Group #23749508 — subgroups

Subgroups — #23749508

Order 9536.

154 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 69 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×C₄⋊Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
2	C₂×#14558715	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#18011818	C₂	1	1	yes	maximal, characteristic
5	#18011818	C₂	1	1	yes	maximal, characteristic
6	#18011818	C₂	1	1	yes	maximal, characteristic
7	#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic
8	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
11	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
12	C₄⋊Dic₁₄₉	C₄	1	4	yes	complemented
13	#14558715	—	2	2	no	—
14	C₄×Dic₁₄₉	—	2	2	no	—
15	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
16	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
18	C₂×Dic₁₄₉	—	2	1	no	—
19	C₂×Dic₁₄₉	—	2	1	no	—
20	C₂×Dic₁₄₉	—	2	1	no	—
21	C₂×Dic₁₄₉	—	2	1	no	—
22	C₂×Dic₁₄₉	—	2	1	no	—
23	C₂×Dic₁₄₉	—	2	1	no	—
24	C₂×Dic₁₄₉	—	2	1	no	—
25	C₂×Dic₁₄₉	—	2	1	no	—
26	C₂×Dic₁₄₉	—	2	1	no	—
27	C₂×Dic₁₄₉	C₂×C₄	1	2	yes	—
28	C₂×Dic₁₄₉	C₂×C₄	1	2	yes	—
29	C₂×Dic₁₄₉	D₄	1	2	yes	—
30	C₂³×C₁₄₉	C₂³	1	1	yes	characteristic
31	C₂×C₄×C₁₄₉	—	2	1	no	—
32	C₂×C₄×C₁₄₉	—	2	1	no	—
33	C₂×C₄×C₁₄₉	—	2	1	no	—
34	C₂×C₄×C₁₄₉	—	2	1	no	—
35	C₂×C₄×C₁₄₉	—	2	1	no	—
36	C₂×C₄×C₁₄₉	—	2	1	no	—
37	C₂×C₄×C₁₄₉	—	2	1	no	—
38	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
39	C₂×C₄×C₁₄₉	Q₈	1	2	yes	—
40	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
41	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
42	C₂²×C₁₄₉	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₁₄₉	#41	1	1	yes	characteristic
44	C₂²×C₁₄₉	#41	1	1	yes	characteristic
45	C₂²×C₁₄₉	#41	1	1	yes	characteristic
46	C₂²×C₁₄₉	#41	1	1	yes	characteristic
47	C₄×C₁₄₉	—	2	2	no	—
48	C₄×C₁₄₉	—	2	2	no	—
49	C₄×C₁₄₉	—	4	1	no	—
50	Dic₁₄₉	—	2	2	no	—
51	Dic₁₄₉	—	2	2	no	—
52	Dic₁₄₉	—	2	2	no	—
53	Dic₁₄₉	—	4	1	no	—
54	C₂×C₁₄₉	#117	1	1	yes	characteristic
55	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
56	C₂×C₁₄₉	C₄×Q₈	1	1	yes	characteristic
57	C₂×C₁₄₉	C₂²⋊Q₈	1	1	yes	characteristic
58	C₂×C₁₄₉	#123	1	1	yes	characteristic
59	C₂×C₁₄₉	#125	1	1	yes	characteristic
60	C₂×C₁₄₉	#126	1	1	yes	characteristic
61	C₁₄₉	#387	1	1	yes	characteristic, complemented, Sylow
62	#387	—	149	1	no	maximal, Sylow
63	C₂×C₄⋊C₄	—	149	1	no	—
64	C₂×C₄⋊C₄	—	149	1	no	—
65	C₂×C₄²	—	149	1	no	—
66	#95	—	149	1	no	—
67	#95	—	149	1	no	—
68	#95	—	149	1	no	—
69	#95	D₁₄₉	1	1	yes	characteristic
70	C₂²×C₄	—	149	1	no	—
71	C₂²×C₄	—	149	1	no	—
72	C₂²×C₄	—	149	1	no	—
73	C₂²×C₄	—	149	1	no	—
74	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
75	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
76	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
77	C₄⋊C₄	—	298	2	no	—
78	C₄⋊C₄	—	149	4	no	—
79	C₄²	—	298	2	no	—
80	C₂³	C₂²×D₁₄₉	1	1	yes	characteristic
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	2	1	no	—
83	C₂×C₄	—	2	1	no	—
84	C₂×C₄	—	2	1	no	—
85	C₂×C₄	—	2	1	no	—
86	C₂×C₄	—	2	1	no	—
87	C₂×C₄	—	2	1	no	—
88	C₂×C₄	—	298	1	no	—
89	C₂×C₄	—	298	1	no	—
90	C₂×C₄	—	298	1	no	—
91	C₂×C₄	—	298	1	no	—
92	C₂×C₄	—	298	1	no	—
93	C₂×C₄	—	298	1	no	—
94	C₂×C₄	—	298	1	no	—
95	C₂×C₄	—	298	1	no	—
96	C₂×C₄	—	298	1	no	—
97	C₂×C₄	—	149	2	no	—
98	C₂×C₄	—	149	2	no	—
99	C₂×C₄	—	149	2	no	—
100	C₂×C₄	C₄×D₁₄₉	1	2	yes	—
101	C₂×C₄	Dic₂₉₈	1	2	yes	—
102	C₂²	C₂×C₄×D₁₄₉	1	1	yes	characteristic
103	C₂²	D₄×D₁₄₉	1	1	yes	characteristic
104	C₂²	C₂×Dic₂₉₈	1	1	yes	characteristic
105	C₂²	#14558735	1	1	yes	characteristic
106	C₂²	#14558735	1	1	yes	characteristic
107	C₂²	#14558736	1	1	yes	characteristic
108	C₂²	#14558737	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	2	2	no	—
111	C₄	—	4	1	no	—
112	C₄	—	298	2	no	—
113	C₄	—	298	2	no	—
114	C₄	—	298	2	no	—
115	C₄	—	596	1	no	—
116	C₂	#18011867	1	1	yes	characteristic
117	C₂	#18011873	1	1	yes	characteristic
118	C₂	C₄×Dic₂₉₈	1	1	yes	characteristic
119	C₂	#18011888	1	1	yes	characteristic
120	C₂	#18011893	1	1	yes	characteristic
121	C₂	#18011902	1	1	yes	characteristic
122	C₂	#18011906	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₁₄₉

