—
826C3×C4C2×#23512yes—
827C3×C4D3×#4112yes—
828C3×C4D3×#4112yes—
829C3×C4D3×#4112yes—
830Dic3—21no—
831Dic3—24no—
832Dic3—22no—
833Dic3—22no—
834Dic3—21no—
835Dic3—34no—
836Dic3—34no—
837Dic3—64no—
838Dic3—64no—
839Dic3—64no—
840Dic3—62no—
841Dic3—62no—
842Dic3—124no—
843Dic3—122no—
844Dic3#101012yes—
845C32#348211yescharacteristic, complemented, Sylow
846C23—32no—
847C23—32no—
848C23—31no—
849Q8—22no—
850Q8—64no—
851Q8—94no—
852Q8—188no—
853Q8—184no—
854D4—34no—
855D4—64no—
856D4—62no—
857D4—184no—
858D4—188no—
859C2×C4—31no—
860C2×C4—31no—
861C2×C4—31no—
862C2×C4—32no—
863C2×C4—32no—
864C2×C4—34no—
865C2×C4—64no—
866C2×C4—62no—
867C2×C4—64no—
868C2×C4—62no—
869C2×C4—64no—
870C2×C4—64no—
871C2×C4—62no—
872C2×C4—92no—
873C2×C4—92no—
874C2×C4—94no—
875C2×C4—184no—
876C2×C4—188no—
877C2×C4—184no—
878C2×C4—188no—
879C2×C4C22×D3212yes—
880C2×C4C22×D3211yescharacteristic
881C2×C4C22×D3212yes—
882C2×C4C22×D3211yescharacteristic
883C2×C4C22×D3211yescharacteristic
884C2×C3—21no—
885C2×C3—21no—
886C2×C3—21no—
887C2×C3—64no—
888C2×C3—122no—
889C2×C3—121no—
890C2×C3C22×#23511yescharacteristic
891C2×C3C2×D3×#4111yescharacteristic
892C2×C3C2×D3×#4111yescharacteristic
893C2×C3C2×D3×#4111yescharacteristic
894C2×C3C2×#101011yescharacteristic
895C2×C3D3×2−1+411yescharacteristic
896D3—24no—
897D3—41no—
898D3—42no—
899C22—34no—
900C22—62no—
901C22—62no—
902C22—61no—
903C22—62no—
904C22—61no—
905C22—62no—
906C22—61no—
907C22—62no—
908C22C23×D3211yescharacteristic
909C4—22no—
910C4—22no—
911C4—21no—
912C4—32no—
913C4—61no—
914C4—62no—
915C4—61no—
916C4—62no—
917C4—64no—
918C4—94no—
919C4—184no—
920C4—182no—
921C4D3×#23512yes—
922C4#6431912yes—
923C3—21no—
924C3#8582611yescharacteristic, complemented
925C3#8698111yescharacteristic, complemented
926C2—64no—
927C2—121no—
928C2—122no—
929C2C2×D3×#23511yescharacteristic
930C2C2×#6431911yescharacteristic
931C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3482
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
2. C3×#5584C2semidirect
3. C3×C4×#239C2semidirect
4. #10595367C2semidirect
5. #10595357C2semidirect
6. #10594581C2semidirect
7. #10594409C2semidirect
8. #10594405C2semidirect
9. #10594358C2semidirect
10. #10593921C2semidirect
11. #10593917C2semidirect
12. #10593905C2semidirect
13. #10593904C2semidirect
14. #10593895C2semidirect
15. C4×#3795C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593859C2semidirect
96. #5584D3semidirect
99. C4×#239D3semidirect
341. #634#41semidirect
350. C3×D12#41semidirect
692. D12#235semidirect
845. C32#3482semidirect
924. C3#85826semidirect
925. C3#86981semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55842
C3×C4×#2392
#105953672
#105953572
#105945812
#105944092
#105944052
#105943582
#105939212
#105939172
#105939052
#105939042
#105938952
C4×#37952
C4×D3×Dic62
#105938592
#869813
#858263