Subgroups — C₂×C₄×C₁₁×C₁₆×C₁₇ #72201213

Order 23936.

432 conjugacy classes of subgroups.

The subgroup lattice has 168 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₈×C₁₁×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₁₁×C₁₆×C₁₇	C₂	1	2	yes	maximal
3	C₄×C₁₁×C₁₆×C₁₇	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₈×C₁₁×C₁₇	C₄	1	1	yes	characteristic
5	C₂²×C₈×C₁₁×C₁₇	C₂²	1	1	yes	characteristic
6	C₂×C₄²×C₁₁×C₁₇	C₄	1	1	yes	characteristic
7	C₄×C₈×C₁₁×C₁₇	C₄	1	2	yes	—
8	C₄×C₈×C₁₁×C₁₇	C₂²	1	2	yes	—
9	C₂×C₁₁×C₁₆×C₁₇	C₄	1	8	yes	direct product factor
10	C₂×C₁₁×C₁₆×C₁₇	C₂²	1	4	yes	—
11	C₂²×C₄×C₁₁×C₁₇	C₈	1	2	yes	—
12	C₂²×C₄×C₁₁×C₁₇	C₂×C₄	1	1	yes	characteristic
13	C₄²×C₁₁×C₁₇	C₈	1	2	yes	—
14	C₄²×C₁₁×C₁₇	C₂×C₄	1	2	yes	—
15	C₂×C₈×C₁₁×C₁₇	C₈	1	4	yes	—
16	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	1	yes	characteristic
17	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	2	yes	—
18	C₂×C₈×C₁₁×C₁₇	C₂×C₄	1	4	yes	—
19	C₂×C₈×C₁₁×C₁₇	C₂³	1	1	yes	characteristic
20	C₁₁×C₁₆×C₁₇	C₂×C₄	1	8	yes	direct product factor
21	C₂×C₄×C₁₆×C₁₇	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂³×C₁₁×C₁₇	C₂×C₈	1	1	yes	characteristic
23	C₂×C₄×C₁₁×C₁₇	C₁₆	1	8	yes	direct product factor
24	C₂×C₄×C₁₁×C₁₇	C₄²	1	2	yes	—
25	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	1	yes	characteristic
26	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	2	yes	—
27	C₂×C₄×C₁₁×C₁₇	C₂×C₈	1	4	yes	—
28	C₂×C₄×C₁₁×C₁₇	C₂²×C₄	1	1	yes	characteristic
29	C₈×C₁₁×C₁₇	C₄²	1	2	yes	—
30	C₈×C₁₁×C₁₇	C₂×C₈	1	4	yes	—
31	C₈×C₁₁×C₁₇	C₂²×C₄	1	2	yes	—
32	C₂×C₄×C₁₁×C₁₆	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂²×C₁₆×C₁₇	C₂×C₁₁	1	2	yes	—
34	C₂×C₄×C₈×C₁₇	C₂×C₁₁	1	1	yes	characteristic
35	C₄×C₁₆×C₁₇	C₂×C₁₁	1	4	yes	direct product factor
36	C₂²×C₁₁×C₁₇	C₄×C₈	1	2	yes	—
37	C₂²×C₁₁×C₁₇	C₂×C₁₆	1	4	yes	—
38	C₂²×C₁₁×C₁₇	C₂²×C₈	1	1	yes	characteristic
39	C₄×C₁₁×C₁₇	C₄×C₈	1	2	yes	—
40	C₄×C₁₁×C₁₇	C₂×C₁₆	1	8	yes	direct product factor
41	C₄×C₁₁×C₁₇	C₂×C₄²	1	1	yes	characteristic
42	C₄×C₁₁×C₁₇	C₂²×C₈	1	1	yes	characteristic
43	C₂²×C₁₁×C₁₆	C₂×C₁₇	1	2	yes	—
44	C₂×C₄×C₈×C₁₁	C₂×C₁₇	1	1	yes	characteristic
45	C₄×C₁₁×C₁₆	C₂×C₁₇	1	4	yes	direct product factor
46	C₂²×C₈×C₁₇	C₄×C₁₁	1	1	yes	characteristic
47	C₂²×C₈×C₁₇	C₂²×C₁₁	1	1	yes	characteristic
