Finite Group Databasebeta

← #11903762

Subgroups — #11903762

Order 1152.

2236 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596192C211yesmaximal, characteristic, complemented
2C3×#5728C211yesmaximal, characteristic, complemented
3C3×#5727C211yesmaximal, characteristic, complemented
4#10595407C212yesmaximal, complemented
5#10595400C212yesmaximal, complemented
6#10595367C212yesmaximal, complemented
7D3×Q8×Dic3C212yesmaximal, complemented
8#10594535C214yesmaximal, complemented
9#10594452C212yesmaximal, complemented
10#10594445C212yesmaximal, complemented
11#10594386C214yesmaximal, complemented
12#10594358C212yesmaximal
13#10594318C212yesmaximal, complemented
14#10593956C211yesmaximal, characteristic, complemented
15C4×#3795C211yesmaximal, characteristic
16C4×D3×Dic6C211yesmaximal, characteristic, complemented
17#10593856C211yesmaximal, characteristic, complemented
18Q8×#237—31nomaximal
19#86277—31nomaximal
20C2×C3×D3×Q8C2212yes—
21C2×#3795C2211yescharacteristic
22C2×D3×Dic6C2211yescharacteristic
23C32×C4⋊Q8C2211yescharacteristic
24Q8×C3⋊Dic3C2212yes—
25#64153C2212yes—
26#64099C2212yes—
27#64098C2214yes—
28#64096C2212yes—
29C4×#634C2211yescharacteristic
30C4×#634C2211yescharacteristic
31C3×#946C2212yes—
32C3×#946C2212yes—
33C3×Q8×Dic3C2212yes—
34C3×#897C2212yes—
35C3×#896C2214yes—
36C3×#893C2212yes—
37C3×#892C2212yes—
38C3×#890C2212yes—
39C3×#888C2212yes—
40C3×#887C2212yes—
41C3×C4×D12C2211yescharacteristic
42C3×C42×D3C2211yescharacteristic
43C3×#869C2211yescharacteristic
44C3×C4×Dic6C2211yescharacteristic
45#63919C2212yes—
46#63918C2212yes—
47C4×#627C2212yes—
48#63902C2214yes—
49C4×#625C2212yes—
50#63899C2214yes—
51#63898C2212yes—
52#63893C2214yes—
53#63893C2214yes—
54Dic3×D12C2211yescharacteristic
55D3×C4⋊Dic3C2212yes—
56D3×C4⋊Dic3C2214yes—
57D3×C4⋊Dic3C2211yescharacteristic
58#63887C2214yes—
59#63887C2214yes—
60#63879C2214yes—
61#63879C2212yes—
62#63877C2214yes—
63#63877C2212yes—
64D3×Dic3⋊C4C2212yes—
65C4×D3×Dic3C2212yes—
66C4×D3×Dic3C2214yes—
67C4×D3×Dic3C2212yes—
68#63872C2212yes—
69#63870C2214yes—
70#63857C2212yes—
71#63851C2214yes—
72#63847C2214yes—
73#63844C2211yescharacteristic
74#63844C2212yes—
75#63844C2211yescharacteristic
76#63843C2214yes—
77#63843C2212yes—
78Dic3×Dic6C2211yescharacteristic
79Dic3×Dic6C2214yes—
80#63841C2211yescharacteristic
81#63839C2214yes—
82#63839C2214yes—
83#63837C2214yes—
84#63837C2212yes—
85C3×D4×Q8—31no—
