Group #23750656 — subgroups

Subgroups — #23750656

Order 9536.

124 conjugacy classes of subgroups; only the 48 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 48 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×#14558745	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	C₂²⋊#11924753	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²⋊#11924753	C₂	1	1	yes	maximal, characteristic, complemented
6	#18011966	C₂	1	1	yes	maximal, characteristic, complemented
7	D₄×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic
8	#14558745	—	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	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
15	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
16	C₄⋊Dic₁₄₉	C₄	1	1	yes	characteristic
17	C₂²⋊Dic₁₄₉	C₄	1	1	yes	characteristic
18	C₂²⋊Dic₁₄₉	C₄	1	1	yes	characteristic
19	C₄×Dic₁₄₉	C₂²	1	1	yes	characteristic
20	C₂×D₄×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	C₂×Dic₁₄₉	—	2	1	no	—
26	C₂×Dic₁₄₉	—	2	1	no	—
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	C₂×C₄	1	1	yes	characteristic
32	C₂×Dic₁₄₉	C₂³	1	1	yes	characteristic
33	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₁₄₉	C₂×C₄	1	1	yes	characteristic
35	D₄×C₁₄₉	—	2	2	no	—
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	—	2	1	no	—
40	C₂²×C₁₄₉	—	2	1	no	—
41	C₂²×C₁₄₉	—	2	1	no	—
42	C₂²×C₁₄₉	M₁₆	1	2	yes	complemented
43	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
44	C₄×C₁₄₉	—	2	1	no	—
45	Dic₁₄₉	—	2	1	no	—
46	Dic₁₄₉	—	2	1	no	—
47	Dic₁₄₉	—	2	1	no	—
48	Dic₁₄₉	C₂×D₄	1	1	yes	characteristic
49	Dic₁₄₉	#41	1	1	yes	characteristic
50	C₂×C₁₄₉	—	2	2	no	—
51	C₂×C₁₄₉	—	4	1	no	—
52	C₂×C₁₄₉	C₄×D₄	1	1	yes	characteristic
53	C₂×C₁₄₉	C₂×M₁₆	1	1	yes	characteristic
54	C₂×C₁₄₉	#131	1	1	yes	characteristic
55	C₁₄₉	#435	1	1	yes	characteristic, complemented, Sylow
56	#435	—	149	1	no	maximal, Sylow
57	C₂×M₁₆	—	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	#97	—	149	1	no	—
64	C₂×D₄	#10597010	1	1	yes	characteristic
65	C₂²×C₄	—	149	1	no	—
66	C₂²×C₄	—	149	1	no	—
67	M₁₆	—	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	—	149	1	no	—
76	C₄²	—	149	1	no	—
77	C₂³	C₂×#10597010	1	1	yes	characteristic
78	C₂³	C₂×#10597010	1	1	yes	characteristic
79	D₄	—	2	2	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	—	149	1	no	—
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	—	2	1	no	—
96	C₂²	—	2	1	no	—
97	C₂²	—	2	1	no	—
98	C₂²	#14558745	1	2	yes	complemented
99	C₂²	C₂²×#10597010	1	1	yes	characteristic
100	C₄	—	2	1	no	—
101	C₄	—	298	1	no	—
102	C₄	—	298	1	no	—
103	C₄	—	298	1	no	—
104	C₄	—	149	1	no	—
105	C₄	—	149	1	no	—
106	C₂	—	2	2	no	—
107	C₂	—	4	1	no	—
108	C₂	D₄×#10597010	1	1	yes	characteristic
109	C₂	C₂×#14558745	1	1	yes	characteristic
110	C₂	#18011998	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14558745

