Group #36369279 — subgroups

Subgroups — #36369279

Order 22144.

272 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 98 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	#26012450	C₂	1	1	yes	maximal, characteristic
2	C₄²×#10621924	C₂	1	1	yes	maximal, characteristic
3	(C₂×#10621924)⋊C₈	C₂	1	4	yes	maximal
4	#97×D₁₇₃	C₂	1	1	yes	maximal, characteristic
5	C₂×D₁₇₃⋊C₈	C₂²	1	2	yes	—
6	C₂×C₄×#10621924	C₄	1	4	yes	—
7	C₂×C₄×#10621924	C₂²	1	2	yes	—
8	#19149734	C₄	1	4	yes	complemented
9	C₂×C₈×D₁₇₃	C₂²	1	2	yes	—
10	C₄²×D₁₇₃	C₂²	1	1	yes	characteristic
11	#19149590	C₄	1	1	yes	characteristic, complemented
12	#19149589	C₄	1	2	yes	complemented
13	#97×C₁₇₃	C₄	1	1	yes	characteristic, complemented
14	C₂²×#10621924	C₂×C₄	1	4	yes	—
15	D₁₇₃⋊C₈	—	2	4	no	—
16	C₂×#13063443	C₂×C₄	1	4	yes	—
17	C₄×#10621924	—	2	8	no	—
18	C₄×#10621924	—	2	4	no	—
19	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
20	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
21	C₂×#13063436	C₂×C₄	1	2	yes	—
22	C₈×D₁₇₃	—	2	4	no	—
23	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
24	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
25	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
26	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
27	C₂×#10621924	—	2	4	no	—
28	C₂×#10621924	—	2	4	no	—
29	C₂×#10621924	M₁₆	1	8	yes	—
30	#13063443	—	2	4	no	—
31	C₂²×D₁₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₂×Dic₁₇₃	C₄²	1	2	yes	—
33	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
34	C₄×D₁₇₃	—	2	4	no	—
35	C₄×D₁₇₃	#41	1	4	yes	—
36	#13063436	—	2	2	no	—
37	C₂×C₄×C₁₇₃	C₄²	1	2	yes	—
38	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
39	C₈×C₁₇₃	—	2	2	no	—
40	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
41	C₂×D₁₇₃	#117	1	2	yes	—
42	C₂×D₁₇₃	C₂×M₁₆	1	4	yes	—
43	#10621924	—	2	8	no	—
44	C₄×C₁₇₃	—	2	2	no	—
45	C₄×C₁₇₃	#117	1	2	yes	—
46	Dic₁₇₃	—	2	2	no	—
47	Dic₁₇₃	#117	1	2	yes	—
48	C₂×C₁₇₃	#376	1	1	yes	characteristic
49	C₂×C₁₇₃	C₄×M₁₆	1	2	yes	—
50	D₁₇₃	#432	1	4	yes	—
51	C₁₇₃	#1745	1	1	yes	characteristic, complemented, Sylow
52	#1745	—	173	1	no	maximal, Sylow
53	C₂×#97	—	173	1	no	—
54	C₂×#97	—	173	1	no	—
55	C₄³	—	173	1	no	—
56	#336	—	173	4	no	—
57	C₂²×C₈	—	173	2	no	—
58	C₂²×C₈	—	173	2	no	—
59	C₂×C₄²	—	173	2	no	—
60	C₂×C₄²	—	173	4	no	—
61	C₂×C₄²	—	173	1	no	—
62	#97	—	173	4	no	—
63	#97	—	173	2	no	—
64	#97	—	173	1	no	—
65	#97	#10621924	1	1	yes	characteristic, complemented
66	C₂²×C₄	—	173	4	no	—
67	C₂²×C₄	—	173	2	no	—
68	C₂²×C₄	—	173	1	no	—
69	C₂×C₈	—	346	4	no	—
70	C₂×C₈	—	346	4	no	—
71	C₂×C₈	—	173	4	no	—
72	C₂×C₈	—	173	2	no	—
73	C₂×C₈	C₂×#10621924	1	2	yes	—
74	C₄²	—	346	8	no	—
75	C₄²	—	346	4	no	—
76	C₄²	—	173	2	no	—
77	C₄²	—	173	1	no	—
78	C₄²	C₂×#10621924	1	1	yes	characteristic
79	C₂³	—	173	1	no	—
80	C₂×C₄	—	346	4	no	—
81	C₂×C₄	—	346	4	no	—
82	C₂×C₄	—	346	4	no	—
83	C₂×C₄	—	173	8	no	—
84	C₂×C₄	—	173	2	no	—
85	C₂×C₄	—	173	1	no	—
86	C₂×C₄	—	173	4	no	—
87	C₂×C₄	C₄×#10621924	1	2	yes	—
88	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
89	C₈	—	2	2	no	—
90	C₈	—	346	4	no	—
91	C₈	—	346	2	no	—
92	C₂²	—	173	2	no	—
93	C₂²	—	173	4	no	—
94	C₂²	C₂×C₄×#10621924	1	1	yes	characteristic
95	C₄	—	2	2	no	—
96	C₄	—	346	8	no	—
97	C₄	—	346	2	no	—
98	C₄	—	173	2	no	—
99	C₄	#19149758	1	2	yes	—
100	C₂	—	173	4	no	—
101	C₂	#26012427	1	1	yes	characteristic
102	C₂	M₁₆×#10621924	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

