Subgroups — #17004308

Order 4352.

632 conjugacy classes of subgroups.

The subgroup lattice has 570 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538862	C₂	1	1	yes	maximal, characteristic
2	#14537762	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527660	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527657	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527655	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527590	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527588	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527587	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×#3622	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527568	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527229	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527194	C₂	1	1	yes	maximal, characteristic
14	#14527063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1588	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763341	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₁₇	C₂²	1	1	yes	characteristic
18	#11763141	C₄	1	1	yes	characteristic
19	#11763121	C₄	1	1	yes	characteristic
20	#11763119	C₄	1	1	yes	characteristic
21	#11763118	C₄	1	1	yes	characteristic
22	#11763030	C₄	1	1	yes	characteristic
23	#11763029	C₄	1	1	yes	characteristic
24	#11762966	C₄	1	1	yes	characteristic
25	#11762946	C₄	1	1	yes	characteristic
26	#11762939	C₂²	1	1	yes	characteristic
27	Q₈×#3622	C₂²	1	1	yes	characteristic
28	C₈×Dic₃₄	—	2	1	no	—
29	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
30	#11762933	—	2	1	no	—
31	#11762933	C₂²	1	1	yes	characteristic
32	#11762933	C₂²	1	1	yes	characteristic
33	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
34	C₄×#63231	C₂²	1	1	yes	characteristic
35	C₄×#63229	C₂²	1	1	yes	characteristic
36	#11762878	—	2	1	no	—
37	D₄×#3622	C₂²	1	1	yes	characteristic
38	#11762872	—	2	1	no	—
39	#11762867	—	2	1	no	—
40	#11762865	C₂²	1	1	yes	characteristic
41	#11762860	C₂²	1	1	yes	characteristic
42	C₄⋊C₈×D₁₇	—	2	1	no	—
43	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
44	#11762767	—	2	1	no	—
45	C₄×#63218	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₁₇	—	2	1	no	—
47	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11762561	C₂²	1	1	yes	characteristic
49	#11762560	C₂²	1	1	yes	characteristic
50	#11762559	C₂²	1	1	yes	characteristic
51	#11762541	C₂²	1	1	yes	characteristic
52	#11762541	C₂²	1	1	yes	characteristic
53	Q₈⋊#3622	C₂²	1	1	yes	characteristic
54	#11762539	C₂²	1	1	yes	characteristic
55	#11762539	C₂²	1	1	yes	characteristic
56	D₄⋊#3622	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	C₈×#3622	C₂²	1	1	yes	characteristic
59	C₈×#3622	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
62	C₁₇×#436	C₂²	1	1	yes	characteristic
63	C₁₇×#335	C₂²	1	1	yes	characteristic
