Subgroups — C₁₇×#18649 #16876393

Order 4352.

868 conjugacy classes of subgroups.

The subgroup lattice has 706 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×#3248	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3113	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1653	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1653	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1652	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1651	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1650	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1648	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1552	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1494	C₂	1	1	yes	maximal, characteristic
15	C₂×C₁₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#557	—	2	1	no	—
17	C₁₇×#557	C₂²	1	1	yes	characteristic
18	C₁₇×#557	C₂²	1	1	yes	characteristic
19	C₁₇×#556	—	2	1	no	—
20	C₁₇×#556	C₂²	1	1	yes	characteristic
21	C₁₇×#552	—	2	2	no	—
22	C₁₇×#552	—	2	1	no	—
23	D₄×Q₈×C₁₇	—	2	1	no	—
24	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#541	—	2	1	no	—
26	C₁₇×#541	—	2	2	no	—
27	C₁₇×#533	—	2	1	no	—
28	C₁₇×#533	C₂²	1	1	yes	characteristic
29	C₁₇×#533	C₂²	1	1	yes	characteristic
30	C₁₇×#529	—	2	1	no	—
31	C₁₇×#529	C₂²	1	1	yes	characteristic
32	C₁₇×#519	—	2	1	no	—
33	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
34	C₁₇×#500	C₂²	1	1	yes	characteristic
35	C₁₇×#500	C₂²	1	1	yes	characteristic
36	C₁₇×#499	—	2	2	no	—
37	C₁₇×#498	C₂²	1	1	yes	characteristic
38	C₁₇×#498	C₂²	1	1	yes	characteristic
39	C₁₇×#483	—	2	1	no	—
40	C₁₇×#479	—	2	1	no	—
41	C₁₇×#475	C₂²	1	1	yes	characteristic
42	C₁₇×#475	C₂²	1	1	yes	characteristic
43	C₁₇×#475	C₂²	1	1	yes	characteristic
44	C₁₇×#474	C₂²	1	1	yes	characteristic
45	C₁₇×#467	—	2	1	no	—
46	C₁₇×#465	—	2	1	no	—
47	C₁₇×#464	—	2	1	no	—
48	C₁₇×#462	C₂²	1	1	yes	characteristic
49	C₁₇×#462	C₂²	1	1	yes	characteristic
50	C₁₇×#462	C₂²	1	1	yes	characteristic
51	C₁₇×#461	C₂²	1	1	yes	characteristic
52	C₁₇×#451	—	2	1	no	—
53	C₁₇×#441	—	2	1	no	—
54	C₁₇×#441	—	2	1	no	—
55	C₁₇×#432	C₂²	1	1	yes	characteristic
56	C₁₇×#427	—	2	2	no	—
57	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
58	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#332	C₂²	1	1	yes	characteristic
60	C₁₇×#332	C₂²	1	1	yes	characteristic
61	C₁₇×#332	C₂²	1	1	yes	characteristic
62	C₁₇×#332	C₂²	1	1	yes	characteristic
63	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
67	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
68	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
69	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
70	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
71	C₂²×Q₈×C₁₇	—	2	1	no	—
72	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
73	C₂×Q₁₆×C₁₇	—	2	1	no	—
74	C₂×Q₁₆×C₁₇	—	2	1	no	—
