Subgroups — C₁₇×#61864 #16919608

Order 4352.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3555	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3388	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3385	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3381	C₂	1	2	yes	maximal, complemented
7	C₁₇×#3380	C₂	1	1	yes	maximal, characteristic, complemented
8	Q₈×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#3376	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3367	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3360	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#3360	C₂	1	2	yes	maximal, complemented
14	C₁₇×#3359	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3244	C₂	1	2	yes	maximal, complemented
16	C₁₇×#3242	C₂	1	2	yes	maximal, complemented
17	C₁₇×#3233	C₂	1	1	yes	maximal, characteristic, complemented
18	C₁₇×#3231	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₇×#3123	C₂	1	2	yes	maximal, complemented
20	C₁₇×#3118	C₂	1	2	yes	maximal
21	C₁₇×#3105	C₂	1	1	yes	maximal, characteristic
22	C₁₇×#3101	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₇×#563	—	2	2	no	—
25	Q₈²×C₁₇	C₂²	1	1	yes	characteristic, complemented
26	C₁₇×#557	C₂²	1	1	yes	characteristic, complemented
27	C₁₇×#557	C₂²	1	2	yes	complemented
28	C₁₇×#556	—	2	1	no	—
29	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
30	C₁₇×#556	C₂²	1	2	yes	complemented
31	C₁₇×#554	—	2	1	no	—
32	C₁₇×#554	—	2	2	no	—
33	C₁₇×#554	C₂²	1	1	yes	characteristic
34	C₁₇×#554	C₂²	1	2	yes	—
35	C₁₇×#554	C₂²	1	1	yes	characteristic
36	C₁₇×#554	C₂²	1	2	yes	—
37	C₁₇×#554	C₂²	1	1	yes	characteristic, complemented
38	C₁₇×#552	—	2	1	no	—
39	D₄×Q₈×C₁₇	—	2	1	no	—
40	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
41	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#544	—	2	1	no	—
43	C₁₇×#544	C₂²	1	2	yes	—
44	C₁₇×#543	—	2	2	no	—
45	C₁₇×#542	C₂²	1	2	yes	—
46	C₁₇×#541	—	2	1	no	—
47	C₁₇×#541	—	2	2	no	—
48	C₁₇×#541	C₂²	1	2	yes	—
49	C₁₇×#533	C₂²	1	1	yes	characteristic
50	C₁₇×#533	C₂²	1	1	yes	characteristic
51	C₁₇×#533	C₂²	1	1	yes	characteristic
52	C₁₇×#529	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
54	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
55	C₁₇×#518	C₂²	1	2	yes	—
56	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
57	C₁₇×#501	C₂²	1	2	yes	complemented
58	C₁₇×#501	C₂²	1	2	yes	complemented
59	C₁₇×#500	C₂²	1	1	yes	characteristic, complemented
60	C₁₇×#499	C₂²	1	2	yes	complemented
61	C₁₇×#499	C₂²	1	2	yes	complemented
62	C₁₇×#498	C₂²	1	1	yes	characteristic, complemented
63	C₁₇×#498	C₂²	1	2	yes	complemented
64	C₁₇×#491	C₂²	1	2	yes	complemented
65	C₁₇×#489	C₂²	1	2	yes	complemented
66	C₁₇×#488	C₂²	1	2	yes	complemented
67	C₁₇×#488	C₂²	1	2	yes	complemented
68	C₁₇×#487	C₂²	1	1	yes	characteristic, complemented
69	C₁₇×#487	C₂²	1	1	yes	characteristic, complemented
70	C₁₇×#487	C₂²	1	2	yes	complemented
71	C₁₇×#485	C₂²	1	2	yes	—
72	C₁₇×#485	C₂²	1	2	yes	—
73	C₁₇×#485	C₂²	1	2	yes	—
74	C₁₇×#484	C₂²	1	1	yes	characteristic
75	C₁₇×#483	C₂²	1	2	yes	—
76	C₁₇×#482	C₂²	1	2	yes	—
77	C₁₇×#481	C₂²	1	1	yes	characteristic
78	C₁₇×#479	C₂²	1	2	yes	complemented
79	C₁₇×#479	C₂²	1	2	yes	complemented
80	C₁₇×#479	C₂²	1	2	yes	complemented
81	C₁₇×#479	C₂²	1	2	yes	complemented
82	C₁₇×#479	C₂²	1	2	yes	complemented
83	C₁₇×#478	C₂²	1	1	yes	characteristic
84	C₁₇×#478	C₂²	1	1	yes	characteristic
85	C₁₇×#478	C₂²	1	2	yes	—
86	C₁₇×#478	C₂²	1	2	yes	—
87	C₁₇×#478	C₂²	1	2	yes	complemented
88	C₁₇×#477	C₂²	1	1	yes	characteristic, complemented
89	C₁₇×#477	C₂²	1	2	yes	complemented
90	C₁₇×#476	C₂²	1	1	yes	characteristic
91	C₁₇×#476	C₂²	1	1	yes	characteristic
92	C₁₇×#476	C₂²	1	2	yes	—
93	C₁₇×#476	C₂²	1	1	yes	characteristic, complemented
94	C₁₇×#476	C₂²	1	2	yes	complemented
95	C₁₇×#475	C₂²	1	1	yes	characteristic, complemented
96	C₁₇×#475	C₂²	1	2	yes	complemented
97	C₁₇×#475	C₂²	1	2	yes	complemented
98	C₁₇×#474	C₂²	1	2	yes	—
99	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
100	C₁₇×#463	C₂²	1	1	yes	characteristic
101	C₁₇×#463	C₂²	1	2	yes	—
102	C₁₇×#463	C₂²	1	2	yes	—
103	C₁₇×#463	C₂²	1	1	yes	characteristic
104	C₁₇×#461	C₂²	1	1	yes	characteristic
105	C₁₇×#461	C₂²	1	1	yes	characteristic
106	C₁₇×#461	C₂²	1	2	yes	—
107	C₁₇×#461	C₂²	1	2	yes	—
108	C₁₇×#450	C₂²	1	2	yes	—
109	C₁₇×#450	C₂²	1	1	yes	characteristic
110	C₁₇×#447	C₂²	1	1	yes	characteristic
111	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
112	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
113	C₁₇×#446	C₂²	1	2	yes	complemented
114	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
115	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
116	C₈×Q₈×C₁₇	C₂²	1	2	yes	complemented
117	C₁₇×#442	C₂²	1	2	yes	—
118	C₁₇×#440	C₂²	1	2	yes	—
119	C₁₇×#440	C₂²	1	2	yes	—
120	C₁₇×#440	C₂²	1	2	yes	—
