Subgroups — #17916709

Order 4352.

1910 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14542728	C₂	1	2	yes	maximal, complemented
2	#14541797	C₂	1	1	yes	maximal, characteristic, complemented
3	#14541652	C₂	1	1	yes	maximal, characteristic, complemented
4	#14541539	C₂	1	2	yes	maximal, complemented
5	#14541187	C₂	1	1	yes	maximal, characteristic, complemented
6	#14541153	C₂	1	1	yes	maximal, characteristic, complemented
7	#14541132	C₂	1	1	yes	maximal, characteristic, complemented
8	#14540987	C₂	1	2	yes	maximal, complemented
9	#14540807	C₂	1	2	yes	maximal, complemented
10	#14540747	C₂	1	2	yes	maximal, complemented
11	#14540471	C₂	1	1	yes	maximal, characteristic, complemented
12	#14540471	C₂	1	1	yes	maximal, characteristic, complemented
13	D₄×D₁₃₆	C₂	1	1	yes	maximal, characteristic, complemented
14	#14539434	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	#14538985	C₂	1	2	yes	maximal, complemented
18	#14538970	C₂	1	2	yes	maximal, complemented
19	#14538924	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	C₂×C₄×D₁₃₆	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	C₂²×D₁₃₆	C₂²	1	1	yes	characteristic
26	C₂²×D₁₃₆	C₂²	1	1	yes	characteristic
27	#11763544	C₂²	1	2	yes	complemented
28	#11763519	C₂²	1	2	yes	complemented
29	#11763510	—	2	2	no	—
30	#11763505	C₂²	1	2	yes	complemented
31	#11763499	C₂²	1	2	yes	—
32	#11763486	—	2	2	no	—
33	#11763484	—	2	2	no	—
34	#11763463	C₂²	1	2	yes	complemented
35	#11763455	C₂²	1	2	yes	complemented
36	#11763455	C₂²	1	2	yes	complemented
37	#11763448	—	2	2	no	—
38	D₄×D₆₈	C₂²	1	2	yes	—
39	#11763430	C₂²	1	2	yes	complemented
40	#11763414	C₂²	1	2	yes	complemented
41	#11763407	—	2	2	no	—
42	#11763393	—	2	2	no	—
43	#11763343	C₂²	1	2	yes	complemented
44	#11763317	—	2	2	no	—
45	#123×D₁₇	—	2	2	no	—
46	#11763289	C₂²	1	2	yes	complemented
47	#11763283	C₂²	1	2	yes	complemented
48	C₂×C₄×D₆₈	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, complemented
53	#11763193	C₂²	1	1	yes	characteristic, complemented
54	#11763186	C₂²	1	1	yes	characteristic
55	#11763174	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	complemented
59	#11763140	C₂²	1	2	yes	complemented
60	#11763134	C₂²	1	2	yes	complemented
61	#11763128	C₂²	1	2	yes	complemented
62	#11763123	C₂²	1	2	yes	complemented
63	#11763123	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	#11763090	C₂²	1	2	yes	complemented
70	#11763062	C₂²	1	2	yes	complemented
71	#11763055	C₂²	1	2	yes	complemented
72	#11763050	C₂²	1	1	yes	characteristic, complemented
73	#11763050	C₂²	1	1	yes	characteristic, complemented
74	#11763045	C₂²	1	1	yes	characteristic
75	#11763045	C₂²	1	1	yes	characteristic
76	#11763045	C₂²	1	1	yes	characteristic, complemented
77	#11763045	C₂²	1	1	yes	characteristic, complemented
78	#11763038	C₂²	1	2	yes	complemented
79	#11763025	C₂²	1	2	yes	complemented
80	#11763025	C₂²	1	2	yes	complemented
81	#11763025	C₂²	1	2	yes	complemented
82	#11763025	C₂²	1	2	yes	complemented
83	#11763010	C₂²	1	2	yes	complemented
84	#11763005	C₂²	1	2	yes	—
85	#11762962	C₂²	1	2	yes	complemented
86	#11762962	C₂²	1	2	yes	complemented
87	#11762956	C₂²	1	2	yes	complemented
88	#11762956	C₂²	1	2	yes	complemented
89	#11762945	C₂²	1	2	yes	—
90	#11762945	C₂²	1	2	yes	—
91	#11762922	C₂²	1	2	yes	complemented
92	#11762922	C₂²	1	2	yes	complemented
93	#11762922	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×#63219	C₂²	1	2	yes	complemented
100	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
101	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
102	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
103	C₄×D₁₃₆	C₂²	1	1	yes	characteristic
104	C₄×D₁₃₆	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₁₃₆	C₂²	1	1	yes	characteristic, complemented
106	C₄×D₁₃₆	C₂²	1	2	yes	complemented
107	C₄×D₁₃₆	C₂²	1	2	yes	complemented
108	C₄×D₁₃₆	C₂²	1	1	yes	characteristic, complemented
109	C₄×D₁₃₆	C₂²	1	1	yes	characteristic, complemented
110	#11762847	C₂²	1	1	yes	characteristic, complemented
111	C₂×#10587489	C₂²	1	1	yes	characteristic, complemented
112	C₂×#10587489	C₂²	1	1	yes	characteristic, complemented
113	#11762815	C₂²	1	2	yes	complemented
114	#11762811	C₂²	1	2	yes	complemented
115	C₂×#10587492	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, complemented
