Subgroups — #17004249

Order 4352.

610 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538821	C₂	1	1	yes	maximal, characteristic
2	#14537715	C₂	1	1	yes	maximal, characteristic
3	C₈×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic
4	#14527657	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527655	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527653	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527603	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527602	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527600	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527600	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527553	C₂	1	1	yes	maximal, characteristic
12	#14527211	C₂	1	1	yes	maximal, characteristic
13	#14527185	C₂	1	1	yes	maximal, characteristic
14	#14527075	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#1587	C₂	1	1	yes	maximal, characteristic, complemented
16	#11763363	C₂²	1	1	yes	characteristic
17	C₄×Q₈×D₁₇	C₂²	1	1	yes	characteristic
18	#11763146	C₄	1	1	yes	characteristic
19	#11763143	C₄	1	1	yes	characteristic
20	#11763103	C₄	1	1	yes	characteristic
21	#11763102	C₄	1	1	yes	characteristic
22	#11763018	C₄	1	1	yes	characteristic
23	#11763017	C₄	1	1	yes	characteristic
24	#11762966	C₄	1	1	yes	characteristic
25	#11762963	C₄	1	1	yes	characteristic
26	#11762939	C₂²	1	1	yes	characteristic
27	#11762937	—	2	1	no	—
28	Q₈×#3622	C₂²	1	1	yes	characteristic
29	Q₈×#3622	C₂²	1	1	yes	characteristic
30	C₈×Dic₃₄	—	2	1	no	—
31	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
32	#11762933	—	2	1	no	—
33	#11762933	—	2	1	no	—
34	#11762933	C₂²	1	1	yes	characteristic
35	#11762933	C₂²	1	1	yes	characteristic
36	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
37	C₄×#63231	C₂²	1	1	yes	characteristic
38	C₄×#63231	C₂²	1	1	yes	characteristic
39	#11762860	C₂²	1	1	yes	characteristic
40	#11762860	C₂²	1	1	yes	characteristic
41	#11762834	—	2	1	no	—
42	#11762831	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₁₇	—	2	1	no	—
44	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
45	#11762766	—	2	1	no	—
46	C₄×C₈×D₁₇	—	2	1	no	—
47	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11762560	C₂²	1	1	yes	characteristic
49	#11762559	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	Q₈⋊#3622	C₂²	1	1	yes	characteristic
55	#11762539	C₂²	1	1	yes	characteristic
56	#11762539	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	#11762531	C₂²	1	1	yes	characteristic
59	#11762530	C₂²	1	1	yes	characteristic
60	C₁₇×#446	C₂²	1	1	yes	characteristic
61	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
62	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#334	C₂²	1	1	yes	characteristic
64	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×Q₈⋊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×Q₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
