Finite Group Databasebeta

← #11664144

Subgroups — #11664144

Order 768.

2194 conjugacy classes of subgroups.

The subgroup lattice has 946 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#3508C211yesmaximal, characteristic, complemented
2C4×#1009C211yesmaximal, characteristic, complemented
3#83435C214yesmaximal, complemented
4#83434C214yesmaximal, complemented
5#83383C212yesmaximal, complemented
6#83376C212yesmaximal, complemented
7#83350C211yesmaximal, characteristic, complemented
8#83349C211yesmaximal, characteristic, complemented
9#83301C212yesmaximal, complemented
10#83300C212yesmaximal, complemented
11#83299C212yesmaximal, complemented
12#83298C212yesmaximal, complemented
13#83165C211yesmaximal, characteristic, complemented
14C2×#5072C211yesmaximal, characteristic, complemented
15#82538C212yesmaximal, complemented
16#82537C212yesmaximal, complemented
17#82515C211yesmaximal, characteristic, complemented
18#60590—31nomaximal, Sylow
19C2×#1009C2211yescharacteristic
20C3×#559—21no—
21C3×#559—21no—
22C3×#550—21no—
23C3×#550—21no—
24C3×#546—22no—
25C3×#546—22no—
26C3×#540C2214yescomplemented
27C3×#535C2212yes—
28C3×#533C2211yescharacteristic, complemented
29C3×#532C2212yescomplemented
30C3×#532C2212yescomplemented
31C2×C3×#127C2211yescharacteristic, complemented
32C3×#518C2212yescomplemented
33C3×C4×#41C2211yescharacteristic
34#5827C2211yescharacteristic
35C2×#932C2212yes—
36C22×#213C2212yes—
37#5574—21no—
38C4×#239—21no—
39#5545—21no—
40#5545—22no—
41C4×D3×D4—21no—
42C4×D3×D4—22no—
43#5523C2211yescharacteristic
44#5523C2212yescomplemented
45#5521C2211yescharacteristic
46#5521C2212yescomplemented
47C4×#235C2211yescharacteristic
48C4×#235C2212yescomplemented
49C2×C4×D12C2211yescharacteristic
50C2×C4×D12C2212yescomplemented
51#5234C2212yes—
52#5215C2212yescomplemented
53C2×#832C2212yescomplemented
54#5094C2211yescharacteristic, complemented
55#5091C2211yescharacteristic, complemented
56#5087C2211yescharacteristic, complemented
57#5087C2212yescomplemented
58#5084C2212yescomplemented
59#5084C2211yescharacteristic, complemented
60#5075C2212yescomplemented
61#5075C2212yescomplemented
62#5072C2212yescomplemented
63#5072C2212yescomplemented
64#5072C2212yescomplemented
65#5072C2214yescomplemented
66#5072C2212yescomplemented
67#5066C2212yescomplemented
68#5066C2214yescomplemented
69#5063C2212yescomplemented
70#5037C2214yescomplemented
71#5037C2214yescomplemented
72#5036C2214yescomplemented
73#5036C2214yescomplemented
74#5035C2214yescomplemented
75#5035C2214yescomplemented
76#5034C2214yescomplemented
77#5033C2214yescomplemented
78#5018C2214yescomplemented