75	C₂×Q₁₆×C₁₇	—	2	1	no	—
76	C₂×SD₁₆×C₁₇	—	2	1	no	—
77	C₂²×C₈×C₁₇	—	2	1	no	—
78	C₂²×C₈×C₁₇	—	2	1	no	—
79	C₁₇×C₄⋊Q₈	—	2	2	no	—
80	C₁₇×C₄⋊Q₈	—	2	1	no	—
81	C₁₇×C₄⋊Q₈	—	2	1	no	—
82	C₁₇×C₄⋊Q₈	—	2	1	no	—
83	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
84	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
85	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
86	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
87	C₁₇×#126	—	2	2	no	—
88	C₁₇×#126	—	2	2	no	—
89	C₁₇×#126	—	2	2	no	—
90	C₁₇×#126	—	2	2	no	—
91	C₁₇×#126	—	2	1	no	—
92	C₁₇×#125	—	2	2	no	—
93	C₁₇×#125	—	2	2	no	—
94	C₁₇×#125	—	2	2	no	—
95	C₁₇×#125	—	2	1	no	—
96	C₁₇×#125	—	2	2	no	—
97	C₁₇×#125	—	2	2	no	—
98	C₁₇×#125	—	2	1	no	—
99	C₁₇×#125	—	2	1	no	—
100	C₁₇×#125	D₄	1	2	yes	—
101	C₁₇×#125	D₄	1	1	yes	characteristic
102	C₁₇×#124	—	2	1	no	—
103	C₁₇×#124	D₄	1	1	yes	characteristic
104	C₁₇×#123	—	2	2	no	—
105	C₁₇×#123	—	2	1	no	—
106	C₁₇×C₂²⋊Q₈	—	2	2	no	—
107	C₁₇×C₂²⋊Q₈	—	2	2	no	—
108	C₁₇×C₂²⋊Q₈	—	2	1	no	—
109	C₁₇×C₂²⋊Q₈	—	2	1	no	—
110	C₁₇×C₂²⋊Q₈	—	2	1	no	—
111	C₁₇×C₂²⋊Q₈	—	2	1	no	—
112	C₁₇×C₂²⋊Q₈	—	2	2	no	—
113	C₁₇×C₂²⋊Q₈	—	2	1	no	—
114	C₁₇×C₂²⋊Q₈	—	2	1	no	—
115	C₁₇×C₂²⋊Q₈	D₄	1	1	yes	characteristic
116	C₁₇×#121	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₇	—	2	2	no	—
118	C₄×Q₈×C₁₇	—	2	2	no	—
119	C₄×Q₈×C₁₇	—	2	1	no	—
120	C₄×Q₈×C₁₇	—	2	1	no	—
121	C₄×Q₈×C₁₇	—	2	1	no	—
122	C₄×Q₈×C₁₇	—	2	1	no	—
123	C₄×Q₈×C₁₇	—	2	1	no	—
124	C₄×Q₈×C₁₇	—	2	1	no	—
125	C₄×Q₈×C₁₇	—	2	1	no	—
126	C₄×Q₈×C₁₇	—	2	1	no	—
127	C₄×Q₈×C₁₇	—	2	1	no	—
128	C₄×Q₈×C₁₇	—	2	1	no	—
129	C₄×Q₈×C₁₇	—	2	1	no	—
130	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
131	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
132	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
133	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
135	C₄×D₄×C₁₇	—	2	2	no	—
136	C₄×D₄×C₁₇	—	2	1	no	—
137	C₄×D₄×C₁₇	—	2	1	no	—
138	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
139	C₁₇×#117	—	2	2	no	—
140	C₁₇×#117	—	2	2	no	—
141	C₁₇×#117	—	2	2	no	—
142	C₁₇×#117	—	2	1	no	—
143	C₁₇×#117	—	2	1	no	—
144	C₁₇×#117	—	2	1	no	—
145	C₁₇×#117	D₄	1	2	yes	—
146	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
147	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
148	C₂×C₄²×C₁₇	—	2	1	no	—
149	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
150	C₁₇×#107	—	2	2	no	—
151	C₁₇×#107	—	2	2	no	—
152	C₁₇×#107	—	2	1	no	—
153	C₁₇×#106	—	2	2	no	—
154	C₁₇×#106	—	2	2	no	—
155	C₁₇×#106	—	2	1	no	—
156	C₁₇×#106	—	2	1	no	—
157	C₁₇×#106	—	2	1	no	—
158	C₁₇×C₄⋊C₈	—	2	1	no	—
159	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
160	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
161	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
162	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
163	C₁₇×#103	—	2	1	no	—
