Subgroups — C₁₇×#61433 #16919177

Order 4352.

1852 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3482	C₂	1	2	yes	maximal, complemented
2	C₁₇×#3393	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3364	C₂	1	2	yes	maximal, complemented
5	C₁₇×#3336	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3334	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3300	C₂	1	4	yes	maximal, complemented
8	C₁₇×#3298	C₂	1	2	yes	maximal, complemented
9	D₄×Q₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3285	C₂	1	2	yes	maximal, complemented
11	C₁₇×#3170	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#3168	C₂	1	2	yes	maximal, complemented
13	C₁₇×#3108	C₂	1	4	yes	maximal, complemented
14	C₁₇×#3107	C₂	1	2	yes	maximal, complemented
15	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄×C₁₇×#135	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄×Q₁₆×C₁₇	C₂	1	2	yes	maximal, complemented
18	C₂×C₁₇×#135	C₂²	1	1	yes	characteristic
19	C₂²×Q₁₆×C₁₇	C₂²	1	2	yes	—
20	C₁₇×#557	C₂²	1	2	yes	—
21	C₁₇×#556	—	2	2	no	—
22	C₁₇×#556	C₂²	1	2	yes	—
23	C₁₇×#552	—	2	4	no	—
24	C₁₇×#552	C₂²	1	4	yes	—
25	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
26	C₁₇×#548	C₂²	1	4	yes	—
27	C₁₇×#547	—	2	2	no	—
28	C₁₇×#547	C₂²	1	2	yes	—
29	C₁₇×#533	—	2	2	no	—
30	C₁₇×#533	C₂²	1	2	yes	—
31	C₁₇×#529	—	2	4	no	—
32	C₁₇×#529	C₂²	1	4	yes	—
33	C₄×#41×C₁₇	—	2	2	no	—
34	C₄×#41×C₁₇	C₂²	1	2	yes	—
35	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₇	C₂²	1	4	yes	—
37	C₁₇×#500	C₂²	1	1	yes	characteristic
38	C₁₇×#499	C₂²	1	2	yes	—
39	C₁₇×#495	C₂²	1	2	yes	—
40	C₁₇×#494	C₂²	1	1	yes	characteristic
41	C₁₇×#488	C₂²	1	4	yes	—
42	C₁₇×#487	C₂²	1	2	yes	—
43	C₁₇×#485	C₂²	1	4	yes	—
44	C₁₇×#483	C₂²	1	4	yes	—
45	C₁₇×#480	C₂²	1	4	yes	—
46	C₁₇×#479	C₂²	1	4	yes	—
47	C₁₇×#479	C₂²	1	4	yes	—
48	C₁₇×#475	C₂²	1	2	yes	—
49	C₁₇×#474	C₂²	1	2	yes	—
50	C₁₇×#467	C₂²	1	2	yes	—
51	C₁₇×#467	C₂²	1	2	yes	—
52	C₁₇×#467	C₂²	1	2	yes	—
53	C₁₇×#466	C₂²	1	2	yes	—
54	C₁₇×#465	C₂²	1	4	yes	—
55	C₁₇×#464	C₂²	1	4	yes	—
56	C₁₇×#464	C₂²	1	4	yes	—
57	C₁₇×#462	C₂²	1	2	yes	—
58	C₁₇×#461	C₂²	1	2	yes	—
59	C₁₇×#452	C₂²	1	4	yes	—
60	C₁₇×#451	C₂²	1	4	yes	—
61	C₁₇×#448	C₂²	1	4	yes	—
62	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
65	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
66	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
67	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
68	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
69	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
70	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
71	C₄×Q₁₆×C₁₇	C₂²	1	1	yes	characteristic
72	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
73	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	—
74	C₄×SD₁₆×C₁₇	C₂²	1	2	yes	—
75	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
76	C₄×D₈×C₁₇	C₂²	1	1	yes	characteristic
77	C₈×D₄×C₁₇	C₂²	1	2	yes	—
78	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
79	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
80	C₈×D₄×C₁₇	C₂²	1	2	yes	—
81	C₁₇×#431	C₂²	1	1	yes	characteristic
82	C₁₇×#431	C₂²	1	2	yes	—
83	C₁₇×#427	C₂²	1	1	yes	characteristic
84	C₂×C₁₇×#107	C₂²	1	2	yes	—
85	C₁₇×#416	C₂²	1	2	yes	—
86	C₂×C₁₇×#103	C₂²	1	4	yes	—
87	C₂×C₄×C₈×C₁₇	C₂²	1	2	yes	—
88	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
