Subgroups — #17023126

Order 4352.

636 conjugacy classes of subgroups.

The subgroup lattice has 486 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14539945	C₂	1	1	yes	maximal, characteristic
2	#14539943	C₂	1	1	yes	maximal, characteristic
3	#14539939	C₂	1	1	yes	maximal, characteristic
4	#14539366	C₂	1	1	yes	maximal, characteristic
5	#14539366	C₂	1	1	yes	maximal, characteristic
6	#14528464	C₂	1	1	yes	maximal, characteristic, complemented
7	#14528462	C₂	1	1	yes	maximal, characteristic, complemented
8	#14528460	C₂	1	1	yes	maximal, characteristic, complemented
9	#14528458	C₂	1	1	yes	maximal, characteristic, complemented
10	#14528432	C₂	1	1	yes	maximal, characteristic, complemented
11	#14528431	C₂	1	1	yes	maximal, characteristic, complemented
12	#14528428	C₂	1	1	yes	maximal, characteristic, complemented
13	#14528427	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527077	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#3231	C₂	1	1	yes	maximal, characteristic
16	#11763366	C₂²	1	1	yes	characteristic
17	#11763366	C₂²	1	1	yes	characteristic
18	#11763214	C₂²	1	1	yes	characteristic
19	#11763212	C₂²	1	1	yes	characteristic
20	#11763212	C₂²	1	1	yes	characteristic
21	#11763212	C₂²	1	1	yes	characteristic
22	#11763212	C₂²	1	1	yes	characteristic
23	#11763207	C₂²	1	1	yes	characteristic
24	#11763205	C₂²	1	1	yes	characteristic
25	#11763205	C₂²	1	1	yes	characteristic
26	#11763188	C₂²	1	1	yes	characteristic
27	#11763188	C₂²	1	1	yes	characteristic
28	#11763161	C₂²	1	1	yes	characteristic
29	#11763161	C₂²	1	1	yes	characteristic
30	#11763161	C₂²	1	1	yes	characteristic
31	#11763161	C₂²	1	1	yes	characteristic
32	#11763160	C₂²	1	1	yes	characteristic
33	#11763160	C₂²	1	1	yes	characteristic
34	#11763159	C₂²	1	1	yes	characteristic
35	#11763159	C₂²	1	1	yes	characteristic
36	#11763159	C₂²	1	1	yes	characteristic
37	#11763159	C₂²	1	1	yes	characteristic
38	#11763151	—	2	2	no	—
39	#11763150	—	2	2	no	—
40	#11763147	—	2	2	no	—
41	#11763117	—	2	2	no	—
42	#11763116	—	2	2	no	—
43	#11763113	—	2	2	no	—
44	#11763048	—	2	2	no	—
45	#11763048	—	2	2	no	—
46	C₄×#63231	—	2	2	no	—
47	C₄×#63231	—	2	2	no	—
48	#11762862	C₂²	1	1	yes	characteristic
49	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
50	#11762531	C₂²	1	1	yes	characteristic
51	#11762531	C₂²	1	1	yes	characteristic
52	#11762530	C₂²	1	1	yes	characteristic
53	#11762530	C₂²	1	1	yes	characteristic
