Finite Group Databasebeta

← #11661696

Subgroups — #11661696

Order 768.

4746 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic
2C2×D3×#137C212yesmaximal, complemented
3C2×#5628C211yesmaximal, characteristic, complemented
4C3×#3007C211yesmaximal, characteristic, complemented
5#84084C211yesmaximal, characteristic, complemented
6#83981C212yesmaximal, complemented
7#82735C211yesmaximal, characteristic, complemented
8#80230C214yesmaximal, complemented
9#80229C214yesmaximal, complemented
10#80185C214yesmaximal, complemented
11#80148C214yesmaximal, complemented
12#78885C212yesmaximal, complemented
13#78881C212yesmaximal, complemented
14#78640C211yesmaximal, characteristic, complemented
15#78630C211yesmaximal, characteristic, complemented
16#60370—31nomaximal, Sylow
17C22×C3×#41C2211yescharacteristic
18#5964—216no—
19C2×#1010—21no—
20C2×#1010C2212yes—
21C2×#1009—21no—
22C2×#1009C2212yes—
23C2×D3×#41—22no—
24C2×D3×#41C2212yes—
25C2×D3×#41C2212yes—
26C2×#1007C2212yes—
27C22×D3×Q8C2211yescharacteristic, complemented
28C2×#1004—21no—
29C2×#1004—21no—
30C2×#1004C2212yes—
31C22×#235—22no—
32C22×#235C2211yescharacteristic
33C22×#235C2211yescharacteristic
34C2×C3×#137C2212yescomplemented
35C2×C3×C22⋊Q8C2211yescharacteristic, complemented
36C2×#951C2212yescomplemented
37C2×#946C2211yescharacteristic, complemented
38C2×#942C2212yescomplemented
39C2×#924C2211yescharacteristic, complemented
40D3×#137—216no—
41C2×#918C2214yescomplemented
42C2×D3×Q16C2214yescomplemented
43C2×#915C2214yescomplemented
44C2×D3×SD16C2214yescomplemented
45C2×#909C2212yescomplemented
46C2×D3×M16C2212yescomplemented
47#5628—22no—
48#5628—22no—
49#5628C2214yescomplemented
50#5628C2214yescomplemented
51C2×#897C2211yescharacteristic, complemented
52C2×#894—21no—
53C2×#892C2211yescharacteristic, complemented
54C2×#888—21no—
55C2×#885—21no—
56C2×#883—21no—
57C3×#452C2214yescomplemented
58C3×#451C2212yescomplemented
59C3×#450C2212yescomplemented
60C3×#417C2212yescomplemented
61C3×#407C2211yescharacteristic, complemented
62#5239C2214yescomplemented
63#5232C2212yescomplemented
64#5228C2212yescomplemented
65#5218C2212yescomplemented
66#5207C2211yescharacteristic, complemented
67#5187C2214yescomplemented
68#5186C2214yescomplemented
69#5173C2214yescomplemented
70#5169C2214yescomplemented
71#5133C2212yescomplemented
72#5126C2212yescomplemented
73#5050C2212yescomplemented
74#5047C2214yescomplemented
75#5046C2212yescomplemented
76#4966C2212yescomplemented
77#4809C2214yescomplemented
78#4808C2214yescomplemented
79#4804C2214yescomplemented
80#4802C2214yescomplemented
81#4783C2214yescomplemented
82#4776C2214yescomplemented
83#4772C2214yescomplemented
84#4770C2214yescomplemented
85#4739C2212yescomplemented
86#4733C2214yescomplemented
87#4731C2212yescomplemented
88#4727C2214yescomplemented
89#4727C2214yescomplemented
90C2×#585—31no—
91C22×#137—32no—
92C2×#536—31no—
93#3011—34no—
94#3011—34no—
95#3009—34no—
96#3009—34no—
97#3007—32no—
98#3007—31no—
99#3007—31no—
