Subgroups — C₂×C₁₇×#2932 #16917880

Order 4352.

2806 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₁₇×#131	C₂	1	2	yes	maximal, complemented
2	C₂×C₁₇×#532	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2932	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₁₇×#435	C₂	1	8	yes	maximal, complemented
5	C₂×C₁₇×#423	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₁₇×#408	C₂	1	2	yes	maximal, complemented
7	C₂²×C₁₇×#97	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#41×C₁₇	C₂²	1	2	yes	—
9	C₂×C₁₇×#131	—	2	16	no	—
10	C₂×C₁₇×#131	C₂²	1	16	yes	complemented
11	C₂²×M₁₆×C₁₇	C₂²	1	2	yes	—
12	C₂²×M₁₆×C₁₇	C₂²	1	4	yes	—
13	C₂³×C₈×C₁₇	C₂²	1	4	yes	—
14	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#532	C₄	1	8	yes	—
17	C₁₇×#532	C₂²	1	8	yes	—
18	C₂×C₁₇×C₄⋊Q₈	C₄	1	1	yes	characteristic
19	C₂×C₁₇×#127	C₄	1	1	yes	characteristic
20	C₂×C₁₇×#124	C₄	1	2	yes	—
21	C₂×C₁₇×#121	C₄	1	4	yes	—
22	C₂×C₄×D₄×C₁₇	C₂²	1	4	yes	—
23	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
24	C₁₇×#435	C₂²	1	64	yes	complemented
25	C₁₇×#423	C₂²	1	8	yes	complemented
26	C₂×C₁₇×C₄⋊C₈	C₂²	1	4	yes	—
27	C₁₇×#408	C₂²	1	16	yes	complemented
28	C₂×C₁₇×C₂²⋊C₈	C₂²	1	8	yes	—
29	C₂×C₁₇×#97	C₂²	1	4	yes	—
30	C₂×C₁₇×#97	C₂²	1	8	yes	complemented
31	C₂×#41×C₁₇	—	2	8	no	—
32	C₂×#41×C₁₇	—	2	8	no	—
33	C₂×#41×C₁₇	C₂×C₄	1	8	yes	—
34	C₂×#41×C₁₇	C₂³	1	8	yes	—
35	C₂²×Q₈×C₁₇	C₂×C₄	1	2	yes	—
36	C₂²×D₄×C₁₇	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₁₇	C₂×C₄	1	2	yes	—
38	C₂²×D₄×C₁₇	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₁₇	C₂×C₄	1	2	yes	—
40	C₂³×C₄×C₁₇	C₂³	1	4	yes	—
41	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
42	C₁₇×#131	—	2	64	no	—
43	C₂×M₁₆×C₁₇	—	2	8	no	—
44	C₂×M₁₆×C₁₇	—	2	16	no	—
45	C₂×M₁₆×C₁₇	C₂³	1	8	yes	—
46	C₂×M₁₆×C₁₇	C₂³	1	16	yes	—
47	C₂²×C₈×C₁₇	—	2	4	no	—
48	C₂²×C₈×C₁₇	—	2	16	no	—
49	C₂²×C₈×C₁₇	D₄	1	8	yes	complemented
50	C₂²×C₈×C₁₇	C₂³	1	16	yes	—
51	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
52	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
53	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
54	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
56	C₁₇×C₄⋊Q₈	C₂×C₄	1	8	yes	—
57	C₁₇×#127	C₂×C₄	1	8	yes	—
58	C₁₇×#124	C₂×C₄	1	16	yes	—
59	C₁₇×#121	C₂×C₄	1	32	yes	—
60	C₄×D₄×C₁₇	C₂×C₄	1	16	yes	—
61	C₄×D₄×C₁₇	C₂³	1	16	yes	—
62	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	8	yes	—
64	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄²×C₁₇	C₂×C₄	1	4	yes	—
67	C₂×C₄²×C₁₇	C₂³	1	4	yes	—
68	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
69	C₁₇×C₄⋊C₈	C₂³	1	16	yes	—
70	C₁₇×C₂²⋊C₈	C₂³	1	32	yes	—
71	C₁₇×#97	C₂³	1	16	yes	—
72	C₂⁴×C₁₇	C₂²×C₄	1	4	yes	—
