Subgroups — #17917045

Order 4352.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14542856	C₂	1	2	yes	maximal, complemented
2	#14541773	C₂	1	1	yes	maximal, characteristic, complemented
3	#14541652	C₂	1	1	yes	maximal, characteristic, complemented
4	#14541613	C₂	1	2	yes	maximal, complemented
5	#14541215	C₂	1	1	yes	maximal, characteristic, complemented
6	#14541187	C₂	1	1	yes	maximal, characteristic, complemented
7	#14541153	C₂	1	1	yes	maximal, characteristic, complemented
8	#14541002	C₂	1	2	yes	maximal, complemented
9	#14540822	C₂	1	2	yes	maximal, complemented
10	#14540762	C₂	1	2	yes	maximal, complemented
11	#14540506	C₂	1	1	yes	maximal, characteristic, complemented
12	#14540471	C₂	1	1	yes	maximal, characteristic, complemented
13	#14540471	C₂	1	1	yes	maximal, characteristic, complemented
14	#14539443	C₂	1	1	yes	maximal, characteristic, complemented
15	#14539423	C₂	1	1	yes	maximal, characteristic, complemented
16	#14539354	C₂	1	1	yes	maximal, characteristic, complemented
17	#14539063	C₂	1	2	yes	maximal, complemented
18	#14539037	C₂	1	2	yes	maximal, complemented
19	#14538895	C₂	1	2	yes	maximal, complemented
20	#14537661	C₂	1	1	yes	maximal, characteristic, complemented
21	#14537637	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#10587590	C₂	1	1	yes	maximal, characteristic, complemented
23	C₁₇×#2966	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10587590	C₂²	1	1	yes	characteristic
25	C₂×#10587590	C₂²	1	1	yes	characteristic
26	C₂²×D₁₃₆	C₂²	1	1	yes	characteristic
27	#11763532	C₂²	1	2	yes	complemented
28	#11763529	C₂²	1	2	yes	—
29	#11763519	C₂²	1	2	yes	complemented
30	#11763505	C₂²	1	2	yes	complemented
31	#11763504	—	2	2	no	—
32	#11763499	C₂²	1	2	yes	—
33	#11763491	—	2	2	no	—
34	#11763489	—	2	2	no	—
35	#11763487	—	2	2	no	—
36	#11763464	C₂²	1	2	yes	complemented
37	#11763455	C₂²	1	2	yes	—
38	#11763455	C₂²	1	2	yes	—
39	#11763430	C₂²	1	2	yes	complemented
40	#11763421	C₂²	1	2	yes	—
41	#11763405	—	2	2	no	—
42	#11763391	—	2	2	no	—
43	#11763343	C₂²	1	2	yes	complemented
44	#11763342	—	2	2	no	—
45	#126×D₁₇	—	2	2	no	—
46	#11763289	C₂²	1	2	yes	complemented
47	#11763283	C₂²	1	2	yes	—
48	C₄×#63252	C₂²	1	2	yes	complemented
49	#11763214	C₂²	1	1	yes	characteristic, complemented
50	#11763211	C₂²	1	1	yes	characteristic, complemented
51	#11763211	C₂²	1	1	yes	characteristic, complemented
52	#11763193	C₂²	1	1	yes	characteristic
53	#11763193	C₂²	1	1	yes	characteristic
54	#11763189	C₂²	1	1	yes	characteristic, complemented
55	#11763178	C₂²	1	2	yes	complemented
56	#11763169	C₂²	1	2	yes	complemented
57	#11763164	C₂²	1	2	yes	complemented
58	#11763151	C₂²	1	2	yes	—
59	#11763151	C₂²	1	2	yes	—
60	#11763151	C₂²	1	2	yes	complemented
61	#11763140	C₂²	1	2	yes	complemented
62	#11763134	C₂²	1	2	yes	complemented
63	#11763128	C₂²	1	2	yes	complemented
64	#11763117	C₂²	1	2	yes	complemented
65	#11763110	C₂²	1	2	yes	complemented
66	#11763110	C₂²	1	2	yes	complemented
67	#11763110	C₂²	1	2	yes	complemented
68	#11763100	C₂²	1	2	yes	complemented
69	#11763095	C₂²	1	2	yes	complemented
70	#11763067	C₂²	1	2	yes	—
71	#11763055	C₂²	1	2	yes	complemented
72	#11763050	C₂²	1	1	yes	characteristic
73	#11763050	C₂²	1	1	yes	characteristic
74	#11763050	C₂²	1	1	yes	characteristic, complemented
75	#11763050	C₂²	1	1	yes	characteristic, complemented
76	#11763045	C₂²	1	1	yes	characteristic
77	#11763045	C₂²	1	1	yes	characteristic
78	#11763038	C₂²	1	2	yes	complemented
79	#11763032	C₂²	1	2	yes	complemented
80	#11763032	C₂²	1	2	yes	complemented
81	#11763025	C₂²	1	2	yes	—
82	#11763025	C₂²	1	2	yes	—
83	#11763015	C₂²	1	2	yes	complemented
84	#11763015	C₂²	1	2	yes	complemented
85	#11762973	C₂²	1	2	yes	complemented
86	#11762973	C₂²	1	2	yes	complemented
87	#11762962	C₂²	1	2	yes	—
88	#11762962	C₂²	1	2	yes	—
89	#11762956	C₂²	1	2	yes	—
90	#11762956	C₂²	1	2	yes	—
91	#11762922	C₂²	1	2	yes	—
92	#11762922	C₂²	1	2	yes	—
93	#11762917	C₂²	1	2	yes	complemented
94	#11762911	C₂²	1	2	yes	complemented
95	#11762911	C₂²	1	2	yes	complemented
96	#11762911	C₂²	1	2	yes	complemented
97	C₄×Dic₆₈	C₂²	1	1	yes	characteristic, complemented
98	C₄×Dic₆₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×Dic₆₈	C₂²	1	1	yes	characteristic, complemented
100	C₄×Dic₆₈	C₂²	1	1	yes	characteristic, complemented
101	C₄×#63219	C₂²	1	2	yes	complemented
102	C₄×#63219	C₂²	1	2	yes	complemented
103	C₄×#63219	C₂²	1	2	yes	complemented
104	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
