Subgroups — #124×C₇₀₁ #36375985

Order 22432.

76 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₇₀₁	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×C₇₀₁	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊C₄×C₇₀₁	C₂	1	4	yes	maximal, complemented
4	C₄²×C₇₀₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×C₇₀₁	C₂²	1	2	yes	—
6	Q₈×C₇₀₁	—	2	2	no	—
7	D₄×C₇₀₁	—	2	2	no	—
8	C₂×C₄×C₇₀₁	C₂²	1	2	yes	—
9	C₂×C₄×C₇₀₁	C₂²	1	2	yes	—
10	C₂×C₄×C₇₀₁	C₂²	1	1	yes	characteristic
11	C₂²×C₇₀₁	—	2	2	no	—
12	C₂²×C₇₀₁	—	2	4	no	—
13	C₂²×C₇₀₁	C₂³	1	1	yes	characteristic
14	C₄×C₇₀₁	—	2	2	no	—
15	C₄×C₇₀₁	—	2	2	no	—
16	C₄×C₇₀₁	D₄	1	2	yes	—
17	C₂×C₇₀₁	—	4	2	no	—
18	C₂×C₇₀₁	C₂×D₄	1	1	yes	characteristic
19	C₂×C₇₀₁	#41	1	2	yes	—
20	C₇₀₁	#124	1	1	yes	characteristic, direct product factor, Sylow
21	#124	C₇₀₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
22	C₂×Q₈	C₂×C₇₀₁	1	1	yes	characteristic, complemented
23	C₂×D₄	C₂×C₇₀₁	1	1	yes	characteristic
24	C₂²⋊C₄	C₂×C₇₀₁	1	4	yes	complemented
25	C₄²	C₂×C₇₀₁	1	1	yes	characteristic, complemented
26	C₂³	C₂²×C₇₀₁	1	2	yes	—
27	Q₈	—	2	2	no	—
28	D₄	—	2	2	no	—
29	C₂×C₄	C₂²×C₇₀₁	1	2	yes	—
30	C₂×C₄	C₂²×C₇₀₁	1	2	yes	—
31	C₂×C₄	C₂²×C₇₀₁	1	1	yes	characteristic
32	C₂²	—	2	2	no	—
33	C₂²	—	2	4	no	—
34	C₂²	C₂³×C₇₀₁	1	1	yes	characteristic
35	C₄	—	2	2	no	—
36	C₄	—	2	2	no	—
37	C₄	D₄×C₇₀₁	1	2	yes	—
38	C₂	—	4	2	no	—
39	C₂	C₂×D₄×C₇₀₁	1	1	yes	characteristic
40	C₂	#41×C₇₀₁	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₇₀₁	C₂³
commutator, Frattini, cosocle	C₂²	C₂³×C₇₀₁
prime radical	C₂×D₄×C₇₀₁	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₇₀₁ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₇₀₁	C₂	semidirect
3. C₂²⋊C₄×C₇₀₁	C₂	semidirect
4. C₄²×C₇₀₁	C₂	semidirect
20. C₇₀₁	#124	direct (N × H)
21. #124	C₇₀₁	direct (N × H)
22. C₂×Q₈	C₂×C₇₀₁	semidirect
24. C₂²⋊C₄	C₂×C₇₀₁	semidirect
25. C₄²	C₂×C₇₀₁	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₇₀₁	2
C₂×D₄×C₇₀₁	2
C₂²⋊C₄×C₇₀₁	2
C₄²×C₇₀₁	2
#124	701

Subgroups — #124×C701 #36375985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #124×C₇₀₁ #36375985