Subgroups — #14543335

Order 2176.

1056 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763563	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763561	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763549	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763547	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763510	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763507	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763505	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763483	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763482	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763463	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763459	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763454	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763454	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763448	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763448	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763430	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763425	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763407	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763403	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763401	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763398	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763396	C₂	1	1	yes	maximal, characteristic, complemented
23	#11763395	C₂	1	1	yes	maximal, characteristic, complemented
24	#11763392	C₂	1	1	yes	maximal, characteristic, complemented
25	#11763392	C₂	1	1	yes	maximal, characteristic, complemented
26	#11763386	C₂	1	1	yes	maximal, characteristic, complemented
27	#11763367	C₂	1	1	yes	maximal, characteristic, complemented
28	#11763354	C₂	1	1	yes	maximal, characteristic, complemented
29	#11763339	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂×#10587584	C₂	1	1	yes	maximal, characteristic, complemented
31	C₁₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
33	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
34	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
35	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
36	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
37	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
38	C₁₇×#126	C₂²	1	1	yes	characteristic, complemented
39	C₁₇×#126	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×#123	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#123	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#121	C₂²	1	1	yes	characteristic
44	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
45	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
47	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
49	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
50	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
51	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
52	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
53	#10587626	C₂²	1	1	yes	characteristic, complemented
54	#10587625	C₂²	1	1	yes	characteristic
55	#10587625	C₂²	1	1	yes	characteristic
56	#10587625	C₂²	1	1	yes	characteristic
57	#10587625	C₂²	1	1	yes	characteristic
58	#10587625	C₂²	1	1	yes	characteristic, complemented
59	#10587625	C₂²	1	1	yes	characteristic, complemented
60	#10587625	C₂²	1	1	yes	characteristic, complemented
61	#10587624	C₂²	1	1	yes	characteristic, complemented
62	#10587623	C₂²	1	1	yes	characteristic
63	#10587623	C₂²	1	1	yes	characteristic
64	#10587623	C₂²	1	1	yes	characteristic
65	#10587623	C₂²	1	1	yes	characteristic, complemented
66	#10587623	C₂²	1	1	yes	characteristic, complemented
67	#10587621	C₂²	1	1	yes	characteristic, complemented
68	#10587621	C₂²	1	1	yes	characteristic, complemented
69	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
70	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
71	#10587616	C₂²	1	1	yes	characteristic
72	#10587616	C₂²	1	1	yes	characteristic
73	#10587616	C₂²	1	1	yes	characteristic
74	#10587616	C₂²	1	1	yes	characteristic, complemented
75	#10587616	C₂²	1	1	yes	characteristic, complemented
76	#10587616	C₂²	1	1	yes	characteristic, complemented
77	#10587616	C₂²	1	1	yes	characteristic, complemented
78	#10587615	C₂²	1	1	yes	characteristic, complemented
79	#10587615	C₂²	1	1	yes	characteristic, complemented
80	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
81	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
82	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
83	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
84	C₂×#63227	C₂²	1	1	yes	characteristic
85	C₂×#63227	C₂²	1	1	yes	characteristic
86	C₂×#63227	C₂²	1	1	yes	characteristic
87	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
88	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
89	#10587612	C₂²	1	1	yes	characteristic, complemented
90	C₂×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic, complemented
91	C₂×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic, complemented
92	#10587610	C₂²	1	1	yes	characteristic, complemented
93	C₂×#63225	C₂²	1	1	yes	characteristic, complemented
94	C₂×C₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
95	#10587584	C₂²	1	1	yes	characteristic, complemented