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, complemented
124	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
125	C₁₇×#433	C₂²	1	1	yes	characteristic, complemented
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, complemented
129	C₁₇×#405	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#63254	—	2	2	no	—
132	C₂×D₄×D₁₇	—	2	2	no	—
133	C₂×#63252	C₂³	1	2	yes	—
134	C₂²×D₆₈	C₂³	1	2	yes	—
135	C₂²×D₆₈	C₂³	1	2	yes	—
136	C₂²×C₄×D₁₇	—	2	2	no	—
137	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
138	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
139	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
140	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
141	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
142	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₁₇×#126	D₄	1	1	yes	characteristic
144	C₁₇×#126	D₄	1	1	yes	characteristic
145	C₁₇×#125	D₄	1	1	yes	characteristic
146	C₁₇×#124	D₄	1	1	yes	characteristic
147	C₁₇×#123	D₄	1	1	yes	characteristic
148	C₁₇×#123	D₄	1	1	yes	characteristic
149	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
150	C₁₇×#121	D₄	1	1	yes	characteristic
151	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
153	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
154	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
155	C₁₇×#117	C₂³	1	1	yes	characteristic
156	C₁₇×#117	C₂³	1	1	yes	characteristic
157	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
158	#10587633	—	2	2	no	—
159	#10587632	—	2	2	no	—
160	#10587625	—	2	2	no	—
161	#10587623	—	2	2	no	—
162	#10587623	—	2	2	no	—
163	#10587621	—	2	2	no	—
164	#10587616	C₂³	1	2	yes	—
165	#10587616	C₂³	1	2	yes	—
166	#10587616	C₂³	1	2	yes	—
167	#10587616	C₂³	1	2	yes	—
168	#10587615	—	2	2	no	—
169	C₄×C₂²⋊D₁₇	—	2	2	no	—
170	C₂×#63227	—	2	2	no	—
171	#10587612	C₂³	1	2	yes	—
172	C₂×C₄⋊Dic₁₇	C₂³	1	2	yes	—
173	C₂×C₄⋊Dic₁₇	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	#10587590	—	2	4	no	—
178	C₂×D₁₃₆	—	2	4	no	—
179	C₂×D₁₃₆	—	2	4	no	—
180	C₂×D₁₃₆	C₂³	1	2	yes	—
181	C₂×D₁₃₆	C₂³	1	2	yes	—
182	C₂×D₁₃₆	C₂³	1	1	yes	characteristic
183	C₂×D₁₃₆	C₂³	1	1	yes	characteristic
184	C₂×D₁₃₆	C₂³	1	2	yes	—
185	C₂×D₁₃₆	C₂³	1	1	yes	characteristic
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	#10587583	—	2	2	no	—
192	#10587582	—	2	2	no	—
193	#10587582	—	2	2	no	—
194	#10587582	—	2	2	no	—
195	#10587581	—	2	2	no	—
196	#10587580	—	2	2	no	—
197	#10587580	—	2	2	no	—
198	#10587580	—	2	2	no	—
199	#10587580	—	2	2	no	—
200	#10587580	—	2	2	no	—
201	#10587580	—	2	2	no	—
202	#10587579	—	2	2	no	—
203	#10587579	—	2	2	no	—
204	#10587579	—	2	2	no	—
205	#10587578	—	2	2	no	—
206	C₄⋊C₄×D₁₇	—	2	2	no	—
207	C₄⋊C₄×D₁₇	—	2	2	no	—
208	#10587575	—	2	2	no	—
209	#10587572	—	2	2	no	—
210	#10587572	—	2	2	no	—
211	#10587571	—	2	2	no	—
212	#10587570	—	2	2	no	—
213	#10587570	—	2	2	no	—
214	#10587570	—	2	2	no	—
215	#10587570	—	2	2	no	—
216	#10587569	—	2	2	no	—
217	#10587569	—	2	2	no	—
218	#10587568	—	2	2	no	—
219	#10587568	—	2	2	no	—
220	#10587567	—	2	2	no	—
221	#10587567	—	2	2	no	—
222	#10587567	—	2	2	no	—
223	C₂²⋊C₄×D₁₇	—	2	2	no	—
224	C₂²⋊C₄×D₁₇	—	2	2	no	—
225	C₂²⋊C₄×D₁₇	—	2	2	no	—
226	C₂²⋊C₄×D₁₇	—	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	#10587560	C₂³	1	2	yes	—
233	C₄×D₆₈	—	2	2	no	—
234	C₄×D₆₈	—	2	2	no	—
235	C₄×D₆₈	C₂³	1	2	yes	—
236	C₄×D₆₈	C₂³	1	2	yes	—
237	C₄×D₆₈	C₂³	1	2	yes	—
238	C₄×D₆₈	C₂³	1	2	yes	—
239	C₄×D₆₈	C₂³	1	2	yes	—
240	C₄×D₆₈	C₂³	1	2	yes	—
241	C₄×D₆₈	C₂³	1	2	yes	—
242	C₄×D₆₈	C₂³	1	2	yes	—
243	#10587558	—	2	2	no	—
244	#10587556	C₂³	1	2	yes	—
245	#10587556	C₂³	1	2	yes	—
246	#10587555	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	#10587492	C₂³	1	2	yes	—
280	#10587492	C₂³	1	2	yes	—
281	#10587492	C₂³	1	2	yes	—
282	#10587492	C₂³	1	2	yes	—
283	#10587489	C₂³	1	1	yes	characteristic
284	#10587489	C₂³	1	1	yes	characteristic
285	#10587489	C₂³	1	1	yes	characteristic
286	#10587489	C₂³	1	2	yes	—
287	#10587489	C₂³	1	2	yes	—
288	#10587489	C₂³	1	2	yes	—
289	#10587489	C₂³	1	1	yes	characteristic
290	#10587488	C₂³	1	2	yes	—
291	#10587488	C₂³	1	2	yes	—
292	#10587488	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	C₂³×D₁₇	—	2	2	no	—
299	C₂×Q₈×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	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
