Subgroups — #17005267

Order 4352.

616 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538796	C₂	1	1	yes	maximal, characteristic
2	#14537802	C₂	1	1	yes	maximal, characteristic, complemented
3	#14527674	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527667	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527632	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527627	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527625	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527613	C₂	1	1	yes	maximal, characteristic, complemented
9	C₈×#63231	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×#63229	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527562	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527244	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527164	C₂	1	1	yes	maximal, characteristic, complemented
14	M₁₆×#3622	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2969	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×#63252	C₂²	1	1	yes	characteristic
17	#11763147	C₄	1	1	yes	characteristic
18	#11763130	C₄	1	1	yes	characteristic
19	#11763113	C₄	1	1	yes	characteristic
20	#11763106	C₄	1	1	yes	characteristic
21	#11763028	C₄	1	1	yes	characteristic
22	#11763021	C₄	1	1	yes	characteristic
23	#11762969	C₄	1	1	yes	characteristic
24	#11762952	C₄	1	1	yes	characteristic
25	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
26	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
27	C₄×#63231	C₂²	1	1	yes	characteristic
28	C₄×#63230	C₂²	1	1	yes	characteristic
29	C₄×#63229	C₂²	1	1	yes	characteristic
30	C₄×#63228	C₂²	1	1	yes	characteristic
31	#11762888	C₂²	1	1	yes	characteristic
32	#11762888	C₂²	1	1	yes	characteristic
33	#11762885	—	2	1	no	—
34	#11762885	—	2	1	no	—
35	#11762866	C₂²	1	1	yes	characteristic
36	#11762864	—	2	1	no	—
37	#11762862	C₂²	1	1	yes	characteristic
38	#11762761	—	2	1	no	—
39	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
40	#11762561	C₂²	1	1	yes	characteristic
41	#11762561	C₂²	1	1	yes	characteristic
42	#11762559	C₂²	1	1	yes	characteristic
43	#11762559	C₂²	1	1	yes	characteristic
44	Q₈⋊#3622	C₂²	1	1	yes	characteristic
45	Q₈⋊#3622	C₂²	1	1	yes	characteristic
46	#11762539	C₂²	1	1	yes	characteristic
47	#11762539	C₂²	1	1	yes	characteristic
48	D₄⋊#3622	C₂²	1	1	yes	characteristic
49	D₄⋊#3622	C₂²	1	1	yes	characteristic
50	#11762536	C₂²	1	1	yes	characteristic
51	#11762536	C₂²	1	1	yes	characteristic
52	#11762530	C₂²	1	1	yes	characteristic
53	#11762530	C₂²	1	1	yes	characteristic
54	C₈×#3622	C₂²	1	1	yes	characteristic
55	C₈×#3622	C₂²	1	1	yes	characteristic
56	C₁₇×#529	C₂²	1	1	yes	characteristic
57	C₁₇×#446	C₂²	1	1	yes	characteristic
58	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#436	—	2	1	no	—
60	C₁₇×#436	C₂²	1	1	yes	characteristic
61	C₁₇×#435	—	2	1	no	—
62	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#433	—	2	1	no	—
64	C₁₇×#431	C₂²	1	1	yes	characteristic
65	C₁₇×#405	—	2	1	no	—
