Group #36369505 — subgroups

Subgroups — #36369505

Order 22144.

212 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 86 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×#19149750	C₂	1	2	yes	maximal
2	C₂×#19149749	C₂	1	2	yes	maximal
3	#26012496	C₂	1	1	yes	maximal, characteristic
4	#26012495	C₂	1	1	yes	maximal, characteristic
5	#97×D₁₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14583836	C₂²	1	2	yes	—
7	C₂×#14583836	C₂²	1	1	yes	characteristic
8	C₂×#14583836	C₂²	1	1	yes	characteristic
9	#19149750	—	2	4	no	—
10	#19149749	—	2	4	no	—
11	#19149746	—	2	2	no	—
12	C₄⋊#13063443	—	2	2	no	—
13	C₂×C₈×D₁₇₃	C₂²	1	2	yes	—
14	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
15	#19149590	C₄	1	1	yes	characteristic
16	#19149589	C₄	1	2	yes	—
17	#97×C₁₇₃	C₄	1	1	yes	characteristic
18	#14583836	—	2	2	no	—
19	#14583836	—	2	2	no	—
20	#14583836	—	2	2	no	—
21	#14583836	—	2	2	no	—
22	C₂×#13063443	—	2	2	no	—
23	C₂×#13063443	—	2	1	no	—
24	C₂×#13063443	—	2	1	no	—
25	C₂×C₄×D₁₇₃	Q₈	1	2	yes	—
26	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
27	C₂×#13063436	C₂×C₄	1	2	yes	—
28	C₈×D₁₇₃	D₄	1	4	yes	—
29	C₈×D₁₇₃	Q₈	1	4	yes	—
30	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
31	C₄×Dic₁₇₃	D₄	1	2	yes	—
32	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
33	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
34	#13063443	—	4	2	no	—
35	#13063443	—	4	1	no	—
36	#13063443	—	4	1	no	—
37	C₂²×D₁₇₃	C₂×Q₈	1	1	yes	characteristic
38	C₂×Dic₁₇₃	C₄⋊C₄	1	2	yes	—
39	C₂×Dic₁₇₃	C₂×D₄	1	1	yes	characteristic
40	C₄×D₁₇₃	—	4	2	no	—
41	C₄×D₁₇₃	C₂×D₄	1	2	yes	—
42	C₄×D₁₇₃	C₂×Q₈	1	2	yes	—
43	#13063436	C₄⋊C₄	1	4	yes	—
44	C₂×C₄×C₁₇₃	C₄⋊C₄	1	2	yes	—
45	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
46	C₈×C₁₇₃	C₄⋊C₄	1	4	yes	—
47	C₂²×C₁₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
