Subgroups — C₄×#11763696 #17960418

Order 4352.

510 conjugacy classes of subgroups.

The subgroup lattice has 170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763696	C₂	1	4	yes	maximal
2	C₄×#10587529	C₂	1	1	yes	maximal, characteristic
3	C₄×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	C₄×C₁₆×D₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×#10587529	C₂²	1	2	yes	—
6	C₄×#63242	C₄	1	1	yes	characteristic
7	C₂×C₈×#595	C₄	1	2	yes	—
8	C₂×C₈×#595	C₂²	1	2	yes	—
9	C₄²×#595	C₄	1	1	yes	characteristic
10	#11763696	C₄	1	16	yes	direct product factor
11	#11763695	C₄	1	2	yes	complemented
12	C₄×#63216	C₄	1	2	yes	complemented
13	C₂×C₁₆×D₁₇	C₂²	1	2	yes	—
14	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
15	C₄×#63214	C₄	1	1	yes	characteristic, complemented
16	C₁₆×Dic₁₇	C₄	1	2	yes	complemented
17	C₄×C₁₆×C₁₇	C₄	1	1	yes	characteristic, complemented
18	C₂×C₄×#595	C₈	1	4	yes	—
19	C₂×C₄×#595	C₂×C₄	1	2	yes	—
20	C₂×#63242	C₂×C₄	1	2	yes	—
21	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
22	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
23	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
24	C₄×#3624	C₈	1	4	yes	—
25	C₂×#63216	C₂×C₄	1	4	yes	—
26	C₈×#595	C₈	1	8	yes	—
27	C₈×#595	C₂×C₄	1	8	yes	—
28	#10587529	C₂×C₄	1	8	yes	—
29	C₂×C₁₆×C₁₇	C₂×C₄	1	2	yes	—
30	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
31	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
32	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂×#63214	C₂×C₄	1	2	yes	—
34	C₄×#3622	C₂×C₄	1	1	yes	characteristic
35	C₁₆×D₁₇	C₂×C₄	1	8	yes	—
36	C₂²×#595	C₂×C₈	1	4	yes	—
37	C₂×C₄×D₁₇	C₂×C₈	1	2	yes	—
38	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
39	C₂×#3624	C₂×C₈	1	4	yes	—
40	C₄×#595	—	2	8	no	—
41	C₄×#595	C₄²	1	4	yes	—
42	C₄×#595	C₂×C₈	1	4	yes	—
43	#63242	C₄²	1	4	yes	—
44	#63242	C₂×C₈	1	4	yes	—
45	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
46	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
47	C₄²×C₁₇	C₄²	1	1	yes	characteristic
48	C₄×Dic₁₇	C₄²	1	1	yes	characteristic
49	C₄×Dic₁₇	C₂×C₈	1	2	yes	—
50	C₂×#3622	C₄²	1	1	yes	characteristic
51	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
52	C₈×D₁₇	C₂×C₈	1	4	yes	—
53	C₈×D₁₇	C₂²×C₄	1	4	yes	—
54	#63216	C₄²	1	8	yes	complemented
55	C₁₆×C₁₇	C₄²	1	4	yes	complemented
56	#63214	C₄²	1	4	yes	complemented
57	C₄×#346	—	17	1	no	maximal, Sylow
58	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
59	C₂×#595	—	2	8	no	—
60	C₂×#595	C₄×C₈	1	8	yes	—
61	C₂×C₄×C₁₇	C₄×C₈	1	2	yes	—
62	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
63	C₂×Dic₁₇	C₄×C₈	1	2	yes	—
64	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
65	C₄×D₁₇	M₃₂	1	8	yes	—
66	C₄×D₁₇	C₂×C₄²	1	2	yes	—
67	C₄×D₁₇	C₂²×C₈	1	2	yes	—
68	#3624	C₄×C₈	1	8	yes	—
69	C₈×C₁₇	C₄×C₈	1	2	yes	—
70	C₈×C₁₇	C₂×C₄²	1	2	yes	—
71	#3622	C₄×C₈	1	2	yes	—
72	#3622	C₂×C₄²	1	2	yes	—
73	C₂×#346	—	17	4	no	—
74	C₂×C₄×C₁₆	—	17	1	no	—
75	C₂×C₄×C₁₆	—	17	1	no	—
76	C₄²×C₈	—	17	1	no	—
77	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
78	C₂×D₁₇	C₂×C₄×C₈	1	2	yes	—
79	C₂×D₁₇	C₂×M₃₂	1	4	yes	—
80	#595	—	2	8	no	—
81	C₄×C₁₇	#346	1	4	yes	complemented
82	C₄×C₁₇	C₄³	1	1	yes	characteristic
83	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
84	Dic₁₇	#346	1	4	yes	complemented
85	Dic₁₇	C₂×C₄×C₈	1	2	yes	—
86	C₂²×C₁₆	—	17	2	no	—
87	C₂²×C₁₆	—	17	2	no	—
88	C₂×C₄×C₈	—	17	2	no	—
89	C₂×C₄×C₈	—	17	2	no	—
90	C₂×C₄×C₈	—	17	1	no	—
91	C₂×C₄×C₈	—	17	1	no	—
92	C₄³	—	17	1	no	—
93	#346	—	17	16	no	—
94	C₄×C₁₆	—	17	2	no	—
95	C₄×C₁₆	—	17	2	no	—
96	C₄×C₁₆	—	17	2	no	—
97	C₄×C₁₆	—	17	1	no	—
98	C₄×C₁₆	#595	1	1	yes	characteristic, complemented
99	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
100	C₂×C₁₇	C₂×#346	1	2	yes	—
101	D₁₇	C₄×M₃₂	1	4	yes	—
102	C₂²×C₈	—	17	2	no	—
103	C₂²×C₈	—	17	1	no	—
104	C₂²×C₈	—	17	1	no	—
105	C₂×C₄²	—	17	2	no	—
106	C₂×C₄²	—	17	1	no	—
107	C₂×C₄²	—	17	4	no	—
108	C₂×C₁₆	—	17	4	no	—
109	C₂×C₁₆	—	17	8	no	—
110	C₂×C₁₆	—	17	2	no	—
111	C₂×C₁₆	—	17	8	no	—
112	C₂×C₁₆	C₂×#595	1	2	yes	—
113	C₄×C₈	—	17	8	no	—
114	C₄×C₈	—	17	8	no	—
115	C₄×C₈	—	17	4	no	—
116	C₄×C₈	—	17	1	no	—
117	C₄×C₈	—	17	1	no	—
118	C₄×C₈	—	17	1	no	—
119	C₄×C₈	C₂×#595	1	1	yes	characteristic
120	C₁₇	C₄×#346	1	1	yes	characteristic, complemented, Sylow
121	C₂²×C₄	—	17	1	no	—
122	C₂²×C₄	—	17	2	no	—
123	C₂²×C₄	—	17	4	no	—
124	C₂×C₈	—	17	4	no	—
125	C₂×C₈	—	17	4	no	—
126	C₂×C₈	—	17	4	no	—
127	C₂×C₈	—	17	1	no	—
128	C₂×C₈	—	17	1	no	—
129	C₂×C₈	—	17	4	no	—
130	C₂×C₈	—	17	4	no	—
131	C₂×C₈	C₄×#595	1	1	yes	characteristic
132	C₂×C₈	C₂²×#595	1	1	yes	characteristic
133	C₄²	—	17	4	no	—
134	C₄²	—	17	4	no	—
135	C₄²	—	17	1	no	—
136	C₄²	—	17	2	no	—
137	C₄²	—	34	8	no	—
138	C₄²	C₄×#595	1	1	yes	characteristic
139	C₁₆	—	17	8	no	—
140	C₁₆	—	17	4	no	—
141	C₁₆	C₄×#595	1	4	yes	complemented
142	C₂³	—	17	1	no	—
143	C₂×C₄	—	17	1	no	—
144	C₂×C₄	—	17	2	no	—
145	C₂×C₄	—	17	2	no	—
146	C₂×C₄	—	17	2	no	—
147	C₂×C₄	—	17	8	no	—
148	C₂×C₄	—	17	8	no	—
149	C₂×C₄	—	34	8	no	—
150	C₂×C₄	C₈×#595	1	2	yes	—
151	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
152	C₈	—	17	8	no	—
153	C₈	—	17	2	no	—
154	C₈	—	17	2	no	—
155	C₈	C₈×#595	1	2	yes	—
156	C₈	C₂×C₄×#595	1	2	yes	—
157	C₂²	—	17	2	no	—
158	C₂²	—	17	4	no	—
159	C₂²	C₂×C₈×#595	1	1	yes	characteristic
160	C₄	—	17	2	no	—
161	C₄	—	17	4	no	—
162	C₄	—	34	8	no	—
163	C₄	#11763696	1	4	yes	direct product factor
164	C₄	C₄²×#595	1	1	yes	characteristic
165	C₄	C₂×C₈×#595	1	1	yes	characteristic
166	C₂	—	17	4	no	—
167	C₂	C₄×C₈×#595	1	1	yes	characteristic
168	C₂	C₂×#11763696	1	2	yes	—