86C3×#533—31no—
87Q8×#67—32no—
88C2×Q8×Dic3—32no—
89#5730—31no—
90#5728—32no—
91#5728D311yescharacteristic, complemented
92#5727D311yescharacteristic, complemented
93#5722—31no—
94#5721—31no—
95#5721—31no—
96#5721—32no—
97#5721—61no—
98#5690—32no—
99#5685—32no—
100#5636—34no—
101#5635—32no—
102#5635—32no—
103#5635—34no—
104#5632—32no—
105#5622—32no—
106#5622—34no—
107#5578—32no—
108#5578—34no—
109C4×D3×Q8—32no—
110C4×D3×Q8—31no—
111Q8×Dic6—31no—
112#5543—32no—
113#5543—31no—
114C4×#237—32no—
115C4×#237—31no—
116#5522—32no—
117#5517—32no—
118C4×#235—31no—
119C2×C4×Dic6—31no—
120C2×C32×Q8C2312yes—
121C2×#634C2311yescharacteristic
122C2×#634C2311yescharacteristic
123C3×D3×Q8—28no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×C4×D3C2314yes—
126C2×C3×C4×D3C2311yescharacteristic
127C2×C3×C4×D3C2312yes—
128C2×C3×C4×D3C2311yescharacteristic
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×Dic6C2314yes—
131C2×C3×Dic6C2312yes—
132C2×C3×Dic6C2311yescharacteristic
133C2×#627C2312yes—
134C2×#627C2314yes—
135C2×#625C2312yes—
136C2×D3×Dic3C2312yes—
137C2×D3×Dic3C2312yes—
138C2×D3×Dic3C2312yes—
139C2×D3×Dic3C2314yes—
140C2×D3×Dic3C2312yes—
141#3795Q818yescomplemented
142D3×Dic6—24no—
143C32×C4⋊C4C2312yes—
144C32×C4⋊C4C2312yes—
145C32×C42C2311yescharacteristic
146C4⋊(C3⋊Dic3)C2311yescharacteristic
147C4⋊(C3⋊Dic3)C2311yescharacteristic
148C4⋊(C3⋊Dic3)C2314yes—
149#3750C2312yes—
150#3750C2312yes—
151#3750C2314yes—
152#3750C2314yes—
153C4×C3⋊Dic3C2312yes—
154C4×C3⋊Dic3C2312yes—
155C4×C3⋊Dic3C2314yes—
156C3×(C2×D3)⋊C4C2314yes—
157C3×(C2×D3)⋊C4C2314yes—
158C3×(C2×D3)⋊C4C2312yes—
159C3×C4⋊Dic3C2311yescharacteristic
160C3×C4⋊Dic3C2312yes—
161C3×C4⋊Dic3C2314yes—
162C3×C4⋊Dic3C2312yes—
163C3×C4⋊Dic3C2311yescharacteristic
164C3×Dic3⋊C4C2314yes—
165C3×Dic3⋊C4C2314yes—
166C3×Dic3⋊C4C2312yes—
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2314yes—
169C3×C4×Dic3C2312yes—
170C3×C4×Dic3C2311yescharacteristic
171C3×C4×Dic3C2311yescharacteristic
172#3724C2312yes—
173#3724C2314yes—
174#3724C2312yes—
175Dic3⋊Dic3C2314yes—
176Dic3⋊Dic3C2312yes—
177Dic3⋊Dic3C2314yes—
178Dic3⋊Dic3C2312yes—
179Dic3⋊Dic3C2314yes—
180(C2×D3)⋊Dic3C2312yes—
181(C2×D3)⋊Dic3C2312yes—
182(C2×D3)⋊Dic3C2314yes—
183Dic32C2312yes—
184Dic32C2312yes—
185Dic32C2312yes—
186Dic32C2314yes—
187Dic32C2312yes—
188Q8×#41—91noSylow
189C22×C3×Q8—32no—
190C2×D3×Q8—31no—
191C2×D3×Q8C2×D312yes—