121	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
122	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
123	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
125	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
126	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₁₇	C₂²	1	2	yes	—
130	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
131	C₁₇×#433	C₂²	1	2	yes	—
132	C₁₇×#433	C₂²	1	2	yes	—
133	C₁₇×#431	C₂²	1	1	yes	characteristic
134	C₁₇×#431	C₂²	1	1	yes	characteristic
135	C₂²×Q₈×C₁₇	—	2	1	no	—
136	C₂²×Q₈×C₁₇	—	2	1	no	—
137	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₁₇	—	2	1	no	—
139	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
140	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
141	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
142	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
143	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
144	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
145	C₁₇×C₄⋊Q₈	—	2	2	no	—
146	C₁₇×C₄⋊Q₈	—	2	2	no	—
147	C₁₇×C₄⋊Q₈	—	2	1	no	—
148	C₁₇×C₄⋊Q₈	—	2	2	no	—
149	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
150	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
151	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
152	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
153	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
154	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
155	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
156	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
157	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
158	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
159	C₁₇×#126	—	2	2	no	—
160	C₁₇×#126	—	2	2	no	—
161	C₁₇×#126	—	2	2	no	—
162	C₁₇×#126	—	2	2	no	—
163	C₁₇×#126	—	2	2	no	—
164	C₁₇×#126	—	2	2	no	—
165	C₁₇×#126	—	2	1	no	—
166	C₁₇×#125	—	2	2	no	—
167	C₁₇×#125	—	2	2	no	—
168	C₁₇×#125	—	2	2	no	—
169	C₁₇×#125	—	2	2	no	—
170	C₁₇×#125	—	2	2	no	—
171	C₁₇×#125	—	2	1	no	—
172	C₁₇×#125	—	2	2	no	—
173	C₁₇×#125	—	2	1	no	—
174	C₁₇×#125	D₄	1	2	yes	—
175	C₁₇×#125	C₂³	1	2	yes	—
176	C₁₇×#125	C₂³	1	1	yes	characteristic
177	C₁₇×#125	C₂³	1	2	yes	—
178	C₁₇×#125	C₂³	1	2	yes	—
179	C₁₇×#125	C₂³	1	2	yes	—
180	C₁₇×#124	—	2	2	no	—
181	C₁₇×#124	C₂³	1	1	yes	characteristic
182	C₁₇×#124	C₂³	1	2	yes	—
183	C₁₇×#123	—	2	1	no	—
184	C₁₇×#123	—	2	2	no	—
185	C₁₇×C₂²⋊Q₈	—	2	1	no	—
186	C₁₇×C₂²⋊Q₈	—	2	1	no	—
187	C₁₇×C₂²⋊Q₈	—	2	1	no	—
188	C₁₇×C₂²⋊Q₈	—	2	1	no	—
189	C₁₇×C₂²⋊Q₈	—	2	2	no	—
190	C₁₇×C₂²⋊Q₈	—	2	2	no	—
191	C₁₇×C₂²⋊Q₈	—	2	2	no	—
192	C₁₇×C₂²⋊Q₈	—	2	1	no	—
193	C₁₇×C₂²⋊Q₈	—	2	1	no	—
194	C₁₇×C₂²⋊Q₈	—	2	1	no	—
195	C₁₇×C₂²⋊Q₈	—	2	1	no	—
196	C₁₇×C₂²⋊Q₈	—	2	1	no	—
197	C₁₇×C₂²⋊Q₈	—	2	2	no	—
198	C₁₇×C₂²⋊Q₈	—	2	2	no	—
199	C₁₇×C₂²⋊Q₈	—	2	2	no	—
200	C₁₇×C₂²⋊Q₈	—	2	2	no	—
201	C₁₇×C₂²⋊Q₈	—	2	2	no	—
202	C₁₇×C₂²⋊Q₈	—	2	2	no	—
203	C₁₇×C₂²⋊Q₈	—	2	2	no	—
204	C₁₇×C₂²⋊Q₈	—	2	2	no	—
205	C₁₇×C₂²⋊Q₈	—	2	2	no	—
206	C₁₇×C₂²⋊Q₈	—	2	2	no	—
207	C₁₇×C₂²⋊Q₈	—	2	2	no	—
208	C₁₇×C₂²⋊Q₈	—	2	2	no	—
209	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
210	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
211	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
212	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
213	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
214	C₁₇×#121	C₂³	1	1	yes	characteristic
215	C₄×Q₈×C₁₇	—	2	1	no	—
216	C₄×Q₈×C₁₇	—	2	1	no	—
217	C₄×Q₈×C₁₇	—	2	2	no	—
218	C₄×Q₈×C₁₇	—	2	1	no	—
219	C₄×Q₈×C₁₇	—	2	1	no	—
220	C₄×Q₈×C₁₇	—	2	1	no	—
221	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
222	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
223	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
224	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
225	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
226	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
227	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
228	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
229	C₄×D₄×C₁₇	—	2	1	no	—
230	C₄×D₄×C₁₇	—	2	2	no	—
231	C₄×D₄×C₁₇	—	2	2	no	—
232	C₄×D₄×C₁₇	—	2	1	no	—
233	C₄×D₄×C₁₇	—	2	1	no	—
234	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
235	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
236	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
237	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
238	C₄×D₄×C₁₇	C₂³	1	2	yes	—
239	C₄×D₄×C₁₇	C₂³	1	2	yes	—
240	C₄×D₄×C₁₇	C₂³	1	2	yes	—
241	C₄×D₄×C₁₇	C₂³	1	2	yes	—
242	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₇	C₂³	1	2	yes	—
244	C₁₇×#117	—	2	1	no	—
245	C₁₇×#117	—	2	2	no	—
246	C₁₇×#117	—	2	1	no	—
247	C₁₇×#117	—	2	1	no	—
248	C₁₇×#117	C₂³	1	2	yes	—
249	C₁₇×#117	C₂³	1	2	yes	—
250	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
251	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
