Subgroups — C₁₇×#18588 #16876332

Order 4352.

898 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3523	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3239	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1652	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1649	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1648	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1491	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1483	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₁₇	—	2	1	no	—
13	C₁₇×#557	—	2	1	no	—
14	C₁₇×#557	C₂²	1	1	yes	characteristic
15	C₁₇×#557	C₂²	1	1	yes	characteristic
16	C₁₇×#556	—	2	1	no	—
17	C₁₇×#556	C₂²	1	1	yes	characteristic
18	C₁₇×#552	—	2	2	no	—
19	C₁₇×#552	—	2	1	no	—
20	D₄×Q₈×C₁₇	—	2	1	no	—
21	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#541	—	2	1	no	—
23	C₁₇×#541	—	2	2	no	—
24	C₁₇×#533	—	2	1	no	—
25	C₁₇×#533	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
27	C₁₇×#529	—	2	1	no	—
28	C₁₇×#529	C₂²	1	1	yes	characteristic
29	C₁₇×#519	—	2	1	no	—
30	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
31	C₁₇×#501	—	2	1	no	—
32	C₁₇×#501	—	2	2	no	—
33	C₁₇×#500	C₂²	1	2	yes	—
34	C₁₇×#498	C₂²	1	2	yes	—
35	C₁₇×#489	—	2	1	no	—
36	C₁₇×#484	—	2	1	no	—
37	C₁₇×#481	—	2	1	no	—
38	C₁₇×#475	C₂²	1	2	yes	—
39	C₁₇×#474	C₂²	1	2	yes	—
40	C₁₇×#462	—	2	1	no	—
41	C₁₇×#462	—	2	1	no	—
42	C₁₇×#462	C₂²	1	2	yes	—
43	C₁₇×#462	C₂²	1	2	yes	—
44	C₁₇×#432	C₂²	1	1	yes	characteristic
45	C₁₇×#428	—	2	2	no	—
46	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
47	C₂×C₁₇×#103	—	2	1	no	—
48	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#332	C₂²	1	2	yes	—
50	C₁₇×#332	C₂²	1	2	yes	—
51	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
53	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
54	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
55	C₂²×Q₈×C₁₇	—	2	1	no	—
56	C₂²×Q₈×C₁₇	—	2	1	no	—
57	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
58	C₂×Q₁₆×C₁₇	—	2	2	no	—
59	C₂×Q₁₆×C₁₇	—	2	2	no	—
60	C₂×Q₁₆×C₁₇	—	4	4	no	—
61	C₂×M₁₆×C₁₇	—	2	1	no	—
62	C₂²×C₈×C₁₇	—	2	1	no	—
63	C₁₇×C₄⋊Q₈	—	2	2	no	—
64	C₁₇×C₄⋊Q₈	—	2	1	no	—
65	C₁₇×C₄⋊Q₈	—	2	1	no	—
66	C₁₇×C₄⋊Q₈	—	2	1	no	—
67	C₁₇×C₄⋊Q₈	—	2	1	no	—
68	C₁₇×C₄⋊Q₈	—	2	1	no	—
69	C₁₇×C₄⋊Q₈	—	2	1	no	—
70	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
71	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₇×#126	—	2	2	no	—
74	C₁₇×#126	—	2	2	no	—
75	C₁₇×#126	—	2	2	no	—
76	C₁₇×#126	—	2	2	no	—
77	C₁₇×#126	—	2	1	no	—
78	C₁₇×#125	—	2	2	no	—
79	C₁₇×#125	—	2	2	no	—
80	C₁₇×#125	—	2	2	no	—
81	C₁₇×#125	—	2	1	no	—
82	C₁₇×#125	—	2	2	no	—
83	C₁₇×#125	—	2	2	no	—
84	C₁₇×#125	—	2	1	no	—
85	C₁₇×#125	D₄	1	1	yes	characteristic
86	C₁₇×#125	D₄	1	2	yes	—
87	C₁₇×#124	—	2	1	no	—
88	C₁₇×#124	D₄	1	1	yes	characteristic
89	C₁₇×#123	—	2	2	no	—
90	C₁₇×#123	—	2	1	no	—
91	C₁₇×C₂²⋊Q₈	—	2	2	no	—
92	C₁₇×C₂²⋊Q₈	—	2	2	no	—
93	C₁₇×C₂²⋊Q₈	—	2	1	no	—
94	C₁₇×C₂²⋊Q₈	—	2	1	no	—
95	C₁₇×C₂²⋊Q₈	—	2	1	no	—
96	C₁₇×C₂²⋊Q₈	—	2	1	no	—
97	C₁₇×C₂²⋊Q₈	—	2	2	no	—
98	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₇×#121	D₄	1	1	yes	characteristic
100	C₄×Q₈×C₁₇	—	2	2	no	—
