Group #22612094 — subgroups

Subgroups — #22612094

Order 9344.

124 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 47 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	#17988988	C₂	1	1	yes	maximal, characteristic
2	#17988681	C₂	1	1	yes	maximal, characteristic
3	#17988414	C₂	1	1	yes	maximal, characteristic
4	#17988405	C₂	1	1	yes	maximal, characteristic
5	#17988392	C₂	1	1	yes	maximal, characteristic
6	#17988390	C₂	1	1	yes	maximal, characteristic
7	#366×C₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×Dic₂₉₂	C₂²	1	1	yes	characteristic
9	#14556582	—	2	1	no	—
10	#14556556	—	2	1	no	—
11	C₂×#11924003	C₂²	1	1	yes	characteristic
12	#14556525	C₂²	1	1	yes	characteristic
13	#14556522	—	2	1	no	—
14	#14556514	—	2	1	no	—
15	C₈×Dic₇₃	C₂²	1	1	yes	characteristic
16	C₂×C₁₆×C₇₃	C₂²	1	1	yes	characteristic
17	#107×C₇₃	C₂²	1	1	yes	characteristic
18	#107×C₇₃	C₂²	1	1	yes	characteristic
19	C₂×Dic₁₄₆	—	2	1	no	—
20	Dic₂₉₂	—	2	1	no	—
21	Dic₂₉₂	Q₈	1	2	yes	—
22	C₂×#10596831	D₄	1	1	yes	characteristic
23	C₄⋊Dic₇₃	—	2	1	no	—
24	C₄⋊Dic₇₃	—	4	1	no	—
25	#11924007	—	4	1	no	—
26	#11924007	—	4	1	no	—
27	C₄×Dic₇₃	—	4	1	no	—
28	C₄×Dic₇₃	D₄	1	1	yes	characteristic
29	#11924003	—	2	1	no	—
30	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
31	C₄⋊C₄×C₇₃	—	2	1	no	—
32	C₄⋊C₄×C₇₃	—	2	1	no	—
33	C₁₆×C₇₃	—	2	1	no	—
34	C₂×C₄×C₇₃	—	4	1	no	—
35	C₂×C₄×C₇₃	—	4	1	no	—
36	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
37	C₂×Dic₇₃	—	4	1	no	—
38	C₂×Dic₇₃	—	4	1	no	—
39	C₂×Dic₇₃	D₈	1	1	yes	characteristic
40	C₂×Dic₇₃	D₈	1	1	yes	characteristic
41	Dic₁₄₆	—	2	2	no	—
42	Dic₁₄₆	—	4	1	no	—
43	C₈×C₇₃	C₂×Q₈	1	1	yes	characteristic
44	C₈×C₇₃	#41	1	1	yes	characteristic
45	#10596831	—	2	1	no	—
46	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
47	C₄×C₇₃	—	8	1	no	—
48	C₄×C₇₃	—	8	1	no	—
49	C₄×C₇₃	C₂²⋊Q₈	1	1	yes	characteristic
50	C₄×C₇₃	#137	1	1	yes	characteristic
51	Dic₇₃	—	2	1	no	—
52	Dic₇₃	—	2	1	no	—
53	Dic₇₃	—	4	2	no	—
54	Dic₇₃	—	8	1	no	—
55	C₂×C₇₃	#474	1	1	yes	characteristic
56	C₂×C₇₃	#508	1	1	yes	characteristic
57	C₂×C₇₃	#510	1	1	yes	characteristic
58	#2229	—	73	1	no	maximal, Sylow
59	C₇₃	#2229	1	1	yes	characteristic, complemented, Sylow
60	#499	—	73	1	no	—
61	C₄×Q₁₆	—	73	1	no	—
62	#367	—	73	1	no	—
63	#366	D₇₃	1	1	yes	characteristic
64	C₄⋊C₁₆	—	73	1	no	—
65	#358	—	73	1	no	—
66	#358	—	73	1	no	—
67	C₂×Q₁₆	—	73	1	no	—
68	#125	—	146	1	no	—
69	C₄×Q₈	—	146	1	no	—
70	C₂×C₁₆	—	73	1	no	—
71	C₂×C₁₆	C₂×D₇₃	1	1	yes	characteristic
72	#107	—	73	1	no	—
73	#107	C₂×D₇₃	1	1	yes	characteristic
74	#107	C₂×D₇₃	1	1	yes	characteristic
75	#106	—	146	1	no	—
76	#103	—	146	1	no	—
77	C₄×C₈	—	73	1	no	—
78	C₂×Q₈	—	146	1	no	—
79	Q₁₆	—	73	2	no	—
80	Q₁₆	—	146	1	no	—
81	C₂×C₈	—	73	1	no	—
82	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
83	C₄⋊C₄	—	2	1	no	—
84	C₄⋊C₄	—	2	1	no	—
85	C₄⋊C₄	—	292	1	no	—
86	C₄⋊C₄	—	292	1	no	—
87	C₄⋊C₄	—	292	1	no	—
88	C₄⋊C₄	—	146	1	no	—
89	C₄²	—	292	1	no	—
90	C₄²	—	73	1	no	—
91	C₁₆	—	2	1	no	—
92	C₁₆	—	146	1	no	—
93	Q₈	—	292	1	no	—
94	Q₈	—	146	2	no	—
95	C₂×C₄	—	4	1	no	—
96	C₂×C₄	—	4	1	no	—
97	C₂×C₄	—	292	1	no	—
98	C₂×C₄	—	292	1	no	—
99	C₂×C₄	—	73	1	no	—
100	C₂×C₄	—	73	1	no	—
101	C₂×C₄	D₄×D₇₃	1	1	yes	characteristic
102	C₈	—	146	1	no	—
103	C₈	Q₈×D₇₃	1	1	yes	characteristic
104	C₈	#11924028	1	1	yes	characteristic
105	C₂²	D₈×D₇₃	1	1	yes	characteristic
106	C₄	—	8	1	no	—
107	C₄	—	8	1	no	—
108	C₄	—	292	2	no	—
109	C₄	—	584	1	no	—
110	C₄	—	146	1	no	—
111	C₄	—	146	1	no	—
112	C₄	#14556569	1	1	yes	characteristic
113	C₄	#14556623	1	1	yes	characteristic
114	C₂	#17988866	1	1	yes	characteristic
115	C₂	#17989016	1	1	yes	characteristic
116	C₂	#17989029	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988988