252	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
253	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
254	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
255	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
256	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
257	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
258	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
259	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
260	C₁₇×#107	C₂³	1	1	yes	characteristic
261	C₁₇×#107	C₂³	1	2	yes	—
262	C₁₇×#107	C₂³	1	2	yes	—
263	C₁₇×#107	C₂³	1	2	yes	—
264	C₁₇×#107	C₂³	1	2	yes	—
265	C₁₇×#107	C₂³	1	1	yes	characteristic
266	C₁₇×#106	C₂³	1	2	yes	—
267	C₁₇×#106	C₂³	1	1	yes	characteristic
268	C₁₇×#106	C₂³	1	2	yes	—
269	C₁₇×#106	C₂³	1	2	yes	—
270	C₁₇×#106	C₂³	1	2	yes	—
271	C₁₇×#106	C₂³	1	2	yes	—
272	C₁₇×#106	C₂³	1	1	yes	characteristic
273	C₁₇×#106	C₂³	1	2	yes	—
274	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
275	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
276	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
277	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
278	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
279	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
280	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
281	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
282	C₁₇×#103	C₂³	1	1	yes	characteristic
283	C₁₇×#103	C₂³	1	2	yes	—
284	C₁₇×#103	C₂³	1	2	yes	—
285	C₁₇×#103	C₂³	1	2	yes	—
286	C₁₇×#103	C₂³	1	2	yes	—
287	C₁₇×#103	C₂³	1	2	yes	—
288	C₁₇×#103	C₂³	1	2	yes	—
289	C₁₇×#103	C₂³	1	2	yes	—
290	C₁₇×#103	C₂³	1	1	yes	characteristic
291	C₁₇×#103	C₂³	1	2	yes	—
292	C₁₇×#102	C₂³	1	2	yes	—
293	C₁₇×#102	C₂³	1	1	yes	characteristic
294	C₁₇×#102	C₂³	1	1	yes	characteristic
295	C₁₇×#102	C₂³	1	1	yes	characteristic
296	C₁₇×#102	C₂³	1	2	yes	—
297	C₁₇×#102	C₂³	1	1	yes	characteristic
298	C₁₇×#102	C₂³	1	1	yes	characteristic
299	C₁₇×#102	C₂³	1	1	yes	characteristic
300	C₁₇×#102	C₂³	1	2	yes	—
301	C₁₇×#102	C₂³	1	2	yes	—
302	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
303	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
304	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
305	C₁₇×#97	C₂³	1	2	yes	—
306	C₁₇×#97	C₂³	1	2	yes	—
307	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₁₇	C₂³	1	2	yes	—
309	C₄×C₈×C₁₇	C₂³	1	2	yes	—
310	C₄×C₈×C₁₇	C₂³	1	2	yes	—
311	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
312	C₂⁴×C₁₇	—	2	1	no	—
313	C₂×Q₈×C₁₇	—	2	1	no	—
314	C₂×Q₈×C₁₇	—	2	1	no	—
315	C₂×Q₈×C₁₇	—	2	2	no	—
316	C₂×Q₈×C₁₇	—	2	2	no	—
317	C₂×Q₈×C₁₇	—	2	1	no	—
318	C₂×Q₈×C₁₇	—	2	2	no	—
319	C₂×Q₈×C₁₇	—	8	2	no	—
320	C₂×Q₈×C₁₇	—	8	2	no	—
321	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
324	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
326	C₂×D₄×C₁₇	—	2	2	no	—
327	C₂×D₄×C₁₇	—	2	2	no	—
328	C₂×D₄×C₁₇	—	2	1	no	—
329	C₂×D₄×C₁₇	—	2	1	no	—
330	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
332	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
333	C₂²×C₄×C₁₇	—	2	1	no	—
334	C₂²×C₄×C₁₇	—	2	1	no	—
335	C₂²×C₄×C₁₇	—	2	1	no	—
336	C₂²×C₄×C₁₇	—	2	1	no	—
337	C₂²×C₄×C₁₇	—	2	2	no	—
338	C₂²×C₄×C₁₇	—	2	1	no	—
339	C₂²×C₄×C₁₇	—	2	1	no	—
340	C₂²×C₄×C₁₇	—	2	2	no	—
341	C₂²×C₄×C₁₇	—	2	2	no	—
342	C₂²×C₄×C₁₇	—	2	2	no	—
343	C₂²×C₄×C₁₇	—	2	2	no	—
344	C₂²×C₄×C₁₇	—	8	2	no	—
345	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
346	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
347	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
348	SD₁₆×C₁₇	—	2	4	no	—
349	SD₁₆×C₁₇	—	2	2	no	—
350	SD₁₆×C₁₇	—	2	4	no	—
351	SD₁₆×C₁₇	—	2	2	no	—
352	D₈×C₁₇	—	2	2	no	—
353	D₈×C₁₇	—	2	2	no	—
354	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
358	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
359	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₁₇	—	2	2	no	—
361	C₄⋊C₄×C₁₇	—	2	1	no	—
362	C₄⋊C₄×C₁₇	—	2	2	no	—
363	C₄⋊C₄×C₁₇	—	2	2	no	—
364	C₄⋊C₄×C₁₇	—	2	2	no	—
365	C₄⋊C₄×C₁₇	—	2	2	no	—
366	C₄⋊C₄×C₁₇	—	2	2	no	—
367	C₄⋊C₄×C₁₇	—	2	2	no	—
368	C₄⋊C₄×C₁₇	—	2	2	no	—
369	C₄⋊C₄×C₁₇	—	2	1	no	—
370	C₄⋊C₄×C₁₇	—	2	2	no	—
371	C₄⋊C₄×C₁₇	—	2	2	no	—
372	C₄⋊C₄×C₁₇	—	2	2	no	—
373	C₄⋊C₄×C₁₇	—	2	2	no	—
374	C₄⋊C₄×C₁₇	—	2	2	no	—
375	C₄⋊C₄×C₁₇	—	2	2	no	—
376	C₄⋊C₄×C₁₇	—	2	2	no	—
377	C₄⋊C₄×C₁₇	—	2	1	no	—
378	C₄⋊C₄×C₁₇	—	2	1	no	—
379	C₄⋊C₄×C₁₇	—	2	2	no	—
380	C₄⋊C₄×C₁₇	—	2	1	no	—
381	C₄⋊C₄×C₁₇	—	2	1	no	—
382	C₄⋊C₄×C₁₇	—	2	1	no	—
383	C₄⋊C₄×C₁₇	—	2	1	no	—
384	C₄⋊C₄×C₁₇	—	2	2	no	—
385	C₄⋊C₄×C₁₇	—	2	1	no	—
386	C₄⋊C₄×C₁₇	—	2	2	no	—
387	C₄⋊C₄×C₁₇	—	2	1	no	—
388	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
389	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
393	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
395	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
