Subgroups — C₁₇×#61929 #16919673

Order 4352.

1654 conjugacy classes of subgroups.

The subgroup lattice has 1090 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×#3507	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3402	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3400	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3398	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3394	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#3393	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3377	C₂	1	2	yes	maximal, complemented
10	C₁₇×#3375	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3372	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3364	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#3361	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#3225	C₂	1	2	yes	maximal, complemented
16	C₁₇×#3223	C₂	1	2	yes	maximal, complemented
17	C₁₇×#3212	C₂	1	1	yes	maximal, characteristic
18	C₁₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
19	C₁₇×#3124	C₂	1	2	yes	maximal, complemented
20	C₁₇×#3120	C₂	1	2	yes	maximal, complemented
21	C₁₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
22	C₁₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#2986	C₂	1	1	yes	maximal, characteristic, complemented
24	C₁₇×#563	—	2	2	no	—
25	C₁₇×#559	C₂²	1	1	yes	characteristic
26	C₁₇×#559	C₂²	1	1	yes	characteristic
27	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
28	C₁₇×#557	C₂²	1	1	yes	characteristic
29	C₁₇×#557	C₂²	1	1	yes	characteristic
30	C₁₇×#557	C₂²	1	1	yes	characteristic
31	C₁₇×#557	C₂²	1	2	yes	—
32	C₁₇×#556	—	2	1	no	—
33	C₁₇×#556	—	2	1	no	—
34	C₁₇×#556	C₂²	1	2	yes	—
35	C₁₇×#556	C₂²	1	2	yes	—
36	C₁₇×#556	C₂²	1	2	yes	—
37	C₁₇×#556	C₂²	1	1	yes	characteristic
38	C₁₇×#554	—	2	1	no	—
39	C₁₇×#554	C₂²	1	1	yes	characteristic
40	C₁₇×#552	—	2	2	no	—
41	C₁₇×#552	—	2	1	no	—
42	C₁₇×#544	—	2	1	no	—
43	C₁₇×#542	C₂²	1	2	yes	—
44	C₁₇×#541	—	2	1	no	—
45	C₁₇×#541	—	2	2	no	—
46	C₁₇×#541	C₂²	1	2	yes	—
47	C₁₇×#539	—	2	2	no	—
48	C₁₇×#536	C₂²	1	2	yes	—
49	C₁₇×#533	C₂²	1	1	yes	characteristic
50	C₁₇×#533	C₂²	1	1	yes	characteristic
51	C₁₇×#532	C₂²	1	1	yes	characteristic
52	C₁₇×#529	—	2	1	no	—
53	C₁₇×#529	—	2	1	no	—
54	C₁₇×#529	C₂²	1	1	yes	characteristic
55	C₁₇×#520	C₂²	1	2	yes	—
56	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
57	C₁₇×#497	C₂²	1	2	yes	—
58	C₁₇×#497	C₂²	1	2	yes	—
59	C₁₇×#495	C₂²	1	2	yes	—
60	C₁₇×#495	C₂²	1	2	yes	—
61	C₁₇×#494	C₂²	1	1	yes	characteristic
62	C₁₇×#494	C₂²	1	2	yes	—
63	C₁₇×#492	C₂²	1	1	yes	characteristic
64	C₁₇×#491	C₂²	1	2	yes	—
65	C₁₇×#489	C₂²	1	2	yes	—
66	C₁₇×#488	C₂²	1	2	yes	—
67	C₁₇×#488	C₂²	1	2	yes	—
68	C₁₇×#487	C₂²	1	1	yes	characteristic
69	C₁₇×#487	C₂²	1	2	yes	—
70	C₁₇×#486	C₂²	1	1	yes	characteristic
71	C₁₇×#484	C₂²	1	2	yes	—
72	C₁₇×#483	C₂²	1	1	yes	characteristic
73	C₁₇×#480	C₂²	1	1	yes	characteristic
74	C₁₇×#479	C₂²	1	1	yes	characteristic
75	C₁₇×#479	C₂²	1	1	yes	characteristic
76	C₁₇×#479	C₂²	1	2	yes	—
77	C₁₇×#478	C₂²	1	2	yes	—
78	C₁₇×#477	C₂²	1	1	yes	characteristic
79	C₁₇×#477	C₂²	1	1	yes	characteristic
80	C₁₇×#477	C₂²	1	2	yes	—
81	C₁₇×#474	C₂²	1	2	yes	—
82	C₁₇×#464	C₂²	1	2	yes	—
83	C₁₇×#464	C₂²	1	2	yes	—
84	C₁₇×#464	C₂²	1	2	yes	—
85	C₁₇×#464	C₂²	1	2	yes	—
86	C₁₇×#464	C₂²	1	2	yes	—
87	C₁₇×#464	C₂²	1	1	yes	characteristic
88	C₁₇×#464	C₂²	1	1	yes	characteristic
89	C₁₇×#464	C₂²	1	2	yes	—
90	C₁₇×#463	C₂²	1	2	yes	—
91	C₁₇×#463	C₂²	1	2	yes	—
92	C₁₇×#462	C₂²	1	1	yes	characteristic
93	C₁₇×#462	C₂²	1	2	yes	—
94	C₁₇×#462	C₂²	1	2	yes	—
95	C₁₇×#462	C₂²	1	2	yes	—
96	C₁₇×#462	C₂²	1	1	yes	characteristic
97	C₁₇×#462	C₂²	1	1	yes	characteristic
98	C₁₇×#462	C₂²	1	2	yes	—
99	C₁₇×#461	C₂²	1	1	yes	characteristic
100	C₁₇×#461	C₂²	1	2	yes	—
101	C₁₇×#461	C₂²	1	2	yes	—
102	C₁₇×#460	C₂²	1	1	yes	characteristic
103	C₁₇×#459	C₂²	1	1	yes	characteristic
104	C₁₇×#452	C₂²	1	2	yes	—
105	C₁₇×#452	C₂²	1	2	yes	—
106	C₁₇×#452	C₂²	1	2	yes	—
107	C₁₇×#451	C₂²	1	1	yes	characteristic
108	C₁₇×#451	C₂²	1	2	yes	—
109	C₁₇×#449	C₂²	1	2	yes	—
110	C₁₇×#448	C₂²	1	1	yes	characteristic
111	C₁₇×#446	C₂²	1	1	yes	characteristic
112	C₁₇×#446	C₂²	1	1	yes	characteristic
113	C₁₇×#446	C₂²	1	2	yes	—
114	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
