Finite Group Databasebeta

← #11661752

Subgroups — #11661752

Order 768.

4714 conjugacy classes of subgroups.

The subgroup lattice has 1142 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#1007C211yesmaximal, characteristic, complemented
2C2×#5779C212yesmaximal, complemented
3#86042C211yesmaximal, characteristic, complemented
4C3×#3004C211yesmaximal, characteristic, complemented
5C2×#5228C211yesmaximal, characteristic, complemented
6#83984C212yesmaximal, complemented
7#82926C211yesmaximal, characteristic, complemented
8#80185C214yesmaximal, complemented
9#80184C212yesmaximal, complemented
10D3×#451C212yesmaximal, complemented
11#80042C214yesmaximal, complemented
12#80039C212yesmaximal, complemented
13#80038C212yesmaximal, complemented
14#78961C212yesmaximal, complemented
15#78957C212yesmaximal, complemented
16#78640C211yesmaximal, characteristic, complemented
17#78631C211yesmaximal, characteristic, complemented
18#60375—31nomaximal, Sylow
19C23×C3×Q8C2211yescharacteristic
20C2×#1010C2211yescharacteristic, complemented
21C2×#1007—216no—
22C2×#1007—22no—
23C2×#1007—21no—
24C2×#1007—21no—
25C2×#1007C2212yes—
26C2×#1007C2214yes—
27C2×#1007C2212yes—
28C22×#239—21no—
29C22×#239C2212yes—
30C22×D3×Q8—21no—
31C22×D3×Q8C2212yes—
32C22×#235—22no—
33C22×#235C2211yescharacteristic
34C22×#235C2211yescharacteristic
35C2×C3×#137C2212yescomplemented
36C3×#525C2211yescharacteristic
37#5833C2211yescharacteristic, complemented
38C2×#950C2212yescomplemented
39C22×#216C2212yescomplemented
40C2×#924C2211yescharacteristic
41#5779—216no—
42C2×#918C2214yescomplemented
43C2×D3×Q16C2214yescomplemented
44C2×#916C2214yescomplemented
45C2×#915C2214yescomplemented
46C2×#909C2212yescomplemented
47C2×#907C2212yescomplemented
48#5655—22no—
49#5628C2212yescomplemented
50D3×C22⋊Q8C2212yes—
51#5608C2212yescomplemented
52#5606C2212yes—
53#5591—22no—
54#5552—21no—
55#5551—21no—
56#5550—21no—
57D4×Dic6—21no—
58#5526C2211yescharacteristic, complemented
59#5523C2211yescharacteristic, complemented
60C3×#451C2212yes—
61C3×#451C2212yescomplemented
62C3×#448C2212yes—
63C3×#448C2212yescomplemented
64C3×#419C2212yescomplemented
65C3×#407C2211yescharacteristic
66#5228C2212yes—
67#5228C2212yes—
68#5228C2214yescomplemented
69C2×#835C2212yescomplemented
70C2×#830C2211yescharacteristic
71#5187C2214yescomplemented
72#5186C2214yescomplemented
73#5172C2214yescomplemented
74#5170C2214yescomplemented
75#5133C2212yescomplemented
76#5129C2212yescomplemented
77#5050C2211yescharacteristic
78#5047C2212yescomplemented
79#5046C2211yescharacteristic
80#5040C2211yescharacteristic
81#5037C2212yescomplemented
82#5036C2211yescharacteristic
83#5002C2212yescomplemented
84#4809C2214yescomplemented
85#4809C2214yescomplemented
86#4808C2214yescomplemented
87#4808C2214yescomplemented
88#4804C2214yescomplemented
89#4803C2214yescomplemented
90#4802C2214yescomplemented
91D3×#103C2214yescomplemented
92#4739C2212yes—
93#4733C2214yescomplemented
