Subgroups — C₁₇×#61582 #16919326

Order 4352.

2570 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄²×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3325	C₂	1	4	yes	maximal, complemented
4	C₁₇×#3324	C₂	1	4	yes	maximal, complemented
5	C₁₇×#3274	C₂	1	4	yes	maximal, complemented
6	C₁₇×#3272	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#3194	C₂	1	4	yes	maximal, complemented
10	C₁₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3003	C₂	1	4	yes	maximal, complemented
13	C₁₇×#2975	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂³×D₄×C₁₇	—	2	1	no	—
15	C₂³×D₄×C₁₇	C₂²	1	2	yes	—
16	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
17	C₁₇×#559	—	2	2	no	—
18	C₁₇×#556	C₂²	1	2	yes	complemented
19	C₁₇×#555	C₂²	1	2	yes	complemented
20	C₁₇×#553	—	2	2	no	—
21	C₁₇×#550	C₂²	1	2	yes	complemented
22	C₁₇×#547	C₂²	1	2	yes	complemented
23	D₄²×C₁₇	—	2	2	no	—
24	D₄²×C₁₇	—	2	2	no	—
25	D₄²×C₁₇	C₂²	1	4	yes	—
26	D₄²×C₁₇	C₂²	1	4	yes	—
27	C₁₇×#538	—	2	2	no	—
28	C₁₇×#535	—	2	1	no	—
29	C₁₇×#533	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#532	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
32	C₁₇×#525	C₂²	1	4	yes	complemented
33	C₂×C₁₇×#121	—	2	1	no	—
34	C₂×C₁₇×#121	C₂²	1	2	yes	—
35	C₂×C₁₇×#120	—	2	2	no	—
36	C₁₇×#520	—	2	1	no	—
37	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₁₇×#493	C₂²	1	2	yes	complemented
40	C₁₇×#492	C₂²	1	2	yes	complemented
41	C₁₇×#486	C₂²	1	2	yes	complemented
42	C₁₇×#486	C₂²	1	2	yes	complemented
43	C₁₇×#483	C₂²	1	2	yes	complemented
44	C₁₇×#482	C₂²	1	8	yes	complemented
45	C₁₇×#480	C₂²	1	2	yes	complemented
46	C₁₇×#476	C₂²	1	2	yes	complemented
47	C₁₇×#474	C₂²	1	2	yes	complemented
48	C₁₇×#469	C₂²	1	8	yes	complemented
49	C₁₇×#468	C₂²	1	8	yes	complemented
50	C₁₇×#461	C₂²	1	2	yes	complemented
51	C₁₇×#460	C₂²	1	4	yes	complemented
52	C₁₇×#459	C₂²	1	4	yes	complemented
53	C₁₇×#459	C₂²	1	2	yes	complemented
54	C₁₇×#450	C₂²	1	2	yes	—
55	C₁₇×#450	C₂²	1	4	yes	complemented
56	C₁₇×#450	C₂²	1	8	yes	complemented
57	C₁₇×#449	C₂²	1	8	yes	complemented
58	C₁₇×#447	C₂²	1	2	yes	—
59	C₁₇×#447	C₂²	1	8	yes	complemented
60	C₁₇×#447	C₂²	1	4	yes	complemented
61	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	complemented
62	C₄×D₈×C₁₇	C₂²	1	4	yes	complemented
63	C₁₇×#436	C₂²	1	4	yes	complemented
64	C₁₇×#436	C₂²	1	4	yes	complemented
65	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
66	C₁₇×#431	C₂²	1	1	yes	characteristic, complemented
67	C₁₇×#418	C₂²	1	8	yes	complemented
68	C₁₇×#407	C₂²	1	4	yes	complemented
69	C₂⁵×C₁₇	—	2	2	no	—
70	C₂×#41×C₁₇	—	2	1	no	—
71	C₂×#41×C₁₇	C₂³	1	4	yes	complemented
72	C₂²×D₄×C₁₇	—	2	2	no	—
73	C₂²×D₄×C₁₇	—	2	4	no	—
74	C₂²×D₄×C₁₇	—	2	4	no	—
75	C₂²×D₄×C₁₇	—	2	2	no	—
76	C₂²×D₄×C₁₇	—	2	1	no	—
77	C₂²×D₄×C₁₇	—	2	4	no	—
78	C₂²×D₄×C₁₇	—	2	1	no	—
79	C₂²×D₄×C₁₇	—	4	8	no	—
80	C₂²×D₄×C₁₇	—	4	8	no	—
81	C₂²×D₄×C₁₇	D₄	1	1	yes	characteristic
82	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
83	C₂²×D₄×C₁₇	C₂³	1	8	yes	—
84	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
85	C₂³×C₄×C₁₇	—	2	1	no	—
86	C₂³×C₄×C₁₇	C₂³	1	2	yes	—
87	C₁₇×AGL(1,ℤ/8)	—	4	16	no	—
88	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
89	C₂×SD₁₆×C₁₇	C₂³	1	8	yes	complemented
90	C₂×D₈×C₁₇	C₂³	1	4	yes	—
91	C₂×D₈×C₁₇	C₂³	1	8	yes	complemented
92	C₂×M₁₆×C₁₇	C₂³	1	8	yes	complemented
93	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
94	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
95	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic, complemented