192C2×#237—31no—
193C2×#235—31no—
194C22×Dic6—31no—
195C3×C4⋊Q8—21no—
196C3×C4⋊Q8—32no—
197C3×C4⋊Q8—31no—
198C3×C4⋊Q8C2×D311yescharacteristic
199C3×C4⋊Q8C2×D311yescharacteristic
200C3×#125—32no—
201C3×C22⋊Q8—32no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—32no—
205C3×C4×Q8—32no—
206C3×C4×Q8—32no—
207C3×C4×Q8—31no—
208C3×C4×D4—32no—
209C3×C4×D4—31no—
210C3×#117—32no—
211C2×C3×C42—31no—
212#946—34no—
213#946—34no—
214#946C2×D312yes—
215#946C2×D312yes—
216Q8×Dic3—32no—
217Q8×Dic3—32no—
218Q8×Dic3—34no—
219Q8×Dic3—32no—
220Q8×Dic3—34no—
221Q8×Dic3—31no—
222Q8×Dic3—62no—
223Q8×Dic3C2×D312yes—
224#944—32no—
225#944—32no—
226#944—34no—
227#944—34no—
228#944—62no—
229D4×Dic3—32no—
230D4×Dic3—31no—
231C4×#67—32no—
232C4×#67—32no—
233C4×#67—34no—
234C4×#67—32no—
235#926—31no—
236C2×C4⋊Dic3—31no—
237C2×C4⋊Dic3—32no—
238C2×C4⋊Dic3—34no—
239#924—32no—
240#924—34no—
241C2×Dic3⋊C4—32no—
242C2×C4×Dic3—32no—
243C2×C4×Dic3—32no—
244C2×C4×Dic3—34no—
245#897—32no—
246#897—34no—
247#897—34no—
248#897C2×D312yes—
249#896—34no—
250#896—34no—
251#896C2×D314yes—
252#893—32no—
253#893C2×D312yes—
254#892—31no—
255#892C2×D312yes—
256D3×C4⋊C4—32no—
257D3×C4⋊C4—31no—
258D3×C4⋊C4—32no—
259D3×C4⋊C4—34no—
260#890—32no—
261#890—32no—
262#890—32no—
263#890—32no—
264#890—62no—
265#890C2×D312yes—
266#889—34no—
267#889—34no—
268#889—34no—
269#889—34no—
270#889—34no—
271#889—34no—
272#889—64no—
273#888—34no—
274#888—34no—
275#888—32no—
276#888—32no—
277#888—32no—
278#888C2×D312yes—
279#887—32no—
280#887—34no—
281#887—32no—
282#887—32no—
283#887—32no—
284#887—31no—
285#887—34no—
286#887—32no—
287#887—31no—
288#887—62no—
289#887C2×D312yes—
290#67⋊C4—34no—
291#67⋊C4—32no—
292#67⋊C4—34no—
293#67⋊C4—34no—
294#878—34no—
295#878—34no—
296#878—34no—
297#878—34no—
298#878—34no—
299#877—34no—
300#877—32no—
301C4×D12—31no—
302C4×D12C2×D311yescharacteristic
303#872—32no—
304#872—34no—
305C42×D3—32no—
306C42×D3—32no—
307C42×D3—34no—
308C42×D3C2×D311yescharacteristic
309#869—32no—
310#869C2×D311yescharacteristic
311C4×Dic6—31no—
312C4×Dic6—34no—
313C4×Dic6—31no—
314C4×Dic6—31no—
315C4×Dic6—31no—
316C4×Dic6—31no—
317C4×Dic6—31no—
318C4×Dic6—32no—
319C4×Dic6—31no—
320C4×Dic6—32no—
321C4×Dic6—34no—
322C4×Dic6—32no—
323C4×Dic6—32no—
324C4×Dic6—61no—
325C4×Dic6—61no—
326C4×Dic6C2×D311yescharacteristic
327C22×C3×D3C2412yes—
328C22×C3×D3C2411yescharacteristic
329C32×Q8—24no—
330C2×C32×C4C2414yes—