105	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
106	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
107	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
108	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
109	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
110	#11762847	C₂²	1	1	yes	characteristic
111	#11762847	C₂²	1	1	yes	characteristic, complemented
112	C₂×#10587489	C₂²	1	1	yes	characteristic, complemented
113	#11762815	C₂²	1	2	yes	—
114	#11762811	C₂²	1	2	yes	complemented
115	#11762806	C₂²	1	2	yes	complemented
116	C₁₇×#529	C₂²	1	1	yes	characteristic
117	C₁₇×#446	C₂²	1	1	yes	characteristic, complemented
118	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
119	C₁₇×#436	C₂²	1	1	yes	characteristic
120	C₁₇×#435	C₂²	1	1	yes	characteristic
121	C₁₇×#435	C₂²	1	1	yes	characteristic, complemented
122	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
123	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
124	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
125	C₁₇×#433	C₂²	1	1	yes	characteristic
126	C₁₇×#433	C₂²	1	1	yes	characteristic, complemented
127	C₁₇×#432	C₂²	1	1	yes	characteristic, complemented
128	C₁₇×#405	C₂²	1	1	yes	characteristic
129	C₁₇×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#63252	C₂³	1	2	yes	—
132	C₂×#63252	C₂³	1	2	yes	—
133	C₂²×D₆₈	C₂³	1	2	yes	—
134	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
135	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
138	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
140	C₁₇×#126	D₄	1	1	yes	characteristic
141	C₁₇×#126	D₄	1	1	yes	characteristic
142	C₁₇×#125	D₄	1	1	yes	characteristic
143	C₁₇×#124	D₄	1	1	yes	characteristic
144	C₁₇×#123	D₄	1	1	yes	characteristic
145	C₁₇×#123	D₄	1	1	yes	characteristic
146	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
147	C₁₇×#121	D₄	1	1	yes	characteristic
148	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
149	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
150	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
151	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
152	C₁₇×#117	C₂³	1	1	yes	characteristic
153	C₁₇×#117	C₂³	1	1	yes	characteristic
154	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
155	#10587632	—	2	2	no	—
156	#10587632	—	2	2	no	—
157	#10587625	—	2	2	no	—
158	#10587624	—	2	2	no	—
159	#10587623	—	2	2	no	—
160	#10587623	—	2	2	no	—
161	#10587622	—	2	2	no	—
162	#10587621	—	2	2	no	—
163	#10587616	C₂³	1	2	yes	—
164	#10587616	C₂³	1	2	yes	—
165	#10587615	—	2	2	no	—
166	C₄×C₂²⋊D₁₇	—	2	2	no	—
167	C₄×C₂²⋊D₁₇	—	2	2	no	—
168	C₄×C₂²⋊D₁₇	—	2	2	no	—
169	#10587612	C₂³	1	2	yes	—
170	#10587612	C₂³	1	2	yes	—
171	C₂×C₄⋊Dic₁₇	C₂³	1	2	yes	—
172	#10587610	C₂³	1	2	yes	—
173	#10587610	C₂³	1	2	yes	—
174	#10587610	C₂³	1	2	yes	—
175	#10587610	C₂³	1	2	yes	—
176	C₂×Dic₆₈	C₂³	1	1	yes	characteristic
177	C₂×Dic₆₈	C₂³	1	1	yes	characteristic
178	C₂×Dic₆₈	C₂³	1	2	yes	—
179	#10587590	—	2	4	no	—
180	#10587590	—	2	4	no	—
181	C₂×D₁₃₆	—	2	4	no	—
182	C₂×D₁₃₆	C₂³	1	2	yes	—
183	C₂×D₁₃₆	C₂³	1	1	yes	characteristic
184	C₂×D₁₃₆	C₂³	1	1	yes	characteristic
185	C₂×#63219	C₂³	1	2	yes	—
186	C₂×#63219	C₂³	1	2	yes	—
187	C₂×#63219	C₂³	1	2	yes	—
188	C₂×#63219	C₂³	1	2	yes	—
189	#10587584	—	2	2	no	—
190	#10587584	—	2	2	no	—
191	#10587584	—	2	2	no	—
192	#10587584	—	2	2	no	—
193	#10587582	—	2	2	no	—
194	#10587582	—	2	2	no	—
195	#10587582	—	2	2	no	—
196	#10587580	—	2	2	no	—
197	#10587580	—	2	2	no	—
198	#10587579	—	2	2	no	—
199	#10587579	—	2	2	no	—
200	#10587578	—	2	2	no	—
201	#10587578	—	2	2	no	—
202	C₄⋊C₄×D₁₇	—	2	2	no	—
203	C₄⋊C₄×D₁₇	—	2	2	no	—
204	C₄⋊C₄×D₁₇	—	2	2	no	—
205	#10587575	—	2	2	no	—
206	#10587575	—	2	2	no	—
207	#10587575	—	2	2	no	—
208	#10587573	—	2	2	no	—
209	#10587571	—	2	2	no	—
210	#10587570	—	2	2	no	—
211	#10587570	—	2	2	no	—
212	#10587569	—	2	2	no	—
213	#10587569	—	2	2	no	—
214	#10587569	—	2	2	no	—
215	#10587569	—	2	2	no	—
216	#10587567	—	2	2	no	—
217	#10587567	—	2	2	no	—
218	#10587567	—	2	2	no	—
219	C₂²⋊C₄×D₁₇	—	2	2	no	—
220	C₂²⋊C₄×D₁₇	—	2	2	no	—
221	C₂²⋊C₄×D₁₇	—	2	2	no	—
222	C₂²⋊C₄×D₁₇	—	2	2	no	—
223	#10587565	—	2	2	no	—
224	#10587565	—	2	2	no	—
225	#10587565	—	2	2	no	—
226	#10587565	—	2	2	no	—
227	#10587565	—	2	2	no	—
228	#10587563	—	2	2	no	—
229	#10587562	—	2	2	no	—
230	#10587561	C₂³	1	2	yes	—
231	#10587561	C₂³	1	2	yes	—
232	C₄×D₆₈	C₂³	1	2	yes	—
233	C₄×D₆₈	C₂³	1	2	yes	—
234	C₄×D₆₈	C₂³	1	2	yes	—
235	C₄×D₆₈	C₂³	1	2	yes	—
236	C₄×D₆₈	C₂³	1	2	yes	—
237	C₄×D₆₈	C₂³	1	2	yes	—
238	#10587558	—	2	2	no	—
