Group #23749688 — subgroups

Subgroups — #23749688

Order 9536.

134 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 61 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	C₂²×#11924746	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₈×D₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×C₂²⋊D₁₄₉	C₂	1	1	yes	maximal, characteristic
4	#18011840	C₂	1	1	yes	maximal, characteristic, complemented
5	#18011823	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²⋊C₈×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
10	C₂×#11924746	—	2	2	no	—
11	C₂×#11924746	C₂²	1	1	yes	characteristic
12	C₂×#11924746	C₂²	1	1	yes	characteristic
13	C₈×D₁₄₉	—	2	2	no	—
14	#14558715	C₄	1	1	yes	characteristic
15	C₂²⋊Dic₁₄₉	C₄	1	1	yes	characteristic
16	#14558713	C₄	1	1	yes	characteristic
17	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
19	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×C₈×C₁₄₉	C₂²	1	1	yes	characteristic
21	C₂²×D₁₄₉	C₂×C₄	1	1	yes	characteristic
22	C₂²⋊D₁₄₉	C₈	1	4	yes	complemented
23	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
24	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
25	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
26	C₄×D₁₄₉	—	2	1	no	—
27	C₄×D₁₄₉	—	2	1	no	—
28	#11924746	—	2	1	no	—
29	#11924746	D₄	1	2	yes	complemented
30	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄×C₁₄₉	—	2	1	no	—
32	C₂×C₄×C₁₄₉	—	2	1	no	—
33	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
34	C₂×C₄×C₁₄₉	C₂³	1	1	yes	characteristic
35	C₈×C₁₄₉	—	2	1	no	—
36	C₈×C₁₄₉	—	2	1	no	—
37	C₂²×C₁₄₉	—	2	1	no	—
38	C₂²×C₁₄₉	—	2	1	no	—
39	C₂²×C₁₄₉	C₂×C₈	1	2	yes	complemented
40	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
41	C₂×D₁₄₉	—	2	1	no	—
42	C₂×D₁₄₉	—	2	1	no	—
43	C₂×D₁₄₉	C₂×C₈	1	2	yes	complemented
44	C₄×C₁₄₉	—	2	1	no	—
45	C₄×C₁₄₉	C₂×D₄	1	1	yes	characteristic
46	C₄×C₁₄₉	#41	1	1	yes	characteristic
47	Dic₁₄₉	—	2	1	no	—
48	Dic₁₄₉	—	2	1	no	—
49	Dic₁₄₉	C₂×C₈	1	2	yes	complemented
50	C₂×C₁₄₉	—	2	2	no	—
51	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
52	C₂×C₁₄₉	C₂²×C₈	1	1	yes	characteristic
53	C₂×C₁₄₉	#131	1	1	yes	characteristic
54	D₁₄₉	—	2	2	no	—
55	C₁₄₉	C₈×D₄	1	1	yes	characteristic, complemented, Sylow
56	C₈×D₄	—	149	1	no	maximal, Sylow
57	C₂²×C₈	—	149	1	no	—
58	C₂²×C₈	—	149	1	no	—
59	C₄×D₄	—	149	1	no	—
60	C₄⋊C₈	—	149	1	no	—
61	C₂²⋊C₈	—	149	1	no	—
62	C₂²⋊C₈	D₁₄₉	1	1	yes	characteristic, complemented
63	C₄×C₈	—	149	1	no	—
64	C₂×D₄	—	149	1	no	—
65	C₂²×C₄	—	149	1	no	—
66	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
67	C₂×C₈	—	298	2	no	—
68	C₂×C₈	—	298	2	no	—
69	C₂×C₈	—	149	1	no	—
70	C₂×C₈	—	149	1	no	—
71	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
72	C₂×C₈	C₂×D₁₄₉	1	1	yes	characteristic
73	C₄⋊C₄	—	149	1	no	—
74	C₂²⋊C₄	—	149	1	no	—
75	C₂²⋊C₄	—	149	1	no	—
76	C₄²	—	149	1	no	—
77	C₂³	—	149	1	no	—
78	C₂³	C₄×D₁₄₉	1	1	yes	characteristic
79	D₄	—	149	4	no	—
80	C₂×C₄	—	2	1	no	—
81	C₂×C₄	—	2	1	no	—
82	C₂×C₄	—	298	1	no	—
83	C₂×C₄	—	298	1	no	—
84	C₂×C₄	—	149	1	no	—
85	C₂×C₄	—	149	1	no	—
86	C₂×C₄	—	149	1	no	—
87	C₂×C₄	C₄×D₁₄₉	1	1	yes	characteristic
88	C₂×C₄	C₂²×D₁₄₉	1	1	yes	characteristic
89	C₈	—	2	1	no	—
90	C₈	—	2	1	no	—
91	C₈	—	298	1	no	—
92	C₈	—	149	2	no	—
93	C₂²	—	2	1	no	—
94	C₂²	—	2	1	no	—
95	C₂²	—	298	1	no	—
96	C₂²	—	298	1	no	—
97	C₂²	—	149	2	no	—
98	C₂²	C₈×D₁₄₉	1	2	yes	complemented
99	C₂²	C₂×C₄×D₁₄₉	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	298	1	no	—
102	C₄	—	298	1	no	—
103	C₄	—	149	2	no	—
104	C₄	D₄×D₁₄₉	1	1	yes	characteristic
105	C₄	#14558735	1	1	yes	characteristic
106	C₂	—	2	2	no	—
107	C₂	—	298	2	no	—
108	C₂	#18011871	1	1	yes	characteristic
109	C₂	C₂×C₈×D₁₄₉	1	1	yes	characteristic
110	C₂	#18011919	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#11924746

