Finite Group Databasebeta

← #11675758

Subgroups — #11675758

Order 768.

2010 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86277C211yesmaximal, characteristic, complemented
2C2×D4×Dic6C211yesmaximal, characteristic, complemented
3C3×#3077C211yesmaximal, characteristic, complemented
4#83341C211yesmaximal, characteristic, complemented
5C4×#932C211yesmaximal, characteristic
6#81159C214yesmaximal, complemented
7#81158C214yesmaximal, complemented
8#81089C212yesmaximal, complemented
9#81053C212yesmaximal, complemented
10#80961C212yesmaximal, complemented
11#80957C212yesmaximal, complemented
12#79240C212yesmaximal, complemented
13#79203C212yesmaximal, complemented
14#79060C211yesmaximal, characteristic, complemented
15#79046C211yesmaximal, characteristic, complemented
16#78917C212yesmaximal, complemented
17#78914C212yesmaximal
18Q8×AGL(1,ℤ/8)—31nomaximal, Sylow
19C23×Dic6—21no—
20C3×#533C2211yescharacteristic
21C2×C3×C4×D4C2211yescharacteristic
22C2×D4×Dic3C2212yes—
23C2×#932C2211yescharacteristic
24C2×#924—21no—
25#5730C2211yescharacteristic, complemented
26#5727C2211yescharacteristic, complemented
27#5722C2211yescharacteristic, complemented
28#5721C2211yescharacteristic, complemented
29#5690C2212yescomplemented
30#5685C2212yescomplemented
31#5636—22no—
32#5635—21no—
33#5632—21no—
34#5578—22no—
35#5578—21no—
36C4×D3×Q8—21no—
37D4×Dic6—21no—
38D4×Dic6—22no—
39D4×Dic6—21no—
40D4×Dic6C2214yes—
41D4×Dic6C2212yes—
42D4×Dic6C2212yes—
43#5522C2212yes—
44#5517C2212yes—
45C2×#888C2212yes—
46C2×#878—22no—
47C4×#235C2211yescharacteristic
48C2×#869C2211yescharacteristic
49C2×C4×Dic6C2211yescharacteristic
50C3×#478C2214yes—
51C3×#476C2212yes—
52C3×#474C2212yes—
53C3×#428C2212yes—
54C3×#423C2211yescharacteristic
55C3×#418C2212yes—
56#5215C2211yescharacteristic
57#5133C2212yes—
58#5121C2212yes—
59#5118C2212yes—
60Dic3×M16C2212yes—
61#5080C2212yescomplemented
62#5078C2212yescomplemented
63#5064C2214yescomplemented
64#5018C2212yes—
65C4×#214C2212yes—
66#5014C2212yes—
67C4×#213C2212yes—
68#4995C2212yes—
69#4995C2212yes—
70#4966C2211yescharacteristic
71#4964C2211yescharacteristic
72C4×#208C2211yescharacteristic
73#4890C2214yescomplemented
74#4876C2214yescomplemented
75#4875C2214yescomplemented
76#4874C2214yescomplemented
77#4870C2214yescomplemented
78#4856C2214yescomplemented
79#4855C2214yescomplemented
80#4854C2214yescomplemented
81#4851C2212yescomplemented
82#4850C2212yescomplemented
83#4846C2212yescomplemented
84#4842C2212yescomplemented
85#4831C2212yescomplemented
86#4830C2212yescomplemented
87#4828C2214yescomplemented
88#4785C2214yes—
89#4766C2214yes—
90#4763C2214yes—
91#4761C2214yes—
92#4759C2214yes—
93#4758C2214yes—
