Subgroups — C₂×Q₈×D₁₁₇₁ #49154097

Order 37472.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₂₃₄₂	C₂	1	3	yes	maximal, complemented
2	Q₈×D₁₁₇₁	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄×D₁₁₇₁	C₂	1	3	yes	maximal
4	C₂×Q₈×C₁₁₇₁	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×D₁₁₇₁	C₂²	1	1	yes	characteristic
6	Dic₂₃₄₂	C₂²	1	12	yes	complemented
7	C₂×Dic₁₁₇₁	C₂²	1	3	yes	—
8	C₄×D₁₁₇₁	C₂²	1	12	yes	—
9	Q₈×C₁₁₇₁	C₂²	1	4	yes	complemented
10	C₂×C₄×C₁₁₇₁	C₂²	1	3	yes	—
11	C₂²×C₁₁₇₁	C₂³	1	1	yes	characteristic
12	C₂×D₁₁₇₁	Q₈	1	4	yes	direct product factor
13	C₂×D₁₁₇₁	C₂³	1	2	yes	—
14	C₄×C₁₁₇₁	C₂³	1	6	yes	—
15	Dic₁₁₇₁	C₂³	1	6	yes	—
16	C₂×C₁₁₇₁	C₂×Q₈	1	2	yes	complemented
17	C₂×C₁₁₇₁	C₂⁴	1	1	yes	characteristic
18	D₁₁₇₁	C₂×Q₈	1	4	yes	direct product factor
19	C₁₁₇₁	C₂²×Q₈	1	1	yes	characteristic, complemented, Sylow
20	C₂²×Q₈	—	1171	1	no	maximal, Sylow
21	C₂×Q₈	—	1171	8	no	—
22	C₂×Q₈	—	1171	3	no	—
23	C₂×Q₈	D₁₁₇₁	1	1	yes	characteristic, direct product factor
24	C₂²×C₄	—	1171	3	no	—
25	C₂³	—	1171	1	no	—
26	Q₈	—	1171	12	no	—
27	Q₈	C₂×D₁₁₇₁	1	4	yes	direct product factor
28	C₂×C₄	—	1171	3	no	—
29	C₂×C₄	—	1171	12	no	—
30	C₂×C₄	C₂×D₁₁₇₁	1	3	yes	—
31	C₂²	—	1171	4	no	—
32	C₂²	—	1171	2	no	—
33	C₂²	C₂²×D₁₁₇₁	1	1	yes	characteristic
34	C₄	—	1171	6	no	—
35	C₄	C₂²×D₁₁₇₁	1	6	yes	—
36	C₂	—	1171	4	no	—
37	C₂	Q₈×D₁₁₇₁	1	2	yes	direct product factor
38	C₂	C₂³×D₁₁₇₁	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₁₁₇₁
commutator, cosocle	C₂×C₁₁₇₁	C₂⁴
Frattini	C₂	C₂³×D₁₁₇₁
Fitting	C₂×Q₈×C₁₁₇₁	C₂
socle	C₂²×C₁₁₇₁	C₂³
prime radical	C₂²×D₁₁₇₁	C₂²
hypercenter	C₂×Q₈	D₁₁₇₁
hypocenter	C₁₁₇₁	C₂²×Q₈
LCS	G ▷ C₂×C₁₁₇₁ ▷ C₁₁₇₁
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×Dic₂₃₄₂	C₂	semidirect
2. Q₈×D₁₁₇₁	C₂	direct (N × H)
4. C₂×Q₈×C₁₁₇₁	C₂	semidirect
6. Dic₂₃₄₂	C₂²	semidirect
9. Q₈×C₁₁₇₁	C₂²	semidirect
12. C₂×D₁₁₇₁	Q₈	direct (N × H)
16. C₂×C₁₁₇₁	C₂×Q₈	semidirect
18. D₁₁₇₁	C₂×Q₈	direct (N × H)
19. C₁₁₇₁	C₂²×Q₈	semidirect
23. C₂×Q₈	D₁₁₇₁	direct (N × H)
27. Q₈	C₂×D₁₁₇₁	direct (N × H)
37. C₂	Q₈×D₁₁₇₁	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Dic₂₃₄₂	2
Q₈×D₁₁₇₁	2
C₂×C₄×D₁₁₇₁	2
C₂×Q₈×C₁₁₇₁	2
C₂²×Q₈	1171

Subgroups — C2×Q8×D1171 #49154097

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈×D₁₁₇₁ #49154097