331C2×C32×C4C2411yescharacteristic
332C2×C32×C4C2411yescharacteristic
333C2×C32×C4C2411yescharacteristic
334C2×C3⋊Dic3C2412yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338#634—22no—
339#634C2×Q814yescomplemented
340C2×C3×Dic3C2412yes—
341C2×C3×Dic3C2411yescharacteristic
342C2×C3×Dic3C2414yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2411yescharacteristic
345C2×C3×Dic3C2411yescharacteristic
346C2×C3×Dic3C2412yes—
347C3×D12C2×Q814yescomplemented
348C3×C4×D3—22no—
349C3×C4×D3—24no—
350C3×C4×D3—28no—
351C3×C4×D3—41no—
352C3×C4×D3C2×Q814yescomplemented
353C3×Dic6—28no—
354C3×Dic6—42no—
355C3×Dic6#4114yescomplemented
356#627—24no—
357#627—44no—
358#625C2×Q818yescomplemented
359D3×Dic3—24no—
360D3×Dic3—42no—
361D3×Dic3—42no—
362D3×Dic3—44no—
363D3×Dic3C2×Q818yescomplemented
364Q82—91no—
365#557—92no—
366#557—91no—
367#554—92no—
368#554—91no—
369#554—92no—
370#554—94no—
371D4×Q8—31no—
372D4×Q8—92no—
373#533—31no—
374#533—92no—
375#533—92no—
376#533—94no—
377C4×#41—91no—
378C4×#41—92no—
379C2×C4×Q8—91no—
380C2×C4×Q8—92no—
381C2×C3×Q8—22no—
382C2×C3×Q8—31no—
383C2×C3×Q8—34no—
384C2×C3×Q8—32no—
385C2×C3×Q8—68no—
386C2×C3×Q8C22×D312yes—
387C2×C3×Q8C22×D312yes—
388C2×C3×D4—31no—
389C22×C3×C4—31no—
390C22×C3×C4—34no—
391C22×C3×C4—32no—
392C22×C3×C4—31no—
393C22×C3×C4—31no—
394C2×#67—32no—
395C2×#67—32no—
396C22×Dic3—32no—
397C22×Dic3—32no—
398C22×Dic3—32no—
399C22×Dic3—34no—
400C22×Dic3—32no—
401D3×Q8—28no—
402D3×Q8—64no—
403#237—38no—
404#235—38no—
405C2×D12C22×D311yescharacteristic
406C2×C4×D3—32no—
407C2×C4×D3—32no—
408C2×C4×D3—32no—
409C2×C4×D3—32no—
410C2×C4×D3—34no—
411C2×C4×D3C22×D312yes—
412C2×C4×D3C22×D314yes—
413C2×C4×D3C22×D311yescharacteristic
414C2×C4×D3C22×D311yescharacteristic
415C2×C4×D3C22×D311yescharacteristic
416C2×Dic6—31no—
417C2×Dic6—31no—
418C2×Dic6—31no—
419C2×Dic6—31no—
420C2×Dic6—32no—
421C2×Dic6—32no—
422C2×Dic6—34no—
423C2×Dic6—34no—
424C2×Dic6—61no—
425C2×Dic6—61no—
426C2×Dic6—64no—
427C2×Dic6C22×D314yes—
428C2×Dic6C22×D312yes—
429C2×Dic6C22×D311yescharacteristic
430C3×C4⋊C4—22no—
431C3×C4⋊C4—22no—
432C3×C4⋊C4—32no—
433C3×C4⋊C4—31no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—32no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4—34no—
438C3×C4⋊C4—31no—
439C3×C4⋊C4—34no—
440C3×C4⋊C4C22×D312yes—
441C3×C4⋊C4C22×D312yes—
442C3×C4⋊C4C22×D312yes—
443C3×C4⋊C4C22×D312yes—
