Subgroups — C₂×#20260561 #27143513

Order 12416.

168 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15690744	C₂	1	2	yes	maximal
2	#20260561	C₂	1	4	yes	maximal, direct product factor
3	C₂²×C₁₆×C₉₇	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊Dic₉₇	—	2	2	no	—
5	#15690744	—	2	2	no	—
6	#15690744	C₂²	1	4	yes	—
7	C₂²×C₈×C₉₇	C₂²	1	1	yes	characteristic
8	C₂×C₁₆×C₉₇	C₄	1	4	yes	complemented
9	C₂×C₁₆×C₉₇	C₂²	1	2	yes	—
10	C₂²×Dic₉₇	—	4	2	no	—
11	C₄⋊Dic₉₇	—	2	4	no	—
12	C₄⋊Dic₉₇	—	4	2	no	—
13	C₂²×C₄×C₉₇	D₄	1	1	yes	characteristic
14	C₂×C₈×C₉₇	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₉₇	D₄	1	1	yes	characteristic
16	C₂×C₈×C₉₇	Q₈	1	2	yes	—
17	C₂×C₈×C₉₇	C₂³	1	1	yes	characteristic
18	C₁₆×C₉₇	C₂×C₄	1	4	yes	complemented
19	C₂³×C₉₇	D₈	1	1	yes	characteristic
20	C₂×C₄×C₉₇	C₄⋊C₄	1	2	yes	—
21	C₂×C₄×C₉₇	D₈	1	1	yes	characteristic
22	C₂×C₄×C₉₇	Q₁₆	1	2	yes	—
23	C₂×C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
24	C₂×Dic₉₇	—	4	4	no	—
25	C₂×Dic₉₇	—	8	4	no	—
26	C₈×C₉₇	C₄⋊C₄	1	2	yes	—
27	C₈×C₉₇	C₂²×C₄	1	1	yes	characteristic
28	C₈×C₉₇	C₂×Q₈	1	1	yes	characteristic
29	C₂²×C₉₇	#107	1	2	yes	—
30	C₂²×C₉₇	D₁₆	1	2	yes	—
31	C₂²×C₉₇	Q₃₂	1	2	yes	—
32	C₂²×C₉₇	C₂×D₈	1	1	yes	characteristic
33	C₄×C₉₇	#107	1	2	yes	—
34	C₄×C₉₇	C₂×C₄⋊C₄	1	1	yes	characteristic
35	C₄×C₉₇	C₂×Q₁₆	1	1	yes	characteristic
36	Dic₉₇	—	8	4	no	—
37	C₂×C₉₇	#366	1	4	yes	complemented
38	C₂×C₉₇	C₂×#107	1	1	yes	characteristic
39	C₂×C₉₇	C₂×D₁₆	1	1	yes	characteristic
40	C₂×C₉₇	C₂×Q₃₂	1	1	yes	characteristic
41	C₂×#366	—	97	1	no	maximal, Sylow
42	C₉₇	C₂×#366	1	1	yes	characteristic, complemented, Sylow
43	C₂²×C₁₆	D₉₇	1	1	yes	characteristic
44	C₂×#107	—	97	2	no	—
45	#366	—	97	4	no	—
46	C₂²×C₈	C₂×D₉₇	1	1	yes	characteristic
47	C₂×C₄⋊C₄	—	194	2	no	—
48	C₂×C₁₆	Dic₉₇	1	4	yes	complemented
49	C₂×C₁₆	C₂×D₉₇	1	2	yes	—
50	#107	—	97	4	no	—
51	#107	—	194	2	no	—
52	C₂²×C₄	—	388	2	no	—
53	C₂²×C₄	D₃₈₈	1	1	yes	characteristic
54	C₂×C₈	Dic₁₉₄	1	2	yes	—
55	C₂×C₈	D₃₈₈	1	1	yes	characteristic
56	C₂×C₈	C₂×Dic₉₇	1	2	yes	—
57	C₂×C₈	C₂²×D₉₇	1	1	yes	characteristic
58	C₄⋊C₄	—	388	2	no	—
59	C₄⋊C₄	—	194	4	no	—
60	C₁₆	C₂×Dic₉₇	1	4	yes	complemented
61	C₂³	D₇₇₆	1	1	yes	characteristic
62	C₂×C₄	—	776	4	no	—
63	C₂×C₄	—	388	4	no	—
64	C₂×C₄	C₄⋊Dic₉₇	1	2	yes	—
65	C₂×C₄	D₇₇₆	1	1	yes	characteristic
66	C₂×C₄	Dic₃₈₈	1	2	yes	—
67	C₂×C₄	C₂×D₃₈₈	1	1	yes	characteristic
68	C₈	C₄⋊Dic₉₇	1	2	yes	—
69	C₈	C₂²×Dic₉₇	1	1	yes	characteristic
70	C₈	C₂×Dic₁₉₄	1	1	yes	characteristic
71	C₂²	#15690744	1	2	yes	—
72	C₂²	D₁₅₅₂	1	2	yes	—
73	C₂²	Dic₇₇₆	1	2	yes	—
74	C₂²	C₂×D₇₇₆	1	1	yes	characteristic
75	C₄	—	776	4	no	—
76	C₄	#15690744	1	2	yes	—
77	C₄	C₂×C₄⋊Dic₉₇	1	1	yes	characteristic
78	C₄	C₂×Dic₃₈₈	1	1	yes	characteristic
79	C₂	#20260561	1	4	yes	direct product factor
80	C₂	C₂×#15690744	1	1	yes	characteristic
81	C₂	C₂×D₁₅₅₂	1	1	yes	characteristic
82	C₂	C₂×Dic₇₇₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	D₇₇₆
commutator	C₈×C₉₇	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₉₇
Fitting	C₂²×C₁₆×C₉₇	C₂
socle, prime radical	C₂³×C₉₇	D₈
cosocle	C₂×C₈×C₉₇	C₂³
hypercenter	C₂²×C₁₆	D₉₇
hypocenter	C₉₇	C₂×#366
LCS	G ▷ C₈×C₉₇ ▷ C₄×C₉₇ ▷ C₂×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

Complements

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

N	H ≅ G/N	type
2. #20260561	C₂	direct (N × H)
8. C₂×C₁₆×C₉₇	C₄	semidirect
18. C₁₆×C₉₇	C₂×C₄	semidirect
37. C₂×C₉₇	#366	semidirect
42. C₉₇	C₂×#366	semidirect
48. C₂×C₁₆	Dic₉₇	semidirect
60. C₁₆	C₂×Dic₉₇	semidirect
79. C₂	#20260561	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×#15690744	2
#20260561	2
C₂²×C₁₆×C₉₇	2
C₂×#366	97

Subgroups — C2×#20260561 #27143513

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20260561 #27143513