Group #22618394 — subgroups

Subgroups — #22618394

Order 9344.

716 conjugacy classes of subgroups; only the 249 normal subgroups are shown.

normal subgroups only

This group has 716 conjugacy classes of subgroups — too many to draw. Only its 249 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×#14556639	C₂	1	1	yes	maximal, characteristic
2	#17989065	C₂	1	1	yes	maximal, characteristic, complemented
3	#17988560	C₂	1	12	yes	maximal, complemented
4	#519×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
5	#14556639	—	2	4	no	—
6	#14556639	—	2	4	no	—
7	C₂×#11924029	C₄	1	4	yes	complemented
8	C₂×#11924028	C₂²	1	6	yes	—
9	C₂×Q₈×D₇₃	C₄	1	4	yes	complemented
10	Q₈×Dic₇₃	—	2	4	no	—
11	#14556550	C₂²	1	6	yes	—
12	#14556505	C₂²	1	16	yes	—
13	C₂²×Q₈×C₇₃	C₂²	1	1	yes	characteristic
14	C₄×Q₈×C₇₃	—	2	4	no	—
15	#117×C₇₃	C₂²	1	6	yes	—
16	#11924029	—	2	16	no	—
17	#11924028	—	2	12	no	—
18	#11924028	—	2	12	no	—
19	C₂×Dic₁₄₆	C₂×C₄	1	6	yes	—
20	Q₈×D₇₃	—	2	16	no	—
21	C₂×D₂₉₂	C₂×C₄	1	6	yes	—
22	C₂×C₂²⋊D₇₃	C₂³	1	4	yes	—
23	C₂×C₄×D₇₃	C₂×C₄	1	12	yes	—
24	C₄⋊Dic₇₃	—	2	6	no	—
25	C₂²⋊Dic₇₃	C₂³	1	4	yes	—
26	C₄×Dic₇₃	—	2	6	no	—
27	C₂×Q₈×C₇₃	C₂×C₄	1	4	yes	—
28	C₂×Q₈×C₇₃	D₄	1	4	yes	—
29	C₂×Q₈×C₇₃	D₄	1	4	yes	—
30	C₂²×C₄×C₇₃	C₂³	1	3	yes	—
31	C₄⋊C₄×C₇₃	—	2	6	no	—
32	C₂²⋊C₄×C₇₃	C₂³	1	4	yes	—
33	C₄²×C₇₃	—	2	6	no	—
34	C₂³×C₇₃	C₂⁴	1	1	yes	characteristic
35	C₂²×D₇₃	C₂²×C₄	1	4	yes	—
36	Q₈×C₇₃	C₂²⋊C₄	1	16	yes	—
37	C₂×C₄×C₇₃	—	2	4	no	—
38	C₂×C₄×C₇₃	C₂²×C₄	1	6	yes	—
39	C₂×C₄×C₇₃	C₂×D₄	1	6	yes	—
40	C₂×C₄×C₇₃	C₂×D₄	1	6	yes	—
41	C₂²⋊D₇₃	—	2	4	no	—
42	C₂²⋊D₇₃	—	2	4	no	—
43	C₂×Dic₇₃	—	2	4	no	—
44	C₂×Dic₇₃	C₂²×C₄	1	4	yes	—
45	D₂₉₂	—	2	12	no	—
46	C₄×D₇₃	—	2	24	no	—
47	Dic₁₄₆	—	2	12	no	—
48	C₂²×C₇₃	—	4	1	no	—
49	C₂²×C₇₃	C₂³×C₄	1	1	yes	characteristic
50	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
51	C₂²×C₇₃	C₂²×D₄	1	1	yes	characteristic
52	C₂×D₇₃	—	2	4	no	—
53	C₂×D₇₃	—	4	4	no	—
54	C₄×C₇₃	—	4	4	no	—
55	C₄×C₇₃	C₂×C₂²⋊C₄	1	12	yes	—
56	Dic₇₃	—	2	4	no	—
57	Dic₇₃	—	4	4	no	—
58	C₂×C₇₃	—	2	1	no	—
59	C₂×C₇₃	—	2	1	no	—
60	C₂×C₇₃	—	2	1	no	—
61	C₂×C₇₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
62	D₇₃	—	4	4	no	—
63	#2884	—	73	1	no	maximal, Sylow
64	C₇₃	#2884	1	1	yes	characteristic, complemented, Sylow
65	C₂×2₋¹⁺⁴	—	73	1	no	—
66	#519	—	73	1	no	—
67	#519	D₇₃	1	1	yes	characteristic, complemented
68	#410	—	73	12	no	—
69	2₋¹⁺⁴	—	146	4	no	—
70	2₋¹⁺⁴	—	146	4	no	—
71	C₂×#41	—	73	4	no	—
72	C₂×#41	—	73	6	no	—
73	C₂²×Q₈	—	73	4	no	—
74	C₂²×Q₈	C₂×D₇₃	1	1	yes	characteristic
75	C₄×Q₈	—	2	4	no	—
76	C₄×Q₈	—	146	4	no	—
77	#117	—	73	6	no	—
78	#117	C₂×D₇₃	1	6	yes	—
79	#99	—	73	16	no	—
80	#41	—	146	16	no	—
81	#41	—	146	12	no	—
82	#41	—	146	12	no	—
83	C₂×Q₈	—	73	6	no	—
84	C₂×Q₈	—	146	16	no	—
85	C₂×Q₈	C₄×D₇₃	1	4	yes	—
86	C₂×Q₈	D₂₉₂	1	4	yes	—
87	C₂×Q₈	C₂²⋊D₇₃	1	4	yes	—
88	C₂×D₄	—	73	4	no	—
89	C₂×D₄	—	73	6	no	—
90	C₂²×C₄	—	73	12	no	—
91	C₂²×C₄	C₂²×D₇₃	1	3	yes	—
92	C₄⋊C₄	—	2	6	no	—
93	C₄⋊C₄	—	146	6	no	—
94	C₂²⋊C₄	—	73	4	no	—
95	C₂²⋊C₄	C₂²×D₇₃	1	4	yes	—
96	C₄²	—	2	6	no	—
97	C₄²	—	146	6	no	—
98	C₂³	—	73	4	no	—
99	C₂³	C₂³×D₇₃	1	1	yes	characteristic
100	Q₈	—	146	12	no	—
101	Q₈	#11924005	1	16	yes	—
102	D₄	—	146	4	no	—
103	D₄	—	146	4	no	—
104	D₄	—	146	12	no	—
105	C₂×C₄	—	2	4	no	—
106	C₂×C₄	—	73	4	no	—
107	C₂×C₄	—	146	4	no	—
108	C₂×C₄	—	146	24	no	—
109	C₂×C₄	C₂×C₄×D₇₃	1	6	yes	—
110	C₂×C₄	C₂×C₂²⋊D₇₃	1	6	yes	—
111	C₂×C₄	C₂×D₂₉₂	1	6	yes	—
112	C₂²	—	4	1	no	—
113	C₂²	—	292	4	no	—
114	C₂²	—	146	4	no	—
115	C₂²	C₂²×C₄×D₇₃	1	1	yes	characteristic
116	C₂²	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
117	C₂²	C₂²×D₂₉₂	1	1	yes	characteristic
118	C₄	—	4	4	no	—
119	C₄	—	292	4	no	—
120	C₄	—	146	4	no	—
121	C₄	C₂×#11924005	1	12	yes	—
122	C₂	—	2	1	no	—
123	C₂	—	2	1	no	—
124	C₂	—	2	1	no	—
125	C₂	—	292	4	no	—
126	C₂	C₂²×#11924005	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#14556639