64	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₈×D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×M₁₆×C₁₇	—	2	1	no	—
70	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
71	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
72	Q₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×#63231	C₂×C₄	1	1	yes	characteristic
74	#10587624	C₂×C₄	1	1	yes	characteristic
75	#10587622	C₂×C₄	1	1	yes	characteristic
76	C₂×#63229	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₇	—	2	1	no	—
78	#10587612	—	2	1	no	—
79	C₂²×#3622	—	2	1	no	—
80	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
81	C₂×#63218	—	2	1	no	—
82	C₂×C₈×D₁₇	—	2	1	no	—
83	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
84	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
85	#10587583	C₂×C₄	1	1	yes	characteristic
86	C₄⋊C₄×D₁₇	—	2	1	no	—
87	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
88	#10587576	C₂×C₄	1	1	yes	characteristic
89	#10587573	—	2	1	no	—
90	#10587573	C₂×C₄	1	1	yes	characteristic
91	#10587569	—	2	1	no	—
92	#10587565	—	2	1	no	—
93	C₄²×D₁₇	—	2	1	no	—
94	C₄²×D₁₇	C₂³	1	1	yes	characteristic
95	C₄×Dic₃₄	—	2	1	no	—
96	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
97	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
98	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
102	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
104	C₁₇×C₂²⋊C₈	—	2	1	no	—
105	C₄×C₈×C₁₇	—	2	1	no	—
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
108	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
109	#10587506	C₂×C₄	1	1	yes	characteristic
110	#10587503	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊#3622	—	2	1	no	—
112	#10587491	—	2	1	no	—
113	#10587491	C₂×C₄	1	1	yes	characteristic
114	#10587491	C₂×C₄	1	1	yes	characteristic
115	#10587489	C₂×C₄	1	1	yes	characteristic
116	#10587487	C₂×C₄	1	1	yes	characteristic
117	#10587487	C₂×C₄	1	1	yes	characteristic
118	#10587486	—	2	1	no	—
119	#10587486	—	2	1	no	—
120	#10587486	—	2	1	no	—
121	#10587485	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	#10587485	—	2	1	no	—
125	#10587485	—	2	1	no	—
126	#10587485	C₂×C₄	1	1	yes	characteristic
127	#10587485	C₂×C₄	1	1	yes	characteristic
128	C₈×Dic₁₇	—	2	1	no	—
129	C₈×Dic₁₇	—	2	1	no	—
130	C₈×Dic₁₇	—	2	1	no	—
131	C₈×Dic₁₇	D₄	1	1	yes	characteristic
132	C₈×Dic₁₇	D₄	1	1	yes	characteristic
133	#10587481	C₂×C₄	1	1	yes	characteristic
134	#10587481	C₂×C₄	1	1	yes	characteristic
135	#10587479	C₂×C₄	1	1	yes	characteristic
136	#10587478	C₂×C₄	1	1	yes	characteristic
137	C₄⋊#3622	—	2	1	no	—
138	C₄⋊#3622	C₂³	1	1	yes	characteristic
139	C₄⋊#3622	C₂³	1	1	yes	characteristic
140	C₄×#3622	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	—	2	1	no	—
147	C₂×C₂²⋊D₁₇	—	2	1	no	—
148	Q₈×D₁₇	—	2	2	no	—
149	Q₈×D₁₇	—	2	2	no	—
150	C₂×C₄×D₁₇	—	2	1	no	—
151	C₂×C₄×D₁₇	—	2	1	no	—
152	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
