Finite Group Databasebeta

← #11675877

Subgroups — #11675877

Order 768.

1778 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86215C211yesmaximal, characteristic, complemented
2#85828C211yesmaximal, characteristic, complemented
3C3×#3079C211yesmaximal, characteristic, complemented
4C2×#5080C211yesmaximal, characteristic, complemented
5C4×#950C211yesmaximal, characteristic
6#81136C212yesmaximal, complemented
7#81104C212yesmaximal, complemented
8#81089C212yesmaximal, complemented
9#81053C212yesmaximal, complemented
10#81043C212yesmaximal, complemented
11#81039C212yesmaximal, complemented
12#80959C212yesmaximal, complemented
13#80958C212yesmaximal, complemented
14#79244C212yesmaximal, complemented
15#79205C212yesmaximal, complemented
16#79060C211yesmaximal, characteristic, complemented
17#79044C211yesmaximal, characteristic, complemented
18#78873C212yesmaximal, complemented
19#78869C212yesmaximal
20#61374—31nomaximal, Sylow
21C2×C3×C4⋊Q8C2211yescharacteristic
22C3×C4×#41C2211yescharacteristic
23#5827C2212yes—
24C2×#950C2211yescharacteristic
25Q8×#67—22no—
26#5730C2212yes—
27#5729—22no—
28#5728—21no—
29#5727C2212yes—
30D3×C4⋊Q8—21no—
31#5722C2212yes—
32#5721C2212yes—
33#5570C2212yes—
34Q8×Dic6C2212yes—
35#5543—22no—
36#5543C2212yes—
37D4×Dic6—22no—
38D4×Dic6C2212yes—
39#5519—22no—
40#5519C2212yes—
41#5511—22no—
42#5504C2212yes—
43#5500C2212yes—
44C4×#235C2211yescharacteristic
45#5470—21no—
46#5470C2211yescharacteristic
47C2×#869—21no—
48C2×#869C2211yescharacteristic
49C3×#477C2212yes—
50C3×#476C2212yes—
51C3×#475C2212yes—
52C3×#474C2212yes—
53C3×#428C2212yes—
54C3×#423C2211yescharacteristic
55C3×#417C2212yes—
56#5233C2211yescharacteristic
57#5133C2212yes—
58#5122C2212yes—
59#5121C2212yes—
60#5119C2212yes—
61#5080C2212yes—
62#5080C2212yes—
63#5080C2212yes—
64#5080C2212yes—
65C4×#216C2211yescharacteristic
66C4×#216C2211yescharacteristic
67C4×#215C2211yescharacteristic
68C4×#215C2211yescharacteristic
69C4×#214C2211yescharacteristic
70C4×#214C2211yescharacteristic
71C4×#213C2211yescharacteristic
72C4×#213C2211yescharacteristic
73#5002C2211yescharacteristic
74#4998C2211yescharacteristic
75C2×#808C2212yes—
76C2×#808C2212yes—
77C2×C4×C3⋊C8C2211yescharacteristic
78#4891C2214yes—
79#4878C2214yes—
80#4877C2214yes—
81#4876C2214yes—
82#4870C2214yes—
83#4856C2214yes—
84#4855C2214yes—
85#4854C2214yes—
86#4851C2212yes—
87#4850C2212yes—
88#4846C2212yes—
89#4842C2212yes—
90#4831C2212yes—
91#4831C2212yes—
92#4830C2212yes—
93#4830C2212yes—
94#4796C2214yes—
95#4791C2214yes—