96	C₁₇×#127	—	2	2	no	—
97	C₁₇×#127	—	2	1	no	—
98	C₁₇×#127	—	2	1	no	—
99	C₁₇×#127	C₂³	1	2	yes	—
100	C₁₇×#127	C₂³	1	2	yes	—
101	C₁₇×#127	C₂³	1	1	yes	characteristic, complemented
102	C₁₇×#126	—	2	4	no	—
103	C₁₇×#125	—	2	1	no	—
104	C₁₇×#124	—	2	2	no	—
105	C₁₇×#124	—	2	4	no	—
106	C₁₇×#124	—	2	1	no	—
107	C₁₇×#123	—	2	4	no	—
108	C₁₇×#123	—	2	4	no	—
109	C₁₇×C₂²⋊Q₈	—	2	1	no	—
110	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
111	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	complemented
112	C₁₇×#121	—	2	2	no	—
113	C₁₇×#121	—	2	2	no	—
114	C₁₇×#121	—	2	4	no	—
115	C₁₇×#121	—	2	1	no	—
116	C₁₇×#121	—	2	4	no	—
117	C₁₇×#121	—	2	4	no	—
118	C₁₇×#121	—	2	4	no	—
119	C₁₇×#121	C₂³	1	8	yes	—
120	C₁₇×#121	C₂³	1	2	yes	—
121	C₁₇×#121	C₂³	1	4	yes	complemented
122	C₁₇×#120	—	2	4	no	—
123	C₁₇×#120	—	2	8	no	—
124	C₁₇×#120	—	2	8	no	—
125	C₄×Q₈×C₁₇	—	2	2	no	—
126	C₄×Q₈×C₁₇	—	2	1	no	—
127	C₄×Q₈×C₁₇	C₂³	1	2	yes	complemented
128	C₄×D₄×C₁₇	—	2	4	no	—
129	C₄×D₄×C₁₇	—	2	4	no	—
130	C₄×D₄×C₁₇	—	2	2	no	—
131	C₄×D₄×C₁₇	—	2	1	no	—
132	C₄×D₄×C₁₇	—	2	1	no	—
133	C₄×D₄×C₁₇	—	2	1	no	—
134	C₄×D₄×C₁₇	D₄	1	2	yes	—
135	C₄×D₄×C₁₇	D₄	1	2	yes	—
136	C₄×D₄×C₁₇	C₂³	1	2	yes	—
137	C₄×D₄×C₁₇	C₂³	1	2	yes	—
138	C₄×D₄×C₁₇	C₂³	1	2	yes	—
139	C₄×D₄×C₁₇	C₂³	1	2	yes	—
140	C₄×D₄×C₁₇	C₂³	1	2	yes	complemented
141	C₁₇×#117	—	2	1	no	—
142	C₁₇×#117	—	2	2	no	—
143	C₁₇×#117	C₂³	1	4	yes	complemented
144	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
145	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
146	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
147	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
148	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
149	C₂×C₂²⋊C₄×C₁₇	D₄	1	2	yes	—
150	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
151	C₁₇×#107	C₂³	1	4	yes	complemented
152	C₁₇×#106	C₂³	1	4	yes	complemented
153	C₁₇×C₄⋊C₈	C₂³	1	2	yes	complemented
154	C₁₇×C₄⋊C₈	C₂³	1	2	yes	complemented
155	C₁₇×#103	C₂³	1	4	yes	complemented
156	C₁₇×#102	C₂³	1	4	yes	—
157	C₁₇×#102	C₂³	1	4	yes	—
158	C₁₇×#102	C₂³	1	8	yes	complemented
159	C₁₇×#102	C₂³	1	8	yes	complemented
160	C₁₇×#102	C₂³	1	4	yes	complemented
161	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
162	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
163	C₁₇×C₂²⋊C₈	C₂³	1	8	yes	complemented
164	C₄×C₈×C₁₇	C₂³	1	2	yes	complemented
165	C₄×C₈×C₁₇	C₂³	1	2	yes	complemented
166	C₂⁴×C₁₇	—	2	1	no	—
167	C₂⁴×C₁₇	—	2	2	no	—
168	C₂⁴×C₁₇	—	2	8	no	—
169	C₂⁴×C₁₇	—	4	8	no	—
170	C₂⁴×C₁₇	—	4	8	no	—
171	C₂⁴×C₁₇	—	8	4	no	—
172	C₂⁴×C₁₇	C₂×D₄	1	2	yes	—
173	#41×C₁₇	—	4	8	no	—
174	#41×C₁₇	—	4	4	no	—
175	C₂×Q₈×C₁₇	—	2	1	no	—
176	C₂×Q₈×C₁₇	—	2	1	no	—
177	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
178	C₂×D₄×C₁₇	—	2	4	no	—
179	C₂×D₄×C₁₇	—	2	16	no	—
180	C₂×D₄×C₁₇	—	2	8	no	—
181	C₂×D₄×C₁₇	—	2	2	no	—
182	C₂×D₄×C₁₇	—	2	4	no	—
183	C₂×D₄×C₁₇	—	2	4	no	—
184	C₂×D₄×C₁₇	—	2	4	no	—
185	C₂×D₄×C₁₇	—	2	1	no	—
186	C₂×D₄×C₁₇	—	2	1	no	—
187	C₂×D₄×C₁₇	—	2	2	no	—
188	C₂×D₄×C₁₇	—	2	2	no	—
189	C₂×D₄×C₁₇	—	2	2	no	—
190	C₂×D₄×C₁₇	—	2	8	no	—
191	C₂×D₄×C₁₇	—	2	2	no	—
192	C₂×D₄×C₁₇	—	2	2	no	—
193	C₂×D₄×C₁₇	—	2	1	no	—
194	C₂×D₄×C₁₇	—	4	8	no	—
195	C₂×D₄×C₁₇	—	4	4	no	—
196	C₂×D₄×C₁₇	—	4	16	no	—
197	C₂×D₄×C₁₇	—	4	16	no	—
198	C₂×D₄×C₁₇	—	4	16	no	—
199	C₂×D₄×C₁₇	—	4	8	no	—
200	C₂×D₄×C₁₇	—	4	8	no	—
201	C₂×D₄×C₁₇	—	4	4	no	—
202	C₂×D₄×C₁₇	—	8	2	no	—
203	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
204	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
205	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
