Subgroups — C₂×C₁₇×#3262 #16918657

Order 4352.

1882 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#542	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3262	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₁₇×#477	C₂	1	2	yes	maximal, complemented
4	C₂×C₁₇×#474	C₂	1	2	yes	maximal, complemented
5	C₂×C₁₇×#468	C₂	1	2	yes	maximal, complemented
6	C₂×C₁₇×#467	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₁₇×#466	C₂	1	1	yes	maximal, characteristic
8	C₂×C₁₇×#464	C₂	1	2	yes	maximal, complemented
9	C₂×C₁₇×#463	C₂	1	2	yes	maximal, complemented
10	C₂×C₁₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
12	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	—
13	C₂²×D₈×C₁₇	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#542	—	2	8	no	—
17	C₁₇×#542	C₂²	1	16	yes	complemented
18	C₂×C₁₇×C₄⋊Q₈	C₂²	1	2	yes	—
19	C₂×C₁₇×#126	—	2	2	no	—
20	C₂×C₁₇×#124	—	2	2	no	—
21	C₂×C₁₇×#124	C₂²	1	2	yes	—
22	C₂×C₁₇×#123	—	2	2	no	—
23	C₂×C₁₇×C₂²⋊Q₈	—	2	2	no	—
24	C₂×C₁₇×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₂×C₁₇×#121	C₂²	1	2	yes	—
26	C₂×C₄×Q₈×C₁₇	C₂²	1	2	yes	—
27	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
28	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
29	C₁₇×#477	C₂²	1	16	yes	complemented
30	C₁₇×#474	C₂²	1	16	yes	complemented
31	C₁₇×#468	C₂²	1	16	yes	complemented
32	C₁₇×#467	C₂²	1	8	yes	complemented
33	C₁₇×#466	C₂²	1	8	yes	—
34	C₁₇×#464	C₂²	1	16	yes	complemented
35	C₁₇×#463	C₂²	1	16	yes	complemented
36	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
37	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×#107	C₂²	1	2	yes	—
39	C₁₇×#424	C₂²	1	8	yes	complemented
40	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
41	C₂×C₁₇×C₄⋊C₈	C₂²	1	2	yes	—
42	C₂×C₁₇×#103	C₂²	1	2	yes	—
43	C₂×C₁₇×#103	C₂²	1	2	yes	—
44	C₂×C₁₇×#102	C₂²	1	2	yes	—
45	C₂×C₁₇×#102	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₇	—	2	2	no	—
47	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₁₇	—	2	2	no	—
49	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₁₇	—	2	2	no	—
51	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₁₇	—	4	2	no	—
53	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
54	C₂×SD₁₆×C₁₇	—	4	4	no	—
55	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	—
56	C₂×D₈×C₁₇	—	4	2	no	—
57	C₂×D₈×C₁₇	C₂³	1	4	yes	—
58	C₂×M₁₆×C₁₇	—	4	2	no	—
59	C₂×M₁₆×C₁₇	C₂³	1	4	yes	—
60	C₂²×C₈×C₁₇	—	4	2	no	—
61	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
62	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
63	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
64	C₂²×C₈×C₁₇	C₂³	1	4	yes	—
65	C₁₇×C₄⋊Q₈	—	2	4	no	—
66	C₁₇×C₄⋊Q₈	C₂³	1	8	yes	—
67	C₁₇×#126	—	2	16	no	—
68	C₁₇×#124	—	2	16	no	—
69	C₁₇×#124	—	2	4	no	—
70	C₁₇×#124	C₂³	1	8	yes	—
71	C₁₇×#123	—	2	16	no	—
72	C₁₇×C₂²⋊Q₈	—	2	4	no	—
73	C₁₇×C₂²⋊Q₈	—	2	16	no	—
74	C₁₇×C₂²⋊Q₈	C₂³	1	8	yes	—
75	C₁₇×#121	—	2	4	no	—
76	C₁₇×#121	C₂³	1	8	yes	—
77	C₄×Q₈×C₁₇	—	2	4	no	—
78	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
79	C₄×D₄×C₁₇	—	2	4	no	—
80	C₄×D₄×C₁₇	C₂³	1	8	yes	—
81	C₁₇×#117	D₄	1	4	yes	—
82	C₁₇×#117	C₂³	1	4	yes	—
83	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	2	yes	—
90	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
