Group #22626267 — subgroups

Subgroups — #22626267

Order 9344.

160 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 76 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×#14556666	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556664	C₂	1	1	yes	maximal, characteristic
3	#17989508	C₂	1	2	yes	maximal, complemented
4	C₄⋊#11924031	C₂	1	2	yes	maximal, complemented
5	#17988544	C₂	1	1	yes	maximal, characteristic
6	#14556666	—	2	2	no	—
7	#14556664	—	2	2	no	—
8	C₂×#11924031	C₂²	1	2	yes	—
9	C₂×#11924031	C₂²	1	2	yes	—
10	C₂×#11924011	C₄	1	1	yes	characteristic
11	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
12	#14556548	C₄	1	1	yes	characteristic
13	#14556501	C₄	1	1	yes	characteristic
14	C₄×#10596831	C₂²	1	1	yes	characteristic
15	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
16	#97×C₇₃	C₄	1	1	yes	characteristic
17	#11924031	—	2	2	no	—
18	#11924031	—	2	2	no	—
19	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
20	#11924011	—	2	2	no	—
21	C₂×#10596831	C₂×C₄	1	1	yes	characteristic
22	C₂×#10596831	C₂³	1	1	yes	characteristic
23	C₈×D₇₃	D₄	1	2	yes	—
24	C₈×D₇₃	Q₈	1	2	yes	—
25	#11924007	C₈	1	2	yes	—
26	#11924005	C₈	1	2	yes	—
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
31	C₂²×D₇₃	C₂×C₈	1	1	yes	characteristic
32	C₂×C₄×C₇₃	C₂×C₈	1	2	yes	—
33	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₂×Dic₇₃	C₂×C₈	1	2	yes	—
35	C₂×Dic₇₃	C₂×C₈	1	1	yes	characteristic
36	C₄×D₇₃	C₄⋊C₄	1	2	yes	—
37	C₄×D₇₃	M₁₆	1	2	yes	—
38	C₈×C₇₃	—	2	1	no	—
39	C₈×C₇₃	C₄⋊C₄	1	2	yes	—
40	#10596831	—	2	1	no	—
41	#10596831	C₂×D₄	1	1	yes	characteristic
42	#10596831	C₂×Q₈	1	1	yes	characteristic
43	C₂²×C₇₃	C₂²×C₈	1	1	yes	characteristic
44	C₂×D₇₃	—	2	2	no	—
45	C₂×D₇₃	C₄⋊C₈	1	2	yes	—
46	C₄×C₇₃	—	2	2	no	—
47	C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
49	Dic₇₃	—	2	2	no	—
50	Dic₇₃	C₄⋊C₈	1	2	yes	—
51	C₂×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
52	C₂×C₇₃	#504	1	2	yes	—
53	D₇₃	—	2	2	no	—
54	#2151	—	73	1	no	maximal, Sylow
55	C₇₃	#2151	1	1	yes	characteristic, complemented, Sylow
56	C₂×M₃₂	—	73	1	no	—
57	C₂²×C₁₆	—	73	1	no	—
58	#405	—	73	1	no	—
59	C₄⋊C₁₆	—	73	2	no	—
60	C₄⋊C₁₆	—	73	2	no	—
61	C₂×M₁₆	—	73	1	no	—
62	C₂²×C₈	—	73	1	no	—
63	#117	—	73	1	no	—
64	M₃₂	—	146	2	no	—
65	C₂×C₁₆	—	73	2	no	—
66	C₂×C₁₆	—	73	2	no	—
67	C₂×C₁₆	—	146	2	no	—
68	#97	—	73	1	no	—
69	#97	#64408	1	1	yes	characteristic
70	C₄×C₈	—	73	1	no	—
71	C₄×C₈	—	73	1	no	—
72	C₂²×C₄	—	73	1	no	—
73	M₁₆	—	146	2	no	—
74	C₂×C₈	—	73	1	no	—
75	C₂×C₈	—	73	2	no	—
76	C₂×C₈	—	73	2	no	—
77	C₂×C₈	—	73	1	no	—
78	C₂×C₈	C₂×#64408	1	1	yes	characteristic
79	C₂×C₈	C₂×#64408	1	1	yes	characteristic
80	C₄⋊C₄	—	73	2	no	—
81	C₂²⋊C₄	—	73	2	no	—
82	C₄²	—	73	1	no	—
83	C₄²	C₂×#64408	1	1	yes	characteristic
84	C₁₆	—	146	2	no	—
85	C₁₆	—	146	2	no	—
86	C₂³	—	73	1	no	—
87	C₂×C₄	—	73	1	no	—
88	C₂×C₄	—	73	2	no	—
89	C₂×C₄	—	73	2	no	—
90	C₂×C₄	—	73	2	no	—
91	C₂×C₄	#11924036	1	2	yes	—
92	C₂×C₄	C₂²×#64408	1	1	yes	characteristic
93	C₈	—	2	1	no	—
94	C₈	—	73	1	no	—
95	C₈	—	73	1	no	—
96	C₈	—	146	1	no	—
97	C₈	C₄⋊#64408	1	2	yes	—
98	C₂²	—	73	2	no	—
99	C₂²	—	146	2	no	—
100	C₂²	C₂×#11924036	1	1	yes	characteristic
101	C₄	—	2	2	no	—
102	C₄	—	73	2	no	—
103	C₄	—	146	2	no	—
104	C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
105	C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
106	C₂	—	146	2	no	—
107	C₂	#17989588	1	1	yes	characteristic
108	C₂	#17989646	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556666

