Group #22608665 — subgroups

Subgroups — #22608665

Order 9344.

254 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 67 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	#17989138	C₂	1	1	yes	maximal, characteristic
2	#17988609	C₂	1	2	yes	maximal, complemented
3	#17988336	C₂	1	1	yes	maximal, characteristic, complemented
4	#17988330	C₂	1	2	yes	maximal, complemented
5	#333×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#11924029	C₄	1	2	yes	—
7	C₂×#11924011	—	2	2	no	—
8	#14556588	C₂²	1	1	yes	characteristic
9	#14556580	C₄	1	2	yes	—
10	#14556566	—	2	2	no	—
11	#14556553	—	2	2	no	—
12	C₄²×D₇₃	C₂²	1	1	yes	characteristic
13	C₄⋊#10596831	C₂²	1	2	yes	—
14	#14556520	—	2	2	no	—
15	C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic
16	C₄⋊C₈×C₇₃	C₂²	1	2	yes	—
17	#11924029	—	4	4	no	—
18	C₂×D₂₉₂	—	2	2	no	—
19	C₂×D₂₉₂	—	2	2	no	—
20	C₂×D₂₉₂	C₂×C₄	1	2	yes	—
21	C₂×C₄×D₇₃	—	2	2	no	—
22	C₂×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
23	C₂×C₄×D₇₃	D₄	1	2	yes	—
24	#11924011	—	4	4	no	—
25	C₂×#10596831	—	2	2	no	—
26	#11924005	—	2	4	no	—
27	C₄×Dic₇₃	C₂×C₄	1	1	yes	characteristic
28	C₄×Dic₇₃	D₄	1	2	yes	—
29	C₂×Q₈×C₇₃	C₂×C₄	1	2	yes	—
30	C₂×C₈×C₇₃	—	2	2	no	—
31	C₄⋊C₄×C₇₃	—	2	2	no	—
32	C₄²×C₇₃	C₂³	1	1	yes	characteristic
33	C₂²×D₇₃	—	2	2	no	—
34	C₂²×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
35	Q₈×C₇₃	—	4	2	no	—
36	C₂×C₄×C₇₃	—	2	2	no	—
37	C₂×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
38	C₂×C₄×C₇₃	C₂×D₄	1	2	yes	—
39	C₂×Dic₇₃	C₂²⋊C₄	1	2	yes	—
40	C₂×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
41	D₂₉₂	—	4	2	no	—
42	D₂₉₂	—	4	4	no	—
43	D₂₉₂	—	4	2	no	—
44	D₂₉₂	—	4	2	no	—
45	C₄×D₇₃	—	2	2	no	—
46	C₄×D₇₃	—	2	2	no	—
47	C₄×D₇₃	—	2	2	no	—
48	C₄×D₇₃	—	4	4	no	—
49	C₈×C₇₃	—	4	2	no	—
50	#10596831	—	4	2	no	—
51	C₂²×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
52	C₂×D₇₃	—	2	1	no	—
53	C₂×D₇₃	—	2	2	no	—
54	C₂×D₇₃	—	4	2	no	—
55	C₂×D₇₃	—	4	4	no	—
56	C₄×C₇₃	—	2	1	no	—
57	C₄×C₇₃	—	4	2	no	—
58	C₄×C₇₃	AGL(1,ℤ/8)	1	2	yes	—
59	C₄×C₇₃	#137	1	2	yes	—
60	Dic₇₃	—	2	2	no	—
61	Dic₇₃	#100	1	2	yes	—
62	C₂×C₇₃	C₂×#100	1	1	yes	characteristic
63	C₂×C₇₃	#417	1	2	yes	—
64	D₇₃	—	4	1	no	—
65	D₇₃	—	8	2	no	—
66	#1560	—	73	1	no	maximal, Sylow
67	C₇₃	#1560	1	1	yes	characteristic, complemented, Sylow
68	#532	—	73	1	no	—
69	#423	—	73	2	no	—
70	#333	—	73	1	no	—
71	#333	D₇₃	1	1	yes	characteristic, complemented
72	#331	—	73	2	no	—
73	C₂×#41	—	73	2	no	—
74	C₂×M₁₆	—	146	2	no	—
75	C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic
76	#127	—	73	1	no	—
77	#124	—	73	2	no	—
78	#121	—	146	2	no	—
79	C₄×D₄	—	146	2	no	—
80	C₂×C₄²	—	73	1	no	—
81	C₄⋊C₈	—	73	2	no	—
82	C₄⋊C₈	—	146	2	no	—
83	C₄⋊C₈	C₂×D₇₃	1	2	yes	—
84	#41	—	292	4	no	—
85	C₂×Q₈	C₄×D₇₃	1	2	yes	—
86	C₂×D₄	—	73	2	no	—
87	C₂×D₄	—	146	2	no	—
88	C₂×D₄	—	146	2	no	—
89	C₂²×C₄	—	73	1	no	—
90	C₂²×C₄	—	73	2	no	—
91	C₂²×C₄	—	146	2	no	—
92	M₁₆	—	292	4	no	—
93	C₂×C₈	—	2	2	no	—
94	C₂×C₈	—	146	2	no	—
95	C₄⋊C₄	—	2	2	no	—
96	C₂²⋊C₄	—	146	4	no	—
97	C₄²	—	73	1	no	—
98	C₄²	—	73	2	no	—
99	C₄²	C₂²×D₇₃	1	1	yes	characteristic
100	C₂³	—	73	1	no	—
101	C₂³	—	146	2	no	—
102	Q₈	—	4	2	no	—
103	D₄	—	292	2	no	—
104	D₄	—	292	4	no	—
105	D₄	—	292	2	no	—
106	D₄	—	292	2	no	—
107	C₂×C₄	—	2	2	no	—
108	C₂×C₄	—	292	4	no	—
109	C₂×C₄	—	73	1	no	—
110	C₂×C₄	—	73	2	no	—
111	C₂×C₄	—	146	2	no	—
112	C₂×C₄	—	146	2	no	—
113	C₂×C₄	—	146	2	no	—
114	C₂×C₄	C₂×C₄×D₇₃	1	1	yes	characteristic
115	C₂×C₄	D₄×D₇₃	1	2	yes	—
116	C₈	—	4	2	no	—
117	C₈	—	292	2	no	—
118	C₂²	—	292	2	no	—
119	C₂²	—	292	4	no	—
120	C₂²	—	146	1	no	—
121	C₂²	—	146	2	no	—
122	C₂²	C₂²⋊C₄×D₇₃	1	1	yes	characteristic
123	C₄	—	2	1	no	—
124	C₄	—	4	2	no	—
125	C₄	—	73	2	no	—
126	C₄	—	146	2	no	—
127	C₄	#14556618	1	2	yes	—
128	C₄	#14556623	1	2	yes	—
129	C₂	—	292	1	no	—
130	C₂	—	584	2	no	—
131	C₂	#100×D₇₃	1	1	yes	characteristic
132	C₂	#17988587	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#17989138

