Subgroups — C₂×Dic₃₁₇₆ #38762950

Order 25408.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₁₅₈₈	C₂	1	2	yes	maximal
2	Dic₃₁₇₆	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₁₆×C₃₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₇₉₄	—	2	2	no	—
5	Dic₁₅₈₈	—	2	2	no	—
6	Dic₁₅₈₈	C₂²	1	4	yes	—
7	C₂×C₈×C₃₉₇	C₂²	1	1	yes	characteristic
8	C₁₆×C₃₉₇	C₂²	1	2	yes	—
9	Dic₇₉₄	—	2	4	no	—
10	Dic₇₉₄	—	4	2	no	—
11	C₂×Dic₃₉₇	—	4	2	no	—
12	C₂×C₄×C₃₉₇	D₄	1	1	yes	characteristic
13	C₈×C₃₉₇	D₄	1	1	yes	characteristic
14	C₈×C₃₉₇	C₂³	1	1	yes	characteristic
15	C₂²×C₃₉₇	D₈	1	1	yes	characteristic
16	C₄×C₃₉₇	D₈	1	1	yes	characteristic
17	C₄×C₃₉₇	C₂×D₄	1	1	yes	characteristic
18	Dic₃₉₇	—	4	4	no	—
19	C₂×C₃₉₇	Q₃₂	1	2	yes	complemented
20	C₂×C₃₉₇	C₂×D₈	1	1	yes	characteristic
21	C₃₉₇	C₂×Q₃₂	1	1	yes	characteristic, complemented, Sylow
22	C₂×Q₃₂	—	397	1	no	maximal, Sylow
23	C₂×Q₁₆	—	397	2	no	—
24	Q₃₂	—	397	4	no	—
25	C₂×C₁₆	D₃₉₇	1	1	yes	characteristic
26	C₂×Q₈	—	794	2	no	—
27	Q₁₆	—	794	2	no	—
28	Q₁₆	—	397	4	no	—
29	C₂×C₈	C₂×D₃₉₇	1	1	yes	characteristic
30	C₁₆	C₂×D₃₉₇	1	2	yes	—
31	Q₈	—	794	4	no	—
32	Q₈	—	1588	2	no	—
33	C₂×C₄	—	1588	2	no	—
34	C₂×C₄	D₁₅₈₈	1	1	yes	characteristic
35	C₈	D₁₅₈₈	1	1	yes	characteristic
36	C₈	C₂²×D₃₉₇	1	1	yes	characteristic
37	C₂²	D₃₁₇₆	1	1	yes	characteristic
38	C₄	—	1588	4	no	—
39	C₄	D₃₁₇₆	1	1	yes	characteristic
40	C₄	C₂×D₁₅₈₈	1	1	yes	characteristic
41	C₂	Dic₃₁₇₆	1	2	yes	direct product factor
42	C₂	C₂×D₃₁₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₃₁₇₆
commutator, cosocle	C₈×C₃₉₇	C₂³
Frattini	C₈	C₂²×D₃₉₇
Fitting	C₂×C₁₆×C₃₉₇	C₂
socle, prime radical	C₂²×C₃₉₇	D₈
hypercenter	C₂×C₁₆	D₃₉₇
hypocenter	C₃₉₇	C₂×Q₃₂
LCS	G ▷ C₈×C₃₉₇ ▷ C₄×C₃₉₇ ▷ C₂×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆

Complements

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

N	H ≅ G/N	type
2. Dic₃₁₇₆	C₂	direct (N × H)
19. C₂×C₃₉₇	Q₃₂	semidirect
21. C₃₉₇	C₂×Q₃₂	semidirect
41. C₂	Dic₃₁₇₆	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×Dic₁₅₈₈	2
Dic₃₁₇₆	2
C₂×C₁₆×C₃₉₇	2
C₂×Q₃₂	397

Subgroups — C2×Dic3176 #38762950

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₃₁₇₆ #38762950