94#4757C2214yes—
95#4756C2214yes—
96Q8×#41—31no—
97C2×D4×Q8—31no—
98#3386—34no—
99#3386—32no—
100#3384—34no—
101#3384—32no—
102Q8×SD16—32no—
103Q8×D8—32no—
104#3165—32no—
105#3165—31no—
106#3079—32no—
107#3079—31no—
108#3077—32no—
109#3077D311yescharacteristic, complemented
110Q8×M16—31no—
111C4×AGL(1,ℤ/8)—32no—
112C4×AGL(1,ℤ/8)—31no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C23×Dic3—22no—
116C2×D3×Q8—21no—
117C2×#235C2311yescharacteristic
118C22×Dic6—21no—
119C22×Dic6—22no—
120C22×Dic6—24no—
121C22×Dic6—22no—
122C22×Dic6—22no—
123C22×Dic6—48no—
124C22×Dic6D411yescharacteristic
125C2×C3×M16C2312yes—
126C3×C4⋊Q8C2311yescharacteristic
127C3×C4⋊Q8C2311yescharacteristic
128C3×#125C2312yes—
129C3×C22⋊Q8—21no—
130C3×C22⋊Q8—21no—
131C3×C4×Q8—21no—
132C3×C4×Q8—21no—
133C3×C4×D4—21no—
134C3×C4×D4—21no—
135C3×C4×D4C2312yes—
136C3×C4×D4C2312yes—
137C3×#117C2312yes—
138C2×C3×C4⋊C4C2311yescharacteristic
139C2×C3×C22⋊C4—21no—
140C2×C3×C42C2311yescharacteristic
141C2×#217—22no—
142#946—21no—
143#946—22no—
144Q8×Dic3—21no—
145#944—21no—
146#944—22no—
147D4×Dic3—22no—
148D4×Dic3—22no—
149D4×Dic3C2314yes—
150D4×Dic3C2314yes—
151C2×#214C2312yes—
152#932Q818yescomplemented
153C2×#213C2312yes—
154C4×#67—21no—
155C4×#67—21no—
156#926C2311yescharacteristic
157C2×C4⋊Dic3—21no—
158C2×C4⋊Dic3D411yescharacteristic
159C2×C4⋊Dic3C2312yes—
160#924—22no—
161#924—24no—
162#924—22no—
163C2×Dic3⋊C4—22no—
164C2×Dic3⋊C4D412yes—
165C2×C4×Dic3C2312yes—
166C2×#208C2311yescharacteristic
167C2×#208C2311yescharacteristic
168#897—21no—
169#897—22no—
170#896—22no—
171#896—22no—
172#896—22no—
173#893C2312yes—
174#893C2312yes—
175D3×C4⋊C4—21no—
176D3×C4⋊C4—22no—
177#890C2312yes—
178#890C2312yes—
179#889—22no—
180#889—22no—
181#889—22no—
182#888—22no—
183#888—21no—
184#888—22no—
185#888—22no—
186#888C2314yes—
187#888C2312yes—
188#888C2314yes—
189#888C2312yes—
190#887—21no—
191#887—22no—
192#887C2312yes—
193#887C2312yes—
194#67⋊C4—22no—
195#67⋊C4—22no—
196#878—22no—
197#878—22no—
198#878—24no—
199#878—24no—
200#878—24no—
201#878—24no—
202C4×D12C2311yescharacteristic
203C4×D12C2311yescharacteristic
204#872—21no—
205#872—22no—
206C42×D3—21no—
207C42×D3—22no—
208#869—21no—
209#869—21no—
210#869C2312yes—
211#869C2312yes—
212C4×Dic6—22no—
213C4×Dic6—22no—
214C4×Dic6D411yescharacteristic
215C4×Dic6D412yes—
216C4×Dic6D411yescharacteristic
217C4×Dic6C2311yescharacteristic
218C4×Dic6C2311yescharacteristic
219C4×Dic6C2312yes—
220C4×Dic6C2311yescharacteristic
221C4×Dic6C2311yescharacteristic
222C3×#107C2314yes—
223C3×#106C2314yes—
224C3×C4⋊C8C2312yes—
225C3×C4⋊C8C2312yes—
226C3×#102C2314yes—
227C3×#102C2314yes—
228#832C2312yes—
229#832C2312yes—
230#821C2314yes—
