Subgroups — #14542715

Order 2176.

1152 conjugacy classes of subgroups.

The subgroup lattice has 1032 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#11763543	C₂	1	1	yes	maximal, characteristic, complemented
2	#11763514	C₂	1	1	yes	maximal, characteristic, complemented
3	#11763510	C₂	1	1	yes	maximal, characteristic, complemented
4	#11763508	C₂	1	1	yes	maximal, characteristic, complemented
5	#11763491	C₂	1	1	yes	maximal, characteristic, complemented
6	#11763488	C₂	1	1	yes	maximal, characteristic, complemented
7	#11763488	C₂	1	1	yes	maximal, characteristic, complemented
8	#11763484	C₂	1	1	yes	maximal, characteristic, complemented
9	#11763483	C₂	1	1	yes	maximal, characteristic, complemented
10	#11763457	C₂	1	1	yes	maximal, characteristic, complemented
11	#11763455	C₂	1	1	yes	maximal, characteristic, complemented
12	#11763448	C₂	1	1	yes	maximal, characteristic, complemented
13	#11763448	C₂	1	1	yes	maximal, characteristic, complemented
14	#11763448	C₂	1	1	yes	maximal, characteristic, complemented
15	#11763443	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763425	C₂	1	1	yes	maximal, characteristic, complemented
17	#11763409	C₂	1	1	yes	maximal, characteristic, complemented
18	#11763407	C₂	1	1	yes	maximal, characteristic, complemented
19	#11763404	C₂	1	1	yes	maximal, characteristic, complemented
20	#11763396	C₂	1	1	yes	maximal, characteristic, complemented
21	#11763395	C₂	1	1	yes	maximal, characteristic, complemented
22	#11763342	C₂	1	1	yes	maximal, characteristic, complemented
23	#11763337	C₂	1	1	yes	maximal, characteristic, complemented
24	#11763319	C₂	1	1	yes	maximal, characteristic, complemented
25	#11763318	C₂	1	1	yes	maximal, characteristic, complemented
26	C₂×#10587580	C₂	1	1	yes	maximal, characteristic, complemented
27	#123×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
28	#11763288	C₂	1	1	yes	maximal, characteristic, complemented
29	#11763281	C₂	1	1	yes	maximal, characteristic, complemented
30	C₄×D₄×D₁₇	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
33	C₂×#63254	C₂²	1	1	yes	characteristic, complemented
34	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
35	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
36	C₂×D₄×D₁₇	C₂²	1	1	yes	characteristic
37	C₂×#63252	C₂²	1	1	yes	characteristic, complemented
38	C₂²×D₆₈	C₂²	1	1	yes	characteristic
39	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
40	C₂²×C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
41	C₁₇×#126	C₂²	1	1	yes	characteristic, complemented
42	C₁₇×#126	C₂²	1	1	yes	characteristic, complemented
43	C₁₇×#125	C₂²	1	1	yes	characteristic, complemented
44	C₁₇×#123	C₂²	1	1	yes	characteristic, complemented
45	C₁₇×#123	C₂²	1	1	yes	characteristic, complemented
46	C₁₇×#121	C₂²	1	1	yes	characteristic
47	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
48	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
49	C₁₇×#121	C₂²	1	1	yes	characteristic, complemented
50	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
51	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
52	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
53	C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
54	C₁₇×#117	C₂²	1	1	yes	characteristic, complemented
55	C₂×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic, complemented
56	#10587626	C₂²	1	1	yes	characteristic
57	#10587625	C₂²	1	1	yes	characteristic, complemented
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, complemented
65	#10587623	C₂²	1	1	yes	characteristic, complemented
66	#10587623	C₂²	1	1	yes	characteristic, complemented
67	#10587623	C₂²	1	1	yes	characteristic, complemented
68	#10587621	C₂²	1	1	yes	characteristic, complemented
69	#10587621	C₂²	1	1	yes	characteristic, complemented
70	#10587621	C₂²	1	1	yes	characteristic, complemented
71	#10587621	C₂²	1	1	yes	characteristic, complemented
72	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
73	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