239	#10587558	—	2	2	no	—
240	C₄²×D₁₇	—	2	2	no	—
241	#10587556	C₂³	1	2	yes	—
242	#10587556	C₂³	1	2	yes	—
243	#10587555	C₂³	1	2	yes	—
244	#10587555	C₂³	1	2	yes	—
245	C₄×Dic₃₄	C₂³	1	2	yes	—
246	C₄×Dic₃₄	C₂³	1	2	yes	—
247	C₄×Dic₃₄	C₂³	1	2	yes	—
248	C₄×Dic₃₄	C₂³	1	2	yes	—
249	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
250	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
251	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
252	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
253	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
254	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
255	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
256	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
257	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
258	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
259	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
260	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
261	C₁₇×#97	C₂³	1	1	yes	characteristic
262	C₁₇×#97	C₂³	1	1	yes	characteristic
263	C₁₇×#97	C₂³	1	1	yes	characteristic
264	C₁₇×#97	C₂³	1	1	yes	characteristic
265	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
266	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
267	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
268	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
269	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
270	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
271	#10587492	C₂³	1	2	yes	—
272	#10587492	C₂³	1	2	yes	—
273	#10587492	C₂³	1	2	yes	—
274	#10587492	C₂³	1	2	yes	—
275	#10587492	C₂³	1	2	yes	—
276	#10587492	C₂³	1	2	yes	—
277	#10587492	C₂³	1	2	yes	—
278	#10587492	C₂³	1	2	yes	—
279	#10587489	C₂³	1	1	yes	characteristic
280	#10587489	C₂³	1	1	yes	characteristic
281	#10587489	C₂³	1	1	yes	characteristic
282	#10587489	C₂³	1	2	yes	—
283	#10587489	C₂³	1	1	yes	characteristic
284	#10587489	C₂³	1	2	yes	—
285	#10587488	C₂³	1	2	yes	—
286	#10587488	C₂³	1	2	yes	—
287	#10587488	C₂³	1	2	yes	—
288	#10587488	C₂³	1	2	yes	—
289	#10587487	C₂³	1	2	yes	—
290	#10587487	C₂³	1	2	yes	—
291	#10587487	C₂³	1	2	yes	—
292	#10587487	C₂³	1	2	yes	—
293	#10587487	C₂³	1	2	yes	—
294	#10587487	C₂³	1	2	yes	—
295	#10587487	C₂³	1	2	yes	—
296	#10587487	C₂³	1	2	yes	—
297	C₂³×D₁₇	—	2	2	no	—
298	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
299	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
300	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
302	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
307	C₂×C₂²⋊D₁₇	—	2	2	no	—
308	C₂×C₂²⋊D₁₇	—	2	2	no	—
309	C₂×C₂²⋊D₁₇	—	2	2	no	—
310	C₂×C₂²⋊D₁₇	—	2	2	no	—
311	C₂²×Dic₁₇	—	2	2	no	—
312	#63252	—	2	4	no	—
313	#63252	—	2	4	no	—
314	#63252	—	4	2	no	—
315	#63252	—	4	2	no	—
316	C₂×D₆₈	—	2	4	no	—
317	C₂×D₆₈	—	2	2	no	—
318	C₂×D₆₈	—	4	2	no	—
319	C₂×D₆₈	C₂⁴	1	2	yes	—
320	C₂×D₆₈	C₂⁴	1	2	yes	—
321	C₂×C₄×D₁₇	—	2	2	no	—
322	C₂×C₄×D₁₇	—	2	2	no	—
323	C₂×C₄×D₁₇	—	2	2	no	—
324	C₂×C₄×D₁₇	—	2	2	no	—
325	C₂×C₄×D₁₇	—	2	2	no	—
326	C₂×C₄×D₁₇	—	2	2	no	—
327	C₂×C₄×D₁₇	—	2	2	no	—
328	C₂×C₄×D₁₇	—	2	2	no	—
329	C₂×Dic₃₄	—	2	2	no	—
330	C₂×Dic₃₄	C₂⁴	1	2	yes	—
331	C₂×Dic₃₄	C₂⁴	1	2	yes	—
332	M₁₆×C₁₇	—	4	1	no	—
333	M₁₆×C₁₇	—	4	1	no	—
334	C₂×C₈×C₁₇	—	2	2	no	—
335	C₂×C₈×C₁₇	—	2	2	no	—
336	C₂×C₈×C₁₇	—	2	2	no	—
337	C₂×C₈×C₁₇	—	4	1	no	—
338	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
346	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
347	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
348	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
351	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
356	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
357	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
359	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
360	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
361	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
362	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
363	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
364	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
365	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
367	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
369	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
370	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
371	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
372	C₂²⋊Dic₁₇	—	2	2	no	—
373	C₂²⋊Dic₁₇	—	2	2	no	—
374	C₂²⋊Dic₁₇	—	2	2	no	—