206	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
207	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₁₇	—	2	1	no	—
209	C₂²×C₄×C₁₇	—	2	2	no	—
210	C₂²×C₄×C₁₇	—	2	2	no	—
211	C₂²×C₄×C₁₇	—	2	2	no	—
212	C₂²×C₄×C₁₇	—	2	4	no	—
213	C₂²×C₄×C₁₇	—	4	4	no	—
214	C₂²×C₄×C₁₇	—	4	4	no	—
215	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
216	C₂²×C₄×C₁₇	C₂×D₄	1	4	yes	—
217	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
218	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
219	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
220	C₂²×C₄×C₁₇	C₂⁴	1	4	yes	—
221	SD₁₆×C₁₇	—	2	8	no	—
222	SD₁₆×C₁₇	—	4	8	no	—
223	D₈×C₁₇	—	2	8	no	—
224	D₈×C₁₇	—	4	8	no	—
225	M₁₆×C₁₇	—	4	8	no	—
226	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
227	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
228	C₄⋊C₄×C₁₇	—	2	1	no	—
229	C₄⋊C₄×C₁₇	—	2	2	no	—
230	C₄⋊C₄×C₁₇	—	2	2	no	—
231	C₄⋊C₄×C₁₇	—	2	4	no	—
232	C₄⋊C₄×C₁₇	—	2	1	no	—
233	C₄⋊C₄×C₁₇	—	2	1	no	—
234	C₄⋊C₄×C₁₇	—	2	1	no	—
235	C₄⋊C₄×C₁₇	—	2	1	no	—
236	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
237	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
239	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
240	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
241	C₂²⋊C₄×C₁₇	—	2	2	no	—
242	C₂²⋊C₄×C₁₇	—	2	4	no	—
243	C₂²⋊C₄×C₁₇	—	2	4	no	—
244	C₂²⋊C₄×C₁₇	—	2	2	no	—
245	C₂²⋊C₄×C₁₇	—	2	2	no	—
246	C₂²⋊C₄×C₁₇	—	2	4	no	—
247	C₂²⋊C₄×C₁₇	—	2	2	no	—
248	C₂²⋊C₄×C₁₇	—	2	2	no	—
249	C₂²⋊C₄×C₁₇	—	2	8	no	—
250	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
251	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
252	C₄²×C₁₇	—	2	4	no	—
253	C₄²×C₁₇	—	2	2	no	—
254	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
255	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
256	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
257	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
258	#61582	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
259	C₂³×C₁₇	—	2	4	no	—
260	C₂³×C₁₇	—	2	4	no	—
261	C₂³×C₁₇	—	2	2	no	—
262	C₂³×C₁₇	—	2	2	no	—
263	C₂³×C₁₇	—	2	4	no	—
264	C₂³×C₁₇	—	4	2	no	—
265	C₂³×C₁₇	—	4	2	no	—
266	C₂³×C₁₇	—	4	16	no	—
267	C₂³×C₁₇	—	4	2	no	—
268	C₂³×C₁₇	—	4	4	no	—
269	C₂³×C₁₇	—	4	16	no	—
270	C₂³×C₁₇	—	4	4	no	—
271	C₂³×C₁₇	—	4	2	no	—
272	C₂³×C₁₇	—	4	4	no	—
273	C₂³×C₁₇	—	8	8	no	—
274	C₂³×C₁₇	—	8	32	no	—
275	C₂³×C₁₇	C₂²×D₄	1	4	yes	—
276	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
277	Q₈×C₁₇	—	2	4	no	—
278	Q₈×C₁₇	—	4	2	no	—
279	Q₈×C₁₇	—	8	1	no	—
280	D₄×C₁₇	—	2	4	no	—
281	D₄×C₁₇	—	2	4	no	—
282	D₄×C₁₇	—	2	4	no	—
283	D₄×C₁₇	—	2	2	no	—
284	D₄×C₁₇	—	2	4	no	—
285	D₄×C₁₇	—	2	8	no	—
286	D₄×C₁₇	—	4	16	no	—
287	D₄×C₁₇	—	4	4	no	—
288	D₄×C₁₇	—	4	16	no	—
289	D₄×C₁₇	—	4	4	no	—
290	D₄×C₁₇	—	4	4	no	—
291	D₄×C₁₇	—	4	4	no	—
292	D₄×C₁₇	—	4	2	no	—
293	D₄×C₁₇	—	8	1	no	—
294	D₄×C₁₇	—	8	2	no	—
295	D₄×C₁₇	—	8	2	no	—
296	D₄×C₁₇	—	8	4	no	—
297	D₄×C₁₇	—	8	4	no	—
298	D₄×C₁₇	H(5,𝔽₂)	1	4	yes	—
299	C₂×C₄×C₁₇	—	2	8	no	—
300	C₂×C₄×C₁₇	—	2	2	no	—
301	C₂×C₄×C₁₇	—	2	2	no	—
302	C₂×C₄×C₁₇	—	2	2	no	—
303	C₂×C₄×C₁₇	—	2	2	no	—
304	C₂×C₄×C₁₇	—	2	2	no	—
305	C₂×C₄×C₁₇	—	4	4	no	—
306	C₂×C₄×C₁₇	—	4	2	no	—
307	C₂×C₄×C₁₇	—	4	1	no	—
308	C₂×C₄×C₁₇	—	4	2	no	—
309	C₂×C₄×C₁₇	—	4	4	no	—
310	C₂×C₄×C₁₇	—	4	4	no	—
311	C₂×C₄×C₁₇	—	4	4	no	—
312	C₂×C₄×C₁₇	—	8	4	no	—
313	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	4	yes	complemented
314	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
315	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
