Group #22609255 — subgroups

Subgroups — #22609255

Order 9344.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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	#17989335	C₂	1	1	yes	maximal, characteristic
2	#17988957	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988947	C₂	1	2	yes	maximal, complemented
4	#17988326	C₂	1	2	yes	maximal, complemented
5	#330×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#14556591	C₂²	1	1	yes	characteristic
7	#14556579	C₂²	1	2	yes	—
8	#14556576	—	2	2	no	—
9	#14556569	—	2	2	no	—
10	#14556566	—	2	2	no	—
11	#14556516	—	2	2	no	—
12	#14556514	—	2	2	no	—
13	#14556513	—	2	2	no	—
14	#14556502	C₂²	1	1	yes	characteristic
15	#125×C₇₃	C₂²	1	1	yes	characteristic
16	#97×C₇₃	C₂²	1	2	yes	—
17	C₂×Dic₁₄₆	—	2	1	no	—
18	C₂×Dic₁₄₆	D₄	1	2	yes	—
19	C₂×D₂₉₂	—	2	2	no	—
20	C₂×D₂₉₂	D₄	1	2	yes	—
21	C₂×C₄×D₇₃	—	2	2	no	—
22	C₂×#10596831	—	2	1	no	—
23	C₄⋊Dic₇₃	—	2	2	no	—
24	#11924007	—	2	2	no	—
25	#11924005	—	2	2	no	—
26	#11924005	—	2	2	no	—
27	#11924005	—	2	2	no	—
28	C₂×C₈×C₇₃	—	2	2	no	—
29	C₄⋊C₄×C₇₃	—	2	2	no	—
30	C₄⋊C₄×C₇₃	D₄	1	2	yes	—
31	C₄²×C₇₃	C₂³	1	1	yes	characteristic
32	C₂²×D₇₃	—	2	2	no	—
33	C₂×C₄×C₇₃	—	2	2	no	—
34	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
35	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
36	C₂×Dic₇₃	—	2	2	no	—
37	C₂×Dic₇₃	—	4	1	no	—
38	D₂₉₂	—	4	2	no	—
39	D₂₉₂	—	8	2	no	—
40	C₄×D₇₃	—	8	2	no	—
41	Dic₁₄₆	—	4	2	no	—
42	Dic₁₄₆	—	4	2	no	—
43	C₈×C₇₃	—	4	2	no	—
44	#10596831	—	4	1	no	—
45	C₂²×C₇₃	#120	1	1	yes	characteristic
46	C₂×D₇₃	—	4	2	no	—
47	C₂×D₇₃	—	4	2	no	—
48	C₂×D₇₃	—	4	2	no	—
49	C₄×C₇₃	—	2	1	no	—
50	C₄×C₇₃	—	2	2	no	—
51	C₄×C₇₃	—	4	2	no	—
52	Dic₇₃	—	4	2	no	—
53	Dic₇₃	—	8	1	no	—
54	C₂×C₇₃	#454	1	1	yes	characteristic
55	C₂×C₇₃	#455	1	2	yes	—
56	D₇₃	—	8	2	no	—
57	#1662	—	73	1	no	maximal, Sylow
58	C₇₃	#1662	1	1	yes	characteristic, complemented, Sylow
59	#562	—	73	1	no	—
60	#491	—	73	1	no	—
61	#489	—	73	2	no	—
62	#330	D₇₃	1	1	yes	characteristic, complemented
63	#329	—	73	2	no	—
64	C₄⋊Q₈	—	73	1	no	—
65	#125	C₂×D₇₃	1	1	yes	characteristic
66	#124	—	73	2	no	—
67	#123	—	146	2	no	—
68	C₂²⋊Q₈	—	146	2	no	—
69	#121	—	146	2	no	—
70	#103	—	146	2	no	—
71	#103	—	146	2	no	—
72	#102	—	146	2	no	—
73	#97	—	73	1	no	—
74	#97	C₂×D₇₃	1	2	yes	—
75	C₂×Q₈	—	73	2	no	—
76	C₂×Q₈	—	146	1	no	—
77	C₂×D₄	—	73	2	no	—
78	C₂×D₄	—	146	2	no	—
79	C₂²×C₄	—	146	2	no	—
80	C₂×C₈	—	2	2	no	—
81	C₂×C₈	—	146	1	no	—
82	C₄⋊C₄	—	2	2	no	—
83	C₄⋊C₄	—	146	2	no	—
84	C₄⋊C₄	—	146	2	no	—
85	C₄⋊C₄	D₂₉₂	1	2	yes	—
86	C₂²⋊C₄	—	146	2	no	—
87	C₂²⋊C₄	—	146	2	no	—
88	C₂²⋊C₄	—	146	2	no	—
89	C₄²	C₂²×D₇₃	1	1	yes	characteristic
90	C₂³	—	146	2	no	—
91	Q₈	—	292	2	no	—
92	Q₈	—	292	2	no	—
93	D₄	—	292	2	no	—
94	D₄	—	584	2	no	—
95	C₂×C₄	—	2	2	no	—
96	C₂×C₄	—	292	1	no	—
97	C₂×C₄	—	584	2	no	—
98	C₂×C₄	—	146	2	no	—
99	C₂×C₄	D₄×D₇₃	1	2	yes	—
100	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
101	C₈	—	4	2	no	—
102	C₈	—	292	1	no	—
103	C₂²	—	292	2	no	—
104	C₂²	—	292	2	no	—
105	C₂²	—	292	2	no	—
106	C₂²	#14556561	1	1	yes	characteristic
107	C₄	—	2	1	no	—
108	C₄	—	2	2	no	—
109	C₄	—	4	2	no	—
110	C₄	—	292	2	no	—
111	C₄	—	584	1	no	—
112	C₂	—	584	2	no	—
113	C₂	#17988762	1	1	yes	characteristic
114	C₂	#17988766	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989335

