Finite Group Databasebeta

← C2×#78992 #11658785

Subgroups — C2×#78992 #11658785

Order 768.

4946 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5964C211yesmaximal, characteristic
2C2×#5745C211yesmaximal, characteristic, complemented
3C2×#5522C211yesmaximal, characteristic, complemented
4C2×C3×#421C211yesmaximal, characteristic, complemented
5C22×#837C211yesmaximal, characteristic, complemented
6C22×#825C211yesmaximal, characteristic, complemented
7C2×#5005C211yesmaximal, characteristic, complemented
8#78992C2116yesmaximal, direct product factor
9C2×#4821C214yesmaximal, complemented
10C2×D3×#104C214yesmaximal, complemented
11C2×#2901—31nomaximal, Sylow
12C22×C3×#41C2211yescharacteristic
13#5964—24no—
14#5964—24no—
15#5964C418yescomplemented
16#5964C2218yes—
17C2×#1010—21no—
18C2×#1010C412yescomplemented
19C2×#1009—21no—
20C2×#1009C412yescomplemented
21C2×D3×#41—22no—
22C2×D3×#41C2214yes—
23C2×#1007C412yescomplemented
24C2×#1004—22no—
25C2×#1004C412yescomplemented
26C22×#235—22no—
27C22×#235C2211yescharacteristic
28C22×#235C2211yescharacteristic
29C22×C3×M16C2211yescharacteristic, complemented
30C2×C3×#117C2211yescharacteristic, complemented
31C22×C4×Dic3C2211yescharacteristic, complemented
32C22×#208C2211yescharacteristic, complemented
33#5745—24no—
34#5745C2218yescomplemented
35C2×#907—22no—
36C2×D3×M16C2214yescomplemented
37C2×#901—22no—
38#5522—24no—
39#5522C2218yescomplemented
40C2×#893—21no—
41C2×#887—21no—
42C2×#67⋊C4—22no—
43C2×#872C2212yescomplemented
44C2×C42×D3C2212yescomplemented
45C3×#421C2218yescomplemented
46C2×C3×#104C2214yescomplemented
47C2×#837C2212yescomplemented
48C2×#837C2212yescomplemented
49C2×#837C2218yescomplemented
50C2×#825C2212yescomplemented
51C2×#825C2212yescomplemented
52C2×#825C2218yescomplemented
53#5005C2218yescomplemented
54C2×#805C2214yescomplemented
55#4821C22132yescomplemented
56D3×#104C22132yescomplemented
57C2×#585—31no—
58C2×#568—31no—
59C2×C4×#41—31no—
60#2901—316no—
61C2×#421—34no—
62C2×#421—31no—
63C2×#421D311yescharacteristic, complemented
64C22×#104—34no—
65C22×#104—31no—
66C22×#104—31no—
67C2×C3×#41—21no—
68C2×C3×#41—21no—
69C2×C3×#41—22no—
70C2×C3×#41—22no—
71C2×C3×#41C2×C412yescomplemented
72C2×C3×#41C2×C414yescomplemented
73C2×C3×#41C2312yes—
74C2×C3×#41C2314yes—
75C22×C3×Q8C2×C411yescharacteristic, complemented
76C22×C3×D4—21no—
77C22×C3×D4C2×C411yescharacteristic, complemented
78C23×C3×C4—21no—
79C23×C3×C4C2311yescharacteristic
80C22×#67—21no—
81C22×#67—24no—
82C22×#67D412yes—
83C23×Dic3—21no—
84#1010—28no—
85#1010—28no—
86#1010—28no—
87#1010C2×C4116yescomplemented
88#1009—28no—
89#1009—28no—
90#1009—28no—
91#1009C2×C4116yescomplemented
92D3×#41—216no—
93D3×#41—216no—
94D3×#41—28no—
95D3×#41—28no—
96D3×#41C2×C4116yescomplemented
97D3×#41C23116yes—