100#3007—32no—
101#3007—31no—
102#3007D311yescharacteristic, complemented
103#2896—32no—
104#2879—31no—
105C2×C3×#41—28no—
106C2×C3×#41—21no—
107C2×C3×#41—21no—
108C2×C3×#41C2312yes—
109C2×C3×#41C2312yes—
110C22×C3×Q8C2311yescharacteristic
111C22×C3×Q8C2311yescharacteristic
112C22×C3×D4—21no—
113C22×C3×D4C2311yescharacteristic
114C23×C3×C4—21no—
115C23×C3×C4C2311yescharacteristic
116C22×#67—21no—
117C22×#67—22no—
118C22×#67—22no—
119C22×#67D411yescharacteristic
120C22×#67D411yescharacteristic
121#1010—216no—
122#1010—28no—
123#1010—28no—
124#1009—216no—
125#1009—28no—
126#1009—28no—
127D3×#41—232no—
128D3×#41—28no—
129D3×#41—28no—
130D3×#41—28no—
131D3×#41D4116yes—
132#1007—28no—
133#1007—28no—
134C2×#239—22no—
135C2×#239C2312yes—
136C2×#239C2312yes—
137C2×D3×Q8—22no—
138C2×D3×Q8—22no—
139C2×D3×Q8—28no—
140C2×D3×Q8C2312yes—
141C2×D3×Q8C2314yes—
142C2×D3×Q8C2312yes—
143#1004—216no—
144#1004—216no—
145#1004—28no—
146#1004—28no—
147C2×#237—22no—
148C2×#237—22no—
149C2×#237—22no—
150C2×#237—22no—
151C2×#237—22no—
152C2×#237C2312yes—
153C2×#237C2312yes—
154C2×D3×D4—22no—
155C2×D3×D4—22no—
156C2×D3×D4—22no—
157C2×D3×D4—22no—
158C2×D3×D4—22no—
159C2×D3×D4C2312yes—
160C2×D3×D4C2312yes—
161C2×#235—232no—
162C2×#235—21no—
163C2×#235—21no—
164C2×#235—22no—
165C2×#235—22no—
166C2×#235—28no—
167C2×#235—22no—
168C2×#235—22no—
169C2×#235—22no—
170C2×#235—28no—
171C2×#235—22no—
172C2×#235D412yes—
173C2×#235D412yes—
174C2×#235C2312yes—
175C2×#235C2312yes—
176C2×#235C2312yes—
177C2×#235C2312yes—
178C22×D12—22no—
179C22×D12D411yescharacteristic
180C22×D12C2311yescharacteristic
181C22×C4×D3—21no—
182C22×C4×D3—22no—
183C22×C4×D3—22no—
184C22×C4×D3—21no—
185C22×C4×D3C2311yescharacteristic
186C22×C4×D3C2311yescharacteristic
187C22×Dic6—22no—
188C22×Dic6—21no—
189C22×Dic6D411yescharacteristic
190C22×Dic6C2311yescharacteristic
191C22×Dic6C2311yescharacteristic
192C3×#137—28no—
193C2×C3×Q16C2314yes—
194C2×C3×SD16C2314yes—
195C2×C3×M16C2312yes—
196C3×C22⋊Q8—21no—
197C3×C22⋊Q8—21no—
198C3×C22⋊Q8C2312yes—
199C3×C22⋊Q8C2312yes—
200C2×C3×C4⋊C4—21no—
201C2×C3×C4⋊C4C2311yescharacteristic
202C2×C3×C22⋊C4—21no—
203C2×#217—21no—
204#951—28no—
205#946—22no—
206#946C2314yes—
207C2×#216C2314yes—
208C2×#216C2314yes—
209#942—28no—
210C2×#215C2314yes—
211C2×#214C2314yes—
212C2×(C2×D3)⋊C4—21no—
213C2×(C2×D3)⋊C4—21no—
214C2×(C2×D3)⋊C4—21no—
215C2×C4⋊Dic3—21no—
216C2×C4⋊Dic3C2311yescharacteristic
217#924—21no—
218#924—21no—
219#924C2312yes—
220#924C2312yes—
221C2×Dic3⋊C4—21no—
222C2×Dic3⋊C4—21no—
223C2×C4×Dic3—21no—
224C2×#208C2312yes—
225#918—216no—
226D3×Q16—216no—
227#915—216no—
228D3×SD16—216no—
229#909—28no—
230D3×M16—28no—
231C2×Dic12C2314yes—
232C2×#204C2314yes—
233C2×ΓL(1,𝔽25)C2314yes—
234C2×D3×C8C2314yes—
235#897—22no—
236#897C2314yes—
237#894—24no—
238#894—24no—
239#892—22no—
240#892C2314yes—
241#888—24no—
242#888—24no—
243#885—24no—
244#885—24no—
245#883—24no—
246#883—24no—
247C3×#103C2314yes—
248C3×#102C2314yes—
249C3×C22⋊C8C2312yes—