94#4731C2212yes—
95#4727C2214yescomplemented
96#4726C2212yes—
97D3×C22⋊C8C2212yes—
98C22×2−1+4—31no—
99C2×#578—32no—
100#3489—31no—
101#3013—34no—
102#3013—32no—
103#3011—34no—
104#3011—32no—
105#3007—32no—
106#3007—31no—
107#3004—32no—
108#3004D311yescharacteristic, complemented
109#3002—32no—
110#3002—31no—
111C2×#451—32no—
112C2×#451—31no—
113#2898—32no—
114#2880—31no—
115C2×C3×#41C2311yescharacteristic
116C22×C3×Q8—28no—
117C22×C3×Q8—21no—
118C22×C3×Q8—21no—
119C22×C3×Q8—21no—
120C22×C3×Q8C2312yes—
121C22×C3×Q8C2312yes—
122C22×C3×Q8C2312yes—
123C23×C3×C4—21no—
124C23×C3×C4C2311yescharacteristic
125C22×#67—21no—
126C22×#67D412yes—
127#1010—28no—
128#1007—216no—
129#1007—216no—
130#1007—232no—
131#1007—28no—
132#1007—216no—
133#1007—216no—
134#1007—28no—
135#1007—28no—
136#1007D4116yescomplemented
137C2×#239—216no—
138C2×#239—216no—
139C2×#239—22no—
140C2×#239—24no—
141C2×#239—22no—
142C2×#239—22no—
143C2×#239—22no—
144C2×#239C2314yes—
145C2×#239C2314yes—
146C2×D3×Q8—216no—
147C2×D3×Q8—216no—
148C2×D3×Q8—22no—
149C2×D3×Q8—22no—
150C2×D3×Q8—22no—
151C2×D3×Q8—24no—
152C2×D3×Q8—22no—
153C2×D3×Q8C2314yes—
154C2×D3×Q8C2312yes—
155C2×D3×Q8C2314yes—
156C2×#237—22no—
157C2×#237C2312yes—
158C2×#235—232no—
159C2×#235—21no—
160C2×#235—21no—
161C2×#235—24no—
162C2×#235—24no—
163C2×#235—24no—
164C2×#235—24no—
165C2×#235—28no—
166C2×#235—28no—
167C2×#235—21no—
168C2×#235D412yes—
169C2×#235D411yescharacteristic
170C2×#235D411yescharacteristic
171C2×#235C2311yescharacteristic
172C2×#235C2312yes—
173C2×#235C2311yescharacteristic
174C2×#235C2312yes—
175C2×#235C2312yes—
176C22×D12—22no—
177C22×D12D411yescharacteristic
178C22×D12C2311yescharacteristic
179C22×C4×D3—22no—
180C22×C4×D3—21no—
181C22×C4×D3—22no—
182C22×C4×D3C2312yes—
183C22×Dic6—22no—
184C22×Dic6—21no—
185C22×Dic6D411yescharacteristic
186C22×Dic6C2311yescharacteristic
187C22×Dic6C2311yescharacteristic
188C3×#137—28no—
189C2×C3×Q16C2314yes—
190C2×C3×SD16C2314yes—
191C2×C3×M16C2312yes—
192C3×#123—21no—
193C3×C22⋊Q8C2311yescharacteristic
194C3×C22⋊Q8C2311yescharacteristic
195C3×#121C2311yescharacteristic
196C3×#121C2311yescharacteristic
197C3×#120—21no—
198C3×C4×D4—21no—
199C3×C4×D4—21no—
200C3×#117C2311yescharacteristic
201C2×#217—21no—
202#950—28no—
203#946C2312yes—
204C2×#216—28no—
205C2×#216C2312yes—
206C2×#216C2314yes—
207C2×#216C2314yes—
208C2×#215C2312yes—
209#939—22no—
210#939—22no—
211#938—22no—
212#938C2312yes—
213#937—22no—
214D4×Dic3—22no—
215C2×#214C2312yes—
216C2×#213C2312yes—
217#930—21no—
218C2×C4⋊Dic3C2311yescharacteristic
219#924—21no—
220#924—21no—
221#924—21no—
222#924C2312yes—
223#924C2312yes—
224C2×Dic3⋊C4—21no—
225C22×C3⋊C8C2312yes—
226#918—216no—
227D3×Q16—216no—
228#916—216no—
229#915—216no—
230#909—28no—
231#907—28no—
232C2×Dic12C2314yes—
233C2×#204C2314yes—
234C2×ΓL(1,𝔽25)C2314yes—
235C2×D3×C8C2314yes—
236#897C2312yes—
237#897C2312yes—
238#896—22no—
239#894—22no—
240#892C2312yes—
