Group #23749526 — subgroups

Subgroups — #23749526

Order 9536.

258 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 83 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×D₅₉₆	C₂	1	1	yes	maximal, characteristic
2	C₂×#14558713	C₂	1	4	yes	maximal, complemented
3	C₂×C₄×Dic₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄⋊C₄×C₁₄₉	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂³×D₁₄₉	C₂²	1	2	yes	—
6	C₂×D₅₉₆	—	2	2	no	—
7	C₂×D₅₉₆	—	2	2	no	—
8	C₂×D₅₉₆	C₄	1	4	yes	complemented
9	C₂²×Dic₁₄₉	C₂²	1	2	yes	—
10	#14558713	—	2	8	no	—
11	C₄×Dic₁₄₉	—	2	2	no	—
12	C₂²×C₄×C₁₄₉	C₂²	1	2	yes	—
13	C₂²×C₄×C₁₄₉	C₂²	1	1	yes	characteristic
14	C₄⋊C₄×C₁₄₉	—	2	2	no	—
15	C₂²×D₁₄₉	—	2	2	no	—
16	C₂²×D₁₄₉	—	2	2	no	—
17	C₂²×D₁₄₉	—	2	4	no	—
18	C₂²×D₁₄₉	—	2	4	no	—
19	C₂²×D₁₄₉	C₂×C₄	1	4	yes	—
20	D₅₉₆	—	2	8	no	—
21	C₂×Dic₁₄₉	—	2	2	no	—
22	C₂×Dic₁₄₉	—	2	2	no	—
23	C₂×Dic₁₄₉	D₄	1	4	yes	complemented
24	C₂³×C₁₄₉	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₁₄₉	—	2	2	no	—
26	C₂×C₄×C₁₄₉	—	2	4	no	—
27	C₂×C₄×C₁₄₉	C₂×C₄	1	2	yes	—
28	C₂×C₄×C₁₄₉	D₄	1	2	yes	—
29	C₂×C₄×C₁₄₉	D₄	1	2	yes	—
30	C₂²×C₁₄₉	C₂²×C₄	1	1	yes	characteristic
31	C₂²×C₁₄₉	C₂×D₄	1	2	yes	—
32	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
33	C₂²×C₁₄₉	C₂×D₄	1	1	yes	characteristic
34	C₂²×C₁₄₉	#41	1	2	yes	—
35	C₂×D₁₄₉	—	2	4	no	—
36	C₂×D₁₄₉	—	2	8	no	—
37	C₂×D₁₄₉	—	4	4	no	—
38	C₂×D₁₄₉	—	4	2	no	—
39	C₂×D₁₄₉	—	4	2	no	—
40	C₄×C₁₄₉	—	4	2	no	—
41	C₄×C₁₄₉	C₂²⋊C₄	1	4	yes	complemented
42	Dic₁₄₉	—	2	4	no	—
43	C₂×C₁₄₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
44	C₂×C₁₄₉	C₄×D₄	1	2	yes	—
45	C₂×C₁₄₉	#121	1	2	yes	—
46	C₂×C₁₄₉	#124	1	1	yes	characteristic
47	C₂×C₁₄₉	#127	1	1	yes	characteristic
48	D₁₄₉	—	4	4	no	—
49	C₁₄₉	#390	1	1	yes	characteristic, complemented, Sylow
50	#390	—	149	1	no	maximal, Sylow
51	C₂²×D₄	—	149	1	no	—
52	C₂×C₄⋊C₄	D₁₄₉	1	1	yes	characteristic, complemented
53	C₂×C₂²⋊C₄	—	149	4	no	—
54	C₂×C₄²	—	149	1	no	—
55	C₂⁴	—	149	2	no	—
56	C₂×D₄	—	298	2	no	—
57	C₂×D₄	—	298	2	no	—
58	C₂×D₄	—	149	4	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	—	2	2	no	—
63	C₂²⋊C₄	—	298	8	no	—
64	C₄²	—	298	2	no	—
65	C₂³	—	298	4	no	—
66	C₂³	—	298	2	no	—
67	C₂³	—	298	2	no	—
68	C₂³	—	298	4	no	—
69	C₂³	—	149	4	no	—
70	C₂³	C₂²×D₁₄₉	1	1	yes	characteristic
71	D₄	—	298	8	no	—
72	C₂×C₄	—	2	4	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	298	2	no	—
75	C₂×C₄	—	298	2	no	—
76	C₂×C₄	—	149	4	no	—
77	C₂×C₄	C₄×D₁₄₉	1	2	yes	—
78	C₂×C₄	C₂²⋊D₁₄₉	1	2	yes	—
79	C₂×C₄	D₅₉₆	1	2	yes	—
80	C₂²	—	298	4	no	—
81	C₂²	—	298	8	no	—
82	C₂²	—	596	2	no	—
83	C₂²	—	596	4	no	—
84	C₂²	—	596	2	no	—
85	C₂²	C₂×C₄×D₁₄₉	1	1	yes	characteristic
86	C₂²	D₄×D₁₄₉	1	2	yes	—
87	C₂²	C₂×C₂²⋊D₁₄₉	1	1	yes	characteristic
88	C₂²	C₂×D₅₉₆	1	1	yes	characteristic
89	C₂²	#14558737	1	2	yes	—
90	C₄	—	4	2	no	—
91	C₄	—	298	4	no	—
92	C₄	#14558713	1	4	yes	complemented
93	C₂	—	596	4	no	—
94	C₂	C₂×#14558713	1	1	yes	characteristic
95	C₂	#18011873	1	2	yes	—
96	C₂	#18011886	1	2	yes	—
97	C₂	#18011900	1	1	yes	characteristic
98	C₂	#18011907	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×D₅₉₆

