Subgroups — C₁₇×#18592 #16876336

Order 4352.

860 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3509	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3255	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1653	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1652	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1650	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1648	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1549	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1489	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1485	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#557	—	2	1	no	—
13	C₁₇×#557	C₂²	1	2	yes	—
14	C₁₇×#556	—	2	1	no	—
15	C₁₇×#556	C₂²	1	2	yes	—
16	C₁₇×#552	—	2	2	no	—
17	C₁₇×#552	—	2	2	no	—
18	C₁₇×#541	—	2	2	no	—
19	C₁₇×#536	—	2	1	no	—
20	C₁₇×#533	—	2	1	no	—
21	C₁₇×#533	—	2	1	no	—
22	C₁₇×#533	C₂²	1	1	yes	characteristic
23	C₁₇×#533	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₇×#519	—	2	1	no	—
26	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
27	C₁₇×#501	—	2	2	no	—
28	C₁₇×#500	C₂²	1	2	yes	—
29	C₁₇×#498	C₂²	1	2	yes	—
30	C₁₇×#485	—	2	1	no	—
31	C₁₇×#475	—	2	1	no	—
32	C₁₇×#475	C₂²	1	2	yes	—
33	C₁₇×#475	C₂²	1	1	yes	characteristic
34	C₁₇×#474	C₂²	1	1	yes	characteristic
35	C₁₇×#470	—	2	2	no	—
36	C₁₇×#462	—	2	1	no	—
37	C₁₇×#462	C₂²	1	2	yes	—
38	C₁₇×#462	C₂²	1	1	yes	characteristic
39	C₁₇×#461	C₂²	1	1	yes	characteristic
40	C₁₇×#452	—	2	1	no	—
41	C₄×Q₁₆×C₁₇	—	2	1	no	—
42	C₄×SD₁₆×C₁₇	—	2	1	no	—
43	C₁₇×#431	C₂²	1	1	yes	characteristic
44	C₁₇×#428	—	2	2	no	—
45	C₁₇×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#332	C₂²	1	2	yes	—
48	C₁₇×#332	C₂²	1	2	yes	—
49	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
51	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
52	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
54	C₂²×Q₈×C₁₇	—	2	1	no	—
55	C₂×Q₁₆×C₁₇	—	2	1	no	—
56	C₂×Q₁₆×C₁₇	—	2	2	no	—
57	C₂×SD₁₆×C₁₇	—	2	1	no	—
58	C₂×M₁₆×C₁₇	—	2	1	no	—
59	C₂×M₁₆×C₁₇	—	2	1	no	—
60	C₁₇×C₄⋊Q₈	—	2	2	no	—
61	C₁₇×C₄⋊Q₈	—	2	1	no	—
62	C₁₇×C₄⋊Q₈	—	2	1	no	—
63	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
64	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
65	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₇×#126	—	2	4	no	—
70	C₁₇×#126	—	2	4	no	—
71	C₁₇×#125	—	2	2	no	—
72	C₁₇×#125	—	2	4	no	—
73	C₁₇×#125	—	2	2	no	—
74	C₁₇×#125	—	2	4	no	—
75	C₁₇×#125	—	2	1	no	—
76	C₁₇×#125	—	2	1	no	—
77	C₁₇×#124	—	2	2	no	—
78	C₁₇×#123	—	2	4	no	—
79	C₁₇×C₂²⋊Q₈	—	2	2	no	—
80	C₁₇×C₂²⋊Q₈	—	2	2	no	—
81	C₁₇×C₂²⋊Q₈	—	2	2	no	—
82	C₁₇×C₂²⋊Q₈	—	2	2	no	—
83	C₁₇×C₂²⋊Q₈	—	2	1	no	—
84	C₁₇×C₂²⋊Q₈	—	2	1	no	—
85	C₁₇×C₂²⋊Q₈	—	2	1	no	—
86	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
87	C₄×Q₈×C₁₇	—	2	2	no	—
88	C₄×Q₈×C₁₇	—	2	2	no	—
89	C₄×Q₈×C₁₇	—	2	2	no	—
90	C₄×Q₈×C₁₇	—	2	2	no	—
91	C₄×Q₈×C₁₇	—	2	2	no	—
92	C₄×Q₈×C₁₇	—	2	2	no	—
93	C₄×Q₈×C₁₇	—	2	1	no	—
94	C₄×Q₈×C₁₇	—	2	1	no	—
95	C₄×Q₈×C₁₇	—	2	1	no	—
96	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
97	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
99	C₄×D₄×C₁₇	—	2	1	no	—
100	C₄×D₄×C₁₇	—	2	1	no	—
101	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
103	C₁₇×#117	—	2	4	no	—
104	C₁₇×#117	—	2	2	no	—
105	C₁₇×#117	—	2	1	no	—
106	C₁₇×#117	—	2	2	no	—
107	C₁₇×#117	—	2	1	no	—
