Subgroups — C₂²×#11763902 #17983001

Order 4352.

1022 conjugacy classes of subgroups.

The subgroup lattice has 174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#10587665	C₂	1	2	yes	maximal
2	C₂×#11763902	C₂	1	12	yes	maximal, direct product factor
3	C₂²×C₈×#595	C₂	1	1	yes	maximal, characteristic
4	C₂×#10587665	C₄	1	12	yes	complemented
5	C₂×#10587665	C₂²	1	12	yes	—
6	C₂²×#63241	C₄	1	4	yes	complemented
7	#11763902	C₂²	1	16	yes	direct product factor
8	C₂²×#63242	C₂²	1	1	yes	characteristic
9	C₂²×C₄×#595	C₄	1	1	yes	characteristic
10	C₂×C₈×#595	C₄	1	6	yes	—
11	C₂×C₈×#595	C₂²	1	6	yes	—
12	C₂²×C₈×D₁₇	C₄	1	1	yes	characteristic
13	C₂³×#595	C₈	1	2	yes	—
14	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
15	C₂²×#3624	C₂×C₄	1	2	yes	—
16	C₂×C₄×#595	C₈	1	6	yes	—
17	C₂×C₄×#595	C₂×C₄	1	6	yes	—
18	C₂×#63242	C₂×C₄	1	3	yes	—
19	C₂×#63242	C₂×C₄	1	6	yes	—
20	C₂×#63242	C₂³	1	3	yes	—
21	C₂×#63241	C₂×C₄	1	24	yes	complemented
22	#10587665	C₂×C₄	1	24	yes	complemented
23	#10587665	C₂³	1	8	yes	—
24	C₂²×C₈×C₁₇	C₈	1	1	yes	characteristic
25	C₂²×#3622	C₈	1	1	yes	characteristic
26	C₂×C₈×D₁₇	C₈	1	6	yes	—
27	C₂×C₈×D₁₇	C₂×C₄	1	6	yes	—
28	C₈×#595	C₂×C₄	1	12	yes	—
29	C₈×#595	C₂³	1	4	yes	—
30	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
31	C₂²×#595	C₁₆	1	16	yes	complemented
32	C₂²×#595	C₂×C₈	1	12	yes	—
33	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
34	C₂²×Dic₁₇	C₄²	1	1	yes	characteristic
35	C₂×C₄×D₁₇	C₄²	1	3	yes	—
36	C₂×C₄×D₁₇	C₂×C₈	1	3	yes	—
37	C₂×C₄×D₁₇	C₂×C₈	1	3	yes	—
38	C₂×C₄×D₁₇	C₂²×C₄	1	3	yes	—
39	C₂×#3624	C₄²	1	6	yes	—
40	C₂×#3624	C₂²×C₄	1	6	yes	—
41	C₄×#595	C₂×C₈	1	12	yes	—
42	C₄×#595	C₂²×C₄	1	4	yes	—
43	#63242	C₄²	1	6	yes	—
44	#63242	C₂²×C₄	1	3	yes	—
45	#63242	C₂²×C₄	1	6	yes	—
46	#63242	C₂⁴	1	1	yes	characteristic
47	#63241	C₂²×C₄	1	16	yes	complemented
48	C₂×C₈×C₁₇	C₂×C₈	1	6	yes	—
49	C₂×#3622	C₂×C₈	1	6	yes	—
50	C₈×D₁₇	C₂×C₈	1	12	yes	—
51	C₈×D₁₇	C₂²×C₄	1	4	yes	—
52	C₂²×C₄×C₁₆	—	17	1	no	maximal, Sylow
53	C₂³×C₁₇	C₄×C₈	1	1	yes	characteristic
54	C₂²×D₁₇	C₄×C₈	1	3	yes	—
55	C₂²×D₁₇	C₂×C₁₆	1	8	yes	—
56	C₂²×D₁₇	C₂²×C₈	1	3	yes	—
