Finite Group Databasebeta

← #11664287

Subgroups — #11664287

Order 768.

2130 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#86205C211yesmaximal, characteristic, complemented
2C4×#1009C211yesmaximal, characteristic, complemented
3C3×#3079C211yesmaximal, characteristic, complemented
4C2×#5084C211yesmaximal, characteristic, complemented
5#82525C211yesmaximal, characteristic, complemented
6#81095C212yesmaximal, complemented
7#81093C212yesmaximal, complemented
8#81046C212yesmaximal, complemented
9#81044C212yesmaximal, complemented
10#81001C214yesmaximal, complemented
11#80952C214yesmaximal, complemented
12#79222C212yesmaximal, complemented
13#79201C212yesmaximal, complemented
14#79055C211yesmaximal, characteristic, complemented
15#79040C211yesmaximal, characteristic, complemented
16#78886C212yesmaximal, complemented
17#78869C212yesmaximal, complemented
18#60597—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C2×C3×C4⋊Q8C2211yescharacteristic, complemented
21C3×C4×#41C2211yescharacteristic
22#5827C2211yescharacteristic
23C2×#950C2212yes—
24#5817—22no—
25C2×#908C2212yes—
26#5734—21no—
27#5733C2214yescomplemented
28#5732—21no—
29#5730—21no—
30#5728C2212yescomplemented
31#5726—21no—
32#5725C2212yescomplemented
33#5574C2212yes—
34C4×#239C2212yes—
35#5545—22no—
36#5545C2212yes—
37C4×D3×D4—22no—
38C4×D3×D4C2212yes—
39#5523—21no—
40#5523C2211yescharacteristic
41#5521—21no—
42#5521C2211yescharacteristic
43#5514—22no—
44#5510C2212yes—
45#5504C2212yescomplemented
46#5477C2211yescharacteristic, complemented
47C4×#235—21no—
48C4×#235C2211yescharacteristic
49C2×C4×D12—21no—
50C2×C4×D12C2211yescharacteristic
51C3×#477C2212yescomplemented
52C3×#476C2212yescomplemented
53C3×#475C2212yescomplemented
54C3×#474C2212yescomplemented
55C3×#428C2212yescomplemented
56C3×#423C2211yescharacteristic, complemented
57C3×#417C2212yes—
58#5133C2212yescomplemented
59#5129C2212yes—
60#5122C2212yescomplemented
61#5084C2214yescomplemented
62#5084C2212yescomplemented
63#5084C2212yescomplemented
64#5031C2211yescharacteristic, complemented
65#5028C2212yescomplemented
66#5027C2211yescharacteristic, complemented
67#5019C2211yescharacteristic, complemented
68#5016C2212yescomplemented
69#5015C2211yescharacteristic, complemented
70#5002C2212yescomplemented
71C2×#809C2212yes—
72C2×#808C2212yescomplemented
73C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
74#4889C2214yescomplemented
75#4888C2214yescomplemented
76#4885C2214yescomplemented
77#4872C2214yescomplemented
78#4869C2214yescomplemented
79#4863C2214yescomplemented
80#4862C2214yescomplemented
81#4852C2214yescomplemented
82#4844C2214yescomplemented
83#4843C2212yescomplemented
84#4841C2212yescomplemented
85#4840C2214yescomplemented
86#4835C2212yescomplemented
87#4833C2212yescomplemented
88#4810C2214yes—
89#4808C2214yes—
90#4789C2214yescomplemented
91#4788C2214yescomplemented