399	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
400	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
401	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
403	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
404	C₂²⋊C₄×C₁₇	—	2	2	no	—
405	C₂²⋊C₄×C₁₇	—	2	2	no	—
406	C₂²⋊C₄×C₁₇	—	2	1	no	—
407	C₂²⋊C₄×C₁₇	—	2	2	no	—
408	C₂²⋊C₄×C₁₇	—	2	2	no	—
409	C₂²⋊C₄×C₁₇	—	2	2	no	—
410	C₂²⋊C₄×C₁₇	—	2	2	no	—
411	C₂²⋊C₄×C₁₇	—	2	1	no	—
412	C₂²⋊C₄×C₁₇	—	2	1	no	—
413	C₂²⋊C₄×C₁₇	—	2	1	no	—
414	C₂²⋊C₄×C₁₇	—	2	1	no	—
415	C₂²⋊C₄×C₁₇	—	2	1	no	—
416	C₂²⋊C₄×C₁₇	—	2	1	no	—
417	C₂²⋊C₄×C₁₇	—	2	2	no	—
418	C₂²⋊C₄×C₁₇	—	2	2	no	—
419	C₂²⋊C₄×C₁₇	—	2	1	no	—
420	C₂²⋊C₄×C₁₇	—	2	2	no	—
421	C₂²⋊C₄×C₁₇	—	2	1	no	—
422	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
423	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
424	C₄²×C₁₇	—	2	2	no	—
425	C₄²×C₁₇	—	2	2	no	—
426	C₄²×C₁₇	—	2	2	no	—
427	C₄²×C₁₇	—	2	2	no	—
428	C₄²×C₁₇	—	2	1	no	—
429	C₄²×C₁₇	—	2	2	no	—
430	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
431	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
432	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
433	C₄²×C₁₇	C₂⁴	1	2	yes	—
434	C₄²×C₁₇	C₂⁴	1	2	yes	—
435	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
436	#61864	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
437	C₂³×C₁₇	—	2	4	no	—
438	C₂³×C₁₇	—	2	1	no	—
439	C₂³×C₁₇	—	2	1	no	—
440	C₂³×C₁₇	—	2	1	no	—
441	C₂³×C₁₇	—	8	1	no	—
442	C₂³×C₁₇	—	8	1	no	—
443	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
444	Q₈×C₁₇	—	2	2	no	—
445	Q₈×C₁₇	—	2	2	no	—
446	Q₈×C₁₇	—	2	1	no	—
447	Q₈×C₁₇	—	2	2	no	—
448	Q₈×C₁₇	—	2	1	no	—
449	Q₈×C₁₇	—	2	2	no	—
450	Q₈×C₁₇	—	4	2	no	—
451	Q₈×C₁₇	—	4	2	no	—
452	Q₈×C₁₇	—	8	1	no	—
453	Q₈×C₁₇	—	8	1	no	—
454	Q₈×C₁₇	—	8	2	no	—
455	Q₈×C₁₇	—	8	2	no	—
456	Q₈×C₁₇	—	8	2	no	—
457	D₄×C₁₇	—	2	4	no	—
458	D₄×C₁₇	—	2	1	no	—
459	D₄×C₁₇	—	2	1	no	—
460	D₄×C₁₇	—	2	1	no	—
461	D₄×C₁₇	—	2	1	no	—
462	D₄×C₁₇	—	8	1	no	—
463	D₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
464	D₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
465	C₂×C₄×C₁₇	—	2	2	no	—
466	C₂×C₄×C₁₇	—	2	1	no	—
467	C₂×C₄×C₁₇	—	2	1	no	—
468	C₂×C₄×C₁₇	—	2	2	no	—
469	C₂×C₄×C₁₇	—	2	1	no	—
470	C₂×C₄×C₁₇	—	2	1	no	—
471	C₂×C₄×C₁₇	—	2	1	no	—
472	C₂×C₄×C₁₇	—	2	2	no	—
473	C₂×C₄×C₁₇	—	2	2	no	—
474	C₂×C₄×C₁₇	—	2	2	no	—
475	C₂×C₄×C₁₇	—	2	1	no	—
476	C₂×C₄×C₁₇	—	2	1	no	—
477	C₂×C₄×C₁₇	—	4	1	no	—
478	C₂×C₄×C₁₇	—	4	2	no	—
479	C₂×C₄×C₁₇	—	4	2	no	—
480	C₂×C₄×C₁₇	—	4	2	no	—
481	C₂×C₄×C₁₇	—	8	2	no	—
482	C₂×C₄×C₁₇	—	8	2	no	—
483	C₂×C₄×C₁₇	—	8	2	no	—
484	C₂×C₄×C₁₇	—	8	1	no	—
485	C₂×C₄×C₁₇	—	8	1	no	—
486	C₂×C₄×C₁₇	—	8	2	no	—
487	C₂×C₄×C₁₇	—	8	2	no	—
488	C₂×C₄×C₁₇	—	8	1	no	—
489	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
492	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
497	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
499	C₈×C₁₇	—	2	1	no	—
500	C₈×C₁₇	—	2	1	no	—
501	C₈×C₁₇	—	2	1	no	—
502	C₈×C₁₇	—	2	2	no	—
503	C₈×C₁₇	—	2	2	no	—
504	C₈×C₁₇	—	2	1	no	—
505	#3555	C₂×C₁₇	1	1	yes	characteristic, complemented
506	#3501	C₂×C₁₇	1	1	yes	characteristic, complemented
507	#3388	C₂×C₁₇	1	2	yes	complemented
508	#3385	C₂×C₁₇	1	1	yes	characteristic, complemented
509	#3384	C₂×C₁₇	1	1	yes	characteristic, complemented
510	#3381	C₂×C₁₇	1	2	yes	complemented
511	#3380	C₂×C₁₇	1	1	yes	characteristic, complemented
512	Q₈×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
513	#3376	C₂×C₁₇	1	2	yes	complemented
514	#3372	C₂×C₁₇	1	1	yes	characteristic, complemented
515	#3367	C₂×C₁₇	1	1	yes	characteristic, complemented
516	#3360	C₂×C₁₇	1	1	yes	characteristic, complemented
517	#3360	C₂×C₁₇	1	2	yes	complemented
518	#3359	C₂×C₁₇	1	1	yes	characteristic, complemented
519	#3244	C₂×C₁₇	1	2	yes	complemented
520	#3242	C₂×C₁₇	1	2	yes	complemented
521	#3233	C₂×C₁₇	1	1	yes	characteristic, complemented
522	#3231	C₂×C₁₇	1	1	yes	characteristic, complemented
523	#3123	C₂×C₁₇	1	2	yes	complemented
524	#3118	C₂×C₁₇	1	2	yes	—
525	#3105	C₂×C₁₇	1	1	yes	characteristic
526	#3101	C₂×C₁₇	1	1	yes	characteristic, complemented
527	#2986	C₂×C₁₇	1	1	yes	characteristic, complemented
528	C₂²×C₁₇	—	2	1	no	—
529	C₂²×C₁₇	—	2	1	no	—
530	C₂²×C₁₇	—	2	2	no	—
531	C₂²×C₁₇	—	2	2	no	—
532	C₂²×C₁₇	—	2	1	no	—
533	C₂²×C₁₇	—	4	1	no	—
534	C₂²×C₁₇	—	4	1	no	—
535	C₂²×C₁₇	—	4	1	no	—
536	C₂²×C₁₇	—	4	1	no	—
537	C₂²×C₁₇	—	4	1	no	—
538	C₂²×C₁₇	—	4	1	no	—
539	C₂²×C₁₇	—	4	1	no	—
540	C₂²×C₁₇	—	8	4	no	—
541	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
542	C₄×C₁₇	—	2	1	no	—
543	C₄×C₁₇	—	2	1	no	—
544	C₄×C₁₇	—	2	2	no	—
545	C₄×C₁₇	—	2	2	no	—
546	C₄×C₁₇	—	2	1	no	—
547	C₄×C₁₇	—	2	1	no	—
548	C₄×C₁₇	—	2	2	no	—
549	C₄×C₁₇	—	2	2	no	—
550	C₄×C₁₇	—	4	2	no	—
551	C₄×C₁₇	—	4	2	no	—
552	C₄×C₁₇	—	4	1	no	—
553	C₄×C₁₇	—	4	2	no	—
554	C₄×C₁₇	—	4	1	no	—