54	C₁₇×#533	C₂²	1	1	yes	characteristic
55	C₁₇×#533	C₂²	1	1	yes	characteristic
56	C₁₇×#500	C₂²	1	1	yes	characteristic
57	C₁₇×#498	C₂²	1	1	yes	characteristic
58	C₁₇×#487	C₂²	1	1	yes	characteristic
59	C₁₇×#487	C₂²	1	1	yes	characteristic
60	C₁₇×#485	—	2	2	no	—
61	C₁₇×#479	—	2	2	no	—
62	C₁₇×#431	C₂²	1	1	yes	characteristic
63	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
66	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₇×#125	—	2	1	no	—
68	C₁₇×#125	—	2	1	no	—
69	C₁₇×C₂²⋊Q₈	—	2	1	no	—
70	C₁₇×C₂²⋊Q₈	—	2	1	no	—
71	C₁₇×C₂²⋊Q₈	—	2	1	no	—
72	C₁₇×C₂²⋊Q₈	—	2	1	no	—
73	C₄×Q₈×C₁₇	—	2	1	no	—
74	C₄×Q₈×C₁₇	—	2	1	no	—
75	C₄×Q₈×C₁₇	—	2	1	no	—
76	C₄×Q₈×C₁₇	—	2	1	no	—
77	C₁₇×#117	—	2	1	no	—
78	C₁₇×#117	—	2	1	no	—
79	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
80	C₂×#63231	—	2	2	no	—
81	C₂×#63231	—	2	2	no	—
82	#10587612	—	2	1	no	—
83	#10587612	—	2	1	no	—
84	#10587610	—	2	1	no	—
85	#10587610	—	2	1	no	—
86	#10587610	—	2	1	no	—
87	#10587610	—	2	1	no	—
88	C₂²×#3622	D₄	1	2	yes	—
89	#10587556	—	2	1	no	—
90	#10587556	—	2	1	no	—
91	#10587555	C₂³	1	1	yes	characteristic
92	#10587555	C₂³	1	1	yes	characteristic
93	#10587555	C₂³	1	1	yes	characteristic
94	#10587555	C₂³	1	1	yes	characteristic
95	C₄×Dic₃₄	—	2	1	no	—
96	C₄×Dic₃₄	—	2	1	no	—
97	C₄×Dic₃₄	—	2	1	no	—
98	C₄×Dic₃₄	—	2	1	no	—
99	C₁₇×#107	—	2	2	no	—
100	C₁₇×#106	—	2	2	no	—
101	C₁₇×C₄⋊C₈	D₄	1	2	yes	—
102	C₁₇×#103	—	2	2	no	—
103	C₁₇×#103	—	2	2	no	—
104	C₁₇×C₂²⋊C₈	D₄	1	2	yes	—
105	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	#10587506	—	2	2	no	—
108	#10587506	—	2	2	no	—
109	#10587506	—	2	2	no	—
110	#10587506	—	2	2	no	—
111	C₂²⋊#3622	D₄	1	2	yes	—
112	#10587489	—	2	2	no	—
113	#10587488	—	2	2	no	—
114	#10587487	—	2	2	no	—
115	#10587487	—	2	2	no	—
116	#10587481	—	2	2	no	—
117	#10587481	—	2	2	no	—
118	#10587481	—	2	2	no	—
119	#10587481	—	2	2	no	—
120	#10587479	—	2	2	no	—
121	#10587479	—	2	2	no	—
122	#10587478	—	2	2	no	—
123	#10587478	—	2	2	no	—
124	#10587478	—	2	2	no	—
125	#10587478	—	2	2	no	—
126	C₄⋊#3622	D₄	1	2	yes	—
127	C₄×#3622	D₄	1	2	yes	—
128	C₄×#3622	C₂³	1	1	yes	characteristic
129	C₄×#3622	C₂³	1	1	yes	characteristic
130	C₄×#3622	C₂³	1	1	yes	characteristic
131	C₄×#3622	C₂³	1	1	yes	characteristic
132	C₂×Q₈×C₁₇	—	2	1	no	—
133	C₂×Q₈×C₁₇	—	2	1	no	—
134	C₂×Q₈×C₁₇	—	2	1	no	—
135	C₂×Q₈×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₃₄	—	2	1	no	—