98#1007—28no—
99#1007C2×C4116yescomplemented
100C2×#239—22no—
101C2×#239C2×C414yescomplemented
102C2×D3×Q8—22no—
103C2×D3×Q8C2×C414yescomplemented
104#1004—216no—
105#1004—216no—
106#1004—28no—
107#1004C2×C4116yescomplemented
108C2×#237—24no—
109C2×#237—24no—
110C2×#237—22no—
111C2×#237C2×C414yescomplemented
112C2×D3×D4—24no—
113C2×D3×D4—24no—
114C2×D3×D4—22no—
115C2×D3×D4C2×C414yescomplemented
116C2×#235—21no—
117C2×#235—21no—
118C2×#235—22no—
119C2×#235—22no—
120C2×#235—24no—
121C2×#235—216no—
122C2×#235—216no—
123C2×#235—22no—
124C2×#235—24no—
125C2×#235—22no—
126C2×#235C2×C412yes—
127C2×#235C2×C412yes—
128C2×#235C2×C414yes—
129C2×#235C2×C412yescomplemented
130C2×#235C2×C414yescomplemented
131C2×#235D412yes—
132C2×#235D412yes—
133C2×#235D414yes—
134C2×#235D414yes—
135C2×#235C2312yes—
136C2×#235C2314yes—
137C2×#235C2314yes—
138C22×D12—22no—
139C22×D12C2×C411yescharacteristic, complemented
140C22×D12D411yescharacteristic
141C22×C4×D3—21no—
142C22×C4×D3—24no—
143C22×C4×D3—22no—
144C22×C4×D3C2312yes—
145C22×Dic6—22no—
146C22×Dic6C2×C411yescharacteristic, complemented
147C22×Dic6D411yescharacteristic
148C2×C3×M16—21no—
149C2×C3×M16—22no—
150C2×C3×M16C2312yes—
151C2×C3×M16C2314yescomplemented
152C22×C3×C8—21no—
153C3×#117—22no—
154C3×#117C2314yescomplemented
155C2×C3×C4⋊C4—21no—
156C2×C3×C22⋊C4—21no—
157C2×C3×C42C2312yes—
158C2×(C2×D3)⋊C4—22no—
159C2×Dic3⋊C4—22no—
160C2×C4×Dic3—21no—
161C2×C4×Dic3—22no—
162C2×C4×Dic3—22no—
163C2×C4×Dic3C2311yescharacteristic
164C2×C4×Dic3C2311yescharacteristic
165C2×C4×Dic3C2314yescomplemented
166C2×#208—21no—
167C2×#208—22no—
168C2×#208C2312yes—
169C2×#208C2314yescomplemented
170C22×C3⋊C8—21no—
171#907—216no—
172D3×M16—28no—
173D3×M16C23116yescomplemented
174#901—216no—
175C2×ΓL(1,𝔽25)—24no—
176C2×D3×C8—24no—
177#893—28no—
178#887—28no—
179#67⋊C4—216no—
180#872—24no—
181#872C2318yescomplemented
182C42×D3—24no—
183C42×D3C2318yescomplemented
184C3×#104C23116yescomplemented
185#837C2318yescomplemented
186#837C2318yescomplemented
187#825C2318yescomplemented
188#825C2318yescomplemented
189#805C23116yescomplemented
190#585—38no—
191#585—38no—
192#585—64no—
193#585—64no—
194C2×2−1+4—32no—
195C2×2−1+4—32no—
196C2×2−1+4—61no—
197C2×H(5,𝔽2)—32no—
198C2×H(5,𝔽2)—32no—
199C2×H(5,𝔽2)—62no—
200C2×H(5,𝔽2)—61no—
201C22×#41—31no—
202C22×#41—34no—
203C22×#41—31no—
204C22×#41—62no—
205C22×#41—62no—
206C22×#41C2×D311yescharacteristic
207#568—38no—
208#568—64no—
209C2×#131—62no—
210C2×#131—62no—
211C22×M16—31no—
212C22×M16—34no—
213C22×M16C2×D311yescharacteristic, complemented
214C4×#41—38no—
215C4×#41—64no—
216C2×C4×Q8—61no—
217C2×C4×D4—62no—
218C2×C4×D4—61no—
219C2×#117—32no—
220C2×#117C2×D311yescharacteristic, complemented
221C22×C42—31no—
222C22×C42—32no—
223#421—38no—
224#421—332no—