108	C₁₇×#117	—	2	1	no	—
109	C₁₇×#117	D₄	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
112	C₂×C₄²×C₁₇	—	2	1	no	—
113	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
114	C₁₇×#107	—	2	4	no	—
115	C₁₇×#107	—	2	1	no	—
116	C₁₇×#106	—	2	4	no	—
117	C₁₇×#106	—	2	1	no	—
118	C₁₇×#106	—	2	2	no	—
119	C₁₇×C₄⋊C₈	—	2	1	no	—
120	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
121	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
123	C₁₇×#103	—	2	1	no	—
124	C₁₇×#103	—	2	2	no	—
125	C₁₇×#103	—	2	1	no	—
126	C₁₇×#103	—	2	1	no	—
127	C₁₇×#103	—	2	2	no	—
128	C₁₇×#102	—	2	1	no	—
129	C₁₇×C₂²⋊C₈	—	2	1	no	—
130	C₁₇×#97	—	2	1	no	—
131	C₄×C₈×C₁₇	—	2	1	no	—
132	C₄×C₈×C₁₇	C₂³	1	2	yes	—
133	#41×C₁₇	—	4	1	no	—
134	#41×C₁₇	—	4	1	no	—
135	C₂×Q₈×C₁₇	—	2	1	no	—
136	C₂×Q₈×C₁₇	—	2	2	no	—
137	C₂×Q₈×C₁₇	—	2	2	no	—
138	C₂×Q₈×C₁₇	—	2	1	no	—
139	C₂×Q₈×C₁₇	—	2	1	no	—
140	C₂×Q₈×C₁₇	—	4	2	no	—
141	C₂×Q₈×C₁₇	—	4	2	no	—
142	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
143	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
144	C₂×D₄×C₁₇	—	2	1	no	—
145	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₁₇	—	2	2	no	—
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂²×C₄×C₁₇	—	2	1	no	—
149	C₂²×C₄×C₁₇	—	2	1	no	—
150	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
153	Q₁₆×C₁₇	—	4	2	no	—
154	Q₁₆×C₁₇	—	8	2	no	—
155	SD₁₆×C₁₇	—	4	2	no	—
156	M₁₆×C₁₇	—	2	4	no	—
157	M₁₆×C₁₇	—	8	1	no	—
158	C₂×C₈×C₁₇	—	2	2	no	—
159	C₂×C₈×C₁₇	—	2	2	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₄⋊C₄×C₁₇	—	2	4	no	—
163	C₄⋊C₄×C₁₇	—	2	4	no	—
164	C₄⋊C₄×C₁₇	—	2	4	no	—
165	C₄⋊C₄×C₁₇	—	2	4	no	—
166	C₄⋊C₄×C₁₇	—	2	1	no	—
167	C₄⋊C₄×C₁₇	—	2	1	no	—
168	C₄⋊C₄×C₁₇	—	2	1	no	—
169	C₄⋊C₄×C₁₇	—	2	2	no	—
170	C₄⋊C₄×C₁₇	—	2	2	no	—
171	C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	2	no	—
173	C₄⋊C₄×C₁₇	—	2	2	no	—
174	C₄⋊C₄×C₁₇	—	2	2	no	—
175	C₄⋊C₄×C₁₇	—	2	1	no	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	—	2	1	no	—
178	C₄⋊C₄×C₁₇	—	2	1	no	—
179	C₄⋊C₄×C₁₇	—	2	1	no	—
180	C₄⋊C₄×C₁₇	—	4	1	no	—
181	C₄⋊C₄×C₁₇	—	4	1	no	—
182	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
184	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
185	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
186	C₂²⋊C₄×C₁₇	—	2	4	no	—
187	C₂²⋊C₄×C₁₇	—	2	4	no	—
188	C₂²⋊C₄×C₁₇	—	2	2	no	—
189	C₂²⋊C₄×C₁₇	—	2	1	no	—
190	C₂²⋊C₄×C₁₇	—	2	1	no	—
191	C₂²⋊C₄×C₁₇	—	2	1	no	—
192	C₂²⋊C₄×C₁₇	—	4	1	no	—
193	C₄²×C₁₇	—	2	4	no	—
194	C₄²×C₁₇	—	2	4	no	—
195	C₄²×C₁₇	—	2	1	no	—
196	C₄²×C₁₇	—	2	1	no	—
197	C₄²×C₁₇	—	2	2	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	4	1	no	—
200	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
201	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
203	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
204	#18592	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₇	—	2	1	no	—
206	C₂³×C₁₇	#120	1	1	yes	characteristic
207	Q₈×C₁₇	—	2	1	no	—
208	Q₈×C₁₇	—	2	1	no	—
209	Q₈×C₁₇	—	2	2	no	—
210	Q₈×C₁₇	—	2	2	no	—
211	Q₈×C₁₇	—	4	4	no	—
212	Q₈×C₁₇	—	4	2	no	—
213	Q₈×C₁₇	—	4	2	no	—
214	Q₈×C₁₇	—	4	2	no	—
215	Q₈×C₁₇	—	4	1	no	—
216	Q₈×C₁₇	—	4	1	no	—
217	Q₈×C₁₇	—	4	1	no	—
218	Q₈×C₁₇	—	4	1	no	—
219	D₄×C₁₇	—	2	1	no	—
220	D₄×C₁₇	—	2	1	no	—