140	C₂×Dic₃₄	—	2	1	no	—
141	C₂×Dic₃₄	—	2	1	no	—
142	C₂×Dic₃₄	—	2	1	no	—
143	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
144	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
145	C₄⋊C₄×C₁₇	—	2	1	no	—
146	C₄⋊C₄×C₁₇	—	2	1	no	—
147	C₄⋊C₄×C₁₇	—	2	1	no	—
148	C₄⋊C₄×C₁₇	—	2	1	no	—
149	C₄⋊C₄×C₁₇	—	2	1	no	—
150	C₄⋊C₄×C₁₇	—	2	1	no	—
151	C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₄⋊C₄×C₁₇	—	2	1	no	—
153	C₄⋊C₄×C₁₇	—	4	1	no	—
154	C₄⋊C₄×C₁₇	—	4	1	no	—
155	C₄⋊C₄×C₁₇	—	4	1	no	—
156	C₄⋊C₄×C₁₇	—	4	1	no	—
157	C₂²⋊C₄×C₁₇	—	4	1	no	—
158	C₂²⋊C₄×C₁₇	—	4	1	no	—
159	C₄²×C₁₇	—	4	1	no	—
160	C₄²×C₁₇	—	4	1	no	—
161	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
165	C₂²⋊Dic₁₇	—	4	1	no	—
166	C₂²⋊Dic₁₇	—	4	1	no	—
167	#63231	—	4	4	no	—
168	#63231	—	4	4	no	—
169	C₄⋊Dic₁₇	—	2	1	no	—
170	C₄⋊Dic₁₇	—	2	1	no	—
171	C₄⋊Dic₁₇	—	2	1	no	—
172	C₄⋊Dic₁₇	—	2	1	no	—
173	C₄⋊Dic₁₇	—	2	1	no	—
174	C₄⋊Dic₁₇	—	2	1	no	—
175	C₄⋊Dic₁₇	—	2	1	no	—
176	C₄⋊Dic₁₇	—	2	1	no	—
177	#63225	—	4	1	no	—
178	#63225	—	4	1	no	—
179	#63225	—	4	1	no	—
180	#63225	—	4	1	no	—
181	C₄×Dic₁₇	—	4	1	no	—
182	C₄×Dic₁₇	—	4	1	no	—
183	C₂×#3622	—	4	2	no	—
184	C₂×#3622	C₂×D₄	1	2	yes	—
185	C₂×#3622	C₂×D₄	1	2	yes	—
186	C₂×#3622	C₂×D₄	1	2	yes	—
187	C₂×#3622	C₂×D₄	1	2	yes	—
188	#19711	—	17	1	no	maximal, Sylow
189	C₂³×C₁₇	#127	1	1	yes	characteristic
190	Q₈×C₁₇	—	4	2	no	—
191	Q₈×C₁₇	—	4	2	no	—
192	Q₈×C₁₇	—	4	2	no	—
193	Q₈×C₁₇	—	4	2	no	—
194	C₂×C₄×C₁₇	—	2	2	no	—
195	C₂×C₄×C₁₇	—	2	2	no	—
196	C₂×C₄×C₁₇	—	2	2	no	—
197	C₂×C₄×C₁₇	—	4	1	no	—
198	C₂×C₄×C₁₇	—	4	1	no	—
199	C₂×C₄×C₁₇	—	4	1	no	—
200	C₂×C₄×C₁₇	—	4	1	no	—
201	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
202	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
203	C₂×C₄×C₁₇	#127	1	1	yes	characteristic
204	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×Dic₁₇	—	4	1	no	—
208	C₂×Dic₁₇	—	4	1	no	—
209	C₂×Dic₁₇	—	4	1	no	—
210	C₂×Dic₁₇	—	4	1	no	—
211	Dic₃₄	—	4	2	no	—
212	Dic₃₄	—	4	2	no	—
213	Dic₃₄	—	4	2	no	—
214	Dic₃₄	—	4	2	no	—
215	C₈×C₁₇	—	2	2	no	—
216	C₈×C₁₇	—	2	2	no	—
217	#3622	—	2	2	no	—
218	#3622	—	2	2	no	—
219	#3622	—	2	2	no	—
220	#3622	—	2	2	no	—
221	#3231	—	17	1	no	—
222	#3231	—	17	1	no	—
223	#3231	—	17	1	no	—
224	#3231	D₁₇	1	1	yes	characteristic
225	#3170	—	17	1	no	—
226	#3170	—	17	1	no	—
227	#1723	—	17	1	no	—
228	#1723	—	17	1	no	—
229	#1723	—	17	1	no	—
230	#1723	—	17	1	no	—