89	C₂×#41×C₁₇	—	2	2	no	—
90	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
91	C₂×#41×C₁₇	C₂³	1	2	yes	—
92	C₂²×Q₈×C₁₇	C₂³	1	4	yes	—
93	C₁₇×#135	—	2	4	no	—
94	C₂×Q₁₆×C₁₇	—	2	8	no	—
95	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
96	C₂×Q₁₆×C₁₇	C₂³	1	4	yes	—
97	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
98	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
99	C₂×SD₁₆×C₁₇	C₂³	1	2	yes	—
100	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
101	C₂×D₈×C₁₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
103	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
106	C₁₇×C₄⋊Q₈	—	2	2	no	—
107	C₁₇×C₄⋊Q₈	—	2	2	no	—
108	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
109	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
110	C₁₇×#126	—	2	4	no	—
111	C₁₇×#126	—	2	4	no	—
112	C₁₇×#126	—	2	4	no	—
113	C₁₇×#125	—	2	4	no	—
114	C₁₇×#125	—	2	4	no	—
115	C₁₇×#125	—	2	2	no	—
116	C₁₇×#125	C₂³	1	4	yes	—
117	C₁₇×#124	—	2	4	no	—
118	C₁₇×#124	C₂³	1	4	yes	—
119	C₁₇×#123	—	2	4	no	—
120	C₁₇×#123	—	2	4	no	—
121	C₁₇×#123	—	2	4	no	—
122	C₁₇×C₂²⋊Q₈	—	2	2	no	—
123	C₁₇×C₂²⋊Q₈	—	2	2	no	—
124	C₁₇×C₂²⋊Q₈	—	2	2	no	—
125	C₁₇×C₂²⋊Q₈	—	2	4	no	—
126	C₁₇×C₂²⋊Q₈	—	2	4	no	—
127	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
128	C₁₇×C₂²⋊Q₈	C₂³	1	4	yes	—
129	C₁₇×#121	—	2	4	no	—
130	C₁₇×#121	C₂³	1	4	yes	—
131	C₄×Q₈×C₁₇	—	2	2	no	—
132	C₄×Q₈×C₁₇	—	2	4	no	—
133	C₄×Q₈×C₁₇	—	2	4	no	—
134	C₄×Q₈×C₁₇	—	2	2	no	—
135	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
136	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
137	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
138	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
139	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
140	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
141	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
142	C₄×D₄×C₁₇	—	2	2	no	—
143	C₄×D₄×C₁₇	—	2	4	no	—
144	C₄×D₄×C₁₇	—	2	2	no	—
145	C₄×D₄×C₁₇	—	2	2	no	—
146	C₄×D₄×C₁₇	—	2	4	no	—
147	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
148	C₄×D₄×C₁₇	D₄	1	2	yes	—
149	C₄×D₄×C₁₇	C₂³	1	2	yes	—
150	C₄×D₄×C₁₇	C₂³	1	2	yes	—
151	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₁₇	C₂³	1	2	yes	—
153	C₁₇×#117	—	2	2	no	—
154	C₁₇×#117	—	2	2	no	—
155	C₁₇×#117	—	2	4	no	—
156	C₁₇×#117	—	2	2	no	—
157	C₁₇×#117	—	2	4	no	—
158	C₁₇×#117	D₄	1	2	yes	—
159	C₁₇×#117	D₄	1	1	yes	characteristic
160	C₁₇×#117	C₂³	1	2	yes	—
161	C₂×C₄⋊C₄×C₁₇	—	2	4	no	—
162	C₂×C₄⋊C₄×C₁₇	C₂³	1	4	yes	—
163	C₂×C₄²×C₁₇	—	2	4	no	—
164	C₂×C₄²×C₁₇	—	2	2	no	—
165	C₂×C₄²×C₁₇	C₂³	1	2	yes	—
166	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
167	C₁₇×#107	C₂³	1	1	yes	characteristic
168	C₁₇×#107	C₂³	1	2	yes	—
169	C₁₇×#107	C₂³	1	2	yes	—
170	C₁₇×#107	C₂³	1	1	yes	characteristic
171	C₁₇×#107	C₂³	1	4	yes	—
172	C₁₇×#106	C₂³	1	4	yes	—
173	C₁₇×#106	C₂³	1	2	yes	—
174	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
175	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
176	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₇×#103	C₂³	1	2	yes	—
179	C₁₇×#103	C₂³	1	4	yes	—
180	C₁₇×#103	C₂³	1	4	yes	—
181	C₁₇×#103	C₂³	1	4	yes	—
182	C₁₇×#103	C₂³	1	2	yes	—
183	C₁₇×#103	C₂³	1	4	yes	—
184	C₁₇×#103	C₂³	1	4	yes	—
185	C₁₇×#102	C₂³	1	2	yes	—
186	C₁₇×#102	C₂³	1	2	yes	—
187	C₁₇×#102	C₂³	1	4	yes	—
