Finite Group Databasebeta

← #11909916

Subgroups — #11909916

Order 1152.

2084 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596038C211yesmaximal, characteristic, complemented
2C3×#5580C211yesmaximal, characteristic
3C3×#5570C211yesmaximal, characteristic, complemented
4#10595389C212yesmaximal, complemented
5#10595367C212yesmaximal, complemented
6#10594488C214yesmaximal, complemented
7#10594429C214yesmaximal, complemented
8#10594427C212yesmaximal
9#10594324C212yesmaximal, complemented
10#10593917C212yesmaximal, complemented
11#10593904C212yesmaximal, complemented
12#10593904C211yesmaximal, characteristic, complemented
13#10593885C212yesmaximal, complemented
14C4×D3×Dic6C211yesmaximal, characteristic, complemented
15#10593879C211yesmaximal, characteristic, complemented
16#10593862C212yesmaximal, complemented
17#10593859C211yesmaximal, characteristic, complemented
18#87025—31nomaximal
19#86129—31nomaximal
20C2×D3×Dic6C2211yescharacteristic
21C2×D3×Dic6C2212yes—
22C32×C4×Q8C2211yescharacteristic
23#64153C2212yes—
24#64098C2214yes—
25#64096C2212yes—
26#64079C2212yes—
27#64078C2211yescharacteristic
28C4×#634C2211yescharacteristic
29C4×#634C2212yes—
30C3×#947C2211yescharacteristic
31C3×#946C2211yescharacteristic
32C3×Q8×Dic3C2212yes—
33C3×#898C2212yes—
34C3×#895C2211yescharacteristic
35C3×#894C2212yes—
36C3×#890C2211yescharacteristic
37C3×#890C2212yes—
38C3×#890C2214yes—
39C3×C4×D12C2211yescharacteristic
40C3×C4×D12C2212yes—
41C3×#872C2212yes—
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×#869C2212yes—
45C3×C4×Dic6C2211yescharacteristic
46C3×C4×Dic6C2212yes—
47#63919C2212yes—
48#63919C2214yes—
49C4×#627C2212yes—
50#63899C2214yes—
51#63899C2214yes—
52#63899C2214yes—
53#63898C2212yes—
54#63898C2214yes—
55D3×C4⋊Dic3C2211yescharacteristic
56#63884C2214yes—
57#63878C2214yes—
58#63877C2214yes—
59#63877C2214yes—
60D3×Dic3⋊C4C2212yes—
61C4×D3×Dic3C2212yes—
62#63869C2212yes—
63#63861C2214yes—
64#63860C2212yes—
65#63859C2214yes—
66#63858C2214yes—
67#63858C2214yes—
68#63857C2212yes—
69#63856C2212yes—
70#63856C2212yes—
71#63856C2212yes—
72#63847C2214yes—
73#63847C2214yes—
74#63847C2214yes—
75#63844C2212yes—
76#63844C2212yes—
77#63844C2211yescharacteristic
78Dic3×Dic6C2212yes—
79Dic3×Dic6C2211yescharacteristic
80#63841C2212yes—
81#63841C2212yes—
82#63838C2214yes—
83#63837C2214yes—
84#63837C2212yes—
85C3×#557—31no—
86C3×#529—31no—
87#5731—32no—
88#5728—31no—
89#5727—31no—
90#5727—32no—
91#5701—34no—
92#5696—34no—
93#5693—34no—
94#5691—32no—
95#5685—32no—
96#5685—32no—
97#5671—32no—
98#5650—34no—
99#5622—32no—
100#5600—32no—
