Subgroups — C₁₇×C₂²⋊#95 #14524439

Order 2176.

1088 conjugacy classes of subgroups.

The subgroup lattice has 188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₁₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₂²⋊C₄×C₁₇	C₂	1	2	yes	maximal
3	C₂×C₁₇×#95	C₂	1	4	yes	maximal, complemented
4	C₂⁵×C₁₇	C₂²	1	1	yes	characteristic
5	C₂³×C₄×C₁₇	—	2	4	no	—
6	C₂³×C₄×C₁₇	—	2	8	no	—
7	C₂³×C₄×C₁₇	C₄	1	4	yes	complemented
8	C₂³×C₄×C₁₇	C₂²	1	4	yes	—
9	C₂³×C₄×C₁₇	C₂²	1	2	yes	—
10	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
11	C₂×C₂²⋊C₄×C₁₇	—	2	4	no	—
12	C₂×C₂²⋊C₄×C₁₇	C₄	1	8	yes	complemented
13	C₁₇×#95	—	2	8	no	—
14	C₂⁴×C₁₇	—	2	4	no	—
15	C₂⁴×C₁₇	—	2	4	no	—
16	C₂⁴×C₁₇	C₂×C₄	1	2	yes	—
17	C₂⁴×C₁₇	C₂×C₄	1	4	yes	—
18	C₂⁴×C₁₇	D₄	1	4	yes	—
19	C₂⁴×C₁₇	D₄	1	2	yes	—
20	C₂⁴×C₁₇	Q₈	1	2	yes	—
21	C₂⁴×C₁₇	C₂³	1	1	yes	characteristic
22	C₂²×C₄×C₁₇	—	2	32	no	—
23	C₂²×C₄×C₁₇	—	2	8	no	—
24	C₂²×C₄×C₁₇	—	2	4	no	—
25	C₂²×C₄×C₁₇	—	2	4	no	—
26	C₂²×C₄×C₁₇	—	2	16	no	—
27	C₂²×C₄×C₁₇	—	2	8	no	—
28	C₂²×C₄×C₁₇	—	2	4	no	—
29	C₂²×C₄×C₁₇	—	2	4	no	—
30	C₂²×C₄×C₁₇	—	2	8	no	—
31	C₂²×C₄×C₁₇	C₂×C₄	1	4	yes	—
32	C₂²×C₄×C₁₇	C₂×C₄	1	8	yes	complemented
33	C₂²×C₄×C₁₇	D₄	1	8	yes	—
34	C₂²⋊C₄×C₁₇	—	2	16	no	—
35	C₂³×C₁₇	—	2	4	no	—
36	C₂³×C₁₇	—	2	4	no	—
37	C₂³×C₁₇	—	2	16	no	—
38	C₂³×C₁₇	—	2	8	no	—
39	C₂³×C₁₇	—	2	8	no	—
40	C₂³×C₁₇	—	2	8	no	—
41	C₂³×C₁₇	—	2	8	no	—
42	C₂³×C₁₇	C₄²	1	4	yes	—
43	C₂³×C₁₇	C₂²⋊C₄	1	8	yes	—
44	C₂³×C₁₇	C₂²⋊C₄	1	4	yes	—
45	C₂³×C₁₇	C₄⋊C₄	1	4	yes	—
46	C₂³×C₁₇	C₄⋊C₄	1	8	yes	—
47	C₂³×C₁₇	C₂²×C₄	1	1	yes	characteristic
48	C₂³×C₁₇	C₂²×C₄	1	2	yes	—
49	C₂³×C₁₇	C₂×D₄	1	2	yes	—
50	C₂³×C₁₇	C₂×D₄	1	1	yes	characteristic
51	C₂³×C₁₇	C₂×D₄	1	4	yes	—
52	C₂³×C₁₇	C₂×Q₈	1	1	yes	characteristic
53	C₂³×C₁₇	#41	1	4	yes	—
54	C₂×C₄×C₁₇	—	2	32	no	—
55	C₂×C₄×C₁₇	—	2	4	no	—
56	C₂×C₄×C₁₇	—	2	4	no	—
57	C₂×C₄×C₁₇	—	2	16	no	—
58	C₂×C₄×C₁₇	—	2	8	no	—
59	C₂×C₄×C₁₇	—	2	16	no	—
60	C₂×C₄×C₁₇	—	4	4	no	—
61	C₂×C₄×C₁₇	—	4	8	no	—
62	C₂×C₄×C₁₇	—	4	4	no	—
63	C₂×C₄×C₁₇	C₂²⋊C₄	1	8	yes	complemented
64	C₂²⋊#95	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
65	C₂²×C₁₇	—	2	8	no	—
66	C₂²×C₁₇	—	2	4	no	—
67	C₂²×C₁₇	—	2	8	no	—
