Group #22608556 — subgroups

Subgroups — #22608556

Order 9344.

196 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 59 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	#125×D₇₃	C₂	1	1	yes	maximal, characteristic
2	#17988642	C₂	1	2	yes	maximal
3	#17988329	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988328	C₂	1	2	yes	maximal, complemented
5	#330×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556583	C₂²	1	1	yes	characteristic
7	#14556582	C₄	1	2	yes	—
8	#14556581	—	2	2	no	—
9	C₄⋊C₄×D₇₃	—	2	2	no	—
10	C₄⋊C₄×D₇₃	C₄	1	2	yes	—
11	C₄²×D₇₃	C₂²	1	1	yes	characteristic
12	#14556520	—	2	2	no	—
13	#14556503	—	2	2	no	—
14	#14556502	C₂²	1	2	yes	—
15	#125×C₇₃	C₂²	1	1	yes	characteristic
16	#97×C₇₃	C₂²	1	2	yes	—
17	C₂×C₄×D₇₃	—	2	2	no	—
18	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×D₇₃	D₄	1	2	yes	—
20	C₂×#10596831	—	2	2	no	—
21	C₄⋊Dic₇₃	—	2	2	no	—
22	C₄⋊Dic₇₃	C₂×C₄	1	2	yes	—
23	#11924007	—	2	2	no	—
24	#11924007	—	2	2	no	—
25	#11924007	—	2	2	no	—
26	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
27	C₄×Dic₇₃	D₄	1	2	yes	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄⋊C₄×C₇₃	C₂×C₄	1	2	yes	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
38	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
39	C₄×D₇₃	—	2	2	no	—
40	C₄×D₇₃	—	4	2	no	—
41	C₄×D₇₃	—	4	4	no	—
42	C₈×C₇₃	—	4	2	no	—
43	#10596831	—	4	2	no	—
44	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
45	C₂×D₇₃	—	2	2	no	—
46	C₂×D₇₃	#101	1	2	yes	—
47	C₄×C₇₃	—	2	1	no	—
48	C₄×C₇₃	—	2	2	no	—
49	C₄×C₇₃	—	4	2	no	—
50	Dic₇₃	—	2	1	no	—
51	Dic₇₃	—	2	2	no	—
52	Dic₇₃	—	4	2	no	—
53	C₂×C₇₃	C₂×#101	1	1	yes	characteristic
54	C₂×C₇₃	#421	1	2	yes	—
55	D₇₃	—	2	2	no	—
56	#1534	—	73	1	no	maximal, Sylow
57	C₇₃	#1534	1	1	yes	characteristic, complemented, Sylow
58	C₂×#125	—	73	1	no	—
59	#432	—	73	2	no	—
60	#330	—	73	1	no	—
61	#330	—	73	2	no	—
62	#330	D₇₃	1	1	yes	characteristic, complemented
63	#125	—	73	2	no	—
64	#125	—	73	1	no	—
65	#125	—	146	2	no	—
66	#125	C₂×D₇₃	1	1	yes	characteristic
67	C₂×C₄⋊C₄	—	73	2	no	—
68	C₂×C₄⋊C₄	—	146	2	no	—
69	C₂×C₄²	—	73	1	no	—
70	C₄⋊C₈	—	146	2	no	—
71	C₂²⋊C₈	—	146	2	no	—
72	#97	—	73	2	no	—
73	#97	C₂×D₇₃	1	2	yes	—
74	C₂²×C₄	—	73	2	no	—
75	C₂²×C₄	—	73	1	no	—
76	C₂²×C₄	—	146	2	no	—
77	C₂×C₈	—	2	2	no	—
78	C₂×C₈	—	146	2	no	—
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	73	2	no	—
81	C₄⋊C₄	—	146	2	no	—
82	C₄⋊C₄	—	146	2	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	—	146	2	no	—
85	C₄⋊C₄	C₄×D₇₃	1	2	yes	—
86	C₄²	—	73	1	no	—
87	C₄²	—	73	2	no	—
88	C₄²	C₂²×D₇₃	1	1	yes	characteristic
89	C₂³	—	73	1	no	—
90	C₂×C₄	—	2	2	no	—
91	C₂×C₄	—	292	2	no	—
92	C₂×C₄	—	292	4	no	—
93	C₂×C₄	—	73	1	no	—
94	C₂×C₄	—	73	2	no	—
95	C₂×C₄	—	146	2	no	—
96	C₂×C₄	—	146	2	no	—
97	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
98	C₂×C₄	D₄×D₇₃	1	2	yes	—
99	C₈	—	4	2	no	—
100	C₈	—	292	2	no	—
101	C₂²	—	73	2	no	—
102	C₂²	—	146	2	no	—
103	C₂²	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
104	C₄	—	2	1	no	—
105	C₄	—	2	2	no	—
106	C₄	—	4	2	no	—
107	C₄	—	292	2	no	—
108	C₄	—	146	1	no	—
109	C₄	—	146	2	no	—
110	C₂	—	146	2	no	—
111	C₂	#101×D₇₃	1	1	yes	characteristic
112	C₂	#17988602	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#125×D₇₃

C₂

yes

maximal, characteristic

#17988642

C₂

yes

maximal

#17988329

C₂

yes

maximal, characteristic, complemented

#17988328

C₂

yes

maximal, complemented

#330×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556583

C₂²

yes

characteristic

#14556582

C₄

yes

—

#14556581

—

C₄⋊C₄×D₇₃

—

C₄⋊C₄×D₇₃

C₄

yes

—

C₄²×D₇₃

C₂²

yes

—

—

C₂²

yes

—

#125×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₂²

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₄

yes

—

#11924007

—

#11924007

—

#11924007

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

#101

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

C₂×#101

yes

characteristic

C₂×C₇₃

#421

yes

—

D₇₃

—

#1534

—

maximal, Sylow

C₇₃

#1534

yes

characteristic, complemented, Sylow

—

—

—

—

D₇₃

yes

characteristic, complemented

#125

—

#125

—

#125

—

146

—

#125

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

C₂×C₄⋊C₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

146

—

C₂²⋊C₈

—

146

—

#97

—

#97

C₂×D₇₃

yes

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

C₄×D₇₃

yes

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

292

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

146

—

C₂×C₄

—

146

—

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

C₂×C₄

D₄×D₇₃

yes

—

C₈

—

100

C₈

—

292

—

101

C₂²

—

102

C₂²

—

146

—

103

C₂²

C₂²⋊C₄×D₇₃

yes

characteristic

104

C₄

—

105

C₄

—

106

C₄

—

107

C₄

—

292

—

108

C₄

—

146

—

109

C₄

—

146

—

110

C₂

—

146

—

111

C₂

#101×D₇₃

yes

characteristic

112

C₂

#17988602

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#330×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#330	D₇₃
hypocenter	C₇₃	#1534
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#330×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
3. #17988329	C₂	semidirect
4. #17988328	C₂	semidirect
5. #330×C₇₃	C₂	semidirect
57. C₇₃	#1534	semidirect
62. #330	D₇₃	semidirect

H ≅ G/N

type

3. #17988329

C₂

semidirect

4. #17988328

C₂

semidirect

5. #330×C₇₃

C₂

semidirect

57. C₇₃

#1534

semidirect

62. #330

D₇₃

semidirect

Subgroups — #22608556

Conjugacy classes of subgroups

Complements