Subgroups — #14526957

Order 2176.

78 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11762608	C₂	1	2	yes	maximal
2	C₁₇×#491	C₂	1	1	yes	maximal, characteristic
3	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
4	C₁₇×#125	C₄	1	1	yes	characteristic
5	C₁₇×#103	—	2	2	no	—
6	C₁₇×#97	C₄	1	1	yes	characteristic
7	#10587507	—	2	2	no	—
8	C₂×Q₈×C₁₇	D₄	1	2	yes	—
9	C₂×C₈×C₁₇	—	2	1	no	—
10	C₄⋊C₄×C₁₇	—	2	1	no	—
11	C₄⋊C₄×C₁₇	—	4	1	no	—
12	C₄⋊C₄×C₁₇	—	4	1	no	—
13	C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
14	#63223	—	4	2	no	—
15	Q₈×C₁₇	—	4	2	no	—
16	C₂×C₄×C₁₇	—	2	1	no	—
17	C₂×C₄×C₁₇	—	2	2	no	—
18	C₂×C₄×C₁₇	—	4	1	no	—
19	C₂×C₄×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
20	C₈×C₁₇	—	4	1	no	—
21	#3622	—	8	2	no	—
22	#1413	—	17	1	no	maximal, Sylow
23	C₂²×C₁₇	#99	1	1	yes	characteristic
24	C₄×C₁₇	—	2	1	no	—
25	C₄×C₁₇	—	4	1	no	—
26	C₄×C₁₇	—	4	2	no	—
27	C₄×C₁₇	—	8	1	no	—
28	#491	D₁₇	1	1	yes	characteristic
29	#356	—	17	2	no	—
30	C₂×C₁₇	—	2	1	no	—
31	C₂×C₁₇	#354	1	1	yes	characteristic
32	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
33	#125	Dic₁₇	1	1	yes	characteristic
34	#103	—	2	2	no	—
35	#101	—	34	2	no	—
36	#97	Dic₁₇	1	1	yes	characteristic
37	C₁₇	#1413	1	1	yes	characteristic, complemented, Sylow
38	C₂×Q₈	C₂²⋊D₁₇	1	2	yes	—
39	M₁₆	—	68	2	no	—
40	C₂×C₈	—	2	1	no	—
41	C₄⋊C₄	—	2	1	no	—
42	C₄⋊C₄	—	4	1	no	—
43	C₄⋊C₄	—	4	1	no	—
44	C₄²	C₂×Dic₁₇	1	1	yes	characteristic
45	Q₈	—	4	2	no	—
46	C₂×C₄	—	2	1	no	—
47	C₂×C₄	—	2	2	no	—
48	C₂×C₄	—	4	1	no	—
49	C₂×C₄	C₂²⋊Dic₁₇	1	1	yes	characteristic
50	C₈	—	4	1	no	—
51	C₈	—	136	2	no	—
52	C₂²	#10587505	1	1	yes	characteristic
53	C₄	—	2	1	no	—
54	C₄	—	4	1	no	—
55	C₄	—	4	2	no	—
56	C₄	—	8	1	no	—
57	C₂	—	2	1	no	—
58	C₂	#11762604	1	1	yes	characteristic

	subgroup	G/H
center	C₂	#11762604
commutator	C₄²×C₁₇	C₂×C₄
Frattini	C₄⋊Q₈	C₂×D₁₇
Fitting	C₁₇×#491	C₂
socle	C₂×C₁₇	#354
prime radical	C₂²×C₁₇	#99
cosocle	C₁₇×C₄⋊Q₈	C₂²
hypercenter	#491	D₁₇
hypocenter	C₁₇	#1413
LCS	G ▷ C₄²×C₁₇ ▷ C₂×C₄×C₁₇ ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂ ◁ C₂² ◁ C₂×C₄ ◁ C₄⋊Q₈ ◁ #491

Complements

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

N	H ≅ G/N	type
37. C₁₇	#1413	semidirect

Maximal subgroups

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

subgroup	index
#11762608	2
C₁₇×#491	2
#1413	17