115	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
116	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
117	C₁₇×#441	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×Q₁₆×C₁₇	C₂²	1	2	yes	—
122	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
123	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
124	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
125	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
126	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
127	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
130	C₄×D₈×C₁₇	C₂²	1	2	yes	—
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	C₂×#41×C₁₇	C₂³	1	2	yes	—
136	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
137	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
138	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
139	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
140	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
141	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
142	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
143	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
144	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
145	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
146	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
147	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
148	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
149	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
150	C₂×D₈×C₁₇	C₂³	1	2	yes	—
151	C₁₇×C₄⋊Q₈	—	2	2	no	—
152	C₁₇×C₄⋊Q₈	—	2	2	no	—
153	C₁₇×C₄⋊Q₈	—	2	1	no	—
154	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
155	C₁₇×C₄⋊Q₈	D₄	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×C₄⋊Q₈	C₂³	1	1	yes	characteristic
160	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
161	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
162	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
163	C₁₇×#127	C₂³	1	1	yes	characteristic
164	C₁₇×#126	—	2	2	no	—
165	C₁₇×#126	—	2	2	no	—
166	C₁₇×#126	—	2	2	no	—
167	C₁₇×#126	—	2	2	no	—
168	C₁₇×#126	—	2	2	no	—
169	C₁₇×#126	—	2	2	no	—
170	C₁₇×#126	—	2	2	no	—
171	C₁₇×#126	—	2	2	no	—
172	C₁₇×#126	—	2	2	no	—
173	C₁₇×#126	—	2	2	no	—
174	C₁₇×#126	—	2	1	no	—
175	C₁₇×#125	—	2	1	no	—
176	C₁₇×#125	—	2	1	no	—
177	C₁₇×#125	—	2	2	no	—
178	C₁₇×#125	—	2	2	no	—
179	C₁₇×#125	—	2	2	no	—
180	C₁₇×#125	—	2	2	no	—
181	C₁₇×#125	—	2	2	no	—
182	C₁₇×#125	—	2	2	no	—
183	C₁₇×#125	—	2	2	no	—
184	C₁₇×#125	—	2	1	no	—
185	C₁₇×#125	—	2	1	no	—
186	C₁₇×#125	D₄	1	2	yes	—
187	C₁₇×#125	C₂³	1	2	yes	—
188	C₁₇×#125	C₂³	1	1	yes	characteristic
189	C₁₇×#124	—	2	1	no	—
190	C₁₇×#124	—	2	1	no	—
191	C₁₇×#124	—	2	2	no	—
192	C₁₇×#124	C₂³	1	1	yes	characteristic
193	C₁₇×#124	C₂³	1	2	yes	—
194	C₁₇×#124	C₂³	1	2	yes	—
195	C₁₇×#124	C₂³	1	2	yes	—
196	C₁₇×#124	C₂³	1	2	yes	—
197	C₁₇×#123	—	2	1	no	—
198	C₁₇×#123	—	2	2	no	—
199	C₁₇×#123	—	2	2	no	—
200	C₁₇×#123	—	2	2	no	—
201	C₁₇×#123	—	2	2	no	—
202	C₁₇×#123	—	2	2	no	—
203	C₁₇×C₂²⋊Q₈	—	2	2	no	—
204	C₁₇×C₂²⋊Q₈	—	2	2	no	—
205	C₁₇×C₂²⋊Q₈	—	2	1	no	—
206	C₁₇×C₂²⋊Q₈	—	2	1	no	—
207	C₁₇×C₂²⋊Q₈	—	2	2	no	—
208	C₁₇×C₂²⋊Q₈	—	2	1	no	—
209	C₁₇×C₂²⋊Q₈	—	2	2	no	—
210	C₁₇×C₂²⋊Q₈	—	2	2	no	—
211	C₁₇×C₂²⋊Q₈	—	2	2	no	—
212	C₁₇×C₂²⋊Q₈	—	2	2	no	—
213	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
214	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
215	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
216	C₁₇×C₂²⋊Q₈	C₂³	1	1	yes	characteristic
217	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
218	C₁₇×#121	—	2	1	no	—
219	C₁₇×#121	—	2	1	no	—
220	C₁₇×#121	C₂³	1	1	yes	characteristic
221	C₄×Q₈×C₁₇	—	2	1	no	—
222	C₄×Q₈×C₁₇	—	2	1	no	—
223	C₄×Q₈×C₁₇	—	2	1	no	—
224	C₄×Q₈×C₁₇	—	2	1	no	—
225	C₄×Q₈×C₁₇	—	2	2	no	—
226	C₄×Q₈×C₁₇	—	2	1	no	—
227	C₄×Q₈×C₁₇	—	2	1	no	—
228	C₄×Q₈×C₁₇	—	2	1	no	—
229	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
230	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
231	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
232	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
233	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
234	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
235	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
