Subgroups — C₁₇×#61892 #16919636

Order 4352.

1770 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#559	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3400	C₂	1	8	yes	maximal, complemented
4	C₁₇×#3375	C₂	1	8	yes	maximal, complemented
5	C₁₇×#3215	C₂	1	4	yes	maximal, complemented
6	C₁₇×#3208	C₂	1	2	yes	maximal
7	C₁₇×#3110	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3104	C₂	1	2	yes	maximal, complemented
9	C₁₇×#2983	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#559	—	2	4	no	—
11	C₁₇×#559	C₂²	1	8	yes	—
12	Q₈²×C₁₇	C₂²	1	4	yes	complemented
13	C₁₇×#557	—	2	4	no	—
14	C₁₇×#557	C₂²	1	4	yes	complemented
15	C₁₇×#544	—	2	1	no	—
16	C₁₇×#544	—	2	2	no	—
17	C₁₇×#533	C₂²	1	2	yes	—
18	C₁₇×#533	C₂²	1	4	yes	—
19	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#124	—	2	1	no	—
21	C₂×C₁₇×#124	C₂²	1	2	yes	—
22	C₂×C₁₇×#123	—	2	2	no	—
23	C₁₇×#519	—	2	1	no	—
24	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₁₇	—	2	1	no	—
27	C₂×C₄×D₄×C₁₇	C₂²	1	2	yes	—
28	C₁₇×#497	C₂²	1	8	yes	complemented
29	C₁₇×#492	C₂²	1	4	yes	—
30	C₁₇×#489	C₂²	1	8	yes	complemented
31	C₁₇×#486	C₂²	1	4	yes	—
32	C₁₇×#484	C₂²	1	4	yes	—
33	C₁₇×#477	C₂²	1	4	yes	complemented
34	C₁₇×#474	C₂²	1	8	yes	complemented
35	C₁₇×#464	C₂²	1	16	yes	complemented
36	C₁₇×#462	C₂²	1	4	yes	complemented
37	C₁₇×#461	C₂²	1	8	yes	complemented
38	C₁₇×#460	C₂²	1	8	yes	—
39	C₁₇×#451	C₂²	1	4	yes	—
40	C₁₇×#450	C₂²	1	8	yes	—
41	C₁₇×#446	C₂²	1	8	yes	complemented
42	C₁₇×#440	C₂²	1	16	yes	complemented
43	C₄×Q₁₆×C₁₇	C₂²	1	8	yes	complemented
44	C₁₇×#432	C₂²	1	4	yes	—
45	C₁₇×#431	C₂²	1	2	yes	—
46	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
47	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
48	C₂²×D₄×C₁₇	—	2	1	no	—
49	C₂²×D₄×C₁₇	—	2	1	no	—
50	C₂²×D₄×C₁₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₁₇	—	2	2	no	—
52	C₂×Q₁₆×C₁₇	C₂³	1	8	yes	—
53	C₂×SD₁₆×C₁₇	C₂³	1	16	yes	—
54	C₁₇×C₄⋊Q₈	—	2	8	no	—
55	C₁₇×C₄⋊Q₈	—	2	4	no	—
56	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
57	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
58	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
59	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
60	C₁₇×#127	—	2	2	no	—
61	C₁₇×#127	C₂³	1	4	yes	—
62	C₁₇×#125	—	2	8	no	—
63	C₁₇×#125	—	2	4	no	—
64	C₁₇×#125	—	2	4	no	—
65	C₁₇×#125	—	2	2	no	—
66	C₁₇×#124	—	2	8	no	—
67	C₁₇×#124	—	2	4	no	—
68	C₁₇×#124	C₂³	1	8	yes	—
69	C₁₇×#123	—	2	16	no	—
70	C₁₇×C₂²⋊Q₈	—	2	4	no	—
71	C₁₇×C₂²⋊Q₈	—	2	2	no	—
72	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
73	C₄×Q₈×C₁₇	—	2	4	no	—
74	C₄×Q₈×C₁₇	—	2	4	no	—
75	C₄×Q₈×C₁₇	—	2	2	no	—
76	C₄×Q₈×C₁₇	—	2	4	no	—
77	C₄×Q₈×C₁₇	—	2	2	no	—
78	C₄×Q₈×C₁₇	D₄	1	4	yes	—
79	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
80	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
81	C₄×Q₈×C₁₇	C₂³	1	8	yes	—
82	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