164	C₁₇×#103	—	2	1	no	—
165	C₁₇×#103	—	2	1	no	—
166	C₁₇×#103	—	2	1	no	—
167	C₁₇×#103	—	2	1	no	—
168	C₁₇×#103	—	2	1	no	—
169	C₁₇×#103	—	2	1	no	—
170	C₁₇×#102	—	2	1	no	—
171	C₁₇×C₂²⋊C₈	—	2	1	no	—
172	C₁₇×#97	—	2	1	no	—
173	C₄×C₈×C₁₇	—	2	1	no	—
174	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
175	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
176	C₂×Q₈×C₁₇	—	2	2	no	—
177	C₂×Q₈×C₁₇	—	2	1	no	—
178	C₂×Q₈×C₁₇	—	2	1	no	—
179	C₂×Q₈×C₁₇	—	2	1	no	—
180	C₂×Q₈×C₁₇	—	2	2	no	—
181	C₂×Q₈×C₁₇	—	2	1	no	—
182	C₂×Q₈×C₁₇	—	2	1	no	—
183	C₂×Q₈×C₁₇	—	4	1	no	—
184	C₂×Q₈×C₁₇	—	4	2	no	—
185	C₂×Q₈×C₁₇	—	4	2	no	—
186	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
188	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
189	C₂×D₄×C₁₇	—	2	1	no	—
190	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₁₇	—	2	2	no	—
192	C₂²×C₄×C₁₇	—	2	1	no	—
193	C₂²×C₄×C₁₇	—	2	1	no	—
194	C₂²×C₄×C₁₇	—	2	1	no	—
195	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
198	Q₁₆×C₁₇	—	4	2	no	—
199	Q₁₆×C₁₇	—	4	2	no	—
200	Q₁₆×C₁₇	—	8	1	no	—
201	SD₁₆×C₁₇	—	8	1	no	—
202	C₂×C₈×C₁₇	—	2	4	no	—
203	C₂×C₈×C₁₇	—	2	1	no	—
204	C₂×C₈×C₁₇	—	2	1	no	—
205	C₂×C₈×C₁₇	—	2	1	no	—
206	C₂×C₈×C₁₇	—	2	1	no	—
207	C₂×C₈×C₁₇	—	2	1	no	—
208	C₂×C₈×C₁₇	—	2	1	no	—
209	C₂×C₈×C₁₇	—	8	1	no	—
210	C₄⋊C₄×C₁₇	—	2	2	no	—
211	C₄⋊C₄×C₁₇	—	2	2	no	—
212	C₄⋊C₄×C₁₇	—	2	2	no	—
213	C₄⋊C₄×C₁₇	—	2	2	no	—
214	C₄⋊C₄×C₁₇	—	2	2	no	—
215	C₄⋊C₄×C₁₇	—	2	2	no	—
216	C₄⋊C₄×C₁₇	—	2	2	no	—
217	C₄⋊C₄×C₁₇	—	2	2	no	—
218	C₄⋊C₄×C₁₇	—	2	2	no	—
219	C₄⋊C₄×C₁₇	—	2	2	no	—
220	C₄⋊C₄×C₁₇	—	2	1	no	—
221	C₄⋊C₄×C₁₇	—	2	1	no	—
222	C₄⋊C₄×C₁₇	—	2	1	no	—
223	C₄⋊C₄×C₁₇	—	2	1	no	—
224	C₄⋊C₄×C₁₇	—	2	1	no	—
225	C₄⋊C₄×C₁₇	—	2	1	no	—
226	C₄⋊C₄×C₁₇	—	2	1	no	—
227	C₄⋊C₄×C₁₇	—	2	1	no	—
228	C₄⋊C₄×C₁₇	—	2	1	no	—
229	C₄⋊C₄×C₁₇	—	2	1	no	—
230	C₄⋊C₄×C₁₇	—	2	1	no	—
231	C₄⋊C₄×C₁₇	—	2	1	no	—
232	C₄⋊C₄×C₁₇	—	2	1	no	—
233	C₄⋊C₄×C₁₇	—	2	1	no	—
234	C₄⋊C₄×C₁₇	—	2	1	no	—
235	C₄⋊C₄×C₁₇	—	4	1	no	—
236	C₄⋊C₄×C₁₇	—	4	1	no	—
237	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
238	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
239	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
240	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
241	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
242	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
243	C₂²⋊C₄×C₁₇	—	2	2	no	—
244	C₂²⋊C₄×C₁₇	—	2	2	no	—
245	C₂²⋊C₄×C₁₇	—	2	2	no	—
246	C₂²⋊C₄×C₁₇	—	2	2	no	—
247	C₂²⋊C₄×C₁₇	—	2	1	no	—
248	C₂²⋊C₄×C₁₇	—	2	1	no	—
249	C₂²⋊C₄×C₁₇	—	2	1	no	—
250	C₂²⋊C₄×C₁₇	—	2	1	no	—
251	C₂²⋊C₄×C₁₇	—	2	1	no	—
252	C₂²⋊C₄×C₁₇	—	4	1	no	—
253	C₄²×C₁₇	—	2	2	no	—
254	C₄²×C₁₇	—	2	2	no	—
255	C₄²×C₁₇	—	2	2	no	—
256	C₄²×C₁₇	—	2	1	no	—
257	C₄²×C₁₇	—	2	2	no	—
258	C₄²×C₁₇	—	2	1	no	—
259	C₄²×C₁₇	—	2	1	no	—
260	C₄²×C₁₇	—	2	1	no	—
261	C₄²×C₁₇	—	2	1	no	—
262	C₄²×C₁₇	—	4	1	no	—
