Group #36361926 — subgroups

Subgroups — #36361926

Order 22144.

472 conjugacy classes of subgroups; only the 213 normal subgroups are shown.

normal subgroups only

This group has 472 conjugacy classes of subgroups — too many to draw. Only its 213 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×#19149671	C₂	1	2	yes	maximal
2	#26011389	C₂	1	8	yes	maximal
3	#26011361	C₂	1	2	yes	maximal
4	#26011357	C₂	1	2	yes	maximal
5	C₄³×C₁₇₃	C₂	1	1	yes	maximal, characteristic
6	#19149671	—	2	8	no	—
7	C₂×C₄⋊Dic₁₇₃	C₂²	1	4	yes	—
8	C₂×C₄⋊Dic₁₇₃	C₂²	1	8	yes	—
9	C₂×#14583805	C₂²	1	8	yes	—
10	#19149586	C₂²	1	8	yes	—
11	C₂×C₄²×C₁₇₃	C₂²	1	4	yes	—
12	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
13	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
14	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic
15	C₂²×Dic₁₇₃	C₂³	1	8	yes	—
16	C₄⋊Dic₁₇₃	—	2	8	no	—
17	C₄⋊Dic₁₇₃	—	2	16	no	—
18	#14583805	—	2	16	no	—
19	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
20	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
21	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
23	C₄²×C₁₇₃	—	2	8	no	—
24	C₄²×C₁₇₃	D₄	1	4	yes	—
25	C₄²×C₁₇₃	Q₈	1	4	yes	—
26	C₄²×C₁₇₃	Q₈	1	4	yes	—
27	C₂×Dic₁₇₃	—	2	8	no	—
28	C₂×Dic₁₇₃	—	2	16	no	—
29	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
30	C₂×C₄×C₁₇₃	—	2	4	no	—
31	C₂×C₄×C₁₇₃	—	2	4	no	—
32	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
33	C₂×C₄×C₁₇₃	C₂×D₄	1	2	yes	—
34	C₂×C₄×C₁₇₃	C₂×Q₈	1	4	yes	—
35	C₂×C₄×C₁₇₃	C₂×Q₈	1	4	yes	—
36	C₂×C₄×C₁₇₃	C₂×Q₈	1	2	yes	—
37	C₂×C₄×C₁₇₃	C₂×Q₈	1	2	yes	—
38	C₂×C₄×C₁₇₃	#41	1	8	yes	—
39	C₂²×C₁₇₃	C₂²×D₄	1	1	yes	characteristic
40	C₂²×C₁₇₃	C₂²×Q₈	1	1	yes	characteristic
41	C₂²×C₁₇₃	C₂²×Q₈	1	1	yes	characteristic
42	C₂²×C₁₇₃	C₂×#41	1	4	yes	—
43	C₄×C₁₇₃	—	2	4	no	—
44	C₄×C₁₇₃	—	2	4	no	—
45	C₄×C₁₇₃	#125	1	8	yes	complemented
46	C₄×C₁₇₃	C₄⋊Q₈	1	4	yes	—
47	Dic₁₇₃	—	4	8	no	—
48	C₂×C₁₇₃	C₂×#125	1	2	yes	—
49	C₂×C₁₇₃	C₂×C₄⋊Q₈	1	1	yes	characteristic
50	C₂×C₁₇₃	#532	1	2	yes	—
51	C₂×C₁₇₃	#533	1	2	yes	—
52	C₁₇₃	#2859	1	1	yes	characteristic, complemented, Sylow
53	#2859	—	173	1	no	maximal, Sylow
54	C₂×#125	—	173	2	no	—
55	#389	—	173	8	no	—
56	#384	—	173	2	no	—
57	#382	—	173	2	no	—
58	C₄³	D₁₇₃	1	1	yes	characteristic
59	#125	—	346	8	no	—
60	C₂×C₄⋊C₄	—	173	8	no	—
61	C₂×C₄⋊C₄	—	173	4	no	—
62	C₂×C₄⋊C₄	—	173	8	no	—
63	C₂×C₄²	C₂×D₁₇₃	1	4	yes	—
64	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
65	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
66	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic
67	#95	—	173	8	no	—
68	C₂²×C₄	—	173	8	no	—
69	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
70	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
71	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
72	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
73	C₄⋊C₄	—	346	16	no	—
74	C₄⋊C₄	—	346	8	no	—
75	C₄⋊C₄	—	346	16	no	—
76	C₄²	—	2	8	no	—
77	C₄²	D₆₉₂	1	4	yes	—
78	C₄²	Dic₃₄₆	1	4	yes	—
79	C₄²	Dic₃₄₆	1	4	yes	—
80	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
81	C₂×C₄	—	2	4	no	—
82	C₂×C₄	—	2	4	no	—
83	C₂×C₄	—	346	8	no	—
84	C₂×C₄	—	346	16	no	—
85	C₂×C₄	C₂×D₆₉₂	1	4	yes	—
86	C₂×C₄	C₂×D₆₉₂	1	2	yes	—
87	C₂×C₄	C₂×Dic₃₄₆	1	4	yes	—
88	C₂×C₄	C₂×Dic₃₄₆	1	4	yes	—
89	C₂×C₄	C₂×Dic₃₄₆	1	2	yes	—
90	C₂×C₄	C₂×Dic₃₄₆	1	2	yes	—
91	C₂×C₄	#14583826	1	8	yes	—
92	C₂²	C₂²×D₆₉₂	1	1	yes	characteristic
93	C₂²	C₂²×Dic₃₄₆	1	1	yes	characteristic
94	C₂²	C₂²×Dic₃₄₆	1	1	yes	characteristic
95	C₂²	C₂×#14583826	1	4	yes	—
96	C₄	—	2	4	no	—
97	C₄	—	2	4	no	—
98	C₄	—	692	8	no	—
99	C₄	#19149671	1	8	yes	complemented
100	C₄	#19149679	1	4	yes	—
101	C₂	C₂×#19149671	1	2	yes	—
102	C₂	C₂×#19149679	1	1	yes	characteristic
103	C₂	#26012041	1	2	yes	—
104	C₂	#26012048	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19149671