101	C₄×Q₈×C₁₇	—	2	2	no	—
102	C₄×Q₈×C₁₇	—	2	1	no	—
103	C₄×Q₈×C₁₇	—	2	1	no	—
104	C₄×Q₈×C₁₇	—	2	1	no	—
105	C₄×Q₈×C₁₇	—	2	1	no	—
106	C₄×Q₈×C₁₇	—	2	1	no	—
107	C₄×Q₈×C₁₇	—	2	1	no	—
108	C₄×Q₈×C₁₇	—	2	1	no	—
109	C₄×Q₈×C₁₇	—	2	1	no	—
110	C₄×Q₈×C₁₇	—	2	1	no	—
111	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
112	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
113	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
114	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
115	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
116	C₄×D₄×C₁₇	—	2	2	no	—
117	C₄×D₄×C₁₇	—	2	1	no	—
118	C₄×D₄×C₁₇	—	2	1	no	—
119	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
120	C₁₇×#117	—	2	2	no	—
121	C₁₇×#117	—	2	2	no	—
122	C₁₇×#117	—	2	2	no	—
123	C₁₇×#117	—	2	1	no	—
124	C₁₇×#117	—	2	1	no	—
125	C₁₇×#117	D₄	1	2	yes	—
126	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
127	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
128	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
129	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
130	C₂×C₄²×C₁₇	—	2	1	no	—
131	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
132	C₁₇×#107	—	2	4	no	—
133	C₁₇×#107	—	2	2	no	—
134	C₁₇×#106	—	2	4	no	—
135	C₁₇×#106	—	2	2	no	—
136	C₁₇×C₄⋊C₈	—	2	1	no	—
137	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
138	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
139	C₁₇×#103	—	2	2	no	—
140	C₁₇×#103	—	2	2	no	—
141	C₁₇×#103	—	2	2	no	—
142	C₁₇×#102	—	2	2	no	—
143	C₁₇×C₂²⋊C₈	—	2	1	no	—
144	C₁₇×#97	—	2	1	no	—
145	C₁₇×#97	—	2	1	no	—
146	C₄×C₈×C₁₇	C₂³	1	2	yes	—
147	C₂×Q₈×C₁₇	—	2	2	no	—
148	C₂×Q₈×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	—	2	1	no	—
151	C₂×Q₈×C₁₇	—	2	2	no	—
152	C₂×Q₈×C₁₇	—	2	2	no	—
153	C₂×Q₈×C₁₇	—	4	1	no	—
154	C₂×Q₈×C₁₇	—	4	2	no	—
155	C₂×Q₈×C₁₇	—	4	2	no	—
156	C₂×Q₈×C₁₇	—	4	2	no	—
157	C₂×Q₈×C₁₇	—	4	2	no	—
158	C₂×Q₈×C₁₇	—	4	1	no	—
159	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
160	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₁₇	—	2	1	no	—
163	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₇	—	2	2	no	—
165	C₂²×C₄×C₁₇	—	2	1	no	—
166	C₂²×C₄×C₁₇	—	2	1	no	—
167	C₂²×C₄×C₁₇	—	2	1	no	—
168	C₂²×C₄×C₁₇	—	4	1	no	—
169	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
172	Q₁₆×C₁₇	—	4	4	no	—
173	Q₁₆×C₁₇	—	4	4	no	—
174	M₁₆×C₁₇	—	2	4	no	—
175	C₂×C₈×C₁₇	—	2	2	no	—
176	C₂×C₈×C₁₇	—	2	2	no	—
177	C₂×C₈×C₁₇	—	2	2	no	—
178	C₂×C₈×C₁₇	—	4	2	no	—
179	C₄⋊C₄×C₁₇	—	2	2	no	—
180	C₄⋊C₄×C₁₇	—	2	2	no	—
181	C₄⋊C₄×C₁₇	—	2	2	no	—
182	C₄⋊C₄×C₁₇	—	2	2	no	—
183	C₄⋊C₄×C₁₇	—	2	2	no	—
184	C₄⋊C₄×C₁₇	—	2	2	no	—
185	C₄⋊C₄×C₁₇	—	2	2	no	—
186	C₄⋊C₄×C₁₇	—	2	2	no	—
187	C₄⋊C₄×C₁₇	—	2	2	no	—
188	C₄⋊C₄×C₁₇	—	2	2	no	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	—	2	1	no	—
191	C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₄⋊C₄×C₁₇	—	2	1	no	—
193	C₄⋊C₄×C₁₇	—	2	1	no	—
194	C₄⋊C₄×C₁₇	—	2	1	no	—
195	C₄⋊C₄×C₁₇	—	2	1	no	—
196	C₄⋊C₄×C₁₇	—	2	1	no	—
197	C₄⋊C₄×C₁₇	—	2	1	no	—
198	C₄⋊C₄×C₁₇	—	2	1	no	—
199	C₄⋊C₄×C₁₇	—	2	1	no	—
200	C₄⋊C₄×C₁₇	—	2	2	no	—
201	C₄⋊C₄×C₁₇	—	2	2	no	—
202	C₄⋊C₄×C₁₇	—	4	1	no	—
203	C₄⋊C₄×C₁₇	—	4	1	no	—