#26012450

C₂

yes

maximal, characteristic

C₄²×#10621924

C₂

yes

maximal, characteristic

(C₂×#10621924)⋊C₈

C₂

yes

maximal

#97×D₁₇₃

C₂

yes

maximal, characteristic

C₂×D₁₇₃⋊C₈

C₂²

yes

—

C₂×C₄×#10621924

C₄

yes

—

C₂×C₄×#10621924

C₂²

yes

—

#19149734

C₄

yes

complemented

C₂×C₈×D₁₇₃

C₂²

yes

—

C₄²×D₁₇₃

C₂²

yes

characteristic

#19149590

C₄

yes

characteristic, complemented

#19149589

C₄

yes

complemented

#97×C₁₇₃

C₄

yes

characteristic, complemented

C₂²×#10621924

C₂×C₄

yes

—

D₁₇₃⋊C₈

—

C₂×#13063443

C₂×C₄

yes

—

C₄×#10621924

—

C₄×#10621924

—

C₂×C₄×D₁₇₃

C₂×C₄

yes

—

C₂×C₄×D₁₇₃

C₂³

yes

characteristic

C₂×#13063436

C₂×C₄

yes

—

C₈×D₁₇₃

—

C₄×Dic₁₇₃

C₂×C₄

yes

—

C₄×Dic₁₇₃

C₂×C₄

yes

characteristic

C₂×C₈×C₁₇₃

C₂×C₄

yes

—

C₄²×C₁₇₃

C₂×C₄

yes

—

—

M₁₆

yes

—

#13063443

—

C₂²×D₁₇₃

C₂²×C₄

yes

characteristic

C₂×Dic₁₇₃

C₄²

yes

—

C₂×Dic₁₇₃

C₂²×C₄

yes

characteristic

C₄×D₁₇₃

—

C₄×D₁₇₃

#41

yes

—

#13063436

—

C₂×C₄×C₁₇₃

C₄²

yes

—

C₂×C₄×C₁₇₃

C₂²×C₄

yes

characteristic

C₈×C₁₇₃

—

C₂²×C₁₇₃

C₂×C₄²

yes

characteristic

C₂×D₁₇₃

#117

yes

—

C₂×D₁₇₃

C₂×M₁₆

yes

—

#10621924

—

C₄×C₁₇₃

—

C₄×C₁₇₃

#117

yes

—

Dic₁₇₃

—

Dic₁₇₃

#117

yes

—

C₂×C₁₇₃

#376

yes

characteristic

C₂×C₁₇₃

C₄×M₁₆

yes

—

D₁₇₃

#432

yes

—

C₁₇₃

#1745

yes

characteristic, complemented, Sylow

#1745

—

173

maximal, Sylow

C₂×#97

—

173

—

C₂×#97

—

173

—

C₄³

—

173

—

#336

—

173

—

C₂²×C₈

—

173

—

C₂²×C₈

—

173

—

C₂×C₄²

—

173

—

C₂×C₄²

—

173

—

C₂×C₄²

—

173

—

#97

—

173

—

#97

—

173

—

#97

—

173

—

#97

#10621924

yes

characteristic, complemented

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

—

173

—

C₂×C₈

—

346

—

C₂×C₈

—

346

—

C₂×C₈

—

173

—

C₂×C₈

—

173

—

C₂×C₈

C₂×#10621924

yes

—

C₄²

—

346

—

C₄²

—

346

—

C₄²

—

173

—

C₄²

—

173

—

C₄²

C₂×#10621924

yes

characteristic

C₂³

—

173

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

—

173

—

C₂×C₄

C₄×#10621924

yes

—

C₂×C₄

C₂²×#10621924

yes

characteristic

C₈

—

C₈

—

346

—

C₈

—

346

—

C₂²

—

173

—

C₂²

—

173

—

C₂²

C₂×C₄×#10621924

yes

characteristic

C₄

—

C₄

—

346

—

C₄

—

346

—

C₄

—

173

—

C₄

#19149758

yes

—

100

C₂

—

173

—

101

C₂

#26012427

yes

characteristic

102

C₂

M₁₆×#10621924

yes

—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#10621924
commutator, socle	C₂²×C₁₇₃	C₂×C₄²
Fitting	#97×C₁₇₃	C₄
prime radical	C₂²×D₁₇₃	C₂²×C₄
cosocle	C₂×C₄×D₁₇₃	C₂³
hypercenter	#97	#10621924
hypocenter	C₁₇₃	#1745
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ #97

subgroup

G/H

center, Frattini

C₂×C₄

C₂²×#10621924

commutator, socle

C₂²×C₁₇₃

C₂×C₄²

Fitting

#97×C₁₇₃

C₄

prime radical

C₂²×D₁₇₃

C₂²×C₄

cosocle

C₂×C₄×D₁₇₃

C₂³

C₁₇₃

G ▷ C₂²×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂×C₄ ◁ #97

N	H ≅ G/N	type
8. #19149734	C₄	semidirect
11. #19149590	C₄	semidirect
12. #19149589	C₄	semidirect
13. #97×C₁₇₃	C₄	semidirect
51. C₁₇₃	#1745	semidirect
65. #97	#10621924	semidirect

H ≅ G/N

type

8. #19149734

C₄

semidirect

11. #19149590

C₄

semidirect

12. #19149589

C₄

semidirect

13. #97×C₁₇₃

C₄

semidirect

51. C₁₇₃

#1745

semidirect

65. #97

#10621924

semidirect

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

subgroup	index
#26012450	2
C₄²×#10621924	2
(C₂×#10621924)⋊C₈	2
#97×D₁₇₃	2
#1745	173

subgroup

index

#97×D₁₇₃

173

Subgroups — #36369279

Conjugacy classes of subgroups

Complements

Maximal subgroups