73	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
74	#41×C₁₇	—	2	32	no	—
75	#41×C₁₇	—	2	16	no	—
76	#41×C₁₇	—	2	16	no	—
77	C₂×Q₈×C₁₇	—	2	8	no	—
78	C₂×Q₈×C₁₇	C₂²×C₄	1	8	yes	—
79	C₂×D₄×C₁₇	—	2	16	no	—
80	C₂×D₄×C₁₇	—	2	8	no	—
81	C₂×D₄×C₁₇	—	4	8	no	—
82	C₂×D₄×C₁₇	C₂²×C₄	1	8	yes	—
83	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	—
84	C₂×D₄×C₁₇	C₂²×C₄	1	16	yes	—
85	C₂²×C₄×C₁₇	—	2	8	no	—
86	C₂²×C₄×C₁₇	—	2	8	no	—
87	C₂²×C₄×C₁₇	—	4	4	no	—
88	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
90	C₂²×C₄×C₁₇	C₂²×C₄	1	4	yes	—
91	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
92	C₂²×C₄×C₁₇	C₂²×C₄	1	8	yes	—
93	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
96	C₂²×C₄×C₁₇	#41	1	4	yes	—
97	C₂²×C₄×C₁₇	C₂⁴	1	8	yes	—
98	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
99	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₁₇	—	2	16	no	—
101	M₁₆×C₁₇	—	2	32	no	—
102	C₂×C₈×C₁₇	—	2	8	no	—
103	C₂×C₈×C₁₇	—	2	4	no	—
104	C₂×C₈×C₁₇	—	2	8	no	—
105	C₂×C₈×C₁₇	—	2	32	no	—
106	C₂×C₈×C₁₇	C₂×D₄	1	8	yes	—
107	C₂×C₈×C₁₇	C₂×D₄	1	16	yes	complemented
108	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
109	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
110	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
111	C₄⋊C₄×C₁₇	C₂²×C₄	1	16	yes	—
112	C₂²⋊C₄×C₁₇	C₂²×C₄	1	32	yes	—
113	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
114	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
115	C₄²×C₁₇	C₂²×C₄	1	4	yes	—
116	C₄²×C₁₇	C₂⁴	1	4	yes	—
117	C₂×#2932	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
118	C₂³×C₁₇	—	2	4	no	—
119	C₂³×C₁₇	—	2	8	no	—
120	C₂³×C₁₇	—	2	16	no	—
121	C₂³×C₁₇	C₄×D₄	1	4	yes	—
122	C₂³×C₁₇	C₂³×C₄	1	8	yes	—
123	C₂³×C₁₇	C₂³×C₄	1	2	yes	—
124	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
125	Q₈×C₁₇	—	2	16	no	—
126	D₄×C₁₇	—	2	32	no	—
127	D₄×C₁₇	—	2	16	no	—
128	D₄×C₁₇	—	4	16	no	—
129	C₂×C₄×C₁₇	—	2	8	no	—
130	C₂×C₄×C₁₇	—	2	4	no	—
131	C₂×C₄×C₁₇	—	2	4	no	—
132	C₂×C₄×C₁₇	—	2	16	no	—
133	C₂×C₄×C₁₇	—	2	8	no	—
134	C₂×C₄×C₁₇	—	2	8	no	—
135	C₂×C₄×C₁₇	—	4	8	no	—
136	C₂×C₄×C₁₇	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₁₇	C₄×D₄	1	8	yes	—
138	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₁₇	C₂³×C₄	1	4	yes	—
140	C₂×C₄×C₁₇	C₂³×C₄	1	8	yes	—
141	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₇	C₂³×C₄	1	2	yes	—
143	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
144	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
145	C₂×C₄×C₁₇	C₂×#41	1	2	yes	—
146	C₂×C₄×C₁₇	C₂×#41	1	4	yes	—
147	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
148	C₈×C₁₇	—	2	8	no	—
149	C₈×C₁₇	—	2	4	no	—
150	C₈×C₁₇	C₂²×D₄	1	8	yes	—
151	C₂²×#131	C₂×C₁₇	1	2	yes	complemented