225#421C2×D318yescomplemented
226C2×#104—32no—
227C2×#104—32no—
228C2×#104—38no—
229C2×#104—32no—
230C2×#104—32no—
231C2×#104—38no—
232C2×#104—34no—
233C2×#104—332no—
234C2×#104C2×D314yescomplemented
235C24×C3—21no—
236C24×C3C2×D411yescharacteristic
237C23×D3—21no—
238C23×D3—24no—
239C23×D3C2×D412yes—
240C3×#41—24no—
241C3×#41—24no—
242C3×#41—24no—
243C3×#41—22no—
244C3×#41—24no—
245C3×#41—22no—
246C3×#41—24no—
247C3×#41C22×C414yes—
248C3×#41C22×C418yescomplemented
249C3×#41C2414yes—
250C2×C3×Q8—21no—
251C2×C3×Q8—22no—
252C2×C3×Q8C22×C412yes—
253C2×C3×Q8C22×C414yescomplemented
254C2×C3×D4—22no—
255C2×C3×D4—24no—
256C2×C3×D4—22no—
257C2×C3×D4—24no—
258C2×C3×D4—21no—
259C2×C3×D4—22no—
260C2×C3×D4C22×C412yes—
261C2×C3×D4C22×C414yescomplemented
262C22×C3×C4—21no—
263C22×C3×C4—22no—
264C22×C3×C4—24no—
265C22×C3×C4—22no—
266C22×C3×C4—24no—
267C22×C3×C4—22no—
268C22×C3×C4C22×C411yescharacteristic
269C22×C3×C4C22×C411yescharacteristic
270C22×C3×C4C22×C412yes—
271C22×C3×C4C2×D411yescharacteristic
272C22×C3×C4C2×D412yes—
273C22×C3×C4C2×D411yescharacteristic
274C22×C3×C4C2×D411yescharacteristic
275C22×C3×C4C2×D412yes—
276C22×C3×C4C2411yescharacteristic
277C22×C3×C4C2412yes—
278C2×#67—22no—
279C2×#67—24no—
280C2×#67—22no—
281C2×#67—24no—
282C2×#67—24no—
283C2×#67—232no—
284C2×#67—24no—
285C2×#67C22⋊C414yes—
286C2×#67C22⋊C414yes—
287C2×#67C22⋊C418yes—
288C2×#67C2×D418yes—
289C22×Dic3—21no—
290C22×Dic3—21no—
291C22×Dic3—24no—
292C22×Dic3—24no—
293C22×Dic3—21no—
294C22×Dic3—44no—
295C22×Dic3C2×D412yes—
296#239—216no—
297#239—28no—
298#239C22×C4116yescomplemented
299D3×Q8—28no—
300D3×Q8—216no—
301D3×Q8C22×C4116yescomplemented
302#237—232no—
303#237—216no—
304#237—216no—
305#237—28no—
306#237—216no—
307#237C22×C4116yescomplemented
308D3×D4—216no—
309D3×D4—216no—
310D3×D4—232no—
311D3×D4—216no—
312D3×D4—28no—
313D3×D4C22×C4116yescomplemented
314#235—24no—
315#235—24no—
316#235—24no—
317#235—24no—
318#235—22no—
319#235—22no—
320#235—24no—
321#235—232no—
322#235—216no—
323#235—216no—
324#235—216no—
325#235—216no—
326#235C22⋊C418yes—
327#235C22⋊C418yes—
328#235C22⋊C418yes—
329#235C22⋊C418yes—
330#235C22×C418yes—
331#235C22×C418yes—
332#235C22×C414yes—
333#235C22×C418yescomplemented
334#235C2×D418yes—
335#235C2×D418yes—
336#235C2414yes—
337C2×D12—24no—
338C2×D12—21no—
339C2×D12—22no—
340C2×D12—216no—
341C2×D12C22⋊C412yes—
342C2×D12C22⋊C412yes—
343C2×D12C22⋊C414yes—
344C2×D12C22×C412yes—
345C2×D12C22×C414yescomplemented
346C2×D12C2×D414yes—
347C2×C4×D3—24no—
348C2×C4×D3—22no—
349C2×C4×D3—24no—
350C2×C4×D3—22no—
351C2×C4×D3—24no—
352C2×C4×D3—24no—
353C2×C4×D3—216no—
354C2×C4×D3—216no—
355C2×C4×D3—28no—
356C2×C4×D3—48no—
357C2×C4×D3C22×C414yes—
358C2×C4×D3C22×C414yes—
359C2×C4×D3C2×D414yes—
360C2×C4×D3C2×D414yes—