250C3×C22⋊C8C2312yes—
251#835C2314yes—
252#832C2314yes—
253#830C2312yes—
254#830C2312yes—
255#821C2314yes—
256(C2×D3)⋊C8C2314yes—
257(C2×D3)⋊C8C2314yes—
258#816C2314yes—
259#810C2314yes—
260#809C2314yes—
261#585—616no—
262C2×2−1+4—32no—
263C2×2−1+4—32no—
264C2×2−1+4—61no—
265C2×H(5,𝔽2)—32no—
266C2×H(5,𝔽2)—32no—
267C2×H(5,𝔽2)—61no—
268C2×H(5,𝔽2)—61no—
269C2×H(5,𝔽2)—61no—
270C22×#41—31no—
271C22×#41—32no—
272C22×#41—32no—
273C22×#41—31no—
274C22×#41—62no—
275C22×#41—62no—
276C22×#41C2×D311yescharacteristic
277C23×Q8—31no—
278C2×#137—32no—
279C2×#137—32no—
280C2×#137—34no—
281C2×#137—34no—
282C2×#137—32no—
283C2×#137—616no—
284C2×#137C2×D312yescomplemented
285C22×Q16—34no—
286C22×SD16—34no—
287C22×M16—32no—
288#536—34no—
289#536—34no—
290#536—62no—
291#536—62no—
292C2×C4⋊Q8—61no—
293C2×#124—61no—
294C2×#123—61no—
295C2×#123—61no—
296C2×C22⋊Q8—31no—
297C2×C22⋊Q8—31no—
298C2×C22⋊Q8—31no—
299C2×C22⋊Q8C2×D311yescharacteristic, complemented
300C2×#117—31no—
301#452—34no—
302#452—34no—
303#452—34no—
304#452—34no—
305#452—34no—
306#452—34no—
307#452—34no—
308#452C2×D314yescomplemented
309#451—32no—
310#451—34no—
311#451—32no—
312#451—34no—
313#451—32no—
314#451C2×D312yescomplemented
315#450—32no—
316#450—34no—
317#450—32no—
318#450—34no—
319#450—32no—
320#450C2×D312yescomplemented
321#419—34no—
322#418—34no—
323#417—32no—
324#417—32no—
325#417—32no—
326#417C2×D312yescomplemented
327#416—34no—
328#416—34no—
329#408—34no—
330#408—34no—
331#407—31no—
332#407—32no—
333#407C2×D311yescharacteristic, complemented
334C24×C3—21no—
335C24×C3C2×D411yescharacteristic
336C23×D3—21no—
337C23×D3—22no—
338C23×D3—22no—
339C23×D3C2×D411yescharacteristic
340C23×D3C2×D411yescharacteristic
341C3×#41—28no—
342C3×#41—28no—
343C3×#41—24no—
344C3×#41—24no—
345C3×#41—24no—
346C3×#41C2×D418yes—
347C2×C3×Q8—24no—
348C2×C3×Q8—21no—
349C2×C3×Q8—21no—
350C2×C3×Q8—24no—
351C2×C3×Q8C2412yes—
352C2×C3×Q8C2412yes—
353C2×C3×D4—28no—
354C2×C3×D4—22no—
355C2×C3×D4—22no—
356C2×C3×D4—24no—
357C2×C3×D4—21no—
358C2×C3×D4C2412yes—
359C22×C3×C4—28no—
360C22×C3×C4—21no—
361C22×C3×C4—22no—
362C22×C3×C4—22no—
363C22×C3×C4—24no—
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4C2×D411yescharacteristic
367C22×C3×C4C2×D411yescharacteristic
368C22×C3×C4C2×D411yescharacteristic
369C22×C3×C4C2411yescharacteristic
370C22×C3×C4C2411yescharacteristic
371C22×C3×C4C2411yescharacteristic
372C2×#67—28no—
373C2×#67—216no—
374C2×#67—216no—
375C2×#67—22no—
376C2×#67—22no—
377C2×#67—24no—
378C2×#67—22no—
379C2×#67—22no—
380C2×#67—24no—
381C2×#67—22no—
382C2×#67—22no—
383C2×#67C2×D412yes—
384C2×#67C2×D412yes—
385C2×#67C2×D412yes—
386C2×#67C2×D412yes—
387C22×Dic3—21no—
388C22×Dic3—22no—
389C22×Dic3—22no—
390C22×Dic3—21no—
391C22×Dic3—21no—
392C22×Dic3C2×D411yescharacteristic
393C22×Dic3C2×D411yescharacteristic
394#239—216no—
395#239—24no—
396#239—24no—
397#239—24no—
398#239C2×D418yes—
399D3×Q8—216no—
400D3×Q8—24no—
401D3×Q8—24no—
402D3×Q8—24no—
403D3×Q8—28no—
404D3×Q8—28no—