155	C₂×Dic₃₄	—	2	1	no	—
156	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
158	SD₁₆×C₁₇	—	2	2	no	—
159	M₁₆×C₁₇	—	4	2	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
164	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
167	C₄⋊C₄×C₁₇	—	2	1	no	—
168	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²⋊C₄×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
173	C₂²⋊Dic₁₇	—	2	1	no	—
174	C₂²⋊Dic₁₇	—	2	1	no	—
175	C₂²⋊Dic₁₇	—	2	1	no	—
176	#63231	—	2	2	no	—
177	#63229	—	2	2	no	—
178	#63227	—	2	1	no	—
179	C₄⋊Dic₁₇	—	2	1	no	—
180	C₄⋊Dic₁₇	—	2	1	no	—
181	C₄⋊Dic₁₇	—	2	1	no	—
182	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
183	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
184	#63225	—	2	1	no	—
185	#63225	—	2	1	no	—
186	#63225	—	2	1	no	—
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	C₄×Dic₁₇	—	2	1	no	—
190	C₄×Dic₁₇	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	—	2	1	no	—
193	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₁₇	#41	1	1	yes	characteristic
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	—	2	1	no	—
199	C₂×#3622	—	4	2	no	—
200	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
201	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
202	C₂×#3622	C₂×D₄	1	1	yes	characteristic
203	C₂×#3622	C₂×D₄	1	1	yes	characteristic
204	Dic₆₈	—	2	2	no	—
205	#63218	—	2	4	no	—
206	C₈×D₁₇	—	2	2	no	—
207	C₈×D₁₇	—	4	1	no	—
208	C₈×D₁₇	—	4	2	no	—
209	#17911	—	17	1	no	maximal, Sylow
210	C₂³×C₁₇	—	2	1	no	—
211	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
212	Q₈×C₁₇	—	2	1	no	—
213	Q₈×C₁₇	#131	1	2	yes	—
214	D₄×C₁₇	—	2	1	no	—
215	D₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	4	1	no	—
220	C₂×C₄×C₁₇	—	4	1	no	—
221	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
224	C₂²⋊D₁₇	—	4	2	no	—
225	C₂×Dic₁₇	—	2	1	no	—
226	C₂×Dic₁₇	—	2	1	no	—
227	C₂×Dic₁₇	—	2	1	no	—
228	C₂×Dic₁₇	—	2	1	no	—
229	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
230	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
231	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
232	C₄×D₁₇	—	2	4	no	—
233	C₄×D₁₇	—	2	2	no	—
234	C₄×D₁₇	—	2	1	no	—
235	C₄×D₁₇	—	2	1	no	—
236	C₄×D₁₇	—	2	1	no	—
237	C₄×D₁₇	—	2	1	no	—
238	C₄×D₁₇	—	4	2	no	—
239	Dic₃₄	—	2	4	no	—
240	Dic₃₄	—	2	1	no	—
241	Dic₃₄	—	2	1	no	—
242	Dic₃₄	—	2	1	no	—
243	Dic₃₄	#131	1	2	yes	—
244	C₈×C₁₇	—	2	2	no	—
245	C₈×C₁₇	—	2	1	no	—
246	C₈×C₁₇	—	2	1	no	—
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	#3622	—	2	2	no	—
252	#3622	—	2	1	no	—
253	#3622	—	2	1	no	—
254	#3622	—	2	1	no	—
255	#3622	—	4	1	no	—
256	#3622	—	4	1	no	—
257	#3622	#137	1	2	yes	—
258	#3108	—	17	1	no	—
259	#2966	—	17	1	no	—
260	C₂×C₈×Q₈	—	17	1	no	—
261	#1588	—	17	1	no	—
262	#1588	D₁₇	1	1	yes	characteristic, complemented
263	#1587	—	17	1	no	—
264	#1587	—	17	1	no	—
265	C₈×Q₁₆	—	17	1	no	—
266	C₈×Q₁₆	—	17	1	no	—
