Subgroups — C₁₇×#19867 #16877611

Order 4352.

692 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3397	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3391	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3304	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3287	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1721	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1688	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1681	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1666	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1642	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1628	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1621	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1621	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1584	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#135	—	2	1	no	—
17	C₁₇×#556	C₂²	1	1	yes	characteristic
18	C₁₇×#550	C₂²	1	1	yes	characteristic
19	C₁₇×#550	C₂²	1	1	yes	characteristic
20	C₁₇×#550	C₂²	1	1	yes	characteristic
21	C₁₇×#496	—	2	1	no	—
22	C₁₇×#493	—	2	1	no	—
23	C₁₇×#493	C₂²	1	1	yes	characteristic
24	C₁₇×#493	C₂²	1	1	yes	characteristic
25	C₁₇×#493	C₂²	1	1	yes	characteristic
26	C₁₇×#492	C₂²	1	1	yes	characteristic
27	C₁₇×#486	C₂²	1	1	yes	characteristic
28	C₁₇×#486	C₂²	1	1	yes	characteristic
29	C₁₇×#482	—	2	1	no	—
30	C₁₇×#475	C₂²	1	1	yes	characteristic
31	C₁₇×#466	—	2	1	no	—
32	C₁₇×#465	—	2	1	no	—
33	C₁₇×#463	—	2	1	no	—
34	C₁₇×#461	C₂²	1	1	yes	characteristic
35	C₁₇×#460	—	2	1	no	—
36	C₁₇×#460	C₂²	1	1	yes	characteristic
37	C₁₇×#460	C₂²	1	1	yes	characteristic
38	C₁₇×#460	C₂²	1	1	yes	characteristic
39	C₁₇×#459	—	2	1	no	—
40	C₁₇×#459	—	2	1	no	—
41	C₁₇×#459	C₂²	1	1	yes	characteristic
42	C₁₇×#459	C₂²	1	1	yes	characteristic
43	C₁₇×#459	C₂²	1	1	yes	characteristic
44	C₁₇×#452	—	2	1	no	—
45	C₁₇×#449	—	2	1	no	—
46	C₁₇×#449	—	2	1	no	—
47	C₁₇×#446	C₂²	1	1	yes	characteristic
48	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#440	—	2	1	no	—
50	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
51	C₄×D₈×C₁₇	—	2	1	no	—
52	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
54	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
55	C₁₇×#416	—	2	1	no	—
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#334	C₂²	1	1	yes	characteristic
58	C₁₇×#332	C₂²	1	1	yes	characteristic
59	C₁₇×#331	C₂²	1	1	yes	characteristic
60	C₁₇×#331	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	—	2	1	no	—
68	C₂×#41×C₁₇	—	2	1	no	—
69	C₂×#41×C₁₇	—	2	1	no	—
70	C₁₇×#135	—	4	4	no	—
71	C₂×Q₁₆×C₁₇	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₁₇	—	2	1	no	—
73	C₂×SD₁₆×C₁₇	—	2	1	no	—
74	C₂×SD₁₆×C₁₇	—	2	1	no	—
75	C₂×SD₁₆×C₁₇	—	2	1	no	—
76	C₂×SD₁₆×C₁₇	—	2	1	no	—
77	C₂×SD₁₆×C₁₇	—	2	1	no	—
78	C₂×D₈×C₁₇	—	2	1	no	—
79	C₂×D₈×C₁₇	—	2	1	no	—
80	C₂×D₈×C₁₇	—	2	1	no	—