C₂

yes

maximal, characteristic, complemented

C₂×C₈×D₁₄₉

C₂

yes

maximal, characteristic, complemented

C₄×C₂²⋊D₁₄₉

C₂

yes

maximal, characteristic

#18011840

C₂

yes

maximal, characteristic, complemented

#18011823

C₂

yes

maximal, characteristic, complemented

C₈×Dic₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂²⋊C₈×C₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂×C₂²⋊D₁₄₉

C₄

yes

characteristic

C₂×C₄×D₁₄₉

C₂²

yes

characteristic

C₂×#11924746

—

C₂×#11924746

C₂²

yes

characteristic

C₂×#11924746

C₂²

yes

characteristic

C₈×D₁₄₉

—

#14558715

C₄

yes

characteristic

C₂²⋊Dic₁₄₉

C₄

yes

characteristic

#14558713

C₄

yes

characteristic

C₄×Dic₁₄₉

C₂²

yes

characteristic

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₂×C₈×C₁₄₉

C₂²

yes

characteristic

C₂×C₈×C₁₄₉

C₂²

yes

characteristic

C₂²×D₁₄₉

C₂×C₄

yes

characteristic

C₂²⋊D₁₄₉

C₈

yes

complemented

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₄×D₁₄₉

—

C₄×D₁₄₉

—

#11924746

—

#11924746

D₄

yes

complemented

C₂³×C₁₄₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂³

yes

characteristic

C₈×C₁₄₉

—

C₈×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

C₂×C₈

yes

complemented

C₂²×C₁₄₉

C₂²×C₄

yes

characteristic

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

C₂×C₈

yes

complemented

C₄×C₁₄₉

—

C₄×C₁₄₉

C₂×D₄

yes

characteristic

C₄×C₁₄₉

#41

yes

characteristic

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

C₂×C₈

yes

complemented

C₂×C₁₄₉

—

C₂×C₁₄₉

C₄×D₄

yes

characteristic

C₂×C₁₄₉

C₂²×C₈

yes

characteristic

C₂×C₁₄₉

#131

yes

characteristic

D₁₄₉

—

C₁₄₉

C₈×D₄

yes

characteristic, complemented, Sylow

C₈×D₄

—

149

maximal, Sylow

C₂²×C₈

—

149

—

C₂²×C₈

—

149

—

C₄×D₄

—

149

—

C₄⋊C₈

—

149

—

C₂²⋊C₈

—

149

—

C₂²⋊C₈

D₁₄₉

yes

characteristic, complemented

C₄×C₈

—

149

—

C₂×D₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

C₂×D₁₄₉

yes

characteristic

C₂×C₈

C₂×D₁₄₉

yes

characteristic

C₄⋊C₄

—

149

—

C₂²⋊C₄

—

149

—

C₂²⋊C₄

—

149

—

C₄²

—

149

—

C₂³

—

149

—

C₂³

C₄×D₁₄₉

yes

