Group #22611634 — subgroups

Subgroups — C₂×#17988392 #22611634

Order 9344.

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

normal subgroups only

This group has 232 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	C₂²×Dic₂₉₂	C₂	1	1	yes	maximal, characteristic
2	C₂×#14556525	C₂	1	1	yes	maximal, characteristic
3	#17988392	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆×C₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂²×Dic₁₄₆	—	2	1	no	—
6	C₂×Dic₂₉₂	—	2	1	no	—
7	C₂×Dic₂₉₂	—	2	2	no	—
8	C₂×Dic₂₉₂	C₄	1	4	yes	complemented
9	C₂×Dic₂₉₂	C₂²	1	2	yes	—
10	C₂×C₄⋊Dic₇₃	—	2	1	no	—
11	#14556525	—	2	1	no	—
12	#14556525	C₂²	1	2	yes	—
13	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₁₆×C₇₃	—	2	2	no	—
15	C₂×C₁₆×C₇₃	C₂²	1	2	yes	—
16	C₂×Dic₁₄₆	—	2	4	no	—
17	C₂×Dic₁₄₆	—	2	2	no	—
18	C₂×Dic₁₄₆	—	4	1	no	—
19	C₂×Dic₁₄₆	—	4	2	no	—
20	C₂²×Dic₇₃	—	4	1	no	—
21	C₂²×Dic₇₃	—	4	1	no	—
22	Dic₂₉₂	—	2	4	no	—
23	Dic₂₉₂	—	2	2	no	—
24	Dic₂₉₂	C₂×C₄	1	4	yes	complemented
25	C₄⋊Dic₇₃	—	2	2	no	—
26	C₄⋊Dic₇₃	—	4	1	no	—
27	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
28	C₂×C₈×C₇₃	C₂×C₄	1	2	yes	—
29	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
30	C₂×C₈×C₇₃	D₄	1	2	yes	—
31	C₂×C₈×C₇₃	C₂³	1	1	yes	characteristic
32	C₁₆×C₇₃	—	2	2	no	—
33	C₂³×C₇₃	D₈	1	1	yes	characteristic
34	C₂×C₄×C₇₃	C₂²⋊C₄	1	2	yes	—
35	C₂×C₄×C₇₃	D₈	1	1	yes	characteristic
36	C₂×C₄×C₇₃	SD₁₆	1	2	yes	—
37	C₂×C₄×C₇₃	C₂×D₄	1	1	yes	characteristic
38	C₂×Dic₇₃	—	4	4	no	—
39	C₂×Dic₇₃	—	4	2	no	—
40	C₂×Dic₇₃	—	4	2	no	—
41	C₂×Dic₇₃	—	8	2	no	—
42	Dic₁₄₆	—	2	4	no	—
43	Dic₁₄₆	—	4	4	no	—
44	Dic₁₄₆	—	4	2	no	—
45	C₈×C₇₃	C₂²⋊C₄	1	2	yes	—
46	C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
47	C₈×C₇₃	C₂×D₄	1	1	yes	characteristic
48	C₂²×C₇₃	#102	1	2	yes	—
49	C₂²×C₇₃	SD₃₂	1	2	yes	—
50	C₂²×C₇₃	Q₃₂	1	2	yes	—
51	C₂²×C₇₃	C₂×D₈	1	1	yes	characteristic
52	C₄×C₇₃	#102	1	2	yes	—
53	C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
54	C₄×C₇₃	C₂×SD₁₆	1	1	yes	characteristic
55	Dic₇₃	—	4	4	no	—
56	Dic₇₃	—	8	2	no	—