48	C₂×C₄²×C₁₇	C₄×C₁₁	1	1	yes	characteristic
49	C₂×C₁₆×C₁₇	C₄×C₁₁	1	8	yes	direct product factor
50	C₂×C₁₆×C₁₇	C₂²×C₁₁	1	4	yes	—
51	C₄×C₈×C₁₇	C₄×C₁₁	1	2	yes	—
52	C₄×C₈×C₁₇	C₂²×C₁₁	1	2	yes	—
53	C₂×C₁₁×C₁₇	C₄×C₁₆	1	4	yes	direct product factor
54	C₂×C₁₁×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
55	C₂×C₁₁×C₁₇	C₂²×C₁₆	1	2	yes	—
56	C₂²×C₈×C₁₁	C₄×C₁₇	1	1	yes	characteristic
57	C₂²×C₈×C₁₁	C₂²×C₁₇	1	1	yes	characteristic
58	C₂×C₄²×C₁₁	C₄×C₁₇	1	1	yes	characteristic
59	C₂×C₁₁×C₁₆	C₄×C₁₇	1	8	yes	direct product factor
60	C₂×C₁₁×C₁₆	C₂²×C₁₇	1	4	yes	—
61	C₄×C₈×C₁₁	C₄×C₁₇	1	2	yes	—
62	C₄×C₈×C₁₁	C₂²×C₁₇	1	2	yes	—
63	C₂²×C₄×C₁₇	C₈×C₁₁	1	2	yes	—
64	C₂²×C₄×C₁₇	C₂×C₄×C₁₁	1	1	yes	characteristic
65	C₂×C₈×C₁₇	C₈×C₁₁	1	4	yes	—
66	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	1	yes	characteristic
67	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	2	yes	—
68	C₂×C₈×C₁₇	C₂×C₄×C₁₁	1	4	yes	—
69	C₂×C₈×C₁₇	C₂³×C₁₁	1	1	yes	characteristic
70	C₄²×C₁₇	C₈×C₁₁	1	2	yes	—
71	C₄²×C₁₇	C₂×C₄×C₁₁	1	2	yes	—
72	C₁₆×C₁₇	C₂×C₄×C₁₁	1	8	yes	direct product factor
73	C₁₁×C₁₇	C₂×C₄×C₁₆	1	1	yes	characteristic, direct product factor, Hall
74	C₂²×C₄×C₁₁	C₈×C₁₇	1	2	yes	—
75	C₂²×C₄×C₁₁	C₂×C₄×C₁₇	1	1	yes	characteristic
76	C₂×C₈×C₁₁	C₈×C₁₇	1	4	yes	—
77	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	1	yes	characteristic
78	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	2	yes	—
79	C₂×C₈×C₁₁	C₂×C₄×C₁₇	1	4	yes	—
80	C₂×C₈×C₁₁	C₂³×C₁₇	1	1	yes	characteristic
81	C₄²×C₁₁	C₈×C₁₇	1	2	yes	—
82	C₄²×C₁₁	C₂×C₄×C₁₇	1	2	yes	—
83	C₁₁×C₁₆	C₂×C₄×C₁₇	1	8	yes	direct product factor
84	C₂³×C₁₇	C₂×C₈×C₁₁	1	1	yes	characteristic
85	C₂×C₄×C₁₇	C₁₁×C₁₆	1	8	yes	direct product factor
86	C₂×C₄×C₁₇	C₄²×C₁₁	1	2	yes	—
87	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	1	yes	characteristic
88	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	2	yes	—
89	C₂×C₄×C₁₇	C₂×C₈×C₁₁	1	4	yes	—
90	C₂×C₄×C₁₇	C₂²×C₄×C₁₁	1	1	yes	characteristic
91	C₈×C₁₇	C₄²×C₁₁	1	2	yes	—
92	C₈×C₁₇	C₂×C₈×C₁₁	1	4	yes	—
93	C₈×C₁₇	C₂²×C₄×C₁₁	1	2	yes	—
94	C₂×C₄×C₁₆	C₁₁×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
95	C₂³×C₁₁	C₂×C₈×C₁₇	1	1	yes	characteristic
96	C₂×C₄×C₁₁	C₁₆×C₁₇	1	8	yes	direct product factor
97	C₂×C₄×C₁₁	C₄²×C₁₇	1	2	yes	—
98	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	1	yes	characteristic
