Subgroups — C₁₇×#61434 #16919178

Order 4352.

1906 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3483	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3340	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3304	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3303	C₂	1	3	yes	maximal, complemented
10	C₁₇×#3284	C₂	1	3	yes	maximal, complemented
11	C₁₇×#3167	C₂	1	3	yes	maximal, complemented
12	C₁₇×#3107	C₂	1	3	yes	maximal, complemented
13	C₁₇×#3106	C₂	1	3	yes	maximal, complemented
14	C₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₇×#135	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₇×#135	C₂²	1	3	yes	—
17	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#557	C₂²	1	1	yes	characteristic
19	C₁₇×#556	C₂²	1	3	yes	—
20	C₁₇×#555	—	2	3	no	—
21	C₁₇×#555	C₂²	1	3	yes	—
22	C₁₇×#552	—	2	3	no	—
23	C₁₇×#550	—	2	1	no	—
24	C₁₇×#550	C₂²	1	3	yes	—
25	C₁₇×#550	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
27	C₁₇×#548	—	2	1	no	—
28	C₁₇×#547	C₂²	1	3	yes	—
29	C₁₇×#533	C₂²	1	3	yes	—
30	C₁₇×#532	—	2	3	no	—
31	C₁₇×#532	C₂²	1	3	yes	—
32	C₁₇×#529	—	2	3	no	—
33	C₄×#41×C₁₇	—	2	1	no	—
34	C₄×#41×C₁₇	C₂²	1	3	yes	—
35	C₄×#41×C₁₇	C₂²	1	3	yes	—
36	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
38	C₁₇×#498	C₂²	1	3	yes	—
39	C₁₇×#492	C₂²	1	3	yes	—
40	C₁₇×#487	C₂²	1	3	yes	—
41	C₁₇×#486	C₂²	1	3	yes	—
42	C₁₇×#485	C₂²	1	6	yes	—
43	C₁₇×#482	C₂²	1	6	yes	—
44	C₁₇×#477	C₂²	1	3	yes	—
45	C₁₇×#476	C₂²	1	3	yes	—
46	C₁₇×#475	C₂²	1	3	yes	—
47	C₁₇×#474	C₂²	1	3	yes	—
48	C₁₇×#465	C₂²	1	6	yes	—
49	C₁₇×#465	C₂²	1	6	yes	—
50	C₁₇×#462	C₂²	1	3	yes	—
51	C₁₇×#461	C₂²	1	3	yes	—
52	C₁₇×#460	C₂²	1	3	yes	—
53	C₁₇×#459	C₂²	1	3	yes	—
54	C₁₇×#452	C₂²	1	6	yes	—
55	C₁₇×#449	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
58	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
59	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
60	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
61	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
62	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
63	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
64	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
65	C₄×D₈×C₁₇	C₂²	1	3	yes	—
66	C₄×D₈×C₁₇	C₂²	1	3	yes	—
67	C₈×D₄×C₁₇	C₂²	1	3	yes	—
68	C₈×D₄×C₁₇	C₂²	1	3	yes	—
69	C₁₇×#431	C₂²	1	3	yes	—
70	C₁₇×#427	C₂²	1	3	yes	—
71	C₁₇×#416	C₂²	1	3	yes	—
72	C₁₇×#416	C₂²	1	3	yes	—
73	C₂×C₄×C₈×C₁₇	C₂²	1	3	yes	—
74	C₂×#41×C₁₇	—	2	1	no	—
75	C₂×#41×C₁₇	—	2	3	no	—
76	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
77	C₂×#41×C₁₇	C₂³	1	3	yes	—
78	C₂×#41×C₁₇	C₂³	1	3	yes	—
79	C₂²×Q₈×C₁₇	—	2	1	no	—
80	C₁₇×#135	—	2	12	no	—
81	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