C₂

yes

maximal, characteristic

C₂×#14558713

C₂

yes

maximal, complemented

C₂×C₄×Dic₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂×C₄⋊C₄×C₁₄₉

C₂

yes

maximal, characteristic, complemented

C₂³×D₁₄₉

C₂²

yes

—

C₂×D₅₉₆

—

C₂×D₅₉₆

—

C₂×D₅₉₆

C₄

yes

complemented

C₂²×Dic₁₄₉

C₂²

yes

—

#14558713

—

C₄×Dic₁₄₉

—

C₂²×C₄×C₁₄₉

C₂²

yes

—

C₂²×C₄×C₁₄₉

C₂²

yes

characteristic

C₄⋊C₄×C₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

—

C₂²×D₁₄₉

C₂×C₄

yes

—

D₅₉₆

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

—

C₂×Dic₁₄₉

D₄

yes

complemented

C₂³×C₁₄₉

C₂³

yes

characteristic

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

—

C₂×C₄×C₁₄₉

C₂×C₄

yes

—

C₂×C₄×C₁₄₉

D₄

yes

—

C₂×C₄×C₁₄₉

D₄

yes

—

C₂²×C₁₄₉

C₂²×C₄

yes

characteristic

C₂²×C₁₄₉

C₂×D₄

yes

—

C₂²×C₁₄₉

C₂×D₄

yes

characteristic

C₂²×C₁₄₉

C₂×D₄

yes

characteristic

C₂²×C₁₄₉

#41

yes

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₂×D₁₄₉

—

C₄×C₁₄₉

—

C₄×C₁₄₉

C₂²⋊C₄

yes

complemented

Dic₁₄₉

—

C₂×C₁₄₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₁₄₉

C₄×D₄

yes

—

C₂×C₁₄₉

#121

yes

—

C₂×C₁₄₉

yes

C₂×C₁₄₉

yes

D₁₄₉

—

C₁₄₉

#390

yes

characteristic, complemented, Sylow

#390

—

149

maximal, Sylow

C₂²×D₄

—

149

—

C₂×C₄⋊C₄

D₁₄₉

yes

characteristic, complemented

C₂×C₂²⋊C₄

—

149

—

C₂×C₄²

—

149

—

C₂⁴

—

149

—

C₂×D₄

—

298

—

C₂×D₄

—

298

—

C₂×D₄

—

149

—

C₂²×C₄

—

149

—

C₂²×C₄

C₂×D₁₄₉

yes

—

C₂²×C₄

C₂×D₁₄₉

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

298

—

C₄²

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

298

—

C₂³

—

149

—

C₂³

C₂²×D₁₄₉

yes

characteristic

D₄

—

298

