Subgroups — #14542988

Order 2176.

1038 conjugacy classes of subgroups.

The subgroup lattice has 982 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	#11763558	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763555	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763555	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763514	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763500	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763491	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763488	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763488	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763486	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763486	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763461	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763460	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763450	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763438	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763434	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763431	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763429	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763407	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763407	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763406	C₂	1	1	yes	maximal, characteristic, complemented
23	#11763405	C₂	1	1	yes	maximal, characteristic, complemented
24	#11763401	C₂	1	1	yes	maximal, characteristic, complemented
25	#11763392	C₂	1	1	yes	maximal, characteristic, complemented
26	#11763384	C₂	1	1	yes	maximal, characteristic, complemented
27	#11763382	C₂	1	1	yes	maximal, characteristic, complemented
28	#11763318	C₂	1	1	yes	maximal, characteristic, complemented
29	C₂×#10587580	C₂	1	1	yes	maximal, characteristic, complemented
30	C₂²⋊Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
31	C₁₇×#554	C₂	1	1	yes	maximal, characteristic, complemented
32	C₂×#63256	C₂²	1	1	yes	characteristic
33	C₂×Q₈×D₁₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#63252	C₂²	1	1	yes	characteristic
35	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
36	C₂²×D₆₈	C₂²	1	1	yes	characteristic
37	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic
38	C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
39	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
40	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
42	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
43	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
44	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
45	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
47	C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic, complemented
48	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
49	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
50	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
51	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
53	#10587633	C₂²	1	1	yes	characteristic
54	#10587633	C₂²	1	1	yes	characteristic, complemented
55	#10587633	C₂²	1	1	yes	characteristic, complemented
56	#10587632	C₂²	1	1	yes	characteristic, complemented
57	#10587632	C₂²	1	1	yes	characteristic, complemented
58	#10587632	C₂²	1	1	yes	characteristic, complemented
59	#10587632	C₂²	1	1	yes	characteristic, complemented
60	#10587632	C₂²	1	1	yes	characteristic, complemented
61	#10587630	C₂²	1	1	yes	characteristic, complemented
62	#10587630	C₂²	1	1	yes	characteristic, complemented
63	#10587625	C₂²	1	1	yes	characteristic
64	#10587623	C₂²	1	1	yes	characteristic
65	#10587623	C₂²	1	1	yes	characteristic
66	#10587621	C₂²	1	1	yes	characteristic
67	#10587616	C₂²	1	1	yes	characteristic
68	#10587616	C₂²	1	1	yes	characteristic, complemented
69	#10587615	C₂²	1	1	yes	characteristic, complemented
70	#10587615	C₂²	1	1	yes	characteristic, complemented
71	#10587615	C₂²	1	1	yes	characteristic, complemented
72	#10587615	C₂²	1	1	yes	characteristic, complemented
73	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
74	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
75	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
76	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
77	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
79	C₂×#63227	C₂²	1	1	yes	characteristic
80	C₂×#63227	C₂²	1	1	yes	characteristic
