Subgroups — #17960423

Order 4352.

478 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763697	C₂	1	3	yes	maximal
2	C₂×C₄×#63216	C₂	1	3	yes	maximal
3	#14528471	C₂	1	1	yes	maximal, characteristic
4	C₂²×#63216	C₂²	1	1	yes	characteristic
5	C₂²×#63216	C₂²	1	3	yes	—
6	#11763697	C₄	1	12	yes	complemented
7	C₄×#63216	C₄	1	12	yes	complemented
8	C₂×#10587474	C₄	1	3	yes	—
9	C₂×C₄×#3622	C₂²	1	3	yes	—
10	C₁₇×#376	C₄	1	1	yes	characteristic
11	C₂×C₄²×C₁₇	C₂×C₄	1	3	yes	—
12	C₂²×#3622	C₂×C₄	1	3	yes	—
13	C₂²×#3622	C₂³	1	1	yes	characteristic
14	C₂×#63216	C₂×C₄	1	6	yes	—
15	C₂×#63216	C₂×C₄	1	6	yes	—
16	C₂×#63216	C₂×C₄	1	12	yes	—
17	C₁₇×#95	C₈	1	4	yes	—
18	#10587474	C₈	1	12	yes	—
19	C₄×#3622	C₂×C₄	1	6	yes	—
20	C₄×#3622	C₂×C₄	1	6	yes	—
21	C₂²×C₄×C₁₇	C₂×C₈	1	6	yes	—
22	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
23	C₄²×C₁₇	C₄²	1	6	yes	—
24	C₄²×C₁₇	C₂×C₈	1	6	yes	—
25	C₂×#3622	C₄²	1	6	yes	—
26	C₂×#3622	C₂×C₈	1	12	yes	—
27	C₂×#3622	C₂²×C₄	1	3	yes	—
28	C₂×#3622	C₂²×C₄	1	3	yes	—
29	#63216	C₄²	1	4	yes	—
30	#63216	C₄²	1	12	yes	—
31	#12539	—	17	1	no	maximal, Sylow
32	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
33	C₂×C₄×C₁₇	—	2	12	no	—
34	C₂×C₄×C₁₇	C₄×C₈	1	12	yes	—
35	C₂×C₄×C₁₇	C₂×C₄²	1	3	yes	—
36	C₂×C₄×C₁₇	C₂²×C₈	1	3	yes	—
37	#3622	C₄×C₈	1	12	yes	—
38	#3622	C₂×C₄²	1	1	yes	characteristic
39	#3622	C₂×C₄²	1	3	yes	—
40	C₂×#346	—	17	3	no	—
41	C₂×C₄×C₁₆	—	17	3	no	—
42	#1726	—	17	1	no	—
43	C₂²×C₁₇	C₂×C₄×C₈	1	3	yes	—
44	C₂²×C₁₇	#504	1	4	yes	—
45	C₄×C₁₇	—	2	12	no	—
46	C₄×C₁₇	C₄³	1	1	yes	characteristic
47	C₄×C₁₇	C₂×C₄×C₈	1	3	yes	—
48	C₂²×C₁₆	—	17	1	no	—
49	C₂²×C₁₆	—	17	3	no	—
50	C₂×#97	—	17	3	no	—
51	C₂×C₄×C₈	—	17	3	no	—
52	#376	#595	1	1	yes	characteristic
53	#346	—	17	12	no	—
54	C₄×C₁₆	—	17	12	no	—
55	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
56	C₂×C₁₇	#2108	1	6	yes	—
57	C₂²×C₈	—	17	1	no	—
58	C₂²×C₈	—	17	3	no	—
59	C₂×C₄²	C₂×#595	1	3	yes	—
60	C₂×C₁₆	—	17	6	no	—
61	C₂×C₁₆	—	17	6	no	—
62	C₂×C₁₆	—	17	12	no	—
63	#97	—	17	12	no	—
64	C₄×C₈	—	17	6	no	—
65	C₄×C₈	—	17	6	no	—
66	#95	#3624	1	4	yes	—
67	C₁₇	#12539	1	1	yes	characteristic, complemented, Sylow
68	C₂²×C₄	C₂×#3624	1	6	yes	—
69	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
70	C₂×C₈	—	17	12	no	—
71	C₂×C₈	—	17	3	no	—
72	C₂×C₈	—	17	3	no	—
73	C₂×C₈	—	17	6	no	—
74	C₄²	#63242	1	6	yes	—
75	C₄²	C₄×#595	1	6	yes	—
76	C₁₆	—	17	4	no	—
77	C₁₆	—	17	12	no	—
78	C₂³	C₂²×#3624	1	1	yes	characteristic
79	C₂×C₄	—	2	12	no	—
80	C₂×C₄	C₄×#3624	1	12	yes	—
81	C₂×C₄	C₂×#63242	1	3	yes	—
82	C₂×C₄	C₂×C₄×#595	1	3	yes	—
83	C₈	—	17	1	no	—
84	C₈	—	17	3	no	—
85	C₈	—	17	12	no	—
86	C₂²	C₂×C₄×#3624	1	3	yes	—
87	C₂²	#11763867	1	4	yes	—
88	C₄	—	2	12	no	—
89	C₄	C₄²×#595	1	1	yes	characteristic
90	C₄	C₄×#63242	1	3	yes	—
91	C₂	C₄²×#3624	1	1	yes	characteristic
92	C₂	#14544993	1	6	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂²×#595
commutator	C₂×C₁₇	C₄²×C₈
Fitting	C₁₇×#376	C₄
socle, prime radical	C₂³×C₁₇	C₂²×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	#376	#595
hypocenter	C₁₇	#12539
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂²×C₄ ◁ #376

Complements

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

N	H ≅ G/N	type
6. #11763697	C₄	semidirect
7. C₄×#63216	C₄	semidirect
67. C₁₇	#12539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763697	2
C₂×C₄×#63216	2
#14528471	2
#12539	17