Subgroups — C₁₇×#62149 #16919893

Order 4352.

1788 conjugacy classes of subgroups.

The subgroup lattice has 490 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×#3483	C₂	1	1	yes	maximal, characteristic
3	Q₈×Q₁₆×C₁₇	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3362	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3357	C₂	1	6	yes	maximal, complemented
6	C₁₇×#3333	C₂	1	6	yes	maximal, complemented
7	C₁₇×#3254	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3226	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	1	yes	characteristic
13	Q₈²×C₁₇	C₂²	1	2	yes	—
14	C₁₇×#557	—	2	1	no	—
15	C₁₇×#555	—	2	3	no	—
16	C₁₇×#555	C₂²	1	3	yes	—
17	C₁₇×#554	C₂²	1	6	yes	—
18	C₁₇×#550	—	2	1	no	—
19	C₁₇×#550	C₂²	1	3	yes	—
20	C₁₇×#550	C₂²	1	1	yes	characteristic
21	D₄×Q₈×C₁₇	—	2	3	no	—
22	C₁₇×#544	—	2	3	no	—
23	C₁₇×#533	C₂²	1	3	yes	—
24	C₁₇×#532	—	2	3	no	—
25	C₁₇×#532	C₂²	1	3	yes	—
26	C₂×C₁₇×C₄⋊Q₈	C₂²	1	3	yes	—
27	C₁₇×#520	—	2	1	no	—
28	C₄×#41×C₁₇	—	2	1	no	—
29	C₄×#41×C₁₇	C₂²	1	3	yes	—
30	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
31	C₁₇×#500	C₂²	1	6	yes	—
32	C₁₇×#486	C₂²	1	6	yes	—
33	C₁₇×#485	C₂²	1	6	yes	—
34	C₁₇×#480	C₂²	1	12	yes	—
35	C₁₇×#477	C₂²	1	6	yes	—
36	C₁₇×#477	C₂²	1	6	yes	—
37	C₁₇×#476	C₂²	1	6	yes	—
38	C₁₇×#475	C₂²	1	3	yes	—
39	C₁₇×#474	C₂²	1	3	yes	—
40	C₁₇×#474	C₂²	1	6	yes	—
41	C₁₇×#468	C₂²	1	12	yes	—
42	C₁₇×#462	C₂²	1	1	yes	characteristic
43	C₁₇×#461	C₂²	1	3	yes	—
44	C₁₇×#460	C₂²	1	6	yes	—
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	—	2	1	no	—
55	C₂×#41×C₁₇	—	2	3	no	—
56	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
57	C₂×#41×C₁₇	C₂³	1	3	yes	—
58	C₂²×Q₈×C₁₇	—	2	3	no	—
59	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
60	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
61	C₂×M₁₆×C₁₇	C₂³	1	6	yes	—
62	C₁₇×C₄⋊Q₈	—	2	3	no	—
63	C₁₇×C₄⋊Q₈	—	2	6	no	—
64	C₁₇×C₄⋊Q₈	—	2	3	no	—
65	C₁₇×C₄⋊Q₈	—	2	3	no	—
66	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
68	C₁₇×C₄⋊Q₈	C₂³	1	6	yes	—
69	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
70	C₁₇×#127	—	2	3	no	—
71	C₁₇×#127	C₂³	1	3	yes	—
72	C₁₇×#125	—	2	6	no	—
73	C₁₇×#125	—	2	3	no	—
74	C₁₇×#124	—	2	6	no	—
75	C₁₇×#124	—	2	3	no	—
76	C₁₇×C₂²⋊Q₈	—	2	3	no	—
77	C₁₇×C₂²⋊Q₈	—	2	12	no	—
78	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
79	C₁₇×#121	—	2	3	no	—
80	C₁₇×#121	—	2	3	no	—
81	C₁₇×#121	—	2	3	no	—
82	C₁₇×#121	—	2	6	no	—
83	C₁₇×#121	C₂³	1	6	yes	—
84	C₄×Q₈×C₁₇	—	2	1	no	—
85	C₄×Q₈×C₁₇	—	2	2	no	—
86	C₄×Q₈×C₁₇	—	2	3	no	—
87	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
88	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