555	C₄×C₁₇	—	4	1	no	—
556	C₄×C₁₇	—	4	1	no	—
557	C₄×C₁₇	—	4	1	no	—
558	C₄×C₁₇	—	4	2	no	—
559	C₄×C₁₇	#577	1	2	yes	—
560	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
561	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	#563	—	2	2	no	—
563	Q₈²	C₂²×C₁₇	1	1	yes	characteristic, complemented
564	#557	C₂²×C₁₇	1	1	yes	characteristic, complemented
565	#557	C₂²×C₁₇	1	2	yes	complemented
566	#556	—	2	1	no	—
567	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
568	#556	C₂²×C₁₇	1	2	yes	complemented
569	#554	—	2	1	no	—
570	#554	—	2	2	no	—
571	#554	C₂²×C₁₇	1	1	yes	characteristic
572	#554	C₂²×C₁₇	1	2	yes	—
573	#554	C₂²×C₁₇	1	1	yes	characteristic
574	#554	C₂²×C₁₇	1	2	yes	—
575	#554	C₂²×C₁₇	1	1	yes	characteristic, complemented
576	#552	—	2	1	no	—
577	D₄×Q₈	—	2	1	no	—
578	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
579	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
580	#544	—	2	1	no	—
581	#544	C₂²×C₁₇	1	2	yes	—
582	#543	—	2	2	no	—
583	#542	C₂²×C₁₇	1	2	yes	—
584	#541	—	2	1	no	—
585	#541	—	2	2	no	—
586	#541	C₂²×C₁₇	1	2	yes	—
587	#533	C₂²×C₁₇	1	1	yes	characteristic
588	#533	C₂²×C₁₇	1	1	yes	characteristic
589	#533	C₂²×C₁₇	1	1	yes	characteristic
590	#529	C₂²×C₁₇	1	1	yes	characteristic
591	C₂×C₂²⋊Q₈	—	2	1	no	—
592	C₂×C₂²⋊Q₈	—	2	1	no	—
593	#518	C₂²×C₁₇	1	2	yes	—
594	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
595	#501	C₂²×C₁₇	1	2	yes	complemented
596	#501	C₂²×C₁₇	1	2	yes	complemented
597	#500	C₂²×C₁₇	1	1	yes	characteristic, complemented
598	#499	C₂²×C₁₇	1	2	yes	complemented
599	#499	C₂²×C₁₇	1	2	yes	complemented
600	#498	C₂²×C₁₇	1	2	yes	complemented
601	#498	C₂²×C₁₇	1	1	yes	characteristic, complemented
602	#491	C₂²×C₁₇	1	2	yes	complemented
603	#489	C₂²×C₁₇	1	2	yes	complemented
604	#488	C₂²×C₁₇	1	2	yes	complemented
605	#488	C₂²×C₁₇	1	2	yes	complemented
606	#487	C₂²×C₁₇	1	2	yes	complemented
607	#487	C₂²×C₁₇	1	1	yes	characteristic, complemented
608	#487	C₂²×C₁₇	1	1	yes	characteristic, complemented
609	#485	C₂²×C₁₇	1	2	yes	—
610	#485	C₂²×C₁₇	1	2	yes	—
611	#485	C₂²×C₁₇	1	2	yes	—
612	#484	C₂²×C₁₇	1	1	yes	characteristic
613	#483	C₂²×C₁₇	1	2	yes	—
614	#482	C₂²×C₁₇	1	2	yes	—
615	#481	C₂²×C₁₇	1	1	yes	characteristic
616	#479	C₂²×C₁₇	1	2	yes	complemented
617	#479	C₂²×C₁₇	1	2	yes	complemented
618	#479	C₂²×C₁₇	1	2	yes	complemented
619	#479	C₂²×C₁₇	1	2	yes	complemented
620	#479	C₂²×C₁₇	1	2	yes	complemented
621	#478	C₂²×C₁₇	1	1	yes	characteristic
622	#478	C₂²×C₁₇	1	1	yes	characteristic
623	#478	C₂²×C₁₇	1	2	yes	—
624	#478	C₂²×C₁₇	1	2	yes	—
625	#478	C₂²×C₁₇	1	2	yes	complemented
626	#477	C₂²×C₁₇	1	2	yes	complemented
627	#477	C₂²×C₁₇	1	1	yes	characteristic, complemented
628	#476	C₂²×C₁₇	1	1	yes	characteristic
629	#476	C₂²×C₁₇	1	1	yes	characteristic
630	#476	C₂²×C₁₇	1	2	yes	—
631	#476	C₂²×C₁₇	1	1	yes	characteristic, complemented
632	#476	C₂²×C₁₇	1	2	yes	complemented
633	#475	C₂²×C₁₇	1	1	yes	characteristic, complemented
634	#475	C₂²×C₁₇	1	2	yes	complemented
635	#475	C₂²×C₁₇	1	2	yes	complemented
636	#474	C₂²×C₁₇	1	2	yes	—
637	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
638	#463	C₂²×C₁₇	1	1	yes	characteristic
639	#463	C₂²×C₁₇	1	2	yes	—
640	#463	C₂²×C₁₇	1	2	yes	—
641	#463	C₂²×C₁₇	1	1	yes	characteristic
642	#461	C₂²×C₁₇	1	1	yes	characteristic
643	#461	C₂²×C₁₇	1	1	yes	characteristic
644	#461	C₂²×C₁₇	1	2	yes	—
645	#461	C₂²×C₁₇	1	2	yes	—
646	#450	C₂²×C₁₇	1	2	yes	—
647	#450	C₂²×C₁₇	1	1	yes	characteristic
648	#447	C₂²×C₁₇	1	1	yes	characteristic
649	#446	C₂²×C₁₇	1	1	yes	characteristic, complemented
650	#446	C₂²×C₁₇	1	1	yes	characteristic, complemented
651	#446	C₂²×C₁₇	1	2	yes	complemented
652	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
653	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
654	C₈×Q₈	C₂²×C₁₇	1	2	yes	complemented
655	#442	C₂²×C₁₇	1	2	yes	—
656	#440	C₂²×C₁₇	1	2	yes	—
657	#440	C₂²×C₁₇	1	2	yes	—
658	#440	C₂²×C₁₇	1	2	yes	—
659	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
660	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
661	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
662	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
663	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
664	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
666	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
667	C₄×D₈	C₂²×C₁₇	1	2	yes	—
668	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
669	#433	C₂²×C₁₇	1	2	yes	—
670	#433	C₂²×C₁₇	1	2	yes	—
671	#431	C₂²×C₁₇	1	1	yes	characteristic
672	#431	C₂²×C₁₇	1	1	yes	characteristic
673	C₂×C₁₇	—	4	1	no	—
674	C₂×C₁₇	—	4	2	no	—
675	C₂×C₁₇	—	4	2	no	—
676	C₂×C₁₇	—	8	1	no	—
677	C₂×C₁₇	#3486	1	1	yes	characteristic
678	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
679	C₂×C₁₇	#3584	1	1	yes	characteristic
680	C₂²×Q₈	—	2	1	no	—