57	C₂×C₇₃	#358	1	4	yes	complemented
58	C₂×C₇₃	C₂×#102	1	1	yes	characteristic
59	C₂×C₇₃	C₂×SD₃₂	1	1	yes	characteristic
60	C₂×C₇₃	C₂×Q₃₂	1	1	yes	characteristic
61	C₂×#358	—	73	1	no	maximal, Sylow
62	C₇₃	C₂×#358	1	1	yes	characteristic, complemented, Sylow
63	C₂²×Q₁₆	—	73	1	no	—
64	C₂²×C₁₆	D₇₃	1	1	yes	characteristic
65	C₂×#107	—	73	1	no	—
66	#358	—	73	4	no	—
67	C₂²×Q₈	—	146	1	no	—
68	C₂×Q₁₆	—	73	4	no	—
69	C₂×Q₁₆	—	73	2	no	—
70	C₂×Q₁₆	—	146	1	no	—
71	C₂×Q₁₆	—	146	2	no	—
72	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
73	C₂×C₄⋊C₄	—	146	1	no	—
74	C₂×C₁₆	—	2	2	no	—
75	C₂×C₁₆	C₂×D₇₃	1	2	yes	—
76	#107	—	73	2	no	—
77	#107	—	146	1	no	—
78	C₂×Q₈	—	292	1	no	—
79	C₂×Q₈	—	292	2	no	—
80	C₂×Q₈	—	146	4	no	—
81	C₂×Q₈	—	146	2	no	—
82	C₂²×C₄	—	292	1	no	—
83	C₂²×C₄	—	292	1	no	—
84	C₂²×C₄	D₂₉₂	1	1	yes	characteristic
85	Q₁₆	—	73	4	no	—
86	Q₁₆	—	146	4	no	—
87	Q₁₆	—	146	2	no	—
88	C₂×C₈	C₄×D₇₃	1	2	yes	—
89	C₂×C₈	D₂₉₂	1	1	yes	characteristic
90	C₂×C₈	C₂²⋊D₇₃	1	2	yes	—
91	C₂×C₈	C₂²×D₇₃	1	1	yes	characteristic
92	C₄⋊C₄	—	292	1	no	—
93	C₄⋊C₄	—	146	2	no	—
94	C₁₆	—	2	2	no	—
95	C₂³	D₅₈₄	1	1	yes	characteristic
96	Q₈	—	292	4	no	—
97	Q₈	—	292	2	no	—
98	Q₈	—	146	4	no	—
99	C₂×C₄	—	292	4	no	—
100	C₂×C₄	—	292	2	no	—
101	C₂×C₄	—	292	2	no	—
102	C₂×C₄	—	584	2	no	—
103	C₂×C₄	#11924005	1	2	yes	—
104	C₂×C₄	D₅₈₄	1	1	yes	characteristic
105	C₂×C₄	#11924017	1	2	yes	—
106	C₂×C₄	C₂×D₂₉₂	1	1	yes	characteristic
107	C₈	#11924005	1	2	yes	—
108	C₈	C₂×C₄×D₇₃	1	1	yes	characteristic
109	C₈	C₂×C₂²⋊D₇₃	1	1	yes	characteristic
110	C₂²	#14556513	1	2	yes	—
111	C₂²	#14556536	1	2	yes	—
112	C₂²	Dic₅₈₄	1	2	yes	—
113	C₂²	C₂×D₅₈₄	1	1	yes	characteristic
114	C₄	—	292	4	no	—
115	C₄	—	584	2	no	—
116	C₄	#14556513	1	2	yes	—
117	C₄	C₂×#11924005	1	1	yes	characteristic
118	C₄	C₂×#11924017	1	1	yes	characteristic
119	C₂	#17988392	1	4	yes	direct product factor
120	C₂	C₂×#14556513	1	1	yes	characteristic
121	C₂	C₂×#14556536	1	1	yes	characteristic
122	C₂	C₂×Dic₅₈₄	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×Dic₂₉₂