71	#10587632	C₂×C₄	1	1	yes	characteristic
72	Q₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
73	#10587630	C₂×C₄	1	1	yes	characteristic
74	C₂×#63231	C₂×C₄	1	1	yes	characteristic
75	C₂×#63231	C₂×C₄	1	1	yes	characteristic
76	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
77	C₂×#63218	—	2	1	no	—
78	C₂×C₈×D₁₇	—	2	1	no	—
79	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
80	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
81	#10587583	C₂×C₄	1	1	yes	characteristic
82	#10587582	—	2	1	no	—
83	C₄⋊C₄×D₁₇	—	2	1	no	—
84	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
85	#10587575	—	2	1	no	—
86	#10587574	C₂×C₄	1	1	yes	characteristic
87	#10587573	—	2	1	no	—
88	#10587573	C₂×C₄	1	1	yes	characteristic
89	#10587558	—	2	1	no	—
90	C₄²×D₁₇	—	2	1	no	—
91	C₄²×D₁₇	C₂³	1	1	yes	characteristic
92	C₄×Dic₃₄	—	2	1	no	—
93	C₄×Dic₃₄	—	2	1	no	—
94	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
95	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
96	C₁₇×#107	C₂×C₄	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	—	2	1	no	—
98	C₁₇×C₄⋊C₈	—	2	1	no	—
99	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
100	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
101	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
102	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
103	C₁₇×#97	—	2	1	no	—
104	C₄×C₈×C₁₇	—	2	1	no	—
105	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
106	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
108	#10587506	C₂×C₄	1	1	yes	characteristic
109	#10587506	C₂×C₄	1	1	yes	characteristic
110	#10587491	—	2	1	no	—
111	#10587491	C₂×C₄	1	1	yes	characteristic
112	#10587491	C₂×C₄	1	1	yes	characteristic
113	#10587489	C₂×C₄	1	1	yes	characteristic
114	#10587487	C₂×C₄	1	1	yes	characteristic
115	#10587487	C₂×C₄	1	1	yes	characteristic
116	#10587486	—	2	1	no	—
117	#10587485	—	2	1	no	—
118	#10587485	—	2	1	no	—
119	#10587485	—	2	1	no	—
120	#10587485	—	2	1	no	—
121	#10587485	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	#10587485	C₂×C₄	1	1	yes	characteristic
125	#10587485	C₂×C₄	1	1	yes	characteristic
126	C₈×Dic₁₇	—	2	1	no	—
127	C₈×Dic₁₇	—	2	1	no	—
128	C₈×Dic₁₇	—	2	1	no	—
129	C₈×Dic₁₇	D₄	1	1	yes	characteristic
130	C₈×Dic₁₇	D₄	1	1	yes	characteristic
131	#10587481	C₂×C₄	1	1	yes	characteristic
132	#10587481	C₂×C₄	1	1	yes	characteristic
133	#10587478	C₂×C₄	1	1	yes	characteristic
134	#10587478	C₂×C₄	1	1	yes	characteristic
135	C₄⋊#3622	—	2	1	no	—
136	C₄⋊#3622	—	2	1	no	—
137	C₄⋊#3622	C₂³	1	1	yes	characteristic
138	C₄⋊#3622	C₂³	1	1	yes	characteristic
139	C₄×#3622	—	2	1	no	—
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×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	Q₈×D₁₇	—	2	2	no	—
147	Q₈×D₁₇	—	2	2	no	—
148	C₂×C₄×D₁₇	—	2	1	no	—
149	C₂×C₄×D₁₇	—	2	1	no	—
150	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