204	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
205	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
206	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
208	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₂²⋊C₄×C₁₇	—	2	2	no	—
211	C₂²⋊C₄×C₁₇	—	2	2	no	—
212	C₂²⋊C₄×C₁₇	—	2	2	no	—
213	C₂²⋊C₄×C₁₇	—	2	2	no	—
214	C₂²⋊C₄×C₁₇	—	2	1	no	—
215	C₂²⋊C₄×C₁₇	—	2	1	no	—
216	C₂²⋊C₄×C₁₇	—	2	1	no	—
217	C₂²⋊C₄×C₁₇	—	2	1	no	—
218	C₂²⋊C₄×C₁₇	—	2	1	no	—
219	C₄²×C₁₇	—	2	2	no	—
220	C₄²×C₁₇	—	2	2	no	—
221	C₄²×C₁₇	—	2	2	no	—
222	C₄²×C₁₇	—	2	1	no	—
223	C₄²×C₁₇	—	2	2	no	—
224	C₄²×C₁₇	—	2	1	no	—
225	C₄²×C₁₇	—	2	1	no	—
226	C₄²×C₁₇	—	2	1	no	—
227	C₄²×C₁₇	—	2	1	no	—
228	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
229	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
230	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
231	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
232	#18588	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂³×C₁₇	—	2	1	no	—
234	C₂³×C₁₇	#120	1	1	yes	characteristic
235	Q₈×C₁₇	—	2	1	no	—
236	Q₈×C₁₇	—	2	1	no	—
237	Q₈×C₁₇	—	2	1	no	—
238	Q₈×C₁₇	—	2	2	no	—
239	Q₈×C₁₇	—	4	2	no	—
240	Q₈×C₁₇	—	4	4	no	—
241	Q₈×C₁₇	—	4	1	no	—
242	Q₈×C₁₇	—	4	1	no	—
243	Q₈×C₁₇	—	4	2	no	—
244	Q₈×C₁₇	—	4	2	no	—
245	Q₈×C₁₇	—	4	2	no	—
246	Q₈×C₁₇	—	8	2	no	—
247	Q₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
248	D₄×C₁₇	—	2	2	no	—
249	D₄×C₁₇	—	4	2	no	—
250	C₂×C₄×C₁₇	—	2	1	no	—
251	C₂×C₄×C₁₇	—	2	2	no	—
252	C₂×C₄×C₁₇	—	2	1	no	—
253	C₂×C₄×C₁₇	—	2	1	no	—
254	C₂×C₄×C₁₇	—	2	2	no	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	1	no	—
257	C₂×C₄×C₁₇	—	2	2	no	—
258	C₂×C₄×C₁₇	—	2	1	no	—
259	C₂×C₄×C₁₇	—	2	1	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	1	no	—
262	C₂×C₄×C₁₇	—	2	2	no	—
263	C₂×C₄×C₁₇	—	4	2	no	—
264	C₂×C₄×C₁₇	—	4	4	no	—
265	C₂×C₄×C₁₇	—	4	2	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	2	no	—
269	C₂×C₄×C₁₇	—	8	2	no	—
270	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
271	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
272	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
273	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
274	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
276	C₈×C₁₇	—	2	4	no	—
277	C₈×C₁₇	—	4	2	no	—
278	C₈×C₁₇	—	4	2	no	—
279	#3523	C₂×C₁₇	1	1	yes	characteristic
280	#3239	C₂×C₁₇	1	1	yes	characteristic
281	#3165	C₂×C₁₇	1	1	yes	characteristic, complemented
282	C₂×#462	C₂×C₁₇	1	1	yes	characteristic, complemented
283	#1653	C₂×C₁₇	1	2	yes	complemented
284	#1652	C₂×C₁₇	1	2	yes	complemented
285	#1649	C₂×C₁₇	1	2	yes	complemented
286	#1648	C₂×C₁₇	1	2	yes	complemented
287	#1552	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#1491	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#1483	C₂×C₁₇	1	1	yes	characteristic
290	C₂²×C₁₇	—	2	1	no	—
291	C₂²×C₁₇	—	2	1	no	—
292	C₂²×C₁₇	—	4	1	no	—
293	C₂²×C₁₇	—	4	1	no	—
294	C₂²×C₁₇	—	4	1	no	—
295	C₂²×C₁₇	#456	1	2	yes	—
296	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	2	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	1	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	2	no	—
