Finite Group Databasebeta

← #11906386

Subgroups — #11906386

Order 1152.

2226 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596193C211yesmaximal, characteristic, complemented
2C3×#5730C211yesmaximal, characteristic, complemented
3C3×D3×C4⋊Q8C211yesmaximal, characteristic, complemented
4#10595400C214yesmaximal, complemented
5#10595369C214yesmaximal, complemented
6#10594532C212yesmaximal, complemented
7#10594531C212yesmaximal, complemented
8#10594387C212yesmaximal, complemented
9#10594376C212yesmaximal, complemented
10D3×#888C212yesmaximal, complemented
11#10594359C212yesmaximal
12#10594344C212yesmaximal, complemented
13#10594318C212yesmaximal, complemented
14#10593956C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic
16#10593873C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18#86926—31nomaximal
19#86215—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3795C2211yescharacteristic
22C2×D3×Dic6C2214yes—
23C32×C4⋊Q8C2211yescharacteristic
24#64153C2214yes—
25#64097C2212yes—
26#64097C2212yes—
27#64096C2212yes—
28#64096C2212yes—
29C4×#634C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#946C2214yes—
32C3×#944C2212yes—
33C3×#897C2212yes—
34C3×#893C2212yes—
35C3×D3×C4⋊C4C2212yes—
36C3×D3×C4⋊C4C2212yes—
37C3×D3×C4⋊C4C2212yes—
38C3×#890C2212yes—
39C3×#888C2212yes—
40C3×#888C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63919C2212yes—
46#63918C2212yes—
47#63918C2211yescharacteristic
48C4×#627C2212yes—
49C4×#625C2214yes—
50C4×#625C2212yes—
51#63898C2212yes—
52#63896C2214yes—
53Dic3×D12C2211yescharacteristic
54D3×C4⋊Dic3C2212yes—
55#63887C2214yes—
56#63887C2214yes—
57#63879C2214yes—
58#63879C2212yes—
59#63878C2214yes—
60#63877C2212yes—
61D3×Dic3⋊C4C2214yes—
62C4×D3×Dic3C2212yes—
63#63872C2212yes—
64#63870C2214yes—
65#63867C2212yes—
66#63866C2211yescharacteristic
67#63857C2214yes—
68#63857C2211yescharacteristic
69#63857C2212yes—
70#63856C2211yescharacteristic
71#63855C2212yes—
72#63851C2214yes—
73#63851C2214yes—
74#63851C2212yes—
75#63847C2214yes—
76#63846C2214yes—
77#63844C2211yescharacteristic
78#63844C2212yes—
79#63843C2214yes—
80#63843C2212yes—
81#63841C2211yescharacteristic
82#63840C2214yes—
83#63839C2214yes—
84#63839C2214yes—
85C3×#554—31no—
86C2×C3×C4⋊Q8—31no—
87Q8×#67—34no—
88#5730—31no—
89#5730D311yescharacteristic, complemented
90#5729—34no—
91#5728—32no—
92#5727—32no—
93D3×C4⋊Q8—32no—
94D3×C4⋊Q8D311yescharacteristic, complemented
95#5722—31no—
96#5722—31no—
97#5722—31no—
98#5722—61no—
99#5721—32no—
100#5689—32no—
101#5685—32no—
102#5635—32no—
103#5632—34no—
104#5623—34no—
105#5622—32no—
106#5578—31no—
107Q8×Dic6—31no—
108#5546—32no—
109#5543—31no—
110D4×Dic6—32no—
111C4×#237—31no—
112#5511—32no—
113#5511—32no—
114#5511—32no—
115#5504—32no—
116#5500—32no—
117C2×#888—32no—
118C4×#235—31no—
119#5470—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2314yes—
123C2×#634C2311yescharacteristic
124C3×D3×Q8—44no—
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2314yes—
130C2×C3×C4×D3C2314yes—
131C2×C3×C4×D3C2311yescharacteristic
