Group #22626118 — subgroups

Subgroups — #22626118

Order 9344.

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

normal subgroups only

This group has 244 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	#17989591	C₂	1	1	yes	maximal, characteristic
2	#17989523	C₂	1	1	yes	maximal, characteristic
3	#17989457	C₂	1	4	yes	maximal
4	#17989143	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924038	C₂²	1	2	yes	—
6	C₂×C₄×#64408	C₂²	1	2	yes	—
7	C₄⋊#10596833	—	2	2	no	—
8	(C₂×#64408)⋊C₄	—	2	2	no	—
9	#14556590	C₄	1	2	yes	complemented
10	#14556583	C₄	1	1	yes	characteristic, complemented
11	#14556569	—	2	2	no	—
12	#14556556	—	2	2	no	—
13	#14556549	C₂²	1	2	yes	—
14	C₄²×D₇₃	C₂²	1	1	yes	characteristic
15	#125×C₇₃	C₄	1	1	yes	characteristic, complemented
16	C₂²×#64408	—	2	2	no	—
17	#11924038	—	2	4	no	—
18	C₂×#10596833	—	2	2	no	—
19	C₄×#64408	—	2	2	no	—
20	C₄×#64408	Q₈	1	4	yes	complemented
21	C₂×Dic₁₄₆	—	2	2	no	—
22	C₂×C₄×D₇₃	D₄	1	2	yes	—
23	C₂×C₄×D₇₃	C₂³	1	1	yes	characteristic
24	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
25	#11924007	—	2	2	no	—
26	#11924007	—	2	2	no	—
27	#11924005	—	2	2	no	—
28	C₄×Dic₇₃	—	2	2	no	—
29	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
30	C₄×Dic₇₃	D₄	1	2	yes	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
33	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×D₇₃	C₂×D₄	1	1	yes	characteristic
35	C₂×#64408	—	2	4	no	—
36	C₂×#64408	—	4	4	no	—
37	C₂×C₄×C₇₃	—	2	2	no	—
38	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
39	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
40	C₂×Dic₇₃	—	2	2	no	—
41	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
42	C₂×Dic₇₃	C₂×D₄	1	1	yes	characteristic
43	C₄×D₇₃	—	4	2	no	—
44	C₄×D₇₃	C₂×Q₈	1	2	yes	—
45	C₄×D₇₃	#41	1	2	yes	—
46	Dic₁₄₆	—	4	4	no	—
47	#10596833	—	4	2	no	—
48	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
49	C₂×D₇₃	—	2	2	no	—
50	C₂×D₇₃	C₂²⋊Q₈	1	2	yes	—
51	#64408	—	4	4	no	—
52	C₄×C₇₃	—	2	2	no	—
53	C₄×C₇₃	—	4	2	no	—
54	C₄×C₇₃	C₄×Q₈	1	2	yes	—
55	Dic₇₃	—	2	2	no	—
56	Dic₇₃	—	4	2	no	—
57	Dic₇₃	#124	1	1	yes	characteristic
58	Dic₇₃	C₄⋊Q₈	1	1	yes	characteristic
59	C₂×C₇₃	#391	1	1	yes	characteristic
60	C₂×C₇₃	#421	1	2	yes	—
61	D₇₃	—	2	2	no	—
62	#1995	—	73	1	no	maximal, Sylow
63	C₇₃	#1995	1	1	yes	characteristic, complemented, Sylow
64	#533	—	73	1	no	—
65	#423	—	73	1	no	—
66	#376	—	73	1	no	—
67	#339	—	73	4	no	—
68	C₂×M₁₆	—	73	2	no	—
69	C₄⋊Q₈	—	73	2	no	—
70	#125	—	73	1	no	—
71	#125	#64408	1	1	yes	characteristic, complemented
72	C₂²⋊Q₈	—	146	2	no	—
73	C₄×Q₈	—	146	2	no	—
74	#117	—	73	2	no	—
75	C₂×C₄²	—	73	1	no	—
76	C₂×C₄²	—	73	2	no	—
77	C₄⋊C₈	—	146	2	no	—
78	#95	—	146	2	no	—
79	C₂×Q₈	—	146	2	no	—
80	C₂²×C₄	—	73	2	no	—
81	C₂²×C₄	—	73	1	no	—
82	C₂²×C₄	—	146	2	no	—
83	M₁₆	—	146	4	no	—
84	C₂×C₈	—	146	2	no	—
85	C₄⋊C₄	—	2	2	no	—
86	C₄⋊C₄	—	73	2	no	—
87	C₄⋊C₄	—	146	2	no	—
88	C₄⋊C₄	—	146	2	no	—
89	C₄⋊C₄	C₂×#64408	1	2	yes	—
90	C₂²⋊C₄	—	146	2	no	—
91	C₄²	—	73	2	no	—
92	C₄²	—	73	1	no	—
93	C₄²	—	73	4	no	—
94	C₄²	—	146	2	no	—
95	C₄²	—	146	2	no	—
96	C₄²	C₂×#64408	1	1	yes	characteristic
97	C₂³	—	73	1	no	—
98	Q₈	—	292	4	no	—
99	C₂×C₄	—	2	2	no	—
100	C₂×C₄	—	292	2	no	—
101	C₂×C₄	—	292	4	no	—
102	C₂×C₄	—	73	1	no	—
103	C₂×C₄	—	73	2	no	—
104	C₂×C₄	—	73	2	no	—
105	C₂×C₄	—	73	2	no	—
106	C₂×C₄	—	146	4	no	—
107	C₂×C₄	—	146	2	no	—
108	C₂×C₄	C₂²⋊#64408	1	2	yes	—
109	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
110	C₈	—	292	2	no	—
111	C₂²	—	73	2	no	—
112	C₂²	—	146	2	no	—
113	C₂²	C₂×C₂²⋊#64408	1	1	yes	characteristic
114	C₄	—	2	2	no	—
115	C₄	—	4	2	no	—
116	C₄	—	292	4	no	—
117	C₄	—	292	2	no	—
118	C₄	—	73	1	no	—
119	C₄	—	73	1	no	—
120	C₄	—	146	2	no	—
121	C₄	Q₈×#64408	1	2	yes	—
122	C₂	—	146	2	no	—
123	C₂	(C₂×#64408)⋊Q₈	1	1	yes	characteristic
124	C₂	#17989584	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989591