82	C₂×SD₁₆×C₁₇	C₂³	1	3	yes	—
83	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
84	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×D₈×C₁₇	C₂³	1	3	yes	—
86	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
87	C₂²×C₈×C₁₇	C₂³	1	3	yes	—
88	C₁₇×C₄⋊Q₈	—	2	3	no	—
89	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₇×#127	—	2	3	no	—
93	C₁₇×#127	C₂³	1	3	yes	—
94	C₁₇×#126	—	2	6	no	—
95	C₁₇×#125	—	2	3	no	—
96	C₁₇×#125	—	2	3	no	—
97	C₁₇×#124	—	2	3	no	—
98	C₁₇×#124	—	2	6	no	—
99	C₁₇×#124	—	2	3	no	—
100	C₁₇×#123	—	2	6	no	—
101	C₁₇×C₂²⋊Q₈	—	2	3	no	—
102	C₁₇×C₂²⋊Q₈	—	2	3	no	—
103	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
104	C₁₇×#121	—	2	3	no	—
105	C₁₇×#121	—	2	3	no	—
106	C₁₇×#121	—	2	3	no	—
107	C₁₇×#121	—	2	3	no	—
108	C₁₇×#121	—	2	6	no	—
109	C₁₇×#121	C₂³	1	6	yes	—
110	C₄×Q₈×C₁₇	—	2	1	no	—
111	C₄×Q₈×C₁₇	—	2	1	no	—
112	C₄×Q₈×C₁₇	—	2	3	no	—
113	C₄×Q₈×C₁₇	—	2	3	no	—
114	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
115	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
116	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
117	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
118	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
120	C₄×D₄×C₁₇	—	2	3	no	—
121	C₄×D₄×C₁₇	—	2	3	no	—
122	C₄×D₄×C₁₇	—	2	3	no	—
123	C₄×D₄×C₁₇	—	2	3	no	—
124	C₄×D₄×C₁₇	—	2	3	no	—
125	C₄×D₄×C₁₇	—	2	3	no	—
126	C₄×D₄×C₁₇	D₄	1	3	yes	—
127	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
128	C₄×D₄×C₁₇	C₂³	1	3	yes	—
129	C₄×D₄×C₁₇	C₂³	1	3	yes	—
130	C₄×D₄×C₁₇	C₂³	1	3	yes	—
131	C₄×D₄×C₁₇	C₂³	1	3	yes	—
132	C₁₇×#117	—	2	3	no	—
133	C₁₇×#117	—	2	3	no	—
134	C₁₇×#117	—	2	3	no	—
135	C₁₇×#117	—	2	3	no	—
136	C₁₇×#117	D₄	1	3	yes	—
137	C₁₇×#117	C₂³	1	3	yes	—
138	C₁₇×#117	C₂³	1	3	yes	—
139	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
140	C₂×C₄²×C₁₇	—	2	3	no	—
141	C₂×C₄²×C₁₇	—	2	3	no	—
142	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
143	C₁₇×#107	C₂³	1	3	yes	—
144	C₁₇×#107	C₂³	1	3	yes	—
145	C₁₇×#106	C₂³	1	3	yes	—
146	C₁₇×#106	C₂³	1	6	yes	—
147	C₁₇×#106	C₂³	1	1	yes	characteristic
148	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₇×#103	C₂³	1	1	yes	characteristic
151	C₁₇×#103	C₂³	1	3	yes	—
152	C₁₇×#103	C₂³	1	3	yes	—
153	C₁₇×#103	C₂³	1	3	yes	—
154	C₁₇×#103	C₂³	1	6	yes	—
155	C₁₇×#102	C₂³	1	1	yes	characteristic
156	C₁₇×#102	C₂³	1	3	yes	—
157	C₁₇×#102	C₂³	1	3	yes	—
158	C₁₇×#102	C₂³	1	3	yes	—
159	C₁₇×#102	C₂³	1	6	yes	—
160	C₁₇×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₄×C₈×C₁₇	C₂³	1	3	yes	—
162	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
163	C₄×C₈×C₁₇	C₂³	1	3	yes	—
164	C₄×C₈×C₁₇	C₂³	1	3	yes	—
165	#41×C₁₇	—	2	4	no	—
166	#41×C₁₇	—	2	6	no	—