153	C₂×Dic₃₄	—	2	1	no	—
154	C₂×Dic₃₄	—	2	1	no	—
155	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
156	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
157	Q₁₆×C₁₇	—	2	2	no	—
158	C₂×C₈×C₁₇	—	2	1	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
162	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
165	C₄⋊C₄×C₁₇	—	2	1	no	—
166	C₄⋊C₄×C₁₇	—	2	1	no	—
167	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₄²×C₁₇	—	2	1	no	—
170	C₄²×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
172	#63231	—	2	2	no	—
173	#63231	—	2	2	no	—
174	#63227	—	2	1	no	—
175	#63227	—	2	1	no	—
176	C₄⋊Dic₁₇	—	2	1	no	—
177	C₄⋊Dic₁₇	—	2	1	no	—
178	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
179	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
180	#63225	—	2	1	no	—
181	#63225	—	2	1	no	—
182	#63225	—	2	1	no	—
183	#63225	—	2	1	no	—
184	#63225	—	2	1	no	—
185	#63225	—	2	1	no	—
186	#63225	—	2	1	no	—
187	#63225	—	2	1	no	—
188	C₄×Dic₁₇	—	2	1	no	—
189	C₄×Dic₁₇	—	2	1	no	—
190	C₄×Dic₁₇	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₁₇	#41	1	1	yes	characteristic
195	C₂×#3622	—	2	1	no	—
196	C₂×#3622	—	2	1	no	—
197	C₂×#3622	—	2	1	no	—
198	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
199	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
200	C₂×#3622	C₂×D₄	1	1	yes	characteristic
201	C₂×#3622	C₂×D₄	1	1	yes	characteristic
202	Dic₆₈	—	2	2	no	—
203	#63218	—	4	2	no	—
204	C₈×D₁₇	—	2	2	no	—
205	C₈×D₁₇	—	2	2	no	—
206	C₈×D₁₇	—	4	2	no	—
207	#17906	—	17	1	no	maximal, Sylow
208	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₁₇	—	2	1	no	—
210	Q₈×C₁₇	—	2	1	no	—
211	Q₈×C₁₇	—	2	1	no	—
212	Q₈×C₁₇	#131	1	2	yes	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
219	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
220	C₂×Dic₁₇	—	2	1	no	—
221	C₂×Dic₁₇	—	2	1	no	—
222	C₂×Dic₁₇	—	2	1	no	—
223	C₂×Dic₁₇	—	2	1	no	—
224	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
225	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
226	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
227	C₄×D₁₇	—	2	4	no	—
228	C₄×D₁₇	—	2	1	no	—
229	C₄×D₁₇	—	2	1	no	—
230	C₄×D₁₇	—	4	1	no	—
231	C₄×D₁₇	—	4	2	no	—
232	C₄×D₁₇	#137	1	2	yes	—
233	C₄×D₁₇	#137	1	2	yes	—
234	Dic₃₄	—	2	4	no	—
235	Dic₃₄	—	2	1	no	—
236	Dic₃₄	—	2	1	no	—
237	Dic₃₄	—	2	1	no	—
238	Dic₃₄	—	4	2	no	—
239	Dic₃₄	#131	1	2	yes	—
240	C₈×C₁₇	—	2	1	no	—
241	C₈×C₁₇	—	2	1	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	—	2	1	no	—
244	C₈×C₁₇	—	4	1	no	—
245	C₈×C₁₇	—	4	1	no	—
246	C₈×C₁₇	—	4	1	no	—
247	#3622	—	2	1	no	—
248	#3622	—	2	1	no	—
249	#3622	—	2	1	no	—
250	#3622	—	2	1	no	—
251	#3622	—	4	1	no	—
252	#3622	—	4	1	no	—
253	#3622	—	4	1	no	—
254	#3104	—	17	1	no	—
255	#2960	—	17	1	no	—
256	C₂×C₈×Q₈	—	17	1	no	—
257	#1587	—	17	1	no	—
258	#1587	—	17	1	no	—
259	#1587	—	17	1	no	—
260	#1587	D₁₇	1	1	yes	characteristic, complemented