444C3×C22⋊C4—32no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C42—21no—
448C3×C42—31no—
449C3×C42—32no—
450C3×C42—31no—
451C3×C42—34no—
452C3×C42—31no—
453C3×C42C22×D311yescharacteristic
454C3×C42C22×D311yescharacteristic
455#217—34no—
456#217—32no—
457#217—32no—
458(C2×D3)⋊C4—32no—
459(C2×D3)⋊C4—34no—
460(C2×D3)⋊C4—32no—
461(C2×D3)⋊C4C22×D312yes—
462(C2×D3)⋊C4C22×D314yes—
463(C2×D3)⋊C4C22×D314yes—
464C4⋊Dic3—31no—
465C4⋊Dic3—31no—
466C4⋊Dic3—31no—
467C4⋊Dic3—34no—
468C4⋊Dic3—31no—
469C4⋊Dic3—34no—
470C4⋊Dic3—32no—
471C4⋊Dic3—34no—
472C4⋊Dic3—32no—
473C4⋊Dic3—34no—
474C4⋊Dic3—34no—
475C4⋊Dic3—61no—
476C4⋊Dic3—61no—
477C4⋊Dic3—64no—
478C4⋊Dic3C22×D311yescharacteristic
479C4⋊Dic3C22×D312yes—
480C4⋊Dic3C22×D311yescharacteristic
481C4⋊Dic3C22×D312yes—
482C4⋊Dic3C22×D314yes—
483Dic3⋊C4—32no—
484Dic3⋊C4—32no—
485Dic3⋊C4—32no—
486Dic3⋊C4—32no—
487Dic3⋊C4—34no—
488Dic3⋊C4—34no—
489Dic3⋊C4—34no—
490Dic3⋊C4—34no—
491Dic3⋊C4—32no—
492Dic3⋊C4—32no—
493Dic3⋊C4—32no—
494Dic3⋊C4—34no—
495Dic3⋊C4—32no—
496Dic3⋊C4—32no—
497Dic3⋊C4—34no—
498Dic3⋊C4—34no—
499Dic3⋊C4—34no—
500Dic3⋊C4—32no—
501Dic3⋊C4—34no—
502Dic3⋊C4—62no—
503Dic3⋊C4—62no—
504Dic3⋊C4—64no—
505Dic3⋊C4—64no—
506Dic3⋊C4C22×D312yes—
507Dic3⋊C4C22×D314yes—
508Dic3⋊C4C22×D314yes—
509C4×Dic3—32no—
510C4×Dic3—32no—
511C4×Dic3—32no—
512C4×Dic3—32no—
513C4×Dic3—34no—
514C4×Dic3—34no—
515C4×Dic3—32no—
516C4×Dic3—32no—
517C4×Dic3—32no—
518C4×Dic3—32no—
519C4×Dic3—34no—
520C4×Dic3—32no—
521C4×Dic3—34no—
522C4×Dic3—32no—
523C4×Dic3—32no—
524C4×Dic3—32no—
525C4×Dic3—62no—
526C4×Dic3—62no—
527C4×Dic3—64no—
528C4×Dic3C22×D311yescharacteristic
529C4×Dic3C22×D312yes—
530C4×Dic3C22×D311yescharacteristic
531C4×Dic3C22×D311yescharacteristic
532C4×Dic3C22×D314yes—
533C22×C32C2511yescharacteristic
534C2×C3×D3—21no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—21no—
538C2×C3×D3C22×Q814yes—
539C2×C3×D3C22×Q812yes—
540C32×C4—24no—
541C32×C4—21no—
542C32×C4C22×Q812yes—
543C32×C4C2×#4112yes—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3—22no—
547C3⋊Dic3C22×Q814yes—
548C3×Dic3—21no—
549C3×Dic3—22no—
550C3×Dic3—21no—
551C3×Dic3—22no—
552C3×Dic3—24no—
553C3×Dic3C22×Q812yes—
554C3×Dic3C2×#4114yes—
555C2×#41—91no—
556C22×Q8—32no—
557C22×Q8—91no—
558C4⋊Q8—32no—
559C4⋊Q8—31no—
560C4⋊Q8—92no—
561C4⋊Q8—92no—
562C4⋊Q8—94no—
563C4⋊Q8—94no—
564C4⋊Q8—92no—
565C4⋊Q8D3211yescharacteristic
566#125—32no—
567#125—94no—
568#125—94no—
569#125—92no—
