Subgroups — #17042176

Order 4352.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538572	C₂	1	1	yes	maximal, characteristic
2	#14537724	C₂	1	1	yes	maximal, characteristic, complemented
3	#14529728	C₂	1	1	yes	maximal, characteristic, complemented
4	#14529559	C₂	1	1	yes	maximal, characteristic, complemented
5	#14529383	C₂	1	1	yes	maximal, characteristic, complemented
6	#14529383	C₂	1	1	yes	maximal, characteristic, complemented
7	#14529059	C₂	1	1	yes	maximal, characteristic
8	#14529059	C₂	1	1	yes	maximal, characteristic
9	#14528804	C₂	1	1	yes	maximal, characteristic
10	#14528669	C₂	1	1	yes	maximal, characteristic, complemented
11	#14528664	C₂	1	1	yes	maximal, characteristic, complemented
12	#14528656	C₂	1	1	yes	maximal, characteristic, complemented
13	#14528626	C₂	1	1	yes	maximal, characteristic
14	#14528619	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#2875	C₂	1	1	yes	maximal, characteristic
16	#11763366	C₂²	1	1	yes	characteristic
17	#11763116	C₄	1	1	yes	characteristic, complemented
18	#11763116	C₄	1	1	yes	characteristic, complemented
19	#11763109	C₄	1	1	yes	characteristic, complemented
20	#11763109	C₄	1	1	yes	characteristic, complemented
21	#11763104	C₄	1	1	yes	characteristic, complemented
22	#11763099	C₄	1	1	yes	characteristic, complemented
23	#11763094	C₄	1	1	yes	characteristic, complemented
24	#11763089	C₄	1	1	yes	characteristic, complemented
25	#11762937	—	2	1	no	—
26	#11762937	—	2	1	no	—
27	#11762937	—	2	1	no	—
28	#11762937	—	2	1	no	—
29	C₂×#10587493	C₂²	1	1	yes	characteristic
30	C₂×#10587493	C₂²	1	1	yes	characteristic
31	#11762845	C₂²	1	1	yes	characteristic
32	#11762845	C₂²	1	1	yes	characteristic
33	#11762835	C₂²	1	1	yes	characteristic
34	#11762835	C₂²	1	1	yes	characteristic
35	#11762833	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
37	C₂×#10587508	C₂²	1	1	yes	characteristic
38	C₂×#10587508	C₂²	1	1	yes	characteristic
39	#11762805	C₂²	1	1	yes	characteristic
40	#11762805	C₂²	1	1	yes	characteristic
41	#11762764	C₂²	1	1	yes	characteristic
42	#11762764	C₂²	1	1	yes	characteristic
43	C₂×#10587486	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₁₇	C₂²	1	1	yes	characteristic
45	C₄×C₄⋊Dic₁₇	C₂²	1	1	yes	characteristic
46	#11762573	C₂²	1	1	yes	characteristic
47	#11762573	C₂²	1	1	yes	characteristic
48	#11762570	C₂²	1	1	yes	characteristic
49	#11762570	C₂²	1	1	yes	characteristic
50	#11762570	C₂²	1	1	yes	characteristic
51	#11762570	C₂²	1	1	yes	characteristic
52	#11762568	C₂²	1	1	yes	characteristic
53	#11762568	C₂²	1	1	yes	characteristic
54	#11762563	C₂²	1	1	yes	characteristic
55	#11762563	C₂²	1	1	yes	characteristic
56	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
57	C₂×C₁₇×#131	C₂²	1	1	yes	characteristic
58	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#405	—	2	1	no	—
60	C₁₇×#405	—	2	1	no	—
61	C₁₇×#405	C₂²	1	1	yes	characteristic
62	C₁₇×#405	C₂²	1	1	yes	characteristic
