Subgroups — C₁₇×#18580 #16876324

Order 4352.

962 conjugacy classes of subgroups.

The subgroup lattice has 646 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, complemented
2	C₁₇×#3217	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₁₇×#460	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1628	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1627	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1626	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1626	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, complemented
12	C₂²×SD₁₆×C₁₇	—	2	1	no	—
13	C₁₇×#557	—	2	1	no	—
14	C₁₇×#557	C₂²	1	1	yes	characteristic, complemented
15	C₁₇×#557	C₂²	1	1	yes	characteristic, complemented
16	C₁₇×#556	—	2	1	no	—
17	C₁₇×#556	C₂²	1	1	yes	characteristic, complemented
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, complemented
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×#127	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×#496	—	2	1	no	—
32	C₁₇×#490	—	2	1	no	—
33	C₁₇×#490	—	2	2	no	—
34	C₁₇×#486	C₂²	1	2	yes	—
35	C₁₇×#486	C₂²	1	2	yes	—
36	C₁₇×#460	—	2	1	no	—
37	C₁₇×#460	—	2	1	no	—
38	C₁₇×#460	C₂²	1	2	yes	—
39	C₁₇×#460	C₂²	1	2	yes	—
40	C₁₇×#460	C₂²	1	2	yes	—
41	C₁₇×#459	C₂²	1	2	yes	—
42	C₁₇×#450	—	2	1	no	—
43	C₁₇×#447	—	2	1	no	—
44	C₁₇×#432	C₂²	1	1	yes	characteristic
45	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
46	C₁₇×#418	—	2	2	no	—
47	C₂×C₁₇×#102	—	2	1	no	—
48	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#332	C₂²	1	2	yes	complemented
50	C₁₇×#332	C₂²	1	2	yes	complemented
51	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
53	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
54	C₁₇×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂²×Q₈×C₁₇	—	2	1	no	—
56	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₁₇	—	2	1	no	—
58	C₂²×D₄×C₁₇	—	2	1	no	—
59	C₂²×D₄×C₁₇	—	2	1	no	—
60	C₂×SD₁₆×C₁₇	—	2	2	no	—
61	C₂×SD₁₆×C₁₇	—	2	2	no	—
62	C₂×SD₁₆×C₁₇	—	2	2	no	—
63	C₂×SD₁₆×C₁₇	—	4	4	no	—
64	C₂×D₈×C₁₇	—	2	2	no	—
65	C₂×M₁₆×C₁₇	—	2	1	no	—
66	C₂²×C₈×C₁₇	—	2	1	no	—
67	C₁₇×C₄⋊Q₈	—	2	2	no	—
68	C₁₇×C₄⋊Q₈	—	2	1	no	—
69	C₁₇×C₄⋊Q₈	—	2	1	no	—
70	C₁₇×C₄⋊Q₈	—	2	1	no	—
71	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
72	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
73	C₁₇×#127	—	2	1	no	—
74	C₁₇×#127	—	2	1	no	—
75	C₁₇×#127	—	2	1	no	—
76	C₁₇×#127	C₂³	1	2	yes	—
77	C₁₇×#126	—	2	2	no	—
78	C₁₇×#126	—	2	2	no	—
79	C₁₇×#126	—	2	2	no	—
80	C₁₇×#126	—	2	2	no	—
81	C₁₇×#126	—	2	1	no	—
82	C₁₇×#125	—	2	2	no	—
83	C₁₇×#125	—	2	2	no	—
84	C₁₇×#125	—	2	2	no	—
85	C₁₇×#125	—	2	1	no	—
86	C₁₇×#125	—	2	2	no	—
87	C₁₇×#125	—	2	2	no	—
88	C₁₇×#125	—	2	1	no	—
89	C₁₇×#125	D₄	1	1	yes	characteristic
90	C₁₇×#125	D₄	1	2	yes	—
91	C₁₇×#124	—	2	1	no	—
92	C₁₇×#124	D₄	1	1	yes	characteristic
93	C₁₇×#123	—	2	2	no	—
94	C₁₇×#123	—	2	1	no	—