81	C₂×D₈×C₁₇	—	2	1	no	—
82	C₂×D₈×C₁₇	—	2	1	no	—
83	C₂×D₈×C₁₇	—	2	1	no	—
84	C₂×D₈×C₁₇	—	2	1	no	—
85	C₂×D₈×C₁₇	—	4	1	no	—
86	C₂×D₈×C₁₇	D₄	1	1	yes	characteristic
87	C₂²×C₈×C₁₇	—	2	1	no	—
88	C₂²×C₈×C₁₇	—	2	1	no	—
89	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
90	C₁₇×#127	—	2	1	no	—
91	C₁₇×#127	—	2	1	no	—
92	C₁₇×#127	—	2	1	no	—
93	C₁₇×#127	C₂³	1	1	yes	characteristic
94	C₁₇×#127	C₂³	1	1	yes	characteristic
95	C₁₇×#127	C₂³	1	1	yes	characteristic
96	C₁₇×#126	—	4	1	no	—
97	C₁₇×#124	—	2	1	no	—
98	C₁₇×C₂²⋊Q₈	—	2	1	no	—
99	C₁₇×#121	—	2	1	no	—
100	C₁₇×#121	—	2	1	no	—
101	C₁₇×#121	—	2	1	no	—
102	C₁₇×#121	—	4	1	no	—
103	C₁₇×#121	—	4	1	no	—
104	C₁₇×#121	—	4	1	no	—
105	C₄×Q₈×C₁₇	—	2	1	no	—
106	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
107	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
108	C₄×D₄×C₁₇	—	2	1	no	—
109	C₄×D₄×C₁₇	—	2	1	no	—
110	C₄×D₄×C₁₇	—	2	1	no	—
111	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
112	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
113	C₁₇×#117	—	2	1	no	—
114	C₁₇×#107	D₄	1	1	yes	characteristic
115	C₁₇×#107	D₄	1	1	yes	characteristic
116	C₁₇×#106	—	2	1	no	—
117	C₁₇×C₄⋊C₈	—	2	1	no	—
118	C₁₇×C₄⋊C₈	—	2	1	no	—
119	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
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	1	no	—
125	C₁₇×#103	D₄	1	1	yes	characteristic
126	C₁₇×#103	D₄	1	1	yes	characteristic
127	C₁₇×#102	—	2	1	no	—
128	C₁₇×#102	—	2	1	no	—
129	C₁₇×#102	—	2	1	no	—
130	C₁₇×#102	—	2	1	no	—
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	—	4	1	no	—
136	C₁₇×#102	D₄	1	1	yes	characteristic
137	C₁₇×#102	D₄	1	1	yes	characteristic
138	C₁₇×C₂²⋊C₈	—	2	1	no	—
139	C₁₇×C₂²⋊C₈	—	2	1	no	—
140	C₁₇×#97	—	2	1	no	—
141	C₄×C₈×C₁₇	—	2	1	no	—
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
145	#41×C₁₇	—	4	2	no	—
146	#41×C₁₇	—	4	2	no	—
147	#41×C₁₇	—	4	2	no	—
148	#41×C₁₇	—	8	1	no	—
149	#41×C₁₇	—	8	1	no	—
150	#41×C₁₇	—	8	1	no	—
151	C₂×Q₈×C₁₇	—	2	1	no	—
152	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
153	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂×D₄×C₁₇	—	2	1	no	—
155	C₂×D₄×C₁₇	—	2	1	no	—
156	C₂×D₄×C₁₇	—	2	1	no	—
157	C₂×D₄×C₁₇	—	2	1	no	—
158	C₂×D₄×C₁₇	—	2	1	no	—
159	C₂×D₄×C₁₇	—	2	1	no	—
160	C₂×D₄×C₁₇	—	2	1	no	—
161	C₂×D₄×C₁₇	—	2	1	no	—
162	C₂×D₄×C₁₇	—	2	1	no	—
163	C₂×D₄×C₁₇	—	4	1	no	—
164	C₂×D₄×C₁₇	—	4	1	no	—
165	C₂×D₄×C₁₇	—	4	1	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	C₂×D₄	1	1	yes	characteristic
170	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂²×C₄×C₁₇	—	2	1	no	—
172	C₂²×C₄×C₁₇	—	2	1	no	—
173	C₂²×C₄×C₁₇	—	4	1	no	—
174	C₂²×C₄×C₁₇	—	4	1	no	—
175	C₂²×C₄×C₁₇	—	4	1	no	—
176	Q₁₆×C₁₇	—	2	2	no	—
177	SD₁₆×C₁₇	—	4	2	no	—
178	SD₁₆×C₁₇	—	4	2	no	—
179	SD₁₆×C₁₇	—	4	2	no	—
180	SD₁₆×C₁₇	—	8	1	no	—
181	SD₁₆×C₁₇	—	8	1	no	—
182	SD₁₆×C₁₇	—	8	1	no	—
183	D₈×C₁₇	—	2	2	no	—