241D3×C4⋊C4—22no—
242D3×C4⋊C4C2312yes—
243#888—22no—
244#886—22no—
245#885—22no—
246#884—22no—
247#883—22no—
248#883—22no—
249#67⋊C4—22no—
250#67⋊C4—22no—
251D3×C22⋊C4—22no—
252#878—22no—
253#878—22no—
254#875—21no—
255C4×D12—21no—
256#869—21no—
257C4×Dic6—21no—
258C3×#103C2314yes—
259C3×#103C2314yes—
260C3×C22⋊C8C2312yes—
261C3×C22⋊C8C2312yes—
262#835C2314yes—
263#835C2314yes—
264#830C2311yescharacteristic
265#830C2311yescharacteristic
266#830C2312yes—
267#821C2314yes—
268(C2×D3)⋊C8C2314yes—
269(C2×D3)⋊C8C2314yes—
270#816C2314yes—
271#810C2312yes—
272#810C2312yes—
273#809C2312yes—
274#809C2312yes—
275C2×2−1+4—31no—
276C2×2−1+4—32no—
277C2×2−1+4—34no—
278C2×2−1+4—32no—
279C2×2−1+4—62no—
280C2×2−1+4—61no—
281C2×2−1+4—61no—
282C2×2−1+4—616no—
283C22×#41—31no—
284C22×#41—32no—
285C22×#41—31no—
286C22×#41—62no—
287C22×#41—61no—
288C23×Q8—32no—
289C23×Q8—61no—
290C23×Q8C2×D311yescharacteristic
291#578—616no—
292C2×#137—34no—
293C2×#137—34no—
294C2×#137—32no—
295C2×#137C2×D312yescomplemented
296C2×#135—32no—
297C2×#135—34no—
298C22×Q16—32no—
299C22×Q16—34no—
300C2×#131—32no—
301D4×Q8—61no—
302#548—61no—
303#547—61no—
304#547—62no—
305#546—61no—
306#546—62no—
307#537—31no—
308#537—32no—
309#536—32no—
310#536—31no—
311#525—32no—
312#525C2×D311yescharacteristic
313C2×C22⋊Q8—31no—
314C2×C22⋊Q8—32no—
315#520—31no—
316#452—34no—
317#452—32no—
318#452—34no—
319#452—34no—
320#452—34no—
321#451—32no—
322#451—32no—
323#451—34no—
324#451—34no—
325#451—31no—
326#451—34no—
327#451—34no—
328#451—32no—
329#451C2×D312yes—
330#451C2×D312yescomplemented
331#450—31no—
332#450—32no—
333#449—34no—
334#449—32no—
335#448—34no—
336#448—31no—
337#448C2×D312yes—
338#448C2×D312yescomplemented
339#447—31no—
340#419—34no—
341#419C2×D312yescomplemented
342#417—32no—
343#417—34no—
344#416—32no—
345#416—34no—
346C2×#103—32no—
347C2×#103—34no—
348#408—32no—
349#408—34no—
350#407—32no—
351#407C2×D311yescharacteristic
352C2×C22⋊C8—31no—
353C2×C22⋊C8—32no—
354C24×C3C2×D411yescharacteristic
355C23×D3—21no—
356C23×D3C2×D412yes—
357C3×#41—24no—
358C2×C3×Q8—28no—
359C2×C3×Q8—28no—
360C2×C3×Q8—28no—
361C2×C3×Q8—28no—
362C2×C3×Q8—28no—
363C2×C3×Q8—22no—
364C2×C3×Q8—22no—
365C2×C3×Q8—22no—
366C2×C3×Q8—24no—
367C2×C3×Q8C2×D418yes—
368C2×C3×Q8C2411yescharacteristic
369C2×C3×Q8C2414yes—
370C2×C3×D4—21no—
371C2×C3×D4—21no—
372C2×C3×D4—21no—
373C2×C3×D4C2411yescharacteristic
374C22×C3×C4—28no—
375C22×C3×C4—22no—
376C22×C3×C4—22no—
377C22×C3×C4—22no—
378C22×C3×C4—24no—
379C22×C3×C4—21no—
380C22×C3×C4C2×D411yescharacteristic
381C22×C3×C4C2×D411yescharacteristic
382C22×C3×C4C2×D411yescharacteristic
383C22×C3×C4C2411yescharacteristic
384C22×C3×C4C2411yescharacteristic
385C22×C3×C4C2411yescharacteristic
386C2×#67—28no—
387C2×#67—22no—
388C2×#67—22no—
389C2×#67—28no—
390C2×#67—22no—
391C2×#67—22no—
392C2×#67C2×D412yes—
393C2×#67C2×D412yes—
394C2×#67C2×D412yes—
395C2×#67C2×D412yes—
396C22×Dic3—21no—
397C22×Dic3—21no—