306	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₂²⋊D₁₇	—	2	2	no	—
309	C₂×C₂²⋊D₁₇	—	2	2	no	—
310	C₂×C₂²⋊D₁₇	—	2	2	no	—
311	C₂×C₂²⋊D₁₇	—	2	2	no	—
312	C₂×C₂²⋊D₁₇	—	2	2	no	—
313	C₂²×Dic₁₇	—	2	2	no	—
314	C₂²×Dic₁₇	—	2	2	no	—
315	#63254	—	8	4	no	—
316	D₄×D₁₇	—	8	4	no	—
317	#63252	—	2	4	no	—
318	#63252	—	4	2	no	—
319	C₂×D₆₈	—	2	4	no	—
320	C₂×D₆₈	—	2	4	no	—
321	C₂×D₆₈	—	2	2	no	—
322	C₂×D₆₈	—	2	2	no	—
323	C₂×D₆₈	—	2	2	no	—
324	C₂×D₆₈	—	2	2	no	—
325	C₂×D₆₈	—	4	2	no	—
326	C₂×D₆₈	—	4	2	no	—
327	C₂×D₆₈	C₂⁴	1	2	yes	—
328	C₂×D₆₈	C₂⁴	1	2	yes	—
329	C₂×D₆₈	C₂⁴	1	2	yes	—
330	C₂×C₄×D₁₇	—	2	2	no	—
331	C₂×C₄×D₁₇	—	2	2	no	—
332	C₂×C₄×D₁₇	—	2	2	no	—
333	C₂×C₄×D₁₇	—	2	2	no	—
334	C₂×C₄×D₁₇	—	2	2	no	—
335	C₂×C₄×D₁₇	—	2	2	no	—
336	C₂×C₄×D₁₇	—	2	2	no	—
337	C₂×C₄×D₁₇	—	2	2	no	—
338	C₂×C₄×D₁₇	—	2	2	no	—
339	C₂×C₄×D₁₇	—	8	4	no	—
340	C₂×Dic₃₄	—	2	2	no	—
341	C₂×Dic₃₄	C₂⁴	1	2	yes	—
342	M₁₆×C₁₇	—	4	1	no	—
343	M₁₆×C₁₇	—	4	1	no	—
344	C₂×C₈×C₁₇	—	2	2	no	—
345	C₂×C₈×C₁₇	—	2	2	no	—
346	C₂×C₈×C₁₇	—	2	2	no	—
347	C₂×C₈×C₁₇	—	4	1	no	—
348	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
351	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
357	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
358	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
360	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
361	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
362	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
364	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
365	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
366	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
368	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
371	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
372	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
374	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
375	C₂²⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
378	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
379	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
380	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
381	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
382	C₂²⋊Dic₁₇	—	2	2	no	—
383	C₂²⋊Dic₁₇	—	2	2	no	—
384	C₂²⋊Dic₁₇	—	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	#63227	—	2	2	no	—
391	#63227	—	2	2	no	—
392	#63227	—	2	2	no	—
393	#63227	—	2	2	no	—
394	#63227	—	2	2	no	—
395	#63227	—	2	2	no	—
396	#63227	—	2	2	no	—
397	#63227	—	2	2	no	—
398	#63227	—	2	2	no	—
399	#63227	—	2	2	no	—
400	#63227	—	2	2	no	—
401	C₄⋊Dic₁₇	—	2	2	no	—
402	C₄⋊Dic₁₇	—	2	2	no	—
403	C₄⋊Dic₁₇	—	2	2	no	—
404	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
405	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
406	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
407	C₄⋊Dic₁₇	C₂⁴	1	2	yes	—
408	#63225	—	2	2	no	—
409	#63225	—	2	2	no	—
410	#63225	—	2	2	no	—
411	#63225	—	2	2	no	—
412	#63225	—	2	2	no	—
413	#63225	—	2	2	no	—
414	#63225	—	2	2	no	—
415	#63225	—	2	2	no	—
416	C₄×Dic₁₇	—	2	2	no	—
417	C₄×Dic₁₇	—	2	2	no	—
418	C₄×Dic₁₇	—	2	2	no	—
419	Dic₆₈	—	2	2	no	—
420	D₁₃₆	—	2	4	no	—
421	D₁₃₆	—	2	4	no	—
422	D₁₃₆	—	2	2	no	—
423	D₁₃₆	—	2	2	no	—
424	D₁₃₆	—	4	2	no	—
425	D₁₃₆	#41	1	4	yes	complemented
426	#63219	—	2	4	no	—
427	#63219	—	4	2	no	—
428	#63219	—	4	2	no	—
429	#61471	—	17	1	no	maximal, Sylow
430	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₁₇	—	2	2	no	—
434	C₂²×D₁₇	—	2	2	no	—
435	C₂²×D₁₇	—	2	2	no	—
436	C₂²×D₁₇	—	4	4	no	—
437	C₂²×D₁₇	—	4	4	no	—
438	C₂²×D₁₇	—	4	4	no	—
439	C₂²×D₁₇	—	8	2	no	—
440	C₂²×D₁₇	—	8	2	no	—
441	C₂²×D₁₇	—	8	2	no	—
442	Q₈×C₁₇	—	4	1	no	—
443	D₄×C₁₇	—	2	2	no	—
444	D₄×C₁₇	—	2	2	no	—
445	D₄×C₁₇	—	4	1	no	—
446	C₂×C₄×C₁₇	—	2	2	no	—
447	C₂×C₄×C₁₇	—	2	1	no	—
448	C₂×C₄×C₁₇	—	2	1	no	—
449	C₂×C₄×C₁₇	—	2	1	no	—
450	C₂×C₄×C₁₇	—	2	1	no	—
451	C₂×C₄×C₁₇	—	2	1	no	—
452	C₂×C₄×C₁₇	—	2	1	no	—
453	C₂×C₄×C₁₇	—	4	1	no	—
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	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
461	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
462	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
463	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
466	C₂²⋊D₁₇	—	4	4	no	—
467	C₂²⋊D₁₇	—	4	4	no	—
468	C₂²⋊D₁₇	—	8	2	no	—
469	C₂²⋊D₁₇	—	8	2	no	—
470	C₂²⋊D₁₇	—	8	2	no	—