361C2×C4×D3C2×D414yes—
362C2×C4×D3C2414yes—
363C2×Dic6—21no—
364C2×Dic6—22no—
365C2×Dic6—24no—
366C2×Dic6—216no—
367C2×Dic6C22⋊C412yes—
368C2×Dic6C22⋊C412yes—
369C2×Dic6C22⋊C414yes—
370C2×Dic6C22×C412yes—
371C2×Dic6C22×C414yescomplemented
372C2×Dic6C2×D414yes—
373C3×M16—22no—
374C3×M16—24no—
375C3×M16C2414yes—
376C2×C3×C8—22no—
377C2×C3×C8—24no—
378C3×C4⋊C4—24no—
379C3×C22⋊C4—24no—
380C3×C42—22no—
381C3×C42C2414yes—
382(C2×D3)⋊C4—28no—
383Dic3⋊C4—28no—
384C4×Dic3—21no—
385C4×Dic3—21no—
386C4×Dic3—24no—
387C4×Dic3—28no—
388C4×Dic3C2412yes—
389C4×Dic3C2412yes—
390#208—24no—
391#208—22no—
392#208C2414yes—
393C2×C3⋊C8—22no—
394C2×C3⋊C8—24no—
395ΓL(1,𝔽25)—216no—
396D3×C8—216no—
3972−1+4—316no—
3982−1+4—316no—
3992−1+4—68no—
4002−1+4—68no—
4012−1+4—68no—
4022−1+4—68no—
403H(5,𝔽2)—316no—
404H(5,𝔽2)—316no—
405H(5,𝔽2)—616no—
406H(5,𝔽2)—616no—
407H(5,𝔽2)—68no—
408H(5,𝔽2)—68no—
409H(5,𝔽2)—68no—
410H(5,𝔽2)—68no—
411C2×#41—21no—
412C2×#41—21no—
413C2×#41—22no—
414C2×#41—22no—
415C2×#41—32no—
416C2×#41—32no—
417C2×#41—34no—
418C2×#41—34no—
419C2×#41—32no—
420C2×#41—32no—
421C2×#41—34no—
422C2×#41—34no—
423C2×#41—316no—
424C2×#41—316no—
425C2×#41—34no—
426C2×#41—34no—
427C2×#41—32no—
428C2×#41—34no—
429C2×#41—32no—
430C2×#41—34no—
431C2×#41—64no—
432C2×#41—64no—
433C2×#41—62no—
434C2×#41—62no—
435C2×#41—616no—
436C2×#41—616no—
437C2×#41—64no—
438C2×#41—68no—
439C2×#41—68no—
440C2×#41—64no—
441C2×#41—62no—
442C2×#41—62no—
443C2×#41—616no—
444C2×#41—616no—
445C2×#41—61no—
446C2×#41—61no—
447C2×#41—62no—
448C2×#41—62no—
449C2×#41C4×D312yescomplemented
450C2×#41C4×D314yescomplemented
451C2×#41C22×D312yes—
452C2×#41C22×D314yes—
453C22×Q8—31no—
454C22×Q8—34no—
455C22×Q8—31no—
456C22×Q8—62no—
457C22×Q8—62no—
458C22×Q8C4×D311yescharacteristic, complemented
459C22×D4—21no—
460C22×D4—32no—
461C22×D4—34no—
462C22×D4—31no—
463C22×D4—31no—
464C22×D4—62no—
465C22×D4—64no—
466C22×D4—62no—
467C22×D4—64no—
468C22×D4—64no—
469C22×D4—61no—
470C22×D4C4×D311yescharacteristic, complemented
471C23×C4—21no—
472C23×C4—32no—
473C23×C4—64no—
474C23×C4—62no—
475C23×C4—61no—
476C23×C4—61no—
477C23×C4C22×D311yescharacteristic
478#131—616no—
479#131—616no—
480C2×M16—21no—
481C2×M16—22no—
482C2×M16—32no—
483C2×M16—34no—
484C2×M16—316no—
485C2×M16—64no—
486C2×M16—68no—
487C2×M16—61no—
488C2×M16—62no—
489C2×M16C22×D312yes—
490C2×M16C22×D314yescomplemented
491C22×C8—21no—
492C22×C8—64no—
493C22×C8—61no—
494C4×Q8—68no—
495C4×D4—616no—
496C4×D4—68no—
497#117—22no—
498#117—38no—
499#117—64no—
500#117C22×D314yescomplemented
501C2×C4⋊C4—21no—
502C2×C4⋊C4—62no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—62no—
505C2×C42—31no—
506C2×C42—34no—
507C2×C42—31no—
508C2×C42—38no—
509C2×C42—64no—
510C2×C42—62no—
511C2×C42—61no—
512C2×C42—62no—
513C2×C42C22×D312yes—