236	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
237	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
238	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
239	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
240	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
241	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
242	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
243	C₄×D₄×C₁₇	—	2	1	no	—
244	C₄×D₄×C₁₇	—	2	1	no	—
245	C₄×D₄×C₁₇	—	2	1	no	—
246	C₄×D₄×C₁₇	—	2	2	no	—
247	C₄×D₄×C₁₇	—	2	2	no	—
248	C₄×D₄×C₁₇	—	2	1	no	—
249	C₄×D₄×C₁₇	—	2	1	no	—
250	C₄×D₄×C₁₇	C₂³	1	2	yes	—
251	C₄×D₄×C₁₇	C₂³	1	2	yes	—
252	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
253	C₄×D₄×C₁₇	C₂³	1	2	yes	—
254	C₁₇×#117	—	2	1	no	—
255	C₁₇×#117	—	2	2	no	—
256	C₁₇×#117	—	2	2	no	—
257	C₁₇×#117	—	2	2	no	—
258	C₁₇×#117	—	2	2	no	—
259	C₁₇×#117	—	2	1	no	—
260	C₁₇×#117	—	2	1	no	—
261	C₁₇×#117	C₂³	1	2	yes	—
262	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
263	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
264	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
265	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
266	C₂×C₄²×C₁₇	—	2	1	no	—
267	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
268	C₁₇×#107	C₂³	1	2	yes	—
269	C₁₇×#107	C₂³	1	1	yes	characteristic
270	C₁₇×#107	C₂³	1	2	yes	—
271	C₁₇×#107	C₂³	1	1	yes	characteristic
272	C₁₇×#106	C₂³	1	1	yes	characteristic
273	C₁₇×#106	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
288	C₁₇×#103	C₂³	1	1	yes	characteristic
289	C₁₇×#103	C₂³	1	1	yes	characteristic
290	C₁₇×#103	C₂³	1	2	yes	—
291	C₁₇×#103	C₂³	1	1	yes	characteristic
292	C₁₇×#103	C₂³	1	1	yes	characteristic
293	C₁₇×#103	C₂³	1	2	yes	—
294	C₁₇×#103	C₂³	1	2	yes	—
295	C₁₇×#103	C₂³	1	2	yes	—
296	C₁₇×#102	C₂³	1	1	yes	characteristic
297	C₁₇×#102	C₂³	1	2	yes	—
298	C₁₇×#102	C₂³	1	1	yes	characteristic
299	C₁₇×#102	C₂³	1	2	yes	—
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	2	yes	—
304	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
309	C₄×C₈×C₁₇	C₂³	1	2	yes	—
310	C₄×C₈×C₁₇	C₂³	1	2	yes	—
311	C₄×C₈×C₁₇	C₂³	1	2	yes	—
312	#41×C₁₇	—	4	2	no	—
313	#41×C₁₇	—	4	2	no	—
314	C₂×Q₈×C₁₇	—	2	1	no	—
315	C₂×Q₈×C₁₇	—	2	1	no	—
316	C₂×Q₈×C₁₇	—	2	2	no	—
317	C₂×Q₈×C₁₇	—	4	1	no	—
318	C₂×Q₈×C₁₇	—	4	1	no	—
319	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
322	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
325	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
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	—	2	1	no	—
331	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
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	2	no	—
336	C₂²×C₄×C₁₇	—	2	1	no	—
337	C₂²×C₄×C₁₇	—	2	2	no	—
338	C₂²×C₄×C₁₇	—	2	2	no	—
339	C₂²×C₄×C₁₇	—	2	2	no	—
340	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
343	Q₁₆×C₁₇	—	4	2	no	—
344	Q₁₆×C₁₇	—	4	2	no	—
345	Q₁₆×C₁₇	—	4	2	no	—
346	Q₁₆×C₁₇	—	4	1	no	—
347	Q₁₆×C₁₇	—	4	2	no	—
348	Q₁₆×C₁₇	—	4	1	no	—
349	Q₁₆×C₁₇	—	4	2	no	—
350	SD₁₆×C₁₇	—	4	1	no	—
351	SD₁₆×C₁₇	—	4	2	no	—
352	SD₁₆×C₁₇	—	4	2	no	—
353	SD₁₆×C₁₇	—	4	2	no	—
354	SD₁₆×C₁₇	—	4	2	no	—
355	SD₁₆×C₁₇	—	4	1	no	—
356	D₈×C₁₇	—	4	2	no	—
357	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
358	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
361	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
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	1	no	—
368	C₄⋊C₄×C₁₇	—	2	1	no	—
369	C₄⋊C₄×C₁₇	—	2	2	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	1	no	—
377	C₄⋊C₄×C₁₇	—	2	2	no	—
378	C₄⋊C₄×C₁₇	—	2	2	no	—
379	C₄⋊C₄×C₁₇	—	2	1	no	—
380	C₄⋊C₄×C₁₇	—	2	2	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	1	no	—
385	C₄⋊C₄×C₁₇	—	2	1	no	—
386	C₄⋊C₄×C₁₇	—	2	1	no	—
387	C₄⋊C₄×C₁₇	—	2	2	no	—
388	C₄⋊C₄×C₁₇	—	2	1	no	—
389	C₄⋊C₄×C₁₇	—	2	1	no	—
390	C₄⋊C₄×C₁₇	—	2	2	no	—
391	C₄⋊C₄×C₁₇	—	2	1	no	—
392	C₄⋊C₄×C₁₇	—	2	1	no	—
393	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
394	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
395	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
396	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
397	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
398	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
