Subgroups — C₁₇×#61887 #16919631

Order 4352.

1740 conjugacy classes of subgroups.

The subgroup lattice has 614 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3480	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3394	C₂	1	3	yes	maximal, complemented
5	C₁₇×#3393	C₂	1	3	yes	maximal, complemented
6	C₁₇×#3392	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3365	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3364	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3359	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#3358	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3212	C₂	1	3	yes	maximal, complemented
12	C₁₇×#3210	C₂	1	3	yes	maximal, complemented
13	C₁₇×#3107	C₂	1	3	yes	maximal, complemented
14	C₁₇×#3102	C₂	1	3	yes	maximal, complemented
15	C₁₇×#2982	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#559	C₂²	1	3	yes	—
17	C₁₇×#557	C₂²	1	1	yes	characteristic
18	C₁₇×#557	C₂²	1	1	yes	characteristic
19	C₁₇×#557	C₂²	1	3	yes	—
20	C₁₇×#556	C₂²	1	3	yes	—
21	C₁₇×#556	C₂²	1	3	yes	—
22	C₁₇×#553	—	2	3	no	—
23	C₁₇×#552	—	2	3	no	—
24	C₁₇×#550	C₂²	1	1	yes	characteristic
25	D₄×Q₈×C₁₇	—	2	1	no	—
26	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
27	C₁₇×#548	—	2	1	no	—
28	C₁₇×#541	—	2	3	no	—
29	C₁₇×#533	C₂²	1	3	yes	—
30	C₁₇×#532	C₂²	1	3	yes	—
31	C₁₇×#529	—	2	3	no	—
32	C₁₇×#529	C₂²	1	3	yes	—
33	C₁₇×#519	—	2	1	no	—
34	C₄×#41×C₁₇	—	2	1	no	—
35	C₄×#41×C₁₇	C₂²	1	3	yes	—
36	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
37	C₁₇×#495	C₂²	1	6	yes	—
38	C₁₇×#494	C₂²	1	3	yes	—
39	C₁₇×#492	C₂²	1	3	yes	—
40	C₁₇×#488	C₂²	1	6	yes	—
41	C₁₇×#487	C₂²	1	3	yes	—
42	C₁₇×#486	C₂²	1	3	yes	—
43	C₁₇×#485	C₂²	1	3	yes	—
44	C₁₇×#482	C₂²	1	1	yes	characteristic
45	C₁₇×#479	C₂²	1	3	yes	—
46	C₁₇×#478	C₂²	1	3	yes	—
47	C₁₇×#475	C₂²	1	3	yes	—
48	C₁₇×#474	C₂²	1	3	yes	—
49	C₁₇×#464	C₂²	1	6	yes	—
50	C₁₇×#464	C₂²	1	6	yes	—
51	C₁₇×#464	C₂²	1	3	yes	—
52	C₁₇×#463	C₂²	1	3	yes	—
53	C₁₇×#462	C₂²	1	3	yes	—
54	C₁₇×#462	C₂²	1	3	yes	—
55	C₁₇×#461	C₂²	1	3	yes	—
56	C₁₇×#461	C₂²	1	3	yes	—
57	C₁₇×#460	C₂²	1	3	yes	—
58	C₁₇×#459	C₂²	1	3	yes	—
59	C₁₇×#452	C₂²	1	3	yes	—
60	C₁₇×#452	C₂²	1	6	yes	—
61	C₁₇×#449	C₂²	1	3	yes	—
62	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
64	C₈×Q₈×C₁₇	C₂²	1	3	yes	—
65	C₈×Q₈×C₁₇	C₂²	1	3	yes	—
66	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
67	C₄×Q₁₆×C₁₇	C₂²	1	6	yes	—
68	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
69	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