231	#1718	—	17	1	no	—
232	#1718	—	17	1	no	—
233	#1718	—	17	1	no	—
234	#1718	—	17	1	no	—
235	#1452	—	17	1	no	—
236	C₂²×C₁₇	—	2	1	no	—
237	C₂²×C₁₇	—	2	1	no	—
238	C₂²×C₁₇	—	2	1	no	—
239	C₂²×C₁₇	C₂×#127	1	1	yes	characteristic
240	C₄×C₁₇	—	2	1	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	8	1	no	—
244	C₄×C₁₇	—	8	1	no	—
245	C₄×C₁₇	—	8	1	no	—
246	C₄×C₁₇	—	8	1	no	—
247	C₄×C₁₇	#575	1	2	yes	—
248	C₄×C₁₇	#578	1	2	yes	—
249	C₄×C₁₇	#578	1	2	yes	—
250	Dic₁₇	—	8	1	no	—
251	Dic₁₇	—	8	1	no	—
252	Dic₁₇	—	8	1	no	—
253	Dic₁₇	—	8	1	no	—
254	#533	—	17	1	no	—
255	#533	—	17	1	no	—
256	#533	C₂×D₁₇	1	1	yes	characteristic
257	#533	C₂×D₁₇	1	1	yes	characteristic
258	#500	—	17	1	no	—
259	#500	—	17	1	no	—
260	#500	—	17	1	no	—
261	#500	—	17	1	no	—
262	#500	—	17	1	no	—
263	#500	C₂×D₁₇	1	1	yes	characteristic
264	#498	—	17	1	no	—
265	#498	—	17	1	no	—
266	#498	—	17	1	no	—
267	#498	C₂×D₁₇	1	1	yes	characteristic
268	#494	—	17	1	no	—
269	#494	—	17	1	no	—
270	#487	—	17	1	no	—
271	#487	—	17	1	no	—
272	#487	—	17	1	no	—
273	#487	—	17	1	no	—
274	#487	—	17	1	no	—
275	#487	—	17	1	no	—
276	#487	—	17	1	no	—
277	#487	—	17	1	no	—
278	#487	—	17	1	no	—
279	#487	—	17	1	no	—
280	#487	C₂×D₁₇	1	1	yes	characteristic
281	#487	C₂×D₁₇	1	1	yes	characteristic
282	#485	—	2	2	no	—
283	#485	—	34	2	no	—
284	#485	—	34	2	no	—
285	#485	—	34	2	no	—
286	#479	—	2	2	no	—
287	#479	—	34	2	no	—
288	#479	—	34	2	no	—
289	#479	—	34	2	no	—
290	#467	—	34	2	no	—
291	#467	—	34	2	no	—
292	C₄×Q₁₆	—	34	2	no	—
293	C₄×Q₁₆	—	34	2	no	—
294	#431	—	17	1	no	—
295	#431	C₂×D₁₇	1	1	yes	characteristic
296	C₂×C₄×C₈	—	17	1	no	—
297	#322	—	17	1	no	—
298	#322	—	17	1	no	—
299	#322	—	17	1	no	—
300	#322	—	17	1	no	—
301	C₂×C₁₇	—	4	1	no	—
302	C₂×C₁₇	#3150	1	1	yes	characteristic
303	C₂×C₁₇	#3156	1	1	yes	characteristic
304	C₂×C₁₇	#3156	1	1	yes	characteristic
305	C₂×Q₁₆	—	34	2	no	—
306	C₂×Q₁₆	—	34	2	no	—
307	C₂²×C₈	—	17	2	no	—
308	C₄⋊Q₈	—	17	1	no	—
309	C₄⋊Q₈	—	17	1	no	—
310	C₄⋊Q₈	—	17	1	no	—
311	C₄⋊Q₈	—	17	1	no	—
312	C₄⋊Q₈	C₂²×D₁₇	1	1	yes	characteristic
313	C₄⋊Q₈	C₂²×D₁₇	1	1	yes	characteristic
314	C₄⋊Q₈	C₂²×D₁₇	1	1	yes	characteristic
315	C₄⋊Q₈	C₂²×D₁₇	1	1	yes	characteristic
316	#125	—	2	1	no	—
317	#125	—	2	1	no	—
318	#125	—	34	1	no	—
319	#125	—	34	1	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	1	no	—
322	C₂²⋊Q₈	—	2	1	no	—
323	C₂²⋊Q₈	—	2	1	no	—
324	C₂²⋊Q₈	—	34	1	no	—
325	C₂²⋊Q₈	—	34	1	no	—