167	#41×C₁₇	—	2	6	no	—
168	#41×C₁₇	—	4	3	no	—
169	#41×C₁₇	—	4	3	no	—
170	#41×C₁₇	—	4	4	no	—
171	#41×C₁₇	—	8	6	no	—
172	C₂×Q₈×C₁₇	—	2	3	no	—
173	C₂×Q₈×C₁₇	—	2	3	no	—
174	C₂×Q₈×C₁₇	—	4	4	no	—
175	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
176	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₇	—	2	3	no	—
179	C₂×D₄×C₁₇	—	2	3	no	—
180	C₂×D₄×C₁₇	—	2	6	no	—
181	C₂×D₄×C₁₇	—	2	3	no	—
182	C₂×D₄×C₁₇	—	2	3	no	—
183	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
184	C₂×D₄×C₁₇	C₂⁴	1	3	yes	—
185	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₁₇	—	2	3	no	—
187	C₂²×C₄×C₁₇	—	2	3	no	—
188	C₂²×C₄×C₁₇	—	2	3	no	—
189	C₂²×C₄×C₁₇	—	2	3	no	—
190	C₂²×C₄×C₁₇	—	2	3	no	—
191	C₂²×C₄×C₁₇	—	2	1	no	—
192	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
193	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
194	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
195	Q₁₆×C₁₇	—	2	6	no	—
196	SD₁₆×C₁₇	—	2	6	no	—
197	SD₁₆×C₁₇	—	4	6	no	—
198	SD₁₆×C₁₇	#41	1	4	yes	complemented
199	D₈×C₁₇	—	2	6	no	—
200	C₂×C₈×C₁₇	—	2	6	no	—
201	C₂×C₈×C₁₇	—	4	3	no	—
202	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
203	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
204	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
205	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
206	C₄⋊C₄×C₁₇	—	2	3	no	—
207	C₄⋊C₄×C₁₇	—	2	3	no	—
208	C₄⋊C₄×C₁₇	—	2	3	no	—
209	C₄⋊C₄×C₁₇	—	2	6	no	—
210	C₄⋊C₄×C₁₇	—	2	3	no	—
211	C₄⋊C₄×C₁₇	—	2	3	no	—
212	C₄⋊C₄×C₁₇	—	2	3	no	—
213	C₄⋊C₄×C₁₇	—	2	3	no	—
214	C₄⋊C₄×C₁₇	—	2	1	no	—
215	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
216	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
217	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
218	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
219	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₇	—	2	6	no	—
222	C₂²⋊C₄×C₁₇	—	2	3	no	—
223	C₂²⋊C₄×C₁₇	—	2	3	no	—
224	C₂²⋊C₄×C₁₇	—	2	3	no	—
225	C₂²⋊C₄×C₁₇	—	2	6	no	—
226	C₂²⋊C₄×C₁₇	—	2	3	no	—
227	C₂²⋊C₄×C₁₇	—	2	3	no	—
228	C₂²⋊C₄×C₁₇	—	2	1	no	—
229	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
230	C₄²×C₁₇	—	2	3	no	—
231	C₄²×C₁₇	—	2	3	no	—
232	C₄²×C₁₇	—	2	3	no	—
233	C₄²×C₁₇	—	2	3	no	—
234	C₄²×C₁₇	—	2	1	no	—
235	C₄²×C₁₇	—	2	3	no	—
236	C₄²×C₁₇	C₂×D₄	1	3	yes	—
237	C₄²×C₁₇	C₂×D₄	1	3	yes	—
238	C₄²×C₁₇	C₂⁴	1	3	yes	—
239	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
240	#61434	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
241	C₂³×C₁₇	—	2	1	no	—
242	C₂³×C₁₇	—	2	3	no	—
243	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
244	Q₈×C₁₇	—	2	1	no	—
245	Q₈×C₁₇	—	2	3	no	—
246	Q₈×C₁₇	—	2	3	no	—
247	Q₈×C₁₇	—	4	6	no	—
248	Q₈×C₁₇	—	8	3	no	—
