Finite Group Databasebeta

← #11664169

Subgroups — #11664169

Order 768.

2074 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86204C211yesmaximal, characteristic, complemented
2C4×#1009C211yesmaximal, characteristic
3C3×#3039C211yesmaximal, characteristic, complemented
4#83982C212yesmaximal
5#83965C212yesmaximal, complemented
6C2×#5083C211yesmaximal, characteristic, complemented
7#82507C211yesmaximal, characteristic, complemented
8#80460C214yesmaximal, complemented
9#80459C212yesmaximal, complemented
10#80457C212yesmaximal, complemented
11#80413C214yesmaximal, complemented
12#80410C212yesmaximal, complemented
13#80408C212yesmaximal, complemented
14#79059C211yesmaximal, characteristic, complemented
15#79040C211yesmaximal, characteristic, complemented
16#78951C212yesmaximal, complemented
17#78947C212yesmaximal, complemented
18#60591—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C2×C3×#137C2212yes—
21C2×C3×C4⋊Q8C2211yescharacteristic, complemented
22C3×C4×#41C2211yescharacteristic
23#5827C2211yescharacteristic
24#5816C2212yes—
25#5812C2212yescomplemented
26C22×#215C2212yes—
27#5732—21no—
28#5732—21no—
29#5731C2214yescomplemented
30#5728C2212yescomplemented
31#5728C2212yescomplemented
32#5721—21no—
33#5721—21no—
34#5574C2212yes—
35C4×#239C2212yes—
36#5545—22no—
37#5545C2212yes—
38C4×D3×D4—22no—
39C4×D3×D4C2212yes—
40#5523—21no—
41#5523C2211yescharacteristic
42#5521—21no—
43#5521C2211yescharacteristic
44#5513—22no—
45#5513—22no—
46C4×#235—21no—
47C4×#235C2211yescharacteristic
48C2×C4×D12—21no—
49C2×C4×D12C2211yescharacteristic
50#5470C2211yescharacteristic, complemented
51C3×#462C2212yescomplemented
52C3×#462C2212yescomplemented
53C3×#461C2212yescomplemented
54C3×#461C2212yescomplemented
55C3×#423C2211yescharacteristic, complemented
56C3×#419C2212yescomplemented
57#5233C2212yes—
58C2×#835C2212yescomplemented
59#5187C2214yes—
60#5187C2214yes—
61#5184C2214yescomplemented
62Dic3×Q16C2214yescomplemented
63#5169C2214yes—
64#5169C2214yes—
65#5164C2214yescomplemented
66Dic3×SD16C2214yescomplemented
67#5131C2212yes—
68#5129C2212yes—
69#5122C2212yescomplemented
70#5121C2212yescomplemented
71#5083C2212yescomplemented
72#5083C2212yescomplemented
73#5083C2214yescomplemented
74#5022C2212yescomplemented
75#5021C2211yescharacteristic, complemented
76#5020C2211yescharacteristic, complemented
77#5009C2212yescomplemented
78#5008C2211yescharacteristic, complemented
79#5007C2211yescharacteristic, complemented
80#4998C2212yescomplemented
81C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
82#4847C2214yescomplemented
83#4846C2212yescomplemented
84#4842C2212yescomplemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4817C2214yescomplemented
89#4817C2214yescomplemented
90#4815C2214yescomplemented
91#4814C2214yescomplemented
92#4811C2214yescomplemented