261	#1579	—	17	1	no	—
262	#1579	—	17	1	no	—
263	#1579	—	17	1	no	—
264	#1579	—	17	1	no	—
265	#1570	—	17	1	no	—
266	#1487	—	17	1	no	—
267	#1481	—	17	1	no	—
268	#1452	—	17	1	no	—
269	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
270	C₂×D₁₇	—	2	1	no	—
271	C₂×D₁₇	—	2	1	no	—
272	C₂×D₁₇	#441	1	2	yes	—
273	C₄×C₁₇	—	2	2	no	—
274	C₄×C₁₇	—	2	1	no	—
275	C₄×C₁₇	—	4	1	no	—
276	C₄×C₁₇	—	4	1	no	—
277	C₄×C₁₇	—	4	1	no	—
278	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
279	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
280	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
281	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
282	Dic₁₇	—	2	1	no	—
283	Dic₁₇	—	2	2	no	—
284	Dic₁₇	—	2	1	no	—
285	Dic₁₇	—	4	1	no	—
286	Dic₁₇	—	4	1	no	—
287	Dic₁₇	—	4	1	no	—
288	Dic₁₇	#441	1	2	yes	—
289	#533	—	17	1	no	—
290	C₂×C₄×Q₈	—	17	1	no	—
291	#484	—	17	1	no	—
292	#484	—	17	1	no	—
293	#477	—	17	1	no	—
294	#477	—	17	1	no	—
295	#462	—	17	1	no	—
296	#462	—	17	1	no	—
297	#451	—	17	1	no	—
298	#451	—	17	1	no	—
299	#446	—	17	1	no	—
300	#446	—	34	1	no	—
301	#446	C₂×D₁₇	1	1	yes	characteristic
302	C₈×Q₈	—	17	1	no	—
303	C₈×Q₈	—	17	1	no	—
304	C₈×Q₈	—	17	1	no	—
305	C₈×Q₈	—	17	1	no	—
306	C₈×Q₈	—	17	1	no	—
307	C₈×Q₈	—	34	1	no	—
308	C₈×Q₈	—	34	1	no	—
309	C₈×Q₈	—	34	1	no	—
310	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
311	C₄×Q₁₆	—	17	1	no	—
312	C₄×Q₁₆	—	17	1	no	—
313	C₄×Q₁₆	—	17	1	no	—
314	C₄×Q₁₆	C₂×D₁₇	1	1	yes	characteristic
315	#431	—	17	1	no	—
316	#431	—	17	1	no	—
317	#424	—	34	1	no	—
318	#423	—	17	1	no	—
319	C₂×C₄⋊C₈	—	17	1	no	—
320	C₂×C₄⋊C₈	—	34	1	no	—
321	#405	—	34	1	no	—
322	C₂×C₄×C₈	—	17	1	no	—
323	C₂×C₄×C₈	—	34	1	no	—
324	#334	—	17	1	no	—
325	#334	—	17	1	no	—
326	#334	—	17	1	no	—
327	#334	C₂×D₁₇	1	1	yes	characteristic
328	Q₈⋊C₈	—	17	1	no	—
329	Q₈⋊C₈	—	17	1	no	—
330	Q₈⋊C₈	—	17	1	no	—
331	Q₈⋊C₈	—	17	1	no	—
332	Q₈⋊C₈	—	17	1	no	—
333	Q₈⋊C₈	—	17	1	no	—
334	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
335	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
336	#322	—	17	1	no	—
337	#322	—	17	1	no	—
338	#322	—	17	1	no	—
339	#322	C₂×D₁₇	1	1	yes	characteristic
340	C₂×C₁₇	#2929	1	1	yes	characteristic
341	C₂×C₁₇	C₂×#441	1	1	yes	characteristic
342	C₂×C₁₇	#2955	1	1	yes	characteristic
343	D₁₇	—	2	2	no	—
344	C₂²×Q₈	—	17	1	no	—
345	C₂×Q₁₆	—	17	1	no	—
346	C₂×Q₁₆	—	17	1	no	—
347	C₂×Q₁₆	—	17	1	no	—
348	C₂×Q₁₆	C₄×D₁₇	1	1	yes	characteristic
349	C₂×M₁₆	—	34	1	no	—
350	C₂²×C₈	—	17	1	no	—
351	C₂²×C₈	—	17	1	no	—
352	C₂²×C₈	—	34	1	no	—
353	C₄⋊Q₈	—	17	1	no	—
354	C₄⋊Q₈	—	17	1	no	—
355	#125	—	34	1	no	—
356	C₂²⋊Q₈	—	17	1	no	—
357	C₂²⋊Q₈	—	17	1	no	—
358	C₂²⋊Q₈	—	34	1	no	—
359	C₄×Q₈	—	17	1	no	—
360	C₄×Q₈	—	17	1	no	—
361	C₄×Q₈	—	17	1	no	—
362	C₄×Q₈	—	17	1	no	—
363	C₄×Q₈	—	34	1	no	—
364	C₄×Q₈	—	34	1	no	—
365	C₄×Q₈	—	34	1	no	—
366	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
