Finite Group Databasebeta

← #11675134

Subgroups — #11675134

Order 768.

1870 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#85788C211yesmaximal, characteristic, complemented
2#85766C211yesmaximal, characteristic, complemented
3C2×C3×C4×D8C211yesmaximal, characteristic, complemented
4#83826C212yesmaximal, complemented
5#82307C211yesmaximal, characteristic, complemented
6#82296C211yesmaximal, characteristic, complemented
7#79572C214yesmaximal, complemented
8#79571C212yesmaximal, complemented
9#79570C212yesmaximal, complemented
10#79569C214yesmaximal, complemented
11#79568C212yesmaximal, complemented
12#79567C212yesmaximal, complemented
13#79162C212yesmaximal, complemented
14#78737C212yesmaximal, complemented
15#78726C212yesmaximal, complemented
16#78463C211yesmaximal, characteristic, complemented
17#78445C211yesmaximal, characteristic, complemented
18#61325—31nomaximal, Sylow
19C22×C3×D8C2211yescharacteristic
20C2×C3×C4×D4C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22#5805C2212yes—
23#5798C2212yes—
24C2×#932C2212yes—
25#5791—22no—
26C2×#924—22no—
27#5563—21no—
28#5559C2214yescomplemented
29#5558—22no—
30#5553C2212yescomplemented
31#5551—21no—
32#5543—21no—
33#5543C2212yescomplemented
34#5542C2212yescomplemented
35#5539—22no—
36#5539C2214yescomplemented
37D4×Dic6—21no—
38D4×Dic6C2212yescomplemented
39#5504C2212yes—
40#5500C2212yes—
41#5494—22no—
42#5483—22no—
43#5477C2211yescharacteristic
44#5470C2211yescharacteristic
45#5470C2211yescharacteristic
46C3×C4×D8C2212yes—
47C3×C4×D8C2212yes—
48C3×C4×D8C2212yes—
49C3×C4×D8C2212yes—
50C2×C3×#107C2211yescharacteristic
51C2×C3×#102C2211yescharacteristic
52C2×C3×#102C2211yescharacteristic
53C2×C3×C4×C8C2211yescharacteristic
54#5215C2212yes—
55#5153C2214yes—
56#5153C2214yes—
57#5150C2214yes—
58#5150C2214yes—
59#5113C2212yes—
60#5113C2212yes—
61#5102C2212yes—
62#5101C2212yes—
63#5019C2212yescomplemented
64#5016C2214yescomplemented
65#5015C2212yescomplemented
66#5009C2214yescomplemented
67#5008C2212yescomplemented
68#5007C2212yescomplemented
69#4966C2212yes—
70#4964C2212yes—
71#4924C2211yescharacteristic
72#4891C2214yescomplemented
73#4890C2214yescomplemented
74#4877C2214yescomplemented
75#4875C2214yescomplemented
76#4785C2214yescomplemented
77#4768C2214yescomplemented
78#4765C2214yescomplemented
79#4764C2214yescomplemented
80#4760C2214yescomplemented
81#4758C2214yescomplemented
82#4757C2214yescomplemented
83#4756C2214yescomplemented
84#4697C2212yescomplemented
85#4697C2212yescomplemented
86#4694C2211yescharacteristic, complemented
87#4694C2211yescharacteristic, complemented
88#4681C2211yescharacteristic, complemented
89#4681C2211yescharacteristic, complemented
90#4679C2212yescomplemented
91#4679C2212yescomplemented
92C8×Dic6C2212yescomplemented
93C8×Dic6C2212yescomplemented
94#3506—31no—
95#3501—31no—
96#3370—34no—
97#3367—32no—
98#3366—32no—
99#3361—34no—
100#3360—32no—
101#3358—32no—
102#3136—32no—
