Finite Group Databasebeta

← #11661729

Subgroups — #11661729

Order 768.

5058 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1009C211yesmaximal, characteristic, complemented
2C2×#5778C212yesmaximal, complemented
3#85985C211yesmaximal, characteristic, complemented
4C3×#3007C211yesmaximal, characteristic, complemented
5#84080C211yesmaximal, characteristic, complemented
6#83982C212yesmaximal, complemented
7C2×#5046C211yesmaximal, characteristic, complemented
8#80231C214yesmaximal, complemented
9#80229C214yesmaximal, complemented
10#80184C212yesmaximal, complemented
11#80182C212yesmaximal, complemented
12#80146C212yesmaximal, complemented
13D3×#450C212yesmaximal, complemented
14#78886C212yesmaximal, complemented
15#78882C212yesmaximal, complemented
16#78637C211yesmaximal, characteristic, complemented
17#78631C211yesmaximal, characteristic, complemented
18#60373—31nomaximal, Sylow
19C22×C3×#41C2211yescharacteristic
20C2×#1009—216no—
21C2×#1009—21no—
22C2×#1009—22no—
23C2×#1009—21no—
24C2×#1009C2212yes—
25C2×#1009C2214yes—
26C2×#1009C2212yes—
27C2×#1007C2211yescharacteristic, complemented
28C22×#239C2212yes—
29C22×D3×D4—22no—
30C22×D3×D4C2212yes—
31C22×#235—21no—
32C22×#235C2211yescharacteristic
33C23×D12—21no—
34C23×D12C2211yescharacteristic
35C2×C3×#137C2212yescomplemented
36C2×C3×C22⋊Q8C2211yescharacteristic, complemented
37C2×#950C2212yescomplemented
38#5816C2211yescharacteristic, complemented
39C22×#215C2212yescomplemented
40#5791C2211yescharacteristic, complemented
41#5778—216no—
42C2×#919C2214yescomplemented
43C2×#918C2214yescomplemented
44C2×#914C2214yescomplemented
45C2×D3×SD16C2214yescomplemented
46C2×#908C2212yescomplemented
47C2×#907C2212yescomplemented
48#5633—21no—
49#5632—21no—
50#5631—21no—
51#5630—21no—
52#5629C2212yescomplemented
53#5628C2212yescomplemented
54#5627C2212yescomplemented
55D3×C22⋊Q8C2212yescomplemented
56#5510C2211yescharacteristic, complemented
57#5507—22no—
58#5504C2211yescharacteristic, complemented
59#5490—22no—
60C3×#452C2214yescomplemented
61C3×#451C2212yescomplemented
62C3×#450C2212yescomplemented
63C3×#417C2212yescomplemented
64C3×#407C2211yescharacteristic, complemented
65#5239C2212yescomplemented
66#5238C2212yescomplemented
67#5233C2212yescomplemented
68#5228C2211yescharacteristic, complemented
69#5227C2211yescharacteristic, complemented
70#5218C2211yescharacteristic, complemented
71#5217C2211yescharacteristic, complemented
72C2×#830C2211yescharacteristic, complemented
73#5187C2214yescomplemented
74#5187C2214yescomplemented
75#5169C2214yescomplemented
76#5169C2214yescomplemented
77#5131C2212yescomplemented
78#5129C2212yescomplemented
79#5046C2212yescomplemented
80#5046C2212yescomplemented
81#5046C2214yescomplemented
82C2×#809C2212yescomplemented
83#4810C2214yescomplemented
84#4808C2214yescomplemented
85#4804C2214yescomplemented
86#4803C2214yescomplemented
87#4776C2214yescomplemented
88#4773C2214yescomplemented
89#4770C2214yescomplemented
90D3×#102C2214yescomplemented
91#4732C2212yescomplemented
92#4732C2212yescomplemented
93#4731C2212yescomplemented
94#4731C2212yescomplemented
95#4727C2214yescomplemented
96#4726C2212yescomplemented
97D3×C22⋊C8C2212yescomplemented
98C22×H(5,𝔽2)—31no—
99C2×#577—32no—
100#3489—31no—
101#3012—34no—
102#3012—32no—
103#3009—34no—
104#3009—32no—
105#3007—32no—
106#3007D311yescharacteristic, complemented