184	D₈×C₁₇	—	4	2	no	—
185	D₈×C₁₇	—	4	2	no	—
186	D₈×C₁₇	—	8	1	no	—
187	D₈×C₁₇	—	8	1	no	—
188	D₈×C₁₇	—	8	1	no	—
189	D₈×C₁₇	—	8	1	no	—
190	D₈×C₁₇	—	8	1	no	—
191	D₈×C₁₇	—	8	2	no	—
192	C₂×C₈×C₁₇	—	2	1	no	—
193	C₂×C₈×C₁₇	—	2	1	no	—
194	C₂×C₈×C₁₇	—	2	1	no	—
195	C₂×C₈×C₁₇	—	2	1	no	—
196	C₂×C₈×C₁₇	—	2	1	no	—
197	C₂×C₈×C₁₇	—	4	2	no	—
198	C₂×C₈×C₁₇	—	8	1	no	—
199	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
200	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
201	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
202	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
208	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
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	1	yes	characteristic
212	C₂²⋊C₄×C₁₇	—	2	1	no	—
213	C₂²⋊C₄×C₁₇	—	2	1	no	—
214	C₂²⋊C₄×C₁₇	—	4	1	no	—
215	C₂²⋊C₄×C₁₇	—	4	1	no	—
216	C₂²⋊C₄×C₁₇	—	4	1	no	—
217	C₂²⋊C₄×C₁₇	—	4	1	no	—
218	C₂²⋊C₄×C₁₇	—	4	1	no	—
219	C₄²×C₁₇	—	2	1	no	—
220	C₄²×C₁₇	—	2	1	no	—
221	C₄²×C₁₇	—	4	1	no	—
222	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
223	#19867	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
224	C₂³×C₁₇	—	2	1	no	—
225	C₂³×C₁₇	—	2	1	no	—
226	C₂³×C₁₇	—	4	1	no	—
227	C₂³×C₁₇	—	4	1	no	—
228	C₂³×C₁₇	—	4	1	no	—
229	Q₈×C₁₇	—	2	1	no	—
230	Q₈×C₁₇	—	2	1	no	—
231	Q₈×C₁₇	—	2	1	no	—
232	Q₈×C₁₇	—	4	1	no	—
233	Q₈×C₁₇	—	4	1	no	—
234	Q₈×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
235	D₄×C₁₇	—	2	1	no	—
236	D₄×C₁₇	—	2	1	no	—
237	D₄×C₁₇	—	2	1	no	—
238	D₄×C₁₇	—	2	1	no	—
239	D₄×C₁₇	—	4	1	no	—
240	D₄×C₁₇	—	4	1	no	—
241	D₄×C₁₇	—	4	1	no	—
242	D₄×C₁₇	—	4	1	no	—
243	D₄×C₁₇	—	4	1	no	—
244	D₄×C₁₇	—	4	1	no	—
245	D₄×C₁₇	—	4	1	no	—
246	D₄×C₁₇	—	4	1	no	—
247	D₄×C₁₇	—	4	1	no	—
248	D₄×C₁₇	—	4	1	no	—
249	D₄×C₁₇	—	4	1	no	—
250	D₄×C₁₇	—	4	1	no	—
251	D₄×C₁₇	—	8	2	no	—
252	D₄×C₁₇	—	8	2	no	—
253	D₄×C₁₇	—	8	1	no	—
254	D₄×C₁₇	—	8	1	no	—
255	D₄×C₁₇	—	8	1	no	—
256	D₄×C₁₇	—	8	2	no	—
257	D₄×C₁₇	—	16	1	no	—
258	D₄×C₁₇	—	16	1	no	—
259	D₄×C₁₇	—	16	1	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	1	no	—
262	C₂×C₄×C₁₇	—	2	1	no	—
263	C₂×C₄×C₁₇	—	2	1	no	—
264	C₂×C₄×C₁₇	—	2	1	no	—
265	C₂×C₄×C₁₇	—	2	1	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	4	1	no	—
270	C₂×C₄×C₁₇	—	4	1	no	—
271	C₂×C₄×C₁₇	—	8	2	no	—
272	C₂×C₄×C₁₇	—	8	2	no	—
273	C₂×C₄×C₁₇	—	8	2	no	—
274	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
275	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
276	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
277	C₈×C₁₇	—	2	1	no	—
278	C₈×C₁₇	—	2	1	no	—
279	C₈×C₁₇	—	2	1	no	—
280	C₈×C₁₇	—	4	1	no	—
281	C₈×C₁₇	—	4	1	no	—
282	C₈×C₁₇	—	4	1	no	—
283	C₈×C₁₇	—	4	1	no	—
284	C₈×C₁₇	—	4	1	no	—
285	C₈×C₁₇	#135	1	2	yes	complemented
286	#3397	C₂×C₁₇	1	1	yes	characteristic, complemented
287	#3391	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#3304	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#3287	C₂×C₁₇	1	1	yes	characteristic, complemented