188	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
189	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
190	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
192	C₄×C₈×C₁₇	C₂³	1	2	yes	—
193	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
194	C₄×C₈×C₁₇	C₂³	1	2	yes	—
195	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
197	C₄×C₈×C₁₇	C₂³	1	2	yes	—
198	#41×C₁₇	—	2	4	no	—
199	#41×C₁₇	—	2	4	no	—
200	#41×C₁₇	—	4	2	no	—
201	#41×C₁₇	—	4	8	no	—
202	C₂×Q₈×C₁₇	—	2	4	no	—
203	C₂×Q₈×C₁₇	—	2	2	no	—
204	C₂×Q₈×C₁₇	—	2	8	no	—
205	C₂×Q₈×C₁₇	—	4	4	no	—
206	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₂×Q₈×C₁₇	C₂⁴	1	4	yes	—
208	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
209	C₂×D₄×C₁₇	—	2	4	no	—
210	C₂×D₄×C₁₇	—	2	2	no	—
211	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
212	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
213	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
214	C₂²×C₄×C₁₇	—	2	4	no	—
215	C₂²×C₄×C₁₇	—	2	4	no	—
216	C₂²×C₄×C₁₇	—	2	2	no	—
217	C₂²×C₄×C₁₇	—	2	2	no	—
218	C₂²×C₄×C₁₇	—	2	2	no	—
219	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
221	C₂²×C₄×C₁₇	C₂×D₄	1	2	yes	—
222	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
223	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
224	C₂²×C₄×C₁₇	C₂⁴	1	2	yes	—
225	Q₁₆×C₁₇	—	2	8	no	—
226	Q₁₆×C₁₇	—	2	4	no	—
227	Q₁₆×C₁₇	—	4	2	no	—
228	Q₁₆×C₁₇	#41	1	4	yes	complemented
229	SD₁₆×C₁₇	—	2	4	no	—
230	SD₁₆×C₁₇	—	4	4	no	—
231	D₈×C₁₇	—	2	2	no	—
232	C₂×C₈×C₁₇	—	2	4	no	—
233	C₂×C₈×C₁₇	—	2	2	no	—
234	C₂×C₈×C₁₇	—	4	2	no	—
235	C₂×C₈×C₁₇	—	4	1	no	—
236	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
239	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
240	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
242	C₄⋊C₄×C₁₇	—	2	2	no	—
243	C₄⋊C₄×C₁₇	—	2	2	no	—
244	C₄⋊C₄×C₁₇	—	2	2	no	—
245	C₄⋊C₄×C₁₇	—	2	4	no	—
246	C₄⋊C₄×C₁₇	—	2	4	no	—
247	C₄⋊C₄×C₁₇	—	2	4	no	—
248	C₄⋊C₄×C₁₇	—	2	4	no	—
249	C₄⋊C₄×C₁₇	—	2	4	no	—
250	C₄⋊C₄×C₁₇	—	2	4	no	—
251	C₄⋊C₄×C₁₇	—	2	2	no	—
252	C₄⋊C₄×C₁₇	—	2	4	no	—
253	C₄⋊C₄×C₁₇	—	2	4	no	—
254	C₄⋊C₄×C₁₇	—	2	2	no	—
255	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
256	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
257	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
258	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
259	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
260	C₄⋊C₄×C₁₇	C₂⁴	1	4	yes	—
261	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
262	C₂²⋊C₄×C₁₇	—	2	4	no	—
263	C₂²⋊C₄×C₁₇	—	2	4	no	—
264	C₂²⋊C₄×C₁₇	—	2	2	no	—
265	C₂²⋊C₄×C₁₇	—	2	4	no	—
266	C₂²⋊C₄×C₁₇	—	2	4	no	—
267	C₂²⋊C₄×C₁₇	—	2	2	no	—
268	C₂²⋊C₄×C₁₇	—	2	2	no	—
269	C₂²⋊C₄×C₁₇	—	2	4	no	—
270	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
271	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
272	C₂²⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
273	C₄²×C₁₇	—	2	4	no	—
274	C₄²×C₁₇	—	2	2	no	—
275	C₄²×C₁₇	—	2	4	no	—
276	C₄²×C₁₇	—	2	2	no	—
277	C₄²×C₁₇	—	2	2	no	—
278	C₄²×C₁₇	—	2	4	no	—
279	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
280	C₄²×C₁₇	C₂×D₄	1	2	yes	—
281	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
282	C₄²×C₁₇	C₂×D₄	1	2	yes	—
283	C₄²×C₁₇	C₂⁴	1	2	yes	—
284	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
285	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