267	C₈×SD₁₆	—	17	1	no	—
268	C₈×SD₁₆	—	17	1	no	—
269	#1573	—	17	1	no	—
270	#1491	—	17	1	no	—
271	#1483	—	17	1	no	—
272	C₈×M₁₆	—	17	1	no	—
273	C₂²×C₁₇	—	4	1	no	—
274	C₂²×C₁₇	—	4	1	no	—
275	C₂²×C₁₇	—	4	1	no	—
276	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
277	C₂×D₁₇	—	2	1	no	—
278	C₂×D₁₇	—	2	1	no	—
279	C₂×D₁₇	#443	1	2	yes	—
280	C₄×C₁₇	—	2	2	no	—
281	C₄×C₁₇	—	2	1	no	—
282	C₄×C₁₇	—	4	1	no	—
283	C₄×C₁₇	—	4	1	no	—
284	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
286	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
287	C₄×C₁₇	#575	1	1	yes	characteristic
288	Dic₁₇	—	2	1	no	—
289	Dic₁₇	—	2	2	no	—
290	Dic₁₇	—	2	1	no	—
291	Dic₁₇	—	2	1	no	—
292	Dic₁₇	—	4	1	no	—
293	Dic₁₇	—	4	1	no	—
294	Dic₁₇	—	4	1	no	—
295	#529	—	17	1	no	—
296	C₂×C₄×Q₈	—	17	1	no	—
297	#483	—	17	1	no	—
298	#480	—	17	1	no	—
299	#479	—	17	1	no	—
300	#479	—	17	1	no	—
301	#464	—	17	1	no	—
302	#464	—	17	1	no	—
303	#451	—	17	1	no	—
304	#448	—	17	1	no	—
305	#446	—	17	1	no	—
306	C₈×Q₈	—	17	1	no	—
307	C₈×Q₈	—	17	1	no	—
308	C₈×Q₈	—	17	1	no	—
309	C₈×Q₈	—	17	1	no	—
310	C₈×Q₈	—	34	1	no	—
311	C₈×Q₈	—	34	1	no	—
312	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
313	C₄×Q₁₆	—	17	1	no	—
314	C₄×Q₁₆	—	17	1	no	—
315	C₄×SD₁₆	—	17	1	no	—
316	C₄×SD₁₆	C₂×D₁₇	1	1	yes	characteristic
317	#436	C₂×D₁₇	1	1	yes	characteristic
318	#435	—	34	1	no	—
319	C₈×D₄	—	17	1	no	—
320	C₈×D₄	—	34	1	no	—
321	#433	—	34	1	no	—
322	#432	—	17	1	no	—
323	#431	—	17	1	no	—
324	C₂×C₄⋊C₈	—	17	1	no	—
325	C₂×C₄⋊C₈	—	34	1	no	—
326	#405	—	34	1	no	—
327	C₄×M₁₆	—	17	1	no	—
328	C₂×C₄×C₈	—	17	1	no	—
329	C₂×C₄×C₈	—	34	1	no	—
330	#335	—	17	1	no	—
331	#335	C₂×D₁₇	1	1	yes	characteristic
332	#334	—	17	1	no	—
333	#334	—	17	1	no	—
334	Q₈⋊C₈	—	17	1	no	—
335	Q₈⋊C₈	—	17	1	no	—
336	Q₈⋊C₈	—	17	1	no	—
337	Q₈⋊C₈	—	17	1	no	—
338	Q₈⋊C₈	—	17	1	no	—
339	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
340	D₄⋊C₈	—	17	1	no	—
341	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
342	#322	—	17	1	no	—
343	#322	C₂×D₁₇	1	1	yes	characteristic
344	C₈²	—	17	1	no	—
345	C₈²	—	17	1	no	—
346	C₂×C₁₇	—	8	1	no	—
347	C₂×C₁₇	#2929	1	1	yes	characteristic
348	C₂×C₁₇	C₄×#137	1	1	yes	characteristic
349	C₂×C₁₇	C₂×#443	1	1	yes	characteristic
350	D₁₇	—	2	2	no	—
351	C₂²×Q₈	—	17	1	no	—
352	C₂×Q₁₆	—	17	1	no	—
353	C₂×Q₁₆	—	17	1	no	—
354	C₂×SD₁₆	—	17	1	no	—
355	C₂×SD₁₆	C₄×D₁₇	1	1	yes	characteristic
356	C₂×M₁₆	—	2	1	no	—
357	C₂×M₁₆	—	34	1	no	—
358	C₂²×C₈	—	17	1	no	—
359	C₂²×C₈	—	17	1	no	—
360	C₂²×C₈	—	34	1	no	—
361	C₂²×C₈	—	34	1	no	—
362	#126	—	34	1	no	—
363	#125	—	17	1	no	—
364	#124	—	17	1	no	—
365	#123	—	34	1	no	—
366	C₂²⋊Q₈	—	17	1	no	—
367	#121	—	17	1	no	—
368	C₄×Q₈	—	17	1	no	—
369	C₄×Q₈	—	17	1	no	—
370	C₄×Q₈	—	17	1	no	—
371	C₄×Q₈	—	17	1	no	—
372	C₄×Q₈	—	34	1	no	—
373	C₄×Q₈	—	34	1	no	—
374	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
375	C₄×D₄	—	34	1	no	—