79C4×#214C2214yescomplemented
80#5014C2214yescomplemented
81#5014C2214yescomplemented
82#5014C2214yescomplemented
83C4×#213C2214yescomplemented
84C4×#213C2214yescomplemented
85C4×#213C2214yescomplemented
86#5002C2212yes—
87#5001C2212yes—
88#5000C2214yescomplemented
89#4998C2212yescomplemented
90#4997C2212yescomplemented
91#4995C2212yescomplemented
92#4926C2212yescomplemented
93#4925C2212yescomplemented
94#4924C2211yescharacteristic, complemented
95C2×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
96#3508D311yescharacteristic, complemented
97C4×H(5,𝔽2)—31no—
98#3122—34no—
99#3119—34no—
100#3115—32no—
101#3109—32no—
102#3106—32no—
103#3100—32no—
104#3096—32no—
105#3077—31no—
106#3076—31no—
107#3038—31no—
108C2×#459—31no—
109#3008—32no—
110#2948—32no—
111#2946—32no—
112#2925—31no—
113C2×C3×#41—22no—
114C2×C3×#41—22no—
115C2×C3×#41C2311yescharacteristic
116C22×C3×D4—21no—
117C22×C3×D4—21no—
118C22×C3×D4C2312yes—
119#1009—24no—
120#1009—24no—
121C2×#239—21no—
122C2×D3×D4—22no—
123C2×D3×D4—21no—
124C2×#235C2312yes—
125C2×#235C2311yescharacteristic
126C22×D12C2312yes—
127C22×D12C2311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3—22no—
130C3×C4⋊Q8C2311yescharacteristic
131C3×C4⋊Q8C2311yescharacteristic
132C3×#127—22no—
133C3×#127—21no—
134C3×#127—21no—
135C3×#127C2312yes—
136C3×#127C2312yes—
137C3×#125C2312yes—
138C3×#124—22no—
139C3×#124—22no—
140C3×#124—22no—
141C3×#123—24no—
142C3×#123—24no—
143C3×C22⋊Q8—21no—
144C3×C22⋊Q8—21no—
145C3×#121—22no—
146C3×#121—22no—
147C3×#121—24no—
148C3×#121—24no—
149C3×#121C2314yes—
150C3×#121C2314yes—
151C3×#120—24no—
152C3×C4×Q8—21no—
153C3×C4×Q8—21no—
154C3×C4×Q8D411yescharacteristic
155C3×C4×Q8D411yescharacteristic
156C3×C4×D4—22no—
157C3×C4×D4—22no—
158C3×C4×D4—22no—
159C3×C4×D4—22no—
160C3×C4×D4D412yes—
161C3×C4×D4D411yescharacteristic
162C3×C4×D4D412yes—
163C3×C4×D4D411yescharacteristic
164C3×C4×D4C2314yes—
165C3×C4×D4C2314yes—
166C3×#117C2312yes—
167C3×#117C2311yescharacteristic
168C3×#117C2312yes—
169C2×C3×C22⋊C4—24no—
170C2×C3×C42C2311yescharacteristic
171C2×C3×C42C2312yes—
172Q8×Dic3—21no—
173D4×Dic3—22no—
174D4×Dic3—21no—
175C2×#214C2314yes—
176#932—28no—
177C2×#213—28no—
178C2×#213C2314yes—
179C2×#213C2314yes—
180C2×#213C2314yes—
181C4×#67—21no—
182C4×#67—21no—
183C4×#67—22no—
184C4×#67—22no—
185C2×(C2×D3)⋊C4—21no—
186C2×(C2×D3)⋊C4—22no—
187#926C2311yescharacteristic
188#926C2312yes—
189C2×C4⋊Dic3C2311yescharacteristic
190C2×C4⋊Dic3C2312yes—
191C2×#208C2312yes—
192C22×C3⋊C8C2312yes—
193#893—21no—
194#893—21no—
195#893—22no—
196#893—22no—
197#892—21no—
198#892—22no—
199D3×C4⋊C4—21no—
