Subgroups — C₁₇×#18643 #16876387

Order 4352.

906 conjugacy classes of subgroups.

The subgroup lattice has 496 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
2	C₁₇×#3230	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₁₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3079	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1637	C₂	1	4	yes	maximal, complemented
6	C₁₇×#1636	C₂	1	4	yes	maximal, complemented
7	C₁₇×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1493	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1476	C₂	1	1	yes	maximal, characteristic
10	Q₈²×C₁₇	—	2	1	no	—
11	C₁₇×#557	C₂²	1	2	yes	—
12	C₁₇×#554	—	2	1	no	—
13	C₁₇×#554	—	2	2	no	—
14	D₄×Q₈×C₁₇	—	2	2	no	—
15	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
16	C₁₇×#544	—	2	1	no	—
17	C₁₇×#544	—	2	2	no	—
18	C₁₇×#533	—	2	1	no	—
19	C₁₇×#533	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×C₄⋊Q₈	—	2	1	no	—
21	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
23	C₁₇×#520	—	2	1	no	—
24	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
25	C₁₇×#500	—	2	1	no	—
26	C₁₇×#487	—	2	1	no	—
27	C₁₇×#487	—	2	2	no	—
28	C₁₇×#487	C₂²	1	4	yes	—
29	C₁₇×#484	—	2	2	no	—
30	C₁₇×#477	C₂²	1	4	yes	—
31	C₁₇×#477	C₂²	1	2	yes	—
32	C₁₇×#476	C₂²	1	2	yes	—
33	C₁₇×#475	—	2	1	no	—
34	C₁₇×#474	—	2	1	no	—
35	C₁₇×#431	C₂²	1	1	yes	characteristic
36	C₁₇×#428	—	2	1	no	—
37	C₁₇×#423	C₂²	1	1	yes	characteristic
38	C₁₇×#417	—	2	1	no	—
39	C₂×C₁₇×#103	—	2	2	no	—
40	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#332	C₂²	1	4	yes	—
42	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
43	C₁₇×Q₈⋊C₈	C₂²	1	4	yes	—
44	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
45	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
46	C₂²×Q₈×C₁₇	—	2	2	no	—
47	C₂²×Q₈×C₁₇	—	2	1	no	—
48	C₂²×Q₈×C₁₇	—	2	1	no	—
49	C₂×M₁₆×C₁₇	—	2	1	no	—
50	C₂²×C₈×C₁₇	—	2	1	no	—
51	C₁₇×C₄⋊Q₈	—	2	2	no	—
52	C₁₇×C₄⋊Q₈	—	2	2	no	—
53	C₁₇×C₄⋊Q₈	—	2	4	no	—
54	C₁₇×C₄⋊Q₈	—	2	2	no	—
55	C₁₇×C₄⋊Q₈	—	2	2	no	—
56	C₁₇×C₄⋊Q₈	—	2	1	no	—
57	C₁₇×C₄⋊Q₈	—	2	1	no	—
58	C₁₇×C₄⋊Q₈	—	2	1	no	—
59	C₁₇×C₄⋊Q₈	—	2	1	no	—
60	C₁₇×C₄⋊Q₈	—	2	1	no	—
61	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
62	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
63	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
64	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
65	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
66	C₁₇×#125	—	2	2	no	—
67	C₁₇×#125	—	2	4	no	—
68	C₁₇×#125	—	2	2	no	—
69	C₁₇×#125	—	2	1	no	—
70	C₁₇×C₂²⋊Q₈	—	2	2	no	—
71	C₁₇×C₂²⋊Q₈	—	2	4	no	—
72	C₁₇×C₂²⋊Q₈	—	2	4	no	—
73	C₁₇×C₂²⋊Q₈	—	2	1	no	—
74	C₁₇×C₂²⋊Q₈	—	2	2	no	—
75	C₁₇×C₂²⋊Q₈	—	2	4	no	—
76	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
77	C₄×Q₈×C₁₇	—	2	2	no	—
78	C₄×Q₈×C₁₇	—	2	2	no	—
79	C₄×Q₈×C₁₇	—	2	2	no	—
80	C₄×Q₈×C₁₇	—	2	1	no	—
81	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
83	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
84	C₄×D₄×C₁₇	—	2	4	no	—