103#3131—31no—
104#3083—32no—
105#3077—31no—
106#3041—32no—
107#3036—31no—
108#2960—31no—
109#2946—32no—
110C2×C4×D8D311yescharacteristic, complemented
111C22×C3×D4C2311yescharacteristic
112C22×C3×D4C2311yescharacteristic
113C23×C3×C4—21no—
114C23×C3×C4—21no—
115C2×#235—22no—
116C2×#235C2312yes—
117C22×Dic6—22no—
118C2×C3×D8—24no—
119C2×C3×D8C2312yes—
120C2×C3×D8C2312yes—
121C22×C3×C8C2311yescharacteristic
122C22×C3×C8C2311yescharacteristic
123C3×C4×D4—21no—
124C3×C4×D4—21no—
125C3×C4×D4—21no—
126C3×C4×D4—21no—
127C3×C4×D4C2312yes—
128C3×C4×D4C2312yes—
129C3×C4×D4C2312yes—
130C3×C4×D4C2312yes—
131C2×C3×C4⋊C4C2311yescharacteristic
132C2×C3×C4⋊C4C2311yescharacteristic
133C2×C3×C22⋊C4—21no—
134C2×C3×C22⋊C4—21no—
135C2×C3×C42C2311yescharacteristic
136#953—24no—
137C2×#217—24no—
138#940C2314yes—
139#938—22no—
140#938—22no—
141#936C2314yes—
142D4×Dic3—22no—
143D4×Dic3—22no—
144D4×Dic3C2314yes—
145D4×Dic3C2314yes—
146C2×#214C2314yes—
147#932—28no—
148C2×#213C2314yes—
149#930—21no—
150#930—21no—
151#930—22no—
152#929—24no—
153C4×#67—24no—
154C4×#67—24no—
155#926—22no—
156#926C2312yes—
157#926C2312yes—
158C2×C4⋊Dic3—22no—
159#924—21no—
160#924—21no—
161#924—22no—
162#924—22no—
163#924—24no—
164#924—22no—
165#924—24no—
166#924D412yes—
167#924D412yes—
168C2×Dic3⋊C4—24no—
169C2×#208C2312yes—
170#893C2314yes—
171#892—22no—
172D3×C4⋊C4—22no—
173#890—22no—
174#890C2314yes—
175#888—22no—
176#888C2314yes—
177#887C2314yes—
178#885—24no—
179#884—24no—
180#883—24no—
181#879—24no—
182#878—24no—
183#878—24no—
184#878—24no—
185#878—24no—
186#875C2312yes—
187#874C2311yescharacteristic
188C4×D12—21no—
189C4×D12—21no—
190#870D412yes—
191#870C2312yes—
192#869D411yescharacteristic
193#869D411yescharacteristic
194#869C2311yescharacteristic
195#869C2311yescharacteristic
196#869C2311yescharacteristic
197C4×Dic6—21no—
198C4×Dic6—21no—
199C4×Dic6C2312yes—
200C4×Dic6C2312yes—
201C3×#107C2312yes—
202C3×#107C2312yes—
203C3×#102C2312yes—
204C3×#102C2312yes—
205C3×#102C2312yes—
206C3×#102C2312yes—
207C3×C4×C8C2311yescharacteristic
208C3×C4×C8C2311yescharacteristic
209C3×C4×C8C2311yescharacteristic
210C3×C4×C8C2311yescharacteristic
211#832C2314yes—
212#832C2314yes—
213#821C2312yes—
214#821C2312yes—
215#821C2312yes—
216#821C2312yes—
217#816C2312yes—
218#816C2312yes—
219#816C2312yes—
220#816C2312yes—
221#815C2314yes—
222Dic3⋊C8C2314yes—
223Dic3⋊C8C2314yes—
224C8×Dic3C2314yes—
225#810C2314yes—
226#809C2314yes—
227#808C2314yes—
228#807C2314yes—
229C4⋊(C3⋊C8)C2312yes—
230C4⋊(C3⋊C8)C2312yes—
231C2×AGL(1,ℤ/8)—32no—
232C22×D8C2×D311yescharacteristic
233#559—34no—
234#556—32no—
235#555—61no—
236#554—32no—
237#554—34no—
238#554—62no—
239#554—61no—
240#553—62no—
241#550—32no—
242D4×Q8—32no—
243D4×Q8—61no—
244#547—61no—
245#544—32no—
246#543—62no—
247#538—62no—
248#535—32no—
249#533—31no—
250#533—31no—
251#532—31no—
252#525—62no—
253C2×C22⋊Q8—62no—
254#520—32no—
255#518—32no—
256C2×C4×D4C2×D311yescharacteristic