200D3×C4⋊C4—22no—
201#67⋊C4—22no—
202#67⋊C4—22no—
203#67⋊C4—22no—
204D3×C22⋊C4—22no—
205D3×C22⋊C4—22no—
206D3×C22⋊C4—22no—
207C4×D12—21no—
208C4×D12—21no—
209C4×D12—22no—
210C4×D12—22no—
211C4×D12C2312yes—
212C4×D12C2312yes—
213C4×D12C2311yescharacteristic
214C4×D12C2312yes—
215C4×D12C2312yes—
216C4×D12C2311yescharacteristic
217C4×D12C2312yes—
218#872—21no—
219#872—22no—
220C42×D3—21no—
221C42×D3—22no—
222C4×Dic6C2311yescharacteristic
223C4×Dic6C2311yescharacteristic
224C4×Dic6C2312yes—
225#832C2314yes—
226#832C2314yes—
227#832C2314yes—
228#832C2314yes—
229#830C2314yes—
230#830C2314yes—
231#810C2312yes—
232#810C2312yes—
233#809C2314yes—
234#809C2314yes—
235#809C2312yes—
236#809C2312yes—
237#808C2314yes—
238#808C2312yes—
239#808C2312yes—
240#807C2314yes—
241#807C2312yes—
242#807C2312yes—
243C4⋊(C3⋊C8)C2311yescharacteristic
244C4⋊(C3⋊C8)C2311yescharacteristic
245C4⋊(C3⋊C8)C2312yes—
246C4⋊(C3⋊C8)C2312yes—
247C4⋊(C3⋊C8)C2312yes—
248#803C2314yes—
249C4×C3⋊C8C2314yes—
250C2×H(5,𝔽2)—31no—
251C2×AGL(1,ℤ/8)—32no—
252C22×D8—32no—
253#559—21no—
254#559—21no—
255#550—21no—
256#550—21no—
257#546—22no—
258#546—22no—
259#540C2×D314yescomplemented
260#535C2×D312yes—
261#533C2×D311yescharacteristic, complemented
262#532C2×D312yescomplemented
263#532C2×D312yescomplemented
264C2×#127C2×D311yescharacteristic, complemented
265#520—31no—
266#520—32no—
267#520—31no—
268#520—61no—
269#518—32no—
270#518—31no—
271#518—62no—
272#518—61no—
273#518C2×D312yescomplemented
274C4×#41—31no—
275C4×#41—32no—
276C4×#41—61no—
277C4×#41C2×D311yescharacteristic
278C2×C4×D4—31no—
279C2×C4×D4—32no—
280C2×C4×D4—62no—
281C2×C4×D4—61no—
282#482—34no—
283#482—34no—
284#481—34no—
285#480—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#460—32no—
296#460—32no—
297#459—32no—
298#459—32no—
299#459—32no—
300#459—34no—
301#459—32no—
302#449—34no—
303#449—34no—
304#447—34no—
305#447—34no—
306#442—34no—
307#442—34no—
308#442—34no—
309#440—34no—
310C4×SD16—34no—
311C4×D8—34no—
312C4×D8—34no—
313C4×D8—34no—
314#433—34no—
315#432—32no—
316#431—32no—
317#428—32no—
318#427—32no—
319#423—31no—
320C2×C4⋊C8—31no—
321#418—32no—
322#418—32no—
323#416—32no—
324C2×#102—32no—
325#408—32no—
326#405—32no—
327C24×C3—22no—
328C23×D3—22no—
329C23×D3—21no—
330C3×#41—22no—
331C3×#41—22no—
332C3×#41—84no—
333C3×#41—84no—
334C2×C3×Q8—21no—
335C2×C3×Q8—21no—
336C2×C3×Q8C2×D411yescharacteristic
337C2×C3×D4—24no—
338C2×C3×D4—24no—
339C2×C3×D4—22no—
340C2×C3×D4—22no—
341C2×C3×D4—22no—
342C2×C3×D4—22no—
343C2×C3×D4—22no—
344C2×C3×D4—24no—
345C2×C3×D4—24no—
346C2×C3×D4—82no—
347C2×C3×D4—82no—
348C2×C3×D4C2×D412yes—