C₂

yes

maximal

#26011389

C₂

yes

maximal

#26011361

C₂

yes

maximal

#26011357

C₂

yes

maximal

C₄³×C₁₇₃

C₂

yes

maximal, characteristic

#19149671

—

C₂×C₄⋊Dic₁₇₃

C₂²

yes

—

C₂×C₄⋊Dic₁₇₃

C₂²

yes

—

C₂×#14583805

C₂²

yes

—

#19149586

C₂²

yes

—

C₂×C₄²×C₁₇₃

C₂²

yes

—

C₂×C₄²×C₁₇₃

C₂²

yes

characteristic

C₂×C₄²×C₁₇₃

C₂²

yes

characteristic

C₂×C₄²×C₁₇₃

C₂²

yes

characteristic

C₂²×Dic₁₇₃

C₂³

yes

—

C₄⋊Dic₁₇₃

—

C₄⋊Dic₁₇₃

—

#14583805

—

C₂²×C₄×C₁₇₃

C₂³

yes

—

C₂²×C₄×C₁₇₃

C₂³

yes

—

C₂²×C₄×C₁₇₃

C₂³

yes

characteristic

C₂²×C₄×C₁₇₃

C₂³

yes

—

C₄²×C₁₇₃

—

C₄²×C₁₇₃

D₄

yes

—

C₄²×C₁₇₃

Q₈

yes

—

C₄²×C₁₇₃

Q₈

yes

—

C₂×Dic₁₇₃

—

C₂×Dic₁₇₃

—

C₂³×C₁₇₃

C₂⁴

yes

characteristic

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

—

C₂×C₄×C₁₇₃

C₂×D₄

yes

—

C₂×C₄×C₁₇₃

C₂×D₄

yes

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂×C₄×C₁₇₃

C₂×Q₈

yes

—

C₂×C₄×C₁₇₃

#41

yes

—

C₂²×C₁₇₃

C₂²×D₄

yes

characteristic

C₂²×C₁₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₇₃

C₂²×Q₈

yes

characteristic

C₂²×C₁₇₃

C₂×#41

yes

—

C₄×C₁₇₃

—

C₄×C₁₇₃

—

C₄×C₁₇₃

#125

yes

complemented

C₄×C₁₇₃

C₄⋊Q₈

yes

—

Dic₁₇₃

—

C₂×C₁₇₃

C₂×#125

yes

—

C₂×C₁₇₃

C₂×C₄⋊Q₈

yes

characteristic

C₂×C₁₇₃

#532

yes

—

C₂×C₁₇₃

#533

yes

—

C₁₇₃

#2859

yes

characteristic, complemented, Sylow

#2859

—

173

maximal, Sylow

C₂×#125

—

173

—

#389

—

173

—

#384

—

173

—

#382

—

173

—

C₄³

D₁₇₃

yes

characteristic

#125

—

346

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄⋊C₄

—

173

—

C₂×C₄²

C₂×D₁₇₃

yes

—

C₂×C₄²

C₂×D₁₇₃

yes

characteristic

C₂×C₄²

C₂×D₁₇₃

yes

characteristic

C₂×C₄²

C₂×D₁₇₃

yes

characteristic

#95

—

173

—

C₂²×C₄

—

173

—

C₂²×C₄