375	C₂²⋊Dic₁₇	—	2	2	no	—
376	C₂²⋊Dic₁₇	—	2	2	no	—
377	C₂²⋊Dic₁₇	—	2	2	no	—
378	#63227	—	2	2	no	—
379	#63227	—	2	2	no	—
380	#63227	—	2	2	no	—
381	#63227	—	2	2	no	—
382	#63227	—	2	2	no	—
383	#63227	—	2	2	no	—
384	#63227	—	2	2	no	—
385	#63227	—	2	2	no	—
386	#63227	—	2	2	no	—
387	#63227	—	2	2	no	—
388	#63227	—	2	2	no	—
389	#63227	—	2	2	no	—
390	C₄⋊Dic₁₇	—	2	2	no	—
391	C₄⋊Dic₁₇	—	2	2	no	—
392	C₄⋊Dic₁₇	—	2	2	no	—
393	C₄⋊Dic₁₇	—	2	2	no	—
394	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
395	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
396	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
397	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
398	#63225	—	2	2	no	—
399	#63225	—	2	2	no	—
400	#63225	—	2	2	no	—
401	#63225	—	2	2	no	—
402	#63225	—	2	2	no	—
403	#63225	—	2	2	no	—
404	#63225	—	2	2	no	—
405	#63225	—	2	2	no	—
406	#63225	—	2	2	no	—
407	#63225	—	2	2	no	—
408	#63225	—	2	2	no	—
409	#63225	—	2	2	no	—
410	C₄×Dic₁₇	—	2	2	no	—
411	C₄×Dic₁₇	—	2	2	no	—
412	C₄×Dic₁₇	—	2	2	no	—
413	C₄×Dic₁₇	—	2	2	no	—
414	C₄×Dic₁₇	—	2	2	no	—
415	C₄×Dic₁₇	—	2	2	no	—
416	Dic₆₈	—	2	2	no	—
417	Dic₆₈	—	2	2	no	—
418	Dic₆₈	—	4	2	no	—
419	D₁₃₆	—	2	4	no	—
420	D₁₃₆	—	2	2	no	—
421	D₁₃₆	#41	1	4	yes	—
422	#63219	—	2	4	no	—
423	#63219	—	2	4	no	—
424	#63219	—	4	2	no	—
425	#63219	—	4	2	no	—
426	#61487	—	17	1	no	maximal, Sylow
427	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
428	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
429	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
430	C₂²×D₁₇	—	2	2	no	—
431	C₂²×D₁₇	—	2	2	no	—
432	C₂²×D₁₇	—	4	4	no	—
433	C₂²×D₁₇	—	8	2	no	—
434	C₂²×D₁₇	—	8	2	no	—
435	Q₈×C₁₇	—	4	1	no	—
436	D₄×C₁₇	—	4	1	no	—
437	D₄×C₁₇	—	4	1	no	—
438	D₄×C₁₇	—	4	1	no	—
439	C₂×C₄×C₁₇	—	2	1	no	—
440	C₂×C₄×C₁₇	—	2	1	no	—
441	C₂×C₄×C₁₇	—	2	1	no	—
442	C₂×C₄×C₁₇	—	2	1	no	—
443	C₂×C₄×C₁₇	—	2	1	no	—
444	C₂×C₄×C₁₇	—	2	1	no	—
445	C₂×C₄×C₁₇	—	4	1	no	—
446	C₂×C₄×C₁₇	—	4	1	no	—
447	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
459	C₂²⋊D₁₇	—	4	4	no	—
460	C₂²⋊D₁₇	—	4	4	no	—
461	C₂²⋊D₁₇	—	8	2	no	—
462	C₂²⋊D₁₇	—	8	2	no	—
463	C₂×Dic₁₇	—	2	2	no	—
464	C₂×Dic₁₇	—	2	2	no	—
465	C₂×Dic₁₇	—	2	2	no	—
466	C₂×Dic₁₇	—	2	2	no	—
467	C₂×Dic₁₇	—	2	2	no	—
468	C₂×Dic₁₇	—	2	2	no	—
469	C₂×Dic₁₇	—	8	2	no	—
470	D₆₈	—	2	2	no	—
471	D₆₈	—	2	2	no	—
472	D₆₈	—	2	2	no	—
473	D₆₈	—	4	4	no	—
474	D₆₈	C₂×#41	1	4	yes	—
475	C₄×D₁₇	—	4	4	no	—
476	C₄×D₁₇	—	4	4	no	—
477	C₄×D₁₇	—	8	2	no	—
478	C₄×D₁₇	—	8	2	no	—
479	C₄×D₁₇	—	8	2	no	—
480	C₄×D₁₇	—	8	2	no	—
481	C₄×D₁₇	—	8	2	no	—
482	C₄×D₁₇	—	8	2	no	—
483	Dic₃₄	—	2	2	no	—
484	Dic₃₄	—	2	2	no	—
485	Dic₃₄	—	2	2	no	—
486	Dic₃₄	—	2	2	no	—
487	Dic₃₄	—	8	2	no	—
488	C₈×C₁₇	—	2	1	no	—
489	C₈×C₁₇	—	2	1	no	—
490	C₈×C₁₇	—	2	1	no	—
491	C₈×C₁₇	—	2	1	no	—
492	C₈×C₁₇	—	2	1	no	—
493	C₈×C₁₇	—	2	1	no	—
494	C₈×C₁₇	—	2	1	no	—
495	C₈×C₁₇	C₂×#41	1	2	yes	—
496	#3521	—	17	2	no	—
497	#3393	—	17	1	no	—
498	#3380	—	17	1	no	—
499	#3376	—	17	2	no	—
500	#3342	—	17	1	no	—
501	#3339	—	17	1	no	—
502	#3336	—	17	1	no	—
503	#3323	—	17	2	no	—
504	#3311	—	17	2	no	—
505	#3307	—	17	2	no	—
506	#3283	—	17	1	no	—
507	#3280	—	17	1	no	—
508	#3280	—	17	1	no	—
509	#3177	—	17	1	no	—
510	#3175	—	17	1	no	—
511	#3168	—	17	1	no	—
512	#3125	—	17	2	no	—
513	#3123	—	17	2	no	—
514	#3111	—	17	2	no	—
515	#2966	D₁₇	1	1	yes	characteristic, complemented
516	#2951	—	17	1	no	—
517	#2948	—	17	1	no	—
518	C₄×#135	—	17	1	no	—
519	C₂²×C₁₇	—	2	1	no	—
520	C₂²×C₁₇	—	2	1	no	—
521	C₂²×C₁₇	—	2	1	no	—
522	C₂²×C₁₇	—	2	1	no	—
523	C₂²×C₁₇	—	2	1	no	—
524	C₂²×C₁₇	—	2	1	no	—
525	C₂²×C₁₇	—	2	1	no	—
526	C₂²×C₁₇	—	2	1	no	—
527	C₂²×C₁₇	—	2	1	no	—
528	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
529	C₂×D₁₇	—	2	4	no	—
530	C₂×D₁₇	—	4	2	no	—
531	C₂×D₁₇	—	4	2	no	—
532	C₂×D₁₇	—	4	2	no	—
533	C₂×D₁₇	—	4	2	no	—
534	C₂×D₁₇	—	4	2	no	—
535	C₂×D₁₇	—	16	4	no	—
536	C₄×C₁₇	—	2	1	no	—
537	C₄×C₁₇	—	2	1	no	—
538	C₄×C₁₇	—	2	1	no	—
539	C₄×C₁₇	—	2	1	no	—
540	C₄×C₁₇	—	2	1	no	—
541	C₄×C₁₇	—	2	1	no	—
542	C₄×C₁₇	—	2	1	no	—
543	C₄×C₁₇	—	2	1	no	—
544	C₄×C₁₇	—	2	1	no	—
545	C₄×C₁₇	—	2	1	no	—
546	C₄×C₁₇	—	2	1	no	—
547	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
548	C₄×C₁₇	#585	1	1	yes	characteristic
549	Dic₁₇	—	4	2	no	—
550	Dic₁₇	—	4	2	no	—
551	Dic₁₇	—	4	2	no	—
552	Dic₁₇	—	4	2	no	—
553	Dic₁₇	—	4	2	no	—
554	Dic₁₇	—	4	2	no	—
555	C₂×#135	—	17	1	no	—
556	C₂×#135	—	17	1	no	—
557	C₂²×D₈	—	17	1	no	—
558	#556	—	17	2	no	—
559	#556	—	17	2	no	—
560	#554	—	17	2	no	—
561	#553	—	17	2	no	—
562	#553	—	34	2	no	—