326	C₂²⋊Q₈	—	34	1	no	—
327	C₂²⋊Q₈	—	34	1	no	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	1	no	—
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	—	34	1	no	—
333	C₄×Q₈	—	34	1	no	—
334	C₄×Q₈	—	34	1	no	—
335	C₄×Q₈	—	34	1	no	—
336	#117	—	2	1	no	—
337	#117	—	2	1	no	—
338	#117	—	34	1	no	—
339	#117	—	34	1	no	—
340	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
341	#107	—	2	2	no	—
342	#107	—	34	2	no	—
343	#107	—	34	2	no	—
344	#107	—	34	2	no	—
345	#107	—	34	2	no	—
346	#107	—	34	2	no	—
347	#106	—	2	2	no	—
348	#106	—	34	2	no	—
349	#106	—	34	2	no	—
350	#106	—	34	2	no	—
351	C₄⋊C₈	—	17	2	no	—
352	C₄⋊C₈	C₂²⋊D₁₇	1	2	yes	—
353	#103	—	2	2	no	—
354	#103	—	2	2	no	—
355	#103	—	34	2	no	—
356	#103	—	34	2	no	—
357	#103	—	34	2	no	—
358	#103	—	34	2	no	—
359	#103	—	34	2	no	—
360	#103	—	34	2	no	—
361	#103	—	34	2	no	—
362	#103	—	34	2	no	—
363	#103	—	34	2	no	—
364	#103	—	34	2	no	—
365	C₂²⋊C₈	—	17	2	no	—
366	C₂²⋊C₈	C₂²⋊D₁₇	1	2	yes	—
367	C₄×C₈	—	17	2	no	—
368	C₄×C₈	—	17	1	no	—
369	C₄×C₈	—	17	1	no	—
370	C₄×C₈	—	17	1	no	—
371	C₄×C₈	—	17	1	no	—
372	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
373	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
374	C₁₇	#19711	1	1	yes	characteristic, complemented, Sylow
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	1	no	—
377	C₂×Q₈	—	2	1	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	34	1	no	—
380	C₂×Q₈	—	34	1	no	—
381	C₂×Q₈	—	34	1	no	—
382	C₂×Q₈	—	34	1	no	—
383	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
384	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
385	C₂²×C₄	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
386	Q₁₆	—	68	4	no	—
387	Q₁₆	—	68	4	no	—
388	C₂×C₈	—	17	2	no	—
389	C₂×C₈	—	17	2	no	—
390	C₂×C₈	—	17	2	no	—
391	C₂×C₈	—	17	2	no	—
392	C₂×C₈	—	68	2	no	—
393	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
394	C₂×C₈	C₂×C₂²⋊D₁₇	1	2	yes	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	4	1	no	—
404	C₄⋊C₄	—	4	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	—	34	1	no	—
408	C₄⋊C₄	—	34	1	no	—
409	C₄⋊C₄	—	34	1	no	—
410	C₄⋊C₄	—	34	1	no	—
411	C₄⋊C₄	—	34	1	no	—
412	C₄⋊C₄	—	34	1	no	—
413	C₄⋊C₄	—	34	1	no	—
414	C₄⋊C₄	—	34	1	no	—
415	C₄⋊C₄	—	68	1	no	—
416	C₄⋊C₄	—	68	1	no	—
417	C₄⋊C₄	—	68	1	no	—
418	C₄⋊C₄	—	68	1	no	—
419	C₂²⋊C₄	—	4	1	no	—
420	C₂²⋊C₄	—	4	1	no	—
421	C₂²⋊C₄	—	68	1	no	—
422	C₂²⋊C₄	—	68	1	no	—
423	C₄²	—	4	1	no	—
424	C₄²	—	4	1	no	—