C₂²×D₁₇₃

yes

—

C₂²×C₄

C₂²×D₁₇₃

yes

—

C₂²×C₄

C₂²×D₁₇₃

yes

characteristic

C₂²×C₄

C₂²×D₁₇₃

yes

—

C₄⋊C₄

—

346

—

C₄⋊C₄

—

346

—

C₄⋊C₄

—

346

—

C₄²

—

C₄²

D₆₉₂

yes

—

C₄²

Dic₃₄₆

yes

—

C₄²

Dic₃₄₆

yes

—

C₂³

C₂³×D₁₇₃

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

346

—

C₂×C₄

—

346

—

C₂×C₄

C₂×D₆₉₂

yes

—

C₂×C₄

C₂×D₆₉₂

yes

—

C₂×C₄

C₂×Dic₃₄₆

yes

—

C₂×C₄

C₂×Dic₃₄₆

yes

—

C₂×C₄

C₂×Dic₃₄₆

yes

—

C₂×C₄

C₂×Dic₃₄₆

yes

—

C₂×C₄

#14583826

yes

—

C₂²

C₂²×D₆₉₂

yes

characteristic

C₂²

C₂²×Dic₃₄₆

yes

characteristic

C₂²

C₂²×Dic₃₄₆

yes

characteristic

C₂²

C₂×#14583826

yes

—

C₄

—

C₄

—

C₄

—

692

—

C₄

#19149671

yes

complemented

100

C₄

#19149679

yes

—

101

C₂

C₂×#19149671

yes

—

102

C₂

C₂×#19149679

yes

characteristic

103

C₂

#26012041

yes

—

104

C₂

#26012048

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₇₃
commutator, socle, prime radical, cosocle	C₂³×C₁₇₃	C₂⁴
Fitting	C₄³×C₁₇₃	C₂
hypercenter	C₄³	D₁₇₃
hypocenter	C₁₇₃	#2859
LCS	G ▷ C₂³×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂³ ◁ C₄³

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₇₃

commutator, socle, prime radical, cosocle

C₂³×C₁₇₃

C₂⁴

Fitting

C₄³×C₁₇₃

C₂

hypercenter

C₄³

D₁₇₃

C₁₇₃

G ▷ C₂³×C₁₇₃ ▷ C₁₇₃

C₁ ◁ C₂³ ◁ C₄³

N	H ≅ G/N	type
45. C₄×C₁₇₃	#125	semidirect
52. C₁₇₃	#2859	semidirect
99. C₄	#19149671	semidirect

H ≅ G/N

type

45. C₄×C₁₇₃

#125

semidirect

52. C₁₇₃

#2859

semidirect

99. C₄

#19149671

semidirect

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

subgroup	index
C₂×#19149671	2
#26011389	2
#26011361	2
#26011357	2
C₄³×C₁₇₃	2
#2859	173

subgroup

index

C₄³×C₁₇₃

173

Subgroups — #36361926

Conjugacy classes of subgroups

Complements

Maximal subgroups