249	Q₈×C₁₇	#135	1	4	yes	complemented
250	Q₈×C₁₇	C₂×#41	1	2	yes	—
251	D₄×C₁₇	—	2	6	no	—
252	D₄×C₁₇	—	2	3	no	—
253	D₄×C₁₇	—	2	1	no	—
254	D₄×C₁₇	—	2	3	no	—
255	D₄×C₁₇	—	4	6	no	—
256	D₄×C₁₇	—	4	6	no	—
257	D₄×C₁₇	—	4	6	no	—
258	D₄×C₁₇	—	8	3	no	—
259	D₄×C₁₇	—	8	6	no	—
260	D₄×C₁₇	C₂×#41	1	2	yes	—
261	C₂×C₄×C₁₇	—	2	1	no	—
262	C₂×C₄×C₁₇	—	2	6	no	—
263	C₂×C₄×C₁₇	—	2	6	no	—
264	C₂×C₄×C₁₇	—	2	3	no	—
265	C₂×C₄×C₁₇	—	2	3	no	—
266	C₂×C₄×C₁₇	—	2	1	no	—
267	C₂×C₄×C₁₇	—	2	1	no	—
268	C₂×C₄×C₁₇	—	2	3	no	—
269	C₂×C₄×C₁₇	—	2	3	no	—
270	C₂×C₄×C₁₇	—	2	3	no	—
271	C₂×C₄×C₁₇	—	4	6	no	—
272	C₂×C₄×C₁₇	—	4	6	no	—
273	C₂×C₄×C₁₇	—	4	6	no	—
274	C₂×C₄×C₁₇	—	4	6	no	—
275	C₂×C₄×C₁₇	—	4	2	no	—
276	C₂×C₄×C₁₇	—	4	6	no	—
277	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
278	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
280	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
281	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
282	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
283	C₈×C₁₇	—	2	3	no	—
284	C₈×C₁₇	—	2	1	no	—
285	C₈×C₁₇	—	2	3	no	—
286	C₈×C₁₇	C₂×#41	1	2	yes	—
287	#3483	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#3482	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#3392	C₂×C₁₇	1	1	yes	characteristic, complemented
290	Q₈×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
291	#3363	C₂×C₁₇	1	1	yes	characteristic, complemented
292	#3358	C₂×C₁₇	1	1	yes	characteristic, complemented
293	#3340	C₂×C₁₇	1	3	yes	complemented
294	#3304	C₂×C₁₇	1	3	yes	complemented
295	#3303	C₂×C₁₇	1	3	yes	complemented
296	#3284	C₂×C₁₇	1	3	yes	complemented
297	#3167	C₂×C₁₇	1	3	yes	complemented
298	#3107	C₂×C₁₇	1	3	yes	complemented
299	#3106	C₂×C₁₇	1	3	yes	complemented
300	C₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
301	C₄×#135	C₂×C₁₇	1	3	yes	complemented
302	C₂²×C₁₇	—	2	3	no	—
303	C₂²×C₁₇	—	2	2	no	—
304	C₂²×C₁₇	—	2	3	no	—
305	C₂²×C₁₇	—	2	3	no	—
306	C₂²×C₁₇	—	4	1	no	—
307	C₂²×C₁₇	—	4	1	no	—
308	C₂²×C₁₇	—	4	3	no	—
309	C₂²×C₁₇	—	4	3	no	—
310	C₂²×C₁₇	—	4	3	no	—
311	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
312	C₄×C₁₇	—	2	3	no	—
313	C₄×C₁₇	—	2	2	no	—
314	C₄×C₁₇	—	2	1	no	—
315	C₄×C₁₇	—	2	3	no	—
316	C₄×C₁₇	—	4	3	no	—
317	C₄×C₁₇	—	4	1	no	—
318	C₄×C₁₇	—	4	3	no	—
319	C₄×C₁₇	—	4	1	no	—
320	C₄×C₁₇	—	4	3	no	—
321	C₄×C₁₇	C₂×#135	1	6	yes	—
322	C₄×C₁₇	#577	1	2	yes	—
323	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
324	C₄×C₁₇	#585	1	1	yes	characteristic
325	C₂×#135	C₂²×C₁₇	1	3	yes	—
326	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
327	#557	C₂²×C₁₇	1	1	yes	characteristic
328	#556	C₂²×C₁₇	1	3	yes	—
329	#555	—	2	3	no	—
330	#555	C₂²×C₁₇	1	3	yes	—
331	#552	—	2	3	no	—
332	#550	—	2	1	no	—