C₂

yes

maximal, characteristic

#17989523

C₂

yes

maximal, characteristic

#17989457

C₂

yes

maximal

#17989143

C₂

yes

maximal, characteristic

C₂×#11924038

C₂²

yes

—

C₂×C₄×#64408

C₂²

yes

—

C₄⋊#10596833

—

(C₂×#64408)⋊C₄

—

#14556590

C₄

yes

complemented

#14556583

C₄

yes

characteristic, complemented

#14556569

—

#14556556

—

#14556549

C₂²

yes

—

C₄²×D₇₃

C₂²

yes

characteristic

#125×C₇₃

C₄

yes

characteristic, complemented

C₂²×#64408

—

—

—

—

Q₈

yes

complemented

C₂×Dic₁₄₆

—

C₂×C₄×D₇₃

D₄

yes

—

C₂×C₄×D₇₃

C₂³

yes

characteristic

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

#11924005

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×D₄

yes

characteristic

C₂×#64408

—

C₂×#64408

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂×D₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₂×Q₈

yes

—

C₄×D₇₃

#41

yes

—

Dic₁₄₆

—

#10596833

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₂²⋊Q₈

yes

—

#64408

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×Q₈

yes

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

#124

yes

characteristic

Dic₇₃

C₄⋊Q₈

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

D₇₃

—

#1995

—

maximal, Sylow

C₇₃

#1995

yes

characteristic, complemented, Sylow

—

—

—

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

#125

#64408

yes

characteristic, complemented

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

#117

—

C₂×C₄²

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

#95

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₂×#64408

yes

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

—

146

—

C₄²

C₂×#64408

yes

characteristic

C₂³

—

Q₈

—

292

—

C₂×C₄

—

100

C₂×C₄

—

292

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

103

C₂×C₄

—

104

C₂×C₄

—

105

C₂×C₄

—

106

C₂×C₄

—

146

—

107

C₂×C₄

—

146

—

108

C₂×C₄

C₂²⋊#64408

yes

—

109

C₂×C₄

C₂²×#64408

yes

characteristic

110

C₈

—

292

—

111

C₂²

—

112

C₂²

—

146

—

113

C₂²

C₂×C₂²⋊#64408

yes

characteristic

114

C₄

—

115

C₄

—

116

C₄

—

292

—

117

C₄

—

292

—

118

C₄

—

119

C₄

—

120

C₄

—

146

—

121

C₄

Q₈×#64408

yes

—

122

C₂

—

146

—

123

C₂

(C₂×#64408)⋊Q₈

yes

characteristic

124

C₂

#17989584

yes

—

	subgroup	G/H
center	C₂²	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#64408
Fitting	#125×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#125	#64408
hypocenter	C₇₃	#1995
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #125

subgroup

G/H

center

C₂²

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#64408

Fitting

#125×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #125

N	H ≅ G/N	type
9. #14556590	C₄	semidirect
10. #14556583	C₄	semidirect
15. #125×C₇₃	C₄	semidirect
20. C₄×#64408	Q₈	semidirect
63. C₇₃	#1995	semidirect
71. #125	#64408	semidirect

H ≅ G/N

type

9. #14556590

C₄

semidirect

10. #14556583

C₄

semidirect

15. #125×C₇₃

C₄

semidirect

20. C₄×#64408

Q₈

semidirect

63. C₇₃

#1995

semidirect

71. #125

#64408

semidirect

Subgroups — #22626118

Conjugacy classes of subgroups

Complements