74	D₄×Dic₁₇	C₂²	1	1	yes	characteristic, complemented
75	#10587616	C₂²	1	1	yes	characteristic, complemented
76	#10587615	C₂²	1	1	yes	characteristic, complemented
77	#10587615	C₂²	1	1	yes	characteristic, complemented
78	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
79	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
80	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic
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	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₁₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
87	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
88	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
89	C₂×#63227	C₂²	1	1	yes	characteristic, complemented
90	#10587610	C₂²	1	1	yes	characteristic, complemented
91	#10587610	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×#63225	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	#10587583	C₂²	1	1	yes	characteristic, complemented
100	#10587583	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	#10587581	C₂²	1	1	yes	characteristic
108	#10587580	C₂²	1	1	yes	characteristic
109	#10587580	C₂²	1	1	yes	characteristic
110	#10587580	C₂²	1	1	yes	characteristic
111	#10587580	C₂²	1	1	yes	characteristic, complemented
112	#10587580	C₂²	1	1	yes	characteristic, complemented
113	#10587580	C₂²	1	1	yes	characteristic, complemented
114	#10587580	C₂²	1	1	yes	characteristic, complemented
115	#10587580	C₂²	1	1	yes	characteristic, complemented
116	#10587580	C₂²	1	1	yes	characteristic, complemented
117	#10587580	C₂²	1	1	yes	characteristic, complemented
118	#10587580	C₂²	1	1	yes	characteristic, complemented
119	#10587580	C₂²	1	1	yes	characteristic, complemented
120	#10587579	C₂²	1	1	yes	characteristic
121	#10587579	C₂²	1	1	yes	characteristic, complemented
122	#10587579	C₂²	1	1	yes	characteristic, complemented
123	#10587578	C₂²	1	1	yes	characteristic, complemented
124	#10587578	C₂²	1	1	yes	characteristic, complemented
125	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
126	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
127	C₄⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
128	#10587575	C₂²	1	1	yes	characteristic, complemented
129	#10587575	C₂²	1	1	yes	characteristic, complemented
130	#10587575	C₂²	1	1	yes	characteristic, complemented
131	#10587575	C₂²	1	1	yes	characteristic, complemented
132	#10587574	C₂²	1	1	yes	characteristic, complemented
133	#10587573	C₂²	1	1	yes	characteristic, complemented
134	#10587573	C₂²	1	1	yes	characteristic, complemented
135	#10587572	C₂²	1	1	yes	characteristic, complemented
136	#10587572	C₂²	1	1	yes	characteristic, complemented
137	#10587571	C₂²	1	1	yes	characteristic, complemented
138	#10587571	C₂²	1	1	yes	characteristic, complemented
139	#10587571	C₂²	1	1	yes	characteristic, complemented
140	#10587571	C₂²	1	1	yes	characteristic, complemented
141	#10587571	C₂²	1	1	yes	characteristic, complemented
142	#10587571	C₂²	1	1	yes	characteristic, complemented
143	#10587570	C₂²	1	1	yes	characteristic
144	#10587570	C₂²	1	1	yes	characteristic
145	#10587570	C₂²	1	1	yes	characteristic
146	#10587570	C₂²	1	1	yes	characteristic, complemented
147	#10587570	C₂²	1	1	yes	characteristic, complemented
148	#10587570	C₂²	1	1	yes	characteristic, complemented
149	#10587569	C₂²	1	1	yes	characteristic, complemented
150	#10587569	C₂²	1	1	yes	characteristic, complemented
151	#10587569	C₂²	1	1	yes	characteristic, complemented
152	#10587569	C₂²	1	1	yes	characteristic, complemented
153	#10587568	C₂²	1	1	yes	characteristic
154	#10587568	C₂²	1	1	yes	characteristic
155	#10587567	C₂²	1	1	yes	characteristic
156	#10587567	C₂²	1	1	yes	characteristic, complemented
157	#10587567	C₂²	1	1	yes	characteristic, complemented
158	#10587567	C₂²	1	1	yes	characteristic, complemented
159	#10587567	C₂²	1	1	yes	characteristic, complemented
160	#10587567	C₂²	1	1	yes	characteristic, complemented
161	#10587567	C₂²	1	1	yes	characteristic, complemented
162	#10587567	C₂²	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