81	C₂×#63227	C₂²	1	1	yes	characteristic
82	#10587610	C₂²	1	1	yes	characteristic
83	#10587610	C₂²	1	1	yes	characteristic
84	#10587610	C₂²	1	1	yes	characteristic
85	#10587610	C₂²	1	1	yes	characteristic, complemented
86	C₂×#63225	C₂²	1	1	yes	characteristic
87	#10587584	C₂²	1	1	yes	characteristic, complemented
88	#10587584	C₂²	1	1	yes	characteristic, complemented
89	#10587584	C₂²	1	1	yes	characteristic, complemented
90	#10587584	C₂²	1	1	yes	characteristic, complemented
91	#10587584	C₂²	1	1	yes	characteristic, complemented
92	#10587584	C₂²	1	1	yes	characteristic, complemented
93	#10587584	C₂²	1	1	yes	characteristic, complemented
94	#10587583	C₂²	1	1	yes	characteristic, complemented
95	#10587583	C₂²	1	1	yes	characteristic, complemented
96	#10587583	C₂²	1	1	yes	characteristic, complemented
97	#10587583	C₂²	1	1	yes	characteristic, complemented
98	#10587582	C₂²	1	1	yes	characteristic, complemented
99	#10587582	C₂²	1	1	yes	characteristic, complemented
100	#10587582	C₂²	1	1	yes	characteristic, complemented
101	#10587582	C₂²	1	1	yes	characteristic, complemented
102	#10587582	C₂²	1	1	yes	characteristic, complemented
103	#10587582	C₂²	1	1	yes	characteristic, complemented
104	#10587582	C₂²	1	1	yes	characteristic, complemented
105	#10587582	C₂²	1	1	yes	characteristic, complemented
106	#10587582	C₂²	1	1	yes	characteristic, complemented
107	#10587582	C₂²	1	1	yes	characteristic, complemented
108	#10587582	C₂²	1	1	yes	characteristic, complemented
109	#10587582	C₂²	1	1	yes	characteristic, complemented
110	#10587581	C₂²	1	1	yes	characteristic
111	#10587581	C₂²	1	1	yes	characteristic
112	#10587581	C₂²	1	1	yes	characteristic
113	#10587580	C₂²	1	1	yes	characteristic
114	#10587580	C₂²	1	1	yes	characteristic
115	#10587580	C₂²	1	1	yes	characteristic
116	#10587580	C₂²	1	1	yes	characteristic
117	#10587580	C₂²	1	1	yes	characteristic
118	#10587580	C₂²	1	1	yes	characteristic
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
124	#10587580	C₂²	1	1	yes	characteristic
125	#10587580	C₂²	1	1	yes	characteristic, complemented
126	#10587580	C₂²	1	1	yes	characteristic, complemented
127	#10587580	C₂²	1	1	yes	characteristic, complemented
128	#10587580	C₂²	1	1	yes	characteristic, complemented
129	#10587580	C₂²	1	1	yes	characteristic, complemented
130	#10587580	C₂²	1	1	yes	characteristic, complemented
131	#10587579	C₂²	1	1	yes	characteristic
132	#10587579	C₂²	1	1	yes	characteristic, complemented
133	#10587579	C₂²	1	1	yes	characteristic, complemented
134	#10587578	C₂²	1	1	yes	characteristic, complemented
135	#10587578	C₂²	1	1	yes	characteristic, complemented
136	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
137	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
138	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
139	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
140	#10587575	C₂²	1	1	yes	characteristic, complemented
141	#10587575	C₂²	1	1	yes	characteristic, complemented
142	#10587575	C₂²	1	1	yes	characteristic, complemented
143	#10587575	C₂²	1	1	yes	characteristic, complemented
144	#10587575	C₂²	1	1	yes	characteristic, complemented
145	#10587575	C₂²	1	1	yes	characteristic, complemented
146	#10587575	C₂²	1	1	yes	characteristic, complemented
147	#10587574	C₂²	1	1	yes	characteristic, complemented
148	#10587574	C₂²	1	1	yes	characteristic, complemented
149	#10587574	C₂²	1	1	yes	characteristic, complemented
150	#10587573	C₂²	1	1	yes	characteristic, complemented
151	#10587572	C₂²	1	1	yes	characteristic
152	#10587571	C₂²	1	1	yes	characteristic, complemented
153	#10587571	C₂²	1	1	yes	characteristic, complemented
154	#10587571	C₂²	1	1	yes	characteristic, complemented
155	#10587570	C₂²	1	1	yes	characteristic
156	#10587570	C₂²	1	1	yes	characteristic
157	#10587570	C₂²	1	1	yes	characteristic, complemented
158	#10587570	C₂²	1	1	yes	characteristic, complemented
159	#10587569	C₂²	1	1	yes	characteristic, complemented
160	#10587569	C₂²	1	1	yes	characteristic, complemented
161	#10587569	C₂²	1	1	yes	characteristic, complemented
162	#10587569	C₂²	1	1	yes	characteristic, complemented
163	#10587568	C₂²	1	1	yes	characteristic
164	#10587568	C₂²	1	1	yes	characteristic
165	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
166	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