681	C₂²×Q₈	—	2	1	no	—
682	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
683	C₂³×C₄	—	2	1	no	—
684	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
685	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
686	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
687	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
688	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
689	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
690	C₄⋊Q₈	—	2	2	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	1	no	—
693	C₄⋊Q₈	—	2	2	no	—
694	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
695	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
696	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
697	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
698	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
699	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
702	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
704	#126	—	2	2	no	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	1	no	—
711	#125	—	2	2	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	1	no	—
717	#125	—	2	2	no	—
718	#125	—	2	1	no	—
719	#125	D₄×C₁₇	1	2	yes	—
720	#125	C₂³×C₁₇	1	1	yes	characteristic
721	#125	C₂³×C₁₇	1	2	yes	—
722	#125	C₂³×C₁₇	1	2	yes	—
723	#125	C₂³×C₁₇	1	2	yes	—
724	#125	C₂³×C₁₇	1	2	yes	—
725	#124	—	2	2	no	—
726	#124	C₂³×C₁₇	1	1	yes	characteristic
727	#124	C₂³×C₁₇	1	2	yes	—
728	#123	—	2	1	no	—
729	#123	—	2	2	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	no	—
734	C₂²⋊Q₈	—	2	2	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	2	1	no	—
738	C₂²⋊Q₈	—	2	1	no	—
739	C₂²⋊Q₈	—	2	1	no	—
740	C₂²⋊Q₈	—	2	1	no	—
741	C₂²⋊Q₈	—	2	1	no	—
742	C₂²⋊Q₈	—	2	2	no	—
743	C₂²⋊Q₈	—	2	2	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	2	no	—
750	C₂²⋊Q₈	—	2	2	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	2	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
755	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
756	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
757	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
758	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
759	#121	C₂³×C₁₇	1	1	yes	characteristic
760	C₄×Q₈	—	2	1	no	—
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	2	no	—
763	C₄×Q₈	—	2	1	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
767	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
768	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
769	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
770	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
771	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
772	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
773	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
774	C₄×D₄	—	2	1	no	—
775	C₄×D₄	—	2	2	no	—
776	C₄×D₄	—	2	2	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	2	1	no	—
779	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
780	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
781	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
782	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
783	C₄×D₄	C₂³×C₁₇	1	2	yes	—
784	C₄×D₄	C₂³×C₁₇	1	2	yes	—
785	C₄×D₄	C₂³×C₁₇	1	2	yes	—
786	C₄×D₄	C₂³×C₁₇	1	2	yes	—
787	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
788	C₄×D₄	C₂³×C₁₇	1	2	yes	—
789	#117	—	2	1	no	—
790	#117	—	2	2	no	—
791	#117	—	2	1	no	—
792	#117	—	2	1	no	—
793	#117	C₂³×C₁₇	1	2	yes	—
794	#117	C₂³×C₁₇	1	2	yes	—
795	C₂×C₄⋊C₄	—	2	2	no	—
796	C₂×C₄⋊C₄	—	2	2	no	—
797	C₂×C₄⋊C₄	—	2	1	no	—
798	C₂×C₄⋊C₄	—	2	1	no	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
801	C₂×C₂²⋊C₄	—	2	1	no	—
802	C₂×C₂²⋊C₄	—	2	2	no	—
803	C₂×C₂²⋊C₄	—	2	2	no	—
804	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
805	#107	C₂³×C₁₇	1	2	yes	—
806	#107	C₂³×C₁₇	1	1	yes	characteristic
807	#107	C₂³×C₁₇	1	1	yes	characteristic
808	#107	C₂³×C₁₇	1	2	yes	—
809	#107	C₂³×C₁₇	1	2	yes	—
810	#107	C₂³×C₁₇	1	2	yes	—
811	#106	C₂³×C₁₇	1	2	yes	—
812	#106	C₂³×C₁₇	1	1	yes	characteristic
813	#106	C₂³×C₁₇	1	2	yes	—
814	#106	C₂³×C₁₇	1	2	yes	—
815	#106	C₂³×C₁₇	1	2	yes	—
816	#106	C₂³×C₁₇	1	2	yes	—
817	#106	C₂³×C₁₇	1	1	yes	characteristic
818	#106	C₂³×C₁₇	1	2	yes	—
819	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
820	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
821	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
822	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
823	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
824	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
825	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
826	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
827	#103	C₂³×C₁₇	1	2	yes	—
828	#103	C₂³×C₁₇	1	2	yes	—
829	#103	C₂³×C₁₇	1	2	yes	—
830	#103	C₂³×C₁₇	1	2	yes	—
