Group #22607939 — subgroups

Subgroups — #22607939

Order 9344.

126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 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	#17988823	C₂	1	1	yes	maximal, characteristic
2	C₂²⋊#11924003	C₂	1	1	yes	maximal, characteristic, complemented
3	#340×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₅₈₄	C₄	1	1	yes	characteristic, complemented
5	#14556565	—	2	1	no	—
6	C₂×#11924003	—	2	1	no	—
7	#14556525	C₄	1	1	yes	characteristic, complemented
8	#14556513	—	2	1	no	—
9	C₂²×C₈×C₇₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₄×C₇₃	—	2	1	no	—
11	C₂×D₂₉₂	—	2	1	no	—
12	C₂×C₂²⋊D₇₃	—	4	1	no	—
13	D₅₈₄	—	4	1	no	—
14	C₄⋊Dic₇₃	—	2	1	no	—
15	#11924005	—	4	1	no	—
16	#11924003	—	4	1	no	—
17	C₂²×C₄×C₇₃	—	4	1	no	—
18	C₂²×C₄×C₇₃	D₄	1	1	yes	characteristic
19	C₂×C₈×C₇₃	—	4	1	no	—
20	C₂×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
21	C₂×C₈×C₇₃	D₄	1	1	yes	characteristic
22	C₄⋊C₄×C₇₃	—	2	2	no	—
23	C₄⋊C₄×C₇₃	—	4	1	no	—
24	C₂³×C₇₃	D₈	1	1	yes	characteristic
25	C₂²×D₇₃	—	4	1	no	—
26	C₂×C₄×C₇₃	—	2	1	no	—
27	C₂×C₄×C₇₃	—	2	1	no	—
28	C₂×C₄×C₇₃	—	4	2	no	—
29	C₂×C₄×C₇₃	—	8	1	no	—
30	C₂×C₄×C₇₃	—	8	1	no	—
31	C₂×C₄×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
32	C₂×C₄×C₇₃	SD₁₆	1	1	yes	characteristic
33	C₂²⋊D₇₃	—	8	1	no	—
34	C₂²⋊D₇₃	—	8	1	no	—
35	C₂×Dic₇₃	—	4	1	no	—
36	D₂₉₂	—	4	1	no	—
37	D₂₉₂	—	4	1	no	—
38	C₈×C₇₃	—	2	1	no	—
39	C₈×C₇₃	—	2	1	no	—
40	C₂²×C₇₃	—	2	1	no	—
41	C₂²×C₇₃	—	2	1	no	—
42	C₂²×C₇₃	#102	1	1	yes	characteristic
43	C₂²×C₇₃	D₁₆	1	1	yes	characteristic
44	C₂²×C₇₃	SD₃₂	1	1	yes	characteristic
45	C₂×D₇₃	—	8	1	no	—
46	C₂×D₇₃	—	8	1	no	—
47	C₂×D₇₃	—	8	1	no	—
48	C₄×C₇₃	—	2	1	no	—
49	C₄×C₇₃	—	8	2	no	—
50	C₄×C₇₃	#99	1	1	yes	characteristic
51	C₄×C₇₃	#104	1	1	yes	characteristic
52	Dic₇₃	—	8	1	no	—
53	C₂×C₇₃	—	2	1	no	—
