Subgroups — C₁₇×#21433 #16879177

Order 4352.

668 conjugacy classes of subgroups.

The subgroup lattice has 212 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2298	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#1924	C₂	1	4	yes	maximal
3	C₁₇×#1917	C₂	1	4	yes	maximal, complemented
4	C₁₇×#1768	C₂	1	2	yes	maximal, complemented
5	C₁₇×#1750	C₂	1	2	yes	maximal
6	C₁₇×#1745	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₁₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
9	C₂×C₁₇×C₄⋊C₈	C₂²	1	4	yes	—
10	C₂×C₁₇×C₂²⋊C₈	C₂²	1	4	yes	—
11	C₂×C₁₇×#97	C₂²	1	4	yes	—
12	C₂×C₁₇×#97	C₂²	1	2	yes	—
13	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
14	C₁₇×#388	C₄	1	4	yes	—
15	C₁₇×#387	C₄	1	4	yes	—
16	C₄×C₄⋊C₄×C₁₇	C₂²	1	2	yes	—
17	C₄×C₂²⋊C₄×C₁₇	C₂²	1	2	yes	—
18	C₁₇×#376	C₂²	1	1	yes	characteristic
19	C₄³×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#336	C₂²	1	4	yes	—
21	C₁₇×#336	C₂²	1	4	yes	—
22	C₁₇×#336	C₂²	1	4	yes	—
23	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
24	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
25	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
26	C₁₇×#117	—	2	4	no	—
27	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
28	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	4	yes	—
29	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	2	yes	—
30	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	4	yes	—
31	C₂×C₄²×C₁₇	C₂×C₄	1	4	yes	—
32	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
33	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
34	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
35	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
36	C₁₇×C₄⋊C₈	—	2	8	no	—
37	C₁₇×C₂²⋊C₈	—	2	8	no	—
38	C₁₇×#97	—	2	8	no	—
39	C₁₇×#97	—	2	4	no	—
40	C₄×C₈×C₁₇	—	2	4	no	—
41	C₁₇×#95	C₂×C₄	1	4	yes	—
42	C₁₇×#95	C₂×C₄	1	4	yes	—
43	C₁₇×#95	C₂×C₄	1	4	yes	—
44	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
45	C₂²×C₄×C₁₇	—	2	4	no	—
46	C₂²×C₄×C₁₇	—	2	2	no	—
47	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
48	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
49	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
50	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
51	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
52	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
53	C₂×C₈×C₁₇	—	2	4	no	—
54	C₂×C₈×C₁₇	—	2	4	no	—
55	C₂×C₈×C₁₇	—	2	4	no	—
56	C₂×C₈×C₁₇	—	2	4	no	—
57	C₂×C₈×C₁₇	—	2	4	no	—
58	C₂×C₈×C₁₇	#41	1	8	yes	—
59	C₄⋊C₄×C₁₇	—	2	4	no	—
60	C₄⋊C₄×C₁₇	—	4	4	no	—
61	C₂²⋊C₄×C₁₇	—	2	4	no	—
62	C₂²⋊C₄×C₁₇	—	4	4	no	—
63	C₄²×C₁₇	—	2	4	no	—
64	C₄²×C₁₇	—	2	4	no	—
65	C₄²×C₁₇	—	2	2	no	—
66	C₄²×C₁₇	—	4	4	no	—
67	C₄²×C₁₇	#41	1	4	yes	—
68	#21433	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
69	C₂³×C₁₇	—	2	1	no	—
70	C₂³×C₁₇	—	2	2	no	—
71	C₂³×C₁₇	—	2	4	no	—
72	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
73	C₂×C₄×C₁₇	—	2	4	no	—
74	C₂×C₄×C₁₇	—	2	2	no	—
75	C₂×C₄×C₁₇	—	2	1	no	—
76	C₂×C₄×C₁₇	—	2	4	no	—
77	C₂×C₄×C₁₇	—	2	4	no	—
78	C₂×C₄×C₁₇	—	2	2	no	—
79	C₂×C₄×C₁₇	—	2	4	no	—
80	C₂×C₄×C₁₇	—	2	4	no	—
81	C₂×C₄×C₁₇	—	2	4	no	—
82	C₂×C₄×C₁₇	—	2	4	no	—
83	C₂×C₄×C₁₇	—	2	4	no	—
84	C₂×C₄×C₁₇	—	4	4	no	—
85	C₂×C₄×C₁₇	#117	1	4	yes	—
86	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
87	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
88	C₈×C₁₇	—	2	8	no	—
89	C₈×C₁₇	—	4	4	no	—
90	#2298	C₂×C₁₇	1	1	yes	characteristic
91	#1924	C₂×C₁₇	1	4	yes	—
92	#1917	C₂×C₁₇	1	4	yes	complemented
93	#1768	C₂×C₁₇	1	2	yes	complemented
94	#1750	C₂×C₁₇	1	2	yes	—
95	#1745	C₂×C₁₇	1	1	yes	characteristic, complemented
96	C₄×#97	C₂×C₁₇	1	1	yes	characteristic, complemented
97	C₂²×C₁₇	—	4	2	no	—
98	C₂²×C₁₇	—	4	4	no	—
99	C₂²×C₁₇	—	4	1	no	—
100	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
101	C₂²×C₁₇	C₄×#41	1	2	yes	—
102	C₂²×C₁₇	#568	1	4	yes	—
103	C₄×C₁₇	—	2	4	no	—
104	C₄×C₁₇	—	4	2	no	—
105	C₄×C₁₇	—	4	4	no	—
106	C₄×C₁₇	—	4	4	no	—
107	C₄×C₁₇	—	4	1	no	—
