Subgroups — #11763844

Order 1088.

122 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63247	C₂	1	2	yes	maximal, complemented
2	D₄×Dic₁₇	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊#3624	C₂	1	2	yes	maximal, complemented
4	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#3624	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×D₄×C₁₇	C₄	1	1	yes	characteristic
7	C₂²×Dic₁₇	C₂²	1	2	yes	—
8	#63247	—	2	4	no	—
9	C₂×#3624	C₂²	1	2	yes	—
10	C₂×#3624	C₂²	1	1	yes	characteristic
11	C₂×#3624	C₂²	1	1	yes	characteristic
12	C₂²⋊Dic₁₇	C₄	1	2	yes	—
13	C₄⋊Dic₁₇	C₄	1	1	yes	characteristic
14	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
15	C₂³×C₁₇	C₂×C₄	1	2	yes	—
16	D₄×C₁₇	—	2	2	no	—
17	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	—	2	2	no	—
19	C₂×Dic₁₇	—	2	2	no	—
20	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
21	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
22	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
23	#3624	—	2	2	no	—
24	#3624	—	2	1	no	—
25	#3624	D₄	1	2	yes	complemented
26	C₂²×C₁₇	—	2	2	no	—
27	C₂²×C₁₇	—	2	2	no	—
28	C₂²×C₁₇	—	2	2	no	—
29	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
30	C₄×C₁₇	M₁₆	1	2	yes	complemented
31	Dic₁₇	—	2	2	no	—
32	Dic₁₇	—	2	1	no	—
33	Dic₁₇	C₂×D₄	1	1	yes	characteristic
34	Dic₁₇	#41	1	1	yes	characteristic
35	#436	—	17	1	no	maximal, Sylow
36	C₂×C₁₇	—	4	2	no	—
37	C₂×C₁₇	C₄×D₄	1	1	yes	characteristic
38	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
39	C₂×C₁₇	#131	1	1	yes	characteristic
40	C₂×M₁₆	—	17	2	no	—
41	C₄×D₄	—	17	1	no	—
42	C₄⋊C₈	—	17	1	no	—
43	C₂²⋊C₈	—	17	2	no	—
44	C₄×C₈	—	17	1	no	—
45	C₁₇	#436	1	1	yes	characteristic, complemented, Sylow
46	C₂×D₄	#595	1	1	yes	characteristic
47	C₂²×C₄	—	17	2	no	—
48	M₁₆	—	34	4	no	—
49	C₂×C₈	—	17	1	no	—
50	C₂×C₈	—	17	1	no	—
51	C₂×C₈	—	17	2	no	—
52	C₄⋊C₄	—	17	1	no	—
53	C₂²⋊C₄	—	17	2	no	—
54	C₄²	—	17	1	no	—
55	C₂³	C₂×#595	1	2	yes	—
56	D₄	—	2	2	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	2	no	—
60	C₂×C₄	—	34	2	no	—
61	C₂×C₄	—	34	2	no	—
62	C₂×C₄	C₂×#595	1	1	yes	characteristic
63	C₈	—	17	2	no	—
64	C₈	—	34	2	no	—
65	C₈	—	34	1	no	—
66	C₂²	—	2	2	no	—
67	C₂²	—	2	2	no	—
68	C₂²	—	2	2	no	—
69	C₂²	C₂²×#595	1	1	yes	characteristic
70	C₄	—	17	1	no	—
71	C₄	—	17	1	no	—
72	C₄	—	34	1	no	—
73	C₄	—	34	2	no	—
74	C₄	#63247	1	2	yes	complemented
75	C₂	—	4	2	no	—
76	C₂	#10587678	1	1	yes	characteristic
77	C₂	D₄×#595	1	1	yes	characteristic
78	C₂	C₂×#63247	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄
Fitting, prime radical	C₂×D₄×C₁₇	C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₂×D₄	#595
hypocenter	C₁₇	#436
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×D₄

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₂×#63247	C₂	semidirect
3. C₂²⋊#3624	C₂	semidirect
4. C₄⋊#3624	C₂	semidirect
5. C₄×#3624	C₂	semidirect
25. #3624	D₄	semidirect
30. C₄×C₁₇	M₁₆	semidirect
45. C₁₇	#436	semidirect
74. C₄	#63247	semidirect

Maximal subgroups

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

subgroup	index
C₂×#63247	2
D₄×Dic₁₇	2
C₂²⋊#3624	2
C₄⋊#3624	2
C₄×#3624	2
#436	17