Subgroups — #17982824

Order 4352.

128 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545889	C₂	1	2	yes	maximal, complemented
2	#14545888	C₂	1	1	yes	maximal, characteristic, complemented
3	#14545887	C₂	1	2	yes	maximal, complemented
4	C₂×#11763891	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545208	C₂	1	1	yes	maximal, characteristic
6	#11763891	C₂²	1	1	yes	characteristic
7	#11763891	C₂²	1	1	yes	characteristic
8	#11763891	C₂²	1	2	yes	—
9	#11763742	C₄	1	2	yes	—
10	#11763741	C₄	1	1	yes	characteristic
11	#11763740	C₂²	1	2	yes	—
12	C₂×#10587467	C₂²	1	1	yes	characteristic
13	#11763227	C₄	1	1	yes	characteristic
14	#10587587	C₈	1	1	yes	characteristic
15	C₁₇×M₃₂	C₈	1	1	yes	characteristic
16	C₂×#63214	C₂×C₄	1	1	yes	characteristic
17	#10587469	C₈	1	2	yes	—
18	C₁₆×D₁₇	C₂×C₄	1	2	yes	—
19	#10587467	C₂×C₄	1	1	yes	characteristic
20	#10587467	C₂×C₄	1	2	yes	—
21	#10587467	C₂³	1	1	yes	characteristic
22	#63252	C₁₆	1	1	yes	characteristic
23	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
24	#63223	C₁₆	1	1	yes	characteristic
25	#63218	C₁₆	1	2	yes	—
26	C₈×D₁₇	C₂×C₈	1	2	yes	—
27	C₁₆×C₁₇	C₂×C₈	1	2	yes	—
28	#63214	C₂×C₈	1	1	yes	characteristic
29	#63214	C₂²×C₄	1	1	yes	characteristic
30	#13737	—	17	1	no	maximal, Sylow
31	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
32	C₂²⋊D₁₇	C₃₂	1	2	yes	—
33	D₆₈	C₃₂	1	1	yes	characteristic
34	C₄×D₁₇	C₂×C₁₆	1	2	yes	—
35	Dic₃₄	C₃₂	1	1	yes	characteristic
36	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
37	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
38	#3622	C₂×C₁₆	1	2	yes	—
39	#2258	—	17	1	no	—
40	M₁₂₈	—	17	1	no	—
41	M₁₂₈	—	17	2	no	—
42	C₂×C₆₄	—	17	1	no	—
43	C₂×C₆₄	—	17	2	no	—
44	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
45	C₂×D₁₇	C₂×C₃₂	1	2	yes	—
46	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
47	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
48	Dic₁₇	C₂×C₃₂	1	2	yes	—
49	#504	—	17	1	no	—
50	M₆₄	—	17	1	no	—
51	M₆₄	—	17	2	no	—
52	C₂×C₃₂	—	17	1	no	—
53	C₂×C₃₂	—	17	2	no	—
54	C₆₄	—	17	1	no	—
55	C₆₄	—	17	1	no	—
56	C₆₄	—	17	2	no	—
57	C₂×C₁₇	—	2	1	no	—
58	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
59	D₁₇	—	2	2	no	—
60	#131	—	17	1	no	—
61	M₃₂	—	17	2	no	—
62	M₃₂	#3633	1	1	yes	characteristic
63	C₂×C₁₆	—	17	1	no	—
64	C₂×C₁₆	—	17	2	no	—
65	C₃₂	—	17	1	no	—
66	C₃₂	—	17	1	no	—
67	C₃₂	—	17	2	no	—
68	C₁₇	#13737	1	1	yes	characteristic, complemented, Sylow
69	#41	—	17	1	no	—
70	M₁₆	—	17	1	no	—
71	M₁₆	—	17	2	no	—
72	C₂×C₈	—	17	2	no	—
73	C₂×C₈	C₂×#3633	1	1	yes	characteristic
74	C₁₆	—	17	1	no	—
75	C₁₆	—	17	1	no	—
76	C₁₆	C₂×#3633	1	2	yes	—
77	Q₈	—	17	1	no	—
78	D₄	—	17	2	no	—
79	D₄	—	17	1	no	—
80	C₂×C₄	—	17	2	no	—
81	C₂×C₄	#10587665	1	1	yes	characteristic
82	C₈	—	17	2	no	—
83	C₈	#10587665	1	1	yes	characteristic
84	C₈	C₂²×#3633	1	1	yes	characteristic
85	C₂²	—	17	2	no	—
86	C₂²	#11763916	1	1	yes	characteristic
87	C₄	—	17	2	no	—
88	C₄	#11763916	1	1	yes	characteristic
89	C₄	C₂×#10587665	1	1	yes	characteristic
90	C₂	—	2	1	no	—
91	C₂	—	34	2	no	—
92	C₂	C₂×#11763916	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₈	C₂²×#3633
commutator, socle	C₂×C₁₇	C₂²×C₃₂
Fitting	C₁₇×M₃₂	C₈
prime radical	#63252	C₁₆
cosocle	#10587467	C₂³
hypercenter	M₃₂	#3633
hypocenter	C₁₇	#13737
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ M₃₂

Complements

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

N	H ≅ G/N	type
1. #14545889	C₂	semidirect
2. #14545888	C₂	semidirect
3. #14545887	C₂	semidirect
4. C₂×#11763891	C₂	semidirect
68. C₁₇	#13737	semidirect

Maximal subgroups

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

subgroup	index
#14545889	2
#14545888	2
#14545887	2
C₂×#11763891	2
#14545208	2
#13737	17