54	C₂×C₇₃	—	2	1	no	—
55	C₂×C₇₃	#327	1	1	yes	characteristic
56	C₂×C₇₃	#357	1	1	yes	characteristic
57	C₂×C₇₃	#360	1	1	yes	characteristic
58	D₇₃	—	16	1	no	—
59	#1347	—	73	1	no	maximal, Sylow
60	C₇₃	#1347	1	1	yes	characteristic, complemented, Sylow
61	#466	—	73	1	no	—
62	C₂²⋊C₁₆	—	73	1	no	—
63	#340	D₇₃	1	1	yes	characteristic, complemented
64	C₂×D₈	—	73	1	no	—
65	C₂²×C₈	C₂×D₇₃	1	1	yes	characteristic
66	#121	—	146	1	no	—
67	C₂×C₄⋊C₄	—	2	1	no	—
68	C₂×C₁₆	—	146	1	no	—
69	#107	—	73	1	no	—
70	#102	—	146	1	no	—
71	C₂×D₄	—	292	1	no	—
72	C₂×D₄	—	146	1	no	—
73	C₂²×C₄	—	4	1	no	—
74	C₂²×C₄	C₂²⋊D₇₃	1	1	yes	characteristic
75	D₈	—	292	1	no	—
76	C₂×C₈	—	4	1	no	—
77	C₂×C₈	C₄×D₇₃	1	1	yes	characteristic
78	C₂×C₈	D₂₉₂	1	1	yes	characteristic
79	C₄⋊C₄	—	2	2	no	—
80	C₄⋊C₄	—	4	1	no	—
81	C₄⋊C₄	—	146	1	no	—
82	C₂²⋊C₄	—	292	1	no	—
83	C₁₆	—	292	1	no	—
84	C₂³	—	292	1	no	—
85	C₂³	#11924013	1	1	yes	characteristic
86	D₄	—	292	1	no	—
87	D₄	—	292	1	no	—
88	D₄	—	584	1	no	—
89	D₄	—	584	1	no	—
90	C₂×C₄	—	2	1	no	—
91	C₂×C₄	—	2	1	no	—
92	C₂×C₄	—	4	2	no	—
93	C₂×C₄	—	8	1	no	—
94	C₂×C₄	—	8	1	no	—
95	C₂×C₄	—	292	1	no	—
96	C₂×C₄	#11924005	1	1	yes	characteristic
97	C₂×C₄	#11924015	1	1	yes	characteristic
98	C₈	—	2	1	no	—
99	C₈	—	2	1	no	—
100	C₂²	—	2	1	no	—
101	C₂²	—	2	1	no	—
102	C₂²	—	584	1	no	—
103	C₂²	—	584	1	no	—
104	C₂²	—	584	1	no	—
105	C₂²	#14556511	1	1	yes	characteristic
106	C₂²	#14556532	1	1	yes	characteristic
107	C₂²	#14556534	1	1	yes	characteristic
108	C₄	—	2	1	no	—
109	C₄	—	8	2	no	—
110	C₄	—	584	1	no	—
111	C₄	#14556505	1	1	yes	characteristic
112	C₄	#14556519	1	1	yes	characteristic
113	C₂	—	2	1	no	—
114	C₂	—	2	1	no	—
115	C₂	—	1168	1	no	—
116	C₂	#17988320	1	1	yes	characteristic
117	C₂	#17988387	1	1	yes	characteristic
118	C₂	#17988396	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#17988823

