Subgroups — C₁₇×#25406 #16883150

Order 4352.

884 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3152	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₇×#473	C₂	1	2	yes	maximal, complemented
3	C₁₇×#3037	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2935	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#2052	C₂	1	2	yes	maximal, complemented
7	C₁₇×#2020	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1908	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#101	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×#137	C₂²	1	2	yes	—
13	C₂×C₁₇×#137	C₂²	1	2	yes	—
14	C₂×C₁₇×#137	C₂²	1	2	yes	—
15	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
16	C₂×C₁₇×#131	C₂²	1	2	yes	—
17	C₁₇×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#497	—	2	2	no	—
21	C₁₇×#494	—	2	1	no	—
22	C₁₇×#492	—	2	1	no	—
23	C₁₇×#473	—	2	8	no	—
24	C₁₇×#464	—	2	2	no	—
25	C₁₇×#462	—	2	1	no	—
26	C₁₇×#462	—	2	2	no	—
27	C₁₇×#462	—	2	1	no	—
28	C₁₇×#462	—	2	1	no	—
29	C₁₇×#460	—	2	1	no	—
30	C₁₇×#436	—	2	1	no	—
31	C₁₇×#435	—	2	2	no	—
32	C₈×D₄×C₁₇	—	2	1	no	—
33	C₂×C₁₇×#108	C₂²	1	2	yes	—
34	C₁₇×#423	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₁₇×#417	C₂²	1	2	yes	—
37	C₂×C₁₇×#103	C₂²	1	2	yes	—
38	C₂×C₁₇×#101	C₂²	1	2	yes	—
39	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×#101	C₂²	1	2	yes	—
41	C₂×C₁₇×#101	C₂²	1	1	yes	characteristic
42	C₁₇×#408	C₂²	1	2	yes	—
43	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
45	C₁₇×#343	C₂²	1	1	yes	characteristic
46	C₁₇×#343	C₂²	1	1	yes	characteristic
47	C₁₇×#341	C₂²	1	2	yes	—
48	C₂×#41×C₁₇	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
50	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
51	C₁₇×#137	—	2	4	no	—
52	C₁₇×#137	—	2	4	no	—
53	C₁₇×#137	—	2	4	no	—
54	C₁₇×#137	—	4	2	no	—
55	C₁₇×#137	—	4	2	no	—
56	C₁₇×#137	—	4	2	no	—
57	C₂×Q₁₆×C₁₇	—	2	2	no	—
58	C₂×Q₁₆×C₁₇	—	2	2	no	—
59	C₂×Q₁₆×C₁₇	—	2	4	no	—
60	C₂×Q₁₆×C₁₇	—	2	2	no	—
61	C₂×Q₁₆×C₁₇	—	2	2	no	—
62	C₂×Q₁₆×C₁₇	—	2	2	no	—
63	C₂×Q₁₆×C₁₇	—	4	2	no	—
64	C₂×SD₁₆×C₁₇	—	2	2	no	—
65	C₂×SD₁₆×C₁₇	—	2	2	no	—
66	C₂×SD₁₆×C₁₇	—	2	2	no	—
67	C₁₇×#131	—	2	4	no	—
68	C₁₇×#131	—	4	2	no	—
69	C₂×M₁₆×C₁₇	—	2	2	no	—
70	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
71	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
72	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₇	—	2	2	no	—
76	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
77	C₁₇×C₄⋊Q₈	—	2	1	no	—
78	C₁₇×C₄⋊Q₈	—	2	1	no	—
79	C₁₇×C₄⋊Q₈	—	2	1	no	—
80	C₁₇×C₄⋊Q₈	—	2	1	no	—
81	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
82	C₁₇×#127	D₄	1	1	yes	characteristic
83	C₁₇×#124	D₄	1	2	yes	—
84	C₁₇×#121	—	2	1	no	—
85	C₁₇×#121	—	2	1	no	—
86	C₄×Q₈×C₁₇	—	2	1	no	—
87	C₄×Q₈×C₁₇	—	2	1	no	—
88	C₄×Q₈×C₁₇	—	2	1	no	—
89	C₄×Q₈×C₁₇	—	2	1	no	—
90	C₄×D₄×C₁₇	—	2	1	no	—
91	C₄×D₄×C₁₇	—	2	1	no	—
92	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₄²×C₁₇	—	2	1	no	—
97	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
98	C₁₇×#108	—	2	4	no	—
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₇×C₄⋊C₈	D₄	1	2	yes	—
103	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₇×#103	—	2	2	no	—