95	C₁₇×C₂²⋊Q₈	—	2	2	no	—
96	C₁₇×C₂²⋊Q₈	—	2	2	no	—
97	C₁₇×C₂²⋊Q₈	—	2	1	no	—
98	C₁₇×C₂²⋊Q₈	—	2	1	no	—
99	C₁₇×C₂²⋊Q₈	—	2	1	no	—
100	C₁₇×C₂²⋊Q₈	—	2	1	no	—
101	C₁₇×C₂²⋊Q₈	—	2	2	no	—
102	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
103	C₁₇×#121	D₄	1	1	yes	characteristic
104	C₄×Q₈×C₁₇	—	2	2	no	—
105	C₄×Q₈×C₁₇	—	2	2	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	—	2	1	no	—
112	C₄×Q₈×C₁₇	—	2	1	no	—
113	C₄×Q₈×C₁₇	—	2	1	no	—
114	C₄×Q₈×C₁₇	—	2	1	no	—
115	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
116	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
118	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
119	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₁₇	—	2	2	no	—
121	C₄×D₄×C₁₇	—	2	1	no	—
122	C₄×D₄×C₁₇	—	2	1	no	—
123	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
124	C₁₇×#117	—	2	2	no	—
125	C₁₇×#117	—	2	2	no	—
126	C₁₇×#117	—	2	2	no	—
127	C₁₇×#117	—	2	1	no	—
128	C₁₇×#117	—	2	1	no	—
129	C₁₇×#117	D₄	1	2	yes	—
130	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
131	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
132	C₂×C₄²×C₁₇	—	2	1	no	—
133	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
134	C₁₇×C₄⋊C₈	—	2	1	no	—
135	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
136	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
137	C₁₇×#102	—	2	2	no	—
138	C₁₇×#102	—	2	2	no	—
139	C₁₇×#102	—	2	4	no	—
140	C₁₇×#102	—	2	4	no	—
141	C₁₇×#102	—	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	C₂⁴×C₁₇	—	4	1	no	—
148	C₂×Q₈×C₁₇	—	2	2	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	—	2	1	no	—
151	C₂×Q₈×C₁₇	—	2	1	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	C₂×D₄	1	1	yes	characteristic
157	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
158	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₇	—	2	1	no	—
160	C₂×D₄×C₁₇	—	2	2	no	—
161	C₂×D₄×C₁₇	—	2	2	no	—
162	C₂×D₄×C₁₇	—	2	2	no	—
163	C₂×D₄×C₁₇	—	4	2	no	—
164	C₂×D₄×C₁₇	—	4	4	no	—
165	C₂×D₄×C₁₇	—	4	2	no	—
166	C₂×D₄×C₁₇	—	4	1	no	—
167	C₂×D₄×C₁₇	—	4	1	no	—
168	C₂×D₄×C₁₇	—	4	1	no	—
169	C₂×D₄×C₁₇	—	8	2	no	—
170	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₇	—	2	2	no	—
172	C₂²×C₄×C₁₇	—	2	1	no	—
173	C₂²×C₄×C₁₇	—	2	1	no	—
174	C₂²×C₄×C₁₇	—	2	1	no	—
175	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
177	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
178	SD₁₆×C₁₇	—	4	4	no	—
179	SD₁₆×C₁₇	—	4	4	no	—
180	SD₁₆×C₁₇	—	8	2	no	—
181	D₈×C₁₇	—	8	2	no	—
182	M₁₆×C₁₇	—	4	2	no	—
183	C₂×C₈×C₁₇	—	2	2	no	—
184	C₂×C₈×C₁₇	—	2	2	no	—
185	C₂×C₈×C₁₇	—	2	2	no	—
186	C₂×C₈×C₁₇	—	4	2	no	—
187	C₄⋊C₄×C₁₇	—	2	2	no	—
188	C₄⋊C₄×C₁₇	—	2	2	no	—
189	C₄⋊C₄×C₁₇	—	2	2	no	—
190	C₄⋊C₄×C₁₇	—	2	2	no	—
191	C₄⋊C₄×C₁₇	—	2	2	no	—
192	C₄⋊C₄×C₁₇	—	2	2	no	—
193	C₄⋊C₄×C₁₇	—	2	2	no	—
194	C₄⋊C₄×C₁₇	—	2	2	no	—
195	C₄⋊C₄×C₁₇	—	2	2	no	—