398C22×Dic3—21no—
399C22×Dic3—22no—
400C22×Dic3C2×D412yes—
401#239—232no—
402#239—216no—
403#239—216no—
404#239—216no—
405#239—28no—
406#239—216no—
407#239—28no—
408#239—28no—
409#239C2×D4116yes—
410D3×Q8—216no—
411D3×Q8—216no—
412D3×Q8—216no—
413D3×Q8—232no—
414D3×Q8—28no—
415D3×Q8—28no—
416D3×Q8—216no—
417D3×Q8—28no—
418D3×Q8—28no—
419D3×Q8C2×D4116yes—
420#237—28no—
421#237—48no—
422#235—232no—
423#235—28no—
424#235—232no—
425#235—28no—
426#235—232no—
427#235—24no—
428#235—24no—
429#235—232no—
430#235—28no—
431#235—24no—
432#235—24no—
433#235—28no—
434#235—24no—
435#235—24no—
436#235—44no—
437#235C2×D418yes—
438#235C2×D418yes—
439C2×D12—216no—
440C2×D12—24no—
441C2×D12—24no—
442C2×D12—21no—
443C2×D12—24no—
444C2×D12—24no—
445C2×D12C2×D411yescharacteristic
446C2×D12C2×D412yes—
447C2×D12C2×D411yescharacteristic
448C2×D12C2412yes—
449C2×C4×D3—216no—
450C2×C4×D3—28no—
451C2×C4×D3—216no—
452C2×C4×D3—24no—
453C2×C4×D3—24no—
454C2×C4×D3—22no—
455C2×C4×D3—22no—
456C2×C4×D3—24no—
457C2×C4×D3—24no—
458C2×C4×D3—28no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3C2×D412yes—
462C2×C4×D3C2×D412yes—
463C2×C4×D3C2412yes—
464C2×C4×D3C2412yes—
465C2×Dic6—216no—
466C2×Dic6—21no—
467C2×Dic6—24no—
468C2×Dic6—24no—
469C2×Dic6—24no—
470C2×Dic6—24no—
471C2×Dic6—24no—
472C2×Dic6—21no—
473C2×Dic6—22no—
474C2×Dic6—44no—
475C2×Dic6C2×D411yescharacteristic
476C2×Dic6C2×D412yes—
477C2×Dic6C2×D411yescharacteristic
478C2×Dic6C2412yes—
479C2×Dic6C2412yes—
480C3×Q16—28no—
481C3×SD16—28no—
482C3×M16—24no—
483C2×C3×C8C2414yes—
484C3×C4⋊C4—21no—
485C3×C4⋊C4—21no—
486C3×C4⋊C4C2411yescharacteristic
487C3×C4⋊C4C2411yescharacteristic
488C3×C22⋊C4—21no—
489C3×C22⋊C4—21no—
490C3×C22⋊C4—21no—
491C3×C22⋊C4—21no—
492C3×C22⋊C4—21no—
493C3×C42—21no—
494#217—22no—
495#217—22no—
496#217—22no—
497#216—28no—
498#216—28no—
499#216—24no—
500#215—24no—
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—
507C4⋊Dic3—21no—
508C4⋊Dic3—22no—
509C4⋊Dic3—22no—
510C4⋊Dic3C2412yes—
511Dic3⋊C4—22no—
512Dic3⋊C4—22no—
513Dic3⋊C4—22no—
514Dic3⋊C4—22no—
515C4×Dic3—22no—
516C2×C3⋊C8—24no—
517C2×C3⋊C8C2412yes—
518C2×C3⋊C8C2412yes—
519Dic12—28no—
520#204—28no—
521ΓL(1,𝔽25)—28no—
522D3×C8—28no—
5232−1+4—316no—
5242−1+4—616no—
5252−1+4—616no—
5262−1+4—68no—
5272−1+4—68no—
5282−1+4—616no—
5292−1+4—632no—
5302−1+4—616no—
5312−1+4—68no—
5322−1+4—68no—
533C2×#41—31no—
534C2×#41—32no—
535C2×#41—31no—
536C2×#41—31no—
537C2×#41—32no—
538C2×#41—31no—
539C2×#41—34no—
540C2×#41—34no—
541C2×#41—32no—
542C2×#41—32no—
543C2×#41—32no—
544C2×#41—64no—
545C2×#41—64no—
546C2×#41—64no—
547C2×#41—64no—
548C2×#41—61no—
549C2×#41—68no—
550C2×#41—68no—
551C2×#41—632no—
552C2×#41—62no—
553C2×#41—62no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—64no—
557C2×#41—62no—
558C2×#41—616no—
559C2×#41—616no—
560C2×#41—61no—
561C2×#41—61no—
562C2×#41C22×D311yescharacteristic
563C22×Q8—28no—
564C22×Q8—21no—
565C22×Q8—21no—
566C22×Q8—21no—