C₂

yes

maximal, characteristic

#17988609

C₂

yes

maximal, complemented

#17988336

C₂

yes

maximal, characteristic, complemented

#17988330

C₂

yes

maximal, complemented

#333×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×#11924029

C₄

yes

—

C₂×#11924011

—

#14556588

C₂²

yes

characteristic

#14556580

C₄

yes

—

#14556566

—

#14556553

—

C₄²×D₇₃

C₂²

yes

characteristic

C₄⋊#10596831

C₂²

yes

—

#14556520

—

C₄⋊Q₈×C₇₃

C₂²

yes

characteristic

C₄⋊C₈×C₇₃

C₂²

yes

—

#11924029

—

C₂×D₂₉₂

—

C₂×D₂₉₂

—

C₂×D₂₉₂

C₂×C₄

yes

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂×C₄

yes

characteristic

C₂×C₄×D₇₃

D₄

yes

—

#11924011

—

C₂×#10596831

—

#11924005

—

C₄×Dic₇₃

C₂×C₄

yes

characteristic

C₄×Dic₇₃

D₄

yes

—

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₂×C₈×C₇₃

—

C₄⋊C₄×C₇₃

—

C₄²×C₇₃

C₂³

yes

characteristic

C₂²×D₇₃

—

C₂²×D₇₃

C₂²⋊C₄

yes

characteristic

Q₈×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

characteristic

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×Dic₇₃

C₂²⋊C₄

yes

—

C₂×Dic₇₃

C₂²⋊C₄

yes

characteristic

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

D₂₉₂

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₄×D₇₃

—

C₈×C₇₃

—

#10596831

—

C₂²×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

AGL(1,ℤ/8)