90	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
91	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
92	C₄×D₄×C₁₇	—	2	6	no	—
93	C₄×D₄×C₁₇	—	2	3	no	—
94	C₄×D₄×C₁₇	—	2	3	no	—
95	C₄×D₄×C₁₇	—	2	3	no	—
96	C₄×D₄×C₁₇	—	2	3	no	—
97	C₄×D₄×C₁₇	D₄	1	3	yes	—
98	C₄×D₄×C₁₇	C₂³	1	3	yes	—
99	C₄×D₄×C₁₇	C₂³	1	3	yes	—
100	C₄×D₄×C₁₇	C₂³	1	3	yes	—
101	C₁₇×#117	—	2	3	no	—
102	C₁₇×#117	—	2	3	no	—
103	C₁₇×#117	—	2	3	no	—
104	C₁₇×#117	D₄	1	3	yes	—
105	C₁₇×#117	C₂³	1	3	yes	—
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×#107	C₂³	1	12	yes	—
112	C₁₇×#106	C₂³	1	6	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	6	yes	—
117	C₁₇×#103	C₂³	1	2	yes	—
118	C₁₇×#103	C₂³	1	6	yes	—
119	C₁₇×#102	C₂³	1	12	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	#41×C₁₇	—	4	4	no	—
127	#41×C₁₇	—	8	6	no	—
128	C₂×Q₈×C₁₇	—	2	3	no	—
129	C₂×Q₈×C₁₇	—	2	6	no	—
130	C₂×Q₈×C₁₇	—	2	3	no	—
131	C₂×Q₈×C₁₇	—	8	6	no	—
132	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
133	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
134	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
135	C₂×D₄×C₁₇	—	2	3	no	—
136	C₂×D₄×C₁₇	—	2	6	no	—
137	C₂×D₄×C₁₇	—	2	3	no	—
138	C₂×D₄×C₁₇	—	2	3	no	—
139	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
140	C₂×D₄×C₁₇	C₂⁴	1	3	yes	—
141	C₂²×C₄×C₁₇	—	2	6	no	—
142	C₂²×C₄×C₁₇	—	2	3	no	—
143	C₂²×C₄×C₁₇	—	2	3	no	—
144	C₂²×C₄×C₁₇	—	2	3	no	—
145	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
146	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
147	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
148	Q₁₆×C₁₇	—	2	4	no	—
149	SD₁₆×C₁₇	—	4	6	no	—
150	M₁₆×C₁₇	—	4	6	no	—
151	C₂×C₈×C₁₇	C₂⁴	1	6	yes	—
152	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
153	C₄⋊C₄×C₁₇	—	2	6	no	—
154	C₄⋊C₄×C₁₇	—	2	1	no	—
155	C₄⋊C₄×C₁₇	—	2	6	no	—
156	C₄⋊C₄×C₁₇	—	2	6	no	—
157	C₄⋊C₄×C₁₇	—	2	1	no	—
158	C₄⋊C₄×C₁₇	—	2	3	no	—
159	C₄⋊C₄×C₁₇	—	2	6	no	—
160	C₄⋊C₄×C₁₇	—	2	3	no	—
161	C₄⋊C₄×C₁₇	—	2	3	no	—
162	C₄⋊C₄×C₁₇	—	2	1	no	—
163	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
164	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
165	C₄⋊C₄×C₁₇	C₂⁴	1	6	yes	—
166	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
167	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
168	C₂²⋊C₄×C₁₇	—	2	6	no	—
169	C₂²⋊C₄×C₁₇	—	2	3	no	—
170	C₂²⋊C₄×C₁₇	—	2	6	no	—
171	C₂²⋊C₄×C₁₇	—	2	3	no	—
172	C₂²⋊C₄×C₁₇	—	2	3	no	—
173	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
174	C₄²×C₁₇	—	2	3	no	—
175	C₄²×C₁₇	—	2	6	no	—
176	C₄²×C₁₇	—	2	3	no	—
177	C₄²×C₁₇	—	2	1	no	—
178	C₄²×C₁₇	C₂×D₄	1	3	yes	—
179	C₄²×C₁₇	C₂×D₄	1	3	yes	—