567C22×Q8—31no—
568C22×Q8—34no—
569C22×Q8—32no—
570C22×Q8—34no—
571C22×Q8—31no—
572C22×Q8—31no—
573C22×Q8—62no—
574C22×Q8—61no—
575C22×Q8—62no—
576C22×Q8—62no—
577C22×Q8—616no—
578C22×Q8—62no—
579C22×Q8—64no—
580C22×Q8—62no—
581C22×Q8—616no—
582C22×Q8C22×D312yes—
583C22×Q8C22×D312yes—
584C22×Q8C22×D312yes—
585C22×D4—32no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—62no—
589C22×D4—61no—
590C23×C4—21no—
591C23×C4—32no—
592C23×C4—62no—
593C23×C4—62no—
594C23×C4—61no—
595C23×C4C22×D311yescharacteristic
596#137—28no—
597#137—68no—
598#137—616no—
599#137—616no—
600#135—616no—
601#135—68no—
602C2×Q16—32no—
603C2×Q16—34no—
604C2×Q16—34no—
605C2×Q16—34no—
606C2×Q16—616no—
607C2×Q16—68no—
608C2×Q16C22×D314yes—
609C2×SD16—32no—
610C2×SD16—32no—
611C2×SD16—34no—
612C2×SD16C22×D314yes—
613C2×D8—32no—
614#131—68no—
615C2×M16—34no—
616C2×M16C22×D312yes—
617C22×C8—32no—
618C22×C8—34no—
619C4⋊Q8—61no—
620C4⋊Q8—62no—
621#124—61no—
622#124—62no—
623#123—21no—
624#123—62no—
625#123—62no—
626#123—62no—
627#123—62no—
628C22⋊Q8—32no—
629C22⋊Q8—32no—
630C22⋊Q8—32no—
631C22⋊Q8—32no—
632C22⋊Q8—32no—
633C22⋊Q8—62no—
634C22⋊Q8—62no—
635C22⋊Q8—62no—
636C22⋊Q8—61no—
637C22⋊Q8—61no—
638C22⋊Q8—61no—
639C22⋊Q8C22×D311yescharacteristic
640C22⋊Q8C22×D311yescharacteristic
641#121—32no—
642#121—62no—
643#121—61no—
644#121—62no—
645#121—62no—
646#121—62no—
647#121C22×D311yescharacteristic
648#121C22×D311yescharacteristic
649#120—21no—
650#120—62no—
651C4×Q8—61no—
652C4×D4—21no—
653C4×D4—21no—
654C4×D4—61no—
655C4×D4—62no—
656C4×D4—62no—
657C4×D4—62no—
658#117—32no—
659#117C22×D311yescharacteristic
660C2×C4⋊C4—31no—
661C2×C4⋊C4—32no—
662C2×C4⋊C4—62no—
663C2×C4⋊C4—61no—
664C2×C22⋊C4—62no—
665C2×C22⋊C4—61no—
666#103—34no—
667#103—34no—
668#103—34no—
669#103—32no—
670#103—32no—
671#103C22×D314yes—
672#103C22×D314yes—
673#102—34no—
674#102—32no—
675#102—32no—
676C22⋊C8—31no—
677C22⋊C8—31no—
678C22⋊C8—32no—
679C22⋊C8—34no—
680C22⋊C8—34no—
681C22⋊C8C22×D312yes—
682C22⋊C8C22×D312yes—
683C23×C3—22no—
684C23×C3—22no—
685C23×C3—21no—
686C23×C3—41no—
687C23×C3C22×D411yescharacteristic
688C23×C3C22×D411yescharacteristic
689C23×C3C22×D411yescharacteristic
690C22×D3—24no—
691C22×D3—24no—
692C22×D3—22no—
693C22×D3—24no—
694C22×D3—42no—
695C22×D3—42no—
696C22×D3—42no—
697C22×D3C22×D412yes—
698C22×D3C22×D412yes—
699C3×Q8—28no—
700C3×Q8—28no—
701C3×Q8—28no—
702C3×Q8—24no—
703C3×Q8—22no—
704C3×Q8C22×D418yes—
705C3×D4—22no—
706C3×D4—42no—
707C3×D4—42no—
708C3×D4—81no—
709C2×C3×C4—28no—
710C2×C3×C4—28no—
711C2×C3×C4—28no—
712C2×C3×C4—22no—
713C2×C3×C4—24no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—21no—
719C2×C3×C4—21no—
720C2×C3×C4—21no—
721C2×C3×C4—42no—
722C2×C3×C4C22×D411yescharacteristic
723C2×C3×C4C22×D411yescharacteristic
724C2×C3×C4C22×D411yescharacteristic
725C2×C3×C4C22×D414yes—
726C2×C3×C4C2511yescharacteristic
727#67—28no—
728#67—24no—
729#67—28no—
730#67—24no—
731#67—24no—
732#67—44no—