231#818C2314yes—
232#817C2314yes—
233#816C2314yes—
234#815C2314yes—
235Dic3⋊C8C2314yes—
236Dic3⋊C8C2314yes—
237C8×Dic3C2314yes—
238#810C2312yes—
239#809C2312yes—
240#808C2314yes—
241#808C2312yes—
242#808C2314yes—
243#807C2312yes—
244#807C2314yes—
245#807C2314yes—
246#803C2312yes—
247C4×C3⋊C8C2312yes—
248C23×Q8—61no—
249C2×AGL(1,ℤ/8)—31no—
250Q82—31no—
251#557—31no—
252#557—32no—
253#554—31no—
254#554—32no—
255#554—61no—
256#554—62no—
257D4×Q8—31no—
258D4×Q8—32no—
259D4×Q8—34no—
260D4×Q8—32no—
261D4×Q8—61no—
262D4×Q8—61no—
263D4×Q8—62no—
264D4×Q8—61no—
265#533—32no—
266#533—62no—
267#533—61no—
268#533C2×D311yescharacteristic
269C2×C4⋊Q8—32no—
270C2×C4⋊Q8—31no—
271C2×C22⋊Q8—62no—
272C2×C22⋊Q8—61no—
273C4×#41—32no—
274C4×#41—31no—
275C2×C4×Q8—31no—
276C2×C4×Q8—61no—
277C2×C4×D4—32no—
278C2×C4×D4C2×D311yescharacteristic
279#501—34no—
280#501—34no—
281#501—34no—
282#500—32no—
283#500—34no—
284#498—32no—
285#498—34no—
286#478—34no—
287#478—34no—
288#478C2×D314yes—
289#477—34no—
290#477—32no—
291#476—34no—
292#476—32no—
293#476—34no—
294#476C2×D312yes—
295#475—34no—
296#475—32no—
297#474—34no—
298#474—32no—
299#474—34no—
300#474C2×D312yes—
301#446—34no—
302#446—32no—
303C8×Q8—32no—
304#442—32no—
305#442—34no—
306#440—32no—
307#440—34no—
308C4×SD16—32no—
309C4×SD16—34no—
310C4×D8—32no—
311C4×D8—34no—
312#428—32no—
313#428—32no—
314#428—32no—
315#428—31no—
316#428C2×D312yes—
317#423—32no—
318#423C2×D311yescharacteristic
319#418—31no—
320#418C2×D312yes—
321#417—32no—
322#417—31no—
323C4×M16—32no—
324C4×M16—31no—
325C24×C3—21no—
326C2×C3×Q8—21no—
327C2×C3×Q8—21no—
328C2×C3×D4—21no—
329C2×C3×D4—22no—
330C2×C3×D4C2×Q814yescomplemented
331C2×C3×D4C2412yes—
332C22×C3×C4—21no—
333C22×C3×C4—22no—
334C22×C3×C4—22no—
335C22×C3×C4—44no—
336C22×C3×C4C2×D411yescharacteristic
337C22×C3×C4C2×D411yescharacteristic
338C22×C3×C4C2411yescharacteristic
339C2×#67—21no—
340C22×Dic3—22no—
341C22×Dic3—24no—
342C22×Dic3—24no—
343C22×Dic3—48no—
344C22×Dic3C2×D412yes—
345C22×Dic3C2×D412yes—
346D3×Q8—44no—
347#235—22no—
348#235C2×Q814yescomplemented
349C2×D12C2411yescharacteristic
350C2×C4×D3—21no—
351C2×C4×D3—21no—
352C2×C4×D3—22no—
353C2×C4×D3—21no—
354C2×C4×D3—22no—
355C2×Dic6—24no—
356C2×Dic6—22no—
357C2×Dic6—22no—
358C2×Dic6—22no—
359C2×Dic6—24no—
360C2×Dic6—24no—
361C2×Dic6—22no—
362C2×Dic6—48no—
363C2×Dic6—416no—
364C2×Dic6—48no—
365C2×Dic6—44no—
366C2×Dic6—48no—
367C2×Dic6C2×D412yes—
368C2×Dic6C2×D411yescharacteristic
369C2×Dic6C2×D411yescharacteristic
370C2×Dic6C2411yescharacteristic
371C3×M16—24no—
372C2×C3×C8C2414yes—
373C3×C4⋊C4—21no—
374C3×C4⋊C4—22no—
375C3×C4⋊C4—21no—
376C3×C4⋊C4—22no—
377C3×C4⋊C4—21no—
378C3×C4⋊C4C2412yes—
379C3×C4⋊C4C2412yes—