105	C₁₇×#103	—	2	2	no	—
106	C₁₇×#103	—	2	2	no	—
107	C₁₇×#102	—	2	2	no	—
108	C₁₇×#101	—	2	4	no	—
109	C₁₇×#101	—	2	2	no	—
110	C₁₇×#101	—	4	2	no	—
111	C₁₇×#101	D₄	1	4	yes	complemented
112	C₁₇×C₂²⋊C₈	—	2	2	no	—
113	C₁₇×C₂²⋊C₈	—	2	2	no	—
114	C₁₇×#97	—	2	1	no	—
115	C₁₇×#97	—	2	1	no	—
116	C₄×C₈×C₁₇	—	2	1	no	—
117	C₄×C₈×C₁₇	—	2	1	no	—
118	#41×C₁₇	—	2	2	no	—
119	#41×C₁₇	—	2	2	no	—
120	#41×C₁₇	—	2	2	no	—
121	#41×C₁₇	—	2	2	no	—
122	C₂×Q₈×C₁₇	—	2	1	no	—
123	C₂×Q₈×C₁₇	—	2	1	no	—
124	C₂×Q₈×C₁₇	—	2	1	no	—
125	C₂×Q₈×C₁₇	—	2	2	no	—
126	C₂×Q₈×C₁₇	—	2	2	no	—
127	C₂×Q₈×C₁₇	—	2	2	no	—
128	C₂×Q₈×C₁₇	—	2	2	no	—
129	C₂×Q₈×C₁₇	—	2	1	no	—
130	C₂×Q₈×C₁₇	—	2	1	no	—
131	C₂×Q₈×C₁₇	—	2	2	no	—
132	C₂×Q₈×C₁₇	—	2	2	no	—
133	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
134	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
135	C₂×D₄×C₁₇	—	2	2	no	—
136	C₂×D₄×C₁₇	—	2	1	no	—
137	C₂×D₄×C₁₇	—	2	1	no	—
138	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	2	no	—
141	C₂²×C₄×C₁₇	—	2	2	no	—
142	C₂²×C₄×C₁₇	—	2	1	no	—
143	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
145	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
146	Q₁₆×C₁₇	—	4	4	no	—
147	Q₁₆×C₁₇	—	4	4	no	—
148	Q₁₆×C₁₇	—	4	4	no	—
149	Q₁₆×C₁₇	—	4	4	no	—
150	Q₁₆×C₁₇	—	4	4	no	—
151	SD₁₆×C₁₇	—	4	4	no	—
152	SD₁₆×C₁₇	—	4	4	no	—
153	SD₁₆×C₁₇	—	4	4	no	—
154	M₁₆×C₁₇	—	2	1	no	—
155	M₁₆×C₁₇	—	2	1	no	—
156	M₁₆×C₁₇	—	2	1	no	—
157	M₁₆×C₁₇	—	2	2	no	—
158	M₁₆×C₁₇	—	2	1	no	—
159	M₁₆×C₁₇	—	2	2	no	—
160	M₁₆×C₁₇	—	2	1	no	—
161	M₁₆×C₁₇	—	4	4	no	—
162	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
163	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
164	M₁₆×C₁₇	#41	1	2	yes	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	2	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	2	no	—
170	C₂×C₈×C₁₇	—	2	2	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	4	4	no	—
173	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
175	C₄⋊C₄×C₁₇	—	2	1	no	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	—	2	1	no	—
178	C₄⋊C₄×C₁₇	—	2	1	no	—
179	C₄⋊C₄×C₁₇	—	4	1	no	—
180	C₄⋊C₄×C₁₇	—	4	1	no	—
181	C₄⋊C₄×C₁₇	—	4	1	no	—
182	C₄⋊C₄×C₁₇	—	4	1	no	—
183	C₄⋊C₄×C₁₇	—	4	1	no	—
184	C₄⋊C₄×C₁₇	—	4	1	no	—
185	C₂²⋊C₄×C₁₇	—	2	2	no	—
186	C₂²⋊C₄×C₁₇	—	2	2	no	—
187	C₄²×C₁₇	—	4	1	no	—
188	C₄²×C₁₇	—	4	1	no	—
189	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
193	#25406	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
194	C₂³×C₁₇	—	2	2	no	—
195	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
196	Q₈×C₁₇	—	2	2	no	—
197	Q₈×C₁₇	—	2	2	no	—
198	Q₈×C₁₇	—	2	2	no	—
199	Q₈×C₁₇	—	2	2	no	—
200	Q₈×C₁₇	—	4	1	no	—
201	Q₈×C₁₇	—	4	1	no	—
202	Q₈×C₁₇	—	4	2	no	—
203	Q₈×C₁₇	—	4	2	no	—
204	Q₈×C₁₇	—	4	2	no	—
205	Q₈×C₁₇	—	4	2	no	—
206	D₄×C₁₇	—	2	2	no	—
207	D₄×C₁₇	—	2	2	no	—
208	D₄×C₁₇	—	4	2	no	—
209	D₄×C₁₇	—	4	2	no	—
210	D₄×C₁₇	—	4	2	no	—
211	D₄×C₁₇	—	8	1	no	—
212	C₂×C₄×C₁₇	—	2	2	no	—
213	C₂×C₄×C₁₇	—	2	2	no	—
214	C₂×C₄×C₁₇	—	2	2	no	—
215	C₂×C₄×C₁₇	—	4	1	no	—
216	C₂×C₄×C₁₇	—	4	1	no	—
217	C₂×C₄×C₁₇	—	4	1	no	—
218	C₂×C₄×C₁₇	—	4	2	no	—
219	C₂×C₄×C₁₇	—	4	2	no	—
220	C₂×C₄×C₁₇	—	4	1	no	—
221	C₂×C₄×C₁₇	—	4	2	no	—
222	C₂×C₄×C₁₇	—	4	2	no	—
223	C₂×C₄×C₁₇	—	4	2	no	—