107#3003—32no—
108#3003—31no—
109#3002—32no—
110#3002—31no—
111C2×#450—32no—
112C2×#450—31no—
113#2897—32no—
114#2880—31no—
115C24×D3—21no—
116C24×D3—22no—
117C2×C3×#41—28no—
118C2×C3×#41—21no—
119C2×C3×#41—21no—
120C2×C3×#41C2312yes—
121C2×C3×#41C2312yes—
122C22×C3×Q8C2311yescharacteristic
123C22×C3×Q8C2311yescharacteristic, complemented
124C22×C3×D4—21no—
125C22×C3×D4C2311yescharacteristic
126C23×C3×C4—21no—
127C23×C3×C4C2311yescharacteristic
128C22×#67—22no—
129C22×#67D412yes—
130#1009—232no—
131#1009—216no—
132#1009—216no—
133#1009—28no—
134#1009—216no—
135#1009—216no—
136#1009—28no—
137#1009—28no—
138#1009D4116yescomplemented
139#1007—28no—
140C2×#239—216no—
141C2×#239—21no—
142C2×#239—22no—
143C2×#239—22no—
144C2×#239C2314yes—
145C2×#239C2314yes—
146C2×#239C2312yescomplemented
147C2×D3×Q8—21no—
148C2×D3×Q8C2312yescomplemented
149C2×D3×D4—232no—
150C2×D3×D4—24no—
151C2×D3×D4—24no—
152C2×D3×D4—24no—
153C2×D3×D4—24no—
154C2×D3×D4—216no—
155C2×D3×D4—22no—
156C2×D3×D4—22no—
157C2×D3×D4C2314yes—
158C2×D3×D4C2314yes—
159C2×#235—216no—
160C2×#235—28no—
161C2×#235—22no—
162C2×#235—24no—
163C2×#235—22no—
164C2×#235—22no—
165C2×#235D411yescharacteristic
166C2×#235D412yes—
167C2×#235D411yescharacteristic
168C2×#235C2311yescharacteristic
169C2×#235C2312yes—
170C2×#235C2311yescharacteristic
171C2×#235C2311yescharacteristic, complemented
172C22×D12—216no—
173C22×D12—22no—
174C22×D12—21no—
175C22×D12—21no—
176C22×D12—21no—
177C22×D12—24no—
178C22×D12—22no—
179C22×D12—22no—
180C22×D12—28no—
181C22×D12D411yescharacteristic
182C22×D12C2312yes—
183C22×D12C2312yes—
184C22×D12C2312yes—
185C22×C4×D3—22no—
186C22×C4×D3C2312yes—
187C22×Dic6D411yescharacteristic
188C3×#137—28no—
189C2×C3×Q16C2314yescomplemented
190C2×C3×SD16C2314yescomplemented
191C2×C3×M16C2312yescomplemented
192C3×C22⋊Q8—21no—
193C3×C22⋊Q8—21no—
194C3×C22⋊Q8C2312yes—
195C3×C22⋊Q8C2312yescomplemented
196C2×C3×C4⋊C4—21no—
197C2×C3×C4⋊C4C2311yescharacteristic, complemented
198C2×C3×C22⋊C4—21no—
199#953—21no—
200#950—28no—
201#947—21no—
202#946C2312yescomplemented
203#946C2312yescomplemented
204#944—21no—
205C2×#216C2312yescomplemented
206C2×#215—28no—
207C2×#215C2314yescomplemented
208C2×#215C2314yescomplemented
209C2×#215C2312yescomplemented
210C2×#214C2312yescomplemented
211C2×#213C2312yescomplemented
212#930—22no—
213#930C2311yescharacteristic
214#930C2311yescharacteristic, complemented
215#929—21no—
216#929—22no—
217C4×#67—21no—
218C4×#67—21no—
219C4×#67—22no—
220#926C2311yescharacteristic, complemented
221#924C2311yescharacteristic
222#924C2311yescharacteristic, complemented
223C22×C3⋊C8C2312yescomplemented
224#919—216no—
225#918—216no—
226#914—216no—
227D3×SD16—216no—
228#908—28no—
229#907—28no—
230C2×D24C2314yescomplemented
231C2×#204C2314yescomplemented
232C2×ΓL(1,𝔽25)C2314yescomplemented
233C2×D3×C8C2314yescomplemented
234#897—21no—
235#897C2312yescomplemented
236#896—22no—
237#896—22no—
238#895—21no—
239#895—22no—
240#895C2312yescomplemented
241#894—22no—
242#894—22no—
243#893—21no—
244#893—22no—
245#892C2312yescomplemented
246D3×C4⋊C4—22no—
247D3×C4⋊C4C2312yescomplemented
248#888—22no—
249#887—21no—
250#885—22no—
251#884—22no—
252#884—22no—
253#883—22no—
254#882—22no—
255#67⋊C4—22no—
256D3×C22⋊C4—22no—
257#878—22no—
258C3×#103C2314yescomplemented
259C3×#102C2314yescomplemented
260C3×C22⋊C8C2312yes—
261C3×C22⋊C8C2312yescomplemented