563	#552	—	17	2	no	—
564	#552	—	34	2	no	—
565	#551	—	34	2	no	—
566	#551	—	34	2	no	—
567	#547	—	17	2	no	—
568	#546	—	17	2	no	—
569	#546	—	17	2	no	—
570	#542	—	17	2	no	—
571	#541	—	17	2	no	—
572	#539	—	34	2	no	—
573	#538	—	34	2	no	—
574	#529	—	17	2	no	—
575	#529	—	34	2	no	—
576	#529	C₂×D₁₇	1	1	yes	characteristic
577	C₂×#126	—	34	2	no	—
578	#520	—	17	2	no	—
579	#518	—	17	2	no	—
580	C₄×#41	—	17	2	no	—
581	#500	—	17	1	no	—
582	#499	—	17	1	no	—
583	#499	—	17	1	no	—
584	#495	—	17	1	no	—
585	#495	—	17	1	no	—
586	#494	—	17	1	no	—
587	#491	—	17	2	no	—
588	#489	—	17	2	no	—
589	#488	—	17	2	no	—
590	#485	—	17	2	no	—
591	#485	—	17	2	no	—
592	#485	—	17	2	no	—
593	#483	—	17	2	no	—
594	#482	—	17	2	no	—
595	#481	—	17	2	no	—
596	#479	—	17	2	no	—
597	#478	—	17	2	no	—
598	#478	—	17	2	no	—
599	#478	—	17	2	no	—
600	#476	—	17	2	no	—
601	#475	—	17	2	no	—
602	#470	—	17	2	no	—
603	#468	—	17	2	no	—
604	#467	—	17	1	no	—
605	#467	—	17	1	no	—
606	#467	—	17	1	no	—
607	#467	—	17	1	no	—
608	#466	—	17	1	no	—
609	#466	—	17	1	no	—
610	#465	—	17	2	no	—
611	#464	—	17	2	no	—
612	#464	—	17	2	no	—
613	#463	—	17	2	no	—
614	#463	—	17	2	no	—
615	#461	—	17	2	no	—
616	#461	—	17	2	no	—
617	#452	—	17	2	no	—
618	#452	—	17	2	no	—
619	#450	—	17	2	no	—
620	#450	—	17	2	no	—
621	#449	—	17	2	no	—
622	#449	—	17	2	no	—
623	#446	C₂×D₁₇	1	1	yes	characteristic, complemented
624	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
625	#442	—	17	2	no	—
626	#442	—	17	2	no	—
627	#441	—	17	2	no	—
628	#440	—	17	2	no	—
629	#440	—	17	2	no	—
630	#440	—	17	2	no	—
631	C₄×Q₁₆	—	17	1	no	—
632	C₄×Q₁₆	—	17	1	no	—
633	C₄×Q₁₆	—	17	1	no	—
634	C₄×Q₁₆	—	17	1	no	—
635	C₄×SD₁₆	—	17	2	no	—
636	C₄×SD₁₆	—	17	2	no	—
637	C₄×SD₁₆	—	17	2	no	—
638	C₄×D₈	—	17	1	no	—
639	C₄×D₈	—	17	1	no	—
640	C₄×D₈	—	17	1	no	—
641	C₄×D₈	—	17	1	no	—
642	C₄×D₈	—	17	1	no	—
643	C₄×D₈	—	17	1	no	—
644	#436	C₂×D₁₇	1	1	yes	characteristic
645	#435	C₂×D₁₇	1	1	yes	characteristic
646	#435	C₂×D₁₇	1	1	yes	characteristic, complemented
647	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
648	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
649	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
650	#433	C₂×D₁₇	1	1	yes	characteristic
651	#433	C₂×D₁₇	1	1	yes	characteristic, complemented
652	#432	C₂×D₁₇	1	1	yes	characteristic, complemented
653	#427	—	17	1	no	—
654	#427	—	17	1	no	—
655	C₂×#107	—	17	1	no	—
656	#418	—	17	2	no	—
657	#417	—	17	2	no	—
658	#416	—	17	2	no	—
659	#405	C₂×D₁₇	1	1	yes	characteristic
660	#405	C₂×D₁₇	1	1	yes	characteristic, complemented
661	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
662	C₂×C₁₇	—	4	1	no	—
663	C₂×C₁₇	—	4	1	no	—
664	C₂×C₁₇	—	4	1	no	—
665	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
666	C₂×C₁₇	#3584	1	1	yes	characteristic
667	C₂×C₁₇	#3584	1	1	yes	characteristic
668	D₁₇	—	4	4	no	—
669	D₁₇	—	8	2	no	—
670	C₂×#41	—	17	2	no	—
671	C₂×#41	—	17	2	no	—
672	C₂²×D₄	—	17	2	no	—
673	#135	—	34	4	no	—
674	#135	—	34	4	no	—
675	C₂×Q₁₆	—	17	1	no	—
676	C₂×Q₁₆	—	17	1	no	—
677	C₂×Q₁₆	—	17	2	no	—
678	C₂×SD₁₆	—	17	2	no	—
679	C₂×SD₁₆	—	17	2	no	—
680	C₂×SD₁₆	—	17	2	no	—
681	C₂×SD₁₆	—	17	2	no	—
682	C₂×D₈	—	17	1	no	—
683	C₂×D₈	—	17	1	no	—
684	C₂×D₈	—	17	2	no	—
685	C₂×D₈	—	34	4	no	—
686	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
687	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
688	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
689	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
690	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
691	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
692	C₄⋊Q₈	—	17	2	no	—
693	C₄⋊Q₈	—	17	2	no	—
694	#126	—	34	2	no	—
695	#126	—	34	2	no	—
696	#126	—	34	2	no	—
697	#126	—	34	2	no	—
698	#126	—	34	2	no	—
699	#126	—	34	2	no	—
700	#126	—	34	2	no	—
701	#126	—	34	2	no	—
702	#126	—	34	2	no	—
703	#126	—	34	2	no	—
704	#126	D₆₈	1	1	yes	characteristic
705	#126	D₆₈	1	1	yes	characteristic
706	#125	—	17	2	no	—
707	#125	—	17	2	no	—
708	#125	—	34	2	no	—
709	#125	—	34	2	no	—
710	#125	—	34	2	no	—
711	#125	D₆₈	1	1	yes	characteristic
712	#124	—	17	2	no	—
713	#124	—	17	2	no	—
714	#124	—	34	2	no	—
715	#124	—	34	2	no	—
716	#124	D₆₈	1	1	yes	characteristic
717	#123	—	34	2	no	—
718	#123	—	34	2	no	—
719	#123	—	34	2	no	—
720	#123	—	34	2	no	—
721	#123	—	34	2	no	—
722	#123	—	34	2	no	—
723	#123	—	34	2	no	—
724	#123	—	34	2	no	—
725	#123	D₆₈	1	1	yes	characteristic
726	#123	D₆₈	1	1	yes	characteristic
727	C₂²⋊Q₈	—	17	2	no	—
728	C₂²⋊Q₈	—	17	2	no	—
729	C₂²⋊Q₈	—	17	2	no	—