96	#10587584	C₂²	1	1	yes	characteristic, complemented
97	#10587584	C₂²	1	1	yes	characteristic, complemented
98	#10587584	C₂²	1	1	yes	characteristic, complemented
99	#10587584	C₂²	1	1	yes	characteristic, complemented
100	#10587584	C₂²	1	1	yes	characteristic, complemented
101	#10587584	C₂²	1	1	yes	characteristic, complemented
102	#10587584	C₂²	1	1	yes	characteristic, complemented
103	#10587584	C₂²	1	1	yes	characteristic, complemented
104	#10587584	C₂²	1	1	yes	characteristic, complemented
105	#10587584	C₂²	1	1	yes	characteristic, complemented
106	#10587584	C₂²	1	1	yes	characteristic, complemented
107	#10587583	C₂²	1	1	yes	characteristic, complemented
108	#10587583	C₂²	1	1	yes	characteristic, complemented
109	#10587583	C₂²	1	1	yes	characteristic, complemented
110	#10587583	C₂²	1	1	yes	characteristic, complemented
111	#10587582	C₂²	1	1	yes	characteristic, complemented
112	#10587582	C₂²	1	1	yes	characteristic, complemented
113	#10587582	C₂²	1	1	yes	characteristic, complemented
114	#10587582	C₂²	1	1	yes	characteristic, complemented
115	#10587582	C₂²	1	1	yes	characteristic, complemented
116	#10587581	C₂²	1	1	yes	characteristic
117	#10587581	C₂²	1	1	yes	characteristic
118	#10587581	C₂²	1	1	yes	characteristic, complemented
119	#10587580	C₂²	1	1	yes	characteristic
120	#10587580	C₂²	1	1	yes	characteristic
121	#10587580	C₂²	1	1	yes	characteristic
122	#10587580	C₂²	1	1	yes	characteristic
123	#10587580	C₂²	1	1	yes	characteristic, complemented
124	#10587580	C₂²	1	1	yes	characteristic, complemented
125	#10587580	C₂²	1	1	yes	characteristic, complemented
126	#10587579	C₂²	1	1	yes	characteristic, complemented
127	#10587579	C₂²	1	1	yes	characteristic, complemented
128	#10587578	C₂²	1	1	yes	characteristic, complemented
129	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
130	#10587576	C₂²	1	1	yes	characteristic, complemented
131	#10587575	C₂²	1	1	yes	characteristic, complemented
132	#10587575	C₂²	1	1	yes	characteristic, complemented
133	#10587574	C₂²	1	1	yes	characteristic, complemented
134	#10587574	C₂²	1	1	yes	characteristic, complemented
135	#10587572	C₂²	1	1	yes	characteristic
136	#10587572	C₂²	1	1	yes	characteristic
137	#10587572	C₂²	1	1	yes	characteristic, complemented
138	#10587572	C₂²	1	1	yes	characteristic, complemented
139	#10587572	C₂²	1	1	yes	characteristic, complemented
140	#10587572	C₂²	1	1	yes	characteristic, complemented
141	#10587571	C₂²	1	1	yes	characteristic
142	#10587571	C₂²	1	1	yes	characteristic
143	#10587571	C₂²	1	1	yes	characteristic, complemented
144	#10587571	C₂²	1	1	yes	characteristic, complemented
145	#10587571	C₂²	1	1	yes	characteristic, complemented
146	#10587571	C₂²	1	1	yes	characteristic, complemented
147	#10587570	C₂²	1	1	yes	characteristic
148	#10587570	C₂²	1	1	yes	characteristic
149	#10587570	C₂²	1	1	yes	characteristic, complemented
150	#10587570	C₂²	1	1	yes	characteristic, complemented
151	#10587570	C₂²	1	1	yes	characteristic, complemented
152	#10587569	C₂²	1	1	yes	characteristic
153	#10587569	C₂²	1	1	yes	characteristic
154	#10587569	C₂²	1	1	yes	characteristic, complemented
155	#10587569	C₂²	1	1	yes	characteristic, complemented
156	#10587569	C₂²	1	1	yes	characteristic, complemented
157	#10587568	C₂²	1	1	yes	characteristic
158	#10587568	C₂²	1	1	yes	characteristic
159	#10587568	C₂²	1	1	yes	characteristic
160	#10587568	C₂²	1	1	yes	characteristic, complemented
161	#10587568	C₂²	1	1	yes	characteristic, complemented
162	#10587567	C₂²	1	1	yes	characteristic, complemented
163	#10587567	C₂²	1	1	yes	characteristic, complemented
164	#10587567	C₂²	1	1	yes	characteristic, complemented
165	#10587567	C₂²	1	1	yes	characteristic, complemented
166	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
167	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
168	#10587565	C₂²	1	1	yes	characteristic, complemented
169	#10587565	C₂²	1	1	yes	characteristic, complemented
170	#10587564	C₂²	1	1	yes	characteristic, complemented
171	#10587564	C₂²	1	1	yes	characteristic, complemented
172	#10587564	C₂²	1	1	yes	characteristic, complemented
173	#10587564	C₂²	1	1	yes	characteristic, complemented
174	#10587564	C₂²	1	1	yes	characteristic, complemented
175	#10587562	C₂²	1	1	yes	characteristic, complemented
176	#10587562	C₂²	1	1	yes	characteristic, complemented
177	#10587561	C₂²	1	1	yes	characteristic
178	#10587561	C₂²	1	1	yes	characteristic
179	#10587561	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
182	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
183	#10587558	C₂²	1	1	yes	characteristic, complemented
184	#10587556	C₂²	1	1	yes	characteristic, complemented
185	#10587555	C₂²	1	1	yes	characteristic, complemented
186	C₄×Dic₃₄	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₇	C₂³	1	1	yes	characteristic
188	C₂³×D₁₇	C₂³	1	1	yes	characteristic
189	C₂³×D₁₇	C₂³	1	1	yes	characteristic
190	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
191	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
193	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
194	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
195	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
196	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