286	#61433	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
287	C₂³×C₁₇	—	2	2	no	—
288	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
289	C₂³×C₁₇	C₂²×D₄	1	2	yes	—
290	Q₈×C₁₇	—	2	2	no	—
291	Q₈×C₁₇	—	2	2	no	—
292	Q₈×C₁₇	—	2	4	no	—
293	Q₈×C₁₇	—	2	4	no	—
294	Q₈×C₁₇	—	4	8	no	—
295	Q₈×C₁₇	—	4	4	no	—
296	Q₈×C₁₇	C₂×#41	1	4	yes	—
297	D₄×C₁₇	—	2	4	no	—
298	D₄×C₁₇	—	2	2	no	—
299	D₄×C₁₇	—	2	2	no	—
300	D₄×C₁₇	—	4	4	no	—
301	D₄×C₁₇	—	4	8	no	—
302	D₄×C₁₇	#135	1	4	yes	complemented
303	C₂×C₄×C₁₇	—	2	4	no	—
304	C₂×C₄×C₁₇	—	2	2	no	—
305	C₂×C₄×C₁₇	—	2	2	no	—
306	C₂×C₄×C₁₇	—	2	4	no	—
307	C₂×C₄×C₁₇	—	2	2	no	—
308	C₂×C₄×C₁₇	—	2	2	no	—
309	C₂×C₄×C₁₇	—	2	1	no	—
310	C₂×C₄×C₁₇	—	2	2	no	—
311	C₂×C₄×C₁₇	—	2	1	no	—
312	C₂×C₄×C₁₇	—	2	2	no	—
313	C₂×C₄×C₁₇	—	2	2	no	—
314	C₂×C₄×C₁₇	—	2	4	no	—
315	C₂×C₄×C₁₇	—	2	4	no	—
316	C₂×C₄×C₁₇	—	4	4	no	—
317	C₂×C₄×C₁₇	—	4	8	no	—
318	C₂×C₄×C₁₇	—	4	8	no	—
319	C₂×C₄×C₁₇	—	4	4	no	—
320	C₂×C₄×C₁₇	—	4	4	no	—
321	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
322	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
324	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
325	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
326	C₂×C₄×C₁₇	C₂²×D₄	1	2	yes	—
327	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
328	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
329	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
330	C₈×C₁₇	—	2	1	no	—
331	C₈×C₁₇	—	2	2	no	—
332	C₈×C₁₇	—	2	1	no	—
333	C₈×C₁₇	—	2	2	no	—
334	C₈×C₁₇	—	2	1	no	—
335	C₈×C₁₇	C₂×#41	1	2	yes	—
336	#3482	C₂×C₁₇	1	2	yes	complemented
337	#3393	C₂×C₁₇	1	1	yes	characteristic, complemented
338	#3383	C₂×C₁₇	1	1	yes	characteristic, complemented
339	#3364	C₂×C₁₇	1	2	yes	complemented
340	#3336	C₂×C₁₇	1	2	yes	complemented
341	#3334	C₂×C₁₇	1	1	yes	characteristic, complemented
342	#3300	C₂×C₁₇	1	4	yes	complemented
343	#3298	C₂×C₁₇	1	2	yes	complemented
344	D₄×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
345	#3285	C₂×C₁₇	1	2	yes	complemented
346	#3170	C₂×C₁₇	1	1	yes	characteristic, complemented
347	#3168	C₂×C₁₇	1	2	yes	complemented
348	#3108	C₂×C₁₇	1	4	yes	complemented
349	#3107	C₂×C₁₇	1	2	yes	complemented
350	C₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
351	C₄×#135	C₂×C₁₇	1	1	yes	characteristic, complemented
352	C₂×C₄×Q₁₆	C₂×C₁₇	1	2	yes	complemented
353	C₂²×C₁₇	—	2	2	no	—
354	C₂²×C₁₇	—	2	2	no	—
355	C₂²×C₁₇	—	2	1	no	—
356	C₂²×C₁₇	—	2	1	no	—
357	C₂²×C₁₇	—	2	1	no	—
358	C₂²×C₁₇	—	4	2	no	—
359	C₂²×C₁₇	—	4	2	no	—
360	C₂²×C₁₇	—	4	2	no	—
361	C₂²×C₁₇	C₂×#135	1	4	yes	—
362	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
363	C₄×C₁₇	—	2	1	no	—
364	C₄×C₁₇	—	2	2	no	—
365	C₄×C₁₇	—	2	4	no	—
366	C₄×C₁₇	—	2	1	no	—
367	C₄×C₁₇	—	2	2	no	—
368	C₄×C₁₇	—	2	2	no	—
369	C₄×C₁₇	—	2	1	no	—
370	C₄×C₁₇	—	4	4	no	—
371	C₄×C₁₇	—	4	2	no	—
372	C₄×C₁₇	—	4	4	no	—
373	C₄×C₁₇	—	4	2	no	—
374	C₄×C₁₇	C₂×#135	1	2	yes	—
375	C₄×C₁₇	#578	1	2	yes	—
376	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
377	C₄×C₁₇	#585	1	1	yes	characteristic
378	C₂×#135	C₂²×C₁₇	1	1	yes	characteristic
379	C₂²×Q₁₆	C₂²×C₁₇	1	2	yes	—
380	#557	C₂²×C₁₇	1	2	yes	—
381	#556	—	2	2	no	—
382	#556	C₂²×C₁₇	1	2	yes	—
383	#552	—	2	4	no	—
384	#552	C₂²×C₁₇	1	4	yes	—
385	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
386	#548	C₂²×C₁₇	1	4	yes	—
387	#547	—	2	2	no	—
388	#547	C₂²×C₁₇	1	2	yes	—
