Subgroups — #11763657

Order 1088.

82 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#10587579	C₂	1	1	yes	maximal, characteristic
2	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#3624	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₆₈	C₄	1	1	yes	characteristic
5	C₂×C₄×D₁₇	—	2	1	no	—
6	C₂×#3624	—	2	1	no	—
7	C₂×#3624	—	2	1	no	—
8	C₄⋊C₄×C₁₇	C₄	1	1	yes	characteristic
9	#63227	—	2	1	no	—
10	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
11	C₂²×D₁₇	—	2	1	no	—
12	C₂×C₄×C₁₇	—	2	1	no	—
13	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
14	C₂×Dic₁₇	D₄	1	1	yes	characteristic
15	C₂×Dic₁₇	D₄	1	1	yes	characteristic
16	D₆₈	—	2	1	no	—
17	D₆₈	C₈	1	2	yes	complemented
18	C₄×D₁₇	—	4	1	no	—
19	C₄×D₁₇	—	4	1	no	—
20	#3624	—	2	2	no	—
21	#3624	—	4	1	no	—
22	C₂²×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
23	C₂×D₁₇	—	2	2	no	—
24	C₂×D₁₇	—	4	1	no	—
25	C₂×D₁₇	—	4	1	no	—
26	C₄×C₁₇	—	4	1	no	—
27	C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
28	C₄×C₁₇	M₁₆	1	1	yes	characteristic
29	Dic₁₇	—	2	1	no	—
30	Dic₁₇	D₈	1	1	yes	characteristic
31	Dic₁₇	SD₁₆	1	1	yes	characteristic
32	D₄⋊C₈	—	17	1	no	maximal, Sylow
33	C₂×C₁₇	C₂²⋊C₈	1	1	yes	characteristic
34	C₂×C₁₇	#102	1	1	yes	characteristic
35	C₂×C₁₇	#104	1	1	yes	characteristic
36	D₁₇	—	4	2	no	—
37	C₄×D₄	—	17	1	no	—
38	C₄⋊C₈	—	17	1	no	—
39	C₄×C₈	—	17	1	no	—
40	C₁₇	D₄⋊C₈	1	1	yes	characteristic, complemented, Sylow
41	C₂×D₄	—	17	1	no	—
42	C₂²×C₄	—	34	1	no	—
43	C₂×C₈	—	34	1	no	—
44	C₂×C₈	—	34	1	no	—
45	C₄⋊C₄	#595	1	1	yes	characteristic
46	C₂²⋊C₄	—	34	1	no	—
47	C₄²	—	17	1	no	—
48	C₂³	—	34	1	no	—
49	D₄	—	17	2	no	—
50	D₄	—	34	1	no	—
51	C₂×C₄	—	2	1	no	—
52	C₂×C₄	—	17	1	no	—
53	C₂×C₄	—	17	1	no	—
54	C₂×C₄	—	68	1	no	—
55	C₂×C₄	—	68	1	no	—
56	C₂×C₄	C₂×#595	1	1	yes	characteristic
57	C₈	—	34	2	no	—
58	C₈	—	68	1	no	—
59	C₂²	—	34	2	no	—
60	C₂²	—	68	1	no	—
61	C₂²	—	68	1	no	—
62	C₂²	C₂²⋊#595	1	1	yes	characteristic
63	C₄	—	4	1	no	—
64	C₄	—	17	1	no	—
65	C₄	—	17	1	no	—
66	C₄	—	34	1	no	—
67	C₄	#63242	1	1	yes	characteristic
68	C₄	#63243	1	1	yes	characteristic
69	C₂	—	68	2	no	—
70	C₂	#10587543	1	1	yes	characteristic
71	C₂	#10587547	1	1	yes	characteristic
72	C₂	#10587550	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²⋊#595
commutator	C₄×C₁₇	C₂×C₈
Frattini	C₂×C₄	C₂×#595
Fitting	C₄⋊C₄×C₁₇	C₄
socle	C₂²×C₁₇	C₂²⋊C₄
prime radical	C₂×D₆₈	C₄
cosocle	C₄×Dic₁₇	C₂²
hypercenter	C₄⋊C₄	#595
hypocenter	C₁₇	D₄⋊C₈
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₄⋊#3624	C₂	semidirect
3. C₄×#3624	C₂	semidirect
17. D₆₈	C₈	semidirect
40. C₁₇	D₄⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#10587579	2
C₄⋊#3624	2
C₄×#3624	2
D₄⋊C₈	17