101#5584—31no—
102#5581—32no—
103#5580D311yescharacteristic
104#5578—32no—
105#5572—32no—
106C4×D3×Q8—31no—
107#5570D311yescharacteristic, complemented
108#5568—32no—
109#5567—31no—
110#5567—31no—
111#5567—61no—
112#5542—31no—
113#5541—32no—
114D4×Dic6—31no—
115D4×Dic6—32no—
116#5518—32no—
117#5516—32no—
118#5470—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2311yescharacteristic
121C2×#634C2312yes—
122C2×#634C2311yescharacteristic
123C2×C3×D12C2312yes—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×Dic6C2311yescharacteristic
130C2×C3×Dic6C2312yes—
131C2×#627C2314yes—
132C2×#627C2312yes—
133C2×D3×Dic3C2312yes—
134C2×D3×Dic3C2314yes—
135C2×D3×Dic3C2312yes—
136D3×Dic6—24no—
137D3×Dic6—28no—
138C32×C4⋊C4C2311yescharacteristic
139C32×C4⋊C4C2312yes—
140C32×C42C2311yescharacteristic
141C32×C42C2312yes—
142C4⋊(C3⋊Dic3)C2312yes—
143C4⋊(C3⋊Dic3)C2311yescharacteristic
144C4⋊(C3⋊Dic3)C2312yes—
145#3750C2312yes—
146#3750C2314yes—
147#3750C2314yes—
148#3750C2314yes—
149C4×C3⋊Dic3C2314yes—
150C4×C3⋊Dic3C2312yes—
151C3×(C2×D3)⋊C4C2312yes—
152C3×(C2×D3)⋊C4C2312yes—
153C3×(C2×D3)⋊C4C2312yes—
154C3×(C2×D3)⋊C4C2312yes—
155C3×(C2×D3)⋊C4C2312yes—
156C3×C4⋊Dic3C2312yes—
157C3×C4⋊Dic3C2314yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2312yes—
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×C4⋊Dic3C2311yescharacteristic
163C3×Dic3⋊C4C2312yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2314yes—
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172#3724C2312yes—
173#3724C2314yes—
174#3724C2314yes—
175#3724C2314yes—
176Dic3⋊Dic3C2314yes—
177Dic3⋊Dic3C2312yes—
178Dic3⋊Dic3C2312yes—
179(C2×D3)⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2314yes—
181(C2×D3)⋊Dic3C2314yes—
182(C2×D3)⋊Dic3C2314yes—
183Dic32C2312yes—
184Dic32C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187#3523—91noSylow
188C2×D3×Q8—31no—
189C2×D3×Q8—32no—
190C22×Dic6—31no—
191C22×Dic6—32no—
192C3×C4⋊Q8—31no—
193C3×C4⋊Q8—32no—
194C3×#126—32no—
195C3×#125—31no—
196C3×#125—32no—
197C3×#125—34no—
198C3×#124—31no—
199C3×#123—32no—
200C3×C22⋊Q8—31no—
201C3×#121—31no—
202C3×C4×Q8—21no—
203C3×C4×Q8—32no—
204C3×C4×Q8—31no—
205C3×C4×Q8—32no—
206C3×C4×Q8C2×D311yescharacteristic
207C3×C4×Q8C2×D311yescharacteristic
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×#117—32no—
211C2×C3×C42—31no—
212#947C2×D311yescharacteristic
213#946—32no—
214#946—32no—
215#946—32no—
216#946C2×D311yescharacteristic
217Q8×Dic3—32no—
218Q8×Dic3—31no—
219Q8×Dic3C2×D312yes—
220#944—32no—
221#944—32no—
222#944—62no—
223#936—32no—
224#935—34no—
225D4×Dic3—34no—
226D4×Dic3—32no—