66	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
67	C₂×#63252	C₂×C₄	1	1	yes	characteristic
68	C₂×M₁₆×C₁₇	—	2	1	no	—
69	C₂×M₁₆×C₁₇	D₄	1	1	yes	characteristic
70	C₂×M₁₆×C₁₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₁₇	—	2	1	no	—
72	C₁₇×#126	—	2	1	no	—
73	C₁₇×#125	C₂×C₄	1	1	yes	characteristic
74	C₁₇×#124	C₂×C₄	1	1	yes	characteristic
75	C₁₇×#123	—	2	1	no	—
76	C₁₇×C₂²⋊Q₈	C₂×C₄	1	1	yes	characteristic
77	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
78	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
79	C₄×D₄×C₁₇	—	2	1	no	—
80	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
81	C₁₇×#117	—	2	1	no	—
82	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
83	C₂×#63231	C₂×C₄	1	1	yes	characteristic
84	C₂×#63230	C₂×C₄	1	1	yes	characteristic
85	C₂×#63229	C₂×C₄	1	1	yes	characteristic
86	C₂×#63228	C₂×C₄	1	1	yes	characteristic
87	C₄×C₂²⋊D₁₇	—	2	1	no	—
88	C₄×C₂²⋊D₁₇	—	2	1	no	—
89	#10587612	C₂×C₄	1	1	yes	characteristic
90	C₂²×#3622	—	2	1	no	—
91	C₂×#63218	—	2	1	no	—
92	C₂×#63218	—	2	1	no	—
93	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
94	C₄×D₆₈	C₂³	1	1	yes	characteristic
95	#10587558	—	2	1	no	—
96	C₄²×D₁₇	—	2	1	no	—
97	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
98	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₁₇×C₂²⋊C₈	—	2	1	no	—
104	C₁₇×C₂²⋊C₈	—	2	1	no	—
105	C₁₇×C₂²⋊C₈	—	2	1	no	—
106	C₁₇×#97	—	2	1	no	—
107	C₁₇×#97	D₄	1	1	yes	characteristic
108	C₁₇×#97	D₄	1	1	yes	characteristic
109	C₄×C₈×C₁₇	—	2	1	no	—
110	C₄×C₈×C₁₇	—	2	1	no	—
111	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
112	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
113	#10587506	C₂×C₄	1	1	yes	characteristic
114	#10587506	C₂×C₄	1	1	yes	characteristic
115	#10587503	C₂×C₄	1	1	yes	characteristic
116	#10587503	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊#3622	—	2	1	no	—
118	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
120	#10587491	—	2	1	no	—
121	#10587491	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	C₈×Dic₁₇	—	2	1	no	—
125	C₈×Dic₁₇	—	2	1	no	—
126	#10587481	C₂×C₄	1	1	yes	characteristic
127	#10587481	C₂×C₄	1	1	yes	characteristic
128	#10587480	C₂×C₄	1	1	yes	characteristic
129	#10587480	C₂×C₄	1	1	yes	characteristic
130	#10587479	C₂×C₄	1	1	yes	characteristic
131	#10587479	C₂×C₄	1	1	yes	characteristic
132	#10587478	C₂×C₄	1	1	yes	characteristic
133	#10587478	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
136	C₄⋊#3622	C₂³	1	1	yes	characteristic
137	C₄⋊#3622	C₂³	1	1	yes	characteristic
138	#10587474	—	2	1	no	—
139	C₄×#3622	—	2	1	no	—
140	C₄×#3622	C₂³	1	1	yes	characteristic
141	C₄×#3622	C₂³	1	1	yes	characteristic
142	C₄×#3622	C₂³	1	1	yes	characteristic
143	C₄×#3622	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×D₄×C₁₇	—	2	1	no	—
146	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
151	C₂×C₂²⋊D₁₇	—	2	1	no	—
152	#63252	—	2	2	no	—
153	#63252	—	4	1	no	—