197	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
198	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
199	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
200	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
201	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
202	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
203	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
204	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
205	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
206	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
207	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
208	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
209	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
210	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
211	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
212	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
213	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
214	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
215	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
216	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
217	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
218	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
219	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
220	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
221	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
222	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
223	#63254	—	4	2	no	—
224	#63254	—	4	2	no	—
225	#63254	—	4	2	no	—
226	#63254	—	4	2	no	—
227	D₄×D₁₇	—	4	2	no	—
228	D₄×D₁₇	—	4	2	no	—
229	C₂×D₆₈	C₂³	1	1	yes	characteristic
230	C₂×D₆₈	C₂³	1	1	yes	characteristic
231	C₂×D₆₈	C₂³	1	1	yes	characteristic
232	C₂×D₆₈	C₂³	1	1	yes	characteristic
233	C₂×D₆₈	C₂³	1	1	yes	characteristic
234	C₂×D₆₈	C₂³	1	1	yes	characteristic
235	C₂×D₆₈	C₂³	1	1	yes	characteristic
236	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
237	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
238	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
239	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
240	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
241	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
242	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
243	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
244	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
245	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
246	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
247	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
248	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
249	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
250	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
251	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
252	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
253	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
254	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
255	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
256	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
257	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
258	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
259	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
260	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
261	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
262	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
263	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
264	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
265	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
266	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
267	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
268	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
269	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
270	C₄²×C₁₇	C₂³	1	1	yes	characteristic
271	C₄²×C₁₇	C₂³	1	1	yes	characteristic
272	C₄²×C₁₇	C₂³	1	1	yes	characteristic
273	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
274	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
275	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
277	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
278	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
279	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
280	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
281	#63227	C₂³	1	1	yes	characteristic
282	#63227	C₂³	1	1	yes	characteristic
283	#63227	C₂³	1	1	yes	characteristic
284	#63227	C₂³	1	1	yes	characteristic
285	#63227	C₂³	1	1	yes	characteristic
286	#63227	C₂³	1	1	yes	characteristic
287	#63227	C₂³	1	1	yes	characteristic
288	#63227	C₂³	1	1	yes	characteristic
289	#63227	C₂³	1	1	yes	characteristic
290	#63227	C₂³	1	1	yes	characteristic
291	#63227	C₂³	1	1	yes	characteristic
292	#63227	C₂³	1	1	yes	characteristic
293	#63227	C₂³	1	1	yes	characteristic
294	#63227	C₂³	1	1	yes	characteristic
295	#63227	C₂³	1	1	yes	characteristic
296	#63227	C₂³	1	1	yes	characteristic
297	#63227	C₂³	1	1	yes	characteristic
298	#63227	C₂³	1	1	yes	characteristic