227#926—32no—
228#926—32no—
229C2×C4⋊Dic3—31no—
230#924—32no—
231#924—32no—
232#924—32no—
233#924—32no—
234C2×Dic3⋊C4—32no—
235C2×C4×Dic3—32no—
236#898—34no—
237#898—34no—
238#898—34no—
239#898C2×D312yes—
240#897—32no—
241#896—34no—
242#896—34no—
243#896—34no—
244#895C2×D311yescharacteristic
245#894—34no—
246#894C2×D312yes—
247#893—34no—
248#893—32no—
249#892—32no—
250#892—32no—
251#892—34no—
252D3×C4⋊C4—32no—
253D3×C4⋊C4—31no—
254#890—32no—
255#890C2×D314yes—
256#890C2×D311yescharacteristic
257#890C2×D312yes—
258#889—34no—
259#889—34no—
260#889—34no—
261#889—34no—
262#889—34no—
263#889—34no—
264#889—34no—
265#889—34no—
266#889—64no—
267#888—34no—
268#888—34no—
269#888—32no—
270#888—32no—
271#887—32no—
272#887—32no—
273#887—34no—
274#887—34no—
275#887—32no—
276#887—32no—
277#887—32no—
278#887—34no—
279#887—31no—
280#887—62no—
281#879—34no—
282#879—34no—
283#879—34no—
284#879—34no—
285#878—34no—
286#878—34no—
287#878—34no—
288#877—34no—
289#877—34no—
290#877—34no—
291#876—34no—
292#875—32no—
293C4×D12C2×D312yes—
294C4×D12C2×D311yescharacteristic
295#872—34no—
296#872—34no—
297#872C2×D312yes—
298C42×D3—32no—
299C42×D3C2×D311yescharacteristic
300#870—32no—
301#870—32no—
302#870—32no—
303#870—62no—
304#869—31no—
305#869—31no—
306#869—61no—
307#869C2×D311yescharacteristic
308#869C2×D312yes—
309C4×Dic6—31no—
310C4×Dic6—32no—
311C4×Dic6—31no—
312C4×Dic6—31no—
313C4×Dic6—32no—
314C4×Dic6—32no—
315C4×Dic6—32no—
316C4×Dic6—32no—
317C4×Dic6—31no—
318C4×Dic6—34no—
319C4×Dic6—32no—
320C4×Dic6—32no—
321C4×Dic6—32no—
322C4×Dic6—61no—
323C4×Dic6—62no—
324C4×Dic6C2×D311yescharacteristic
325C4×Dic6C2×D312yes—
326C22×C3×D3C2412yes—
327C22×C3×D3C2411yescharacteristic
328C32×Q8—22no—
329C2×C32×C4C2412yes—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2412yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2414yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337#634—24no—
338#634#4114yes—
339C2×C3×Dic3C2411yescharacteristic
340C2×C3×Dic3C2411yescharacteristic
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2414yes—
345C2×C3×Dic3C2411yescharacteristic
346C3×D12—24no—
347C3×D12—22no—
348C3×C4×D3—22no—
349C3×C4×D3—22no—
350C3×C4×D3—24no—
351C3×C4×D3—22no—
352C3×Dic6—22no—
353C3×Dic6—24no—
354#627—28no—
355#627—24no—
356D3×Dic3—24no—
357D3×Dic3—24no—
358D3×Dic3—28no—
359#557—31no—
360#557—92no—
361#557—91no—
362#556—91no—
363#556—92no—
364#552—92no—
365#552—94no—
366D4×Q8—92no—
367D4×Q8—91no—
368#541—92no—
369#541—94no—
370#533—91no—
371#533—92no—
372#529—31no—
373#529—92no—
374#519—92no—
375C2×C4×Q8—91no—
376C2×C3×Q8—21no—