349C2×C3×D4C2×D411yescharacteristic
350C2×C3×D4C2414yes—
351C22×C3×C4—24no—
352C22×C3×C4—24no—
353C22×C3×C4C2×D412yes—
354C22×C3×C4C2×D411yescharacteristic
355C22×C3×C4C2×D412yes—
356C22×C3×C4C2×D411yescharacteristic
357C22×C3×C4C2412yes—
358C22×C3×C4C2411yescharacteristic
359C2×#67—22no—
360C2×#67—21no—
361C22×Dic3—22no—
362C22×Dic3—21no—
363#239—28no—
364D3×D4—216no—
365D3×D4—28no—
366#235—22no—
367#235—24no—
368#235—24no—
369#235#4114yescomplemented
370C2×D12—22no—
371C2×D12—21no—
372C2×D12—22no—
373C2×D12—24no—
374C2×D12—24no—
375C2×D12#4114yescomplemented
376C2×D12C2411yescharacteristic
377C2×D12C2412yes—
378C2×C4×D3—22no—
379C2×C4×D3—21no—
380C2×C4×D3—21no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—21no—
384C2×C4×D3—22no—
385C2×C4×D3—22no—
386C2×C4×D3—22no—
387C2×C4×D3—82no—
388C2×C4×D3—84no—
389C2×Dic6C2411yescharacteristic
390C3×C4⋊C4—21no—
391C3×C4⋊C4—21no—
392C3×C4⋊C4—22no—
393C3×C4⋊C4—22no—
394C3×C4⋊C4C2×D411yescharacteristic
395C3×C4⋊C4C2×D412yes—
396C3×C4⋊C4C2×D411yescharacteristic
397C3×C4⋊C4C2×D412yes—
398C3×C4⋊C4C2412yes—
399C3×C4⋊C4C2412yes—
400C3×C22⋊C4—22no—
401C3×C22⋊C4—24no—
402C3×C22⋊C4—24no—
403C3×C22⋊C4—24no—
404C3×C22⋊C4—24no—
405C3×C22⋊C4C2×D412yes—
406C3×C22⋊C4C2×D412yes—
407C3×C22⋊C4C2×D412yes—
408C3×C42—22no—
409C3×C42C2×D412yes—
410C3×C42C2×D411yescharacteristic
411C3×C42C2×D412yes—
412C3×C42C2×D411yescharacteristic
413C3×C42C2412yes—
414C3×C42C2411yescharacteristic
415C3×C42C2411yescharacteristic
416#217—22no—
417#217—21no—
418#214—28no—
419#213—28no—
420#213—28no—
421#213—28no—
422(C2×D3)⋊C4—21no—
423(C2×D3)⋊C4—22no—
424(C2×D3)⋊C4—22no—
425(C2×D3)⋊C4—21no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—22no—
428(C2×D3)⋊C4—22no—
429C4⋊Dic3—22no—
430C4⋊Dic3—21no—
431C4⋊Dic3C2412yes—
432C4⋊Dic3C2411yescharacteristic
433C4⋊Dic3C2411yescharacteristic
434Dic3⋊C4—21no—
435Dic3⋊C4—22no—
436Dic3⋊C4—21no—
437C4×Dic3—21no—
438C4×Dic3—22no—
439C4×Dic3—21no—
440C4×Dic3—22no—
441C4×Dic3—21no—
442#208—24no—
443C2×C3⋊C8—24no—
444C2×C3⋊C8C2412yes—
445C2×C3⋊C8C2414yes—
446C2×C3⋊C8C2412yes—
447H(5,𝔽2)—64no—
448H(5,𝔽2)—64no—
449C2×#41—22no—
450C2×#41—22no—
451C2×#41—31no—
452C2×#41—32no—
453C2×#41—61no—
454C2×#41C22×D311yescharacteristic
455C22×D4—21no—
456C22×D4—21no—
457C22×D4—31no—
458C22×D4—32no—
459C22×D4—62no—
460C22×D4—61no—
461C22×D4C22×D312yes—
462C23×C4—62no—
463C23×C4—61no—
464AGL(1,ℤ/8)—68no—
465C2×SD16—34no—
466C2×D8—34no—
467C2×D8—34no—
468C2×D8—34no—
469C2×D8—68no—
470C2×M16—32no—
471C22×C8—32no—
472C4⋊Q8C22×D311yescharacteristic
473C4⋊Q8C22×D311yescharacteristic
474#127—22no—
475#127—21no—