221	D₄×C₁₇	—	4	2	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	2	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	2	no	—
230	C₂×C₄×C₁₇	—	2	2	no	—
231	C₂×C₄×C₁₇	—	2	4	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	4	2	no	—
234	C₂×C₄×C₁₇	—	4	4	no	—
235	C₂×C₄×C₁₇	—	4	1	no	—
236	C₂×C₄×C₁₇	—	4	1	no	—
237	C₂×C₄×C₁₇	—	4	2	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
241	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
242	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
243	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
244	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
246	C₈×C₁₇	—	2	4	no	—
247	C₈×C₁₇	—	4	1	no	—
248	C₈×C₁₇	—	4	1	no	—
249	C₈×C₁₇	—	4	2	no	—
250	#3509	C₂×C₁₇	1	1	yes	characteristic
251	#3255	C₂×C₁₇	1	1	yes	characteristic, complemented
252	#3165	C₂×C₁₇	1	1	yes	characteristic, complemented
253	#3107	C₂×C₁₇	1	1	yes	characteristic
254	#1653	C₂×C₁₇	1	2	yes	complemented
255	#1652	C₂×C₁₇	1	2	yes	complemented
256	#1650	C₂×C₁₇	1	2	yes	complemented
257	#1648	C₂×C₁₇	1	2	yes	complemented
258	#1549	C₂×C₁₇	1	1	yes	characteristic, complemented
259	#1489	C₂×C₁₇	1	1	yes	characteristic
260	#1485	C₂×C₁₇	1	1	yes	characteristic, complemented
261	C₂²×C₁₇	—	2	1	no	—
262	C₂²×C₁₇	—	2	1	no	—
263	C₂²×C₁₇	—	2	1	no	—
264	C₂²×C₁₇	—	4	1	no	—
265	C₂²×C₁₇	—	4	1	no	—
266	C₂²×C₁₇	—	4	1	no	—
267	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
268	C₄×C₁₇	—	2	1	no	—
269	C₄×C₁₇	—	2	1	no	—
270	C₄×C₁₇	—	2	1	no	—
271	C₄×C₁₇	—	4	1	no	—
272	C₄×C₁₇	—	4	4	no	—
273	C₄×C₁₇	—	4	1	no	—
274	C₄×C₁₇	—	4	2	no	—
275	C₄×C₁₇	—	4	1	no	—
276	C₄×C₁₇	—	4	2	no	—
277	C₄×C₁₇	—	8	1	no	—
278	C₄×C₁₇	—	8	1	no	—
279	C₄×C₁₇	#456	1	2	yes	—
280	C₄×C₁₇	#575	1	1	yes	characteristic
281	C₄×C₁₇	#575	1	1	yes	characteristic
282	C₄×C₁₇	#577	1	1	yes	characteristic
283	C₄×C₁₇	#578	1	1	yes	characteristic
284	#557	—	2	1	no	—
285	#557	C₂²×C₁₇	1	2	yes	—
286	#556	—	2	1	no	—
287	#556	C₂²×C₁₇	1	2	yes	—
288	#552	—	2	2	no	—
289	#552	—	2	2	no	—
290	#541	—	2	2	no	—
291	#536	—	2	1	no	—
292	#533	—	2	1	no	—
293	#533	—	2	1	no	—
294	#533	C₂²×C₁₇	1	1	yes	characteristic
295	#533	C₂²×C₁₇	1	1	yes	characteristic
296	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
297	#519	—	2	1	no	—
298	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
299	#501	—	2	2	no	—
300	#500	C₂²×C₁₇	1	2	yes	—
301	#498	C₂²×C₁₇	1	2	yes	—
302	#485	—	2	1	no	—
303	#475	—	2	1	no	—
304	#475	C₂²×C₁₇	1	1	yes	characteristic
305	#475	C₂²×C₁₇	1	2	yes	—
306	#474	C₂²×C₁₇	1	1	yes	characteristic
307	#470	—	2	2	no	—
308	#462	—	2	1	no	—
309	#462	C₂²×C₁₇	1	1	yes	characteristic
310	#462	C₂²×C₁₇	1	2	yes	—
311	#461	C₂²×C₁₇	1	1	yes	characteristic
312	#452	—	2	1	no	—
313	C₄×Q₁₆	—	2	1	no	—
314	C₄×SD₁₆	—	2	1	no	—
315	#431	C₂²×C₁₇	1	1	yes	characteristic
316	#428	—	2	2	no	—
317	#423	C₂²×C₁₇	1	1	yes	characteristic
318	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
319	#332	C₂²×C₁₇	1	2	yes	—
320	#332	C₂²×C₁₇	1	2	yes	—
321	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
322	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
323	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
324	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
325	C₂×C₁₇	—	4	1	no	—
326	C₂×C₁₇	—	8	1	no	—
327	C₂×C₁₇	#3005	1	1	yes	characteristic
328	C₂×C₁₇	#3013	1	1	yes	characteristic
329	C₂×C₁₇	C₂×#456	1	1	yes	characteristic