377C2×C3×Q8—32no—
378C2×C3×Q8—31no—
379C2×C3×Q8C22×D311yescharacteristic
380C2×C3×Q8C22×D311yescharacteristic
381C2×C3×D4—32no—
382C2×C3×D4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—31no—
385C22×C3×C4—31no—
386C22×C3×C4—32no—
387C22×Dic3—34no—
388C22×Dic3—32no—
389C22×Dic3—32no—
390D3×Q8—64no—
391D3×Q8—68no—
392C2×D12C22×D311yescharacteristic
393C2×D12C22×D312yes—
394C2×C4×D3—32no—
395C2×C4×D3—32no—
396C2×C4×D3—34no—
397C2×C4×D3C22×D311yescharacteristic
398C2×C4×D3C22×D311yescharacteristic
399C2×C4×D3C22×D311yescharacteristic
400C2×C4×D3C22×D312yes—
401C2×Dic6—31no—
402C2×Dic6—31no—
403C2×Dic6—32no—
404C2×Dic6—32no—
405C2×Dic6—32no—
406C2×Dic6—34no—
407C2×Dic6—32no—
408C2×Dic6—34no—
409C2×Dic6—61no—
410C2×Dic6—62no—
411C2×Dic6—64no—
412C2×Dic6—68no—
413C2×Dic6C22×D311yescharacteristic
414C2×Dic6C22×D312yes—
415C3×C4⋊C4—21no—
416C3×C4⋊C4—22no—
417C3×C4⋊C4—31no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—31no—
423C3×C4⋊C4—32no—
424C3×C4⋊C4—32no—
425C3×C4⋊C4—34no—
426C3×C4⋊C4—34no—
427C3×C4⋊C4—32no—
428C3×C4⋊C4C22×D311yescharacteristic
429C3×C4⋊C4C22×D311yescharacteristic
430C3×C4⋊C4C22×D312yes—
431C3×C4⋊C4C22×D312yes—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4—32no—
436C3×C22⋊C4—32no—
437C3×C42—21no—
438C3×C42—22no—
439C3×C42—31no—
440C3×C42—31no—
441C3×C42—31no—
442C3×C42—32no—
443C3×C42—34no—
444C3×C42C22×D311yescharacteristic
445C3×C42C22×D312yes—
446C3×C42C22×D311yescharacteristic
447C3×C42C22×D312yes—
448#217—34no—
449#217—34no—
450#217—34no—
451#217—34no—
452(C2×D3)⋊C4—34no—
453(C2×D3)⋊C4—34no—
454(C2×D3)⋊C4—34no—
455(C2×D3)⋊C4—34no—
456(C2×D3)⋊C4C22×D312yes—
457(C2×D3)⋊C4C22×D312yes—
458(C2×D3)⋊C4C22×D312yes—
459(C2×D3)⋊C4C22×D312yes—
460(C2×D3)⋊C4C22×D312yes—
461C4⋊Dic3—32no—
462C4⋊Dic3—31no—
463C4⋊Dic3—32no—
464C4⋊Dic3—31no—
465C4⋊Dic3—32no—
466C4⋊Dic3—32no—
467C4⋊Dic3—32no—
468C4⋊Dic3—32no—
469C4⋊Dic3—34no—
470C4⋊Dic3—62no—
471C4⋊Dic3—61no—
472C4⋊Dic3—62no—
473C4⋊Dic3C22×D311yescharacteristic
474C4⋊Dic3C22×D311yescharacteristic
475C4⋊Dic3C22×D312yes—
476C4⋊Dic3C22×D312yes—
477C4⋊Dic3C22×D314yes—
478C4⋊Dic3C22×D314yes—
479C4⋊Dic3C22×D312yes—
480Dic3⋊C4—34no—
481Dic3⋊C4—32no—
482Dic3⋊C4—34no—
483Dic3⋊C4—32no—
484Dic3⋊C4—34no—
485Dic3⋊C4—34no—
486Dic3⋊C4—34no—
487Dic3⋊C4—34no—
488Dic3⋊C4—32no—
489Dic3⋊C4—32no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—34no—
496Dic3⋊C4—34no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—62no—
500Dic3⋊C4—64no—
501Dic3⋊C4—64no—
502Dic3⋊C4—64no—
503Dic3⋊C4C22×D312yes—
504Dic3⋊C4C22×D312yes—
505Dic3⋊C4C22×D314yes—
506Dic3⋊C4C22×D312yes—
507C4×Dic3—32no—