93#4805C2214yescomplemented
94#4788C2214yescomplemented
95#4788C2214yescomplemented
96#3509—31no—
97C4×H(5,𝔽2)—31no—
98#3123—34no—
99#3120—34no—
100#3116—32no—
101#3110—32no—
102#3107—32no—
103#3101—32no—
104#3097—32no—
105#3077—31no—
106#3076—31no—
107#3039D311yescharacteristic, complemented
108C2×#461—31no—
109#3009—32no—
110#2949—32no—
111#2947—32no—
112#2925—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8C2312yes—
115#1009—24no—
116#1009—24no—
117C2×#239C2312yes—
118C2×D3×D4—22no—
119C2×D3×D4C2312yes—
120C2×#235—21no—
121C2×#235C2311yescharacteristic
122C22×D12—21no—
123C22×D12C2311yescharacteristic
124C22×C4×D3—21no—
125C22×C4×D3—22no—
126C3×#137—28no—
127C2×C3×Q16C2314yes—
128C2×C3×SD16C2314yes—
129C2×C3×M16C2312yes—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8—21no—
132C3×C4⋊Q8C2312yes—
133C3×C4⋊Q8C2312yes—
134C3×C4×Q8C2311yescharacteristic
135C3×C4×Q8C2311yescharacteristic
136C3×C4×D4—21no—
137C3×C4×D4—21no—
138C3×C4×D4C2311yescharacteristic
139C3×C4×D4C2311yescharacteristic
140C3×#117—21no—
141C3×#117C2311yescharacteristic
142C2×C3×C4⋊C4—21no—
143C2×C3×C4⋊C4—21no—
144C2×C3×C42—21no—
145C2×C3×C42C2311yescharacteristic
146#947—22no—
147#946C2314yes—
148#946C2314yes—
149Q8×Dic3—22no—
150Q8×Dic3—22no—
151Q8×Dic3C2314yes—
152Q8×Dic3C2314yes—
153Q8×Dic3C2312yes—
154#944—22no—
155C2×#215—28no—
156C2×#215C2314yes—
157C2×#215C2314yes—
158D4×Dic3—22no—
159D4×Dic3C2312yes—
160#929—24no—
161C4×#67—22no—
162C4×#67—22no—
163C4×#67D412yes—
164C4×#67D412yes—
165C2×(C2×D3)⋊C4—21no—
166C2×(C2×D3)⋊C4—22no—
167#926—24no—
168#926—21no—
169#926C2312yes—
170#926C2311yescharacteristic
171C2×C4⋊Dic3—21no—
172C2×C4⋊Dic3C2311yescharacteristic
173#924—21no—
174#924—21no—
175C22×C3⋊C8C2312yes—
176#898—24no—
177#898—24no—
178#897—22no—
179#897—22no—
180#893—22no—
181#893—22no—
182#893C2312yes—
183#893C2312yes—
184#892—22no—
185#892—22no—
186#892—22no—
187#892C2312yes—
188D3×C4⋊C4—22no—
189D3×C4⋊C4C2312yes—
190#890—22no—
191#890—22no—
192#889—24no—
193#889—24no—
194#887—22no—
195#887—22no—
196#67⋊C4—22no—
197#67⋊C4—22no—
198#67⋊C4—22no—
199D3×C22⋊C4—22no—
200D3×C22⋊C4—22no—
201D3×C22⋊C4—22no—
202C4×D12—21no—
203C4×D12—22no—
204C4×D12—21no—
205C4×D12—21no—
206C4×D12—22no—
207C4×D12—21no—
208C4×D12—21no—
209C4×D12D411yescharacteristic
210C4×D12D411yescharacteristic
211C4×D12C2312yes—
212C4×D12C2312yes—
213#872—22no—
214#872C2312yes—
215C42×D3—22no—
216C42×D3C2312yes—
217#870C2312yes—
218#869C2311yescharacteristic
219#869C2311yescharacteristic
220C4×Dic6—21no—
221C4×Dic6—21no—
222C4×Dic6—21no—
223C4×Dic6D411yescharacteristic
224C4×Dic6D411yescharacteristic
225C3×C4⋊C8C2312yes—
226C3×C4⋊C8C2312yes—
227C3×#103C2314yes—
228C3×#103C2314yes—
229#835C2314yes—
230#835C2314yes—
231#835C2312yes—
232#835C2312yes—
233#832C2312yes—
234#832C2312yes—
235#821C2314yes—
236#821C2314yes—
