Subgroups — #14545119

Order 2176.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10587538	C₂	1	1	yes	maximal, characteristic
2	C₂²×#63216	C₂	1	1	yes	maximal, characteristic
3	C₄⋊#63216	C₂	1	4	yes	maximal, complemented
4	#11762765	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#117	C₄	1	1	yes	characteristic
6	C₂×#63223	C₄	1	1	yes	characteristic
7	C₂²×#3622	C₂²	1	1	yes	characteristic
8	#10587538	—	2	2	no	—
9	C₂×#63216	—	2	2	no	—
10	C₂×#63216	C₂²	1	2	yes	—
11	C₂×#63216	C₂²	1	2	yes	—
12	#10587474	C₄	1	2	yes	—
13	C₄×#3622	C₂²	1	2	yes	—
14	C₂²×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
15	C₄⋊C₄×C₁₇	C₈	1	2	yes	—
16	C₂²⋊C₄×C₁₇	C₈	1	2	yes	—
17	C₄²×C₁₇	C₂×C₄	1	2	yes	—
18	#63223	—	2	2	no	—
19	C₂×#3622	C₂×C₄	1	2	yes	—
20	C₂×#3622	C₂×C₄	1	1	yes	characteristic
21	C₂×#3622	D₄	1	2	yes	—
22	C₂×#3622	Q₈	1	2	yes	—
23	C₂×#3622	C₂³	1	1	yes	characteristic
24	#63216	—	2	2	no	—
25	#63216	—	2	2	no	—
26	C₂³×C₁₇	C₂×C₈	1	1	yes	characteristic
27	C₂×C₄×C₁₇	C₄⋊C₄	1	2	yes	—
28	C₂×C₄×C₁₇	C₂×C₈	1	4	yes	—
29	C₂×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
30	C₂×C₄×C₁₇	M₁₆	1	2	yes	—
31	C₂×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
32	#3622	—	2	2	no	—
33	#3622	C₄⋊C₄	1	2	yes	—
34	#3622	C₂×D₄	1	1	yes	characteristic
35	#3622	C₂×Q₈	1	1	yes	characteristic
36	#2151	—	17	1	no	maximal, Sylow
37	C₂²×C₁₇	—	2	2	no	—
38	C₂²×C₁₇	C₄⋊C₈	1	2	yes	—
39	C₂²×C₁₇	C₂²×C₈	1	1	yes	characteristic
40	C₄×C₁₇	—	2	4	no	—
41	C₄×C₁₇	C₄⋊C₈	1	2	yes	—
42	C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
43	C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
44	C₂×M₃₂	—	17	1	no	—
45	C₂²×C₁₆	—	17	1	no	—
46	#405	—	17	1	no	—
47	C₄⋊C₁₆	—	17	4	no	—
48	C₂×C₁₇	—	2	2	no	—
49	C₂×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
50	C₂×C₁₇	#504	1	2	yes	—
51	C₂×M₁₆	—	17	1	no	—
52	C₂²×C₈	—	17	1	no	—
53	#117	#595	1	1	yes	characteristic
54	M₃₂	—	34	2	no	—
55	C₂×C₁₆	—	17	2	no	—
56	C₂×C₁₆	—	17	2	no	—
57	C₂×C₁₆	—	34	2	no	—
58	#97	—	17	2	no	—
59	C₄×C₈	—	17	2	no	—
60	C₁₇	#2151	1	1	yes	characteristic, complemented, Sylow
61	C₂²×C₄	C₂×#595	1	1	yes	characteristic
62	M₁₆	—	34	2	no	—
63	C₂×C₈	—	17	2	no	—
64	C₂×C₈	—	17	2	no	—
65	C₂×C₈	—	17	1	no	—
66	C₂×C₈	—	17	1	no	—
67	C₂×C₈	—	17	2	no	—
68	C₄⋊C₄	#3624	1	2	yes	—
69	C₂²⋊C₄	#3624	1	2	yes	—
70	C₄²	C₂×#595	1	2	yes	—
71	C₁₆	—	34	2	no	—
72	C₁₆	—	34	2	no	—
73	C₂³	C₂×#3624	1	1	yes	characteristic
74	C₂×C₄	#63243	1	2	yes	—
75	C₂×C₄	C₄⋊#595	1	2	yes	—
76	C₂×C₄	C₂×#3624	1	4	yes	—
77	C₂×C₄	C₂×#3624	1	1	yes	characteristic
78	C₂×C₄	C₂²×#595	1	1	yes	characteristic
79	C₈	—	17	1	no	—
80	C₈	—	17	2	no	—
81	C₈	—	17	1	no	—
82	C₈	—	34	2	no	—
83	C₂²	—	2	2	no	—
84	C₂²	C₄⋊#3624	1	2	yes	—
85	C₂²	C₂²×#3624	1	1	yes	characteristic
86	C₄	—	2	4	no	—
87	C₄	C₄⋊#3624	1	2	yes	—
88	C₄	C₂×#63243	1	1	yes	characteristic
89	C₄	C₂×C₄⋊#595	1	1	yes	characteristic
90	C₂	—	2	2	no	—
91	C₂	C₂×C₄⋊#3624	1	1	yes	characteristic
92	C₂	#11763867	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂²×C₈
Fitting	C₁₇×#117	C₄
prime radical	C₂³×C₁₇	C₂×C₈
cosocle	C₂×#3622	C₂³
hypercenter	#117	#595
hypocenter	C₁₇	#2151
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #117

Complements

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

N	H ≅ G/N	type
3. C₄⋊#63216	C₂	semidirect
60. C₁₇	#2151	semidirect

Maximal subgroups

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

subgroup	index
C₂×#10587538	2
C₂²×#63216	2
C₄⋊#63216	2
#11762765	2
#2151	17