399	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
400	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
402	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
403	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
404	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₁₇	—	2	2	no	—
408	C₂²⋊C₄×C₁₇	—	2	1	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	2	no	—
414	C₂²⋊C₄×C₁₇	—	2	2	no	—
415	C₂²⋊C₄×C₁₇	—	2	2	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	2	no	—
420	C₂²⋊C₄×C₁₇	—	2	2	no	—
421	C₂²⋊C₄×C₁₇	—	2	2	no	—
422	C₂²⋊C₄×C₁₇	—	2	1	no	—
423	C₂²⋊C₄×C₁₇	—	2	2	no	—
424	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
425	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
426	C₄²×C₁₇	—	2	2	no	—
427	C₄²×C₁₇	—	2	1	no	—
428	C₄²×C₁₇	—	2	1	no	—
429	C₄²×C₁₇	—	2	2	no	—
430	C₄²×C₁₇	—	2	2	no	—
431	C₄²×C₁₇	—	2	2	no	—
432	C₄²×C₁₇	—	2	2	no	—
433	C₄²×C₁₇	—	2	2	no	—
434	C₄²×C₁₇	—	2	1	no	—
435	C₄²×C₁₇	—	2	1	no	—
436	C₄²×C₁₇	—	2	1	no	—
437	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
438	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
439	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
440	C₄²×C₁₇	C₂⁴	1	2	yes	—
441	C₄²×C₁₇	C₂⁴	1	2	yes	—
442	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
443	#61929	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
444	C₂³×C₁₇	—	2	1	no	—
445	C₂³×C₁₇	—	2	2	no	—
446	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
447	Q₈×C₁₇	—	2	2	no	—
448	Q₈×C₁₇	—	2	2	no	—
449	Q₈×C₁₇	—	2	1	no	—
450	Q₈×C₁₇	—	2	2	no	—
451	Q₈×C₁₇	—	2	2	no	—
452	Q₈×C₁₇	—	2	1	no	—
453	Q₈×C₁₇	—	2	1	no	—
454	Q₈×C₁₇	—	2	2	no	—
455	Q₈×C₁₇	—	2	1	no	—
456	Q₈×C₁₇	—	2	1	no	—
457	Q₈×C₁₇	—	2	1	no	—
458	Q₈×C₁₇	—	2	2	no	—
459	Q₈×C₁₇	—	4	2	no	—
460	Q₈×C₁₇	—	4	2	no	—
461	Q₈×C₁₇	—	8	1	no	—
462	Q₈×C₁₇	—	8	2	no	—
463	D₄×C₁₇	—	2	1	no	—
464	D₄×C₁₇	—	2	2	no	—
465	D₄×C₁₇	—	2	1	no	—
466	D₄×C₁₇	—	2	2	no	—
467	D₄×C₁₇	—	4	4	no	—
468	D₄×C₁₇	—	4	2	no	—
469	D₄×C₁₇	—	8	1	no	—
470	D₄×C₁₇	—	8	1	no	—
471	C₂×C₄×C₁₇	—	2	2	no	—
472	C₂×C₄×C₁₇	—	2	1	no	—
473	C₂×C₄×C₁₇	—	2	1	no	—
474	C₂×C₄×C₁₇	—	2	1	no	—
475	C₂×C₄×C₁₇	—	2	1	no	—
476	C₂×C₄×C₁₇	—	2	2	no	—
477	C₂×C₄×C₁₇	—	2	1	no	—
478	C₂×C₄×C₁₇	—	2	1	no	—
479	C₂×C₄×C₁₇	—	2	1	no	—
480	C₂×C₄×C₁₇	—	2	1	no	—
481	C₂×C₄×C₁₇	—	2	1	no	—
482	C₂×C₄×C₁₇	—	2	2	no	—
483	C₂×C₄×C₁₇	—	2	2	no	—
484	C₂×C₄×C₁₇	—	4	1	no	—
485	C₂×C₄×C₁₇	—	4	4	no	—
486	C₂×C₄×C₁₇	—	4	2	no	—
487	C₂×C₄×C₁₇	—	4	2	no	—
488	C₂×C₄×C₁₇	—	8	2	no	—
489	C₂×C₄×C₁₇	—	8	2	no	—
490	C₂×C₄×C₁₇	—	8	2	no	—
491	C₂×C₄×C₁₇	—	8	1	no	—
492	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
500	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
501	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
502	C₈×C₁₇	—	2	2	no	—
503	C₈×C₁₇	—	2	1	no	—
504	C₈×C₁₇	—	2	1	no	—
505	C₈×C₁₇	—	2	2	no	—
506	C₈×C₁₇	—	2	1	no	—
507	C₈×C₁₇	—	2	1	no	—
508	#3555	C₂×C₁₇	1	1	yes	characteristic, complemented
509	#3507	C₂×C₁₇	1	1	yes	characteristic, complemented
510	#3402	C₂×C₁₇	1	2	yes	complemented
511	#3400	C₂×C₁₇	1	1	yes	characteristic, complemented
512	#3398	C₂×C₁₇	1	1	yes	characteristic, complemented
513	#3395	C₂×C₁₇	1	1	yes	characteristic, complemented
514	#3394	C₂×C₁₇	1	1	yes	characteristic, complemented
515	#3393	C₂×C₁₇	1	2	yes	complemented
516	#3377	C₂×C₁₇	1	2	yes	complemented
517	#3375	C₂×C₁₇	1	1	yes	characteristic, complemented
518	#3372	C₂×C₁₇	1	1	yes	characteristic, complemented
519	#3364	C₂×C₁₇	1	2	yes	complemented
520	#3363	C₂×C₁₇	1	1	yes	characteristic, complemented
521	#3361	C₂×C₁₇	1	1	yes	characteristic, complemented
522	#3225	C₂×C₁₇	1	2	yes	complemented
523	#3223	C₂×C₁₇	1	2	yes	complemented
524	#3212	C₂×C₁₇	1	1	yes	characteristic
525	#3210	C₂×C₁₇	1	1	yes	characteristic, complemented
526	#3124	C₂×C₁₇	1	2	yes	complemented
527	#3120	C₂×C₁₇	1	2	yes	complemented
528	#3108	C₂×C₁₇	1	1	yes	characteristic, complemented
529	#3104	C₂×C₁₇	1	1	yes	characteristic, complemented
530	#2986	C₂×C₁₇	1	1	yes	characteristic, complemented
531	C₂²×C₁₇	—	2	1	no	—
532	C₂²×C₁₇	—	2	1	no	—
533	C₂²×C₁₇	—	2	1	no	—
534	C₂²×C₁₇	—	4	2	no	—
535	C₂²×C₁₇	—	4	1	no	—
536	C₂²×C₁₇	—	4	2	no	—
537	C₂²×C₁₇	—	4	1	no	—
538	C₂²×C₁₇	—	4	1	no	—
539	C₂²×C₁₇	—	4	2	no	—
540	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