48	C₂×D₁₇₃	—	2	2	no	—
49	C₂×D₁₇₃	C₄⋊Q₈	1	2	yes	—
50	C₄×C₁₇₃	—	2	2	no	—
51	C₄×C₁₇₃	C₂×C₄⋊C₄	1	2	yes	—
52	Dic₁₇₃	—	2	2	no	—
53	Dic₁₇₃	#127	1	1	yes	characteristic
54	Dic₁₇₃	C₄⋊Q₈	1	1	yes	characteristic
55	C₂×C₁₇₃	#384	1	1	yes	characteristic
56	C₂×C₁₇₃	#430	1	2	yes	—
57	D₁₇₃	—	2	2	no	—
58	C₁₇₃	#1849	1	1	yes	characteristic, complemented, Sylow
59	#1849	—	173	1	no	maximal, Sylow
60	C₂×#108	—	173	2	no	—
61	C₂×#108	—	173	2	no	—
62	#423	—	173	1	no	—
63	#423	—	173	1	no	—
64	C₂×#97	—	173	1	no	—
65	C₂×M₁₆	—	173	2	no	—
66	C₂×M₁₆	—	173	1	no	—
67	C₂×M₁₆	—	173	1	no	—
68	C₂²×C₈	—	173	2	no	—
69	C₂×C₄²	—	173	1	no	—
70	#108	—	346	4	no	—
71	#108	—	346	4	no	—
72	C₄⋊C₈	—	346	2	no	—
73	C₄⋊C₈	—	346	2	no	—
74	#97	—	173	2	no	—
75	#97	—	173	1	no	—
76	#97	#10621924	1	1	yes	characteristic
77	C₂²×C₄	—	173	1	no	—
78	C₂²×C₄	—	173	2	no	—
79	M₁₆	—	346	2	no	—
80	M₁₆	—	346	2	no	—
81	M₁₆	—	346	2	no	—
82	M₁₆	—	346	2	no	—
83	C₂×C₈	—	346	2	no	—
84	C₂×C₈	—	346	1	no	—
85	C₂×C₈	—	346	1	no	—
86	C₂×C₈	—	173	2	no	—
87	C₂×C₈	—	173	4	no	—
88	C₂×C₈	—	173	4	no	—
89	C₂×C₈	C₂×#10621924	1	2	yes	—
90	C₄²	—	173	2	no	—
91	C₄²	—	173	1	no	—
92	C₄²	C₂×#10621924	1	1	yes	characteristic
93	C₂³	—	173	1	no	—
94	C₂×C₄	—	173	2	no	—
95	C₂×C₄	—	173	1	no	—
96	C₂×C₄	—	173	2	no	—
97	C₂×C₄	—	173	2	no	—
98	C₂×C₄	—	692	2	no	—
99	C₂×C₄	C₄⋊#10621924	1	2	yes	—
100	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
101	C₈	—	173	4	no	—
102	C₈	—	692	2	no	—
103	C₈	—	692	1	no	—
104	C₈	—	692	1	no	—
105	C₈	C₄⋊#10621924	1	4	yes	—
106	C₂²	—	346	2	no	—
107	C₂²	—	173	2	no	—
108	C₂²	C₂×C₄⋊#10621924	1	1	yes	characteristic
109	C₄	—	2	2	no	—
110	C₄	—	346	2	no	—
111	C₄	—	173	1	no	—
112	C₄	—	173	1	no	—
113	C₄	C₂×C₄⋊#10621924	1	2	yes	—
114	C₂	—	346	2	no	—
115	C₂	#26012437	1	1	yes	characteristic
116	C₂	#26012506	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149750