257C2×C4×D4C2×D311yescharacteristic
258#490—34no—
259#489—34no—
260#488—34no—
261#488—32no—
262#488—32no—
263#487—31no—
264#487—31no—
265#486—34no—
266#486—31no—
267#486—31no—
268#479—34no—
269#478—34no—
270#478—34no—
271#477—34no—
272#476—32no—
273#474—32no—
274#474—34no—
275#463—34no—
276#463—34no—
277#463—34no—
278#461—32no—
279#459—34no—
280#459—34no—
281#459—32no—
282#446—32no—
283#446—32no—
284C8×Q8—32no—
285C8×Q8—32no—
286#442—34no—
287#440—34no—
288C4×SD16—34no—
289C4×D8—34no—
290C4×D8C2×D312yes—
291C4×D8C2×D312yes—
292C4×D8C2×D312yes—
293C4×D8C2×D312yes—
294#428—32no—
295C2×#107C2×D311yescharacteristic
296#424—32no—
297#423—31no—
298#418—32no—
299#417—32no—
300#416—32no—
301#416—32no—
302C2×#102C2×D311yescharacteristic
303C2×#102C2×D311yescharacteristic
304#405—32no—
305C2×C4×C8C2×D311yescharacteristic
306C24×C3—21no—
307C24×C3—21no—
308C2×C3×D4—21no—
309C2×C3×D4—21no—
310C2×C3×D4—22no—
311C2×C3×D4—22no—
312C2×C3×D4—22no—
313C2×C3×D4#4114yescomplemented
314C2×C3×D4C2412yes—
315C2×C3×D4C2412yes—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—22no—
319C22×C3×C4—22no—
320C22×C3×C4—22no—
321C22×C3×C4—22no—
322C22×C3×C4—82no—
323C22×C3×C4—82no—
324C22×C3×C4C2×D411yescharacteristic
325C22×C3×C4C2×D411yescharacteristic
326C22×C3×C4C2411yescharacteristic
327C2×#67—22no—
328C2×#67—24no—
329C2×#67—24no—
330C22×Dic3—24no—
331C22×Dic3—24no—
332#235—24no—
333#235—24no—
334#235—84no—
335C2×D12—21no—
336C2×D12—21no—
337C2×D12C2412yes—
338C2×C4×D3—22no—
339C2×C4×D3—24no—
340C2×Dic6—21no—
341C2×Dic6—21no—
342C2×Dic6—24no—
343C2×Dic6—84no—
344C2×Dic6C2×D412yes—
345C2×Dic6C2×D412yes—
346C2×Dic6C2412yes—
347C3×D8—24no—
348C3×D8—24no—
349C2×C3×C8—22no—
350C2×C3×C8—22no—
351C2×C3×C8C2411yescharacteristic
352C2×C3×C8C2411yescharacteristic
353C2×C3×C8C2411yescharacteristic
354C2×C3×C8C2411yescharacteristic
355C3×C4⋊C4—21no—
356C3×C4⋊C4—21no—
357C3×C4⋊C4C2412yes—
358C3×C4⋊C4C2412yes—
359C3×C22⋊C4—22no—
360C3×C22⋊C4—22no—
361C3×C22⋊C4—22no—
362C3×C22⋊C4—22no—
363C3×C42C2×D411yescharacteristic
364C3×C42C2×D411yescharacteristic
365C3×C42C2411yescharacteristic
366C3×C42C2411yescharacteristic
367#217—22no—
368#217—24no—
369#217—24no—
370#217—24no—
371#217—24no—
372#217C2×D414yes—
373#214—28no—
374#213—28no—
375(C2×D3)⋊C4—22no—
376(C2×D3)⋊C4—22no—
377(C2×D3)⋊C4—24no—
378C4⋊Dic3—21no—
379C4⋊Dic3—21no—
380C4⋊Dic3—21no—
381C4⋊Dic3—21no—
382C4⋊Dic3—24no—
383C4⋊Dic3C2×D412yes—
384C4⋊Dic3C2×D412yes—
385C4⋊Dic3C2×D412yes—
386C4⋊Dic3C2×D412yes—
387C4⋊Dic3C2412yes—
388C4⋊Dic3C2412yes—
389Dic3⋊C4—22no—
390Dic3⋊C4—22no—
391Dic3⋊C4—24no—
392Dic3⋊C4—24no—
393Dic3⋊C4—24no—
394Dic3⋊C4C2×D414yes—
395Dic3⋊C4C2×D414yes—
396C4×Dic3—22no—
397C4×Dic3—24no—
398C4×Dic3C2414yes—
399#208—24no—
400C2×C3⋊C8C2414yes—
401C2×#41—32no—
402C2×#41—62no—
403C22×Q8—62no—
404C22×D4C22×D311yescharacteristic
405C22×D4C22×D311yescharacteristic
406C23×C4—21no—
407C23×C4—21no—
408AGL(1,ℤ/8)—68no—
409C2×SD16—34no—
410C2×D8—24no—