730	C₂²⋊Q₈	—	17	2	no	—
731	C₂²⋊Q₈	—	34	2	no	—
732	C₂²⋊Q₈	—	34	2	no	—
733	C₂²⋊Q₈	—	34	2	no	—
734	C₂²⋊Q₈	—	34	2	no	—
735	C₂²⋊Q₈	—	34	2	no	—
736	C₂²⋊Q₈	D₆₈	1	1	yes	characteristic
737	#121	—	17	2	no	—
738	#121	—	17	2	no	—
739	#121	—	34	2	no	—
740	#121	—	34	2	no	—
741	#121	—	34	2	no	—
742	#121	—	34	2	no	—
743	#121	D₆₈	1	1	yes	characteristic
744	#120	—	34	2	no	—
745	#120	—	34	2	no	—
746	C₄×Q₈	—	17	2	no	—
747	C₄×Q₈	—	17	2	no	—
748	C₄×Q₈	—	17	2	no	—
749	C₄×Q₈	—	17	2	no	—
750	C₄×Q₈	—	34	2	no	—
751	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
752	C₄×D₄	—	17	2	no	—
753	C₄×D₄	—	17	2	no	—
754	C₄×D₄	—	17	2	no	—
755	C₄×D₄	—	17	2	no	—
756	C₄×D₄	—	17	2	no	—
757	C₄×D₄	—	17	2	no	—
758	C₄×D₄	—	34	2	no	—
759	C₄×D₄	—	34	2	no	—
760	C₄×D₄	—	34	2	no	—
761	C₄×D₄	—	34	2	no	—
762	C₄×D₄	—	34	2	no	—
763	C₄×D₄	—	34	2	no	—
764	C₄×D₄	—	34	2	no	—
765	C₄×D₄	—	34	2	no	—
766	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
767	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
768	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
769	#117	—	17	2	no	—
770	#117	—	17	2	no	—
771	#117	—	34	2	no	—
772	#117	—	34	2	no	—
773	#117	—	34	2	no	—
774	#117	—	34	2	no	—
775	#117	—	34	2	no	—
776	#117	C₂²×D₁₇	1	1	yes	characteristic
777	#117	C₂²×D₁₇	1	1	yes	characteristic
778	C₂×C₄⋊C₄	—	17	2	no	—
779	C₂×C₄⋊C₄	—	34	2	no	—
780	C₂×C₄⋊C₄	—	34	2	no	—
781	C₂×C₄⋊C₄	—	34	2	no	—
782	C₂×C₂²⋊C₄	—	34	2	no	—
783	C₂×C₂²⋊C₄	—	34	2	no	—
784	C₂×C₂²⋊C₄	—	34	2	no	—
785	C₂×C₂²⋊C₄	—	34	2	no	—
786	C₂×C₄²	—	34	2	no	—
787	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
788	#107	—	17	1	no	—
789	#107	—	17	1	no	—
790	#107	—	17	2	no	—
791	#107	—	17	1	no	—
792	#107	—	17	1	no	—
793	#107	—	17	2	no	—
794	#106	—	17	2	no	—
795	#106	—	17	2	no	—
796	#106	—	17	2	no	—
797	#106	—	17	2	no	—
798	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
799	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
800	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
801	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
802	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
803	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
804	#103	—	17	2	no	—
805	#103	—	17	2	no	—
806	#103	—	17	2	no	—
807	#103	—	17	2	no	—
808	#103	—	17	2	no	—
809	#103	—	17	2	no	—
810	#103	—	17	2	no	—
811	#103	—	17	2	no	—
812	#102	—	17	2	no	—
813	#102	—	17	2	no	—
814	#102	—	17	2	no	—
815	#102	—	17	2	no	—
816	#102	—	17	2	no	—
817	#102	—	17	2	no	—
818	#102	—	17	2	no	—
819	#102	—	17	2	no	—
820	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
821	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
822	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
823	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
824	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
825	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
826	#97	C₂²×D₁₇	1	1	yes	characteristic
827	#97	C₂²×D₁₇	1	1	yes	characteristic
828	#97	C₂²×D₁₇	1	1	yes	characteristic
829	#97	C₂²×D₁₇	1	1	yes	characteristic
830	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
831	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
832	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
833	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
836	C₁₇	#61487	1	1	yes	characteristic, complemented, Sylow
837	C₂⁴	—	34	2	no	—
838	#41	—	34	4	no	—
839	#41	—	34	4	no	—
840	#41	—	68	2	no	—
841	#41	—	68	2	no	—
842	C₂×Q₈	—	17	2	no	—
843	C₂×Q₈	—	17	2	no	—
844	C₂×Q₈	—	34	2	no	—
845	C₂×Q₈	C₂×D₆₈	1	1	yes	characteristic
846	C₂×D₄	—	17	2	no	—
847	C₂×D₄	—	17	2	no	—
848	C₂×D₄	—	34	4	no	—
849	C₂×D₄	—	34	2	no	—
850	C₂×D₄	—	34	2	no	—
851	C₂×D₄	—	34	2	no	—
852	C₂×D₄	—	34	2	no	—
853	C₂×D₄	—	34	2	no	—
854	C₂×D₄	—	68	2	no	—
855	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
856	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
857	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
858	C₂²×C₄	—	34	2	no	—
859	C₂²×C₄	—	34	2	no	—
860	C₂²×C₄	—	34	2	no	—
861	C₂²×C₄	—	34	2	no	—
862	C₂²×C₄	—	34	2	no	—
863	C₂²×C₄	—	34	2	no	—
864	C₂²×C₄	—	34	2	no	—
865	C₂²×C₄	—	34	2	no	—
866	C₂²×C₄	—	34	2	no	—
867	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
868	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
869	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
870	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
872	Q₁₆	—	34	2	no	—
873	Q₁₆	—	34	2	no	—
874	Q₁₆	—	68	2	no	—
875	SD₁₆	—	34	4	no	—
876	SD₁₆	—	34	4	no	—
877	SD₁₆	—	68	2	no	—
878	SD₁₆	—	68	2	no	—