180	C₄²×C₁₇	C₂⁴	1	3	yes	—
181	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
182	#62149	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
183	C₂³×C₁₇	—	2	3	no	—
184	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
185	Q₈×C₁₇	—	2	1	no	—
186	Q₈×C₁₇	—	2	2	no	—
187	Q₈×C₁₇	—	2	2	no	—
188	Q₈×C₁₇	—	4	6	no	—
189	Q₈×C₁₇	—	8	6	no	—
190	Q₈×C₁₇	—	8	3	no	—
191	Q₈×C₁₇	#137	1	4	yes	—
192	Q₈×C₁₇	2₋¹⁺⁴	1	2	yes	—
193	D₄×C₁₇	—	2	6	no	—
194	D₄×C₁₇	—	2	3	no	—
195	D₄×C₁₇	—	2	3	no	—
196	D₄×C₁₇	—	4	6	no	—
197	D₄×C₁₇	—	4	6	no	—
198	D₄×C₁₇	—	8	3	no	—
199	D₄×C₁₇	—	8	6	no	—
200	C₂×C₄×C₁₇	—	2	1	no	—
201	C₂×C₄×C₁₇	—	2	6	no	—
202	C₂×C₄×C₁₇	—	2	6	no	—
203	C₂×C₄×C₁₇	—	2	3	no	—
204	C₂×C₄×C₁₇	—	2	3	no	—
205	C₂×C₄×C₁₇	—	2	1	no	—
206	C₂×C₄×C₁₇	—	2	2	no	—
207	C₂×C₄×C₁₇	—	2	3	no	—
208	C₂×C₄×C₁₇	—	2	6	no	—
209	C₂×C₄×C₁₇	—	4	6	no	—
210	C₂×C₄×C₁₇	—	4	6	no	—
211	C₂×C₄×C₁₇	—	4	6	no	—
212	C₂×C₄×C₁₇	—	8	6	no	—
213	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
214	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
216	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
217	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
219	C₈×C₁₇	—	2	2	no	—
220	C₈×C₁₇	—	2	6	no	—
221	#3503	C₂×C₁₇	1	1	yes	characteristic, complemented
222	#3483	C₂×C₁₇	1	1	yes	characteristic
223	Q₈×Q₁₆	C₂×C₁₇	1	2	yes	complemented
224	#3362	C₂×C₁₇	1	2	yes	complemented
225	#3357	C₂×C₁₇	1	6	yes	complemented
226	#3333	C₂×C₁₇	1	6	yes	complemented
227	#3254	C₂×C₁₇	1	3	yes	complemented
228	#3226	C₂×C₁₇	1	3	yes	complemented
229	#3107	C₂×C₁₇	1	3	yes	complemented
230	#3079	C₂×C₁₇	1	3	yes	complemented
231	#2991	C₂×C₁₇	1	1	yes	characteristic, complemented
232	C₂²×C₁₇	—	2	3	no	—
233	C₂²×C₁₇	—	2	3	no	—
234	C₂²×C₁₇	—	2	3	no	—
235	C₂²×C₁₇	—	4	3	no	—
236	C₂²×C₁₇	—	4	3	no	—
237	C₂²×C₁₇	—	4	3	no	—
238	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
239	C₄×C₁₇	—	2	3	no	—
240	C₄×C₁₇	—	2	2	no	—
241	C₄×C₁₇	—	2	1	no	—
242	C₄×C₁₇	—	2	3	no	—
243	C₄×C₁₇	—	4	2	no	—
244	C₄×C₁₇	—	4	1	no	—
245	C₄×C₁₇	—	4	3	no	—
246	C₄×C₁₇	—	4	6	no	—
247	C₄×C₁₇	C₂×#137	1	6	yes	—
248	C₄×C₁₇	#576	1	2	yes	—
249	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
250	C₄×C₁₇	#585	1	1	yes	characteristic
251	Q₈²	C₂²×C₁₇	1	2	yes	—
252	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
253	#557	—	2	1	no	—
254	#555	—	2	3	no	—
255	#555	C₂²×C₁₇	1	3	yes	—
256	#554	C₂²×C₁₇	1	6	yes	—
257	#550	—	2	1	no	—
258	#550	C₂²×C₁₇	1	3	yes	—
259	#550	C₂²×C₁₇	1	1	yes	characteristic
260	D₄×Q₈	—	2	3	no	—
261	#544	—	2	3	no	—
262	#533	C₂²×C₁₇	1	3	yes	—
263	#532	—	2	3	no	—
264	#532	C₂²×C₁₇	1	3	yes	—
265	C₂×C₄⋊Q₈	C₂²×C₁₇	1	3	yes	—