262#835C2312yescomplemented
263#835C2312yescomplemented
264#832C2312yescomplemented
265#832C2312yescomplemented
266#830C2311yescharacteristic
267#830C2311yescharacteristic
268#830C2312yescomplemented
269#821C2314yescomplemented
270#821C2314yescomplemented
271(C2×D3)⋊C8C2314yescomplemented
272(C2×D3)⋊C8C2314yescomplemented
273#809C2314yescomplemented
274#809C2314yescomplemented
275C2×2−1+4—31no—
276C2×H(5,𝔽2)—32no—
277C2×H(5,𝔽2)—34no—
278C2×H(5,𝔽2)—32no—
279C2×H(5,𝔽2)—61no—
280C2×H(5,𝔽2)—62no—
281C2×H(5,𝔽2)—61no—
282C2×H(5,𝔽2)—616no—
283C22×#41—31no—
284C22×#41—32no—
285C22×#41—61no—
286C22×#41C2×D311yescharacteristic
287C23×D4—32no—
288C23×D4—31no—
289C23×D4—61no—
290C23×D4—62no—
291#577—616no—
292C2×#137—34no—
293C2×#137C2×D312yescomplemented
294C2×AGL(1,ℤ/8)—34no—
295C2×AGL(1,ℤ/8)—32no—
296C2×#135—32no—
297C2×#135—34no—
298C22×SD16—32no—
299C22×SD16—34no—
300C2×#131—32no—
301D4×Q8—61no—
302#548—61no—
303#547—62no—
304#547—61no—
305#546—62no—
306#546—61no—
307#537—32no—
308#537—31no—
309#536—31no—
310#536—32no—
311#525—31no—
312#525—32no—
313C2×C22⋊Q8—32no—
314C2×C22⋊Q8C2×D311yescharacteristic, complemented
315#520—31no—
316#452—32no—
317#452—34no—
318#452—34no—
319#452—34no—
320#452C2×D314yescomplemented
321#451—31no—
322#451C2×D312yescomplemented
323#450—31no—
324#450—34no—
325#450—34no—
326#450—32no—
327#450—32no—
328#450—34no—
329#450—34no—
330#450—32no—
331#450—32no—
332#450C2×D312yescomplemented
333#449—32no—
334#449—34no—
335#448—31no—
336#447—31no—
337#447—34no—
338#447—32no—
339#447—32no—
340#418—32no—
341#418—34no—
342#417—34no—
343#417C2×D312yescomplemented
344#416—32no—
345#416—34no—
346C2×#102—32no—
347C2×#102—34no—
348#408—32no—
349#408—34no—
350#407—32no—
351#407C2×D311yescharacteristic, complemented
352C2×C22⋊C8—31no—
353C2×C22⋊C8—32no—
354C24×C3—21no—
355C24×C3C2×D411yescharacteristic
356C23×D3—22no—
357C23×D3—28no—
358C23×D3—216no—
359C23×D3—22no—
360C23×D3—22no—
361C23×D3—24no—
362C23×D3—24no—
363C23×D3—84no—
364C23×D3—82no—
365C23×D3—84no—
366C23×D3—82no—
367C23×D3C2×D412yes—
368C3×#41—28no—
369C3×#41—28no—
370C3×#41—24no—
371C3×#41—24no—
372C3×#41—24no—
373C3×#41C2×D418yes—
374C2×C3×Q8—24no—
375C2×C3×Q8—21no—
376C2×C3×Q8—21no—
377C2×C3×Q8—24no—
378C2×C3×Q8C2412yes—
379C2×C3×Q8C2412yes—
380C2×C3×D4—28no—
381C2×C3×D4—22no—
382C2×C3×D4—22no—
383C2×C3×D4—24no—
384C2×C3×D4—21no—
385C2×C3×D4C2412yes—
386C22×C3×C4—28no—
387C22×C3×C4—21no—
388C22×C3×C4—22no—
389C22×C3×C4—22no—
390C22×C3×C4—24no—
391C22×C3×C4—21no—
392C22×C3×C4—21no—
393C22×C3×C4C2×D411yescharacteristic
394C22×C3×C4C2×D411yescharacteristic
395C22×C3×C4C2×D411yescharacteristic
396C22×C3×C4C2411yescharacteristic
397C22×C3×C4C2411yescharacteristic
398C22×C3×C4C2411yescharacteristic
399C2×#67—216no—
400C2×#67—28no—
401C2×#67—21no—
402C2×#67—21no—
403C2×#67—21no—
404C2×#67—24no—
405C2×#67—24no—
406C2×#67C2×D412yes—
407C2×#67C2×D412yes—
408C2×#67C2×D412yes—
409C2×#67C2×D412yes—
410C22×Dic3C2×D412yes—
411#239—216no—
412#239—216no—
413#239—28no—
414#239—28no—
415#239—28no—
416#239—28no—
417#239—44no—
418#239C2×D4116yes—
419D3×Q8—28no—
420D3×Q8—44no—
421D3×D4—232no—
422D3×D4—232no—
423D3×D4—216no—
424D3×D4—232no—
425D3×D4—216no—
426D3×D4—28no—
427D3×D4—232no—
428D3×D4—28no—
429D3×D4—28no—
430D3×D4C2×D4116yes—
431#235—216no—
432#235—232no—
433#235—24no—
434#235—28no—
435#235—24no—
436#235—28no—