63	C₄×M₁₆×C₁₇	—	2	1	no	—
64	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
65	C₂×C₁₇×#97	—	2	1	no	—
66	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	C₂³	1	1	yes	characteristic
68	C₁₇×#131	—	2	2	no	—
69	C₁₇×#131	—	2	2	no	—
70	C₁₇×#131	—	2	2	no	—
71	C₁₇×#131	Q₈	1	4	yes	complemented
72	C₂×M₁₆×C₁₇	—	2	1	no	—
73	C₂×M₁₆×C₁₇	—	2	1	no	—
74	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₇	—	2	1	no	—
77	C₂²×C₈×C₁₇	—	2	1	no	—
78	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
80	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
81	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
82	C₄×D₄×C₁₇	—	2	1	no	—
83	C₄×D₄×C₁₇	—	2	1	no	—
84	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
85	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
86	C₁₇×#117	—	2	1	no	—
87	C₁₇×#117	C₂³	1	1	yes	characteristic
88	C₂×C₄²×C₁₇	—	2	1	no	—
89	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
90	#10587612	C₂³	1	1	yes	characteristic
91	#10587612	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊Dic₁₇	—	2	1	no	—
93	#10587610	—	2	1	no	—
94	#10587610	—	2	1	no	—
95	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₁₇	C₂³	1	1	yes	characteristic
97	C₂×#63223	C₂³	1	1	yes	characteristic
98	C₂×#63223	C₂³	1	1	yes	characteristic
99	C₂²×#3622	C₂³	1	1	yes	characteristic
100	C₂²×#3622	C₂³	1	1	yes	characteristic
101	#10587556	C₂×C₄	1	1	yes	characteristic
102	#10587556	C₂×C₄	1	1	yes	characteristic
103	#10587555	C₂×C₄	1	1	yes	characteristic
104	#10587555	C₂×C₄	1	1	yes	characteristic
105	C₄×Dic₃₄	—	2	1	no	—
106	C₄×Dic₃₄	—	2	1	no	—
107	C₁₇×#97	—	2	1	no	—
108	C₁₇×#97	—	2	1	no	—
109	C₁₇×#97	—	2	1	no	—
110	C₁₇×#97	D₄	1	1	yes	characteristic
111	C₁₇×#97	D₄	1	1	yes	characteristic
112	C₁₇×#97	D₄	1	1	yes	characteristic
113	C₁₇×#97	D₄	1	1	yes	characteristic
114	C₄×C₈×C₁₇	—	2	1	no	—
115	C₄×C₈×C₁₇	—	2	1	no	—
116	C₄×C₈×C₁₇	—	2	1	no	—
117	#10587508	—	2	2	no	—
118	#10587508	—	2	2	no	—
119	#10587506	C₂×C₄	1	1	yes	characteristic
120	#10587506	C₂×C₄	1	1	yes	characteristic
121	#10587506	C₂×C₄	1	1	yes	characteristic
122	#10587506	C₂×C₄	1	1	yes	characteristic
123	#10587503	C₂×C₄	1	1	yes	characteristic
124	#10587503	C₂×C₄	1	1	yes	characteristic
125	#10587503	C₂×C₄	1	1	yes	characteristic
126	#10587503	C₂×C₄	1	1	yes	characteristic
127	#10587502	—	2	1	no	—
128	#10587493	—	2	2	no	—
129	#10587493	—	2	2	no	—
130	#10587486	—	2	1	no	—
131	#10587486	—	2	1	no	—
132	#10587486	—	2	2	no	—
133	#10587485	—	2	1	no	—
134	#10587485	—	2	1	no	—
135	#10587485	—	2	1	no	—
136	#10587485	—	2	1	no	—
137	C₈×Dic₁₇	—	2	1	no	—
138	C₈×Dic₁₇	—	2	1	no	—
139	C₈×Dic₁₇	—	2	2	no	—
140	#10587479	C₂×C₄	1	1	yes	characteristic
141	#10587479	C₂×C₄	1	1	yes	characteristic
142	#10587479	C₂×C₄	1	1	yes	characteristic
143	#10587479	C₂×C₄	1	1	yes	characteristic
144	#10587478	C₂×C₄	1	1	yes	characteristic
145	#10587478	C₂×C₄	1	1	yes	characteristic