570#125—94no—
571#125—92no—
572C22⋊Q8—32no—
573C22⋊Q8—32no—
574C22⋊Q8—32no—
575C22⋊Q8—34no—
576C22⋊Q8—94no—
577C22⋊Q8—94no—
578C22⋊Q8—94no—
579C22⋊Q8—94no—
580C22⋊Q8—94no—
581C22⋊Q8—94no—
582C22⋊Q8—92no—
583C4×Q8—32no—
584C4×Q8—32no—
585C4×Q8—31no—
586C4×Q8—92no—
587C4×Q8—91no—
588C4×Q8—92no—
589C4×Q8—91no—
590C4×Q8—92no—
591C4×Q8—94no—
592C4×Q8—91no—
593C4×Q8—94no—
594C4×Q8—92no—
595C4×Q8—94no—
596C4×Q8—92no—
597C4×Q8—92no—
598C4×Q8—91no—
599C4×Q8—91no—
600C4×D4—32no—
601C4×D4—31no—
602C4×D4—91no—
603C4×D4—94no—
604C4×D4—94no—
605C4×D4—92no—
606C4×D4—92no—
607C4×D4—92no—
608#117—32no—
609#117—92no—
610#117—94no—
611#117—91no—
612C2×C4⋊C4—92no—
613C2×C4⋊C4—91no—
614C2×C4⋊C4—94no—
615C2×C4⋊C4—92no—
616C2×C42—31no—
617C2×C42—92no—
618C2×C42—94no—
619C2×C42—92no—
620C23×C3—32no—
621C23×C3—31no—
622C22×D3C23×D312yes—
623C22×D3C23×D311yescharacteristic
624C3×Q8—24no—
625C3×Q8—24no—
626C3×Q8—34no—
627C3×Q8—44no—
628C3×Q8—68no—
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—32no—
637C2×C3×C4—34no—
638C2×C3×C4—31no—
639C2×C3×C4—32no—
640C2×C3×C4—32no—
641C2×C3×C4—34no—
642C2×C3×C4—31no—
643C2×C3×C4—68no—
644C2×C3×C4—62no—
645C2×C3×C4—64no—
646C2×C3×C4—121no—
647C2×C3×C4C23×D314yes—
648C2×C3×C4C23×D314yes—
649C2×C3×C4C23×D311yescharacteristic
650C2×C3×C4C23×D311yescharacteristic
651C2×C3×C4C23×D311yescharacteristic
652C2×C3×C4C23×D311yescharacteristic
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D311yescharacteristic
655#67—38no—
656#67—38no—
657C2×Dic3—32no—
658C2×Dic3—32no—
659C2×Dic3—38no—
660C2×Dic3—32no—
661C2×Dic3—32no—
662C2×Dic3—32no—
663C2×Dic3—32no—
664C2×Dic3—32no—
665C2×Dic3—32no—
666C2×Dic3—62no—
667C2×Dic3—62no—
668C2×Dic3—62no—
669C2×Dic3—62no—
670C2×Dic3—64no—
671C2×Dic3—124no—
672C2×Dic3—122no—
673C2×Dic3—122no—
674C2×Dic3C23×D311yescharacteristic
675C2×Dic3C23×D312yes—
676C2×Dic3C23×D312yes—
677C2×Dic3C23×D314yes—
678C2×Dic3C23×D311yescharacteristic
679C2×Dic3C23×D312yes—
680C2×Dic3C23×D311yescharacteristic
681D12D3×Q814yescomplemented
682C4×D3—24no—
683C4×D3—22no—
684C4×D3—28no—
685C4×D3—38no—
686C4×D3—41no—
687C4×D3—64no—
688C4×D3—122no—
689C4×D3—122no—
690C4×D3—124no—
691C4×D3D3×Q814yescomplemented
692Dic6—28no—
693Dic6—34no—
694Dic6—34no—
695Dic6—42no—
696Dic6—64no—
697Dic6—64no—
698Dic6—62no—
699Dic6—62no—
700Dic6—64no—
701Dic6—122no—
702Dic6—124no—
703Dic6—124no—
704Dic6#23714yescomplemented
705C2×C32C23×Q811yescharacteristic