471	C₂×Dic₁₇	—	2	2	no	—
472	C₂×Dic₁₇	—	2	2	no	—
473	C₂×Dic₁₇	—	2	2	no	—
474	C₂×Dic₁₇	—	2	2	no	—
475	C₂×Dic₁₇	—	2	2	no	—
476	C₂×Dic₁₇	—	4	4	no	—
477	C₂×Dic₁₇	—	8	2	no	—
478	D₆₈	—	2	2	no	—
479	D₆₈	—	2	2	no	—
480	D₆₈	—	2	2	no	—
481	D₆₈	—	2	2	no	—
482	D₆₈	—	2	2	no	—
483	D₆₈	—	4	4	no	—
484	D₆₈	—	4	4	no	—
485	D₆₈	—	8	2	no	—
486	D₆₈	—	8	2	no	—
487	D₆₈	C₂×#41	1	4	yes	—
488	C₄×D₁₇	—	4	4	no	—
489	C₄×D₁₇	—	8	2	no	—
490	C₄×D₁₇	—	8	2	no	—
491	C₄×D₁₇	—	8	2	no	—
492	C₄×D₁₇	—	8	2	no	—
493	C₄×D₁₇	—	8	2	no	—
494	C₄×D₁₇	—	8	2	no	—
495	C₄×D₁₇	—	8	2	no	—
496	C₄×D₁₇	—	8	2	no	—
497	Dic₃₄	—	2	2	no	—
498	Dic₃₄	—	2	2	no	—
499	Dic₃₄	—	8	2	no	—
500	C₈×C₁₇	—	2	1	no	—
501	C₈×C₁₇	—	2	1	no	—
502	C₈×C₁₇	—	2	1	no	—
503	C₈×C₁₇	—	2	1	no	—
504	C₈×C₁₇	—	2	1	no	—
505	C₈×C₁₇	—	2	1	no	—
506	C₈×C₁₇	—	2	1	no	—
507	C₈×C₁₇	C₂×#41	1	2	yes	—
508	#3513	—	17	2	no	—
509	#3396	—	17	1	no	—
510	#3380	—	17	1	no	—
511	#3370	—	17	2	no	—
512	#3339	—	17	1	no	—
513	#3336	—	17	1	no	—
514	#3334	—	17	1	no	—
515	#3322	—	17	2	no	—
516	#3310	—	17	2	no	—
517	#3306	—	17	2	no	—
518	#3280	—	17	1	no	—
519	#3280	—	17	1	no	—
520	D₄×D₈	—	17	1	no	—
521	#3176	—	17	1	no	—
522	#3175	—	17	1	no	—
523	#3168	—	17	1	no	—
524	#3119	—	17	2	no	—
525	#3118	—	17	2	no	—
526	#3114	—	17	2	no	—
527	#2966	D₁₇	1	1	yes	characteristic, complemented
528	#2951	—	17	1	no	—
529	#2948	—	17	1	no	—
530	C₂×C₄×D₈	—	17	1	no	—
531	C₂²×C₁₇	—	2	1	no	—
532	C₂²×C₁₇	—	2	1	no	—
533	C₂²×C₁₇	—	2	1	no	—
534	C₂²×C₁₇	—	2	1	no	—
535	C₂²×C₁₇	—	2	1	no	—
536	C₂²×C₁₇	—	2	1	no	—
537	C₂²×C₁₇	—	2	1	no	—
538	C₂²×C₁₇	—	2	1	no	—
539	C₂²×C₁₇	#576	1	2	yes	—
540	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
541	C₂×D₁₇	—	2	4	no	—
542	C₂×D₁₇	—	4	2	no	—
543	C₂×D₁₇	—	4	2	no	—
544	C₂×D₁₇	—	4	2	no	—
545	C₂×D₁₇	—	4	2	no	—
546	C₂×D₁₇	—	4	2	no	—
547	C₂×D₁₇	—	4	2	no	—
548	C₂×D₁₇	—	4	2	no	—
549	C₂×D₁₇	—	4	2	no	—
550	C₂×D₁₇	—	8	8	no	—
551	C₂×D₁₇	—	16	4	no	—
552	C₄×C₁₇	—	2	1	no	—
553	C₄×C₁₇	—	2	1	no	—
554	C₄×C₁₇	—	2	1	no	—
555	C₄×C₁₇	—	2	1	no	—
556	C₄×C₁₇	—	2	1	no	—
557	C₄×C₁₇	—	2	1	no	—
558	C₄×C₁₇	—	2	1	no	—
559	C₄×C₁₇	—	2	1	no	—
560	C₄×C₁₇	—	2	1	no	—
561	C₄×C₁₇	—	2	1	no	—
562	C₄×C₁₇	—	2	1	no	—
563	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
564	C₄×C₁₇	#585	1	1	yes	characteristic
565	Dic₁₇	—	4	2	no	—
566	Dic₁₇	—	4	2	no	—
567	Dic₁₇	—	4	2	no	—
568	Dic₁₇	—	4	2	no	—
569	Dic₁₇	—	4	2	no	—
570	C₂×#135	—	17	1	no	—
571	C₂²×D₈	—	17	1	no	—
572	C₂²×D₈	—	17	1	no	—
573	#559	—	17	2	no	—
574	#554	—	17	2	no	—
575	#553	—	17	2	no	—
576	#553	—	34	2	no	—
577	#552	—	17	2	no	—
578	#551	—	34	2	no	—
579	#551	—	34	2	no	—
580	#547	—	17	2	no	—
581	#546	—	17	2	no	—
582	#546	—	17	2	no	—
583	#546	—	34	2	no	—
584	D₄²	—	17	2	no	—
585	#542	—	17	2	no	—
586	#540	—	17	2	no	—
587	#539	—	34	2	no	—
588	#538	—	34	2	no	—
589	#529	—	17	2	no	—
590	#529	C₂×D₁₇	1	1	yes	characteristic
591	#525	—	34	2	no	—
592	C₂×#123	—	34	2	no	—
593	#520	—	17	2	no	—
594	#518	—	17	2	no	—
595	C₂×C₄×D₄	—	17	2	no	—
596	#500	—	17	1	no	—
597	#499	—	17	1	no	—
598	#499	—	17	1	no	—
599	#495	—	17	1	no	—
600	#495	—	17	1	no	—
601	#493	—	17	1	no	—
602	#490	—	17	2	no	—
603	#489	—	17	2	no	—
604	#488	—	17	2	no	—
605	#485	—	17	2	no	—
606	#483	—	17	2	no	—
607	#482	—	17	2	no	—
608	#481	—	17	2	no	—
609	#480	—	17	2	no	—
610	#480	—	17	2	no	—
611	#479	—	17	2	no	—
612	#478	—	17	2	no	—
613	#478	—	17	2	no	—
614	#478	—	17	2	no	—
615	#476	—	17	2	no	—
616	#474	—	17	2	no	—
617	#469	—	17	2	no	—
618	#468	—	17	2	no	—
619	#467	—	17	1	no	—
620	#467	—	17	1	no	—
621	#466	—	17	1	no	—
622	#466	—	17	1	no	—
623	#466	—	17	1	no	—
624	#466	—	17	1	no	—
625	#465	—	17	2	no	—
626	#463	—	17	2	no	—
627	#463	—	17	2	no	—
628	#463	—	17	2	no	—
629	#463	—	17	2	no	—
630	#460	—	17	2	no	—
631	#459	—	17	2	no	—
632	#450	—	17	2	no	—
633	#450	—	17	2	no	—
634	#449	—	17	2	no	—
635	#449	—	17	2	no	—
636	#447	—	17	2	no	—
637	#447	—	17	2	no	—
638	#446	C₂×D₁₇	1	1	yes	characteristic, complemented
639	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
640	#442	—	17	2	no	—
641	#442	—	17	2	no	—
642	#442	—	17	2	no	—
643	#440	—	17	2	no	—
644	#440	—	17	2	no	—
645	#440	—	17	2	no	—
646	C₄×Q₁₆	—	17	1	no	—
647	C₄×Q₁₆	—	17	1	no	—
648	C₄×SD₁₆	—	17	2	no	—
649	C₄×D₈	—	17	1	no	—
650	C₄×D₈	—	17	1	no	—
651	C₄×D₈	—	17	2	no	—
652	C₄×D₈	—	17	2	no	—
653	C₄×D₈	—	17	1	no	—
654	C₄×D₈	—	17	1	no	—