514#104—38no—
515#104—38no—
516#104—38no—
517#104—38no—
518#104—316no—
519#104C22×D3116yescomplemented
520C23×C3—22no—
521C23×C3—24no—
522C23×C3—42no—
523C23×C3—82no—
524C23×C3C2×C22⋊C411yescharacteristic
525C23×C3C2×C22⋊C411yescharacteristic
526C23×C3C2×C22⋊C412yes—
527C23×C3C22×D411yescharacteristic
528C23×C3C22×D412yes—
529C22×D3—22no—
530C22×D3—24no—
531C22×D3—216no—
532C22×D3—44no—
533C22×D3—88no—
534C22×D3—82no—
535C22×D3C2×C22⋊C414yes—
536C22×D3C2×C22⋊C414yes—
537C22×D3C22×D414yes—
538C3×Q8—22no—
539C3×Q8—24no—
540C3×Q8C23×C414yes—
541C3×D4—24no—
542C3×D4—28no—
543C3×D4—24no—
544C3×D4—22no—
545C3×D4—24no—
546C3×D4C23×C414yes—
547C2×C3×C4—22no—
548C2×C3×C4—24no—
549C2×C3×C4—28no—
550C2×C3×C4—24no—
551C2×C3×C4—24no—
552C2×C3×C4—24no—
553C2×C3×C4—44no—
554C2×C3×C4C2×C22⋊C411yescharacteristic
555C2×C3×C4C2×C22⋊C412yes—
556C2×C3×C4C2×C22⋊C411yescharacteristic
557C2×C3×C4C2×C22⋊C412yes—
558C2×C3×C4C2×C22⋊C412yes—
559C2×C3×C4C2×C22⋊C412yes—
560C2×C3×C4C2×C22⋊C412yes—
561C2×C3×C4C23×C411yescharacteristic
562C2×C3×C4C23×C412yes—
563C2×C3×C4C23×C411yescharacteristic
564C2×C3×C4C23×C412yes—
565C2×C3×C4C22×D411yescharacteristic
566C2×C3×C4C22×D412yes—
567C2×C3×C4C22×D412yes—
568C2×C3×C4C22×D412yes—
569C2×C3×C4C22×D411yescharacteristic
570C2×C3×C4C22×D411yescharacteristic
571C2×C3×C4C2511yescharacteristic
572#67—28no—
573#67—24no—
574#67—24no—
575#67—216no—
576#67—216no—
577#67C2×C22⋊C4116yes—
578#67C2×C22⋊C4116yes—
579C2×Dic3—24no—
580C2×Dic3—22no—
581C2×Dic3—24no—
582C2×Dic3—22no—
583C2×Dic3—216no—
584C2×Dic3—22no—
585C2×Dic3—48no—
586C2×Dic3—42no—
587C2×Dic3C2×C22⋊C414yes—
588C2×Dic3C2×C22⋊C414yes—
589C2×Dic3C22×D414yes—
590D12—216no—
591D12—24no—
592D12—22no—
593D12C2×C22⋊C418yes—
594D12C2×C22⋊C418yes—
595D12C23×C414yes—
596C4×D3—216no—
597C4×D3—24no—
598C4×D3—28no—
599C4×D3—24no—
600C4×D3—216no—
601C4×D3—416no—
602C4×D3C2×C22⋊C418yes—
603C4×D3C2×C22⋊C418yes—
604C4×D3C23×C418yes—
605C4×D3C22×D418yes—
606Dic6—24no—
607Dic6—22no—
608Dic6—216no—
609Dic6C2×C22⋊C418yes—
610Dic6C2×C22⋊C418yes—
611Dic6C23×C414yes—
612C3×C8—24no—
613C3⋊C8—24no—
614C24—21no—
615C24—32no—
616C24—64no—
617C24—61no—
618C24D3×D411yescharacteristic
619#41—24no—
620#41—24no—
621#41—24no—
622#41—24no—
623#41—22no—
624#41—22no—
625#41—24no—
626#41—38no—
627#41—38no—
628#41—38no—
629#41—38no—
630#41—38no—
631#41—38no—
632#41—38no—
633#41—38no—
634#41—316no—
635#41—316no—
636#41—34no—
637#41—38no—
638#41—34no—
639#41—616no—
640#41—616no—
641#41—632no—
642#41—616no—
643#41—616no—
644#41—616no—
645#41—616no—
646#41—68no—
647#41—68no—
648#41—632no—
649#41—616no—
650#41—616no—
651#41—64no—
652#41—64no—
653#41—64no—
654#41—64no—
655#41—62no—
656#41—62no—
657#41—64no—
658#41C2×C4×D314yes—
659#41C2×C4×D318yescomplemented
660#41C23×D314yes—
