Subgroups — C₁₇×#19846 #16877590

Order 4352.

566 conjugacy classes of subgroups.

The subgroup lattice has 546 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3375	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#3365	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1719	C₂	1	1	yes	maximal, characteristic
6	C₁₇×#1704	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1682	C₂	1	1	yes	maximal, characteristic
8	C₁₇×#1678	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1676	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1645	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1636	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1630	C₂	1	1	yes	maximal, characteristic
13	C₁₇×#1623	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1579	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#559	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
18	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#557	C₂²	1	1	yes	characteristic
20	C₁₇×#500	—	2	1	no	—
21	C₁₇×#500	C₂²	1	1	yes	characteristic
22	C₁₇×#492	C₂²	1	1	yes	characteristic
23	C₁₇×#489	—	2	1	no	—
24	C₁₇×#488	—	2	1	no	—
25	C₁₇×#487	—	2	1	no	—
26	C₁₇×#487	C₂²	1	1	yes	characteristic
27	C₁₇×#487	C₂²	1	1	yes	characteristic
28	C₁₇×#486	C₂²	1	1	yes	characteristic
29	C₁₇×#486	C₂²	1	1	yes	characteristic
30	C₁₇×#478	—	2	1	no	—
31	C₁₇×#477	—	2	1	no	—
32	C₁₇×#477	—	2	1	no	—
33	C₁₇×#477	—	2	1	no	—
34	C₁₇×#477	C₂²	1	1	yes	characteristic
35	C₁₇×#477	C₂²	1	1	yes	characteristic
36	C₁₇×#477	C₂²	1	1	yes	characteristic
37	C₁₇×#477	C₂²	1	1	yes	characteristic
38	C₁₇×#475	C₂²	1	1	yes	characteristic
39	C₁₇×#474	—	2	1	no	—
40	C₁₇×#464	—	2	1	no	—
41	C₁₇×#464	—	2	1	no	—
42	C₁₇×#462	—	2	1	no	—
43	C₁₇×#462	C₂²	1	1	yes	characteristic
44	C₁₇×#460	C₂²	1	1	yes	characteristic
45	C₁₇×#460	C₂²	1	1	yes	characteristic
46	C₁₇×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
50	C₁₇×#440	—	2	1	no	—
51	C₄×Q₁₆×C₁₇	—	2	1	no	—
52	C₄×Q₁₆×C₁₇	—	2	1	no	—
53	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
54	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
55	C₄×SD₁₆×C₁₇	—	2	1	no	—
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#334	C₂²	1	1	yes	characteristic
58	C₁₇×#333	C₂²	1	1	yes	characteristic
59	C₁₇×#333	C₂²	1	1	yes	characteristic
60	C₁₇×#332	C₂²	1	1	yes	characteristic
61	C₁₇×#331	C₂²	1	1	yes	characteristic
62	C₁₇×Q₈⋊C₈	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×#322	C₂²	1	1	yes	characteristic
67	C₂×Q₁₆×C₁₇	—	2	1	no	—
68	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
69	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₇	—	2	1	no	—
71	C₂×SD₁₆×C₁₇	—	2	1	no	—
72	C₂×SD₁₆×C₁₇	—	4	1	no	—
73	C₁₇×C₄⋊Q₈	—	2	1	no	—
74	C₁₇×C₄⋊Q₈	—	2	1	no	—
75	C₁₇×C₄⋊Q₈	—	2	1	no	—