224	C₂×C₄×C₁₇	—	8	1	no	—
225	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
226	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
227	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
228	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
233	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
235	C₈×C₁₇	—	2	2	no	—
236	C₈×C₁₇	—	2	2	no	—
237	C₈×C₁₇	—	2	2	no	—
238	C₈×C₁₇	—	2	2	no	—
239	C₈×C₁₇	—	2	2	no	—
240	C₈×C₁₇	—	4	2	no	—
241	C₈×C₁₇	—	4	1	no	—
242	#3152	C₂×C₁₇	1	1	yes	characteristic
243	C₂×#473	C₂×C₁₇	1	2	yes	complemented
244	#3037	C₂×C₁₇	1	1	yes	characteristic
245	C₂×#462	C₂×C₁₇	1	1	yes	characteristic, complemented
246	#2935	C₂×C₁₇	1	1	yes	characteristic
247	#2052	C₂×C₁₇	1	2	yes	complemented
248	#2020	C₂×C₁₇	1	2	yes	complemented
249	#1966	C₂×C₁₇	1	1	yes	characteristic, complemented
250	#1950	C₂×C₁₇	1	1	yes	characteristic, complemented
251	#1908	C₂×C₁₇	1	2	yes	complemented
252	C₄×#101	C₂×C₁₇	1	1	yes	characteristic, complemented
253	C₂²×C₁₇	—	2	1	no	—
254	C₂²×C₁₇	—	2	1	no	—
255	C₂²×C₁₇	—	4	2	no	—
256	C₂²×C₁₇	—	4	2	no	—
257	C₂²×C₁₇	—	4	2	no	—
258	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
259	C₂²×C₁₇	#532	1	1	yes	characteristic
260	C₂²×C₁₇	#540	1	1	yes	characteristic
261	C₄×C₁₇	—	2	1	no	—
262	C₄×C₁₇	—	2	1	no	—
263	C₄×C₁₇	—	2	1	no	—
264	C₄×C₁₇	—	4	2	no	—
265	C₄×C₁₇	—	4	2	no	—
266	C₄×C₁₇	—	8	2	no	—
267	C₄×C₁₇	—	8	1	no	—
268	C₄×C₁₇	#473	1	2	yes	complemented
269	C₄×C₁₇	D₄²	1	1	yes	characteristic
270	C₄×C₁₇	D₄²	1	1	yes	characteristic
271	C₄×C₁₇	#546	1	1	yes	characteristic
272	C₄×C₁₇	#550	1	1	yes	characteristic
273	C₂×#137	C₂²×C₁₇	1	2	yes	—
274	C₂×#137	C₂²×C₁₇	1	2	yes	—
275	C₂×#137	C₂²×C₁₇	1	2	yes	—
276	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	—
277	C₂×#131	C₂²×C₁₇	1	2	yes	—
278	#532	C₂²×C₁₇	1	1	yes	characteristic
279	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
280	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
281	#497	—	2	2	no	—
282	#494	—	2	1	no	—
283	#492	—	2	1	no	—
284	#473	—	2	8	no	—
285	#464	—	2	2	no	—
286	#462	—	2	1	no	—
287	#462	—	2	1	no	—
288	#462	—	2	2	no	—
289	#462	—	2	1	no	—
290	#460	—	2	1	no	—
291	#436	—	2	1	no	—
292	#435	—	2	2	no	—
293	C₈×D₄	—	2	1	no	—
294	C₂×#108	C₂²×C₁₇	1	2	yes	—
295	#423	C₂²×C₁₇	1	1	yes	characteristic
296	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
297	#417	C₂²×C₁₇	1	2	yes	—
298	C₂×#103	C₂²×C₁₇	1	2	yes	—
299	C₂×#101	C₂²×C₁₇	1	2	yes	—
300	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
301	C₂×#101	C₂²×C₁₇	1	2	yes	—
302	C₂×#101	C₂²×C₁₇	1	1	yes	characteristic
303	#408	C₂²×C₁₇	1	2	yes	—
304	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
305	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
306	#343	C₂²×C₁₇	1	1	yes	characteristic
307	#343	C₂²×C₁₇	1	1	yes	characteristic
308	#341	C₂²×C₁₇	1	2	yes	—
309	C₂×C₁₇	—	2	1	no	—
310	C₂×C₁₇	—	2	1	no	—
311	C₂×C₁₇	—	8	2	no	—
312	C₂×C₁₇	#2428	1	1	yes	characteristic
313	C₂×C₁₇	C₂×#473	1	1	yes	characteristic
314	C₂×C₁₇	#3069	1	1	yes	characteristic
315	C₂×#41	C₂³×C₁₇	1	2	yes	—
316	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
317	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