132C2×C3×Dic6C2314yes—
133C2×C3×Dic6C2311yescharacteristic
134C2×C3×Dic6C2312yes—
135C2×#627C2312yes—
136C2×#627C2314yes—
137C2×#625C2312yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141#3795Q818yescomplemented
142D3×Dic6—48no—
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148#3750C2312yes—
149#3750C2312yes—
150#3750C2314yes—
151#3750C2314yes—
152C4×C3⋊Dic3C2312yes—
153C4×C3⋊Dic3C2312yes—
154C4×C3⋊Dic3C2314yes—
155C3×(C2×D3)⋊C4C2314yes—
156C3×(C2×D3)⋊C4C2312yes—
157C3×C4⋊Dic3C2312yes—
158C3×C4⋊Dic3C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2314yes—
161C3×C4⋊Dic3C2311yescharacteristic
162C3×Dic3⋊C4C2314yes—
163C3×Dic3⋊C4C2314yes—
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2311yescharacteristic
170#3724C2314yes—
171#3724C2312yes—
172#3724C2312yes—
173Dic3⋊Dic3C2314yes—
174Dic3⋊Dic3C2314yes—
175Dic3⋊Dic3C2312yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2312yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2312yes—
183(C2×D3)⋊Dic3C2312yes—
184(C2×D3)⋊Dic3C2314yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188#3503—91noSylow
189C22×C3×Q8—32no—
190C2×D3×Q8—34no—
191C2×D3×Q8C2×D312yes—
192C2×#237—31no—
193C2×#235—31no—
194C22×Dic6—34no—
195C3×C4⋊Q8—21no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—32no—
198C3×C4⋊Q8—32no—
199C3×C4⋊Q8—31no—
200C3×C4⋊Q8C2×D311yescharacteristic
201C3×C4⋊Q8C2×D311yescharacteristic
202C3×#125—32no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—32no—
205C3×C4×Q8—31no—
206C3×C4×D4—32no—
207C3×C4×D4—31no—
208C2×C3×C4⋊C4—32no—
209C2×C3×C4⋊C4—32no—
210C2×C3×C4⋊C4—32no—
211C2×C3×C42—31no—
212#946—31no—
213#946—34no—
214#946—34no—
215#946C2×D314yes—
216Q8×Dic3—32no—
217Q8×Dic3—34no—
218#944—34no—
219#944—34no—
220#944—34no—
221#944—34no—
222#944—31no—
223#944—64no—
224#944C2×D312yes—
225D4×Dic3—32no—
226D4×Dic3—31no—
227C4×#67—34no—
228C4×#67—32no—
229C4×#67—32no—
230C4×#67—34no—
231C4×#67—32no—
232C4×#67—34no—
233#926—31no—
234#926—32no—
235C2×C4⋊Dic3—32no—
236#924—31no—
237#924—31no—
238#924—34no—
239#924—32no—
240#924—32no—
241#924—34no—
242#924—34no—
243C2×Dic3⋊C4—34no—
244C2×C4×Dic3—32no—
245#897—34no—
246#897—32no—
247#897—31no—
248#897C2×D312yes—
249#896—32no—
250#896—34no—
251#896—34no—
252#896—34no—
253#893—32no—
254#893C2×D312yes—
255#892—31no—
256#892—34no—
257D3×C4⋊C4—34no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4C2×D312yes—
260D3×C4⋊C4C2×D312yes—
261D3×C4⋊C4C2×D312yes—
262#890—32no—
263#890—32no—
264#890—34no—
265#890C2×D312yes—
266#889—34no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—32no—
272#888—34no—
273#888—34no—
274#888—32no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888—32no—
279#888—32no—
280#888—34no—
281#888—34no—
282#888—32no—
283#888—31no—
284#888—62no—
285#888—62no—
286#888C2×D312yes—
287#888C2×D312yes—
288#887—34no—
289#887—32no—
290#887—32no—
291#887—32no—
292#887—32no—
293#887—32no—
294#887—31no—
295#887—32no—
296#887—62no—
297#887—62no—
298#67⋊C4—32no—
299#67⋊C4—34no—
300#878—34no—
301#878—34no—
302#878—34no—
303#877—34no—
