Subgroups — C₂×Dic₁₅₅₂ #27144041

Order 12416.

104 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Dic₇₇₆	C₂	1	2	yes	maximal
2	Dic₁₅₅₂	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₃₂×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×Dic₃₈₈	—	2	2	no	—
5	Dic₇₇₆	—	2	2	no	—
6	Dic₇₇₆	C₂²	1	4	yes	—
7	C₂×C₁₆×C₉₇	C₂²	1	1	yes	characteristic
8	C₃₂×C₉₇	C₂²	1	2	yes	—
9	C₂×Dic₁₉₄	—	4	2	no	—
10	Dic₃₈₈	—	2	4	no	—
11	Dic₃₈₈	—	4	2	no	—
12	C₂×C₈×C₉₇	D₄	1	1	yes	characteristic
13	C₁₆×C₉₇	D₄	1	1	yes	characteristic
14	C₁₆×C₉₇	C₂³	1	1	yes	characteristic
15	C₂×C₄×C₉₇	D₈	1	1	yes	characteristic
16	C₂×Dic₉₇	—	8	2	no	—
17	Dic₁₉₄	—	4	4	no	—
18	Dic₁₉₄	—	8	2	no	—
19	C₈×C₉₇	D₈	1	1	yes	characteristic
20	C₈×C₉₇	C₂×D₄	1	1	yes	characteristic
21	C₂²×C₉₇	D₁₆	1	1	yes	characteristic
22	C₄×C₉₇	D₁₆	1	1	yes	characteristic
23	C₄×C₉₇	C₂×D₈	1	1	yes	characteristic
24	Dic₉₇	—	8	4	no	—
25	C₂×C₉₇	Q₆₄	1	2	yes	complemented
26	C₂×C₉₇	C₂×D₁₆	1	1	yes	characteristic
27	C₂×Q₆₄	—	97	1	no	maximal, Sylow
28	C₉₇	C₂×Q₆₄	1	1	yes	characteristic, complemented, Sylow
29	C₂×Q₃₂	—	97	2	no	—
30	Q₆₄	—	97	4	no	—
31	C₂×C₃₂	D₉₇	1	1	yes	characteristic
32	C₂×Q₁₆	—	194	2	no	—
33	Q₃₂	—	97	4	no	—
34	Q₃₂	—	194	2	no	—
35	C₂×C₁₆	C₂×D₉₇	1	1	yes	characteristic
36	C₃₂	C₂×D₉₇	1	2	yes	—
37	C₂×Q₈	—	388	2	no	—
38	Q₁₆	—	388	2	no	—
39	Q₁₆	—	194	4	no	—
40	C₂×C₈	D₃₈₈	1	1	yes	characteristic
41	C₁₆	D₃₈₈	1	1	yes	characteristic
42	C₁₆	C₂²×D₉₇	1	1	yes	characteristic
43	Q₈	—	776	2	no	—
44	Q₈	—	388	4	no	—
45	C₂×C₄	—	776	2	no	—
46	C₂×C₄	D₇₇₆	1	1	yes	characteristic
47	C₈	D₇₇₆	1	1	yes	characteristic
48	C₈	C₂×D₃₈₈	1	1	yes	characteristic
49	C₂²	D₁₅₅₂	1	1	yes	characteristic
50	C₄	—	776	4	no	—
51	C₄	D₁₅₅₂	1	1	yes	characteristic
52	C₄	C₂×D₇₇₆	1	1	yes	characteristic
53	C₂	Dic₁₅₅₂	1	2	yes	direct product factor
54	C₂	C₂×D₁₅₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₁₅₅₂
commutator, cosocle	C₁₆×C₉₇	C₂³
Frattini	C₁₆	C₂²×D₉₇
Fitting	C₂×C₃₂×C₉₇	C₂
socle, prime radical	C₂²×C₉₇	D₁₆
hypercenter	C₂×C₃₂	D₉₇
hypocenter	C₉₇	C₂×Q₆₄
LCS	G ▷ C₁₆×C₉₇ ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ C₂×C₁₆ ◁ C₂×C₃₂

Complements

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

N	H ≅ G/N	type
2. Dic₁₅₅₂	C₂	direct (N × H)
25. C₂×C₉₇	Q₆₄	semidirect
28. C₉₇	C₂×Q₆₄	semidirect
53. C₂	Dic₁₅₅₂	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×Dic₇₇₆	2
Dic₁₅₅₂	2
C₂×C₃₂×C₉₇	2
C₂×Q₆₄	97

Subgroups — C2×Dic1552 #27144041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Dic₁₅₅₂ #27144041