167	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
168	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic
169	#10587565	C₂²	1	1	yes	characteristic, complemented
170	#10587564	C₂²	1	1	yes	characteristic
171	#10587564	C₂²	1	1	yes	characteristic
172	#10587564	C₂²	1	1	yes	characteristic
173	#10587563	C₂²	1	1	yes	characteristic
174	#10587563	C₂²	1	1	yes	characteristic
175	#10587562	C₂²	1	1	yes	characteristic, complemented
176	#10587562	C₂²	1	1	yes	characteristic, complemented
177	#10587562	C₂²	1	1	yes	characteristic, complemented
178	#10587562	C₂²	1	1	yes	characteristic, complemented
179	#10587561	C₂²	1	1	yes	characteristic
180	#10587561	C₂²	1	1	yes	characteristic, complemented
181	C₄×D₆₈	C₂²	1	1	yes	characteristic
182	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
183	#10587558	C₂²	1	1	yes	characteristic, complemented
184	#10587558	C₂²	1	1	yes	characteristic, complemented
185	#10587558	C₂²	1	1	yes	characteristic, complemented
186	#10587556	C₂²	1	1	yes	characteristic, complemented
187	C₂³×D₁₇	C₂³	1	1	yes	characteristic
188	C₂³×D₁₇	C₂³	1	1	yes	characteristic
189	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
190	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
191	C₂×Q₈×C₁₇	C₂³	1	1	yes	characteristic
192	C₂×D₄×C₁₇	C₂³	1	1	yes	characteristic
193	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
194	C₂²×C₄×C₁₇	C₂³	1	1	yes	characteristic
195	C₂²×C₄×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	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
200	C₂×C₂²⋊D₁₇	C₂³	1	1	yes	characteristic
201	C₂×C₂²⋊D₁₇	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	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
206	C₂²×Dic₁₇	C₂³	1	1	yes	characteristic
207	#63256	—	4	2	no	—
208	Q₈×D₁₇	—	4	2	no	—
209	#63252	—	4	2	no	—
210	#63252	—	4	2	no	—
211	C₂×D₆₈	—	4	2	no	—
212	C₂×D₆₈	C₂³	1	1	yes	characteristic
213	C₂×D₆₈	C₂³	1	1	yes	characteristic
214	C₂×D₆₈	C₂³	1	1	yes	characteristic
215	C₂×D₆₈	C₂³	1	1	yes	characteristic
216	C₂×D₆₈	C₂³	1	1	yes	characteristic
217	C₂×D₆₈	C₂³	1	1	yes	characteristic
218	C₂×D₆₈	C₂³	1	1	yes	characteristic
219	C₂×D₆₈	C₂³	1	1	yes	characteristic
220	C₂×C₄×D₁₇	—	4	2	no	—
221	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
222	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
223	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
224	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
225	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
226	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
227	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
228	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
229	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
230	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
231	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
232	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
233	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
234	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
235	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
236	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
237	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
238	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
239	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
240	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
241	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
242	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
243	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
244	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
245	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
246	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
247	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
248	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
249	C₄⋊C₄×C₁₇	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	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
259	C₂²⋊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	C₄²×C₁₇	C₂³	1	1	yes	characteristic
265	C₄²×C₁₇	C₂³	1	1	yes	characteristic
266	C₄²×C₁₇	C₂³	1	1	yes	characteristic
267	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
268	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
269	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
270	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
