Group #22609788 — subgroups

Subgroups — #22609788

Order 9344.

260 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 141 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×C₄⋊#10596831	C₂	1	2	yes	maximal
2	C₂×#14556502	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10596831	C₂	1	1	yes	maximal, characteristic
4	#17988342	C₂	1	2	yes	maximal
5	#376×C₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10596831	C₂²	1	2	yes	—
7	C₂²×#10596831	C₂²	1	2	yes	—
8	C₄⋊#10596831	C₄	1	8	yes	complemented
9	#14556502	—	2	2	no	—
10	C₄×#10596831	—	2	2	no	—
11	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
12	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₇₃	C₂²	1	1	yes	characteristic
14	#95×C₇₃	C₄	1	4	yes	—
15	C₂×#10596831	—	2	2	no	—
16	C₂×#10596831	—	2	2	no	—
17	C₂×#10596831	—	2	2	no	—
18	C₂×#10596831	—	2	2	no	—
19	C₂×#10596831	C₂×C₄	1	4	yes	—
20	C₂×#10596831	C₂×C₄	1	4	yes	—
21	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
22	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
23	C₂²×C₄×C₇₃	C₂×C₄	1	2	yes	—
24	C₂²×C₄×C₇₃	C₂³	1	1	yes	characteristic
25	C₄²×C₇₃	—	2	2	no	—
26	C₄²×C₇₃	C₂×C₄	1	4	yes	—
27	C₄²×C₇₃	D₄	1	2	yes	—
28	C₄²×C₇₃	Q₈	1	2	yes	—
29	C₂³×C₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×C₄×C₇₃	—	2	4	no	—
31	C₂×C₄×C₇₃	—	2	4	no	—
32	C₂×C₄×C₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	—	2	4	no	—
34	C₂×C₄×C₇₃	C₄²	1	4	yes	—
35	C₂×C₄×C₇₃	C₄⋊C₄	1	4	yes	—
36	C₂×C₄×C₇₃	C₂²×C₄	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×Q₈	1	1	yes	characteristic
39	C₂×C₄×C₇₃	#41	1	2	yes	—
40	#10596831	—	2	4	no	—
41	#10596831	—	2	4	no	—
42	C₂²×C₇₃	C₂×C₄²	1	1	yes	characteristic
43	C₂²×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
44	C₂²×C₇₃	#117	1	1	yes	characteristic
45	C₂²×C₇₃	#131	1	4	yes	—
46	C₄×C₇₃	—	2	4	no	—
47	C₄×C₇₃	—	2	4	no	—
48	C₄×C₇₃	—	4	2	no	—
49	C₄×C₇₃	C₄×D₄	1	2	yes	—
50	C₄×C₇₃	C₄×Q₈	1	2	yes	—
51	C₂×C₇₃	C₄×C₄⋊C₄	1	1	yes	characteristic
52	C₂×C₇₃	#405	1	2	yes	—
53	C₂×C₇₃	#424	1	2	yes	—
54	C₂×C₇₃	#433	1	2	yes	—
55	#1768	—	73	1	no	maximal, Sylow
56	C₇₃	#1768	1	1	yes	characteristic, complemented, Sylow
57	C₂×C₄⋊C₈	—	73	2	no	—
58	C₂×#97	—	73	1	no	—
59	C₂×C₄×C₈	—	73	1	no	—
60	#376	D₇₃	1	1	yes	characteristic
61	#336	—	73	2	no	—
62	C₂²×C₈	—	73	2	no	—
63	C₂²×C₈	—	73	2	no	—
64	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₇₃	1	1	yes	characteristic
67	C₄⋊C₈	—	73	8	no	—
68	#97	—	146	2	no	—
69	C₄×C₈	—	146	2	no	—
70	#95	Dic₇₃	1	4	yes	—
71	C₂²×C₄	C₂×Dic₇₃	1	2	yes	—
72	C₂²×C₄	C₂×Dic₇₃	1	2	yes	—
73	C₂²×C₄	C₂×Dic₇₃	1	2	yes	—
74	C₂²×C₄	C₂²×D₇₃	1	1	yes	characteristic
75	C₂×C₈	—	73	4	no	—
76	C₂×C₈	—	73	4	no	—
77	C₂×C₈	—	146	2	no	—
78	C₂×C₈	—	146	2	no	—
79	C₂×C₈	—	146	2	no	—
80	C₂×C₈	—	146	2	no	—
81	C₄²	—	2	2	no	—
82	C₄²	Dic₁₄₆	1	2	yes	—
83	C₄²	C₄×D₇₃	1	4	yes	—
84	C₄²	D₂₉₂	1	2	yes	—
85	C₂³	C₂²×Dic₇₃	1	1	yes	characteristic
86	C₂×C₄	—	2	4	no	—
87	C₂×C₄	—	2	4	no	—
88	C₂×C₄	—	2	2	no	—
89	C₂×C₄	—	2	4	no	—
90	C₂×C₄	C₄×Dic₇₃	1	4	yes	—
91	C₂×C₄	C₄⋊Dic₇₃	1	4	yes	—
92	C₂×C₄	C₂×C₄×D₇₃	1	2	yes	—
93	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
94	C₂×C₄	C₂×Dic₁₄₆	1	1	yes	characteristic
95	C₂×C₄	#11924028	1	2	yes	—
96	C₈	—	146	4	no	—
97	C₈	—	146	4	no	—
98	C₂²	C₂×C₄×Dic₇₃	1	1	yes	characteristic
99	C₂²	C₂×C₄⋊Dic₇₃	1	1	yes	characteristic
100	C₂²	#14556550	1	1	yes	characteristic
101	C₂²	#14556598	1	4	yes	—
102	C₄	—	2	4	no	—
103	C₄	—	2	4	no	—
104	C₄	—	4	2	no	—
105	C₄	C₄×D₂₉₂	1	2	yes	—
106	C₄	C₄×Dic₁₄₆	1	2	yes	—
107	C₂	C₄×C₄⋊Dic₇₃	1	1	yes	characteristic
108	C₂	#17988543	1	2	yes	—
109	C₂	#17988614	1	2	yes	—
110	C₂	#17988648	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×C₄⋊#10596831