76	C₁₇×C₄⋊Q₈	—	2	1	no	—
77	C₁₇×C₄⋊Q₈	—	2	1	no	—
78	C₁₇×C₄⋊Q₈	—	4	1	no	—
79	C₁₇×C₄⋊Q₈	—	4	1	no	—
80	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₇×#127	C₂³	1	1	yes	characteristic
84	C₁₇×#125	—	2	1	no	—
85	C₁₇×#125	—	4	1	no	—
86	C₁₇×#124	—	2	1	no	—
87	C₁₇×#124	—	2	1	no	—
88	C₁₇×#123	—	4	1	no	—
89	C₄×Q₈×C₁₇	—	2	1	no	—
90	C₄×Q₈×C₁₇	—	2	1	no	—
91	C₄×Q₈×C₁₇	—	2	1	no	—
92	C₄×Q₈×C₁₇	—	2	1	no	—
93	C₄×Q₈×C₁₇	—	2	1	no	—
94	C₄×Q₈×C₁₇	—	2	1	no	—
95	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
98	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₇	—	2	1	no	—
100	C₄×D₄×C₁₇	—	2	1	no	—
101	C₁₇×#107	—	2	1	no	—
102	C₁₇×#107	—	2	1	no	—
103	C₁₇×#107	—	2	1	no	—
104	C₁₇×#107	—	2	1	no	—
105	C₁₇×#107	—	2	1	no	—
106	C₁₇×#107	—	2	1	no	—
107	C₁₇×#107	D₄	1	1	yes	characteristic
108	C₁₇×#107	D₄	1	1	yes	characteristic
109	C₁₇×#106	—	2	1	no	—
110	C₁₇×C₄⋊C₈	—	2	1	no	—
111	C₁₇×C₄⋊C₈	—	2	1	no	—
112	C₁₇×C₄⋊C₈	—	2	1	no	—
113	C₁₇×C₄⋊C₈	—	2	1	no	—
114	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₇×#103	—	2	1	no	—
119	C₁₇×#103	—	2	1	no	—
120	C₁₇×#103	—	2	1	no	—
121	C₁₇×#103	—	2	1	no	—
122	C₁₇×#103	—	2	1	no	—
123	C₁₇×#103	—	2	1	no	—
124	C₁₇×#103	—	2	1	no	—
125	C₁₇×#103	—	2	1	no	—
126	C₁₇×#103	—	4	1	no	—
127	C₁₇×#103	D₄	1	1	yes	characteristic
128	C₁₇×#103	D₄	1	1	yes	characteristic
129	C₁₇×#103	D₄	1	1	yes	characteristic
130	C₁₇×#103	D₄	1	1	yes	characteristic
131	C₁₇×#102	—	2	1	no	—
132	C₁₇×#102	—	2	1	no	—
133	C₁₇×#102	—	2	1	no	—
134	C₁₇×#102	—	2	1	no	—
135	C₁₇×#102	—	2	1	no	—
136	C₁₇×#102	—	2	1	no	—
137	C₁₇×#97	—	2	1	no	—
138	C₄×C₈×C₁₇	—	2	1	no	—
139	C₄×C₈×C₁₇	—	2	1	no	—
140	C₄×C₈×C₁₇	—	2	1	no	—
141	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	C₂×Q₈×C₁₇	—	2	1	no	—
145	C₂×Q₈×C₁₇	—	2	1	no	—
146	C₂×Q₈×C₁₇	—	2	1	no	—
147	C₂×Q₈×C₁₇	—	4	1	no	—
148	C₂×Q₈×C₁₇	—	4	1	no	—
149	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂×D₄×C₁₇	—	2	1	no	—
154	C₂×D₄×C₁₇	—	2	1	no	—
155	C₂×D₄×C₁₇	—	2	1	no	—
156	C₂²×C₄×C₁₇	—	4	1	no	—
157	Q₁₆×C₁₇	—	2	2	no	—
158	Q₁₆×C₁₇	—	2	2	no	—
159	Q₁₆×C₁₇	—	4	2	no	—
160	SD₁₆×C₁₇	—	4	2	no	—
161	SD₁₆×C₁₇	—	4	2	no	—
162	SD₁₆×C₁₇	—	8	2	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	—	2	1	no	—
174	C₄⋊C₄×C₁₇	—	2	1	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	—	2	1	no	—
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	4	1	no	—
183	C₄⋊C₄×C₁₇	—	4	1	no	—
184	C₄⋊C₄×C₁₇	—	4	1	no	—
185	C₄⋊C₄×C₁₇	—	4	1	no	—
186	C₄⋊C₄×C₁₇	—	4	1	no	—
187	C₄⋊C₄×C₁₇	—	4	1	no	—
188	C₄⋊C₄×C₁₇	—	4	1	no	—
189	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
190	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₇	—	4	1	no	—
194	C₂²⋊C₄×C₁₇	—	4	1	no	—
195	C₂²⋊C₄×C₁₇	—	4	1	no	—
196	C₄²×C₁₇	—	2	1	no	—