237(C2×D3)⋊C8C2314yes—
238(C2×D3)⋊C8C2314yes—
239#818C2314yes—
240#817C2314yes—
241#815C2314yes—
242C8×Dic3C2314yes—
243#808C2312yes—
244#808C2312yes—
245#807C2312yes—
246#807C2312yes—
247C4⋊(C3⋊C8)C2311yescharacteristic
248C4⋊(C3⋊C8)C2311yescharacteristic
249C4⋊(C3⋊C8)C2312yes—
250C2×H(5,𝔽2)—31no—
251C2×#137C2×D312yes—
252C22×SD16—32no—
253#557—61no—
254#557—61no—
255#556—61no—
256#556—61no—
257#552—62no—
258#552—62no—
259#541—34no—
260#536—32no—
261#533—32no—
262#533—32no—
263#533—31no—
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
265#520—31no—
266#520—31no—
267#520—32no—
268#520—61no—
269#519—32no—
270#518—32no—
271#518—31no—
272#518—61no—
273#518—62no—
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—61no—
277C4×#41C2×D311yescharacteristic
278C2×C4×D4—32no—
279C2×C4×D4—31no—
280C2×C4×D4—61no—
281C2×C4×D4—62no—
282#485—34no—
283#485—34no—
284#484—34no—
285#483—34no—
286#479—32no—
287#478—32no—
288#478—34no—
289#477—31no—
290#476—31no—
291#476—32no—
292#475—31no—
293#474—31no—
294#474—32no—
295#462C2×D312yescomplemented
296#462C2×D312yescomplemented
297#461—32no—
298#461—32no—
299#461—34no—
300#461C2×D312yescomplemented
301#461C2×D312yescomplemented
302#452—34no—
303#452—34no—
304#450—34no—
305#450—34no—
306#441—34no—
307#440—34no—
308#440—34no—
309#440—34no—
310C4×Q16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×SD16—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423C2×D311yescharacteristic, complemented
320C2×C4⋊C8—31no—
321#419C2×D312yescomplemented
322#418—32no—
323#416—32no—
324C2×#103—32no—
325#408—32no—
326#405—32no—
327C23×D3—21no—
328C23×D3—22no—
329C3×#41—22no—
330C3×#41#4114yes—
331C2×C3×Q8—22no—
332C2×C3×Q8—24no—
333C2×C3×Q8—24no—
334C2×C3×Q8C2414yes—
335C2×C3×Q8C2411yescharacteristic
336C2×C3×D4—21no—
337C2×C3×D4C2411yescharacteristic
338C22×C3×C4—21no—
339C22×C3×C4—22no—
340C22×C3×C4—21no—
341C22×C3×C4—21no—
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2×D411yescharacteristic
344C22×C3×C4C2411yescharacteristic
345C2×#67—22no—
346C2×#67C2×D412yes—
347C22×Dic3—21no—
348C22×Dic3—22no—
349#239—24no—
350#239—24no—
351D3×D4—216no—
352D3×D4—24no—
353D3×D4—24no—
354#235—28no—
355#235—22no—
356#235—22no—
357C2×D12—28no—
358C2×D12—22no—
359C2×D12—21no—
360C2×D12—22no—
361C2×D12C2×D411yescharacteristic
362C2×D12#4114yes—
363C2×D12C2412yes—
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—22no—
370C2×C4×D3—84no—
371C2×C4×D3—82no—
372C2×C4×D3C2×D412yes—
373C2×C4×D3C2×D412yes—
374C2×C4×D3C2412yes—
375C2×Dic6—21no—
376C2×Dic6—21no—
377C2×Dic6C2×D411yescharacteristic
378C3×Q16—28no—
379C3×SD16—28no—
380C3×M16—24no—
381C2×C3×C8C2414yes—
382C3×C4⋊C4—22no—
383C3×C4⋊C4—22no—
384C3×C4⋊C4—22no—
385C3×C4⋊C4—22no—
386C3×C4⋊C4—21no—
387C3×C4⋊C4—21no—
388C3×C4⋊C4C2411yescharacteristic
389C3×C4⋊C4C2411yescharacteristic
