Subgroups — C₁₇×#62147 #16919891

Order 4352.

1734 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3482	C₂	1	1	yes	maximal, characteristic
3	Q₈×SD₁₆×C₁₇	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3363	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3356	C₂	1	6	yes	maximal, complemented
6	C₁₇×#3331	C₂	1	6	yes	maximal, complemented
7	C₁₇×#3255	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3229	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3107	C₂	1	3	yes	maximal, complemented
10	C₁₇×#3079	C₂	1	3	yes	maximal, complemented
11	C₁₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
12	Q₈²×C₁₇	C₂²	1	2	yes	—
13	C₁₇×#557	—	2	1	no	—
14	C₁₇×#557	C₂²	1	1	yes	characteristic
15	C₁₇×#556	C₂²	1	3	yes	—
16	C₁₇×#554	C₂²	1	6	yes	—
17	C₁₇×#552	—	2	3	no	—
18	D₄×Q₈×C₁₇	—	2	3	no	—
19	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#548	—	2	1	no	—
21	C₁₇×#547	C₂²	1	3	yes	—
22	C₁₇×#544	—	2	3	no	—
23	C₁₇×#533	C₂²	1	3	yes	—
24	C₁₇×#533	C₂²	1	3	yes	—
25	C₂×C₁₇×C₄⋊Q₈	C₂²	1	3	yes	—
26	C₁₇×#529	—	2	3	no	—
27	C₁₇×#520	—	2	1	no	—
28	C₄×#41×C₁₇	C₂²	1	3	yes	—
29	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
31	C₁₇×#498	C₂²	1	6	yes	—
32	C₁₇×#487	C₂²	1	6	yes	—
33	C₁₇×#485	C₂²	1	6	yes	—
34	C₁₇×#483	C₂²	1	12	yes	—
35	C₁₇×#477	C₂²	1	6	yes	—
36	C₁₇×#476	C₂²	1	6	yes	—
37	C₁₇×#475	C₂²	1	3	yes	—
38	C₁₇×#475	C₂²	1	6	yes	—
39	C₁₇×#475	C₂²	1	6	yes	—
40	C₁₇×#474	C₂²	1	3	yes	—
41	C₁₇×#470	C₂²	1	12	yes	—
42	C₁₇×#462	C₂²	1	3	yes	—
43	C₁₇×#462	C₂²	1	6	yes	—
44	C₁₇×#461	C₂²	1	1	yes	characteristic
45	C₁₇×#452	C₂²	1	6	yes	—
46	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
47	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
48	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
49	C₁₇×#436	C₂²	1	6	yes	—
50	C₁₇×#431	C₂²	1	3	yes	—
51	C₁₇×#428	C₂²	1	6	yes	—
52	C₁₇×#423	C₂²	1	3	yes	—
53	C₁₇×#417	C₂²	1	6	yes	—
54	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
55	C₂×#41×C₁₇	C₂³	1	3	yes	—
56	C₂²×Q₈×C₁₇	—	2	1	no	—
57	C₂²×Q₈×C₁₇	—	2	3	no	—
58	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
59	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
60	C₂×M₁₆×C₁₇	C₂³	1	6	yes	—
61	C₁₇×C₄⋊Q₈	—	2	6	no	—
62	C₁₇×C₄⋊Q₈	—	2	3	no	—
63	C₁₇×C₄⋊Q₈	—	2	3	no	—
64	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
65	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
66	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
67	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
68	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
69	C₁₇×#126	—	2	6	no	—
70	C₁₇×#125	—	2	3	no	—
71	C₁₇×#125	—	2	6	no	—
72	C₁₇×#125	—	2	3	no	—
73	C₁₇×#125	—	2	3	no	—
74	C₁₇×#124	—	2	3	no	—
75	C₁₇×#123	—	2	6	no	—
76	C₁₇×C₂²⋊Q₈	—	2	3	no	—
77	C₁₇×C₂²⋊Q₈	—	2	3	no	—
78	C₁₇×C₂²⋊Q₈	—	2	3	no	—
79	C₁₇×C₂²⋊Q₈	—	2	12	no	—