290	#1721	C₂×C₁₇	1	1	yes	characteristic, complemented
291	#1688	C₂×C₁₇	1	1	yes	characteristic, complemented
292	#1681	C₂×C₁₇	1	1	yes	characteristic, complemented
293	#1667	C₂×C₁₇	1	1	yes	characteristic, complemented
294	#1666	C₂×C₁₇	1	1	yes	characteristic, complemented
295	#1642	C₂×C₁₇	1	1	yes	characteristic, complemented
296	#1628	C₂×C₁₇	1	1	yes	characteristic, complemented
297	#1621	C₂×C₁₇	1	1	yes	characteristic, complemented
298	#1621	C₂×C₁₇	1	1	yes	characteristic, complemented
299	#1584	C₂×C₁₇	1	1	yes	characteristic, complemented
300	#1580	C₂×C₁₇	1	1	yes	characteristic, complemented
301	C₂²×C₁₇	—	4	1	no	—
302	C₂²×C₁₇	—	4	1	no	—
303	C₂²×C₁₇	—	4	1	no	—
304	C₂²×C₁₇	—	4	1	no	—
305	C₂²×C₁₇	—	4	1	no	—
306	C₂²×C₁₇	—	4	1	no	—
307	C₂²×C₁₇	—	8	1	no	—
308	C₂²×C₁₇	—	8	1	no	—
309	C₂²×C₁₇	—	8	1	no	—
310	C₂²×C₁₇	—	8	1	no	—
311	C₂²×C₁₇	—	8	1	no	—
312	C₂²×C₁₇	—	8	1	no	—
313	C₂²×C₁₇	—	8	1	no	—
314	C₂²×C₁₇	—	8	1	no	—
315	C₂²×C₁₇	—	8	1	no	—
316	C₂²×C₁₇	D₄²	1	1	yes	characteristic
317	C₄×C₁₇	—	2	2	no	—
318	C₄×C₁₇	—	2	1	no	—
319	C₄×C₁₇	—	4	1	no	—
320	C₄×C₁₇	—	4	1	no	—
321	C₄×C₁₇	—	4	1	no	—
322	C₄×C₁₇	—	4	1	no	—
323	C₄×C₁₇	—	4	1	no	—
324	C₄×C₁₇	—	8	1	no	—
325	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
326	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
327	C₄×C₁₇	#576	1	1	yes	characteristic
328	C₄×C₁₇	#576	1	1	yes	characteristic
329	C₂×#135	—	2	1	no	—
330	#556	C₂²×C₁₇	1	1	yes	characteristic
331	#550	C₂²×C₁₇	1	1	yes	characteristic
332	#550	C₂²×C₁₇	1	1	yes	characteristic
333	#550	C₂²×C₁₇	1	1	yes	characteristic
334	#496	—	2	1	no	—
335	#493	—	2	1	no	—
336	#493	C₂²×C₁₇	1	1	yes	characteristic
337	#493	C₂²×C₁₇	1	1	yes	characteristic
338	#493	C₂²×C₁₇	1	1	yes	characteristic
339	#492	C₂²×C₁₇	1	1	yes	characteristic
340	#486	C₂²×C₁₇	1	1	yes	characteristic
341	#486	C₂²×C₁₇	1	1	yes	characteristic
342	#482	—	2	1	no	—
343	#475	C₂²×C₁₇	1	1	yes	characteristic
344	#466	—	2	1	no	—
345	#465	—	2	1	no	—
346	#463	—	2	1	no	—
347	#461	C₂²×C₁₇	1	1	yes	characteristic
348	#460	—	2	1	no	—
349	#460	C₂²×C₁₇	1	1	yes	characteristic
350	#460	C₂²×C₁₇	1	1	yes	characteristic
351	#460	C₂²×C₁₇	1	1	yes	characteristic
352	#459	—	2	1	no	—
353	#459	—	2	1	no	—
354	#459	C₂²×C₁₇	1	1	yes	characteristic
355	#459	C₂²×C₁₇	1	1	yes	characteristic
356	#459	C₂²×C₁₇	1	1	yes	characteristic
357	#452	—	2	1	no	—
358	#449	—	2	1	no	—
359	#449	—	2	1	no	—
360	#446	C₂²×C₁₇	1	1	yes	characteristic
361	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
362	#440	—	2	1	no	—
363	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
364	C₄×D₈	—	2	1	no	—
365	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
366	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
367	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
368	#416	—	2	1	no	—