389	#533	—	2	2	no	—
390	#533	C₂²×C₁₇	1	2	yes	—
391	#529	—	2	4	no	—
392	#529	C₂²×C₁₇	1	4	yes	—
393	C₄×#41	—	2	2	no	—
394	C₄×#41	C₂²×C₁₇	1	2	yes	—
395	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
396	C₂×C₄×Q₈	C₂²×C₁₇	1	4	yes	—
397	#500	C₂²×C₁₇	1	1	yes	characteristic
398	#499	C₂²×C₁₇	1	2	yes	—
399	#495	C₂²×C₁₇	1	2	yes	—
400	#494	C₂²×C₁₇	1	1	yes	characteristic
401	#488	C₂²×C₁₇	1	4	yes	—
402	#487	C₂²×C₁₇	1	2	yes	—
403	#485	C₂²×C₁₇	1	4	yes	—
404	#483	C₂²×C₁₇	1	4	yes	—
405	#480	C₂²×C₁₇	1	4	yes	—
406	#479	C₂²×C₁₇	1	4	yes	—
407	#479	C₂²×C₁₇	1	4	yes	—
408	#475	C₂²×C₁₇	1	2	yes	—
409	#474	C₂²×C₁₇	1	2	yes	—
410	#467	C₂²×C₁₇	1	2	yes	—
411	#467	C₂²×C₁₇	1	2	yes	—
412	#467	C₂²×C₁₇	1	2	yes	—
413	#466	C₂²×C₁₇	1	2	yes	—
414	#465	C₂²×C₁₇	1	4	yes	—
415	#464	C₂²×C₁₇	1	4	yes	—
416	#464	C₂²×C₁₇	1	4	yes	—
417	#462	C₂²×C₁₇	1	2	yes	—
418	#461	C₂²×C₁₇	1	2	yes	—
419	#452	C₂²×C₁₇	1	4	yes	—
420	#451	C₂²×C₁₇	1	4	yes	—
421	#448	C₂²×C₁₇	1	4	yes	—
422	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
423	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
424	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
426	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
427	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
428	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
429	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
430	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
431	C₄×Q₁₆	C₂²×C₁₇	1	1	yes	characteristic
432	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	—
433	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
434	C₄×SD₁₆	C₂²×C₁₇	1	2	yes	—
435	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
436	C₄×D₈	C₂²×C₁₇	1	1	yes	characteristic
437	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
438	C₈×D₄	C₂²×C₁₇	1	2	yes	—
439	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
440	C₈×D₄	C₂²×C₁₇	1	2	yes	—
441	#431	C₂²×C₁₇	1	1	yes	characteristic
442	#431	C₂²×C₁₇	1	2	yes	—
443	#427	C₂²×C₁₇	1	1	yes	characteristic
444	C₂×#107	C₂²×C₁₇	1	2	yes	—
445	#416	C₂²×C₁₇	1	2	yes	—
446	C₂×#103	C₂²×C₁₇	1	4	yes	—
447	C₂×C₄×C₈	C₂²×C₁₇	1	2	yes	—
448	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
449	C₂×C₁₇	—	2	4	no	—
450	C₂×C₁₇	—	4	1	no	—
451	C₂×C₁₇	—	8	2	no	—
452	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
453	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
454	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
455	C₂×#41	—	2	2	no	—
456	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
457	C₂×#41	C₂³×C₁₇	1	2	yes	—
458	C₂²×Q₈	C₂³×C₁₇	1	4	yes	—
459	#135	—	2	4	no	—
460	C₂×Q₁₆	—	2	8	no	—
461	C₂×Q₁₆	C₂³×C₁₇	1	4	yes	—
462	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
463	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
464	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
465	C₂×SD₁₆	C₂³×C₁₇	1	2	yes	—
466	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
467	C₂×D₈	C₂³×C₁₇	1	1	yes	characteristic
468	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
469	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
470	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
471	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
472	C₄⋊Q₈	—	2	2	no	—
473	C₄⋊Q₈	—	2	2	no	—
474	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