304#877—32no—
305C4×D12—31no—
306C4×D12C2×D311yescharacteristic
307#872—32no—
308#872—32no—
309C42×D3—32no—
310C42×D3C2×D311yescharacteristic
311#870—32no—
312#869—31no—
313#869—32no—
314#869—31no—
315#869C2×D311yescharacteristic
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—31no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—31no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2411yescharacteristic
328C22×C3×D3C2412yes—
329C32×Q8—42no—
330C2×C32×C4C2411yescharacteristic
331C2×C32×C4C2414yes—
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—22no—
339#634—44no—
340#634C2×Q814yescomplemented
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2414yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2411yescharacteristic
347C2×C3×Dic3C2411yescharacteristic
348C3×D12C2×Q814yescomplemented
349C3×C4×D3—22no—
350C3×C4×D3—24no—
351C3×C4×D3—22no—
352C3×C4×D3—44no—
353C3×C4×D3—44no—
354C3×C4×D3C2×Q814yescomplemented
355C3×Dic6—22no—
356C3×Dic6—28no—
357C3×Dic6—42no—
358#627—24no—
359#627—44no—
360#625C2×Q818yescomplemented
361D3×Dic3—24no—
362D3×Dic3—44no—
363D3×Dic3C2×Q818yescomplemented
364Q82—91no—
365Q82—91no—
366#557—92no—
367#554—31no—
368#554—92no—
369#554—92no—
370#554—91no—
371D4×Q8—92no—
372D4×Q8—94no—
373#544—92no—
374#544—94no—
375#533—91no—
376#533—92no—
377C2×C4⋊Q8—31no—
378C2×C4⋊Q8—92no—
379#520—92no—
380C4×#41—91no—
381C2×C3×Q8—22no—
382C2×C3×Q8—31no—
383C2×C3×Q8—34no—
384C2×C3×Q8—32no—
385C2×C3×Q8—124no—
386C2×C3×Q8C22×D312yes—
387C2×C3×Q8C22×D312yes—
388C2×C3×D4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—32no—
391C22×C3×C4—31no—
392C22×C3×C4—31no—
393C22×C3×C4—34no—
394C22×C3×C4—34no—
395C2×#67—32no—
396C2×#67—32no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399C22×Dic3—34no—
400D3×Q8—44no—
401D3×Q8—128no—
402#237—38no—
403#235—38no—
404C2×D12C22×D311yescharacteristic
405C2×C4×D3—32no—
406C2×C4×D3—32no—
407C2×C4×D3—34no—
408C2×C4×D3C22×D312yes—
409C2×C4×D3C22×D311yescharacteristic
410C2×C4×D3C22×D311yescharacteristic
411C2×C4×D3C22×D314yes—
412C2×C4×D3C22×D314yes—
413C2×C4×D3C22×D311yescharacteristic
414C2×Dic6—31no—
415C2×Dic6—31no—
416C2×Dic6—31no—
417C2×Dic6—31no—
418C2×Dic6—32no—
419C2×Dic6—32no—
420C2×Dic6—34no—
421C2×Dic6—34no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—61no—
425C2×Dic6—61no—
426C2×Dic6—64no—
427C2×Dic6—128no—
428C2×Dic6C22×D311yescharacteristic
429C2×Dic6C22×D314yes—
430C2×Dic6C22×D312yes—
431C3×C4⋊C4—22no—
432C3×C4⋊C4—22no—
433C3×C4⋊C4—32no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—31no—
437C3×C4⋊C4—31no—
438C3×C4⋊C4—34no—
439C3×C4⋊C4—32no—
440C3×C4⋊C4—34no—
441C3×C4⋊C4—34no—
442C3×C4⋊C4C22×D312yes—
443C3×C4⋊C4C22×D312yes—
444C3×C4⋊C4C22×D312yes—
445C3×C4⋊C4C22×D312yes—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—32no—
448C3×C42—21no—
449C3×C42—31no—
450C3×C42—32no—
451C3×C42—31no—
452C3×C42—31no—
453C3×C42C22×D311yescharacteristic
454C3×C42C22×D311yescharacteristic
455#217—34no—
456#217—32no—
457#217—32no—
458#217—32no—
459#217—32no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4—32no—
