Group #22610908 — subgroups

Subgroups — #22610908

Order 9344.

284 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 101 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	#17989144	C₂	1	1	yes	maximal, characteristic
2	#17988611	C₂	1	1	yes	maximal, characteristic
3	#17988347	C₂	1	4	yes	maximal
4	C₄³×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	C₂²	1	2	yes	—
6	#14556591	C₄	1	2	yes	complemented
7	#14556583	C₄	1	2	yes	complemented
8	#14556570	—	2	2	no	—
9	C₄×Dic₁₄₆	—	2	2	no	—
10	#14556550	C₂²	1	2	yes	—
11	C₄⋊#10596831	—	2	2	no	—
12	C₂×C₄²×C₇₃	—	2	2	no	—
13	C₂×C₄²×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂×Dic₁₄₆	—	2	2	no	—
16	#11924012	—	2	4	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₄⋊Dic₇₃	—	2	2	no	—
19	C₄⋊Dic₇₃	C₂×C₄	1	4	yes	—
20	#11924007	—	2	4	no	—
21	C₂²⋊Dic₇₃	—	2	2	no	—
22	C₄×Dic₇₃	—	2	2	no	—
23	C₂²×C₄×C₇₃	—	2	2	no	—
24	C₂²×C₄×C₇₃	D₄	1	2	yes	—
25	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
26	C₄²×C₇₃	—	2	8	no	—
27	C₄²×C₇₃	—	2	2	no	—
28	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
29	C₄²×C₇₃	C₂×C₄	1	1	yes	characteristic
30	C₄²×C₇₃	D₄	1	2	yes	—
31	C₄²×C₇₃	Q₈	1	4	yes	complemented
32	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	—	2	8	no	—
34	C₂×C₄×C₇₃	—	2	4	no	—
35	C₂×C₄×C₇₃	—	2	4	no	—
36	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
38	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
40	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
41	C₂×C₄×C₇₃	#41	1	2	yes	—
42	C₂×Dic₇₃	—	2	4	no	—
43	Dic₁₄₆	—	4	4	no	—
44	#10596831	—	4	2	no	—
45	C₂²×C₇₃	—	2	2	no	—
46	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
47	C₂²×C₇₃	C₂²⋊Q₈	1	2	yes	—
48	C₄×C₇₃	—	2	8	no	—
49	C₄×C₇₃	—	2	2	no	—
50	C₄×C₇₃	#104	1	4	yes	—
51	C₄×C₇₃	C₄×Q₈	1	2	yes	—
52	C₄×C₇₃	#124	1	1	yes	characteristic
53	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
54	Dic₇₃	—	4	4	no	—
55	C₂×C₇₃	—	2	2	no	—
56	C₂×C₇₃	#391	1	1	yes	characteristic
57	C₂×C₇₃	C₂×#104	1	2	yes	—
58	#1994	—	73	1	no	maximal, Sylow
59	C₇₃	#1994	1	1	yes	characteristic, complemented, Sylow
60	#533	—	73	1	no	—
61	#423	—	73	1	no	—
62	C₄³	D₇₃	1	1	yes	characteristic
63	#339	—	73	4	no	—
64	C₂×M₁₆	—	73	2	no	—
65	C₄⋊Q₈	—	73	2	no	—
66	#125	—	73	2	no	—
67	C₂²⋊Q₈	—	146	2	no	—
68	C₄×Q₈	—	146	2	no	—
69	#117	—	73	2	no	—
70	C₂×C₄²	—	2	2	no	—
71	C₂×C₄²	C₂×D₇₃	1	2	yes	—
72	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
73	C₄⋊C₈	—	146	2	no	—
74	C₂×Q₈	—	146	2	no	—
75	C₂²×C₄	—	2	2	no	—
76	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
77	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
78	M₁₆	—	146	4	no	—
79	C₂×C₈	—	146	2	no	—
80	C₄⋊C₄	—	73	4	no	—
81	C₄⋊C₄	—	146	4	no	—
82	C₄⋊C₄	—	146	2	no	—
83	C₂²⋊C₄	—	146	2	no	—
84	C₄²	—	2	8	no	—
85	C₄²	—	2	2	no	—
86	C₄²	—	146	2	no	—
87	C₄²	Dic₁₄₆	1	4	yes	complemented
88	C₄²	C₄×D₇₃	1	1	yes	characteristic
89	C₄²	C₄×D₇₃	1	1	yes	characteristic
90	C₄²	D₂₉₂	1	2	yes	—
91	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
92	Q₈	—	292	4	no	—
93	C₂×C₄	—	2	8	no	—
94	C₂×C₄	—	2	4	no	—
95	C₂×C₄	—	2	4	no	—
96	C₂×C₄	—	146	4	no	—
97	C₂×C₄	#11924005	1	2	yes	—
98	C₂×C₄	#11924005	1	2	yes	—
99	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
100	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
101	C₂×C₄	C₂×Dic₁₄₆	1	2	yes	—
102	C₂×C₄	#11924028	1	2	yes	—
103	C₈	—	292	2	no	—
104	C₂²	—	2	2	no	—
105	C₂²	C₂×#11924005	1	1	yes	characteristic
106	C₂²	#14556570	1	2	yes	—
107	C₄	—	2	8	no	—
108	C₄	—	2	2	no	—
109	C₄	—	292	4	no	—
110	C₄	#14556519	1	4	yes	—
111	C₄	C₄×Dic₁₄₆	1	2	yes	—
112	C₄	#14556579	1	1	yes	characteristic
113	C₄	#14556591	1	1	yes	characteristic
114	C₂	—	2	2	no	—
115	C₂	#17988493	1	1	yes	characteristic
116	C₂	C₂×#14556519	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989144