152	C₂×#532	C₂×C₁₇	1	1	yes	characteristic
153	#2932	C₂×C₁₇	1	16	yes	direct product factor
154	C₂×#435	C₂×C₁₇	1	8	yes	complemented
155	C₂×#423	C₂×C₁₇	1	1	yes	characteristic, complemented
156	C₂×#408	C₂×C₁₇	1	2	yes	complemented
157	C₂²×#97	C₂×C₁₇	1	1	yes	characteristic, complemented
158	C₂²×C₁₇	—	2	8	no	—
159	C₂²×C₁₇	—	2	4	no	—
160	C₂²×C₁₇	—	2	8	no	—
161	C₂²×C₁₇	—	2	16	no	—
162	C₂²×C₁₇	—	4	16	no	—
163	C₂²×C₁₇	C₂×C₄×D₄	1	4	yes	—
164	C₂²×C₁₇	C₂×C₄×D₄	1	2	yes	—
165	C₂²×C₁₇	#568	1	4	yes	—
166	C₂²×C₁₇	C₂⁴×C₄	1	1	yes	characteristic
167	C₄×C₁₇	—	2	8	no	—
168	C₄×C₁₇	—	2	4	no	—
169	C₄×C₁₇	—	2	4	no	—
170	C₄×C₁₇	C₂×C₄×D₄	1	2	yes	—
171	C₄×C₁₇	C₂×C₄×D₄	1	4	yes	—
172	C₄×C₁₇	C₂³×D₄	1	1	yes	characteristic
173	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
174	C₂²×#41	C₂²×C₁₇	1	2	yes	—
175	C₂×#131	—	2	16	no	—
176	C₂×#131	C₂²×C₁₇	1	16	yes	complemented
177	C₂²×M₁₆	C₂²×C₁₇	1	2	yes	—
178	C₂²×M₁₆	C₂²×C₁₇	1	4	yes	—
179	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
180	C₂³×C₈	C₂²×C₁₇	1	4	yes	—
181	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
182	#532	C₄×C₁₇	1	8	yes	—
183	#532	C₂²×C₁₇	1	8	yes	—
184	C₂×C₄⋊Q₈	C₄×C₁₇	1	1	yes	characteristic
185	C₂×#127	C₄×C₁₇	1	1	yes	characteristic
186	C₂×#124	C₄×C₁₇	1	2	yes	—
187	C₂×#121	C₄×C₁₇	1	4	yes	—
188	C₂×C₄×D₄	C₂²×C₁₇	1	4	yes	—
189	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
190	#435	C₂²×C₁₇	1	64	yes	complemented
191	#423	C₂²×C₁₇	1	8	yes	complemented
192	C₂×C₄⋊C₈	C₂²×C₁₇	1	4	yes	—
193	#408	C₂²×C₁₇	1	16	yes	complemented
194	C₂×C₂²⋊C₈	C₂²×C₁₇	1	8	yes	—
195	C₂×#97	C₂²×C₁₇	1	4	yes	—
196	C₂×#97	C₂²×C₁₇	1	8	yes	complemented
197	C₂×C₁₇	—	2	4	no	—
198	C₂×C₁₇	—	4	8	no	—
199	C₂×C₁₇	#2932	1	4	yes	direct product factor
200	C₂×C₁₇	C₂²×C₄×D₄	1	1	yes	characteristic
201	C₂×C₁₇	C₂×#568	1	2	yes	—
202	C₂×#41	—	2	8	no	—
203	C₂×#41	—	2	8	no	—
204	C₂×#41	C₂×C₄×C₁₇	1	8	yes	—
205	C₂×#41	C₂³×C₁₇	1	8	yes	—
206	C₂²×Q₈	C₂×C₄×C₁₇	1	2	yes	—
207	C₂²×D₄	C₂×C₄×C₁₇	1	4	yes	—
208	C₂²×D₄	C₂×C₄×C₁₇	1	2	yes	—
209	C₂²×D₄	C₂×C₄×C₁₇	1	4	yes	—
210	C₂³×C₄	C₂×C₄×C₁₇	1	2	yes	—
211	C₂³×C₄	C₂³×C₁₇	1	4	yes	—
212	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
213	#131	—	2	64	no	—
214	C₂×M₁₆	—	2	8	no	—
215	C₂×M₁₆	—	2	16	no	—
216	C₂×M₁₆	C₂³×C₁₇	1	8	yes	—
217	C₂×M₁₆	C₂³×C₁₇	1	16	yes	—
218	C₂²×C₈	—	2	4	no	—
219	C₂²×C₈	—	2	16	no	—
220	C₂²×C₈	D₄×C₁₇	1	8	yes	complemented
221	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
222	C₂²×C₈	C₂³×C₁₇	1	16	yes	—
223	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
224	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
225	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
226	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