197	C₄²×C₁₇	—	2	1	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	2	1	no	—
200	C₄²×C₁₇	—	4	1	no	—
201	C₄²×C₁₇	—	4	1	no	—
202	C₄²×C₁₇	—	4	1	no	—
203	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
204	#19846	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₇	—	4	1	no	—
206	Q₈×C₁₇	—	2	1	no	—
207	Q₈×C₁₇	—	2	1	no	—
208	Q₈×C₁₇	—	2	1	no	—
209	Q₈×C₁₇	—	2	1	no	—
210	Q₈×C₁₇	—	2	1	no	—
211	Q₈×C₁₇	—	2	1	no	—
212	Q₈×C₁₇	—	4	1	no	—
213	Q₈×C₁₇	—	4	1	no	—
214	Q₈×C₁₇	—	8	1	no	—
215	Q₈×C₁₇	—	8	1	no	—
216	Q₈×C₁₇	—	16	1	no	—
217	Q₈×C₁₇	—	16	1	no	—
218	Q₈×C₁₇	#135	1	2	yes	—
219	Q₈×C₁₇	#137	1	2	yes	—
220	D₄×C₁₇	—	4	1	no	—
221	D₄×C₁₇	—	4	1	no	—
222	D₄×C₁₇	—	4	1	no	—
223	D₄×C₁₇	—	4	1	no	—
224	D₄×C₁₇	—	8	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	1	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	4	1	no	—
234	C₂×C₄×C₁₇	—	4	1	no	—
235	C₂×C₄×C₁₇	—	4	1	no	—
236	C₂×C₄×C₁₇	—	16	1	no	—
237	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₈×C₁₇	—	2	1	no	—
241	C₈×C₁₇	—	2	1	no	—
242	C₈×C₁₇	—	2	1	no	—
243	C₈×C₁₇	—	2	1	no	—
244	C₈×C₁₇	—	4	1	no	—
245	C₈×C₁₇	—	4	1	no	—
246	C₈×C₁₇	—	4	1	no	—
247	C₈×C₁₇	—	4	1	no	—
248	C₈×C₁₇	—	4	1	no	—
249	Q₈×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
250	#3375	C₂×C₁₇	1	1	yes	characteristic
251	#3365	C₂×C₁₇	1	1	yes	characteristic
252	#3363	C₂×C₁₇	1	1	yes	characteristic, complemented
253	#1719	C₂×C₁₇	1	1	yes	characteristic
254	#1704	C₂×C₁₇	1	1	yes	characteristic, complemented
255	#1682	C₂×C₁₇	1	1	yes	characteristic
256	#1678	C₂×C₁₇	1	1	yes	characteristic
257	#1676	C₂×C₁₇	1	1	yes	characteristic, complemented
258	#1645	C₂×C₁₇	1	1	yes	characteristic, complemented
259	#1636	C₂×C₁₇	1	1	yes	characteristic, complemented
260	#1630	C₂×C₁₇	1	1	yes	characteristic
261	#1623	C₂×C₁₇	1	1	yes	characteristic
262	#1584	C₂×C₁₇	1	1	yes	characteristic, complemented
263	#1579	C₂×C₁₇	1	1	yes	characteristic, complemented
264	C₂²×C₁₇	—	8	1	no	—
265	C₂²×C₁₇	—	8	1	no	—
266	C₂²×C₁₇	—	8	1	no	—
267	C₂²×C₁₇	D₄²	1	1	yes	characteristic
268	C₄×C₁₇	—	2	2	no	—
269	C₄×C₁₇	—	2	2	no	—
270	C₄×C₁₇	—	2	1	no	—
271	C₄×C₁₇	—	4	1	no	—
272	C₄×C₁₇	—	4	1	no	—
273	C₄×C₁₇	—	4	1	no	—
274	C₄×C₁₇	—	4	1	no	—
275	C₄×C₁₇	—	4	1	no	—
276	C₄×C₁₇	—	4	1	no	—
277	C₄×C₁₇	—	8	1	no	—
278	C₄×C₁₇	—	8	1	no	—
279	C₄×C₁₇	—	8	1	no	—
280	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
281	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
282	C₄×C₁₇	#578	1	1	yes	characteristic
283	C₄×C₁₇	#578	1	1	yes	characteristic
284	#559	C₂²×C₁₇	1	1	yes	characteristic
285	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
286	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
287	#557	C₂²×C₁₇	1	1	yes	characteristic
288	#500	—	2	1	no	—
289	#500	C₂²×C₁₇	1	1	yes	characteristic