380C3×C4⋊C4C2412yes—
381C3×C22⋊C4—22no—
382C3×C22⋊C4—22no—
383C3×C22⋊C4—22no—
384C3×C42—22no—
385C3×C42C2×D411yescharacteristic
386C3×C42C2×D411yescharacteristic
387C3×C42C2411yescharacteristic
388C3×C42C2411yescharacteristic
389#217—21no—
390#217—24no—
391#217—24no—
392#214C2×Q818yescomplemented
393#213C2×Q818yescomplemented
394(C2×D3)⋊C4—21no—
395(C2×D3)⋊C4—21no—
396(C2×D3)⋊C4—22no—
397(C2×D3)⋊C4—22no—
398C4⋊Dic3—22no—
399C4⋊Dic3—22no—
400C4⋊Dic3—22no—
401C4⋊Dic3—22no—
402C4⋊Dic3—22no—
403C4⋊Dic3C2×D411yescharacteristic
404C4⋊Dic3C2×D412yes—
405C4⋊Dic3C2×D411yescharacteristic
406C4⋊Dic3C2414yes—
407C4⋊Dic3C2411yescharacteristic
408C4⋊Dic3C2411yescharacteristic
409Dic3⋊C4—21no—
410Dic3⋊C4—21no—
411Dic3⋊C4—22no—
412Dic3⋊C4—22no—
413Dic3⋊C4—22no—
414Dic3⋊C4—22no—
415Dic3⋊C4—22no—
416Dic3⋊C4—22no—
417Dic3⋊C4—24no—
418Dic3⋊C4—24no—
419Dic3⋊C4C2×D412yes—
420Dic3⋊C4C2×D412yes—
421Dic3⋊C4C2×D412yes—
422Dic3⋊C4C2×D412yes—
423C4×Dic3—21no—
424C4×Dic3—21no—
425C4×Dic3—21no—
426C4×Dic3—22no—
427C4×Dic3—22no—
428C4×Dic3C2×D412yes—
429C4×Dic3C2×D412yes—
430C4×Dic3C2412yes—
431C4×Dic3C2412yes—
432#208—22no—
433#208C2×Q814yescomplemented
434C2×C3⋊C8C2412yes—
435C2×C3⋊C8C2412yes—
436C2×#41—31no—
437C22×Q8—31no—
438C22×Q8—62no—
439C22×Q8—62no—
440C22×Q8—64no—
441C22×Q8—62no—
442C22×Q8—61no—
443C22×Q8—61no—
444C22×Q8—128no—
445C22×D4C22×D311yescharacteristic
446C23×C4—21no—
447C23×C4—62no—
448AGL(1,ℤ/8)—38no—
449C2×SD16—32no—
450C2×D8—32no—
451C2×M16—31no—
452C2×M16—31no—
453C2×M16C22×D312yes—
454C4⋊Q8—34no—
455C4⋊Q8—34no—
456C4⋊Q8—32no—
457C4⋊Q8—32no—
458C4⋊Q8—32no—
459C4⋊Q8—32no—
460C4⋊Q8—62no—
461C4⋊Q8—62no—
462C4⋊Q8—61no—
463C4⋊Q8—62no—
464C4⋊Q8—62no—
465C4⋊Q8—61no—
466C4⋊Q8—61no—
467C4⋊Q8—61no—
468C4⋊Q8C22×D311yescharacteristic
469C4⋊Q8C22×D311yescharacteristic
470#125—32no—
471#125—32no—
472#125—62no—
473#125—62no—
474#125—62no—
475#125C22×D312yes—
476C22⋊Q8—21no—
477C22⋊Q8—21no—
478C22⋊Q8—64no—
479C22⋊Q8—64no—
480C22⋊Q8—64no—
481C22⋊Q8—64no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—62no—
485C22⋊Q8—62no—
486C22⋊Q8—62no—
487C22⋊Q8—62no—
488C22⋊Q8—61no—
489C22⋊Q8—62no—
490C22⋊Q8—64no—
491C22⋊Q8—62no—
492C22⋊Q8—61no—
493C22⋊Q8—62no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—31no—
497C4×Q8—32no—
498C4×Q8—31no—
499C4×Q8—31no—
500C4×Q8—32no—
501C4×Q8—31no—
502C4×Q8—32no—
503C4×Q8—32no—
504C4×Q8—31no—
505C4×Q8—31no—
506C4×Q8—62no—
507C4×Q8—62no—
508C4×Q8—62no—
509C4×Q8—61no—
510C4×Q8—61no—
511C4×D4—21no—
512C4×D4—21no—
513C4×D4—34no—
514C4×D4—34no—
515C4×D4—32no—
516C4×D4—32no—
517C4×D4—31no—
518C4×D4—31no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—61no—
524C4×D4—61no—
525C4×D4C22×D312yes—