831	#103	C₂³×C₁₇	1	1	yes	characteristic
832	#103	C₂³×C₁₇	1	2	yes	—
833	#103	C₂³×C₁₇	1	1	yes	characteristic
834	#103	C₂³×C₁₇	1	2	yes	—
835	#103	C₂³×C₁₇	1	2	yes	—
836	#103	C₂³×C₁₇	1	2	yes	—
837	#102	C₂³×C₁₇	1	2	yes	—
838	#102	C₂³×C₁₇	1	1	yes	characteristic
839	#102	C₂³×C₁₇	1	1	yes	characteristic
840	#102	C₂³×C₁₇	1	1	yes	characteristic
841	#102	C₂³×C₁₇	1	2	yes	—
842	#102	C₂³×C₁₇	1	1	yes	characteristic
843	#102	C₂³×C₁₇	1	1	yes	characteristic
844	#102	C₂³×C₁₇	1	1	yes	characteristic
845	#102	C₂³×C₁₇	1	2	yes	—
846	#102	C₂³×C₁₇	1	2	yes	—
847	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
848	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
849	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
850	#97	C₂³×C₁₇	1	2	yes	—
851	#97	C₂³×C₁₇	1	2	yes	—
852	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
854	C₄×C₈	C₂³×C₁₇	1	2	yes	—
855	C₄×C₈	C₂³×C₁₇	1	2	yes	—
856	C₄×C₈	C₂³×C₁₇	1	2	yes	—
857	C₁₇	#61864	1	1	yes	characteristic, direct product factor, Sylow
858	C₂⁴	—	2	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	2	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	8	2	no	—
866	C₂×Q₈	—	8	2	no	—
867	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
868	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
869	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
870	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
871	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
877	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
878	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	1	no	—
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	2	no	—
890	C₂²×C₄	—	8	2	no	—
891	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
892	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
893	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
894	SD₁₆	—	2	4	no	—
895	SD₁₆	—	2	2	no	—
896	SD₁₆	—	2	4	no	—
897	SD₁₆	—	2	2	no	—
898	D₈	—	2	2	no	—
899	D₈	—	2	2	no	—
900	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
901	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
902	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
904	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
905	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
906	C₄⋊C₄	—	2	2	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	2	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	2	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	2	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	2	no	—
925	C₄⋊C₄	—	2	2	no	—
926	C₄⋊C₄	—	2	1	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
935	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
936	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
937	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
938	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
940	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
941	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
942	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
943	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
944	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
945	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
946	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
947	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	2	1	no	—
962	C₂²⋊C₄	—	2	1	no	—
963	C₂²⋊C₄	—	2	1	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	1	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
969	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	2	2	no	—
976	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
977	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
978	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
979	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
980	C₄²	C₂⁴×C₁₇	1	2	yes	—
981	C₄²	C₂⁴×C₁₇	1	2	yes	—
982	C₂³	—	2	4	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	8	1	no	—
987	C₂³	—	8	1	no	—
988	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
989	Q₈	—	2	2	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	4	2	no	—
997	Q₈	—	8	2	no	—
998	Q₈	—	8	2	no	—
999	Q₈	—	8	1	no	—
1000	Q₈	—	8	1	no	—
1001	Q₈	—	8	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
1009	D₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	2	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	8	1	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	8	2	no	—
1030	C₂×C₄	—	8	2	no	—
1031	C₂×C₄	—	8	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	1	no	—
1034	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1035	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1036	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1037	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1038	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1039	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1040	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1042	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1043	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	2	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	8	4	no	—