462(C2×D3)⋊C4—32no—
463(C2×D3)⋊C4—32no—
464(C2×D3)⋊C4—34no—
465(C2×D3)⋊C4C22×D312yes—
466(C2×D3)⋊C4C22×D314yes—
467C4⋊Dic3—31no—
468C4⋊Dic3—31no—
469C4⋊Dic3—31no—
470C4⋊Dic3—31no—
471C4⋊Dic3—32no—
472C4⋊Dic3—32no—
473C4⋊Dic3—32no—
474C4⋊Dic3—32no—
475C4⋊Dic3—34no—
476C4⋊Dic3—34no—
477C4⋊Dic3—34no—
478C4⋊Dic3—61no—
479C4⋊Dic3—61no—
480C4⋊Dic3C22×D312yes—
481C4⋊Dic3C22×D311yescharacteristic
482C4⋊Dic3C22×D311yescharacteristic
483C4⋊Dic3C22×D312yes—
484C4⋊Dic3C22×D314yes—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—32no—
488Dic3⋊C4—32no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—34no—
492Dic3⋊C4—34no—
493Dic3⋊C4—32no—
494Dic3⋊C4—32no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—32no—
498Dic3⋊C4—34no—
499Dic3⋊C4—32no—
500Dic3⋊C4—32no—
501Dic3⋊C4—32no—
502Dic3⋊C4—34no—
503Dic3⋊C4—34no—
504Dic3⋊C4—34no—
505Dic3⋊C4—34no—
506Dic3⋊C4—62no—
507Dic3⋊C4—62no—
508Dic3⋊C4—64no—
509Dic3⋊C4—64no—
510Dic3⋊C4C22×D312yes—
511Dic3⋊C4C22×D314yes—
512Dic3⋊C4C22×D314yes—
513Dic3⋊C4C22×D314yes—
514C4×Dic3—32no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—34no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—34no—
526C4×Dic3—62no—
527C4×Dic3—62no—
528C4×Dic3—64no—
529C4×Dic3C22×D311yescharacteristic
530C4×Dic3C22×D312yes—
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D311yescharacteristic
533C22×C32C2511yescharacteristic
534C2×C3×D3—22no—
535C2×C3×D3—21no—
536C2×C3×D3—21no—
537C2×C3×D3—22no—
538C2×C3×D3C22×Q814yes—
539C2×C3×D3C22×Q812yes—
540C32×C4—24no—
541C32×C4—21no—
542C32×C4C22×Q812yes—
543C32×C42−1+412yes—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3—22no—
547C3⋊Dic3C22×Q814yes—
548C3×Dic3—24no—
549C3×Dic3—22no—
550C3×Dic3—22no—
551C3×Dic3—21no—
552C3×Dic3—22no—
553C3×Dic3C22×Q812yes—
554C3×Dic3H(5,𝔽2)12yes—
555C2×#41—91no—
556C22×Q8—32no—
557C22×Q8—94no—
558C4⋊Q8—32no—
559C4⋊Q8—32no—
560C4⋊Q8—32no—
561C4⋊Q8—31no—
562C4⋊Q8—91no—
563C4⋊Q8—92no—
564C4⋊Q8—91no—
565C4⋊Q8—94no—
566C4⋊Q8—92no—
567C4⋊Q8—94no—
568C4⋊Q8—94no—
569C4⋊Q8—94no—
570C4⋊Q8—92no—
571C4⋊Q8—92no—
572C4⋊Q8D3211yescharacteristic
573#125—32no—
574#125—92no—
575#125—94no—
576#125—94no—
577#125—94no—
578#125—92no—
579C22⋊Q8—34no—
580C22⋊Q8—32no—
581C22⋊Q8—94no—
582C22⋊Q8—94no—
583C22⋊Q8—94no—
584C22⋊Q8—92no—
585C22⋊Q8—91no—
586C22⋊Q8—92no—
587C22⋊Q8—94no—
588C22⋊Q8—94no—
589C22⋊Q8—94no—
590C22⋊Q8—91no—
591C4×Q8—31no—
592C4×Q8—92no—
593C4×Q8—91no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—92no—
599C4×Q8—91no—
600C4×Q8—91no—
601C4×D4—32no—
602C4×D4—31no—
603C4×D4—91no—
604C4×D4—92no—
605C4×D4—94no—
606C4×D4—92no—
607C4×D4—92no—
608C4×D4—94no—
609#117—92no—
610#117—92no—
611#117—94no—
612#117—91no—
613C2×C4⋊C4—32no—
614C2×C4⋊C4—32no—
615C2×C4⋊C4—32no—
616C2×C4⋊C4—94no—
617C2×C4⋊C4—92no—
618C2×C42—31no—
619C2×C42—92no—
620C23×C3—31no—
621C23×C3—32no—
622C22×D3C23×D311yescharacteristic
623C22×D3C23×D312yes—
624C3×Q8—42no—
625C3×Q8—42no—
626C3×Q8—68no—
627C3×Q8—62no—
628C3×Q8—82no—
629C3×Q8—122no—
630C3×D4—34no—
631C2×C3×C4—21no—
632C2×C3×C4—21no—