316	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
317	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
321	C₈×C₁₇	—	2	4	no	—
322	C₈×C₁₇	—	2	4	no	—
323	#3506	C₂×C₁₇	1	1	yes	characteristic, complemented
324	C₂×D₄²	C₂×C₁₇	1	1	yes	characteristic, complemented
325	#3325	C₂×C₁₇	1	4	yes	complemented
326	#3324	C₂×C₁₇	1	4	yes	complemented
327	#3274	C₂×C₁₇	1	4	yes	complemented
328	#3272	C₂×C₁₇	1	4	yes	complemented
329	#3208	C₂×C₁₇	1	1	yes	characteristic, complemented
330	#3205	C₂×C₁₇	1	1	yes	characteristic, complemented
331	#3194	C₂×C₁₇	1	4	yes	complemented
332	#3101	C₂×C₁₇	1	1	yes	characteristic, complemented
333	#3100	C₂×C₁₇	1	1	yes	characteristic, complemented
334	#3003	C₂×C₁₇	1	4	yes	complemented
335	#2975	C₂×C₁₇	1	1	yes	characteristic, complemented
336	C₂²×C₁₇	—	2	1	no	—
337	C₂²×C₁₇	—	2	1	no	—
338	C₂²×C₁₇	—	2	4	no	—
339	C₂²×C₁₇	—	2	4	no	—
340	C₂²×C₁₇	—	2	4	no	—
341	C₂²×C₁₇	—	2	4	no	—
342	C₂²×C₁₇	—	4	8	no	—
343	C₂²×C₁₇	—	4	8	no	—
344	C₂²×C₁₇	—	4	2	no	—
345	C₂²×C₁₇	—	4	2	no	—
346	C₂²×C₁₇	—	4	2	no	—
347	C₂²×C₁₇	—	4	4	no	—
348	C₂²×C₁₇	—	4	2	no	—
349	C₂²×C₁₇	—	4	4	no	—
350	C₂²×C₁₇	—	4	2	no	—
351	C₂²×C₁₇	—	4	4	no	—
352	C₂²×C₁₇	—	8	8	no	—
353	C₂²×C₁₇	—	8	32	no	—
354	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
355	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
356	C₄×C₁₇	—	2	1	no	—
357	C₄×C₁₇	—	2	1	no	—
358	C₄×C₁₇	—	2	1	no	—
359	C₄×C₁₇	—	2	4	no	—
360	C₄×C₁₇	—	4	2	no	—
361	C₄×C₁₇	—	4	2	no	—
362	C₄×C₁₇	—	4	2	no	—
363	C₄×C₁₇	—	4	2	no	—
364	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
365	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
366	C₄×C₁₇	C₂×H(5,𝔽₂)	1	2	yes	—
367	C₂³×D₄	—	2	1	no	—
368	C₂³×D₄	C₂²×C₁₇	1	2	yes	—
369	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	8	yes	complemented
370	#559	—	2	2	no	—
371	#556	C₂²×C₁₇	1	2	yes	complemented
372	#555	C₂²×C₁₇	1	2	yes	complemented
373	#553	—	2	2	no	—
374	#550	C₂²×C₁₇	1	2	yes	complemented
375	#547	C₂²×C₁₇	1	2	yes	complemented
376	D₄²	—	2	2	no	—
377	D₄²	—	2	2	no	—
378	D₄²	C₂²×C₁₇	1	4	yes	—
379	D₄²	C₂²×C₁₇	1	4	yes	—
380	#538	—	2	2	no	—
381	#535	—	2	1	no	—
382	#533	C₂²×C₁₇	1	1	yes	characteristic, complemented
383	#532	C₂²×C₁₇	1	1	yes	characteristic, complemented
384	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
385	#525	C₂²×C₁₇	1	4	yes	complemented
386	C₂×#121	—	2	1	no	—
387	C₂×#121	C₂²×C₁₇	1	2	yes	—
388	C₂×#120	—	2	2	no	—
389	#520	—	2	1	no	—
390	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
391	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
392	#493	C₂²×C₁₇	1	2	yes	complemented
393	#492	C₂²×C₁₇	1	2	yes	complemented
394	#486	C₂²×C₁₇	1	2	yes	complemented
395	#486	C₂²×C₁₇	1	2	yes	complemented
396	#483	C₂²×C₁₇	1	2	yes	complemented
397	#482	C₂²×C₁₇	1	8	yes	complemented
398	#480	C₂²×C₁₇	1	2	yes	complemented
399	#476	C₂²×C₁₇	1	2	yes	complemented
400	#474	C₂²×C₁₇	1	2	yes	complemented
401	#469	C₂²×C₁₇	1	8	yes	complemented
402	#468	C₂²×C₁₇	1	8	yes	complemented
403	#461	C₂²×C₁₇	1	2	yes	complemented
404	#460	C₂²×C₁₇	1	4	yes	complemented
405	#459	C₂²×C₁₇	1	2	yes	complemented
406	#459	C₂²×C₁₇	1	4	yes	complemented
407	#450	C₂²×C₁₇	1	2	yes	—
408	#450	C₂²×C₁₇	1	4	yes	complemented
409	#450	C₂²×C₁₇	1	8	yes	complemented
410	#449	C₂²×C₁₇	1	8	yes	complemented
411	#447	C₂²×C₁₇	1	2	yes	—
412	#447	C₂²×C₁₇	1	4	yes	complemented
413	#447	C₂²×C₁₇	1	8	yes	complemented
414	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	complemented
415	C₄×D₈	C₂²×C₁₇	1	4	yes	complemented