271	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
272	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
273	#63227	C₂³	1	1	yes	characteristic
274	#63227	C₂³	1	1	yes	characteristic
275	#63227	C₂³	1	1	yes	characteristic
276	#63227	C₂³	1	1	yes	characteristic
277	#63227	C₂³	1	1	yes	characteristic
278	#63227	C₂³	1	1	yes	characteristic
279	#63227	C₂³	1	1	yes	characteristic
280	#63227	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	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
308	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
309	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
310	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
311	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
312	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
313	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
314	C₄⋊Dic₁₇	C₂³	1	1	yes	characteristic
315	#63225	C₂³	1	1	yes	characteristic
316	#63225	C₂³	1	1	yes	characteristic
317	#63225	C₂³	1	1	yes	characteristic
318	#63225	C₂³	1	1	yes	characteristic
319	#63225	C₂³	1	1	yes	characteristic
320	#63225	C₂³	1	1	yes	characteristic
321	#63225	C₂³	1	1	yes	characteristic
322	#63225	C₂³	1	1	yes	characteristic
323	#63225	C₂³	1	1	yes	characteristic
324	#63225	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	C₂²×D₁₇	—	2	2	no	—
351	C₂²×D₁₇	—	2	2	no	—
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	C₂⁴	1	1	yes	characteristic
357	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
358	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
359	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
360	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
361	Q₈×C₁₇	—	4	1	no	—
362	Q₈×C₁₇	—	4	1	no	—
363	Q₈×C₁₇	—	4	1	no	—
364	D₄×C₁₇	—	2	2	no	—
365	C₂×C₄×C₁₇	—	4	1	no	—
366	C₂×C₄×C₁₇	—	4	1	no	—
367	C₂×C₄×C₁₇	—	4	1	no	—
368	C₂×C₄×C₁₇	—	4	1	no	—
369	C₂×C₄×C₁₇	—	4	1	no	—
370	C₂×C₄×C₁₇	—	4	1	no	—
371	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
372	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
376	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
377	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	C₂²⋊D₁₇	—	2	2	no	—
385	C₂²⋊D₁₇	—	2	2	no	—
386	C₂²⋊D₁₇	—	4	1	no	—
387	C₂²⋊D₁₇	—	4	1	no	—
388	C₂²⋊D₁₇	—	4	1	no	—
389	C₂²⋊D₁₇	—	4	1	no	—
390	C₂×Dic₁₇	—	2	2	no	—
391	C₂×Dic₁₇	—	4	1	no	—
392	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
393	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
394	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
395	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
396	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
397	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
398	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
399	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
400	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
401	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
402	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
403	D₆₈	—	2	2	no	—
404	D₆₈	—	2	2	no	—
405	D₆₈	—	2	2	no	—
406	D₆₈	—	4	1	no	—
407	D₆₈	—	4	1	no	—
408	D₆₈	—	4	1	no	—
409	D₆₈	—	4	1	no	—
410	D₆₈	—	4	1	no	—
411	C₄×D₁₇	—	2	2	no	—
412	C₄×D₁₇	—	2	2	no	—
413	C₄×D₁₇	—	2	2	no	—
414	C₄×D₁₇	—	2	2	no	—
415	C₄×D₁₇	—	4	1	no	—
416	C₄×D₁₇	—	4	1	no	—
417	C₄×D₁₇	—	4	1	no	—
418	C₄×D₁₇	—	4	1	no	—
419	C₄×D₁₇	—	4	1	no	—
420	C₄×D₁₇	—	4	1	no	—
421	C₄×D₁₇	—	4	1	no	—
422	C₄×D₁₇	—	4	1	no	—
423	C₄×D₁₇	—	4	1	no	—
424	C₄×D₁₇	—	4	1	no	—
425	C₄×D₁₇	—	4	1	no	—
426	Dic₃₄	—	4	1	no	—
427	Dic₃₄	—	4	1	no	—
428	Dic₃₄	—	4	1	no	—
429	Dic₃₄	—	4	1	no	—
430	Dic₃₄	—	4	1	no	—
431	Dic₃₄	—	4	1	no	—
432	#3535	—	17	1	no	maximal, Sylow
433	C₂²×C₁₇	—	2	1	no	—
434	C₂²×C₁₇	—	2	1	no	—
435	C₂²×C₁₇	—	2	1	no	—
436	C₂²×C₁₇	—	2	1	no	—
437	C₂²×C₁₇	—	2	1	no	—
438	C₂²×C₁₇	2₋¹⁺⁴	1	2	yes	—
439	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
440	C₂×D₁₇	—	2	1	no	—
441	C₂×D₁₇	—	2	1	no	—
442	C₂×D₁₇	—	2	1	no	—
443	C₂×D₁₇	—	2	1	no	—
444	C₂×D₁₇	—	2	1	no	—
445	C₂×D₁₇	—	2	1	no	—
446	C₂×D₁₇	—	2	1	no	—
447	C₂×D₁₇	—	2	1	no	—
448	C₂×D₁₇	—	2	1	no	—
449	C₂×D₁₇	—	2	1	no	—
450	C₂×D₁₇	—	2	1	no	—
451	C₂×D₁₇	—	2	1	no	—
452	C₂×D₁₇	—	2	1	no	—
453	C₂×D₁₇	—	2	1	no	—
454	C₂×D₁₇	—	4	4	no	—
455	C₂×D₁₇	—	8	2	no	—
456	C₂×D₁₇	H(5,𝔽₂)	1	2	yes	—
457	C₄×C₁₇	—	2	1	no	—
458	C₄×C₁₇	—	2	1	no	—
459	C₄×C₁₇	—	2	1	no	—