146	#10587478	C₂×C₄	1	1	yes	characteristic
147	#10587478	C₂×C₄	1	1	yes	characteristic
148	C₄⋊#3622	—	2	1	no	—
149	C₄⋊#3622	—	2	1	no	—
150	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
151	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
152	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
153	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
154	#41×C₁₇	—	2	1	no	—
155	#41×C₁₇	—	2	1	no	—
156	#41×C₁₇	C₂×Q₈	1	2	yes	—
157	#41×C₁₇	#41	1	2	yes	—
158	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×D₄×C₁₇	—	2	1	no	—
160	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	—	2	1	no	—
162	C₂²×C₄×C₁₇	—	2	1	no	—
163	C₂²×C₄×C₁₇	—	2	1	no	—
164	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
166	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
167	C₂²×Dic₁₇	—	2	1	no	—
168	C₂²×Dic₁₇	—	2	1	no	—
169	C₂×Dic₃₄	—	2	1	no	—
170	C₂×Dic₃₄	—	2	1	no	—
171	M₁₆×C₁₇	—	2	4	no	—
172	M₁₆×C₁₇	—	2	1	no	—
173	M₁₆×C₁₇	—	2	1	no	—
174	M₁₆×C₁₇	—	2	4	no	—
175	M₁₆×C₁₇	C₂×Q₈	1	2	yes	—
176	M₁₆×C₁₇	#41	1	2	yes	—
177	C₂×C₈×C₁₇	—	2	4	no	—
178	C₂×C₈×C₁₇	—	2	1	no	—
179	C₂×C₈×C₁₇	—	2	1	no	—
180	C₂×C₈×C₁₇	—	2	1	no	—
181	C₂×C₈×C₁₇	—	2	1	no	—
182	C₂×C₈×C₁₇	—	2	4	no	—
183	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₂×C₈×C₁₇	C₂×Q₈	1	2	yes	—
188	C₂×C₈×C₁₇	#41	1	2	yes	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	—	2	1	no	—
191	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₇	—	2	1	no	—
194	C₂²⋊C₄×C₁₇	—	2	1	no	—
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₄²×C₁₇	—	2	1	no	—
197	C₄²×C₁₇	—	2	1	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
200	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
201	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₂²⋊Dic₁₇	—	2	1	no	—
204	C₂²⋊Dic₁₇	—	2	1	no	—
205	C₄⋊Dic₁₇	—	2	1	no	—
206	C₄⋊Dic₁₇	—	2	1	no	—
207	C₄⋊Dic₁₇	—	4	2	no	—
208	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
209	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
210	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
211	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
212	#63225	—	2	1	no	—
213	#63225	—	2	1	no	—
214	#63225	—	2	1	no	—
215	#63225	—	2	1	no	—
216	C₄×Dic₁₇	—	2	1	no	—
217	C₄×Dic₁₇	—	2	1	no	—
218	C₄×Dic₁₇	—	2	1	no	—
219	C₄×Dic₁₇	—	2	1	no	—
220	C₄×Dic₁₇	—	2	1	no	—
221	C₄×Dic₁₇	—	2	1	no	—
222	#63223	—	2	1	no	—
223	#63223	—	2	1	no	—
224	#63223	—	2	1	no	—
225	#63223	—	2	1	no	—
226	C₂×#3622	—	2	1	no	—
227	C₂×#3622	—	2	1	no	—
228	C₂×#3622	—	2	1	no	—
229	C₂×#3622	—	2	1	no	—
230	C₂×#3622	—	2	1	no	—
231	C₂×#3622	—	2	1	no	—
232	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
233	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
234	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
235	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
236	#21629	—	17	1	no	maximal, Sylow
237	C₂³×C₁₇	—	2	1	no	—
238	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