879	D₈	—	17	4	no	—
880	D₈	—	34	4	no	—
881	D₈	—	34	2	no	—
882	M₁₆	—	4	1	no	—
883	M₁₆	—	4	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	2	2	no	—
886	C₂×C₈	—	2	2	no	—
887	C₂×C₈	—	4	1	no	—
888	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
892	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
896	C₄⋊C₄	—	17	2	no	—
897	C₄⋊C₄	—	17	2	no	—
898	C₄⋊C₄	—	17	2	no	—
899	C₄⋊C₄	—	17	2	no	—
900	C₄⋊C₄	—	34	2	no	—
901	C₄⋊C₄	—	34	2	no	—
902	C₄⋊C₄	—	34	2	no	—
903	C₄⋊C₄	—	34	2	no	—
904	C₄⋊C₄	—	34	2	no	—
905	C₄⋊C₄	—	34	2	no	—
906	C₄⋊C₄	—	34	2	no	—
907	C₄⋊C₄	—	34	2	no	—
908	C₄⋊C₄	—	34	2	no	—
909	C₄⋊C₄	—	34	2	no	—
910	C₄⋊C₄	—	34	2	no	—
911	C₄⋊C₄	—	34	2	no	—
912	C₄⋊C₄	—	34	2	no	—
913	C₄⋊C₄	—	34	2	no	—
914	C₄⋊C₄	—	34	2	no	—
915	C₄⋊C₄	—	34	2	no	—
916	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
917	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
918	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
919	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
920	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
921	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
922	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
923	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
924	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
925	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
926	C₂²⋊C₄	—	34	2	no	—
927	C₂²⋊C₄	—	34	2	no	—
928	C₂²⋊C₄	—	34	2	no	—
929	C₂²⋊C₄	—	34	2	no	—
930	C₂²⋊C₄	—	34	2	no	—
931	C₂²⋊C₄	—	34	2	no	—
932	C₂²⋊C₄	—	34	2	no	—
933	C₂²⋊C₄	—	34	2	no	—
934	C₂²⋊C₄	—	34	2	no	—
935	C₂²⋊C₄	—	34	2	no	—
936	C₂²⋊C₄	—	34	2	no	—
937	C₂²⋊C₄	—	34	2	no	—
938	C₂²⋊C₄	—	34	2	no	—
939	C₂²⋊C₄	—	34	2	no	—
940	C₂²⋊C₄	—	34	2	no	—
941	C₂²⋊C₄	—	34	2	no	—
942	C₂²⋊C₄	—	34	2	no	—
943	C₂²⋊C₄	—	34	2	no	—
944	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
945	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
946	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
947	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
948	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
949	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
950	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
951	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
952	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
953	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
954	C₄²	—	34	2	no	—
955	C₄²	—	34	2	no	—
956	C₄²	—	34	2	no	—
957	C₄²	—	34	2	no	—
958	C₄²	—	34	2	no	—
959	C₄²	—	34	2	no	—
960	C₄²	C₂×D₆₈	1	1	yes	characteristic
961	C₄²	C₂×D₆₈	1	1	yes	characteristic
962	C₄²	C₂³×D₁₇	1	1	yes	characteristic
963	C₄²	C₂³×D₁₇	1	1	yes	characteristic
964	C₄²	C₂³×D₁₇	1	1	yes	characteristic
965	C₄²	C₂³×D₁₇	1	1	yes	characteristic
966	C₂³	—	34	2	no	—
967	C₂³	—	34	2	no	—
968	C₂³	—	68	4	no	—
969	C₂³	—	136	2	no	—
970	C₂³	—	136	2	no	—
971	C₂³	C₂²×D₆₈	1	1	yes	characteristic
972	C₂³	C₂²×D₆₈	1	1	yes	characteristic
973	C₂³	C₂²×D₆₈	1	1	yes	characteristic
974	Q₈	—	4	1	no	—
975	Q₈	—	34	2	no	—
976	Q₈	—	34	2	no	—
977	Q₈	—	34	2	no	—
978	Q₈	—	34	2	no	—
979	Q₈	—	136	2	no	—
980	D₄	—	4	1	no	—
981	D₄	—	4	1	no	—
982	D₄	—	4	1	no	—
983	D₄	—	17	4	no	—
984	D₄	—	34	2	no	—
985	D₄	—	34	2	no	—
986	D₄	—	34	2	no	—
987	D₄	—	68	4	no	—
988	D₄	—	68	4	no	—
989	D₄	—	68	4	no	—
990	D₄	—	136	2	no	—
991	D₄	—	136	2	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	1	no	—
995	C₂×C₄	—	2	1	no	—
996	C₂×C₄	—	2	1	no	—
997	C₂×C₄	—	2	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	4	1	no	—
1000	C₂×C₄	—	34	2	no	—
1001	C₂×C₄	—	34	2	no	—
1002	C₂×C₄	—	34	2	no	—
1003	C₂×C₄	—	34	2	no	—
1004	C₂×C₄	—	34	2	no	—
1005	C₂×C₄	—	34	2	no	—
1006	C₂×C₄	—	68	4	no	—
1007	C₂×C₄	—	68	4	no	—
1008	C₂×C₄	—	136	2	no	—
1009	C₂×C₄	—	136	2	no	—
1010	C₂×C₄	—	136	2	no	—
1011	C₂×C₄	—	136	2	no	—
1012	C₂×C₄	—	136	2	no	—
1013	C₂×C₄	—	136	2	no	—
1014	C₂×C₄	—	136	2	no	—
1015	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1016	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1017	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1018	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1019	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1020	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1021	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1022	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1023	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1024	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1025	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₁₇	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	2	1	no	—
