Group #36369283 — subgroups

Subgroups — #36369283

Order 22144.

240 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 240 conjugacy classes of subgroups — too many to draw. Only its 90 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	C₄×D₁₇₃⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#26012427	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	C₂²	1	2	yes	—
7	C₄×#13063443	C₄	1	4	yes	complemented
8	(C₂×#10621924)⋊C₄	C₄	1	4	yes	—
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	4	no	—
18	C₂×C₄×D₁₇₃	C₂×C₄	1	2	yes	—
19	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
20	C₂×#13063436	C₂×C₄	1	2	yes	—
21	C₈×D₁₇₃	—	2	4	no	—
22	C₄×Dic₁₇₃	C₂×C₄	1	2	yes	—
23	C₄×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
24	C₂×C₈×C₁₇₃	C₂×C₄	1	2	yes	—
25	C₄²×C₁₇₃	C₂×C₄	1	1	yes	characteristic
26	C₂×#10621924	—	2	4	no	—
27	C₂×#10621924	—	2	8	no	—
28	#13063443	—	2	4	no	—
29	C₂²×D₁₇₃	C₂²×C₄	1	1	yes	characteristic
30	C₂×Dic₁₇₃	C₄²	1	2	yes	—
31	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
32	C₄×D₁₇₃	—	2	4	no	—
33	C₄×D₁₇₃	#41	1	4	yes	—
34	#13063436	—	2	2	no	—
35	C₂×C₄×C₁₇₃	C₄²	1	2	yes	—
36	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
37	C₈×C₁₇₃	—	2	2	no	—
38	C₂²×C₁₇₃	C₂×C₄²	1	1	yes	characteristic
39	C₂×D₁₇₃	#117	1	2	yes	—
40	C₂×D₁₇₃	#131	1	4	yes	—
41	#10621924	—	4	4	no	—
42	C₄×C₁₇₃	—	2	2	no	—
43	C₄×C₁₇₃	#117	1	2	yes	—
44	Dic₁₇₃	—	2	2	no	—
45	Dic₁₇₃	#117	1	2	yes	—
46	C₂×C₁₇₃	#376	1	1	yes	characteristic
47	C₂×C₁₇₃	#405	1	2	yes	—
48	D₁₇₃	#433	1	4	yes	—
49	C₁₇₃	#1746	1	1	yes	characteristic, complemented, Sylow
50	#1746	—	173	1	no	maximal, Sylow
51	C₂×#97	—	173	1	no	—
52	C₂×C₄×C₈	—	173	1	no	—
53	#376	—	173	1	no	—
54	#336	—	173	4	no	—
55	C₂²×C₈	—	173	2	no	—
56	C₂²×C₈	—	173	2	no	—
57	C₂×C₄²	—	173	2	no	—
58	C₂×C₄²	—	173	1	no	—
59	#97	—	173	2	no	—
60	#97	—	173	1	no	—
61	#97	#10621924	1	1	yes	characteristic, complemented
62	C₄×C₈	—	173	4	no	—
63	#95	—	173	4	no	—
64	C₂²×C₄	—	173	4	no	—
65	C₂²×C₄	—	173	2	no	—
66	C₂²×C₄	—	173	1	no	—
67	C₂×C₈	—	346	4	no	—
68	C₂×C₈	—	346	4	no	—
69	C₂×C₈	—	173	4	no	—
70	C₂×C₈	—	173	2	no	—
71	C₂×C₈	C₂×#10621924	1	2	yes	—
72	C₄²	—	346	4	no	—
73	C₄²	—	173	2	no	—
74	C₄²	—	173	1	no	—
75	C₄²	C₂×#10621924	1	1	yes	characteristic
76	C₂³	—	173	1	no	—
77	C₂×C₄	—	346	4	no	—
78	C₂×C₄	—	346	4	no	—
79	C₂×C₄	—	346	8	no	—
80	C₂×C₄	—	173	2	no	—
81	C₂×C₄	—	173	1	no	—
82	C₂×C₄	—	173	4	no	—
83	C₂×C₄	C₄×#10621924	1	2	yes	—
84	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
85	C₈	—	2	2	no	—
86	C₈	—	346	4	no	—
87	C₈	—	346	2	no	—
88	C₂²	—	173	2	no	—
89	C₂²	—	173	4	no	—
90	C₂²	C₂×C₄×#10621924	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	346	2	no	—
93	C₄	—	173	2	no	—
94	C₄	—	692	4	no	—
95	C₄	#19149758	1	2	yes	—
96	C₂	—	173	4	no	—
97	C₂	#26012427	1	1	yes	characteristic
98	C₂	#26012457	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₄×D₁₇₃⋊C₈

C₂

yes

maximal, characteristic

#26012427

C₂

yes

maximal, characteristic

(C₂×#10621924)⋊C₈

C₂

yes

maximal

#97×D₁₇₃

C₂

yes

maximal, characteristic

C₂×D₁₇₃⋊C₈

C₂²

yes

—

C₂×C₄×#10621924

C₂²

yes

—

C₄×#13063443

C₄

yes

complemented

(C₂×#10621924)⋊C₄

C₄

yes

—

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

—

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

—

—

—

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

#131

yes

—

#10621924

—

C₄×C₁₇₃

—

C₄×C₁₇₃

#117

yes

—

Dic₁₇₃

—

Dic₁₇₃

#117

yes

—

C₂×C₁₇₃

#376

yes

characteristic

C₂×C₁₇₃

#405

yes

—

D₁₇₃

#433

yes

—

C₁₇₃

#1746

yes

characteristic, complemented, Sylow

#1746

—

173

maximal, Sylow

C₂×#97

—

173

—

C₂×C₄×C₈

—

173

—

#376

—

173

—

#336

—

173

—

C₂²×C₈

—

173

—

C₂²×C₈

—

173

—

C₂×C₄²

—

173

—

C₂×C₄²

—

173

—

#97

—

173

—

#97

—

173

—

#97

#10621924

yes

characteristic, complemented

C₄×C₈

—

173

—

#95

—

173

—

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

—

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

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

—

173

—

C₄

—

692

—

C₄

#19149758

yes

—

C₂

—

173

—

C₂

#26012427

yes

characteristic

C₂

#26012457

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	#1746
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
7. C₄×#13063443	C₄	semidirect
11. #19149590	C₄	semidirect
12. #19149589	C₄	semidirect
13. #97×C₁₇₃	C₄	semidirect
49. C₁₇₃	#1746	semidirect
61. #97	#10621924	semidirect

H ≅ G/N

type

7. C₄×#13063443

C₄

semidirect

11. #19149590

C₄

semidirect

12. #19149589

C₄

semidirect

13. #97×C₁₇₃

C₄

semidirect

49. C₁₇₃

#1746

semidirect

61. #97

#10621924

semidirect

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

subgroup	index
C₄×D₁₇₃⋊C₈	2
#26012427	2
(C₂×#10621924)⋊C₈	2
#97×D₁₇₃	2
#1746	173

subgroup

index

C₄×D₁₇₃⋊C₈

#26012427

(C₂×#10621924)⋊C₈

#97×D₁₇₃

#1746

173

Subgroups — #36369283

Conjugacy classes of subgroups

Complements

Maximal subgroups