299	#63227	C₂³	1	1	yes	characteristic
300	#63227	C₂³	1	1	yes	characteristic
301	#63227	C₂³	1	1	yes	characteristic
302	#63227	C₂³	1	1	yes	characteristic
303	#63227	C₂³	1	1	yes	characteristic
304	#63227	C₂³	1	1	yes	characteristic
305	#63227	C₂³	1	1	yes	characteristic
306	#63227	C₂³	1	1	yes	characteristic
307	#63227	C₂³	1	1	yes	characteristic
308	#63227	C₂³	1	1	yes	characteristic
309	#63227	C₂³	1	1	yes	characteristic
310	#63227	C₂³	1	1	yes	characteristic
311	#63227	C₂³	1	1	yes	characteristic
312	#63227	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
315	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
316	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
317	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
318	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
319	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
320	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
321	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
322	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
323	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
324	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
325	#63225	C₂³	1	1	yes	characteristic
326	#63225	C₂³	1	1	yes	characteristic
327	#63225	C₂³	1	1	yes	characteristic
328	#63225	C₂³	1	1	yes	characteristic
329	#63225	C₂³	1	1	yes	characteristic
330	#63225	C₂³	1	1	yes	characteristic
331	#63225	C₂³	1	1	yes	characteristic
332	#63225	C₂³	1	1	yes	characteristic
333	#63225	C₂³	1	1	yes	characteristic
334	#63225	C₂³	1	1	yes	characteristic
335	#63225	C₂³	1	1	yes	characteristic
336	#63225	C₂³	1	1	yes	characteristic
337	#63225	C₂³	1	1	yes	characteristic
338	#63225	C₂³	1	1	yes	characteristic
339	#63225	C₂³	1	1	yes	characteristic
340	#63225	C₂³	1	1	yes	characteristic
341	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
342	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
343	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
344	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
345	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
346	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
347	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
348	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
349	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
350	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
351	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
352	C₂²×D₁₇	—	2	2	no	—
353	C₂²×D₁₇	—	4	1	no	—
354	C₂²×D₁₇	—	4	1	no	—
355	C₂²×D₁₇	—	4	1	no	—
356	C₂²×D₁₇	—	4	1	no	—
357	C₂²×D₁₇	—	4	1	no	—
358	C₂²×D₁₇	—	4	1	no	—
359	C₂²×D₁₇	—	4	1	no	—
360	C₂²×D₁₇	—	4	1	no	—
361	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
362	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
363	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
364	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
365	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
366	D₄×C₁₇	—	2	2	no	—
367	D₄×C₁₇	—	2	2	no	—
368	D₄×C₁₇	—	2	2	no	—
369	D₄×C₁₇	—	4	1	no	—
370	D₄×C₁₇	—	4	1	no	—
371	D₄×C₁₇	—	4	1	no	—
372	C₂×C₄×C₁₇	—	4	1	no	—
373	C₂×C₄×C₁₇	—	4	1	no	—
374	C₂×C₄×C₁₇	—	4	1	no	—
375	C₂×C₄×C₁₇	—	4	1	no	—
376	C₂×C₄×C₁₇	—	4	1	no	—
377	C₂×C₄×C₁₇	—	4	1	no	—
378	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
379	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
380	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
381	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
382	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
383	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
384	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
385	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
386	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
387	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
388	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
389	C₂²⋊D₁₇	—	2	2	no	—
390	C₂²⋊D₁₇	—	2	2	no	—
391	C₂²⋊D₁₇	—	2	2	no	—
392	C₂²⋊D₁₇	—	4	1	no	—
393	C₂²⋊D₁₇	—	4	1	no	—
394	C₂²⋊D₁₇	—	4	1	no	—
395	C₂²⋊D₁₇	—	4	1	no	—
396	C₂²⋊D₁₇	—	4	1	no	—
397	C₂²⋊D₁₇	—	4	1	no	—
398	C₂²⋊D₁₇	—	4	1	no	—
399	C₂²⋊D₁₇	—	4	1	no	—
400	C₂²⋊D₁₇	—	4	1	no	—
401	C₂²⋊D₁₇	—	4	1	no	—
402	C₂²⋊D₁₇	—	4	1	no	—
403	C₂×Dic₁₇	—	2	2	no	—
404	C₂×Dic₁₇	—	2	2	no	—
405	C₂×Dic₁₇	—	4	1	no	—
406	C₂×Dic₁₇	—	4	1	no	—
407	C₂×Dic₁₇	—	4	1	no	—
408	C₂×Dic₁₇	—	4	1	no	—
409	C₂×Dic₁₇	—	4	1	no	—
410	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
411	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
412	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
413	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
414	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
415	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
416	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
417	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
418	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
419	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
420	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
421	D₆₈	—	4	1	no	—
422	D₆₈	—	4	1	no	—
423	D₆₈	—	4	1	no	—
424	D₆₈	—	4	1	no	—
425	D₆₈	—	4	1	no	—
426	D₆₈	—	4	1	no	—
427	D₆₈	—	4	1	no	—
428	C₄×D₁₇	—	4	1	no	—
429	C₄×D₁₇	—	4	1	no	—
