Group #22625500 — subgroups

Subgroups — #22625500

Order 9344.

168 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 168 conjugacy classes of subgroups — too many to draw. Only its 70 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	#17989590	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊#10596833	C₂	1	1	yes	maximal, characteristic
3	#17989451	C₂	1	2	yes	maximal, complemented
4	#17989450	C₂	1	2	yes	maximal, complemented
5	#17988637	C₂	1	1	yes	maximal, characteristic
6	C₂×#11924037	—	2	1	no	—
7	C₂²×#10596833	—	2	1	no	—
8	#14556658	—	2	1	no	—
9	C₄⋊#10596833	—	2	1	no	—
10	C₄⋊#10596833	C₂²	1	1	yes	characteristic
11	C₄⋊#10596833	C₂²	1	2	yes	—
12	C₄⋊#10596833	C₂²	1	1	yes	characteristic
13	C₂×C₄×Dic₇₃	C₂²	1	1	yes	characteristic
14	#14556520	C₄	1	2	yes	—
15	C₂²⋊#10596831	C₄	1	1	yes	characteristic
16	C₈×Dic₇₃	C₂²	1	2	yes	—
17	C₂²⋊C₈×C₇₃	C₄	1	1	yes	characteristic
18	#11924037	—	4	2	no	—
19	C₂×#10596833	—	2	2	no	—
20	C₂×#10596833	—	2	1	no	—
21	C₂×#10596833	—	2	1	no	—
22	C₂×#10596833	—	4	2	no	—
23	C₂²×Dic₇₃	D₄	1	1	yes	characteristic
24	C₂²×Dic₇₃	Q₈	1	1	yes	characteristic
25	C₂×#10596831	C₂×C₄	1	2	yes	—
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	D₄	1	1	yes	characteristic
28	C₄×Dic₇₃	Q₈	1	1	yes	characteristic
29	C₄×Dic₇₃	C₂³	1	1	yes	characteristic
30	C₂²×C₄×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
32	C₂³×C₇₃	C₄⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₄⋊C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	4	1	no	—
37	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
38	C₂×Dic₇₃	C₄⋊C₄	1	1	yes	characteristic
39	C₂×Dic₇₃	D₈	1	2	yes	—
40	C₂×Dic₇₃	Q₁₆	1	2	yes	—
41	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
42	C₂×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
43	#10596833	—	4	2	no	—
44	#10596833	—	4	1	no	—
45	#10596833	—	4	1	no	—
46	C₈×C₇₃	—	2	2	no	—
47	#10596831	—	2	2	no	—
48	C₂²×C₇₃	—	2	1	no	—
49	C₂²×C₇₃	—	2	1	no	—
50	C₂²×C₇₃	#107	1	2	yes	—
51	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
52	C₄×C₇₃	—	2	1	no	—
53	C₄×C₇₃	#131	1	2	yes	—
54	Dic₇₃	—	2	1	no	—
55	Dic₇₃	—	2	1	no	—
56	Dic₇₃	#107	1	2	yes	—
57	Dic₇₃	C₂×D₈	1	1	yes	characteristic
58	Dic₇₃	C₂×Q₁₆	1	1	yes	characteristic
59	C₂×C₇₃	—	2	2	no	—
60	C₂×C₇₃	#424	1	1	yes	characteristic
61	C₂×C₇₃	C₂×#107	1	1	yes	characteristic
62	C₂×C₇₃	#430	1	1	yes	characteristic
63	#1571	—	73	1	no	maximal, Sylow
64	C₇₃	#1571	1	1	yes	characteristic, complemented, Sylow
65	#431	—	73	1	no	—
66	#423	—	73	1	no	—
67	C₂×C₄⋊C₈	—	73	1	no	—
68	#335	—	73	2	no	—
69	#335	—	73	2	no	—
70	C₂×M₁₆	—	146	1	no	—
71	C₂²×C₈	—	146	1	no	—
72	C₂×C₄²	—	73	1	no	—
73	C₄⋊C₈	—	73	2	no	—
74	C₄⋊C₈	—	73	2	no	—
75	C₄⋊C₈	—	73	1	no	—
76	C₄⋊C₈	—	73	1	no	—
77	C₄⋊C₈	—	146	1	no	—
78	C₄⋊C₈	—	146	1	no	—
79	C₂²⋊C₈	—	73	1	no	—
80	C₂²⋊C₈	#64408	1	1	yes	characteristic
81	C₄×C₈	—	73	2	no	—
82	C₂²×C₄	—	73	1	no	—
83	C₂²×C₄	—	73	1	no	—
84	C₂²×C₄	C₂×#64408	1	1	yes	characteristic
85	M₁₆	—	292	2	no	—
86	C₂×C₈	—	292	2	no	—
87	C₂×C₈	—	73	2	no	—
88	C₂×C₈	—	146	2	no	—
89	C₂×C₈	—	146	1	no	—
90	C₂×C₈	—	146	1	no	—
91	C₂×C₈	C₂×#64408	1	2	yes	—
92	C₄²	—	73	1	no	—
93	C₄²	—	73	1	no	—
94	C₄²	—	73	1	no	—
95	C₄²	—	73	1	no	—
96	C₂³	C₄⋊#64408	1	1	yes	characteristic
97	C₂×C₄	—	2	2	no	—
98	C₂×C₄	—	292	1	no	—
99	C₂×C₄	—	73	2	no	—
100	C₂×C₄	—	73	2	no	—
101	C₂×C₄	—	73	1	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	1	no	—
104	C₂×C₄	—	73	1	no	—
105	C₂×C₄	C₄⋊#64408	1	1	yes	characteristic
106	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
107	C₈	—	2	2	no	—
108	C₈	—	292	2	no	—
109	C₈	—	292	1	no	—
110	C₈	—	292	1	no	—
111	C₈	—	146	2	no	—
112	C₂²	—	2	1	no	—
113	C₂²	—	2	1	no	—
114	C₂²	#14556660	1	2	yes	—
115	C₂²	C₂×C₄⋊#64408	1	1	yes	characteristic
116	C₄	—	2	1	no	—
117	C₄	—	73	1	no	—
118	C₄	—	73	2	no	—
119	C₄	—	73	1	no	—
120	C₄	—	146	1	no	—
121	C₄	—	146	1	no	—
122	C₄	#14556678	1	2	yes	—
123	C₂	—	2	2	no	—
124	C₂	#17989593	1	1	yes	characteristic
125	C₂	C₂×#14556660	1	1	yes	characteristic
126	C₂	#17989602	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989590

