Group #22610913 — subgroups

Subgroups — #22610913

Order 9344.

244 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 97 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	#17988611	C₂	1	1	yes	maximal, characteristic
2	#17988433	C₂	1	1	yes	maximal, characteristic
3	#17988346	C₂	1	4	yes	maximal
4	#533×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×#11924012	C₂²	1	2	yes	—
6	C₂×C₄×Dic₇₃	C₂²	1	2	yes	—
7	C₄⋊#10596831	—	2	2	no	—
8	#14556498	—	2	2	no	—
9	C₄⋊Q₈×C₇₃	C₄	1	2	yes	complemented
10	#125×C₇₃	C₄	1	2	yes	complemented
11	C₂²⋊Q₈×C₇₃	—	2	2	no	—
12	C₄×Q₈×C₇₃	—	2	2	no	—
13	#117×C₇₃	C₂²	1	2	yes	—
14	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
15	C₂²×Dic₇₃	—	2	2	no	—
16	#11924012	—	2	4	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₄×Dic₇₃	—	2	2	no	—
19	C₄×Dic₇₃	Q₈	1	4	yes	complemented
20	C₂×Q₈×C₇₃	—	2	2	no	—
21	C₂²×C₄×C₇₃	D₄	1	2	yes	—
22	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
23	C₄⋊C₄×C₇₃	—	2	4	no	—
24	C₄⋊C₄×C₇₃	—	2	2	no	—
25	C₄⋊C₄×C₇₃	C₂×C₄	1	4	yes	—
26	C₂²⋊C₄×C₇₃	—	2	2	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	C₂³×C₇₃	C₂×D₄	1	1	yes	characteristic
32	Q₈×C₇₃	—	4	4	no	—
33	C₂×C₄×C₇₃	—	2	4	no	—
34	C₂×C₄×C₇₃	—	4	2	no	—
35	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
36	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
39	C₂×C₄×C₇₃	C₂×Q₈	1	2	yes	—
40	C₂×C₄×C₇₃	#41	1	2	yes	—
41	C₂×Dic₇₃	—	2	4	no	—
42	C₂×Dic₇₃	—	4	4	no	—
43	#10596831	—	4	2	no	—
44	C₂²×C₇₃	—	2	2	no	—
45	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
46	C₂²×C₇₃	C₂²⋊Q₈	1	2	yes	—
47	C₄×C₇₃	—	2	2	no	—
48	C₄×C₇₃	—	2	2	no	—
49	C₄×C₇₃	—	4	4	no	—
50	C₄×C₇₃	C₄×Q₈	1	2	yes	—
51	C₄×C₇₃	#124	1	1	yes	characteristic
52	C₄×C₇₃	C₄⋊Q₈	1	1	yes	characteristic
53	Dic₇₃	—	4	4	no	—
54	C₂×C₇₃	—	2	2	no	—
55	C₂×C₇₃	#391	1	1	yes	characteristic
56	C₂×C₇₃	#421	1	2	yes	—
57	#1995	—	73	1	no	maximal, Sylow
58	C₇₃	#1995	1	1	yes	characteristic, complemented, Sylow
59	#533	D₇₃	1	1	yes	characteristic
60	#423	—	73	1	no	—
61	#376	—	73	1	no	—
62	#339	—	73	4	no	—
63	C₂×M₁₆	—	73	2	no	—
64	C₄⋊Q₈	Dic₇₃	1	2	yes	complemented
65	#125	Dic₇₃	1	2	yes	complemented
66	C₂²⋊Q₈	—	2	2	no	—
67	C₄×Q₈	—	2	2	no	—
68	#117	C₂×D₇₃	1	2	yes	—
69	C₂×C₄²	—	73	2	no	—
70	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
71	C₄⋊C₈	—	146	2	no	—
72	#95	—	146	2	no	—
73	C₂×Q₈	—	2	2	no	—
74	C₂²×C₄	—	146	2	no	—
75	C₂²×C₄	C₂²⋊D₇₃	1	2	yes	—
76	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
77	M₁₆	—	146	4	no	—
78	C₂×C₈	—	146	2	no	—
79	C₄⋊C₄	—	2	4	no	—
80	C₄⋊C₄	—	2	2	no	—
81	C₄⋊C₄	C₂×Dic₇₃	1	4	yes	—
82	C₂²⋊C₄	—	2	2	no	—
83	C₄²	—	2	2	no	—
84	C₄²	—	73	4	no	—
85	C₄²	—	146	2	no	—
86	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
87	C₄²	C₂×Dic₇₃	1	1	yes	characteristic
88	C₄²	C₂²⋊D₇₃	1	2	yes	—
89	C₂³	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
90	Q₈	—	4	4	no	—
91	C₂×C₄	—	2	4	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	—	292	4	no	—
94	C₂×C₄	—	146	4	no	—
95	C₂×C₄	C₂²⋊Dic₇₃	1	2	yes	—
96	C₂×C₄	C₂²⋊Dic₇₃	1	2	yes	—
97	C₂×C₄	C₂²×Dic₇₃	1	1	yes	characteristic
98	C₂×C₄	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
99	C₂×C₄	Q₈×D₇₃	1	2	yes	—
100	C₂×C₄	#11924029	1	2	yes	—
101	C₈	—	292	2	no	—
102	C₂²	—	2	2	no	—
103	C₂²	C₂×C₂²⋊Dic₇₃	1	1	yes	characteristic
104	C₂²	#14556567	1	2	yes	—
105	C₄	—	2	2	no	—
106	C₄	—	2	2	no	—
107	C₄	—	4	4	no	—
108	C₄	—	292	4	no	—
109	C₄	Q₈×Dic₇₃	1	2	yes	—
110	C₄	#14556580	1	1	yes	characteristic
111	C₄	#14556589	1	1	yes	characteristic
112	C₂	—	2	2	no	—
113	C₂	#17988494	1	1	yes	characteristic
114	C₂	#17988604	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17988611