460	C₄×C₁₇	—	2	1	no	—
461	C₄×C₁₇	—	2	1	no	—
462	C₄×C₁₇	—	2	1	no	—
463	C₄×C₁₇	—	2	1	no	—
464	C₄×C₁₇	—	2	1	no	—
465	C₄×C₁₇	—	2	1	no	—
466	C₄×C₁₇	—	2	1	no	—
467	C₄×C₁₇	—	2	1	no	—
468	C₄×C₁₇	—	2	1	no	—
469	C₄×C₁₇	—	2	1	no	—
470	Dic₁₇	—	2	1	no	—
471	Dic₁₇	—	2	1	no	—
472	Dic₁₇	—	2	1	no	—
473	Dic₁₇	—	2	1	no	—
474	Dic₁₇	—	2	1	no	—
475	Dic₁₇	—	2	1	no	—
476	Dic₁₇	—	2	1	no	—
477	Dic₁₇	—	2	1	no	—
478	Dic₁₇	—	2	1	no	—
479	Dic₁₇	—	2	1	no	—
480	Dic₁₇	—	2	1	no	—
481	#563	—	17	1	no	—
482	#563	—	17	1	no	—
483	#562	—	17	1	no	—
484	#562	—	17	1	no	—
485	#554	—	17	1	no	—
486	#554	D₁₇	1	1	yes	characteristic, complemented
487	#552	—	17	1	no	—
488	#552	—	17	1	no	—
489	#551	—	17	1	no	—
490	#551	—	17	1	no	—
491	#551	—	17	1	no	—
492	#551	—	17	1	no	—
493	#547	—	17	1	no	—
494	#547	—	17	1	no	—
495	#546	—	17	1	no	—
496	#546	—	17	1	no	—
497	#544	—	17	1	no	—
498	#543	—	17	1	no	—
499	#542	—	17	1	no	—
500	#542	—	17	1	no	—
501	#539	—	17	1	no	—
502	#539	—	17	1	no	—
503	#539	—	17	1	no	—
504	#539	—	17	1	no	—
505	#539	—	17	1	no	—
506	#538	—	17	1	no	—
507	#536	—	17	1	no	—
508	#536	—	17	1	no	—
509	#525	—	17	1	no	—
510	C₂×#123	—	17	1	no	—
511	C₂×C₂²⋊Q₈	—	17	1	no	—
512	C₂×C₁₇	—	2	2	no	—
513	C₂×C₁₇	—	4	1	no	—
514	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
515	C₂×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
516	C₂×C₁₇	#585	1	1	yes	characteristic
517	D₁₇	—	2	2	no	—
518	D₁₇	—	4	1	no	—
519	D₁₇	—	4	1	no	—
520	D₁₇	—	4	1	no	—
521	D₁₇	—	4	1	no	—
522	C₂×#41	—	17	1	no	—
523	C₂×#41	—	17	1	no	—
524	C₂×#41	—	17	1	no	—
525	C₂²×Q₈	—	17	1	no	—
526	C₂²×D₄	—	17	1	no	—
527	C₂³×C₄	—	17	1	no	—
528	C₄⋊Q₈	—	17	1	no	—
529	C₄⋊Q₈	—	17	1	no	—
530	C₄⋊Q₈	—	17	1	no	—
531	C₄⋊Q₈	—	17	1	no	—
532	C₄⋊Q₈	—	17	1	no	—
533	C₄⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
534	#126	—	17	1	no	—
535	#126	—	17	1	no	—
536	#126	—	17	1	no	—
537	#126	—	17	1	no	—
538	#126	—	17	1	no	—
539	#126	—	17	1	no	—
540	#126	—	17	1	no	—
541	#126	—	17	1	no	—
542	#126	—	17	1	no	—
543	#126	—	17	1	no	—
544	#126	—	17	1	no	—
545	#126	—	17	1	no	—
546	#125	—	17	1	no	—
547	#125	—	17	1	no	—
548	#125	—	17	1	no	—
549	#125	—	17	1	no	—
550	#125	—	17	1	no	—
551	#125	—	17	1	no	—
552	#125	—	17	1	no	—
553	#125	—	17	1	no	—
554	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
555	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
556	#124	—	17	1	no	—
557	#124	—	17	1	no	—
558	#124	—	17	1	no	—
559	#124	—	17	1	no	—
560	#124	—	17	1	no	—
561	#124	—	17	1	no	—
562	#124	—	17	1	no	—
563	#124	—	17	1	no	—
564	#123	—	17	1	no	—
565	#123	—	17	1	no	—
566	#123	—	17	1	no	—
567	#123	—	17	1	no	—
568	#123	—	17	1	no	—
569	#123	—	17	1	no	—
570	#123	—	17	1	no	—
571	#123	—	17	1	no	—
572	#123	—	17	1	no	—
573	#123	—	17	1	no	—
574	#123	—	17	1	no	—
575	#123	—	17	1	no	—
576	#123	—	17	1	no	—
577	#123	—	17	1	no	—
578	#123	—	17	1	no	—
579	#123	—	17	1	no	—
580	#123	—	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	C₂²⋊Q₈	—	17	1	no	—
593	C₂²⋊Q₈	—	17	1	no	—
594	C₂²⋊Q₈	—	17	1	no	—
595	C₂²⋊Q₈	—	17	1	no	—
596	C₂²⋊Q₈	—	17	1	no	—
597	C₂²⋊Q₈	—	17	1	no	—
598	C₂²⋊Q₈	—	17	1	no	—
599	C₂²⋊Q₈	—	17	1	no	—
600	C₂²⋊Q₈	—	17	1	no	—
601	C₂²⋊Q₈	—	17	1	no	—
602	C₂²⋊Q₈	—	17	1	no	—
603	C₂²⋊Q₈	—	17	1	no	—
604	C₂²⋊Q₈	—	17	1	no	—
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	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
621	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
622	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic
623	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
624	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
625	C₂²⋊Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
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	#120	—	17	1	no	—
637	#120	—	17	1	no	—
638	#120	—	17	1	no	—
639	#120	—	17	1	no	—
640	C₄×Q₈	—	17	1	no	—
641	C₄×Q₈	C₂×D₁₇	1	1	yes	characteristic, complemented
642	C₄×D₄	—	17	1	no	—
643	C₄×D₄	—	17	1	no	—
644	C₄×D₄	—	17	1	no	—
645	C₄×D₄	—	17	1	no	—
646	C₄×D₄	—	17	1	no	—
647	C₄×D₄	—	17	1	no	—
648	C₄×D₄	—	17	1	no	—
649	C₄×D₄	—	17	1	no	—
650	C₄×D₄	—	17	1	no	—
651	C₄×D₄	—	17	1	no	—
652	C₄×D₄	—	17	1	no	—
653	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
654	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
655	C₄×D₄	C₂×D₁₇	1	1	yes	characteristic
656	#117	—	17	1	no	—
657	#117	—	17	1	no	—
658	#117	—	17	1	no	—
659	#117	—	17	1	no	—