390C3×C22⋊C4—21no—
391C3×C22⋊C4—21no—
392C3×C22⋊C4—21no—
393C3×C42—21no—
394C3×C42—21no—
395C3×C42—21no—
396C3×C42C2×D411yescharacteristic
397C3×C42C2×D411yescharacteristic
398C3×C42C2411yescharacteristic
399C3×C42C2411yescharacteristic
400#217—22no—
401#217—22no—
402#217C2×D412yes—
403#215—28no—
404#215—28no—
405(C2×D3)⋊C4—22no—
406(C2×D3)⋊C4—24no—
407(C2×D3)⋊C4—24no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4C2×D412yes—
413(C2×D3)⋊C4C2×D412yes—
414C4⋊Dic3—21no—
415C4⋊Dic3—21no—
416C4⋊Dic3—21no—
417C4⋊Dic3—22no—
418C4⋊Dic3—24no—
419C4⋊Dic3—24no—
420C4⋊Dic3C2×D411yescharacteristic
421C4⋊Dic3C2×D411yescharacteristic
422C4⋊Dic3C2412yes—
423C4⋊Dic3C2412yes—
424C4⋊Dic3C2412yes—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—22no—
428Dic3⋊C4—24no—
429Dic3⋊C4—24no—
430Dic3⋊C4C2×D412yes—
431Dic3⋊C4C2×D412yes—
432C4×Dic3—22no—
433C4×Dic3—22no—
434C4×Dic3—22no—
435C4×Dic3—24no—
436C4×Dic3—24no—
437C4×Dic3C2×D412yes—
438C4×Dic3C2×D412yes—
439C4×Dic3C2412yes—
440C2×C3⋊C8—24no—
441C2×C3⋊C8C2412yes—
442C2×C3⋊C8C2412yes—
443H(5,𝔽2)—64no—
444H(5,𝔽2)—64no—
445C2×#41—31no—
446C2×#41—32no—
447C2×#41—61no—
448C2×#41C22×D311yescharacteristic
449C22×Q8C22×D312yes—
450C22×D4—32no—
451C22×D4—31no—
452C22×D4—61no—
453C22×D4—62no—
454C23×C4—62no—
455C23×C4—61no—
456#137—28no—
457C2×Q16C22×D314yes—
458C2×SD16—34no—
459C2×SD16—34no—
460C2×SD16—68no—
461C2×SD16C22×D314yes—
462C2×M16C22×D312yes—
463C22×C8—32no—
464C4⋊Q8—21no—
465C4⋊Q8—21no—
466C4⋊Q8—31no—
467C4⋊Q8—31no—
468C4⋊Q8—62no—
469C4⋊Q8C22×D312yes—
470C4⋊Q8C22×D312yes—
471#126—64no—
472#126—64no—
473#125—32no—
474#125—62no—
475#125—62no—
476#125—64no—
477#125—64no—
478#124—62no—
479#123—64no—
480C22⋊Q8—34no—
481C22⋊Q8—34no—
482C22⋊Q8—62no—
483C22⋊Q8—62no—
484C22⋊Q8—61no—
485C22⋊Q8—61no—
486C4×Q8—31no—
487C4×Q8—31no—
488C4×Q8—32no—
489C4×Q8—34no—
490C4×Q8—34no—
491C4×Q8—61no—
492C4×Q8—62no—
493C4×Q8—62no—
494C4×Q8—62no—
495C4×Q8—62no—
496C4×Q8—61no—
497C4×Q8—61no—
498C4×Q8C22×D311yescharacteristic
499C4×Q8C22×D311yescharacteristic
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—32no—
503C4×D4—32no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—31no—
508C4×D4—31no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—62no—
512C4×D4—61no—
513C4×D4—61no—
514C4×D4—62no—
515C4×D4—61no—
516C4×D4—62no—
517C4×D4—62no—
518C4×D4—62no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—61no—
525C4×D4—61no—
526C4×D4C22×D311yescharacteristic
527C4×D4C22×D311yescharacteristic
528#117—21no—
529#117—31no—
530#117—32no—
531#117—32no—
532#117—32no—
533#117—62no—
534#117—62no—
535#117—64no—
536#117—62no—
537#117—62no—
538#117—61no—
539#117C22×D311yescharacteristic
540C2×C4⋊C4—21no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4—31no—
543C2×C4⋊C4—32no—
544C2×C4⋊C4—62no—
545C2×C4⋊C4—61no—
546C2×C22⋊C4—62no—