83	C₄×D₄×C₁₇	—	2	8	no	—
84	C₄×D₄×C₁₇	—	2	4	no	—
85	C₄×D₄×C₁₇	C₂³	1	8	yes	—
86	C₁₇×#117	—	2	4	no	—
87	C₁₇×#117	—	2	2	no	—
88	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	2	no	—
95	C₂×C₄²×C₁₇	—	2	1	no	—
96	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
97	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
98	C₁₇×#107	C₂³	1	8	yes	—
99	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
100	C₁₇×C₄⋊C₈	C₂³	1	8	yes	—
101	C₁₇×#103	C₂³	1	8	yes	—
102	C₁₇×#103	C₂³	1	8	yes	—
103	C₁₇×#102	C₂³	1	16	yes	—
104	C₁₇×C₂²⋊C₈	C₂³	1	4	yes	—
105	C₁₇×#97	C₂³	1	8	yes	—
106	C₄×C₈×C₁₇	C₂³	1	4	yes	—
107	C₂⁴×C₁₇	—	2	2	no	—
108	C₂×Q₈×C₁₇	—	2	4	no	—
109	C₂×Q₈×C₁₇	—	2	1	no	—
110	C₂×Q₈×C₁₇	—	2	4	no	—
111	C₂×Q₈×C₁₇	—	2	2	no	—
112	C₂×Q₈×C₁₇	—	4	2	no	—
113	C₂×Q₈×C₁₇	C₂×D₄	1	4	yes	—
114	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
115	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
116	C₂×D₄×C₁₇	—	2	2	no	—
117	C₂×D₄×C₁₇	—	2	4	no	—
118	C₂×D₄×C₁₇	—	2	4	no	—
119	C₂×D₄×C₁₇	—	4	4	no	—
120	C₂×D₄×C₁₇	—	4	4	no	—
121	C₂×D₄×C₁₇	—	8	2	no	—
122	C₂×D₄×C₁₇	C₂⁴	1	4	yes	—
123	C₂²×C₄×C₁₇	—	2	1	no	—
124	C₂²×C₄×C₁₇	—	2	1	no	—
125	C₂²×C₄×C₁₇	—	2	8	no	—
126	C₂²×C₄×C₁₇	—	8	4	no	—
127	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₁₇	—	4	8	no	—
133	SD₁₆×C₁₇	—	4	16	no	—
134	C₂×C₈×C₁₇	C₂⁴	1	8	yes	—
135	C₄⋊C₄×C₁₇	—	2	4	no	—
136	C₄⋊C₄×C₁₇	—	2	2	no	—
137	C₄⋊C₄×C₁₇	—	2	8	no	—
138	C₄⋊C₄×C₁₇	—	2	4	no	—
139	C₄⋊C₄×C₁₇	—	2	4	no	—
140	C₄⋊C₄×C₁₇	—	2	4	no	—
141	C₄⋊C₄×C₁₇	—	2	4	no	—
142	C₄⋊C₄×C₁₇	—	2	2	no	—
143	C₄⋊C₄×C₁₇	—	2	4	no	—
144	C₄⋊C₄×C₁₇	—	2	2	no	—
145	C₄⋊C₄×C₁₇	—	2	1	no	—
146	C₄⋊C₄×C₁₇	C₂×D₄	1	8	yes	—
147	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
148	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
149	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
150	C₂²⋊C₄×C₁₇	—	2	4	no	—
151	C₂²⋊C₄×C₁₇	—	2	8	no	—
152	C₂²⋊C₄×C₁₇	—	2	8	no	—
153	C₂²⋊C₄×C₁₇	—	2	8	no	—
154	C₄²×C₁₇	—	2	4	no	—
155	C₄²×C₁₇	—	2	8	no	—
156	C₄²×C₁₇	—	2	4	no	—
157	C₄²×C₁₇	C₂×D₄	1	4	yes	—
158	C₄²×C₁₇	C₂×D₄	1	2	yes	—
159	C₄²×C₁₇	C₂⁴	1	4	yes	—
160	C₄²×C₁₇	C₂⁴	1	2	yes	—
161	#61892	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
162	C₂³×C₁₇	—	2	4	no	—
163	C₂³×C₁₇	—	4	4	no	—
164	C₂³×C₁₇	—	4	4	no	—
165	C₂³×C₁₇	—	4	4	no	—
166	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₁₇	—	2	8	no	—
168	Q₈×C₁₇	—	2	8	no	—
169	Q₈×C₁₇	—	2	4	no	—
170	Q₈×C₁₇	—	4	2	no	—
171	Q₈×C₁₇	—	8	4	no	—
172	Q₈×C₁₇	—	8	2	no	—
173	D₄×C₁₇	—	2	8	no	—
174	D₄×C₁₇	—	4	4	no	—
175	D₄×C₁₇	—	4	8	no	—
176	D₄×C₁₇	—	8	4	no	—
177	C₂×C₄×C₁₇	—	2	4	no	—
178	C₂×C₄×C₁₇	—	2	2	no	—
179	C₂×C₄×C₁₇	—	2	4	no	—
180	C₂×C₄×C₁₇	—	2	4	no	—
181	C₂×C₄×C₁₇	—	2	2	no	—
182	C₂×C₄×C₁₇	—	2	2	no	—
183	C₂×C₄×C₁₇	—	4	2	no	—
184	C₂×C₄×C₁₇	—	4	1	no	—
185	C₂×C₄×C₁₇	—	4	2	no	—
186	C₂×C₄×C₁₇	—	4	2	no	—
187	C₂×C₄×C₁₇	—	8	8	no	—
188	C₂×C₄×C₁₇	#137	1	4	yes	—