70	C₄×SD₁₆×C₁₇	C₂²	1	6	yes	—
71	C₄×D₈×C₁₇	C₂²	1	3	yes	—
72	C₁₇×#431	C₂²	1	3	yes	—
73	C₁₇×#431	C₂²	1	3	yes	—
74	C₂×#41×C₁₇	—	2	1	no	—
75	C₂×#41×C₁₇	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₇	—	2	1	no	—
77	C₂²×Q₈×C₁₇	D₄	1	1	yes	characteristic
78	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
79	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
80	C₂×SD₁₆×C₁₇	C₂³	1	3	yes	—
81	C₂×SD₁₆×C₁₇	C₂³	1	6	yes	—
82	C₂×SD₁₆×C₁₇	C₂³	1	3	yes	—
83	C₂×D₈×C₁₇	C₂³	1	3	yes	—
84	C₁₇×C₄⋊Q₈	—	2	3	no	—
85	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
86	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
88	C₁₇×#127	C₂³	1	3	yes	—
89	C₁₇×#126	—	2	6	no	—
90	C₁₇×#126	—	2	6	no	—
91	C₁₇×#126	—	2	3	no	—
92	C₁₇×#125	—	2	3	no	—
93	C₁₇×#125	—	2	6	no	—
94	C₁₇×#125	—	2	3	no	—
95	C₁₇×#125	—	2	3	no	—
96	C₁₇×#125	C₂³	1	3	yes	—
97	C₁₇×#124	—	2	3	no	—
98	C₁₇×#124	C₂³	1	3	yes	—
99	C₁₇×#124	C₂³	1	6	yes	—
100	C₁₇×#123	—	2	3	no	—
101	C₁₇×#123	—	2	6	no	—
102	C₁₇×C₂²⋊Q₈	—	2	3	no	—
103	C₁₇×C₂²⋊Q₈	—	2	3	no	—
104	C₁₇×C₂²⋊Q₈	—	2	3	no	—
105	C₁₇×C₂²⋊Q₈	—	2	3	no	—
106	C₁₇×C₂²⋊Q₈	C₂³	1	3	yes	—
107	C₁₇×#121	—	2	3	no	—
108	C₁₇×#121	—	2	3	no	—
109	C₁₇×#121	—	2	3	no	—
110	C₁₇×#121	C₂³	1	1	yes	characteristic
111	C₄×Q₈×C₁₇	—	2	1	no	—
112	C₄×Q₈×C₁₇	—	2	1	no	—
113	C₄×Q₈×C₁₇	—	2	3	no	—
114	C₄×Q₈×C₁₇	—	2	3	no	—
115	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
116	C₄×Q₈×C₁₇	D₄	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	3	yes	—
120	C₄×Q₈×C₁₇	C₂³	1	6	yes	—
121	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
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	—	2	3	no	—
127	C₄×D₄×C₁₇	—	2	3	no	—
128	C₄×D₄×C₁₇	—	2	3	no	—
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	—	2	3	no	—
137	C₁₇×#117	C₂³	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₁₇	D₄	1	3	yes	—
139	C₂×C₄²×C₁₇	—	2	3	no	—
140	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
141	C₁₇×#107	C₂³	1	3	yes	—
142	C₁₇×#107	C₂³	1	1	yes	characteristic
143	C₁₇×#106	C₂³	1	3	yes	—
144	C₁₇×#106	C₂³	1	1	yes	characteristic
145	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
146	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
147	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₇×#103	C₂³	1	3	yes	—
150	C₁₇×#103	C₂³	1	3	yes	—
151	C₁₇×#103	C₂³	1	3	yes	—
152	C₁₇×#103	C₂³	1	3	yes	—
153	C₁₇×#103	C₂³	1	6	yes	—
154	C₁₇×#102	C₂³	1	1	yes	characteristic
155	C₁₇×#102	C₂³	1	3	yes	—
156	C₁₇×#102	C₂³	1	1	yes	characteristic