C₂

yes

maximal, characteristic

#17988957

C₂

yes

maximal, characteristic, complemented

#17988947

C₂

yes

maximal, complemented

#17988326

C₂

yes

maximal, complemented

#330×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556591

C₂²

yes

characteristic

#14556579

C₂²

yes

—

—

—

—

—

—

—

C₂²

yes

characteristic

#125×C₇₃

C₂²

yes

characteristic

#97×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

D₄

yes

—

C₂×D₂₉₂

—

C₂×D₂₉₂

D₄

yes

—

C₂×C₄×D₇₃

—

C₂×#10596831

—

C₄⋊Dic₇₃

—

—

—

—

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

D₄

yes

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

#120

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

#454

yes

characteristic

C₂×C₇₃

#455

yes

—

D₇₃

—

#1662

—

maximal, Sylow

C₇₃

#1662

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#329

—

C₄⋊Q₈

—

#125

C₂×D₇₃

yes

characteristic

#124

—

#123

—

146

—

C₂²⋊Q₈

—

146

—

#121

—

146

—

#103

—

146

—

#103

—

146

—

#102

—

146

—

#97

—

#97

C₂×D₇₃

yes

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂²×C₄

—

146

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₄⋊C₄

—

146

—

C₄⋊C₄

D₂₉₂

yes

—

C₂²⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₂²⋊C₄

—

146

—

C₄²

C₂²×D₇₃

yes

characteristic

C₂³

—

146

—

Q₈

—

292

—

Q₈

—

292

—

D₄

—

292

—

D₄

—

584

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

—

584

—

C₂×C₄

—

146

—

C₂×C₄

D₄×D₇₃

yes

—

100

C₂×C₄

C₂×D₂₉₂

yes

characteristic

101

C₈

—

102

C₈

—

292

—

103

C₂²

—

292

—

104

C₂²

—

292

—

105

C₂²

—

292

—

106

C₂²

#14556561

yes

characteristic

107

C₄

—

108

C₄

—

109

C₄

—

110

C₄

—

292

—

111

C₄

—

584

—

112

C₂

—

584

—

113

C₂

#17988762

yes

characteristic

114

C₂

#17988766

yes

—

	subgroup	G/H
center	C₂²	#14556561
commutator	C₄²×C₇₃	C₂³
Frattini	C₄²	C₂²×D₇₃
Fitting	#330×C₇₃	C₂
socle	C₂²×C₇₃	#120
hypercenter	#330	D₇₃
hypocenter	C₇₃	#1662
LCS	G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #330

subgroup

G/H

center

C₂²

#14556561

commutator

C₄²×C₇₃

C₂³

Frattini

C₄²

C₂²×D₇₃

Fitting

#330×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₄²×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #330

N	H ≅ G/N	type
2. #17988957	C₂	semidirect
3. #17988947	C₂	semidirect
4. #17988326	C₂	semidirect
5. #330×C₇₃	C₂	semidirect
58. C₇₃	#1662	semidirect
62. #330	D₇₃	semidirect

H ≅ G/N

type

2. #17988957

C₂

semidirect

3. #17988947

C₂

semidirect

4. #17988326

C₂

semidirect

5. #330×C₇₃

C₂

semidirect

58. C₇₃

#1662

semidirect

62. #330

D₇₃

semidirect

Subgroups — #22609255

Conjugacy classes of subgroups

Complements