239	Q₈×C₁₇	—	2	1	no	—
240	Q₈×C₁₇	C₄×Q₈	1	2	yes	—
241	D₄×C₁₇	—	2	2	no	—
242	D₄×C₁₇	—	2	2	no	—
243	D₄×C₁₇	—	2	1	no	—
244	D₄×C₁₇	C₄×Q₈	1	2	yes	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	2	2	no	—
247	C₂×C₄×C₁₇	—	2	2	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	4	1	no	—
251	C₂×C₄×C₁₇	—	4	1	no	—
252	C₂×C₄×C₁₇	—	8	1	no	—
253	C₂×C₄×C₁₇	—	8	1	no	—
254	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
259	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
260	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
261	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
263	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
264	C₂×Dic₁₇	—	2	2	no	—
265	C₂×Dic₁₇	—	2	1	no	—
266	C₂×Dic₁₇	—	2	1	no	—
267	C₂×Dic₁₇	—	2	1	no	—
268	C₂×Dic₁₇	—	2	1	no	—
269	C₂×Dic₁₇	—	4	1	no	—
270	C₂×Dic₁₇	—	4	1	no	—
271	C₂×Dic₁₇	—	4	1	no	—
272	C₂×Dic₁₇	—	4	1	no	—
273	C₂×Dic₁₇	—	4	1	no	—
274	Dic₃₄	—	8	1	no	—
275	Dic₃₄	—	8	1	no	—
276	C₈×C₁₇	—	2	2	no	—
277	C₈×C₁₇	—	2	1	no	—
278	C₈×C₁₇	—	2	2	no	—
279	C₈×C₁₇	—	2	1	no	—
280	C₈×C₁₇	C₂²⋊Q₈	1	2	yes	—
281	C₈×C₁₇	C₂²⋊Q₈	1	2	yes	—
282	#3622	—	2	1	no	—
283	#3622	—	2	1	no	—
284	#3622	—	2	1	no	—
285	#3622	—	2	1	no	—
286	#3622	—	4	1	no	—
287	#3622	—	4	1	no	—
288	#3076	—	17	1	no	—
289	#2961	—	17	1	no	—
290	#2875	D₁₇	1	1	yes	characteristic
291	#1986	—	17	1	no	—
292	#1950	—	17	1	no	—
293	#1922	—	17	1	no	—
294	#1922	—	17	1	no	—
295	#1866	—	17	1	no	—
296	#1866	—	17	1	no	—
297	#1806	—	17	1	no	—
298	#1773	—	17	1	no	—
299	#1772	—	17	1	no	—
300	#1771	—	17	1	no	—
301	#1765	—	17	1	no	—
302	#1764	—	17	1	no	—
303	C₂²×C₁₇	—	2	1	no	—
304	C₂²×C₁₇	—	2	1	no	—
305	C₂²×C₁₇	—	2	2	no	—
306	C₂²×C₁₇	—	4	1	no	—
307	C₂²×C₁₇	—	4	1	no	—
308	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
309	C₂²×C₁₇	#529	1	1	yes	characteristic
310	C₂²×C₁₇	#533	1	1	yes	characteristic
311	C₄×C₁₇	—	2	1	no	—
312	C₄×C₁₇	—	2	1	no	—
313	C₄×C₁₇	—	2	1	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	2	no	—
316	C₄×C₁₇	—	4	1	no	—
317	C₄×C₁₇	—	4	1	no	—
318	C₄×C₁₇	C₂×C₄×Q₈	1	1	yes	characteristic
319	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
320	C₄×C₁₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
321	C₄×C₁₇	#525	1	1	yes	characteristic
322	Dic₁₇	—	4	2	no	—
323	Dic₁₇	—	4	1	no	—
324	Dic₁₇	—	4	1	no	—
325	Dic₁₇	—	4	1	no	—
326	Dic₁₇	—	4	1	no	—
327	Dic₁₇	—	8	1	no	—
328	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
329	C₂×#131	C₂×D₁₇	1	1	yes	characteristic
330	#533	—	17	1	no	—
331	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
332	#479	—	17	1	no	—
333	#479	—	17	1	no	—
334	#478	—	17	1	no	—
335	#478	—	17	1	no	—
336	#477	—	17	1	no	—
337	#476	—	17	1	no	—
338	#475	—	17	1	no	—
339	#474	—	17	1	no	—
340	#446	—	34	1	no	—
341	#446	—	34	1	no	—
342	#446	—	34	1	no	—
343	#446	—	34	1	no	—
344	C₂×#108	—	17	1	no	—
345	C₂×#108	—	17	1	no	—
346	#427	—	17	1	no	—
347	#427	—	17	1	no	—
348	#424	—	17	1	no	—