660	#117	—	17	1	no	—
661	#117	—	17	1	no	—
662	#117	—	17	1	no	—
663	C₂×C₄⋊C₄	—	17	1	no	—
664	C₂×C₄⋊C₄	—	17	1	no	—
665	C₂×C₄⋊C₄	—	17	1	no	—
666	C₂×C₄⋊C₄	—	17	1	no	—
667	C₂×C₄⋊C₄	—	17	1	no	—
668	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic
669	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
670	C₂×C₂²⋊C₄	—	17	1	no	—
671	C₂×C₂²⋊C₄	—	17	1	no	—
672	C₂×C₂²⋊C₄	—	17	1	no	—
673	C₂×C₂²⋊C₄	—	17	1	no	—
674	C₂×C₂²⋊C₄	—	17	1	no	—
675	C₂×C₂²⋊C₄	—	17	1	no	—
676	C₂×C₂²⋊C₄	—	17	1	no	—
677	C₁₇	#3535	1	1	yes	characteristic, complemented, Sylow
678	C₂⁴	—	17	1	no	—
679	C₂⁴	—	17	1	no	—
680	#41	—	68	2	no	—
681	#41	—	68	2	no	—
682	#41	—	68	2	no	—
683	C₂×Q₈	—	17	1	no	—
684	C₂×Q₈	—	17	1	no	—
685	C₂×Q₈	—	17	1	no	—
686	C₂×Q₈	—	17	1	no	—
687	C₂×Q₈	—	17	1	no	—
688	C₂×Q₈	—	17	1	no	—
689	C₂×Q₈	—	68	2	no	—
690	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
691	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
692	C₂×Q₈	C₂²×D₁₇	1	1	yes	characteristic
693	C₂×D₄	—	17	1	no	—
694	C₂×D₄	—	17	1	no	—
695	C₂×D₄	—	17	1	no	—
696	C₂×D₄	—	17	1	no	—
697	C₂×D₄	—	17	1	no	—
698	C₂×D₄	—	17	1	no	—
699	C₂×D₄	—	17	1	no	—
700	C₂×D₄	—	17	1	no	—
701	C₂×D₄	—	17	1	no	—
702	C₂×D₄	—	17	1	no	—
703	C₂×D₄	—	17	1	no	—
704	C₂×D₄	—	17	1	no	—
705	C₂×D₄	—	17	1	no	—
706	C₂×D₄	—	17	1	no	—
707	C₂×D₄	—	68	2	no	—
708	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
709	C₂²×C₄	—	17	1	no	—
710	C₂²×C₄	—	17	1	no	—
711	C₂²×C₄	—	17	1	no	—
712	C₂²×C₄	—	17	1	no	—
713	C₂²×C₄	—	17	1	no	—
714	C₂²×C₄	—	17	1	no	—
715	C₂²×C₄	—	17	1	no	—
716	C₂²×C₄	—	17	1	no	—
717	C₂²×C₄	—	17	1	no	—
718	C₂²×C₄	—	17	1	no	—
719	C₂²×C₄	—	17	1	no	—
720	C₂²×C₄	—	17	1	no	—
721	C₂²×C₄	—	17	1	no	—
722	C₂²×C₄	—	17	1	no	—
723	C₂²×C₄	—	17	1	no	—
724	C₂²×C₄	—	17	1	no	—
725	C₂²×C₄	—	17	1	no	—
726	C₂²×C₄	—	68	2	no	—
727	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
728	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
729	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
730	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
731	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
732	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
733	C₄⋊C₄	—	17	1	no	—
734	C₄⋊C₄	—	17	1	no	—
735	C₄⋊C₄	—	17	1	no	—
736	C₄⋊C₄	—	17	1	no	—
737	C₄⋊C₄	—	17	1	no	—
738	C₄⋊C₄	—	17	1	no	—
739	C₄⋊C₄	—	17	1	no	—
740	C₄⋊C₄	—	17	1	no	—
741	C₄⋊C₄	—	17	1	no	—
742	C₄⋊C₄	—	17	1	no	—
743	C₄⋊C₄	—	17	1	no	—
744	C₄⋊C₄	—	17	1	no	—
745	C₄⋊C₄	—	17	1	no	—
746	C₄⋊C₄	—	17	1	no	—
747	C₄⋊C₄	—	17	1	no	—
748	C₄⋊C₄	—	17	1	no	—
749	C₄⋊C₄	—	17	1	no	—
750	C₄⋊C₄	—	17	1	no	—
751	C₄⋊C₄	—	17	1	no	—
752	C₄⋊C₄	—	17	1	no	—
753	C₄⋊C₄	—	17	1	no	—
754	C₄⋊C₄	—	17	1	no	—
755	C₄⋊C₄	—	17	1	no	—
756	C₄⋊C₄	—	17	1	no	—
757	C₄⋊C₄	—	17	1	no	—
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	C₂²×D₁₇	1	1	yes	characteristic
768	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
769	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
770	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
771	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
772	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
773	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
774	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
775	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
776	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
777	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
778	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
779	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
780	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
781	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
782	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
783	C₂²⋊C₄	—	17	1	no	—
784	C₂²⋊C₄	—	17	1	no	—
785	C₂²⋊C₄	—	17	1	no	—
786	C₂²⋊C₄	—	17	1	no	—
787	C₂²⋊C₄	—	17	1	no	—
788	C₂²⋊C₄	—	17	1	no	—
789	C₂²⋊C₄	—	17	1	no	—
790	C₂²⋊C₄	—	17	1	no	—
791	C₂²⋊C₄	—	17	1	no	—
792	C₂²⋊C₄	—	17	1	no	—
793	C₂²⋊C₄	—	17	1	no	—
794	C₂²⋊C₄	—	17	1	no	—
795	C₂²⋊C₄	—	17	1	no	—
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	C₂²×D₁₇	1	1	yes	characteristic
824	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
825	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
826	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
827	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
828	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