333	#550	C₂²×C₁₇	1	3	yes	—
334	#550	C₂²×C₁₇	1	1	yes	characteristic
335	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
336	#548	—	2	1	no	—
337	#547	C₂²×C₁₇	1	3	yes	—
338	#533	C₂²×C₁₇	1	3	yes	—
339	#532	—	2	3	no	—
340	#532	C₂²×C₁₇	1	3	yes	—
341	#529	—	2	3	no	—
342	C₄×#41	—	2	1	no	—
343	C₄×#41	C₂²×C₁₇	1	3	yes	—
344	C₄×#41	C₂²×C₁₇	1	3	yes	—
345	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
346	C₂×C₄×Q₈	—	2	1	no	—
347	#498	C₂²×C₁₇	1	3	yes	—
348	#492	C₂²×C₁₇	1	3	yes	—
349	#487	C₂²×C₁₇	1	3	yes	—
350	#486	C₂²×C₁₇	1	3	yes	—
351	#485	C₂²×C₁₇	1	6	yes	—
352	#482	C₂²×C₁₇	1	6	yes	—
353	#477	C₂²×C₁₇	1	3	yes	—
354	#476	C₂²×C₁₇	1	3	yes	—
355	#475	C₂²×C₁₇	1	3	yes	—
356	#474	C₂²×C₁₇	1	3	yes	—
357	#465	C₂²×C₁₇	1	6	yes	—
358	#465	C₂²×C₁₇	1	6	yes	—
359	#462	C₂²×C₁₇	1	3	yes	—
360	#461	C₂²×C₁₇	1	3	yes	—
361	#460	C₂²×C₁₇	1	3	yes	—
362	#459	C₂²×C₁₇	1	3	yes	—
363	#452	C₂²×C₁₇	1	6	yes	—
364	#449	C₂²×C₁₇	1	6	yes	—
365	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
366	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
367	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
368	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
369	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
370	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
371	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
372	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
373	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
374	C₄×D₈	C₂²×C₁₇	1	3	yes	—
375	C₄×D₈	C₂²×C₁₇	1	3	yes	—
376	C₈×D₄	C₂²×C₁₇	1	3	yes	—
377	C₈×D₄	C₂²×C₁₇	1	3	yes	—
378	#431	C₂²×C₁₇	1	3	yes	—
379	#427	C₂²×C₁₇	1	3	yes	—
380	#416	C₂²×C₁₇	1	3	yes	—
381	#416	C₂²×C₁₇	1	3	yes	—
382	C₂×C₄×C₈	C₂²×C₁₇	1	3	yes	—
383	C₂×C₁₇	—	4	3	no	—
384	C₂×C₁₇	—	4	2	no	—
385	C₂×C₁₇	—	8	3	no	—
386	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
387	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
388	C₂×C₁₇	C₂×#577	1	1	yes	characteristic
389	C₂×#41	—	2	1	no	—
390	C₂×#41	—	2	3	no	—
391	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
392	C₂×#41	C₂³×C₁₇	1	3	yes	—
393	C₂×#41	C₂³×C₁₇	1	3	yes	—
394	C₂²×Q₈	—	2	1	no	—
395	#135	—	2	12	no	—
396	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
397	C₂×SD₁₆	C₂³×C₁₇	1	3	yes	—
398	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
399	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
400	C₂×D₈	C₂³×C₁₇	1	3	yes	—
401	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
402	C₂²×C₈	C₂³×C₁₇	1	3	yes	—
403	C₄⋊Q₈	—	2	3	no	—
404	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
405	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
406	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