376	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
377	#117	—	34	1	no	—
378	C₂×C₄⋊C₄	—	17	1	no	—
379	C₂×C₄⋊C₄	—	34	1	no	—
380	C₂×C₄²	—	17	1	no	—
381	C₂×C₄²	—	34	1	no	—
382	#107	—	17	1	no	—
383	#107	—	17	1	no	—
384	#106	—	17	1	no	—
385	#106	C₄×D₁₇	1	1	yes	characteristic
386	C₄⋊C₈	—	2	1	no	—
387	C₄⋊C₈	—	17	1	no	—
388	C₄⋊C₈	—	17	1	no	—
389	C₄⋊C₈	—	17	1	no	—
390	C₄⋊C₈	—	17	1	no	—
391	C₄⋊C₈	—	34	1	no	—
392	C₄⋊C₈	—	34	1	no	—
393	C₄⋊C₈	—	34	1	no	—
394	C₄⋊C₈	—	34	1	no	—
395	C₄⋊C₈	—	34	1	no	—
396	C₄⋊C₈	—	34	1	no	—
397	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
398	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
399	#103	—	17	1	no	—
400	#103	—	17	1	no	—
401	#103	—	17	1	no	—
402	#103	—	17	1	no	—
403	#103	—	17	1	no	—
404	#103	C₄×D₁₇	1	1	yes	characteristic
405	#102	—	17	1	no	—
406	#102	C₄×D₁₇	1	1	yes	characteristic
407	C₂²⋊C₈	—	2	1	no	—
408	C₂²⋊C₈	—	17	1	no	—
409	C₂²⋊C₈	—	17	1	no	—
410	C₂²⋊C₈	—	34	1	no	—
411	C₂²⋊C₈	—	34	1	no	—
412	#97	—	34	1	no	—
413	#97	—	34	1	no	—
414	#97	—	34	1	no	—
415	C₄×C₈	—	2	1	no	—
416	C₄×C₈	—	17	1	no	—
417	C₄×C₈	—	17	1	no	—
418	C₄×C₈	—	17	1	no	—
419	C₄×C₈	—	17	1	no	—
420	C₄×C₈	—	17	1	no	—
421	C₄×C₈	—	34	1	no	—
422	C₄×C₈	—	34	1	no	—
423	C₄×C₈	—	34	1	no	—
424	C₄×C₈	—	34	1	no	—
425	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
426	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
427	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
428	C₁₇	#17911	1	1	yes	characteristic, complemented, Sylow
429	C₂×Q₈	—	17	1	no	—
430	C₂×Q₈	—	17	1	no	—
431	C₂×Q₈	—	34	1	no	—
432	C₂×Q₈	—	34	2	no	—
433	C₂×Q₈	—	34	2	no	—
434	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
435	C₂×D₄	—	34	1	no	—
436	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	17	1	no	—
439	C₂²×C₄	—	17	1	no	—
440	C₂²×C₄	—	17	1	no	—
441	C₂²×C₄	—	34	1	no	—
442	C₂²×C₄	—	34	1	no	—
443	Q₁₆	—	34	2	no	—
444	Q₁₆	—	34	2	no	—
445	SD₁₆	—	2	2	no	—
446	SD₁₆	—	34	2	no	—
447	M₁₆	—	4	2	no	—
448	M₁₆	—	34	4	no	—
449	C₂×C₈	—	2	1	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	17	1	no	—
453	C₂×C₈	—	17	1	no	—
454	C₂×C₈	—	17	1	no	—
455	C₂×C₈	—	17	1	no	—
456	C₂×C₈	—	34	2	no	—
457	C₂×C₈	—	34	1	no	—
458	C₂×C₈	—	34	1	no	—
459	C₂×C₈	—	34	1	no	—
460	C₂×C₈	—	68	1	no	—
461	C₂×C₈	—	68	2	no	—
462	C₂×C₈	—	68	2	no	—
463	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
464	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
465	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
466	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	17	1	no	—
469	C₄⋊C₄	—	17	1	no	—
470	C₄⋊C₄	—	34	1	no	—
471	C₄⋊C₄	—	34	1	no	—
472	C₄⋊C₄	—	34	1	no	—
473	C₄⋊C₄	—	34	1	no	—
474	C₄⋊C₄	—	34	1	no	—
475	C₄⋊C₄	—	34	1	no	—
476	C₄⋊C₄	—	34	1	no	—
477	C₄⋊C₄	—	34	1	no	—
478	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
479	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
480	C₂²⋊C₄	—	2	1	no	—
481	C₂²⋊C₄	—	34	1	no	—