475	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
476	#126	—	2	4	no	—
477	#126	—	2	4	no	—
478	#126	—	2	4	no	—
479	#125	—	2	4	no	—
480	#125	—	2	4	no	—
481	#125	—	2	2	no	—
482	#125	C₂³×C₁₇	1	4	yes	—
483	#124	—	2	4	no	—
484	#124	C₂³×C₁₇	1	4	yes	—
485	#123	—	2	4	no	—
486	#123	—	2	4	no	—
487	#123	—	2	4	no	—
488	C₂²⋊Q₈	—	2	2	no	—
489	C₂²⋊Q₈	—	2	2	no	—
490	C₂²⋊Q₈	—	2	2	no	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	2	4	no	—
493	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
494	C₂²⋊Q₈	C₂³×C₁₇	1	4	yes	—
495	#121	—	2	4	no	—
496	#121	C₂³×C₁₇	1	4	yes	—
497	C₄×Q₈	—	2	2	no	—
498	C₄×Q₈	—	2	4	no	—
499	C₄×Q₈	—	2	4	no	—
500	C₄×Q₈	—	2	2	no	—
501	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
502	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
503	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
504	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
505	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
506	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
507	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
508	C₄×D₄	—	2	2	no	—
509	C₄×D₄	—	2	4	no	—
510	C₄×D₄	—	2	2	no	—
511	C₄×D₄	—	2	2	no	—
512	C₄×D₄	—	2	4	no	—
513	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
514	C₄×D₄	D₄×C₁₇	1	2	yes	—
515	C₄×D₄	C₂³×C₁₇	1	2	yes	—
516	C₄×D₄	C₂³×C₁₇	1	2	yes	—
517	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
518	C₄×D₄	C₂³×C₁₇	1	2	yes	—
519	#117	—	2	2	no	—
520	#117	—	2	2	no	—
521	#117	—	2	4	no	—
522	#117	—	2	2	no	—
523	#117	—	2	4	no	—
524	#117	D₄×C₁₇	1	2	yes	—
525	#117	D₄×C₁₇	1	1	yes	characteristic
526	#117	C₂³×C₁₇	1	2	yes	—
527	C₂×C₄⋊C₄	—	2	4	no	—
528	C₂×C₄⋊C₄	C₂³×C₁₇	1	4	yes	—
529	C₂×C₄²	—	2	4	no	—
530	C₂×C₄²	—	2	2	no	—
531	C₂×C₄²	C₂³×C₁₇	1	2	yes	—
532	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
533	#107	C₂³×C₁₇	1	1	yes	characteristic
534	#107	C₂³×C₁₇	1	2	yes	—
535	#107	C₂³×C₁₇	1	4	yes	—
536	#107	C₂³×C₁₇	1	1	yes	characteristic
537	#107	C₂³×C₁₇	1	2	yes	—
538	#106	C₂³×C₁₇	1	2	yes	—
539	#106	C₂³×C₁₇	1	4	yes	—
540	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
541	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
542	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
543	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
544	#103	C₂³×C₁₇	1	2	yes	—
545	#103	C₂³×C₁₇	1	4	yes	—
546	#103	C₂³×C₁₇	1	4	yes	—
547	#103	C₂³×C₁₇	1	4	yes	—
548	#103	C₂³×C₁₇	1	2	yes	—
549	#103	C₂³×C₁₇	1	4	yes	—
550	#103	C₂³×C₁₇	1	4	yes	—
551	#102	C₂³×C₁₇	1	2	yes	—
552	#102	C₂³×C₁₇	1	2	yes	—
553	#102	C₂³×C₁₇	1	4	yes	—
554	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
555	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
556	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
557	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
558	C₄×C₈	C₂³×C₁₇	1	2	yes	—
559	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
560	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
561	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
562	C₄×C₈	C₂³×C₁₇	1	2	yes	—
563	C₄×C₈	C₂³×C₁₇	1	2	yes	—
564	C₁₇	#61433	1	1	yes	characteristic, direct product factor, Sylow
565	#41	—	2	4	no	—
566	#41	—	2	4	no	—
567	#41	—	4	2	no	—
568	#41	—	4	8	no	—
569	C₂×Q₈	—	2	4	no	—
570	C₂×Q₈	—	2	2	no	—
571	C₂×Q₈	—	2	8	no	—
572	C₂×Q₈	—	4	4	no	—
573	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