508C4×Dic3—32no—
509C4×Dic3—34no—
510C4×Dic3—34no—
511C4×Dic3—32no—
512C4×Dic3—34no—
513C4×Dic3—32no—
514C4×Dic3—34no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—34no—
518C4×Dic3—34no—
519C4×Dic3—64no—
520C4×Dic3—62no—
521C4×Dic3C22×D311yescharacteristic
522C4×Dic3C22×D312yes—
523C4×Dic3C22×D314yes—
524C4×Dic3C22×D311yescharacteristic
525C4×Dic3C22×D311yescharacteristic
526C22×C32C2511yescharacteristic
527C2×C3×D3—21no—
528C2×C3×D3—21no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D32−1+412yes—
533C32×C4—21no—
534C32×C4—22no—
535C32×C4—22no—
536C32×C4C2×#4112yes—
537C32×C42−1+412yes—
538C3⋊Dic3—22no—
539C3⋊Dic3—24no—
540C3⋊Dic3C2×#4114yes—
541C3×Dic3—22no—
542C3×Dic3—24no—
543C3×Dic3—22no—
544C3×Dic3—21no—
545C3×Dic3—22no—
546C3×Dic3—21no—
547C3×Dic3—21no—
548C22×Q8—91no—
549C22×Q8—92no—
550C4⋊Q8—31no—
551C4⋊Q8—32no—
552C4⋊Q8—92no—
553C4⋊Q8—94no—
554C4⋊Q8—92no—
555C4⋊Q8—91no—
556#126—32no—
557#126—94no—
558#126—94no—
559#126—94no—
560#126—94no—
561#125—31no—
562#125—32no—
563#125—34no—
564#125—92no—
565#125—94no—
566#125—94no—
567#125—94no—
568#125—94no—
569#125—92no—
570#124—31no—
571#124—92no—
572#123—32no—
573#123—94no—
574C22⋊Q8—31no—
575C22⋊Q8—94no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—92no—
579C22⋊Q8—92no—
580C22⋊Q8—92no—
581C22⋊Q8—92no—
582#121—31no—
583C4×Q8—32no—
584C4×Q8—31no—
585C4×Q8—32no—
586C4×Q8—92no—
587C4×Q8—91no—
588C4×Q8—92no—
589C4×Q8—94no—
590C4×Q8—92no—
591C4×Q8—92no—
592C4×Q8—91no—
593C4×Q8—92no—
594C4×Q8—94no—
595C4×Q8—92no—
596C4×Q8—91no—
597C4×Q8—92no—
598C4×Q8D3211yescharacteristic
599C4×D4—32no—
600C4×D4—31no—
601C4×D4—94no—
602C4×D4—92no—
603#117—32no—
604#117—94no—
605#117—94no—
606#117—94no—
607#117—92no—
608#117—92no—
609C2×C4⋊C4—92no—
610C2×C4⋊C4—91no—
611C2×C42—31no—
612C2×C42—92no—
613C23×C3—31no—
614C23×C3—32no—
615C22×D3C23×D312yes—
616C22×D3C23×D311yescharacteristic
617C3×Q8—22no—
618C3×Q8—22no—
619C3×Q8—42no—
620C3×Q8—62no—
621C3×Q8—64no—
622C3×D4—64no—
623C3×D4—62no—
624C2×C3×C4—21no—
625C2×C3×C4—21no—
626C2×C3×C4—22no—
627C2×C3×C4—22no—
628C2×C3×C4—21no—
629C2×C3×C4—31no—
630C2×C3×C4—31no—
631C2×C3×C4—32no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—34no—
635C2×C3×C4—31no—
636C2×C3×C4—62no—
637C2×C3×C4—62no—
638C2×C3×C4—62no—
639C2×C3×C4—64no—
640C2×C3×C4C23×D312yes—
641C2×C3×C4C23×D312yes—
642C2×C3×C4C23×D312yes—
643C2×C3×C4C23×D311yescharacteristic
644C2×C3×C4C23×D312yes—
645C2×C3×C4C23×D311yescharacteristic
646C2×C3×C4C23×D311yescharacteristic
647C2×C3×C4C23×D311yescharacteristic
648C2×C3×C4C23×D311yescharacteristic
649C2×C3×C4C23×D311yescharacteristic