526C4×D4C22×D312yes—
527#117—31no—
528#117—62no—
529#117—61no—
530#117C22×D312yes—
531C2×C4⋊C4—32no—
532C2×C4⋊C4—31no—
533C2×C4⋊C4—32no—
534C2×C4⋊C4—62no—
535C2×C4⋊C4—61no—
536C2×C4⋊C4—62no—
537C2×C4⋊C4—61no—
538C2×C4⋊C4C22×D311yescharacteristic
539C2×C22⋊C4—21no—
540C2×C22⋊C4—62no—
541C2×C42—32no—
542C2×C42—62no—
543C2×C42—61no—
544C2×C42C22×D311yescharacteristic
545#107—34no—
546#107—32no—
547#107—34no—
548#107—34no—
549#107C22×D314yes—
550#106—34no—
551#106—32no—
552#106—34no—
553#106—34no—
554#106C22×D314yes—
555C4⋊C8—34no—
556C4⋊C8—34no—
557C4⋊C8C22×D312yes—
558C4⋊C8C22×D312yes—
559#103—34no—
560#103—32no—
561#102—32no—
562#102—32no—
563#102—34no—
564#102—32no—
565#102C22×D314yes—
566#102C22×D314yes—
567#97—34no—
568#97—32no—
569C4×C8—34no—
570C4×C8—32no—
571C23×C3—24no—
572C23×C3—22no—
573C23×C3—42no—
574C23×C3—42no—
575C23×C3C22×D411yescharacteristic
576C22×D3—21no—
577C3×Q8—42no—
578C3×Q8—81no—
579C3×D4—24no—
580C3×D4—22no—
581C3×D4C22×Q814yes—
582C2×C3×C4—22no—
583C2×C3×C4—22no—
584C2×C3×C4—22no—
585C2×C3×C4—22no—
586C2×C3×C4—41no—
587C2×C3×C4—44no—
588C2×C3×C4—42no—
589C2×C3×C4—44no—
590C2×C3×C4C22×D411yescharacteristic
591C2×C3×C4C22×D411yescharacteristic
592C2×C3×C4C22×D411yescharacteristic
593C2×C3×C4C22×D411yescharacteristic
594C2×C3×C4C22×D411yescharacteristic
595C2×C3×C4C22×Q812yes—
596C2×C3×C42−1+412yes—
597C2×C3×C4C2511yescharacteristic
598#67—24no—
599C2×Dic3—21no—
600C2×Dic3—24no—
601C2×Dic3—21no—
602C2×Dic3—21no—
603C2×Dic3—24no—
604C2×Dic3—42no—
605C2×Dic3—48no—
606C2×Dic3—44no—
607C2×Dic3—48no—
608C2×Dic3C22×D412yes—
609C2×Dic3C22×D412yes—
610C2×Dic3C22×D412yes—
611C2×Dic3C22×D412yes—
612D12—21no—
613D12C22×Q812yescomplemented
614C4×D3—24no—
615C4×D3—42no—
616C4×D3—44no—
617C4×D3—82no—
618C4×D3—81no—
619Dic6—22no—
620Dic6—21no—
621Dic6—24no—
622Dic6—48no—
623Dic6—44no—
624Dic6—44no—
625Dic6—48no—
626Dic6—44no—
627Dic6—82no—
628Dic6AGL(1,ℤ/8)14yescomplemented
629Dic6C22×Q812yescomplemented
630C3×C8—24no—
631C3⋊C8—22no—
632C3⋊C8C22×Q814yescomplemented
633C24—21no—
634#41—34no—
635#41—62no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—31no—
639C2×Q8—32no—
640C2×Q8—31no—
641C2×Q8—31no—
642C2×Q8—62no—
643C2×Q8—64no—
644C2×Q8—64no—
645C2×Q8—62no—
646C2×Q8—64no—
647C2×Q8—62no—
648C2×Q8—62no—
649C2×Q8—124no—
650C2×Q8—128no—
651C2×Q8—128no—
652C2×Q8—1216no—
653C2×Q8—128no—
654C2×Q8—124no—
655C2×D4—21no—
656C2×D4—22no—
657C2×D4—31no—
658C2×D4—61no—
659C2×D4D3×Q814yescomplemented
660C2×D4C23×D312yes—
661C22×C4—21no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—32no—
665C22×C4—32no—
666C22×C4—44no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—64no—
670C22×C4—64no—
671C22×C4—61no—
672C22×C4—62no—