430	C₄×D₁₇	—	4	1	no	—
431	C₄×D₁₇	—	4	1	no	—
432	C₄×D₁₇	—	4	1	no	—
433	C₄×D₁₇	—	4	1	no	—
434	C₄×D₁₇	—	4	1	no	—
435	C₄×D₁₇	—	4	1	no	—
436	C₄×D₁₇	—	4	1	no	—
437	Dic₃₄	—	4	1	no	—
438	Dic₃₄	—	4	1	no	—
439	Dic₃₄	—	4	1	no	—
440	Dic₃₄	—	4	1	no	—
441	Dic₃₄	—	4	1	no	—
442	#3560	—	17	1	no	maximal, Sylow
443	C₂²×C₁₇	—	2	1	no	—
444	C₂²×C₁₇	—	2	1	no	—
445	C₂²×C₁₇	—	2	1	no	—
446	C₂²×C₁₇	—	2	1	no	—
447	C₂²×C₁₇	—	2	1	no	—
448	C₂²×C₁₇	—	2	1	no	—
449	C₂²×C₁₇	—	2	1	no	—
450	C₂²×C₁₇	—	2	1	no	—
451	C₂²×C₁₇	—	2	1	no	—
452	C₂²×C₁₇	—	2	1	no	—
453	C₂²×C₁₇	—	2	1	no	—
454	C₂²×C₁₇	H(5,𝔽₂)	1	2	yes	—
455	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
456	C₂×D₁₇	—	2	1	no	—
457	C₂×D₁₇	—	2	1	no	—
458	C₂×D₁₇	—	2	1	no	—
459	C₂×D₁₇	—	2	1	no	—
460	C₂×D₁₇	—	2	1	no	—
461	C₂×D₁₇	—	2	1	no	—
462	C₂×D₁₇	—	2	1	no	—
463	C₂×D₁₇	—	2	1	no	—
464	C₂×D₁₇	—	2	1	no	—
465	C₂×D₁₇	—	2	1	no	—
466	C₂×D₁₇	—	2	1	no	—
467	C₂×D₁₇	—	2	1	no	—
468	C₂×D₁₇	—	2	1	no	—
469	C₂×D₁₇	—	2	1	no	—
470	C₂×D₁₇	—	2	1	no	—
471	C₂×D₁₇	—	8	2	no	—
472	C₂×D₁₇	—	8	2	no	—
473	C₂×D₁₇	—	8	2	no	—
474	C₄×C₁₇	—	2	1	no	—
475	C₄×C₁₇	—	2	1	no	—
476	C₄×C₁₇	—	2	1	no	—
477	C₄×C₁₇	—	2	1	no	—
478	C₄×C₁₇	—	2	1	no	—
479	C₄×C₁₇	—	2	1	no	—
480	C₄×C₁₇	—	2	1	no	—
481	C₄×C₁₇	—	2	1	no	—
482	C₄×C₁₇	—	2	1	no	—
483	C₄×C₁₇	—	2	1	no	—
484	C₄×C₁₇	—	2	1	no	—
485	Dic₁₇	—	2	1	no	—
486	Dic₁₇	—	2	1	no	—
487	Dic₁₇	—	2	1	no	—
488	Dic₁₇	—	2	1	no	—
489	Dic₁₇	—	2	1	no	—
490	Dic₁₇	—	2	1	no	—
491	Dic₁₇	—	2	1	no	—
492	Dic₁₇	—	2	1	no	—
493	Dic₁₇	—	2	1	no	—
494	Dic₁₇	—	2	1	no	—
495	Dic₁₇	—	2	1	no	—
496	#563	—	17	1	no	—
497	#563	—	17	1	no	—
498	#560	—	17	1	no	—
499	#560	—	17	1	no	—
500	#553	—	17	1	no	—
501	#553	—	17	1	no	—
502	#553	—	17	1	no	—
503	#553	D₁₇	1	1	yes	characteristic, complemented
504	#551	—	17	1	no	—
505	#551	—	17	1	no	—
506	#547	—	17	1	no	—
507	#547	—	17	1	no	—
508	#546	—	17	1	no	—
509	#546	—	17	1	no	—
510	#546	—	17	1	no	—
511	#546	—	17	1	no	—
512	#542	—	17	1	no	—
513	#542	—	17	1	no	—
514	#539	—	17	1	no	—
515	#539	—	17	1	no	—
516	#539	—	17	1	no	—
517	#538	—	17	1	no	—
518	#538	—	17	1	no	—
519	#538	—	17	1	no	—
520	#538	—	17	1	no	—
521	#538	—	17	1	no	—
522	#537	—	17	1	no	—
523	#534	—	17	1	no	—
524	#532	—	17	1	no	—
525	#529	—	17	1	no	—
526	C₂×#126	—	17	1	no	—
527	C₂×C₁₇	—	2	2	no	—
528	C₂×C₁₇	—	4	1	no	—
529	C₂×C₁₇	—	4	1	no	—
530	C₂×C₁₇	—	4	1	no	—
531	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
532	C₂×C₁₇	#585	1	1	yes	characteristic
533	C₂×C₁₇	#585	1	1	yes	characteristic
534	D₁₇	—	4	1	no	—
535	D₁₇	—	4	1	no	—
536	D₁₇	—	4	1	no	—
537	D₁₇	—	4	1	no	—
538	D₁₇	—	4	1	no	—
539	C₂×#41	—	17	1	no	—
540	C₂×#41	—	17	1	no	—
541	C₂×#41	—	17	1	no	—
542	C₂×#41	—	17	1	no	—
543	C₂²×D₄	—	17	1	no	—
544	C₂²×D₄	—	17	1	no	—
545	C₄⋊Q₈	—	17	1	no	—
546	C₄⋊Q₈	—	17	1	no	—
547	C₄⋊Q₈	—	17	1	no	—
548	#127	—	17	1	no	—
549	#126	—	17	1	no	—
550	#126	—	17	1	no	—
551	#126	—	17	1	no	—
552	#126	—	17	1	no	—
553	#126	—	17	1	no	—
554	#126	—	17	1	no	—
555	#126	—	17	1	no	—
556	#126	—	17	1	no	—
557	#126	—	17	1	no	—
558	#126	—	17	1	no	—
559	#126	—	17	1	no	—
560	#126	—	17	1	no	—
561	#126	—	17	1	no	—
562	#126	—	17	1	no	—
563	#126	—	17	1	no	—
564	#126	—	17	1	no	—
565	#126	C₂×D₁₇	1	1	yes	characteristic, complemented
566	#126	C₂×D₁₇	1	1	yes	characteristic, complemented
567	#125	—	17	1	no	—
568	#125	—	17	1	no	—
569	#125	—	17	1	no	—
570	#125	—	17	1	no	—
571	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
572	#124	—	17	1	no	—
573	#124	—	17	1	no	—
574	#124	—	17	1	no	—
575	#124	—	17	1	no	—
576	#124	—	17	1	no	—
577	#124	—	17	1	no	—
578	#124	—	17	1	no	—
579	#124	—	17	1	no	—
580	#124	—	17	1	no	—
581	#123	—	17	1	no	—
582	#123	—	17	1	no	—
583	#123	—	17	1	no	—
584	#123	—	17	1	no	—
585	#123	—	17	1	no	—
586	#123	—	17	1	no	—
587	#123	—	17	1	no	—
588	#123	—	17	1	no	—
589	#123	—	17	1	no	—
590	#123	—	17	1	no	—
591	#123	—	17	1	no	—
592	#123	—	17	1	no	—
593	#123	—	17	1	no	—
594	#123	—	17	1	no	—
595	#123	—	17	1	no	—
596	#123	—	17	1	no	—
597	#123	—	17	1	no	—
598	#123	—	17	1	no	—
599	#123	—	17	1	no	—
600	#123	—	17	1	no	—
601	#123	—	17	1	no	—
602	#123	—	17	1	no	—
603	#123	C₂×D₁₇	1	1	yes	characteristic, complemented
604	#123	C₂×D₁₇	1	1	yes	characteristic, complemented
605	C₂²⋊Q₈	—	17	1	no	—
606	C₂²⋊Q₈	—	17	1	no	—
607	C₂²⋊Q₈	—	17	1	no	—
608	C₂²⋊Q₈	—	17	1	no	—
609	C₂²⋊Q₈	—	17	1	no	—
610	C₂²⋊Q₈	—	17	1	no	—
611	C₂²⋊Q₈	—	17	1	no	—
612	C₂²⋊Q₈	—	17	1	no	—
613	C₂²⋊Q₈	—	17	1	no	—
614	C₂²⋊Q₈	—	17	1	no	—
615	C₂²⋊Q₈	—	17	1	no	—
616	C₂²⋊Q₈	—	17	1	no	—
617	C₂²⋊Q₈	—	17	1	no	—
618	C₂²⋊Q₈	—	17	1	no	—
619	C₂²⋊Q₈	—	17	1	no	—
620	#121	—	17	1	no	—
621	#121	—	17	1	no	—
622	#121	—	17	1	no	—
623	#121	—	17	1	no	—
624	#121	—	17	1	no	—
625	#121	—	17	1	no	—
626	#121	—	17	1	no	—
627	#121	—	17	1	no	—
628	#121	—	17	1	no	—
629	#121	—	17	1	no	—
630	#121	—	17	1	no	—
631	#121	—	17	1	no	—
632	#121	—	17	1	no	—
633	#121	—	17	1	no	—
634	#121	—	17	1	no	—
635	#121	—	17	1	no	—
636	#121	—	17	1	no	—
637	#121	—	17	1	no	—
638	#121	—	17	1	no	—
639	#121	—	17	1	no	—
640	#121	—	17	1	no	—
641	#121	—	17	1	no	—
642	#121	—	17	1	no	—
643	#121	C₂×D₁₇	1	1	yes	characteristic
644	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
645	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
646	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