154	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₄×D₁₇	—	2	1	no	—
156	C₂×C₄×D₁₇	—	2	1	no	—
157	C₂×C₄×D₁₇	—	2	1	no	—
158	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
159	M₁₆×C₁₇	—	2	2	no	—
160	M₁₆×C₁₇	—	2	2	no	—
161	M₁₆×C₁₇	—	4	2	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	4	2	no	—
165	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
167	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₇	—	2	1	no	—
170	C₄⋊C₄×C₁₇	—	2	1	no	—
171	C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₇	—	2	1	no	—
176	C₂²⋊C₄×C₁₇	—	2	1	no	—
177	C₂²⋊C₄×C₁₇	—	2	1	no	—
178	C₂²⋊C₄×C₁₇	—	2	1	no	—
179	C₂²⋊C₄×C₁₇	—	2	1	no	—
180	C₄²×C₁₇	—	2	1	no	—
181	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
182	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₁₇	#41	1	1	yes	characteristic
184	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
185	C₂²⋊Dic₁₇	—	2	1	no	—
186	#63231	—	2	2	no	—
187	#63230	—	4	1	no	—
188	#63229	—	2	2	no	—
189	#63228	—	4	1	no	—
190	#63227	—	2	1	no	—
191	#63227	—	2	1	no	—
192	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
194	#63225	—	2	1	no	—
195	#63225	—	2	1	no	—
196	C₄×Dic₁₇	—	2	1	no	—
197	C₄×Dic₁₇	—	2	1	no	—
198	C₄×Dic₁₇	—	2	1	no	—
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	2	1	no	—
201	C₂×#3622	—	2	1	no	—
202	C₂×#3622	—	2	1	no	—
203	C₂×#3622	—	4	2	no	—
204	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
205	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
206	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
207	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
208	#63218	—	4	2	no	—
209	#63218	—	4	2	no	—
210	#17999	—	17	1	no	maximal, Sylow
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
213	C₂²×D₁₇	—	2	1	no	—
214	Q₈×C₁₇	—	2	1	no	—
215	Q₈×C₁₇	—	2	1	no	—
216	D₄×C₁₇	—	2	1	no	—
217	D₄×C₁₇	—	2	1	no	—
218	D₄×C₁₇	—	8	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	4	1	no	—
227	C₂×C₄×C₁₇	—	4	1	no	—
228	C₂×C₄×C₁₇	—	4	1	no	—
229	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
233	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
235	C₂²⋊D₁₇	—	4	2	no	—
236	C₂×Dic₁₇	—	2	1	no	—
237	C₂×Dic₁₇	—	2	1	no	—
238	C₂×Dic₁₇	—	2	1	no	—
239	D₆₈	—	2	1	no	—
240	D₆₈	—	2	1	no	—
241	C₄×D₁₇	—	4	2	no	—
242	C₄×D₁₇	—	4	1	no	—
243	C₄×D₁₇	—	4	1	no	—
244	C₄×D₁₇	—	8	1	no	—
245	Dic₃₄	—	2	1	no	—
246	Dic₃₄	#131	1	2	yes	—
247	C₈×C₁₇	—	2	1	no	—
248	C₈×C₁₇	—	2	1	no	—
249	C₈×C₁₇	—	4	1	no	—
250	C₈×C₁₇	—	4	1	no	—
251	C₈×C₁₇	#135	1	2	yes	—
252	C₈×C₁₇	#135	1	2	yes	—
253	#3622	—	2	2	no	—
254	#3622	—	2	1	no	—
255	#3622	—	2	1	no	—
256	#3622	—	2	1	no	—
257	#3622	—	2	1	no	—
258	#3622	—	4	1	no	—
259	#3622	—	4	1	no	—
260	#3622	—	4	1	no	—
261	#3102	—	17	1	no	—
262	#2971	—	17	1	no	—
263	#2969	D₁₇	1	1	yes	characteristic, complemented
264	#1590	—	17	1	no	—
265	#1589	—	17	1	no	—
266	#1584	—	17	1	no	—
267	#1583	—	17	1	no	—
268	#1583	—	17	1	no	—
269	#1581	—	17	1	no	—
270	C₈×Q₁₆	—	17	1	no	—
271	C₈×SD₁₆	—	17	1	no	—
272	#1572	—	17	1	no	—