349	#424	—	17	1	no	—
350	#423	—	17	1	no	—
351	C₂×C₄⋊C₈	—	17	1	no	—
352	C₂×#104	—	17	1	no	—
353	C₂×#104	—	17	1	no	—
354	#416	—	17	1	no	—
355	#416	—	17	1	no	—
356	#405	—	2	1	no	—
357	#405	—	2	1	no	—
358	#405	—	17	1	no	—
359	#405	—	17	1	no	—
360	#405	C₂×D₁₇	1	1	yes	characteristic
361	#405	C₂×D₁₇	1	1	yes	characteristic
362	C₄×M₁₆	—	2	1	no	—
363	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
364	C₂×#97	—	2	1	no	—
365	C₂×#97	—	17	1	no	—
366	C₂×#97	C₂×D₁₇	1	1	yes	characteristic
367	C₂×C₄×C₈	—	17	1	no	—
368	C₄×C₄⋊C₄	—	17	1	no	—
369	#341	—	17	1	no	—
370	#341	—	17	1	no	—
371	#339	—	17	1	no	—
372	#339	—	17	1	no	—
373	#339	—	17	1	no	—
374	#339	—	17	1	no	—
375	#339	—	17	1	no	—
376	#339	—	17	1	no	—
377	#336	—	17	1	no	—
378	#336	—	17	1	no	—
379	C₂×C₁₇	—	2	1	no	—
380	C₂×C₁₇	—	2	1	no	—
381	C₂×C₁₇	—	4	2	no	—
382	C₂×C₁₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
383	C₂×C₁₇	#2956	1	1	yes	characteristic
384	C₂×C₁₇	#2957	1	1	yes	characteristic
385	C₂×#41	C₂²×D₁₇	1	1	yes	characteristic
386	#131	—	2	2	no	—
387	#131	—	2	2	no	—
388	#131	—	2	2	no	—
389	#131	Dic₃₄	1	4	yes	complemented
390	C₂×M₁₆	—	2	1	no	—
391	C₂×M₁₆	—	2	1	no	—
392	C₂×M₁₆	—	17	1	no	—
393	C₂×M₁₆	—	17	1	no	—
394	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
395	C₂×M₁₆	C₂²×D₁₇	1	1	yes	characteristic
396	C₂²×C₈	—	2	1	no	—
397	C₂²×C₈	—	2	1	no	—
398	C₂²×C₈	—	17	1	no	—
399	C₂²×C₈	—	17	1	no	—
400	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
401	C₂²×C₈	C₂²×D₁₇	1	1	yes	characteristic
402	C₄⋊Q₈	—	17	1	no	—
403	C₄⋊Q₈	—	17	1	no	—
404	#125	—	17	1	no	—
405	#125	—	17	1	no	—
406	C₂²⋊Q₈	—	34	1	no	—
407	C₂²⋊Q₈	—	34	1	no	—
408	C₄×Q₈	—	34	1	no	—
409	C₄×Q₈	—	34	1	no	—
410	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
411	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
412	C₄×D₄	—	2	1	no	—
413	C₄×D₄	—	2	1	no	—
414	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
415	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
416	#117	—	2	1	no	—
417	#117	—	17	1	no	—
418	#117	—	17	1	no	—
419	#117	C₂²×D₁₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	—	34	1	no	—
421	C₂×C₄²	—	2	1	no	—
422	C₂×C₄²	—	17	1	no	—
423	C₂×C₄²	—	17	1	no	—
424	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
425	#108	—	34	2	no	—
426	#108	—	34	2	no	—
427	#107	—	17	1	no	—
428	#107	—	17	1	no	—
429	#107	—	17	1	no	—
430	#107	—	17	1	no	—
431	#106	—	17	1	no	—
432	#106	—	17	1	no	—
433	#106	—	17	1	no	—
434	#106	—	17	1	no	—
435	C₄⋊C₈	—	17	1	no	—
436	C₄⋊C₈	—	17	1	no	—
437	C₄⋊C₈	—	17	1	no	—
438	C₄⋊C₈	—	17	1	no	—
439	C₄⋊C₈	—	34	1	no	—
440	C₄⋊C₈	—	34	1	no	—
441	C₄⋊C₈	—	34	1	no	—
442	C₄⋊C₈	—	34	1	no	—
443	C₄⋊C₈	—	34	1	no	—
444	C₄⋊C₈	—	34	1	no	—
445	#104	—	34	2	no	—
446	#104	—	34	2	no	—
447	#103	—	17	1	no	—
448	#103	—	17	1	no	—
449	#103	—	17	1	no	—
450	#103	—	17	1	no	—
451	#102	—	17	1	no	—
452	#102	—	17	1	no	—
453	#102	—	17	1	no	—
454	#102	—	17	1	no	—