108	C₄×C₁₇	#529	1	4	yes	—
109	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
110	C₂×C₄⋊C₈	C₂²×C₁₇	1	4	yes	—
111	C₂×C₂²⋊C₈	C₂²×C₁₇	1	4	yes	—
112	C₂×#97	C₂²×C₁₇	1	4	yes	—
113	C₂×#97	C₂²×C₁₇	1	2	yes	—
114	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
115	#388	C₄×C₁₇	1	4	yes	—
116	#387	C₄×C₁₇	1	4	yes	—
117	C₄×C₄⋊C₄	C₂²×C₁₇	1	2	yes	—
118	C₄×C₂²⋊C₄	C₂²×C₁₇	1	2	yes	—
119	#376	C₂²×C₁₇	1	1	yes	characteristic
120	C₄³	C₂²×C₁₇	1	1	yes	characteristic
121	#336	C₂²×C₁₇	1	4	yes	—
122	#336	C₂²×C₁₇	1	4	yes	—
123	#336	C₂²×C₁₇	1	4	yes	—
124	C₂×C₁₇	—	8	1	no	—
125	C₂×C₁₇	#2298	1	1	yes	characteristic
126	C₂×C₁₇	#2923	1	2	yes	—
127	C₂×C₁₇	#2967	1	4	yes	—
128	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
129	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
130	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
131	#117	—	2	4	no	—
132	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
133	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	4	yes	—
134	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	2	yes	—
135	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	4	yes	—
136	C₂×C₄²	C₂×C₄×C₁₇	1	4	yes	—
137	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
138	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
139	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
140	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
141	C₄⋊C₈	—	2	8	no	—
142	C₂²⋊C₈	—	2	8	no	—
143	#97	—	2	8	no	—
144	#97	—	2	4	no	—
145	C₄×C₈	—	2	4	no	—
146	#95	C₂×C₄×C₁₇	1	4	yes	—
147	#95	C₂×C₄×C₁₇	1	4	yes	—
148	#95	C₂×C₄×C₁₇	1	4	yes	—
149	C₁₇	#21433	1	1	yes	characteristic, direct product factor, Sylow
150	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
151	C₂²×C₄	—	2	4	no	—
152	C₂²×C₄	—	2	2	no	—
153	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
154	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
155	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
156	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
157	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
158	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
159	C₂×C₈	—	2	4	no	—
160	C₂×C₈	—	2	4	no	—
161	C₂×C₈	—	2	4	no	—
162	C₂×C₈	—	2	4	no	—
163	C₂×C₈	—	2	4	no	—
164	C₂×C₈	#41×C₁₇	1	8	yes	—
165	C₄⋊C₄	—	2	4	no	—
166	C₄⋊C₄	—	4	4	no	—
167	C₂²⋊C₄	—	2	4	no	—
168	C₂²⋊C₄	—	4	4	no	—
169	C₄²	—	2	4	no	—
170	C₄²	—	2	4	no	—
171	C₄²	—	2	2	no	—
172	C₄²	—	4	4	no	—
173	C₄²	#41×C₁₇	1	4	yes	—
174	C₂³	—	2	1	no	—
175	C₂³	—	2	2	no	—
176	C₂³	—	2	4	no	—
177	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
178	C₂×C₄	—	2	4	no	—
179	C₂×C₄	—	2	2	no	—
180	C₂×C₄	—	2	1	no	—
181	C₂×C₄	—	2	4	no	—
182	C₂×C₄	—	2	4	no	—
183	C₂×C₄	—	2	2	no	—
184	C₂×C₄	—	2	4	no	—
185	C₂×C₄	—	2	4	no	—
186	C₂×C₄	—	2	4	no	—
187	C₂×C₄	—	2	4	no	—
188	C₂×C₄	—	2	4	no	—
189	C₂×C₄	—	4	4	no	—
190	C₂×C₄	C₁₇×#117	1	4	yes	—
191	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
192	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
193	C₈	—	2	8	no	—
194	C₈	—	4	4	no	—
195	C₂²	—	4	4	no	—
196	C₂²	—	4	1	no	—
197	C₂²	—	4	2	no	—
198	C₂²	C₂×C₁₇×#117	1	1	yes	characteristic
199	C₂²	C₄×#41×C₁₇	1	2	yes	—
200	C₂²	C₁₇×#568	1	4	yes	—
201	C₄	—	2	4	no	—
202	C₄	—	4	4	no	—
203	C₄	—	4	4	no	—
204	C₄	—	4	1	no	—
205	C₄	—	4	2	no	—
206	C₄	C₁₇×#529	1	4	yes	—
207	C₂	—	8	1	no	—
208	C₂	C₁₇×#2298	1	1	yes	characteristic
209	C₂	C₁₇×#2923	1	2	yes	—
210	C₂	C₁₇×#2967	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#1917	C₂	semidirect
4. C₁₇×#1768	C₂	semidirect
6. C₁₇×#1745	C₂	semidirect
7. C₄×C₁₇×#97	C₂	semidirect
68. #21433	C₁₇	direct (N × H)
92. #1917	C₂×C₁₇	semidirect
93. #1768	C₂×C₁₇	semidirect
95. #1745	C₂×C₁₇	semidirect
96. C₄×#97	C₂×C₁₇	semidirect
149. C₁₇	#21433	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#2298	2
C₁₇×#1924	2
C₁₇×#1917	2
C₁₇×#1768	2
C₁₇×#1750	2
C₁₇×#1745	2
C₄×C₁₇×#97	2
#21433	17

Subgroups — C17×#21433 #16879177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#21433 #16879177