263	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
264	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
265	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
266	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
267	#18649	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
268	C₂³×C₁₇	—	2	1	no	—
269	C₂³×C₁₇	#120	1	1	yes	characteristic
270	Q₈×C₁₇	—	2	1	no	—
271	Q₈×C₁₇	—	2	1	no	—
272	Q₈×C₁₇	—	2	1	no	—
273	Q₈×C₁₇	—	2	1	no	—
274	Q₈×C₁₇	—	2	1	no	—
275	Q₈×C₁₇	—	4	2	no	—
276	Q₈×C₁₇	—	4	4	no	—
277	Q₈×C₁₇	—	4	1	no	—
278	Q₈×C₁₇	—	4	1	no	—
279	Q₈×C₁₇	—	4	1	no	—
280	Q₈×C₁₇	—	4	1	no	—
281	Q₈×C₁₇	—	4	1	no	—
282	Q₈×C₁₇	—	4	1	no	—
283	Q₈×C₁₇	—	4	1	no	—
284	Q₈×C₁₇	—	4	1	no	—
285	Q₈×C₁₇	#135	1	2	yes	—
286	D₄×C₁₇	—	2	1	no	—
287	D₄×C₁₇	—	2	1	no	—
288	D₄×C₁₇	—	4	2	no	—
289	C₂×C₄×C₁₇	—	2	1	no	—
290	C₂×C₄×C₁₇	—	2	2	no	—
291	C₂×C₄×C₁₇	—	2	1	no	—
292	C₂×C₄×C₁₇	—	2	1	no	—
293	C₂×C₄×C₁₇	—	2	1	no	—
294	C₂×C₄×C₁₇	—	2	1	no	—
295	C₂×C₄×C₁₇	—	2	1	no	—
296	C₂×C₄×C₁₇	—	2	1	no	—
297	C₂×C₄×C₁₇	—	2	2	no	—
298	C₂×C₄×C₁₇	—	2	1	no	—
299	C₂×C₄×C₁₇	—	2	1	no	—
300	C₂×C₄×C₁₇	—	2	1	no	—
301	C₂×C₄×C₁₇	—	2	1	no	—
302	C₂×C₄×C₁₇	—	2	2	no	—
303	C₂×C₄×C₁₇	—	4	2	no	—
304	C₂×C₄×C₁₇	—	4	4	no	—
305	C₂×C₄×C₁₇	—	4	2	no	—
306	C₂×C₄×C₁₇	—	4	1	no	—
307	C₂×C₄×C₁₇	—	4	1	no	—
308	C₂×C₄×C₁₇	—	4	1	no	—
309	C₂×C₄×C₁₇	—	4	1	no	—
310	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
311	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
312	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
313	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
316	C₈×C₁₇	—	2	2	no	—
317	C₈×C₁₇	—	2	2	no	—
318	C₈×C₁₇	—	4	1	no	—
319	C₈×C₁₇	—	4	1	no	—
320	C₈×C₁₇	—	4	1	no	—
321	C₈×C₁₇	—	4	1	no	—
322	#3523	C₂×C₁₇	1	1	yes	characteristic
323	#3248	C₂×C₁₇	1	1	yes	characteristic
324	#3160	C₂×C₁₇	1	1	yes	characteristic, complemented
325	#3113	C₂×C₁₇	1	1	yes	characteristic, complemented
326	#1653	C₂×C₁₇	1	1	yes	characteristic, complemented
327	#1653	C₂×C₁₇	1	1	yes	characteristic, complemented
328	#1652	C₂×C₁₇	1	1	yes	characteristic, complemented
329	#1651	C₂×C₁₇	1	1	yes	characteristic, complemented
330	#1650	C₂×C₁₇	1	1	yes	characteristic, complemented
331	#1649	C₂×C₁₇	1	1	yes	characteristic, complemented
332	#1648	C₂×C₁₇	1	1	yes	characteristic, complemented
333	#1648	C₂×C₁₇	1	1	yes	characteristic, complemented
334	#1552	C₂×C₁₇	1	1	yes	characteristic, complemented
335	#1494	C₂×C₁₇	1	1	yes	characteristic
336	C₂×Q₈⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
337	C₂²×C₁₇	—	2	1	no	—
338	C₂²×C₁₇	—	2	1	no	—
339	C₂²×C₁₇	—	4	1	no	—
340	C₂²×C₁₇	—	4	1	no	—
341	C₂²×C₁₇	—	4	1	no	—
342	C₂²×C₁₇	#456	1	2	yes	—
343	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
344	C₄×C₁₇	—	2	1	no	—
345	C₄×C₁₇	—	2	2	no	—
346	C₄×C₁₇	—	2	1	no	—
347	C₄×C₁₇	—	2	1	no	—
348	C₄×C₁₇	—	2	1	no	—