273	#1494	—	17	1	no	—
274	#1476	—	17	1	no	—
275	C₈×M₁₆	—	17	1	no	—
276	C₂²×C₁₇	—	2	1	no	—
277	C₂²×C₁₇	—	2	1	no	—
278	C₂²×C₁₇	—	2	1	no	—
279	C₂²×C₁₇	—	4	1	no	—
280	C₂²×C₁₇	—	4	1	no	—
281	C₂²×C₁₇	—	4	1	no	—
282	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×D₁₇	—	4	1	no	—
284	C₂×D₁₇	—	4	1	no	—
285	C₂×D₁₇	—	4	1	no	—
286	C₄×C₁₇	—	2	1	no	—
287	C₄×C₁₇	—	2	1	no	—
288	C₄×C₁₇	—	2	1	no	—
289	C₄×C₁₇	—	2	1	no	—
290	C₄×C₁₇	—	4	1	no	—
291	C₄×C₁₇	—	4	1	no	—
292	C₄×C₁₇	—	4	1	no	—
293	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
294	C₄×C₁₇	#568	1	1	yes	characteristic
295	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
296	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
297	Dic₁₇	—	2	2	no	—
298	Dic₁₇	—	4	1	no	—
299	Dic₁₇	—	4	1	no	—
300	#529	C₂×D₁₇	1	1	yes	characteristic
301	C₄×#41	—	17	1	no	—
302	#485	—	17	1	no	—
303	#482	—	17	1	no	—
304	#479	—	17	1	no	—
305	#478	—	17	1	no	—
306	#464	—	17	1	no	—
307	#463	—	17	1	no	—
308	#452	—	17	1	no	—
309	#449	—	17	1	no	—
310	#446	C₂×D₁₇	1	1	yes	characteristic
311	C₈×Q₈	—	17	1	no	—
312	C₈×Q₈	—	17	1	no	—
313	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
314	C₄×Q₁₆	—	17	1	no	—
315	C₄×SD₁₆	—	17	1	no	—
316	C₄×SD₁₆	—	17	1	no	—
317	C₄×D₈	—	17	1	no	—
318	#436	—	2	1	no	—
319	#436	—	17	1	no	—
320	#436	—	17	1	no	—
321	#436	—	34	1	no	—
322	#436	—	34	1	no	—
323	#436	C₂×D₁₇	1	1	yes	characteristic
324	#435	—	2	1	no	—
325	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
326	#433	—	2	1	no	—
327	#432	—	17	1	no	—
328	#432	—	34	1	no	—
329	#431	—	17	1	no	—
330	#431	C₂×D₁₇	1	1	yes	characteristic
331	#405	—	2	1	no	—
332	C₄×M₁₆	—	34	1	no	—
333	C₄×M₁₆	C₂×D₁₇	1	1	yes	characteristic
334	C₂×C₄×C₈	—	17	1	no	—
335	#335	—	17	1	no	—
336	#335	—	17	1	no	—
337	#334	—	17	1	no	—
338	#334	—	17	1	no	—
339	Q₈⋊C₈	—	17	1	no	—
340	Q₈⋊C₈	—	17	1	no	—
341	Q₈⋊C₈	—	17	1	no	—
342	Q₈⋊C₈	—	17	1	no	—
343	D₄⋊C₈	—	17	1	no	—
344	D₄⋊C₈	—	17	1	no	—
345	D₄⋊C₈	—	17	1	no	—
346	D₄⋊C₈	—	17	1	no	—
347	#322	—	17	1	no	—
348	#322	—	17	1	no	—
349	C₈²	—	17	1	no	—
350	C₈²	—	17	1	no	—
351	C₂×C₁₇	—	4	1	no	—
352	C₂×C₁₇	—	8	1	no	—
353	C₂×C₁₇	#2933	1	1	yes	characteristic
354	C₂×C₁₇	C₄×#135	1	1	yes	characteristic
355	C₂×C₁₇	#2956	1	1	yes	characteristic
356	D₁₇	—	8	1	no	—
357	C₂×#41	—	17	1	no	—
358	C₂×Q₁₆	—	17	1	no	—
359	C₂×SD₁₆	—	17	1	no	—
360	C₂×SD₁₆	—	17	1	no	—
361	C₂×D₈	—	17	1	no	—
362	C₂×M₁₆	—	2	1	no	—
363	C₂×M₁₆	—	34	1	no	—
364	C₂×M₁₆	—	34	1	no	—
365	C₂×M₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
366	C₂×M₁₆	C₂²⋊D₁₇	1	1	yes	characteristic
367	C₂²×C₈	—	2	1	no	—
368	C₂²×C₈	—	34	1	no	—
369	#126	—	2	1	no	—
370	#125	C₄×D₁₇	1	1	yes	characteristic
371	#124	C₄×D₁₇	1	1	yes	characteristic
372	#123	—	2	1	no	—
373	C₂²⋊Q₈	C₄×D₁₇	1	1	yes	characteristic
374	#121	C₄×D₁₇	1	1	yes	characteristic
375	C₄×Q₈	—	17	1	no	—
376	C₄×Q₈	—	17	1	no	—
377	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	17	1	no	—
380	C₄×D₄	—	17	1	no	—
381	C₄×D₄	—	34	1	no	—
