Group #11762736 — subgroups

Subgroups — #11762736

Order 1088.

170 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 170 conjugacy classes of subgroups — too many to draw. Only its 57 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×#63227	C₂	1	1	yes	maximal, characteristic
2	C₂×#63227	C₂	1	2	yes	maximal
3	C₂×C₄⋊Dic₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#95	C₂	1	1	yes	maximal, characteristic, complemented
5	#10587502	C₂	1	2	yes	maximal, complemented
6	C₂³×D₁₇	C₂²	1	1	yes	characteristic
7	C₂²×C₄×C₁₇	C₂²	1	2	yes	—
8	C₂²×C₄×C₁₇	C₂²	1	1	yes	characteristic
9	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
10	C₂²×Dic₁₇	C₂²	1	2	yes	—
11	#63227	—	2	4	no	—
12	#63227	—	2	2	no	—
13	C₄⋊Dic₁₇	—	2	2	no	—
14	C₂³×C₁₇	C₂³	1	1	yes	characteristic
15	C₂²×D₁₇	—	2	1	no	—
16	C₂²×D₁₇	—	2	2	no	—
17	C₂²×D₁₇	—	2	2	no	—
18	C₂²×D₁₇	—	2	1	no	—
19	C₂²×D₁₇	D₄	1	2	yes	—
20	C₂×C₄×C₁₇	—	2	2	no	—
21	C₂×C₄×C₁₇	—	2	2	no	—
22	C₂×C₄×C₁₇	—	2	2	no	—
23	C₂×C₄×C₁₇	—	2	2	no	—
24	C₂×C₄×C₁₇	D₄	1	2	yes	—
25	C₂×Dic₁₇	—	2	2	no	—
26	C₂×Dic₁₇	—	2	1	no	—
27	C₂×Dic₁₇	—	2	2	no	—
28	C₂×Dic₁₇	—	2	2	no	—
29	C₂×Dic₁₇	—	2	2	no	—
30	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
31	C₂²×C₁₇	C₂×D₄	1	1	yes	characteristic
32	C₂²×C₁₇	#41	1	2	yes	—
33	C₂²×C₁₇	#41	1	2	yes	—
34	C₂²×C₁₇	#41	1	1	yes	characteristic
35	C₂×D₁₇	—	2	2	no	—
36	C₂×D₁₇	—	2	4	no	—
37	C₂×D₁₇	—	4	1	no	—
38	C₂×D₁₇	—	4	1	no	—
39	C₂×D₁₇	—	4	2	no	—
40	C₄×C₁₇	—	2	2	no	—
41	C₄×C₁₇	—	4	2	no	—
42	Dic₁₇	—	4	2	no	—
43	Dic₁₇	—	4	1	no	—
44	#397	—	17	1	no	maximal, Sylow
45	C₂×C₁₇	#121	1	1	yes	characteristic
46	C₂×C₁₇	#123	1	2	yes	—
47	C₂×C₁₇	#123	1	1	yes	characteristic
48	C₂×C₁₇	#124	1	1	yes	characteristic
49	C₂×C₁₇	#126	1	2	yes	—
50	D₁₇	—	4	2	no	—
51	C₂×C₄⋊C₄	—	17	1	no	—
52	C₂×C₂²⋊C₄	—	17	2	no	—
53	C₂×C₂²⋊C₄	—	17	1	no	—
54	#95	—	17	2	no	—
55	#95	D₁₇	1	1	yes	characteristic, complemented
56	C₁₇	#397	1	1	yes	characteristic, complemented, Sylow
57	C₂⁴	—	17	1	no	—
58	C₂²×C₄	—	17	1	no	—
59	C₂²×C₄	—	17	2	no	—
60	C₂²×C₄	C₂×D₁₇	1	2	yes	—
61	C₂²×C₄	C₂×D₁₇	1	1	yes	characteristic
62	C₄⋊C₄	—	34	2	no	—
63	C₂²⋊C₄	—	34	4	no	—
64	C₂²⋊C₄	—	34	2	no	—
65	C₂³	—	17	2	no	—
66	C₂³	—	34	1	no	—
67	C₂³	—	34	2	no	—
68	C₂³	—	34	2	no	—
69	C₂³	—	34	1	no	—
70	C₂³	C₂²×D₁₇	1	1	yes	characteristic
71	C₂×C₄	—	2	2	no	—
72	C₂×C₄	—	2	2	no	—
73	C₂×C₄	—	2	2	no	—
74	C₂×C₄	—	2	2	no	—
75	C₂×C₄	—	34	1	no	—
76	C₂×C₄	—	34	2	no	—
77	C₂×C₄	—	34	2	no	—
78	C₂×C₄	—	34	2	no	—
79	C₂×C₄	—	34	2	no	—
80	C₂×C₄	D₆₈	1	2	yes	—
81	C₂²	—	34	4	no	—
82	C₂²	—	34	2	no	—
83	C₂²	—	68	1	no	—
84	C₂²	—	68	1	no	—
85	C₂²	—	68	2	no	—
86	C₂²	C₂×D₆₈	1	1	yes	characteristic
87	C₂²	#63252	1	2	yes	—
88	C₂²	D₄×D₁₇	1	1	yes	characteristic
89	C₂²	#63254	1	2	yes	—
90	C₂²	#63256	1	1	yes	characteristic
91	C₄	—	2	2	no	—
92	C₄	—	4	2	no	—
93	C₄	—	68	1	no	—
94	C₄	—	68	2	no	—
95	C₂	—	68	2	no	—
96	C₂	#10587561	1	1	yes	characteristic
97	C₂	#10587569	1	2	yes	—
98	C₂	#10587572	1	1	yes	characteristic
99	C₂	#10587581	1	1	yes	characteristic
100	C₂	#10587584	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#63227