189	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
190	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
192	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
193	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
194	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
195	C₈×C₁₇	—	2	8	no	—
196	#3502	C₂×C₁₇	1	1	yes	characteristic, complemented
197	C₂×#559	C₂×C₁₇	1	1	yes	characteristic
198	#3400	C₂×C₁₇	1	8	yes	complemented
199	#3375	C₂×C₁₇	1	8	yes	complemented
200	#3215	C₂×C₁₇	1	4	yes	complemented
201	#3208	C₂×C₁₇	1	2	yes	—
202	#3110	C₂×C₁₇	1	4	yes	complemented
203	#3104	C₂×C₁₇	1	2	yes	complemented
204	#2983	C₂×C₁₇	1	1	yes	characteristic, complemented
205	C₂²×C₁₇	—	2	1	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	4	4	no	—
208	C₂²×C₁₇	—	4	4	no	—
209	C₂²×C₁₇	—	4	4	no	—
210	C₂²×C₁₇	—	8	8	no	—
211	C₂²×C₁₇	C₂×#137	1	2	yes	—
212	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
213	C₄×C₁₇	—	2	4	no	—
214	C₄×C₁₇	—	2	2	no	—
215	C₄×C₁₇	—	2	1	no	—
216	C₄×C₁₇	—	2	4	no	—
217	C₄×C₁₇	—	4	2	no	—
218	C₄×C₁₇	—	4	4	no	—
219	C₄×C₁₇	—	4	2	no	—
220	C₄×C₁₇	—	4	4	no	—
221	C₄×C₁₇	C₂×#137	1	4	yes	—
222	C₄×C₁₇	#585	1	2	yes	—
223	#559	—	2	4	no	—
224	#559	C₂²×C₁₇	1	8	yes	—
225	Q₈²	C₂²×C₁₇	1	4	yes	complemented
226	#557	—	2	4	no	—
227	#557	C₂²×C₁₇	1	4	yes	complemented
228	#544	—	2	1	no	—
229	#544	—	2	2	no	—
230	#533	C₂²×C₁₇	1	2	yes	—
231	#533	C₂²×C₁₇	1	4	yes	—
232	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
233	C₂×#124	—	2	1	no	—
234	C₂×#124	C₂²×C₁₇	1	2	yes	—
235	C₂×#123	—	2	2	no	—
236	#519	—	2	1	no	—
237	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
239	C₂×C₄×D₄	—	2	1	no	—
240	C₂×C₄×D₄	C₂²×C₁₇	1	2	yes	—
241	#497	C₂²×C₁₇	1	8	yes	complemented
242	#492	C₂²×C₁₇	1	4	yes	—
243	#489	C₂²×C₁₇	1	8	yes	complemented
244	#486	C₂²×C₁₇	1	4	yes	—
245	#484	C₂²×C₁₇	1	4	yes	—
246	#477	C₂²×C₁₇	1	4	yes	complemented
247	#474	C₂²×C₁₇	1	8	yes	complemented
248	#464	C₂²×C₁₇	1	16	yes	complemented
249	#462	C₂²×C₁₇	1	4	yes	complemented
250	#461	C₂²×C₁₇	1	8	yes	complemented
251	#460	C₂²×C₁₇	1	8	yes	—
252	#451	C₂²×C₁₇	1	4	yes	—
253	#450	C₂²×C₁₇	1	8	yes	—
254	#446	C₂²×C₁₇	1	8	yes	complemented
255	#440	C₂²×C₁₇	1	16	yes	complemented
256	C₄×Q₁₆	C₂²×C₁₇	1	8	yes	complemented
257	#432	C₂²×C₁₇	1	4	yes	—
258	#431	C₂²×C₁₇	1	2	yes	—
259	C₂×C₁₇	—	2	2	no	—
260	C₂×C₁₇	—	8	4	no	—
261	C₂×C₁₇	#3487	1	1	yes	characteristic
262	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
263	C₂×C₁₇	#3585	1	1	yes	characteristic
264	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
265	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
266	C₂²×D₄	—	2	1	no	—
267	C₂²×D₄	—	2	1	no	—
268	C₂²×D₄	C₂³×C₁₇	1	2	yes	—
269	C₂³×C₄	—	2	2	no	—
270	C₂×Q₁₆	C₂³×C₁₇	1	8	yes	—
271	C₂×SD₁₆	C₂³×C₁₇	1	16	yes	—
272	C₄⋊Q₈	—	2	4	no	—
273	C₄⋊Q₈	—	2	8	no	—
274	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