196	C₄⋊C₄×C₁₇	—	2	2	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	1	no	—
201	C₄⋊C₄×C₁₇	—	2	1	no	—
202	C₄⋊C₄×C₁₇	—	2	1	no	—
203	C₄⋊C₄×C₁₇	—	2	1	no	—
204	C₄⋊C₄×C₁₇	—	2	1	no	—
205	C₄⋊C₄×C₁₇	—	2	1	no	—
206	C₄⋊C₄×C₁₇	—	2	1	no	—
207	C₄⋊C₄×C₁₇	—	2	1	no	—
208	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
212	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
213	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
214	C₂²⋊C₄×C₁₇	—	2	2	no	—
215	C₂²⋊C₄×C₁₇	—	2	2	no	—
216	C₂²⋊C₄×C₁₇	—	2	2	no	—
217	C₂²⋊C₄×C₁₇	—	2	2	no	—
218	C₂²⋊C₄×C₁₇	—	2	1	no	—
219	C₂²⋊C₄×C₁₇	—	2	1	no	—
220	C₂²⋊C₄×C₁₇	—	2	1	no	—
221	C₂²⋊C₄×C₁₇	—	2	1	no	—
222	C₂²⋊C₄×C₁₇	—	2	1	no	—
223	C₄²×C₁₇	—	2	2	no	—
224	C₄²×C₁₇	—	2	2	no	—
225	C₄²×C₁₇	—	2	2	no	—
226	C₄²×C₁₇	—	2	1	no	—
227	C₄²×C₁₇	—	2	2	no	—
228	C₄²×C₁₇	—	2	1	no	—
229	C₄²×C₁₇	—	2	1	no	—
230	C₄²×C₁₇	—	2	1	no	—
231	C₄²×C₁₇	—	2	1	no	—
232	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
233	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
234	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
235	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
236	#18580	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
237	C₂³×C₁₇	—	2	1	no	—
238	C₂³×C₁₇	—	4	2	no	—
239	C₂³×C₁₇	—	8	2	no	—
240	C₂³×C₁₇	—	8	2	no	—
241	C₂³×C₁₇	—	8	2	no	—
242	C₂³×C₁₇	#120	1	1	yes	characteristic
243	Q₈×C₁₇	—	2	1	no	—
244	Q₈×C₁₇	—	2	1	no	—
245	Q₈×C₁₇	—	2	1	no	—
246	Q₈×C₁₇	—	2	2	no	—
247	Q₈×C₁₇	—	4	2	no	—
248	Q₈×C₁₇	—	4	4	no	—
249	Q₈×C₁₇	—	4	1	no	—
250	Q₈×C₁₇	—	4	1	no	—
251	Q₈×C₁₇	—	4	2	no	—
252	Q₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
253	D₄×C₁₇	—	2	2	no	—
254	D₄×C₁₇	—	4	4	no	—
255	D₄×C₁₇	—	4	2	no	—
256	D₄×C₁₇	—	4	2	no	—
257	D₄×C₁₇	—	4	2	no	—
258	D₄×C₁₇	—	4	2	no	—
259	D₄×C₁₇	—	4	2	no	—
260	D₄×C₁₇	—	8	2	no	—
261	D₄×C₁₇	—	8	2	no	—
262	D₄×C₁₇	—	8	2	no	—
263	C₂×C₄×C₁₇	—	2	1	no	—
264	C₂×C₄×C₁₇	—	2	2	no	—
265	C₂×C₄×C₁₇	—	2	1	no	—
266	C₂×C₄×C₁₇	—	2	1	no	—
267	C₂×C₄×C₁₇	—	2	2	no	—
268	C₂×C₄×C₁₇	—	2	1	no	—
269	C₂×C₄×C₁₇	—	2	1	no	—
270	C₂×C₄×C₁₇	—	2	2	no	—
271	C₂×C₄×C₁₇	—	2	1	no	—
272	C₂×C₄×C₁₇	—	2	1	no	—
273	C₂×C₄×C₁₇	—	2	1	no	—
274	C₂×C₄×C₁₇	—	2	1	no	—
275	C₂×C₄×C₁₇	—	2	2	no	—
276	C₂×C₄×C₁₇	—	4	2	no	—
277	C₂×C₄×C₁₇	—	4	4	no	—
278	C₂×C₄×C₁₇	—	4	2	no	—
279	C₂×C₄×C₁₇	—	4	1	no	—
280	C₂×C₄×C₁₇	—	4	1	no	—
281	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
282	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
283	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
284	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
285	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
286	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
287	C₈×C₁₇	—	4	2	no	—
288	C₈×C₁₇	—	4	2	no	—
289	C₈×C₁₇	—	4	2	no	—
290	#3523	C₂×C₁₇	1	1	yes	characteristic, complemented
291	#3217	C₂×C₁₇	1	1	yes	characteristic
292	#3138	C₂×C₁₇	1	1	yes	characteristic, complemented