85	C₄×D₄×C₁₇	—	2	2	no	—
86	C₄×D₄×C₁₇	—	2	1	no	—
87	C₄×D₄×C₁₇	—	2	1	no	—
88	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
89	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₁₇×#117	—	2	2	no	—
91	C₁₇×#117	—	2	1	no	—
92	C₁₇×#117	—	2	1	no	—
93	C₁₇×#117	D₄	1	1	yes	characteristic
94	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
95	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
96	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
102	C₁₇×#107	—	2	4	no	—
103	C₁₇×#107	—	2	2	no	—
104	C₁₇×#106	—	2	2	no	—
105	C₁₇×C₄⋊C₈	—	2	1	no	—
106	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
107	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
108	C₁₇×#103	—	2	2	no	—
109	C₁₇×#103	—	2	4	no	—
110	C₁₇×#103	—	2	8	no	—
111	C₁₇×#102	—	2	2	no	—
112	C₁₇×C₂²⋊C₈	—	2	1	no	—
113	C₄×C₈×C₁₇	—	2	1	no	—
114	C₄×C₈×C₁₇	—	2	1	no	—
115	C₄×C₈×C₁₇	C₂³	1	2	yes	—
116	#41×C₁₇	—	2	2	no	—
117	#41×C₁₇	Q₁₆	1	4	yes	—
118	C₂×Q₈×C₁₇	—	2	4	no	—
119	C₂×Q₈×C₁₇	—	2	1	no	—
120	C₂×Q₈×C₁₇	—	2	2	no	—
121	C₂×Q₈×C₁₇	—	2	2	no	—
122	C₂×Q₈×C₁₇	—	2	2	no	—
123	C₂×Q₈×C₁₇	—	4	4	no	—
124	C₂×Q₈×C₁₇	—	4	1	no	—
125	C₂×Q₈×C₁₇	—	8	2	no	—
126	C₂×Q₈×C₁₇	—	8	4	no	—
127	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
128	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₁₇	—	2	1	no	—
130	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₁₇	—	2	1	no	—
132	C₂²×C₄×C₁₇	—	2	4	no	—
133	C₂²×C₄×C₁₇	—	2	2	no	—
134	C₂²×C₄×C₁₇	—	2	1	no	—
135	C₂²×C₄×C₁₇	—	2	1	no	—
136	C₂²×C₄×C₁₇	—	4	1	no	—
137	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
140	M₁₆×C₁₇	—	4	2	no	—
141	C₂×C₈×C₁₇	—	2	2	no	—
142	C₂×C₈×C₁₇	—	2	2	no	—
143	C₂×C₈×C₁₇	—	2	2	no	—
144	C₂×C₈×C₁₇	—	4	2	no	—
145	C₄⋊C₄×C₁₇	—	2	4	no	—
146	C₄⋊C₄×C₁₇	—	2	4	no	—
147	C₄⋊C₄×C₁₇	—	2	4	no	—
148	C₄⋊C₄×C₁₇	—	2	4	no	—
149	C₄⋊C₄×C₁₇	—	2	2	no	—
150	C₄⋊C₄×C₁₇	—	2	2	no	—
151	C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₄⋊C₄×C₁₇	—	2	1	no	—
153	C₄⋊C₄×C₁₇	—	2	1	no	—
154	C₄⋊C₄×C₁₇	—	2	2	no	—
155	C₄⋊C₄×C₁₇	—	2	1	no	—
156	C₄⋊C₄×C₁₇	—	2	2	no	—
157	C₄⋊C₄×C₁₇	—	2	1	no	—
158	C₄⋊C₄×C₁₇	—	2	2	no	—
159	C₄⋊C₄×C₁₇	—	2	2	no	—
160	C₄⋊C₄×C₁₇	—	2	2	no	—
161	C₄⋊C₄×C₁₇	—	4	1	no	—
162	C₄⋊C₄×C₁₇	—	4	1	no	—
163	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
164	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
165	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
166	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
167	C₂²⋊C₄×C₁₇	—	2	4	no	—
168	C₂²⋊C₄×C₁₇	—	2	1	no	—
169	C₂²⋊C₄×C₁₇	—	2	2	no	—
170	C₂²⋊C₄×C₁₇	—	2	1	no	—
171	C₂²⋊C₄×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	—	2	4	no	—
173	C₄²×C₁₇	—	2	1	no	—
174	C₄²×C₁₇	—	2	1	no	—
175	C₄²×C₁₇	—	2	2	no	—
176	C₄²×C₁₇	—	2	1	no	—
177	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
181	#18643	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
182	C₂³×C₁₇	—	2	1	no	—
183	C₂³×C₁₇	#120	1	1	yes	characteristic
184	Q₈×C₁₇	—	2	1	no	—
185	Q₈×C₁₇	—	2	4	no	—
186	Q₈×C₁₇	—	4	4	no	—