541	C₄×C₁₇	—	2	1	no	—
542	C₄×C₁₇	—	2	1	no	—
543	C₄×C₁₇	—	2	2	no	—
544	C₄×C₁₇	—	2	2	no	—
545	C₄×C₁₇	—	2	1	no	—
546	C₄×C₁₇	—	2	1	no	—
547	C₄×C₁₇	—	2	2	no	—
548	C₄×C₁₇	—	2	2	no	—
549	C₄×C₁₇	—	4	1	no	—
550	C₄×C₁₇	—	4	1	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	2	no	—
558	C₄×C₁₇	—	4	1	no	—
559	C₄×C₁₇	#578	1	2	yes	—
560	C₄×C₁₇	#585	1	1	yes	characteristic
561	C₄×C₁₇	#585	1	1	yes	characteristic
562	#563	—	2	2	no	—
563	#559	C₂²×C₁₇	1	1	yes	characteristic
564	#559	C₂²×C₁₇	1	1	yes	characteristic
565	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
566	#557	C₂²×C₁₇	1	1	yes	characteristic
567	#557	C₂²×C₁₇	1	1	yes	characteristic
568	#557	C₂²×C₁₇	1	1	yes	characteristic
569	#557	C₂²×C₁₇	1	2	yes	—
570	#556	—	2	1	no	—
571	#556	—	2	1	no	—
572	#556	C₂²×C₁₇	1	2	yes	—
573	#556	C₂²×C₁₇	1	2	yes	—
574	#556	C₂²×C₁₇	1	2	yes	—
575	#556	C₂²×C₁₇	1	1	yes	characteristic
576	#554	—	2	1	no	—
577	#554	C₂²×C₁₇	1	1	yes	characteristic
578	#552	—	2	2	no	—
579	#552	—	2	1	no	—
580	#544	—	2	1	no	—
581	#542	C₂²×C₁₇	1	2	yes	—
582	#541	—	2	1	no	—
583	#541	—	2	2	no	—
584	#541	C₂²×C₁₇	1	2	yes	—
585	#539	—	2	2	no	—
586	#536	C₂²×C₁₇	1	2	yes	—
587	#533	C₂²×C₁₇	1	1	yes	characteristic
588	#533	C₂²×C₁₇	1	1	yes	characteristic
589	#532	C₂²×C₁₇	1	1	yes	characteristic
590	#529	—	2	1	no	—
591	#529	—	2	1	no	—
592	#529	C₂²×C₁₇	1	1	yes	characteristic
593	#520	C₂²×C₁₇	1	2	yes	—
594	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
595	#497	C₂²×C₁₇	1	2	yes	—
596	#497	C₂²×C₁₇	1	2	yes	—
597	#495	C₂²×C₁₇	1	2	yes	—
598	#495	C₂²×C₁₇	1	2	yes	—
599	#494	C₂²×C₁₇	1	2	yes	—
600	#494	C₂²×C₁₇	1	1	yes	characteristic
601	#492	C₂²×C₁₇	1	1	yes	characteristic
602	#491	C₂²×C₁₇	1	2	yes	—
603	#489	C₂²×C₁₇	1	2	yes	—
604	#488	C₂²×C₁₇	1	2	yes	—
605	#488	C₂²×C₁₇	1	2	yes	—
606	#487	C₂²×C₁₇	1	2	yes	—
607	#487	C₂²×C₁₇	1	1	yes	characteristic
608	#486	C₂²×C₁₇	1	1	yes	characteristic
609	#484	C₂²×C₁₇	1	2	yes	—
610	#483	C₂²×C₁₇	1	1	yes	characteristic
611	#480	C₂²×C₁₇	1	1	yes	characteristic
612	#479	C₂²×C₁₇	1	1	yes	characteristic
613	#479	C₂²×C₁₇	1	1	yes	characteristic
614	#479	C₂²×C₁₇	1	2	yes	—
615	#478	C₂²×C₁₇	1	2	yes	—
616	#477	C₂²×C₁₇	1	1	yes	characteristic
617	#477	C₂²×C₁₇	1	1	yes	characteristic
618	#477	C₂²×C₁₇	1	2	yes	—
619	#474	C₂²×C₁₇	1	2	yes	—
620	#464	C₂²×C₁₇	1	1	yes	characteristic
621	#464	C₂²×C₁₇	1	1	yes	characteristic
622	#464	C₂²×C₁₇	1	2	yes	—
623	#464	C₂²×C₁₇	1	2	yes	—
624	#464	C₂²×C₁₇	1	2	yes	—
625	#464	C₂²×C₁₇	1	2	yes	—
626	#464	C₂²×C₁₇	1	2	yes	—
627	#464	C₂²×C₁₇	1	2	yes	—
628	#463	C₂²×C₁₇	1	2	yes	—
629	#463	C₂²×C₁₇	1	2	yes	—
630	#462	C₂²×C₁₇	1	1	yes	characteristic
631	#462	C₂²×C₁₇	1	1	yes	characteristic
632	#462	C₂²×C₁₇	1	1	yes	characteristic
633	#462	C₂²×C₁₇	1	2	yes	—
634	#462	C₂²×C₁₇	1	2	yes	—
635	#462	C₂²×C₁₇	1	2	yes	—
636	#462	C₂²×C₁₇	1	2	yes	—
637	#461	C₂²×C₁₇	1	2	yes	—
638	#461	C₂²×C₁₇	1	1	yes	characteristic
639	#461	C₂²×C₁₇	1	2	yes	—
640	#460	C₂²×C₁₇	1	1	yes	characteristic
641	#459	C₂²×C₁₇	1	1	yes	characteristic
642	#452	C₂²×C₁₇	1	2	yes	—
643	#452	C₂²×C₁₇	1	2	yes	—
644	#452	C₂²×C₁₇	1	2	yes	—
645	#451	C₂²×C₁₇	1	2	yes	—
646	#451	C₂²×C₁₇	1	1	yes	characteristic
647	#449	C₂²×C₁₇	1	2	yes	—
648	#448	C₂²×C₁₇	1	1	yes	characteristic
649	#446	C₂²×C₁₇	1	1	yes	characteristic
650	#446	C₂²×C₁₇	1	1	yes	characteristic
651	#446	C₂²×C₁₇	1	2	yes	—
652	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
653	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
654	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
655	#441	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×Q₁₆	C₂²×C₁₇	1	2	yes	—
660	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
661	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
662	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
663	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
664	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
665	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
666	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
667	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
668	C₄×D₈	C₂²×C₁₇	1	2	yes	—
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	—	8	2	no	—
675	C₂×C₁₇	—	8	1	no	—
676	C₂×C₁₇	#3487	1	1	yes	characteristic
