Group #20260808 — subgroups

Subgroups — #20260808

Order 6208.

124 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 53 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#13095494	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₉₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₃₈₈	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#11715895	C₂	1	1	yes	maximal, characteristic, complemented
5	#15690722	C₂	1	1	yes	maximal, characteristic, complemented
6	#15690722	C₂	1	1	yes	maximal, characteristic, complemented
7	#97×C₉₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₈₈	C₄	1	1	yes	characteristic
9	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
10	C₂×C₄×D₉₇	C₂²	1	1	yes	characteristic
11	#13095494	—	2	2	no	—
12	C₂×#11715895	C₂²	1	1	yes	characteristic
13	C₂×#11715895	C₂²	1	1	yes	characteristic
14	C₈×D₉₇	—	2	2	no	—
15	C₄⋊Dic₉₇	C₄	1	1	yes	characteristic
16	#13095488	C₄	1	1	yes	characteristic
17	#13095488	C₄	1	1	yes	characteristic
18	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₉₇	C₂²	1	1	yes	characteristic
20	C₄²×C₉₇	C₂²	1	1	yes	characteristic
21	C₂²×D₉₇	C₂×C₄	1	1	yes	characteristic
22	C₂²×D₉₇	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
24	C₂×C₄×C₉₇	C₂×C₄	1	1	yes	characteristic
25	C₂×C₄×C₉₇	C₂³	1	1	yes	characteristic
26	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
27	C₂×Dic₉₇	C₂×C₄	1	1	yes	characteristic
28	D₃₈₈	—	2	2	no	—
29	C₄×D₉₇	—	2	1	no	—
30	C₄×D₉₇	—	2	1	no	—
31	C₄×D₉₇	—	2	1	no	—
32	C₄×D₉₇	—	2	1	no	—
33	C₈×C₉₇	—	2	1	no	—
34	C₈×C₉₇	D₄	1	2	yes	complemented
35	#11715895	—	2	1	no	—
36	#11715895	—	2	1	no	—
37	C₂²×C₉₇	C₂²×C₄	1	1	yes	characteristic
38	C₂×D₉₇	—	2	1	no	—
39	C₂×D₉₇	—	2	1	no	—
40	C₂×D₉₇	—	2	1	no	—
41	C₂×D₉₇	—	2	1	no	—
42	C₂×D₉₇	—	2	1	no	—
43	C₂×D₉₇	M₁₆	1	2	yes	complemented
44	C₄×C₉₇	—	2	1	no	—
45	C₄×C₉₇	—	2	1	no	—
46	C₄×C₉₇	C₂×D₄	1	1	yes	characteristic
47	C₄×C₉₇	#41	1	1	yes	characteristic
48	Dic₉₇	—	2	1	no	—
49	Dic₉₇	—	2	1	no	—
50	C₂×C₉₇	C₄×D₄	1	1	yes	characteristic
51	C₂×C₉₇	C₂×M₁₆	1	1	yes	characteristic
52	C₂×C₉₇	#131	1	1	yes	characteristic
53	D₉₇	—	2	2	no	—
54	D₉₇	—	4	1	no	—
55	C₉₇	#435	1	1	yes	characteristic, complemented, Sylow
56	#435	—	97	1	no	maximal, Sylow
57	C₂×M₁₆	—	97	1	no	—
58	C₂²×C₈	—	97	1	no	—
59	C₄×D₄	—	97	1	no	—
60	C₄⋊C₈	—	97	1	no	—
61	C₂²⋊C₈	—	97	1	no	—
62	C₂²⋊C₈	—	97	1	no	—
63	#97	D₉₇	1	1	yes	characteristic, complemented
64	C₂×D₄	—	97	1	no	—
65	C₂²×C₄	—	97	1	no	—
66	C₂²×C₄	—	97	1	no	—
67	M₁₆	—	194	2	no	—
68	C₂×C₈	—	97	1	no	—
69	C₂×C₈	—	97	1	no	—
70	C₂×C₈	—	194	2	no	—
71	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
72	C₂×C₈	C₂×D₉₇	1	1	yes	characteristic
73	C₄⋊C₄	—	97	1	no	—
74	C₂²⋊C₄	—	97	1	no	—
75	C₂²⋊C₄	—	97	1	no	—
76	C₄²	C₂×D₉₇	1	1	yes	characteristic
77	C₂³	—	97	1	no	—
78	C₂³	—	97	1	no	—
79	D₄	—	194	2	no	—
80	C₂×C₄	—	97	1	no	—
81	C₂×C₄	—	97	1	no	—
82	C₂×C₄	—	194	1	no	—
83	C₂×C₄	—	194	1	no	—
84	C₂×C₄	—	194	1	no	—
85	C₂×C₄	—	194	1	no	—
86	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
87	C₂×C₄	C₄×D₉₇	1	1	yes	characteristic
88	C₂×C₄	C₂²×D₉₇	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	194	1	no	—
91	C₈	—	194	1	no	—
92	C₈	D₃₈₈	1	2	yes	complemented
93	C₂²	—	97	2	no	—
94	C₂²	—	194	1	no	—
95	C₂²	—	194	1	no	—
96	C₂²	—	194	1	no	—
97	C₂²	—	194	1	no	—
98	C₂²	—	194	1	no	—
99	C₂²	C₂×C₄×D₉₇	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	194	1	no	—
103	C₄	—	194	1	no	—
104	C₄	C₂×D₃₈₈	1	1	yes	characteristic
105	C₄	#13095511	1	1	yes	characteristic
106	C₂	—	388	1	no	—
107	C₂	—	194	2	no	—
108	C₂	C₄×D₃₈₈	1	1	yes	characteristic
109	C₂	M₁₆×D₉₇	1	1	yes	characteristic
110	C₂	#15690818	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#13095494