437#235—24no—
438#235—216no—
439#235—24no—
440#235—48no—
441#235C2×D418yes—
442C2×D12—28no—
443C2×D12—216no—
444C2×D12—28no—
445C2×D12—232no—
446C2×D12—216no—
447C2×D12—28no—
448C2×D12—24no—
449C2×D12—24no—
450C2×D12—22no—
451C2×D12—22no—
452C2×D12—22no—
453C2×D12—24no—
454C2×D12—24no—
455C2×D12—216no—
456C2×D12—28no—
457C2×D12—28no—
458C2×D12—22no—
459C2×D12—22no—
460C2×D12C2×D412yes—
461C2×D12C2×D411yescharacteristic
462C2×D12C2×D418yes—
463C2×D12C2×D411yescharacteristic
464C2×D12C2411yescharacteristic
465C2×D12C2414yes—
466C2×C4×D3—216no—
467C2×C4×D3—24no—
468C2×C4×D3—24no—
469C2×C4×D3—28no—
470C2×C4×D3—22no—
471C2×C4×D3—21no—
472C2×C4×D3—22no—
473C2×C4×D3—22no—
474C2×C4×D3C2×D412yes—
475C2×C4×D3C2×D412yes—
476C2×C4×D3C2412yes—
477C2×C4×D3C2412yes—
478C2×Dic6—24no—
479C2×Dic6—22no—
480C2×Dic6C2×D412yes—
481C2×Dic6C2×D411yescharacteristic
482C2×Dic6C2×D411yescharacteristic
483C2×Dic6C2411yescharacteristic
484C3×Q16—28no—
485C3×SD16—28no—
486C3×M16—24no—
487C2×C3×C8C2414yes—
488C3×C4⋊C4—21no—
489C3×C4⋊C4—22no—
490C3×C4⋊C4—22no—
491C3×C4⋊C4C2412yes—
492C3×C22⋊C4—22no—
493C3×C22⋊C4—22no—
494#217—21no—
495#217—21no—
496#217—21no—
497#216—24no—
498#215—24no—
499#215—28no—
500#215—28no—
501#214—24no—
502#213—24no—
503(C2×D3)⋊C4—22no—
504(C2×D3)⋊C4—22no—
505(C2×D3)⋊C4—22no—
506(C2×D3)⋊C4—22no—
507(C2×D3)⋊C4—21no—
508(C2×D3)⋊C4—21no—
509(C2×D3)⋊C4—22no—
510C4⋊Dic3—22no—
511C4⋊Dic3C2411yescharacteristic
512C4⋊Dic3C2411yescharacteristic
513Dic3⋊C4—21no—
514Dic3⋊C4—21no—
515Dic3⋊C4—22no—
516Dic3⋊C4—22no—
517Dic3⋊C4—22no—
518C4×Dic3—21no—
519C4×Dic3—22no—
520C2×C3⋊C8—24no—
521C2×C3⋊C8C2412yes—
522C2×C3⋊C8C2412yes—
523D24—28no—
524#204—28no—
525ΓL(1,𝔽25)—28no—
526D3×C8—28no—
527C25—62no—
528C25—61no—
5292−1+4—68no—
530H(5,𝔽2)—316no—
531H(5,𝔽2)—616no—
532H(5,𝔽2)—68no—
533H(5,𝔽2)—616no—
534H(5,𝔽2)—68no—
535H(5,𝔽2)—616no—
536H(5,𝔽2)—632no—
537H(5,𝔽2)—616no—
538H(5,𝔽2)—68no—
539C2×#41—28no—
540C2×#41—21no—
541C2×#41—21no—
542C2×#41—31no—
543C2×#41—32no—
544C2×#41—31no—
545C2×#41—31no—
546C2×#41—32no—
547C2×#41—31no—
548C2×#41—34no—
549C2×#41—32no—
550C2×#41—34no—
551C2×#41—31no—
552C2×#41—62no—
553C2×#41—62no—
554C2×#41—64no—
555C2×#41—62no—
556C2×#41—68no—
557C2×#41—616no—
558C2×#41—62no—
559C2×#41—62no—
560C2×#41—61no—
561C2×#41—616no—
562C2×#41C22×D312yes—
563C2×#41C22×D312yes—
564C22×Q8—31no—
565C22×Q8—32no—
566C22×Q8—61no—
567C22×Q8C22×D311yescharacteristic
568C22×Q8C22×D311yescharacteristic, complemented
569C22×D4—21no—
570C22×D4—34no—
571C22×D4—32no—
572C22×D4—34no—
573C22×D4—31no—
574C22×D4—32no—
575C22×D4—32no—
576C22×D4—32no—
577C22×D4—68no—
578C22×D4—62no—
579C22×D4—64no—
580C22×D4—62no—
581C22×D4—62no—
582C22×D4—616no—
583C22×D4—62no—
584C22×D4—62no—
585C22×D4—62no—
586C22×D4—616no—
587C22×D4—64no—
588C22×D4—64no—
589C22×D4—64no—
590C22×D4—64no—
591C22×D4—632no—
592C22×D4—61no—
593C22×D4—61no—
594C22×D4—61no—
595C22×D4C22×D311yescharacteristic
596C23×C4—21no—
597C23×C4—32no—
598C23×C4—62no—
599C23×C4C22×D311yescharacteristic
600#137—28no—
601#137—616no—
602AGL(1,ℤ/8)—68no—
603AGL(1,ℤ/8)—616no—
604#135—616no—
605#135—68no—
606C2×Q16—32no—
607C2×Q16C22×D314yescomplemented
608C2×SD16—34no—
609C2×SD16—34no—
610C2×SD16—32no—
611C2×SD16—32no—
612C2×SD16—34no—
613C2×SD16—616no—
614C2×SD16—68no—
615C2×SD16C22×D314yescomplemented
616C2×D8—32no—
617C2×D8—34no—
618#131—68no—
619C2×M16—34no—