91	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
96	C₂×C₄²×C₁₇	—	2	2	no	—
97	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
98	C₁₇×#107	C₂³	1	4	yes	—
99	C₁₇×#107	C₂³	1	4	yes	—
100	C₁₇×#107	C₂³	1	8	yes	—
101	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
102	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
103	C₁₇×#103	C₂³	1	8	yes	—
104	C₁₇×#103	C₂³	1	8	yes	—
105	C₁₇×#102	C₂³	1	8	yes	—
106	C₁₇×#102	C₂³	1	8	yes	—
107	C₂⁴×C₁₇	—	2	2	no	—
108	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
109	C₂×Q₈×C₁₇	—	2	2	no	—
110	C₂×Q₈×C₁₇	—	2	8	no	—
111	C₂×Q₈×C₁₇	—	2	4	no	—
112	C₂×Q₈×C₁₇	—	2	4	no	—
113	C₂×Q₈×C₁₇	—	8	4	no	—
114	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
115	C₂×D₄×C₁₇	—	2	8	no	—
116	C₂×D₄×C₁₇	—	2	2	no	—
117	C₂×D₄×C₁₇	—	2	4	no	—
118	C₂×D₄×C₁₇	—	2	4	no	—
119	C₂×D₄×C₁₇	—	8	4	no	—
120	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
121	C₂²×C₄×C₁₇	—	2	2	no	—
122	C₂²×C₄×C₁₇	—	2	2	no	—
123	C₂²×C₄×C₁₇	—	2	2	no	—
124	C₂²×C₄×C₁₇	—	2	2	no	—
125	C₂²×C₄×C₁₇	—	2	2	no	—
126	C₂²×C₄×C₁₇	—	2	8	no	—
127	C₂²×C₄×C₁₇	—	8	4	no	—
128	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
133	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
134	Q₁₆×C₁₇	—	4	4	no	—
135	SD₁₆×C₁₇	—	4	8	no	—
136	D₈×C₁₇	—	4	4	no	—
137	M₁₆×C₁₇	—	4	4	no	—
138	C₂×C₈×C₁₇	—	2	2	no	—
139	C₂×C₈×C₁₇	—	2	2	no	—
140	C₂×C₈×C₁₇	—	2	4	no	—
141	C₂×C₈×C₁₇	—	4	4	no	—
142	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
143	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
144	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₁₇	—	2	8	no	—
146	C₄⋊C₄×C₁₇	—	2	8	no	—
147	C₄⋊C₄×C₁₇	—	2	2	no	—
148	C₄⋊C₄×C₁₇	—	2	8	no	—
149	C₄⋊C₄×C₁₇	—	2	2	no	—
150	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
151	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
152	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
153	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
154	C₂²⋊C₄×C₁₇	—	2	8	no	—
155	C₂²⋊C₄×C₁₇	—	2	8	no	—
156	C₂²⋊C₄×C₁₇	—	2	8	no	—
157	C₂²⋊C₄×C₁₇	—	2	8	no	—
158	C₂²⋊C₄×C₁₇	—	2	8	no	—
159	C₂²⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
160	C₄²×C₁₇	—	2	8	no	—
161	C₄²×C₁₇	C₂×D₄	1	4	yes	—
162	C₄²×C₁₇	C₂⁴	1	4	yes	—
163	C₂×#3262	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂³×C₁₇	—	2	2	no	—
165	C₂³×C₁₇	—	2	2	no	—
166	C₂³×C₁₇	—	2	2	no	—
167	C₂³×C₁₇	—	2	4	no	—
168	C₂³×C₁₇	—	4	4	no	—
169	C₂³×C₁₇	—	4	4	no	—
170	C₂³×C₁₇	—	4	4	no	—
171	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
172	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₁₇	—	2	4	no	—
174	Q₈×C₁₇	—	2	4	no	—
175	Q₈×C₁₇	—	4	4	no	—
176	Q₈×C₁₇	—	8	8	no	—
177	D₄×C₁₇	—	2	4	no	—
178	D₄×C₁₇	—	2	4	no	—
179	D₄×C₁₇	—	4	4	no	—
180	D₄×C₁₇	—	8	8	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	4	no	—
183	C₂×C₄×C₁₇	—	2	4	no	—
184	C₂×C₄×C₁₇	—	2	4	no	—
185	C₂×C₄×C₁₇	—	2	2	no	—
186	C₂×C₄×C₁₇	—	2	2	no	—
187	C₂×C₄×C₁₇	—	2	4	no	—
188	C₂×C₄×C₁₇	—	2	4	no	—
189	C₂×C₄×C₁₇	—	2	4	no	—
190	C₂×C₄×C₁₇	—	4	4	no	—
191	C₂×C₄×C₁₇	—	4	4	no	—
192	C₂×C₄×C₁₇	—	4	4	no	—
193	C₂×C₄×C₁₇	—	8	8	no	—
194	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
195	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
196	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