96#4789C2214yes—
97#4788C2214yes—
98#4785C2214yes—
99#4766C2214yes—
100#4761C2214yes—
101#4758C2214yes—
102#3503—31no—
103#3503—31no—
104#3387—32no—
105#3387—32no—
106#3384—32no—
107#3384—32no—
108#3381—32no—
109#3381—32no—
110Q8×SD16—32no—
111Q8×SD16—32no—
112#3163—32no—
113C2×#498—31no—
114#3084—32no—
115#3084—32no—
116#3079—31no—
117#3079D311yescharacteristic, complemented
118#2960—31no—
119#2952—32no—
120C4×#135—31no—
121C2×C3×#41C2311yescharacteristic
122C22×C3×Q8—21no—
123C2×D3×Q8—22no—
124C2×#235C2311yescharacteristic
125C22×Dic6—21no—
126C22×Dic6—22no—
127C2×C3×M16C2312yes—
128C3×C4⋊Q8—21no—
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8C2312yes—
131C3×C4⋊Q8C2312yes—
132C3×C4×Q8C2311yescharacteristic
133C3×C4×Q8C2311yescharacteristic
134C3×C4×D4—21no—
135C3×C4×D4—21no—
136C3×C4×D4C2311yescharacteristic
137C3×C4×D4C2311yescharacteristic
138C3×#117—21no—
139C3×#117C2311yescharacteristic
140C2×C3×C4⋊C4—21no—
141C2×C3×C4⋊C4C2312yes—
142C2×C3×C42—21no—
143C2×C3×C42C2311yescharacteristic
144#950Q818yescomplemented
145#946—22no—
146#946—24no—
147Q8×Dic3—22no—
148Q8×Dic3C2314yes—
149#944—22no—
150#944—24no—
151C2×#216C2311yescharacteristic
152C2×#215C2311yescharacteristic
153D4×Dic3—24no—
154D4×Dic3C2314yes—
155C2×#214C2311yescharacteristic
156C2×#213C2311yescharacteristic
157C4×#67—21no—
158C4×#67—21no—
159C4×#67—24no—
160#926—22no—
161#926C2311yescharacteristic
162#926C2312yes—
163C2×C4⋊Dic3—21no—
164C2×C4⋊Dic3—22no—
165C2×C4⋊Dic3—22no—
166C2×C4⋊Dic3C2312yes—
167#924—22no—
168#924—24no—
169#924—22no—
170#924D412yes—
171#924D412yes—
172C22×C3⋊C8C2311yescharacteristic
173C22×C3⋊C8C2311yescharacteristic
174#897—22no—
175#896—24no—
176#893C2314yes—
177#892—22no—
178D3×C4⋊C4—22no—
179D3×C4⋊C4—22no—
180#890—22no—
181#890—24no—
182#890C2314yes—
183#890C2314yes—
184#889—24no—
185#888—22no—
186#888—22no—
187#888—24no—
188#888C2314yes—
189#888C2314yes—
190#887—22no—
191#887C2314yes—
192#878—24no—
193#878—24no—
194#878—24no—
195C4×D12C2311yescharacteristic
196C4×D12C2311yescharacteristic
197#872—21no—
198C42×D3—21no—
199#870—22no—
200#870D412yes—
201#869—22no—
202#869—21no—
203#869—21no—
204#869—22no—
205#869—22no—
206#869D411yescharacteristic
207#869D411yescharacteristic
208#869C2312yes—
209#869C2312yes—
210C4×Dic6—22no—
211C4×Dic6—22no—
212C4×Dic6C2311yescharacteristic
213C4×Dic6C2311yescharacteristic
214C4×Dic6C2312yes—
215C4×Dic6C2312yes—
216C3×#107C2314yes—
217C3×#106C2314yes—
218C3×C4⋊C8C2312yes—
219C3×C4⋊C8C2312yes—
220C3×#103C2314yes—
221C3×#102C2314yes—