416	#436	C₂²×C₁₇	1	4	yes	complemented
417	#436	C₂²×C₁₇	1	4	yes	complemented
418	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
419	#431	C₂²×C₁₇	1	1	yes	characteristic, complemented
420	#418	C₂²×C₁₇	1	8	yes	complemented
421	#407	C₂²×C₁₇	1	4	yes	complemented
422	C₂×C₁₇	—	2	2	no	—
423	C₂×C₁₇	—	4	4	no	—
424	C₂×C₁₇	—	4	4	no	—
425	C₂×C₁₇	—	8	2	no	—
426	C₂×C₁₇	—	8	4	no	—
427	C₂×C₁₇	#3484	1	1	yes	characteristic
428	C₂×C₁₇	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
429	C₂×C₁₇	#3585	1	1	yes	characteristic
430	C₂⁵	—	2	2	no	—
431	C₂×#41	—	2	1	no	—
432	C₂×#41	C₂³×C₁₇	1	4	yes	complemented
433	C₂²×D₄	—	2	2	no	—
434	C₂²×D₄	—	2	4	no	—
435	C₂²×D₄	—	2	4	no	—
436	C₂²×D₄	—	2	2	no	—
437	C₂²×D₄	—	2	1	no	—
438	C₂²×D₄	—	2	4	no	—
439	C₂²×D₄	—	2	1	no	—
440	C₂²×D₄	—	4	8	no	—
441	C₂²×D₄	—	4	8	no	—
442	C₂²×D₄	D₄×C₁₇	1	1	yes	characteristic
443	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
444	C₂²×D₄	C₂³×C₁₇	1	8	yes	—
445	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
446	C₂³×C₄	—	2	1	no	—
447	C₂³×C₄	C₂³×C₁₇	1	2	yes	—
448	AGL(1,ℤ/8)	—	4	16	no	—
449	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
450	C₂×SD₁₆	C₂³×C₁₇	1	8	yes	complemented
451	C₂×D₈	C₂³×C₁₇	1	4	yes	—
452	C₂×D₈	C₂³×C₁₇	1	8	yes	complemented
453	C₂×M₁₆	C₂³×C₁₇	1	8	yes	complemented
454	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic, complemented
455	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic, complemented
456	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic, complemented
457	#127	—	2	2	no	—
458	#127	—	2	1	no	—
459	#127	—	2	1	no	—
460	#127	C₂³×C₁₇	1	2	yes	—
461	#127	C₂³×C₁₇	1	2	yes	—
462	#127	C₂³×C₁₇	1	1	yes	characteristic, complemented
463	#126	—	2	4	no	—
464	#125	—	2	1	no	—
465	#124	—	2	2	no	—
466	#124	—	2	4	no	—
467	#124	—	2	1	no	—
468	#123	—	2	4	no	—
469	#123	—	2	4	no	—
470	C₂²⋊Q₈	—	2	1	no	—
471	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
472	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	complemented
473	#121	—	2	2	no	—
474	#121	—	2	2	no	—
475	#121	—	2	4	no	—
476	#121	—	2	1	no	—
477	#121	—	2	4	no	—
478	#121	—	2	4	no	—
479	#121	—	2	4	no	—
480	#121	C₂³×C₁₇	1	8	yes	—
481	#121	C₂³×C₁₇	1	2	yes	—
482	#121	C₂³×C₁₇	1	4	yes	complemented
483	#120	—	2	4	no	—
484	#120	—	2	8	no	—
485	#120	—	2	8	no	—
486	C₄×Q₈	—	2	2	no	—
487	C₄×Q₈	—	2	1	no	—
488	C₄×Q₈	C₂³×C₁₇	1	2	yes	complemented
489	C₄×D₄	—	2	4	no	—
490	C₄×D₄	—	2	4	no	—
491	C₄×D₄	—	2	2	no	—
492	C₄×D₄	—	2	1	no	—
493	C₄×D₄	—	2	1	no	—
494	C₄×D₄	—	2	1	no	—
495	C₄×D₄	D₄×C₁₇	1	2	yes	—
496	C₄×D₄	D₄×C₁₇	1	2	yes	—
497	C₄×D₄	C₂³×C₁₇	1	2	yes	—
498	C₄×D₄	C₂³×C₁₇	1	2	yes	—
499	C₄×D₄	C₂³×C₁₇	1	2	yes	—
500	C₄×D₄	C₂³×C₁₇	1	2	yes	—
501	C₄×D₄	C₂³×C₁₇	1	2	yes	complemented
502	#117	—	2	1	no	—
503	#117	—	2	2	no	—
504	#117	C₂³×C₁₇	1	4	yes	complemented
505	C₂×C₄⋊C₄	—	2	2	no	—
506	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
507	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
508	C₂×C₂²⋊C₄	—	2	1	no	—
509	C₂×C₂²⋊C₄	—	2	2	no	—
510	C₂×C₂²⋊C₄	D₄×C₁₇	1	2	yes	—
511	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
512	#107	C₂³×C₁₇	1	4	yes	complemented
513	#106	C₂³×C₁₇	1	4	yes	complemented
514	C₄⋊C₈	C₂³×C₁₇	1	2	yes	complemented
515	C₄⋊C₈	C₂³×C₁₇	1	2	yes	complemented
516	#103	C₂³×C₁₇	1	4	yes	complemented
517	#102	C₂³×C₁₇	1	4	yes	—
518	#102	C₂³×C₁₇	1	4	yes	—
519	#102	C₂³×C₁₇	1	8	yes	complemented
520	#102	C₂³×C₁₇	1	8	yes	complemented
521	#102	C₂³×C₁₇	1	4	yes	complemented
522	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
