Subgroups — #17948412

Order 4352.

98 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14543806	C₂	1	1	yes	maximal, characteristic
2	#14543806	C₂	1	1	yes	maximal, characteristic
3	#14526700	C₂	1	1	yes	maximal, characteristic
4	C₄⋊#63216	—	2	1	no	—
5	C₄⋊#63216	—	2	1	no	—
6	C₄×#63214	C₄	1	1	yes	characteristic
7	C₈×#3622	C₂²	1	1	yes	characteristic
8	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic
9	C₂×#63216	—	4	1	no	—
10	C₂×#63216	—	4	1	no	—
11	C₂×C₁₆×C₁₇	—	2	1	no	—
12	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₂×#63214	C₈	1	1	yes	characteristic
14	C₂×#63214	C₈	1	1	yes	characteristic
15	C₄×#3622	D₄	1	1	yes	characteristic
16	C₄×#3622	Q₈	1	1	yes	characteristic
17	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
18	C₂×C₈×C₁₇	M₁₆	1	1	yes	characteristic
19	C₄²×C₁₇	C₄⋊C₄	1	1	yes	characteristic
20	C₂×#3622	—	2	1	no	—
21	C₂×#3622	SD₁₆	1	1	yes	characteristic
22	C₂×#3622	SD₁₆	1	1	yes	characteristic
23	#63216	—	8	1	no	—
24	#63216	—	8	1	no	—
25	C₁₆×C₁₇	—	2	2	no	—
26	#63214	—	2	1	no	—
27	#63214	C₁₆	1	2	yes	complemented
28	#7099	—	17	1	no	maximal, Sylow
29	C₂×C₄×C₁₇	C₄⋊C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	#106	1	1	yes	characteristic
31	C₂×C₄×C₁₇	#108	1	1	yes	characteristic
32	C₈×C₁₇	—	2	1	no	—
33	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
34	C₈×C₁₇	M₃₂	1	1	yes	characteristic
35	#3622	—	2	1	no	—
36	#3622	—	2	1	no	—
37	#3622	—	4	1	no	—
38	#1367	—	17	1	no	—
39	#1367	—	17	1	no	—
40	#1311	—	17	1	no	—
41	C₂²×C₁₇	#334	1	1	yes	characteristic
42	C₄×C₁₇	—	2	1	no	—
43	C₄×C₁₇	C₄⋊C₁₆	1	1	yes	characteristic
44	C₄×C₁₇	#364	1	1	yes	characteristic
45	C₄×C₁₇	#365	1	1	yes	characteristic
46	C₄×C₁₇	#365	1	1	yes	characteristic
47	C₄⋊C₁₆	—	34	1	no	—
48	C₄⋊C₁₆	—	34	1	no	—
49	C₄×C₁₆	—	17	1	no	—
50	C₄×C₁₆	#595	1	1	yes	characteristic
51	C₈²	—	17	1	no	—
52	C₂×C₁₇	#1367	1	1	yes	characteristic
53	C₂×C₁₇	#1368	1	1	yes	characteristic
54	C₂×C₁₇	#1369	1	1	yes	characteristic
55	C₂×C₁₆	—	2	1	no	—
56	C₂×C₁₆	—	17	1	no	—
57	C₂×C₁₆	—	17	1	no	—
58	C₂×C₁₆	—	68	1	no	—
59	C₂×C₁₆	—	68	1	no	—
60	C₄×C₈	—	17	1	no	—
61	C₄×C₈	—	17	1	no	—
62	C₄×C₈	C₂×#595	1	1	yes	characteristic
63	C₁₇	#7099	1	1	yes	characteristic, complemented, Sylow
64	C₂×C₈	—	17	1	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	34	1	no	—
67	C₂×C₈	#63242	1	1	yes	characteristic
68	C₂×C₈	#63247	1	1	yes	characteristic
69	C₄²	C₄⋊#595	1	1	yes	characteristic
70	C₁₆	—	2	2	no	—
71	C₁₆	—	17	2	no	—
72	C₁₆	—	34	1	no	—
73	C₁₆	—	136	1	no	—
74	C₁₆	—	136	1	no	—
75	C₂×C₄	#10587533	1	1	yes	characteristic
76	C₂×C₄	#10587536	1	1	yes	characteristic
77	C₂×C₄	#10587544	1	1	yes	characteristic
78	C₈	—	2	1	no	—
79	C₈	—	34	1	no	—
80	C₈	—	34	1	no	—
81	C₈	—	68	1	no	—
82	C₈	#10587529	1	1	yes	characteristic
83	C₈	#10587530	1	1	yes	characteristic
84	C₂²	#11763671	1	1	yes	characteristic
85	C₄	—	2	1	no	—
86	C₄	#11763730	1	1	yes	characteristic
87	C₄	#11763732	1	1	yes	characteristic
88	C₄	#11763733	1	1	yes	characteristic
89	C₄	#11763734	1	1	yes	characteristic
90	C₂	#14543807	1	1	yes	characteristic
91	C₂	#14543810	1	1	yes	characteristic
92	C₂	#14543812	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	#10587533
commutator	C₈×C₁₇	C₂×C₁₆
Frattini	C₄×C₈	C₂×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle, prime radical	C₂²×C₁₇	#334
cosocle	C₈×#3622	C₂²
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	#7099
LCS	G ▷ C₈×C₁₇ ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
27. #63214	C₁₆	semidirect
63. C₁₇	#7099	semidirect

Maximal subgroups

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

subgroup	index
#14543806	2
#14526700	2
#7099	17