222#835C2311yescharacteristic
223#835C2311yescharacteristic
224#832C2311yescharacteristic
225#832C2311yescharacteristic
226#821C2314yes—
227#818C2314yes—
228#817C2314yes—
229#816C2314yes—
230#815C2314yes—
231Dic3⋊C8C2314yes—
232Dic3⋊C8C2314yes—
233C8×Dic3C2314yes—
234#810C2311yescharacteristic
235#810C2311yescharacteristic
236#809C2311yescharacteristic
237#809C2311yescharacteristic
238#808C2314yes—
239#808C2314yes—
240#808C2311yescharacteristic
241#808C2314yes—
242#808C2314yes—
243#808C2311yescharacteristic
244#807C2311yescharacteristic
245#807C2311yescharacteristic
246C4×C3⋊C8C2311yescharacteristic
247C4×C3⋊C8C2311yescharacteristic
248C4×C3⋊C8C2311yescharacteristic
249C4×C3⋊C8C2311yescharacteristic
250C2×#135—31no—
251Q82—32no—
252Q82—32no—
253#557—32no—
254#557—32no—
255#554—32no—
256#554—32no—
257#554—62no—
258#554—62no—
259D4×Q8—32no—
260D4×Q8—32no—
261D4×Q8—62no—
262D4×Q8—62no—
263#544—32no—
264#544—32no—
265#544—62no—
266#544—62no—
267#533—31no—
268#533—61no—
269#533—61no—
270C2×C4⋊Q8—31no—
271C2×C4⋊Q8—61no—
272C2×C4⋊Q8—61no—
273C2×C4⋊Q8C2×D311yescharacteristic
274#520—32no—
275#520—32no—
276C4×#41—31no—
277C4×#41C2×D311yescharacteristic
278#501—34no—
279#501—34no—
280#499—34no—
281#498—32no—
282#498—32no—
283#498—32no—
284#498—32no—
285#498—34no—
286#479—34no—
287#479—34no—
288#478—34no—
289#478—34no—
290#477—32no—
291#477C2×D312yes—
292#476—34no—
293#476—32no—
294#476—34no—
295#476C2×D312yes—
296#475—34no—
297#475—32no—
298#475—34no—
299#475C2×D312yes—
300#474—32no—
301#474C2×D312yes—
302#446—32no—
303#446—32no—
304C8×Q8—32no—
305C8×Q8—32no—
306#442—34no—
307#441—34no—
308C4×Q16—31no—
309C4×Q16—31no—
310C4×SD16—31no—
311C4×SD16—31no—
312C4×SD16—31no—
313C4×SD16—31no—
314C4×SD16—34no—
315C4×SD16—34no—
316C4×D8—31no—
317C4×D8—31no—
318#428—32no—
319#428C2×D312yes—
320#427—31no—
321C2×#106—32no—
322C2×#106—32no—
323#424—32no—
324#423C2×D311yescharacteristic
325#417—32no—
326#417C2×D312yes—
327#416—31no—
328#416—31no—
329#405—32no—
330C2×C4×C8—31no—
331C3×#41—22no—
332C3×#41C2×Q814yescomplemented
333C2×C3×Q8—22no—
334C2×C3×Q8—22no—
335C2×C3×Q8—82no—
336C2×C3×Q8C2411yescharacteristic
337C2×C3×D4—21no—
338C2×C3×D4C2411yescharacteristic
339C22×C3×C4—21no—
340C22×C3×C4—22no—
341C22×C3×C4—21no—
342C22×C3×C4—21no—
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2×D411yescharacteristic
345C22×C3×C4C2411yescharacteristic
346C2×#67—21no—
347C22×Dic3—22no—
348C22×Dic3—24no—
349D3×Q8—84no—
350#235—22no—
351#235C2×Q814yescomplemented
352C2×D12C2411yescharacteristic