266	#520	—	2	1	no	—
267	C₄×#41	—	2	1	no	—
268	C₄×#41	C₂²×C₁₇	1	3	yes	—
269	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
270	#500	C₂²×C₁₇	1	6	yes	—
271	#486	C₂²×C₁₇	1	6	yes	—
272	#485	C₂²×C₁₇	1	6	yes	—
273	#480	C₂²×C₁₇	1	12	yes	—
274	#477	C₂²×C₁₇	1	6	yes	—
275	#477	C₂²×C₁₇	1	6	yes	—
276	#476	C₂²×C₁₇	1	6	yes	—
277	#475	C₂²×C₁₇	1	3	yes	—
278	#474	C₂²×C₁₇	1	6	yes	—
279	#474	C₂²×C₁₇	1	3	yes	—
280	#468	C₂²×C₁₇	1	12	yes	—
281	#462	C₂²×C₁₇	1	1	yes	characteristic
282	#461	C₂²×C₁₇	1	3	yes	—
283	#460	C₂²×C₁₇	1	6	yes	—
284	#452	C₂²×C₁₇	1	6	yes	—
285	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
286	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
287	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
288	#436	C₂²×C₁₇	1	6	yes	—
289	#431	C₂²×C₁₇	1	3	yes	—
290	#428	C₂²×C₁₇	1	6	yes	—
291	#423	C₂²×C₁₇	1	3	yes	—
292	#417	C₂²×C₁₇	1	6	yes	—
293	C₂×C₁₇	—	4	3	no	—
294	C₂×C₁₇	—	8	3	no	—
295	C₂×C₁₇	#3489	1	1	yes	characteristic
296	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
297	C₂×C₁₇	C₂×#576	1	1	yes	characteristic
298	C₂×#41	—	2	1	no	—
299	C₂×#41	—	2	3	no	—
300	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
301	C₂×#41	C₂³×C₁₇	1	3	yes	—
302	C₂²×Q₈	—	2	3	no	—
303	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
304	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
305	C₂×M₁₆	C₂³×C₁₇	1	6	yes	—
306	C₄⋊Q₈	—	2	3	no	—
307	C₄⋊Q₈	—	2	6	no	—
308	C₄⋊Q₈	—	2	3	no	—
309	C₄⋊Q₈	—	2	3	no	—
310	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
312	C₄⋊Q₈	C₂³×C₁₇	1	6	yes	—
313	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
314	#127	—	2	3	no	—
315	#127	C₂³×C₁₇	1	3	yes	—
316	#125	—	2	6	no	—
317	#125	—	2	3	no	—
318	#124	—	2	6	no	—
319	#124	—	2	3	no	—
320	C₂²⋊Q₈	—	2	3	no	—
321	C₂²⋊Q₈	—	2	12	no	—
322	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
323	#121	—	2	3	no	—
324	#121	—	2	3	no	—
325	#121	—	2	3	no	—
326	#121	—	2	6	no	—
327	#121	C₂³×C₁₇	1	6	yes	—
328	C₄×Q₈	—	2	1	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	3	no	—
331	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
332	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
333	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
334	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
335	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
336	C₄×D₄	—	2	6	no	—
337	C₄×D₄	—	2	3	no	—
338	C₄×D₄	—	2	3	no	—
339	C₄×D₄	—	2	3	no	—
340	C₄×D₄	—	2	3	no	—
341	C₄×D₄	D₄×C₁₇	1	3	yes	—
342	C₄×D₄	C₂³×C₁₇	1	3	yes	—
343	C₄×D₄	C₂³×C₁₇	1	3	yes	—
344	C₄×D₄	C₂³×C₁₇	1	3	yes	—
345	#117	—	2	3	no	—
346	#117	—	2	3	no	—
347	#117	—	2	3	no	—
348	#117	D₄×C₁₇	1	3	yes	—