349	C₄×C₁₇	—	4	1	no	—
350	C₄×C₁₇	—	4	2	no	—
351	C₄×C₁₇	—	4	1	no	—
352	C₄×C₁₇	—	4	1	no	—
353	C₄×C₁₇	—	4	2	no	—
354	C₄×C₁₇	—	4	1	no	—
355	C₄×C₁₇	—	4	1	no	—
356	C₄×C₁₇	—	4	1	no	—
357	C₄×C₁₇	—	8	1	no	—
358	C₄×C₁₇	—	8	1	no	—
359	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
360	C₄×C₁₇	#575	1	1	yes	characteristic
361	C₄×C₁₇	#577	1	1	yes	characteristic
362	C₄×C₁₇	#578	1	1	yes	characteristic
363	#557	—	2	1	no	—
364	#557	C₂²×C₁₇	1	1	yes	characteristic
365	#557	C₂²×C₁₇	1	1	yes	characteristic
366	#556	—	2	1	no	—
367	#556	C₂²×C₁₇	1	1	yes	characteristic
368	#552	—	2	2	no	—
369	#552	—	2	1	no	—
370	D₄×Q₈	—	2	1	no	—
371	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
372	#541	—	2	2	no	—
373	#541	—	2	1	no	—
374	#533	—	2	1	no	—
375	#533	C₂²×C₁₇	1	1	yes	characteristic
376	#533	C₂²×C₁₇	1	1	yes	characteristic
377	#529	—	2	1	no	—
378	#529	C₂²×C₁₇	1	1	yes	characteristic
379	#519	—	2	1	no	—
380	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
381	#500	C₂²×C₁₇	1	1	yes	characteristic
382	#500	C₂²×C₁₇	1	1	yes	characteristic
383	#499	—	2	2	no	—
384	#498	C₂²×C₁₇	1	1	yes	characteristic
385	#498	C₂²×C₁₇	1	1	yes	characteristic
386	#483	—	2	1	no	—
387	#479	—	2	1	no	—
388	#475	C₂²×C₁₇	1	1	yes	characteristic
389	#475	C₂²×C₁₇	1	1	yes	characteristic
390	#475	C₂²×C₁₇	1	1	yes	characteristic
391	#474	C₂²×C₁₇	1	1	yes	characteristic
392	#467	—	2	1	no	—
393	#465	—	2	1	no	—
394	#464	—	2	1	no	—
395	#462	C₂²×C₁₇	1	1	yes	characteristic
396	#462	C₂²×C₁₇	1	1	yes	characteristic
397	#462	C₂²×C₁₇	1	1	yes	characteristic
398	#461	C₂²×C₁₇	1	1	yes	characteristic
399	#451	—	2	1	no	—
400	#441	—	2	1	no	—
401	#441	—	2	1	no	—
402	#432	C₂²×C₁₇	1	1	yes	characteristic
403	#427	—	2	2	no	—
404	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
405	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
406	#332	C₂²×C₁₇	1	1	yes	characteristic
407	#332	C₂²×C₁₇	1	1	yes	characteristic
408	#332	C₂²×C₁₇	1	1	yes	characteristic
409	#332	C₂²×C₁₇	1	1	yes	characteristic
410	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
411	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
412	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
413	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
414	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
415	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
416	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
417	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
418	C₂×C₁₇	—	2	2	no	—
419	C₂×C₁₇	—	8	1	no	—
420	C₂×C₁₇	#3002	1	1	yes	characteristic
421	C₂×C₁₇	#3013	1	1	yes	characteristic
422	C₂×C₁₇	C₂×#456	1	1	yes	characteristic
423	C₂²×Q₈	—	2	1	no	—
424	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
425	C₂×Q₁₆	—	2	1	no	—
426	C₂×Q₁₆	—	2	1	no	—
427	C₂×Q₁₆	—	2	1	no	—
428	C₂×SD₁₆	—	2	1	no	—
429	C₂²×C₈	—	2	1	no	—