80	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
81	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
82	C₁₇×#121	—	2	3	no	—
83	C₄×Q₈×C₁₇	—	2	1	no	—
84	C₄×Q₈×C₁₇	—	2	2	no	—
85	C₄×Q₈×C₁₇	—	2	3	no	—
86	C₄×Q₈×C₁₇	—	2	3	no	—
87	C₄×Q₈×C₁₇	—	2	3	no	—
88	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
90	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
91	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
92	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₇	—	2	6	no	—
94	C₄×D₄×C₁₇	—	2	3	no	—
95	C₄×D₄×C₁₇	—	2	3	no	—
96	C₄×D₄×C₁₇	D₄	1	3	yes	—
97	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×D₄×C₁₇	C₂³	1	3	yes	—
99	C₄×D₄×C₁₇	C₂³	1	3	yes	—
100	C₁₇×#117	—	2	3	no	—
101	C₁₇×#117	—	2	3	no	—
102	C₁₇×#117	—	2	3	no	—
103	C₁₇×#117	D₄	1	3	yes	—
104	C₁₇×#117	C₂³	1	3	yes	—
105	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
106	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
107	C₂×C₄⋊C₄×C₁₇	C₂³	1	6	yes	—
108	C₂×C₄²×C₁₇	—	2	3	no	—
109	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
110	C₁₇×#107	C₂³	1	6	yes	—
111	C₁₇×#106	C₂³	1	6	yes	—
112	C₁₇×#106	C₂³	1	12	yes	—
113	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
114	C₁₇×C₄⋊C₈	C₂³	1	6	yes	—
115	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₇×#103	C₂³	1	12	yes	—
117	C₁₇×#103	C₂³	1	6	yes	—
118	C₁₇×#103	C₂³	1	2	yes	—
119	C₁₇×#103	C₂³	1	6	yes	—
120	C₁₇×#102	C₂³	1	6	yes	—
121	C₁₇×C₂²⋊C₈	C₂³	1	6	yes	—
122	C₄×C₈×C₁₇	C₂³	1	6	yes	—
123	#41×C₁₇	—	2	4	no	—
124	#41×C₁₇	—	2	6	no	—
125	#41×C₁₇	—	4	3	no	—
126	C₂×Q₈×C₁₇	—	2	3	no	—
127	C₂×Q₈×C₁₇	—	2	3	no	—
128	C₂×Q₈×C₁₇	—	2	6	no	—
129	C₂×Q₈×C₁₇	—	4	4	no	—
130	C₂×Q₈×C₁₇	—	8	6	no	—
131	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
132	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
133	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
134	C₂×D₄×C₁₇	—	2	3	no	—
135	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
136	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	—	2	6	no	—
138	C₂²×C₄×C₁₇	—	2	3	no	—
139	C₂²×C₄×C₁₇	—	2	3	no	—
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
142	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
143	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
144	Q₁₆×C₁₇	—	4	6	no	—
145	SD₁₆×C₁₇	—	2	4	no	—
146	M₁₆×C₁₇	—	4	6	no	—
147	C₂×C₈×C₁₇	C₂⁴	1	6	yes	—
148	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
149	C₄⋊C₄×C₁₇	—	2	6	no	—
150	C₄⋊C₄×C₁₇	—	2	1	no	—
151	C₄⋊C₄×C₁₇	—	2	6	no	—
152	C₄⋊C₄×C₁₇	—	2	6	no	—
153	C₄⋊C₄×C₁₇	—	2	3	no	—
154	C₄⋊C₄×C₁₇	—	2	3	no	—
155	C₄⋊C₄×C₁₇	—	2	3	no	—
156	C₄⋊C₄×C₁₇	—	2	6	no	—
157	C₄⋊C₄×C₁₇	—	2	3	no	—
158	C₄⋊C₄×C₁₇	—	2	1	no	—
159	C₄⋊C₄×C₁₇	—	2	3	no	—
160	C₄⋊C₄×C₁₇	—	2	3	no	—
161	C₄⋊C₄×C₁₇	—	2	6	no	—
162	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