C₂

yes

maximal, characteristic, complemented

C₂²×#11924753

C₂

yes

maximal, characteristic, complemented

#18011978

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11924753

C₂

yes

maximal, characteristic, complemented

C₂²⋊#11924753

C₂

yes

maximal, characteristic, complemented

#18011966

C₂

yes

maximal, characteristic, complemented

D₄×Dic₁₄₉

C₂

yes

maximal, characteristic

#14558745

—

C₂×#11924753

—

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂×#11924753

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₄⋊Dic₁₄₉

C₄

yes

characteristic

C₂²⋊Dic₁₄₉

C₄

yes

characteristic

C₂²⋊Dic₁₄₉

C₄

yes

characteristic

C₄×Dic₁₄₉

C₂²

yes

characteristic

C₂×D₄×C₁₄₉

C₄

yes

—

—

—

D₄

yes

complemented

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂×C₄

yes

characteristic

C₂×Dic₁₄₉

C₂³

yes

characteristic

C₂³×C₁₄₉

C₂×C₄

yes

characteristic

C₂³×C₁₄₉

C₂×C₄

yes

characteristic

D₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂×C₄

yes

characteristic

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

—

C₂²×C₁₄₉

M₁₆

yes

complemented

C₂²×C₁₄₉

C₂²×C₄

yes

characteristic

C₄×C₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

C₂×D₄

yes

characteristic

Dic₁₄₉

#41

yes

characteristic

C₂×C₁₄₉

—

C₂×C₁₄₉

—

C₂×C₁₄₉

C₄×D₄

yes

characteristic

C₂×C₁₄₉

C₂×M₁₆

yes

C₂×C₁₄₉

yes

C₁₄₉

yes

characteristic, complemented, Sylow

#435

—

149

maximal, Sylow

C₂×M₁₆

—

149

—

C₂²×C₈

—

149

—

C₄×D₄

—

149

—

C₄⋊C₈

—

149

—

C₂²⋊C₈

—

149

—

C₂²⋊C₈

—

149

—

#97

—

149

—

C₂×D₄

#10597010

yes

characteristic

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

M₁₆

—

298

—

C₂×C₈

—

298

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₂×C₈

—

149

—

C₄⋊C₄

—

149

—

C₂²⋊C₄

—

149

—

C₂²⋊C₄

—

149

—

C₄²

—

149

—

C₂³

yes

C₂³

yes

D₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

—

149

—

C₂×C₄

C₂×#10597010

yes

characteristic

C₈

—

298

—

C₈

—

298

—

C₈

—

298

—

C₈

—

149

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

yes

C₂²

yes

100

C₄

—

101

C₄

—

298

—

102

C₄

—

298

—

103

C₄

—

298

—

104

C₄

—

149

—

105

C₄

—

149

—

106

C₂

—

107

C₂

—

108

C₂

D₄×#10597010

yes

characteristic

109

C₂

C₂×#14558745

yes

characteristic

110

C₂

#18011998

yes

characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#10597010
commutator, socle	C₂²×C₁₄₉	C₂²×C₄
Fitting, prime radical	C₂×D₄×C₁₄₉	C₄
cosocle	C₂×Dic₁₄₉	C₂³
hypercenter	C₂×D₄	#10597010
hypocenter	C₁₄₉	#435
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂² ◁ C₂×D₄

subgroup

G/H

center, Frattini

C₂²

C₂²×#10597010

commutator, socle

C₂²×C₁₄₉

C₂²×C₄

Fitting, prime radical

C₂×D₄×C₁₄₉

C₄

cosocle

C₂×Dic₁₄₉

C₂³

C₂×D₄

C₁₄₉

G ▷ C₂²×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂² ◁ C₂×D₄

N	H ≅ G/N	type
1. C₂×#14558745	C₂	semidirect
2. C₂²×#11924753	C₂	semidirect
3. #18011978	C₂	semidirect
4. C₂²⋊#11924753	C₂	semidirect
5. C₂²⋊#11924753	C₂	semidirect
6. #18011966	C₂	semidirect
24. #11924753	D₄	semidirect
42. C₂²×C₁₄₉	M₁₆	semidirect
55. C₁₄₉	#435	semidirect
98. C₂²	#14558745	semidirect

H ≅ G/N

type

1. C₂×#14558745

C₂

semidirect

2. C₂²×#11924753

C₂

semidirect

3. #18011978

C₂

semidirect

4. C₂²⋊#11924753

C₂

semidirect

5. C₂²⋊#11924753

C₂

semidirect

6. #18011966

C₂

semidirect

24. #11924753

D₄

semidirect

42. C₂²×C₁₄₉

M₁₆

semidirect

55. C₁₄₉

#435

semidirect

98. C₂²

#14558745

semidirect

Subgroups — #23750656

Conjugacy classes of subgroups

Complements