Subgroups — C₂×#14545888 #17982820

Order 4352.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545888	C₂	1	4	yes	maximal, direct product factor
2	C₂×#11763891	C₂	1	2	yes	maximal, complemented
3	C₂²×#10587467	C₂	1	1	yes	maximal, characteristic
4	#11763891	C₂²	1	4	yes	complemented
5	C₂×#10587467	C₄	1	2	yes	—
6	C₂×#10587467	C₄	1	1	yes	characteristic
7	C₂×#10587467	C₂²	1	1	yes	characteristic
8	C₂×#10587467	C₂²	1	2	yes	—
9	C₂²×#63214	C₄	1	1	yes	characteristic
10	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
11	C₂×#63214	C₈	1	2	yes	—
12	C₂×#63214	C₈	1	1	yes	characteristic
13	C₂×#63214	C₂×C₄	1	2	yes	—
14	C₂×#63214	C₂×C₄	1	1	yes	characteristic
15	#10587467	C₂×C₄	1	1	yes	characteristic
16	#10587467	C₂×C₄	1	2	yes	—
17	#10587467	C₂³	1	1	yes	characteristic
18	C₂²×C₄×C₁₇	C₁₆	1	1	yes	characteristic
19	C₂×C₈×C₁₇	C₁₆	1	1	yes	characteristic
20	C₂×C₈×C₁₇	C₁₆	1	2	yes	—
21	C₂×C₈×C₁₇	C₂×C₈	1	2	yes	—
22	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
23	#63214	C₂×C₈	1	1	yes	characteristic
24	#63214	C₂×C₈	1	2	yes	—
25	#63214	C₂²×C₄	1	1	yes	characteristic
26	C₂×M₁₂₈	—	17	1	no	maximal, Sylow
27	C₂³×C₁₇	C₃₂	1	1	yes	characteristic
28	C₂×C₄×C₁₇	C₃₂	1	2	yes	—
29	C₂×C₄×C₁₇	C₃₂	1	1	yes	characteristic
30	C₂×C₄×C₁₇	C₂×C₁₆	1	2	yes	—
31	C₂×C₄×C₁₇	C₂×C₁₆	1	1	yes	characteristic
32	C₈×C₁₇	C₂×C₁₆	1	2	yes	—
33	C₈×C₁₇	C₂×C₁₆	1	1	yes	characteristic
34	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
35	C₂²×C₃₂	—	17	1	no	—
36	M₁₂₈	—	17	4	no	—
37	C₂×C₆₄	—	17	2	no	—
38	C₂²×C₁₇	—	2	2	no	—
39	C₂²×C₁₇	C₂×C₃₂	1	2	yes	—
40	C₂²×C₁₇	C₂×C₃₂	1	1	yes	characteristic
41	C₄×C₁₇	C₂×C₃₂	1	2	yes	—
42	C₄×C₁₇	C₂×C₃₂	1	1	yes	characteristic
43	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
44	C₂²×C₁₆	—	17	1	no	—
45	C₂×C₃₂	—	17	2	no	—
46	C₂×C₃₂	—	17	1	no	—
47	C₂×C₃₂	—	17	1	no	—
48	C₂×C₃₂	—	17	2	no	—
49	C₆₄	—	17	4	no	—
50	C₂×C₁₇	—	2	2	no	—
51	C₂×C₁₇	M₁₂₈	1	2	yes	complemented
52	C₂×C₁₇	C₂²×C₃₂	1	1	yes	characteristic
53	C₂²×C₈	#3633	1	1	yes	characteristic
54	C₂×C₁₆	—	17	2	no	—
55	C₂×C₁₆	—	17	2	no	—
56	C₂×C₁₆	—	17	1	no	—
57	C₂×C₁₆	—	17	1	no	—
58	C₃₂	—	17	1	no	—
59	C₃₂	—	17	1	no	—
60	C₃₂	—	17	2	no	—
61	C₁₇	C₂×M₁₂₈	1	1	yes	characteristic, complemented, Sylow
62	C₂²×C₄	#63241	1	1	yes	characteristic
63	C₂×C₈	#63241	1	1	yes	characteristic
64	C₂×C₈	#63241	1	2	yes	—
65	C₂×C₈	C₂×#3633	1	2	yes	—
66	C₂×C₈	C₂×#3633	1	1	yes	characteristic
67	C₁₆	—	17	1	no	—
68	C₁₆	—	17	1	no	—
69	C₁₆	—	17	2	no	—
70	C₂³	#10587528	1	1	yes	characteristic
71	C₂×C₄	#10587528	1	2	yes	—
72	C₂×C₄	#10587528	1	1	yes	characteristic
73	C₂×C₄	C₂×#63241	1	2	yes	—
74	C₂×C₄	C₂×#63241	1	1	yes	characteristic
75	C₈	C₂×#63241	1	2	yes	—
76	C₈	C₂×#63241	1	1	yes	characteristic
77	C₈	C₂²×#3633	1	1	yes	characteristic
78	C₂²	—	2	2	no	—
79	C₂²	C₂×#10587528	1	2	yes	—
80	C₂²	C₂×#10587528	1	1	yes	characteristic
81	C₄	C₂×#10587528	1	2	yes	—
82	C₄	C₂×#10587528	1	1	yes	characteristic
83	C₄	C₂²×#63241	1	1	yes	characteristic
84	C₂	—	2	2	no	—
85	C₂	#14545888	1	2	yes	direct product factor
86	C₂	C₂²×#10587528	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×#3633
commutator	C₂×C₁₇	C₂²×C₃₂
Frattini	C₈	C₂²×#3633
Fitting	C₂²×C₈×C₁₇	C₈
socle	C₂²×C₁₇	C₂×C₃₂
prime radical	C₂³×C₁₇	C₃₂
cosocle	#10587467	C₂³
hypercenter	C₂²×C₈	#3633
hypocenter	C₁₇	C₂×M₁₂₈
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
1. #14545888	C₂	direct (N × H)
2. C₂×#11763891	C₂	semidirect
4. #11763891	C₂²	semidirect
51. C₂×C₁₇	M₁₂₈	semidirect
61. C₁₇	C₂×M₁₂₈	semidirect
85. C₂	#14545888	direct (N × H)

Maximal subgroups

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

subgroup	index
#14545888	2
C₂×#11763891	2
C₂²×#10587467	2
C₂×M₁₂₈	17

Subgroups — C2×#14545888 #17982820

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14545888 #17982820