68	C₂²×C₁₇	—	2	4	no	—
69	C₂²×C₁₇	—	2	16	no	—
70	C₂²×C₁₇	—	2	16	no	—
71	C₂²×C₁₇	#95	1	8	yes	complemented
72	C₂²×C₁₇	C₂×C₄²	1	1	yes	characteristic
73	C₂²×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
75	C₂²×C₁₇	C₂×C₂²⋊C₄	1	2	yes	—
76	C₂²×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
77	C₂²×C₁₇	C₂×C₄⋊C₄	1	2	yes	—
78	C₂²×C₁₇	#117	1	2	yes	—
79	C₂²×C₁₇	C₄×D₄	1	8	yes	—
80	C₂²×C₁₇	#120	1	4	yes	—
81	C₂²×C₁₇	#121	1	4	yes	—
82	C₂²×C₁₇	C₂²⋊Q₈	1	4	yes	—
83	C₂²×C₁₇	#123	1	4	yes	—
84	C₄×C₁₇	—	2	8	no	—
85	C₄×C₁₇	—	4	8	no	—
86	C₂⁴×C₄	C₂×C₁₇	1	1	yes	characteristic
87	C₂²×C₂²⋊C₄	C₂×C₁₇	1	2	yes	—
88	C₂×#95	C₂×C₁₇	1	4	yes	complemented
89	C₂×C₁₇	—	2	8	no	—
90	C₂×C₁₇	C₂×#95	1	1	yes	characteristic
91	C₂×C₁₇	C₄×C₂²⋊C₄	1	2	yes	—
92	C₂×C₁₇	#379	1	1	yes	characteristic
93	C₂×C₁₇	#380	1	2	yes	—
94	C₂×C₁₇	#381	1	1	yes	characteristic
95	C₂×C₁₇	#385	1	4	yes	—
96	C₂×C₁₇	#386	1	4	yes	—
97	C₂⁵	C₂²×C₁₇	1	1	yes	characteristic
98	C₂³×C₄	—	2	4	no	—
99	C₂³×C₄	—	2	8	no	—
100	C₂³×C₄	C₄×C₁₇	1	4	yes	complemented
101	C₂³×C₄	C₂²×C₁₇	1	4	yes	—
102	C₂³×C₄	C₂²×C₁₇	1	2	yes	—
103	C₂×C₂²⋊C₄	—	2	4	no	—
104	C₂×C₂²⋊C₄	—	2	4	no	—
105	C₂×C₂²⋊C₄	C₄×C₁₇	1	8	yes	complemented
106	#95	—	2	8	no	—
107	C₁₇	C₂²⋊#95	1	1	yes	characteristic, direct product factor, Sylow
108	C₂⁴	—	2	4	no	—
109	C₂⁴	—	2	4	no	—
110	C₂⁴	C₂×C₄×C₁₇	1	4	yes	—
111	C₂⁴	C₂×C₄×C₁₇	1	2	yes	—
112	C₂⁴	D₄×C₁₇	1	2	yes	—
113	C₂⁴	D₄×C₁₇	1	4	yes	—
114	C₂⁴	Q₈×C₁₇	1	2	yes	—
115	C₂⁴	C₂³×C₁₇	1	1	yes	characteristic
116	C₂²×C₄	—	2	32	no	—
117	C₂²×C₄	—	2	8	no	—
118	C₂²×C₄	—	2	4	no	—
119	C₂²×C₄	—	2	4	no	—
120	C₂²×C₄	—	2	16	no	—
121	C₂²×C₄	—	2	8	no	—
122	C₂²×C₄	—	2	4	no	—
123	C₂²×C₄	—	2	4	no	—
124	C₂²×C₄	—	2	8	no	—
125	C₂²×C₄	C₂×C₄×C₁₇	1	4	yes	—
126	C₂²×C₄	C₂×C₄×C₁₇	1	8	yes	complemented
127	C₂²×C₄	D₄×C₁₇	1	8	yes	—
128	C₂²⋊C₄	—	2	16	no	—
129	C₂³	—	2	8	no	—
130	C₂³	—	2	8	no	—
131	C₂³	—	2	4	no	—
132	C₂³	—	2	4	no	—
133	C₂³	—	2	16	no	—
134	C₂³	—	2	8	no	—
135	C₂³	—	2	8	no	—
136	C₂³	C₄²×C₁₇	1	4	yes	—
137	C₂³	C₂²⋊C₄×C₁₇	1	8	yes	—
138	C₂³	C₂²⋊C₄×C₁₇	1	4	yes	—
139	C₂³	C₄⋊C₄×C₁₇	1	4	yes	—
140	C₂³	C₄⋊C₄×C₁₇	1	8	yes	—
141	C₂³	C₂²×C₄×C₁₇	1	1	yes	characteristic