620C2×M16C22×D312yescomplemented
621C22×C8—32no—
622C22×C8—34no—
623C4⋊Q8—62no—
624C4⋊Q8—61no—
625#124—62no—
626#124—61no—
627#123—62no—
628#123—62no—
629#123—62no—
630#123—62no—
631#123—61no—
632C22⋊Q8—21no—
633C22⋊Q8—21no—
634C22⋊Q8—32no—
635C22⋊Q8—32no—
636C22⋊Q8—31no—
637C22⋊Q8—31no—
638C22⋊Q8—32no—
639C22⋊Q8—62no—
640C22⋊Q8—62no—
641C22⋊Q8—62no—
642C22⋊Q8—61no—
643C22⋊Q8C22×D312yes—
644C22⋊Q8C22×D312yescomplemented
645#121—31no—
646#121—31no—
647#121—32no—
648#121—62no—
649#121—62no—
650#121—62no—
651#121—61no—
652#121—62no—
653#120—62no—
654#120—61no—
655C4×Q8—61no—
656C4×D4—62no—
657C4×D4—62no—
658C4×D4—61no—
659C4×D4—62no—
660C4×D4—61no—
661C4×D4—61no—
662#117—31no—
663#117—32no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—32no—
666C2×C4⋊C4—62no—
667C2×C4⋊C4C22×D311yescharacteristic, complemented
668C2×C22⋊C4—21no—
669C2×C22⋊C4—62no—
670#103—32no—
671#103—32no—
672#103C22×D314yescomplemented
673#102—32no—
674#102—32no—
675#102—34no—
676#102—34no—
677#102—34no—
678#102—34no—
679#102C22×D314yescomplemented
680C22⋊C8—31no—
681C22⋊C8—31no—
682C22⋊C8—32no—
683C22⋊C8—34no—
684C22⋊C8—34no—
685C22⋊C8C22×D312yes—
686C22⋊C8C22×D312yescomplemented
687C23×C3—24no—
688C23×C3—22no—
689C23×C3—22no—
690C23×C3—22no—
691C23×C3—41no—
692C23×C3—42no—
693C23×C3—42no—
694C23×C3C22×D411yescharacteristic
695C23×C3C22×D411yescharacteristic
696C23×C3C22×D411yescharacteristic
697C22×D3—28no—
698C22×D3—24no—
699C22×D3—24no—
700C22×D3—216no—
701C22×D3—28no—
702C22×D3—28no—
703C22×D3—24no—
704C22×D3—216no—
705C22×D3—21no—
706C22×D3—42no—
707C22×D3—44no—
708C22×D3—44no—
709C22×D3—84no—
710C22×D3—84no—
711C22×D3—84no—
712C22×D3—84no—
713C22×D3—82no—
714C22×D3—82no—
715C22×D3—82no—
716C22×D3—82no—
717C22×D3—832no—
718C22×D3—816no—
719C22×D3C22×D412yes—
720C22×D3C22×D412yes—
721C3×Q8—24no—
722C3×Q8—22no—
723C3×Q8—24no—
724C3×Q8—42no—
725C3×Q8C22×D414yes—
726C3×D4—28no—
727C3×D4—24no—
728C3×D4—28no—
729C3×D4—22no—
730C3×D4C22×D414yes—
731C2×C3×C4—24no—
732C2×C3×C4—28no—
733C2×C3×C4—22no—
734C2×C3×C4—22no—
735C2×C3×C4—22no—
736C2×C3×C4—28no—
737C2×C3×C4—22no—
738C2×C3×C4—22no—
739C2×C3×C4—22no—
740C2×C3×C4—22no—
741C2×C3×C4—22no—
742C2×C3×C4—42no—
743C2×C3×C4—81no—
744C2×C3×C4C22×D411yescharacteristic
745C2×C3×C4C22×D411yescharacteristic
746C2×C3×C4C22×D411yescharacteristic
747C2×C3×C4C22×D414yes—
748C2×C3×C4C2511yescharacteristic
749#67—216no—
750#67—24no—
751#67—24no—
752#67—24no—
753#67—216no—
754#67—42no—
755#67—42no—
756#67—81no—
757#67#12018yes—
758C2×Dic3—24no—
759C2×Dic3—21no—
760C2×Dic3—21no—
761C2×Dic3—21no—
762C2×Dic3C22×D412yes—
763C2×Dic3C22×D412yes—
764D12—28no—
765D12—216no—
766D12—28no—
767D12—24no—
768D12—216no—
769D12—22no—
770D12—28no—
771D12—24no—
772D12—22no—
773D12—44no—
774D12—82no—
775D12#12014yes—
776D12C22×D418yes—
777C4×D3—216no—
778C4×D3—24no—
779C4×D3—24no—
780C4×D3—216no—
781C4×D3—24no—
782C4×D3—44no—
783C4×D3—42no—
784C4×D3—44no—
785C4×D3—82no—
786C4×D3C22×D418yes—
787Dic6—22no—
788Dic6—24no—
789Dic6—22no—
790Dic6—44no—
791Dic6#12014yes—
792C3×C8—24no—
793C3⋊C8—22no—
794C3⋊C8—22no—
795C24—21no—
796C24—32no—
797C24—64no—
798C24—64no—
799C24—616no—
800C24—68no—
801C24—62no—
802C24—62no—
803C24—62no—
804C24—242no—
805C24—244no—
806C24—242no—
807C24—244no—
808C24D3×D411yescharacteristic
809#41—28no—
810#41—28no—
811#41—24no—
812#41—24no—
813#41—24no—
814#41—38no—
815#41—316no—
