Subgroups — #11763815

Order 1088.

114 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#63247	C₂	1	1	yes	maximal, characteristic
2	C₂²×#3624	C₂	1	1	yes	maximal, characteristic
3	#10587563	C₂	1	1	yes	maximal, characteristic
4	#10587544	C₂	1	2	yes	maximal, complemented
5	C₄⋊#3624	C₂	1	2	yes	maximal, complemented
6	C₂²×Dic₁₇	C₂²	1	1	yes	characteristic
7	#63247	—	2	2	no	—
8	C₂×#3624	—	2	2	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⋊C₄×C₁₇	C₄	1	1	yes	characteristic
13	C₂²⋊Dic₁₇	C₄	1	1	yes	characteristic
14	#63225	C₄	1	2	yes	—
15	C₄×Dic₁₇	C₂²	1	2	yes	—
16	C₂³×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₄×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₁₇	D₄	1	2	yes	—
21	C₂×Dic₁₇	Q₈	1	2	yes	—
22	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
23	#3624	—	2	2	no	—
24	#3624	—	2	1	no	—
25	#3624	—	2	1	no	—
26	C₂²×C₁₇	—	2	2	no	—
27	C₂²×C₁₇	C₄⋊C₄	1	2	yes	—
28	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₁₇	—	2	2	no	—
30	Dic₁₇	—	2	2	no	—
31	Dic₁₇	C₄⋊C₄	1	2	yes	—
32	Dic₁₇	C₂×D₄	1	1	yes	characteristic
33	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
34	#424	—	17	1	no	maximal, Sylow
35	C₂×C₁₇	—	2	2	no	—
36	C₂×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
37	C₂×C₁₇	#131	1	2	yes	—
38	C₂×M₁₆	—	17	1	no	—
39	C₂²×C₈	—	17	1	no	—
40	#117	—	17	1	no	—
41	C₄⋊C₈	—	17	2	no	—
42	C₄⋊C₈	—	17	2	no	—
43	C₁₇	#424	1	1	yes	characteristic, complemented, Sylow
44	C₂²×C₄	—	17	1	no	—
45	M₁₆	—	34	2	no	—
46	C₂×C₈	—	17	2	no	—
47	C₂×C₈	—	17	1	no	—
48	C₂×C₈	—	17	1	no	—
49	C₂×C₈	—	34	2	no	—
50	C₄⋊C₄	—	17	2	no	—
51	C₂²⋊C₄	—	17	1	no	—
52	C₂²⋊C₄	#595	1	1	yes	characteristic
53	C₄²	—	17	2	no	—
54	C₂³	C₂×#595	1	1	yes	characteristic
55	C₂×C₄	—	17	2	no	—
56	C₂×C₄	—	17	2	no	—
57	C₂×C₄	—	17	1	no	—
58	C₂×C₄	—	17	1	no	—
59	C₂×C₄	—	17	2	no	—
60	C₂×C₄	C₂×#595	1	2	yes	—
61	C₈	—	34	2	no	—
62	C₈	—	34	1	no	—
63	C₈	—	34	1	no	—
64	C₂²	—	2	2	no	—
65	C₂²	C₄⋊#595	1	2	yes	—
66	C₂²	C₂²×#595	1	1	yes	characteristic
67	C₄	—	2	2	no	—
68	C₄	—	17	1	no	—
69	C₄	—	17	2	no	—
70	C₄	—	17	1	no	—
71	C₄	—	34	2	no	—
72	C₂	—	2	2	no	—
73	C₂	C₂×C₄⋊#595	1	1	yes	characteristic
74	C₂	#10587678	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₄
Fitting	C₂²⋊C₄×C₁₇	C₄
prime radical	C₂³×C₁₇	C₂×C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₂²⋊C₄	#595
hypocenter	C₁₇	#424
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. #10587544	C₂	semidirect
5. C₄⋊#3624	C₂	semidirect
43. C₁₇	#424	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
C₂²×#3624	2
#10587563	2
#10587544	2
C₄⋊#3624	2
#424	17