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₉₇

C₂

yes

maximal, characteristic, complemented

C₄×D₃₈₈

C₂

yes

maximal, characteristic

C₄⋊#11715895

C₂

yes

maximal, characteristic, complemented

#15690722

C₂

yes

maximal, characteristic, complemented

#15690722

C₂

yes

maximal, characteristic, complemented

#97×C₉₇

C₂

yes

maximal, characteristic, complemented

C₂×D₃₈₈

C₄

yes

characteristic

C₂×C₄×D₉₇

C₂²

yes

characteristic

C₂×C₄×D₉₇

C₂²

yes

characteristic

#13095494

—

C₂×#11715895

C₂²

yes

characteristic

C₂×#11715895

C₂²

yes

characteristic

C₈×D₉₇

—

C₄⋊Dic₉₇

C₄

yes

characteristic

#13095488

C₄

yes

characteristic

#13095488

C₄

yes

characteristic

C₂×C₈×C₉₇

C₂²

yes

characteristic

C₂×C₈×C₉₇

C₂²

yes

characteristic

C₄²×C₉₇

C₂²

yes

characteristic

C₂²×D₉₇

C₂×C₄

yes

characteristic

C₂²×D₉₇

C₂×C₄

yes

characteristic

C₂×C₄×C₉₇

C₂×C₄

yes

characteristic

C₂×C₄×C₉₇

C₂×C₄

yes

characteristic

C₂×C₄×C₉₇

C₂³

yes

characteristic

C₂×Dic₉₇

C₂×C₄

yes

characteristic

C₂×Dic₉₇

C₂×C₄

yes

characteristic

D₃₈₈

—

C₄×D₉₇

—

C₄×D₉₇

—

C₄×D₉₇

—

C₄×D₉₇

—

C₈×C₉₇

—

C₈×C₉₇

D₄

yes

complemented

#11715895

—

#11715895

—

C₂²×C₉₇

C₂²×C₄

yes

characteristic

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

—

C₂×D₉₇

M₁₆

yes

complemented

C₄×C₉₇

—

C₄×C₉₇

—

C₄×C₉₇

C₂×D₄

yes

characteristic

C₄×C₉₇

#41

yes

characteristic

Dic₉₇

—

Dic₉₇

—

C₂×C₉₇

C₄×D₄

yes

characteristic

C₂×C₉₇

C₂×M₁₆

yes

characteristic

C₂×C₉₇

#131

yes

characteristic

D₉₇

—

D₉₇

—

C₉₇

#435

yes

characteristic, complemented, Sylow

#435

—

maximal, Sylow

C₂×M₁₆

—

C₂²×C₈

—

C₄×D₄

—

C₄⋊C₈

—

C₂²⋊C₈

—

C₂²⋊C₈

—

#97

D₉₇

yes

characteristic, complemented

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

—

M₁₆

—

194

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

194

—

C₂×C₈

C₂×D₉₇

yes

characteristic

C₂×C₈

C₂×D₉₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₄²

C₂×D₉₇

yes

characteristic

C₂³

—

C₂³

—

D₄

—

194

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

—

194

—

C₂×C₄

C₄×D₉₇

yes

characteristic

C₂×C₄

C₄×D₉₇

yes

characteristic

C₂×C₄

C₂²×D₉₇

yes

characteristic

C₈

—

C₈

—

194

—

C₈

—

194

—

C₈

D₃₈₈

yes

complemented

C₂²

—

C₂²

—

194

—

C₂²

—

194

—

C₂²

—

194

—

C₂²

—

194

—

C₂²

—

194

—

C₂²

C₂×C₄×D₉₇

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

194

—

103

C₄

—

194

—

104

C₄

C₂×D₃₈₈

yes

characteristic

105

C₄

#13095511

yes

characteristic

106

C₂

—

388

—

107

C₂

—

194

—

108

C₂

C₄×D₃₈₈

yes

characteristic

109

C₂

M₁₆×D₉₇

yes

characteristic

110

C₂

#15690818

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₉₇
commutator, socle	C₂²×C₉₇	C₂²×C₄
Fitting	#97×C₉₇	C₂
hypercenter	#97	D₉₇
hypocenter	C₉₇	#435
LCS	G ▷ C₂²×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×D₉₇

commutator, socle

C₂²×C₉₇

C₂²×C₄

Fitting

#97×C₉₇

C₂

D₉₇

C₉₇

G ▷ C₂²×C₉₇ ▷ C₉₇

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
1. C₂×#13095494	C₂	semidirect
2. C₂×C₈×D₉₇	C₂	semidirect
4. C₄⋊#11715895	C₂	semidirect
5. #15690722	C₂	semidirect
6. #15690722	C₂	semidirect
7. #97×C₉₇	C₂	semidirect
34. C₈×C₉₇	D₄	semidirect
43. C₂×D₉₇	M₁₆	semidirect
55. C₉₇	#435	semidirect
63. #97	D₉₇	semidirect
92. C₈	D₃₈₈	semidirect

H ≅ G/N

type

1. C₂×#13095494

C₂

semidirect

2. C₂×C₈×D₉₇

C₂

semidirect

4. C₄⋊#11715895

C₂

semidirect

5. #15690722

C₂

semidirect

6. #15690722

C₂

semidirect

7. #97×C₉₇

C₂

semidirect

34. C₈×C₉₇

D₄

semidirect

43. C₂×D₉₇

M₁₆

semidirect

55. C₉₇

#435

semidirect

63. #97

D₉₇

semidirect

92. C₈

D₃₈₈

semidirect

Subgroups — #20260808

Conjugacy classes of subgroups

Complements