353C2×C4×D3—21no—
354C2×C4×D3—21no—
355C2×C4×D3—21no—
356C2×C4×D3—24no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—24no—
361C2×Dic6—84no—
362C2×Dic6—82no—
363C2×Dic6C2×D412yes—
364C2×Dic6C2×D412yes—
365C2×Dic6C2411yescharacteristic
366C3×M16—24no—
367C2×C3×C8C2414yes—
368C3×C4⋊C4—22no—
369C3×C4⋊C4—21no—
370C3×C4⋊C4—22no—
371C3×C4⋊C4—22no—
372C3×C4⋊C4—21no—
373C3×C4⋊C4C2411yescharacteristic
374C3×C4⋊C4C2411yescharacteristic
375C3×C4⋊C4C2414yes—
376C3×C22⋊C4—21no—
377C3×C22⋊C4—21no—
378C3×C22⋊C4—21no—
379C3×C42—21no—
380C3×C42—21no—
381C3×C42—21no—
382C3×C42C2×D411yescharacteristic
383C3×C42C2×D411yescharacteristic
384C3×C42C2411yescharacteristic
385C3×C42C2411yescharacteristic
386#217—21no—
387#217—24no—
388#217C2×D414yes—
389#216C2×Q814yescomplemented
390#215C2×Q814yescomplemented
391#214C2×Q814yescomplemented
392#213C2×Q814yescomplemented
393(C2×D3)⋊C4—21no—
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—24no—
396C4⋊Dic3—22no—
397C4⋊Dic3—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—24no—
400C4⋊Dic3—24no—
401C4⋊Dic3—24no—
402C4⋊Dic3C2×D412yes—
403C4⋊Dic3C2×D412yes—
404C4⋊Dic3C2×D412yes—
405C4⋊Dic3C2×D412yes—
406C4⋊Dic3C2411yescharacteristic
407C4⋊Dic3C2411yescharacteristic
408C4⋊Dic3C2414yes—
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—24no—
412Dic3⋊C4—24no—
413Dic3⋊C4—24no—
414Dic3⋊C4—24no—
415Dic3⋊C4—24no—
416Dic3⋊C4C2×D414yes—
417Dic3⋊C4C2×D414yes—
418C4×Dic3—21no—
419C4×Dic3—21no—
420C4×Dic3—21no—
421C4×Dic3—24no—
422C4×Dic3—24no—
423C4×Dic3C2414yes—
424C2×C3⋊C8—22no—
425C2×C3⋊C8C2×Q814yescomplemented
426C2×C3⋊C8C2411yescharacteristic
427C2×C3⋊C8C2411yescharacteristic
428C2×C3⋊C8C2411yescharacteristic
429C2×C3⋊C8C2411yescharacteristic
430C2×#41—31no—
431C2×#41C22×D311yescharacteristic
432C22×Q8—21no—
433C22×Q8—62no—
434C22×Q8—62no—
435C22×Q8—61no—
436#135—38no—
437C2×Q16—31no—
438C2×SD16—31no—
439C2×SD16—31no—
440C2×D8—31no—
441C2×M16C22×D312yes—
442C22×C8—31no—
443C22×C8—31no—
444C4⋊Q8—21no—
445C4⋊Q8—21no—
446C4⋊Q8—34no—
447C4⋊Q8—34no—
448C4⋊Q8—31no—
449C4⋊Q8—31no—
450C4⋊Q8—32no—
451C4⋊Q8—32no—
452C4⋊Q8—62no—
453C4⋊Q8—62no—
454C4⋊Q8—62no—
455C4⋊Q8—62no—
456C4⋊Q8—62no—
457C4⋊Q8—64no—
458C4⋊Q8—64no—
459C4⋊Q8—62no—
460C4⋊Q8—61no—
461C4⋊Q8—61no—
462C4⋊Q8C22×D312yes—
463C4⋊Q8C22×D312yes—
464#125—34no—
465#125—34no—
466#125—32no—
467#125—62no—
468#125—62no—
469#125—64no—
470#125—64no—
471C22⋊Q8—32no—
472C22⋊Q8—32no—
473C22⋊Q8—64no—
474C22⋊Q8—64no—
475C22⋊Q8—64no—
476C22⋊Q8—64no—
477C22⋊Q8—64no—
478C22⋊Q8—62no—