382	C₄×D₄	—	34	1	no	—
383	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
384	#117	—	2	1	no	—
385	#117	—	17	1	no	—
386	#117	—	34	1	no	—
387	C₂×C₄²	—	34	1	no	—
388	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
389	#107	—	17	1	no	—
390	#107	—	17	1	no	—
391	#106	—	17	1	no	—
392	#106	—	17	1	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	17	1	no	—
396	C₄⋊C₈	—	17	1	no	—
397	C₄⋊C₈	—	17	1	no	—
398	C₄⋊C₈	—	17	1	no	—
399	C₄⋊C₈	—	34	1	no	—
400	C₄⋊C₈	—	34	1	no	—
401	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
402	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
403	#103	—	17	1	no	—
404	#103	—	17	1	no	—
405	#103	—	17	1	no	—
406	#103	—	17	1	no	—
407	#102	—	17	1	no	—
408	#102	—	17	1	no	—
409	#102	—	17	1	no	—
410	#102	—	17	1	no	—
411	C₂²⋊C₈	—	2	1	no	—
412	C₂²⋊C₈	—	2	1	no	—
413	C₂²⋊C₈	—	2	1	no	—
414	C₂²⋊C₈	—	17	1	no	—
415	C₂²⋊C₈	—	17	1	no	—
416	C₂²⋊C₈	—	34	1	no	—
417	C₂²⋊C₈	—	34	1	no	—
418	C₂²⋊C₈	—	34	1	no	—
419	#97	—	2	1	no	—
420	#97	—	34	1	no	—
421	#97	C₂²⋊D₁₇	1	1	yes	characteristic
422	#97	C₂²⋊D₁₇	1	1	yes	characteristic
423	C₄×C₈	—	2	1	no	—
424	C₄×C₈	—	2	1	no	—
425	C₄×C₈	—	17	1	no	—
426	C₄×C₈	—	17	1	no	—
427	C₄×C₈	—	17	1	no	—
428	C₄×C₈	—	17	1	no	—
429	C₄×C₈	—	34	1	no	—
430	C₄×C₈	—	34	1	no	—
431	C₄×C₈	—	34	1	no	—
432	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
434	C₁₇	#17999	1	1	yes	characteristic, complemented, Sylow
435	#41	—	34	2	no	—
436	#41	—	68	1	no	—
437	C₂×Q₈	—	17	1	no	—
438	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	17	1	no	—
441	C₂×D₄	—	34	1	no	—
442	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	34	1	no	—
445	C₂²×C₄	—	34	1	no	—
446	C₂²×C₄	—	34	1	no	—
447	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
448	C₂²×C₄	#63252	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
450	Q₁₆	—	34	2	no	—
451	SD₁₆	—	34	2	no	—
452	SD₁₆	—	68	1	no	—
453	D₈	—	68	1	no	—
454	M₁₆	—	2	2	no	—
455	M₁₆	—	2	2	no	—
456	M₁₆	—	4	2	no	—
457	M₁₆	—	68	2	no	—
458	M₁₆	—	68	2	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	4	2	no	—
462	C₂×C₈	—	17	1	no	—
463	C₂×C₈	—	17	1	no	—
464	C₂×C₈	—	17	1	no	—
465	C₂×C₈	—	17	1	no	—
466	C₂×C₈	—	34	1	no	—
467	C₂×C₈	—	34	1	no	—
468	C₂×C₈	—	34	1	no	—
469	C₂×C₈	—	34	1	no	—
470	C₂×C₈	—	68	2	no	—
471	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
472	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
473	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
474	C₂×C₈	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	1	no	—
478	C₄⋊C₄	—	2	1	no	—
479	C₄⋊C₄	—	17	1	no	—
480	C₄⋊C₄	—	17	1	no	—
481	C₄⋊C₄	—	34	1	no	—
482	C₄⋊C₄	—	34	1	no	—
483	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
484	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	1	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	34	1	no	—
491	C₂²⋊C₄	—	34	1	no	—
492	C₂²⋊C₄	—	34	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	34	1	no	—
495	C₄²	—	34	1	no	—
496	C₄²	—	34	1	no	—