647	#120	—	17	1	no	—
648	#120	—	17	1	no	—
649	#120	—	17	1	no	—
650	#120	—	17	1	no	—
651	#120	—	17	1	no	—
652	#120	—	17	1	no	—
653	#120	—	17	1	no	—
654	#120	—	17	1	no	—
655	#120	—	17	1	no	—
656	#120	—	17	1	no	—
657	C₄×Q₈	—	17	1	no	—
658	C₄×D₄	—	17	1	no	—
659	C₄×D₄	—	17	1	no	—
660	C₄×D₄	—	17	1	no	—
661	C₄×D₄	—	17	1	no	—
662	C₄×D₄	—	17	1	no	—
663	C₄×D₄	—	17	1	no	—
664	C₄×D₄	—	17	1	no	—
665	C₄×D₄	—	17	1	no	—
666	C₄×D₄	—	17	1	no	—
667	C₄×D₄	—	17	1	no	—
668	C₄×D₄	—	17	1	no	—
669	C₄×D₄	—	17	1	no	—
670	C₄×D₄	—	17	1	no	—
671	C₄×D₄	—	17	1	no	—
672	C₄×D₄	—	17	1	no	—
673	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
674	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
675	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
676	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic, complemented
677	#117	—	17	1	no	—
678	#117	—	17	1	no	—
679	#117	—	17	1	no	—
680	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
681	C₂×C₄⋊C₄	—	17	1	no	—
682	C₂×C₄⋊C₄	—	17	1	no	—
683	C₂×C₄⋊C₄	—	17	1	no	—
684	C₂×C₄⋊C₄	—	17	1	no	—
685	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
686	C₂×C₂²⋊C₄	—	17	1	no	—
687	C₂×C₂²⋊C₄	—	17	1	no	—
688	C₂×C₂²⋊C₄	—	17	1	no	—
689	C₂×C₂²⋊C₄	—	17	1	no	—
690	C₂×C₂²⋊C₄	—	17	1	no	—
691	C₂×C₂²⋊C₄	—	17	1	no	—
692	C₂×C₂²⋊C₄	—	17	1	no	—
693	C₂×C₄²	—	17	1	no	—
694	C₁₇	#3560	1	1	yes	characteristic, complemented, Sylow
695	C₂⁴	—	17	1	no	—
696	C₂⁴	—	17	1	no	—
697	C₂⁴	—	17	1	no	—
698	#41	—	68	2	no	—
699	#41	—	68	2	no	—
700	#41	—	68	2	no	—
701	#41	—	68	2	no	—
702	C₂×Q₈	—	17	1	no	—
703	C₂×Q₈	—	17	1	no	—
704	C₂×Q₈	—	17	1	no	—
705	C₂×Q₈	—	17	1	no	—
706	C₂×Q₈	—	17	1	no	—
707	C₂×D₄	—	17	1	no	—
708	C₂×D₄	—	17	1	no	—
709	C₂×D₄	—	17	1	no	—
710	C₂×D₄	—	17	1	no	—
711	C₂×D₄	—	17	1	no	—
712	C₂×D₄	—	17	1	no	—
713	C₂×D₄	—	17	1	no	—
714	C₂×D₄	—	17	1	no	—
715	C₂×D₄	—	17	1	no	—
716	C₂×D₄	—	17	1	no	—
717	C₂×D₄	—	17	1	no	—
718	C₂×D₄	—	17	1	no	—
719	C₂×D₄	—	17	1	no	—
720	C₂×D₄	—	17	1	no	—
721	C₂×D₄	—	17	1	no	—
722	C₂×D₄	—	17	1	no	—
723	C₂×D₄	—	17	1	no	—
724	C₂×D₄	—	17	1	no	—
725	C₂×D₄	—	17	1	no	—
726	C₂×D₄	—	17	1	no	—
727	C₂×D₄	—	17	1	no	—
728	C₂×D₄	—	68	2	no	—
729	C₂×D₄	—	68	2	no	—
730	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
731	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
732	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
733	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
734	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
735	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
736	C₂²×C₄	—	17	1	no	—
737	C₂²×C₄	—	17	1	no	—
738	C₂²×C₄	—	17	1	no	—
739	C₂²×C₄	—	17	1	no	—
740	C₂²×C₄	—	17	1	no	—
741	C₂²×C₄	—	17	1	no	—
742	C₂²×C₄	—	17	1	no	—
743	C₂²×C₄	—	17	1	no	—
744	C₂²×C₄	—	17	1	no	—
745	C₂²×C₄	—	17	1	no	—
746	C₂²×C₄	—	17	1	no	—
747	C₂²×C₄	—	17	1	no	—
748	C₂²×C₄	—	17	1	no	—
749	C₂²×C₄	—	17	1	no	—
750	C₂²×C₄	—	17	1	no	—
751	C₂²×C₄	—	17	1	no	—
752	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
753	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
754	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
755	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
756	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
757	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
758	C₄⋊C₄	—	17	1	no	—
759	C₄⋊C₄	—	17	1	no	—
760	C₄⋊C₄	—	17	1	no	—
761	C₄⋊C₄	—	17	1	no	—
762	C₄⋊C₄	—	17	1	no	—
763	C₄⋊C₄	—	17	1	no	—
764	C₄⋊C₄	—	17	1	no	—
765	C₄⋊C₄	—	17	1	no	—
766	C₄⋊C₄	—	17	1	no	—
767	C₄⋊C₄	—	17	1	no	—
768	C₄⋊C₄	—	17	1	no	—
769	C₄⋊C₄	—	17	1	no	—
770	C₄⋊C₄	—	17	1	no	—
771	C₄⋊C₄	—	17	1	no	—
772	C₄⋊C₄	—	17	1	no	—
773	C₄⋊C₄	—	17	1	no	—
774	C₄⋊C₄	—	17	1	no	—
775	C₄⋊C₄	—	17	1	no	—
776	C₄⋊C₄	—	17	1	no	—
777	C₄⋊C₄	—	17	1	no	—
778	C₄⋊C₄	—	17	1	no	—
779	C₄⋊C₄	—	17	1	no	—
780	C₄⋊C₄	—	17	1	no	—
781	C₄⋊C₄	—	17	1	no	—
782	C₄⋊C₄	—	17	1	no	—
783	C₄⋊C₄	—	17	1	no	—
784	C₄⋊C₄	—	17	1	no	—
785	C₄⋊C₄	—	17	1	no	—
786	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
787	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
788	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
789	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
790	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
791	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
792	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
793	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
794	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
795	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
796	C₂²⋊C₄	—	17	1	no	—
797	C₂²⋊C₄	—	17	1	no	—
798	C₂²⋊C₄	—	17	1	no	—
799	C₂²⋊C₄	—	17	1	no	—
800	C₂²⋊C₄	—	17	1	no	—
801	C₂²⋊C₄	—	17	1	no	—
802	C₂²⋊C₄	—	17	1	no	—
803	C₂²⋊C₄	—	17	1	no	—
804	C₂²⋊C₄	—	17	1	no	—
805	C₂²⋊C₄	—	17	1	no	—
806	C₂²⋊C₄	—	17	1	no	—
807	C₂²⋊C₄	—	17	1	no	—
808	C₂²⋊C₄	—	17	1	no	—
809	C₂²⋊C₄	—	17	1	no	—
810	C₂²⋊C₄	—	17	1	no	—
811	C₂²⋊C₄	—	17	1	no	—
812	C₂²⋊C₄	—	17	1	no	—
813	C₂²⋊C₄	—	17	1	no	—
814	C₂²⋊C₄	—	17	1	no	—
815	C₂²⋊C₄	—	17	1	no	—
816	C₂²⋊C₄	—	17	1	no	—
817	C₂²⋊C₄	—	17	1	no	—
818	C₂²⋊C₄	—	17	1	no	—
819	C₂²⋊C₄	—	17	1	no	—
820	C₂²⋊C₄	—	17	1	no	—
821	C₂²⋊C₄	—	17	1	no	—
822	C₂²⋊C₄	—	17	1	no	—
823	C₂²⋊C₄	—	17	1	no	—
824	C₂²⋊C₄	—	17	1	no	—
825	C₂²⋊C₄	—	17	1	no	—
826	C₂²⋊C₄	—	17	1	no	—
827	C₂²⋊C₄	—	17	1	no	—
828	C₂²⋊C₄	—	17	1	no	—