733#67—82no—
734#67#12018yes—
735C2×Dic3—24no—
736C2×Dic3—22no—
737C2×Dic3—24no—
738C2×Dic3—22no—
739C2×Dic3—22no—
740C2×Dic3—42no—
741C2×Dic3—44no—
742C2×Dic3—81no—
743C2×Dic3C22×D412yes—
744C2×Dic3C22×D412yes—
745D12—216no—
746D12—24no—
747D12—216no—
748D12—24no—
749D12—22no—
750D12—22no—
751D12#12014yes—
752D12C22×D414yes—
753C4×D3—216no—
754C4×D3—216no—
755C4×D3—28no—
756C4×D3—216no—
757C4×D3—24no—
758C4×D3—28no—
759C4×D3—24no—
760C4×D3—216no—
761C4×D3—24no—
762C4×D3—44no—
763C4×D3—82no—
764C4×D3C22×D418yes—
765Dic6—216no—
766Dic6—24no—
767Dic6—22no—
768Dic6—22no—
769Dic6—216no—
770Dic6—24no—
771Dic6—24no—
772Dic6—42no—
773Dic6—44no—
774Dic6#12014yes—
775Dic6C22×D414yes—
776C3×C8—24no—
777C3⋊C8—22no—
778C3⋊C8—22no—
779C24—32no—
780C24—61no—
781C24D3×D411yescharacteristic
782#41—24no—
783#41—38no—
784#41—316no—
785#41—38no—
786#41—68no—
787#41—68no—
788#41—64no—
789#41—64no—
790#41—632no—
791#41—64no—
792#41—64no—
793#41—632no—
794#41—632no—
795#41—632no—
796#41—68no—
797#41—68no—
798#41—68no—
799#41—68no—
800#41—68no—
801#41—616no—
802#41—616no—
803#41—616no—
804#41—632no—
805#41—616no—
806#41—68no—
807#41—64no—
808#41—64no—
809#41—124no—
810#41—128no—
811C2×Q8—28no—
812C2×Q8—28no—
813C2×Q8—28no—
814C2×Q8—28no—
815C2×Q8—28no—
816C2×Q8—22no—
817C2×Q8—22no—
818C2×Q8—22no—
819C2×Q8—24no—
820C2×Q8—31no—
821C2×Q8—32no—
822C2×Q8—31no—
823C2×Q8—316no—
824C2×Q8—32no—
825C2×Q8—32no—
826C2×Q8—64no—
827C2×Q8—64no—
828C2×Q8—62no—
829C2×Q8—64no—
830C2×Q8—64no—
831C2×Q8—616no—
832C2×Q8—68no—
833C2×Q8—68no—
834C2×Q8—68no—
835C2×Q8—616no—
836C2×Q8—616no—
837C2×Q8—632no—
838C2×Q8—616no—
839C2×Q8—616no—
840C2×Q8—68no—
841C2×Q8—61no—
842C2×Q8—61no—
843C2×Q8—64no—
844C2×Q8—124no—
845C2×Q8D3×D418yes—
846C2×Q8C23×D311yescharacteristic
847C2×Q8C23×D314yes—
848C2×D4—21no—
849C2×D4—21no—
850C2×D4—21no—
851C2×D4—32no—
852C2×D4—32no—
853C2×D4—32no—
854C2×D4—32no—
855C2×D4—31no—
856C2×D4—32no—
857C2×D4—31no—
858C2×D4—32no—
859C2×D4—64no—
860C2×D4—64no—
861C2×D4—64no—
862C2×D4—64no—
863C2×D4—616no—
864C2×D4—68no—
865C2×D4—68no—
866C2×D4—62no—
867C2×D4—62no—
868C2×D4—62no—
869C2×D4—62no—
870C2×D4—61no—
871C2×D4C23×D311yescharacteristic
872C22×C4—28no—
873C22×C4—22no—
874C22×C4—22no—
875C22×C4—22no—
876C22×C4—24no—
877C22×C4—21no—
878C22×C4—32no—
879C22×C4—32no—
880C22×C4—32no—
881C22×C4—32no—
882C22×C4—32no—
883C22×C4—68no—
884C22×C4—64no—
885C22×C4—64no—
886C22×C4—64no—
887C22×C4—64no—
888C22×C4—616no—
889C22×C4—616no—
890C22×C4—68no—
891C22×C4—62no—
892C22×C4—62no—
893C22×C4—62no—
894C22×C4—61no—
895C22×C4—62no—
896C22×C4—62no—
897C22×C4—61no—
898C22×C4—61no—
899C22×C4D3×D411yescharacteristic
900C22×C4D3×D411yescharacteristic
901C22×C4D3×D411yescharacteristic
902C22×C4C23×D311yescharacteristic
903C22×C4C23×D311yescharacteristic
904C22×C4C23×D311yescharacteristic
905Q16—28no—
906Q16—68no—
907Q16—64no—
908Q16—68no—
909Q16—68no—
910SD16—28no—
911SD16—68no—
912SD16—64no—
913SD16—64no—
914D8—64no—