816#41—68no—
817#41—68no—
818#41—64no—
819#41—64no—
820#41—616no—
821#41—632no—
822#41—616no—
823#41—68no—
824#41—68no—
825#41—68no—
826#41—616no—
827#41—616no—
828#41—68no—
829#41—64no—
830#41—64no—
831#41—128no—
832#41—124no—
833#41D3×D418yes—
834C2×Q8—24no—
835C2×Q8—21no—
836C2×Q8—21no—
837C2×Q8—24no—
838C2×Q8—31no—
839C2×Q8—32no—
840C2×Q8—31no—
841C2×Q8—31no—
842C2×Q8—62no—
843C2×Q8—64no—
844C2×Q8—68no—
845C2×Q8—124no—
846C2×Q8C23×D312yes—
847C2×Q8C23×D312yes—
848C2×D4—28no—
849C2×D4—22no—
850C2×D4—22no—
851C2×D4—24no—
852C2×D4—21no—
853C2×D4—32no—
854C2×D4—316no—
855C2×D4—32no—
856C2×D4—32no—
857C2×D4—32no—
858C2×D4—31no—
859C2×D4—38no—
860C2×D4—32no—
861C2×D4—31no—
862C2×D4—34no—
863C2×D4—31no—
864C2×D4—68no—
865C2×D4—64no—
866C2×D4—68no—
867C2×D4—616no—
868C2×D4—64no—
869C2×D4—64no—
870C2×D4—616no—
871C2×D4—68no—
872C2×D4—632no—
873C2×D4—68no—
874C2×D4—616no—
875C2×D4—68no—
876C2×D4—62no—
877C2×D4—62no—
878C2×D4—68no—
879C2×D4—64no—
880C2×D4—64no—
881C2×D4—68no—
882C2×D4—632no—
883C2×D4—616no—
884C2×D4—632no—
885C2×D4—616no—
886C2×D4—632no—
887C2×D4—632no—
888C2×D4—68no—
889C2×D4—616no—
890C2×D4—68no—
891C2×D4—61no—
892C2×D4—61no—
893C2×D4—61no—
894C2×D4—62no—
895C2×D4—62no—
896C2×D4—62no—
897C2×D4—64no—
898C2×D4C23×D312yes—
899C22×C4—28no—
900C22×C4—21no—
901C22×C4—22no—
902C22×C4—22no—
903C22×C4—24no—
904C22×C4—21no—
905C22×C4—21no—
906C22×C4—32no—
907C22×C4—32no—
908C22×C4—32no—
909C22×C4—32no—
910C22×C4—32no—
911C22×C4—68no—
912C22×C4—64no—
913C22×C4—64no—
914C22×C4—62no—
915C22×C4—616no—
916C22×C4—62no—
917C22×C4—62no—
918C22×C4—61no—
919C22×C4D3×D411yescharacteristic
920C22×C4D3×D411yescharacteristic
921C22×C4D3×D411yescharacteristic
922C22×C4C23×D311yescharacteristic
923C22×C4C23×D311yescharacteristic
924C22×C4C23×D311yescharacteristic
925Q16—28no—
926Q16—64no—
927SD16—28no—
928SD16—68no—
929SD16—68no—
930SD16—68no—
931SD16—64no—
932SD16—64no—
933D8—68no—
934D8—64no—
935M16—24no—
936M16—68no—
937C2×C8—32no—
938C2×C8—32no—
939C2×C8—68no—
940C2×C8—64no—
941C2×C8C23×D314yes—
942C4⋊C4—22no—
943C4⋊C4—22no—
944C4⋊C4—21no—
945C4⋊C4—31no—
946C4⋊C4—31no—
947C4⋊C4—62no—
948C4⋊C4—62no—
949C4⋊C4—62no—
950C4⋊C4—62no—
951C4⋊C4—61no—
952C4⋊C4—61no—
953C4⋊C4C23×D312yes—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—62no—
957C22⋊C4—62no—
958C22⋊C4—62no—
959C22⋊C4—62no—
960C22⋊C4—62no—
961C22⋊C4—61no—
962C22⋊C4—61no—
963C22⋊C4—61no—
964C22⋊C4—61no—
965C22⋊C4—61no—
966C42—62no—
967C42—61no—
968C22×C3—21no—
969C22×C3—21no—
970C22×C3—21no—
971C22×C3—21no—
972C22×C3—21no—
973C22×C3—21no—
974C22×C3—24no—
975C22×C3—21no—
976C22×C3—44no—
977C22×C3—48no—
978C22×C3—42no—
979C22×C3—42no—
980C22×C3C2×#12012yes—
981C22×C3#57712yescomplemented
982C22×C3C23×D411yescharacteristic
983C2×D3—22no—
984C2×D3—22no—
985C2×D3—22no—
986C2×D3—22no—
987C2×D3—28no—
988C2×D3—22no—
989C2×D3—48no—
990C2×D3—416no—
991C2×D3—44no—
992C2×D3—44no—
993C2×D3—41no—
994C2×D3—41no—
995C2×D3—41no—
996C2×D3—816no—
997C2×D3—88no—
998C2×D3—816no—
999C2×D3—88no—
1000C2×D3C2×#12014yes—
1001C3×C4—21no—
1002C3×C4—24no—
1003C3×C4—21no—
1004C3×C4—42no—
1005C3×C4—42no—
1006C3×C4C2×#12012yes—
1007C3×C4C23×D412yes—
1008Dic3—22no—
1009Dic3—41no—
1010Dic3—41no—
1011Dic3—41no—
1012Dic3C2×#12014yes—
1013C23—24no—
1014C23—22no—
1015C23—22no—
1016C23—22no—
1017C23—32no—
1018C23—32no—
1019C23—41no—
1020C23—42no—
1021C23—42no—