411C2×D8—34no—
412C2×D8C22×D312yes—
413C2×D8C22×D312yes—
414C2×M16—32no—
415C22×C8C22×D311yescharacteristic
416C22×C8C22×D311yescharacteristic
417C4⋊Q8—34no—
418C4⋊Q8—31no—
419C4⋊Q8—31no—
420C4⋊Q8—31no—
421C4⋊Q8—31no—
422C4⋊Q8—31no—
423C4⋊Q8—62no—
424#127—34no—
425#127—31no—
426#126—64no—
427#125—34no—
428#125—32no—
429#125—32no—
430#125—62no—
431#124—34no—
432#124—32no—
433#124—64no—
434#123—64no—
435#123—64no—
436C22⋊Q8—32no—
437C22⋊Q8—32no—
438C22⋊Q8—64no—
439C22⋊Q8—64no—
440C22⋊Q8—64no—
441C22⋊Q8—64no—
442C22⋊Q8—64no—
443C22⋊Q8—62no—
444C22⋊Q8—64no—
445C22⋊Q8—62no—
446C22⋊Q8—62no—
447C22⋊Q8—61no—
448C22⋊Q8—61no—
449#121—64no—
450#121—62no—
451#121—62no—
452#121—62no—
453#121—61no—
454#121—61no—
455#120—64no—
456C4×Q8—32no—
457C4×Q8—32no—
458C4×Q8—34no—
459C4×Q8—61no—
460C4×Q8—61no—
461C4×D4—21no—
462C4×D4—21no—
463C4×D4—21no—
464C4×D4—21no—
465C4×D4—34no—
466C4×D4—34no—
467C4×D4—34no—
468C4×D4—64no—
469C4×D4—64no—
470C4×D4—62no—
471C4×D4—62no—
472C4×D4—61no—
473C4×D4—61no—
474C4×D4C22×D312yes—
475C4×D4C22×D312yes—
476C4×D4C22×D312yes—
477C4×D4C22×D312yes—
478#117—32no—
479#117—32no—
480#117—62no—
481#117—62no—
482C2×C4⋊C4—62no—
483C2×C4⋊C4—64no—
484C2×C4⋊C4—62no—
485C2×C4⋊C4C22×D311yescharacteristic
486C2×C4⋊C4C22×D311yescharacteristic
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—64no—
490C2×C42C22×D311yescharacteristic
491#107—34no—
492#107C22×D312yes—
493#107C22×D312yes—
494#106—34no—
495C4⋊C8—34no—
496C4⋊C8—34no—
497C4⋊C8—32no—
498C4⋊C8—32no—
499#103—32no—
500#103—32no—
501#103—32no—
502#103—32no—
503#103—34no—
504#102—34no—
505#102—34no—
506#102—32no—
507#102—32no—
508#102—32no—
509#102—32no—
510#102—34no—
511#102C22×D312yes—
512#102C22×D312yes—
513#102C22×D312yes—
514#102C22×D312yes—
515#97—34no—
516C4×C8—34no—
517C4×C8C22×D311yescharacteristic
518C4×C8C22×D311yescharacteristic
519C4×C8C22×D311yescharacteristic
520C4×C8C22×D311yescharacteristic
521C23×C3—22no—
522C23×C3—24no—
523C23×C3—22no—
524C23×C3—42no—
525C23×C3—81no—
526C23×C3—81no—
527C23×C3—81no—
528C23×C3—81no—
529C23×C3C22×D411yescharacteristic
530C22×D3—22no—
531C3×D4—24no—
532C3×D4—22no—
533C3×D4—22no—
534C3×D4—22no—
535C3×D4—42no—
536C3×D4C2×#4114yes—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—41no—
541C2×C3×C4—44no—
542C2×C3×C4—44no—
543C2×C3×C4—82no—
544C2×C3×C4—82no—
545C2×C3×C4—81no—
546C2×C3×C4—81no—
547C2×C3×C4C22×D411yescharacteristic
548C2×C3×C4C22×D411yescharacteristic
549C2×C3×C4C22×D411yescharacteristic
550C2×C3×C4C22×D411yescharacteristic
551C2×C3×C4C22×D411yescharacteristic
552C2×C3×C4C2×#4112yes—
553C2×C3×C42−1+412yes—
554C2×C3×C4C2511yescharacteristic
555#67—44no—
556#67—84no—
557#67—84no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—84no—
562C2×Dic3—84no—
563C2×Dic3C22×D414yes—
564C2×Dic3C22×D414yes—
565D12—22no—
566D12—22no—
567D12—42no—
568D12—81no—
569C4×D3—44no—
570C4×D3—84no—
571Dic6—24no—
572Dic6—22no—
573Dic6—22no—
574Dic6—42no—
575Dic6—42no—