829	C₄²	—	17	1	no	—
830	C₄²	—	17	1	no	—
831	C₄²	—	17	1	no	—
832	C₄²	—	17	1	no	—
833	C₄²	—	17	1	no	—
834	C₄²	—	17	1	no	—
835	C₄²	—	17	1	no	—
836	C₄²	C₂²×D₁₇	1	1	yes	characteristic
837	C₄²	C₂²×D₁₇	1	1	yes	characteristic
838	C₄²	C₂²×D₁₇	1	1	yes	characteristic
839	C₂³	—	17	1	no	—
840	C₂³	—	17	1	no	—
841	C₂³	—	17	1	no	—
842	C₂³	—	17	1	no	—
843	C₂³	—	17	1	no	—
844	C₂³	—	34	2	no	—
845	C₂³	—	34	2	no	—
846	C₂³	—	34	2	no	—
847	C₂³	—	68	1	no	—
848	C₂³	—	68	1	no	—
849	C₂³	—	68	1	no	—
850	C₂³	C₂³×D₁₇	1	1	yes	characteristic
851	C₂³	C₂³×D₁₇	1	1	yes	characteristic
852	Q₈	—	4	1	no	—
853	Q₈	—	4	1	no	—
854	Q₈	—	4	1	no	—
855	Q₈	—	68	1	no	—
856	Q₈	—	68	1	no	—
857	Q₈	—	68	1	no	—
858	Q₈	—	68	1	no	—
859	Q₈	—	68	1	no	—
860	Q₈	—	68	1	no	—
861	D₄	—	2	2	no	—
862	D₄	—	34	2	no	—
863	D₄	—	34	2	no	—
864	D₄	—	34	2	no	—
865	D₄	—	34	2	no	—
866	D₄	—	34	2	no	—
867	D₄	—	68	1	no	—
868	D₄	—	68	1	no	—
869	D₄	—	68	1	no	—
870	D₄	—	68	1	no	—
871	D₄	—	68	1	no	—
872	D₄	—	68	1	no	—
873	D₄	—	68	1	no	—
874	D₄	—	68	1	no	—
875	D₄	—	68	1	no	—
876	C₂×C₄	—	4	1	no	—
877	C₂×C₄	—	4	1	no	—
878	C₂×C₄	—	4	1	no	—
879	C₂×C₄	—	4	1	no	—
880	C₂×C₄	—	4	1	no	—
881	C₂×C₄	—	4	1	no	—
882	C₂×C₄	—	17	1	no	—
883	C₂×C₄	—	17	1	no	—
884	C₂×C₄	—	17	1	no	—
885	C₂×C₄	—	17	1	no	—
886	C₂×C₄	—	17	1	no	—
887	C₂×C₄	—	17	1	no	—
888	C₂×C₄	—	17	1	no	—
889	C₂×C₄	—	17	1	no	—
890	C₂×C₄	—	17	1	no	—
891	C₂×C₄	—	17	1	no	—
892	C₂×C₄	—	17	1	no	—
893	C₂×C₄	—	34	2	no	—
894	C₂×C₄	—	34	2	no	—
895	C₂×C₄	—	34	2	no	—
896	C₂×C₄	—	34	2	no	—
897	C₂×C₄	—	34	2	no	—
898	C₂×C₄	—	68	1	no	—
899	C₂×C₄	—	68	1	no	—
900	C₂×C₄	—	68	1	no	—
901	C₂×C₄	—	68	1	no	—
902	C₂×C₄	—	68	1	no	—
903	C₂×C₄	—	68	1	no	—
904	C₂×C₄	—	68	1	no	—
905	C₂×C₄	—	68	1	no	—
906	C₂×C₄	—	68	1	no	—
907	C₂×C₄	—	68	1	no	—
908	C₂×C₄	—	68	1	no	—
909	C₂×C₄	—	68	1	no	—
910	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
911	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
912	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
913	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
914	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
915	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
916	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
917	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
918	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
919	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
920	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
921	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
922	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
923	C₂²	—	2	1	no	—
924	C₂²	—	2	1	no	—
925	C₂²	—	2	1	no	—
926	C₂²	—	2	1	no	—
927	C₂²	—	2	1	no	—
928	C₂²	—	17	2	no	—
929	C₂²	—	34	1	no	—
930	C₂²	—	34	1	no	—
931	C₂²	—	34	1	no	—
932	C₂²	—	34	1	no	—
933	C₂²	—	34	1	no	—
934	C₂²	—	34	1	no	—
935	C₂²	—	34	1	no	—
936	C₂²	—	34	1	no	—
937	C₂²	—	34	1	no	—
938	C₂²	—	34	1	no	—
939	C₂²	—	34	1	no	—
940	C₂²	—	34	1	no	—
941	C₂²	—	34	1	no	—
942	C₂²	—	34	1	no	—
943	C₂²	—	68	4	no	—
944	C₂²	—	136	2	no	—
945	C₂²	#10587694	1	2	yes	—
946	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
947	C₄	—	2	1	no	—
948	C₄	—	2	1	no	—
949	C₄	—	2	1	no	—
950	C₄	—	2	1	no	—
951	C₄	—	2	1	no	—
952	C₄	—	2	1	no	—
953	C₄	—	2	1	no	—
954	C₄	—	2	1	no	—
955	C₄	—	2	1	no	—
956	C₄	—	2	1	no	—
957	C₄	—	2	1	no	—
958	C₄	—	2	1	no	—
959	C₄	—	2	1	no	—
960	C₄	—	34	1	no	—
961	C₄	—	34	1	no	—
962	C₄	—	34	1	no	—
963	C₄	—	34	1	no	—
964	C₄	—	34	1	no	—
965	C₄	—	34	1	no	—
966	C₄	—	34	1	no	—
967	C₄	—	34	1	no	—
968	C₄	—	34	1	no	—
969	C₄	—	34	1	no	—
970	C₄	—	34	1	no	—
971	C₂	—	2	2	no	—
972	C₂	—	4	1	no	—
973	C₂	—	34	2	no	—
974	C₂	—	68	1	no	—
975	C₂	—	68	1	no	—
976	C₂	—	68	1	no	—
977	C₂	—	68	1	no	—
978	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
979	C₂	C₂×#10587694	1	1	yes	characteristic
980	C₂	#11763645	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₇
commutator, socle, cosocle	C₂²×C₁₇	C₂⁵
Fitting	C₁₇×#554	C₂
hypercenter	#554	D₁₇
hypocenter	C₁₇	#3535
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ #554

Complements

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

N	H ≅ G/N	type
1. #11763563	C₂	semidirect
2. #11763558	C₂	semidirect
3. #11763555	C₂	semidirect
4. #11763555	C₂	semidirect
5. #11763514	C₂	semidirect
6. #11763500	C₂	semidirect
7. #11763491	C₂	semidirect
8. #11763488	C₂	semidirect