1031	C₈	—	2	1	no	—
1032	C₈	—	2	1	no	—
1033	C₈	—	2	1	no	—
1034	C₈	#41×D₁₇	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	2	1	no	—
1039	C₂²	—	2	1	no	—
1040	C₂²	—	2	1	no	—
1041	C₂²	—	2	1	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	272	4	no	—
1045	C₂²	—	34	4	no	—
1046	C₂²	—	68	2	no	—
1047	C₂²	—	68	2	no	—
1048	C₂²	—	68	2	no	—
1049	C₂²	—	68	2	no	—
1050	C₂²	—	68	2	no	—
1051	C₂²	C₂³×D₆₈	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	2	1	no	—
1058	C₄	—	2	1	no	—
1059	C₄	—	2	1	no	—
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	68	2	no	—
1064	C₄	—	68	2	no	—
1065	C₄	—	68	2	no	—
1066	C₄	—	68	2	no	—
1067	C₄	—	68	2	no	—
1068	C₄	—	68	2	no	—
1069	C₄	C₂×#41×D₁₇	1	1	yes	characteristic
1070	C₄	#11763645	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	4	1	no	—
1073	C₂	—	4	1	no	—
1074	C₂	—	68	4	no	—
1075	C₂	—	136	2	no	—
1076	C₂	#41×D₆₈	1	1	yes	characteristic
1077	C₂	#14543558	1	1	yes	characteristic
1078	C₂	#14543558	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×D₆₈
commutator, cosocle	C₂×C₄×C₁₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₁₇
Fitting	C₁₇×#2966	C₂
socle	C₂²×C₁₇	C₂³×D₄
hypercenter	#2966	D₁₇
hypocenter	C₁₇	#61487
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #2966

Complements

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

N	H ≅ G/N	type
1. #14542856	C₂	semidirect
2. #14541773	C₂	semidirect
3. #14541652	C₂	semidirect
4. #14541613	C₂	semidirect
5. #14541215	C₂	semidirect
6. #14541187	C₂	semidirect
7. #14541153	C₂	semidirect
8. #14541002	C₂	semidirect
9. #14540822	C₂	semidirect
10. #14540762	C₂	semidirect
11. #14540506	C₂	semidirect
12. #14540471	C₂	semidirect
13. #14540471	C₂	semidirect
14. #14539443	C₂	semidirect
15. #14539423	C₂	semidirect
16. #14539354	C₂	semidirect
17. #14539063	C₂	semidirect
18. #14539037	C₂	semidirect
19. #14538895	C₂	semidirect
20. #14537661	C₂	semidirect
21. #14537637	C₂	semidirect
22. C₄×#10587590	C₂	semidirect
23. C₁₇×#2966	C₂	semidirect
27. #11763532	C₂²	semidirect
29. #11763519	C₂²	semidirect
30. #11763505	C₂²	semidirect
36. #11763464	C₂²	semidirect
39. #11763430	C₂²	semidirect
43. #11763343	C₂²	semidirect
46. #11763289	C₂²	semidirect
48. C₄×#63252	C₂²	semidirect
49. #11763214	C₂²	semidirect
50. #11763211	C₂²	semidirect
51. #11763211	C₂²	semidirect
54. #11763189	C₂²	semidirect
55. #11763178	C₂²	semidirect
56. #11763169	C₂²	semidirect
57. #11763164	C₂²	semidirect
60. #11763151	C₂²	semidirect
61. #11763140	C₂²	semidirect
62. #11763134	C₂²	semidirect
63. #11763128	C₂²	semidirect
64. #11763117	C₂²	semidirect
65. #11763110	C₂²	semidirect
66. #11763110	C₂²	semidirect
67. #11763110	C₂²	semidirect
68. #11763100	C₂²	semidirect
69. #11763095	C₂²	semidirect
71. #11763055	C₂²	semidirect
74. #11763050	C₂²	semidirect
75. #11763050	C₂²	semidirect
78. #11763038	C₂²	semidirect
79. #11763032	C₂²	semidirect
80. #11763032	C₂²	semidirect
83. #11763015	C₂²	semidirect
84. #11763015	C₂²	semidirect
85. #11762973	C₂²	semidirect
86. #11762973	C₂²	semidirect
93. #11762917	C₂²	semidirect
94. #11762911	C₂²	semidirect
95. #11762911	C₂²	semidirect
96. #11762911	C₂²	semidirect
97. C₄×Dic₆₈	C₂²	semidirect
98. C₄×Dic₆₈	C₂²	semidirect
99. C₄×Dic₆₈	C₂²	semidirect
100. C₄×Dic₆₈	C₂²	semidirect
101. C₄×#63219	C₂²	semidirect
102. C₄×#63219	C₂²	semidirect
103. C₄×#63219	C₂²	semidirect
111. #11762847	C₂²	semidirect
112. C₂×#10587489	C₂²	semidirect
114. #11762811	C₂²	semidirect
115. #11762806	C₂²	semidirect
117. C₁₇×#446	C₂²	semidirect
118. C₈×Q₈×C₁₇	C₂²	semidirect
121. C₁₇×#435	C₂²	semidirect
124. C₈×D₄×C₁₇	C₂²	semidirect
126. C₁₇×#433	C₂²	semidirect
127. C₁₇×#432	C₂²	semidirect
129. C₁₇×#405	C₂²	semidirect
130. C₂×C₄×C₈×C₁₇	C₂²	semidirect
515. #2966	D₁₇	semidirect
623. #446	C₂×D₁₇	semidirect
624. C₈×Q₈	C₂×D₁₇	semidirect
646. #435	C₂×D₁₇	semidirect
649. C₈×D₄	C₂×D₁₇	semidirect
651. #433	C₂×D₁₇	semidirect
652. #432	C₂×D₁₇	semidirect
660. #405	C₂×D₁₇	semidirect
661. C₂×C₄×C₈	C₂×D₁₇	semidirect
836. C₁₇	#61487	semidirect

Maximal subgroups

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

subgroup	index
#14542856	2
#14541773	2
#14541652	2
#14541613	2
#14541215	2
#14541187	2
#14541153	2
#14541002	2
#14540822	2
#14540762	2
#14540506	2
#14540471	2
#14539443	2
#14539423	2
#14539354	2
#14539063	2
#14539037	2
#14538895	2
#14537661	2
#14537637	2
C₄×#10587590	2
C₁₇×#2966	2
#61487	17