574	C₂×Q₈	C₂⁴×C₁₇	1	4	yes	—
575	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
576	C₂×D₄	—	2	2	no	—
577	C₂×D₄	—	2	4	no	—
578	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
579	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
580	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
581	C₂²×C₄	—	2	4	no	—
582	C₂²×C₄	—	2	4	no	—
583	C₂²×C₄	—	2	2	no	—
584	C₂²×C₄	—	2	2	no	—
585	C₂²×C₄	—	2	2	no	—
586	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
587	C₂²×C₄	C₂×D₄×C₁₇	1	2	yes	—
588	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
589	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
590	C₂²×C₄	C₂⁴×C₁₇	1	2	yes	—
591	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
592	Q₁₆	—	2	8	no	—
593	Q₁₆	—	2	4	no	—
594	Q₁₆	—	4	2	no	—
595	Q₁₆	#41×C₁₇	1	4	yes	complemented
596	SD₁₆	—	2	4	no	—
597	SD₁₆	—	4	4	no	—
598	D₈	—	2	2	no	—
599	C₂×C₈	—	2	4	no	—
600	C₂×C₈	—	2	2	no	—
601	C₂×C₈	—	4	2	no	—
602	C₂×C₈	—	4	1	no	—
603	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
604	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
605	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
606	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
607	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
608	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
609	C₄⋊C₄	—	2	2	no	—
610	C₄⋊C₄	—	2	4	no	—
611	C₄⋊C₄	—	2	4	no	—
612	C₄⋊C₄	—	2	4	no	—
613	C₄⋊C₄	—	2	4	no	—
614	C₄⋊C₄	—	2	2	no	—
615	C₄⋊C₄	—	2	4	no	—
616	C₄⋊C₄	—	2	4	no	—
617	C₄⋊C₄	—	2	2	no	—
618	C₄⋊C₄	—	2	2	no	—
619	C₄⋊C₄	—	2	4	no	—
620	C₄⋊C₄	—	2	2	no	—
621	C₄⋊C₄	—	2	4	no	—
622	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
623	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
624	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
625	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
626	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
627	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
628	C₄⋊C₄	C₂⁴×C₁₇	1	4	yes	—
629	C₂²⋊C₄	—	2	4	no	—
630	C₂²⋊C₄	—	2	4	no	—
631	C₂²⋊C₄	—	2	2	no	—
632	C₂²⋊C₄	—	2	4	no	—
633	C₂²⋊C₄	—	2	2	no	—
634	C₂²⋊C₄	—	2	2	no	—
635	C₂²⋊C₄	—	2	4	no	—
636	C₂²⋊C₄	—	2	4	no	—
637	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
638	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
639	C₂²⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
640	C₄²	—	2	2	no	—
641	C₄²	—	2	2	no	—
642	C₄²	—	2	4	no	—
643	C₄²	—	2	4	no	—
644	C₄²	—	2	2	no	—
645	C₄²	—	2	4	no	—
646	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
647	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
648	C₄²	C₂×D₄×C₁₇	1	2	yes	—
649	C₄²	C₂×D₄×C₁₇	1	2	yes	—
650	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
651	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
652	C₄²	C₂⁴×C₁₇	1	2	yes	—
653	C₂³	—	2	2	no	—
654	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
655	C₂³	C₂²×D₄×C₁₇	1	2	yes	—
656	Q₈	—	2	2	no	—
657	Q₈	—	2	2	no	—
658	Q₈	—	2	4	no	—
659	Q₈	—	2	4	no	—
660	Q₈	—	4	8	no	—
661	Q₈	—	4	4	no	—
662	Q₈	C₂×#41×C₁₇	1	4	yes	—
663	D₄	—	2	4	no	—
664	D₄	—	2	2	no	—
665	D₄	—	2	2	no	—
666	D₄	—	4	4	no	—
667	D₄	—	4	8	no	—
668	D₄	C₁₇×#135	1	4	yes	complemented
669	C₂×C₄	—	2	4	no	—
670	C₂×C₄	—	2	2	no	—
671	C₂×C₄	—	2	2	no	—
672	C₂×C₄	—	2	4	no	—
673	C₂×C₄	—	2	2	no	—
674	C₂×C₄	—	2	2	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	2	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	2	no	—