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

298

—

C₂×C₄

—

298

—

C₂×C₄

—

149

—

C₂×C₄

C₄×D₁₄₉

yes

—

C₂×C₄

C₂²⋊D₁₄₉

yes

—

C₂×C₄

D₅₉₆

yes

—

C₂²

—

298

—

C₂²

—

298

—

C₂²

—

596

—

C₂²

—

596

—

C₂²

—

596

—

C₂²

C₂×C₄×D₁₄₉

yes

characteristic

C₂²

D₄×D₁₄₉

yes

—

C₂²

C₂×C₂²⋊D₁₄₉

yes

characteristic

C₂²

C₂×D₅₉₆

yes

characteristic

C₂²

#14558737

yes

—

C₄

—

C₄

—

298

—

C₄

#14558713

yes

complemented

C₂

—

596

—

C₂

C₂×#14558713

yes

characteristic

C₂

#18011873

yes

—

C₂

#18011886

yes

—

C₂

yes

C₂

yes

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₄₉
commutator	C₂²×C₁₄₉	C₂²×C₄
Fitting	C₂×C₄⋊C₄×C₁₄₉	C₂
socle, cosocle	C₂³×C₁₄₉	C₂³
prime radical	C₂²×D₅₉₆	C₂
hypercenter	C₂×C₄⋊C₄	D₁₄₉
hypocenter	C₁₄₉	#390
LCS	G ▷ C₂²×C₁₄₉ ▷ C₁₄₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₄₉

commutator

C₂²×C₁₄₉

C₂²×C₄

Fitting

C₂×C₄⋊C₄×C₁₄₉

C₂

socle, cosocle

C₂³×C₁₄₉

C₂³

prime radical

C₂²×D₅₉₆

C₂

hypercenter

C₂×C₄⋊C₄

D₁₄₉

C₁₄₉

G ▷ C₂²×C₁₄₉ ▷ C₁₄₉

C₁ ◁ C₂³ ◁ C₂×C₄⋊C₄

N	H ≅ G/N	type
2. C₂×#14558713	C₂	semidirect
3. C₂×C₄×Dic₁₄₉	C₂	semidirect
4. C₂×C₄⋊C₄×C₁₄₉	C₂	semidirect
8. C₂×D₅₉₆	C₄	semidirect
23. C₂×Dic₁₄₉	D₄	semidirect
41. C₄×C₁₄₉	C₂²⋊C₄	semidirect
49. C₁₄₉	#390	semidirect
52. C₂×C₄⋊C₄	D₁₄₉	semidirect
92. C₄	#14558713	semidirect

H ≅ G/N

type

2. C₂×#14558713

C₂

semidirect

3. C₂×C₄×Dic₁₄₉

C₂

semidirect

4. C₂×C₄⋊C₄×C₁₄₉

C₂

semidirect

8. C₂×D₅₉₆

C₄

semidirect

23. C₂×Dic₁₄₉

D₄

semidirect

41. C₄×C₁₄₉

C₂²⋊C₄

semidirect

49. C₁₄₉

#390

semidirect

52. C₂×C₄⋊C₄

D₁₄₉

semidirect

92. C₄

#14558713

semidirect

Subgroups — #23749526

Conjugacy classes of subgroups

Complements