197	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×C₄×C₁₇	H(5,𝔽₂)	1	2	yes	—
199	C₂×C₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
200	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
201	C₈×C₁₇	—	2	2	no	—
202	C₈×C₁₇	—	2	2	no	—
203	C₈×C₁₇	—	2	4	no	—
204	C₂×#542	C₂×C₁₇	1	2	yes	complemented
205	#3262	C₂×C₁₇	1	16	yes	direct product factor
206	C₂×#477	C₂×C₁₇	1	2	yes	complemented
207	C₂×#474	C₂×C₁₇	1	2	yes	complemented
208	C₂×#468	C₂×C₁₇	1	2	yes	complemented
209	C₂×#467	C₂×C₁₇	1	1	yes	characteristic, complemented
210	C₂×#466	C₂×C₁₇	1	1	yes	characteristic
211	C₂×#464	C₂×C₁₇	1	2	yes	complemented
212	C₂×#463	C₂×C₁₇	1	2	yes	complemented
213	C₂×#424	C₂×C₁₇	1	1	yes	characteristic, complemented
214	C₂²×C₁₇	—	2	2	no	—
215	C₂²×C₁₇	—	2	2	no	—
216	C₂²×C₁₇	—	2	2	no	—
217	C₂²×C₁₇	—	4	4	no	—
218	C₂²×C₁₇	—	4	4	no	—
219	C₂²×C₁₇	—	4	4	no	—
220	C₂²×C₁₇	—	4	4	no	—
221	C₂²×C₁₇	—	8	8	no	—
222	C₂²×C₁₇	#537	1	2	yes	—
223	C₂²×C₁₇	#576	1	2	yes	—
224	C₂²×C₁₇	#578	1	2	yes	—
225	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
226	C₄×C₁₇	—	2	2	no	—
227	C₄×C₁₇	—	2	4	no	—
228	C₄×C₁₇	—	2	4	no	—
229	C₄×C₁₇	—	4	4	no	—
230	C₄×C₁₇	—	4	4	no	—
231	C₄×C₁₇	—	4	4	no	—
232	C₄×C₁₇	#537	1	2	yes	—
233	C₄×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
234	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
235	C₂²×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
236	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	—
237	C₂²×D₈	C₂²×C₁₇	1	1	yes	characteristic
238	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
239	C₂³×C₈	C₂²×C₁₇	1	1	yes	characteristic
240	#542	—	2	8	no	—
241	#542	C₂²×C₁₇	1	16	yes	complemented
242	C₂×C₄⋊Q₈	C₂²×C₁₇	1	2	yes	—
243	C₂×#126	—	2	2	no	—
244	C₂×#124	—	2	2	no	—
245	C₂×#124	C₂²×C₁₇	1	2	yes	—
246	C₂×#123	—	2	2	no	—
247	C₂×C₂²⋊Q₈	—	2	2	no	—
248	C₂×C₂²⋊Q₈	C₂²×C₁₇	1	2	yes	—
249	C₂×#121	C₂²×C₁₇	1	2	yes	—
250	C₂×C₄×Q₈	C₂²×C₁₇	1	2	yes	—
251	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
252	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
253	#477	C₂²×C₁₇	1	16	yes	complemented
254	#474	C₂²×C₁₇	1	16	yes	complemented
255	#468	C₂²×C₁₇	1	16	yes	complemented
256	#467	C₂²×C₁₇	1	8	yes	complemented
257	#466	C₂²×C₁₇	1	8	yes	—
258	#464	C₂²×C₁₇	1	16	yes	complemented
259	#463	C₂²×C₁₇	1	16	yes	complemented
260	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
261	C₂×#107	C₂²×C₁₇	1	2	yes	—
262	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
263	#424	C₂²×C₁₇	1	8	yes	complemented
264	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
265	C₂×C₄⋊C₈	C₂²×C₁₇	1	2	yes	—
266	C₂×#103	C₂²×C₁₇	1	2	yes	—
267	C₂×#103	C₂²×C₁₇	1	2	yes	—
268	C₂×#102	C₂²×C₁₇	1	2	yes	—
269	C₂×#102	C₂²×C₁₇	1	2	yes	—
270	C₂×C₁₇	—	4	2	no	—
271	C₂×C₁₇	—	8	4	no	—
272	C₂×C₁₇	#3262	1	4	yes	direct product factor
273	C₂×C₁₇	C₂×#537	1	1	yes	characteristic
274	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
275	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
276	C₂²×Q₈	—	2	2	no	—
277	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
278	C₂²×D₄	—	2	2	no	—
279	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
280	C₂³×C₄	—	2	2	no	—
281	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
282	C₂×Q₁₆	—	4	2	no	—
283	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