1022C23—64no—
1023C23—616no—
1024C23—68no—
1025C23—68no—
1026C23—616no—
1027C23—64no—
1028C23—64no—
1029C23—68no—
1030C23—61no—
1031C23—122no—
1032C23—124no—
1033C23—124no—
1034C23—242no—
1035C23—242no—
1036C23—242no—
1037C23—242no—
1038C23—244no—
1039C23—244no—
1040C23—244no—
1041C23—244no—
1042C23—2416no—
1043C23—2432no—
1044C23C2×D3×D411yescharacteristic
1045C23C2×D3×D411yescharacteristic
1046C23C2×D3×D411yescharacteristic
1047Q8—24no—
1048Q8—22no—
1049Q8—24no—
1050Q8—34no—
1051Q8—42no—
1052Q8—64no—
1053Q8—62no—
1054Q8—62no—
1055Q8—124no—
1056Q8C2×D3×D414yes—
1057D4—28no—
1058D4—24no—
1059D4—28no—
1060D4—22no—
1061D4—38no—
1062D4—38no—
1063D4—34no—
1064D4—64no—
1065D4—616no—
1066D4—68no—
1067D4—616no—
1068D4—68no—
1069D4—64no—
1070D4—616no—
1071D4—64no—
1072D4—616no—
1073D4—64no—
1074D4—64no—
1075D4—62no—
1076D4—68no—
1077D4—62no—
1078D4—124no—
1079D4—122no—
1080D4—122no—
1081D4—242no—
1082D4—241no—
1083D4C2×D3×D414yes—
1084C2×C4—24no—
1085C2×C4—28no—
1086C2×C4—22no—
1087C2×C4—22no—
1088C2×C4—22no—
1089C2×C4—22no—
1090C2×C4—22no—
1091C2×C4—28no—
1092C2×C4—22no—
1093C2×C4—22no—
1094C2×C4—22no—
1095C2×C4—32no—
1096C2×C4—38no—
1097C2×C4—32no—
1098C2×C4—42no—
1099C2×C4—64no—
1100C2×C4—616no—
1101C2×C4—64no—
1102C2×C4—616no—
1103C2×C4—64no—
1104C2×C4—64no—
1105C2×C4—61no—
1106C2×C4—61no—
1107C2×C4—61no—
1108C2×C4—81no—
1109C2×C4—124no—
1110C2×C4—124no—
1111C2×C4—122no—
1112C2×C4—242no—
1113C2×C4C2×D3×D411yescharacteristic
1114C2×C4C2×D3×D411yescharacteristic
1115C2×C4C2×D3×D414yes—
1116C2×C4C2×D3×D411yescharacteristic
1117C2×C4C24×D311yescharacteristic
1118C8—24no—
1119C8—62no—
1120C8—62no—
1121C2×C3—22no—
1122C2×C3—22no—
1123C2×C3—41no—
1124C2×C3—44no—
1125C2×C3C22×#12011yescharacteristic
1126C2×C3C2×#57711yescharacteristic
1127C2×C3#358511yescharacteristic
1128D3—24no—
1129D3—42no—
1130D3—48no—
1131D3—81no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—21no—
1137C22—24no—
1138C22—21no—
1139C22—21no—
1140C22—34no—
1141C22—44no—
1142C22—48no—
1143C22—42no—
1144C22—42no—
1145C22—62no—
1146C22—62no—
1147C22—68no—
1148C22—62no—
1149C22—62no—
1150C22—62no—
1151C22—128no—
1152C22—1216no—
1153C22—124no—
1154C22—124no—
1155C22—121no—
1156C22—121no—
1157C22—121no—
1158C22—248no—
1159C22—2416no—
1160C22—248no—
1161C22—2416no—
1162C22D3×#12012yes—
1163C22#577812yescomplemented
1164C22C22×D3×D411yescharacteristic
1165C4—21no—
1166C4—24no—
1167C4—21no—
1168C4—34no—
1169C4—42no—
1170C4—42no—
1171C4—62no—
1172C4—121no—
1173C4—121no—
1174C4—121no—
1175C4D3×#12012yes—
1176C4C22×D3×D412yes—
1177C3#6037311yescharacteristic, complemented, Sylow
1178C2—22no—
1179C2—22no—
1180C2—41no—
1181C2—44no—
1182C2—64no—
1183C2—122no—
1184C2—128no—
1185C2—241no—
1186C2C2×D3×#12011yescharacteristic
1187C2C2×#577811yescharacteristic
1188C2#8720011yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3007C2
socleC22×C3C23×D4
hypercenter#3007D3
hypocenterC3#60373
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3007

Complements

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

NH ≅ G/Ntype
1. C22×#1009C2semidirect
2. C2×#5778C2semidirect
3. #85985C2semidirect
4. C3×#3007C2semidirect
5. #84080C2semidirect
6. #83982C2semidirect
7. C2×#5046C2semidirect
8. #80231C2semidirect
9. #80229C2semidirect
10. #80184C2semidirect
11. #80182C2semidirect
12. #80146C2semidirect
13. D3×#450C2semidirect
14. #78886C2semidirect