547C2×C22⋊C4—62no—
548C2×C22⋊C4—62no—
549C2×C22⋊C4—62no—
550C2×C22⋊C4—61no—
551C2×C42—21no—
552C2×C42—32no—
553C2×C42—62no—
554C2×C42C22×D311yescharacteristic
555#107—34no—
556#107—32no—
557#107—32no—
558#106—34no—
559#106—32no—
560#106—32no—
561C4⋊C8—31no—
562C4⋊C8—31no—
563C4⋊C8—32no—
564C4⋊C8C22×D312yes—
565C4⋊C8C22×D312yes—
566#103—34no—
567#103—34no—
568#103—32no—
569#103—32no—
570#103C22×D314yes—
571#103C22×D314yes—
572#102—32no—
573#102—32no—
574#102—34no—
575#102—34no—
576C22⋊C8—34no—
577C22⋊C8—34no—
578#97—34no—
579C4×C8—34no—
580C23×C3—21no—
581C23×C3C22×D411yescharacteristic
582C22×D3—22no—
583C22×D3—28no—
584C22×D3—24no—
585C22×D3—82no—
586C22×D3—82no—
587C22×D3—81no—
588C22×D3—81no—
589C22×D3C22×D412yes—
590C3×Q8—21no—
591C3×Q8—24no—
592C3×Q8—24no—
593C3×Q8—44no—
594C3×Q8C2×#4112yes—
595C3×D4—24no—
596C3×D4—21no—
597C3×D4C2×#4112yes—
598C2×C3×C4—21no—
599C2×C3×C4—24no—
600C2×C3×C4—22no—
601C2×C3×C4—24no—
602C2×C3×C4—21no—
603C2×C3×C4—21no—
604C2×C3×C4—41no—
605C2×C3×C4—44no—
606C2×C3×C4—42no—
607C2×C3×C4—81no—
608C2×C3×C4C22×D411yescharacteristic
609C2×C3×C4C22×D411yescharacteristic
610C2×C3×C4C22×D411yescharacteristic
611C2×C3×C4C22×D411yescharacteristic
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C2×#4112yes—
614C2×C3×C4C2×#4112yes—
615C2×C3×C4C2511yescharacteristic
616#67—28no—
617#67—24no—
618C2×Dic3—22no—
619C2×Dic3—22no—
620C2×Dic3—22no—
621C2×Dic3—82no—
622C2×Dic3—81no—
623C2×Dic3C22×D412yes—
624C2×Dic3C22×D412yes—
625C2×Dic3C22×D412yes—
626D12—28no—
627D12—22no—
628D12—24no—
629D12—22no—
630D12C2×#4114yes—
631C4×D3—28no—
632C4×D3—24no—
633C4×D3—22no—
634C4×D3—22no—
635C4×D3—42no—
636C4×D3—44no—
637C4×D3—82no—
638C4×D3—82no—
639C4×D3—82no—
640C4×D3—82no—
641Dic6—22no—
642Dic6—42no—
643Dic6—42no—
644C3×C8—24no—
645C3⋊C8—22no—
646C3⋊C8—22no—
647C24—62no—
648C24—61no—
649#41—22no—
650#41—68no—
651#41—64no—
652#41—64no—
653#41—62no—
654#41—62no—
655#41#23714yes—
656C2×Q8—22no—
657C2×Q8—24no—
658C2×Q8—24no—
659C2×Q8—31no—
660C2×Q8—61no—
661C2×Q8—61no—
662C2×Q8C23×D314yes—
663C2×Q8C23×D311yescharacteristic
664C2×D4—21no—
665C2×D4—32no—
666C2×D4—31no—
667C2×D4—34no—
668C2×D4—32no—
669C2×D4—62no—
670C2×D4—68no—
671C2×D4—62no—
672C2×D4—64no—
673C2×D4—616no—
674C2×D4—64no—
675C2×D4—61no—
676C2×D4—62no—
677C2×D4C23×D311yescharacteristic
678C22×C4—21no—
679C22×C4—22no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—32no—
683C22×C4—32no—
684C22×C4—32no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—62no—
688C22×C4—62no—
689C22×C4—62no—
690C22×C4—61no—
691C22×C4—62no—
692C22×C4—62no—
693C22×C4—242no—
694C22×C4—244no—
695C22×C4D3×D411yescharacteristic
696C22×C4D3×D411yescharacteristic
697C22×C4C23×D311yescharacteristic
698Q16—28no—
699SD16—28no—
700SD16—68no—
701SD16—68no—
702M16—24no—
703C2×C8—32no—
704C2×C8—32no—