284	C₂×SD₁₆	—	4	4	no	—
285	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	—
286	C₂×D₈	—	4	2	no	—
287	C₂×D₈	C₂³×C₁₇	1	4	yes	—
288	C₂×M₁₆	—	4	2	no	—
289	C₂×M₁₆	C₂³×C₁₇	1	4	yes	—
290	C₂²×C₈	—	4	2	no	—
291	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
292	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
293	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
294	C₂²×C₈	C₂³×C₁₇	1	4	yes	—
295	C₄⋊Q₈	—	2	4	no	—
296	C₄⋊Q₈	C₂³×C₁₇	1	8	yes	—
297	#126	—	2	16	no	—
298	#124	—	2	16	no	—
299	#124	—	2	4	no	—
300	#124	C₂³×C₁₇	1	8	yes	—
301	#123	—	2	16	no	—
302	C₂²⋊Q₈	—	2	4	no	—
303	C₂²⋊Q₈	—	2	16	no	—
304	C₂²⋊Q₈	C₂³×C₁₇	1	8	yes	—
305	#121	—	2	4	no	—
306	#121	C₂³×C₁₇	1	8	yes	—
307	C₄×Q₈	—	2	4	no	—
308	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
309	C₄×D₄	—	2	4	no	—
310	C₄×D₄	C₂³×C₁₇	1	8	yes	—
311	#117	D₄×C₁₇	1	4	yes	—
312	#117	C₂³×C₁₇	1	4	yes	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
317	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₁₇	1	2	yes	—
320	C₂×C₂²⋊C₄	—	2	2	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₂²⋊C₄	—	2	2	no	—
325	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
326	C₂×C₄²	—	2	2	no	—
327	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
328	#107	C₂³×C₁₇	1	4	yes	—
329	#107	C₂³×C₁₇	1	4	yes	—
330	#107	C₂³×C₁₇	1	8	yes	—
331	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
332	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
333	#103	C₂³×C₁₇	1	8	yes	—
334	#103	C₂³×C₁₇	1	8	yes	—
335	#102	C₂³×C₁₇	1	8	yes	—
336	#102	C₂³×C₁₇	1	8	yes	—
337	C₁₇	C₂×#3262	1	1	yes	characteristic, direct product factor, Sylow
338	C₂⁴	—	2	2	no	—
339	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	8	no	—
342	C₂×Q₈	—	2	4	no	—
343	C₂×Q₈	—	2	4	no	—
344	C₂×Q₈	—	8	4	no	—
345	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	2	4	no	—
349	C₂×D₄	—	2	4	no	—
350	C₂×D₄	—	8	4	no	—
351	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	8	no	—
358	C₂²×C₄	—	8	4	no	—
359	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
360	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
361	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
363	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
364	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
365	Q₁₆	—	4	4	no	—
366	SD₁₆	—	4	8	no	—
367	D₈	—	4	4	no	—
368	M₁₆	—	4	4	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	4	no	—
372	C₂×C₈	—	4	4	no	—
373	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
374	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
375	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
376	C₄⋊C₄	—	2	8	no	—
377	C₄⋊C₄	—	2	8	no	—
378	C₄⋊C₄	—	2	8	no	—
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	2	2	no	—
381	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
382	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
383	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
384	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₂²⋊C₄	—	2	8	no	—
387	C₂²⋊C₄	—	2	8	no	—
388	C₂²⋊C₄	—	2	8	no	—
389	C₂²⋊C₄	—	2	8	no	—
390	C₂²⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
391	C₄²	—	2	8	no	—
392	C₄²	C₂×D₄×C₁₇	1	4	yes	—
393	C₄²	C₂⁴×C₁₇	1	4	yes	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	2	no	—
