Group #23750652 — subgroups

Subgroups — #23750652

Order 9536.

134 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 56 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×D₁₄₉⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#11924753	C₂	1	1	yes	maximal, characteristic, complemented
3	#18011978	C₂	1	1	yes	maximal, characteristic, complemented
4	#18011968	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊#11924753	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×#11924753	C₂	1	1	yes	maximal, characteristic, complemented
7	#18011871	C₂	1	1	yes	maximal, characteristic
8	D₁₄₉⋊C₈	—	2	2	no	—
9	C₂×#11924753	—	2	2	no	—
10	C₂×#11924753	C₂²	1	1	yes	characteristic
11	C₂×#11924753	C₂²	1	1	yes	characteristic
12	C₂×#11924753	C₂²	1	1	yes	characteristic
13	C₂×#11924753	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊D₁₄₉	C₄	1	1	yes	characteristic
15	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₁₄₉	C₂²	1	1	yes	characteristic
17	#14558715	C₄	1	1	yes	characteristic
18	#14558713	C₄	1	1	yes	characteristic
19	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
20	C₂²⋊C₄×C₁₄₉	C₄	1	1	yes	characteristic
21	#11924753	—	2	1	no	—
22	#11924753	—	2	1	no	—
23	#11924753	—	2	1	no	—
24	#11924753	D₄	1	2	yes	complemented
25	C₂²×D₁₄₉	C₂×C₄	1	1	yes	characteristic
26	C₂²⋊D₁₄₉	C₈	1	4	yes	complemented
27	C₂×Dic₁₄₉	—	2	1	no	—
28	C₂×Dic₁₄₉	—	2	1	no	—
29	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
30	C₂×Dic₁₄₉	C₂×C₄	1	1	yes	characteristic
31	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
32	C₄×D₁₄₉	—	2	1	no	—
33	C₄×D₁₄₉	—	2	1	no	—
34	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×C₁₄₉	C₂×C₄	1	1	yes	characteristic
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	—	2	1	no	—
46	Dic₁₄₉	—	2	1	no	—
47	Dic₁₄₉	C₂×C₈	1	2	yes	complemented
48	Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
49	Dic₁₄₉	#41	1	1	yes	characteristic
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	—	149	1	no	—
63	C₄×C₈	—	149	1	no	—
64	C₂×D₄	—	149	1	no	—
65	C₂²×C₄	—	149	1	no	—
66	C₂²×C₄	—	149	1	no	—
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	—	149	1	no	—
72	C₂×C₈	—	149	1	no	—
73	C₄⋊C₄	—	149	1	no	—
74	C₂²⋊C₄	—	149	1	no	—
75	C₂²⋊C₄	#10597010	1	1	yes	characteristic
76	C₄²	—	149	1	no	—
77	C₂³	—	149	1	no	—
78	C₂³	C₂×#10597010	1	1	yes	characteristic
79	D₄	—	149	4	no	—
80	C₂×C₄	—	298	1	no	—
81	C₂×C₄	—	298	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	C₂×#10597010	1	1	yes	characteristic
88	C₂×C₄	C₂×#10597010	1	1	yes	characteristic
89	C₈	—	298	1	no	—
90	C₈	—	298	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	D₁₄₉⋊C₈	1	2	yes	complemented
99	C₂²	C₂²×#10597010	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	2	1	no	—
102	C₄	—	298	1	no	—
103	C₄	—	149	1	no	—
104	C₄	—	149	1	no	—
105	C₄	—	149	2	no	—
106	C₂	—	2	2	no	—
107	C₂	—	298	2	no	—
108	C₂	D₄×#10597010	1	1	yes	characteristic
109	C₂	C₂×D₁₄₉⋊C₈	1	1	yes	characteristic
110	C₂	#18011998	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₄₉⋊C₈