92#4785C2214yescomplemented
93#4776C2214yes—
94#4773C2214yes—
95#4758C2214yescomplemented
96#3511—31no—
97C4×H(5,𝔽2)—31no—
98#3125—34no—
99#3118—34no—
100#3116—32no—
101#3109—32no—
102#3106—32no—
103#3101—32no—
104#3099—32no—
105#3079D311yescharacteristic, complemented
106C2×#476—31no—
107#3036—31no—
108#3035—31no—
109#3012—32no—
110#2952—32no—
111#2946—32no—
112#2925—31no—
113C2×C3×#41C2311yescharacteristic
114C22×C3×Q8—21no—
115#1009—24no—
116#1009—24no—
117C2×#239—22no—
118C2×#239C2312yes—
119C2×D3×D4—22no—
120C2×D3×D4C2312yes—
121C2×#235—21no—
122C2×#235C2311yescharacteristic
123C2×#235C2312yes—
124C22×D12—21no—
125C22×D12C2311yescharacteristic
126C22×C4×D3—21no—
127C22×C4×D3—22no—
128C2×C3×M16C2312yes—
129C3×C4⋊Q8—21no—
130C3×C4⋊Q8—21no—
131C3×C4⋊Q8C2312yes—
132C3×C4⋊Q8C2312yes—
133C3×C4×Q8C2311yescharacteristic
134C3×C4×Q8C2311yescharacteristic
135C3×C4×D4—21no—
136C3×C4×D4—21no—
137C3×C4×D4C2311yescharacteristic
138C3×C4×D4C2311yescharacteristic
139C3×#117—21no—
140C3×#117C2311yescharacteristic
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4C2312yes—
143C2×C3×C42—21no—
144C2×C3×C42C2311yescharacteristic
145#950—28no—
146#947—24no—
147#947—22no—
148#946—22no—
149#946—24no—
150Q8×Dic3—22no—
151Q8×Dic3C2312yes—
152C2×#216C2312yes—
153C2×#215C2312yes—
154D4×Dic3—22no—
155D4×Dic3C2312yes—
156C2×#214C2312yes—
157C2×#213C2312yes—
158#930—21no—
159#930—21no—
160#930—24no—
161C4×#67—24no—
162C4×#67—22no—
163C4×#67—22no—
164C4×#67D412yes—
165C4×#67D412yes—
166C2×(C2×D3)⋊C4—21no—
167C2×(C2×D3)⋊C4—22no—
168#926—21no—
169#926C2311yescharacteristic
170C2×C4⋊Dic3—21no—
171C2×C4⋊Dic3C2311yescharacteristic
172C22×C3⋊C8C2312yes—
173#908—28no—
174C2×D24C2314yes—
175C2×#204C2314yes—
176#898—24no—
177#897—22no—
178#897C2314yes—
179#895—22no—
180#895—22no—
181#895C2314yes—
182#894—24no—
183#893—22no—
184#893—22no—
185#893—22no—
186#893C2312yes—
187#893C2314yes—
188#893C2312yes—
189#892—22no—
190#892—22no—
191#892—22no—
192#892C2312yes—
193D3×C4⋊C4—22no—
194D3×C4⋊C4—22no—
195D3×C4⋊C4C2312yes—
196#890—22no—
197#887C2314yes—
198#67⋊C4—22no—
199#67⋊C4—22no—
200#67⋊C4—22no—
201D3×C22⋊C4—22no—
202D3×C22⋊C4—22no—
203D3×C22⋊C4—22no—
204#875C2312yes—
205#874C2311yescharacteristic
206C4×D12—21no—
207C4×D12—22no—
208C4×D12—21no—
209C4×D12—21no—
210C4×D12—21no—
211C4×D12—21no—
212C4×D12—22no—
213C4×D12—21no—
214C4×D12—21no—
215C4×D12D411yescharacteristic
216C4×D12D411yescharacteristic
217C4×D12C2312yes—
218C4×D12C2312yes—
219#872—22no—
220#872C2312yes—
221C42×D3—22no—
222C42×D3C2312yes—
223#869C2311yescharacteristic
224C4×Dic6—21no—
225C4×Dic6D411yescharacteristic
226C4×Dic6D411yescharacteristic
227C3×#107C2314yes—
228C3×#106C2314yes—
229C3×C4⋊C8C2312yes—
230C3×C4⋊C8C2312yes—
231C3×#103C2314yes—
232C3×#102C2314yes—
233#821C2314yes—
234(C2×D3)⋊C8C2314yes—
235(C2×D3)⋊C8C2314yes—
236#816C2314yes—
237#815C2314yes—