479C22⋊Q8—62no—
480C22⋊Q8—62no—
481C22⋊Q8—64no—
482C22⋊Q8—62no—
483C4×Q8—32no—
484C4×Q8—32no—
485C4×Q8—34no—
486C4×Q8—34no—
487C4×Q8—31no—
488C4×Q8—31no—
489C4×Q8—62no—
490C4×Q8—62no—
491C4×Q8—62no—
492C4×Q8—62no—
493C4×Q8C22×D311yescharacteristic
494C4×Q8C22×D311yescharacteristic
495C4×D4—21no—
496C4×D4—21no—
497C4×D4—34no—
498C4×D4—34no—
499C4×D4—31no—
500C4×D4—31no—
501C4×D4—64no—
502C4×D4—64no—
503C4×D4—61no—
504C4×D4—61no—
505C4×D4C22×D311yescharacteristic
506C4×D4C22×D311yescharacteristic
507#117—21no—
508#117—32no—
509#117—31no—
510#117—62no—
511#117—62no—
512#117—61no—
513#117C22×D311yescharacteristic
514C2×C4⋊C4—21no—
515C2×C4⋊C4—32no—
516C2×C4⋊C4—62no—
517C2×C4⋊C4—62no—
518C2×C4⋊C4—62no—
519C2×C4⋊C4—62no—
520C2×C4⋊C4—61no—
521C2×C4⋊C4C22×D312yes—
522C2×C42—21no—
523C2×C42—61no—
524C2×C42C22×D311yescharacteristic
525#107—34no—
526#107—31no—
527#107—31no—
528#107C22×D314yes—
529#106—34no—
530#106—34no—
531#106—34no—
532#106—34no—
533#106—34no—
534#106—31no—
535#106—31no—
536#106C22×D314yes—
537C4⋊C8—34no—
538C4⋊C8—34no—
539C4⋊C8C22×D312yes—
540C4⋊C8C22×D312yes—
541#103—31no—
542#103—31no—
543#103—34no—
544#103—31no—
545#103—31no—
546#103C22×D314yes—
547#102—31no—
548#102—31no—
549#102—34no—
550#102—31no—
551#102—31no—
552#102C22×D314yes—
553#97—34no—
554C4×C8—34no—
555C4×C8—31no—
556C4×C8—31no—
557C4×C8—31no—
558C4×C8—31no—
559C23×C3—21no—
560C23×C3C22×D411yescharacteristic
561C22×D3—21no—
562C3×Q8—21no—
563C3×Q8—44no—
564C3×Q8—82no—
565C3×Q8C22×Q812yes—
566C3×D4—24no—
567C3×D4—21no—
568C3×D4C22×Q812yes—
569C2×C3×C4—21no—
570C2×C3×C4—24no—
571C2×C3×C4—22no—
572C2×C3×C4—22no—
573C2×C3×C4—24no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—42no—
577C2×C3×C4—42no—
578C2×C3×C4—82no—
579C2×C3×C4C22×D411yescharacteristic
580C2×C3×C4C22×D411yescharacteristic
581C2×C3×C4C22×D411yescharacteristic
582C2×C3×C4C22×D411yescharacteristic
583C2×C3×C4C22×D411yescharacteristic
584C2×C3×C4C22×Q812yes—
585C2×C3×C42−1+412yes—
586C2×C3×C4C2511yescharacteristic
587#67—24no—
588C2×Dic3—21no—
589C2×Dic3—21no—
590C2×Dic3—21no—
591C2×Dic3—24no—
592C2×Dic3—84no—
593C2×Dic3—82no—
594C2×Dic3C22×D414yes—
595C2×Dic3C22×D414yes—
596D12—21no—
597D12C22×Q812yes—
598C4×D3—24no—
599C4×D3—42no—
600C4×D3—42no—
601C4×D3—84no—
602Dic6—24no—
603Dic6—24no—
604Dic6—21no—
605Dic6—44no—
606Dic6—84no—
607Dic6—84no—
608Dic6—82no—
609Dic6C22×Q812yes—
610C3×C8—24no—
611C3⋊C8—21no—
612C3⋊C8—21no—
613C3⋊C8C22×Q812yes—
614C3⋊C8C22×Q812yes—
615#41—22no—
616#41—34no—
617#41—62no—