407	#127	—	2	3	no	—
408	#127	C₂³×C₁₇	1	3	yes	—
409	#126	—	2	6	no	—
410	#125	—	2	3	no	—
411	#125	—	2	3	no	—
412	#124	—	2	3	no	—
413	#124	—	2	6	no	—
414	#124	—	2	3	no	—
415	#123	—	2	6	no	—
416	C₂²⋊Q₈	—	2	3	no	—
417	C₂²⋊Q₈	—	2	3	no	—
418	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
419	#121	—	2	3	no	—
420	#121	—	2	3	no	—
421	#121	—	2	3	no	—
422	#121	—	2	3	no	—
423	#121	—	2	6	no	—
424	#121	C₂³×C₁₇	1	6	yes	—
425	C₄×Q₈	—	2	1	no	—
426	C₄×Q₈	—	2	1	no	—
427	C₄×Q₈	—	2	3	no	—
428	C₄×Q₈	—	2	3	no	—
429	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
430	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
431	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
432	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
433	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
434	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
435	C₄×D₄	—	2	3	no	—
436	C₄×D₄	—	2	3	no	—
437	C₄×D₄	—	2	3	no	—
438	C₄×D₄	—	2	3	no	—
439	C₄×D₄	—	2	3	no	—
440	C₄×D₄	—	2	3	no	—
441	C₄×D₄	D₄×C₁₇	1	3	yes	—
442	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
443	C₄×D₄	C₂³×C₁₇	1	3	yes	—
444	C₄×D₄	C₂³×C₁₇	1	3	yes	—
445	C₄×D₄	C₂³×C₁₇	1	3	yes	—
446	C₄×D₄	C₂³×C₁₇	1	3	yes	—
447	#117	—	2	3	no	—
448	#117	—	2	3	no	—
449	#117	—	2	3	no	—
450	#117	—	2	3	no	—
451	#117	D₄×C₁₇	1	3	yes	—
452	#117	C₂³×C₁₇	1	3	yes	—
453	#117	C₂³×C₁₇	1	3	yes	—
454	C₂×C₄⋊C₄	—	2	3	no	—
455	C₂×C₄²	—	2	3	no	—
456	C₂×C₄²	—	2	3	no	—
457	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
458	#107	C₂³×C₁₇	1	3	yes	—
459	#107	C₂³×C₁₇	1	3	yes	—
460	#106	C₂³×C₁₇	1	1	yes	characteristic
461	#106	C₂³×C₁₇	1	3	yes	—
462	#106	C₂³×C₁₇	1	6	yes	—
463	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
464	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
465	#103	C₂³×C₁₇	1	1	yes	characteristic
466	#103	C₂³×C₁₇	1	3	yes	—
467	#103	C₂³×C₁₇	1	3	yes	—
468	#103	C₂³×C₁₇	1	3	yes	—
469	#103	C₂³×C₁₇	1	6	yes	—
470	#102	C₂³×C₁₇	1	1	yes	characteristic
471	#102	C₂³×C₁₇	1	3	yes	—
472	#102	C₂³×C₁₇	1	3	yes	—
473	#102	C₂³×C₁₇	1	3	yes	—
474	#102	C₂³×C₁₇	1	6	yes	—
475	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
476	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
477	C₄×C₈	C₂³×C₁₇	1	3	yes	—
478	C₄×C₈	C₂³×C₁₇	1	3	yes	—
479	C₄×C₈	C₂³×C₁₇	1	3	yes	—
480	C₁₇	#61434	1	1	yes	characteristic, direct product factor, Sylow
481	#41	—	2	4	no	—
482	#41	—	2	6	no	—
483	#41	—	2	6	no	—
484	#41	—	4	3	no	—
485	#41	—	4	3	no	—
486	#41	—	4	4	no	—
487	#41	—	8	6	no	—
488	C₂×Q₈	—	2	3	no	—
489	C₂×Q₈	—	2	3	no	—
490	C₂×Q₈	—	4	4	no	—
491	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
493	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
494	C₂×D₄	—	2	3	no	—