655	C₄×D₈	—	17	1	no	—
656	C₄×D₈	—	17	1	no	—
657	C₄×D₈	—	17	1	no	—
658	C₄×D₈	—	17	1	no	—
659	#436	C₂×D₁₇	1	1	yes	characteristic, complemented
660	#435	C₂×D₁₇	1	1	yes	characteristic
661	#435	C₂×D₁₇	1	1	yes	characteristic, complemented
662	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
663	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
664	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
665	#433	C₂×D₁₇	1	1	yes	characteristic, complemented
666	#433	C₂×D₁₇	1	1	yes	characteristic, complemented
667	#432	C₂×D₁₇	1	1	yes	characteristic, complemented
668	#427	—	17	1	no	—
669	C₂×#107	—	17	1	no	—
670	C₂×#107	—	17	1	no	—
671	#418	—	17	2	no	—
672	#417	—	17	2	no	—
673	C₂×#102	—	17	2	no	—
674	#405	C₂×D₁₇	1	1	yes	characteristic, complemented
675	#405	C₂×D₁₇	1	1	yes	characteristic, complemented
676	C₂×C₄×C₈	C₂×D₁₇	1	1	yes	characteristic, complemented
677	C₂×C₁₇	—	2	2	no	—
678	C₂×C₁₇	—	4	1	no	—
679	C₂×C₁₇	—	4	1	no	—
680	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
681	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
682	C₂×C₁₇	#3584	1	1	yes	characteristic
683	D₁₇	—	4	4	no	—
684	D₁₇	—	8	2	no	—
685	D₁₇	—	8	2	no	—
686	C₂×#41	—	17	2	no	—
687	C₂×#41	—	34	2	no	—
688	C₂²×D₄	—	17	2	no	—
689	C₂²×D₄	—	17	2	no	—
690	C₂²×D₄	—	34	2	no	—
691	C₂³×C₄	—	34	2	no	—
692	#135	—	34	4	no	—
693	C₂×Q₁₆	—	17	1	no	—
694	C₂×SD₁₆	—	17	2	no	—
695	C₂×SD₁₆	—	17	2	no	—
696	C₂×SD₁₆	—	17	2	no	—
697	C₂×D₈	—	17	1	no	—
698	C₂×D₈	—	17	2	no	—
699	C₂×D₈	—	17	1	no	—
700	C₂×D₈	—	17	1	no	—
701	C₂×D₈	—	17	2	no	—
702	C₂×D₈	—	17	2	no	—
703	C₂×D₈	—	34	4	no	—
704	C₂×D₈	—	34	4	no	—
705	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
706	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
707	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
708	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
709	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
710	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
711	C₄⋊Q₈	—	17	2	no	—
712	#127	—	17	2	no	—
713	#126	—	34	2	no	—
714	#126	—	34	2	no	—
715	#126	—	34	2	no	—
716	#126	—	34	2	no	—
717	#126	D₆₈	1	1	yes	characteristic
718	#126	D₆₈	1	1	yes	characteristic
719	#125	—	17	2	no	—
720	#125	—	17	2	no	—
721	#125	—	34	2	no	—
722	#125	D₆₈	1	1	yes	characteristic
723	#124	—	17	2	no	—
724	#124	—	17	2	no	—
725	#124	—	34	2	no	—
726	#124	—	34	2	no	—
727	#124	D₆₈	1	1	yes	characteristic
728	#123	—	34	2	no	—
729	#123	—	34	2	no	—
730	#123	—	34	2	no	—
731	#123	—	34	2	no	—
732	#123	—	34	2	no	—
733	#123	—	34	2	no	—
734	#123	—	34	2	no	—
735	#123	—	34	2	no	—
736	#123	—	34	2	no	—
737	#123	—	34	2	no	—
738	#123	—	34	2	no	—
739	#123	—	34	2	no	—
740	#123	D₆₈	1	1	yes	characteristic
741	#123	D₆₈	1	1	yes	characteristic
742	C₂²⋊Q₈	—	17	2	no	—
743	C₂²⋊Q₈	—	17	2	no	—
744	C₂²⋊Q₈	—	34	2	no	—
745	C₂²⋊Q₈	—	34	2	no	—
746	C₂²⋊Q₈	—	34	2	no	—
747	C₂²⋊Q₈	—	34	2	no	—
748	C₂²⋊Q₈	—	34	2	no	—
749	C₂²⋊Q₈	D₆₈	1	1	yes	characteristic
750	#121	—	17	2	no	—
751	#121	—	17	2	no	—
752	#121	—	17	2	no	—
753	#121	—	17	2	no	—
754	#121	—	34	2	no	—
755	#121	—	34	2	no	—
756	#121	—	34	2	no	—
757	#121	—	34	2	no	—
758	#121	—	34	2	no	—
759	#121	—	34	2	no	—
760	#121	D₆₈	1	1	yes	characteristic
761	#120	—	34	2	no	—
762	#120	—	34	2	no	—
763	#120	—	34	2	no	—
764	#120	—	34	2	no	—
765	C₄×Q₈	—	17	2	no	—
766	C₄×Q₈	—	17	2	no	—
767	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
768	C₄×D₄	—	17	2	no	—
769	C₄×D₄	—	17	2	no	—
770	C₄×D₄	—	17	2	no	—
771	C₄×D₄	—	17	2	no	—
772	C₄×D₄	—	17	2	no	—
773	C₄×D₄	—	17	2	no	—
774	C₄×D₄	—	17	2	no	—
775	C₄×D₄	—	17	2	no	—
776	C₄×D₄	—	34	2	no	—
777	C₄×D₄	—	34	2	no	—
778	C₄×D₄	—	34	2	no	—
779	C₄×D₄	—	34	2	no	—
780	C₄×D₄	—	34	2	no	—
781	C₄×D₄	—	34	2	no	—
782	C₄×D₄	—	34	2	no	—
783	C₄×D₄	—	34	2	no	—
784	C₄×D₄	—	34	2	no	—
785	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
786	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
787	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
788	#117	—	17	2	no	—
789	#117	—	34	2	no	—
790	#117	—	34	2	no	—
791	#117	—	34	2	no	—
792	#117	C₂²×D₁₇	1	1	yes	characteristic
793	#117	C₂²×D₁₇	1	1	yes	characteristic
794	C₂×C₄⋊C₄	—	17	2	no	—
795	C₂×C₄⋊C₄	—	17	2	no	—
796	C₂×C₄⋊C₄	—	34	2	no	—
797	C₂×C₄⋊C₄	—	34	2	no	—
798	C₂×C₂²⋊C₄	—	34	2	no	—
799	C₂×C₂²⋊C₄	—	34	2	no	—
800	C₂×C₂²⋊C₄	—	34	2	no	—
801	C₂×C₂²⋊C₄	—	34	2	no	—