164	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
165	C₂²⋊C₄×D₁₇	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	C₂²⋊C₄×D₁₇	C₂²	1	1	yes	characteristic, complemented
169	#10587565	C₂²	1	1	yes	characteristic, complemented
170	#10587565	C₂²	1	1	yes	characteristic, complemented
171	#10587564	C₂²	1	1	yes	characteristic, complemented
172	#10587564	C₂²	1	1	yes	characteristic, complemented
173	#10587563	C₂²	1	1	yes	characteristic, complemented
174	#10587563	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, complemented
178	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
179	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
180	C₄×D₆₈	C₂²	1	1	yes	characteristic, complemented
181	#10587558	C₂²	1	1	yes	characteristic, complemented
182	#10587558	C₂²	1	1	yes	characteristic, complemented
183	#10587558	C₂²	1	1	yes	characteristic, complemented
184	#10587558	C₂²	1	1	yes	characteristic, complemented
185	C₄²×D₁₇	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	C₂³×D₁₇	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	C₂×D₄×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	C₂²×C₄×C₁₇	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	C₂²×Dic₁₇	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	#63254	—	2	4	no	—
222	#63254	—	4	2	no	—
223	D₄×D₁₇	—	2	4	no	—
224	D₄×D₁₇	—	2	4	no	—
225	D₄×D₁₇	—	4	2	no	—
226	#63252	—	4	2	no	—
227	C₂×D₆₈	—	4	2	no	—
228	C₂×D₆₈	C₂³	1	1	yes	characteristic
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×C₄×D₁₇	—	4	2	no	—
235	C₂×C₄×D₁₇	—	4	2	no	—
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×C₄×D₁₇	C₂³	1	1	yes	characteristic
246	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
247	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
248	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
249	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
250	C₂×C₄×D₁₇	C₂³	1	1	yes	characteristic
251	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
252	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
253	C₂×Dic₃₄	C₂³	1	1	yes	characteristic
254	C₂×Dic₃₄	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	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
261	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
262	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
263	C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
264	C₄⋊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	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
271	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
272	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
273	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
274	C₂²⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
275	C₄²×C₁₇	C₂³	1	1	yes	characteristic
276	C₄²×C₁₇	C₂³	1	1	yes	characteristic
277	C₄²×C₁₇	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	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
282	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
283	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
284	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
285	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
286	C₂²⋊Dic₁₇	C₂³	1	1	yes	characteristic
287	C₂²⋊Dic₁₇	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	#63227	C₂³	1	1	yes	characteristic
314	#63227	C₂³	1	1	yes	characteristic
315	#63227	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	#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	#63225	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	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
349	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
350	C₄×Dic₁₇	C₂³	1	1	yes	characteristic
351	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
352	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
353	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
354	C₂³×C₁₇	C₂⁴	1	1	yes	characteristic
355	C₂²×D₁₇	—	2	2	no	—
356	C₂²×D₁₇	—	2	2	no	—
357	C₂²×D₁₇	—	2	2	no	—
358	C₂²×D₁₇	—	2	2	no	—