C₂

yes

maximal

C₂×#14556502

C₂

yes

maximal, characteristic

C₂×C₄×#10596831

C₂

yes

maximal, characteristic

#17988342

C₂

yes

maximal

#376×C₇₃

C₂

yes

maximal, characteristic

C₂²×#10596831

C₂²

yes

—

C₂²×#10596831

C₂²

yes

—

C₄⋊#10596831

C₄

yes

complemented

#14556502

—

C₄×#10596831

—

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

C₂×C₄²×C₇₃

C₂²

yes

characteristic

#95×C₇₃

C₄

yes

—

—

—

—

—

C₂×C₄

yes

—

C₂×#10596831

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂×C₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂×C₄

yes

—

C₄²×C₇₃

D₄

yes

—

C₄²×C₇₃

Q₈

yes

—

C₂³×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₄²

yes

—

C₂×C₄×C₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×C₄×C₇₃

C₂×Q₈

yes

characteristic

C₂×C₄×C₇₃

#41

yes

—

#10596831

—

#10596831

—

C₂²×C₇₃

C₂×C₄²

yes

characteristic

C₂²×C₇₃

C₂×C₄⋊C₄

yes

C₂²×C₇₃

yes

C₂²×C₇₃

yes

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₄×D₄

yes

—

C₄×C₇₃

C₄×Q₈

yes

—

C₂×C₇₃

C₄×C₄⋊C₄

yes

characteristic

C₂×C₇₃

#405

yes

—

C₂×C₇₃

#424

yes

—

C₂×C₇₃

#433

yes

—

#1768

—

maximal, Sylow

C₇₃

#1768

yes

characteristic, complemented, Sylow

C₂×C₄⋊C₈

—

C₂×#97

—

C₂×C₄×C₈

—

#376

D₇₃

yes

characteristic

#336

—

C₂²×C₈

—

C₂²×C₈

—

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₂×C₄²

C₂×D₇₃

yes

characteristic

C₄⋊C₈

—

#97

—

146

—

C₄×C₈

—

146

—

#95

Dic₇₃

yes

—

C₂²×C₄

C₂×Dic₇₃

yes

—

C₂²×C₄

C₂×Dic₇₃

yes

—

C₂²×C₄

C₂×Dic₇₃

yes

—

C₂²×C₄

C₂²×D₇₃

yes

characteristic

C₂×C₈

—

C₂×C₈

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₂×C₈

—

146

—

C₄²

—

C₄²

Dic₁₄₆

yes

—

C₄²

C₄×D₇₃

yes

—

C₄²

D₂₉₂

yes

—

C₂³

C₂²×Dic₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

C₄×Dic₇₃

yes

—

C₂×C₄

C₄⋊Dic₇₃

yes

—

C₂×C₄

C₂×C₄×D₇₃

yes

—

C₂×C₄

C₂×D₂₉₂

yes

characteristic

C₂×C₄

C₂×Dic₁₄₆

yes

characteristic

C₂×C₄

#11924028

yes

—

C₈

—

146

—

C₈

—

146

—

C₂²

C₂×C₄×Dic₇₃

yes

characteristic

C₂²

C₂×C₄⋊Dic₇₃

yes

characteristic

100

C₂²

#14556550

yes

characteristic

101

C₂²

#14556598

yes

—

102

C₄

—

103

C₄

—

104

C₄

—

105

C₄

C₄×D₂₉₂

yes

—

106

C₄

C₄×Dic₁₄₆

yes

—

107

C₂

C₄×C₄⋊Dic₇₃

yes

characteristic

108

C₂

#17988543

yes

—

109

C₂

#17988614

yes

—

110

C₂

#17988648

yes

—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×D₇₃
commutator	C₂²×C₇₃	C₂×C₄²
Fitting	#376×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×C₄
hypercenter	#376	D₇₃
hypocenter	C₇₃	#1768
LCS	G ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂²×C₄ ◁ #376

subgroup

G/H

center, Frattini

C₂²×C₄

C₂²×D₇₃

commutator

C₂²×C₇₃

C₂×C₄²

Fitting

#376×C₇₃

C₂

socle

C₂³×C₇₃

C₂²×C₄

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₇₃

C₁ ◁ C₂²×C₄ ◁ #376

N	H ≅ G/N	type
8. C₄⋊#10596831	C₄	semidirect
56. C₇₃	#1768	semidirect

H ≅ G/N

type

8. C₄⋊#10596831

C₄

semidirect

56. C₇₃

#1768

semidirect

Subgroups — #22609788

Conjugacy classes of subgroups

Complements