482	C₂²⋊C₄	—	34	1	no	—
483	C₂²⋊C₄	—	34	1	no	—
484	C₂²⋊C₄	—	34	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	17	1	no	—
487	C₄²	—	17	1	no	—
488	C₄²	—	17	1	no	—
489	C₄²	—	34	1	no	—
490	C₄²	—	34	1	no	—
491	C₄²	—	34	1	no	—
492	C₄²	—	34	1	no	—
493	C₄²	C₂³×D₁₇	1	1	yes	characteristic
494	C₂³	—	2	1	no	—
495	C₂³	—	17	1	no	—
496	Q₈	—	2	1	no	—
497	Q₈	—	17	2	no	—
498	Q₈	—	34	4	no	—
499	Q₈	—	34	1	no	—
500	Q₈	—	34	1	no	—
501	Q₈	—	34	1	no	—
502	Q₈	#10587593	1	2	yes	—
503	D₄	—	2	1	no	—
504	D₄	—	2	1	no	—
505	D₄	—	68	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	17	1	no	—
512	C₂×C₄	—	17	1	no	—
513	C₂×C₄	—	17	1	no	—
514	C₂×C₄	—	34	2	no	—
515	C₂×C₄	—	34	4	no	—
516	C₂×C₄	—	34	1	no	—
517	C₂×C₄	—	34	1	no	—
518	C₂×C₄	—	34	1	no	—
519	C₂×C₄	—	34	1	no	—
520	C₂×C₄	—	34	1	no	—
521	C₂×C₄	—	34	1	no	—
522	C₂×C₄	—	34	1	no	—
523	C₂×C₄	—	34	1	no	—
524	C₂×C₄	—	68	2	no	—
525	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
527	C₂×C₄	#41×D₁₇	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	1	no	—
530	C₈	—	2	1	no	—
531	C₈	—	2	1	no	—
532	C₈	—	2	1	no	—
533	C₈	—	4	1	no	—
534	C₈	—	4	1	no	—
535	C₈	—	17	2	no	—
536	C₈	—	34	2	no	—
537	C₈	—	34	1	no	—
538	C₈	—	34	1	no	—
539	C₈	—	34	1	no	—
540	C₈	—	68	1	no	—
541	C₈	—	68	1	no	—
542	C₂²	—	4	1	no	—
543	C₂²	—	4	1	no	—
544	C₂²	—	4	1	no	—
545	C₂²	—	17	2	no	—
546	C₂²	—	34	1	no	—
547	C₂²	—	34	1	no	—
548	C₂²	C₄×D₄×D₁₇	1	1	yes	characteristic
549	C₄	—	2	2	no	—
550	C₄	—	2	1	no	—
551	C₄	—	4	1	no	—
552	C₄	—	4	1	no	—
553	C₄	—	34	1	no	—
554	C₄	—	34	2	no	—
555	C₄	—	34	1	no	—
556	C₄	—	34	1	no	—
557	C₄	—	68	1	no	—
558	C₄	—	68	1	no	—
559	C₄	—	68	1	no	—
560	C₄	#131×D₁₇	1	1	yes	characteristic
561	C₄	C₂×#10587593	1	1	yes	characteristic
562	C₄	#137×D₁₇	1	1	yes	characteristic
563	C₄	#11763605	1	1	yes	characteristic
564	C₂	—	8	1	no	—
565	C₂	—	34	2	no	—
566	C₂	#14537475	1	1	yes	characteristic
567	C₂	#14537606	1	1	yes	characteristic
568	C₂	D₁₇×#443	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1588	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#10587624	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1588	D₁₇
hypocenter	C₁₇	#17911
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
3. C₈×Q₈×D₁₇	C₂	semidirect
4. #14527660	C₂	semidirect
5. #14527657	C₂	semidirect
6. #14527655	C₂	semidirect
7. #14527590	C₂	semidirect
8. #14527588	C₂	semidirect
9. #14527587	C₂	semidirect
10. SD₁₆×#3622	C₂	semidirect
11. #14527568	C₂	semidirect
12. #14527229	C₂	semidirect
14. #14527063	C₂	semidirect
15. C₁₇×#1588	C₂	semidirect
262. #1588	D₁₇	semidirect
428. C₁₇	#17911	semidirect

Maximal subgroups

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

subgroup	index
#14538862	2
#14537762	2
C₈×Q₈×D₁₇	2
#14527660	2
#14527657	2
#14527655	2
#14527590	2
#14527588	2
#14527587	2
SD₁₆×#3622	2
#14527568	2
#14527229	2
#14527194	2
#14527063	2
C₁₇×#1588	2
#17911	17