C₂

yes

maximal, characteristic

C₂×#14558715

C₂

yes

maximal, characteristic

C₂×C₄×Dic₁₄₉

C₂

yes

maximal, characteristic

#18011818

C₂

yes

maximal, characteristic

#18011818

C₂

yes

maximal, characteristic

#18011818

C₂

yes

maximal, characteristic

#95×C₁₄₉

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₄⋊Dic₁₄₉

C₄

yes

complemented

#14558715

—

C₄×Dic₁₄₉

—

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₂×C₄

yes

—

C₂×Dic₁₄₉

C₂×C₄

yes

—

C₂×Dic₁₄₉

D₄

yes

—

C₂³×C₁₄₉

C₂³

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂×C₄

yes

—

C₂×C₄×C₁₄₉

Q₈

yes

—

C₂²×C₁₄₉

C₂²×C₄

yes

characteristic

C₂²×C₁₄₉

C₂×D₄

yes

characteristic

C₂²×C₁₄₉

C₂×Q₈

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

C₂²×C₁₄₉

yes

C₄×C₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

C₂×C₁₄₉

#117

yes

characteristic

C₂×C₁₄₉

C₄×D₄

yes

characteristic

C₂×C₁₄₉

C₄×Q₈

yes

characteristic

C₂×C₁₄₉

C₂²⋊Q₈

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₁₄₉

yes

characteristic, complemented, Sylow

#387

—

149

maximal, Sylow

C₂×C₄⋊C₄

—

149

—

C₂×C₄⋊C₄

—

149

—

C₂×C₄²

—

149

—

#95

—

149

—

#95

—

149

—

#95

—

149

—

#95

D₁₄₉

yes

characteristic

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₄⋊C₄

—

298

—

C₄⋊C₄

—

149

—

C₄²

—

298

—

C₂³

C₂²×D₁₄₉

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

100

C₂×C₄

C₄×D₁₄₉

yes

—

101

C₂×C₄

Dic₂₉₈

yes

—

102

C₂²

C₂×C₄×D₁₄₉

yes

characteristic

103

C₂²

D₄×D₁₄₉

yes

characteristic

104

C₂²

C₂×Dic₂₉₈

yes

characteristic

105

C₂²

#14558735

yes

characteristic

106

C₂²

#14558735

yes

characteristic

107

C₂²

#14558736

yes

characteristic

108

C₂²

#14558737

yes

characteristic

109

C₄

—

110

C₄

—

111

C₄

—

112

C₄

—

298

—

113

C₄

—

298

—

114

C₄

—

298

—

115

C₄

—

596

—

116

C₂

#18011867

yes

characteristic

117

C₂

#18011873

yes

characteristic

118

C₂

C₄×Dic₂₉₈

yes

characteristic

119

C₂

#18011888

yes

characteristic

120

C₂

#18011893

yes

characteristic

121

C₂

#18011902

yes

characteristic

122

C₂

#18011906

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₄₉
commutator	C₂²×C₁₄₉	C₂²×C₄
Fitting	#95×C₁₄₉	C₂
socle, prime radical, cosocle	C₂³×C₁₄₉	C₂³
hypercenter	#95	D₁₄₉
hypocenter	C₁₄₉	#387
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₄₉

commutator

C₂²×C₁₄₉

C₂²×C₄

Fitting

#95×C₁₄₉

C₂

socle, prime radical, cosocle

C₂³×C₁₄₉

C₂³

D₁₄₉

C₁₄₉

G ▷ C₂²×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
12. C₄⋊Dic₁₄₉	C₄	semidirect
61. C₁₄₉	#387	semidirect

H ≅ G/N

type

12. C₄⋊Dic₁₄₉

C₄

semidirect

61. C₁₄₉

#387

semidirect

Subgroups — #23749508

Conjugacy classes of subgroups

Complements