C₂

yes

maximal, characteristic

C₂×#14556525

C₂

yes

maximal, characteristic

#17988392

C₂

yes

maximal, direct product factor

C₂²×C₁₆×C₇₃

C₂

yes

maximal, characteristic

C₂²×Dic₁₄₆

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

—

C₂×Dic₂₉₂

C₄

yes

complemented

C₂×Dic₂₉₂

C₂²

yes

—

C₂×C₄⋊Dic₇₃

—

#14556525

—

#14556525

C₂²

yes

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₁₆×C₇₃

—

C₂×C₁₆×C₇₃

C₂²

yes

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

—

C₂²×Dic₇₃

—

C₂²×Dic₇₃

—

Dic₂₉₂

—

Dic₂₉₂

—

Dic₂₉₂

C₂×C₄

yes

complemented

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

—

C₂×C₈×C₇₃

C₂³

yes

characteristic

C₁₆×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

D₈

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

characteristic

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

—

Dic₁₄₆

—

Dic₁₄₆

—

Dic₁₄₆

—

C₈×C₇₃

C₂²⋊C₄

yes

—

C₈×C₇₃

C₂²×C₄

yes

characteristic

C₈×C₇₃

C₂×D₄

yes

characteristic

C₂²×C₇₃

#102

yes

—

C₂²×C₇₃

SD₃₂

yes

—

C₂²×C₇₃

Q₃₂

yes

—

C₂²×C₇₃

C₂×D₈

yes

characteristic

C₄×C₇₃

#102

yes

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₄×C₇₃

C₂×SD₁₆

yes

characteristic

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

C₂×SD₃₂

yes

characteristic

C₂×C₇₃

C₂×Q₃₂

yes

—

C₇₃

yes

characteristic, complemented, Sylow

C₂²×Q₁₆

—

C₂²×C₁₆

D₇₃

yes

characteristic

C₂×#107

—

#358

—

C₂²×Q₈

—

146

—

C₂×Q₁₆

—

C₂×Q₁₆

—

C₂×Q₁₆

—

146

—

C₂×Q₁₆

—

146

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

C₂×C₄⋊C₄

—

146

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₇₃

yes

—

#107

—

#107

—

146

—

C₂×Q₈

—

292

—

C₂×Q₈

—

292

—

C₂×Q₈

—

146

—

C₂×Q₈

—

146

—

C₂²×C₄

—

292

—

C₂²×C₄

—

292

—

C₂²×C₄

D₂₉₂

yes

characteristic

Q₁₆

—

Q₁₆

—

146

—

Q₁₆

—

146

—

C₂×C₈

C₄×D₇₃

yes

—

C₂×C₈

D₂₉₂

yes

characteristic

C₂×C₈

C₂²⋊D₇₃

yes

—

C₂×C₈

C₂²×D₇₃

yes

characteristic

C₄⋊C₄

—

292

—

C₄⋊C₄

—

146

—

C₁₆

—

C₂³

D₅₈₄

yes

characteristic

Q₈

—

292

—

Q₈

—

292

—

Q₈

—

146

—

C₂×C₄

—

292

—

100

C₂×C₄

—

292

—

101

C₂×C₄

—

292

—

102

C₂×C₄

—

584

—

103

C₂×C₄

#11924005

yes

—

104

C₂×C₄

D₅₈₄

yes

characteristic

105

C₂×C₄

#11924017

yes

—

106

C₂×C₄

C₂×D₂₉₂

yes

characteristic

107

C₈

#11924005

yes

—

108

C₈

C₂×C₄×D₇₃

yes

characteristic

109

C₈

C₂×C₂²⋊D₇₃

yes

characteristic

110

C₂²

#14556513

yes

—

111

C₂²

#14556536

yes

—

112

C₂²

Dic₅₈₄

yes

—

113

C₂²

C₂×D₅₈₄

yes

characteristic

114

C₄

—

292

—

115

C₄

—

584

—

116

C₄

#14556513

yes

—

117

C₄

C₂×#11924005

yes

characteristic

118

C₄

C₂×#11924017

yes

characteristic

119

C₂

#17988392

yes

direct product factor

120

C₂

C₂×#14556513

yes

characteristic

121

C₂

C₂×#14556536

yes

characteristic

122

C₂

C₂×Dic₅₈₄

yes

characteristic

	subgroup	G/H
center	C₂³	D₅₈₄
commutator	C₈×C₇₃	C₂²×C₄
Frattini	C₂×C₈	C₂²×D₇₃
Fitting	C₂²×C₁₆×C₇₃	C₂
socle	C₂³×C₇₃	D₈
hypercenter	C₂²×C₁₆	D₇₃
hypocenter	C₇₃	C₂×#358
LCS	G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

subgroup

G/H

center

C₂³

D₅₈₄

commutator

C₈×C₇₃

C₂²×C₄

Frattini

C₂×C₈

C₂²×D₇₃

Fitting

C₂²×C₁₆×C₇₃

C₂

socle

C₂³×C₇₃

D₈

hypercenter

C₂²×C₁₆

D₇₃

hypocenter

C₇₃

C₂×#358

LCS

G ▷ C₈×C₇₃ ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂³ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆

N	H ≅ G/N	type
3. #17988392	C₂	direct (N × H)
8. C₂×Dic₂₉₂	C₄	semidirect
24. Dic₂₉₂	C₂×C₄	semidirect
57. C₂×C₇₃	#358	semidirect
62. C₇₃	C₂×#358	semidirect
119. C₂	#17988392	direct (N × H)

H ≅ G/N

type

3. #17988392

C₂

direct (N × H)

8. C₂×Dic₂₉₂

C₄

semidirect

24. Dic₂₉₂

C₂×C₄

semidirect

57. C₂×C₇₃

#358

semidirect

62. C₇₃

C₂×#358

semidirect

119. C₂

#17988392

direct (N × H)

Subgroups — C₂×#17988392 #22611634

Conjugacy classes of subgroups

Complements

Subgroups — C2×#17988392 #22611634

Conjugacy classes of subgroups

Complements

Subgroups — C₂×#17988392 #22611634