369	#335	C₂²×C₁₇	1	1	yes	characteristic
370	#334	C₂²×C₁₇	1	1	yes	characteristic
371	#332	C₂²×C₁₇	1	1	yes	characteristic
372	#331	C₂²×C₁₇	1	1	yes	characteristic
373	#331	C₂²×C₁₇	1	1	yes	characteristic
374	#331	C₂²×C₁₇	1	1	yes	characteristic
375	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
376	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
377	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
378	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
379	#322	C₂²×C₁₇	1	1	yes	characteristic
380	C₂×C₁₇	—	8	1	no	—
381	C₂×C₁₇	—	8	1	no	—
382	C₂×C₁₇	—	16	1	no	—
383	C₂×C₁₇	—	16	1	no	—
384	C₂×C₁₇	—	16	1	no	—
385	C₂×C₁₇	#3264	1	1	yes	characteristic
386	C₂×C₁₇	#3287	1	1	yes	characteristic
387	C₂×C₁₇	#3288	1	1	yes	characteristic
388	C₂×#41	—	2	1	no	—
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	1	no	—
391	#135	—	4	4	no	—
392	C₂×Q₁₆	D₄×C₁₇	1	1	yes	characteristic
393	C₂×SD₁₆	—	2	1	no	—
394	C₂×SD₁₆	—	2	1	no	—
395	C₂×SD₁₆	—	2	1	no	—
396	C₂×SD₁₆	—	2	1	no	—
397	C₂×SD₁₆	—	2	1	no	—
398	C₂×SD₁₆	—	2	1	no	—
399	C₂×D₈	—	2	1	no	—
400	C₂×D₈	—	2	1	no	—
401	C₂×D₈	—	2	1	no	—
402	C₂×D₈	—	2	1	no	—
403	C₂×D₈	—	2	1	no	—
404	C₂×D₈	—	2	1	no	—
405	C₂×D₈	—	2	1	no	—
406	C₂×D₈	—	4	1	no	—
407	C₂×D₈	D₄×C₁₇	1	1	yes	characteristic
408	C₂²×C₈	—	2	1	no	—
409	C₂²×C₈	—	2	1	no	—
410	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
411	#127	—	2	1	no	—
412	#127	—	2	1	no	—
413	#127	—	2	1	no	—
414	#127	C₂³×C₁₇	1	1	yes	characteristic
415	#127	C₂³×C₁₇	1	1	yes	characteristic
416	#127	C₂³×C₁₇	1	1	yes	characteristic
417	#126	—	4	1	no	—
418	#124	—	2	1	no	—
419	C₂²⋊Q₈	—	2	1	no	—
420	#121	—	2	1	no	—
421	#121	—	2	1	no	—
422	#121	—	2	1	no	—
423	#121	—	4	1	no	—
424	#121	—	4	1	no	—
425	#121	—	4	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
429	C₄×D₄	—	2	1	no	—
430	C₄×D₄	—	2	1	no	—
431	C₄×D₄	—	2	1	no	—
432	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
433	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
434	#117	—	2	1	no	—
435	#107	D₄×C₁₇	1	1	yes	characteristic
436	#107	D₄×C₁₇	1	1	yes	characteristic
437	#106	—	2	1	no	—
438	C₄⋊C₈	—	2	1	no	—
439	C₄⋊C₈	—	2	1	no	—
440	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
441	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
442	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
443	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
444	#103	—	2	1	no	—
445	#103	—	2	1	no	—
446	#103	D₄×C₁₇	1	1	yes	characteristic
447	#103	D₄×C₁₇	1	1	yes	characteristic
448	#102	—	2	1	no	—
449	#102	—	2	1	no	—
450	#102	—	2	1	no	—
451	#102	—	2	1	no	—
452	#102	—	2	1	no	—
453	#102	—	2	1	no	—
454	#102	—	2	1	no	—
455	#102	—	2	1	no	—
456	#102	—	4	1	no	—
457	#102	D₄×C₁₇	1	1	yes	characteristic
458	#102	D₄×C₁₇	1	1	yes	characteristic
459	C₂²⋊C₈	—	2	1	no	—
460	C₂²⋊C₈	—	2	1	no	—
461	#97	—	2	1	no	—
462	C₄×C₈	—	2	1	no	—