476#127—21no—
477#127C22×D312yes—
478#127C22×D312yes—
479#125C22×D312yes—
480#124—22no—
481#124—22no—
482#124—22no—
483#123—24no—
484#123—24no—
485C22⋊Q8—21no—
486C22⋊Q8—21no—
487#121—22no—
488#121—22no—
489#121—24no—
490#121—24no—
491#121C22×D314yes—
492#121C22×D314yes—
493#120—24no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—31no—
497C4×Q8—32no—
498C4×Q8—31no—
499C4×Q8—61no—
500C4×Q8#6711yescharacteristic
501C4×Q8#6711yescharacteristic
502C4×D4—22no—
503C4×D4—22no—
504C4×D4—22no—
505C4×D4—22no—
506C4×D4—32no—
507C4×D4—31no—
508C4×D4—32no—
509C4×D4—32no—
510C4×D4—32no—
511C4×D4—32no—
512C4×D4—31no—
513C4×D4—62no—
514C4×D4—61no—
515C4×D4—62no—
516C4×D4—61no—
517C4×D4—62no—
518C4×D4—61no—
519C4×D4—61no—
520C4×D4—62no—
521C4×D4—61no—
522C4×D4—62no—
523C4×D4—62no—
524C4×D4—62no—
525C4×D4—62no—
526C4×D4—62no—
527C4×D4—61no—
528C4×D4—62no—
529C4×D4—61no—
530C4×D4#6712yes—
531C4×D4#6711yescharacteristic
532C4×D4#6712yes—
533C4×D4#6711yescharacteristic
534C4×D4C22×D314yes—
535C4×D4C22×D314yes—
536#117—31no—
537#117—32no—
538#117—61no—
539#117—62no—
540#117—62no—
541#117—61no—
542#117C22×D312yes—
543#117C22×D311yescharacteristic
544#117C22×D312yes—
545C2×C4⋊C4—31no—
546C2×C4⋊C4—32no—
547C2×C4⋊C4—61no—
548C2×C4⋊C4—62no—
549C2×C22⋊C4—24no—
550C2×C22⋊C4—62no—
551C2×C22⋊C4—61no—
552C2×C22⋊C4—62no—
553C2×C22⋊C4—62no—
554C2×C22⋊C4—62no—
555C2×C42—62no—
556C2×C42—61no—
557C2×C42C22×D311yescharacteristic
558C2×C42C22×D312yes—
559#107—32no—
560#107—32no—
561#107—34no—
562#106—32no—
563#106—32no—
564#106—34no—
565C4⋊C8—31no—
566C4⋊C8—31no—
567C4⋊C8—32no—
568C4⋊C8—32no—
569C4⋊C8—32no—
570#103—32no—
571#103—32no—
572#102—34no—
573#102—34no—
574#102—34no—
575#102—34no—
576#102—32no—
577#102—32no—
578#102—34no—
579#102—34no—
580C22⋊C8—34no—
581C22⋊C8—34no—
582#97—34no—
583C4×C8—34no—
584C23×C3—24no—
585C23×C3—44no—
586C23×C3—82no—
587C23×C3—82no—
588C23×C3C22×D412yes—
589C23×C3C22×D411yescharacteristic
590C22×D3—22no—
591C22×D3—21no—
592C22×D3—28no—
593C22×D3—24no—
594C22×D3—81no—
595C22×D3—82no—
596C22×D3—81no—
597C22×D3—82no—
598C3×Q8—22no—
599C3×Q8—42no—
600C3×Q8—42no—
601C3×D4—24no—
602C3×D4—22no—
603C3×D4—24no—
604C3×D4—24no—
605C3×D4—44no—
606C3×D4—44no—
607C3×D4—44no—
608C3×D4—82no—
609C3×D4—82no—
610C3×D4—84no—
611C3×D4—84no—
612C2×C3×C4—22no—
613C2×C3×C4—24no—
614C2×C3×C4—22no—
615C2×C3×C4—22no—
616C2×C3×C4—22no—
617C2×C3×C4—22no—
618C2×C3×C4—41no—
619C2×C3×C4—42no—
620C2×C3×C4—84no—
621C2×C3×C4—84no—
622C2×C3×C4C22×D412yes—
623C2×C3×C4C22×D412yes—
624C2×C3×C4C22×D411yescharacteristic
625C2×C3×C4C22×D411yescharacteristic
626C2×C3×C4C22×D412yes—