359	C₂²×D₁₇	—	2	2	no	—
360	C₂²×D₁₇	—	2	2	no	—
361	C₂²×D₁₇	—	4	1	no	—
362	C₂²×D₁₇	—	4	1	no	—
363	C₂²×D₁₇	—	4	1	no	—
364	C₂²×D₁₇	—	4	1	no	—
365	C₂²×D₁₇	—	4	1	no	—
366	C₂²×D₁₇	—	4	1	no	—
367	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
368	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
369	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
370	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
371	C₂²×D₁₇	C₂⁴	1	1	yes	characteristic
372	D₄×C₁₇	—	2	2	no	—
373	D₄×C₁₇	—	2	2	no	—
374	D₄×C₁₇	—	2	2	no	—
375	D₄×C₁₇	—	4	1	no	—
376	D₄×C₁₇	—	4	1	no	—
377	D₄×C₁₇	—	4	1	no	—
378	C₂×C₄×C₁₇	—	4	1	no	—
379	C₂×C₄×C₁₇	—	4	1	no	—
380	C₂×C₄×C₁₇	—	4	1	no	—
381	C₂×C₄×C₁₇	—	4	1	no	—
382	C₂×C₄×C₁₇	—	4	1	no	—
383	C₂×C₄×C₁₇	—	4	1	no	—
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	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
390	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
391	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
392	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
393	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
394	C₂×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
395	C₂²⋊D₁₇	—	2	2	no	—
396	C₂²⋊D₁₇	—	2	2	no	—
397	C₂²⋊D₁₇	—	2	2	no	—
398	C₂²⋊D₁₇	—	2	2	no	—
399	C₂²⋊D₁₇	—	2	2	no	—
400	C₂²⋊D₁₇	—	4	1	no	—
401	C₂²⋊D₁₇	—	4	1	no	—
402	C₂²⋊D₁₇	—	4	1	no	—
403	C₂²⋊D₁₇	—	4	1	no	—
404	C₂²⋊D₁₇	—	4	1	no	—
405	C₂²⋊D₁₇	—	4	1	no	—
406	C₂²⋊D₁₇	#41	1	4	yes	complemented
407	C₂×Dic₁₇	—	2	2	no	—
408	C₂×Dic₁₇	—	2	2	no	—
409	C₂×Dic₁₇	—	4	1	no	—
410	C₂×Dic₁₇	—	4	1	no	—
411	C₂×Dic₁₇	—	4	1	no	—
412	C₂×Dic₁₇	—	4	1	no	—
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	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
422	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
423	C₂×Dic₁₇	C₂⁴	1	1	yes	characteristic
424	D₆₈	—	2	2	no	—
425	D₆₈	—	2	2	no	—
426	D₆₈	—	2	2	no	—
427	D₆₈	—	2	2	no	—
428	D₆₈	—	4	1	no	—
429	D₆₈	—	4	1	no	—
430	C₄×D₁₇	—	2	2	no	—
431	C₄×D₁₇	—	2	2	no	—
432	C₄×D₁₇	—	2	2	no	—
433	C₄×D₁₇	—	2	2	no	—
434	C₄×D₁₇	—	2	2	no	—
435	C₄×D₁₇	—	2	2	no	—
436	C₄×D₁₇	—	4	1	no	—
437	C₄×D₁₇	—	4	1	no	—
438	C₄×D₁₇	—	4	1	no	—
439	C₄×D₁₇	—	4	1	no	—
440	C₄×D₁₇	—	4	1	no	—
441	C₄×D₁₇	—	4	1	no	—
442	C₄×D₁₇	—	4	1	no	—
443	C₄×D₁₇	—	4	1	no	—
444	C₄×D₁₇	—	4	1	no	—
445	Dic₃₄	—	2	2	no	—
446	Dic₃₄	—	4	1	no	—
447	Dic₃₄	—	4	1	no	—
448	Dic₃₄	—	4	1	no	—
449	#3513	—	17	1	no	maximal, Sylow
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	—	2	1	no	—
455	C₂²×C₁₇	—	2	1	no	—
456	C₂²×C₁₇	—	2	1	no	—
457	C₂²×C₁₇	—	2	1	no	—
458	C₂²×C₁₇	—	2	1	no	—
459	C₂²×C₁₇	—	2	1	no	—
460	C₂²×C₁₇	—	2	1	no	—
461	C₂²×C₁₇	C₂×#41	1	2	yes	—
462	C₂²×C₁₇	C₂⁵	1	1	yes	characteristic
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	—	2	1	no	—
472	C₂×D₁₇	—	2	1	no	—
473	C₂×D₁₇	—	2	1	no	—
474	C₂×D₁₇	—	2	1	no	—
475	C₂×D₁₇	—	2	1	no	—
476	C₂×D₁₇	—	4	4	no	—
477	C₂×D₁₇	—	4	4	no	—
478	C₂×D₁₇	—	8	2	no	—
479	C₂×D₁₇	—	8	2	no	—
480	C₂×D₁₇	C₂×#41	1	2	yes	—
481	C₂×D₁₇	H(5,𝔽₂)	1	2	yes	—
482	C₄×C₁₇	—	2	1	no	—
483	C₄×C₁₇	—	2	1	no	—
484	C₄×C₁₇	—	2	1	no	—
485	C₄×C₁₇	—	2	1	no	—
486	C₄×C₁₇	—	2	1	no	—
487	C₄×C₁₇	—	2	1	no	—
488	C₄×C₁₇	—	2	1	no	—
489	C₄×C₁₇	—	2	1	no	—
490	C₄×C₁₇	—	2	1	no	—
491	C₄×C₁₇	—	2	1	no	—
492	C₄×C₁₇	—	2	1	no	—
493	Dic₁₇	—	2	1	no	—
494	Dic₁₇	—	2	1	no	—
495	Dic₁₇	—	2	1	no	—
496	Dic₁₇	—	2	1	no	—
497	Dic₁₇	—	2	1	no	—
498	Dic₁₇	—	2	1	no	—
499	Dic₁₇	—	2	1	no	—
500	Dic₁₇	—	2	1	no	—
501	Dic₁₇	—	2	1	no	—
502	Dic₁₇	—	2	1	no	—
503	Dic₁₇	C₂×#41	1	2	yes	—
504	#559	—	17	1	no	—
505	#554	—	17	1	no	—
506	#553	—	17	1	no	—
507	#553	—	17	1	no	—
508	#553	D₁₇	1	1	yes	characteristic, complemented
509	#552	—	17	1	no	—
510	#551	—	17	1	no	—
511	#551	—	17	1	no	—
512	#551	—	17	1	no	—
513	#551	—	17	1	no	—
514	#547	—	17	1	no	—
515	#546	—	17	1	no	—
516	#546	—	17	1	no	—
517	#546	—	17	1	no	—
518	#546	—	17	1	no	—
519	D₄²	—	17	1	no	—
520	#542	—	17	1	no	—
521	#540	—	17	1	no	—
522	#539	—	17	1	no	—
523	#539	—	17	1	no	—
524	#538	—	17	1	no	—
525	#538	—	17	1	no	—
526	#529	—	17	1	no	—
527	#529	—	17	1	no	—
528	#525	—	17	1	no	—