405D3×Q8—48no—
406D3×Q8C2×D418yes—
407#237—216no—
408#237—216no—
409#237—216no—
410#237—216no—
411#237—24no—
412#237—216no—
413#237—24no—
414#237—24no—
415#237C2×D418yes—
416D3×D4—216no—
417D3×D4—216no—
418D3×D4—216no—
419D3×D4—216no—
420D3×D4—216no—
421D3×D4—24no—
422D3×D4—24no—
423D3×D4—24no—
424D3×D4C2×D418yes—
425#235—28no—
426#235—216no—
427#235—216no—
428#235—216no—
429#235—28no—
430#235—216no—
431#235—216no—
432#235—24no—
433#235—24no—
434#235—28no—
435#235—216no—
436#235—28no—
437#235—24no—
438#235—24no—
439#235—24no—
440#235—24no—
441#235—24no—
442#235C2×D418yes—
443C2×D12—216no—
444C2×D12—24no—
445C2×D12—22no—
446C2×D12—22no—
447C2×D12—21no—
448C2×D12—24no—
449C2×D12C2×D412yes—
450C2×D12C2×D412yes—
451C2×D12C2412yes—
452C2×C4×D3—28no—
453C2×C4×D3—216no—
454C2×C4×D3—22no—
455C2×C4×D3—22no—
456C2×C4×D3—22no—
457C2×C4×D3—22no—
458C2×C4×D3—24no—
459C2×C4×D3—22no—
460C2×C4×D3—22no—
461C2×C4×D3—216no—
462C2×C4×D3—24no—
463C2×C4×D3—44no—
464C2×C4×D3C2×D412yes—
465C2×C4×D3C2×D412yes—
466C2×C4×D3C2×D418yes—
467C2×C4×D3C2412yes—
468C2×C4×D3C2412yes—
469C2×Dic6—216no—
470C2×Dic6—21no—
471C2×Dic6—24no—
472C2×Dic6—22no—
473C2×Dic6—22no—
474C2×Dic6—24no—
475C2×Dic6—24no—
476C2×Dic6—21no—
477C2×Dic6—24no—
478C2×Dic6—44no—
479C2×Dic6C2×D412yes—
480C2×Dic6C2×D412yes—
481C2×Dic6C2412yes—
482C2×Dic6C2412yes—
483C3×Q16—28no—
484C3×SD16—28no—
485C3×M16—24no—
486C2×C3×C8C2414yes—
487C3×C4⋊C4—22no—
488C3×C4⋊C4—22no—
489C3×C4⋊C4—21no—
490C3×C4⋊C4C2412yes—
491C3×C22⋊C4—22no—
492C3×C22⋊C4—22no—
493#217—22no—
494#217—22no—
495#216—28no—
496#216—28no—
497#215—28no—
498#214—28no—
499(C2×D3)⋊C4—24no—
500(C2×D3)⋊C4—24no—
501(C2×D3)⋊C4—24no—
502C4⋊Dic3—21no—
503C4⋊Dic3—24no—
504C4⋊Dic3C2412yes—
505Dic3⋊C4—22no—
506Dic3⋊C4—22no—
507Dic3⋊C4—24no—
508C4×Dic3—24no—
509#208—24no—
510C2×C3⋊C8C2414yes—
511Dic12—28no—
512#204—28no—
513ΓL(1,𝔽25)—28no—
514D3×C8—28no—
5152−1+4—68no—
5162−1+4—68no—
5172−1+4—68no—
5182−1+4—68no—
5192−1+4—616no—
520H(5,𝔽2)—68no—
521H(5,𝔽2)—68no—
522H(5,𝔽2)—616no—
523H(5,𝔽2)—616no—
524H(5,𝔽2)—68no—
525H(5,𝔽2)—68no—
526H(5,𝔽2)—616no—
527C2×#41—28no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—32no—
531C2×#41—32no—
532C2×#41—32no—
533C2×#41—32no—
534C2×#41—316no—
535C2×#41—32no—
536C2×#41—32no—
537C2×#41—32no—
538C2×#41—32no—
539C2×#41—32no—
540C2×#41—32no—
541C2×#41—62no—
542C2×#41—62no—
543C2×#41—68no—
544C2×#41—62no—
545C2×#41—62no—
546C2×#41—62no—
547C2×#41—62no—
548C2×#41—68no—
549C2×#41—632no—
550C2×#41—62no—
551C2×#41—62no—
552C2×#41—68no—
553C2×#41—62no—
554C2×#41—62no—
555C2×#41—62no—
556C2×#41—62no—
557C2×#41—68no—
558C2×#41—632no—
559C2×#41—68no—
560C2×#41—61no—
561C2×#41—61no—
562C2×#41C22×D312yes—
563C2×#41C22×D312yes—
564C22×Q8—31no—
565C22×Q8—32no—
566C22×Q8—34no—
567C22×Q8—32no—
568C22×Q8—31no—
569C22×Q8—31no—
570C22×Q8—61no—
571C22×Q8—62no—
572C22×Q8—62no—
573C22×Q8—68no—
574C22×Q8—62no—
575C22×Q8C22×D311yescharacteristic
576C22×Q8C22×D311yescharacteristic
577C22×D4—21no—
578C22×D4—32no—