C₂

yes

maximal, characteristic

#17988611

C₂

yes

maximal, characteristic

#17988347

C₂

yes

maximal

C₄³×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

#14556591

C₄

yes

complemented

#14556583

C₄

yes

complemented

#14556570

—

C₄×Dic₁₄₆

—

#14556550

C₂²

yes

—

C₄⋊#10596831

—

C₂×C₄²×C₇₃

—

C₂×C₄²×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×Dic₁₄₆

—

#11924012

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

C₂²⋊Dic₇₃

—

C₄×Dic₇₃

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

Q₈

yes

complemented

C₂³×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

—

C₂×C₄×C₇₃

#41

yes

—

C₂×Dic₇₃

—

Dic₁₄₆

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

#104

yes

—

C₄×C₇₃

C₄×Q₈

yes

—

C₄×C₇₃

#124

yes

characteristic

C₄×C₇₃

C₄⋊Q₈

yes

characteristic

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

#391

yes

characteristic

C₂×C₇₃

C₂×#104

yes

—

#1994

—

maximal, Sylow

C₇₃

#1994

yes

characteristic, complemented, Sylow

#533

—

#423

—

C₄³

D₇₃

yes

characteristic

#339

—

C₂×M₁₆

—

C₄⋊Q₈

—

#125

—

C₂²⋊Q₈

—

146

—

C₄×Q₈

—

146

—

#117

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

Dic₁₄₆

yes

complemented

C₄²

C₄×D₇₃

yes

characteristic

C₄²

C₄×D₇₃

yes

characteristic

C₄²

D₂₉₂

yes

—

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

Q₈

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

#11924005

yes

—

C₂×C₄

#11924005

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

100

C₂×C₄

C₂×D₂₉₂

yes

characteristic

101

C₂×C₄

C₂×Dic₁₄₆

yes

—

102

C₂×C₄

#11924028

yes

—

103

C₈

—

292

—

104

C₂²

—

105

C₂²

C₂×#11924005

yes

characteristic

106

C₂²

#14556570

yes

—

107

C₄

—

108

C₄

—

109

C₄

—

292

—

110

C₄

#14556519

yes

—

111

C₄

C₄×Dic₁₄₆

yes

—

112

C₄

#14556579

yes

characteristic

113

C₄

#14556591

yes

characteristic

114

C₂

—

115

C₂

#17988493

yes

characteristic

116

C₂

C₂×#14556519

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×D₂₉₂
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	C₄³×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	C₄³	D₇₃
hypocenter	C₇₃	#1994
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄³

subgroup

G/H

center

C₂×C₄

C₂×D₂₉₂

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

C₄³×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

hypercenter

C₄³

D₇₃

hypocenter

C₇₃

#1994

LCS

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₄³

N	H ≅ G/N	type
6. #14556591	C₄	semidirect
7. #14556583	C₄	semidirect
31. C₄²×C₇₃	Q₈	semidirect
59. C₇₃	#1994	semidirect
87. C₄²	Dic₁₄₆	semidirect

H ≅ G/N

type

6. #14556591

C₄

semidirect

7. #14556583

C₄

semidirect

31. C₄²×C₇₃

Q₈

semidirect

59. C₇₃

#1994

semidirect

87. C₄²

Dic₁₄₆

semidirect

Subgroups — #22610908

Conjugacy classes of subgroups

Complements