290	#492	C₂²×C₁₇	1	1	yes	characteristic
291	#489	—	2	1	no	—
292	#488	—	2	1	no	—
293	#487	—	2	1	no	—
294	#487	C₂²×C₁₇	1	1	yes	characteristic
295	#487	C₂²×C₁₇	1	1	yes	characteristic
296	#486	C₂²×C₁₇	1	1	yes	characteristic
297	#486	C₂²×C₁₇	1	1	yes	characteristic
298	#478	—	2	1	no	—
299	#477	—	2	1	no	—
300	#477	—	2	1	no	—
301	#477	—	2	1	no	—
302	#477	C₂²×C₁₇	1	1	yes	characteristic
303	#477	C₂²×C₁₇	1	1	yes	characteristic
304	#477	C₂²×C₁₇	1	1	yes	characteristic
305	#477	C₂²×C₁₇	1	1	yes	characteristic
306	#475	C₂²×C₁₇	1	1	yes	characteristic
307	#474	—	2	1	no	—
308	#464	—	2	1	no	—
309	#464	—	2	1	no	—
310	#462	—	2	1	no	—
311	#462	C₂²×C₁₇	1	1	yes	characteristic
312	#460	C₂²×C₁₇	1	1	yes	characteristic
313	#460	C₂²×C₁₇	1	1	yes	characteristic
314	#446	C₂²×C₁₇	1	1	yes	characteristic
315	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
316	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
318	#440	—	2	1	no	—
319	C₄×Q₁₆	—	2	1	no	—
320	C₄×Q₁₆	—	2	1	no	—
321	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
322	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
323	C₄×SD₁₆	—	2	1	no	—
324	#335	C₂²×C₁₇	1	1	yes	characteristic
325	#334	C₂²×C₁₇	1	1	yes	characteristic
326	#333	C₂²×C₁₇	1	1	yes	characteristic
327	#333	C₂²×C₁₇	1	1	yes	characteristic
328	#332	C₂²×C₁₇	1	1	yes	characteristic
329	#331	C₂²×C₁₇	1	1	yes	characteristic
330	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
331	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
332	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
333	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
334	#322	C₂²×C₁₇	1	1	yes	characteristic
335	C₂×C₁₇	—	16	1	no	—
336	C₂×C₁₇	#3270	1	1	yes	characteristic
337	C₂×C₁₇	#3285	1	1	yes	characteristic
338	C₂×C₁₇	#3288	1	1	yes	characteristic
339	C₂×Q₁₆	—	2	1	no	—
340	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
341	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
342	C₂×SD₁₆	—	2	1	no	—
343	C₂×SD₁₆	—	2	1	no	—
344	C₂×SD₁₆	—	4	1	no	—
345	C₄⋊Q₈	—	2	1	no	—
346	C₄⋊Q₈	—	2	1	no	—
347	C₄⋊Q₈	—	2	1	no	—
348	C₄⋊Q₈	—	2	1	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	4	1	no	—
351	C₄⋊Q₈	—	4	1	no	—
352	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
353	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
354	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
355	#127	C₂³×C₁₇	1	1	yes	characteristic
356	#125	—	2	1	no	—
357	#125	—	4	1	no	—
358	#124	—	2	1	no	—
359	#124	—	2	1	no	—
360	#123	—	4	1	no	—
361	C₄×Q₈	—	2	1	no	—
362	C₄×Q₈	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	—	2	1	no	—
366	C₄×Q₈	—	2	1	no	—
367	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
368	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