523	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
524	C₂²⋊C₈	C₂³×C₁₇	1	8	yes	complemented
525	C₄×C₈	C₂³×C₁₇	1	2	yes	complemented
526	C₄×C₈	C₂³×C₁₇	1	2	yes	complemented
527	C₁₇	#61582	1	1	yes	characteristic, direct product factor, Sylow
528	C₂⁴	—	2	1	no	—
529	C₂⁴	—	2	2	no	—
530	C₂⁴	—	2	8	no	—
531	C₂⁴	—	4	8	no	—
532	C₂⁴	—	4	8	no	—
533	C₂⁴	—	8	4	no	—
534	C₂⁴	C₂×D₄×C₁₇	1	2	yes	—
535	#41	—	4	8	no	—
536	#41	—	4	4	no	—
537	C₂×Q₈	—	2	1	no	—
538	C₂×Q₈	—	2	1	no	—
539	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
540	C₂×D₄	—	2	4	no	—
541	C₂×D₄	—	2	16	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	2	8	no	—
544	C₂×D₄	—	2	4	no	—
545	C₂×D₄	—	2	4	no	—
546	C₂×D₄	—	2	4	no	—
547	C₂×D₄	—	2	1	no	—
548	C₂×D₄	—	2	1	no	—
549	C₂×D₄	—	2	8	no	—
550	C₂×D₄	—	2	2	no	—
551	C₂×D₄	—	2	2	no	—
552	C₂×D₄	—	2	2	no	—
553	C₂×D₄	—	2	1	no	—
554	C₂×D₄	—	2	2	no	—
555	C₂×D₄	—	2	2	no	—
556	C₂×D₄	—	4	8	no	—
557	C₂×D₄	—	4	4	no	—
558	C₂×D₄	—	4	16	no	—
559	C₂×D₄	—	4	16	no	—
560	C₂×D₄	—	4	16	no	—
561	C₂×D₄	—	4	8	no	—
562	C₂×D₄	—	4	8	no	—
563	C₂×D₄	—	4	4	no	—
564	C₂×D₄	—	8	2	no	—
565	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
566	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
567	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
568	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
569	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
570	C₂²×C₄	—	2	1	no	—
571	C₂²×C₄	—	2	2	no	—
572	C₂²×C₄	—	2	2	no	—
573	C₂²×C₄	—	2	2	no	—
574	C₂²×C₄	—	2	4	no	—
575	C₂²×C₄	—	4	4	no	—
576	C₂²×C₄	—	4	4	no	—
577	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
578	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
579	C₂²×C₄	C₂×D₄×C₁₇	1	4	yes	—
580	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
581	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
582	C₂²×C₄	C₂⁴×C₁₇	1	4	yes	—
583	SD₁₆	—	2	8	no	—
584	SD₁₆	—	4	8	no	—
585	D₈	—	2	8	no	—
586	D₈	—	4	8	no	—
587	M₁₆	—	4	8	no	—
588	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
589	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
590	C₄⋊C₄	—	2	1	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	1	no	—
594	C₄⋊C₄	—	2	2	no	—
595	C₄⋊C₄	—	2	1	no	—
596	C₄⋊C₄	—	2	1	no	—
597	C₄⋊C₄	—	2	2	no	—
598	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
599	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
600	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
601	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
602	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	4	no	—
605	C₂²⋊C₄	—	2	4	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	8	no	—
609	C₂²⋊C₄	—	2	4	no	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
613	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
614	C₄²	—	2	4	no	—
615	C₄²	—	2	2	no	—
616	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
617	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
618	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
619	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
620	C₂³	—	2	4	no	—
621	C₂³	—	2	4	no	—
622	C₂³	—	2	2	no	—
623	C₂³	—	2	2	no	—
624	C₂³	—	2	4	no	—
625	C₂³	—	4	2	no	—
626	C₂³	—	4	2	no	—
627	C₂³	—	4	16	no	—
628	C₂³	—	4	2	no	—
629	C₂³	—	4	4	no	—
630	C₂³	—	4	16	no	—
631	C₂³	—	4	4	no	—
632	C₂³	—	4	2	no	—
633	C₂³	—	4	4	no	—
634	C₂³	—	8	8	no	—
635	C₂³	—	8	32	no	—
636	C₂³	C₂²×D₄×C₁₇	1	4	yes	—
637	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
638	Q₈	—	2	4	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	8	1	no	—
641	D₄	—	2	4	no	—