627C2×C3×C4C22×D411yescharacteristic
628C2×C3×C4C22×D411yescharacteristic
629C2×C3×C4C22×D411yescharacteristic
630C2×C3×C4C2×#4112yes—
631C2×C3×C4C2×#4112yes—
632C2×C3×C4C2511yescharacteristic
633#67—28no—
634#67—24no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—22no—
638C2×Dic3—21no—
639C2×Dic3—81no—
640C2×Dic3—82no—
641D12—28no—
642D12—24no—
643D12—21no—
644D12—22no—
645D12C2×#4112yes—
646D12C2×#4114yes—
647C4×D3—28no—
648C4×D3—24no—
649C4×D3—42no—
650C4×D3—44no—
651C4×D3—82no—
652C4×D3—81no—
653C4×D3—82no—
654C4×D3—82no—
655C4×D3—82no—
656Dic6—21no—
657Dic6C2×#4112yes—
658C3⋊C8—22no—
659C3⋊C8—22no—
660C3⋊C8—24no—
661C24—22no—
662C24—62no—
663C24—61no—
664#41—22no—
665#41—22no—
666#41—34no—
667#41—64no—
668#41—64no—
669#41—68no—
670#41—62no—
671#41—84no—
672#41—84no—
673C2×Q8—21no—
674C2×Q8—21no—
675C2×Q8—31no—
676C2×Q8C2×#6711yescharacteristic
677C2×D4—24no—
678C2×D4—24no—
679C2×D4—24no—
680C2×D4—24no—
681C2×D4—22no—
682C2×D4—22no—
683C2×D4—22no—
684C2×D4—22no—
685C2×D4—22no—
686C2×D4—34no—
687C2×D4—32no—
688C2×D4—31no—
689C2×D4—64no—
690C2×D4—64no—
691C2×D4—616no—
692C2×D4—68no—
693C2×D4—62no—
694C2×D4—61no—
695C2×D4—62no—
696C2×D4—62no—
697C2×D4—61no—
698C2×D4—82no—
699C2×D4—82no—
700C2×D4C2×#6712yes—
701C2×D4C2×#6711yescharacteristic
702C2×D4C23×D314yes—
703C22×C4—24no—
704C22×C4—24no—
705C22×C4—62no—
706C22×C4—61no—
707C22×C4—62no—
708C22×C4—61no—
709C22×C4—62no—
710C22×C4—61no—
711C22×C4—62no—
712C22×C4—61no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—242no—
717C22×C4—244no—
718C22×C4C2×#6712yes—
719C22×C4C2×#6711yescharacteristic
720C22×C4C2×#6712yes—
721C22×C4C2×#6711yescharacteristic
722C22×C4C23×D312yes—
723C22×C4C23×D311yescharacteristic
724SD16—68no—
725D8—68no—
726D8—68no—
727D8—68no—
728M16—64no—
729C2×C8—32no—
730C2×C8—34no—
731C2×C8—32no—
732C2×C8—64no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—22no—
736C4⋊C4—22no—
737C4⋊C4—32no—
738C4⋊C4—31no—
739C4⋊C4—31no—
740C4⋊C4—62no—
741C4⋊C4—61no—
742C4⋊C4—62no—
743C4⋊C4—61no—
744C4⋊C4—61no—
745C4⋊C4C2×#6711yescharacteristic
746C4⋊C4C2×#6712yes—
747C4⋊C4C2×#6711yescharacteristic
748C4⋊C4C2×#6712yes—
749C4⋊C4C23×D312yes—
750C4⋊C4C23×D312yes—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—24no—
754C22⋊C4—24no—
755C22⋊C4—24no—
756C22⋊C4—62no—
757C22⋊C4—61no—
758C22⋊C4—62no—
759C22⋊C4—61no—
760C22⋊C4—62no—
761C22⋊C4—62no—
762C22⋊C4—62no—
763C22⋊C4—61no—
764C22⋊C4—62no—
765C22⋊C4C2×#6712yes—
766C22⋊C4C2×#6712yes—
767C22⋊C4C2×#6712yes—
768C42—22no—
769C42—61no—
770C42—62no—
771C42—61no—
772C42—62no—
773C42—61no—
774C42C2×#6712yes—
775C42C2×#6711yescharacteristic