455	#97	—	2	1	no	—
456	#97	—	2	1	no	—
457	#97	—	2	1	no	—
458	#97	—	34	2	no	—
459	#97	—	34	1	no	—
460	#97	—	34	1	no	—
461	#97	C₂²⋊D₁₇	1	1	yes	characteristic
462	#97	C₂²⋊D₁₇	1	1	yes	characteristic
463	#97	C₂²⋊D₁₇	1	1	yes	characteristic
464	#97	C₂²⋊D₁₇	1	1	yes	characteristic
465	C₄×C₈	—	2	1	no	—
466	C₄×C₈	—	2	1	no	—
467	C₄×C₈	—	2	1	no	—
468	C₄×C₈	—	34	2	no	—
469	C₄×C₈	—	34	1	no	—
470	C₄×C₈	—	34	1	no	—
471	#95	—	34	1	no	—
472	C₁₇	#21629	1	1	yes	characteristic, complemented, Sylow
473	#41	—	2	1	no	—
474	#41	—	2	1	no	—
475	#41	C₂×Dic₃₄	1	2	yes	—
476	#41	#63252	1	2	yes	—
477	C₂×Q₈	—	34	1	no	—
478	C₂×Q₈	—	34	1	no	—
479	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
482	C₂²×C₄	—	2	1	no	—
483	C₂²×C₄	—	2	1	no	—
484	C₂²×C₄	—	2	1	no	—
485	C₂²×C₄	—	34	1	no	—
486	C₂²×C₄	—	34	1	no	—
487	C₂²×C₄	#63252	1	1	yes	characteristic
488	C₂²×C₄	#63252	1	1	yes	characteristic
489	C₂²×C₄	C₂³×D₁₇	1	1	yes	characteristic
490	M₁₆	—	2	4	no	—
491	M₁₆	—	2	1	no	—
492	M₁₆	—	2	1	no	—
493	M₁₆	—	2	4	no	—
494	M₁₆	—	34	1	no	—
495	M₁₆	—	34	1	no	—
496	M₁₆	—	34	1	no	—
497	M₁₆	—	34	1	no	—
498	M₁₆	C₂×Dic₃₄	1	2	yes	—
499	M₁₆	#63252	1	2	yes	—
500	C₂×C₈	—	2	4	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	4	no	—
506	C₂×C₈	—	17	1	no	—
507	C₂×C₈	—	17	1	no	—
508	C₂×C₈	—	17	1	no	—
509	C₂×C₈	—	17	1	no	—
510	C₂×C₈	—	34	1	no	—
511	C₂×C₈	—	34	1	no	—
512	C₂×C₈	—	34	1	no	—
513	C₂×C₈	—	34	1	no	—
514	C₂×C₈	—	34	1	no	—
515	C₂×C₈	—	34	1	no	—
516	C₂×C₈	C₂×Dic₃₄	1	2	yes	—
517	C₂×C₈	#63252	1	2	yes	—
518	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
519	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
520	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
521	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	17	1	no	—
525	C₄⋊C₄	—	17	1	no	—
526	C₄⋊C₄	—	17	1	no	—
527	C₄⋊C₄	—	17	1	no	—
528	C₄⋊C₄	—	34	1	no	—
529	C₄⋊C₄	—	34	1	no	—
530	C₄⋊C₄	—	34	1	no	—
531	C₄⋊C₄	—	34	1	no	—
532	C₄⋊C₄	—	34	1	no	—
533	C₄⋊C₄	—	34	1	no	—
534	C₄⋊C₄	—	68	2	no	—
535	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	1	no	—
538	C₂²⋊C₄	—	2	1	no	—
539	C₂²⋊C₄	—	2	1	no	—
540	C₂²⋊C₄	—	34	1	no	—
541	C₂²⋊C₄	—	34	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	34	1	no	—
546	C₄²	—	34	1	no	—
547	C₄²	—	34	1	no	—
548	C₄²	—	34	1	no	—
549	C₄²	—	34	1	no	—
550	C₄²	—	34	1	no	—
551	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
552	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
553	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
554	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
555	C₂³	—	2	1	no	—
556	C₂³	C₂×#63252	1	1	yes	characteristic
557	Q₈	—	2	1	no	—
558	Q₈	—	136	1	no	—
559	Q₈	—	136	1	no	—
560	Q₈	C₄×Dic₃₄	1	2	yes	—
561	D₄	—	2	2	no	—
562	D₄	—	2	2	no	—
563	D₄	—	2	1	no	—
564	D₄	C₄×Dic₃₄	1	2	yes	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	4	1	no	—
571	C₂×C₄	—	4	1	no	—
572	C₂×C₄	—	8	1	no	—
573	C₂×C₄	—	8	1	no	—
574	C₂×C₄	—	34	2	no	—