618#41D3×Q814yescomplemented
619C2×Q8—22no—
620C2×Q8—22no—
621C2×Q8—32no—
622C2×Q8—32no—
623C2×Q8—31no—
624C2×Q8—64no—
625C2×Q8—64no—
626C2×Q8—62no—
627C2×Q8—62no—
628C2×Q8—82no—
629C2×Q8—242no—
630C2×Q8—244no—
631C2×Q8—244no—
632C2×Q8C23×D311yescharacteristic
633C2×D4—21no—
634C2×D4—31no—
635C2×D4—61no—
636C2×D4C23×D311yescharacteristic
637C22×C4—21no—
638C22×C4—22no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—64no—
642C22×C4—64no—
643C22×C4—61no—
644C22×C4—62no—
645C22×C4—61no—
646C22×C4—61no—
647C22×C4D3×D411yescharacteristic
648C22×C4D3×D411yescharacteristic
649C22×C4C23×D311yescharacteristic
650Q16—34no—
651SD16—34no—
652SD16—34no—
653D8—34no—
654M16—24no—
655C2×C8—34no—
656C2×C8—31no—
657C2×C8—31no—
658C2×C8—31no—
659C2×C8—31no—
660C2×C8—62no—
661C2×C8C23×D314yes—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—32no—
668C4⋊C4—32no—
669C4⋊C4—32no—
670C4⋊C4—32no—
671C4⋊C4—34no—
672C4⋊C4—34no—
673C4⋊C4—34no—
674C4⋊C4—31no—
675C4⋊C4—31no—
676C4⋊C4—64no—
677C4⋊C4—64no—
678C4⋊C4—64no—
679C4⋊C4—64no—
680C4⋊C4—64no—
681C4⋊C4—64no—
682C4⋊C4—64no—
683C4⋊C4—64no—
684C4⋊C4—62no—
685C4⋊C4—62no—
686C4⋊C4—62no—
687C4⋊C4—61no—
688C4⋊C4—61no—
689C4⋊C4C23×D311yescharacteristic
690C4⋊C4C23×D311yescharacteristic
691C4⋊C4C23×D314yes—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—34no—
696C22⋊C4—64no—
697C22⋊C4—64no—
698C22⋊C4—61no—
699C22⋊C4—61no—
700C22⋊C4—61no—
701C42—21no—
702C42—21no—
703C42—21no—
704C42—34no—
705C42—64no—
706C42—64no—
707C42—61no—
708C42—61no—
709C42—61no—
710C42D3×D411yescharacteristic
711C42D3×D411yescharacteristic
712C42C23×D311yescharacteristic
713C42C23×D311yescharacteristic
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—22no—
717C22×C3—41no—
718C22×C3—41no—
719C22×C3D4×Q812yes—
720C22×C3C23×D411yescharacteristic
721C2×D3—22no—
722C2×D3—41no—
723C2×D3—41no—
724C3×C4—22no—
725C3×C4—21no—
726C3×C4—21no—
727C3×C4—41no—
728C3×C4—44no—
729C3×C4—41no—
730C3×C4D4×Q812yes—
731C3×C4#57712yes—
732C3×C4#57712yes—
733C3×C4C23×Q811yescharacteristic
734C3×C4C2×2−1+411yescharacteristic
735Dic3—22no—
736Dic3—24no—
737Dic3—24no—
738Dic3—44no—
739Dic3—41no—
740Dic3—41no—
741C23—21no—
742C23—61no—
743C23C2×D3×D411yescharacteristic
744Q8—21no—
745Q8—32no—
746Q8—44no—
747Q8—61no—
748Q8—64no—
749Q8—64no—
750Q8—82no—
751Q8—124no—
752Q8—242no—
753Q8—244no—
754Q8—244no—
755Q8C2×D3×Q812yes—
756D4—24no—
757D4—21no—
758D4—32no—
759D4—64no—
760D4—61no—
761D4C2×D3×Q812yes—
762C2×C4—21no—
763C2×C4—24no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—24no—