187	Q₈×C₁₇	—	4	4	no	—
188	Q₈×C₁₇	—	4	2	no	—
189	Q₈×C₁₇	—	8	2	no	—
190	Q₈×C₁₇	—	8	4	no	—
191	Q₈×C₁₇	—	8	2	no	—
192	Q₈×C₁₇	C₂×Q₁₆	1	2	yes	—
193	D₄×C₁₇	—	2	4	no	—
194	D₄×C₁₇	—	2	1	no	—
195	D₄×C₁₇	C₂×Q₁₆	1	2	yes	—
196	C₂×C₄×C₁₇	—	2	1	no	—
197	C₂×C₄×C₁₇	—	2	2	no	—
198	C₂×C₄×C₁₇	—	2	4	no	—
199	C₂×C₄×C₁₇	—	2	2	no	—
200	C₂×C₄×C₁₇	—	2	2	no	—
201	C₂×C₄×C₁₇	—	2	1	no	—
202	C₂×C₄×C₁₇	—	2	1	no	—
203	C₂×C₄×C₁₇	—	2	2	no	—
204	C₂×C₄×C₁₇	—	2	4	no	—
205	C₂×C₄×C₁₇	—	4	2	no	—
206	C₂×C₄×C₁₇	—	4	2	no	—
207	C₂×C₄×C₁₇	—	4	2	no	—
208	C₂×C₄×C₁₇	—	8	2	no	—
209	C₂×C₄×C₁₇	—	8	4	no	—
210	C₂×C₄×C₁₇	—	8	2	no	—
211	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
212	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
213	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₁₇	C₂×Q₁₆	1	2	yes	—
215	C₂×C₄×C₁₇	#137	1	2	yes	—
216	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
217	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
218	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
219	C₈×C₁₇	—	4	2	no	—
220	C₈×C₁₇	—	4	2	no	—
221	C₈×C₁₇	—	4	2	no	—
222	#3503	C₂×C₁₇	1	1	yes	characteristic
223	#3230	C₂×C₁₇	1	1	yes	characteristic, complemented
224	C₂×#487	C₂×C₁₇	1	1	yes	characteristic, complemented
225	#3079	C₂×C₁₇	1	1	yes	characteristic
226	#1637	C₂×C₁₇	1	4	yes	complemented
227	#1636	C₂×C₁₇	1	4	yes	complemented
228	#1549	C₂×C₁₇	1	1	yes	characteristic, complemented
229	#1493	C₂×C₁₇	1	1	yes	characteristic, complemented
230	#1476	C₂×C₁₇	1	1	yes	characteristic
231	C₂²×C₁₇	—	2	1	no	—
232	C₂²×C₁₇	—	2	1	no	—
233	C₂²×C₁₇	—	2	2	no	—
234	C₂²×C₁₇	—	4	1	no	—
235	C₂²×C₁₇	—	4	1	no	—
236	C₂²×C₁₇	#451	1	2	yes	—
237	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
238	C₄×C₁₇	—	2	2	no	—
239	C₄×C₁₇	—	2	1	no	—
240	C₄×C₁₇	—	2	1	no	—
241	C₄×C₁₇	—	4	1	no	—
242	C₄×C₁₇	—	4	2	no	—
243	C₄×C₁₇	—	4	4	no	—
244	C₄×C₁₇	—	4	1	no	—
245	C₄×C₁₇	—	4	2	no	—
246	C₄×C₁₇	—	8	2	no	—
247	C₄×C₁₇	#451	1	2	yes	—
248	C₄×C₁₇	#454	1	2	yes	—
249	C₄×C₁₇	C₂²×Q₁₆	1	1	yes	characteristic
250	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
251	C₄×C₁₇	#577	1	2	yes	—
252	Q₈²	—	2	1	no	—
253	#557	C₂²×C₁₇	1	2	yes	—
254	#554	—	2	1	no	—
255	#554	—	2	2	no	—
256	D₄×Q₈	—	2	2	no	—
257	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
258	#544	—	2	2	no	—
259	#544	—	2	1	no	—
260	#533	—	2	1	no	—
261	#533	C₂²×C₁₇	1	1	yes	characteristic
262	C₂×C₄⋊Q₈	—	2	1	no	—
263	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
264	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
265	#520	—	2	1	no	—
266	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
267	#500	—	2	1	no	—
268	#487	—	2	2	no	—
269	#487	—	2	1	no	—
270	#487	C₂²×C₁₇	1	4	yes	—
271	#484	—	2	2	no	—
272	#477	C₂²×C₁₇	1	2	yes	—
273	#477	C₂²×C₁₇	1	4	yes	—
274	#476	C₂²×C₁₇	1	2	yes	—
275	#475	—	2	1	no	—
276	#474	—	2	1	no	—
277	#431	C₂²×C₁₇	1	1	yes	characteristic
278	#428	—	2	1	no	—
279	#423	C₂²×C₁₇	1	1	yes	characteristic
280	#417	—	2	1	no	—
281	C₂×#103	—	2	2	no	—
