Subgroups — #44526041

Order 30944.

50 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₃₈₆₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₉₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄⋊C₄×C₉₆₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×D₉₆₇	—	2	1	no	—
5	D₃₈₆₈	—	2	1	no	—
6	D₃₈₆₈	C₄	1	2	yes	complemented
7	C₉₆₇⋊C₈	—	2	1	no	—
8	C₂×C₄×C₉₆₇	—	2	1	no	—
9	C₂×C₄×C₉₆₇	C₂²	1	1	yes	characteristic
10	C₂²×C₉₆₇	D₄	1	1	yes	characteristic
11	C₂×D₉₆₇	—	2	2	no	—
12	C₂×D₉₆₇	—	4	1	no	—
13	C₂×D₉₆₇	—	4	1	no	—
14	C₄×C₉₆₇	—	4	1	no	—
15	C₄×C₉₆₇	C₂×C₄	1	1	yes	characteristic
16	C₄×C₉₆₇	D₄	1	1	yes	characteristic
17	C₂×C₉₆₇	C₂²⋊C₄	1	1	yes	characteristic
18	C₂×C₉₆₇	D₈	1	1	yes	characteristic
19	C₂×C₉₆₇	SD₁₆	1	1	yes	characteristic
20	D₉₆₇	—	4	2	no	—
21	C₉₆₇	#102	1	1	yes	characteristic, complemented, Sylow
22	#102	—	967	1	no	maximal, Sylow
23	C₂×D₄	—	967	1	no	—
24	C₂×C₈	—	967	1	no	—
25	C₄⋊C₄	D₉₆₇	1	1	yes	characteristic, complemented
26	C₂³	—	1934	1	no	—
27	D₄	—	1934	1	no	—
28	D₄	—	967	2	no	—
29	C₂×C₄	—	2	1	no	—
30	C₂×C₄	C₂×D₉₆₇	1	1	yes	characteristic
31	C₈	—	1934	1	no	—
32	C₂²	—	3868	1	no	—
33	C₂²	—	3868	1	no	—
34	C₂²	—	1934	2	no	—
35	C₂²	C₂²⋊D₉₆₇	1	1	yes	characteristic
36	C₄	—	4	1	no	—
37	C₄	C₄×D₉₆₇	1	1	yes	characteristic
38	C₄	D₃₈₆₈	1	1	yes	characteristic
39	C₂	—	3868	2	no	—
40	C₂	(C₂×D₉₆₇)⋊C₄	1	1	yes	characteristic
41	C₂	#29509156	1	1	yes	characteristic
42	C₂	#29509158	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊D₉₆₇
commutator	C₄×C₉₆₇	C₂×C₄
Frattini	C₂×C₄	C₂×D₉₆₇
Fitting	C₄⋊C₄×C₉₆₇	C₂
socle	C₂²×C₉₆₇	D₄
prime radical	C₂×D₃₈₆₈	C₂
cosocle	C₂×C₄×C₉₆₇	C₂²
hypercenter	C₄⋊C₄	D₉₆₇
hypocenter	C₉₆₇	#102
LCS	G ▷ C₄×C₉₆₇ ▷ C₂×C₉₆₇ ▷ C₉₆₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₉₆₇⋊C₈	C₂	semidirect
3. C₄⋊C₄×C₉₆₇	C₂	semidirect
6. D₃₈₆₈	C₄	semidirect
21. C₉₆₇	#102	semidirect
25. C₄⋊C₄	D₉₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₃₈₆₈	2
C₂×C₉₆₇⋊C₈	2
C₄⋊C₄×C₉₆₇	2
#102	967