673C22×C4—61no—
674C22×C4—61no—
675C22×C4—128no—
676C22×C4D3×D411yescharacteristic
677C22×C4D3×D411yescharacteristic
678C22×C4C23×D311yescharacteristic
679SD16—38no—
680D8—38no—
681M16—24no—
682M16—34no—
683M16—62no—
684C2×C8—32no—
685C2×C8—32no—
686C2×C8C23×D314yes—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—22no—
692C4⋊C4—32no—
693C4⋊C4—31no—
694C4⋊C4—32no—
695C4⋊C4—32no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—31no—
699C4⋊C4—31no—
700C4⋊C4—31no—
701C4⋊C4—34no—
702C4⋊C4—62no—
703C4⋊C4—62no—
704C4⋊C4—62no—
705C4⋊C4—64no—
706C4⋊C4—64no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C4⋊C4—62no—
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—62no—
715C4⋊C4—61no—
716C4⋊C4—61no—
717C4⋊C4C23×D312yes—
718C4⋊C4C23×D312yes—
719C4⋊C4C23×D312yes—
720C22⋊C4—22no—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—64no—
726C22⋊C4—64no—
727C22⋊C4—61no—
728C22⋊C4—61no—
729C22⋊C4—61no—
730C42—22no—
731C42—32no—
732C42—32no—
733C42—32no—
734C42—32no—
735C42—62no—
736C42—62no—
737C42—61no—
738C42—61no—
739C42—61no—
740C42D3×D411yescharacteristic
741C42D3×D411yescharacteristic
742C42C23×D311yescharacteristic
743C42C23×D311yescharacteristic
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—24no—
747C22×C3—48no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3D4×Q812yes—
751C22×C3C23×D411yescharacteristic
752C2×D3—22no—
753C2×D3—41no—
754C2×D3—41no—
755C3×C4—21no—
756C3×C4—21no—
757C3×C4—21no—
758C3×C4—42no—
759C3×C4—42no—
760C3×C4—42no—
761C3×C4D4×Q812yes—
762C3×C4C2×AGL(1,ℤ/8)12yes—
763C3×C4C23×Q811yescharacteristic
764C3×C4C2×2−1+411yescharacteristic
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—41no—
770Dic3—44no—
771Dic3—41no—
772Dic3C2×AGL(1,ℤ/8)14yes—
773C23—24no—
774C23—22no—
775C23—42no—
776C23—42no—
777C23—61no—
778C23C2×D3×D411yescharacteristic
779Q8—34no—
780Q8—32no—
781Q8—42no—
782Q8—64no—
783Q8—61no—
784Q8—62no—
785Q8—81no—
786Q8—124no—
787Q8—128no—
788Q8—124no—
789Q8—128no—
790Q8—124no—
791Q8—242no—
792D4—24no—
793D4—22no—
794D4—32no—
795D4—64no—
796D4—61no—
797D4C2×D3×Q814yes—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—32no—
803C2×C4—32no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—41no—
807C2×C4—44no—
808C2×C4—42no—
809C2×C4—44no—
810C2×C4—64no—
811C2×C4—61no—
812C2×C4—64no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—64no—
816C2×C4—124no—
817C2×C4—128no—
818C2×C4—122no—
819C2×C4—128no—
820C2×C4—124no—
821C2×C4—122no—
822C2×C4—241no—
823C2×C4—242no—
824C2×C4C2×D3×D411yescharacteristic
825C2×C4C2×D3×D411yescharacteristic
826C2×C4C2×D3×D411yescharacteristic
827C2×C4C2×D3×D411yescharacteristic
828C2×C4C2×D3×D411yescharacteristic