349	#117	C₂³×C₁₇	1	3	yes	—
350	C₂×C₄⋊C₄	—	2	3	no	—
351	C₂×C₄⋊C₄	C₂³×C₁₇	1	6	yes	—
352	C₂×C₄²	—	2	3	no	—
353	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
354	#107	C₂³×C₁₇	1	12	yes	—
355	#107	C₂³×C₁₇	1	6	yes	—
356	#106	C₂³×C₁₇	1	6	yes	—
357	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
358	C₄⋊C₈	C₂³×C₁₇	1	6	yes	—
359	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
360	#103	C₂³×C₁₇	1	6	yes	—
361	#103	C₂³×C₁₇	1	2	yes	—
362	#103	C₂³×C₁₇	1	6	yes	—
363	#102	C₂³×C₁₇	1	12	yes	—
364	#102	C₂³×C₁₇	1	6	yes	—
365	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
366	C₄×C₈	C₂³×C₁₇	1	6	yes	—
367	C₁₇	#62149	1	1	yes	characteristic, direct product factor, Sylow
368	#41	—	2	4	no	—
369	#41	—	2	6	no	—
370	#41	—	4	3	no	—
371	#41	—	4	4	no	—
372	#41	—	8	6	no	—
373	C₂×Q₈	—	2	3	no	—
374	C₂×Q₈	—	2	6	no	—
375	C₂×Q₈	—	2	3	no	—
376	C₂×Q₈	—	8	6	no	—
377	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
378	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
379	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
380	C₂×D₄	—	2	3	no	—
381	C₂×D₄	—	2	6	no	—
382	C₂×D₄	—	2	3	no	—
383	C₂×D₄	—	2	3	no	—
384	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
385	C₂×D₄	C₂⁴×C₁₇	1	3	yes	—
386	C₂²×C₄	—	2	6	no	—
387	C₂²×C₄	—	2	3	no	—
388	C₂²×C₄	—	2	3	no	—
389	C₂²×C₄	—	2	3	no	—
390	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
391	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
392	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
393	Q₁₆	—	2	4	no	—
394	SD₁₆	—	4	6	no	—
395	M₁₆	—	4	6	no	—
396	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
397	C₂×C₈	C₂⁴×C₁₇	1	6	yes	—
398	C₄⋊C₄	—	2	3	no	—
399	C₄⋊C₄	—	2	6	no	—
400	C₄⋊C₄	—	2	6	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	3	no	—
404	C₄⋊C₄	—	2	3	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	6	no	—
407	C₄⋊C₄	—	2	6	no	—
408	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
409	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
410	C₄⋊C₄	C₂⁴×C₁₇	1	6	yes	—
411	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
412	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
413	C₂²⋊C₄	—	2	6	no	—
414	C₂²⋊C₄	—	2	3	no	—
415	C₂²⋊C₄	—	2	6	no	—
416	C₂²⋊C₄	—	2	3	no	—
417	C₂²⋊C₄	—	2	3	no	—
418	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
419	C₄²	—	2	1	no	—
420	C₄²	—	2	3	no	—
421	C₄²	—	2	3	no	—
422	C₄²	—	2	6	no	—
423	C₄²	C₂×D₄×C₁₇	1	3	yes	—
424	C₄²	C₂×D₄×C₁₇	1	3	yes	—
425	C₄²	C₂⁴×C₁₇	1	3	yes	—
426	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
427	C₂³	—	2	3	no	—
428	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