661C2×Q8—21no—
662C2×Q8—22no—
663C2×Q8—32no—
664C2×Q8—32no—
665C2×Q8—34no—
666C2×Q8—34no—
667C2×Q8—316no—
668C2×Q8—32no—
669C2×Q8—34no—
670C2×Q8—64no—
671C2×Q8—616no—
672C2×Q8—68no—
673C2×Q8—616no—
674C2×Q8—61no—
675C2×Q8—62no—
676C2×Q8C2×C4×D312yes—
677C2×Q8C2×C4×D314yescomplemented
678C2×D4—22no—
679C2×D4—24no—
680C2×D4—22no—
681C2×D4—24no—
682C2×D4—21no—
683C2×D4—22no—
684C2×D4—34no—
685C2×D4—34no—
686C2×D4—38no—
687C2×D4—38no—
688C2×D4—316no—
689C2×D4—32no—
690C2×D4—32no—
691C2×D4—34no—
692C2×D4—32no—
693C2×D4—34no—
694C2×D4—34no—
695C2×D4—616no—
696C2×D4—64no—
697C2×D4—68no—
698C2×D4—64no—
699C2×D4—632no—
700C2×D4—616no—
701C2×D4—616no—
702C2×D4—616no—
703C2×D4—632no—
704C2×D4—64no—
705C2×D4—62no—
706C2×D4—64no—
707C2×D4—62no—
708C2×D4—64no—
709C2×D4—61no—
710C2×D4—62no—
711C2×D4C2×C4×D312yes—
712C2×D4C2×C4×D314yescomplemented
713C22×C4—21no—
714C22×C4—22no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—22no—
718C22×C4—22no—
719C22×C4—32no—
720C22×C4—34no—
721C22×C4—34no—
722C22×C4—34no—
723C22×C4—34no—
724C22×C4—34no—
725C22×C4—34no—
726C22×C4—64no—
727C22×C4—616no—
728C22×C4—616no—
729C22×C4—64no—
730C22×C4—68no—
731C22×C4—64no—
732C22×C4—61no—
733C22×C4—61no—
734C22×C4—62no—
735C22×C4—64no—
736C22×C4—64no—
737C22×C4—62no—
738C22×C4—61no—
739C22×C4—64no—
740C22×C4—128no—
741C22×C4—124no—
742C22×C4C2×C4×D311yescharacteristic
743C22×C4C2×C4×D311yescharacteristic
744C22×C4C2×C4×D312yes—
745C22×C4D3×D411yescharacteristic
746C22×C4D3×D412yes—
747C22×C4D3×D412yes—
748C22×C4D3×D411yescharacteristic
749C22×C4D3×D411yescharacteristic
750C22×C4C23×D312yes—
751C22×C4C23×D311yescharacteristic
752M16—22no—
753M16—24no—
754M16—34no—
755M16—616no—
756M16—62no—
757M16—64no—
758M16C23×D314yes—
759C2×C8—24no—
760C2×C8—22no—
761C2×C8—616no—
762C2×C8—64no—
763C2×C8—62no—
764C4⋊C4—24no—
765C4⋊C4—68no—
766C22⋊C4—24no—
767C22⋊C4—68no—
768C42—22no—
769C42—32no—
770C42—32no—
771C42—68no—
772C42—61no—
773C42—61no—
774C42—64no—
775C42C23×D314yes—
776C22×C3—22no—
777C22×C3—22no—
778C22×C3—22no—
779C22×C3—24no—
780C22×C3—42no—
781C22×C3—42no—
782C22×C3—44no—
783C22×C3—84no—
784C22×C3C22×C22⋊C412yes—
785C22×C3C22×C22⋊C411yescharacteristic
786C22×C3C22×C22⋊C412yes—
787C22×C3C22×C22⋊C411yescharacteristic
788C22×C3C23×D411yescharacteristic
789C2×D3—28no—
790C2×D3—24no—
791C2×D3—44no—
792C2×D3—44no—
793C2×D3—44no—
794C2×D3—816no—
795C2×D3—84no—
796C2×D3C22×C22⋊C418yes—
797C3×C4—24no—
798C3×C4—44no—
799C3×C4C22×C22⋊C412yes—
800C3×C4C22×C22⋊C411yescharacteristic
801C3×C4C22×C22⋊C412yes—
802C3×C4C22×C22⋊C411yescharacteristic
803C3×C4C24×C411yescharacteristic
804C3×C4C23×D411yescharacteristic
805Dic3—24no—
806Dic3—24no—
807Dic3—42no—
808Dic3C22×C22⋊C418yes—
809C23—22no—
810C23—24no—
811C23—34no—
812C23—34no—
813C23—34no—