529	#525	—	17	1	no	—
530	C₂×#123	—	17	1	no	—
531	C₂×#123	—	17	1	no	—
532	#520	—	17	1	no	—
533	#518	—	17	1	no	—
534	C₂×C₄×D₄	—	17	1	no	—
535	C₂×C₁₇	—	2	2	no	—
536	C₂×C₁₇	—	4	1	no	—
537	C₂×C₁₇	—	4	1	no	—
538	C₂×C₁₇	—	4	1	no	—
539	C₂×C₁₇	C₂²×#41	1	1	yes	characteristic
540	C₂×C₁₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
541	C₂×C₁₇	#585	1	1	yes	characteristic
542	D₁₇	—	2	2	no	—
543	D₁₇	—	2	2	no	—
544	D₁₇	—	4	1	no	—
545	D₁₇	—	4	1	no	—
546	D₁₇	—	4	1	no	—
547	C₂×#41	—	17	1	no	—
548	C₂×#41	—	17	1	no	—
549	C₂×#41	—	17	1	no	—
550	C₂²×D₄	—	17	1	no	—
551	C₂²×D₄	—	17	1	no	—
552	C₂²×D₄	—	17	1	no	—
553	C₂²×D₄	—	17	1	no	—
554	C₂³×C₄	—	17	1	no	—
555	C₂³×C₄	—	17	1	no	—
556	C₄⋊Q₈	—	17	1	no	—
557	#127	—	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	—	17	1	no	—
566	#126	C₂×D₁₇	1	1	yes	characteristic, complemented
567	#126	C₂×D₁₇	1	1	yes	characteristic, complemented
568	#125	—	17	1	no	—
569	#125	—	17	1	no	—
570	#125	—	17	1	no	—
571	#125	—	17	1	no	—
572	#125	C₂×D₁₇	1	1	yes	characteristic, complemented
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	#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	#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	—	17	1	no	—
604	#123	C₂×D₁₇	1	1	yes	characteristic, complemented
605	#123	C₂×D₁₇	1	1	yes	characteristic, complemented
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	#121	—	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	C₂×D₁₇	1	1	yes	characteristic
633	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
634	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
635	#121	C₂×D₁₇	1	1	yes	characteristic, complemented
636	#120	—	17	1	no	—
637	#120	—	17	1	no	—
638	#120	—	17	1	no	—
639	#120	—	17	1	no	—
640	#120	—	17	1	no	—
641	#120	—	17	1	no	—
642	#120	—	17	1	no	—
643	#120	—	17	1	no	—
644	C₄×Q₈	—	17	1	no	—
645	C₄×Q₈	—	17	1	no	—
646	C₄×Q₈	—	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	—	17	1	no	—
654	C₄×D₄	—	17	1	no	—
655	C₄×D₄	—	17	1	no	—
656	C₄×D₄	—	17	1	no	—
657	C₄×D₄	—	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	C₂×D₁₇	1	1	yes	characteristic, complemented
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	#117	—	17	1	no	—
677	#117	—	17	1	no	—
678	#117	—	17	1	no	—
679	#117	—	17	1	no	—
680	#117	—	17	1	no	—
681	#117	—	17	1	no	—
682	#117	—	17	1	no	—
683	#117	—	17	1	no	—
684	#117	C₂×D₁₇	1	1	yes	characteristic, complemented
685	C₂×C₄⋊C₄	—	17	1	no	—
686	C₂×C₄⋊C₄	—	17	1	no	—
687	C₂×C₄⋊C₄	—	17	1	no	—
688	C₂×C₄⋊C₄	—	17	1	no	—
689	C₂×C₄⋊C₄	—	17	1	no	—
690	C₂×C₄⋊C₄	C₂×D₁₇	1	1	yes	characteristic, complemented
691	C₂×C₂²⋊C₄	—	17	1	no	—
692	C₂×C₂²⋊C₄	—	17	1	no	—
693	C₂×C₂²⋊C₄	—	17	1	no	—
694	C₂×C₂²⋊C₄	—	17	1	no	—
695	C₂×C₂²⋊C₄	—	17	1	no	—
696	C₂×C₂²⋊C₄	—	17	1	no	—
697	C₂×C₂²⋊C₄	—	17	1	no	—
698	C₂×C₂²⋊C₄	—	17	1	no	—
699	C₂×C₂²⋊C₄	—	17	1	no	—
700	C₂×C₂²⋊C₄	—	17	1	no	—
701	C₂×C₄²	—	17	1	no	—
702	C₁₇	#3513	1	1	yes	characteristic, complemented, Sylow
703	C₂⁴	—	17	1	no	—
704	C₂⁴	—	17	1	no	—
705	C₂⁴	—	17	1	no	—
706	C₂⁴	—	17	1	no	—
707	#41	—	34	4	no	—
708	#41	—	68	2	no	—
709	#41	—	68	2	no	—
710	C₂×Q₈	—	17	1	no	—
711	C₂×Q₈	—	17	1	no	—
712	C₂×Q₈	—	17	1	no	—
713	C₂×Q₈	—	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	—	17	1	no	—
729	C₂×D₄	—	17	1	no	—
730	C₂×D₄	—	17	1	no	—
731	C₂×D₄	—	17	1	no	—
732	C₂×D₄	—	34	4	no	—
733	C₂×D₄	—	34	4	no	—
734	C₂×D₄	—	68	2	no	—
735	C₂×D₄	—	68	2	no	—
736	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
737	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
738	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
739	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
740	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
741	C₂×D₄	C₂²×D₁₇	1	1	yes	characteristic
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	—	17	1	no	—
753	C₂²×C₄	—	17	1	no	—
754	C₂²×C₄	—	17	1	no	—
755	C₂²×C₄	—	17	1	no	—
756	C₂²×C₄	—	17	1	no	—
757	C₂²×C₄	—	17	1	no	—
758	C₂²×C₄	—	17	1	no	—
759	C₂²×C₄	—	17	1	no	—
760	C₂²×C₄	—	17	1	no	—
761	C₂²×C₄	—	17	1	no	—
762	C₂²×C₄	—	17	1	no	—