318	#137	—	2	4	no	—
319	#137	—	2	4	no	—
320	#137	—	2	4	no	—
321	#137	—	4	2	no	—
322	#137	—	4	2	no	—
323	#137	—	4	2	no	—
324	C₂×Q₁₆	—	2	4	no	—
325	C₂×Q₁₆	—	2	2	no	—
326	C₂×Q₁₆	—	2	2	no	—
327	C₂×Q₁₆	—	2	2	no	—
328	C₂×Q₁₆	—	2	2	no	—
329	C₂×Q₁₆	—	2	2	no	—
330	C₂×Q₁₆	—	4	2	no	—
331	C₂×SD₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	#131	—	2	4	no	—
335	#131	—	4	2	no	—
336	C₂×M₁₆	—	2	2	no	—
337	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
338	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
339	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
340	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
341	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
342	C₂²×C₈	—	2	2	no	—
343	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
349	#127	D₄×C₁₇	1	1	yes	characteristic
350	#124	D₄×C₁₇	1	2	yes	—
351	#121	—	2	1	no	—
352	#121	—	2	1	no	—
353	C₄×Q₈	—	2	1	no	—
354	C₄×Q₈	—	2	1	no	—
355	C₄×Q₈	—	2	1	no	—
356	C₄×Q₈	—	2	1	no	—
357	C₄×D₄	—	2	1	no	—
358	C₄×D₄	—	2	1	no	—
359	C₂×C₄⋊C₄	—	2	1	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	—	2	1	no	—
362	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
363	C₂×C₄²	—	2	1	no	—
364	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
365	#108	—	2	4	no	—
366	C₄⋊C₈	—	2	1	no	—
367	C₄⋊C₈	—	2	1	no	—
368	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
369	C₄⋊C₈	D₄×C₁₇	1	2	yes	—
370	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
371	#103	—	2	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#102	—	2	2	no	—
375	#101	—	2	4	no	—
376	#101	—	2	2	no	—
377	#101	—	4	2	no	—
378	#101	D₄×C₁₇	1	4	yes	complemented
379	C₂²⋊C₈	—	2	2	no	—
380	C₂²⋊C₈	—	2	2	no	—
381	#97	—	2	1	no	—
382	#97	—	2	1	no	—
383	C₄×C₈	—	2	1	no	—
384	C₄×C₈	—	2	1	no	—
385	C₁₇	#25406	1	1	yes	characteristic, direct product factor, Sylow
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	2	1	no	—
392	C₂×Q₈	—	2	1	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	2	no	—
400	C₂×Q₈	—	2	2	no	—
401	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
402	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
403	C₂×D₄	—	2	2	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	1	no	—
411	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
412	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
413	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
414	Q₁₆	—	4	4	no	—
415	Q₁₆	—	4	4	no	—
416	Q₁₆	—	4	4	no	—
417	Q₁₆	—	4	4	no	—
418	Q₁₆	—	4	4	no	—
419	SD₁₆	—	4	4	no	—
420	SD₁₆	—	4	4	no	—
421	SD₁₆	—	4	4	no	—
422	M₁₆	—	2	1	no	—
423	M₁₆	—	2	1	no	—
424	M₁₆	—	2	1	no	—
425	M₁₆	—	2	2	no	—
426	M₁₆	—	2	1	no	—
427	M₁₆	—	2	1	no	—
428	M₁₆	—	2	2	no	—
429	M₁₆	—	4	4	no	—
430	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
431	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
432	M₁₆	#41×C₁₇	1	2	yes	—
433	C₂×C₈	—	2	1	no	—
434	C₂×C₈	—	2	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	4	4	no	—
441	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
442	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄⋊C₄	—	4	1	no	—
449	C₄⋊C₄	—	4	1	no	—
450	C₄⋊C₄	—	4	1	no	—
451	C₄⋊C₄	—	4	1	no	—