463	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
464	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
465	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
466	C₁₇	#19867	1	1	yes	characteristic, direct product factor, Sylow
467	#41	—	4	2	no	—
468	#41	—	4	2	no	—
469	#41	—	4	2	no	—
470	#41	—	8	1	no	—
471	#41	—	8	1	no	—
472	#41	—	8	1	no	—
473	C₂×Q₈	—	2	1	no	—
474	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
475	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	1	no	—
478	C₂×D₄	—	2	1	no	—
479	C₂×D₄	—	2	1	no	—
480	C₂×D₄	—	2	1	no	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	1	no	—
483	C₂×D₄	—	2	1	no	—
484	C₂×D₄	—	2	1	no	—
485	C₂×D₄	—	4	1	no	—
486	C₂×D₄	—	4	1	no	—
487	C₂×D₄	—	4	1	no	—
488	C₂×D₄	—	4	1	no	—
489	C₂×D₄	—	4	1	no	—
490	C₂×D₄	—	4	1	no	—
491	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
493	C₂²×C₄	—	2	1	no	—
494	C₂²×C₄	—	2	1	no	—
495	C₂²×C₄	—	4	1	no	—
496	C₂²×C₄	—	4	1	no	—
497	C₂²×C₄	—	4	1	no	—
498	Q₁₆	—	2	2	no	—
499	SD₁₆	—	4	2	no	—
500	SD₁₆	—	4	2	no	—
501	SD₁₆	—	4	2	no	—
502	SD₁₆	—	8	1	no	—
503	SD₁₆	—	8	1	no	—
504	SD₁₆	—	8	1	no	—
505	D₈	—	2	2	no	—
506	D₈	—	4	2	no	—
507	D₈	—	4	2	no	—
508	D₈	—	8	1	no	—
509	D₈	—	8	1	no	—
510	D₈	—	8	1	no	—
511	D₈	—	8	1	no	—
512	D₈	—	8	1	no	—
513	D₈	—	8	2	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	2	1	no	—
518	C₂×C₈	—	2	1	no	—
519	C₂×C₈	—	4	2	no	—
520	C₂×C₈	—	8	1	no	—
521	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
522	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
523	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
524	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
525	C₄⋊C₄	—	2	1	no	—
526	C₄⋊C₄	—	2	1	no	—
527	C₄⋊C₄	—	2	1	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	4	1	no	—
530	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
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	1	yes	characteristic
534	C₂²⋊C₄	—	2	1	no	—
535	C₂²⋊C₄	—	2	1	no	—
536	C₂²⋊C₄	—	4	1	no	—
537	C₂²⋊C₄	—	4	1	no	—
538	C₂²⋊C₄	—	4	1	no	—
539	C₂²⋊C₄	—	4	1	no	—
540	C₂²⋊C₄	—	4	1	no	—
541	C₄²	—	2	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	4	1	no	—
544	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	4	1	no	—
548	C₂³	—	4	1	no	—
549	C₂³	—	4	1	no	—
550	Q₈	—	2	1	no	—
551	Q₈	—	2	1	no	—
552	Q₈	—	2	1	no	—
553	Q₈	—	4	1	no	—
554	Q₈	—	4	1	no	—
555	Q₈	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
556	D₄	—	2	1	no	—
557	D₄	—	2	1	no	—
558	D₄	—	2	1	no	—
559	D₄	—	2	1	no	—
560	D₄	—	4	1	no	—
561	D₄	—	4	1	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	D₄	—	4	1	no	—
565	D₄	—	4	1	no	—
566	D₄	—	4	1	no	—
567	D₄	—	4	1	no	—
568	D₄	—	4	1	no	—
569	D₄	—	4	1	no	—
570	D₄	—	4	1	no	—
571	D₄	—	4	1	no	—
572	D₄	—	8	2	no	—
573	D₄	—	8	2	no	—
574	D₄	—	8	1	no	—
575	D₄	—	8	1	no	—
576	D₄	—	8	1	no	—
577	D₄	—	8	2	no	—
578	D₄	—	16	1	no	—
579	D₄	—	16	1	no	—