763	C₂²×C₄	—	68	2	no	—
764	C₂²×C₄	—	68	2	no	—
765	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
766	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
767	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
768	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
769	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
770	C₂²×C₄	C₂²×D₁₇	1	1	yes	characteristic
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	—	17	1	no	—
787	C₄⋊C₄	—	17	1	no	—
788	C₄⋊C₄	—	17	1	no	—
789	C₄⋊C₄	—	17	1	no	—
790	C₄⋊C₄	—	17	1	no	—
791	C₄⋊C₄	—	17	1	no	—
792	C₄⋊C₄	—	17	1	no	—
793	C₄⋊C₄	—	17	1	no	—
794	C₄⋊C₄	—	17	1	no	—
795	C₄⋊C₄	—	17	1	no	—
796	C₄⋊C₄	—	17	1	no	—
797	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
798	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
799	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
800	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
801	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
802	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
803	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
804	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
805	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
806	C₄⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
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	—	17	1	no	—
837	C₂²⋊C₄	—	17	1	no	—
838	C₂²⋊C₄	—	17	1	no	—
839	C₂²⋊C₄	—	17	1	no	—
840	C₂²⋊C₄	—	17	1	no	—
841	C₂²⋊C₄	—	17	1	no	—
842	C₂²⋊C₄	—	17	1	no	—
843	C₂²⋊C₄	—	17	1	no	—
844	C₂²⋊C₄	—	17	1	no	—
845	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
846	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
847	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
848	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
849	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
850	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
851	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
852	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
853	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
854	C₂²⋊C₄	C₂²×D₁₇	1	1	yes	characteristic
855	C₄²	—	17	1	no	—
856	C₄²	—	17	1	no	—
857	C₄²	—	17	1	no	—
858	C₄²	—	17	1	no	—
859	C₄²	—	17	1	no	—
860	C₄²	—	17	1	no	—
861	C₄²	—	17	1	no	—
862	C₄²	—	17	1	no	—
863	C₄²	—	17	1	no	—
864	C₄²	C₂²×D₁₇	1	1	yes	characteristic
865	C₄²	C₂²×D₁₇	1	1	yes	characteristic
866	C₄²	C₂²×D₁₇	1	1	yes	characteristic
867	C₂³	—	17	1	no	—
868	C₂³	—	17	1	no	—
869	C₂³	—	17	1	no	—
870	C₂³	—	17	1	no	—
871	C₂³	—	17	1	no	—
872	C₂³	—	34	2	no	—
873	C₂³	—	34	2	no	—
874	C₂³	—	34	2	no	—
875	C₂³	—	34	2	no	—
876	C₂³	—	34	2	no	—
877	C₂³	—	34	2	no	—
878	C₂³	—	68	1	no	—
879	C₂³	—	68	1	no	—
880	C₂³	—	68	1	no	—
881	C₂³	—	68	1	no	—
882	C₂³	—	68	1	no	—
883	C₂³	—	68	1	no	—
884	C₂³	C₂³×D₁₇	1	1	yes	characteristic
885	C₂³	C₂³×D₁₇	1	1	yes	characteristic
886	C₂³	C₂³×D₁₇	1	1	yes	characteristic
887	C₂³	C₂³×D₁₇	1	1	yes	characteristic
888	Q₈	—	34	2	no	—
889	Q₈	—	68	1	no	—
890	Q₈	—	68	1	no	—
891	Q₈	—	68	1	no	—
892	D₄	—	2	2	no	—
893	D₄	—	2	2	no	—
894	D₄	—	2	2	no	—
895	D₄	—	4	1	no	—
896	D₄	—	4	1	no	—
897	D₄	—	4	1	no	—
898	D₄	—	17	4	no	—
899	D₄	—	34	2	no	—
900	D₄	—	34	2	no	—
901	D₄	—	34	2	no	—
902	D₄	—	34	2	no	—
903	D₄	—	34	2	no	—
904	D₄	—	34	2	no	—
905	D₄	—	34	2	no	—
906	D₄	—	34	2	no	—
907	D₄	—	34	2	no	—
908	D₄	—	68	1	no	—
909	D₄	—	68	1	no	—
910	D₄	—	68	1	no	—
911	D₄	—	68	1	no	—
912	D₄	—	68	1	no	—
913	D₄	—	68	1	no	—
914	D₄	—	68	1	no	—
915	D₄	—	68	1	no	—
916	C₂×C₄	—	4	1	no	—
917	C₂×C₄	—	4	1	no	—
918	C₂×C₄	—	4	1	no	—
919	C₂×C₄	—	4	1	no	—
920	C₂×C₄	—	4	1	no	—
921	C₂×C₄	—	4	1	no	—
922	C₂×C₄	—	17	1	no	—
923	C₂×C₄	—	17	1	no	—
924	C₂×C₄	—	17	1	no	—
925	C₂×C₄	—	17	1	no	—
926	C₂×C₄	—	17	1	no	—
927	C₂×C₄	—	17	1	no	—
928	C₂×C₄	—	17	1	no	—
929	C₂×C₄	—	17	1	no	—
930	C₂×C₄	—	17	1	no	—
931	C₂×C₄	—	17	1	no	—
932	C₂×C₄	—	17	1	no	—
933	C₂×C₄	—	34	2	no	—
934	C₂×C₄	—	34	2	no	—
935	C₂×C₄	—	34	2	no	—
936	C₂×C₄	—	34	2	no	—
937	C₂×C₄	—	34	2	no	—
938	C₂×C₄	—	34	2	no	—
939	C₂×C₄	—	34	2	no	—
940	C₂×C₄	—	34	2	no	—
941	C₂×C₄	—	68	1	no	—