238C8×Dic3C2314yes—
239#810C2312yes—
240#810C2312yes—
241#809C2312yes—
242#809C2314yes—
243#809C2312yes—
244#809C2314yes—
245#808C2314yes—
246#808C2314yes—
247C4⋊(C3⋊C8)C2311yescharacteristic
248C4⋊(C3⋊C8)C2312yes—
249C4⋊(C3⋊C8)C2311yescharacteristic
250C2×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)—32no—
252C2×#135—32no—
253#556—61no—
254#555—61no—
255#554—61no—
256#553—62no—
257#548—62no—
258#547—61no—
259#542—34no—
260#537—32no—
261#533—32no—
262#532—32no—
263#532—31no—
264C2×C4⋊Q8C2×D311yescharacteristic, complemented
265#520—31no—
266#520—31no—
267#520—32no—
268#520—32no—
269#520—61no—
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#483—34no—
284#482—34no—
285#481—34no—
286#477C2×D312yescomplemented
287#476—32no—
288#476—32no—
289#476—34no—
290#476C2×D312yescomplemented
291#475C2×D312yescomplemented
292#474C2×D312yescomplemented
293#464—32no—
294#463—32no—
295#463—34no—
296#462—31no—
297#461—31no—
298#461—32no—
299#460—31no—
300#459—31no—
301#459—32no—
302#452—34no—
303#450—34no—
304#449—34no—
305#447—34no—
306#442—34no—
307#442—34no—
308#441—34no—
309#440—34no—
310C4×SD16—34no—
311C4×SD16—34no—
312C4×SD16—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428C2×D312yescomplemented
318C2×#106—32no—
319#423C2×D311yescharacteristic, complemented
320C2×C4⋊C8—31no—
321#417—32no—
322#417C2×D312yes—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C23×D3—21no—
328C23×D3—22no—
329C3×#41—22no—
330C3×#41#4114yescomplemented
331C2×C3×Q8—22no—
332C2×C3×Q8—22no—
333C2×C3×Q8—82no—
334C2×C3×Q8C2411yescharacteristic
335C2×C3×D4—21no—
336C2×C3×D4C2411yescharacteristic
337C22×C3×C4—21no—
338C22×C3×C4—22no—
339C22×C3×C4—21no—
340C22×C3×C4—21no—
341C22×C3×C4C2×D411yescharacteristic
342C22×C3×C4C2×D411yescharacteristic
343C22×C3×C4C2411yescharacteristic
344C2×#67—22no—
345C2×#67—22no—
346C2×#67C2×D412yes—
347C22×Dic3—21no—
348C22×Dic3—22no—
349#239—24no—
350#239—24no—
351#239—84no—
352D3×D4—216no—
353D3×D4—24no—
354D3×D4—24no—
355#235—28no—
356#235—22no—
357#235—22no—
358#235—24no—
359#235—24no—
360C2×D12—28no—
361C2×D12—22no—
362C2×D12—21no—
363C2×D12—22no—
364C2×D12—21no—
365C2×D12—21no—
366C2×D12—24no—
367C2×D12C2×D411yescharacteristic
368C2×D12#4114yescomplemented
369C2×D12C2412yes—
370C2×D12C2412yes—
371C2×C4×D3—22no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—24no—
379C2×C4×D3—84no—
380C2×C4×D3—82no—
381C2×C4×D3C2×D412yes—
382C2×C4×D3C2×D412yes—
383C2×C4×D3C2412yes—
384C2×Dic6C2×D411yescharacteristic
385C2×Dic6C2412yes—
386C3×M16—24no—
387C2×C3×C8C2414yes—
388C3×C4⋊C4—22no—
389C3×C4⋊C4—21no—
390C3×C4⋊C4—22no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4C2414yes—
394C3×C4⋊C4C2411yescharacteristic
395C3×C4⋊C4C2411yescharacteristic
396C3×C22⋊C4—21no—
397C3×C22⋊C4—21no—
398C3×C22⋊C4—21no—
399C3×C42—21no—
400C3×C42—21no—
401C3×C42—21no—
402C3×C42C2×D411yescharacteristic