642	D₄	—	2	4	no	—
643	D₄	—	2	4	no	—
644	D₄	—	2	2	no	—
645	D₄	—	2	4	no	—
646	D₄	—	2	8	no	—
647	D₄	—	4	16	no	—
648	D₄	—	4	4	no	—
649	D₄	—	4	16	no	—
650	D₄	—	4	4	no	—
651	D₄	—	4	4	no	—
652	D₄	—	4	4	no	—
653	D₄	—	4	2	no	—
654	D₄	—	8	2	no	—
655	D₄	—	8	2	no	—
656	D₄	—	8	1	no	—
657	D₄	—	8	4	no	—
658	D₄	—	8	4	no	—
659	D₄	C₁₇×H(5,𝔽₂)	1	4	yes	—
660	C₂×C₄	—	2	8	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	2	no	—
664	C₂×C₄	—	2	2	no	—
665	C₂×C₄	—	2	2	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	1	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	4	4	no	—
671	C₂×C₄	—	4	4	no	—
672	C₂×C₄	—	4	4	no	—
673	C₂×C₄	—	8	4	no	—
674	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	4	yes	complemented
675	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
676	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
677	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
678	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
679	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
680	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
681	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
682	C₈	—	2	4	no	—
683	C₈	—	2	4	no	—
684	C₂²	—	2	1	no	—
685	C₂²	—	2	1	no	—
686	C₂²	—	2	4	no	—
687	C₂²	—	2	4	no	—
688	C₂²	—	2	4	no	—
689	C₂²	—	2	4	no	—
690	C₂²	—	4	8	no	—
691	C₂²	—	4	8	no	—
692	C₂²	—	4	2	no	—
693	C₂²	—	4	2	no	—
694	C₂²	—	4	2	no	—
695	C₂²	—	4	4	no	—
696	C₂²	—	4	2	no	—
697	C₂²	—	4	4	no	—
698	C₂²	—	4	2	no	—
699	C₂²	—	4	4	no	—
700	C₂²	—	8	8	no	—
701	C₂²	—	8	32	no	—
702	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	2	yes	—
703	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
704	C₄	—	2	1	no	—
705	C₄	—	2	4	no	—
706	C₄	—	2	1	no	—
707	C₄	—	2	1	no	—
708	C₄	—	4	2	no	—
709	C₄	—	4	2	no	—
710	C₄	—	4	2	no	—
711	C₄	—	4	2	no	—
712	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	2	yes	—
713	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	2	yes	—
714	C₄	C₂×C₁₇×H(5,𝔽₂)	1	2	yes	—
715	C₂	—	2	2	no	—
716	C₂	—	4	4	no	—
717	C₂	—	4	4	no	—
718	C₂	—	8	4	no	—
719	C₂	—	8	2	no	—
720	C₂	C₁₇×#3484	1	1	yes	characteristic
721	C₂	C₂²×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
722	C₂	C₁₇×#3585	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3506	C₂	semidirect
2. C₂×D₄²×C₁₇	C₂	semidirect
3. C₁₇×#3325	C₂	semidirect
4. C₁₇×#3324	C₂	semidirect
5. C₁₇×#3274	C₂	semidirect
6. C₁₇×#3272	C₂	semidirect
7. C₁₇×#3208	C₂	semidirect
8. C₁₇×#3205	C₂	semidirect
9. C₁₇×#3194	C₂	semidirect
10. C₁₇×#3101	C₂	semidirect
11. C₁₇×#3100	C₂	semidirect
12. C₁₇×#3003	C₂	semidirect
13. C₁₇×#2975	C₂	semidirect
16. C₂×C₁₇×AGL(1,ℤ/8)	C₂²	semidirect
18. C₁₇×#556	C₂²	semidirect
19. C₁₇×#555	C₂²	semidirect
21. C₁₇×#550	C₂²	semidirect
22. C₁₇×#547	C₂²	semidirect
29. C₁₇×#533	C₂²	semidirect
30. C₁₇×#532	C₂²	semidirect
32. C₁₇×#525	C₂²	semidirect
39. C₁₇×#493	C₂²	semidirect
40. C₁₇×#492	C₂²	semidirect
41. C₁₇×#486	C₂²	semidirect
42. C₁₇×#486	C₂²	semidirect
43. C₁₇×#483	C₂²	semidirect
44. C₁₇×#482	C₂²	semidirect
45. C₁₇×#480	C₂²	semidirect
46. C₁₇×#476	C₂²	semidirect
47. C₁₇×#474	C₂²	semidirect
48. C₁₇×#469	C₂²	semidirect
49. C₁₇×#468	C₂²	semidirect
50. C₁₇×#461	C₂²	semidirect
51. C₁₇×#460	C₂²	semidirect
52. C₁₇×#459	C₂²	semidirect
53. C₁₇×#459	C₂²	semidirect
55. C₁₇×#450	C₂²	semidirect
56. C₁₇×#450	C₂²	semidirect
57. C₁₇×#449	C₂²	semidirect
59. C₁₇×#447	C₂²	semidirect
60. C₁₇×#447	C₂²	semidirect
61. C₄×SD₁₆×C₁₇	C₂²	semidirect
62. C₄×D₈×C₁₇	C₂²	semidirect
63. C₁₇×#436	C₂²	semidirect