163	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
164	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
165	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
166	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₇	—	2	6	no	—
168	C₂²⋊C₄×C₁₇	—	2	6	no	—
169	C₂²⋊C₄×C₁₇	—	2	3	no	—
170	C₂²⋊C₄×C₁₇	—	2	3	no	—
171	C₂²⋊C₄×C₁₇	—	2	1	no	—
172	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
173	C₄²×C₁₇	—	2	3	no	—
174	C₄²×C₁₇	—	2	6	no	—
175	C₄²×C₁₇	—	2	3	no	—
176	C₄²×C₁₇	—	2	3	no	—
177	C₄²×C₁₇	C₂×D₄	1	3	yes	—
178	C₄²×C₁₇	C₂×D₄	1	3	yes	—
179	C₄²×C₁₇	C₂⁴	1	3	yes	—
180	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
181	#62147	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₇	—	2	1	no	—
183	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
184	Q₈×C₁₇	—	2	2	no	—
185	Q₈×C₁₇	—	2	3	no	—
186	Q₈×C₁₇	—	2	2	no	—
187	Q₈×C₁₇	—	2	3	no	—
188	Q₈×C₁₇	—	4	6	no	—
189	Q₈×C₁₇	—	4	6	no	—
190	Q₈×C₁₇	—	8	6	no	—
191	Q₈×C₁₇	#137	1	4	yes	—
192	D₄×C₁₇	—	2	6	no	—
193	D₄×C₁₇	—	2	1	no	—
194	D₄×C₁₇	—	4	6	no	—
195	D₄×C₁₇	2₋¹⁺⁴	1	2	yes	—
196	C₂×C₄×C₁₇	—	2	6	no	—
197	C₂×C₄×C₁₇	—	2	6	no	—
198	C₂×C₄×C₁₇	—	2	3	no	—
199	C₂×C₄×C₁₇	—	2	3	no	—
200	C₂×C₄×C₁₇	—	2	1	no	—
201	C₂×C₄×C₁₇	—	2	2	no	—
202	C₂×C₄×C₁₇	—	2	3	no	—
203	C₂×C₄×C₁₇	—	2	3	no	—
204	C₂×C₄×C₁₇	—	2	6	no	—
205	C₂×C₄×C₁₇	—	4	6	no	—
206	C₂×C₄×C₁₇	—	4	6	no	—
207	C₂×C₄×C₁₇	—	4	2	no	—
208	C₂×C₄×C₁₇	—	8	6	no	—
209	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
210	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
212	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
213	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
215	C₈×C₁₇	—	2	2	no	—
216	C₈×C₁₇	—	2	6	no	—
217	#3503	C₂×C₁₇	1	1	yes	characteristic, complemented
218	#3482	C₂×C₁₇	1	1	yes	characteristic
219	Q₈×SD₁₆	C₂×C₁₇	1	2	yes	complemented
220	#3363	C₂×C₁₇	1	2	yes	complemented
221	#3356	C₂×C₁₇	1	6	yes	complemented
222	#3331	C₂×C₁₇	1	6	yes	complemented
223	#3255	C₂×C₁₇	1	3	yes	complemented
224	#3229	C₂×C₁₇	1	3	yes	complemented
225	#3107	C₂×C₁₇	1	3	yes	complemented
226	#3079	C₂×C₁₇	1	3	yes	complemented
227	#2991	C₂×C₁₇	1	1	yes	characteristic, complemented
228	C₂²×C₁₇	—	2	3	no	—
229	C₂²×C₁₇	—	2	2	no	—
230	C₂²×C₁₇	—	2	3	no	—
231	C₂²×C₁₇	—	2	3	no	—
232	C₂²×C₁₇	—	4	1	no	—
233	C₂²×C₁₇	—	4	1	no	—
234	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
235	C₄×C₁₇	—	2	3	no	—
236	C₄×C₁₇	—	2	1	no	—
237	C₄×C₁₇	—	2	3	no	—
238	C₄×C₁₇	—	4	3	no	—
239	C₄×C₁₇	—	4	2	no	—
240	C₄×C₁₇	—	4	3	no	—
241	C₄×C₁₇	—	4	1	no	—
242	C₄×C₁₇	—	4	6	no	—
243	C₄×C₁₇	C₂×#137	1	6	yes	—
244	C₄×C₁₇	#577	1	2	yes	—
245	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
246	C₄×C₁₇	#585	1	1	yes	characteristic
247	Q₈²	C₂²×C₁₇	1	2	yes	—
248	#557	—	2	1	no	—
249	#557	C₂²×C₁₇	1	1	yes	characteristic
250	#556	C₂²×C₁₇	1	3	yes	—