C₂

yes

maximal, characteristic

C₂×C₄⋊#10596833

C₂

yes

maximal, characteristic

#17989451

C₂

yes

maximal, complemented

#17989450

C₂

yes

maximal, complemented

#17988637

C₂

yes

maximal, characteristic

—

—

—

—

C₂²

yes

characteristic

C₄⋊#10596833

C₂²

yes

—

C₄⋊#10596833

C₂²

yes

characteristic

C₂×C₄×Dic₇₃

C₂²

yes

characteristic

#14556520

C₄

yes

—

C₂²⋊#10596831

C₄

yes

characteristic

C₈×Dic₇₃

C₂²

yes

—

C₂²⋊C₈×C₇₃

C₄

yes

—

—

—

—

—

C₂²×Dic₇₃

D₄

yes

characteristic

C₂²×Dic₇₃

Q₈

yes

characteristic

C₂×#10596831

C₂×C₄

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

characteristic

C₄×Dic₇₃

Q₈

yes

characteristic

C₄×Dic₇₃

C₂³

yes

characteristic

C₂²×C₄×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂³×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

C₄⋊C₄

yes

characteristic

C₂×Dic₇₃

D₈

yes

—

C₂×Dic₇₃

Q₁₆

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

C₂×Q₈

yes

—

—

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#107

yes

—

C₂²×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

#131

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#107

yes

—

Dic₇₃

C₂×D₈

yes

characteristic

Dic₇₃

C₂×Q₁₆

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#431

—

#423

—

C₂×C₄⋊C₈

—

#335

—

#335

—

C₂×M₁₆

—

146

—

C₂²×C₈

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

C₂²⋊C₈

#64408

yes

characteristic

C₄×C₈

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×#64408

yes

characteristic

M₁₆

—

292

—

C₂×C₈

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂×#64408

yes

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

C₂³

C₄⋊#64408

yes

characteristic

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

C₄⋊#64408

yes

characteristic

106

C₂×C₄

C₂²×#64408

yes

characteristic

107

C₈

—

108

C₈

—

292

—

109

C₈

—

292

—

110

C₈

—

292

—

111

C₈

—

146

—

112

C₂²

—

113

C₂²

—

114

C₂²

#14556660

yes

—

115

C₂²

C₂×C₄⋊#64408

yes

characteristic

116

C₄

—

117

C₄

—

118

C₄

—

119

C₄

—

120

C₄

—

146

—

121

C₄

—

146

—

122

C₄

#14556678

yes

—

123

C₂

—

124

C₂

#17989593

yes

characteristic

125

C₂

C₂×#14556660

yes

characteristic

126

C₂

#17989602

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×C₄⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	C₂²⋊C₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₄⋊C₄
hypercenter	C₂²⋊C₈	#64408
hypocenter	C₇₃	#1571
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center

C₂²

C₂×C₄⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

C₂²⋊C₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₄⋊C₄

C₂²⋊C₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
3. #17989451	C₂	semidirect
4. #17989450	C₂	semidirect
64. C₇₃	#1571	semidirect

H ≅ G/N

type

3. #17989451

C₂

semidirect

4. #17989450

C₂

semidirect

64. C₇₃

#1571

semidirect

Subgroups — #22625500

Conjugacy classes of subgroups

Complements