Group #22612035 — subgroups

Subgroups — #22612035

Order 9344.

170 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 49 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×D₁₁₆₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#14556530	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988824	C₂	1	2	yes	maximal, complemented
4	#17988387	C₂	1	2	yes	maximal, complemented
5	#367×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₅₈₄	C₂²	1	2	yes	—
7	C₂×C₈×D₇₃	C₂²	1	1	yes	characteristic
8	#14556566	—	2	2	no	—
9	D₁₁₆₈	—	2	2	no	—
10	#14556530	—	2	2	no	—
11	C₂×#11924003	C₂²	1	1	yes	characteristic
12	#14556511	—	2	2	no	—
13	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
14	#107×C₇₃	C₂²	1	2	yes	—
15	C₂×D₂₉₂	—	2	2	no	—
16	C₂×D₂₉₂	—	4	2	no	—
17	C₂×C₄×D₇₃	D₄	1	1	yes	characteristic
18	D₅₈₄	—	2	2	no	—
19	D₅₈₄	—	2	2	no	—
20	C₂×#10596831	D₄	1	1	yes	characteristic
21	C₈×D₇₃	—	2	1	no	—
22	C₈×D₇₃	—	2	1	no	—
23	#11924005	—	4	2	no	—
24	#11924003	—	2	1	no	—
25	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
26	C₄⋊C₄×C₇₃	—	2	2	no	—
27	C₁₆×C₇₃	D₄	1	2	yes	complemented
28	C₂²×D₇₃	—	4	2	no	—
29	C₂²×D₇₃	D₈	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	4	2	no	—
31	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
32	C₂×Dic₇₃	D₈	1	1	yes	characteristic
33	D₂₉₂	—	4	2	no	—
34	D₂₉₂	—	4	2	no	—
35	D₂₉₂	—	8	4	no	—
36	C₄×D₇₃	—	2	1	no	—
37	C₄×D₇₃	—	2	1	no	—
38	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₈×C₇₃	#41	1	1	yes	characteristic
40	#10596831	—	2	1	no	—
41	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
42	C₂×D₇₃	—	2	1	no	—
43	C₂×D₇₃	—	2	2	no	—
44	C₂×D₇₃	—	8	2	no	—
45	C₂×D₇₃	—	8	2	no	—
46	C₂×D₇₃	—	8	2	no	—
47	C₄×C₇₃	—	8	2	no	—
48	C₄×C₇₃	#121	1	1	yes	characteristic
49	C₄×C₇₃	#135	1	1	yes	characteristic
50	Dic₇₃	—	2	1	no	—
51	C₂×C₇₃	#466	1	1	yes	characteristic
52	C₂×C₇₃	#509	1	2	yes	—
53	D₇₃	—	4	1	no	—
54	D₇₃	—	16	2	no	—
55	#2218	—	73	1	no	maximal, Sylow
56	C₇₃	#2218	1	1	yes	characteristic, complemented, Sylow
57	C₂×D₁₆	—	73	1	no	—
58	C₂×M₃₂	—	73	1	no	—
59	#466	—	73	2	no	—
60	#367	D₇₃	1	1	yes	characteristic, complemented
61	#357	—	73	2	no	—
62	C₂×D₈	—	73	2	no	—
63	C₂²×C₈	—	73	1	no	—
64	#121	—	146	2	no	—
65	D₁₆	—	146	2	no	—
66	M₃₂	—	146	2	no	—
67	C₂×C₁₆	—	73	1	no	—
68	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
69	#107	C₂×D₇₃	1	2	yes	—
70	#102	—	146	2	no	—
71	C₂×D₄	—	292	2	no	—
72	C₂×D₄	—	146	2	no	—
73	C₂²×C₄	—	73	1	no	—
74	D₈	—	146	2	no	—
75	D₈	—	146	2	no	—
76	C₂×C₈	—	73	1	no	—
77	C₂×C₈	—	146	1	no	—
78	C₂×C₈	—	146	1	no	—
79	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
80	C₄⋊C₄	—	2	2	no	—
81	C₂²⋊C₄	—	292	2	no	—
82	C₁₆	—	146	1	no	—
83	C₁₆	D₂₉₂	1	2	yes	complemented
84	C₂³	—	292	2	no	—
85	C₂³	—	73	1	no	—
86	D₄	—	292	2	no	—
87	D₄	—	292	2	no	—
88	D₄	—	584	4	no	—
89	C₂×C₄	—	4	2	no	—
90	C₂×C₄	—	73	1	no	—
91	C₂×C₄	—	146	1	no	—
92	C₂×C₄	—	146	1	no	—
93	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
94	C₈	—	146	1	no	—
95	C₈	C₂×D₂₉₂	1	1	yes	characteristic
96	C₈	#11924029	1	1	yes	characteristic
97	C₂²	—	584	2	no	—
98	C₂²	—	584	2	no	—
99	C₂²	—	584	2	no	—
100	C₂²	—	146	2	no	—
101	C₂²	—	146	1	no	—
102	C₂²	D₈×D₇₃	1	1	yes	characteristic
103	C₄	—	8	2	no	—
104	C₄	—	146	1	no	—
105	C₄	#14556566	1	1	yes	characteristic
106	C₄	#14556614	1	1	yes	characteristic
107	C₂	—	292	1	no	—
108	C₂	—	1168	2	no	—
109	C₂	#17988824	1	1	yes	characteristic
110	C₂	#17989024	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₁₁₆₈