829	C₂²⋊C₄	—	17	1	no	—
830	C₂²⋊C₄	—	17	1	no	—
831	C₂²⋊C₄	—	17	1	no	—
832	C₂²⋊C₄	—	17	1	no	—
833	C₂²⋊C₄	—	17	1	no	—
834	C₂²⋊C₄	—	17	1	no	—
835	C₂²⋊C₄	—	17	1	no	—
836	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
837	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
838	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
839	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
840	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
841	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
842	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
843	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
844	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
845	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
846	C₄²	—	17	1	no	—
847	C₄²	—	17	1	no	—
848	C₄²	—	17	1	no	—
849	C₄²	—	17	1	no	—
850	C₄²	—	17	1	no	—
851	C₄²	—	17	1	no	—
852	C₄²	—	17	1	no	—
853	C₄²	C₂²×D₁₇	1	1	yes	characteristic
854	C₄²	C₂²×D₁₇	1	1	yes	characteristic
855	C₄²	C₂²×D₁₇	1	1	yes	characteristic
856	C₂³	—	17	1	no	—
857	C₂³	—	17	1	no	—
858	C₂³	—	17	1	no	—
859	C₂³	—	17	1	no	—
860	C₂³	—	17	1	no	—
861	C₂³	—	34	2	no	—
862	C₂³	—	68	1	no	—
863	C₂³	—	68	1	no	—
864	C₂³	—	68	1	no	—
865	C₂³	—	68	1	no	—
866	C₂³	—	68	1	no	—
867	C₂³	—	68	1	no	—
868	C₂³	—	68	1	no	—
869	C₂³	—	68	1	no	—
870	C₂³	C₂³×D₁₇	1	1	yes	characteristic
871	C₂³	C₂³×D₁₇	1	1	yes	characteristic
872	C₂³	C₂³×D₁₇	1	1	yes	characteristic
873	C₂³	C₂³×D₁₇	1	1	yes	characteristic
874	Q₈	—	68	1	no	—
875	Q₈	—	68	1	no	—
876	Q₈	—	68	1	no	—
877	Q₈	—	68	1	no	—
878	Q₈	—	68	1	no	—
879	D₄	—	2	2	no	—
880	D₄	—	2	2	no	—
881	D₄	—	2	2	no	—
882	D₄	—	4	1	no	—
883	D₄	—	4	1	no	—
884	D₄	—	4	1	no	—
885	D₄	—	34	2	no	—
886	D₄	—	34	2	no	—
887	D₄	—	34	2	no	—
888	D₄	—	68	1	no	—
889	D₄	—	68	1	no	—
890	D₄	—	68	1	no	—
891	D₄	—	68	1	no	—
892	D₄	—	68	1	no	—
893	D₄	—	68	1	no	—
894	D₄	—	68	1	no	—
895	D₄	—	68	1	no	—
896	D₄	—	68	1	no	—
897	D₄	—	68	1	no	—
898	D₄	—	68	1	no	—
899	D₄	—	68	1	no	—
900	D₄	—	68	1	no	—
901	D₄	—	68	1	no	—
902	D₄	—	68	1	no	—
903	D₄	—	68	1	no	—
904	D₄	—	68	1	no	—
905	D₄	—	68	1	no	—
906	C₂×C₄	—	4	1	no	—
907	C₂×C₄	—	4	1	no	—
908	C₂×C₄	—	4	1	no	—
909	C₂×C₄	—	4	1	no	—
910	C₂×C₄	—	4	1	no	—
911	C₂×C₄	—	4	1	no	—
912	C₂×C₄	—	17	1	no	—
913	C₂×C₄	—	17	1	no	—
914	C₂×C₄	—	17	1	no	—
915	C₂×C₄	—	17	1	no	—
916	C₂×C₄	—	17	1	no	—
917	C₂×C₄	—	17	1	no	—
918	C₂×C₄	—	17	1	no	—
919	C₂×C₄	—	17	1	no	—
920	C₂×C₄	—	17	1	no	—
921	C₂×C₄	—	17	1	no	—
922	C₂×C₄	—	17	1	no	—
923	C₂×C₄	—	34	2	no	—
924	C₂×C₄	—	34	2	no	—
925	C₂×C₄	—	68	1	no	—
926	C₂×C₄	—	68	1	no	—
927	C₂×C₄	—	68	1	no	—
928	C₂×C₄	—	68	1	no	—
929	C₂×C₄	—	68	1	no	—
930	C₂×C₄	—	68	1	no	—
931	C₂×C₄	—	68	1	no	—
932	C₂×C₄	—	68	1	no	—
933	C₂×C₄	—	68	1	no	—
934	C₂×C₄	—	68	1	no	—
935	C₂×C₄	—	68	1	no	—
936	C₂×C₄	—	68	1	no	—
937	C₂×C₄	—	68	1	no	—
938	C₂×C₄	—	68	1	no	—
939	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
940	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
941	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
942	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
943	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
944	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
945	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
946	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
947	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
948	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
949	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
950	C₂²	—	2	1	no	—
951	C₂²	—	2	1	no	—
952	C₂²	—	2	1	no	—
953	C₂²	—	2	1	no	—
954	C₂²	—	2	1	no	—
955	C₂²	—	2	1	no	—
956	C₂²	—	2	1	no	—
957	C₂²	—	2	1	no	—
958	C₂²	—	2	1	no	—
959	C₂²	—	2	1	no	—
960	C₂²	—	2	1	no	—
961	C₂²	—	34	1	no	—
962	C₂²	—	34	1	no	—
963	C₂²	—	34	1	no	—
964	C₂²	—	34	1	no	—
965	C₂²	—	34	1	no	—
966	C₂²	—	34	1	no	—
967	C₂²	—	34	1	no	—
968	C₂²	—	34	1	no	—
969	C₂²	—	34	1	no	—
970	C₂²	—	34	1	no	—
971	C₂²	—	34	1	no	—
972	C₂²	—	34	1	no	—
973	C₂²	—	34	1	no	—
974	C₂²	—	34	1	no	—
975	C₂²	—	34	1	no	—
976	C₂²	—	136	2	no	—
977	C₂²	—	136	2	no	—
978	C₂²	—	136	2	no	—
979	C₂²	#10587696	1	2	yes	—
980	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
981	C₄	—	2	1	no	—
982	C₄	—	2	1	no	—
983	C₄	—	2	1	no	—
984	C₄	—	2	1	no	—
985	C₄	—	2	1	no	—
986	C₄	—	2	1	no	—
987	C₄	—	2	1	no	—
988	C₄	—	2	1	no	—
989	C₄	—	2	1	no	—
990	C₄	—	2	1	no	—
991	C₄	—	2	1	no	—
992	C₄	—	34	1	no	—
993	C₄	—	34	1	no	—
994	C₄	—	34	1	no	—
995	C₄	—	34	1	no	—
996	C₄	—	34	1	no	—
997	C₄	—	34	1	no	—
998	C₄	—	34	1	no	—
999	C₄	—	34	1	no	—
1000	C₄	—	34	1	no	—
1001	C₄	—	34	1	no	—
1002	C₄	—	34	1	no	—
1003	C₂	—	2	2	no	—
1004	C₂	—	4	1	no	—
1005	C₂	—	4	1	no	—
1006	C₂	—	4	1	no	—
1007	C₂	—	68	1	no	—
1008	C₂	—	68	1	no	—
1009	C₂	—	68	1	no	—
1010	C₂	—	68	1	no	—
1011	C₂	—	68	1	no	—
1012	C₂	C₂×#10587696	1	1	yes	characteristic
1013	C₂	#11763644	1	1	yes	characteristic
1014	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#553	C₂
hypercenter	#553	D₁₇
hypocenter	C₁₇	#3560
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #11763563	C₂	semidirect
2. #11763561	C₂	semidirect
3. #11763549	C₂	semidirect
4. #11763547	C₂	semidirect
5. #11763510	C₂	semidirect
6. #11763507	C₂	semidirect
7. #11763505	C₂	semidirect
8. #11763483	C₂	semidirect