403C3×C42C2×D411yescharacteristic
404C3×C42C2411yescharacteristic
405C3×C42C2411yescharacteristic
406#217—22no—
407#217C2×D412yes—
408#216—24no—
409#215—24no—
410#214—24no—
411#213—24no—
412(C2×D3)⋊C4—22no—
413(C2×D3)⋊C4—24no—
414(C2×D3)⋊C4—22no—
415(C2×D3)⋊C4—22no—
416(C2×D3)⋊C4—22no—
417(C2×D3)⋊C4—22no—
418(C2×D3)⋊C4—22no—
419(C2×D3)⋊C4—22no—
420(C2×D3)⋊C4—24no—
421(C2×D3)⋊C4—24no—
422(C2×D3)⋊C4C2×D412yes—
423(C2×D3)⋊C4C2×D412yes—
424C4⋊Dic3—21no—
425C4⋊Dic3—21no—
426C4⋊Dic3—21no—
427C4⋊Dic3—22no—
428C4⋊Dic3—24no—
429C4⋊Dic3C2×D411yescharacteristic
430C4⋊Dic3C2×D411yescharacteristic
431C4⋊Dic3C2412yes—
432Dic3⋊C4—22no—
433Dic3⋊C4—24no—
434Dic3⋊C4C2×D412yes—
435Dic3⋊C4C2×D412yes—
436C4×Dic3—22no—
437C4×Dic3—22no—
438C4×Dic3—24no—
439C4×Dic3C2×D412yes—
440C4×Dic3C2×D412yes—
441C4×Dic3C2412yes—
442C2×C3⋊C8—24no—
443C2×C3⋊C8C2412yes—
444C2×C3⋊C8C2412yes—
445D24—28no—
446#204—28no—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—31no—
450C2×#41—32no—
451C2×#41—32no—
452C2×#41—61no—
453C2×#41—62no—
454C2×#41C22×D311yescharacteristic
455C22×Q8—21no—
456C22×D4—32no—
457C22×D4—31no—
458C22×D4—61no—
459C22×D4—62no—
460C23×C4—62no—
461C23×C4—61no—
462AGL(1,ℤ/8)—68no—
463#135—68no—
464C2×Q16—32no—
465C2×SD16—32no—
466C2×SD16—32no—
467C2×SD16—34no—
468C2×D8—32no—
469C2×D8—34no—
470C2×M16C22×D312yes—
471C22×C8—32no—
472C4⋊Q8—21no—
473C4⋊Q8—21no—
474C4⋊Q8—31no—
475C4⋊Q8C22×D312yes—
476C4⋊Q8C22×D312yes—
477#127—31no—
478#126—64no—
479#125—62no—
480#124—32no—
481#124—62no—
482#124—64no—
483#123—64no—
484C22⋊Q8—34no—
485C22⋊Q8—62no—
486C22⋊Q8—64no—
487C22⋊Q8—62no—
488#121—34no—
489#121—62no—
490#121—62no—
491#121—64no—
492#121—61no—
493#121—61no—
494C4×Q8—31no—
495C4×Q8—31no—
496C4×Q8—32no—
497C4×Q8—34no—
498C4×Q8—61no—
499C4×Q8—62no—
500C4×Q8C22×D311yescharacteristic
501C4×Q8C22×D311yescharacteristic
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—32no—
505C4×D4—32no—
506C4×D4—32no—
507C4×D4—32no—
508C4×D4—32no—
509C4×D4—34no—
510C4×D4—31no—
511C4×D4—31no—
512C4×D4—32no—
513C4×D4—32no—
514C4×D4—62no—
515C4×D4—61no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—62no—
520C4×D4—62no—
521C4×D4—62no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—64no—
526C4×D4—62no—
527C4×D4—62no—
528C4×D4—62no—
529C4×D4—61no—
530C4×D4—61no—
531C4×D4—61no—
532C4×D4—61no—
533C4×D4C22×D311yescharacteristic
534C4×D4C22×D311yescharacteristic
535#117—21no—
536#117—31no—
537#117—32no—
538#117—32no—
539#117—62no—
540#117—62no—
541#117—62no—
542#117—62no—
543#117—61no—
544#117C22×D311yescharacteristic
545C2×C4⋊C4—21no—
546C2×C4⋊C4—31no—
547C2×C4⋊C4—32no—
548C2×C4⋊C4—62no—
549C2×C4⋊C4—62no—
550C2×C4⋊C4—61no—
551C2×C4⋊C4C22×D312yes—
552C2×C22⋊C4—62no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C22⋊C4—62no—
556C2×C22⋊C4—61no—
557C2×C42—21no—
558C2×C42—32no—
559C2×C42—62no—
560C2×C42C22×D311yescharacteristic