330	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
331	C₂²×Q₈	—	2	1	no	—
332	C₂×Q₁₆	—	2	1	no	—
333	C₂×Q₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	1	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₂×M₁₆	—	2	1	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	2	1	no	—
339	C₄⋊Q₈	—	2	1	no	—
340	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
341	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
342	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
343	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
344	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
345	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
346	#126	—	2	4	no	—
347	#126	—	2	4	no	—
348	#125	—	2	2	no	—
349	#125	—	2	4	no	—
350	#125	—	2	2	no	—
351	#125	—	2	4	no	—
352	#125	—	2	1	no	—
353	#125	—	2	1	no	—
354	#124	—	2	2	no	—
355	#123	—	2	4	no	—
356	C₂²⋊Q₈	—	2	2	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	2	no	—
359	C₂²⋊Q₈	—	2	2	no	—
360	C₂²⋊Q₈	—	2	1	no	—
361	C₂²⋊Q₈	—	2	1	no	—
362	C₂²⋊Q₈	—	2	1	no	—
363	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
364	C₄×Q₈	—	2	2	no	—
365	C₄×Q₈	—	2	2	no	—
366	C₄×Q₈	—	2	2	no	—
367	C₄×Q₈	—	2	2	no	—
368	C₄×Q₈	—	2	2	no	—
369	C₄×Q₈	—	2	2	no	—
370	C₄×Q₈	—	2	1	no	—
371	C₄×Q₈	—	2	1	no	—
372	C₄×Q₈	—	2	1	no	—
373	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
374	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
375	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
379	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
380	#117	—	2	4	no	—
381	#117	—	2	2	no	—
382	#117	—	2	1	no	—
383	#117	—	2	2	no	—
384	#117	—	2	1	no	—
385	#117	—	2	1	no	—
386	#117	D₄×C₁₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
389	C₂×C₄²	—	2	1	no	—
390	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
391	#107	—	2	4	no	—
392	#107	—	2	1	no	—
393	#106	—	2	4	no	—
394	#106	—	2	1	no	—
395	#106	—	2	2	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
398	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
399	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
400	#103	—	2	1	no	—
401	#103	—	2	2	no	—
402	#103	—	2	1	no	—
403	#103	—	2	1	no	—
404	#103	—	2	2	no	—
405	#102	—	2	1	no	—
406	C₂²⋊C₈	—	2	1	no	—
407	#97	—	2	1	no	—
408	C₄×C₈	—	2	1	no	—
409	C₄×C₈	C₂³×C₁₇	1	2	yes	—
410	C₁₇	#18592	1	1	yes	characteristic, direct product factor, Sylow
411	#41	—	4	1	no	—
412	#41	—	4	1	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	1	no	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	2	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	4	2	no	—
419	C₂×Q₈	—	4	2	no	—
420	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
421	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
422	C₂×D₄	—	2	1	no	—
423	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
430	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
431	Q₁₆	—	4	2	no	—
432	Q₁₆	—	8	2	no	—
433	SD₁₆	—	4	2	no	—
434	M₁₆	—	2	4	no	—
435	M₁₆	—	8	1	no	—
436	C₂×C₈	—	2	2	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	2	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	4	no	—
443	C₄⋊C₄	—	2	4	no	—
444	C₄⋊C₄	—	2	2	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	2	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	1	no	—