9. #11763482	C₂	semidirect
10. #11763463	C₂	semidirect
11. #11763459	C₂	semidirect
12. #11763454	C₂	semidirect
13. #11763454	C₂	semidirect
14. #11763448	C₂	semidirect
15. #11763448	C₂	semidirect
16. #11763430	C₂	semidirect
17. #11763425	C₂	semidirect
18. #11763407	C₂	semidirect
19. #11763403	C₂	semidirect
20. #11763401	C₂	semidirect
21. #11763398	C₂	semidirect
22. #11763396	C₂	semidirect
23. #11763395	C₂	semidirect
24. #11763392	C₂	semidirect
25. #11763392	C₂	semidirect
26. #11763386	C₂	semidirect
27. #11763367	C₂	semidirect
28. #11763354	C₂	semidirect
29. #11763339	C₂	semidirect
30. C₂×#10587584	C₂	semidirect
31. C₁₇×#553	C₂	semidirect
32. C₂×#63254	C₂²	semidirect
33. C₂×#63254	C₂²	semidirect
34. C₂×#63254	C₂²	semidirect
35. C₂×#63254	C₂²	semidirect
38. C₁₇×#126	C₂²	semidirect
39. C₁₇×#126	C₂²	semidirect
40. C₁₇×#125	C₂²	semidirect
41. C₁₇×#123	C₂²	semidirect
42. C₁₇×#123	C₂²	semidirect
44. C₁₇×#121	C₂²	semidirect
45. C₁₇×#121	C₂²	semidirect
46. C₁₇×#121	C₂²	semidirect
47. C₄×D₄×C₁₇	C₂²	semidirect
48. C₄×D₄×C₁₇	C₂²	semidirect
49. C₄×D₄×C₁₇	C₂²	semidirect
50. C₄×D₄×C₁₇	C₂²	semidirect
51. C₁₇×#117	C₂²	semidirect
52. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
53. #10587626	C₂²	semidirect
58. #10587625	C₂²	semidirect
59. #10587625	C₂²	semidirect
60. #10587625	C₂²	semidirect
61. #10587624	C₂²	semidirect
65. #10587623	C₂²	semidirect
66. #10587623	C₂²	semidirect
67. #10587621	C₂²	semidirect
68. #10587621	C₂²	semidirect
69. D₄×Dic₁₇	C₂²	semidirect
70. D₄×Dic₁₇	C₂²	semidirect
74. #10587616	C₂²	semidirect
75. #10587616	C₂²	semidirect
76. #10587616	C₂²	semidirect
77. #10587616	C₂²	semidirect
78. #10587615	C₂²	semidirect
79. #10587615	C₂²	semidirect
80. C₄×C₂²⋊D₁₇	C₂²	semidirect
81. C₄×C₂²⋊D₁₇	C₂²	semidirect
82. C₄×C₂²⋊D₁₇	C₂²	semidirect
83. C₄×C₂²⋊D₁₇	C₂²	semidirect
87. C₂×#63227	C₂²	semidirect
88. C₂×#63227	C₂²	semidirect
89. #10587612	C₂²	semidirect
90. C₂×C₄⋊Dic₁₇	C₂²	semidirect
91. C₂×C₄⋊Dic₁₇	C₂²	semidirect
92. #10587610	C₂²	semidirect
93. C₂×#63225	C₂²	semidirect
94. C₂×C₄×Dic₁₇	C₂²	semidirect
95. #10587584	C₂²	semidirect
96. #10587584	C₂²	semidirect
97. #10587584	C₂²	semidirect
98. #10587584	C₂²	semidirect
99. #10587584	C₂²	semidirect
100. #10587584	C₂²	semidirect
101. #10587584	C₂²	semidirect
102. #10587584	C₂²	semidirect
103. #10587584	C₂²	semidirect
104. #10587584	C₂²	semidirect
105. #10587584	C₂²	semidirect
106. #10587584	C₂²	semidirect
107. #10587583	C₂²	semidirect
108. #10587583	C₂²	semidirect
109. #10587583	C₂²	semidirect
110. #10587583	C₂²	semidirect
111. #10587582	C₂²	semidirect
112. #10587582	C₂²	semidirect
113. #10587582	C₂²	semidirect
114. #10587582	C₂²	semidirect
115. #10587582	C₂²	semidirect
118. #10587581	C₂²	semidirect
123. #10587580	C₂²	semidirect
124. #10587580	C₂²	semidirect
125. #10587580	C₂²	semidirect
126. #10587579	C₂²	semidirect
127. #10587579	C₂²	semidirect
128. #10587578	C₂²	semidirect
129. C₄⋊C₄×D₁₇	C₂²	semidirect
130. #10587576	C₂²	semidirect
131. #10587575	C₂²	semidirect
132. #10587575	C₂²	semidirect
133. #10587574	C₂²	semidirect
134. #10587574	C₂²	semidirect
137. #10587572	C₂²	semidirect
138. #10587572	C₂²	semidirect
139. #10587572	C₂²	semidirect
140. #10587572	C₂²	semidirect
143. #10587571	C₂²	semidirect
144. #10587571	C₂²	semidirect
145. #10587571	C₂²	semidirect
146. #10587571	C₂²	semidirect
149. #10587570	C₂²	semidirect
150. #10587570	C₂²	semidirect
151. #10587570	C₂²	semidirect
154. #10587569	C₂²	semidirect
155. #10587569	C₂²	semidirect
156. #10587569	C₂²	semidirect
160. #10587568	C₂²	semidirect
161. #10587568	C₂²	semidirect
162. #10587567	C₂²	semidirect
163. #10587567	C₂²	semidirect
164. #10587567	C₂²	semidirect
165. #10587567	C₂²	semidirect
166. C₂²⋊C₄×D₁₇	C₂²	semidirect
167. C₂²⋊C₄×D₁₇	C₂²	semidirect
168. #10587565	C₂²	semidirect
169. #10587565	C₂²	semidirect
170. #10587564	C₂²	semidirect
171. #10587564	C₂²	semidirect
172. #10587564	C₂²	semidirect
173. #10587564	C₂²	semidirect
174. #10587564	C₂²	semidirect
175. #10587562	C₂²	semidirect
176. #10587562	C₂²	semidirect
179. #10587561	C₂²	semidirect
180. C₄×D₆₈	C₂²	semidirect
181. C₄×D₆₈	C₂²	semidirect
182. C₄×D₆₈	C₂²	semidirect
183. #10587558	C₂²	semidirect
184. #10587556	C₂²	semidirect
185. #10587555	C₂²	semidirect
186. C₄×Dic₃₄	C₂²	semidirect
503. #553	D₁₇	semidirect
565. #126	C₂×D₁₇	semidirect
566. #126	C₂×D₁₇	semidirect
571. #125	C₂×D₁₇	semidirect
603. #123	C₂×D₁₇	semidirect
604. #123	C₂×D₁₇	semidirect
644. #121	C₂×D₁₇	semidirect
645. #121	C₂×D₁₇	semidirect
646. #121	C₂×D₁₇	semidirect
673. C₄×D₄	C₂×D₁₇	semidirect
674. C₄×D₄	C₂×D₁₇	semidirect
675. C₄×D₄	C₂×D₁₇	semidirect
676. C₄×D₄	C₂×D₁₇	semidirect
680. #117	C₂×D₁₇	semidirect
685. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
694. C₁₇	#3560	semidirect

Maximal subgroups

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

subgroup	index
#11763563	2
#11763561	2
#11763549	2
#11763547	2
#11763510	2
#11763507	2
#11763505	2
#11763483	2
#11763482	2
#11763463	2
#11763459	2
#11763454	2
#11763448	2
#11763430	2
#11763425	2
#11763407	2
#11763403	2
#11763401	2
#11763398	2
#11763396	2
#11763395	2
#11763392	2
#11763386	2
#11763367	2
#11763354	2
#11763339	2
C₂×#10587584	2
C₁₇×#553	2
#3560	17