705C2×C8—64no—
706C2×C8C23×D314yes—
707C4⋊C4—22no—
708C4⋊C4—22no—
709C4⋊C4—22no—
710C4⋊C4—22no—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—31no—
714C4⋊C4—32no—
715C4⋊C4—31no—
716C4⋊C4—32no—
717C4⋊C4—32no—
718C4⋊C4—32no—
719C4⋊C4—32no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—64no—
723C4⋊C4—64no—
724C4⋊C4—64no—
725C4⋊C4—64no—
726C4⋊C4—61no—
727C4⋊C4—61no—
728C4⋊C4—61no—
729C4⋊C4—62no—
730C4⋊C4—62no—
731C4⋊C4C23×D311yescharacteristic
732C4⋊C4C23×D311yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—32no—
737C22⋊C4—32no—
738C22⋊C4—32no—
739C22⋊C4—62no—
740C22⋊C4—62no—
741C22⋊C4—62no—
742C22⋊C4—64no—
743C22⋊C4—64no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4—62no—
747C22⋊C4—62no—
748C42—21no—
749C42—21no—
750C42—21no—
751C42—32no—
752C42—32no—
753C42—32no—
754C42—62no—
755C42—62no—
756C42—64no—
757C42—64no—
758C42—62no—
759C42D3×D411yescharacteristic
760C42D3×D411yescharacteristic
761C42C23×D311yescharacteristic
762C42C23×D311yescharacteristic
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—22no—
766C22×C3—41no—
767C22×C3—41no—
768C22×C3#52512yes—
769C22×C3C23×D411yescharacteristic
770C2×D3—22no—
771C2×D3—22no—
772C2×D3—24no—
773C2×D3—22no—
774C2×D3—42no—
775C2×D3—42no—
776C2×D3—84no—
777C2×D3—88no—
778C3×C4—21no—
779C3×C4—21no—
780C3×C4—22no—
781C3×C4—21no—
782C3×C4—41no—
783C3×C4—44no—
784C3×C4—41no—
785C3×C4#52512yes—
786C3×C4#57712yes—
787C3×C4C22×#4111yescharacteristic
788C3×C4C22×#4111yescharacteristic
789Dic3—22no—
790Dic3—22no—
791Dic3—22no—
792Dic3—42no—
793Dic3—42no—
794Dic3—42no—
795C23—21no—
796C23—32no—
797C23—68no—
798C23—62no—
799C23—64no—
800C23—241no—
801C23—241no—
802C23—242no—
803C23—242no—
804C23C2×D3×D411yescharacteristic
805Q8—21no—
806Q8—24no—
807Q8—24no—
808Q8—44no—
809Q8—62no—
810Q8—122no—
811Q8—122no—
812Q8C2×#23712yes—
813D4—24no—
814D4—21no—
815D4—34no—
816D4—68no—
817D4—68no—
818D4—64no—
819D4—62no—
820D4—64no—
821D4—62no—
822D4C2×#23712yes—
823C2×C4—21no—
824C2×C4—22no—
825C2×C4—24no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—24no—
829C2×C4—32no—
830C2×C4—32no—
831C2×C4—32no—
832C2×C4—41no—
833C2×C4—44no—
834C2×C4—42no—
835C2×C4—68no—
836C2×C4—62no—
837C2×C4—62no—
838C2×C4—64no—
839C2×C4—62no—
840C2×C4—62no—
841C2×C4—62no—
842C2×C4—81no—
843C2×C4—122no—
844C2×C4—124no—
845C2×C4—242no—
846C2×C4—242no—
847C2×C4—242no—
848C2×C4—242no—
849C2×C4—242no—
850C2×C4—241no—
851C2×C4C2×D3×D411yescharacteristic
852C2×C4C2×D3×D411yescharacteristic
853C2×C4C2×D3×D411yescharacteristic
854C2×C4C2×D3×D411yescharacteristic
855C2×C4C2×D3×D411yescharacteristic
856C2×C4C2×#23712yes—
857C2×C4D3×#4112yes—
858C2×C4C24×D311yescharacteristic
859C8—24no—
860C8—62no—
861C8—62no—
862C2×C3—22no—
863C2×C3—42no—
864C2×C3C2×#52511yescharacteristic
865C2×C3C2×#57711yescharacteristic
866C2×C3#358611yescharacteristic