575	C₂×C₄	—	34	1	no	—
576	C₂×C₄	—	34	1	no	—
577	C₂×C₄	—	34	1	no	—
578	C₂×C₄	—	34	1	no	—
579	C₂×C₄	—	68	1	no	—
580	C₂×C₄	—	68	1	no	—
581	C₂×C₄	—	68	1	no	—
582	C₂×C₄	—	68	1	no	—
583	C₂×C₄	—	68	1	no	—
584	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
585	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
586	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
587	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
588	C₂×C₄	C₂²×Dic₃₄	1	1	yes	characteristic
589	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
590	C₂×C₄	C₂×#63252	1	1	yes	characteristic
591	C₂×C₄	C₂×#63252	1	1	yes	characteristic
592	C₂×C₄	C₂×#63252	1	1	yes	characteristic
593	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
594	C₈	—	2	2	no	—
595	C₈	—	2	1	no	—
596	C₈	—	2	2	no	—
597	C₈	—	2	1	no	—
598	C₈	—	34	1	no	—
599	C₈	—	34	1	no	—
600	C₈	—	34	1	no	—
601	C₈	—	34	1	no	—
602	C₈	—	68	1	no	—
603	C₈	—	68	1	no	—
604	C₈	#10587610	1	2	yes	—
605	C₈	#10587610	1	2	yes	—
606	C₂²	—	2	1	no	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	2	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
612	C₂²	#11763343	1	1	yes	characteristic
613	C₂²	#11763366	1	1	yes	characteristic
614	C₄	—	2	1	no	—
615	C₄	—	2	1	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	4	1	no	—
620	C₄	—	4	1	no	—
621	C₄	—	68	2	no	—
622	C₄	—	68	1	no	—
623	C₄	—	68	1	no	—
624	C₄	—	68	1	no	—
625	C₄	—	68	1	no	—
626	C₄	—	136	1	no	—
627	C₄	C₂×C₄×Dic₃₄	1	1	yes	characteristic
628	C₄	C₄×#63252	1	1	yes	characteristic
629	C₄	C₂×#10587610	1	1	yes	characteristic
630	C₄	#11763320	1	1	yes	characteristic
631	C₂	—	2	1	no	—
632	C₂	—	2	1	no	—
633	C₂	—	4	2	no	—
634	C₂	C₄×#10587610	1	1	yes	characteristic
635	C₂	#14537691	1	1	yes	characteristic
636	C₂	#14537699	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₁₇
Fitting	C₁₇×#2875	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#41×C₁₇	C₂³
cosocle	C₂²×C₄×C₁₇	C₂⁴
hypercenter	#2875	D₁₇
hypocenter	C₁₇	#21629
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×#97 ◁ #2875

Complements

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

N	H ≅ G/N	type
2. #14537724	C₂	semidirect
3. #14529728	C₂	semidirect
4. #14529559	C₂	semidirect
5. #14529383	C₂	semidirect
6. #14529383	C₂	semidirect
10. #14528669	C₂	semidirect
11. #14528664	C₂	semidirect
12. #14528656	C₂	semidirect
17. #11763116	C₄	semidirect
18. #11763116	C₄	semidirect
19. #11763109	C₄	semidirect
20. #11763109	C₄	semidirect
21. #11763104	C₄	semidirect
22. #11763099	C₄	semidirect
23. #11763094	C₄	semidirect
24. #11763089	C₄	semidirect
71. C₁₇×#131	Q₈	semidirect
389. #131	Dic₃₄	semidirect
472. C₁₇	#21629	semidirect

Maximal subgroups

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

subgroup	index
#14538572	2
#14537724	2
#14529728	2
#14529559	2
#14529383	2
#14529059	2
#14528804	2
#14528669	2
#14528664	2
#14528656	2
#14528626	2
#14528619	2
C₁₇×#2875	2
#21629	17