275	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
276	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
277	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
278	#127	—	2	2	no	—
279	#127	C₂³×C₁₇	1	4	yes	—
280	#125	—	2	4	no	—
281	#125	—	2	8	no	—
282	#125	—	2	4	no	—
283	#125	—	2	2	no	—
284	#124	—	2	8	no	—
285	#124	—	2	4	no	—
286	#124	C₂³×C₁₇	1	8	yes	—
287	#123	—	2	16	no	—
288	C₂²⋊Q₈	—	2	4	no	—
289	C₂²⋊Q₈	—	2	2	no	—
290	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
291	C₄×Q₈	—	2	4	no	—
292	C₄×Q₈	—	2	4	no	—
293	C₄×Q₈	—	2	2	no	—
294	C₄×Q₈	—	2	4	no	—
295	C₄×Q₈	—	2	2	no	—
296	C₄×Q₈	D₄×C₁₇	1	4	yes	—
297	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
298	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
299	C₄×Q₈	C₂³×C₁₇	1	8	yes	—
300	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
301	C₄×D₄	—	2	8	no	—
302	C₄×D₄	—	2	4	no	—
303	C₄×D₄	C₂³×C₁₇	1	8	yes	—
304	#117	—	2	4	no	—
305	#117	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	1	no	—
307	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
308	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
309	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₄²	—	2	1	no	—
314	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
315	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
316	#107	C₂³×C₁₇	1	8	yes	—
317	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
318	C₄⋊C₈	C₂³×C₁₇	1	8	yes	—
319	#103	C₂³×C₁₇	1	8	yes	—
320	#103	C₂³×C₁₇	1	8	yes	—
321	#102	C₂³×C₁₇	1	16	yes	—
322	C₂²⋊C₈	C₂³×C₁₇	1	4	yes	—
323	#97	C₂³×C₁₇	1	8	yes	—
324	C₄×C₈	C₂³×C₁₇	1	4	yes	—
325	C₁₇	#61892	1	1	yes	characteristic, direct product factor, Sylow
326	C₂⁴	—	2	2	no	—
327	C₂×Q₈	—	2	4	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	4	2	no	—
332	C₂×Q₈	C₂×D₄×C₁₇	1	4	yes	—
333	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
334	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	4	no	—
337	C₂×D₄	—	2	4	no	—
338	C₂×D₄	—	4	4	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	C₂⁴×C₁₇	1	4	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	—	8	4	no	—
346	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
350	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
351	Q₁₆	—	4	8	no	—
352	SD₁₆	—	4	16	no	—
353	C₂×C₈	C₂⁴×C₁₇	1	8	yes	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	1	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	4	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	8	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
366	C₄⋊C₄	C₂×D₄×C₁₇	1	8	yes	—
367	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
368	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	8	no	—
371	C₂²⋊C₄	—	2	8	no	—
372	C₂²⋊C₄	—	2	8	no	—
373	C₄²	—	2	4	no	—
374	C₄²	—	2	8	no	—
375	C₄²	—	2	4	no	—
376	C₄²	C₂×D₄×C₁₇	1	4	yes	—
377	C₄²	C₂×D₄×C₁₇	1	2	yes	—
378	C₄²	C₂⁴×C₁₇	1	2	yes	—