706C2×C32C22×#4111yescharacteristic
707C2×C32#58511yescharacteristic
708C3×D3—22no—
709C3×D3—24no—
710#41—98no—
711C2×Q8—31no—
712C2×Q8—34no—
713C2×Q8—32no—
714C2×Q8—68no—
715C2×Q8—92no—
716C2×Q8—94no—
717C2×Q8—91no—
718C2×Q8—91no—
719C2×Q8—184no—
720C2×Q8C2×D3212yes—
721C2×D4—31no—
722C2×D4—92no—
723C22×C4—31no—
724C22×C4—31no—
725C22×C4—34no—
726C22×C4—32no—
727C22×C4—31no—
728C22×C4—92no—
729C22×C4—92no—
730C22×C4—92no—
731C22×C4—92no—
732C22×C4—94no—
733C4⋊C4—32no—
734C4⋊C4—31no—
735C4⋊C4—34no—
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—31no—
739C4⋊C4—34no—
740C4⋊C4—34no—
741C4⋊C4—92no—
742C4⋊C4—92no—
743C4⋊C4—92no—
744C4⋊C4—94no—
745C4⋊C4—94no—
746C4⋊C4—92no—
747C4⋊C4—94no—
748C4⋊C4—94no—
749C4⋊C4—91no—
750C4⋊C4—92no—
751C4⋊C4—94no—
752C4⋊C4—94no—
753C4⋊C4—92no—
754C4⋊C4—91no—
755C4⋊C4—94no—
756C4⋊C4C2×D3212yes—
757C4⋊C4C2×D3212yes—
758C22⋊C4—34no—
759C22⋊C4—34no—
760C22⋊C4—32no—
761C22⋊C4—92no—
762C22⋊C4—94no—
763C22⋊C4—92no—
764C42—31no—
765C42—31no—
766C42—31no—
767C42—34no—
768C42—32no—
769C42—92no—
770C42—92no—
771C42—92no—
772C42—92no—
773C42—94no—
774C42—94no—
775C42—92no—
776C42—92no—
777C42C2×D3211yescharacteristic
778C22×C3—21no—
779C22×C3—34no—
780C22×C3—32no—
781C22×C3—61no—
782C22×C3—62no—
783C22×C3—62no—
784C22×C3—61no—
785C22×C3C24×D311yescharacteristic
786C22×C3C24×D311yescharacteristic
787C2×D3—22no—
788C2×D3—21no—
789C2×D3—21no—
790C2×D3—22no—
791C2×D3C2×D3×Q814yes—
792C2×D3C2×D3×Q812yes—
793C3×C4—24no—
794C3×C4—24no—
795C3×C4—21no—
796C3×C4—21no—
797C3×C4—22no—
798C3×C4—22no—
799C3×C4—32no—
800C3×C4—34no—
801C3×C4—44no—
802C3×C4—41no—
803C3×C4—61no—
804C3×C4—62no—
805C3×C4—62no—
806C3×C4—64no—
807C3×C4—61no—
808C3×C4C2×#23712yes—
809C3×C4C2×D3×Q812yes—
810C3×C4C2×D3×Q812yes—
811C3×C4D3×#4112yes—
812Dic3—22no—
813Dic3—21no—
814Dic3—24no—
815Dic3—21no—
816Dic3—22no—
817Dic3—34no—
818Dic3—34no—
819Dic3—64no—
820Dic3—62no—
821Dic3—62no—
822Dic3—62no—
823Dic3—62no—
824Dic3—62no—
825Dic3—62no—
826Dic3—122no—
827Dic3—122no—
828Dic3—122no—
829Dic3C2×#23714yes—
830Dic3C2×D3×Q812yes—
831C32Q8×#4111yescharacteristic, complemented, Sylow
832C23—31no—
833C23—32no—
834Q8—24no—
835Q8—34no—
836Q8—68no—
837Q8—94no—
838Q8—122no—
839Q8—184no—
840Q8—182no—
841Q8—364no—
842D4—34no—
843D4—98no—
844C2×C4—31no—
845C2×C4—32no—
846C2×C4—34no—
847C2×C4—31no—
848C2×C4—31no—
849C2×C4—32no—
850C2×C4—34no—
851C2×C4—32no—