561#107C22×D314yes—
562#106—34no—
563#106—34no—
564#106C22×D314yes—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8C22×D312yes—
569C4⋊C8C22×D312yes—
570#103—34no—
571#103—32no—
572#103—32no—
573#103C22×D314yes—
574#102—34no—
575#102—34no—
576#102—34no—
577#102—32no—
578#102—32no—
579#102C22×D314yes—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—21no—
585C23×C3C22×D411yescharacteristic
586C22×D3—22no—
587C22×D3—28no—
588C22×D3—24no—
589C22×D3—22no—
590C22×D3—82no—
591C22×D3—82no—
592C22×D3—81no—
593C22×D3—81no—
594C22×D3C22×D412yes—
595C3×Q8—21no—
596C3×Q8—44no—
597C3×Q8—82no—
598C3×Q8C2×#4112yes—
599C3×D4—24no—
600C3×D4—21no—
601C3×D4C2×#4112yes—
602C2×C3×C4—21no—
603C2×C3×C4—24no—
604C2×C3×C4—22no—
605C2×C3×C4—21no—
606C2×C3×C4—24no—
607C2×C3×C4—21no—
608C2×C3×C4—41no—
609C2×C3×C4—42no—
610C2×C3×C4—81no—
611C2×C3×C4—82no—
612C2×C3×C4C22×D411yescharacteristic
613C2×C3×C4C22×D411yescharacteristic
614C2×C3×C4C22×D411yescharacteristic
615C2×C3×C4C22×D411yescharacteristic
616C2×C3×C4C22×D411yescharacteristic
617C2×C3×C4C2×#4112yes—
618C2×C3×C4C2×#4112yes—
619C2×C3×C4C2511yescharacteristic
620#67—28no—
621#67—24no—
622#67—44no—
623C2×Dic3—22no—
624C2×Dic3—22no—
625C2×Dic3—82no—
626C2×Dic3—81no—
627C2×Dic3C22×D412yes—
628C2×Dic3C22×D412yes—
629C2×Dic3C22×D412yes—
630D12—28no—
631D12—22no—
632D12—24no—
633D12—22no—
634D12—22no—
635D12—22no—
636D12—42no—
637D12—42no—
638D12—84no—
639D12C2×#4114yes—
640C4×D3—28no—
641C4×D3—24no—
642C4×D3—22no—
643C4×D3—22no—
644C4×D3—42no—
645C4×D3—44no—
646C4×D3—44no—
647C4×D3—82no—
648C4×D3—82no—
649C4×D3—84no—
650C4×D3—82no—
651C4×D3—82no—
652Dic6—22no—
653Dic6—22no—
654Dic6—22no—
655C3×C8—24no—
656C3⋊C8—22no—
657C3⋊C8—22no—
658C24—62no—
659C24—61no—
660#41—22no—
661#41—68no—
662#41—64no—
663#41—64no—
664#41—62no—
665#41—62no—
666#41—64no—
667#41—64no—
668#41—244no—
669#41#23914yescomplemented
670C2×Q8—22no—
671C2×Q8—22no—
672C2×Q8—31no—
673C2×Q8—32no—
674C2×Q8—82no—
675C2×Q8C23×D311yescharacteristic
676C2×D4—21no—
677C2×D4—32no—
678C2×D4—31no—
679C2×D4—34no—
680C2×D4—32no—
681C2×D4—32no—
682C2×D4—62no—
683C2×D4—68no—
684C2×D4—64no—
685C2×D4—62no—
686C2×D4—64no—
687C2×D4—616no—
688C2×D4—64no—
689C2×D4—62no—
690C2×D4—61no—
691C2×D4—61no—
692C2×D4—61no—
693C2×D4—62no—
694C2×D4C23×D311yescharacteristic
695C22×C4—21no—
696C22×C4—22no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—32no—
700C22×C4—32no—
701C22×C4—32no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—64no—
706C22×C4—62no—
707C22×C4—62no—
708C22×C4—61no—
709C22×C4—62no—
710C22×C4—62no—
711C22×C4—62no—
712C22×C4—242no—
713C22×C4—244no—
714C22×C4D3×D411yescharacteristic
715C22×C4D3×D411yescharacteristic
716C22×C4C23×D311yescharacteristic
717Q16—64no—
718SD16—68no—
719SD16—64no—
720SD16—64no—
721D8—68no—
722D8—64no—
723M16—24no—
724C2×C8—32no—
725C2×C8—32no—
726C2×C8—64no—
727C2×C8C23×D314yes—