379	C₄²	C₂⁴×C₁₇	1	4	yes	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	4	no	—
382	C₂³	—	4	4	no	—
383	C₂³	—	4	4	no	—
384	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
385	Q₈	—	2	8	no	—
386	Q₈	—	2	8	no	—
387	Q₈	—	2	4	no	—
388	Q₈	—	4	2	no	—
389	Q₈	—	8	4	no	—
390	Q₈	—	8	2	no	—
391	D₄	—	2	8	no	—
392	D₄	—	4	4	no	—
393	D₄	—	4	8	no	—
394	D₄	—	8	4	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	8	8	no	—
406	C₂×C₄	C₁₇×#137	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
408	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
409	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
411	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
412	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
413	C₈	—	2	8	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	4	4	no	—
419	C₂²	—	8	8	no	—
420	C₂²	C₂×C₁₇×#137	1	2	yes	—
421	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
422	C₄	—	2	1	no	—
423	C₄	—	2	4	no	—
424	C₄	—	2	4	no	—
425	C₄	—	2	2	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	4	no	—
430	C₄	C₂×C₁₇×#137	1	4	yes	—
431	C₄	C₁₇×#585	1	2	yes	—
432	C₂	—	2	2	no	—
433	C₂	—	8	4	no	—
434	C₂	C₁₇×#3487	1	1	yes	characteristic
435	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
436	C₂	C₁₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₂×C₁₇×#127	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3502	C₂	semidirect
3. C₁₇×#3400	C₂	semidirect
4. C₁₇×#3375	C₂	semidirect
5. C₁₇×#3215	C₂	semidirect
7. C₁₇×#3110	C₂	semidirect
8. C₁₇×#3104	C₂	semidirect
9. C₁₇×#2983	C₂	semidirect
12. Q₈²×C₁₇	C₂²	semidirect
14. C₁₇×#557	C₂²	semidirect
28. C₁₇×#497	C₂²	semidirect
30. C₁₇×#489	C₂²	semidirect
33. C₁₇×#477	C₂²	semidirect
34. C₁₇×#474	C₂²	semidirect
35. C₁₇×#464	C₂²	semidirect
36. C₁₇×#462	C₂²	semidirect
37. C₁₇×#461	C₂²	semidirect
41. C₁₇×#446	C₂²	semidirect
42. C₁₇×#440	C₂²	semidirect
43. C₄×Q₁₆×C₁₇	C₂²	semidirect
161. #61892	C₁₇	direct (N × H)
196. #3502	C₂×C₁₇	semidirect
198. #3400	C₂×C₁₇	semidirect
199. #3375	C₂×C₁₇	semidirect
200. #3215	C₂×C₁₇	semidirect
202. #3110	C₂×C₁₇	semidirect
203. #3104	C₂×C₁₇	semidirect
204. #2983	C₂×C₁₇	semidirect
225. Q₈²	C₂²×C₁₇	semidirect
227. #557	C₂²×C₁₇	semidirect
241. #497	C₂²×C₁₇	semidirect
243. #489	C₂²×C₁₇	semidirect
246. #477	C₂²×C₁₇	semidirect
247. #474	C₂²×C₁₇	semidirect
248. #464	C₂²×C₁₇	semidirect
249. #462	C₂²×C₁₇	semidirect
250. #461	C₂²×C₁₇	semidirect
254. #446	C₂²×C₁₇	semidirect
255. #440	C₂²×C₁₇	semidirect
256. C₄×Q₁₆	C₂²×C₁₇	semidirect
325. C₁₇	#61892	direct (N × H)

Maximal subgroups

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

subgroup	index
C₁₇×#3502	2
C₂×C₁₇×#559	2
C₁₇×#3400	2
C₁₇×#3375	2
C₁₇×#3215	2
C₁₇×#3208	2
C₁₇×#3110	2
C₁₇×#3104	2
C₁₇×#2983	2
#61892	17

Subgroups — C17×#61892 #16919636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61892 #16919636