C₂

yes

maximal, characteristic

#17988433

C₂

yes

maximal, characteristic

#17988346

C₂

yes

maximal

#533×C₇₃

C₂

yes

maximal, characteristic

C₂×#11924012

C₂²

yes

—

C₂×C₄×Dic₇₃

C₂²

yes

—

C₄⋊#10596831

—

#14556498

—

C₄⋊Q₈×C₇₃

C₄

yes

complemented

#125×C₇₃

C₄

yes

complemented

C₂²⋊Q₈×C₇₃

—

C₄×Q₈×C₇₃

—

#117×C₇₃

C₂²

yes

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂²×Dic₇₃

—

#11924012

—

C₂×#10596831

—

C₄×Dic₇₃

—

C₄×Dic₇₃

Q₈

yes

complemented

C₂×Q₈×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₂²⋊C₄×C₇₃

—

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

C₂×C₄

yes

characteristic

C₄²×C₇₃

D₄

yes

—

C₂³×C₇₃

C₂×D₄

yes

characteristic

Q₈×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

—

C₂×Dic₇₃

—

#10596831

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂²×C₇₃

C₂²⋊Q₈

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

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

#421

yes

—

#1995

—

maximal, Sylow

C₇₃

#1995

yes

characteristic, complemented, Sylow

#533

D₇₃

yes

—

—

—

C₂×M₁₆

—

C₄⋊Q₈

Dic₇₃

yes

complemented

#125

Dic₇₃

yes

complemented

C₂²⋊Q₈

—

C₄×Q₈

—

#117

C₂×D₇₃

yes

—

C₂×C₄²

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

146

—

#95

—

146

—

C₂×Q₈

—

C₂²×C₄

—

146

—

C₂²×C₄

C₂²⋊D₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

M₁₆

—

146

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

C₂×Dic₇₃

yes

—

C₂²⋊C₄

—

C₄²

—

C₄²

—

C₄²

—

146

—

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂×Dic₇₃

yes

characteristic

C₄²

C₂²⋊D₇₃

yes

—

C₂³

C₂×C₂²⋊D₇₃

yes

characteristic

Q₈

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

146

—

C₂×C₄

C₂²⋊Dic₇₃

yes

—

C₂×C₄

C₂²⋊Dic₇₃

yes

—

C₂×C₄

C₂²×Dic₇₃

yes

characteristic

C₂×C₄

C₂×C₂²⋊D₇₃

yes

characteristic

C₂×C₄

Q₈×D₇₃

yes

—

100

C₂×C₄

#11924029

yes

—

101

C₈

—

292

—

102

C₂²

—

103

C₂²

C₂×C₂²⋊Dic₇₃

yes

characteristic

104

C₂²

#14556567

yes

—

105

C₄

—

106

C₄

—

107

C₄

—

108

C₄

—

292

—

109

C₄

Q₈×Dic₇₃

yes

—

110

C₄

#14556580

yes

characteristic

111

C₄

#14556589

yes

characteristic

112

C₂

—

113

C₂

#17988494

yes

characteristic

114

C₂

#17988604

yes

—

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₂²×C₄	C₂²×D₇₃
Fitting	#533×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#533	D₇₃
hypocenter	C₇₃	#1995
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₂²×C₄

C₂²×D₇₃

Fitting

#533×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #533

N	H ≅ G/N	type
9. C₄⋊Q₈×C₇₃	C₄	semidirect
10. #125×C₇₃	C₄	semidirect
19. C₄×Dic₇₃	Q₈	semidirect
58. C₇₃	#1995	semidirect
64. C₄⋊Q₈	Dic₇₃	semidirect
65. #125	Dic₇₃	semidirect

H ≅ G/N

type

9. C₄⋊Q₈×C₇₃

C₄

semidirect

10. #125×C₇₃

C₄

semidirect

19. C₄×Dic₇₃

Q₈

semidirect

58. C₇₃

#1995

semidirect

64. C₄⋊Q₈

Dic₇₃

semidirect

65. #125

Dic₇₃

semidirect

Subgroups — #22610913

Conjugacy classes of subgroups

Complements