C₂

yes

maximal, characteristic

C₂²⋊#11924003

C₂

yes

maximal, characteristic, complemented

#340×C₇₃

C₂

yes

maximal, characteristic, complemented

C₂×D₅₈₄

C₄

yes

characteristic, complemented

#14556565

—

C₂×#11924003

—

#14556525

C₄

yes

characteristic, complemented

#14556513

—

C₂²×C₈×C₇₃

C₂²

yes

characteristic

C₂×C₄⋊C₄×C₇₃

—

C₂×D₂₉₂

—

C₂×C₂²⋊D₇₃

—

D₅₈₄

—

C₄⋊Dic₇₃

—

#11924005

—

#11924003

—

C₂²×C₄×C₇₃

—

C₂²×C₄×C₇₃

D₄

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₇₃

D₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

—

C₂³×C₇₃

D₈

yes

characteristic

C₂²×D₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

SD₁₆

yes

characteristic

C₂²⋊D₇₃

—

C₂²⋊D₇₃

—

C₂×Dic₇₃

—

D₂₉₂

—

D₂₉₂

—

C₈×C₇₃

—

C₈×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

—

C₂²×C₇₃

#102

yes

characteristic

C₂²×C₇₃

D₁₆

yes

characteristic

C₂²×C₇₃

SD₃₂

yes

characteristic

C₂×D₇₃

—

C₂×D₇₃

—

C₂×D₇₃

—

C₄×C₇₃

—

C₄×C₇₃

—

C₄×C₇₃

yes

C₄×C₇₃

yes

Dic₇₃

—

C₂×C₇₃

—

C₂×C₇₃

—

C₂×C₇₃

yes

C₂×C₇₃

yes

C₂×C₇₃

yes

D₇₃

—

#1347

—

maximal, Sylow

C₇₃

#1347

yes

characteristic, complemented, Sylow

#466

—

C₂²⋊C₁₆

—

#340

D₇₃

yes

characteristic, complemented

C₂×D₈

—

C₂²×C₈

C₂×D₇₃

yes

characteristic

#121

—

146

—

C₂×C₄⋊C₄

—

C₂×C₁₆

—

146

—

#107

—

#102

—

146

—

C₂×D₄

—

292

—

C₂×D₄

—

146

—

C₂²×C₄

—

C₂²×C₄

C₂²⋊D₇₃

yes

characteristic

D₈

—

292

—

C₂×C₈

—

C₂×C₈

C₄×D₇₃

yes

characteristic

C₂×C₈

D₂₉₂

yes

characteristic

C₄⋊C₄

—

C₄⋊C₄

—

C₄⋊C₄

—

146

—

C₂²⋊C₄

—

292

—

C₁₆

—

292

—

C₂³

—

292

—

C₂³

#11924013

yes

characteristic

D₄

—

292

—

D₄

—

292

—

D₄

—

584

—

D₄

—

584

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

292

—

C₂×C₄

yes

C₂×C₄

yes

C₈

—

C₈

—

100

C₂²

—

101

C₂²

—

102

C₂²

—

584

—

103

C₂²

—

584

—

104

C₂²

—

584

—

105

C₂²

#14556511

yes

characteristic

106

C₂²

#14556532

yes

characteristic

107

C₂²

#14556534

yes

characteristic

108

C₄

—

109

C₄

—

110

C₄

—

584

—

111

C₄

#14556505

yes

characteristic

112

C₄

#14556519

yes

characteristic

113

C₂

—

114

C₂

—

115

C₂

—

1168

—

116

C₂

#17988320

yes

characteristic

117

C₂

#17988387

yes

characteristic

118

C₂

#17988396

yes

characteristic

	subgroup	G/H
center	C₂²	#14556511
commutator	C₂×C₈×C₇₃	C₂×C₄
Frattini	C₂²×C₈	C₂×D₇₃
Fitting	#340×C₇₃	C₂
socle	C₂²×C₇₃	#102
hypercenter	#340	D₇₃
hypocenter	C₇₃	#1347
LCS	G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #340

subgroup

G/H

center

C₂²

#14556511

commutator

C₂×C₈×C₇₃

C₂×C₄

Frattini

C₂²×C₈

C₂×D₇₃

Fitting

#340×C₇₃

C₂

C₂²×C₇₃

D₇₃

C₇₃

G ▷ C₂×C₈×C₇₃ ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ #340

N	H ≅ G/N	type
2. C₂²⋊#11924003	C₂	semidirect
3. #340×C₇₃	C₂	semidirect
4. C₂×D₅₈₄	C₄	semidirect
7. #14556525	C₄	semidirect
60. C₇₃	#1347	semidirect
63. #340	D₇₃	semidirect

H ≅ G/N

type

2. C₂²⋊#11924003

C₂

semidirect

3. #340×C₇₃

C₂

semidirect

4. C₂×D₅₈₄

C₄

semidirect

7. #14556525

C₄

semidirect

60. C₇₃

#1347

semidirect

63. #340

D₇₃

semidirect

Subgroups — #22607939

Conjugacy classes of subgroups

Complements