814C23—42no—
815C23—616no—
816C23—62no—
817C23—64no—
818C23—82no—
819C23—124no—
820C23—242no—
821C23—248no—
822C23D3×C22⋊C411yescharacteristic
823C23D3×C22⋊C411yescharacteristic
824C23D3×C22⋊C412yes—
825C23C2×D3×D411yescharacteristic
826C23C2×D3×D412yes—
827Q8—22no—
828Q8—24no—
829Q8—38no—
830Q8—38no—
831Q8—34no—
832Q8—616no—
833Q8—64no—
834Q8—62no—
835Q8C22×C4×D314yes—
836D4—24no—
837D4—24no—
838D4—28no—
839D4—22no—
840D4—24no—
841D4—316no—
842D4—316no—
843D4—34no—
844D4—38no—
845D4—38no—
846D4—616no—
847D4—616no—
848D4—616no—
849D4—64no—
850D4—68no—
851D4—64no—
852D4—64no—
853D4—62no—
854D4C22×C4×D314yes—
855C2×C4—22no—
856C2×C4—24no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—28no—
860C2×C4—24no—
861C2×C4—34no—
862C2×C4—34no—
863C2×C4—34no—
864C2×C4—38no—
865C2×C4—38no—
866C2×C4—38no—
867C2×C4—38no—
868C2×C4—44no—
869C2×C4—616no—
870C2×C4—616no—
871C2×C4—616no—
872C2×C4—64no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—64no—
876C2×C4—64no—
877C2×C4—64no—
878C2×C4—68no—
879C2×C4—62no—
880C2×C4—1216no—
881C2×C4—128no—
882C2×C4—122no—
883C2×C4D3×C22⋊C411yescharacteristic
884C2×C4D3×C22⋊C412yes—
885C2×C4D3×C22⋊C411yescharacteristic
886C2×C4D3×C22⋊C412yes—
887C2×C4D3×C22⋊C412yes—
888C2×C4D3×C22⋊C412yes—
889C2×C4D3×C22⋊C412yes—
890C2×C4C22×C4×D311yescharacteristic
891C2×C4C22×C4×D311yescharacteristic
892C2×C4C22×C4×D312yes—
893C2×C4C22×C4×D312yes—
894C2×C4C2×D3×D412yes—
895C2×C4C2×D3×D412yes—
896C2×C4C2×D3×D411yescharacteristic
897C2×C4C2×D3×D411yescharacteristic
898C2×C4C2×D3×D412yes—
899C2×C4C2×D3×D411yescharacteristic
900C2×C4C24×D311yescharacteristic
901C8—24no—
902C8—64no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—22no—
906C2×C3—22no—
907C2×C3—44no—
908C2×C3#290112yescomplemented
909C2×C3C23×C22⋊C411yescharacteristic
910D3—28no—
911D3—44no—
912C22—22no—
913C22—22no—
914C22—22no—
915C22—24no—
916C22—38no—
917C22—42no—
918C22—42no—
919C22—44no—
920C22—68no—
921C22—64no—
922C22—84no—
923C22—124no—
924C22—124no—
925C22—124no—
926C22—244no—
927C22—2416no—
928C22C2×D3×C22⋊C412yes—
929C22C2×D3×C22⋊C411yescharacteristic
930C22C2×D3×C22⋊C412yes—
931C22C2×D3×C22⋊C411yescharacteristic
932C22C22×D3×D411yescharacteristic
933C4—24no—
934C4—38no—
935C4—44no—
936C4—64no—
937C4—64no—
938C4—122no—
939C4C2×D3×C22⋊C411yescharacteristic
940C4C2×D3×C22⋊C412yes—
941C4C2×D3×C22⋊C411yescharacteristic
942C4C2×D3×C22⋊C412yes—
943C4C23×C4×D311yescharacteristic
944C4C22×D3×D411yescharacteristic
945C3C2×#290111yescharacteristic, complemented, Sylow
946C2—21no—
947C2—22no—
948C2—21no—
949C2—22no—
950C2—44no—
951C2—68no—
952C2—124no—
953C2#7899212yesdirect product factor
954C2C22×D3×C22⋊C411yescharacteristic
subgroupG/H
centerC2×C4C2×D3×D4
commutatorC3×C4C24×C4
FrattiniC2×C4C24×D3
FittingC2×C3×#421C2