9. #11763488	C₂	semidirect
10. #11763486	C₂	semidirect
11. #11763486	C₂	semidirect
12. #11763461	C₂	semidirect
13. #11763460	C₂	semidirect
14. #11763455	C₂	semidirect
15. #11763450	C₂	semidirect
16. #11763438	C₂	semidirect
17. #11763434	C₂	semidirect
18. #11763431	C₂	semidirect
19. #11763429	C₂	semidirect
20. #11763407	C₂	semidirect
21. #11763407	C₂	semidirect
22. #11763406	C₂	semidirect
23. #11763405	C₂	semidirect
24. #11763401	C₂	semidirect
25. #11763392	C₂	semidirect
26. #11763384	C₂	semidirect
27. #11763382	C₂	semidirect
28. #11763318	C₂	semidirect
29. C₂×#10587580	C₂	semidirect
30. C₂²⋊Q₈×D₁₇	C₂	semidirect
31. C₁₇×#554	C₂	semidirect
33. C₂×Q₈×D₁₇	C₂²	semidirect
35. C₂×#63252	C₂²	semidirect
38. C₁₇×C₄⋊Q₈	C₂²	semidirect
39. C₁₇×#125	C₂²	semidirect
40. C₁₇×#125	C₂²	semidirect
44. C₁₇×C₂²⋊Q₈	C₂²	semidirect
45. C₁₇×C₂²⋊Q₈	C₂²	semidirect
46. C₁₇×C₂²⋊Q₈	C₂²	semidirect
47. C₄×Q₈×C₁₇	C₂²	semidirect
52. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
54. #10587633	C₂²	semidirect
55. #10587633	C₂²	semidirect
56. #10587632	C₂²	semidirect
57. #10587632	C₂²	semidirect
58. #10587632	C₂²	semidirect
59. #10587632	C₂²	semidirect
60. #10587632	C₂²	semidirect
61. #10587630	C₂²	semidirect
62. #10587630	C₂²	semidirect
68. #10587616	C₂²	semidirect
69. #10587615	C₂²	semidirect
70. #10587615	C₂²	semidirect
71. #10587615	C₂²	semidirect
72. #10587615	C₂²	semidirect
76. C₄×C₂²⋊D₁₇	C₂²	semidirect
77. C₄×C₂²⋊D₁₇	C₂²	semidirect
78. C₄×C₂²⋊D₁₇	C₂²	semidirect
85. #10587610	C₂²	semidirect
87. #10587584	C₂²	semidirect
88. #10587584	C₂²	semidirect
89. #10587584	C₂²	semidirect
90. #10587584	C₂²	semidirect
91. #10587584	C₂²	semidirect
92. #10587584	C₂²	semidirect
93. #10587584	C₂²	semidirect
94. #10587583	C₂²	semidirect
95. #10587583	C₂²	semidirect
96. #10587583	C₂²	semidirect
97. #10587583	C₂²	semidirect
98. #10587582	C₂²	semidirect
99. #10587582	C₂²	semidirect
100. #10587582	C₂²	semidirect
101. #10587582	C₂²	semidirect
102. #10587582	C₂²	semidirect
103. #10587582	C₂²	semidirect
104. #10587582	C₂²	semidirect
105. #10587582	C₂²	semidirect
106. #10587582	C₂²	semidirect
107. #10587582	C₂²	semidirect
108. #10587582	C₂²	semidirect
109. #10587582	C₂²	semidirect
125. #10587580	C₂²	semidirect
126. #10587580	C₂²	semidirect
127. #10587580	C₂²	semidirect
128. #10587580	C₂²	semidirect
129. #10587580	C₂²	semidirect
130. #10587580	C₂²	semidirect
132. #10587579	C₂²	semidirect
133. #10587579	C₂²	semidirect
134. #10587578	C₂²	semidirect
135. #10587578	C₂²	semidirect
136. C₄⋊C₄×D₁₇	C₂²	semidirect
137. C₄⋊C₄×D₁₇	C₂²	semidirect
138. C₄⋊C₄×D₁₇	C₂²	semidirect
139. C₄⋊C₄×D₁₇	C₂²	semidirect
140. #10587575	C₂²	semidirect
141. #10587575	C₂²	semidirect
142. #10587575	C₂²	semidirect
143. #10587575	C₂²	semidirect
144. #10587575	C₂²	semidirect
145. #10587575	C₂²	semidirect
146. #10587575	C₂²	semidirect
147. #10587574	C₂²	semidirect
148. #10587574	C₂²	semidirect
149. #10587574	C₂²	semidirect
150. #10587573	C₂²	semidirect
152. #10587571	C₂²	semidirect
153. #10587571	C₂²	semidirect
154. #10587571	C₂²	semidirect
157. #10587570	C₂²	semidirect
158. #10587570	C₂²	semidirect
159. #10587569	C₂²	semidirect
160. #10587569	C₂²	semidirect
161. #10587569	C₂²	semidirect
162. #10587569	C₂²	semidirect
169. #10587565	C₂²	semidirect
175. #10587562	C₂²	semidirect
176. #10587562	C₂²	semidirect
177. #10587562	C₂²	semidirect
178. #10587562	C₂²	semidirect
180. #10587561	C₂²	semidirect
182. C₄×D₆₈	C₂²	semidirect
183. #10587558	C₂²	semidirect
184. #10587558	C₂²	semidirect
185. #10587558	C₂²	semidirect
186. #10587556	C₂²	semidirect
486. #554	D₁₇	semidirect
533. C₄⋊Q₈	C₂×D₁₇	semidirect
554. #125	C₂×D₁₇	semidirect
555. #125	C₂×D₁₇	semidirect
623. C₂²⋊Q₈	C₂×D₁₇	semidirect
624. C₂²⋊Q₈	C₂×D₁₇	semidirect
625. C₂²⋊Q₈	C₂×D₁₇	semidirect
641. C₄×Q₈	C₂×D₁₇	semidirect
669. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
677. C₁₇	#3535	semidirect

Maximal subgroups

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

subgroup	index
#11763563	2
#11763558	2
#11763555	2
#11763514	2
#11763500	2
#11763491	2
#11763488	2
#11763486	2
#11763461	2
#11763460	2
#11763455	2
#11763450	2
#11763438	2
#11763434	2
#11763431	2
#11763429	2
#11763407	2
#11763406	2
#11763405	2
#11763401	2
#11763392	2
#11763384	2
#11763382	2
#11763318	2
C₂×#10587580	2
C₂²⋊Q₈×D₁₇	2
C₁₇×#554	2
#3535	17