650C2×Dic3—32no—
651C2×Dic3—32no—
652C2×Dic3—34no—
653C2×Dic3—34no—
654C2×Dic3—32no—
655C2×Dic3—32no—
656C2×Dic3—62no—
657C2×Dic3—62no—
658C2×Dic3—64no—
659C2×Dic3—64no—
660C2×Dic3—68no—
661C2×Dic3—64no—
662C2×Dic3C23×D311yescharacteristic
663C2×Dic3C23×D311yescharacteristic
664C2×Dic3C23×D312yes—
665C2×Dic3C23×D312yes—
666C2×Dic3C23×D314yes—
667C2×Dic3C23×D312yes—
668C2×Dic3C23×D311yescharacteristic
669D12—24no—
670D12—22no—
671C4×D3—22no—
672C4×D3—22no—
673C4×D3—24no—
674C4×D3—22no—
675C4×D3—64no—
676C4×D3—68no—
677C4×D3—64no—
678Dic6—22no—
679Dic6—24no—
680Dic6—34no—
681Dic6—34no—
682Dic6—64no—
683Dic6—64no—
684Dic6—68no—
685Dic6—68no—
686Dic6—64no—
687Dic6—64no—
688Dic6—64no—
689Dic6—124no—
690C2×C32C22×#4111yescharacteristic
691C2×C32C2×2−1+411yescharacteristic
692C2×C32C2×2−1+411yescharacteristic
693C3×D3—22no—
694C3×D3—42no—
695C2×Q8—31no—
696C2×Q8—32no—
697C2×Q8—92no—
698C2×Q8—94no—
699C2×Q8—91no—
700C2×Q8—92no—
701C2×Q8—184no—
702C2×Q8—188no—
703C2×Q8C2×D3211yescharacteristic
704C2×D4—32no—
705C2×D4—31no—
706C22×C4—31no—
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—32no—
710C22×C4—92no—
711C22×C4—92no—
712C22×C4—94no—
713C4⋊C4—31no—
714C4⋊C4—32no—
715C4⋊C4—32no—
716C4⋊C4—32no—
717C4⋊C4—34no—
718C4⋊C4—32no—
719C4⋊C4—31no—
720C4⋊C4—32no—
721C4⋊C4—32no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—92no—
725C4⋊C4—92no—
726C4⋊C4—92no—
727C4⋊C4—94no—
728C4⋊C4—94no—
729C4⋊C4—94no—
730C4⋊C4—94no—
731C4⋊C4—92no—
732C4⋊C4—91no—
733C4⋊C4—94no—
734C4⋊C4—92no—
735C4⋊C4—94no—
736C4⋊C4—92no—
737C4⋊C4—94no—
738C4⋊C4C2×D3211yescharacteristic
739C4⋊C4C2×D3212yes—
740C22⋊C4—32no—
741C22⋊C4—32no—
742C22⋊C4—32no—
743C22⋊C4—32no—
744C22⋊C4—32no—
745C22⋊C4—94no—
746C22⋊C4—94no—
747C22⋊C4—94no—
748C22⋊C4—94no—
749C42—31no—
750C42—31no—
751C42—31no—
752C42—32no—
753C42—34no—
754C42—92no—
755C42—92no—
756C42—94no—
757C42—94no—
758C42—92no—
759C42—94no—
760C42C2×D3211yescharacteristic
761C42C2×D3212yes—
762C22×C3—21no—
763C22×C3—32no—
764C22×C3—61no—
765C22×C3—61no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3C24×D311yescharacteristic
770C22×C3C24×D311yescharacteristic
771C2×D3—21no—
772C2×D3—21no—
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3#101012yes—
777C3×C4—22no—
778C3×C4—21no—
779C3×C4—22no—
780C3×C4—22no—
781C3×C4—21no—
782C3×C4—22no—
783C3×C4—22no—
784C3×C4—22no—
785C3×C4—42no—
786C3×C4—41no—
787C3×C4—42no—
788C3×C4—61no—
789C3×C4—62no—
790C3×C4—61no—
791C3×C4—62no—
792C3×C4—64no—
793C3×C4—62no—
794C3×C4—61no—
795C3×C4#100712yes—
796C3×C4D3×#4112yes—
797C3×C4D3×#4112yes—
798C3×C4#101012yes—