369	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
370	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	#107	—	2	1	no	—
374	#107	—	2	1	no	—
375	#107	—	2	1	no	—
376	#107	—	2	1	no	—
377	#107	—	2	1	no	—
378	#107	—	2	1	no	—
379	#107	D₄×C₁₇	1	1	yes	characteristic
380	#107	D₄×C₁₇	1	1	yes	characteristic
381	#106	—	2	1	no	—
382	C₄⋊C₈	—	2	1	no	—
383	C₄⋊C₈	—	2	1	no	—
384	C₄⋊C₈	—	2	1	no	—
385	C₄⋊C₈	—	2	1	no	—
386	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
387	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
388	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
389	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
390	#103	—	2	1	no	—
391	#103	—	2	1	no	—
392	#103	—	2	1	no	—
393	#103	—	2	1	no	—
394	#103	—	2	1	no	—
395	#103	—	2	1	no	—
396	#103	—	2	1	no	—
397	#103	—	2	1	no	—
398	#103	—	4	1	no	—
399	#103	D₄×C₁₇	1	1	yes	characteristic
400	#103	D₄×C₁₇	1	1	yes	characteristic
401	#103	D₄×C₁₇	1	1	yes	characteristic
402	#103	D₄×C₁₇	1	1	yes	characteristic
403	#102	—	2	1	no	—
404	#102	—	2	1	no	—
405	#102	—	2	1	no	—
406	#102	—	2	1	no	—
407	#102	—	2	1	no	—
408	#102	—	2	1	no	—
409	#97	—	2	1	no	—
410	C₄×C₈	—	2	1	no	—
411	C₄×C₈	—	2	1	no	—
412	C₄×C₈	—	2	1	no	—
413	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
414	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
415	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
416	C₁₇	#19846	1	1	yes	characteristic, direct product factor, Sylow
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	4	1	no	—
421	C₂×Q₈	—	4	1	no	—
422	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
423	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
424	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
425	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
426	C₂×D₄	—	2	1	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂²×C₄	—	4	1	no	—
430	Q₁₆	—	2	2	no	—
431	Q₁₆	—	2	2	no	—
432	Q₁₆	—	4	2	no	—
433	SD₁₆	—	4	2	no	—
434	SD₁₆	—	4	2	no	—
435	SD₁₆	—	8	2	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	1	no	—
438	C₂×C₈	—	2	1	no	—
439	C₂×C₈	—	2	1	no	—
440	C₂×C₈	—	2	1	no	—
441	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
442	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
443	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
444	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	1	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	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	4	1	no	—
456	C₄⋊C₄	—	4	1	no	—
457	C₄⋊C₄	—	4	1	no	—
458	C₄⋊C₄	—	4	1	no	—
459	C₄⋊C₄	—	4	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
463	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
464	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