580	D₄	—	16	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	2	1	no	—
585	C₂×C₄	—	2	1	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	8	2	no	—
593	C₂×C₄	—	8	2	no	—
594	C₂×C₄	—	8	2	no	—
595	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
596	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
597	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
598	C₈	—	2	1	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	1	no	—
601	C₈	—	4	1	no	—
602	C₈	—	4	1	no	—
603	C₈	—	4	1	no	—
604	C₈	—	4	1	no	—
605	C₈	—	4	1	no	—
606	C₈	C₁₇×#135	1	2	yes	complemented
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	—	4	1	no	—
612	C₂²	—	4	1	no	—
613	C₂²	—	8	1	no	—
614	C₂²	—	8	1	no	—
615	C₂²	—	8	1	no	—
616	C₂²	—	8	1	no	—
617	C₂²	—	8	1	no	—
618	C₂²	—	8	1	no	—
619	C₂²	—	8	1	no	—
620	C₂²	—	8	1	no	—
621	C₂²	—	8	1	no	—
622	C₂²	D₄²×C₁₇	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	2	1	no	—
625	C₄	—	4	1	no	—
626	C₄	—	4	1	no	—
627	C₄	—	4	1	no	—
628	C₄	—	4	1	no	—
629	C₄	—	4	1	no	—
630	C₄	—	8	1	no	—
631	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
632	C₄	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₄	C₁₇×#576	1	1	yes	characteristic
634	C₄	C₁₇×#576	1	1	yes	characteristic
635	C₂	—	8	1	no	—
636	C₂	—	8	1	no	—
637	C₂	—	16	1	no	—
638	C₂	—	16	1	no	—
639	C₂	—	16	1	no	—
640	C₂	C₁₇×#3264	1	1	yes	characteristic
641	C₂	C₁₇×#3287	1	1	yes	characteristic
642	C₂	C₁₇×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
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. C₁₇×#3397	C₂	semidirect
2. C₁₇×#3391	C₂	semidirect
3. C₁₇×#3304	C₂	semidirect
4. C₁₇×#3287	C₂	semidirect
5. C₁₇×#1721	C₂	semidirect
6. C₁₇×#1688	C₂	semidirect
7. C₁₇×#1681	C₂	semidirect
8. C₁₇×#1667	C₂	semidirect
9. C₁₇×#1666	C₂	semidirect
10. C₁₇×#1642	C₂	semidirect
11. C₁₇×#1628	C₂	semidirect
12. C₁₇×#1621	C₂	semidirect
13. C₁₇×#1621	C₂	semidirect
14. C₁₇×#1584	C₂	semidirect
15. C₁₇×#1580	C₂	semidirect
223. #19867	C₁₇	direct (N × H)
285. C₈×C₁₇	#135	semidirect
286. #3397	C₂×C₁₇	semidirect
287. #3391	C₂×C₁₇	semidirect
288. #3304	C₂×C₁₇	semidirect
289. #3287	C₂×C₁₇	semidirect
290. #1721	C₂×C₁₇	semidirect
291. #1688	C₂×C₁₇	semidirect
292. #1681	C₂×C₁₇	semidirect
293. #1667	C₂×C₁₇	semidirect
294. #1666	C₂×C₁₇	semidirect
295. #1642	C₂×C₁₇	semidirect
296. #1628	C₂×C₁₇	semidirect
297. #1621	C₂×C₁₇	semidirect
298. #1621	C₂×C₁₇	semidirect
299. #1584	C₂×C₁₇	semidirect
300. #1580	C₂×C₁₇	semidirect
466. C₁₇	#19867	direct (N × H)
606. C₈	C₁₇×#135	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3397	2
C₁₇×#3391	2
C₁₇×#3304	2
C₁₇×#3287	2
C₁₇×#1721	2
C₁₇×#1688	2
C₁₇×#1681	2
C₁₇×#1667	2
C₁₇×#1666	2
C₁₇×#1642	2
C₁₇×#1628	2
C₁₇×#1621	2
C₁₇×#1584	2
C₁₇×#1580	2
#19867	17

Subgroups — C17×#19867 #16877611

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19867 #16877611