64. C₁₇×#436	C₂²	semidirect
65. C₁₇×#431	C₂²	semidirect
66. C₁₇×#431	C₂²	semidirect
67. C₁₇×#418	C₂²	semidirect
68. C₁₇×#407	C₂²	semidirect
71. C₂×#41×C₁₇	C₂³	semidirect
89. C₂×SD₁₆×C₁₇	C₂³	semidirect
91. C₂×D₈×C₁₇	C₂³	semidirect
92. C₂×M₁₆×C₁₇	C₂³	semidirect
93. C₁₇×C₄⋊Q₈	C₂³	semidirect
94. C₁₇×C₄⋊Q₈	C₂³	semidirect
95. C₁₇×C₄⋊Q₈	C₂³	semidirect
101. C₁₇×#127	C₂³	semidirect
111. C₁₇×C₂²⋊Q₈	C₂³	semidirect
121. C₁₇×#121	C₂³	semidirect
127. C₄×Q₈×C₁₇	C₂³	semidirect
140. C₄×D₄×C₁₇	C₂³	semidirect
143. C₁₇×#117	C₂³	semidirect
151. C₁₇×#107	C₂³	semidirect
152. C₁₇×#106	C₂³	semidirect
153. C₁₇×C₄⋊C₈	C₂³	semidirect
154. C₁₇×C₄⋊C₈	C₂³	semidirect
155. C₁₇×#103	C₂³	semidirect
158. C₁₇×#102	C₂³	semidirect
159. C₁₇×#102	C₂³	semidirect
160. C₁₇×#102	C₂³	semidirect
163. C₁₇×C₂²⋊C₈	C₂³	semidirect
164. C₄×C₈×C₁₇	C₂³	semidirect
165. C₄×C₈×C₁₇	C₂³	semidirect
258. #61582	C₁₇	direct (N × H)
313. C₂×C₄×C₁₇	AGL(1,ℤ/8)	semidirect
323. #3506	C₂×C₁₇	semidirect
324. C₂×D₄²	C₂×C₁₇	semidirect
325. #3325	C₂×C₁₇	semidirect
326. #3324	C₂×C₁₇	semidirect
327. #3274	C₂×C₁₇	semidirect
328. #3272	C₂×C₁₇	semidirect
329. #3208	C₂×C₁₇	semidirect
330. #3205	C₂×C₁₇	semidirect
331. #3194	C₂×C₁₇	semidirect
332. #3101	C₂×C₁₇	semidirect
333. #3100	C₂×C₁₇	semidirect
334. #3003	C₂×C₁₇	semidirect
335. #2975	C₂×C₁₇	semidirect
369. C₂×AGL(1,ℤ/8)	C₂²×C₁₇	semidirect
371. #556	C₂²×C₁₇	semidirect
372. #555	C₂²×C₁₇	semidirect
374. #550	C₂²×C₁₇	semidirect
375. #547	C₂²×C₁₇	semidirect
382. #533	C₂²×C₁₇	semidirect
383. #532	C₂²×C₁₇	semidirect
385. #525	C₂²×C₁₇	semidirect
392. #493	C₂²×C₁₇	semidirect
393. #492	C₂²×C₁₇	semidirect
394. #486	C₂²×C₁₇	semidirect
395. #486	C₂²×C₁₇	semidirect
396. #483	C₂²×C₁₇	semidirect
397. #482	C₂²×C₁₇	semidirect
398. #480	C₂²×C₁₇	semidirect
399. #476	C₂²×C₁₇	semidirect
400. #474	C₂²×C₁₇	semidirect
401. #469	C₂²×C₁₇	semidirect
402. #468	C₂²×C₁₇	semidirect
403. #461	C₂²×C₁₇	semidirect
404. #460	C₂²×C₁₇	semidirect
405. #459	C₂²×C₁₇	semidirect
406. #459	C₂²×C₁₇	semidirect
408. #450	C₂²×C₁₇	semidirect
409. #450	C₂²×C₁₇	semidirect
410. #449	C₂²×C₁₇	semidirect
412. #447	C₂²×C₁₇	semidirect
413. #447	C₂²×C₁₇	semidirect
414. C₄×SD₁₆	C₂²×C₁₇	semidirect
415. C₄×D₈	C₂²×C₁₇	semidirect
416. #436	C₂²×C₁₇	semidirect
417. #436	C₂²×C₁₇	semidirect
418. #431	C₂²×C₁₇	semidirect
419. #431	C₂²×C₁₇	semidirect
420. #418	C₂²×C₁₇	semidirect
421. #407	C₂²×C₁₇	semidirect
432. C₂×#41	C₂³×C₁₇	semidirect
450. C₂×SD₁₆	C₂³×C₁₇	semidirect
452. C₂×D₈	C₂³×C₁₇	semidirect
453. C₂×M₁₆	C₂³×C₁₇	semidirect
454. C₄⋊Q₈	C₂³×C₁₇	semidirect
455. C₄⋊Q₈	C₂³×C₁₇	semidirect
456. C₄⋊Q₈	C₂³×C₁₇	semidirect
462. #127	C₂³×C₁₇	semidirect
472. C₂²⋊Q₈	C₂³×C₁₇	semidirect
482. #121	C₂³×C₁₇	semidirect
488. C₄×Q₈	C₂³×C₁₇	semidirect
501. C₄×D₄	C₂³×C₁₇	semidirect
504. #117	C₂³×C₁₇	semidirect
512. #107	C₂³×C₁₇	semidirect
513. #106	C₂³×C₁₇	semidirect
514. C₄⋊C₈	C₂³×C₁₇	semidirect
515. C₄⋊C₈	C₂³×C₁₇	semidirect
516. #103	C₂³×C₁₇	semidirect
519. #102	C₂³×C₁₇	semidirect
520. #102	C₂³×C₁₇	semidirect
521. #102	C₂³×C₁₇	semidirect
524. C₂²⋊C₈	C₂³×C₁₇	semidirect
525. C₄×C₈	C₂³×C₁₇	semidirect
526. C₄×C₈	C₂³×C₁₇	semidirect
527. C₁₇	#61582	direct (N × H)
674. C₂×C₄	C₁₇×AGL(1,ℤ/8)	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3506	2
C₂×D₄²×C₁₇	2
C₁₇×#3325	2
C₁₇×#3324	2
C₁₇×#3274	2
C₁₇×#3272	2
C₁₇×#3208	2
C₁₇×#3205	2
C₁₇×#3194	2
C₁₇×#3101	2
C₁₇×#3100	2
C₁₇×#3003	2
C₁₇×#2975	2
#61582	17

Subgroups — C17×#61582 #16919326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61582 #16919326