1063	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	4	1	no	—
1081	C₄	C₁₇×#577	1	2	yes	—
1082	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
1083	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	—	4	2	no	—
1087	C₂	—	8	1	no	—
1088	C₂	C₁₇×#3486	1	1	yes	characteristic
1089	C₂	C₂×C₁₇×#577	1	1	yes	characteristic
1090	C₂	C₁₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#447	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3555	C₂	semidirect
2. C₁₇×#3501	C₂	semidirect
3. C₁₇×#3388	C₂	semidirect
4. C₁₇×#3385	C₂	semidirect
5. C₁₇×#3384	C₂	semidirect
6. C₁₇×#3381	C₂	semidirect
7. C₁₇×#3380	C₂	semidirect
8. Q₈×SD₁₆×C₁₇	C₂	semidirect
9. C₁₇×#3376	C₂	semidirect
10. C₁₇×#3372	C₂	semidirect
11. C₁₇×#3367	C₂	semidirect
12. C₁₇×#3360	C₂	semidirect
13. C₁₇×#3360	C₂	semidirect
14. C₁₇×#3359	C₂	semidirect
15. C₁₇×#3244	C₂	semidirect
16. C₁₇×#3242	C₂	semidirect
17. C₁₇×#3233	C₂	semidirect
18. C₁₇×#3231	C₂	semidirect
19. C₁₇×#3123	C₂	semidirect
22. C₁₇×#3101	C₂	semidirect
23. C₁₇×#2986	C₂	semidirect
25. Q₈²×C₁₇	C₂²	semidirect
26. C₁₇×#557	C₂²	semidirect
27. C₁₇×#557	C₂²	semidirect
29. C₁₇×#556	C₂²	semidirect
30. C₁₇×#556	C₂²	semidirect
37. C₁₇×#554	C₂²	semidirect
57. C₁₇×#501	C₂²	semidirect
58. C₁₇×#501	C₂²	semidirect
59. C₁₇×#500	C₂²	semidirect
60. C₁₇×#499	C₂²	semidirect
61. C₁₇×#499	C₂²	semidirect
62. C₁₇×#498	C₂²	semidirect
63. C₁₇×#498	C₂²	semidirect
64. C₁₇×#491	C₂²	semidirect
65. C₁₇×#489	C₂²	semidirect
66. C₁₇×#488	C₂²	semidirect
67. C₁₇×#488	C₂²	semidirect
68. C₁₇×#487	C₂²	semidirect
69. C₁₇×#487	C₂²	semidirect
70. C₁₇×#487	C₂²	semidirect
78. C₁₇×#479	C₂²	semidirect
79. C₁₇×#479	C₂²	semidirect
80. C₁₇×#479	C₂²	semidirect
81. C₁₇×#479	C₂²	semidirect
82. C₁₇×#479	C₂²	semidirect
87. C₁₇×#478	C₂²	semidirect
88. C₁₇×#477	C₂²	semidirect
89. C₁₇×#477	C₂²	semidirect
93. C₁₇×#476	C₂²	semidirect
94. C₁₇×#476	C₂²	semidirect
95. C₁₇×#475	C₂²	semidirect
96. C₁₇×#475	C₂²	semidirect
97. C₁₇×#475	C₂²	semidirect
99. C₁₇×#474	C₂²	semidirect
111. C₁₇×#446	C₂²	semidirect
112. C₁₇×#446	C₂²	semidirect
113. C₁₇×#446	C₂²	semidirect
114. C₈×Q₈×C₁₇	C₂²	semidirect
115. C₈×Q₈×C₁₇	C₂²	semidirect
116. C₈×Q₈×C₁₇	C₂²	semidirect
436. #61864	C₁₇	direct (N × H)
505. #3555	C₂×C₁₇	semidirect
506. #3501	C₂×C₁₇	semidirect
507. #3388	C₂×C₁₇	semidirect
508. #3385	C₂×C₁₇	semidirect
509. #3384	C₂×C₁₇	semidirect
510. #3381	C₂×C₁₇	semidirect
511. #3380	C₂×C₁₇	semidirect
512. Q₈×SD₁₆	C₂×C₁₇	semidirect
513. #3376	C₂×C₁₇	semidirect
514. #3372	C₂×C₁₇	semidirect
515. #3367	C₂×C₁₇	semidirect
516. #3360	C₂×C₁₇	semidirect
517. #3360	C₂×C₁₇	semidirect
518. #3359	C₂×C₁₇	semidirect
519. #3244	C₂×C₁₇	semidirect
520. #3242	C₂×C₁₇	semidirect
521. #3233	C₂×C₁₇	semidirect
522. #3231	C₂×C₁₇	semidirect
523. #3123	C₂×C₁₇	semidirect
526. #3101	C₂×C₁₇	semidirect
527. #2986	C₂×C₁₇	semidirect
563. Q₈²	C₂²×C₁₇	semidirect
564. #557	C₂²×C₁₇	semidirect
565. #557	C₂²×C₁₇	semidirect
567. #556	C₂²×C₁₇	semidirect
568. #556	C₂²×C₁₇	semidirect
575. #554	C₂²×C₁₇	semidirect
595. #501	C₂²×C₁₇	semidirect
596. #501	C₂²×C₁₇	semidirect
597. #500	C₂²×C₁₇	semidirect
598. #499	C₂²×C₁₇	semidirect
599. #499	C₂²×C₁₇	semidirect
600. #498	C₂²×C₁₇	semidirect
601. #498	C₂²×C₁₇	semidirect
602. #491	C₂²×C₁₇	semidirect
603. #489	C₂²×C₁₇	semidirect
604. #488	C₂²×C₁₇	semidirect
605. #488	C₂²×C₁₇	semidirect
606. #487	C₂²×C₁₇	semidirect
607. #487	C₂²×C₁₇	semidirect
608. #487	C₂²×C₁₇	semidirect
616. #479	C₂²×C₁₇	semidirect
617. #479	C₂²×C₁₇	semidirect
618. #479	C₂²×C₁₇	semidirect
619. #479	C₂²×C₁₇	semidirect
620. #479	C₂²×C₁₇	semidirect
625. #478	C₂²×C₁₇	semidirect
626. #477	C₂²×C₁₇	semidirect
627. #477	C₂²×C₁₇	semidirect
631. #476	C₂²×C₁₇	semidirect
632. #476	C₂²×C₁₇	semidirect
633. #475	C₂²×C₁₇	semidirect
634. #475	C₂²×C₁₇	semidirect
635. #475	C₂²×C₁₇	semidirect
637. #474	C₂²×C₁₇	semidirect
649. #446	C₂²×C₁₇	semidirect
650. #446	C₂²×C₁₇	semidirect
651. #446	C₂²×C₁₇	semidirect
652. C₈×Q₈	C₂²×C₁₇	semidirect
653. C₈×Q₈	C₂²×C₁₇	semidirect
654. C₈×Q₈	C₂²×C₁₇	semidirect
857. C₁₇	#61864	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×#3555	2
C₁₇×#3501	2
C₁₇×#3388	2
C₁₇×#3385	2
C₁₇×#3384	2
C₁₇×#3381	2
C₁₇×#3380	2
Q₈×SD₁₆×C₁₇	2
C₁₇×#3376	2
C₁₇×#3372	2
C₁₇×#3367	2
C₁₇×#3360	2
C₁₇×#3359	2
C₁₇×#3244	2
C₁₇×#3242	2
C₁₇×#3233	2
C₁₇×#3231	2
C₁₇×#3123	2
C₁₇×#3118	2
C₁₇×#3105	2
C₁₇×#3101	2
C₁₇×#2986	2
#61864	17

Subgroups — C17×#61864 #16919608

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61864 #16919608