430	C₂²×C₈	—	2	1	no	—
431	C₄⋊Q₈	—	2	2	no	—
432	C₄⋊Q₈	—	2	1	no	—
433	C₄⋊Q₈	—	2	1	no	—
434	C₄⋊Q₈	—	2	1	no	—
435	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
436	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
437	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
438	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
439	#126	—	2	2	no	—
440	#126	—	2	2	no	—
441	#126	—	2	2	no	—
442	#126	—	2	2	no	—
443	#126	—	2	1	no	—
444	#125	—	2	2	no	—
445	#125	—	2	2	no	—
446	#125	—	2	2	no	—
447	#125	—	2	1	no	—
448	#125	—	2	2	no	—
449	#125	—	2	2	no	—
450	#125	—	2	1	no	—
451	#125	—	2	1	no	—
452	#125	D₄×C₁₇	1	1	yes	characteristic
453	#125	D₄×C₁₇	1	2	yes	—
454	#124	—	2	1	no	—
455	#124	D₄×C₁₇	1	1	yes	characteristic
456	#123	—	2	2	no	—
457	#123	—	2	1	no	—
458	C₂²⋊Q₈	—	2	2	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	1	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	—	2	1	no	—
464	C₂²⋊Q₈	—	2	2	no	—
465	C₂²⋊Q₈	—	2	1	no	—
466	C₂²⋊Q₈	—	2	1	no	—
467	C₂²⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
468	#121	D₄×C₁₇	1	1	yes	characteristic
469	C₄×Q₈	—	2	2	no	—
470	C₄×Q₈	—	2	2	no	—
471	C₄×Q₈	—	2	1	no	—
472	C₄×Q₈	—	2	1	no	—
473	C₄×Q₈	—	2	1	no	—
474	C₄×Q₈	—	2	1	no	—
475	C₄×Q₈	—	2	1	no	—
476	C₄×Q₈	—	2	1	no	—
477	C₄×Q₈	—	2	1	no	—
478	C₄×Q₈	—	2	1	no	—
479	C₄×Q₈	—	2	1	no	—
480	C₄×Q₈	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
483	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
484	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
485	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
486	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	2	1	no	—
489	C₄×D₄	—	2	1	no	—
490	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
491	#117	—	2	2	no	—
492	#117	—	2	2	no	—
493	#117	—	2	2	no	—
494	#117	—	2	1	no	—
495	#117	—	2	1	no	—
496	#117	—	2	1	no	—
497	#117	D₄×C₁₇	1	2	yes	—
498	C₂×C₄⋊C₄	—	2	1	no	—
499	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
500	C₂×C₄²	—	2	1	no	—
501	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
502	#107	—	2	2	no	—
503	#107	—	2	2	no	—
504	#107	—	2	1	no	—
505	#106	—	2	2	no	—
506	#106	—	2	2	no	—
507	#106	—	2	1	no	—
508	#106	—	2	1	no	—
509	#106	—	2	1	no	—
510	C₄⋊C₈	—	2	1	no	—
511	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
512	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
513	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
514	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
515	#103	—	2	1	no	—
516	#103	—	2	1	no	—
517	#103	—	2	1	no	—
518	#103	—	2	1	no	—
519	#103	—	2	1	no	—
520	#103	—	2	1	no	—
521	#103	—	2	1	no	—
522	#102	—	2	1	no	—
523	C₂²⋊C₈	—	2	1	no	—
524	#97	—	2	1	no	—
525	C₄×C₈	—	2	1	no	—
526	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
527	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