465	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₂²⋊C₄	—	4	1	no	—
469	C₄²	—	2	1	no	—
470	C₄²	—	2	1	no	—
471	C₄²	—	2	1	no	—
472	C₄²	—	2	1	no	—
473	C₄²	—	4	1	no	—
474	C₄²	—	4	1	no	—
475	C₄²	—	4	1	no	—
476	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
477	C₂³	—	4	1	no	—
478	Q₈	—	2	1	no	—
479	Q₈	—	2	1	no	—
480	Q₈	—	2	1	no	—
481	Q₈	—	2	1	no	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	1	no	—
484	Q₈	—	4	1	no	—
485	Q₈	—	4	1	no	—
486	Q₈	—	8	1	no	—
487	Q₈	—	8	1	no	—
488	Q₈	—	16	1	no	—
489	Q₈	—	16	1	no	—
490	Q₈	C₁₇×#135	1	2	yes	—
491	Q₈	C₁₇×#137	1	2	yes	—
492	D₄	—	4	1	no	—
493	D₄	—	4	1	no	—
494	D₄	—	4	1	no	—
495	D₄	—	4	1	no	—
496	D₄	—	8	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	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	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	4	1	no	—
507	C₂×C₄	—	4	1	no	—
508	C₂×C₄	—	16	1	no	—
509	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
510	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
511	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	2	1	no	—
516	C₈	—	4	1	no	—
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	1	no	—
520	C₈	—	4	1	no	—
521	C₂²	—	8	1	no	—
522	C₂²	—	8	1	no	—
523	C₂²	—	8	1	no	—
524	C₂²	D₄²×C₁₇	1	1	yes	characteristic
525	C₄	—	2	2	no	—
526	C₄	—	2	2	no	—
527	C₄	—	2	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	1	no	—
531	C₄	—	4	1	no	—
532	C₄	—	4	1	no	—
533	C₄	—	4	1	no	—
534	C₄	—	8	1	no	—
535	C₄	—	8	1	no	—
536	C₄	—	8	1	no	—
537	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
538	C₄	C₂×C₁₇×#137	1	1	yes	characteristic
539	C₄	C₁₇×#578	1	1	yes	characteristic
540	C₄	C₁₇×#578	1	1	yes	characteristic
541	C₂	—	16	1	no	—
542	C₂	C₁₇×#3270	1	1	yes	characteristic
543	C₂	C₁₇×#3285	1	1	yes	characteristic
544	C₂	C₁₇×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#127	C₂³
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. Q₈×Q₁₆×C₁₇	C₂	semidirect
4. C₁₇×#3363	C₂	semidirect
6. C₁₇×#1704	C₂	semidirect
9. C₁₇×#1676	C₂	semidirect
10. C₁₇×#1645	C₂	semidirect
11. C₁₇×#1636	C₂	semidirect
14. C₁₇×#1584	C₂	semidirect
15. C₁₇×#1579	C₂	semidirect
204. #19846	C₁₇	direct (N × H)
249. Q₈×Q₁₆	C₂×C₁₇	semidirect
252. #3363	C₂×C₁₇	semidirect
254. #1704	C₂×C₁₇	semidirect
257. #1676	C₂×C₁₇	semidirect
258. #1645	C₂×C₁₇	semidirect
259. #1636	C₂×C₁₇	semidirect
262. #1584	C₂×C₁₇	semidirect
263. #1579	C₂×C₁₇	semidirect
416. C₁₇	#19846	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
Q₈×Q₁₆×C₁₇	2
C₁₇×#3375	2
C₁₇×#3365	2
C₁₇×#3363	2
C₁₇×#1719	2
C₁₇×#1704	2
C₁₇×#1682	2
C₁₇×#1678	2
C₁₇×#1676	2
C₁₇×#1645	2
C₁₇×#1636	2
C₁₇×#1630	2
C₁₇×#1623	2
C₁₇×#1584	2
C₁₇×#1579	2
#19846	17

Subgroups — C17×#19846 #16877590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19846 #16877590