497	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
498	C₄²	#63252	1	1	yes	characteristic
499	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
500	C₄²	C₂³×D₁₇	1	1	yes	characteristic
501	C₂³	—	2	1	no	—
502	C₂³	—	34	1	no	—
503	C₂³	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
504	Q₈	—	2	1	no	—
505	Q₈	—	2	1	no	—
506	Q₈	—	17	2	no	—
507	Q₈	—	34	1	no	—
508	D₄	—	2	1	no	—
509	D₄	—	2	1	no	—
510	D₄	—	8	1	no	—
511	D₄	—	34	1	no	—
512	D₄	—	34	1	no	—
513	D₄	—	68	2	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	34	1	no	—
525	C₂×C₄	—	34	1	no	—
526	C₂×C₄	—	34	1	no	—
527	C₂×C₄	—	68	2	no	—
528	C₂×C₄	—	68	1	no	—
529	C₂×C₄	—	68	1	no	—
530	C₂×C₄	—	136	1	no	—
531	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
532	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
533	C₂×C₄	C₄×C₂²⋊D₁₇	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
535	C₂×C₄	C₂×#63252	1	1	yes	characteristic
536	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	34	2	no	—
542	C₈	—	34	1	no	—
543	C₈	—	34	1	no	—
544	C₈	—	34	1	no	—
545	C₈	—	34	1	no	—
546	C₈	—	68	1	no	—
547	C₈	—	68	1	no	—
548	C₈	—	68	1	no	—
549	C₈	#10587636	1	2	yes	—
550	C₈	#10587636	1	2	yes	—
551	C₂²	—	2	1	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	4	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	68	1	no	—
558	C₂²	—	68	1	no	—
559	C₂²	—	68	1	no	—
560	C₂²	C₂×C₄×C₂²⋊D₁₇	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	1	no	—
567	C₄	—	4	1	no	—
568	C₄	—	34	2	no	—
569	C₄	—	68	1	no	—
570	C₄	—	68	1	no	—
571	C₄	#131×D₁₇	1	1	yes	characteristic
572	C₄	#11763574	1	1	yes	characteristic
573	C₄	C₂×#10587636	1	1	yes	characteristic
574	C₄	C₂×#10587636	1	1	yes	characteristic
575	C₂	—	4	1	no	—
576	C₂	—	8	1	no	—
577	C₂	—	136	1	no	—
578	C₂	#14537506	1	1	yes	characteristic
579	C₂	C₄×#10587636	1	1	yes	characteristic
580	C₂	#14537691	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#2969	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#11762952	C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#2969	D₁₇
hypocenter	C₁₇	#17999
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×M₁₆ ◁ #2969

Complements

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

N	H ≅ G/N	type
2. #14537802	C₂	semidirect
3. #14527674	C₂	semidirect
4. #14527667	C₂	semidirect
5. #14527632	C₂	semidirect
6. #14527627	C₂	semidirect
7. #14527625	C₂	semidirect
8. #14527613	C₂	semidirect
9. C₈×#63231	C₂	semidirect
10. C₈×#63229	C₂	semidirect
11. #14527562	C₂	semidirect
12. #14527244	C₂	semidirect
13. #14527164	C₂	semidirect
14. M₁₆×#3622	C₂	semidirect
15. C₁₇×#2969	C₂	semidirect
263. #2969	D₁₇	semidirect
434. C₁₇	#17999	semidirect

Maximal subgroups

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

subgroup	index
#14538796	2
#14537802	2
#14527674	2
#14527667	2
#14527632	2
#14527627	2
#14527625	2
#14527613	2
C₈×#63231	2
C₈×#63229	2
#14527562	2
#14527244	2
#14527164	2
M₁₆×#3622	2
C₁₇×#2969	2
#17999	17