Subgroups — C₂×#14531078 #17192433

Order 4352.

470 conjugacy classes of subgroups.

The subgroup lattice has 118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14531078	C₂	1	8	yes	maximal, direct product factor
2	C₂×#11762643	C₂	1	3	yes	maximal, complemented
3	C₂²×#10587465	C₂	1	3	yes	maximal, complemented
4	C₂×C₁₇×#504	C₂	1	1	yes	maximal, characteristic
5	#11762643	C₂²	1	12	yes	complemented
6	C₂×#10587465	C₂²	1	1	yes	characteristic
7	C₂×#10587465	C₂²	1	3	yes	—
8	C₂×#10587465	C₂²	1	12	yes	complemented
9	C₂×C₁₇×#131	C₄	1	1	yes	characteristic
10	C₁₇×#504	C₄	1	4	yes	—
11	C₁₇×#504	C₂²	1	4	yes	—
12	C₂×C₁₇×M₃₂	C₄	1	3	yes	—
13	C₂²×C₁₆×C₁₇	C₂²	1	3	yes	—
14	C₂×#41×C₁₇	C₈	1	1	yes	characteristic
15	C₁₇×#131	C₈	1	4	yes	—
16	C₁₇×#131	C₂×C₄	1	4	yes	—
17	C₂×M₁₆×C₁₇	C₈	1	3	yes	—
18	C₂²×C₈×C₁₇	C₂×C₄	1	3	yes	—
19	C₁₇×M₃₂	C₂×C₄	1	12	yes	—
20	C₂×C₁₆×C₁₇	C₂×C₄	1	3	yes	—
21	C₂×C₁₆×C₁₇	C₂×C₄	1	6	yes	—
22	C₂×C₁₆×C₁₇	C₂³	1	6	yes	—
23	C₂×C₁₆×C₁₇	C₂³	1	1	yes	characteristic
24	#10587465	C₂³	1	2	yes	—
25	#10587465	C₂³	1	6	yes	—
26	#41×C₁₇	C₁₆	1	4	yes	—
27	#41×C₁₇	C₂×C₈	1	4	yes	—
28	C₂×Q₈×C₁₇	C₁₆	1	1	yes	characteristic
29	C₂×D₄×C₁₇	C₁₆	1	3	yes	—
30	C₂²×C₄×C₁₇	C₂×C₈	1	3	yes	—
31	M₁₆×C₁₇	C₂×C₈	1	12	yes	—
32	C₂×C₈×C₁₇	C₂×C₈	1	3	yes	—
33	C₂×C₈×C₁₇	C₂×C₈	1	6	yes	—
34	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
35	C₂×C₈×C₁₇	C₂²×C₄	1	6	yes	—
36	C₁₆×C₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₁₆×C₁₇	C₂²×C₄	1	6	yes	—
38	C₁₆×C₁₇	C₂⁴	1	1	yes	characteristic
39	C₂×#2258	—	17	1	no	maximal, Sylow
40	C₂³×C₁₇	C₂×C₁₆	1	3	yes	—
41	Q₈×C₁₇	C₂×C₁₆	1	4	yes	—
42	D₄×C₁₇	C₂×C₁₆	1	12	yes	—
43	C₂×C₄×C₁₇	C₂×C₁₆	1	3	yes	—
44	C₂×C₄×C₁₇	C₂×C₁₆	1	6	yes	—
45	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
46	C₂×C₄×C₁₇	C₂²×C₈	1	6	yes	—
47	C₈×C₁₇	C₂²×C₈	1	1	yes	characteristic
48	C₈×C₁₇	C₂²×C₈	1	6	yes	—
49	C₈×C₁₇	C₂³×C₄	1	1	yes	characteristic
50	C₂×#504	D₁₇	1	1	yes	characteristic
51	#2258	—	17	8	no	—
52	C₂×M₆₄	—	17	3	no	—
53	C₂²×C₃₂	—	17	3	no	—
54	C₂²×C₁₇	—	2	6	no	—
55	C₂²×C₁₇	C₂²×C₁₆	1	6	yes	—
56	C₂²×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
57	C₄×C₁₇	C₂²×C₁₆	1	1	yes	characteristic
58	C₄×C₁₇	C₂²×C₁₆	1	6	yes	—
59	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
60	C₂×#131	Dic₁₇	1	1	yes	characteristic
61	#504	Dic₁₇	1	4	yes	—
62	#504	C₂×D₁₇	1	4	yes	—
63	C₂×M₃₂	Dic₁₇	1	3	yes	—
64	C₂²×C₁₆	C₂×D₁₇	1	3	yes	—
65	M₆₄	—	17	12	no	—
66	C₂×C₃₂	—	17	12	no	—
67	C₂×C₃₂	—	17	1	no	—
68	C₂×C₃₂	—	17	3	no	—