251	#554	C₂²×C₁₇	1	6	yes	—
252	#552	—	2	3	no	—
253	D₄×Q₈	—	2	3	no	—
254	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
255	#548	—	2	1	no	—
256	#547	C₂²×C₁₇	1	3	yes	—
257	#544	—	2	3	no	—
258	#533	C₂²×C₁₇	1	3	yes	—
259	#533	C₂²×C₁₇	1	3	yes	—
260	C₂×C₄⋊Q₈	C₂²×C₁₇	1	3	yes	—
261	#529	—	2	3	no	—
262	#520	—	2	1	no	—
263	C₄×#41	C₂²×C₁₇	1	3	yes	—
264	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
265	C₂×C₄×Q₈	—	2	1	no	—
266	#498	C₂²×C₁₇	1	6	yes	—
267	#487	C₂²×C₁₇	1	6	yes	—
268	#485	C₂²×C₁₇	1	6	yes	—
269	#483	C₂²×C₁₇	1	12	yes	—
270	#477	C₂²×C₁₇	1	6	yes	—
271	#476	C₂²×C₁₇	1	6	yes	—
272	#475	C₂²×C₁₇	1	6	yes	—
273	#475	C₂²×C₁₇	1	6	yes	—
274	#475	C₂²×C₁₇	1	3	yes	—
275	#474	C₂²×C₁₇	1	3	yes	—
276	#470	C₂²×C₁₇	1	12	yes	—
277	#462	C₂²×C₁₇	1	6	yes	—
278	#462	C₂²×C₁₇	1	3	yes	—
279	#461	C₂²×C₁₇	1	1	yes	characteristic
280	#452	C₂²×C₁₇	1	6	yes	—
281	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
282	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
283	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
284	#436	C₂²×C₁₇	1	6	yes	—
285	#431	C₂²×C₁₇	1	3	yes	—
286	#428	C₂²×C₁₇	1	6	yes	—
287	#423	C₂²×C₁₇	1	3	yes	—
288	#417	C₂²×C₁₇	1	6	yes	—
289	C₂×C₁₇	—	4	3	no	—
290	C₂×C₁₇	—	4	2	no	—
291	C₂×C₁₇	#3489	1	1	yes	characteristic
292	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
293	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
294	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
295	C₂×#41	C₂³×C₁₇	1	3	yes	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	—	2	3	no	—
298	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
299	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
300	C₂×M₁₆	C₂³×C₁₇	1	6	yes	—
301	C₄⋊Q₈	—	2	6	no	—
302	C₄⋊Q₈	—	2	3	no	—
303	C₄⋊Q₈	—	2	3	no	—
304	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
305	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
306	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
307	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
308	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
309	#126	—	2	6	no	—
310	#125	—	2	3	no	—
311	#125	—	2	6	no	—
312	#125	—	2	3	no	—
313	#125	—	2	3	no	—
314	#124	—	2	3	no	—
315	#123	—	2	6	no	—
316	C₂²⋊Q₈	—	2	3	no	—
317	C₂²⋊Q₈	—	2	3	no	—
318	C₂²⋊Q₈	—	2	3	no	—
319	C₂²⋊Q₈	—	2	12	no	—
320	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
321	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
322	#121	—	2	3	no	—
323	C₄×Q₈	—	2	1	no	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	3	no	—
326	C₄×Q₈	—	2	3	no	—
327	C₄×Q₈	—	2	3	no	—
328	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
329	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
330	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
331	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