942	C₂×C₄	—	68	1	no	—
943	C₂×C₄	—	68	1	no	—
944	C₂×C₄	—	68	1	no	—
945	C₂×C₄	—	68	1	no	—
946	C₂×C₄	—	68	1	no	—
947	C₂×C₄	—	68	1	no	—
948	C₂×C₄	—	68	1	no	—
949	C₂×C₄	—	68	1	no	—
950	C₂×C₄	—	68	1	no	—
951	C₂×C₄	—	68	1	no	—
952	C₂×C₄	—	68	1	no	—
953	C₂×C₄	—	68	1	no	—
954	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
955	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
956	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
957	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
958	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
959	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
960	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
961	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
962	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
963	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
964	C₂×C₄	C₂³×D₁₇	1	1	yes	characteristic
965	C₂²	—	2	1	no	—
966	C₂²	—	2	1	no	—
967	C₂²	—	2	1	no	—
968	C₂²	—	2	1	no	—
969	C₂²	—	2	1	no	—
970	C₂²	—	2	1	no	—
971	C₂²	—	2	1	no	—
972	C₂²	—	2	1	no	—
973	C₂²	—	2	1	no	—
974	C₂²	—	2	1	no	—
975	C₂²	—	2	1	no	—
976	C₂²	—	17	2	no	—
977	C₂²	—	17	2	no	—
978	C₂²	—	34	1	no	—
979	C₂²	—	34	1	no	—
980	C₂²	—	34	1	no	—
981	C₂²	—	34	1	no	—
982	C₂²	—	34	1	no	—
983	C₂²	—	34	1	no	—
984	C₂²	—	34	1	no	—
985	C₂²	—	34	1	no	—
986	C₂²	—	34	1	no	—
987	C₂²	—	34	1	no	—
988	C₂²	—	34	1	no	—
989	C₂²	—	34	1	no	—
990	C₂²	—	34	1	no	—
991	C₂²	—	68	4	no	—
992	C₂²	—	68	4	no	—
993	C₂²	—	136	2	no	—
994	C₂²	—	136	2	no	—
995	C₂²	#41×D₁₇	1	2	yes	—
996	C₂²	C₂⁴×D₁₇	1	1	yes	characteristic
997	C₄	—	2	1	no	—
998	C₄	—	2	1	no	—
999	C₄	—	2	1	no	—
1000	C₄	—	2	1	no	—
1001	C₄	—	2	1	no	—
1002	C₄	—	2	1	no	—
1003	C₄	—	2	1	no	—
1004	C₄	—	2	1	no	—
1005	C₄	—	2	1	no	—
1006	C₄	—	2	1	no	—
1007	C₄	—	2	1	no	—
1008	C₄	—	17	2	no	—
1009	C₄	—	34	1	no	—
1010	C₄	—	34	1	no	—
1011	C₄	—	34	1	no	—
1012	C₄	—	34	1	no	—
1013	C₄	—	34	1	no	—
1014	C₄	—	34	1	no	—
1015	C₄	—	34	1	no	—
1016	C₄	—	34	1	no	—
1017	C₄	—	34	1	no	—
1018	C₄	—	34	1	no	—
1019	C₂	—	2	2	no	—
1020	C₂	—	4	1	no	—
1021	C₂	—	4	1	no	—
1022	C₂	—	4	1	no	—
1023	C₂	—	34	2	no	—
1024	C₂	—	34	2	no	—
1025	C₂	—	68	1	no	—
1026	C₂	—	68	1	no	—
1027	C₂	—	68	1	no	—
1028	C₂	C₂×#41×D₁₇	1	1	yes	characteristic
1029	C₂	H(5,𝔽₂)×D₁₇	1	1	yes	characteristic
1030	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	#3513
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. #11763543	C₂	semidirect
2. #11763514	C₂	semidirect
3. #11763510	C₂	semidirect
4. #11763508	C₂	semidirect
5. #11763491	C₂	semidirect
6. #11763488	C₂	semidirect
7. #11763488	C₂	semidirect
8. #11763484	C₂	semidirect
9. #11763483	C₂	semidirect
10. #11763457	C₂	semidirect
11. #11763455	C₂	semidirect
12. #11763448	C₂	semidirect
13. #11763448	C₂	semidirect
14. #11763448	C₂	semidirect
15. #11763443	C₂	semidirect
16. #11763425	C₂	semidirect
17. #11763409	C₂	semidirect
18. #11763407	C₂	semidirect
19. #11763404	C₂	semidirect
20. #11763396	C₂	semidirect
21. #11763395	C₂	semidirect
22. #11763342	C₂	semidirect
23. #11763337	C₂	semidirect
24. #11763319	C₂	semidirect
25. #11763318	C₂	semidirect
26. C₂×#10587580	C₂	semidirect
27. #123×D₁₇	C₂	semidirect
28. #11763288	C₂	semidirect
29. #11763281	C₂	semidirect
30. C₄×D₄×D₁₇	C₂	semidirect
31. C₁₇×#553	C₂	semidirect
33. C₂×#63254	C₂²	semidirect
37. C₂×#63252	C₂²	semidirect
39. C₂²×C₄×D₁₇	C₂²	semidirect
40. C₂²×C₄×D₁₇	C₂²	semidirect
41. C₁₇×#126	C₂²	semidirect
42. C₁₇×#126	C₂²	semidirect
43. C₁₇×#125	C₂²	semidirect
44. C₁₇×#123	C₂²	semidirect
45. C₁₇×#123	C₂²	semidirect
47. C₁₇×#121	C₂²	semidirect
48. C₁₇×#121	C₂²	semidirect
49. C₁₇×#121	C₂²	semidirect
50. C₄×D₄×C₁₇	C₂²	semidirect
51. C₄×D₄×C₁₇	C₂²	semidirect
52. C₄×D₄×C₁₇	C₂²	semidirect
53. C₄×D₄×C₁₇	C₂²	semidirect
54. C₁₇×#117	C₂²	semidirect
55. C₂×C₄⋊C₄×C₁₇	C₂²	semidirect
57. #10587625	C₂²	semidirect
58. #10587625	C₂²	semidirect
59. #10587625	C₂²	semidirect
60. #10587625	C₂²	semidirect
61. #10587624	C₂²	semidirect
64. #10587623	C₂²	semidirect
65. #10587623	C₂²	semidirect