495	C₂×D₄	—	2	3	no	—
496	C₂×D₄	—	2	6	no	—
497	C₂×D₄	—	2	3	no	—
498	C₂×D₄	—	2	3	no	—
499	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
500	C₂×D₄	C₂⁴×C₁₇	1	3	yes	—
501	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	3	no	—
504	C₂²×C₄	—	2	3	no	—
505	C₂²×C₄	—	2	3	no	—
506	C₂²×C₄	—	2	3	no	—
507	C₂²×C₄	—	2	3	no	—
508	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
509	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
510	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
511	Q₁₆	—	2	6	no	—
512	SD₁₆	—	2	6	no	—
513	SD₁₆	—	4	6	no	—
514	SD₁₆	#41×C₁₇	1	4	yes	complemented
515	D₈	—	2	6	no	—
516	C₂×C₈	—	2	6	no	—
517	C₂×C₈	—	4	3	no	—
518	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
519	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
520	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
521	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
522	C₄⋊C₄	—	2	3	no	—
523	C₄⋊C₄	—	2	6	no	—
524	C₄⋊C₄	—	2	1	no	—
525	C₄⋊C₄	—	2	3	no	—
526	C₄⋊C₄	—	2	3	no	—
527	C₄⋊C₄	—	2	3	no	—
528	C₄⋊C₄	—	2	3	no	—
529	C₄⋊C₄	—	2	3	no	—
530	C₄⋊C₄	—	2	3	no	—
531	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
532	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
533	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
534	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
535	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
536	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
537	C₂²⋊C₄	—	2	6	no	—
538	C₂²⋊C₄	—	2	3	no	—
539	C₂²⋊C₄	—	2	3	no	—
540	C₂²⋊C₄	—	2	1	no	—
541	C₂²⋊C₄	—	2	6	no	—
542	C₂²⋊C₄	—	2	3	no	—
543	C₂²⋊C₄	—	2	3	no	—
544	C₂²⋊C₄	—	2	3	no	—
545	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	3	no	—
548	C₄²	—	2	3	no	—
549	C₄²	—	2	3	no	—
550	C₄²	—	2	3	no	—
551	C₄²	—	2	3	no	—
552	C₄²	C₂×D₄×C₁₇	1	3	yes	—
553	C₄²	C₂×D₄×C₁₇	1	3	yes	—
554	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
555	C₄²	C₂⁴×C₁₇	1	3	yes	—
556	C₂³	—	2	1	no	—
557	C₂³	—	2	3	no	—
558	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
559	Q₈	—	2	1	no	—
560	Q₈	—	2	3	no	—
561	Q₈	—	2	3	no	—
562	Q₈	—	4	6	no	—
563	Q₈	—	8	3	no	—
564	Q₈	C₁₇×#135	1	4	yes	complemented
565	Q₈	C₂×#41×C₁₇	1	2	yes	—
566	D₄	—	2	6	no	—
567	D₄	—	2	3	no	—
568	D₄	—	2	1	no	—
569	D₄	—	2	3	no	—
570	D₄	—	4	6	no	—
571	D₄	—	4	6	no	—
572	D₄	—	4	6	no	—
573	D₄	—	8	3	no	—
574	D₄	—	8	6	no	—
575	D₄	C₂×#41×C₁₇	1	2	yes	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	6	no	—
578	C₂×C₄	—	2	6	no	—
579	C₂×C₄	—	2	3	no	—
580	C₂×C₄	—	2	3	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	3	no	—
584	C₂×C₄	—	2	3	no	—
585	C₂×C₄	—	2	3	no	—
586	C₂×C₄	—	4	6	no	—
587	C₂×C₄	—	4	6	no	—
588	C₂×C₄	—	4	6	no	—
589	C₂×C₄	—	4	6	no	—