633C2×C3×C4—24no—
634C2×C3×C4—21no—
635C2×C3×C4—31no—
636C2×C3×C4—31no—
637C2×C3×C4—34no—
638C2×C3×C4—32no—
639C2×C3×C4—32no—
640C2×C3×C4—34no—
641C2×C3×C4—31no—
642C2×C3×C4—32no—
643C2×C3×C4—62no—
644C2×C3×C4—64no—
645C2×C3×C4—62no—
646C2×C3×C4—124no—
647C2×C3×C4—124no—
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D314yes—
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655C2×C3×C4C23×D311yescharacteristic
656#67—38no—
657#67—38no—
658C2×Dic3—32no—
659C2×Dic3—32no—
660C2×Dic3—38no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—32no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—62no—
671C2×Dic3—64no—
672C2×Dic3—124no—
673C2×Dic3C23×D312yes—
674C2×Dic3C23×D312yes—
675C2×Dic3C23×D314yes—
676C2×Dic3C23×D311yescharacteristic
677C2×Dic3C23×D312yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D311yescharacteristic
680D12D3×Q814yescomplemented
681C4×D3—22no—
682C4×D3—24no—
683C4×D3—22no—
684C4×D3—38no—
685C4×D3—44no—
686C4×D3—44no—
687C4×D3—64no—
688C4×D3—124no—
689C4×D3D3×Q814yescomplemented
690Dic6—22no—
691Dic6—28no—
692Dic6—34no—
693Dic6—34no—
694Dic6—42no—
695Dic6—64no—
696Dic6—64no—
697Dic6—64no—
698Dic6—62no—
699Dic6—62no—
700Dic6—64no—
701Dic6—124no—
702Dic6—124no—
703Dic6—124no—
704Dic6—124no—
705Dic6—244no—
706C2×C32C23×Q811yescharacteristic
707C2×C32C2×H(5,𝔽2)11yescharacteristic
708C2×C32C2×2−1+411yescharacteristic
709C3×D3—24no—
710C3×D3—22no—
711#41—98no—
712C2×Q8—31no—
713C2×Q8—34no—
714C2×Q8—32no—
715C2×Q8—92no—
716C2×Q8—94no—
717C2×Q8—91no—
718C2×Q8—91no—
719C2×Q8—94no—
720C2×Q8—124no—
721C2×Q8—368no—
722C2×Q8C2×D3212yes—
723C2×D4—31no—
724C2×D4—92no—
725C22×C4—31no—
726C22×C4—31no—
727C22×C4—31no—
728C22×C4—32no—
729C22×C4—34no—
730C22×C4—34no—
731C22×C4—92no—
732C22×C4—92no—
733C22×C4—94no—
734C4⋊C4—31no—
735C4⋊C4—34no—
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—34no—
739C4⋊C4—34no—
740C4⋊C4—31no—
741C4⋊C4—32no—
742C4⋊C4—34no—
743C4⋊C4—92no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—92no—
747C4⋊C4—92no—
748C4⋊C4—92no—
749C4⋊C4—92no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—91no—
754C4⋊C4—94no—
755C4⋊C4—92no—
756C4⋊C4—91no—
757C4⋊C4—94no—
758C4⋊C4—92no—
759C4⋊C4C2×D3212yes—
760C4⋊C4C2×D3212yes—
761C22⋊C4—34no—
762C22⋊C4—32no—
763C22⋊C4—92no—
764C22⋊C4—92no—
765C22⋊C4—92no—
766C22⋊C4—92no—
767C22⋊C4—94no—
768C42—31no—
769C42—31no—
770C42—31no—
771C42—32no—
772C42—92no—
773C42—92no—
774C42—94no—
775C42—92no—
776C42—94no—
777C42—92no—
778C42C2×D3211yescharacteristic
779C22×C3—21no—
780C22×C3—34no—
781C22×C3—32no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—61no—
785C22×C3—61no—
786C22×C3C24×D311yescharacteristic
787C22×C3C24×D311yescharacteristic
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—22no—
791C2×D3—22no—
792C2×D3C2×D3×Q814yes—
793C2×D3C2×D3×Q812yes—
794C3×C4—24no—
795C3×C4—21no—
796C3×C4—24no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—22no—
800C3×C4—32no—
801C3×C4—32no—
802C3×C4—44no—
803C3×C4—41no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—62no—