99	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	2	yes	—
100	C₂×C₄×C₁₁	C₂×C₈×C₁₇	1	4	yes	—
101	C₂×C₄×C₁₁	C₂²×C₄×C₁₇	1	1	yes	characteristic
102	C₈×C₁₁	C₄²×C₁₇	1	2	yes	—
103	C₈×C₁₁	C₂×C₈×C₁₇	1	4	yes	—
104	C₈×C₁₁	C₂²×C₄×C₁₇	1	2	yes	—
105	C₂²×C₁₇	C₄×C₈×C₁₁	1	2	yes	—
106	C₂²×C₁₇	C₂×C₁₁×C₁₆	1	4	yes	—
107	C₂²×C₁₇	C₂²×C₈×C₁₁	1	1	yes	characteristic
108	C₄×C₁₇	C₄×C₈×C₁₁	1	2	yes	—
109	C₄×C₁₇	C₂×C₁₁×C₁₆	1	8	yes	direct product factor
110	C₄×C₁₇	C₂×C₄²×C₁₁	1	1	yes	characteristic
111	C₄×C₁₇	C₂²×C₈×C₁₁	1	1	yes	characteristic
112	C₂²×C₁₆	C₂×C₁₁×C₁₇	1	2	yes	—
113	C₂×C₄×C₈	C₂×C₁₁×C₁₇	1	1	yes	characteristic
114	C₄×C₁₆	C₂×C₁₁×C₁₇	1	4	yes	direct product factor
115	C₂²×C₁₁	C₄×C₈×C₁₇	1	2	yes	—
116	C₂²×C₁₁	C₂×C₁₆×C₁₇	1	4	yes	—
117	C₂²×C₁₁	C₂²×C₈×C₁₇	1	1	yes	characteristic
118	C₄×C₁₁	C₄×C₈×C₁₇	1	2	yes	—
119	C₄×C₁₁	C₂×C₁₆×C₁₇	1	8	yes	direct product factor
120	C₄×C₁₁	C₂×C₄²×C₁₇	1	1	yes	characteristic
121	C₄×C₁₁	C₂²×C₈×C₁₇	1	1	yes	characteristic
122	C₂×C₁₇	C₄×C₁₁×C₁₆	1	4	yes	direct product factor
123	C₂×C₁₇	C₂×C₄×C₈×C₁₁	1	1	yes	characteristic
124	C₂×C₁₇	C₂²×C₁₁×C₁₆	1	2	yes	—
125	C₂²×C₈	C₄×C₁₁×C₁₇	1	1	yes	characteristic
126	C₂²×C₈	C₂²×C₁₁×C₁₇	1	1	yes	characteristic
127	C₂×C₄²	C₄×C₁₁×C₁₇	1	1	yes	characteristic
128	C₂×C₁₆	C₄×C₁₁×C₁₇	1	8	yes	direct product factor
129	C₂×C₁₆	C₂²×C₁₁×C₁₇	1	4	yes	—
130	C₄×C₈	C₄×C₁₁×C₁₇	1	2	yes	—
131	C₄×C₈	C₂²×C₁₁×C₁₇	1	2	yes	—
132	C₂×C₁₁	C₄×C₁₆×C₁₇	1	4	yes	direct product factor
133	C₂×C₁₁	C₂×C₄×C₈×C₁₇	1	1	yes	characteristic
134	C₂×C₁₁	C₂²×C₁₆×C₁₇	1	2	yes	—
135	C₁₇	C₂×C₄×C₁₁×C₁₆	1	1	yes	characteristic, direct product factor, Sylow
136	C₂²×C₄	C₈×C₁₁×C₁₇	1	2	yes	—
137	C₂²×C₄	C₂×C₄×C₁₁×C₁₇	1	1	yes	characteristic
138	C₂×C₈	C₈×C₁₁×C₁₇	1	4	yes	—
139	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	1	yes	characteristic
140	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	2	yes	—
141	C₂×C₈	C₂×C₄×C₁₁×C₁₇	1	4	yes	—
142	C₂×C₈	C₂³×C₁₁×C₁₇	1	1	yes	characteristic
143	C₄²	C₈×C₁₁×C₁₇	1	2	yes	—
144	C₄²	C₂×C₄×C₁₁×C₁₇	1	2	yes	—
145	C₁₆	C₂×C₄×C₁₁×C₁₇	1	8	yes	direct product factor
146	C₁₁	C₂×C₄×C₁₆×C₁₇	1	1	yes	characteristic, direct product factor, Sylow
147	C₂³	C₂×C₈×C₁₁×C₁₇	1	1	yes	characteristic
148	C₂×C₄	C₁₁×C₁₆×C₁₇	1	8	yes	direct product factor
149	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	1	yes	characteristic