579C22×D4—31no—
580C22×D4—31no—
581C22×D4—32no—
582C22×D4—31no—
583C22×D4—31no—
584C22×D4—62no—
585C22×D4—62no—
586C22×D4—62no—
587C22×D4—62no—
588C22×D4—62no—
589C22×D4—62no—
590C22×D4—62no—
591C22×D4—62no—
592C22×D4—61no—
593C22×D4C22×D311yescharacteristic
594C23×C4—21no—
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—62no—
598C23×C4—62no—
599C23×C4—61no—
600C23×C4—61no—
601C23×C4C22×D311yescharacteristic
602#137—28no—
603#137—68no—
604#137—616no—
605#137—616no—
606#137—68no—
607#137—68no—
608C2×Q16—34no—
609C2×Q16—34no—
610C2×Q16—34no—
611C2×Q16—616no—
612C2×Q16C22×D314yes—
613C2×SD16—34no—
614C2×SD16—34no—
615C2×SD16—34no—
616C2×SD16—616no—
617C2×SD16C22×D314yes—
618C2×M16—32no—
619C2×M16—34no—
620C2×M16—68no—
621C2×M16C22×D312yes—
622C22×C8—34no—
623C4⋊Q8—64no—
624C4⋊Q8—64no—
625#124—64no—
626#124—64no—
627#123—64no—
628#123—64no—
629#123—64no—
630#123—64no—
631C22⋊Q8—21no—
632C22⋊Q8—21no—
633C22⋊Q8—34no—
634C22⋊Q8—32no—
635C22⋊Q8—32no—
636C22⋊Q8—34no—
637C22⋊Q8—62no—
638C22⋊Q8—62no—
639C22⋊Q8—61no—
640C22⋊Q8—61no—
641C22⋊Q8C22×D312yes—
642C22⋊Q8C22×D312yes—
643#117—34no—
644#117—62no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—31no—
647C2×C4⋊C4—61no—
648C2×C4⋊C4—61no—
649C2×C4⋊C4—61no—
650C2×C4⋊C4C22×D311yescharacteristic
651C2×C22⋊C4—21no—
652C2×C22⋊C4—61no—
653C2×C22⋊C4—61no—
654C2×C22⋊C4—61no—
655C2×C22⋊C4—61no—
656C2×C42—61no—
657#103—34no—
658#103—34no—
659#103—34no—
660#103C22×D314yes—
661#102—34no—
662#102—34no—
663#102—34no—
664#102C22×D314yes—
665C22⋊C8—32no—
666C22⋊C8—32no—
667C22⋊C8—34no—
668C22⋊C8—34no—
669C22⋊C8C22×D312yes—
670C22⋊C8C22×D312yes—
671C23×C3—24no—
672C23×C3—22no—
673C23×C3—22no—
674C23×C3—41no—
675C23×C3—41no—
676C23×C3—81no—
677C23×C3—81no—
678C23×C3C22×D411yescharacteristic
679C23×C3C22×D411yescharacteristic
680C23×C3C22×D411yescharacteristic
681C22×D3—22no—
682C22×D3—28no—
683C22×D3—24no—
684C22×D3—22no—
685C22×D3—28no—
686C22×D3—41no—
687C22×D3—41no—
688C22×D3—41no—
689C22×D3—41no—
690C22×D3—82no—
691C22×D3—82no—
692C22×D3—82no—
693C22×D3—82no—
694C22×D3—81no—
695C22×D3—81no—
696C22×D3#12014yes—
697C22×D3C22×D412yes—
698C22×D3C22×D412yes—
699C3×Q8—24no—
700C3×Q8—22no—
701C3×Q8—24no—
702C3×Q8—42no—
703C3×Q8C22×D414yes—
704C3×D4—28no—
705C3×D4—24no—
706C3×D4—28no—
707C3×D4—22no—
708C3×D4C22×D414yes—
709C2×C3×C4—28no—
710C2×C3×C4—24no—
711C2×C3×C4—22no—
712C2×C3×C4—22no—
713C2×C3×C4—28no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—42no—
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—28no—
729#67—28no—
730#67—28no—
731#67—24no—
732#67—24no—
733#67—28no—
734#67—24no—
735#67—24no—
736#67—28no—
737C2×Dic3—28no—
738C2×Dic3—24no—
739C2×Dic3—22no—
740C2×Dic3—22no—
741C2×Dic3—28no—
742C2×Dic3—22no—
743C2×Dic3—22no—
744C2×Dic3—42no—
745C2×Dic3—42no—
746C2×Dic3#12014yes—
747C2×Dic3C22×D412yes—
748C2×Dic3C22×D412yes—
749D12—24no—
750D12—28no—
751D12—24no—
752D12—28no—
753D12—24no—
754D12—22no—
755D12C22×D414yes—
756C4×D3—28no—
757C4×D3—28no—
758C4×D3—28no—
