Group #22626158 — subgroups

Subgroups — #22626158

Order 9344.

260 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 98 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×#14556665	C₂	1	2	yes	maximal, complemented
2	C₂²⋊#11924031	C₂	1	4	yes	maximal, complemented
3	C₂³×#10596831	C₂	1	1	yes	maximal, characteristic
4	#14556665	—	2	4	no	—
5	C₂×#11924031	C₂²	1	4	yes	complemented
6	C₂²×#10596831	—	2	4	no	—
7	C₂²×#10596831	C₄	1	2	yes	—
8	C₂²×#10596831	C₄	1	1	yes	characteristic
9	C₂²×#10596831	C₂²	1	2	yes	—
10	C₂²×#10596831	C₂²	1	1	yes	characteristic
11	C₂³×C₄×C₇₃	C₄	1	1	yes	characteristic
12	#11924031	—	2	4	no	—
13	C₂×#10596831	—	2	2	no	—
14	C₂×#10596831	—	2	4	no	—
15	C₂×#10596831	—	2	4	no	—
16	C₂×#10596831	C₂×C₄	1	2	yes	—
17	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
18	C₂×#10596831	D₄	1	4	yes	—
19	C₂×#10596831	C₂³	1	1	yes	characteristic
20	C₂⁴×C₇₃	C₈	1	1	yes	characteristic
21	C₂²×C₄×C₇₃	—	2	2	no	—
22	C₂²×C₄×C₇₃	—	2	2	no	—
23	C₂²×C₄×C₇₃	C₈	1	1	yes	characteristic
24	C₂²×C₄×C₇₃	C₈	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
26	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₇₃	—	2	2	no	—
28	C₂³×C₇₃	—	2	4	no	—
29	C₂³×C₇₃	C₂×C₈	1	1	yes	characteristic
30	C₂³×C₇₃	C₂×C₈	1	2	yes	—
31	C₂×C₄×C₇₃	—	2	2	no	—
32	C₂×C₄×C₇₃	—	2	4	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	—	2	2	no	—
35	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
38	C₂×C₄×C₇₃	M₁₆	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	#10596831	—	2	2	no	—
41	#10596831	C₂²⋊C₄	1	2	yes	—
42	#10596831	C₂×D₄	1	2	yes	—
43	C₂²×C₇₃	—	2	8	no	—
44	C₂²×C₇₃	—	2	2	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	—	2	2	no	—
47	C₂²×C₇₃	C₂²⋊C₈	1	2	yes	—
48	C₂²×C₇₃	M₃₂	1	4	yes	complemented
49	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	C₂²⋊C₈	1	2	yes	—
52	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
53	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
54	C₂×C₇₃	—	2	2	no	—
55	C₂×C₇₃	—	2	4	no	—
56	C₂×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
57	C₂×C₇₃	C₂×M₃₂	1	2	yes	—
58	#2112	—	73	1	no	maximal, Sylow
59	C₇₃	#2112	1	1	yes	characteristic, complemented, Sylow
60	C₂³×C₈	—	73	1	no	—
61	C₂×M₃₂	—	73	2	no	—
62	C₂²⋊C₁₆	—	73	4	no	—
63	C₂³×C₄	#64408	1	1	yes	characteristic
64	C₂²×C₈	—	73	1	no	—
65	C₂²×C₈	—	73	2	no	—
66	C₂²×C₈	—	73	2	no	—
67	C₂²×C₈	—	73	1	no	—
68	C₂²×C₈	—	146	4	no	—
69	M₃₂	—	146	4	no	—
70	C₂×C₁₆	—	73	4	no	—
71	C₂⁴	#10596833	1	1	yes	characteristic
72	C₂²×C₄	—	2	2	no	—
73	C₂²×C₄	—	2	2	no	—
74	C₂²×C₄	#10596833	1	1	yes	characteristic
75	C₂²×C₄	#10596833	1	2	yes	—
76	C₂²×C₄	C₂×#64408	1	2	yes	—
77	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
78	C₂×C₈	—	73	4	no	—
79	C₂×C₈	—	73	1	no	—
80	C₂×C₈	—	73	1	no	—
81	C₂×C₈	—	73	2	no	—
82	C₂×C₈	—	146	4	no	—
83	C₂×C₈	—	146	4	no	—
84	C₂×C₈	—	146	2	no	—
85	C₁₆	—	146	4	no	—
86	C₂³	—	2	2	no	—
87	C₂³	—	2	4	no	—
88	C₂³	C₂×#10596833	1	1	yes	characteristic
89	C₂³	C₂×#10596833	1	2	yes	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	2	2	no	—
92	C₂×C₄	—	2	4	no	—
93	C₂×C₄	—	2	2	no	—
94	C₂×C₄	C₂²⋊#64408	1	2	yes	—
95	C₂×C₄	C₂×#10596833	1	2	yes	—
96	C₂×C₄	C₂×#10596833	1	1	yes	characteristic
97	C₂×C₄	#11924037	1	2	yes	—
98	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
99	C₈	—	73	2	no	—
100	C₈	—	73	2	no	—
101	C₈	—	146	2	no	—
102	C₂²	—	2	8	no	—
103	C₂²	—	2	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	—	2	2	no	—
106	C₂²	C₂²⋊#10596833	1	2	yes	—
107	C₂²	#14556665	1	4	yes	complemented
108	C₂²	C₂²×#10596833	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	C₂²⋊#10596833	1	2	yes	—
111	C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
112	C₄	C₂×#11924037	1	1	yes	characteristic
113	C₂	—	2	2	no	—
114	C₂	—	2	4	no	—
115	C₂	C₂×C₂²⋊#10596833	1	1	yes	characteristic
116	C₂	C₂×#14556665	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556665