915M16—24no—
916M16—68no—
917C2×C8—32no—
918C2×C8—32no—
919C2×C8—68no—
920C2×C8—64no—
921C2×C8C23×D314yes—
922C4⋊C4—21no—
923C4⋊C4—21no—
924C4⋊C4—32no—
925C4⋊C4—62no—
926C4⋊C4—62no—
927C4⋊C4—62no—
928C4⋊C4—62no—
929C4⋊C4—61no—
930C4⋊C4—62no—
931C4⋊C4—62no—
932C4⋊C4C23×D311yescharacteristic
933C4⋊C4C23×D311yescharacteristic
934C22⋊C4—21no—
935C22⋊C4—21no—
936C22⋊C4—21no—
937C22⋊C4—21no—
938C22⋊C4—21no—
939C22⋊C4—62no—
940C22⋊C4—62no—
941C22⋊C4—62no—
942C22⋊C4—62no—
943C22⋊C4—62no—
944C22⋊C4—62no—
945C22⋊C4—62no—
946C42—21no—
947C42—62no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—21no—
954C22×C3—21no—
955C22×C3—44no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3C2×#12012yes—
960C22×C3#57812yescomplemented
961C22×C3C23×D411yescharacteristic
962C2×D3—22no—
963C2×D3—22no—
964C2×D3—22no—
965C2×D3—22no—
966C2×D3—24no—
967C2×D3—22no—
968C2×D3—48no—
969C2×D3—48no—
970C2×D3—42no—
971C2×D3—42no—
972C2×D3C2×#12014yes—
973C3×C4—28no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—41no—
977C3×C4—41no—
978C3×C4—41no—
979C3×C4C2×#12012yes—
980C3×C4C23×D412yes—
981Dic3—22no—
982Dic3—24no—
983Dic3—42no—
984Dic3—42no—
985Dic3C2×#12014yes—
986C23—22no—
987C23—22no—
988C23—21no—
989C23—32no—
990C23—32no—
991C23—41no—
992C23—64no—
993C23—64no—
994C23—62no—
995C23—64no—
996C23—122no—
997C23—122no—
998C23—122no—
999C23C2×D3×D411yescharacteristic
1000C23C2×D3×D411yescharacteristic
1001C23C2×D3×D411yescharacteristic
1002Q8—28no—
1003Q8—28no—
1004Q8—24no—
1005Q8—28no—
1006Q8—22no—
1007Q8—34no—
1008Q8—34no—
1009Q8—616no—
1010Q8—64no—
1011Q8—616no—
1012Q8—64no—
1013Q8—62no—
1014Q8—62no—
1015Q8—64no—
1016Q8—124no—
1017Q8—122no—
1018Q8C2×D3×D418yes—
1019D4—22no—
1020D4—38no—
1021D4—34no—
1022D4—34no—
1023D4—42no—
1024D4—42no—
1025D4—64no—
1026D4—616no—
1027D4—616no—
1028D4—64no—
1029D4—64no—
1030D4—64no—
1031D4—68no—
1032D4—64no—
1033D4—68no—
1034D4—62no—
1035D4—62no—
1036D4—81no—
1037D4—124no—
1038D4—242no—
1039C2×C4—28no—
1040C2×C4—28no—
1041C2×C4—24no—
1042C2×C4—28no—
1043C2×C4—22no—
1044C2×C4—22no—
1045C2×C4—22no—
1046C2×C4—22no—
1047C2×C4—22no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—21no—
1051C2×C4—32no—
1052C2×C4—38no—
1053C2×C4—32no—
1054C2×C4—42no—
1055C2×C4—64no—
1056C2×C4—616no—
1057C2×C4—64no—
1058C2×C4—616no—
1059C2×C4—616no—
1060C2×C4—616no—
1061C2×C4—68no—
1062C2×C4—64no—
1063C2×C4—64no—
1064C2×C4—62no—
1065C2×C4—64no—
1066C2×C4—68no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—124no—
1070C2×C4—124no—
1071C2×C4—122no—
1072C2×C4—242no—
1073C2×C4—241no—
1074C2×C4C2×D3×D411yescharacteristic
1075C2×C4C2×D3×D411yescharacteristic
1076C2×C4C2×D3×D414yes—
1077C2×C4C2×D3×D411yescharacteristic
1078C2×C4C24×D311yescharacteristic
1079C8—24no—
1080C8—62no—
1081C8—62no—
1082C2×C3—22no—
1083C2×C3—22no—
1084C2×C3—41no—
1085C2×C3—81no—
1086C2×C3C22×#12011yescharacteristic
1087C2×C3C2×#57811yescharacteristic
1088C2×C3#358611yescharacteristic