776C42C2×#6712yes—
777C42C2×#6711yescharacteristic
778C42C23×D312yes—
779C42C23×D311yescharacteristic
780C42C23×D311yescharacteristic
781C22×C3—21no—
782C22×C3—21no—
783C22×C3—22no—
784C22×C3—22no—
785C22×C3—22no—
786C22×C3—44no—
787C22×C3—44no—
788C22×C3—44no—
789C22×C3—164no—
790C22×C3#52512yes—
791C22×C3C23×D411yescharacteristic
792C2×D3—24no—
793C2×D3—22no—
794C2×D3—42no—
795C2×D3—41no—
796C2×D3—42no—
797C2×D3—41no—
798C2×D3—84no—
799C2×D3—88no—
800C3×C4—22no—
801C3×C4—21no—
802C3×C4—21no—
803C3×C4—22no—
804C3×C4—22no—
805C3×C4—21no—
806C3×C4—42no—
807C3×C4—42no—
808C3×C4#52512yes—
809C3×C4#57612yes—
810C3×C4C22×#4111yescharacteristic
811C3×C4C22×#4111yescharacteristic
812Dic3—22no—
813Dic3—41no—
814Dic3—41no—
815Dic3—42no—
816C23—24no—
817C23—44no—
818C23—68no—
819C23—62no—
820C23—61no—
821C23—64no—
822C23—82no—
823C23—82no—
824C23—241no—
825C23—242no—
826C23—241no—
827C23—242no—
828C23C22×#6712yes—
829C23C22×#6711yescharacteristic
830Q8—22no—
831Q8—32no—
832Q8—42no—
833Q8—42no—
834Q8—61no—
835D4—24no—
836D4—24no—
837D4—24no—
838D4—22no—
839D4—34no—
840D4—32no—
841D4—44no—
842D4—44no—
843D4—44no—
844D4—68no—
845D4—68no—
846D4—64no—
847D4—61no—
848D4—62no—
849D4—64no—
850D4—82no—
851D4—82no—
852D4—84no—
853D4—84no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—24no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—68no—
863C2×C4—61no—
864C2×C4—64no—
865C2×C4—61no—
866C2×C4—62no—
867C2×C4—61no—
868C2×C4—84no—
869C2×C4—84no—
870C2×C4—124no—
871C2×C4—122no—
872C2×C4—242no—
873C2×C4—242no—
874C2×C4—242no—
875C2×C4—242no—
876C2×C4—241no—
877C2×C4—241no—
878C2×C4—242no—
879C2×C4D3×#4112yes—
880C2×C4D3×#4112yes—
881C2×C4C22×#6712yes—
882C2×C4C22×#6712yes—
883C2×C4C22×#6711yescharacteristic
884C2×C4C22×#6711yescharacteristic
885C2×C4C22×#6712yes—
886C2×C4C22×#6711yescharacteristic
887C2×C4C22×#6711yescharacteristic
888C2×C4C22×#6711yescharacteristic
889C2×C4C24×D311yescharacteristic
890C8—62no—
891C8—62no—
892C8—64no—
893C2×C3—22no—
894C2×C3—42no—
895C2×C3—84no—
896C2×C3C2×#52511yescharacteristic
897C2×C3C2×#57611yescharacteristic
898C2×C3#358511yescharacteristic
899D3—44no—
900D3—42no—
901C22—21no—
902C22—21no—
903C22—22no—
904C22—22no—
905C22—22no—
906C22—44no—
907C22—44no—
908C22—44no—
909C22—64no—
910C22—62no—
911C22—122no—
912C22—121no—
913C22—122no—
914C22—121no—
915C22—164no—
916C22—244no—
917C22—248no—
918C22#582812yes—
919C22C23×#6711yescharacteristic
920C4—22no—
921C4—22no—
922C4—21no—
923C4—21no—
924C4—22no—
925C4—21no—
926C4—42no—
927C4—42no—
928C4—62no—
929C4—121no—
930C4—122no—
931C4—121no—
932C4#582812yes—
933C4#583512yes—