293	C₂×#460	C₂×C₁₇	1	1	yes	characteristic, complemented
294	#1628	C₂×C₁₇	1	2	yes	complemented
295	#1627	C₂×C₁₇	1	2	yes	complemented
296	#1626	C₂×C₁₇	1	2	yes	complemented
297	#1626	C₂×C₁₇	1	2	yes	complemented
298	#1552	C₂×C₁₇	1	1	yes	characteristic, complemented
299	#1491	C₂×C₁₇	1	1	yes	characteristic, complemented
300	#1483	C₂×C₁₇	1	1	yes	characteristic, complemented
301	C₂²×C₁₇	—	2	1	no	—
302	C₂²×C₁₇	—	2	1	no	—
303	C₂²×C₁₇	—	4	1	no	—
304	C₂²×C₁₇	—	4	1	no	—
305	C₂²×C₁₇	—	4	1	no	—
306	C₂²×C₁₇	—	8	2	no	—
307	C₂²×C₁₇	—	8	2	no	—
308	C₂²×C₁₇	—	8	2	no	—
309	C₂²×C₁₇	—	16	4	no	—
310	C₂²×C₁₇	#454	1	2	yes	—
311	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
312	C₄×C₁₇	—	2	1	no	—
313	C₄×C₁₇	—	2	2	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	1	no	—
316	C₄×C₁₇	—	2	1	no	—
317	C₄×C₁₇	—	4	1	no	—
318	C₄×C₁₇	—	4	2	no	—
319	C₄×C₁₇	—	4	1	no	—
320	C₄×C₁₇	—	4	1	no	—
321	C₄×C₁₇	—	4	2	no	—
322	C₄×C₁₇	—	4	1	no	—
323	C₄×C₁₇	—	4	1	no	—
324	C₄×C₁₇	—	4	1	no	—
325	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
326	C₄×C₁₇	#575	1	1	yes	characteristic
327	C₄×C₁₇	#577	1	2	yes	—
328	C₂²×SD₁₆	—	2	1	no	—
329	#557	—	2	1	no	—
330	#557	C₂²×C₁₇	1	1	yes	characteristic, complemented
331	#557	C₂²×C₁₇	1	1	yes	characteristic, complemented
332	#556	—	2	1	no	—
333	#556	C₂²×C₁₇	1	1	yes	characteristic, complemented
334	#552	—	2	2	no	—
335	#552	—	2	1	no	—
336	D₄×Q₈	—	2	1	no	—
337	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic, complemented
338	#541	—	2	2	no	—
339	#541	—	2	1	no	—
340	#533	—	2	1	no	—
341	#533	C₂²×C₁₇	1	1	yes	characteristic
342	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
343	#529	—	2	1	no	—
344	#529	C₂²×C₁₇	1	1	yes	characteristic
345	#519	—	2	1	no	—
346	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
347	#496	—	2	1	no	—
348	#490	—	2	2	no	—
349	#490	—	2	1	no	—
350	#486	C₂²×C₁₇	1	2	yes	—
351	#486	C₂²×C₁₇	1	2	yes	—
352	#460	—	2	1	no	—
353	#460	—	2	1	no	—
354	#460	C₂²×C₁₇	1	2	yes	—
355	#460	C₂²×C₁₇	1	2	yes	—
356	#460	C₂²×C₁₇	1	2	yes	—
357	#459	C₂²×C₁₇	1	2	yes	—
358	#450	—	2	1	no	—
359	#447	—	2	1	no	—
360	#432	C₂²×C₁₇	1	1	yes	characteristic
361	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
362	#418	—	2	2	no	—
363	C₂×#102	—	2	1	no	—
364	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
365	#332	C₂²×C₁₇	1	2	yes	complemented
366	#332	C₂²×C₁₇	1	2	yes	complemented
367	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	complemented
368	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	complemented
369	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	complemented
370	D₄⋊C₈	C₂²×C₁₇	1	2	yes	complemented
371	C₂×C₁₇	—	2	2	no	—
372	C₂×C₁₇	—	8	1	no	—
373	C₂×C₁₇	—	16	2	no	—
374	C₂×C₁₇	#3006	1	1	yes	characteristic
375	C₂×C₁₇	#3010	1	1	yes	characteristic
376	C₂×C₁₇	C₂×#454	1	1	yes	characteristic
377	C₂²×Q₈	—	2	1	no	—
