Group #23749552 — subgroups

Subgroups — #23749552

Order 9536.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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, complemented
2	C₂×#14558713	C₂	1	1	yes	maximal, characteristic
3	C₂×#14558713	C₂	1	2	yes	maximal
4	#18011818	C₂	1	2	yes	maximal, complemented
5	#95×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂³×D₁₄₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₁₄₉	C₂²	1	1	yes	characteristic
8	C₂²×Dic₁₄₉	C₂²	1	2	yes	—
9	C₄⋊Dic₁₄₉	—	2	2	no	—
10	#14558713	—	2	4	no	—
11	#14558713	—	2	2	no	—
12	C₂²×C₄×C₁₄₉	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₂²×D₁₄₉	—	2	1	no	—
15	C₂²×D₁₄₉	—	2	2	no	—
16	C₂²×D₁₄₉	—	2	2	no	—
17	C₂²×D₁₄₉	—	2	1	no	—
18	C₂²×D₁₄₉	D₄	1	2	yes	—
19	C₂×Dic₁₄₉	—	2	2	no	—
20	C₂×Dic₁₄₉	—	2	1	no	—
21	C₂×Dic₁₄₉	—	2	2	no	—
22	C₂×Dic₁₄₉	—	2	2	no	—
23	C₂×Dic₁₄₉	—	2	2	no	—
24	C₂³×C₁₄₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₄₉	—	2	2	no	—
26	C₂×C₄×C₁₄₉	—	2	2	no	—
27	C₂×C₄×C₁₄₉	—	2	2	no	—
28	C₂×C₄×C₁₄₉	—	2	2	no	—
29	C₂×C₄×C₁₄₉	D₄	1	2	yes	—
30	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₁₄₉	#41	1	2	yes	—
33	C₂²×C₁₄₉	#41	1	2	yes	—
34	C₂²×C₁₄₉	#41	1	1	yes	characteristic
35	C₂×D₁₄₉	—	2	2	no	—
36	C₂×D₁₄₉	—	2	4	no	—
37	C₂×D₁₄₉	—	4	1	no	—
38	C₂×D₁₄₉	—	4	1	no	—
39	C₂×D₁₄₉	—	4	2	no	—
40	C₄×C₁₄₉	—	2	2	no	—
41	C₄×C₁₄₉	—	4	2	no	—
42	Dic₁₄₉	—	4	2	no	—
43	Dic₁₄₉	—	4	1	no	—
44	C₂×C₁₄₉	#121	1	1	yes	characteristic
45	C₂×C₁₄₉	#123	1	2	yes	—
46	C₂×C₁₄₉	#123	1	1	yes	characteristic
47	C₂×C₁₄₉	#124	1	1	yes	characteristic
48	C₂×C₁₄₉	#126	1	2	yes	—
49	D₁₄₉	—	4	2	no	—
50	C₁₄₉	#397	1	1	yes	characteristic, complemented, Sylow
51	#397	—	149	1	no	maximal, Sylow
52	C₂×C₄⋊C₄	—	149	1	no	—
53	C₂×C₂²⋊C₄	—	149	2	no	—
54	C₂×C₂²⋊C₄	—	149	1	no	—
55	#95	—	149	2	no	—
56	#95	D₁₄₉	1	1	yes	characteristic, complemented
57	C₂⁴	—	149	1	no	—
58	C₂²×C₄	—	149	1	no	—
59	C₂²×C₄	—	149	2	no	—
60	C₂²×C₄	C₂×D₁₄₉	1	2	yes	—
61	C₂²×C₄	C₂×D₁₄₉	1	1	yes	characteristic
62	C₄⋊C₄	—	298	2	no	—
63	C₂²⋊C₄	—	298	4	no	—
64	C₂²⋊C₄	—	298	2	no	—
65	C₂³	—	298	1	no	—
66	C₂³	—	298	2	no	—
67	C₂³	—	298	2	no	—
68	C₂³	—	298	1	no	—
69	C₂³	—	149	2	no	—
70	C₂³	C₂²×D₁₄₉	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	298	2	no	—
76	C₂×C₄	—	298	1	no	—
77	C₂×C₄	—	298	2	no	—
78	C₂×C₄	—	298	2	no	—
79	C₂×C₄	—	298	2	no	—
80	C₂×C₄	D₅₉₆	1	2	yes	—
81	C₂²	—	298	2	no	—
82	C₂²	—	298	4	no	—
83	C₂²	—	596	2	no	—
84	C₂²	—	596	1	no	—
85	C₂²	—	596	1	no	—
86	C₂²	D₄×D₁₄₉	1	1	yes	characteristic
87	C₂²	C₂×D₅₉₆	1	1	yes	characteristic
88	C₂²	#14558735	1	2	yes	—
89	C₂²	#14558736	1	2	yes	—
90	C₂²	#14558737	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	4	2	no	—
93	C₄	—	596	2	no	—
94	C₄	—	596	1	no	—
95	C₂	—	596	2	no	—
96	C₂	#18011886	1	1	yes	characteristic
97	C₂	#18011893	1	2	yes	—
98	C₂	#18011895	1	1	yes	characteristic
99	C₂	#18011899	1	1	yes	characteristic
100	C₂	#18011906	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊Dic₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂×#14558713