304	C₄×C₁₇	—	4	1	no	—
305	C₄×C₁₇	—	4	1	no	—
306	C₄×C₁₇	—	4	2	no	—
307	C₄×C₁₇	—	4	1	no	—
308	C₄×C₁₇	—	4	1	no	—
309	C₄×C₁₇	—	4	1	no	—
310	C₄×C₁₇	—	8	2	no	—
311	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
312	C₄×C₁₇	#575	1	1	yes	characteristic
313	C₄×C₁₇	#578	1	2	yes	—
314	C₂²×Q₁₆	—	2	1	no	—
315	#557	—	2	1	no	—
316	#557	C₂²×C₁₇	1	1	yes	characteristic
317	#557	C₂²×C₁₇	1	1	yes	characteristic
318	#556	—	2	1	no	—
319	#556	C₂²×C₁₇	1	1	yes	characteristic
320	#552	—	2	2	no	—
321	#552	—	2	1	no	—
322	D₄×Q₈	—	2	1	no	—
323	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
324	#541	—	2	2	no	—
325	#541	—	2	1	no	—
326	#533	—	2	1	no	—
327	#533	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
329	#529	—	2	1	no	—
330	#529	C₂²×C₁₇	1	1	yes	characteristic
331	#519	—	2	1	no	—
332	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
333	#501	—	2	2	no	—
334	#501	—	2	1	no	—
335	#500	C₂²×C₁₇	1	2	yes	—
336	#498	C₂²×C₁₇	1	2	yes	—
337	#489	—	2	1	no	—
338	#484	—	2	1	no	—
339	#481	—	2	1	no	—
340	#475	C₂²×C₁₇	1	2	yes	—
341	#474	C₂²×C₁₇	1	2	yes	—
342	#462	—	2	1	no	—
343	#462	—	2	1	no	—
344	#462	C₂²×C₁₇	1	2	yes	—
345	#462	C₂²×C₁₇	1	2	yes	—
346	#432	C₂²×C₁₇	1	1	yes	characteristic
347	#428	—	2	2	no	—
348	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×#103	—	2	1	no	—
350	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
351	#332	C₂²×C₁₇	1	2	yes	—
352	#332	C₂²×C₁₇	1	2	yes	—
353	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
354	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
355	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
356	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
357	C₂×C₁₇	—	2	2	no	—
358	C₂×C₁₇	—	8	1	no	—
359	C₂×C₁₇	#3006	1	1	yes	characteristic
360	C₂×C₁₇	#3011	1	1	yes	characteristic
361	C₂×C₁₇	C₂×#456	1	1	yes	characteristic
362	C₂²×Q₈	—	2	1	no	—
363	C₂²×Q₈	—	2	1	no	—
364	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
365	C₂×Q₁₆	—	2	2	no	—
366	C₂×Q₁₆	—	2	2	no	—
367	C₂×Q₁₆	—	4	4	no	—
368	C₂×M₁₆	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₄⋊Q₈	—	2	2	no	—
371	C₄⋊Q₈	—	2	1	no	—
372	C₄⋊Q₈	—	2	1	no	—
373	C₄⋊Q₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	1	no	—
375	C₄⋊Q₈	—	2	1	no	—
376	C₄⋊Q₈	—	2	1	no	—
377	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
378	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
379	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
380	#126	—	2	2	no	—
381	#126	—	2	2	no	—
382	#126	—	2	2	no	—
383	#126	—	2	2	no	—
384	#126	—	2	1	no	—
385	#125	—	2	2	no	—
386	#125	—	2	2	no	—
387	#125	—	2	2	no	—
388	#125	—	2	1	no	—
389	#125	—	2	2	no	—
390	#125	—	2	2	no	—
391	#125	—	2	1	no	—
392	#125	D₄×C₁₇	1	1	yes	characteristic
393	#125	D₄×C₁₇	1	2	yes	—
394	#124	—	2	1	no	—
395	#124	D₄×C₁₇	1	1	yes	characteristic
396	#123	—	2	2	no	—
397	#123	—	2	1	no	—
398	C₂²⋊Q₈	—	2	2	no	—
399	C₂²⋊Q₈	—	2	2	no	—
400	C₂²⋊Q₈	—	2	1	no	—
401	C₂²⋊Q₈	—	2	1	no	—
402	C₂²⋊Q₈	—	2	1	no	—
403	C₂²⋊Q₈	—	2	1	no	—
404	C₂²⋊Q₈	—	2	2	no	—
405	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
406	#121	D₄×C₁₇	1	1	yes	characteristic
407	C₄×Q₈	—	2	2	no	—