378	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
379	C₂²×D₄	—	2	1	no	—
380	C₂²×D₄	—	2	1	no	—
381	C₂²×D₄	—	2	1	no	—
382	C₂×SD₁₆	—	2	2	no	—
383	C₂×SD₁₆	—	2	2	no	—
384	C₂×SD₁₆	—	2	2	no	—
385	C₂×SD₁₆	—	4	4	no	—
386	C₂×D₈	—	2	2	no	—
387	C₂×M₁₆	—	2	1	no	—
388	C₂²×C₈	—	2	1	no	—
389	C₄⋊Q₈	—	2	2	no	—
390	C₄⋊Q₈	—	2	1	no	—
391	C₄⋊Q₈	—	2	1	no	—
392	C₄⋊Q₈	—	2	1	no	—
393	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
394	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
395	#127	—	2	1	no	—
396	#127	—	2	1	no	—
397	#127	—	2	1	no	—
398	#127	C₂³×C₁₇	1	2	yes	—
399	#126	—	2	2	no	—
400	#126	—	2	2	no	—
401	#126	—	2	2	no	—
402	#126	—	2	2	no	—
403	#126	—	2	1	no	—
404	#125	—	2	2	no	—
405	#125	—	2	2	no	—
406	#125	—	2	2	no	—
407	#125	—	2	1	no	—
408	#125	—	2	2	no	—
409	#125	—	2	2	no	—
410	#125	—	2	1	no	—
411	#125	D₄×C₁₇	1	1	yes	characteristic
412	#125	D₄×C₁₇	1	2	yes	—
413	#124	—	2	1	no	—
414	#124	D₄×C₁₇	1	1	yes	characteristic
415	#123	—	2	2	no	—
416	#123	—	2	1	no	—
417	C₂²⋊Q₈	—	2	2	no	—
418	C₂²⋊Q₈	—	2	2	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	C₂²⋊Q₈	—	2	1	no	—
421	C₂²⋊Q₈	—	2	1	no	—
422	C₂²⋊Q₈	—	2	1	no	—
423	C₂²⋊Q₈	—	2	2	no	—
424	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
425	#121	D₄×C₁₇	1	1	yes	characteristic
426	C₄×Q₈	—	2	2	no	—
427	C₄×Q₈	—	2	2	no	—
428	C₄×Q₈	—	2	1	no	—
429	C₄×Q₈	—	2	1	no	—
430	C₄×Q₈	—	2	1	no	—
431	C₄×Q₈	—	2	1	no	—
432	C₄×Q₈	—	2	1	no	—
433	C₄×Q₈	—	2	1	no	—
434	C₄×Q₈	—	2	1	no	—
435	C₄×Q₈	—	2	1	no	—
436	C₄×Q₈	—	2	1	no	—
437	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
438	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
439	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
440	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
441	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
442	C₄×D₄	—	2	2	no	—
443	C₄×D₄	—	2	1	no	—
444	C₄×D₄	—	2	1	no	—
445	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
446	#117	—	2	2	no	—
447	#117	—	2	2	no	—
448	#117	—	2	2	no	—
449	#117	—	2	1	no	—
450	#117	—	2	1	no	—
451	#117	D₄×C₁₇	1	2	yes	—
452	C₂×C₄⋊C₄	—	2	1	no	—
453	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
454	C₂×C₄²	—	2	1	no	—
455	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
456	C₄⋊C₈	—	2	1	no	—
457	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
458	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
459	#102	—	2	2	no	—
460	#102	—	2	2	no	—
461	#102	—	2	4	no	—
462	#102	—	2	4	no	—
463	#102	—	2	2	no	—
464	#102	—	2	2	no	—
465	C₂²⋊C₈	—	2	1	no	—
466	#97	—	2	1	no	—
467	#97	—	2	1	no	—
468	C₄×C₈	C₂³×C₁₇	1	2	yes	—
469	C₁₇	#18580	1	1	yes	characteristic, direct product factor, Sylow
470	C₂⁴	—	4	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	—	2	1	no	—
475	C₂×Q₈	—	2	2	no	—
476	C₂×Q₈	—	4	1	no	—
477	C₂×Q₈	—	4	2	no	—
478	C₂×Q₈	—	4	2	no	—
479	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