677	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
678	C₂×C₁₇	#3584	1	1	yes	characteristic
679	C₂×#41	C₂³×C₁₇	1	2	yes	—
680	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
681	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
682	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
683	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
684	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
685	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
686	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
687	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
688	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
689	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
690	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
691	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
692	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
693	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
694	C₂×D₈	C₂³×C₁₇	1	2	yes	—
695	C₄⋊Q₈	—	2	2	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	2	1	no	—
698	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
699	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
702	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
703	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
704	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
705	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
706	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
707	#127	C₂³×C₁₇	1	1	yes	characteristic
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	2	no	—
712	#126	—	2	2	no	—
713	#126	—	2	2	no	—
714	#126	—	2	2	no	—
715	#126	—	2	2	no	—
716	#126	—	2	2	no	—
717	#126	—	2	2	no	—
718	#126	—	2	1	no	—
719	#125	—	2	1	no	—
720	#125	—	2	1	no	—
721	#125	—	2	2	no	—
722	#125	—	2	2	no	—
723	#125	—	2	2	no	—
724	#125	—	2	2	no	—
725	#125	—	2	2	no	—
726	#125	—	2	2	no	—
727	#125	—	2	2	no	—
728	#125	—	2	1	no	—
729	#125	—	2	1	no	—
730	#125	D₄×C₁₇	1	2	yes	—
731	#125	C₂³×C₁₇	1	1	yes	characteristic
732	#125	C₂³×C₁₇	1	2	yes	—
733	#124	—	2	1	no	—
734	#124	—	2	1	no	—
735	#124	—	2	2	no	—
736	#124	C₂³×C₁₇	1	1	yes	characteristic
737	#124	C₂³×C₁₇	1	2	yes	—
738	#124	C₂³×C₁₇	1	2	yes	—
739	#124	C₂³×C₁₇	1	2	yes	—
740	#124	C₂³×C₁₇	1	2	yes	—
741	#123	—	2	1	no	—
742	#123	—	2	2	no	—
743	#123	—	2	2	no	—
744	#123	—	2	2	no	—
745	#123	—	2	2	no	—
746	#123	—	2	2	no	—
747	C₂²⋊Q₈	—	2	2	no	—
748	C₂²⋊Q₈	—	2	2	no	—
749	C₂²⋊Q₈	—	2	1	no	—
750	C₂²⋊Q₈	—	2	1	no	—
751	C₂²⋊Q₈	—	2	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
758	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
759	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
760	C₂²⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
761	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
762	#121	—	2	1	no	—
763	#121	—	2	1	no	—
764	#121	C₂³×C₁₇	1	1	yes	characteristic
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	2	1	no	—
768	C₄×Q₈	—	2	1	no	—
769	C₄×Q₈	—	2	2	no	—
770	C₄×Q₈	—	2	1	no	—
771	C₄×Q₈	—	2	1	no	—
772	C₄×Q₈	—	2	1	no	—
773	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
774	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
775	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
776	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
777	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
778	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
779	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
780	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
781	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
782	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
783	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
784	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
785	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
786	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
787	C₄×D₄	—	2	1	no	—
788	C₄×D₄	—	2	1	no	—
789	C₄×D₄	—	2	1	no	—
790	C₄×D₄	—	2	2	no	—
791	C₄×D₄	—	2	2	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	C₂³×C₁₇	1	2	yes	—
795	C₄×D₄	C₂³×C₁₇	1	2	yes	—
796	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
797	C₄×D₄	C₂³×C₁₇	1	2	yes	—
798	#117	—	2	1	no	—
799	#117	—	2	2	no	—
800	#117	—	2	2	no	—
801	#117	—	2	2	no	—