C₂

yes

maximal, characteristic

#17989065

C₂

yes

maximal, characteristic, complemented

#17988560

C₂

yes

maximal, complemented

#519×C₇₃

C₂

yes

maximal, characteristic, complemented

#14556639

—

#14556639

—

C₂×#11924029

C₄

yes

complemented

C₂×#11924028

C₂²

yes

—

C₂×Q₈×D₇₃

C₄

yes

complemented

Q₈×Dic₇₃

—

#14556550

C₂²

yes

—

#14556505

C₂²

yes

—

C₂²×Q₈×C₇₃

C₂²

yes

characteristic

C₄×Q₈×C₇₃

—

#117×C₇₃

C₂²

yes

—

#11924029

—

#11924028

—

#11924028

—

C₂×Dic₁₄₆

C₂×C₄

yes

—

Q₈×D₇₃

—

C₂×D₂₉₂

C₂×C₄

yes

—

C₂×C₂²⋊D₇₃

C₂³

yes

—

C₂×C₄×D₇₃

C₂×C₄

yes

—

C₄⋊Dic₇₃

—

C₂²⋊Dic₇₃

C₂³

yes

—

C₄×Dic₇₃

—

C₂×Q₈×C₇₃

C₂×C₄

yes

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂×Q₈×C₇₃

D₄

yes

—

C₂²×C₄×C₇₃

C₂³

yes

—

C₄⋊C₄×C₇₃

—

C₂²⋊C₄×C₇₃

C₂³

yes

—

C₄²×C₇₃

—

C₂³×C₇₃

C₂⁴

yes

characteristic

C₂²×D₇₃

C₂²×C₄

yes

—

Q₈×C₇₃

C₂²⋊C₄

yes

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²×C₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂×C₄×C₇₃