802	C₂×C₂²⋊C₄	—	34	2	no	—
803	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
804	#107	—	17	1	no	—
805	#107	—	17	1	no	—
806	#107	—	17	2	no	—
807	#107	—	17	1	no	—
808	#107	—	17	2	no	—
809	#107	—	17	1	no	—
810	#107	—	17	2	no	—
811	#106	—	17	2	no	—
812	#106	—	17	2	no	—
813	#106	—	17	2	no	—
814	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
815	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
816	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
817	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
818	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
819	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
820	#103	—	17	2	no	—
821	#103	—	17	2	no	—
822	#103	—	17	2	no	—
823	#103	—	17	2	no	—
824	#102	—	17	2	no	—
825	#102	—	17	2	no	—
826	#102	—	17	2	no	—
827	#102	—	17	2	no	—
828	#102	—	17	2	no	—
829	#102	—	17	2	no	—
830	#102	—	17	2	no	—
831	#102	—	17	2	no	—
832	#102	—	17	2	no	—
833	#102	—	17	2	no	—
834	#102	—	17	2	no	—
835	#102	—	17	2	no	—
836	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
837	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
838	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
839	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
840	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
841	C₂²⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
842	#97	C₂²×D₁₇	1	1	yes	characteristic
843	#97	C₂²×D₁₇	1	1	yes	characteristic
844	#97	C₂²×D₁₇	1	1	yes	characteristic
845	#97	C₂²×D₁₇	1	1	yes	characteristic
846	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
847	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
848	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
849	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
850	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
852	C₁₇	#61471	1	1	yes	characteristic, complemented, Sylow
853	C₂⁴	—	34	2	no	—
854	C₂⁴	—	34	2	no	—
855	#41	—	34	4	no	—
856	#41	—	68	2	no	—
857	#41	—	136	4	no	—
858	C₂×Q₈	—	17	2	no	—
859	C₂×Q₈	—	34	2	no	—
860	C₂×Q₈	C₂×D₆₈	1	1	yes	characteristic
861	C₂×D₄	—	17	2	no	—
862	C₂×D₄	—	17	2	no	—
863	C₂×D₄	—	17	2	no	—
864	C₂×D₄	—	34	4	no	—
865	C₂×D₄	—	34	4	no	—
866	C₂×D₄	—	34	2	no	—
867	C₂×D₄	—	34	2	no	—
868	C₂×D₄	—	34	2	no	—
869	C₂×D₄	—	34	2	no	—
870	C₂×D₄	—	34	2	no	—
871	C₂×D₄	—	34	2	no	—
872	C₂×D₄	—	34	2	no	—
873	C₂×D₄	—	34	2	no	—
874	C₂×D₄	—	34	2	no	—
875	C₂×D₄	—	68	2	no	—
876	C₂×D₄	—	68	2	no	—
877	C₂×D₄	—	136	4	no	—
878	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
879	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
880	C₂×D₄	C₂×D₆₈	1	1	yes	characteristic
881	C₂²×C₄	—	34	2	no	—
882	C₂²×C₄	—	34	2	no	—
883	C₂²×C₄	—	34	2	no	—
884	C₂²×C₄	—	34	2	no	—
885	C₂²×C₄	—	34	2	no	—
886	C₂²×C₄	—	34	2	no	—
887	C₂²×C₄	—	34	2	no	—
888	C₂²×C₄	—	34	2	no	—
889	C₂²×C₄	—	34	2	no	—
890	C₂²×C₄	—	34	2	no	—
891	C₂²×C₄	—	34	2	no	—
892	C₂²×C₄	—	136	4	no	—
893	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
894	C₂²×C₄	C₂×D₆₈	1	1	yes	characteristic
895	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
896	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
897	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
898	Q₁₆	—	34	2	no	—
899	SD₁₆	—	34	4	no	—
900	SD₁₆	—	68	2	no	—
901	SD₁₆	—	68	2	no	—
902	D₈	—	17	4	no	—
903	D₈	—	34	4	no	—
904	D₈	—	34	4	no	—
905	D₈	—	34	2	no	—
906	D₈	—	34	2	no	—
907	D₈	—	68	2	no	—
908	M₁₆	—	4	1	no	—
909	M₁₆	—	4	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	2	2	no	—
912	C₂×C₈	—	2	2	no	—
913	C₂×C₈	—	4	1	no	—
914	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
916	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
917	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₁₇	1	1	yes	characteristic
922	C₄⋊C₄	—	17	2	no	—
923	C₄⋊C₄	—	17	2	no	—
924	C₄⋊C₄	—	17	2	no	—
925	C₄⋊C₄	—	17	2	no	—
926	C₄⋊C₄	—	34	2	no	—
927	C₄⋊C₄	—	34	2	no	—
928	C₄⋊C₄	—	34	2	no	—
929	C₄⋊C₄	—	34	2	no	—
930	C₄⋊C₄	—	34	2	no	—
931	C₄⋊C₄	—	34	2	no	—
932	C₄⋊C₄	—	34	2	no	—
933	C₄⋊C₄	—	34	2	no	—
934	C₄⋊C₄	—	34	2	no	—
935	C₄⋊C₄	—	34	2	no	—
936	C₄⋊C₄	—	34	2	no	—
937	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
938	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
939	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
940	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