759C4×D3—28no—
760C4×D3—28no—
761C4×D3—24no—
762C4×D3—22no—
763C4×D3—22no—
764C4×D3—28no—
765C4×D3—48no—
766C4×D3#12018yes—
767C4×D3C22×D414yes—
768C4×D3C22×D414yes—
769Dic6—24no—
770Dic6—28no—
771Dic6—22no—
772Dic6—24no—
773Dic6—28no—
774Dic6—24no—
775Dic6—24no—
776Dic6—42no—
777Dic6—48no—
778Dic6C22×D414yes—
779C3×C8—24no—
780C3⋊C8—24no—
781C24—21no—
782C24—31no—
783C24—31no—
784C24—62no—
785C24—62no—
786C24—61no—
787C24D3×D411yescharacteristic
788#41—28no—
789#41—28no—
790#41—24no—
791#41—24no—
792#41—24no—
793#41—38no—
794#41—38no—
795#41—38no—
796#41—68no—
797#41—616no—
798#41—68no—
799#41—64no—
800#41—64no—
801#41—64no—
802#41—64no—
803#41—64no—
804#41—64no—
805#41—68no—
806#41—616no—
807#41—616no—
808#41—616no—
809#41—616no—
810#41—616no—
811#41—68no—
812#41—616no—
813#41—64no—
814#41—64no—
815#41—64no—
816#41—616no—
817#41—616no—
818#41—616no—
819#41—616no—
820#41—64no—
821#41—616no—
822#41—64no—
823#41—64no—
824#41—64no—
825#41D3×D418yes—
826C2×Q8—24no—
827C2×Q8—21no—
828C2×Q8—21no—
829C2×Q8—24no—
830C2×Q8—32no—
831C2×Q8—32no—
832C2×Q8—38no—
833C2×Q8—32no—
834C2×Q8—32no—
835C2×Q8—62no—
836C2×Q8—62no—
837C2×Q8—64no—
838C2×Q8—64no—
839C2×Q8—64no—
840C2×Q8—616no—
841C2×Q8—64no—
842C2×Q8—68no—
843C2×Q8—68no—
844C2×Q8—64no—
845C2×Q8—616no—
846C2×Q8—64no—
847C2×Q8—61no—
848C2×Q8—61no—
849C2×Q8—64no—
850C2×Q8—124no—
851C2×Q8—128no—
852C2×Q8C23×D312yes—
853C2×Q8C23×D312yes—
854C2×D4—28no—
855C2×D4—22no—
856C2×D4—22no—
857C2×D4—24no—
858C2×D4—21no—
859C2×D4—38no—
860C2×D4—32no—
861C2×D4—32no—
862C2×D4—32no—
863C2×D4—32no—
864C2×D4—32no—
865C2×D4—32no—
866C2×D4—32no—
867C2×D4—64no—
868C2×D4—64no—
869C2×D4—62no—
870C2×D4—62no—
871C2×D4—616no—
872C2×D4—64no—
873C2×D4—62no—
874C2×D4—62no—
875C2×D4—64no—
876C2×D4—64no—
877C2×D4—616no—
878C2×D4—616no—
879C2×D4—616no—
880C2×D4—616no—
881C2×D4—616no—
882C2×D4—64no—
883C2×D4—62no—
884C2×D4—62no—
885C2×D4—616no—
886C2×D4—616no—
887C2×D4—68no—
888C2×D4—62no—
889C2×D4—62no—
890C2×D4—64no—
891C2×D4—61no—
892C2×D4C23×D312yes—
893C22×C4—28no—
894C22×C4—21no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—24no—
898C22×C4—21no—
899C22×C4—21no—
900C22×C4—31no—
901C22×C4—32no—
902C22×C4—38no—
903C22×C4—32no—
904C22×C4—31no—
905C22×C4—32no—
906C22×C4—32no—
907C22×C4—62no—
908C22×C4—62no—
909C22×C4—616no—
910C22×C4—62no—
911C22×C4—62no—
912C22×C4—616no—
913C22×C4—68no—
914C22×C4—64no—
915C22×C4—62no—
916C22×C4—62no—
917C22×C4—61no—
918C22×C4—64no—
919C22×C4—62no—
920C22×C4—62no—
921C22×C4—61no—
922C22×C4—61no—
923C22×C4—124no—
924C22×C4D3×D411yescharacteristic
925C22×C4D3×D411yescharacteristic
926C22×C4D3×D411yescharacteristic
927C22×C4C23×D311yescharacteristic
928C22×C4C23×D311yescharacteristic
929C22×C4C23×D311yescharacteristic
930Q16—28no—
931Q16—68no—
932Q16—68no—
933Q16—68no—
934SD16—28no—
935SD16—68no—
936SD16—68no—
937SD16—68no—
938M16—24no—
939M16—68no—
940M16—64no—
941C2×C8—34no—
942C2×C8—68no—
943C2×C8C23×D314yes—
944C4⋊C4—22no—
945C4⋊C4—22no—
946C4⋊C4—21no—