C₂×D₄

yes

—

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

C₂×Dic₇₃

C₂²×C₄

yes

—

D₂₉₂

—

C₄×D₇₃

—

Dic₁₄₆

—

C₂²×C₇₃

—

C₂²×C₇₃

C₂³×C₄

yes

characteristic

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂²×C₇₃

C₂²×D₄

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

C₂×C₂²⋊C₄

yes

—

Dic₇₃

—

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

C₂²×C₂²⋊C₄

yes

characteristic

D₇₃

—

#2884

—

maximal, Sylow

C₇₃

#2884

yes

characteristic, complemented, Sylow

C₂×2₋¹⁺⁴

—

#519

—

#519

D₇₃

yes

characteristic, complemented

#410

—

2₋¹⁺⁴

—

146

—

2₋¹⁺⁴

—

146

—

C₂×#41

—

C₂×#41

—

C₂²×Q₈

—

C₂²×Q₈

C₂×D₇₃

yes

characteristic

C₄×Q₈

—

C₄×Q₈

—

146

—

#117

—

#117

C₂×D₇₃

yes

—

#99

—

#41

—

146

—

#41

—

146

—

#41

—

146

—

C₂×Q₈

—

C₂×Q₈

—

146

—

C₂×Q₈

C₄×D₇₃

yes

—

C₂×Q₈

D₂₉₂

yes

—

C₂×Q₈

C₂²⋊D₇₃

yes

—

C₂×D₄

—

C₂×D₄

—

C₂²×C₄

—

C₂²×C₄

C₂²×D₇₃

yes

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

C₂²⋊C₄

C₂²×D₇₃

yes

—

C₄²

—

C₄²

—

146

—

C₂³

—

C₂³

C₂³×D₇₃

yes

characteristic

100

Q₈

—

146

—

101

Q₈

#11924005

yes

—

102

D₄

—

146

—

103

D₄

—

146

—

104

D₄

—

146

—

105

C₂×C₄

—

106

C₂×C₄

—

107

C₂×C₄

—

146

—

108

C₂×C₄

—

146

—

109

C₂×C₄

C₂×C₄×D₇₃

yes

—

110

C₂×C₄

C₂×C₂²⋊D₇₃

yes

—

111

C₂×C₄

C₂×D₂₉₂

yes

—

112

C₂²

—

113

C₂²

—

292

—

114

C₂²

—

146

—

115

C₂²

C₂²×C₄×D₇₃

yes

characteristic

116

C₂²

C₂²×C₂²⋊D₇₃

yes

characteristic

117

C₂²

C₂²×D₂₉₂

yes

characteristic

118

C₄

—

119

C₄

—

292

—

120

C₄

—

146

—

121

C₄

C₂×#11924005

yes

—

122

C₂

—

123

C₂

—

124

C₂

—

125

C₂

—

292

—

126

C₂

C₂²×#11924005

yes

characteristic

	subgroup	G/H
center	C₂	C₂²×#11924005
commutator	C₂²×C₇₃	C₂³×C₄
Frattini	C₂³	C₂³×D₇₃
Fitting	#519×C₇₃	C₂
socle	C₂×C₇₃	C₂²×C₂²⋊C₄
hypercenter	#519	D₇₃
hypocenter	C₇₃	#2884
LCS	G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂ ◁ C₂²×Q₈ ◁ #519

subgroup

G/H

center

C₂

C₂²×#11924005

commutator

C₂²×C₇₃

C₂³×C₄

Frattini

C₂³

C₂³×D₇₃

Fitting

#519×C₇₃

C₂

socle

C₂×C₇₃

C₂²×C₂²⋊C₄

D₇₃

C₇₃

G ▷ C₂²×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂ ◁ C₂²×Q₈ ◁ #519

N	H ≅ G/N	type
2. #17989065	C₂	semidirect
3. #17988560	C₂	semidirect
4. #519×C₇₃	C₂	semidirect
7. C₂×#11924029	C₄	semidirect
9. C₂×Q₈×D₇₃	C₄	semidirect
64. C₇₃	#2884	semidirect
67. #519	D₇₃	semidirect

H ≅ G/N

type

2. #17989065

C₂

semidirect

3. #17988560

C₂

semidirect

4. #519×C₇₃

C₂

semidirect

7. C₂×#11924029

C₄

semidirect

9. C₂×Q₈×D₇₃

C₄

semidirect

64. C₇₃

#2884

semidirect

67. #519

D₇₃

semidirect

Subgroups — #22618394

Conjugacy classes of subgroups

Complements