142	C₂³	C₂²×C₄×C₁₇	1	2	yes	—
143	C₂³	C₂×D₄×C₁₇	1	4	yes	—
144	C₂³	C₂×D₄×C₁₇	1	2	yes	—
145	C₂³	C₂×D₄×C₁₇	1	1	yes	characteristic
146	C₂³	C₂×Q₈×C₁₇	1	1	yes	characteristic
147	C₂³	#41×C₁₇	1	4	yes	—
148	C₂×C₄	—	2	32	no	—
149	C₂×C₄	—	2	4	no	—
150	C₂×C₄	—	2	4	no	—
151	C₂×C₄	—	2	16	no	—
152	C₂×C₄	—	2	8	no	—
153	C₂×C₄	—	2	16	no	—
154	C₂×C₄	—	4	4	no	—
155	C₂×C₄	—	4	4	no	—
156	C₂×C₄	—	4	8	no	—
157	C₂×C₄	C₂²⋊C₄×C₁₇	1	8	yes	complemented
158	C₂²	—	2	8	no	—
159	C₂²	—	2	4	no	—
160	C₂²	—	2	8	no	—
161	C₂²	—	2	4	no	—
162	C₂²	—	2	16	no	—
163	C₂²	—	2	16	no	—
164	C₂²	C₁₇×#95	1	8	yes	complemented
165	C₂²	C₂×C₄²×C₁₇	1	1	yes	characteristic
166	C₂²	C₂×C₂²⋊C₄×C₁₇	1	1	yes	characteristic
167	C₂²	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
168	C₂²	C₂×C₂²⋊C₄×C₁₇	1	2	yes	—
169	C₂²	C₂×C₄⋊C₄×C₁₇	1	1	yes	characteristic
170	C₂²	C₂×C₄⋊C₄×C₁₇	1	2	yes	—
171	C₂²	C₁₇×#117	1	2	yes	—
172	C₂²	C₄×D₄×C₁₇	1	8	yes	—
173	C₂²	C₁₇×#120	1	4	yes	—
174	C₂²	C₁₇×#121	1	4	yes	—
175	C₂²	C₁₇×C₂²⋊Q₈	1	4	yes	—
176	C₂²	C₁₇×#123	1	4	yes	—
177	C₄	—	2	8	no	—
178	C₄	—	4	8	no	—
179	C₂	—	2	8	no	—
180	C₂	C₂×C₁₇×#95	1	1	yes	characteristic
181	C₂	C₄×C₂²⋊C₄×C₁₇	1	2	yes	—
182	C₂	C₁₇×#379	1	1	yes	characteristic
183	C₂	C₁₇×#380	1	2	yes	—
184	C₂	C₁₇×#381	1	1	yes	characteristic
185	C₂	C₁₇×#385	1	4	yes	—
186	C₂	C₁₇×#386	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₁₇	C₂³
commutator	C₂²	C₂×C₄²×C₁₇
Frattini, cosocle	C₂⁴	C₂³×C₁₇
prime radical	C₂⁵×C₁₇	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₁₇×#95	C₂	semidirect
7. C₂³×C₄×C₁₇	C₄	semidirect
12. C₂×C₂²⋊C₄×C₁₇	C₄	semidirect
32. C₂²×C₄×C₁₇	C₂×C₄	semidirect
63. C₂×C₄×C₁₇	C₂²⋊C₄	semidirect
64. C₂²⋊#95	C₁₇	direct (N × H)
71. C₂²×C₁₇	#95	semidirect
88. C₂×#95	C₂×C₁₇	semidirect
100. C₂³×C₄	C₄×C₁₇	semidirect
105. C₂×C₂²⋊C₄	C₄×C₁₇	semidirect
107. C₁₇	C₂²⋊#95	direct (N × H)
126. C₂²×C₄	C₂×C₄×C₁₇	semidirect
157. C₂×C₄	C₂²⋊C₄×C₁₇	semidirect
164. C₂²	C₁₇×#95	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×C₁₇	2
C₂²×C₂²⋊C₄×C₁₇	2
C₂×C₁₇×#95	2
C₂²⋊#95	17

Subgroups — C17×C22⋊#95 #14524439

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×C₂²⋊#95 #14524439