769C2×C4—34no—
770C2×C4—34no—
771C2×C4—42no—
772C2×C4—42no—
773C2×C4—61no—
774C2×C4—64no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—64no—
778C2×C4—82no—
779C2×C4—122no—
780C2×C4—122no—
781C2×C4—244no—
782C2×C4—244no—
783C2×C4—242no—
784C2×C4C2×D3×D411yescharacteristic
785C2×C4C2×D3×D411yescharacteristic
786C2×C4C2×D3×D411yescharacteristic
787C2×C4C2×D3×D411yescharacteristic
788C2×C4C2×D3×D411yescharacteristic
789C2×C4C2×D3×Q812yes—
790C2×C4#101012yes—
791C2×C4C24×D311yescharacteristic
792C8—24no—
793C8—32no—
794C8—32no—
795C8—61no—
796C8—61no—
797C2×C3—22no—
798C2×C3—42no—
799C2×C3C2×D4×Q811yescharacteristic
800C2×C3C2×#57711yescharacteristic
801C2×C3C2×#57711yescharacteristic
802D3—42no—
803C22—21no—
804C22—21no—
805C22—22no—
806C22—41no—
807C22—41no—
808C22—62no—
809C22—121no—
810C22—121no—
811C22#563212yes—
812C22C22×D3×D411yescharacteristic
813C4—21no—
814C4—21no—
815C4—22no—
816C4—41no—
817C4—44no—
818C4—41no—
819C4—64no—
820C4—64no—
821C4—62no—
822C4—121no—
823C4—121no—
824C4—124no—
825C4#563212yes—
826C4#577512yes—
827C4#577812yes—
828C4C22×D3×Q811yescharacteristic
829C4C2×#101011yescharacteristic
830C3#6137411yescharacteristic, complemented, Sylow
831C2—22no—
832C2—42no—
833C2—122no—
834C2C2×#563211yescharacteristic
835C2C2×#577511yescharacteristic
836C2C2×#577811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3079C2
socleC22×C3C23×D4
prime radicalC2×#950C22
hypercenter#3079D3
hypocenterC3#61374
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3079

Complements

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

NH ≅ G/Ntype
1. #86215C2semidirect
2. #85828C2semidirect
3. C3×#3079C2semidirect
4. C2×#5080C2semidirect
6. #81136C2semidirect
7. #81104C2semidirect
8. #81089C2semidirect
9. #81053C2semidirect
10. #81043C2semidirect
11. #81039C2semidirect
12. #80959C2semidirect
13. #80958C2semidirect
14. #79244C2semidirect
15. #79205C2semidirect
16. #79060C2semidirect
17. #79044C2semidirect
18. #78873C2semidirect
117. #3079D3semidirect
144. #950Q8semidirect
332. C3×#41C2×Q8semidirect
351. #235C2×Q8semidirect
389. #216C2×Q8semidirect
390. #215C2×Q8semidirect
391. #214C2×Q8semidirect
392. #213C2×Q8semidirect
425. C2×C3⋊C8C2×Q8semidirect
618. #41D3×Q8semidirect
830. C3#61374semidirect

Maximal subgroups

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

subgroupindex
#862152
#858282
C3×#30792
C2×#50802
C4×#9502
#811362
#811042
#810892
#810532
#810432
#810392
#809592
#809582
#792442
#792052
#790602
#790442
#788732
#788692
#613743