947C4⋊C4—32no—
948C4⋊C4—64no—
949C4⋊C4—64no—
950C4⋊C4—61no—
951C4⋊C4—62no—
952C4⋊C4—62no—
953C4⋊C4C23×D312yes—
954C22⋊C4—22no—
955C22⋊C4—22no—
956C22⋊C4—64no—
957C22⋊C4—64no—
958C22⋊C4—64no—
959C22⋊C4—62no—
960C22⋊C4—62no—
961C42—64no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—21no—
969C22×C3—24no—
970C22×C3—21no—
971C22×C3—42no—
972C22×C3—42no—
973C22×C3—82no—
974C22×C3—84no—
975C22×C3C2×#12012yes—
976C22×C3C23×D411yescharacteristic
977C2×D3—22no—
978C2×D3—22no—
979C2×D3—22no—
980C2×D3—22no—
981C2×D3—22no—
982C2×D3—24no—
983C2×D3—44no—
984C2×D3—42no—
985C2×D3—42no—
986C2×D3—88no—
987C2×D3—82no—
988C2×D3—88no—
989C2×D3—84no—
990C2×D3C2×#12014yes—
991C3×C4—21no—
992C3×C4—24no—
993C3×C4—21no—
994C3×C4—42no—
995C3×C4—42no—
996C3×C4C2×#12012yes—
997C3×C4C23×D412yes—
998Dic3—22no—
999Dic3—24no—
1000Dic3—42no—
1001Dic3—42no—
1002Dic3C2×#12014yes—
1003C23—24no—
1004C23—22no—
1005C23—22no—
1006C23—32no—
1007C23—34no—
1008C23—32no—
1009C23—41no—
1010C23—41no—
1011C23—68no—
1012C23—64no—
1013C23—68no—
1014C23—62no—
1015C23—62no—
1016C23—81no—
1017C23—81no—
1018C23—121no—
1019C23—121no—
1020C23—121no—
1021C23—121no—
1022C23—241no—
1023C23—241no—
1024C23—242no—
1025C23—242no—
1026C23—242no—
1027C23—242no—
1028C23C2×D3×D411yescharacteristic
1029C23C2×D3×D411yescharacteristic
1030C23C2×D3×D411yescharacteristic
1031Q8—24no—
1032Q8—22no—
1033Q8—24no—
1034Q8—34no—
1035Q8—42no—
1036Q8—64no—
1037Q8—68no—
1038Q8—64no—
1039Q8—64no—
1040Q8—68no—
1041Q8—62no—
1042Q8—64no—
1043Q8—128no—
1044Q8—122no—
1045Q8C2×D3×D414yes—
1046D4—28no—
1047D4—24no—
1048D4—28no—
1049D4—22no—
1050D4—34no—
1051D4—64no—
1052D4—64no—
1053D4—68no—
1054D4—64no—
1055D4—68no—
1056D4—64no—
1057D4—64no—
1058D4—68no—
1059D4—64no—
1060D4—64no—
1061D4—68no—
1062D4—68no—
1063D4—68no—
1064D4—68no—
1065D4—68no—
1066D4—62no—
1067D4C2×D3×D414yes—
1068C2×C4—24no—
1069C2×C4—28no—
1070C2×C4—22no—
1071C2×C4—22no—
1072C2×C4—22no—
1073C2×C4—22no—
1074C2×C4—22no—
1075C2×C4—28no—
1076C2×C4—22no—
1077C2×C4—22no—
1078C2×C4—22no—
1079C2×C4—32no—
1080C2×C4—34no—
1081C2×C4—34no—
1082C2×C4—34no—
1083C2×C4—38no—
1084C2×C4—32no—
1085C2×C4—42no—
1086C2×C4—42no—
1087C2×C4—68no—
1088C2×C4—68no—
1089C2×C4—68no—
1090C2×C4—68no—
1091C2×C4—68no—
1092C2×C4—68no—
1093C2×C4—68no—
1094C2×C4—64no—
1095C2×C4—62no—
1096C2×C4—62no—
1097C2×C4—62no—
1098C2×C4—62no—
1099C2×C4—64no—
1100C2×C4—68no—
1101C2×C4—62no—
1102C2×C4—62no—
1103C2×C4—128no—
1104C2×C4—122no—
1105C2×C4—122no—
1106C2×C4C2×D3×D411yescharacteristic
1107C2×C4C2×D3×D411yescharacteristic
1108C2×C4C2×D3×D414yes—
1109C2×C4C2×D3×D411yescharacteristic
1110C2×C4C24×D311yescharacteristic
1111C8—24no—
1112C8—64no—
1113C2×C3—22no—
1114C2×C3—41no—
1115C2×C3—44no—
1116C2×C3—41no—
1117C2×C3C22×#12011yescharacteristic
1118C2×C3#358611yescharacteristic
1119C2×C3#358611yescharacteristic
1120D3—24no—
1121D3—42no—
1122D3—44no—
1123C22—21no—
1124C22—21no—
1125C22—21no—
1126C22—21no—
1127C22—24no—
1128C22—21no—
1129C22—21no—
1130C22—21no—
1131C22—21no—