282	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
283	#332	C₂²×C₁₇	1	4	yes	—
284	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
285	Q₈⋊C₈	C₂²×C₁₇	1	4	yes	—
286	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
287	C₂×C₁₇	—	2	2	no	—
288	C₂×C₁₇	—	4	2	no	—
289	C₂×C₁₇	C₂×#451	1	1	yes	characteristic
290	C₂×C₁₇	#3009	1	1	yes	characteristic
291	C₂×C₁₇	C₂×#454	1	1	yes	characteristic
292	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	—	2	1	no	—
296	C₂×M₁₆	—	2	1	no	—
297	C₂²×C₈	—	2	1	no	—
298	C₄⋊Q₈	—	2	2	no	—
299	C₄⋊Q₈	—	2	2	no	—
300	C₄⋊Q₈	—	2	4	no	—
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	—	2	1	no	—
306	C₄⋊Q₈	—	2	1	no	—
307	C₄⋊Q₈	—	2	1	no	—
308	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
309	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
310	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
311	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
312	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
313	#125	—	2	2	no	—
314	#125	—	2	4	no	—
315	#125	—	2	2	no	—
316	#125	—	2	1	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	4	no	—
320	C₂²⋊Q₈	—	2	1	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	—	2	4	no	—
323	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
324	C₄×Q₈	—	2	2	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
329	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
330	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
331	C₄×D₄	—	2	4	no	—
332	C₄×D₄	—	2	2	no	—
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	—	2	1	no	—
335	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
336	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
337	#117	—	2	2	no	—
338	#117	—	2	1	no	—
339	#117	—	2	1	no	—
340	#117	D₄×C₁₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	—	2	2	no	—
342	C₂×C₄⋊C₄	—	2	2	no	—
343	C₂×C₄⋊C₄	—	2	1	no	—
344	C₂×C₄⋊C₄	—	2	1	no	—
345	C₂×C₄⋊C₄	—	2	1	no	—
346	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
349	#107	—	2	2	no	—
350	#107	—	2	4	no	—
351	#106	—	2	2	no	—
352	C₄⋊C₈	—	2	1	no	—
353	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
354	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
355	#103	—	2	2	no	—
356	#103	—	2	4	no	—
357	#103	—	2	8	no	—
358	#102	—	2	2	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₄×C₈	—	2	1	no	—
361	C₄×C₈	—	2	1	no	—
362	C₄×C₈	C₂³×C₁₇	1	2	yes	—
363	C₁₇	#18643	1	1	yes	characteristic, direct product factor, Sylow
364	#41	—	2	2	no	—
365	#41	Q₁₆×C₁₇	1	4	yes	—
366	C₂×Q₈	—	2	4	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	2	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×Q₈	—	4	1	no	—
373	C₂×Q₈	—	8	2	no	—
374	C₂×Q₈	—	8	4	no	—
375	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
376	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
377	C₂×D₄	—	2	1	no	—
378	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	4	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	1	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	4	1	no	—