C₂

yes

maximal, complemented

C₂²⋊#11924031

C₂

yes

maximal, complemented

C₂³×#10596831

C₂

yes

maximal, characteristic

#14556665

—

C₂×#11924031

C₂²

yes

complemented

C₂²×#10596831

—

C₂²×#10596831

C₄

yes

—

C₂²×#10596831

C₄

yes

characteristic

C₂²×#10596831

C₂²

yes

—

C₂²×#10596831

C₂²

yes

characteristic

C₂³×C₄×C₇₃

C₄

yes

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

D₄

yes

—

C₂×#10596831

C₂³

yes

characteristic

C₂⁴×C₇₃

C₈

yes

characteristic

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

C₈

yes

characteristic

C₂²×C₄×C₇₃

C₈

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂³×C₇₃

—

C₂³×C₇₃

—

C₂³×C₇₃

C₂×C₈

yes

characteristic

C₂³×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

M₁₆

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

#10596831

—

#10596831

C₂²⋊C₄

yes

—

#10596831

C₂×D₄

yes

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂²⋊C₈

yes

—

C₂²×C₇₃

M₃₂

yes

complemented

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊C₈

yes

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

C₂×C₇₃

C₂×M₃₂

yes

—

#2112

—

maximal, Sylow

C₇₃

#2112

yes

characteristic, complemented, Sylow

C₂³×C₈

—

C₂×M₃₂

—

C₂²⋊C₁₆

—

C₂³×C₄

#64408

yes

characteristic

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂²×C₈

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂⁴

#10596833

yes

characteristic

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

#10596833

yes

characteristic

C₂²×C₄

#10596833

yes

—

C₂²×C₄

C₂×#64408

yes

—

C₂²×C₄

C₂×#64408

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₁₆

—

146

—

C₂³

—

C₂³

—

C₂³

C₂×#10596833

yes

characteristic

C₂³

C₂×#10596833

yes

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₂²⋊#64408

yes

—

C₂×C₄

C₂×#10596833

yes

—

C₂×C₄

C₂×#10596833

yes

characteristic

C₂×C₄

#11924037

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

100

C₈

—

101

C₈

—

146

—

102

C₂²

—

103

C₂²

—

104

C₂²

—

105

C₂²

—

106

C₂²

C₂²⋊#10596833

yes

—

107

C₂²

#14556665

yes

complemented

108

C₂²

C₂²×#10596833

yes

characteristic

109

C₄

—

110

C₄

C₂²⋊#10596833

yes

—

111

C₄

C₂×C₂²⋊#64408

yes

characteristic

112

C₄

C₂×#11924037

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

C₂×C₂²⋊#10596833

yes

characteristic

116

C₂

C₂×#14556665

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	C₂³×C₄×C₇₃	C₄
hypercenter	C₂³×C₄	#64408
hypocenter	C₇₃	#2112
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

C₂³×C₄×C₇₃

C₄

C₂³×C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ C₂³×C₄

N	H ≅ G/N	type
1. C₂×#14556665	C₂	semidirect
2. C₂²⋊#11924031	C₂	semidirect
5. C₂×#11924031	C₂²	semidirect
48. C₂²×C₇₃	M₃₂	semidirect
59. C₇₃	#2112	semidirect
107. C₂²	#14556665	semidirect

H ≅ G/N

type

1. C₂×#14556665

C₂

semidirect

2. C₂²⋊#11924031

C₂

semidirect

5. C₂×#11924031

C₂²

semidirect

48. C₂²×C₇₃

M₃₂

semidirect

59. C₇₃

#2112

semidirect

107. C₂²

#14556665

semidirect

Subgroups — #22626158

Conjugacy classes of subgroups

Complements