528	C₁₇	#18649	1	1	yes	characteristic, direct product factor, Sylow
529	C₂×Q₈	—	2	2	no	—
530	C₂×Q₈	—	2	1	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	1	no	—
533	C₂×Q₈	—	2	2	no	—
534	C₂×Q₈	—	2	1	no	—
535	C₂×Q₈	—	2	1	no	—
536	C₂×Q₈	—	4	1	no	—
537	C₂×Q₈	—	4	2	no	—
538	C₂×Q₈	—	4	2	no	—
539	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
540	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
541	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
542	C₂×D₄	—	2	1	no	—
543	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
544	C₂²×C₄	—	2	2	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
549	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
550	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
551	Q₁₆	—	4	2	no	—
552	Q₁₆	—	4	2	no	—
553	Q₁₆	—	8	1	no	—
554	SD₁₆	—	8	1	no	—
555	C₂×C₈	—	2	4	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	2	1	no	—
560	C₂×C₈	—	2	1	no	—
561	C₂×C₈	—	2	1	no	—
562	C₂×C₈	—	8	1	no	—
563	C₄⋊C₄	—	2	2	no	—
564	C₄⋊C₄	—	2	2	no	—
565	C₄⋊C₄	—	2	2	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	—	2	2	no	—
568	C₄⋊C₄	—	2	2	no	—
569	C₄⋊C₄	—	2	2	no	—
570	C₄⋊C₄	—	2	2	no	—
571	C₄⋊C₄	—	2	1	no	—
572	C₄⋊C₄	—	2	1	no	—
573	C₄⋊C₄	—	2	1	no	—
574	C₄⋊C₄	—	2	1	no	—
575	C₄⋊C₄	—	2	1	no	—
576	C₄⋊C₄	—	2	1	no	—
577	C₄⋊C₄	—	2	1	no	—
578	C₄⋊C₄	—	2	1	no	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	1	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	2	no	—
584	C₄⋊C₄	—	2	1	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	4	1	no	—
589	C₄⋊C₄	—	4	1	no	—
590	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
591	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
592	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
593	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
594	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
595	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
596	C₂²⋊C₄	—	2	2	no	—
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	1	no	—
600	C₂²⋊C₄	—	2	2	no	—
601	C₂²⋊C₄	—	2	1	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	1	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	4	1	no	—
606	C₄²	—	2	2	no	—
607	C₄²	—	2	2	no	—
608	C₄²	—	2	2	no	—
609	C₄²	—	2	1	no	—
610	C₄²	—	2	1	no	—
611	C₄²	—	2	1	no	—
612	C₄²	—	2	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	2	no	—
615	C₄²	—	4	1	no	—
616	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
617	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
618	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
619	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
620	C₂³	—	2	1	no	—
621	C₂³	C₁₇×#120	1	1	yes	characteristic
622	Q₈	—	2	1	no	—
623	Q₈	—	2	1	no	—
624	Q₈	—	2	1	no	—
625	Q₈	—	2	1	no	—
626	Q₈	—	2	1	no	—
627	Q₈	—	4	2	no	—
628	Q₈	—	4	4	no	—
629	Q₈	—	4	1	no	—
630	Q₈	—	4	1	no	—
631	Q₈	—	4	1	no	—