728C4⋊C4—22no—
729C4⋊C4—22no—
730C4⋊C4—21no—
731C4⋊C4—22no—
732C4⋊C4—21no—
733C4⋊C4—31no—
734C4⋊C4—31no—
735C4⋊C4—32no—
736C4⋊C4—32no—
737C4⋊C4—32no—
738C4⋊C4—62no—
739C4⋊C4—62no—
740C4⋊C4—64no—
741C4⋊C4—64no—
742C4⋊C4—61no—
743C4⋊C4—61no—
744C4⋊C4—61no—
745C4⋊C4C23×D314yes—
746C4⋊C4C23×D311yescharacteristic
747C4⋊C4C23×D311yescharacteristic
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—32no—
752C22⋊C4—32no—
753C22⋊C4—32no—
754C22⋊C4—62no—
755C22⋊C4—62no—
756C22⋊C4—64no—
757C22⋊C4—64no—
758C22⋊C4—62no—
759C22⋊C4—64no—
760C22⋊C4—62no—
761C22⋊C4—62no—
762C22⋊C4—62no—
763C22⋊C4—62no—
764C22⋊C4—62no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42—32no—
769C42—32no—
770C42—32no—
771C42—62no—
772C42—62no—
773C42—64no—
774C42D3×D411yescharacteristic
775C42D3×D411yescharacteristic
776C42C23×D311yescharacteristic
777C42C23×D311yescharacteristic
778C22×C3—21no—
779C22×C3—21no—
780C22×C3—22no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3#52512yes—
784C22×C3C23×D411yescharacteristic
785C2×D3—22no—
786C2×D3—22no—
787C2×D3—24no—
788C2×D3—22no—
789C2×D3—42no—
790C2×D3—42no—
791C2×D3—42no—
792C2×D3—42no—
793C2×D3—42no—
794C2×D3—84no—
795C2×D3—88no—
796C3×C4—21no—
797C3×C4—21no—
798C3×C4—22no—
799C3×C4—21no—
800C3×C4—41no—
801C3×C4—44no—
802C3×C4—41no—
803C3×C4#52512yes—
804C3×C4#57712yes—
805C3×C4C22×#4111yescharacteristic
806C3×C4C22×#4111yescharacteristic
807Dic3—22no—
808Dic3—22no—
809Dic3—22no—
810Dic3—42no—
811Dic3—42no—
812C23—21no—
813C23—32no—
814C23—68no—
815C23—62no—
816C23—64no—
817C23—62no—
818C23—241no—
819C23—241no—
820C23—242no—
821C23—242no—
822C23C2×D3×D411yescharacteristic
823Q8—21no—
824Q8—44no—
825Q8—62no—
826Q8—62no—
827Q8—62no—
828Q8—82no—
829Q8C2×#23912yes—
830D4—24no—
831D4—21no—
832D4—34no—
833D4—68no—
834D4—68no—
835D4—64no—
836D4—62no—
837D4—62no—
838D4—62no—
839D4—64no—
840D4—62no—
841D4—122no—
842D4—124no—
843D4—122no—
844D4—244no—
845D4C2×#23912yes—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—24no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—24no—
852C2×C4—32no—
853C2×C4—32no—
854C2×C4—32no—
855C2×C4—41no—
856C2×C4—42no—
857C2×C4—68no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—64no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—122no—
866C2×C4—124no—
867C2×C4—124no—
868C2×C4—242no—
869C2×C4—242no—
870C2×C4—244no—
871C2×C4—242no—
872C2×C4—242no—
873C2×C4—242no—
874C2×C4—241no—
875C2×C4C2×D3×D411yescharacteristic
876C2×C4C2×D3×D411yescharacteristic
877C2×C4C2×D3×D411yescharacteristic
878C2×C4C2×D3×D411yescharacteristic
879C2×C4C2×D3×D411yescharacteristic
880C2×C4C2×#23912yes—
881C2×C4D3×#4112yes—
882C2×C4C24×D311yescharacteristic
883C8—24no—
884C8—62no—
885C8—62no—
886C2×C3—22no—
887C2×C3—42no—
888C2×C3C2×#52511yescharacteristic
889C2×C3C2×#57711yescharacteristic
890C2×C3#358511yescharacteristic
891D3—42no—
892D3—44no—