1089D3—24no—
1090D3—42no—
1091D3—44no—
1092C22—21no—
1093C22—21no—
1094C22—21no—
1095C22—21no—
1096C22—21no—
1097C22—21no—
1098C22—21no—
1099C22—34no—
1100C22—44no—
1101C22—41no—
1102C22—41no—
1103C22—41no—
1104C22—62no—
1105C22—62no—
1106C22—64no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—128no—
1111C22—128no—
1112C22—122no—
1113C22—122no—
1114C22D3×#12012yes—
1115C22#577912yescomplemented
1116C22C22×D3×D411yescharacteristic
1117C4—28no—
1118C4—21no—
1119C4—21no—
1120C4—34no—
1121C4—41no—
1122C4—41no—
1123C4—41no—
1124C4—62no—
1125C4—64no—
1126C4—122no—
1127C4—122no—
1128C4D3×#12012yes—
1129C4C22×D3×D412yes—
1130C3#6037511yescharacteristic, complemented, Sylow
1131C2—22no—
1132C2—22no—
1133C2—41no—
1134C2—64no—
1135C2—81no—
1136C2—122no—
1137C2—124no—
1138C2C2×D3×#12011yescharacteristic
1139C2C2×#577911yescharacteristic
1140C2#8719711yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3004C2
socleC22×C3C23×D4
hypercenter#3004D3
hypocenterC3#60375
LCSG ▷ C2×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3004

Complements

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

NH ≅ G/Ntype
1. C22×#1007C2semidirect
2. C2×#5779C2semidirect
3. #86042C2semidirect
4. C3×#3004C2semidirect
5. C2×#5228C2semidirect
6. #83984C2semidirect
7. #82926C2semidirect
8. #80185C2semidirect
9. #80184C2semidirect
10. D3×#451C2semidirect
11. #80042C2semidirect
12. #80039C2semidirect
13. #80038C2semidirect
14. #78961C2semidirect
15. #78957C2semidirect
16. #78640C2semidirect
17. #78631C2semidirect
20. C2×#1010C22semidirect
35. C2×C3×#137C22semidirect
37. #5833C22semidirect
38. C2×#950C22semidirect
39. C22×#216C22semidirect
42. C2×#918C22semidirect
43. C2×D3×Q16C22semidirect
44. C2×#916C22semidirect
45. C2×#915C22semidirect
46. C2×#909C22semidirect
47. C2×#907C22semidirect
49. #5628C22semidirect
51. #5608C22semidirect
58. #5526C22semidirect
59. #5523C22semidirect
61. C3×#451C22semidirect
63. C3×#448C22semidirect
64. C3×#419C22semidirect
68. #5228C22semidirect
69. C2×#835C22semidirect
71. #5187C22semidirect
72. #5186C22semidirect
73. #5172C22semidirect
74. #5170C22semidirect
75. #5133C22semidirect
76. #5129C22semidirect
78. #5047C22semidirect
81. #5037C22semidirect
83. #5002C22semidirect
84. #4809C22semidirect
85. #4809C22semidirect
86. #4808C22semidirect
87. #4808C22semidirect
88. #4804C22semidirect
89. #4803C22semidirect
90. #4802C22semidirect
91. D3×#103C22semidirect
93. #4733C22semidirect
95. #4727C22semidirect
108. #3004D3semidirect
136. #1007D4semidirect
295. C2×#137C2×D3semidirect
330. #451C2×D3semidirect
338. #448C2×D3semidirect
341. #419C2×D3semidirect
960. C22×C3#578semidirect
1115. C22#5779semidirect
1130. C3#60375semidirect

Maximal subgroups

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

subgroupindex
C22×#10072
C2×#57792
#860422
C3×#30042
C2×#52282
#839842
#829262
#801852
#801842
D3×#4512
#800422
#800392
#800382
#789612
#789572
#786402
#786312
#603753