453	C₄⋊C₄	—	2	2	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	2	1	no	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
461	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
462	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
463	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₂²⋊C₄	—	2	4	no	—
466	C₂²⋊C₄	—	2	1	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	1	no	—
469	C₂²⋊C₄	—	2	1	no	—
470	C₂²⋊C₄	—	4	1	no	—
471	C₄²	—	2	4	no	—
472	C₄²	—	2	4	no	—
473	C₄²	—	2	1	no	—
474	C₄²	—	2	2	no	—
475	C₄²	—	2	1	no	—
476	C₄²	—	2	1	no	—
477	C₄²	—	4	1	no	—
478	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
479	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
480	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
482	C₂³	—	2	1	no	—
483	C₂³	C₁₇×#120	1	1	yes	characteristic
484	Q₈	—	2	1	no	—
485	Q₈	—	2	1	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	4	4	no	—
489	Q₈	—	4	2	no	—
490	Q₈	—	4	2	no	—
491	Q₈	—	4	2	no	—
492	Q₈	—	4	1	no	—
493	Q₈	—	4	1	no	—
494	Q₈	—	4	1	no	—
495	Q₈	—	4	1	no	—
496	D₄	—	2	1	no	—
497	D₄	—	2	1	no	—
498	D₄	—	4	2	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	4	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	4	1	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	1	no	—
516	C₂×C₄	—	4	1	no	—
517	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
518	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
519	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
520	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
521	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
522	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
523	C₈	—	2	4	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	4	2	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	4	1	no	—
531	C₂²	—	4	1	no	—
532	C₂²	—	4	1	no	—
533	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	2	1	no	—
537	C₄	—	4	1	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	1	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	2	no	—
543	C₄	—	8	1	no	—
544	C₄	—	8	1	no	—
545	C₄	C₁₇×#456	1	2	yes	—
546	C₄	C₁₇×#575	1	1	yes	characteristic
547	C₄	C₁₇×#575	1	1	yes	characteristic
548	C₄	C₁₇×#577	1	1	yes	characteristic
549	C₄	C₁₇×#578	1	1	yes	characteristic
550	C₂	—	4	1	no	—
551	C₂	—	8	1	no	—
552	C₂	C₁₇×#3005	1	1	yes	characteristic
553	C₂	C₁₇×#3013	1	1	yes	characteristic
554	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	C₂×#41×C₁₇	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
2. C₁₇×#3255	C₂	semidirect
3. C₁₇×#3165	C₂	semidirect
5. C₁₇×#1653	C₂	semidirect
6. C₁₇×#1652	C₂	semidirect
7. C₁₇×#1650	C₂	semidirect
8. C₁₇×#1648	C₂	semidirect
9. C₁₇×#1549	C₂	semidirect
11. C₁₇×#1485	C₂	semidirect
204. #18592	C₁₇	direct (N × H)
251. #3255	C₂×C₁₇	semidirect
252. #3165	C₂×C₁₇	semidirect
254. #1653	C₂×C₁₇	semidirect
255. #1652	C₂×C₁₇	semidirect
256. #1650	C₂×C₁₇	semidirect
257. #1648	C₂×C₁₇	semidirect
258. #1549	C₂×C₁₇	semidirect
260. #1485	C₂×C₁₇	semidirect
410. C₁₇	#18592	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×#3509	2
C₁₇×#3255	2
C₁₇×#3165	2
C₁₇×#3107	2
C₁₇×#1653	2
C₁₇×#1652	2
C₁₇×#1650	2
C₁₇×#1648	2
C₁₇×#1549	2
C₁₇×#1489	2
C₁₇×#1485	2
#18592	17

Subgroups — C17×#18592 #16876336

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18592 #16876336