C₂

yes

maximal, characteristic

C₂×#14558713

C₂

yes

maximal

#18011818

C₂

yes

maximal, complemented

#95×C₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

characteristic

C₂²×Dic₁₄₉

C₂²

yes

—

C₄⋊Dic₁₄₉

—

#14558713

—

#14558713

—

C₂²×C₄×C₁₄₉

C₂²

yes

—

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

D₄

yes

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂³×C₁₄₉

C₂³

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

D₄

yes

—

C₂²×C₁₄₉

C₂×D₄

yes

characteristic

C₂²×C₁₄₉

C₂×D₄

yes

characteristic

C₂²×C₁₄₉

#41

yes

—

C₂²×C₁₄₉

#41

yes

—

C₂²×C₁₄₉

#41

yes

characteristic

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

—

Dic₁₄₉

—

Dic₁₄₉

—

C₂×C₁₄₉

#121

yes

characteristic

C₂×C₁₄₉

#123

yes

—

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

—

D₁₄₉

—

C₁₄₉

#397

yes

characteristic, complemented, Sylow

#397

—

149

maximal, Sylow

C₂×C₄⋊C₄

—

149

—

C₂×C₂²⋊C₄

—

149

—

C₂×C₂²⋊C₄

—

149

—

#95

—

149

—

#95

D₁₄₉

yes

characteristic, complemented

C₂⁴

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×D₁₄₉

yes

—

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₄⋊C₄

—

298

—

C₂²⋊C₄

—

298

—

C₂²⋊C₄

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

149

—

C₂³

C₂²×D₁₄₉

yes

characteristic

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

D₅₉₆

yes

—

C₂²

—

298

—

C₂²

—

298

—

C₂²

—

596

—

C₂²

—

596

—

C₂²

—

596

—

C₂²

D₄×D₁₄₉

yes

characteristic

C₂²

C₂×D₅₉₆

yes

characteristic

C₂²

#14558735

yes

—

C₂²

#14558736

yes

—

C₂²

#14558737

yes

characteristic

C₄

—

C₄

—

C₄

—

596

—

C₄

—

596

—

C₂

—

596

—

C₂

#18011886

yes

characteristic

C₂

#18011893

yes

—

C₂

yes

C₂

yes

100

C₂

#18011906

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₄₉
commutator, socle, cosocle	C₂³×C₁₄₉	C₂³
Fitting	#95×C₁₄₉	C₂
prime radical	C₂³×D₁₄₉	C₂²
hypercenter	#95	D₁₄₉
hypocenter	C₁₄₉	#397
LCS	G ▷ C₂³×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₄₉

commutator, socle, cosocle

C₂³×C₁₄₉

C₂³

Fitting

#95×C₁₄₉

C₂

prime radical

C₂³×D₁₄₉

C₂²

D₁₄₉

C₁₄₉

G ▷ C₂³×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
1. C₂×C₄⋊Dic₁₄₉	C₂	semidirect
4. #18011818	C₂	semidirect
5. #95×C₁₄₉	C₂	semidirect
50. C₁₄₉	#397	semidirect
56. #95	D₁₄₉	semidirect

H ≅ G/N

type

1. C₂×C₄⋊Dic₁₄₉

C₂

semidirect

4. #18011818

C₂

semidirect

5. #95×C₁₄₉

C₂

semidirect

50. C₁₄₉

#397

semidirect

56. #95

D₁₄₉

semidirect

Subgroups — #23749552

Conjugacy classes of subgroups

Complements