227	C₄⋊Q₈	C₂×C₄×C₁₇	1	8	yes	—
228	#127	C₂×C₄×C₁₇	1	8	yes	—
229	#124	C₂×C₄×C₁₇	1	16	yes	—
230	#121	C₂×C₄×C₁₇	1	32	yes	—
231	C₄×D₄	C₂×C₄×C₁₇	1	16	yes	—
232	C₄×D₄	C₂³×C₁₇	1	16	yes	—
233	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	4	yes	—
234	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	8	yes	—
235	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
236	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
237	C₂×C₄²	C₂×C₄×C₁₇	1	4	yes	—
238	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
239	C₂×C₄²	C₂³×C₁₇	1	4	yes	—
240	C₄⋊C₈	C₂³×C₁₇	1	16	yes	—
241	C₂²⋊C₈	C₂³×C₁₇	1	32	yes	—
242	#97	C₂³×C₁₇	1	16	yes	—
243	C₁₇	C₂×#2932	1	1	yes	characteristic, direct product factor, Sylow
244	C₂⁴	C₂²×C₄×C₁₇	1	4	yes	—
245	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
246	#41	—	2	16	no	—
247	#41	—	2	16	no	—
248	#41	—	2	32	no	—
249	C₂×Q₈	—	2	8	no	—
250	C₂×Q₈	C₂²×C₄×C₁₇	1	8	yes	—
251	C₂×D₄	—	2	16	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	4	8	no	—
254	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	—
255	C₂×D₄	C₂²×C₄×C₁₇	1	8	yes	—
256	C₂×D₄	C₂²×C₄×C₁₇	1	16	yes	—
257	C₂²×C₄	—	2	8	no	—
258	C₂²×C₄	—	2	8	no	—
259	C₂²×C₄	—	4	4	no	—
260	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
261	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
262	C₂²×C₄	C₂²×C₄×C₁₇	1	4	yes	—
263	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
264	C₂²×C₄	C₂²×C₄×C₁₇	1	8	yes	—
265	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
267	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
268	C₂²×C₄	#41×C₁₇	1	4	yes	—
269	C₂²×C₄	C₂⁴×C₁₇	1	8	yes	—
270	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
271	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
272	M₁₆	—	2	16	no	—
273	M₁₆	—	2	32	no	—
274	C₂×C₈	—	2	8	no	—
275	C₂×C₈	—	2	4	no	—
276	C₂×C₈	—	2	8	no	—
277	C₂×C₈	—	2	32	no	—
278	C₂×C₈	C₂×D₄×C₁₇	1	8	yes	—
279	C₂×C₈	C₂×D₄×C₁₇	1	16	yes	complemented
280	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
281	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
282	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
283	C₄⋊C₄	C₂²×C₄×C₁₇	1	16	yes	—
284	C₂²⋊C₄	C₂²×C₄×C₁₇	1	32	yes	—
285	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
286	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
287	C₄²	C₂²×C₄×C₁₇	1	4	yes	—
288	C₄²	C₂⁴×C₁₇	1	4	yes	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	16	no	—
292	C₂³	C₄×D₄×C₁₇	1	4	yes	—
293	C₂³	C₂³×C₄×C₁₇	1	8	yes	—
294	C₂³	C₂³×C₄×C₁₇	1	2	yes	—
295	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
296	Q₈	—	2	16	no	—
297	D₄	—	2	32	no	—
298	D₄	—	2	16	no	—
299	D₄	—	4	16	no	—
300	C₂×C₄	—	2	8	no	—