	subgroup	G/H
center	C₄×C₈	C₂×#595
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂×C₈	C₂²×#595
Fitting	C₄×C₁₆×C₁₇	C₄
socle	C₂²×C₁₇	C₂×C₄×C₈
prime radical	C₂²×D₁₇	C₂²×C₈
cosocle	C₂×C₈×D₁₇	C₂³
hypercenter	C₄×C₁₆	#595
hypocenter	C₁₇	C₄×#346
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄×C₈ ◁ C₄×C₁₆

Complements

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

N	H ≅ G/N	type
10. #11763696	C₄	direct (N × H)
11. #11763695	C₄	semidirect
12. C₄×#63216	C₄	semidirect
15. C₄×#63214	C₄	semidirect
16. C₁₆×Dic₁₇	C₄	semidirect
17. C₄×C₁₆×C₁₇	C₄	semidirect
54. #63216	C₄²	semidirect
55. C₁₆×C₁₇	C₄²	semidirect
56. #63214	C₄²	semidirect
81. C₄×C₁₇	#346	semidirect
84. Dic₁₇	#346	semidirect
98. C₄×C₁₆	#595	semidirect
120. C₁₇	C₄×#346	semidirect
141. C₁₆	C₄×#595	semidirect
163. C₄	#11763696	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#11763696	2
C₄×#10587529	2
C₄×C₈×#595	2
C₄×C₁₆×D₁₇	2
C₄×#346	17

Subgroups — C4×#11763696 #17960418

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763696 #17960418