679	C₂×C₄	—	2	2	no	—
680	C₂×C₄	—	2	4	no	—
681	C₂×C₄	—	2	4	no	—
682	C₂×C₄	—	4	4	no	—
683	C₂×C₄	—	4	8	no	—
684	C₂×C₄	—	4	8	no	—
685	C₂×C₄	—	4	4	no	—
686	C₂×C₄	—	4	4	no	—
687	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
688	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
689	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
690	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
691	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
692	C₂×C₄	C₂²×D₄×C₁₇	1	2	yes	—
693	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
694	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
695	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
696	C₈	—	2	1	no	—
697	C₈	—	2	2	no	—
698	C₈	—	2	1	no	—
699	C₈	—	2	2	no	—
700	C₈	—	2	1	no	—
701	C₈	C₂×#41×C₁₇	1	2	yes	—
702	C₂²	—	2	2	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	2	1	no	—
705	C₂²	—	2	1	no	—
706	C₂²	—	2	1	no	—
707	C₂²	—	4	2	no	—
708	C₂²	—	4	2	no	—
709	C₂²	—	4	2	no	—
710	C₂²	C₂×C₁₇×#135	1	4	yes	—
711	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
712	C₄	—	2	1	no	—
713	C₄	—	2	2	no	—
714	C₄	—	2	4	no	—
715	C₄	—	2	1	no	—
716	C₄	—	2	2	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	4	4	no	—
720	C₄	—	4	2	no	—
721	C₄	—	4	4	no	—
722	C₄	—	4	2	no	—
723	C₄	C₂×C₁₇×#135	1	2	yes	—
724	C₄	C₁₇×#578	1	2	yes	—
725	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
726	C₄	C₁₇×#585	1	1	yes	characteristic
727	C₂	—	2	4	no	—
728	C₂	—	4	1	no	—
729	C₂	—	8	2	no	—
730	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
731	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
732	C₂	C₂×C₁₇×#578	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
socle	C₂²×C₁₇	C₂³×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3482	C₂	semidirect
2. C₁₇×#3393	C₂	semidirect
3. C₁₇×#3383	C₂	semidirect
4. C₁₇×#3364	C₂	semidirect
5. C₁₇×#3336	C₂	semidirect
6. C₁₇×#3334	C₂	semidirect
7. C₁₇×#3300	C₂	semidirect
8. C₁₇×#3298	C₂	semidirect
9. D₄×Q₁₆×C₁₇	C₂	semidirect
10. C₁₇×#3285	C₂	semidirect
11. C₁₇×#3170	C₂	semidirect
12. C₁₇×#3168	C₂	semidirect
13. C₁₇×#3108	C₂	semidirect
14. C₁₇×#3107	C₂	semidirect
15. C₈×#41×C₁₇	C₂	semidirect
16. C₄×C₁₇×#135	C₂	semidirect
17. C₂×C₄×Q₁₆×C₁₇	C₂	semidirect
228. Q₁₆×C₁₇	#41	semidirect
286. #61433	C₁₇	direct (N × H)
302. D₄×C₁₇	#135	semidirect
336. #3482	C₂×C₁₇	semidirect
337. #3393	C₂×C₁₇	semidirect
338. #3383	C₂×C₁₇	semidirect
339. #3364	C₂×C₁₇	semidirect
340. #3336	C₂×C₁₇	semidirect
341. #3334	C₂×C₁₇	semidirect
342. #3300	C₂×C₁₇	semidirect
343. #3298	C₂×C₁₇	semidirect
344. D₄×Q₁₆	C₂×C₁₇	semidirect
345. #3285	C₂×C₁₇	semidirect
346. #3170	C₂×C₁₇	semidirect
347. #3168	C₂×C₁₇	semidirect
348. #3108	C₂×C₁₇	semidirect
349. #3107	C₂×C₁₇	semidirect
350. C₈×#41	C₂×C₁₇	semidirect
351. C₄×#135	C₂×C₁₇	semidirect
352. C₂×C₄×Q₁₆	C₂×C₁₇	semidirect
564. C₁₇	#61433	direct (N × H)
595. Q₁₆	#41×C₁₇	semidirect
668. D₄	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×#3482	2
C₁₇×#3393	2
C₁₇×#3383	2
C₁₇×#3364	2
C₁₇×#3336	2
C₁₇×#3334	2
C₁₇×#3300	2
C₁₇×#3298	2
D₄×Q₁₆×C₁₇	2
C₁₇×#3285	2
C₁₇×#3170	2
C₁₇×#3168	2
C₁₇×#3108	2
C₁₇×#3107	2
C₈×#41×C₁₇	2
C₄×C₁₇×#135	2
C₂×C₄×Q₁₆×C₁₇	2
#61433	17

Subgroups — C17×#61433 #16919177

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61433 #16919177