57	C₂×#595	C₂×C₁₆	1	48	yes	complemented
58	C₂×#595	C₂²×C₈	1	8	yes	—
59	C₂×C₄×C₁₇	C₄×C₈	1	3	yes	—
60	C₂×C₄×C₁₇	C₂²×C₈	1	3	yes	—
61	C₂×Dic₁₇	C₄×C₈	1	3	yes	—
62	C₂×Dic₁₇	C₂×C₄²	1	3	yes	—
63	C₄×D₁₇	C₄×C₈	1	6	yes	—
64	C₄×D₁₇	C₂×C₄²	1	3	yes	—
65	C₄×D₁₇	C₂²×C₈	1	3	yes	—
66	C₄×D₁₇	C₂²×C₈	1	3	yes	—
67	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
68	#3624	C₂×C₄²	1	6	yes	—
69	#3624	C₂³×C₄	1	2	yes	—
70	C₈×C₁₇	C₂²×C₈	1	4	yes	—
71	#3622	C₂²×C₈	1	4	yes	—
72	C₂³×C₁₆	—	17	2	no	—
73	C₂²×C₄×C₈	—	17	1	no	—
74	C₂×C₄×C₁₆	—	17	12	no	—
75	C₂²×C₁₇	C₄×C₁₆	1	4	yes	complemented
76	C₂²×C₁₇	C₂×C₄×C₈	1	3	yes	—
77	C₂×D₁₇	C₄×C₁₆	1	12	yes	complemented
78	C₂×D₁₇	C₂×C₄×C₈	1	3	yes	—
79	C₂×D₁₇	C₂²×C₁₆	1	12	yes	—
80	C₂×D₁₇	C₂³×C₈	1	1	yes	characteristic
81	#595	C₂²×C₁₆	1	16	yes	complemented
82	C₄×C₁₇	C₂×C₄×C₈	1	3	yes	—
83	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
84	Dic₁₇	C₂×C₄×C₈	1	3	yes	—
85	Dic₁₇	C₂²×C₄²	1	1	yes	characteristic
86	C₂³×C₈	—	17	1	no	—
87	C₂³×C₈	—	17	1	no	—
88	C₂²×C₄²	—	17	1	no	—
89	C₂²×C₁₆	—	17	12	no	—
90	C₂²×C₁₆	—	17	4	no	—
91	C₂²×C₁₆	—	17	12	no	—
92	C₂×C₄×C₈	—	17	6	no	—
93	C₂×C₄×C₈	—	17	6	no	—
94	C₄×C₁₆	—	17	16	no	—
95	C₂×C₁₇	C₂×C₄×C₁₆	1	6	yes	complemented
96	C₂×C₁₇	C₂²×C₄×C₈	1	1	yes	characteristic
97	D₁₇	C₂×C₄×C₁₆	1	6	yes	complemented
98	D₁₇	C₂³×C₁₆	1	2	yes	—
99	C₂³×C₄	—	17	2	no	—
100	C₂³×C₄	—	17	1	no	—
101	C₂²×C₈	—	17	3	no	—
102	C₂²×C₈	—	17	6	no	—
103	C₂²×C₈	—	17	3	no	—
104	C₂²×C₈	—	17	2	no	—
105	C₂²×C₈	—	17	1	no	—
106	C₂²×C₈	—	17	6	no	—
107	C₂²×C₈	—	17	6	no	—
108	C₂²×C₈	#3633	1	1	yes	characteristic
109	C₂×C₄²	—	17	6	no	—
110	C₂×C₄²	—	17	6	no	—
111	C₂×C₁₆	—	17	24	no	—
112	C₂×C₁₆	—	17	8	no	—
113	C₂×C₁₆	—	17	24	no	—
114	C₄×C₈	—	17	4	no	—
115	C₄×C₈	—	17	12	no	—
116	C₁₇	C₂²×C₄×C₁₆	1	1	yes	characteristic, complemented, Sylow
117	C₂⁴	—	17	1	no	—
118	C₂²×C₄	—	17	16	no	—
119	C₂²×C₄	—	17	12	no	—
120	C₂²×C₄	—	17	1	no	—
121	C₂²×C₄	—	17	3	no	—
122	C₂²×C₄	—	17	3	no	—
123	C₂²×C₄	—	17	3	no	—
124	C₂²×C₄	—	17	3	no	—
125	C₂²×C₄	C₂×#3633	1	1	yes	characteristic
126	C₂×C₈	—	17	6	no	—
127	C₂×C₈	—	17	3	no	—
128	C₂×C₈	—	17	6	no	—
129	C₂×C₈	—	17	1	no	—