15. #78882C2semidirect
16. #78637C2semidirect
17. #78631C2semidirect
27. C2×#1007C22semidirect
35. C2×C3×#137C22semidirect
36. C2×C3×C22⋊Q8C22semidirect
37. C2×#950C22semidirect
38. #5816C22semidirect
39. C22×#215C22semidirect
40. #5791C22semidirect
42. C2×#919C22semidirect
43. C2×#918C22semidirect
44. C2×#914C22semidirect
45. C2×D3×SD16C22semidirect
46. C2×#908C22semidirect
47. C2×#907C22semidirect
52. #5629C22semidirect
53. #5628C22semidirect
54. #5627C22semidirect
55. D3×C22⋊Q8C22semidirect
56. #5510C22semidirect
58. #5504C22semidirect
60. C3×#452C22semidirect
61. C3×#451C22semidirect
62. C3×#450C22semidirect
63. C3×#417C22semidirect
64. C3×#407C22semidirect
65. #5239C22semidirect
66. #5238C22semidirect
67. #5233C22semidirect
68. #5228C22semidirect
69. #5227C22semidirect
70. #5218C22semidirect
71. #5217C22semidirect
72. C2×#830C22semidirect
73. #5187C22semidirect
74. #5187C22semidirect
75. #5169C22semidirect
76. #5169C22semidirect
77. #5131C22semidirect
78. #5129C22semidirect
79. #5046C22semidirect
80. #5046C22semidirect
81. #5046C22semidirect
82. C2×#809C22semidirect
83. #4810C22semidirect
84. #4808C22semidirect
85. #4804C22semidirect
86. #4803C22semidirect
87. #4776C22semidirect
88. #4773C22semidirect
89. #4770C22semidirect
90. D3×#102C22semidirect
91. #4732C22semidirect
92. #4732C22semidirect
93. #4731C22semidirect
94. #4731C22semidirect
95. #4727C22semidirect
96. #4726C22semidirect
97. D3×C22⋊C8C22semidirect
106. #3007D3semidirect
123. C22×C3×Q8C23semidirect
138. #1009D4semidirect
146. C2×#239C23semidirect
148. C2×D3×Q8C23semidirect
171. C2×#235C23semidirect
189. C2×C3×Q16C23semidirect
190. C2×C3×SD16C23semidirect
191. C2×C3×M16C23semidirect
195. C3×C22⋊Q8C23semidirect
197. C2×C3×C4⋊C4C23semidirect
202. #946C23semidirect
203. #946C23semidirect
205. C2×#216C23semidirect
207. C2×#215C23semidirect
208. C2×#215C23semidirect
209. C2×#215C23semidirect
210. C2×#214C23semidirect
211. C2×#213C23semidirect
214. #930C23semidirect
220. #926C23semidirect
222. #924C23semidirect
223. C22×C3⋊C8C23semidirect
230. C2×D24C23semidirect
231. C2×#204C23semidirect
232. C2×ΓL(1,𝔽25)C23semidirect
233. C2×D3×C8C23semidirect
235. #897C23semidirect
240. #895C23semidirect
245. #892C23semidirect
247. D3×C4⋊C4C23semidirect
258. C3×#103C23semidirect
259. C3×#102C23semidirect
261. C3×C22⋊C8C23semidirect
262. #835C23semidirect
263. #835C23semidirect
264. #832C23semidirect
265. #832C23semidirect
268. #830C23semidirect
269. #821C23semidirect
270. #821C23semidirect
271. (C2×D3)⋊C8C23semidirect
272. (C2×D3)⋊C8C23semidirect
273. #809C23semidirect
274. #809C23semidirect
293. C2×#137C2×D3semidirect
314. C2×C22⋊Q8C2×D3semidirect
320. #452C2×D3semidirect
322. #451C2×D3semidirect
332. #450C2×D3semidirect
343. #417C2×D3semidirect
351. #407C2×D3semidirect
568. C22×Q8C22×D3semidirect
607. C2×Q16C22×D3semidirect
615. C2×SD16C22×D3semidirect
620. C2×M16C22×D3semidirect
644. C22⋊Q8C22×D3semidirect
667. C2×C4⋊C4C22×D3semidirect
672. #103C22×D3semidirect
679. #102C22×D3semidirect
686. C22⋊C8C22×D3semidirect
981. C22×C3#577semidirect
1163. C22#5778semidirect
1177. C3#60373semidirect

Maximal subgroups

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

subgroupindex
C22×#10092
C2×#57782
#859852
C3×#30072
#840802
#839822
C2×#50462
#802312
#802292
#801842
#801822
#801462
D3×#4502
#788862
#788822
#786372
#786312
#603733