385	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
388	M₁₆	—	4	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	4	2	no	—
393	C₄⋊C₄	—	2	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	4	no	—
396	C₄⋊C₄	—	2	4	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	4	1	no	—
410	C₄⋊C₄	—	4	1	no	—
411	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
412	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
413	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
414	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
415	C₂²⋊C₄	—	2	4	no	—
416	C₂²⋊C₄	—	2	2	no	—
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₄²	—	2	4	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
428	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	C₁₇×#120	1	1	yes	characteristic
431	Q₈	—	2	1	no	—
432	Q₈	—	2	4	no	—
433	Q₈	—	4	4	no	—
434	Q₈	—	4	4	no	—
435	Q₈	—	4	2	no	—
436	Q₈	—	8	2	no	—
437	Q₈	—	8	4	no	—
438	Q₈	—	8	2	no	—
439	Q₈	C₂×Q₁₆×C₁₇	1	2	yes	—
440	D₄	—	2	4	no	—
441	D₄	—	2	1	no	—
442	D₄	C₂×Q₁₆×C₁₇	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	4	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	8	2	no	—
456	C₂×C₄	—	8	4	no	—
457	C₂×C₄	—	8	2	no	—
458	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
459	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
460	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
461	C₂×C₄	C₂×Q₁₆×C₁₇	1	2	yes	—
462	C₂×C₄	C₁₇×#137	1	2	yes	—
463	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
464	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
465	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
466	C₈	—	4	2	no	—
467	C₈	—	4	2	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	C₁₇×#451	1	2	yes	—
475	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	2	no	—
481	C₄	—	4	4	no	—
482	C₄	—	4	1	no	—
483	C₄	—	4	2	no	—
484	C₄	—	8	2	no	—
485	C₄	C₁₇×#451	1	2	yes	—
486	C₄	C₁₇×#454	1	2	yes	—
487	C₄	C₂²×Q₁₆×C₁₇	1	1	yes	characteristic
488	C₄	C₂×C₁₇×#137	1	1	yes	characteristic
489	C₄	C₁₇×#577	1	2	yes	—
490	C₂	—	2	2	no	—
491	C₂	—	4	2	no	—
492	C₂	C₂×C₁₇×#451	1	1	yes	characteristic
493	C₂	C₁₇×#3009	1	1	yes	characteristic
494	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	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×#3230	C₂	semidirect
3. C₂×C₁₇×#487	C₂	semidirect
5. C₁₇×#1637	C₂	semidirect
6. C₁₇×#1636	C₂	semidirect
7. C₁₇×#1549	C₂	semidirect
8. C₁₇×#1493	C₂	semidirect
181. #18643	C₁₇	direct (N × H)
223. #3230	C₂×C₁₇	semidirect
224. C₂×#487	C₂×C₁₇	semidirect
226. #1637	C₂×C₁₇	semidirect
227. #1636	C₂×C₁₇	semidirect
228. #1549	C₂×C₁₇	semidirect
229. #1493	C₂×C₁₇	semidirect
363. C₁₇	#18643	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×#3230	2
C₂×C₁₇×#487	2
C₁₇×#3079	2
C₁₇×#1637	2
C₁₇×#1636	2
C₁₇×#1549	2
C₁₇×#1493	2
C₁₇×#1476	2
#18643	17

Subgroups — C17×#18643 #16876387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18643 #16876387