130	C₂×C₈	—	17	6	no	—
131	C₂×C₈	—	17	6	no	—
132	C₂×C₈	—	17	6	no	—
133	C₂×C₈	—	17	4	no	—
134	C₂×C₈	—	17	12	no	—
135	C₂×C₈	C₂×#3633	1	6	yes	—
136	C₄²	—	17	12	no	—
137	C₄²	—	17	4	no	—
138	C₁₆	—	17	16	no	—
139	C₂³	—	17	8	no	—
140	C₂³	—	17	3	no	—
141	C₂³	—	17	3	no	—
142	C₂³	C₄×#3633	1	1	yes	characteristic
143	C₂×C₄	—	17	8	no	—
144	C₂×C₄	—	17	48	no	—
145	C₂×C₄	—	17	3	no	—
146	C₂×C₄	—	17	3	no	—
147	C₂×C₄	—	17	3	no	—
148	C₂×C₄	—	17	3	no	—
149	C₂×C₄	—	17	6	no	—
150	C₂×C₄	—	17	1	no	—
151	C₂×C₄	—	17	3	no	—
152	C₂×C₄	C₄×#3633	1	3	yes	—
153	C₂×C₄	C₂²×#3633	1	3	yes	—
154	C₈	—	17	2	no	—
155	C₈	—	17	6	no	—
156	C₈	—	17	4	no	—
157	C₈	C₂²×#3633	1	4	yes	—
158	C₂²	—	17	12	no	—
159	C₂²	—	17	12	no	—
160	C₂²	—	17	1	no	—
161	C₂²	—	17	3	no	—
162	C₂²	#11763902	1	4	yes	direct product factor
163	C₂²	C₂×C₄×#3633	1	3	yes	—
164	C₄	—	17	16	no	—
165	C₄	—	17	1	no	—
166	C₄	—	17	3	no	—
167	C₄	C₂×C₄×#3633	1	3	yes	—
168	C₄	C₂³×#3633	1	1	yes	characteristic
169	C₂	—	17	2	no	—
170	C₂	—	17	6	no	—
171	C₂	C₂×#11763902	1	6	yes	direct product factor
172	C₂	C₂²×C₄×#3633	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	#3633
commutator, hypocenter	C₁₇	C₂²×C₄×C₁₆
Frattini	C₄	C₂³×#3633
Fitting	C₂²×C₈×C₁₇	C₈
socle	C₂³×C₁₇	C₄×C₈
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	#63242	C₂⁴
LCS	G ▷ C₁₇
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
2. C₂×#11763902	C₂	direct (N × H)
4. C₂×#10587665	C₄	semidirect
6. C₂²×#63241	C₄	semidirect
7. #11763902	C₂²	direct (N × H)
21. C₂×#63241	C₂×C₄	semidirect
22. #10587665	C₂×C₄	semidirect
31. C₂²×#595	C₁₆	semidirect
47. #63241	C₂²×C₄	semidirect
57. C₂×#595	C₂×C₁₆	semidirect
75. C₂²×C₁₇	C₄×C₁₆	semidirect
77. C₂×D₁₇	C₄×C₁₆	semidirect
81. #595	C₂²×C₁₆	semidirect
95. C₂×C₁₇	C₂×C₄×C₁₆	semidirect
97. D₁₇	C₂×C₄×C₁₆	semidirect
116. C₁₇	C₂²×C₄×C₁₆	semidirect
162. C₂²	#11763902	direct (N × H)
171. C₂	C₂×#11763902	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#10587665	2
C₂×#11763902	2
C₂²×C₈×#595	2
C₂²×C₄×C₁₆	17

Subgroups — C22×#11763902 #17983001

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#11763902 #17983001