480	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	2	no	—
484	C₂×D₄	—	2	2	no	—
485	C₂×D₄	—	2	2	no	—
486	C₂×D₄	—	4	2	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	2	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	—	4	1	no	—
492	C₂×D₄	—	8	2	no	—
493	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
494	C₂²×C₄	—	2	2	no	—
495	C₂²×C₄	—	2	1	no	—
496	C₂²×C₄	—	2	1	no	—
497	C₂²×C₄	—	2	1	no	—
498	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
499	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
500	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
501	SD₁₆	—	4	4	no	—
502	SD₁₆	—	4	4	no	—
503	SD₁₆	—	8	2	no	—
504	D₈	—	8	2	no	—
505	M₁₆	—	4	2	no	—
506	C₂×C₈	—	2	2	no	—
507	C₂×C₈	—	2	2	no	—
508	C₂×C₈	—	2	2	no	—
509	C₂×C₈	—	4	2	no	—
510	C₄⋊C₄	—	2	2	no	—
511	C₄⋊C₄	—	2	2	no	—
512	C₄⋊C₄	—	2	2	no	—
513	C₄⋊C₄	—	2	2	no	—
514	C₄⋊C₄	—	2	2	no	—
515	C₄⋊C₄	—	2	2	no	—
516	C₄⋊C₄	—	2	2	no	—
517	C₄⋊C₄	—	2	2	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	2	1	no	—
521	C₄⋊C₄	—	2	1	no	—
522	C₄⋊C₄	—	2	1	no	—
523	C₄⋊C₄	—	2	1	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	2	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
533	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
534	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
535	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	2	no	—
538	C₂²⋊C₄	—	2	2	no	—
539	C₂²⋊C₄	—	2	2	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	2	no	—
542	C₂²⋊C₄	—	2	1	no	—
543	C₂²⋊C₄	—	2	1	no	—
544	C₂²⋊C₄	—	2	1	no	—
545	C₂²⋊C₄	—	2	1	no	—
546	C₄²	—	2	2	no	—
547	C₄²	—	2	2	no	—
548	C₄²	—	2	2	no	—
549	C₄²	—	2	1	no	—
550	C₄²	—	2	1	no	—
551	C₄²	—	2	1	no	—
552	C₄²	—	2	1	no	—
553	C₄²	—	2	1	no	—
554	C₄²	—	2	2	no	—
555	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
556	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
557	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
558	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
559	C₂³	—	2	1	no	—
560	C₂³	—	4	2	no	—
561	C₂³	—	8	2	no	—
562	C₂³	—	8	2	no	—
563	C₂³	—	8	2	no	—
564	C₂³	C₁₇×#120	1	1	yes	characteristic
565	Q₈	—	2	1	no	—
566	Q₈	—	2	1	no	—
567	Q₈	—	2	1	no	—
568	Q₈	—	2	2	no	—
569	Q₈	—	4	2	no	—
570	Q₈	—	4	4	no	—
571	Q₈	—	4	1	no	—
572	Q₈	—	4	1	no	—
573	Q₈	—	4	2	no	—
574	Q₈	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
575	D₄	—	2	2	no	—
576	D₄	—	4	4	no	—
577	D₄	—	4	2	no	—
578	D₄	—	4	2	no	—
579	D₄	—	4	2	no	—
580	D₄	—	4	2	no	—
581	D₄	—	4	2	no	—
582	D₄	—	8	2	no	—
583	D₄	—	8	2	no	—
584	D₄	—	8	2	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	1	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	1	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	2	no	—
593	C₂×C₄	—	2	1	no	—
594	C₂×C₄	—	2	1	no	—
595	C₂×C₄	—	2	1	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	2	no	—
598	C₂×C₄	—	4	2	no	—