332	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
333	C₄×D₄	—	2	6	no	—
334	C₄×D₄	—	2	3	no	—
335	C₄×D₄	—	2	3	no	—
336	C₄×D₄	D₄×C₁₇	1	3	yes	—
337	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
338	C₄×D₄	C₂³×C₁₇	1	3	yes	—
339	C₄×D₄	C₂³×C₁₇	1	3	yes	—
340	#117	—	2	3	no	—
341	#117	—	2	3	no	—
342	#117	—	2	3	no	—
343	#117	D₄×C₁₇	1	3	yes	—
344	#117	C₂³×C₁₇	1	3	yes	—
345	C₂×C₄⋊C₄	—	2	3	no	—
346	C₂×C₄⋊C₄	—	2	3	no	—
347	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
348	C₂×C₄²	—	2	3	no	—
349	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
350	#107	C₂³×C₁₇	1	6	yes	—
351	#106	C₂³×C₁₇	1	12	yes	—
352	#106	C₂³×C₁₇	1	6	yes	—
353	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
354	C₄⋊C₈	C₂³×C₁₇	1	6	yes	—
355	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
356	#103	C₂³×C₁₇	1	12	yes	—
357	#103	C₂³×C₁₇	1	6	yes	—
358	#103	C₂³×C₁₇	1	2	yes	—
359	#103	C₂³×C₁₇	1	6	yes	—
360	#102	C₂³×C₁₇	1	6	yes	—
361	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
362	C₄×C₈	C₂³×C₁₇	1	6	yes	—
363	C₁₇	#62147	1	1	yes	characteristic, direct product factor, Sylow
364	#41	—	2	4	no	—
365	#41	—	2	6	no	—
366	#41	—	4	3	no	—
367	C₂×Q₈	—	2	3	no	—
368	C₂×Q₈	—	2	3	no	—
369	C₂×Q₈	—	2	6	no	—
370	C₂×Q₈	—	4	4	no	—
371	C₂×Q₈	—	8	6	no	—
372	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
373	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
374	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
375	C₂×D₄	—	2	3	no	—
376	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
377	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
378	C₂²×C₄	—	2	6	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	3	no	—
381	C₂²×C₄	—	2	3	no	—
382	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
383	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
384	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
385	Q₁₆	—	4	6	no	—
386	SD₁₆	—	2	4	no	—
387	M₁₆	—	4	6	no	—
388	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
389	C₂×C₈	C₂⁴×C₁₇	1	6	yes	—
390	C₄⋊C₄	—	2	3	no	—
391	C₄⋊C₄	—	2	6	no	—
392	C₄⋊C₄	—	2	3	no	—
393	C₄⋊C₄	—	2	6	no	—
394	C₄⋊C₄	—	2	6	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	3	no	—
397	C₄⋊C₄	—	2	3	no	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	—	2	3	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	6	no	—
402	C₄⋊C₄	—	2	6	no	—
403	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
404	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
405	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
406	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
407	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
408	C₂²⋊C₄	—	2	6	no	—
409	C₂²⋊C₄	—	2	6	no	—
410	C₂²⋊C₄	—	2	3	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	2	3	no	—
413	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