1132C22—34no—
1133C22—42no—
1134C22—42no—
1135C22—62no—
1136C22—62no—
1137C22—64no—
1138C22—62no—
1139C22—62no—
1140C22—62no—
1141C22—82no—
1142C22—84no—
1143C22—124no—
1144C22—122no—
1145C22—122no—
1146C22—242no—
1147C22—248no—
1148C22—244no—
1149C22—248no—
1150C22D3×#12012yes—
1151C22C22×D3×D411yescharacteristic
1152C4—21no—
1153C4—24no—
1154C4—21no—
1155C4—34no—
1156C4—42no—
1157C4—42no—
1158C4—62no—
1159C4—64no—
1160C4—122no—
1161C4—122no—
1162C4D3×#12012yes—
1163C4C22×D3×D412yes—
1164C3#6037011yescharacteristic, complemented, Sylow
1165C2—22no—
1166C2—41no—
1167C2—41no—
1168C2—44no—
1169C2—64no—
1170C2—122no—
1171C2—124no—
1172C2C2×D3×#12011yescharacteristic
1173C2#8719711yescharacteristic
1174C2#8720111yescharacteristic
subgroupG/H
centerC22C22×D3×D4
commutator, cosocleC2×C3×C4C25
FrattiniC2×C4C24×D3
FittingC3×#3007C2
socleC22×C3C23×D4
prime radicalC2×#5964C2
hypercenter#3007D3
hypocenterC3#60370
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
2. C2×D3×#137C2semidirect
3. C2×#5628C2semidirect
4. C3×#3007C2semidirect
5. #84084C2semidirect
6. #83981C2semidirect
7. #82735C2semidirect
8. #80230C2semidirect
9. #80229C2semidirect
10. #80185C2semidirect
11. #80148C2semidirect
12. #78885C2semidirect
13. #78881C2semidirect
14. #78640C2semidirect
15. #78630C2semidirect
27. C22×D3×Q8C22semidirect
34. C2×C3×#137C22semidirect
35. C2×C3×C22⋊Q8C22semidirect
36. C2×#951C22semidirect
37. C2×#946C22semidirect
38. C2×#942C22semidirect
39. C2×#924C22semidirect
41. C2×#918C22semidirect
42. C2×D3×Q16C22semidirect
43. C2×#915C22semidirect
44. C2×D3×SD16C22semidirect
45. C2×#909C22semidirect
46. C2×D3×M16C22semidirect
49. #5628C22semidirect
50. #5628C22semidirect
51. C2×#897C22semidirect
53. C2×#892C22semidirect
57. C3×#452C22semidirect
58. C3×#451C22semidirect
59. C3×#450C22semidirect
60. C3×#417C22semidirect
61. C3×#407C22semidirect
62. #5239C22semidirect
63. #5232C22semidirect
64. #5228C22semidirect
65. #5218C22semidirect
66. #5207C22semidirect
67. #5187C22semidirect
68. #5186C22semidirect
69. #5173C22semidirect
70. #5169C22semidirect
71. #5133C22semidirect
72. #5126C22semidirect
73. #5050C22semidirect
74. #5047C22semidirect
75. #5046C22semidirect
76. #4966C22semidirect
77. #4809C22semidirect
78. #4808C22semidirect
79. #4804C22semidirect
80. #4802C22semidirect
81. #4783C22semidirect
82. #4776C22semidirect
83. #4772C22semidirect
84. #4770C22semidirect
85. #4739C22semidirect
86. #4733C22semidirect
87. #4731C22semidirect
88. #4727C22semidirect
89. #4727C22semidirect
102. #3007D3semidirect
284. C2×#137C2×D3semidirect
299. C2×C22⋊Q8C2×D3semidirect
308. #452C2×D3semidirect
314. #451C2×D3semidirect
320. #450C2×D3semidirect
326. #417C2×D3semidirect
333. #407C2×D3semidirect
1164. C3#60370semidirect

Maximal subgroups

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

subgroupindex
C2×#59642
C2×D3×#1372
C2×#56282
C3×#30072
#840842
#839812
#827352
#802302
#802292
#801852
#801482
#788852
#788812
#786402
#786302
#603703