Group #22627005 — subgroups

Subgroups — #22627005

Order 9344.

148 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 148 conjugacy classes of subgroups — too many to draw. Only its 51 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	#17989706	C₂	1	2	yes	maximal
2	C₄×#11924036	C₂	1	1	yes	maximal, characteristic
3	#14556688	C₄	1	4	yes	complemented
4	#14556687	—	2	2	no	—
5	#14556686	—	2	2	no	—
6	C₂×#11924036	C₄	1	1	yes	characteristic
7	C₂×#11924036	C₂²	1	1	yes	characteristic
8	C₄×#10596833	—	2	2	no	—
9	C₄²×D₇₃	C₄	1	1	yes	characteristic
10	#11924040	—	2	4	no	—
11	#11924036	—	2	1	no	—
12	#11924036	C₈	1	2	yes	—
13	#11924036	C₂×C₄	1	2	yes	—
14	#11924036	D₄	1	1	yes	characteristic
15	#11924036	Q₈	1	1	yes	characteristic
16	C₂×#10596833	—	2	1	no	—
17	C₂×#10596833	D₄	1	2	yes	—
18	C₂×C₄×D₇₃	—	2	1	no	—
19	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	C₄×Dic₇₃	—	2	1	no	—
21	C₄×Dic₇₃	C₈	1	1	yes	characteristic
22	C₄²×C₇₃	C₈	1	1	yes	characteristic
23	C₂²×D₇₃	M₁₆	1	1	yes	characteristic
24	C₂×C₄×C₇₃	—	2	1	no	—
25	C₂×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
26	C₂×Dic₇₃	—	2	1	no	—
27	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
28	C₄×D₇₃	—	2	4	no	—
29	C₄×D₇₃	C₄²	1	1	yes	characteristic
30	C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
31	C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
32	C₄×D₇₃	M₁₆	1	1	yes	characteristic
33	#10596833	—	2	2	no	—
34	#10596833	C₂²⋊C₄	1	2	yes	—
35	#10596833	C₄⋊C₄	1	2	yes	—
36	C₂²×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
37	C₂×D₇₃	—	2	2	no	—
38	C₂×D₇₃	#97	1	1	yes	characteristic
39	C₂×D₇₃	C₄⋊C₈	1	1	yes	characteristic
40	C₄×C₇₃	—	2	2	no	—
41	C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
42	C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
43	Dic₇₃	—	2	2	no	—
44	Dic₇₃	#95	1	1	yes	characteristic
45	Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
46	C₂×C₇₃	—	2	1	no	—
47	C₂×C₇₃	#336	1	1	yes	characteristic
48	D₇₃	—	2	1	no	—
49	D₇₃	#364	1	2	yes	—
50	#1376	—	73	1	no	maximal, Sylow
51	C₇₃	#1376	1	1	yes	characteristic, complemented, Sylow
52	C₂×M₃₂	—	73	2	no	—
53	C₂×C₄×C₈	—	73	1	no	—
54	C₂²×C₈	—	73	1	no	—
55	C₂²×C₈	—	73	1	no	—
56	C₂×C₄²	—	73	1	no	—
57	M₃₂	—	73	4	no	—
58	M₃₂	—	146	2	no	—
59	C₂×C₁₆	—	146	2	no	—
60	C₄×C₈	—	146	2	no	—
61	C₂²×C₄	—	73	1	no	—
62	C₂²×C₄	—	146	1	no	—
63	C₂×C₈	—	73	2	no	—
64	C₂×C₈	—	73	2	no	—
65	C₂×C₈	—	73	1	no	—
66	C₂×C₈	—	73	1	no	—
67	C₂×C₈	—	73	2	no	—
68	C₂×C₈	—	146	1	no	—
69	C₂×C₈	—	146	1	no	—
70	C₄²	—	73	1	no	—
71	C₄²	—	146	1	no	—
72	C₄²	#10596842	1	1	yes	characteristic
73	C₁₆	—	146	4	no	—
74	C₂³	—	73	1	no	—
75	C₂×C₄	—	2	1	no	—
76	C₂×C₄	—	73	1	no	—
77	C₂×C₄	—	73	1	no	—
78	C₂×C₄	—	73	1	no	—
79	C₂×C₄	—	73	1	no	—
80	C₂×C₄	—	73	1	no	—
81	C₂×C₄	—	146	4	no	—
82	C₂×C₄	—	146	1	no	—
83	C₂×C₄	C₂×#10596842	1	1	yes	characteristic
84	C₈	—	73	2	no	—
85	C₈	—	73	2	no	—
86	C₈	—	146	2	no	—
87	C₂²	—	73	1	no	—
88	C₂²	—	73	1	no	—
89	C₂²	—	146	2	no	—
90	C₂²	C₂²⋊#10596842	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	73	1	no	—
93	C₄	—	73	1	no	—
94	C₄	—	146	2	no	—
95	C₄	C₄×#10596842	1	1	yes	characteristic
96	C₄	C₄⋊#10596842	1	1	yes	characteristic
97	C₂	—	2	1	no	—
98	C₂	—	73	2	no	—
99	C₂	—	146	1	no	—
100	C₂	(C₂×#10596842)⋊C₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17989706