632	Q₈	—	4	1	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	1	no	—
635	Q₈	—	4	1	no	—
636	Q₈	—	4	1	no	—
637	Q₈	C₁₇×#135	1	2	yes	—
638	D₄	—	2	1	no	—
639	D₄	—	2	1	no	—
640	D₄	—	4	2	no	—
641	C₂×C₄	—	2	1	no	—
642	C₂×C₄	—	2	2	no	—
643	C₂×C₄	—	2	1	no	—
644	C₂×C₄	—	2	1	no	—
645	C₂×C₄	—	2	1	no	—
646	C₂×C₄	—	2	1	no	—
647	C₂×C₄	—	2	1	no	—
648	C₂×C₄	—	2	1	no	—
649	C₂×C₄	—	2	2	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	4	2	no	—
656	C₂×C₄	—	4	4	no	—
657	C₂×C₄	—	4	2	no	—
658	C₂×C₄	—	4	1	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
663	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
664	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
666	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
667	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
668	C₈	—	2	2	no	—
669	C₈	—	2	2	no	—
670	C₈	—	4	1	no	—
671	C₈	—	4	1	no	—
672	C₈	—	4	1	no	—
673	C₈	—	4	1	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	4	1	no	—
677	C₂²	—	4	1	no	—
678	C₂²	—	4	1	no	—
679	C₂²	C₁₇×#456	1	2	yes	—
680	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
681	C₄	—	2	1	no	—
682	C₄	—	2	2	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	1	no	—
685	C₄	—	2	1	no	—
686	C₄	—	4	1	no	—
687	C₄	—	4	2	no	—
688	C₄	—	4	1	no	—
689	C₄	—	4	1	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	1	no	—
692	C₄	—	4	1	no	—
693	C₄	—	4	1	no	—
694	C₄	—	8	1	no	—
695	C₄	—	8	1	no	—
696	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
697	C₄	C₁₇×#575	1	1	yes	characteristic
698	C₄	C₁₇×#577	1	1	yes	characteristic
699	C₄	C₁₇×#578	1	1	yes	characteristic
700	C₂	—	2	2	no	—
701	C₂	—	8	1	no	—
702	C₂	C₁₇×#3002	1	1	yes	characteristic
703	C₂	C₁₇×#3013	1	1	yes	characteristic
704	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×#3160	C₂	semidirect
4. C₁₇×#3113	C₂	semidirect
5. C₁₇×#1653	C₂	semidirect
6. C₁₇×#1653	C₂	semidirect
7. C₁₇×#1652	C₂	semidirect
8. C₁₇×#1651	C₂	semidirect
9. C₁₇×#1650	C₂	semidirect
10. C₁₇×#1649	C₂	semidirect
11. C₁₇×#1648	C₂	semidirect
12. C₁₇×#1648	C₂	semidirect
13. C₁₇×#1552	C₂	semidirect
15. C₂×C₁₇×Q₈⋊C₈	C₂	semidirect
267. #18649	C₁₇	direct (N × H)
324. #3160	C₂×C₁₇	semidirect
325. #3113	C₂×C₁₇	semidirect
326. #1653	C₂×C₁₇	semidirect
327. #1653	C₂×C₁₇	semidirect
328. #1652	C₂×C₁₇	semidirect
329. #1651	C₂×C₁₇	semidirect
330. #1650	C₂×C₁₇	semidirect
331. #1649	C₂×C₁₇	semidirect
332. #1648	C₂×C₁₇	semidirect
333. #1648	C₂×C₁₇	semidirect
334. #1552	C₂×C₁₇	semidirect
336. C₂×Q₈⋊C₈	C₂×C₁₇	semidirect
528. C₁₇	#18649	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×#3248	2
C₁₇×#3160	2
C₁₇×#3113	2
C₁₇×#1653	2
C₁₇×#1652	2
C₁₇×#1651	2
C₁₇×#1650	2
C₁₇×#1649	2
C₁₇×#1648	2
C₁₇×#1552	2
C₁₇×#1494	2
C₂×C₁₇×Q₈⋊C₈	2
#18649	17

Subgroups — C17×#18649 #16876393

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18649 #16876393