yes

—

C₄×C₇₃

#137

yes

—

Dic₇₃

—

Dic₇₃

#100

yes

—

C₂×C₇₃

C₂×#100

yes

characteristic

C₂×C₇₃

#417

yes

—

D₇₃

—

D₇₃

—

#1560

—

maximal, Sylow

C₇₃

#1560

yes

characteristic, complemented, Sylow

—

—

—

D₇₃

yes

characteristic, complemented

#331

—

C₂×#41

—

C₂×M₁₆

—

146

—

C₄⋊Q₈

C₂×D₇₃

yes

—

—

—

146

—

C₄×D₄

—

146

—

C₂×C₄²

—

C₄⋊C₈

—

C₄⋊C₈

—

146

—

C₄⋊C₈

C₂×D₇₃

yes

—

#41

—

292

—

C₂×Q₈

C₄×D₇₃

yes

—

C₂×D₄

—

C₂×D₄

—

146

—

C₂×D₄

—

146

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

—

146

—

M₁₆

—

292

—

C₂×C₈

—

C₂×C₈

—

146

—

C₄⋊C₄

—

C₂²⋊C₄

—

146

—

C₄²

—

C₄²

—

C₄²

C₂²×D₇₃

yes

characteristic

100

C₂³

—

101

C₂³

—

146

—

102

Q₈

—

103

D₄

—

292

—

104

D₄

—

292

—

105

D₄

—

292

—

106

D₄

—

292

—

107

C₂×C₄

—

108

C₂×C₄

—

292

—

109

C₂×C₄

—

110

C₂×C₄

—

111

C₂×C₄

—

146

—

112

C₂×C₄

—

146

—

113

C₂×C₄

—

146

—

114

C₂×C₄

C₂×C₄×D₇₃

yes

characteristic

115

C₂×C₄

D₄×D₇₃

yes

—

116

C₈

—

117

C₈

—

292

—

118

C₂²

—

292

—

119

C₂²

—

292

—

120

C₂²

—

146

—

121

C₂²

—

146

—

122

C₂²

C₂²⋊C₄×D₇₃

yes

characteristic

123

C₄

—

124

C₄

—

125

C₄

—

126

C₄

—

146

—

127

C₄

#14556618

yes

—

128

C₄

#14556623

yes

—

129

C₂

—

292

—

130

C₂

—

584

—

131

C₂

#100×D₇₃

yes

characteristic

132

C₂

#17988587

yes

—

	subgroup	G/H
center	C₂²	C₂²⋊C₄×D₇₃
commutator	C₂×C₄×C₇₃	C₂²×C₄
Frattini	C₄²	C₂²×D₇₃
Fitting	#333×C₇₃	C₂
socle	C₂²×C₇₃	C₂×C₂²⋊C₄
hypercenter	#333	D₇₃
hypocenter	C₇₃	#1560
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #333

subgroup

G/H

center

C₂²

C₂²⋊C₄×D₇₃

commutator

C₂×C₄×C₇₃

C₂²×C₄

Frattini

C₄²

C₂²×D₇₃

Fitting

#333×C₇₃

C₂

socle

C₂²×C₇₃

C₂×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂²×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #333

N	H ≅ G/N	type
2. #17988609	C₂	semidirect
3. #17988336	C₂	semidirect
4. #17988330	C₂	semidirect
5. #333×C₇₃	C₂	semidirect
67. C₇₃	#1560	semidirect
71. #333	D₇₃	semidirect

H ≅ G/N

type

2. #17988609

C₂

semidirect

3. #17988336

C₂

semidirect

4. #17988330

C₂

semidirect

5. #333×C₇₃

C₂

semidirect

67. C₇₃

#1560

semidirect

71. #333

D₇₃

semidirect

Subgroups — #22608665

Conjugacy classes of subgroups

Complements