408	C₄×Q₈	—	2	2	no	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	1	no	—
413	C₄×Q₈	—	2	1	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
419	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
420	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
421	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
422	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
423	C₄×D₄	—	2	2	no	—
424	C₄×D₄	—	2	1	no	—
425	C₄×D₄	—	2	1	no	—
426	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
427	#117	—	2	2	no	—
428	#117	—	2	2	no	—
429	#117	—	2	2	no	—
430	#117	—	2	1	no	—
431	#117	—	2	1	no	—
432	#117	D₄×C₁₇	1	2	yes	—
433	C₂×C₄⋊C₄	—	2	1	no	—
434	C₂×C₄⋊C₄	—	2	1	no	—
435	C₂×C₄⋊C₄	—	2	1	no	—
436	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
437	C₂×C₄²	—	2	1	no	—
438	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
439	#107	—	2	4	no	—
440	#107	—	2	2	no	—
441	#106	—	2	4	no	—
442	#106	—	2	2	no	—
443	C₄⋊C₈	—	2	1	no	—
444	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
445	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
446	#103	—	2	2	no	—
447	#103	—	2	2	no	—
448	#103	—	2	2	no	—
449	#102	—	2	2	no	—
450	C₂²⋊C₈	—	2	1	no	—
451	#97	—	2	1	no	—
452	#97	—	2	1	no	—
453	C₄×C₈	C₂³×C₁₇	1	2	yes	—
454	C₁₇	#18588	1	1	yes	characteristic, direct product factor, Sylow
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	1	no	—
457	C₂×Q₈	—	2	1	no	—
458	C₂×Q₈	—	2	1	no	—
459	C₂×Q₈	—	2	2	no	—
460	C₂×Q₈	—	2	2	no	—
461	C₂×Q₈	—	4	1	no	—
462	C₂×Q₈	—	4	2	no	—
463	C₂×Q₈	—	4	2	no	—
464	C₂×Q₈	—	4	2	no	—
465	C₂×Q₈	—	4	2	no	—
466	C₂×Q₈	—	4	1	no	—
467	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
468	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
469	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	4	1	no	—
477	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
480	Q₁₆	—	4	4	no	—
481	Q₁₆	—	4	4	no	—
482	M₁₆	—	2	4	no	—
483	C₂×C₈	—	2	2	no	—
484	C₂×C₈	—	2	2	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	4	2	no	—
487	C₄⋊C₄	—	2	2	no	—
488	C₄⋊C₄	—	2	2	no	—
489	C₄⋊C₄	—	2	2	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	2	no	—
492	C₄⋊C₄	—	2	2	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	2	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	2	no	—
504	C₄⋊C₄	—	2	1	no	—
505	C₄⋊C₄	—	2	1	no	—
506	C₄⋊C₄	—	2	1	no	—
507	C₄⋊C₄	—	2	2	no	—
508	C₄⋊C₄	—	2	2	no	—
509	C₄⋊C₄	—	2	2	no	—
510	C₄⋊C₄	—	4	1	no	—
511	C₄⋊C₄	—	4	1	no	—
512	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
514	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
515	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
516	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
517	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	2	2	no	—
520	C₂²⋊C₄	—	2	2	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	2	no	—
523	C₂²⋊C₄	—	2	1	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	1	no	—
527	C₄²	—	2	2	no	—
528	C₄²	—	2	2	no	—
529	C₄²	—	2	2	no	—
530	C₄²	—	2	1	no	—
531	C₄²	—	2	1	no	—
532	C₄²	—	2	1	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	2	no	—
536	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