425	C₄²	—	68	1	no	—
426	C₄²	—	68	1	no	—
427	C₄²	D₄×D₁₇	1	1	yes	characteristic
428	C₄²	D₄×D₁₇	1	1	yes	characteristic
429	C₄²	C₂×C₂²⋊D₁₇	1	1	yes	characteristic
430	C₄²	C₂³×D₁₇	1	1	yes	characteristic
431	C₂³	#10587626	1	1	yes	characteristic
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	—	4	2	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	68	2	no	—
437	Q₈	—	68	2	no	—
438	Q₈	—	68	2	no	—
439	Q₈	—	68	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	68	1	no	—
448	C₂×C₄	—	68	1	no	—
449	C₂×C₄	—	68	1	no	—
450	C₂×C₄	—	68	1	no	—
451	C₂×C₄	#10587626	1	1	yes	characteristic
452	C₂×C₄	#10587626	1	1	yes	characteristic
453	C₂×C₄	#10587626	1	1	yes	characteristic
454	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
455	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
456	C₂×C₄	C₂²×C₂²⋊D₁₇	1	1	yes	characteristic
457	C₈	—	2	2	no	—
458	C₈	—	2	2	no	—
459	C₈	—	34	2	no	—
460	C₈	—	34	2	no	—
461	C₈	—	34	2	no	—
462	C₈	—	34	2	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	C₂×#10587626	1	1	yes	characteristic
467	C₄	—	2	1	no	—
468	C₄	—	2	1	no	—
469	C₄	—	2	1	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	1	no	—
474	C₄	—	136	1	no	—
475	C₄	—	136	1	no	—
476	C₄	—	136	1	no	—
477	C₄	—	136	1	no	—
478	C₄	#11763606	1	2	yes	—
479	C₄	#11763624	1	2	yes	—
480	C₄	#11763625	1	2	yes	—
481	C₂	—	4	1	no	—
482	C₂	#14539227	1	1	yes	characteristic
483	C₂	#14539275	1	1	yes	characteristic
484	C₂	#14539277	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#10587626
commutator, cosocle	C₄²×C₁₇	C₂⁴
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#3231	C₂
socle	C₂²×C₁₇	C₂×#127
prime radical	C₂³×C₁₇	#127
hypercenter	#3231	D₁₇
hypocenter	C₁₇	#19711
LCS	G ▷ C₄²×C₁₇ ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3231

Complements

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

N	H ≅ G/N	type
6. #14528464	C₂	semidirect
7. #14528462	C₂	semidirect
8. #14528460	C₂	semidirect
9. #14528458	C₂	semidirect
10. #14528432	C₂	semidirect
11. #14528431	C₂	semidirect
12. #14528428	C₂	semidirect
13. #14528427	C₂	semidirect
374. C₁₇	#19711	semidirect

Maximal subgroups

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

subgroup	index
#14539945	2
#14539943	2
#14539939	2
#14539366	2
#14528464	2
#14528462	2
#14528460	2
#14528458	2
#14528432	2
#14528431	2
#14528428	2
#14528427	2
#14527077	2
C₁₇×#3231	2
#19711	17