590	C₂×C₄	—	4	6	no	—
591	C₂×C₄	—	4	2	no	—
592	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
593	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
594	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
595	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
596	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
597	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
598	C₈	—	2	3	no	—
599	C₈	—	2	1	no	—
600	C₈	—	2	3	no	—
601	C₈	C₂×#41×C₁₇	1	2	yes	—
602	C₂²	—	2	3	no	—
603	C₂²	—	2	2	no	—
604	C₂²	—	2	3	no	—
605	C₂²	—	2	3	no	—
606	C₂²	—	4	1	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	3	no	—
609	C₂²	—	4	3	no	—
610	C₂²	—	4	3	no	—
611	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
612	C₄	—	2	3	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	3	no	—
616	C₄	—	4	3	no	—
617	C₄	—	4	1	no	—
618	C₄	—	4	3	no	—
619	C₄	—	4	3	no	—
620	C₄	—	4	1	no	—
621	C₄	C₂×C₁₇×#135	1	6	yes	—
622	C₄	C₁₇×#577	1	2	yes	—
623	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
624	C₄	C₁₇×#585	1	1	yes	characteristic
625	C₂	—	4	3	no	—
626	C₂	—	4	2	no	—
627	C₂	—	8	3	no	—
628	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
629	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
630	C₂	C₂×C₁₇×#577	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×#3483	C₂	semidirect
2. C₁₇×#3482	C₂	semidirect
3. C₁₇×#3392	C₂	semidirect
4. Q₈×SD₁₆×C₁₇	C₂	semidirect
5. C₁₇×#3363	C₂	semidirect
6. C₁₇×#3358	C₂	semidirect
7. C₁₇×#3340	C₂	semidirect
8. C₁₇×#3304	C₂	semidirect
9. C₁₇×#3303	C₂	semidirect
10. C₁₇×#3284	C₂	semidirect
11. C₁₇×#3167	C₂	semidirect
12. C₁₇×#3107	C₂	semidirect
13. C₁₇×#3106	C₂	semidirect
14. C₈×#41×C₁₇	C₂	semidirect
15. C₄×C₁₇×#135	C₂	semidirect
198. SD₁₆×C₁₇	#41	semidirect
240. #61434	C₁₇	direct (N × H)
249. Q₈×C₁₇	#135	semidirect
287. #3483	C₂×C₁₇	semidirect
288. #3482	C₂×C₁₇	semidirect
289. #3392	C₂×C₁₇	semidirect
290. Q₈×SD₁₆	C₂×C₁₇	semidirect
291. #3363	C₂×C₁₇	semidirect
292. #3358	C₂×C₁₇	semidirect
293. #3340	C₂×C₁₇	semidirect
294. #3304	C₂×C₁₇	semidirect
295. #3303	C₂×C₁₇	semidirect
296. #3284	C₂×C₁₇	semidirect
297. #3167	C₂×C₁₇	semidirect
298. #3107	C₂×C₁₇	semidirect
299. #3106	C₂×C₁₇	semidirect
300. C₈×#41	C₂×C₁₇	semidirect
301. C₄×#135	C₂×C₁₇	semidirect
480. C₁₇	#61434	direct (N × H)
514. SD₁₆	#41×C₁₇	semidirect
564. Q₈	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×#3483	2
C₁₇×#3482	2
C₁₇×#3392	2
Q₈×SD₁₆×C₁₇	2
C₁₇×#3363	2
C₁₇×#3358	2
C₁₇×#3340	2
C₁₇×#3304	2
C₁₇×#3303	2
C₁₇×#3284	2
C₁₇×#3167	2
C₁₇×#3107	2
C₁₇×#3106	2
C₈×#41×C₁₇	2
C₄×C₁₇×#135	2
#61434	17

Subgroups — C17×#61434 #16919178

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61434 #16919178