537	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
538	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
539	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
540	C₂³	—	2	1	no	—
541	C₂³	C₁₇×#120	1	1	yes	characteristic
542	Q₈	—	2	1	no	—
543	Q₈	—	2	1	no	—
544	Q₈	—	2	1	no	—
545	Q₈	—	2	2	no	—
546	Q₈	—	4	2	no	—
547	Q₈	—	4	4	no	—
548	Q₈	—	4	1	no	—
549	Q₈	—	4	1	no	—
550	Q₈	—	4	2	no	—
551	Q₈	—	4	2	no	—
552	Q₈	—	4	2	no	—
553	Q₈	—	8	2	no	—
554	Q₈	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
555	D₄	—	2	2	no	—
556	D₄	—	4	2	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	2	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	2	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	2	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	1	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	4	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	1	no	—
574	C₂×C₄	—	4	1	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	8	2	no	—
577	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
578	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
579	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
580	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
581	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
582	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
583	C₈	—	2	4	no	—
584	C₈	—	4	2	no	—
585	C₈	—	4	2	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	2	1	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	1	no	—
591	C₂²	C₁₇×#456	1	2	yes	—
592	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
593	C₄	—	2	1	no	—
594	C₄	—	2	2	no	—
595	C₄	—	2	1	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	4	1	no	—
599	C₄	—	4	2	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	1	no	—
602	C₄	—	4	2	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	1	no	—
605	C₄	—	4	1	no	—
606	C₄	—	8	2	no	—
607	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
608	C₄	C₁₇×#575	1	1	yes	characteristic
609	C₄	C₁₇×#578	1	2	yes	—
610	C₂	—	2	2	no	—
611	C₂	—	8	1	no	—
612	C₂	C₁₇×#3006	1	1	yes	characteristic
613	C₂	C₁₇×#3011	1	1	yes	characteristic
614	C₂	C₂×C₁₇×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#121	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ 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
3. C₁₇×#3165	C₂	semidirect
4. C₂×C₁₇×#462	C₂	semidirect
5. C₁₇×#1653	C₂	semidirect
6. C₁₇×#1652	C₂	semidirect
7. C₁₇×#1649	C₂	semidirect
8. C₁₇×#1648	C₂	semidirect
9. C₁₇×#1552	C₂	semidirect
10. C₁₇×#1491	C₂	semidirect
232. #18588	C₁₇	direct (N × H)
281. #3165	C₂×C₁₇	semidirect
282. C₂×#462	C₂×C₁₇	semidirect
283. #1653	C₂×C₁₇	semidirect
284. #1652	C₂×C₁₇	semidirect
285. #1649	C₂×C₁₇	semidirect
286. #1648	C₂×C₁₇	semidirect
287. #1552	C₂×C₁₇	semidirect
288. #1491	C₂×C₁₇	semidirect
454. C₁₇	#18588	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×#3523	2
C₁₇×#3239	2
C₁₇×#3165	2
C₂×C₁₇×#462	2
C₁₇×#1653	2
C₁₇×#1652	2
C₁₇×#1649	2
C₁₇×#1648	2
C₁₇×#1552	2
C₁₇×#1491	2
C₁₇×#1483	2
#18588	17

Subgroups — C17×#18588 #16876332

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18588 #16876332