802	#117	—	2	2	no	—
803	#117	—	2	1	no	—
804	#117	—	2	1	no	—
805	#117	C₂³×C₁₇	1	2	yes	—
806	C₂×C₄⋊C₄	—	2	1	no	—
807	C₂×C₄⋊C₄	—	2	2	no	—
808	C₂×C₄⋊C₄	—	2	1	no	—
809	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
810	C₂×C₄²	—	2	1	no	—
811	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
812	#107	C₂³×C₁₇	1	2	yes	—
813	#107	C₂³×C₁₇	1	1	yes	characteristic
814	#107	C₂³×C₁₇	1	2	yes	—
815	#107	C₂³×C₁₇	1	1	yes	characteristic
816	#106	C₂³×C₁₇	1	1	yes	characteristic
817	#106	C₂³×C₁₇	1	1	yes	characteristic
818	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
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	2	yes	—
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	#103	C₂³×C₁₇	1	2	yes	—
827	#103	C₂³×C₁₇	1	1	yes	characteristic
828	#103	C₂³×C₁₇	1	1	yes	characteristic
829	#103	C₂³×C₁₇	1	1	yes	characteristic
830	#103	C₂³×C₁₇	1	1	yes	characteristic
831	#103	C₂³×C₁₇	1	2	yes	—
832	#103	C₂³×C₁₇	1	1	yes	characteristic
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	#103	C₂³×C₁₇	1	2	yes	—
838	#103	C₂³×C₁₇	1	2	yes	—
839	#103	C₂³×C₁₇	1	2	yes	—
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	2	yes	—
844	#102	C₂³×C₁₇	1	2	yes	—
845	#102	C₂³×C₁₇	1	2	yes	—
846	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
847	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
848	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
849	#97	C₂³×C₁₇	1	2	yes	—
850	#97	C₂³×C₁₇	1	2	yes	—
851	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
852	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
853	C₄×C₈	C₂³×C₁₇	1	2	yes	—
854	C₄×C₈	C₂³×C₁₇	1	2	yes	—
855	C₄×C₈	C₂³×C₁₇	1	2	yes	—
856	C₁₇	#61929	1	1	yes	characteristic, direct product factor, Sylow
857	#41	—	4	2	no	—
858	#41	—	4	2	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	1	no	—
861	C₂×Q₈	—	2	2	no	—
862	C₂×Q₈	—	4	1	no	—
863	C₂×Q₈	—	4	1	no	—
864	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
865	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
866	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
867	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
868	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
869	C₂×Q₈	C₂⁴×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	1	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
877	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
878	C₂²×C₄	—	2	1	no	—
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	2	2	no	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
886	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
887	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
888	Q₁₆	—	4	2	no	—
889	Q₁₆	—	4	2	no	—
890	Q₁₆	—	4	2	no	—
891	Q₁₆	—	4	1	no	—
892	Q₁₆	—	4	2	no	—
893	Q₁₆	—	4	1	no	—
894	Q₁₆	—	4	2	no	—
895	SD₁₆	—	4	1	no	—
896	SD₁₆	—	4	2	no	—
897	SD₁₆	—	4	2	no	—
898	SD₁₆	—	4	2	no	—
899	SD₁₆	—	4	2	no	—
900	SD₁₆	—	4	1	no	—
901	D₈	—	4	2	no	—
902	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
903	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
904	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
905	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
906	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
907	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	2	1	no	—
924	C₄⋊C₄	—	2	1	no	—
925	C₄⋊C₄	—	2	1	no	—
926	C₄⋊C₄	—	2	2	no	—
927	C₄⋊C₄	—	2	2	no	—
928	C₄⋊C₄	—	2	2	no	—
929	C₄⋊C₄	—	2	2	no	—
930	C₄⋊C₄	—	2	1	no	—
931	C₄⋊C₄	—	2	2	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
939	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
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	1	yes	characteristic
943	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
944	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
945	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
946	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
947	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
949	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	1	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	2	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	2	1	no	—
960	C₂²⋊C₄	—	2	2	no	—
961	C₂²⋊C₄	—	2	2	no	—
962	C₂²⋊C₄	—	2	2	no	—
