Subgroups — C₄×#11763651 #17950264

Order 4352.

654 conjugacy classes of subgroups.

The subgroup lattice has 178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄²×#3624	C₂	1	1	yes	maximal, characteristic
2	C₄²×#3624	C₂	1	1	yes	maximal, characteristic
3	C₂×#11763651	C₂	1	4	yes	maximal
4	C₄×C₈×Dic₁₇	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×#3624	C₄	1	4	yes	—
6	C₂×C₄×#3624	C₄	1	4	yes	—
7	C₂×C₄×#3624	C₂²	1	2	yes	—
8	C₂×C₄×#3624	C₂²	1	2	yes	—
9	#11763651	C₄	1	16	yes	direct product factor
10	C₂×C₄×#3622	C₄	1	1	yes	characteristic
11	C₂×C₈×Dic₁₇	C₄	1	2	yes	—
12	C₂×C₈×Dic₁₇	C₂²	1	2	yes	—
13	C₄²×Dic₁₇	C₂²	1	1	yes	characteristic
14	C₂×C₄×C₈×C₁₇	C₄	1	1	yes	characteristic
15	C₂²×#3624	C₂×C₄	1	4	yes	—
16	C₂²×#3624	C₂×C₄	1	4	yes	—
17	C₂²×C₈×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
21	C₂×C₄×Dic₁₇	C₂×C₄	1	2	yes	—
22	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
23	C₂²×#3622	C₂×C₄	1	2	yes	—
24	C₄×#3624	—	2	8	no	—
25	C₄×#3624	C₈	1	16	yes	complemented
26	C₄×#3624	C₂×C₄	1	8	yes	—
27	C₄×#3624	C₂×C₄	1	8	yes	—
28	C₄×C₈×C₁₇	—	2	2	no	—
29	C₈×Dic₁₇	—	2	4	no	—
30	C₈×Dic₁₇	C₂×C₄	1	8	yes	—
31	C₄×#3622	—	2	2	no	—
32	C₂²×C₄×C₁₇	C₄²	1	2	yes	—
33	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
34	C₂²×Dic₁₇	C₄²	1	2	yes	—
35	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
36	C₂²×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
37	C₂×#3624	—	2	8	no	—
38	C₂×#3624	C₄²	1	8	yes	—
39	C₂×#3624	C₄²	1	8	yes	—
40	C₂×#3624	C₂×C₈	1	16	yes	—
41	C₂×C₈×C₁₇	—	2	2	no	—
42	C₂×C₈×C₁₇	—	2	2	no	—
43	C₂×C₈×C₁₇	C₄²	1	4	yes	—
44	C₄²×C₁₇	M₁₆	1	2	yes	—
45	C₄²×C₁₇	M₁₆	1	2	yes	—
46	C₄×Dic₁₇	C₂×C₈	1	8	yes	—
47	C₄×Dic₁₇	M₁₆	1	4	yes	—
48	C₄×Dic₁₇	M₁₆	1	8	yes	—
49	C₄×Dic₁₇	C₂²×C₄	1	4	yes	—
50	C₂×#3622	—	2	2	no	—
51	C₂×#3622	—	2	2	no	—
52	C₂×#3622	C₄²	1	4	yes	—
53	C₄×#322	—	17	1	no	maximal, Sylow
54	C₂³×C₁₇	C₂×C₄²	1	1	yes	characteristic
55	C₂×C₄×C₁₇	C₄×C₈	1	4	yes	—
56	C₂×C₄×C₁₇	#97	1	4	yes	—
57	C₂×C₄×C₁₇	#97	1	4	yes	—
58	C₂×C₄×C₁₇	C₂×C₄²	1	2	yes	—
59	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
60	C₂×C₄×C₁₇	C₂×M₁₆	1	2	yes	—
61	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
62	C₂×Dic₁₇	C₄×C₈	1	4	yes	—
63	C₂×Dic₁₇	#97	1	4	yes	—
64	C₂×Dic₁₇	#97	1	4	yes	—
65	C₂×Dic₁₇	C₂×C₄²	1	2	yes	—
66	C₂×Dic₁₇	C₂×C₄²	1	2	yes	—
67	C₂×Dic₁₇	C₂²×C₈	1	4	yes	—
68	C₂×Dic₁₇	C₂×M₁₆	1	4	yes	—
69	#3624	—	2	8	no	—
70	#3624	C₄×C₈	1	16	yes	complemented
71	C₈×C₁₇	—	2	4	no	—
72	#3622	—	2	4	no	—
73	C₄²×C₈	—	17	1	no	—
74	C₄²×C₈	—	17	1	no	—
75	C₄²×C₈	—	17	1	no	—
76	C₂×#322	—	17	4	no	—
77	C₂²×C₁₇	C₄³	1	1	yes	characteristic
78	C₂²×C₁₇	C₂×C₄×C₈	1	2	yes	—
79	C₂²×C₁₇	C₂×#97	1	2	yes	—
80	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
81	C₂²×C₁₇	C₂×#97	1	1	yes	characteristic
82	C₄×C₁₇	#322	1	8	yes	complemented
83	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
84	C₄×C₁₇	C₄×M₁₆	1	2	yes	—
85	Dic₁₇	#322	1	8	yes	complemented
86	Dic₁₇	C₂×C₄×C₈	1	4	yes	—
87	Dic₁₇	C₄×M₁₆	1	4	yes	—
88	C₂×C₄×C₈	—	17	4	no	—
89	C₂×C₄×C₈	—	17	2	no	—
90	C₂×C₄×C₈	—	17	2	no	—
91	C₂×C₄×C₈	—	17	2	no	—
92	C₂×C₄×C₈	—	17	4	no	—