301	C₂×C₄	—	2	4	no	—
302	C₂×C₄	—	2	4	no	—
303	C₂×C₄	—	2	16	no	—
304	C₂×C₄	—	2	8	no	—
305	C₂×C₄	—	2	8	no	—
306	C₂×C₄	—	4	8	no	—
307	C₂×C₄	C₄×D₄×C₁₇	1	4	yes	—
308	C₂×C₄	C₄×D₄×C₁₇	1	8	yes	—
309	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
310	C₂×C₄	C₂³×C₄×C₁₇	1	4	yes	—
311	C₂×C₄	C₂³×C₄×C₁₇	1	8	yes	—
312	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
313	C₂×C₄	C₂³×C₄×C₁₇	1	2	yes	—
314	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
315	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
316	C₂×C₄	C₂×#41×C₁₇	1	2	yes	—
317	C₂×C₄	C₂×#41×C₁₇	1	4	yes	—
318	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
319	C₈	—	2	8	no	—
320	C₈	—	2	4	no	—
321	C₈	C₂²×D₄×C₁₇	1	8	yes	—
322	C₂²	—	2	4	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	16	no	—
325	C₂²	—	2	8	no	—
326	C₂²	—	4	16	no	—
327	C₂²	C₂×C₄×D₄×C₁₇	1	4	yes	—
328	C₂²	C₂×C₄×D₄×C₁₇	1	2	yes	—
329	C₂²	C₁₇×#568	1	4	yes	—
330	C₂²	C₂⁴×C₄×C₁₇	1	1	yes	characteristic
331	C₄	—	2	4	no	—
332	C₄	—	2	4	no	—
333	C₄	—	2	8	no	—
334	C₄	C₂×C₄×D₄×C₁₇	1	2	yes	—
335	C₄	C₂×C₄×D₄×C₁₇	1	4	yes	—
336	C₄	C₂³×D₄×C₁₇	1	1	yes	characteristic
337	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
338	C₂	—	2	4	no	—
339	C₂	—	4	8	no	—
340	C₂	C₁₇×#2932	1	4	yes	direct product factor
341	C₂	C₂²×C₄×D₄×C₁₇	1	1	yes	characteristic
342	C₂	C₂×C₁₇×#568	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₁₇
Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂×C₁₇×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×C₁₇×#131	C₂	semidirect
3. C₁₇×#2932	C₂	direct (N × H)
4. C₂×C₁₇×#435	C₂	semidirect
5. C₂×C₁₇×#423	C₂	semidirect
6. C₂×C₁₇×#408	C₂	semidirect
7. C₂²×C₁₇×#97	C₂	semidirect
10. C₂×C₁₇×#131	C₂²	semidirect
24. C₁₇×#435	C₂²	semidirect
25. C₁₇×#423	C₂²	semidirect
27. C₁₇×#408	C₂²	semidirect
30. C₂×C₁₇×#97	C₂²	semidirect
49. C₂²×C₈×C₁₇	D₄	semidirect
107. C₂×C₈×C₁₇	C₂×D₄	semidirect
117. C₂×#2932	C₁₇	direct (N × H)
151. C₂²×#131	C₂×C₁₇	semidirect
153. #2932	C₂×C₁₇	direct (N × H)
154. C₂×#435	C₂×C₁₇	semidirect
155. C₂×#423	C₂×C₁₇	semidirect
156. C₂×#408	C₂×C₁₇	semidirect
157. C₂²×#97	C₂×C₁₇	semidirect
176. C₂×#131	C₂²×C₁₇	semidirect
190. #435	C₂²×C₁₇	semidirect
191. #423	C₂²×C₁₇	semidirect
193. #408	C₂²×C₁₇	semidirect
196. C₂×#97	C₂²×C₁₇	semidirect
199. C₂×C₁₇	#2932	direct (N × H)
220. C₂²×C₈	D₄×C₁₇	semidirect
243. C₁₇	C₂×#2932	direct (N × H)
279. C₂×C₈	C₂×D₄×C₁₇	semidirect
340. C₂	C₁₇×#2932	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×C₁₇×#131	2
C₂×C₁₇×#532	2
C₁₇×#2932	2
C₂×C₁₇×#435	2
C₂×C₁₇×#423	2
C₂×C₁₇×#408	2
C₂²×C₁₇×#97	2
C₂×#2932	17

Subgroups — C2×C17×#2932 #16917880

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#2932 #16917880