C₂

yes

maximal, characteristic

C₂×#63227

C₂

yes

maximal

C₂×C₄⋊Dic₁₇

C₂

yes

maximal, characteristic, complemented

C₁₇×#95

C₂

yes

maximal, characteristic, complemented

#10587502

C₂

yes

maximal, complemented

C₂³×D₁₇

C₂²

yes

characteristic

C₂²×C₄×C₁₇

C₂²

yes

—

C₂²×C₄×C₁₇

C₂²

yes

characteristic

C₂²×Dic₁₇

C₂²

yes

characteristic

C₂²×Dic₁₇

C₂²

yes

—

#63227

—

#63227

—

C₄⋊Dic₁₇

—

C₂³×C₁₇

C₂³

yes

characteristic

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

—

C₂²×D₁₇

D₄

yes

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

—

C₂×C₄×C₁₇

D₄

yes

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂×Dic₁₇

—

C₂²×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₁₇

C₂×D₄

yes

characteristic

C₂²×C₁₇

#41

yes

—

C₂²×C₁₇

#41

yes

—

C₂²×C₁₇

#41

yes

characteristic

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₂×D₁₇

—

C₄×C₁₇

—

C₄×C₁₇

—

Dic₁₇

—

Dic₁₇

—

—

C₂×C₁₇

yes

C₂×C₁₇

yes

—

C₂×C₁₇

yes

C₂×C₁₇

yes

C₂×C₁₇

yes

—

D₁₇

—

C₂×C₄⋊C₄

—

C₂×C₂²⋊C₄

—

C₂×C₂²⋊C₄

—

#95

—

#95

D₁₇

yes

characteristic, complemented

C₁₇

#397

yes

characteristic, complemented, Sylow

C₂⁴

—

C₂²×C₄

—

C₂²×C₄

—

C₂²×C₄

C₂×D₁₇

yes

—

C₂²×C₄

C₂×D₁₇

yes

characteristic

C₄⋊C₄

—

C₂²⋊C₄

—

C₂²⋊C₄

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

—

C₂³

C₂²×D₁₇

yes

characteristic

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

—

C₂×C₄

D₆₈

yes

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

—

C₂²

C₂×D₆₈

yes

characteristic

C₂²

#63252

yes

—

C₂²

D₄×D₁₇

yes

characteristic

C₂²

#63254

yes

—

C₂²

#63256

yes

characteristic

C₄

—

C₄

—

C₄

—

C₄

—

C₂

—

C₂

#10587561

yes

characteristic

C₂

#10587569

yes

—

C₂

yes

C₂

yes

100

C₂

#10587584

yes

—

	subgroup	G/H
center, Frattini	C₂³	C₂²×D₁₇
commutator, socle, cosocle	C₂³×C₁₇	C₂³
Fitting	C₁₇×#95	C₂
prime radical	C₂³×D₁₇	C₂²
hypercenter	#95	D₁₇
hypocenter	C₁₇	#397
LCS	G ▷ C₂³×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂³ ◁ #95

subgroup

G/H

center, Frattini

C₂³

C₂²×D₁₇

commutator, socle, cosocle

C₂³×C₁₇

C₂³

Fitting

C₁₇×#95

C₂

prime radical

C₂³×D₁₇

C₂²

D₁₇

C₁₇

G ▷ C₂³×C₁₇ ▷ C₁₇

C₁ ◁ C₂³ ◁ #95

N	H ≅ G/N	type
3. C₂×C₄⋊Dic₁₇	C₂	semidirect
4. C₁₇×#95	C₂	semidirect
5. #10587502	C₂	semidirect
55. #95	D₁₇	semidirect
56. C₁₇	#397	semidirect

H ≅ G/N

type

3. C₂×C₄⋊Dic₁₇

C₂

semidirect

4. C₁₇×#95

C₂

semidirect

5. #10587502

C₂

semidirect

55. #95

D₁₇

semidirect

56. C₁₇

#397

semidirect

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

subgroup	index
C₂×#63227	2
C₂×C₄⋊Dic₁₇	2
C₁₇×#95	2
#10587502	2
#397	17

subgroup

index

C₂×#63227

C₂×C₄⋊Dic₁₇

C₁₇×#95

#10587502

#397

Subgroups — #11762736

Conjugacy classes of subgroups

Complements

Maximal subgroups