93	C₂×C₄×C₈	—	17	2	no	—
94	C₂×C₄×C₈	—	17	1	no	—
95	C₂×C₄×C₈	#595	1	1	yes	characteristic
96	C₄³	—	17	1	no	—
97	#322	—	17	16	no	—
98	C₂×C₁₇	C₂×#322	1	2	yes	—
99	C₂×C₁₇	C₂×#322	1	2	yes	—
100	C₂×C₁₇	C₄²×C₈	1	1	yes	characteristic
101	C₂×C₁₇	C₄×#97	1	1	yes	characteristic
102	C₂×C₁₇	C₄×#97	1	1	yes	characteristic
103	C₂²×C₈	—	17	4	no	—
104	C₂²×C₈	—	17	4	no	—
105	C₂²×C₈	—	17	2	no	—
106	C₂²×C₈	C₂×#595	1	2	yes	—
107	C₂×C₄²	—	17	2	no	—
108	C₂×C₄²	—	17	2	no	—
109	C₂×C₄²	—	17	1	no	—
110	C₂×C₄²	—	17	1	no	—
111	C₂×C₄²	C₂×#595	1	1	yes	characteristic
112	C₄×C₈	—	2	2	no	—
113	C₄×C₈	—	17	8	no	—
114	C₄×C₈	—	17	8	no	—
115	C₄×C₈	—	17	16	no	—
116	C₄×C₈	—	17	8	no	—
117	C₄×C₈	—	34	4	no	—
118	C₄×C₈	—	34	8	no	—
119	C₄×C₈	—	34	2	no	—
120	C₁₇	C₄×#322	1	1	yes	characteristic, complemented, Sylow
121	C₂²×C₄	—	17	2	no	—
122	C₂²×C₄	—	17	1	no	—
123	C₂²×C₄	—	17	1	no	—
124	C₂²×C₄	C₄×#595	1	2	yes	—
125	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
126	C₂×C₈	—	2	2	no	—
127	C₂×C₈	—	2	2	no	—
128	C₂×C₈	—	17	8	no	—
129	C₂×C₈	—	17	16	no	—
130	C₂×C₈	—	17	8	no	—
131	C₂×C₈	—	17	4	no	—
132	C₂×C₈	—	34	8	no	—
133	C₂×C₈	—	34	2	no	—
134	C₂×C₈	—	34	2	no	—
135	C₂×C₈	C₄×#595	1	4	yes	—
136	C₄²	—	17	4	no	—
137	C₄²	—	17	4	no	—
138	C₄²	—	17	8	no	—
139	C₄²	—	17	8	no	—
140	C₄²	#63243	1	2	yes	—
141	C₄²	#63247	1	2	yes	—
142	C₂³	C₂×C₄×#595	1	1	yes	characteristic
143	C₂×C₄	—	17	2	no	—
144	C₂×C₄	—	17	2	no	—
145	C₂×C₄	—	17	4	no	—
146	C₂×C₄	—	17	4	no	—
147	C₂×C₄	—	17	4	no	—
148	C₂×C₄	—	17	4	no	—
149	C₂×C₄	—	17	4	no	—
150	C₂×C₄	C₈×#595	1	4	yes	—
151	C₂×C₄	#10587532	1	4	yes	—
152	C₂×C₄	#10587542	1	4	yes	—
153	C₂×C₄	C₂×#63243	1	1	yes	characteristic
154	C₂×C₄	D₁₇⋊M₁₆	1	2	yes	—
155	C₂×C₄	C₂×C₄×#595	1	2	yes	—
156	C₂×C₄	C₂×#63247	1	1	yes	characteristic
157	C₈	—	2	4	no	—
158	C₈	—	17	16	no	—
159	C₈	—	34	8	no	—
160	C₈	—	34	4	no	—
161	C₂²	C₄²×#595	1	1	yes	characteristic
162	C₂²	C₂×C₈×#595	1	2	yes	—
163	C₂²	C₂×#10587532	1	2	yes	—
164	C₂²	C₂×#10587542	1	1	yes	characteristic
165	C₂²	#11763768	1	1	yes	characteristic
166	C₄	—	17	4	no	—
167	C₄	—	17	4	no	—
168	C₄	—	17	8	no	—
169	C₄	#11763651	1	8	yes	direct product factor
170	C₄	C₄×#63247	1	2	yes	—
171	C₄	C₄×#63243	1	2	yes	—
172	C₂	C₂×#11763651	1	2	yes	—
173	C₂	#14543980	1	2	yes	—
174	C₂	C₄×C₈×#595	1	1	yes	characteristic
175	C₂	C₄×#10587532	1	1	yes	characteristic
176	C₂	C₄×#10587542	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄²	C₂×#595
commutator	C₂×C₁₇	C₄²×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₂×C₄×C₈×C₁₇	C₄
socle, prime radical	C₂³×C₁₇	C₂×C₄²
cosocle	C₂×C₄×Dic₁₇	C₂³
hypercenter	C₂×C₄×C₈	#595
hypocenter	C₁₇	C₄×#322
LCS	G ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
9. #11763651	C₄	direct (N × H)
25. C₄×#3624	C₈	semidirect
70. #3624	C₄×C₈	semidirect
82. C₄×C₁₇	#322	semidirect
85. Dic₁₇	#322	semidirect
120. C₁₇	C₄×#322	semidirect
169. C₄	#11763651	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄²×#3624	2
C₂×#11763651	2
C₄×C₈×Dic₁₇	2
C₄×#322	17

Subgroups — C4×#11763651 #17950264

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#11763651 #17950264