C₂

yes

maximal, characteristic

#17988681

C₂

yes

maximal, characteristic

#17988414

C₂

yes

maximal, characteristic

#17988405

C₂

yes

maximal, characteristic

#17988392

C₂

yes

maximal, characteristic

#17988390

C₂

yes

maximal, characteristic

#366×C₇₃

C₂

yes

maximal, characteristic

C₂×Dic₂₉₂

C₂²

yes

—

—

C₂²

yes

characteristic

#14556525

C₂²

yes

characteristic

#14556522

—

#14556514

—

C₈×Dic₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

characteristic

#107×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

Dic₂₉₂

—

Dic₂₉₂

Q₈

yes

—

C₂×#10596831

D₄

yes

characteristic

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

#11924007

—

#11924007

—

C₄×Dic₇₃

—

C₄×Dic₇₃

D₄

yes

characteristic

#11924003

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₁₆×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

D₈

yes

characteristic

C₂×Dic₇₃

D₈

yes

characteristic

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂×Q₈

yes

C₈×C₇₃

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂²⋊Q₈

yes

characteristic

C₄×C₇₃

#137

yes

characteristic

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

—

C₇₃

yes

characteristic, complemented, Sylow

#499

—

C₄×Q₁₆

—

#367

—

#366

D₇₃

yes

characteristic

C₄⋊C₁₆

—

#358

—

#358

—

C₂×Q₁₆

—

#125

—

146

—

C₄×Q₈

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

characteristic

#107

—

#107

C₂×D₇₃

yes

characteristic

#107

C₂×D₇₃

yes

characteristic

#106

—

146

—

#103

—

146

—

C₄×C₈

—

C₂×Q₈

—

146

—

Q₁₆

—

Q₁₆

—

146

—

C₂×C₈

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₄²

—

292

—

C₄²

—

C₁₆

—

C₁₆

—

146

—

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

100

C₂×C₄

—

101

C₂×C₄

D₄×D₇₃

yes

characteristic

102

C₈

—

146

—

103

C₈

Q₈×D₇₃

yes

characteristic

104

C₈

#11924028

yes

characteristic

105

C₂²

D₈×D₇₃

yes

characteristic

106

C₄

—

107

C₄

—

108

C₄

—

292

—

109

C₄

—

584

—

110

C₄

—

146

—

111

C₄

—

146

—

112

C₄

#14556569

yes

characteristic

113

C₄

#14556623

yes

characteristic

114

C₂

#17988866

yes

characteristic

115

C₂

#17989016

yes

characteristic

116

C₂

#17989029

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₇₃
commutator	C₂×C₈×C₇₃	C₂³
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	#366×C₇₃	C₂
socle	C₂²×C₇₃	C₂×D₈
hypercenter	#366	D₇₃
hypocenter	C₇₃	#2229
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #366

subgroup

G/H

center

C₂²

D₈×D₇₃

commutator

C₂×C₈×C₇₃

C₂³

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

#366×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 ◁ #366

N	H ≅ G/N	type
59. C₇₃	#2229	semidirect

H ≅ G/N

type

59. C₇₃

#2229

semidirect

Subgroups — #22612094

Conjugacy classes of subgroups

Complements