941	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
942	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
943	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
944	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
945	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
946	C₄⋊C₄	C₂×D₆₈	1	1	yes	characteristic
947	C₂²⋊C₄	—	34	2	no	—
948	C₂²⋊C₄	—	34	2	no	—
949	C₂²⋊C₄	—	34	2	no	—
950	C₂²⋊C₄	—	34	2	no	—
951	C₂²⋊C₄	—	34	2	no	—
952	C₂²⋊C₄	—	34	2	no	—
953	C₂²⋊C₄	—	34	2	no	—
954	C₂²⋊C₄	—	34	2	no	—
955	C₂²⋊C₄	—	34	2	no	—
956	C₂²⋊C₄	—	34	2	no	—
957	C₂²⋊C₄	—	34	2	no	—
958	C₂²⋊C₄	—	34	2	no	—
959	C₂²⋊C₄	—	34	2	no	—
960	C₂²⋊C₄	—	34	2	no	—
961	C₂²⋊C₄	—	34	2	no	—
962	C₂²⋊C₄	—	34	2	no	—
963	C₂²⋊C₄	—	34	2	no	—
964	C₂²⋊C₄	—	34	2	no	—
965	C₂²⋊C₄	—	34	2	no	—
966	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
967	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
968	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
969	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
970	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
971	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
972	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
973	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
974	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
975	C₂²⋊C₄	C₂×D₆₈	1	1	yes	characteristic
976	C₄²	—	34	2	no	—
977	C₄²	—	34	2	no	—
978	C₄²	—	34	2	no	—
979	C₄²	C₂×D₆₈	1	1	yes	characteristic
980	C₄²	C₂×D₆₈	1	1	yes	characteristic
981	C₄²	C₂³×D₁₇	1	1	yes	characteristic
982	C₄²	C₂³×D₁₇	1	1	yes	characteristic
983	C₄²	C₂³×D₁₇	1	1	yes	characteristic
984	C₄²	C₂³×D₁₇	1	1	yes	characteristic
985	C₂³	—	34	2	no	—
986	C₂³	—	34	2	no	—
987	C₂³	—	34	2	no	—
988	C₂³	—	68	4	no	—
989	C₂³	—	68	4	no	—
990	C₂³	—	68	4	no	—
991	C₂³	—	136	2	no	—
992	C₂³	—	136	2	no	—
993	C₂³	—	136	2	no	—
994	C₂³	C₂²×D₆₈	1	1	yes	characteristic
995	C₂³	C₂²×D₆₈	1	1	yes	characteristic
996	C₂³	C₂²×D₆₈	1	1	yes	characteristic
997	Q₈	—	4	1	no	—
998	Q₈	—	34	2	no	—
999	Q₈	—	34	2	no	—
1000	Q₈	—	136	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	4	1	no	—
1004	D₄	—	17	4	no	—
1005	D₄	—	34	2	no	—
1006	D₄	—	34	2	no	—
1007	D₄	—	34	2	no	—
1008	D₄	—	34	2	no	—
1009	D₄	—	34	2	no	—
1010	D₄	—	68	4	no	—
1011	D₄	—	68	4	no	—
1012	D₄	—	68	4	no	—
1013	D₄	—	68	4	no	—
1014	D₄	—	136	2	no	—
1015	D₄	—	136	2	no	—
1016	D₄	—	136	2	no	—
1017	D₄	—	136	2	no	—
1018	D₄	—	136	2	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	1	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	—	4	1	no	—
1027	C₂×C₄	—	34	2	no	—
1028	C₂×C₄	—	34	2	no	—
1029	C₂×C₄	—	34	2	no	—
1030	C₂×C₄	—	34	2	no	—
1031	C₂×C₄	—	34	2	no	—
1032	C₂×C₄	—	68	4	no	—
1033	C₂×C₄	—	68	4	no	—
1034	C₂×C₄	—	136	2	no	—
1035	C₂×C₄	—	136	2	no	—
1036	C₂×C₄	—	136	2	no	—
1037	C₂×C₄	—	136	2	no	—
1038	C₂×C₄	—	136	2	no	—
1039	C₂×C₄	—	136	2	no	—
1040	C₂×C₄	—	136	2	no	—
1041	C₂×C₄	—	136	2	no	—
1042	C₂×C₄	—	136	2	no	—
1043	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1044	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1045	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1046	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1047	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1048	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1049	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1050	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1051	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1052	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1053	C₂×C₄	C₂²×D₆₈	1	1	yes	characteristic
1054	C₂×C₄	C₂⁴×D₁₇	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	2	1	no	—
1059	C₈	—	2	1	no	—
1060	C₈	—	2	1	no	—
1061	C₈	—	2	1	no	—
1062	C₈	#41×D₁₇	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	1	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	2	1	no	—
1068	C₂²	—	2	1	no	—
1069	C₂²	—	2	1	no	—
1070	C₂²	—	2	1	no	—
1071	C₂²	—	272	4	no	—
1072	C₂²	—	34	4	no	—
1073	C₂²	—	68	2	no	—
1074	C₂²	—	68	2	no	—
1075	C₂²	—	68	2	no	—
1076	C₂²	—	68	2	no	—
1077	C₂²	—	68	2	no	—
1078	C₂²	—	68	2	no	—
1079	C₂²	—	68	2	no	—
1080	C₂²	—	68	2	no	—
1081	C₂²	—	136	8	no	—
1082	C₂²	#11763614	1	2	yes	—
1083	C₂²	C₂³×D₆₈	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	1	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	2	1	no	—