893D3—82no—
894C22—21no—
895C22—21no—
896C22—22no—
897C22—41no—
898C22—41no—
899C22—62no—
900C22—62no—
901C22—64no—
902C22—62no—
903C22—122no—
904C22—122no—
905C22—122no—
906C22—122no—
907C22—122no—
908C22—244no—
909C22—248no—
910C22#562712yes—
911C22C22×D3×D411yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—22no—
916C4—41no—
917C4—44no—
918C4—41no—
919C4—62no—
920C4—62no—
921C4—62no—
922C4—122no—
923C4—122no—
924C4#562712yes—
925C4#577812yes—
926C4C22×#23911yescharacteristic
927C4C2×D3×#4111yescharacteristic
928C3#6059711yescharacteristic, complemented, Sylow
929C2—22no—
930C2—42no—
931C2—122no—
932C2—124no—
933C2—242no—
934C2C2×#562711yescharacteristic
935C2#8719211yescharacteristic
936C2C2×#577811yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3079C2
socleC22×C3C23×D4
hypercenter#3079D3
hypocenterC3#60597
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. #86205C2semidirect
2. C4×#1009C2semidirect
3. C3×#3079C2semidirect
4. C2×#5084C2semidirect
5. #82525C2semidirect
6. #81095C2semidirect
7. #81093C2semidirect
8. #81046C2semidirect
9. #81044C2semidirect
10. #81001C2semidirect
11. #80952C2semidirect
12. #79222C2semidirect
13. #79201C2semidirect
14. #79055C2semidirect
15. #79040C2semidirect
16. #78886C2semidirect
17. #78869C2semidirect
20. C2×C3×C4⋊Q8C22semidirect
27. #5733C22semidirect
30. #5728C22semidirect
32. #5725C22semidirect
45. #5504C22semidirect
46. #5477C22semidirect
51. C3×#477C22semidirect
52. C3×#476C22semidirect
53. C3×#475C22semidirect
54. C3×#474C22semidirect
55. C3×#428C22semidirect
56. C3×#423C22semidirect
58. #5133C22semidirect
60. #5122C22semidirect
61. #5084C22semidirect
62. #5084C22semidirect
63. #5084C22semidirect
64. #5031C22semidirect
65. #5028C22semidirect
66. #5027C22semidirect
67. #5019C22semidirect
68. #5016C22semidirect
69. #5015C22semidirect
70. #5002C22semidirect
72. C2×#808C22semidirect
73. C2×C4⋊(C3⋊C8)C22semidirect
74. #4889C22semidirect
75. #4888C22semidirect
76. #4885C22semidirect
77. #4872C22semidirect
78. #4869C22semidirect
79. #4863C22semidirect
80. #4862C22semidirect
81. #4852C22semidirect
82. #4844C22semidirect
83. #4843C22semidirect
84. #4841C22semidirect
85. #4840C22semidirect
86. #4835C22semidirect
87. #4833C22semidirect
90. #4789C22semidirect
91. #4788C22semidirect
92. #4785C22semidirect
95. #4758C22semidirect
105. #3079D3semidirect
264. C2×C4⋊Q8C2×D3semidirect
286. #477C2×D3semidirect
290. #476C2×D3semidirect
291. #475C2×D3semidirect
292. #474C2×D3semidirect
317. #428C2×D3semidirect
319. #423C2×D3semidirect
330. C3×#41#41semidirect
368. C2×D12#41semidirect
669. #41#239semidirect
928. C3#60597semidirect

Maximal subgroups

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

subgroupindex
#862052
C4×#10092
C3×#30792
C2×#50842
#825252
#810952
#810932
#810462
#810442
#810012
#809522
#792222
#792012
#790552
#790402
#788862
#788692
#605973