576Dic6—84no—
577Dic6—81no—
578C3×C8—21no—
579C3×C8—21no—
580C3×C8—21no—
581C3×C8—21no—
582C3⋊C8—24no—
583C24—21no—
584C24—21no—
585#41—64no—
586#41—64no—
587#41—244no—
588C2×Q8—32no—
589C2×Q8—32no—
590C2×Q8—32no—
591C2×Q8—64no—
592C2×Q8—61no—
593C2×Q8—61no—
594C2×Q8—244no—
595C2×D4—22no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—22no—
599C2×D4—22no—
600C2×D4—32no—
601C2×D4—64no—
602C2×D4—64no—
603C2×D4—62no—
604C2×D4—61no—
605C2×D4—61no—
606C2×D4#23514yescomplemented
607C2×D4C23×D312yes—
608C2×D4C23×D312yes—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—64no—
616C22×C4—64no—
617C22×C4—64no—
618C22×C4—62no—
619C22×C4—82no—
620C22×C4—82no—
621C22×C4D3×D411yescharacteristic
622C22×C4D3×D411yescharacteristic
623C22×C4C23×D311yescharacteristic
624SD16—68no—
625D8—24no—
626D8—24no—
627D8—68no—
628M16—64no—
629C2×C8—22no—
630C2×C8—22no—
631C2×C8—34no—
632C2×C8C23×D311yescharacteristic
633C2×C8C23×D311yescharacteristic
634C2×C8C23×D311yescharacteristic
635C2×C8C23×D311yescharacteristic
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—32no—
639C4⋊C4—32no—
640C4⋊C4—34no—
641C4⋊C4—32no—
642C4⋊C4—34no—
643C4⋊C4—32no—
644C4⋊C4—32no—
645C4⋊C4—32no—
646C4⋊C4—64no—
647C4⋊C4—64no—
648C4⋊C4—64no—
649C4⋊C4—64no—
650C4⋊C4—62no—
651C4⋊C4—61no—
652C4⋊C4—61no—
653C4⋊C4—61no—
654C4⋊C4—62no—
655C4⋊C4—61no—
656C4⋊C4C23×D312yes—
657C4⋊C4C23×D312yes—
658C22⋊C4—22no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—34no—
663C22⋊C4—64no—
664C22⋊C4—64no—
665C22⋊C4—64no—
666C22⋊C4—64no—
667C22⋊C4—64no—
668C22⋊C4—62no—
669C22⋊C4—62no—
670C22⋊C4—62no—
671C42—34no—
672C42—64no—
673C42—62no—
674C42D3×D411yescharacteristic
675C42D3×D411yescharacteristic
676C42C23×D311yescharacteristic
677C42C23×D311yescharacteristic
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—24no—
681C22×C3—42no—
682C22×C3—42no—
683C22×C3—42no—
684C22×C3—42no—
685C22×C3—42no—
686C22×C3—84no—
687C22×C3—84no—
688C22×C3#54812yes—
689C22×C3C23×D411yescharacteristic
690C2×D3—42no—
691C2×D3—42no—
692C2×D3—42no—
693C3×C4—21no—
694C3×C4—21no—
695C3×C4—21no—
696C3×C4—42no—
697C3×C4—42no—
698C3×C4#54812yes—
699C3×C4#57612yes—
700C3×C4C22×#4111yescharacteristic
701C3×C4C2×2−1+411yescharacteristic
702Dic3—24no—
703Dic3—24no—
704Dic3—42no—
705Dic3—42no—
706Dic3—42no—
707C23—22no—
708C23—24no—
709C23—22no—
710C23—42no—
711C23—62no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—81no—
716C23C2×D3×D411yescharacteristic
717Q8—64no—
718Q8—62no—
719Q8—62no—
720Q8—122no—
721Q8—122no—
722Q8—241no—
723Q8—244no—
724D4—22no—
725D4—22no—
726D4—22no—
727D4—24no—
728D4—42no—
729D4—62no—
730D4—62no—
731D4—124no—
732D4—122no—
733D4—241no—
734D4—244no—
735D4—244no—
736D4C2×#23514yes—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—34no—
741C2×C4—34no—
742C2×C4—41no—
743C2×C4—44no—
744C2×C4—44no—
745C2×C4—62no—
746C2×C4—62no—
747C2×C4—62no—
748C2×C4—82no—
749C2×C4—82no—
750C2×C4—81no—
751C2×C4—81no—
752C2×C4—124no—