397	C₂³	—	2	4	no	—
398	C₂³	—	4	4	no	—
399	C₂³	—	4	4	no	—
400	C₂³	—	4	4	no	—
401	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
402	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
403	Q₈	—	2	4	no	—
404	Q₈	—	2	4	no	—
405	Q₈	—	4	4	no	—
406	Q₈	—	8	8	no	—
407	D₄	—	2	4	no	—
408	D₄	—	2	4	no	—
409	D₄	—	4	4	no	—
410	D₄	—	8	8	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	4	4	no	—
421	C₂×C₄	—	4	4	no	—
422	C₂×C₄	—	4	4	no	—
423	C₂×C₄	—	8	8	no	—
424	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
425	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
426	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
427	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
428	C₂×C₄	C₁₇×H(5,𝔽₂)	1	2	yes	—
429	C₂×C₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
430	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	2	4	no	—
434	C₂²	—	2	2	no	—
435	C₂²	—	2	2	no	—
436	C₂²	—	2	2	no	—
437	C₂²	—	4	4	no	—
438	C₂²	—	4	4	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	8	8	no	—
442	C₂²	C₁₇×#537	1	2	yes	—
443	C₂²	C₁₇×#576	1	2	yes	—
444	C₂²	C₁₇×#578	1	2	yes	—
445	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
446	C₄	—	2	4	no	—
447	C₄	—	2	4	no	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	4	4	no	—
452	C₄	C₁₇×#537	1	2	yes	—
453	C₄	C₂×C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
454	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
455	C₂	—	4	2	no	—
456	C₂	—	8	4	no	—
457	C₂	C₁₇×#3262	1	4	yes	direct product factor
458	C₂	C₂×C₁₇×#537	1	1	yes	characteristic
459	C₂	C₂×C₁₇×#576	1	1	yes	characteristic
460	C₂	C₂×C₁₇×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#466	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂×C₁₇×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#542	C₂	semidirect
2. C₁₇×#3262	C₂	direct (N × H)
3. C₂×C₁₇×#477	C₂	semidirect
4. C₂×C₁₇×#474	C₂	semidirect
5. C₂×C₁₇×#468	C₂	semidirect
6. C₂×C₁₇×#467	C₂	semidirect
8. C₂×C₁₇×#464	C₂	semidirect
9. C₂×C₁₇×#463	C₂	semidirect
10. C₂×C₁₇×#424	C₂	semidirect
17. C₁₇×#542	C₂²	semidirect
29. C₁₇×#477	C₂²	semidirect
30. C₁₇×#474	C₂²	semidirect
31. C₁₇×#468	C₂²	semidirect
32. C₁₇×#467	C₂²	semidirect
34. C₁₇×#464	C₂²	semidirect
35. C₁₇×#463	C₂²	semidirect
39. C₁₇×#424	C₂²	semidirect
163. C₂×#3262	C₁₇	direct (N × H)
204. C₂×#542	C₂×C₁₇	semidirect
205. #3262	C₂×C₁₇	direct (N × H)
206. C₂×#477	C₂×C₁₇	semidirect
207. C₂×#474	C₂×C₁₇	semidirect
208. C₂×#468	C₂×C₁₇	semidirect
209. C₂×#467	C₂×C₁₇	semidirect
211. C₂×#464	C₂×C₁₇	semidirect
212. C₂×#463	C₂×C₁₇	semidirect
213. C₂×#424	C₂×C₁₇	semidirect
241. #542	C₂²×C₁₇	semidirect
253. #477	C₂²×C₁₇	semidirect
254. #474	C₂²×C₁₇	semidirect
255. #468	C₂²×C₁₇	semidirect
256. #467	C₂²×C₁₇	semidirect
258. #464	C₂²×C₁₇	semidirect
259. #463	C₂²×C₁₇	semidirect
263. #424	C₂²×C₁₇	semidirect
272. C₂×C₁₇	#3262	direct (N × H)
337. C₁₇	C₂×#3262	direct (N × H)
457. C₂	C₁₇×#3262	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×C₁₇×#542	2
C₁₇×#3262	2
C₂×C₁₇×#477	2
C₂×C₁₇×#474	2
C₂×C₁₇×#468	2
C₂×C₁₇×#467	2
C₂×C₁₇×#466	2
C₂×C₁₇×#464	2
C₂×C₁₇×#463	2
C₂×C₁₇×#424	2
C₂×#3262	17

Subgroups — C2×C17×#3262 #16918657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₁₇×#3262 #16918657