69	C₂×C₁₇	—	2	6	no	—
70	C₂×C₁₇	#2258	1	2	yes	complemented
71	C₂×C₁₇	C₂³×C₁₆	1	1	yes	characteristic
72	C₂×#41	#3622	1	1	yes	characteristic
73	#131	#3622	1	4	yes	—
74	#131	C₂×Dic₁₇	1	4	yes	—
75	C₂×M₁₆	#3622	1	3	yes	—
76	C₂²×C₈	C₂×Dic₁₇	1	3	yes	—
77	M₃₂	C₂×Dic₁₇	1	12	yes	—
78	C₂×C₁₆	C₂×Dic₁₇	1	3	yes	—
79	C₂×C₁₆	C₂×Dic₁₇	1	6	yes	—
80	C₂×C₁₆	C₂²×D₁₇	1	6	yes	—
81	C₂×C₁₆	C₂²×D₁₇	1	1	yes	characteristic
82	C₃₂	—	17	2	no	—
83	C₃₂	—	17	6	no	—
84	C₁₇	C₂×#2258	1	1	yes	characteristic, complemented, Sylow
85	#41	#63214	1	4	yes	—
86	#41	C₂×#3622	1	4	yes	—
87	C₂×Q₈	#63214	1	1	yes	characteristic
88	C₂×D₄	#63214	1	3	yes	—
89	C₂²×C₄	C₂×#3622	1	3	yes	—
90	M₁₆	C₂×#3622	1	12	yes	—
91	C₂×C₈	C₂×#3622	1	3	yes	—
92	C₂×C₈	C₂×#3622	1	6	yes	—
93	C₂×C₈	C₂²×Dic₁₇	1	1	yes	characteristic
94	C₂×C₈	C₂²×Dic₁₇	1	6	yes	—
95	C₁₆	C₂²×Dic₁₇	1	1	yes	characteristic
96	C₁₆	C₂²×Dic₁₇	1	6	yes	—
97	C₁₆	C₂³×D₁₇	1	1	yes	characteristic
98	C₂³	C₂×#63214	1	3	yes	—
99	Q₈	C₂×#63214	1	4	yes	—
100	D₄	C₂×#63214	1	12	yes	—
101	C₂×C₄	C₂×#63214	1	3	yes	—
102	C₂×C₄	C₂×#63214	1	6	yes	—
103	C₂×C₄	C₂²×#3622	1	1	yes	characteristic
104	C₂×C₄	C₂²×#3622	1	6	yes	—
105	C₈	C₂²×#3622	1	1	yes	characteristic
106	C₈	C₂²×#3622	1	6	yes	—
107	C₈	C₂³×Dic₁₇	1	1	yes	characteristic
108	C₂²	—	2	6	no	—
109	C₂²	C₂²×#63214	1	6	yes	—
110	C₂²	C₂²×#63214	1	1	yes	characteristic
111	C₄	C₂²×#63214	1	1	yes	characteristic
112	C₄	C₂²×#63214	1	6	yes	—
113	C₄	C₂³×#3622	1	1	yes	characteristic
114	C₂	—	2	6	no	—
115	C₂	#14531078	1	2	yes	direct product factor
116	C₂	C₂³×#63214	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₁₆	C₂²×D₁₇
commutator	C₂×C₁₇	C₂³×C₁₆
Frattini	C₁₆	C₂³×D₁₇
Fitting	C₂×C₁₇×#504	C₂
socle	C₂²×C₁₇	C₂²×C₁₆
prime radical	C₂×#41×C₁₇	C₈
cosocle	C₁₆×C₁₇	C₂⁴
hypercenter	C₂×#504	D₁₇
hypocenter	C₁₇	C₂×#2258
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₁₆ ◁ C₂×#504

Complements

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

N	H ≅ G/N	type
1. #14531078	C₂	direct (N × H)
2. C₂×#11762643	C₂	semidirect
3. C₂²×#10587465	C₂	semidirect
5. #11762643	C₂²	semidirect
8. C₂×#10587465	C₂²	semidirect
70. C₂×C₁₇	#2258	semidirect
84. C₁₇	C₂×#2258	semidirect
115. C₂	#14531078	direct (N × H)

Maximal subgroups

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

subgroup	index
#14531078	2
C₂×#11762643	2
C₂²×#10587465	2
C₂×C₁₇×#504	2
C₂×#2258	17

Subgroups — C2×#14531078 #17192433

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#14531078 #17192433