66. #10587623	C₂²	semidirect
67. #10587623	C₂²	semidirect
68. #10587621	C₂²	semidirect
69. #10587621	C₂²	semidirect
70. #10587621	C₂²	semidirect
71. #10587621	C₂²	semidirect
72. D₄×Dic₁₇	C₂²	semidirect
73. D₄×Dic₁₇	C₂²	semidirect
74. D₄×Dic₁₇	C₂²	semidirect
75. #10587616	C₂²	semidirect
76. #10587615	C₂²	semidirect
77. #10587615	C₂²	semidirect
81. C₄×C₂²⋊D₁₇	C₂²	semidirect
82. C₄×C₂²⋊D₁₇	C₂²	semidirect
83. C₄×C₂²⋊D₁₇	C₂²	semidirect
84. C₄×C₂²⋊D₁₇	C₂²	semidirect
85. C₄×C₂²⋊D₁₇	C₂²	semidirect
86. C₂×#63227	C₂²	semidirect
87. C₂×#63227	C₂²	semidirect
88. C₂×#63227	C₂²	semidirect
89. C₂×#63227	C₂²	semidirect
90. #10587610	C₂²	semidirect
91. #10587610	C₂²	semidirect
92. #10587610	C₂²	semidirect
93. C₂×#63225	C₂²	semidirect
94. C₂×#63225	C₂²	semidirect
95. #10587584	C₂²	semidirect
96. #10587584	C₂²	semidirect
97. #10587584	C₂²	semidirect
98. #10587584	C₂²	semidirect
99. #10587583	C₂²	semidirect
100. #10587583	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
111. #10587580	C₂²	semidirect
112. #10587580	C₂²	semidirect
113. #10587580	C₂²	semidirect
114. #10587580	C₂²	semidirect
115. #10587580	C₂²	semidirect
116. #10587580	C₂²	semidirect
117. #10587580	C₂²	semidirect
118. #10587580	C₂²	semidirect
119. #10587580	C₂²	semidirect
121. #10587579	C₂²	semidirect
122. #10587579	C₂²	semidirect
123. #10587578	C₂²	semidirect
124. #10587578	C₂²	semidirect
125. C₄⋊C₄×D₁₇	C₂²	semidirect
126. C₄⋊C₄×D₁₇	C₂²	semidirect
127. C₄⋊C₄×D₁₇	C₂²	semidirect
128. #10587575	C₂²	semidirect
129. #10587575	C₂²	semidirect
130. #10587575	C₂²	semidirect
131. #10587575	C₂²	semidirect
132. #10587574	C₂²	semidirect
133. #10587573	C₂²	semidirect
134. #10587573	C₂²	semidirect
135. #10587572	C₂²	semidirect
136. #10587572	C₂²	semidirect
137. #10587571	C₂²	semidirect
138. #10587571	C₂²	semidirect
139. #10587571	C₂²	semidirect
140. #10587571	C₂²	semidirect
141. #10587571	C₂²	semidirect
142. #10587571	C₂²	semidirect
146. #10587570	C₂²	semidirect
147. #10587570	C₂²	semidirect
148. #10587570	C₂²	semidirect
149. #10587569	C₂²	semidirect
150. #10587569	C₂²	semidirect
151. #10587569	C₂²	semidirect
152. #10587569	C₂²	semidirect
156. #10587567	C₂²	semidirect
157. #10587567	C₂²	semidirect
158. #10587567	C₂²	semidirect
159. #10587567	C₂²	semidirect
160. #10587567	C₂²	semidirect
161. #10587567	C₂²	semidirect
162. #10587567	C₂²	semidirect
163. C₂²⋊C₄×D₁₇	C₂²	semidirect
164. C₂²⋊C₄×D₁₇	C₂²	semidirect
165. C₂²⋊C₄×D₁₇	C₂²	semidirect
166. C₂²⋊C₄×D₁₇	C₂²	semidirect
167. C₂²⋊C₄×D₁₇	C₂²	semidirect
168. C₂²⋊C₄×D₁₇	C₂²	semidirect
169. #10587565	C₂²	semidirect
170. #10587565	C₂²	semidirect
171. #10587564	C₂²	semidirect
172. #10587564	C₂²	semidirect
173. #10587563	C₂²	semidirect
174. #10587563	C₂²	semidirect
175. #10587562	C₂²	semidirect
176. #10587562	C₂²	semidirect
177. #10587561	C₂²	semidirect
178. C₄×D₆₈	C₂²	semidirect
179. C₄×D₆₈	C₂²	semidirect
180. C₄×D₆₈	C₂²	semidirect
181. #10587558	C₂²	semidirect
182. #10587558	C₂²	semidirect
183. #10587558	C₂²	semidirect
184. #10587558	C₂²	semidirect
185. C₄²×D₁₇	C₂²	semidirect
186. C₄×Dic₃₄	C₂²	semidirect
406. C₂²⋊D₁₇	#41	semidirect
508. #553	D₁₇	semidirect
566. #126	C₂×D₁₇	semidirect
567. #126	C₂×D₁₇	semidirect
572. #125	C₂×D₁₇	semidirect
604. #123	C₂×D₁₇	semidirect
605. #123	C₂×D₁₇	semidirect
633. #121	C₂×D₁₇	semidirect
634. #121	C₂×D₁₇	semidirect
635. #121	C₂×D₁₇	semidirect
672. C₄×D₄	C₂×D₁₇	semidirect
673. C₄×D₄	C₂×D₁₇	semidirect
674. C₄×D₄	C₂×D₁₇	semidirect
675. C₄×D₄	C₂×D₁₇	semidirect
684. #117	C₂×D₁₇	semidirect
690. C₂×C₄⋊C₄	C₂×D₁₇	semidirect
702. C₁₇	#3513	semidirect

Maximal subgroups

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

subgroup	index
#11763543	2
#11763514	2
#11763510	2
#11763508	2
#11763491	2
#11763488	2
#11763484	2
#11763483	2
#11763457	2
#11763455	2
#11763448	2
#11763443	2
#11763425	2
#11763409	2
#11763407	2
#11763404	2
#11763396	2
#11763395	2
#11763342	2
#11763337	2
#11763319	2
#11763318	2
C₂×#10587580	2
#123×D₁₇	2
#11763288	2
#11763281	2
C₄×D₄×D₁₇	2
C₁₇×#553	2
#3513	17