934C4C2×D3×#4111yescharacteristic
935C4C2×D3×#4111yescharacteristic
936C3#6059011yescharacteristic, complemented, Sylow
937C2—22no—
938C2—42no—
939C2—84no—
940C2—124no—
941C2—122no—
942C2C2×#582811yescharacteristic
943C2C2×#583511yescharacteristic
944C2#8727711yescharacteristic
subgroupG/H
centerC22C23×#67
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3508C2
socleC22×C3C23×D4
hypercenter#3508D3
hypocenterC3#60590
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. C3×#3508C2semidirect
2. C4×#1009C2semidirect
3. #83435C2semidirect
4. #83434C2semidirect
5. #83383C2semidirect
6. #83376C2semidirect
7. #83350C2semidirect
8. #83349C2semidirect
9. #83301C2semidirect
10. #83300C2semidirect
11. #83299C2semidirect
12. #83298C2semidirect
13. #83165C2semidirect
14. C2×#5072C2semidirect
15. #82538C2semidirect
16. #82537C2semidirect
17. #82515C2semidirect
26. C3×#540C22semidirect
28. C3×#533C22semidirect
29. C3×#532C22semidirect
30. C3×#532C22semidirect
31. C2×C3×#127C22semidirect
32. C3×#518C22semidirect
44. #5523C22semidirect
46. #5521C22semidirect
48. C4×#235C22semidirect
50. C2×C4×D12C22semidirect
52. #5215C22semidirect
53. C2×#832C22semidirect
54. #5094C22semidirect
55. #5091C22semidirect
56. #5087C22semidirect
57. #5087C22semidirect
58. #5084C22semidirect
59. #5084C22semidirect
60. #5075C22semidirect
61. #5075C22semidirect
62. #5072C22semidirect
63. #5072C22semidirect
64. #5072C22semidirect
65. #5072C22semidirect
66. #5072C22semidirect
67. #5066C22semidirect
68. #5066C22semidirect
69. #5063C22semidirect
70. #5037C22semidirect
71. #5037C22semidirect
72. #5036C22semidirect
73. #5036C22semidirect
74. #5035C22semidirect
75. #5035C22semidirect
76. #5034C22semidirect
77. #5033C22semidirect
78. #5018C22semidirect
79. C4×#214C22semidirect
80. #5014C22semidirect
81. #5014C22semidirect
82. #5014C22semidirect
83. C4×#213C22semidirect
84. C4×#213C22semidirect
85. C4×#213C22semidirect
88. #5000C22semidirect
89. #4998C22semidirect
90. #4997C22semidirect
91. #4995C22semidirect
92. #4926C22semidirect
93. #4925C22semidirect
94. #4924C22semidirect
95. C2×C4⋊(C3⋊C8)C22semidirect
96. #3508D3semidirect
259. #540C2×D3semidirect
261. #533C2×D3semidirect
262. #532C2×D3semidirect
263. #532C2×D3semidirect
264. C2×#127C2×D3semidirect
273. #518C2×D3semidirect
369. #235#41semidirect
375. C2×D12#41semidirect
936. C3#60590semidirect

Maximal subgroups

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

subgroupindex
C3×#35082
C4×#10092
#834352
#834342
#833832
#833762
#833502
#833492
#833012
#833002
#832992
#832982
#831652
C2×#50722
#825382
#825372
#825152
#605903