367	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
368	#117	—	34	1	no	—
369	C₂×C₄⋊C₄	—	17	1	no	—
370	C₂×C₄⋊C₄	—	34	1	no	—
371	C₂×C₄²	—	17	1	no	—
372	C₂×C₄²	—	34	1	no	—
373	#107	—	17	1	no	—
374	#107	—	17	1	no	—
375	#107	—	17	1	no	—
376	#107	C₄×D₁₇	1	1	yes	characteristic
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	—	2	1	no	—
379	C₄⋊C₈	—	17	1	no	—
380	C₄⋊C₈	—	17	1	no	—
381	C₄⋊C₈	—	17	1	no	—
382	C₄⋊C₈	—	17	1	no	—
383	C₄⋊C₈	—	34	1	no	—
384	C₄⋊C₈	—	34	1	no	—
385	C₄⋊C₈	—	34	1	no	—
386	C₄⋊C₈	—	34	1	no	—
387	C₄⋊C₈	—	34	1	no	—
388	C₄⋊C₈	—	34	1	no	—
389	C₄⋊C₈	—	34	1	no	—
390	C₄⋊C₈	—	34	1	no	—
391	C₄⋊C₈	—	34	1	no	—
392	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
393	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
394	#103	—	17	1	no	—
395	#103	—	17	1	no	—
396	#103	—	17	1	no	—
397	#103	—	17	1	no	—
398	#103	—	17	1	no	—
399	#103	—	17	1	no	—
400	#103	C₄×D₁₇	1	1	yes	characteristic
401	#103	C₄×D₁₇	1	1	yes	characteristic
402	C₂²⋊C₈	—	17	1	no	—
403	C₂²⋊C₈	—	17	1	no	—
404	C₂²⋊C₈	—	34	1	no	—
405	#97	—	2	1	no	—
406	#97	—	34	1	no	—
407	C₄×C₈	—	2	1	no	—
408	C₄×C₈	—	17	1	no	—
409	C₄×C₈	—	17	1	no	—
410	C₄×C₈	—	17	1	no	—
411	C₄×C₈	—	17	1	no	—
412	C₄×C₈	—	17	1	no	—
413	C₄×C₈	—	34	1	no	—
414	C₄×C₈	—	34	1	no	—
415	C₄×C₈	—	34	1	no	—
416	C₄×C₈	—	34	1	no	—
417	C₄×C₈	—	34	1	no	—
418	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
419	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
420	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
421	C₁₇	#17906	1	1	yes	characteristic, complemented, Sylow
422	C₂×Q₈	—	17	1	no	—
423	C₂×Q₈	—	17	1	no	—
424	C₂×Q₈	—	34	1	no	—
425	C₂×Q₈	—	34	1	no	—
426	C₂×Q₈	—	34	2	no	—
427	C₂×Q₈	—	34	2	no	—
428	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
429	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
430	C₂²×C₄	—	17	1	no	—
431	C₂²×C₄	—	17	1	no	—
432	C₂²×C₄	—	17	1	no	—
433	C₂²×C₄	—	34	1	no	—
434	C₂²×C₄	—	34	1	no	—
435	Q₁₆	—	2	2	no	—
436	Q₁₆	—	34	2	no	—
437	Q₁₆	—	34	2	no	—
438	Q₁₆	—	34	2	no	—
439	M₁₆	—	68	2	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	—	2	1	no	—
442	C₂×C₈	—	2	1	no	—
443	C₂×C₈	—	17	1	no	—
444	C₂×C₈	—	17	1	no	—
445	C₂×C₈	—	17	1	no	—
446	C₂×C₈	—	17	1	no	—
447	C₂×C₈	—	34	2	no	—
448	C₂×C₈	—	34	2	no	—
449	C₂×C₈	—	34	1	no	—
450	C₂×C₈	—	34	1	no	—
451	C₂×C₈	—	34	1	no	—
452	C₂×C₈	—	68	2	no	—
453	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
454	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
455	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
456	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	17	1	no	—
460	C₄⋊C₄	—	17	1	no	—
461	C₄⋊C₄	—	34	1	no	—
462	C₄⋊C₄	—	34	1	no	—
463	C₄⋊C₄	—	34	1	no	—
464	C₄⋊C₄	—	34	1	no	—
465	C₄⋊C₄	—	34	1	no	—
466	C₄⋊C₄	—	34	1	no	—
467	C₄⋊C₄	—	34	1	no	—
468	C₄⋊C₄	—	34	1	no	—
469	C₄⋊C₄	—	34	1	no	—
470	C₄⋊C₄	—	34	1	no	—
471	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