852C2×C4—68no—
853C2×C4—64no—
854C2×C4—62no—
855C2×C4—98no—
856C2×C4—92no—
857C2×C4—92no—
858C2×C4—92no—
859C2×C4—92no—
860C2×C4—121no—
861C2×C4—184no—
862C2×C4—362no—
863C2×C4—364no—
864C2×C4—362no—
865C2×C4C22×D3214yes—
866C2×C4C22×D3211yescharacteristic
867C2×C4C22×D3211yescharacteristic
868C2×C4C22×D3211yescharacteristic
869C2×C3—21no—
870C2×C3—21no—
871C2×C3—21no—
872C2×C3—64no—
873C2×C3—62no—
874C2×C3C22×#23711yescharacteristic
875C2×C3C22×D3×Q811yescharacteristic
876C2×C3C22×D3×Q811yescharacteristic
877C2×C3C2×D3×#4111yescharacteristic
878C2×C3#596411yescharacteristic
879C2×C3#596811yescharacteristic
880D3—22no—
881D3—24no—
882C22—32no—
883C22—34no—
884C22—62no—
885C22—61no—
886C22—61no—
887C22—62no—
888C22C23×D3211yescharacteristic
889C4—24no—
890C4—21no—
891C4—34no—
892C4—32no—
893C4—62no—
894C4—61no—
895C4—61no—
896C4—64no—
897C4—62no—
898C4—94no—
899C4—182no—
900C4—182no—
901C4—182no—
902C4D3×#23712yes—
903C4D32×Q812yes—
904C3—21no—
905C3#8627711yescharacteristic, complemented
906C3Q8×#23711yescharacteristic, complemented
907C2—62no—
908C2—64no—
909C2C2×D3×#23711yescharacteristic
910C2C2×D32×Q811yescharacteristic
911C2#1059668811yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4⋊Q8C22
prime radicalC2×#3795C22
hypercenterC4⋊Q8D32
hypocenterC32Q8×#41
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #10596192C2semidirect
2. C3×#5728C2semidirect
3. C3×#5727C2semidirect
4. #10595407C2semidirect
5. #10595400C2semidirect
6. #10595367C2semidirect
7. D3×Q8×Dic3C2semidirect
8. #10594535C2semidirect
9. #10594452C2semidirect
10. #10594445C2semidirect
11. #10594386C2semidirect
13. #10594318C2semidirect
14. #10593956C2semidirect
16. C4×D3×Dic6C2semidirect
17. #10593856C2semidirect
91. #5728D3semidirect
92. #5727D3semidirect
141. #3795Q8semidirect
339. #634C2×Q8semidirect
347. C3×D12C2×Q8semidirect
352. C3×C4×D3C2×Q8semidirect
355. C3×Dic6#41semidirect
358. #625C2×Q8semidirect
363. D3×Dic3C2×Q8semidirect
681. D12D3×Q8semidirect
691. C4×D3D3×Q8semidirect
704. Dic6#237semidirect
831. C32Q8×#41semidirect
905. C3#86277semidirect
906. C3Q8×#237semidirect

Maximal subgroups

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

subgroupindex
#105961922
C3×#57282
C3×#57272
#105954072
#105954002
#105953672
D3×Q8×Dic32
#105945352
#105944522
#105944452
#105943862
#105943582
#105943182
#105939562
C4×#37952
C4×D3×Dic62
#105938562
Q8×#2373
#862773