452	C₄⋊C₄	—	4	1	no	—
453	C₂²⋊C₄	—	2	2	no	—
454	C₂²⋊C₄	—	2	2	no	—
455	C₄²	—	4	1	no	—
456	C₄²	—	4	1	no	—
457	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
458	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
459	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
460	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
461	C₂³	—	2	2	no	—
462	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
463	Q₈	—	2	2	no	—
464	Q₈	—	2	2	no	—
465	Q₈	—	2	2	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	4	1	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	2	no	—
471	Q₈	—	4	2	no	—
472	Q₈	—	4	2	no	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	2	no	—
478	D₄	—	8	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	8	1	no	—
492	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
493	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
494	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
495	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
496	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
497	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
498	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
499	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
500	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
501	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	2	2	no	—
504	C₈	—	2	2	no	—
505	C₈	—	2	2	no	—
506	C₈	—	2	2	no	—
507	C₈	—	4	2	no	—
508	C₈	—	4	1	no	—
509	C₂²	—	2	1	no	—
510	C₂²	—	2	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	2	no	—
513	C₂²	—	4	2	no	—
514	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
515	C₂²	C₁₇×#532	1	1	yes	characteristic
516	C₂²	C₁₇×#540	1	1	yes	characteristic
517	C₄	—	2	1	no	—
518	C₄	—	2	1	no	—
519	C₄	—	2	1	no	—
520	C₄	—	4	2	no	—
521	C₄	—	4	2	no	—
522	C₄	—	8	1	no	—
523	C₄	—	8	2	no	—
524	C₄	C₁₇×#473	1	2	yes	complemented
525	C₄	D₄²×C₁₇	1	1	yes	characteristic
526	C₄	D₄²×C₁₇	1	1	yes	characteristic
527	C₄	C₁₇×#546	1	1	yes	characteristic
528	C₄	C₁₇×#550	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	2	no	—
532	C₂	C₁₇×#2428	1	1	yes	characteristic
533	C₂	C₂×C₁₇×#473	1	1	yes	characteristic
534	C₂	C₁₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₁₇×#473	C₂	semidirect
4. C₂×C₁₇×#462	C₂	semidirect
6. C₁₇×#2052	C₂	semidirect
7. C₁₇×#2020	C₂	semidirect
8. C₁₇×#1966	C₂	semidirect
9. C₁₇×#1950	C₂	semidirect
10. C₁₇×#1908	C₂	semidirect
11. C₄×C₁₇×#101	C₂	semidirect
111. C₁₇×#101	D₄	semidirect
193. #25406	C₁₇	direct (N × H)
243. C₂×#473	C₂×C₁₇	semidirect
245. C₂×#462	C₂×C₁₇	semidirect
247. #2052	C₂×C₁₇	semidirect
248. #2020	C₂×C₁₇	semidirect
249. #1966	C₂×C₁₇	semidirect
250. #1950	C₂×C₁₇	semidirect
251. #1908	C₂×C₁₇	semidirect
252. C₄×#101	C₂×C₁₇	semidirect
268. C₄×C₁₇	#473	semidirect
378. #101	D₄×C₁₇	semidirect
385. C₁₇	#25406	direct (N × H)
524. C₄	C₁₇×#473	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3152	2
C₂×C₁₇×#473	2
C₁₇×#3037	2
C₂×C₁₇×#462	2
C₁₇×#2935	2
C₁₇×#2052	2
C₁₇×#2020	2
C₁₇×#1966	2
C₁₇×#1950	2
C₁₇×#1908	2
C₄×C₁₇×#101	2
#25406	17

Subgroups — C17×#25406 #16883150

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25406 #16883150