414	C₄²	—	2	3	no	—
415	C₄²	—	2	3	no	—
416	C₄²	—	2	3	no	—
417	C₄²	—	2	6	no	—
418	C₄²	C₂×D₄×C₁₇	1	3	yes	—
419	C₄²	C₂×D₄×C₁₇	1	3	yes	—
420	C₄²	C₂⁴×C₁₇	1	3	yes	—
421	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
422	C₂³	—	2	1	no	—
423	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
424	Q₈	—	2	2	no	—
425	Q₈	—	2	3	no	—
426	Q₈	—	2	2	no	—
427	Q₈	—	2	3	no	—
428	Q₈	—	4	6	no	—
429	Q₈	—	4	6	no	—
430	Q₈	—	8	6	no	—
431	Q₈	C₁₇×#137	1	4	yes	—
432	D₄	—	2	6	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	6	no	—
435	D₄	C₁₇×2₋¹⁺⁴	1	2	yes	—
436	C₂×C₄	—	2	6	no	—
437	C₂×C₄	—	2	6	no	—
438	C₂×C₄	—	2	3	no	—
439	C₂×C₄	—	2	3	no	—
440	C₂×C₄	—	2	1	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	3	no	—
443	C₂×C₄	—	2	3	no	—
444	C₂×C₄	—	2	6	no	—
445	C₂×C₄	—	4	6	no	—
446	C₂×C₄	—	4	6	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	8	6	no	—
449	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
450	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
452	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
453	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
454	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	2	6	no	—
457	C₂²	—	2	3	no	—
458	C₂²	—	2	2	no	—
459	C₂²	—	2	3	no	—
460	C₂²	—	2	3	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
464	C₄	—	2	3	no	—
465	C₄	—	2	1	no	—
466	C₄	—	2	3	no	—
467	C₄	—	4	3	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	3	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	6	no	—
472	C₄	C₂×C₁₇×#137	1	6	yes	—
473	C₄	C₁₇×#577	1	2	yes	—
474	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
475	C₄	C₁₇×#585	1	1	yes	characteristic
476	C₂	—	4	3	no	—
477	C₂	—	4	2	no	—
478	C₂	C₁₇×#3489	1	1	yes	characteristic
479	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
480	C₂	C₂×C₁₇×#577	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3503	C₂	semidirect
3. Q₈×SD₁₆×C₁₇	C₂	semidirect
4. C₁₇×#3363	C₂	semidirect
5. C₁₇×#3356	C₂	semidirect
6. C₁₇×#3331	C₂	semidirect
7. C₁₇×#3255	C₂	semidirect
8. C₁₇×#3229	C₂	semidirect
9. C₁₇×#3107	C₂	semidirect
10. C₁₇×#3079	C₂	semidirect
11. C₁₇×#2991	C₂	semidirect
181. #62147	C₁₇	direct (N × H)
217. #3503	C₂×C₁₇	semidirect
219. Q₈×SD₁₆	C₂×C₁₇	semidirect
220. #3363	C₂×C₁₇	semidirect
221. #3356	C₂×C₁₇	semidirect
222. #3331	C₂×C₁₇	semidirect
223. #3255	C₂×C₁₇	semidirect
224. #3229	C₂×C₁₇	semidirect
225. #3107	C₂×C₁₇	semidirect
226. #3079	C₂×C₁₇	semidirect
227. #2991	C₂×C₁₇	semidirect
363. C₁₇	#62147	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×#3503	2
C₁₇×#3482	2
Q₈×SD₁₆×C₁₇	2
C₁₇×#3363	2
C₁₇×#3356	2
C₁₇×#3331	2
C₁₇×#3255	2
C₁₇×#3229	2
C₁₇×#3107	2
C₁₇×#3079	2
C₁₇×#2991	2
#62147	17

Subgroups — C17×#62147 #16919891

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62147 #16919891