C₂

yes

maximal

C₄×#11924036

C₂

yes

maximal, characteristic

#14556688

C₄

yes

—

—

C₄

yes

characteristic

C₂×#11924036

C₂²

yes

characteristic

C₄×#10596833

—

C₄²×D₇₃

C₄

yes

—

—

C₈

yes

—

#11924036

C₂×C₄

yes

—

#11924036

D₄

yes

characteristic

#11924036

Q₈

yes

characteristic

C₂×#10596833

—

C₂×#10596833

D₄

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

—

C₄×Dic₇₃

C₈

yes

characteristic

C₄²×C₇₃

C₈

yes

characteristic

C₂²×D₇₃

M₁₆

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₈

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

C₄²

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

characteristic

C₄×D₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

M₁₆

yes

characteristic

#10596833

—

#10596833

C₂²⋊C₄

yes

—

#10596833

C₄⋊C₄

yes

—

C₂²×C₇₃

C₂²⋊C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#97

yes

characteristic

C₂×D₇₃

C₄⋊C₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

C₄×C₈

yes

characteristic

C₄×C₇₃

C₄⋊C₈

yes

characteristic

Dic₇₃

—

Dic₇₃

#95

yes

characteristic

Dic₇₃

C₂²⋊C₈

yes

characteristic

C₂×C₇₃

—

C₂×C₇₃

#336

yes

characteristic

D₇₃

—

D₇₃

#364

yes

—

#1376

—

maximal, Sylow

C₇₃

#1376

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂×C₄×C₈

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

—

M₃₂

—

M₃₂

—

146

—

C₂×C₁₆

—

146

—

C₄×C₈

—

146

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

—

146

—

C₄²

#10596842

yes

characteristic

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×#10596842

yes

characteristic

C₈

—

C₈

—

C₈

—

146

—

C₂²

—

C₂²

—

C₂²

—

146

—

C₂²

C₂²⋊#10596842

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

146

—

C₄

yes

C₄

yes

C₂

—

C₂

—

C₂

—

146

—

100

C₂

(C₂×#10596842)⋊C₄

yes

characteristic

	subgroup	G/H
center	C₄	C₄⋊#10596842
commutator	C₄×C₇₃	C₄×C₈
Frattini	C₂×C₄	C₂×#10596842
Fitting	C₄²×C₇₃	C₈
socle	C₂×C₇₃	#336
hypercenter	C₄²	#10596842
hypocenter	C₇₃	#1376
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

subgroup

G/H

center

C₄

C₄⋊#10596842

commutator

C₄×C₇₃

C₄×C₈

Frattini

C₂×C₄

C₂×#10596842

Fitting

C₄²×C₇₃

C₈

C₂×C₇₃

C₄²

C₇₃

G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₄ ◁ C₂×C₄ ◁ C₄²

N	H ≅ G/N	type
3. #14556688	C₄	semidirect
51. C₇₃	#1376	semidirect

H ≅ G/N

type

3. #14556688

C₄

semidirect

51. C₇₃

#1376

semidirect

Subgroups — #22627005

Conjugacy classes of subgroups

Complements