799Dic3—22no—
800Dic3—24no—
801Dic3—22no—
802Dic3—21no—
803Dic3—21no—
804Dic3—21no—
805Dic3—22no—
806Dic3—34no—
807Dic3—34no—
808Dic3—64no—
809Dic3—64no—
810Dic3—64no—
811Dic3—62no—
812Dic3—62no—
813Dic3—124no—
814Dic3—122no—
815C32#352311yescharacteristic, complemented, Sylow
816C23—31no—
817C23—32no—
818Q8—22no—
819Q8—62no—
820Q8—64no—
821Q8—94no—
822Q8—184no—
823Q8—188no—
824Q8—184no—
825D4—64no—
826D4—62no—
827C2×C4—32no—
828C2×C4—31no—
829C2×C4—31no—
830C2×C4—31no—
831C2×C4—32no—
832C2×C4—34no—
833C2×C4—32no—
834C2×C4—62no—
835C2×C4—62no—
836C2×C4—62no—
837C2×C4—64no—
838C2×C4—92no—
839C2×C4—94no—
840C2×C4—92no—
841C2×C4—184no—
842C2×C4—188no—
843C2×C4—184no—
844C2×C4C22×D3212yes—
845C2×C4C22×D3211yescharacteristic
846C2×C4C22×D3212yes—
847C2×C4C22×D3211yescharacteristic
848C2×C4C22×D3211yescharacteristic
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—62no—
853C2×C3—122no—
854C2×C3C2×#100711yescharacteristic
855C2×C3C2×D3×#4111yescharacteristic
856C2×C3C2×D3×#4111yescharacteristic
857C2×C3C2×#101011yescharacteristic
858C2×C3C2×#101011yescharacteristic
859C2×C3D3×2−1+411yescharacteristic
860D3—22no—
861D3—42no—
862C22—32no—
863C22—61no—
864C22—61no—
865C22—62no—
866C22—62no—
867C22—62no—
868C22C23×D3211yescharacteristic
869C4—22no—
870C4—21no—
871C4—22no—
872C4—61no—
873C4—61no—
874C4—62no—
875C4—62no—
876C4—64no—
877C4—61no—
878C4—62no—
879C4—94no—
880C4—184no—
881C4—182no—
882C4#6429712yes—
883C4#6431912yes—
884C3—21no—
885C3#8612911yescharacteristic, complemented
886C3#8702511yescharacteristic, complemented
887C2—62no—
888C2—122no—
889C2C2×#6429711yescharacteristic
890C2C2×#6431911yescharacteristic
891C2D3×#101011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
prime radicalC3×#895C22
hypercenterC4×Q8D32
hypocenterC32#3523
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596038C2semidirect
3. C3×#5570C2semidirect
4. #10595389C2semidirect
5. #10595367C2semidirect
6. #10594488C2semidirect
7. #10594429C2semidirect
9. #10594324C2semidirect
10. #10593917C2semidirect
11. #10593904C2semidirect
12. #10593904C2semidirect
13. #10593885C2semidirect
14. C4×D3×Dic6C2semidirect
15. #10593879C2semidirect
16. #10593862C2semidirect
17. #10593859C2semidirect
107. #5570D3semidirect
815. C32#3523semidirect
885. C3#86129semidirect
886. C3#87025semidirect

Maximal subgroups

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

subgroupindex
#105960382
C3×#55802
C3×#55702
#105953892
#105953672
#105944882
#105944292
#105944272
#105943242
#105939172
#105939042
#105938852
C4×D3×Dic62
#105938792
#105938622
#105938592
#870253
#861293