963	C₂²⋊C₄	—	2	2	no	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	1	no	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
970	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	1	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	2	2	no	—
978	C₄²	—	2	1	no	—
979	C₄²	—	2	2	no	—
980	C₄²	—	2	2	no	—
981	C₄²	—	2	2	no	—
982	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
983	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
984	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
985	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
986	C₄²	C₂⁴×C₁₇	1	2	yes	—
987	C₄²	C₂⁴×C₁₇	1	2	yes	—
988	C₂³	—	2	1	no	—
989	C₂³	—	2	2	no	—
990	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
991	Q₈	—	2	2	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	2	2	no	—
996	Q₈	—	2	1	no	—
997	Q₈	—	2	1	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	2	1	no	—
1000	Q₈	—	2	1	no	—
1001	Q₈	—	2	1	no	—
1002	Q₈	—	2	2	no	—
1003	Q₈	—	4	2	no	—
1004	Q₈	—	4	2	no	—
1005	Q₈	—	8	1	no	—
1006	Q₈	—	8	2	no	—
1007	D₄	—	2	1	no	—
1008	D₄	—	2	2	no	—
1009	D₄	—	2	1	no	—
1010	D₄	—	2	2	no	—
1011	D₄	—	4	4	no	—
1012	D₄	—	4	2	no	—
1013	D₄	—	8	1	no	—
1014	D₄	—	8	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	1	no	—
1024	C₂×C₄	—	2	1	no	—
1025	C₂×C₄	—	2	1	no	—
1026	C₂×C₄	—	2	2	no	—
1027	C₂×C₄	—	2	2	no	—
1028	C₂×C₄	—	4	1	no	—
1029	C₂×C₄	—	4	4	no	—
1030	C₂×C₄	—	4	2	no	—
1031	C₂×C₄	—	4	2	no	—
1032	C₂×C₄	—	8	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	8	1	no	—
1036	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
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	2	yes	—
1040	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1041	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1042	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1043	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
1044	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
1045	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
1046	C₈	—	2	2	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	2	2	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	2	no	—
1075	C₄	—	4	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	1	no	—
1080	C₄	C₁₇×#578	1	2	yes	—
1081	C₄	C₁₇×#585	1	1	yes	characteristic
1082	C₄	C₁₇×#585	1	1	yes	characteristic
1083	C₂	—	4	1	no	—
1084	C₂	—	8	2	no	—
1085	C₂	—	8	1	no	—
1086	C₂	C₁₇×#3487	1	1	yes	characteristic
1087	C₂	C₂×C₁₇×#578	1	1	yes	characteristic
1088	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×#3212	C₂
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×#3507	C₂	semidirect
3. C₁₇×#3402	C₂	semidirect
4. C₁₇×#3400	C₂	semidirect
5. C₁₇×#3398	C₂	semidirect
6. C₁₇×#3395	C₂	semidirect
7. C₁₇×#3394	C₂	semidirect
8. C₁₇×#3393	C₂	semidirect
9. C₁₇×#3377	C₂	semidirect
10. C₁₇×#3375	C₂	semidirect
11. C₁₇×#3372	C₂	semidirect
12. C₁₇×#3364	C₂	semidirect
13. C₁₇×#3363	C₂	semidirect
14. C₁₇×#3361	C₂	semidirect
15. C₁₇×#3225	C₂	semidirect
16. C₁₇×#3223	C₂	semidirect
18. C₁₇×#3210	C₂	semidirect
19. C₁₇×#3124	C₂	semidirect
20. C₁₇×#3120	C₂	semidirect
21. C₁₇×#3108	C₂	semidirect
22. C₁₇×#3104	C₂	semidirect
23. C₁₇×#2986	C₂	semidirect
443. #61929	C₁₇	direct (N × H)
508. #3555	C₂×C₁₇	semidirect
509. #3507	C₂×C₁₇	semidirect
510. #3402	C₂×C₁₇	semidirect
511. #3400	C₂×C₁₇	semidirect
512. #3398	C₂×C₁₇	semidirect
513. #3395	C₂×C₁₇	semidirect
514. #3394	C₂×C₁₇	semidirect
515. #3393	C₂×C₁₇	semidirect
516. #3377	C₂×C₁₇	semidirect
517. #3375	C₂×C₁₇	semidirect
518. #3372	C₂×C₁₇	semidirect
519. #3364	C₂×C₁₇	semidirect
520. #3363	C₂×C₁₇	semidirect
521. #3361	C₂×C₁₇	semidirect
522. #3225	C₂×C₁₇	semidirect
523. #3223	C₂×C₁₇	semidirect
525. #3210	C₂×C₁₇	semidirect
526. #3124	C₂×C₁₇	semidirect
527. #3120	C₂×C₁₇	semidirect
528. #3108	C₂×C₁₇	semidirect
529. #3104	C₂×C₁₇	semidirect
530. #2986	C₂×C₁₇	semidirect
856. C₁₇	#61929	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×#3507	2
C₁₇×#3402	2
C₁₇×#3400	2
C₁₇×#3398	2
C₁₇×#3395	2
C₁₇×#3394	2
C₁₇×#3393	2
C₁₇×#3377	2
C₁₇×#3375	2
C₁₇×#3372	2
C₁₇×#3364	2
C₁₇×#3363	2
C₁₇×#3361	2
C₁₇×#3225	2
C₁₇×#3223	2
C₁₇×#3212	2
C₁₇×#3210	2
C₁₇×#3124	2
C₁₇×#3120	2
C₁₇×#3108	2
C₁₇×#3104	2
C₁₇×#2986	2
#61929	17

Subgroups — C17×#61929 #16919673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61929 #16919673