Subgroups — #11763860

Order 1088.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
2	#10587544	C₂	1	2	yes	maximal
3	#10587542	C₂	1	2	yes	maximal
4	C₄⋊#3624	C₂	1	1	yes	maximal, characteristic
5	C₄×#3624	C₂	1	1	yes	maximal, characteristic
6	C₂×Q₈×C₁₇	C₄	1	1	yes	characteristic
7	C₂×#3624	C₂²	1	1	yes	characteristic
8	C₂×#3624	C₂²	1	2	yes	—
9	C₂×#3624	C₂²	1	1	yes	characteristic
10	C₄⋊Dic₁₇	C₄	1	2	yes	—
11	C₄⋊Dic₁₇	C₄	1	1	yes	characteristic
12	C₄×Dic₁₇	C₂²	1	1	yes	characteristic
13	C₄×Dic₁₇	C₂²	1	2	yes	—
14	Q₈×C₁₇	—	2	2	no	—
15	C₂×C₄×C₁₇	C₂×C₄	1	2	yes	—
16	C₂×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×Dic₁₇	C₂×C₄	1	1	yes	characteristic
18	C₂×Dic₁₇	C₂×C₄	1	2	yes	—
19	C₂×Dic₁₇	C₂³	1	1	yes	characteristic
20	#3624	—	2	1	no	—
21	#3624	—	2	2	no	—
22	#3624	Q₈	1	2	yes	complemented
23	C₂²×C₁₇	C₂²×C₄	1	1	yes	characteristic
24	C₄×C₁₇	—	2	2	no	—
25	C₄×C₁₇	M₁₆	1	2	yes	—
26	Dic₁₇	—	2	1	no	—
27	Dic₁₇	—	2	2	no	—
28	Dic₁₇	C₂×Q₈	1	1	yes	characteristic
29	Dic₁₇	#41	1	1	yes	characteristic
30	#446	—	17	1	no	maximal, Sylow
31	C₂×C₁₇	C₄×Q₈	1	1	yes	characteristic
32	C₂×C₁₇	C₂×M₁₆	1	1	yes	characteristic
33	C₂×C₁₇	#131	1	1	yes	characteristic
34	C₄×Q₈	—	17	1	no	—
35	C₄⋊C₈	—	17	1	no	—
36	C₄⋊C₈	—	17	2	no	—
37	#97	—	17	2	no	—
38	C₄×C₈	—	17	1	no	—
39	C₁₇	#446	1	1	yes	characteristic, complemented, Sylow
40	C₂×Q₈	#595	1	1	yes	characteristic
41	C₂×C₈	—	17	1	no	—
42	C₂×C₈	—	17	1	no	—
43	C₂×C₈	—	17	2	no	—
44	C₄⋊C₄	—	17	2	no	—
45	C₄⋊C₄	—	17	1	no	—
46	C₄²	—	17	1	no	—
47	C₄²	—	17	2	no	—
48	Q₈	—	2	2	no	—
49	C₂×C₄	—	17	1	no	—
50	C₂×C₄	—	17	1	no	—
51	C₂×C₄	—	17	2	no	—
52	C₂×C₄	C₂×#595	1	2	yes	—
53	C₂×C₄	C₂×#595	1	1	yes	characteristic
54	C₈	—	17	2	no	—
55	C₈	—	34	1	no	—
56	C₈	—	34	2	no	—
57	C₂²	C₂²×#595	1	1	yes	characteristic
58	C₄	—	2	2	no	—
59	C₄	—	17	1	no	—
60	C₄	—	17	1	no	—
61	C₄	—	34	1	no	—
62	C₄	—	34	2	no	—
63	C₄	#63247	1	2	yes	—
64	C₂	#10587680	1	1	yes	characteristic
65	C₂	Q₈×#595	1	1	yes	characteristic
66	C₂	C₂×#63247	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂²×#595
commutator, socle, prime radical	C₂²×C₁₇	C₂²×C₄
Fitting	C₂×Q₈×C₁₇	C₄
cosocle	C₂×Dic₁₇	C₂³
hypercenter	C₂×Q₈	#595
hypocenter	C₁₇	#446
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
22. #3624	Q₈	semidirect
39. C₁₇	#446	semidirect

Maximal subgroups

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

subgroup	index
Q₈×Dic₁₇	2
#10587544	2
#10587542	2
C₄⋊#3624	2
C₄×#3624	2
#446	17