C₂

yes

maximal, characteristic, complemented

C₂×#14556530

C₂

yes

maximal, characteristic, complemented

#17988824

C₂

yes

maximal, complemented

#17988387

C₂

yes

maximal, complemented

#367×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×D₅₈₄

C₂²

yes

—

C₂×C₈×D₇₃

C₂²

yes

characteristic

#14556566

—

D₁₁₆₈

—

#14556530

—

C₂×#11924003

C₂²

yes

characteristic

#14556511

—

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×C₄×D₇₃

D₄

yes

characteristic

D₅₈₄

—

D₅₈₄

—

C₂×#10596831

D₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

#11924005

—

#11924003

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

D₄

yes

complemented

C₂²×D₇₃

—

C₂²×D₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

C₂×D₄

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

#466

yes

characteristic

C₂×C₇₃

#509

yes

—

D₇₃

—

D₇₃

—

#2218

—

maximal, Sylow

C₇₃

#2218

yes

characteristic, complemented, Sylow

C₂×D₁₆

—

C₂×M₃₂

—

#466

—

#367

D₇₃

yes

characteristic, complemented

#357

—

C₂×D₈

—

C₂²×C₈

—

#121

—

146

—

D₁₆

—

146

—

M₃₂

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#107

C₂×D₇₃

yes

—

#102

—

146

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂²×C₄

—

D₈

—

146

—

D₈

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

292

—

C₁₆

—

146

—

C₁₆

D₂₉₂

yes

complemented

C₂³

—

292

—

C₂³

—

D₄

—

292

—

D₄

—

292

—

D₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

characteristic

C₈

—

146

—

C₈

C₂×D₂₉₂

yes

characteristic

C₈

#11924029

yes

characteristic

C₂²

—

584

—

C₂²

—

584

—

C₂²

—

584

—

100

C₂²

—

146

—

101

C₂²

—

146

—

102

C₂²

D₈×D₇₃

yes

characteristic

103

C₄

—

104

C₄

—

146

—

105

C₄

#14556566

yes

characteristic

106

C₄

#14556614

yes

characteristic

107

C₂

—

292

—

108

C₂

—

1168

—

109

C₂

#17988824

yes

characteristic

110

C₂

#17989024

yes

—

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#367×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#367	D₇₃
hypocenter	C₇₃	#2218
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#367×C₇₃

C₂

socle

C₂²×C₇₃

C₂×D₈

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #367

N	H ≅ G/N	type
1. C₂×D₁₁₆₈	C₂	semidirect
2. C₂×#14556530	C₂	semidirect
3. #17988824	C₂	semidirect
4. #17988387	C₂	semidirect
5. #367×C₇₃	C₂	semidirect
27. C₁₆×C₇₃	D₄	semidirect
56. C₇₃	#2218	semidirect
60. #367	D₇₃	semidirect
83. C₁₆	D₂₉₂	semidirect

H ≅ G/N

type

1. C₂×D₁₁₆₈

C₂

semidirect

2. C₂×#14556530

C₂

semidirect

3. #17988824

C₂

semidirect

4. #17988387

C₂

semidirect

5. #367×C₇₃

C₂

semidirect

27. C₁₆×C₇₃

D₄

semidirect

56. C₇₃

#2218

semidirect

60. #367

D₇₃

semidirect

83. C₁₆

D₂₉₂

semidirect

Subgroups — #22612035

Conjugacy classes of subgroups

Complements