150	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	2	yes	—
151	C₂×C₄	C₂×C₈×C₁₁×C₁₇	1	4	yes	—
152	C₂×C₄	C₄²×C₁₁×C₁₇	1	2	yes	—
153	C₂×C₄	C₂²×C₄×C₁₁×C₁₇	1	1	yes	characteristic
154	C₈	C₂×C₈×C₁₁×C₁₇	1	4	yes	—
155	C₈	C₄²×C₁₁×C₁₇	1	2	yes	—
156	C₈	C₂²×C₄×C₁₁×C₁₇	1	2	yes	—
157	C₂²	C₂×C₁₁×C₁₆×C₁₇	1	4	yes	—
158	C₂²	C₄×C₈×C₁₁×C₁₇	1	2	yes	—
159	C₂²	C₂²×C₈×C₁₁×C₁₇	1	1	yes	characteristic
160	C₄	C₂×C₁₁×C₁₆×C₁₇	1	8	yes	direct product factor
161	C₄	C₄×C₈×C₁₁×C₁₇	1	2	yes	—
162	C₄	C₂×C₄²×C₁₁×C₁₇	1	1	yes	characteristic
163	C₄	C₂²×C₈×C₁₁×C₁₇	1	1	yes	characteristic
164	C₂	C₄×C₁₁×C₁₆×C₁₇	1	4	yes	direct product factor
165	C₂	C₂²×C₁₁×C₁₆×C₁₇	1	2	yes	—
166	C₂	C₂×C₄×C₈×C₁₁×C₁₇	1	1	yes	characteristic

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₈	C₂³×C₁₁×C₁₇
socle, prime radical	C₂³×C₁₁×C₁₇	C₂×C₈
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₄×C₁₁×C₁₆×C₁₇	C₂	direct (N × H)
9. C₂×C₁₁×C₁₆×C₁₇	C₄	direct (N × H)
20. C₁₁×C₁₆×C₁₇	C₂×C₄	direct (N × H)
21. C₂×C₄×C₁₆×C₁₇	C₁₁	direct (N × H)
23. C₂×C₄×C₁₁×C₁₇	C₁₆	direct (N × H)
32. C₂×C₄×C₁₁×C₁₆	C₁₇	direct (N × H)
35. C₄×C₁₆×C₁₇	C₂×C₁₁	direct (N × H)
40. C₄×C₁₁×C₁₇	C₂×C₁₆	direct (N × H)
45. C₄×C₁₁×C₁₆	C₂×C₁₇	direct (N × H)
49. C₂×C₁₆×C₁₇	C₄×C₁₁	direct (N × H)
53. C₂×C₁₁×C₁₇	C₄×C₁₆	direct (N × H)
59. C₂×C₁₁×C₁₆	C₄×C₁₇	direct (N × H)
72. C₁₆×C₁₇	C₂×C₄×C₁₁	direct (N × H)
73. C₁₁×C₁₇	C₂×C₄×C₁₆	direct (N × H)
83. C₁₁×C₁₆	C₂×C₄×C₁₇	direct (N × H)
85. C₂×C₄×C₁₇	C₁₁×C₁₆	direct (N × H)
94. C₂×C₄×C₁₆	C₁₁×C₁₇	direct (N × H)
96. C₂×C₄×C₁₁	C₁₆×C₁₇	direct (N × H)
109. C₄×C₁₇	C₂×C₁₁×C₁₆	direct (N × H)
114. C₄×C₁₆	C₂×C₁₁×C₁₇	direct (N × H)
119. C₄×C₁₁	C₂×C₁₆×C₁₇	direct (N × H)
122. C₂×C₁₇	C₄×C₁₁×C₁₆	direct (N × H)
128. C₂×C₁₆	C₄×C₁₁×C₁₇	direct (N × H)
132. C₂×C₁₁	C₄×C₁₆×C₁₇	direct (N × H)
135. C₁₇	C₂×C₄×C₁₁×C₁₆	direct (N × H)
145. C₁₆	C₂×C₄×C₁₁×C₁₇	direct (N × H)
146. C₁₁	C₂×C₄×C₁₆×C₁₇	direct (N × H)
148. C₂×C₄	C₁₁×C₁₆×C₁₇	direct (N × H)
160. C₄	C₂×C₁₁×C₁₆×C₁₇	direct (N × H)
164. C₂	C₄×C₁₁×C₁₆×C₁₇	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×C₄×C₈×C₁₁×C₁₇	2
C₂²×C₁₁×C₁₆×C₁₇	2
C₄×C₁₁×C₁₆×C₁₇	2
C₂×C₄×C₁₆×C₁₇	11
C₂×C₄×C₁₁×C₁₆	17

Subgroups — C2×C4×C11×C16×C17 #72201213

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×C₁₁×C₁₆×C₁₇ #72201213