807C3×C4—61no—
808C3×C4—64no—
809C3×C4C2×D3×Q812yes—
810C3×C4C2×D3×Q812yes—
811C3×C4#100712yes—
812C3×C4#101012yes—
813Dic3—24no—
814Dic3—21no—
815Dic3—22no—
816Dic3—22no—
817Dic3—22no—
818Dic3—34no—
819Dic3—34no—
820Dic3—64no—
821Dic3—64no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—62no—
827Dic3—62no—
828Dic3—122no—
829Dic3—122no—
830Dic3#100412yes—
831Dic3C2×D3×Q812yes—
832C32#350311yescharacteristic, complemented, Sylow
833C23—32no—
834C23—31no—
835Q8—42no—
836Q8—68no—
837Q8—62no—
838Q8—94no—
839Q8—122no—
840Q8—184no—
841Q8—182no—
842Q8—364no—
843Q8—364no—
844D4—34no—
845D4—98no—
846C2×C4—31no—
847C2×C4—31no—
848C2×C4—34no—
849C2×C4—31no—
850C2×C4—32no—
851C2×C4—32no—
852C2×C4—32no—
853C2×C4—34no—
854C2×C4—62no—
855C2×C4—62no—
856C2×C4—64no—
857C2×C4—98no—
858C2×C4—92no—
859C2×C4—92no—
860C2×C4—92no—
861C2×C4—92no—
862C2×C4—124no—
863C2×C4—124no—
864C2×C4—184no—
865C2×C4—364no—
866C2×C4C22×D3211yescharacteristic
867C2×C4C22×D3214yes—
868C2×C4C22×D3211yescharacteristic
869C2×C4C22×D3211yescharacteristic
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—21no—
873C2×C3—62no—
874C2×C3—64no—
875C2×C3C2×#100411yescharacteristic
876C2×C3C22×D3×Q811yescharacteristic
877C2×C3C22×D3×Q811yescharacteristic
878C2×C3C2×#100711yescharacteristic
879C2×C3C2×#101011yescharacteristic
880C2×C3D3×H(5,𝔽2)11yescharacteristic
881D3—24no—
882D3—22no—
883C22—32no—
884C22—34no—
885C22—61no—
886C22—62no—
887C22—62no—
888C22—61no—
889C22C23×D3211yescharacteristic
890C4—21no—
891C4—24no—
892C4—32no—
893C4—32no—
894C4—62no—
895C4—64no—
896C4—61no—
897C4—62no—
898C4—62no—
899C4—94no—
900C4—182no—
901C4—182no—
902C4—182no—
903C4#6431512yes—
904C4D32×Q812yes—
905C3—21no—
906C3#8621511yescharacteristic, complemented
907C3#8692611yescharacteristic, complemented
908C2—62no—
909C2—64no—
910C2D3×#100411yescharacteristic
911C2C2×#6431511yescharacteristic
912C2C2×D32×Q811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3795C22
hypercenterC4⋊Q8D32
hypocenterC32#3503
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596193C2semidirect
2. C3×#5730C2semidirect
3. C3×D3×C4⋊Q8C2semidirect
4. #10595400C2semidirect
5. #10595369C2semidirect
6. #10594532C2semidirect
7. #10594531C2semidirect
8. #10594387C2semidirect
9. #10594376C2semidirect
10. D3×#888C2semidirect
12. #10594344C2semidirect
13. #10594318C2semidirect
14. #10593956C2semidirect
16. #10593873C2semidirect
17. #10593856C2semidirect
89. #5730D3semidirect
94. D3×C4⋊Q8D3semidirect
141. #3795Q8semidirect
340. #634C2×Q8semidirect
348. C3×D12C2×Q8semidirect
354. C3×C4×D3C2×Q8semidirect
360. #625C2×Q8semidirect
363. D3×Dic3C2×Q8semidirect
680. D12D3×Q8semidirect
689. C4×D3D3×Q8semidirect
832. C32#3503semidirect
906. C3#86215semidirect
907. C3#86926semidirect

Maximal subgroups

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

subgroupindex
#105961932
C3×#57302
C3×D3×C4⋊Q82
#105954002
#105953692
#105945322
#105945312
#105943872
#105943762
D3×#8882
#105943592
#105943442
#105943182
#105939562
C4×#37952
#105938732
#105938562
#869263
#862153