Subgroups — #44526150

Order 30944.

60 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509170	C₂	1	1	yes	maximal, characteristic
2	Q₈×D₉₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Dic₃₈₆₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#29509161	C₂	1	1	yes	maximal, characteristic, complemented
5	#29509159	C₂	1	1	yes	maximal, characteristic, complemented
6	#29509154	C₂	1	1	yes	maximal, characteristic, complemented
7	SD₁₆×C₉₆₇	C₂	1	1	yes	maximal, characteristic, complemented
8	Dic₁₉₃₄	—	2	1	no	—
9	Dic₁₉₃₄	C₂²	1	1	yes	characteristic
10	Dic₁₉₃₄	C₂²	1	1	yes	characteristic
11	C₂²⋊D₉₆₇	—	2	1	no	—
12	C₂×Dic₉₆₇	—	2	1	no	—
13	C₄×D₉₆₇	—	2	1	no	—
14	C₄×D₉₆₇	C₂²	1	1	yes	characteristic
15	C₉₆₇⋊C₈	C₂²	1	1	yes	characteristic
16	Q₈×C₉₆₇	C₂²	1	1	yes	characteristic
17	D₄×C₉₆₇	C₂²	1	1	yes	characteristic
18	C₈×C₉₆₇	C₂²	1	1	yes	characteristic
19	C₂²×C₉₆₇	—	2	1	no	—
20	C₂×D₉₆₇	D₄	1	1	yes	characteristic
21	C₄×C₉₆₇	—	2	1	no	—
22	C₄×C₉₆₇	C₂³	1	1	yes	characteristic
23	Dic₉₆₇	—	2	1	no	—
24	Dic₉₆₇	—	2	1	no	—
25	Dic₉₆₇	D₄	1	1	yes	characteristic
26	C₂×C₉₆₇	—	4	1	no	—
27	C₂×C₉₆₇	C₂×D₄	1	1	yes	characteristic
28	D₉₆₇	—	2	1	no	—
29	C₉₆₇	#137	1	1	yes	characteristic, complemented, Sylow
30	#137	—	967	1	no	maximal, Sylow
31	#41	—	967	1	no	—
32	C₂×Q₈	—	967	1	no	—
33	Q₁₆	—	967	1	no	—
34	Q₁₆	—	967	1	no	—
35	SD₁₆	—	967	1	no	—
36	SD₁₆	D₉₆₇	1	1	yes	characteristic, complemented
37	M₁₆	—	967	1	no	—
38	Q₈	—	1934	1	no	—
39	Q₈	—	967	1	no	—
40	Q₈	—	967	1	no	—
41	Q₈	C₂×D₉₆₇	1	1	yes	characteristic
42	D₄	—	1934	1	no	—
43	D₄	C₂×D₉₆₇	1	1	yes	characteristic
44	C₂×C₄	—	1934	1	no	—
45	C₂×C₄	—	1934	1	no	—
46	C₂×C₄	—	967	1	no	—
47	C₈	—	967	1	no	—
48	C₈	C₂×D₉₆₇	1	1	yes	characteristic
49	C₂²	—	2	1	no	—
50	C₂²	—	967	1	no	—
51	C₄	—	2	1	no	—
52	C₄	—	1934	1	no	—
53	C₄	—	1934	1	no	—
54	C₄	—	967	1	no	—
55	C₄	C₂²×D₉₆₇	1	1	yes	characteristic
56	C₂	—	4	1	no	—
57	C₂	—	1934	1	no	—
58	C₂	D₄×D₉₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂	D₄×D₉₆₇
commutator, cosocle	C₄×C₉₆₇	C₂³
Frattini	C₄	C₂²×D₉₆₇
Fitting	SD₁₆×C₉₆₇	C₂
socle	C₂×C₉₆₇	C₂×D₄
prime radical	#29509170	C₂
hypercenter	SD₁₆	D₉₆₇
hypocenter	C₉₆₇	#137
LCS	G ▷ C₄×C₉₆₇ ▷ C₂×C₉₆₇ ▷ C₉₆₇
UCS	C₁ ◁ C₂ ◁ C₄ ◁ SD₁₆

Complements

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

N	H ≅ G/N	type
2. Q₈×D₉₆₇	C₂	semidirect
3. Dic₃₈₆₈	C₂	semidirect
4. #29509161	C₂	semidirect
5. #29509159	C₂	semidirect
6. #29509154	C₂	semidirect
7. SD₁₆×C₉₆₇	C₂	semidirect
29. C₉₆₇	#137	semidirect
36. SD₁₆	D₉₆₇	semidirect

Maximal subgroups

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

subgroup	index
#29509170	2
Q₈×D₉₆₇	2
Dic₃₈₆₈	2
#29509161	2
#29509159	2
#29509154	2
SD₁₆×C₉₆₇	2
#137	967