1094	C₄	—	2	1	no	—
1095	C₄	—	68	2	no	—
1096	C₄	—	68	2	no	—
1097	C₄	—	68	2	no	—
1098	C₄	—	68	2	no	—
1099	C₄	—	68	2	no	—
1100	C₄	C₂×#41×D₁₇	1	1	yes	characteristic
1101	C₄	#11763645	1	1	yes	characteristic
1102	C₂	—	2	2	no	—
1103	C₂	—	4	1	no	—
1104	C₂	—	4	1	no	—
1105	C₂	—	68	4	no	—
1106	C₂	—	136	2	no	—
1107	C₂	—	136	2	no	—
1108	C₂	#41×D₆₈	1	1	yes	characteristic
1109	C₂	C₂×#11763614	1	1	yes	characteristic
1110	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	#61471
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. #14542728	C₂	semidirect
2. #14541797	C₂	semidirect
3. #14541652	C₂	semidirect
4. #14541539	C₂	semidirect
5. #14541187	C₂	semidirect
6. #14541153	C₂	semidirect
7. #14541132	C₂	semidirect
8. #14540987	C₂	semidirect
9. #14540807	C₂	semidirect
10. #14540747	C₂	semidirect
11. #14540471	C₂	semidirect
12. #14540471	C₂	semidirect
13. D₄×D₁₃₆	C₂	semidirect
14. #14539434	C₂	semidirect
15. #14539423	C₂	semidirect
16. #14539354	C₂	semidirect
17. #14538985	C₂	semidirect
18. #14538970	C₂	semidirect
19. #14538924	C₂	semidirect
20. #14537661	C₂	semidirect
21. #14537637	C₂	semidirect
22. C₂×C₄×D₁₃₆	C₂	semidirect
23. C₁₇×#2966	C₂	semidirect
27. #11763544	C₂²	semidirect
28. #11763519	C₂²	semidirect
30. #11763505	C₂²	semidirect
34. #11763463	C₂²	semidirect
35. #11763455	C₂²	semidirect
36. #11763455	C₂²	semidirect
39. #11763430	C₂²	semidirect
40. #11763414	C₂²	semidirect
43. #11763343	C₂²	semidirect
46. #11763289	C₂²	semidirect
47. #11763283	C₂²	semidirect
48. C₂×C₄×D₆₈	C₂²	semidirect
49. #11763214	C₂²	semidirect
50. #11763211	C₂²	semidirect
51. #11763211	C₂²	semidirect
52. #11763193	C₂²	semidirect
53. #11763193	C₂²	semidirect
55. #11763174	C₂²	semidirect
56. #11763169	C₂²	semidirect
57. #11763164	C₂²	semidirect
58. #11763151	C₂²	semidirect
59. #11763140	C₂²	semidirect
60. #11763134	C₂²	semidirect
61. #11763128	C₂²	semidirect
62. #11763123	C₂²	semidirect
63. #11763123	C₂²	semidirect
64. #11763117	C₂²	semidirect
65. #11763110	C₂²	semidirect
66. #11763110	C₂²	semidirect
67. #11763110	C₂²	semidirect
68. #11763100	C₂²	semidirect
69. #11763090	C₂²	semidirect
70. #11763062	C₂²	semidirect
71. #11763055	C₂²	semidirect
72. #11763050	C₂²	semidirect
73. #11763050	C₂²	semidirect
76. #11763045	C₂²	semidirect
77. #11763045	C₂²	semidirect
78. #11763038	C₂²	semidirect
79. #11763025	C₂²	semidirect
80. #11763025	C₂²	semidirect
81. #11763025	C₂²	semidirect
82. #11763025	C₂²	semidirect
83. #11763010	C₂²	semidirect
85. #11762962	C₂²	semidirect
86. #11762962	C₂²	semidirect
87. #11762956	C₂²	semidirect
88. #11762956	C₂²	semidirect
91. #11762922	C₂²	semidirect
92. #11762922	C₂²	semidirect
93. #11762922	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×#63219	C₂²	semidirect
104. C₄×D₁₃₆	C₂²	semidirect
105. C₄×D₁₃₆	C₂²	semidirect
106. C₄×D₁₃₆	C₂²	semidirect
107. C₄×D₁₃₆	C₂²	semidirect
108. C₄×D₁₃₆	C₂²	semidirect
109. C₄×D₁₃₆	C₂²	semidirect
110. #11762847	C₂²	semidirect
111. C₂×#10587489	C₂²	semidirect
112. C₂×#10587489	C₂²	semidirect
113. #11762815	C₂²	semidirect
114. #11762811	C₂²	semidirect
115. C₂×#10587492	C₂²	semidirect
117. C₁₇×#446	C₂²	semidirect
118. C₈×Q₈×C₁₇	C₂²	semidirect
119. C₁₇×#436	C₂²	semidirect
121. C₁₇×#435	C₂²	semidirect
123. C₈×D₄×C₁₇	C₂²	semidirect
124. C₈×D₄×C₁₇	C₂²	semidirect
125. C₁₇×#433	C₂²	semidirect
126. C₁₇×#433	C₂²	semidirect
127. C₁₇×#432	C₂²	semidirect
128. C₁₇×#405	C₂²	semidirect
129. C₁₇×#405	C₂²	semidirect
130. C₂×C₄×C₈×C₁₇	C₂²	semidirect
425. D₁₃₆	#41	semidirect
527. #2966	D₁₇	semidirect
638. #446	C₂×D₁₇	semidirect
639. C₈×Q₈	C₂×D₁₇	semidirect
659. #436	C₂×D₁₇	semidirect
661. #435	C₂×D₁₇	semidirect
663. C₈×D₄	C₂×D₁₇	semidirect
664. C₈×D₄	C₂×D₁₇	semidirect
665. #433	C₂×D₁₇	semidirect
666. #433	C₂×D₁₇	semidirect
667. #432	C₂×D₁₇	semidirect
674. #405	C₂×D₁₇	semidirect
675. #405	C₂×D₁₇	semidirect
676. C₂×C₄×C₈	C₂×D₁₇	semidirect
852. C₁₇	#61471	semidirect

Maximal subgroups

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

subgroup	index
#14542728	2
#14541797	2
#14541652	2
#14541539	2
#14541187	2
#14541153	2
#14541132	2
#14540987	2
#14540807	2
#14540747	2
#14540471	2
D₄×D₁₃₆	2
#14539434	2
#14539423	2
#14539354	2
#14538985	2
#14538970	2
#14538924	2
#14537661	2
#14537637	2
C₂×C₄×D₁₃₆	2
C₁₇×#2966	2
#61471	17