C₂

yes

maximal, characteristic, complemented

C₂²×#11924753

C₂

yes

maximal, characteristic, complemented

#18011978

C₂

yes

maximal, characteristic, complemented

#18011968

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11924753

C₂

yes

maximal, characteristic, complemented

C₄×#11924753

C₂

yes

maximal, characteristic, complemented

#18011871

C₂

yes

maximal, characteristic

D₁₄₉⋊C₈

—

C₂×#11924753

—

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂×C₂²⋊D₁₄₉

C₄

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂×C₄×D₁₄₉

C₂²

yes

characteristic

#14558715

C₄

yes

characteristic

#14558713

C₄

yes

characteristic

C₄×Dic₁₄₉

C₂²

yes

characteristic

C₂²⋊C₄×C₁₄₉

C₄

yes

—

—

—

D₄

yes

complemented

C₂²×D₁₄₉

C₂×C₄

yes

characteristic

C₂²⋊D₁₄₉

C₈

yes

complemented

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂³

yes

characteristic

C₄×D₁₄₉

—

C₄×D₁₄₉

—

C₂³×C₁₄₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×C₄

yes

characteristic

C₂×C₄×C₁₄₉

C₂×C₄

yes

characteristic

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

—

Dic₁₄₉

—

Dic₁₄₉

C₂×C₈

yes

complemented

Dic₁₄₉

C₂×D₄

yes

characteristic

Dic₁₄₉

#41

yes

characteristic

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

—

149

—

C₄×C₈

—

149

—

C₂×D₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂×C₈

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₄⋊C₄

—

149

—

C₂²⋊C₄

—

149

—

C₂²⋊C₄

#10597010

yes

characteristic

C₄²

—

149

—

C₂³

—

149

—

C₂³

C₂×#10597010

yes

characteristic

D₄

—

149

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

298

—

C₈

—

298

—

C₈

—

298

—

C₈

—

149

—

C₂²

—

C₂²

—

C₂²

—

298

—

C₂²

—

298

—

C₂²

—

149

—

C₂²

D₁₄₉⋊C₈

yes

complemented

C₂²

C₂²×#10597010

yes

characteristic

100

C₄

—

101

C₄

—

102

C₄

—

298

—

103

C₄

—

149

—

104

C₄

—

149

—

105

C₄

—

149

—

106

C₂

—

107

C₂

—

298

—

108

C₂

D₄×#10597010

yes

characteristic

109

C₂

C₂×D₁₄₉⋊C₈

yes

characteristic

110

C₂

#18011998

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10597010
commutator	C₂×C₁₄₉	C₂²×C₈
Fitting	C₂²⋊C₄×C₁₄₉	C₄
socle	C₂²×C₁₄₉	C₂²×C₄
prime radical	C₂×C₂²⋊D₁₄₉	C₄
cosocle	C₂×Dic₁₄₉	C₂³
hypercenter	C₂²⋊C₄	#10597010
hypocenter	C₁₄₉	C₈×D₄
LCS	G ▷ C₂×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

subgroup

G/H

center, Frattini

C₂²

C₂²×#10597010

commutator

C₂×C₁₄₉

C₂²×C₈

Fitting

C₂²⋊C₄×C₁₄₉

C₄

socle

C₂²×C₁₄₉

C₂²×C₄

prime radical

C₂×C₂²⋊D₁₄₉

C₄

cosocle

C₂×Dic₁₄₉

C₂³

hypercenter

C₂²⋊C₄

#10597010

hypocenter

C₁₄₉

C₈×D₄

LCS

G ▷ C₂×C₁₄₉ ▷ C₁₄₉

UCS

C₁ ◁ C₂² ◁ C₂²⋊C₄

N	H ≅ G/N	type
1. C₂×D₁₄₉⋊C₈	C₂	semidirect
2. C₂²×#11924753	C₂	semidirect
3. #18011978	C₂	semidirect
4. #18011968	C₂	semidirect
5. C₂²⋊#11924753	C₂	semidirect
6. C₄×#11924753	C₂	semidirect
24. #11924753	D₄	semidirect
26. C₂²⋊D₁₄₉	C₈	semidirect
39. C₂²×C₁₄₉	C₂×C₈	semidirect
43. C₂×D₁₄₉	C₂×C₈	semidirect
47. Dic₁₄₉	C₂×C₈	semidirect
55. C₁₄₉	C₈×D₄	semidirect
98. C₂²	D₁₄₉⋊C₈	semidirect

H ≅ G/N

type

1. C₂×D₁₄₉⋊C₈

C₂

semidirect

2. C₂²×#11924753

C₂

semidirect

3. #18011978

C₂

semidirect

4. #18011968

C₂

semidirect

5. C₂²⋊#11924753

C₂

semidirect

6. C₄×#11924753

C₂

semidirect

24. #11924753

D₄

semidirect

26. C₂²⋊D₁₄₉

C₈

semidirect

39. C₂²×C₁₄₉

C₂×C₈

semidirect

43. C₂×D₁₄₉

C₂×C₈

semidirect

47. Dic₁₄₉

C₂×C₈

semidirect

55. C₁₄₉

C₈×D₄

semidirect

98. C₂²

D₁₄₉⋊C₈

semidirect

Subgroups — #23750652

Conjugacy classes of subgroups

Complements