867D3—42no—
868D3—44no—
869C22—21no—
870C22—21no—
871C22—22no—
872C22—41no—
873C22—41no—
874C22—62no—
875C22—62no—
876C22—64no—
877C22—62no—
878C22—122no—
879C22—122no—
880C22—244no—
881C22—248no—
882C22#560612yes—
883C22C22×D3×D411yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—22no—
888C4—41no—
889C4—41no—
890C4—44no—
891C4—62no—
892C4—62no—
893C4—62no—
894C4—122no—
895C4—122no—
896C4—122no—
897C4#560612yes—
898C4#577812yes—
899C4C22×#23711yescharacteristic
900C4C2×D3×#4111yescharacteristic
901C3#6059111yescharacteristic, complemented, Sylow
902C2—22no—
903C2—42no—
904C2—122no—
905C2—124no—
906C2C2×#560611yescharacteristic
907C2C2×#577811yescharacteristic
908C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3039C2
socleC22×C3C23×D4
prime radicalC2×#1009C22
hypercenter#3039D3
hypocenterC3#60591
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3039

Complements

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

NH ≅ G/Ntype
1. #86204C2semidirect
3. C3×#3039C2semidirect
5. #83965C2semidirect
6. C2×#5083C2semidirect
7. #82507C2semidirect
8. #80460C2semidirect
9. #80459C2semidirect
10. #80457C2semidirect
11. #80413C2semidirect
12. #80410C2semidirect
13. #80408C2semidirect
14. #79059C2semidirect
15. #79040C2semidirect
16. #78951C2semidirect
17. #78947C2semidirect
21. C2×C3×C4⋊Q8C22semidirect
25. #5812C22semidirect
29. #5731C22semidirect
30. #5728C22semidirect
31. #5728C22semidirect
50. #5470C22semidirect
51. C3×#462C22semidirect
52. C3×#462C22semidirect
53. C3×#461C22semidirect
54. C3×#461C22semidirect
55. C3×#423C22semidirect
56. C3×#419C22semidirect
58. C2×#835C22semidirect
61. #5184C22semidirect
62. Dic3×Q16C22semidirect
65. #5164C22semidirect
66. Dic3×SD16C22semidirect
69. #5122C22semidirect
70. #5121C22semidirect
71. #5083C22semidirect
72. #5083C22semidirect
73. #5083C22semidirect
74. #5022C22semidirect
75. #5021C22semidirect
76. #5020C22semidirect
77. #5009C22semidirect
78. #5008C22semidirect
79. #5007C22semidirect
80. #4998C22semidirect
81. C2×C4⋊(C3⋊C8)C22semidirect
82. #4847C22semidirect
83. #4846C22semidirect
84. #4842C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
88. #4817C22semidirect
89. #4817C22semidirect
90. #4815C22semidirect
91. #4814C22semidirect
92. #4811C22semidirect
93. #4805C22semidirect
94. #4788C22semidirect
95. #4788C22semidirect
107. #3039D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
295. #462C2×D3semidirect
296. #462C2×D3semidirect
300. #461C2×D3semidirect
301. #461C2×D3semidirect
319. #423C2×D3semidirect
321. #419C2×D3semidirect
901. C3#60591semidirect

Maximal subgroups

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

subgroupindex
#862042
C4×#10092
C3×#30392
#839822
#839652
C2×#50832
#825072
#804602
#804592
#804572
#804132
#804102
#804082
#790592
#790402
#789512
#789472
#605913