472	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
473	C₂²⋊C₄	—	34	1	no	—
474	C₂²⋊C₄	—	34	1	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	17	1	no	—
478	C₄²	—	17	1	no	—
479	C₄²	—	17	1	no	—
480	C₄²	—	34	1	no	—
481	C₄²	—	34	1	no	—
482	C₄²	—	34	1	no	—
483	C₄²	—	34	1	no	—
484	C₄²	C₂³×D₁₇	1	1	yes	characteristic
485	C₂³	—	17	1	no	—
486	Q₈	—	2	1	no	—
487	Q₈	—	2	1	no	—
488	Q₈	—	2	1	no	—
489	Q₈	—	17	2	no	—
490	Q₈	—	34	4	no	—
491	Q₈	—	34	1	no	—
492	Q₈	—	34	1	no	—
493	Q₈	—	34	1	no	—
494	Q₈	—	68	2	no	—
495	Q₈	#10587593	1	2	yes	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	17	1	no	—
501	C₂×C₄	—	17	2	no	—
502	C₂×C₄	—	17	2	no	—
503	C₂×C₄	—	17	1	no	—
504	C₂×C₄	—	17	1	no	—
505	C₂×C₄	—	34	4	no	—
506	C₂×C₄	—	34	1	no	—
507	C₂×C₄	—	34	1	no	—
508	C₂×C₄	—	34	1	no	—
509	C₂×C₄	—	34	1	no	—
510	C₂×C₄	—	34	1	no	—
511	C₂×C₄	—	34	1	no	—
512	C₂×C₄	—	68	1	no	—
513	C₂×C₄	—	68	2	no	—
514	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
515	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
516	C₂×C₄	#41×D₁₇	1	1	yes	characteristic
517	C₈	—	2	1	no	—
518	C₈	—	2	1	no	—
519	C₈	—	2	1	no	—
520	C₈	—	2	1	no	—
521	C₈	—	4	1	no	—
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	34	1	no	—
525	C₈	—	34	1	no	—
526	C₈	—	34	1	no	—
527	C₈	—	34	1	no	—
528	C₈	—	68	1	no	—
529	C₈	—	68	1	no	—
530	C₈	—	68	1	no	—
531	C₂²	—	17	2	no	—
532	C₂²	—	34	1	no	—
533	C₂²	—	34	1	no	—
534	C₂²	C₄×D₄×D₁₇	1	1	yes	characteristic
535	C₄	—	2	2	no	—
536	C₄	—	2	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	1	no	—
539	C₄	—	4	1	no	—
540	C₄	—	17	2	no	—
541	C₄	—	34	1	no	—
542	C₄	—	34	2	no	—
543	C₄	—	34	1	no	—
544	C₄	—	68	1	no	—
545	C₄	—	68	1	no	—
546	C₄	—	68	1	no	—
547	C₄	#131×D₁₇	1	1	yes	characteristic
548	C₄	C₂×#10587593	1	1	yes	characteristic
549	C₄	#137×D₁₇	1	1	yes	characteristic
550	C₄	#137×D₁₇	1	1	yes	characteristic
551	C₂	—	34	2	no	—
552	C₂	#14537475	1	1	yes	characteristic
553	C₂	D₁₇×#441	1	1	yes	characteristic
554	C₂	#14537682	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×#1587	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂²×D₁₇	C₄×D₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1587	D₁₇
hypocenter	C₁₇	#17906
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1587

Complements

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

N	H ≅ G/N	type
4. #14527657	C₂	semidirect
5. #14527655	C₂	semidirect
6. #14527653	C₂	semidirect
7. #14527603	C₂	semidirect
8. #14527602	C₂	semidirect
9. #14527600	C₂	semidirect
10. #14527600	C₂	semidirect
15. C₁₇×#1587	C₂	semidirect
260. #1587	D₁₇	semidirect
421. C₁₇	#17906	semidirect

Maximal subgroups

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

subgroup	index
#14538821	2
#14537715	2
C₈×Q₈×D₁₇	2
#14527657	2
#14527655	2
#14527653	2
#14527603	2
#14527602	2
#14527600	2
#14527553	2
#14527211	2
#14527185	2
#14527075	2
C₁₇×#1587	2
#17906	17