C₂

yes

maximal, characteristic

C₂×#14556664

C₂

yes

maximal, characteristic

#17989508

C₂

yes

maximal, complemented

C₄⋊#11924031

C₂

yes

maximal, complemented

#17988544

C₂

yes

maximal, characteristic

#14556666

—

#14556664

—

C₂×#11924031

C₂²

yes

—

C₂×#11924031

C₂²

yes

—

C₂×#11924011

C₄

yes

characteristic

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556548

C₄

yes

characteristic

#14556501

C₄

yes

characteristic

C₄×#10596831

C₂²

yes

characteristic

C₈×Dic₇₃

C₂²

yes

characteristic

#97×C₇₃

C₄

yes

characteristic

#11924031

—

#11924031

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

#11924011

—

C₂×#10596831

C₂×C₄

yes

characteristic

C₂×#10596831

C₂³

yes

characteristic

C₈×D₇₃

D₄

yes

—

C₈×D₇₃

Q₈

yes

—

#11924007

C₈

yes

—

#11924005

C₈

yes

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₂²×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×C₇₃

C₂×C₈

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₇₃

C₂×C₈

yes

—

C₂×Dic₇₃

C₂×C₈

yes

characteristic

C₄×D₇₃

C₄⋊C₄

yes

—

C₄×D₇₃

M₁₆

yes

—

C₈×C₇₃

—

C₈×C₇₃

C₄⋊C₄

yes

—

#10596831

—

#10596831

C₂×D₄

yes

characteristic

#10596831

C₂×Q₈

yes

characteristic

C₂²×C₇₃

C₂²×C₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

C₄⋊C₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₄⋊C₄

yes

characteristic

C₄×C₇₃

C₂×M₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

C₄⋊C₈

yes

—

C₂×C₇₃

C₂×C₄⋊C₈

yes

characteristic

C₂×C₇₃

#504

yes

—

D₇₃

—

#2151

—

maximal, Sylow

C₇₃

#2151

yes

characteristic, complemented, Sylow

C₂×M₃₂

—

C₂²×C₁₆

—

#405

—

C₄⋊C₁₆

—

C₄⋊C₁₆

—

C₂×M₁₆

—

C₂²×C₈

—

#117

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

—

C₂×C₁₆

—

146

—

—

yes

C₄×C₈

—

C₄×C₈

—

C₂²×C₄

—

M₁₆

—

146

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

C₂×C₈

yes

C₂×C₈

yes

C₄⋊C₄

—

C₂²⋊C₄

—

C₄²

—

C₄²

C₂×#64408

yes

characteristic

C₁₆

—

146

—

C₁₆

—

146

—

C₂³

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

#11924036

yes

—

C₂×C₄

C₂²×#64408

yes

characteristic

C₈

—

C₈

—

C₈

—

C₈

—

146

—

C₈

C₄⋊#64408

yes

—

C₂²

—

C₂²

—

146

—

100

C₂²

C₂×#11924036

yes

characteristic

101

C₄

—

102

C₄

—

103

C₄

—

146

—

104

C₄

C₂×C₄⋊#64408

yes

characteristic

105

C₄

D₇₃⋊M₁₆

yes

characteristic

106

C₂

—

146

—

107

C₂

#17989588

yes

characteristic

108

C₂

#17989646

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#64408
commutator, socle	C₂²×C₇₃	C₂²×C₈
Fitting	#97×C₇₃	C₄
hypercenter	#97	#64408
hypocenter	C₇₃	#2151
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#64408

commutator, socle

C₂²×C₇₃

C₂²×C₈

Fitting

#97×C₇₃

C₄

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
3. #17989508	C₂	semidirect
4. C₄⋊#11924031	C₂	semidirect
55. C₇₃	#2151	semidirect

H ≅ G/N

type

3. #17989508

C₂

semidirect

4. C₄⋊#11924031

C₂

semidirect

55. C₇₃

#2151

semidirect

Subgroups — #22626267

Conjugacy classes of subgroups

Complements