829C2×C4C2×D3×Q812yes—
830C2×C4#101012yes—
831C2×C4C24×D311yescharacteristic
832C8—24no—
833C8—34no—
834C8—62no—
835C2×C3—22no—
836C2×C3—44no—
837C2×C3C2×D4×Q811yescharacteristic
838C2×C3C22×AGL(1,ℤ/8)11yescharacteristic
839C2×C3#358611yescharacteristic
840D3—42no—
841C22—21no—
842C22—21no—
843C22—24no—
844C22—48no—
845C22—42no—
846C22—42no—
847C22—62no—
848C22—121no—
849C22—121no—
850C22#563212yes—
851C22C22×D3×D411yescharacteristic
852C4—21no—
853C4—21no—
854C4—21no—
855C4—34no—
856C4—42no—
857C4—42no—
858C4—42no—
859C4—62no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—124no—
864C4—121no—
865C4—121no—
866C4#563212yes—
867C4D3×AGL(1,ℤ/8)12yes—
868C4C22×D3×Q811yescharacteristic
869C4C2×#101011yescharacteristic
870C3Q8×AGL(1,ℤ/8)11yescharacteristic, complemented, Sylow
871C2—22no—
872C2—44no—
873C2—122no—
874C2C2×#563211yescharacteristic
875C2C2×D3×AGL(1,ℤ/8)11yescharacteristic
876C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3077C2
socleC22×C3C23×D4
prime radicalC2×#932C22
hypercenter#3077D3
hypocenterC3Q8×AGL(1,ℤ/8)
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3077

Complements

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

NH ≅ G/Ntype
1. #86277C2semidirect
2. C2×D4×Dic6C2semidirect
3. C3×#3077C2semidirect
4. #83341C2semidirect
6. #81159C2semidirect
7. #81158C2semidirect
8. #81089C2semidirect
9. #81053C2semidirect
10. #80961C2semidirect
11. #80957C2semidirect
12. #79240C2semidirect
13. #79203C2semidirect
14. #79060C2semidirect
15. #79046C2semidirect
16. #78917C2semidirect
25. #5730C22semidirect
26. #5727C22semidirect
27. #5722C22semidirect
28. #5721C22semidirect
29. #5690C22semidirect
30. #5685C22semidirect
61. #5080C22semidirect
62. #5078C22semidirect
63. #5064C22semidirect
73. #4890C22semidirect
74. #4876C22semidirect
75. #4875C22semidirect
76. #4874C22semidirect
77. #4870C22semidirect
78. #4856C22semidirect
79. #4855C22semidirect
80. #4854C22semidirect
81. #4851C22semidirect
82. #4850C22semidirect
83. #4846C22semidirect
84. #4842C22semidirect
85. #4831C22semidirect
86. #4830C22semidirect
87. #4828C22semidirect
109. #3077D3semidirect
152. #932Q8semidirect
330. C2×C3×D4C2×Q8semidirect
348. #235C2×Q8semidirect
392. #214C2×Q8semidirect
393. #213C2×Q8semidirect
433. #208C2×Q8semidirect
613. D12C22×Q8semidirect
628. Dic6AGL(1,ℤ/8)semidirect
629. Dic6C22×Q8semidirect
632. C3⋊C8C22×Q8semidirect
659. C2×D4D3×Q8semidirect
870. C3Q8×AGL(1,ℤ/8)semidirect

Maximal subgroups

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

subgroupindex
#862772
C2×D4×Dic62
C3×#30772
#833412
C4×#9322
#811592
#811582
#810892
#810532
#809612
#809572
#792402
#792032
#790602
#790462
#789172
#789142
Q8×AGL(1,ℤ/8)3