socleC22×C3C22×C22⋊C4
prime radicalC2×#5964C2
cosocleC2×C3×C4C25
hypercenterC2×#421D3
hypocenterC3C2×#2901
LCSG ▷ C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#5745C2semidirect
3. C2×#5522C2semidirect
4. C2×C3×#421C2semidirect
5. C22×#837C2semidirect
6. C22×#825C2semidirect
7. C2×#5005C2semidirect
8. #78992C2direct (N × H)
9. C2×#4821C2semidirect
10. C2×D3×#104C2semidirect
15. #5964C4semidirect
18. C2×#1010C4semidirect
20. C2×#1009C4semidirect
23. C2×#1007C4semidirect
25. C2×#1004C4semidirect
29. C22×C3×M16C22semidirect
30. C2×C3×#117C22semidirect
31. C22×C4×Dic3C22semidirect
32. C22×#208C22semidirect
34. #5745C22semidirect
36. C2×D3×M16C22semidirect
39. #5522C22semidirect
43. C2×#872C22semidirect
44. C2×C42×D3C22semidirect
45. C3×#421C22semidirect
46. C2×C3×#104C22semidirect
47. C2×#837C22semidirect
48. C2×#837C22semidirect
49. C2×#837C22semidirect
50. C2×#825C22semidirect
51. C2×#825C22semidirect
52. C2×#825C22semidirect
53. #5005C22semidirect
54. C2×#805C22semidirect
55. #4821C22semidirect
56. D3×#104C22semidirect
63. C2×#421D3semidirect
71. C2×C3×#41C2×C4semidirect
72. C2×C3×#41C2×C4semidirect
75. C22×C3×Q8C2×C4semidirect
77. C22×C3×D4C2×C4semidirect
87. #1010C2×C4semidirect
91. #1009C2×C4semidirect
96. D3×#41C2×C4semidirect
99. #1007C2×C4semidirect
101. C2×#239C2×C4semidirect
103. C2×D3×Q8C2×C4semidirect
107. #1004C2×C4semidirect
111. C2×#237C2×C4semidirect
115. C2×D3×D4C2×C4semidirect
129. C2×#235C2×C4semidirect
130. C2×#235C2×C4semidirect
139. C22×D12C2×C4semidirect
146. C22×Dic6C2×C4semidirect
151. C2×C3×M16C23semidirect
154. C3×#117C23semidirect
165. C2×C4×Dic3C23semidirect
169. C2×#208C23semidirect
173. D3×M16C23semidirect
181. #872C23semidirect
183. C42×D3C23semidirect
184. C3×#104C23semidirect
185. #837C23semidirect
186. #837C23semidirect
187. #825C23semidirect
188. #825C23semidirect
189. #805C23semidirect
213. C22×M16C2×D3semidirect
220. C2×#117C2×D3semidirect
225. #421C2×D3semidirect
234. C2×#104C2×D3semidirect
248. C3×#41C22×C4semidirect
253. C2×C3×Q8C22×C4semidirect
261. C2×C3×D4C22×C4semidirect
298. #239C22×C4semidirect
301. D3×Q8C22×C4semidirect
307. #237C22×C4semidirect
313. D3×D4C22×C4semidirect
333. #235C22×C4semidirect
345. C2×D12C22×C4semidirect
371. C2×Dic6C22×C4semidirect
449. C2×#41C4×D3semidirect
450. C2×#41C4×D3semidirect
458. C22×Q8C4×D3semidirect
470. C22×D4C4×D3semidirect
490. C2×M16C22×D3semidirect
500. #117C22×D3semidirect
519. #104C22×D3semidirect
659. #41C2×C4×D3semidirect
677. C2×Q8C2×C4×D3semidirect
712. C2×D4C2×C4×D3semidirect
908. C2×C3#2901semidirect
945. C3C2×#2901semidirect
953. C2#78992direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#59642
C2×#57452
C2×#55222
C2×C3×#4212
C22×#8372
C22×#8252
C2×#50052
#789922
C2×#48212
C2×D3×#1042
C2×#29013