753C2×C4—244no—
754C2×C4—244no—
755C2×C4—244no—
756C2×C4C2×#23512yes—
757C2×C4C2×D3×D411yescharacteristic
758C2×C4C2×D3×D411yescharacteristic
759C2×C4C2×D3×D411yescharacteristic
760C2×C4C2×D3×D411yescharacteristic
761C2×C4C2×D3×D411yescharacteristic
762C2×C4#101012yes—
763C2×C4C24×D311yescharacteristic
764C8—21no—
765C8—21no—
766C8—21no—
767C8—21no—
768C8—64no—
769C2×C3—22no—
770C2×C3—44no—
771C2×C3—82no—
772C2×C3C2×#54811yescharacteristic
773C2×C3C2×#57611yescharacteristic
774C2×C3#358411yescharacteristic
775D3—82no—
776C22—21no—
777C22—21no—
778C22—24no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22—84no—
785C22—84no—
786C22—122no—
787C22—122no—
788C22—122no—
789C22#555212yes—
790C22C22×D3×D411yescharacteristic
791C4—21no—
792C4—21no—
793C4—21no—
794C4—42no—
795C4—42no—
796C4—64no—
797C4—64no—
798C4—122no—
799C4—122no—
800C4—122no—
801C4#555212yes—
802C4#575712yes—
803C4C22×#23511yescharacteristic
804C4C2×#101011yescharacteristic
805C3#6132511yescharacteristic, complemented, Sylow
806C2—22no—
807C2—44no—
808C2—82no—
809C2—242no—
810C2C2×#555211yescharacteristic
811C2C2×#575711yescharacteristic
812C2#8718711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC2×C3×C4×D8C2
socleC22×C3C23×D4
hypercenterC2×C4×D8D3
hypocenterC3#61325
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D8

Complements

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

NH ≅ G/Ntype
1. #85788C2semidirect
2. #85766C2semidirect
3. C2×C3×C4×D8C2semidirect
4. #83826C2semidirect
5. #82307C2semidirect
6. #82296C2semidirect
7. #79572C2semidirect
8. #79571C2semidirect
9. #79570C2semidirect
10. #79569C2semidirect
11. #79568C2semidirect
12. #79567C2semidirect
13. #79162C2semidirect
14. #78737C2semidirect
15. #78726C2semidirect
16. #78463C2semidirect
17. #78445C2semidirect
28. #5559C22semidirect
30. #5553C22semidirect
33. #5543C22semidirect
34. #5542C22semidirect
36. #5539C22semidirect
38. D4×Dic6C22semidirect
63. #5019C22semidirect
64. #5016C22semidirect
65. #5015C22semidirect
66. #5009C22semidirect
67. #5008C22semidirect
68. #5007C22semidirect
72. #4891C22semidirect
73. #4890C22semidirect
74. #4877C22semidirect
75. #4875C22semidirect
76. #4785C22semidirect
77. #4768C22semidirect
78. #4765C22semidirect
79. #4764C22semidirect
80. #4760C22semidirect
81. #4758C22semidirect
82. #4757C22semidirect
83. #4756C22semidirect
84. #4697C22semidirect
85. #4697C22semidirect
86. #4694C22semidirect
87. #4694C22semidirect
88. #4681C22semidirect
89. #4681C22semidirect
90. #4679C22semidirect
91. #4679C22semidirect
92. C8×Dic6C22semidirect
93. C8×Dic6C22semidirect
110. C2×C4×D8D3semidirect
313. C2×C3×D4#41semidirect
606. C2×D4#235semidirect
805. C3#61325semidirect

Maximal subgroups

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

subgroupindex
#857882
#857662
C2×C3×C4×D82
#838262
#823072
#822962
#795722
#795712
#795702
#795692
#795682
#795672
#791622
#787372
#787262
#784632
#784452
#613253