C₂

yes

maximal

C₂×#19149749

C₂

yes

maximal

#26012496

C₂

yes

maximal, characteristic

#26012495

C₂

yes

maximal, characteristic

#97×D₁₇₃

C₂

yes

maximal, characteristic

C₂×#14583836

C₂²

yes

—

C₂×#14583836

C₂²

yes

characteristic

C₂×#14583836

C₂²

yes

—

—

—

—

C₂×C₈×D₁₇₃

C₂²

yes

—

C₄²×D₁₇₃

C₂²

yes

characteristic

#19149590

C₄

yes

characteristic

#19149589

C₄

yes

—

#97×C₁₇₃

C₄

yes

—

—

—

—

—

—

—

C₂×C₄×D₁₇₃

Q₈

yes

—

C₂×C₄×D₁₇₃

C₂³

yes

characteristic

C₂×#13063436

C₂×C₄

yes

—

C₈×D₁₇₃

D₄

yes

—

C₈×D₁₇₃

Q₈

yes

—

C₄×Dic₁₇₃

C₂×C₄

yes

characteristic

C₄×Dic₁₇₃

D₄

yes

—

C₂×C₈×C₁₇₃

C₂×C₄

yes

—

C₄²×C₁₇₃

C₂×C₄

yes

—

—

—

C₂²×D₁₇₃

C₂×Q₈

yes

characteristic

C₂×Dic₁₇₃

C₄⋊C₄

yes

—

C₂×Dic₁₇₃

C₂×D₄

yes

characteristic

C₄×D₁₇₃

—

C₄×D₁₇₃

C₂×D₄

yes

—

C₄×D₁₇₃

C₂×Q₈

yes

—

#13063436

C₄⋊C₄

yes

—

C₂×C₄×C₁₇₃

C₄⋊C₄

yes

—

C₂×C₄×C₁₇₃

C₂²×C₄

yes

characteristic

C₈×C₁₇₃

C₄⋊C₄

yes

—

C₂²×C₁₇₃

C₂×C₄⋊C₄

yes

characteristic

C₂×D₁₇₃

—

C₂×D₁₇₃

C₄⋊Q₈

yes

—

C₄×C₁₇₃

—

C₄×C₁₇₃

C₂×C₄⋊C₄

yes

—

Dic₁₇₃

—

Dic₁₇₃

#127

yes

characteristic

Dic₁₇₃

C₄⋊Q₈

yes

C₂×C₁₇₃

yes

C₂×C₁₇₃

yes

—

D₁₇₃

—

C₁₇₃

#1849

yes

characteristic, complemented, Sylow

#1849

—

173

maximal, Sylow

C₂×#108

—

173

—

C₂×#108

—

173

—

#423

—

173

—

#423

—

173

—

C₂×#97

—

173

—

C₂×M₁₆

—

173

—

C₂×M₁₆

—

173

—

C₂×M₁₆

—

173

—

C₂²×C₈

—

173

—

C₂×C₄²

—

173

—

#108

—

346

—

#108

—

346

—

C₄⋊C₈

—

346

—

C₄⋊C₈

—

346

—

#97

—

173

—

#97

—

173

—

#97

#10621924

yes

characteristic

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

M₁₆

—

346

—

M₁₆

—

346

—

M₁₆

—

346

—

M₁₆

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

C₂×#10621924

yes

—

C₄²

—

173

—

C₄²

—

173

—

C₄²

C₂×#10621924

yes

characteristic

C₂³

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

692

—

C₂×C₄

C₄⋊#10621924

yes

—

100

C₂×C₄

C₂²×#10621924

yes

characteristic

101

C₈

—

173

—

102

C₈

—

692

—

103

C₈

—

692

—

104

C₈

—

692

—

105

C₈

C₄⋊#10621924

yes

—

106

C₂²

—

346

—

107

C₂²

—

173

—

108

C₂²

C₂×C₄⋊#10621924

yes

characteristic

109

C₄

—

110

C₄

—

346

—

111

C₄

—

173

—

112

C₄

—

173

—

113

C₄

C₂×C₄⋊#10621924

yes

—

114

C₂

—

346

—

115

C₂

#26012437

yes

characteristic

116

C₂

#26012506

yes

—

	subgroup	G/H
center	C₂²	C₂×C₄⋊#10621924
commutator	C₂×C₄×C₁₇₃	C₂²×C₄
Frattini	C₂×C₄	C₂²×#10621924
Fitting	#97×C₁₇₃	C₄
socle	C₂²×C₁₇₃	C₂×C₄⋊C₄
prime radical	C₂²×D₁₇₃	C₂×Q₈
cosocle	C₂×C₄×D₁₇₃	C₂³
hypercenter	#97	#10621924
hypocenter	C₁₇₃	#1849
LCS	G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #97

subgroup

G/H

center

C₂²

C₂×C₄⋊#10621924

commutator

C₂×C₄×C₁₇₃

C₂²×C₄

Frattini

C₂×C₄

C₂²×#10621924

Fitting

#97×C₁₇₃

C₄

socle

C₂²×C₁₇₃

C₂×C₄⋊C₄

prime radical

C₂²×D₁₇₃

C₂×Q₈

cosocle

C₂×C₄×D₁₇₃

C₂³

C₁₇₃

G ▷ C₂×C₄×C₁₇₃ ▷ C₂×C₁₇₃ ▷ C₁₇₃

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #97

N	H ≅ G/N	type
58. C₁₇₃	#1849	semidirect

H ≅ G/N

type

58. C₁₇₃

#1849

semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×#19149750	2
C₂×#19149749	2
#26012496	2
#26012495	2
#97×D₁₇₃	2
#1849	173

subgroup

index

#97×D₁₇₃

173

Subgroups — #36369505

Conjugacy classes of subgroups

Complements

Maximal subgroups