characteristic

D₄

—

149

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

C₄×D₁₄₉

yes

characteristic

C₂×C₄

C₂²×D₁₄₉

yes

characteristic

C₈

—

C₈

—

C₈

—

298

—

C₈

—

149

—

C₂²

—

C₂²

—

C₂²

—

298

—

C₂²

—

298

—

C₂²

—

149

—

C₂²

C₈×D₁₄₉

yes

complemented

C₂²

C₂×C₄×D₁₄₉

yes

characteristic

100

C₄

—

101

C₄

—

298

—

102

C₄

—

298

—

103

C₄

—

149

—

104

C₄

D₄×D₁₄₉

yes

characteristic

105

C₄

#14558735

yes

characteristic

106

C₂

—

107

C₂

—

298

—

108

C₂

#18011871

yes

characteristic

109

C₂

C₂×C₈×D₁₄₉

yes

characteristic

110

C₂

#18011919

yes

characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×D₁₄₉
commutator	C₂×C₁₄₉	C₂²×C₈
Fitting	C₂²⋊C₈×C₁₄₉	C₂
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical	C₂×C₂²⋊D₁₄₉	C₄
cosocle	C₂×C₄×C₁₄₉	C₂³
hypercenter	C₂²⋊C₈	D₁₄₉
hypocenter	C₁₄₉	C₈×D₄
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×D₁₄₉

commutator

C₂×C₁₄₉

C₂²×C₈

Fitting

C₂²⋊C₈×C₁₄₉

C₂

socle

C₂²×C₁₄₉

C₂²×C₄

prime radical

C₂×C₂²⋊D₁₄₉

C₄

cosocle

C₂×C₄×C₁₄₉

C₂³

hypercenter

C₂²⋊C₈

D₁₄₉

hypocenter

C₁₄₉

C₈×D₄

LCS

G ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂×C₄ ◁ C₂²⋊C₈

N	H ≅ G/N	type
1. C₂²×#11924746	C₂	semidirect
2. C₂×C₈×D₁₄₉	C₂	semidirect
4. #18011840	C₂	semidirect
5. #18011823	C₂	semidirect
6. C₈×Dic₁₄₉	C₂	semidirect
7. C₂²⋊C₈×C₁₄₉	C₂	semidirect
22. C₂²⋊D₁₄₉	C₈	semidirect
29. #11924746	D₄	semidirect
39. C₂²×C₁₄₉	C₂×C₈	semidirect
43. C₂×D₁₄₉	C₂×C₈	semidirect
49. Dic₁₄₉	C₂×C₈	semidirect
55. C₁₄₉	C₈×D₄	semidirect
62. C₂²⋊C₈	D₁₄₉	semidirect
98. C₂²	C₈×D₁₄₉	semidirect

H ≅ G/N

type

1. C₂²×#11924746

C₂

semidirect

2. C₂×C₈×D₁₄₉

C₂

semidirect

4. #18011840

C₂

semidirect

5. #18011823

C₂

semidirect

6. C₈×Dic₁₄₉

C₂

semidirect

7. C₂²⋊C₈×C₁₄₉

C₂

semidirect

22. C₂²⋊D₁₄₉

C₈

semidirect

29. #11924746

D₄

semidirect

39. C₂²×C₁₄₉

C₂×C₈

semidirect

43. C₂×D₁₄₉

C₂×C₈

semidirect

49. Dic₁₄₉

C₂×C₈

semidirect

55. C₁₄₉

C₈×D₄

semidirect

62. C₂²⋊C₈

D₁₄₉

semidirect

98. C₂²

C₈×D₁₄₉

semidirect

Subgroups — #23749688

Conjugacy classes of subgroups

Complements