599	C₂×C₄	—	4	4	no	—
600	C₂×C₄	—	4	2	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
604	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
605	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
606	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
607	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
608	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
609	C₈	—	4	2	no	—
610	C₈	—	4	2	no	—
611	C₈	—	4	2	no	—
612	C₂²	—	2	1	no	—
613	C₂²	—	2	1	no	—
614	C₂²	—	4	1	no	—
615	C₂²	—	4	1	no	—
616	C₂²	—	4	1	no	—
617	C₂²	—	8	2	no	—
618	C₂²	—	8	2	no	—
619	C₂²	—	8	2	no	—
620	C₂²	—	16	4	no	—
621	C₂²	C₁₇×#454	1	2	yes	—
622	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
623	C₄	—	2	1	no	—
624	C₄	—	2	2	no	—
625	C₄	—	2	1	no	—
626	C₄	—	2	1	no	—
627	C₄	—	2	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	2	no	—
630	C₄	—	4	1	no	—
631	C₄	—	4	1	no	—
632	C₄	—	4	2	no	—
633	C₄	—	4	1	no	—
634	C₄	—	4	1	no	—
635	C₄	—	4	1	no	—
636	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
637	C₄	C₁₇×#575	1	1	yes	characteristic
638	C₄	C₁₇×#577	1	2	yes	—
639	C₂	—	2	2	no	—
640	C₂	—	8	1	no	—
641	C₂	—	16	2	no	—
642	C₂	C₁₇×#3006	1	1	yes	characteristic
643	C₂	C₁₇×#3010	1	1	yes	characteristic
644	C₂	C₂×C₁₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3217	C₂
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
1. C₁₇×#3523	C₂	semidirect
3. C₁₇×#3138	C₂	semidirect
4. C₂×C₁₇×#460	C₂	semidirect
5. C₁₇×#1628	C₂	semidirect
6. C₁₇×#1627	C₂	semidirect
7. C₁₇×#1626	C₂	semidirect
8. C₁₇×#1626	C₂	semidirect
9. C₁₇×#1552	C₂	semidirect
10. C₁₇×#1491	C₂	semidirect
11. C₁₇×#1483	C₂	semidirect
14. C₁₇×#557	C₂²	semidirect
15. C₁₇×#557	C₂²	semidirect
17. C₁₇×#556	C₂²	semidirect
21. D₄×Q₈×C₁₇	C₂²	semidirect
49. C₁₇×#332	C₂²	semidirect
50. C₁₇×#332	C₂²	semidirect
51. C₁₇×Q₈⋊C₈	C₂²	semidirect
52. C₁₇×Q₈⋊C₈	C₂²	semidirect
53. C₁₇×Q₈⋊C₈	C₂²	semidirect
54. C₁₇×D₄⋊C₈	C₂²	semidirect
236. #18580	C₁₇	direct (N × H)
290. #3523	C₂×C₁₇	semidirect
292. #3138	C₂×C₁₇	semidirect
293. C₂×#460	C₂×C₁₇	semidirect
294. #1628	C₂×C₁₇	semidirect
295. #1627	C₂×C₁₇	semidirect
296. #1626	C₂×C₁₇	semidirect
297. #1626	C₂×C₁₇	semidirect
298. #1552	C₂×C₁₇	semidirect
299. #1491	C₂×C₁₇	semidirect
300. #1483	C₂×C₁₇	semidirect
330. #557	C₂²×C₁₇	semidirect
331. #557	C₂²×C₁₇	semidirect
333. #556	C₂²×C₁₇	semidirect
337. D₄×Q₈	C₂²×C₁₇	semidirect
365. #332	C₂²×C₁₇	semidirect
366. #332	C₂²×C₁₇	semidirect
367. Q₈⋊C₈	C₂²×C₁₇	semidirect
368. Q₈⋊C₈	C₂²×C₁₇	semidirect
369. Q₈⋊C₈	C₂²×C₁₇	semidirect
370. D₄⋊C₈	C₂²×C₁₇	semidirect
469. C₁₇	#18580	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×#3217	2
C₁₇×#3138	2
C₂×C₁₇×#460	2
C₁₇×#1628	2
C₁₇×#1627	2
C₁₇×#1626	2
C₁₇×#1552	2
C₁₇×#1491	2
C₁₇×#1483	2
#18580	17

Subgroups — C17×#18580 #16876324

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18580 #16876324