429	Q₈	—	2	1	no	—
430	Q₈	—	2	2	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	4	6	no	—
433	Q₈	—	8	6	no	—
434	Q₈	—	8	3	no	—
435	Q₈	C₁₇×#137	1	4	yes	—
436	Q₈	C₁₇×2₋¹⁺⁴	1	2	yes	—
437	D₄	—	2	6	no	—
438	D₄	—	2	3	no	—
439	D₄	—	2	3	no	—
440	D₄	—	4	6	no	—
441	D₄	—	4	6	no	—
442	D₄	—	8	3	no	—
443	D₄	—	8	6	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	6	no	—
446	C₂×C₄	—	2	6	no	—
447	C₂×C₄	—	2	3	no	—
448	C₂×C₄	—	2	3	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	3	no	—
452	C₂×C₄	—	2	6	no	—
453	C₂×C₄	—	4	6	no	—
454	C₂×C₄	—	4	6	no	—
455	C₂×C₄	—	4	6	no	—
456	C₂×C₄	—	8	6	no	—
457	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
458	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
459	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
460	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
461	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
462	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	2	6	no	—
465	C₂²	—	2	3	no	—
466	C₂²	—	2	3	no	—
467	C₂²	—	2	3	no	—
468	C₂²	—	4	3	no	—
469	C₂²	—	4	3	no	—
470	C₂²	—	4	3	no	—
471	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
472	C₄	—	2	3	no	—
473	C₄	—	2	2	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	3	no	—
476	C₄	—	4	2	no	—
477	C₄	—	4	1	no	—
478	C₄	—	4	3	no	—
479	C₄	—	4	6	no	—
480	C₄	C₂×C₁₇×#137	1	6	yes	—
481	C₄	C₁₇×#576	1	2	yes	—
482	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
483	C₄	C₁₇×#585	1	1	yes	characteristic
484	C₂	—	4	3	no	—
485	C₂	—	8	3	no	—
486	C₂	C₁₇×#3489	1	1	yes	characteristic
487	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
488	C₂	C₂×C₁₇×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3483	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×Q₁₆×C₁₇	C₂	semidirect
4. C₁₇×#3362	C₂	semidirect
5. C₁₇×#3357	C₂	semidirect
6. C₁₇×#3333	C₂	semidirect
7. C₁₇×#3254	C₂	semidirect
8. C₁₇×#3226	C₂	semidirect
9. C₁₇×#3107	C₂	semidirect
10. C₁₇×#3079	C₂	semidirect
11. C₁₇×#2991	C₂	semidirect
182. #62149	C₁₇	direct (N × H)
221. #3503	C₂×C₁₇	semidirect
223. Q₈×Q₁₆	C₂×C₁₇	semidirect
224. #3362	C₂×C₁₇	semidirect
225. #3357	C₂×C₁₇	semidirect
226. #3333	C₂×C₁₇	semidirect
227. #3254	C₂×C₁₇	semidirect
228. #3226	C₂×C₁₇	semidirect
229. #3107	C₂×C₁₇	semidirect
230. #3079	C₂×C₁₇	semidirect
231. #2991	C₂×C₁₇	semidirect
367. C₁₇	#62149	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×#3483	2
Q₈×Q₁₆×C₁₇	2
C₁₇×#3362	2
C₁₇×#3357	2
C₁₇×#3333	2
C₁₇×#3254	2
C₁₇×#3226	2
C₁₇×#3107	2
C₁₇×#3079	2
C₁₇×#2991	2
#62149	17

Subgroups — C17×#62149 #16919893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62149 #16919893