157	C₁₇×#102	C₂³	1	3	yes	—
158	C₁₇×#102	C₂³	1	6	yes	—
159	C₁₇×C₂²⋊C₈	C₂³	1	3	yes	—
160	C₁₇×C₂²⋊C₈	C₂³	1	1	yes	characteristic
161	C₄×C₈×C₁₇	C₂³	1	3	yes	—
162	C₄×C₈×C₁₇	C₂³	1	3	yes	—
163	C₄×C₈×C₁₇	C₂³	1	6	yes	—
164	#41×C₁₇	—	4	3	no	—
165	#41×C₁₇	—	4	3	no	—
166	#41×C₁₇	—	4	4	no	—
167	C₂×Q₈×C₁₇	—	2	4	no	—
168	C₂×Q₈×C₁₇	—	2	3	no	—
169	C₂×Q₈×C₁₇	—	4	4	no	—
170	C₂×Q₈×C₁₇	C₂×D₄	1	3	yes	—
171	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
173	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
174	C₂×D₄×C₁₇	—	2	1	no	—
175	C₂×D₄×C₁₇	—	2	3	no	—
176	C₂×D₄×C₁₇	—	2	3	no	—
177	C₂×D₄×C₁₇	—	2	3	no	—
178	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
179	C₂×D₄×C₁₇	C₂⁴	1	3	yes	—
180	C₂²×C₄×C₁₇	—	2	3	no	—
181	C₂²×C₄×C₁₇	—	2	3	no	—
182	C₂²×C₄×C₁₇	—	2	3	no	—
183	C₂²×C₄×C₁₇	—	2	3	no	—
184	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
185	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
186	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
187	Q₁₆×C₁₇	—	4	6	no	—
188	Q₁₆×C₁₇	—	4	3	no	—
189	SD₁₆×C₁₇	—	4	3	no	—
190	SD₁₆×C₁₇	—	4	3	no	—
191	SD₁₆×C₁₇	—	4	6	no	—
192	D₈×C₁₇	—	4	3	no	—
193	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
194	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
195	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
196	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
197	C₄⋊C₄×C₁₇	—	2	3	no	—
198	C₄⋊C₄×C₁₇	—	2	6	no	—
199	C₄⋊C₄×C₁₇	—	2	3	no	—
200	C₄⋊C₄×C₁₇	—	2	3	no	—
201	C₄⋊C₄×C₁₇	—	2	3	no	—
202	C₄⋊C₄×C₁₇	—	2	3	no	—
203	C₄⋊C₄×C₁₇	—	2	3	no	—
204	C₄⋊C₄×C₁₇	—	2	3	no	—
205	C₄⋊C₄×C₁₇	—	2	3	no	—
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	C₂×D₄	1	3	yes	—
210	C₄⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
211	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
212	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
213	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
214	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
215	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
216	C₂²⋊C₄×C₁₇	—	2	3	no	—
217	C₂²⋊C₄×C₁₇	—	2	1	no	—
218	C₂²⋊C₄×C₁₇	—	2	3	no	—
219	C₂²⋊C₄×C₁₇	—	2	3	no	—
220	C₂²⋊C₄×C₁₇	—	2	6	no	—
221	C₂²⋊C₄×C₁₇	—	2	3	no	—
222	C₂²⋊C₄×C₁₇	—	2	3	no	—
223	C₂²⋊C₄×C₁₇	—	2	6	no	—
224	C₂²⋊C₄×C₁₇	—	2	1	no	—
225	C₂²⋊C₄×C₁₇	—	2	3	no	—
226	C₄²×C₁₇	—	2	3	no	—
227	C₄²×C₁₇	—	2	6	no	—
228	C₄²×C₁₇	—	2	3	no	—
229	C₄²×C₁₇	—	2	3	no	—
230	C₄²×C₁₇	—	2	1	no	—
231	C₄²×C₁₇	C₂×D₄	1	3	yes	—
232	C₄²×C₁₇	C₂×D₄	1	3	yes	—
233	C₄²×C₁₇	C₂⁴	1	3	yes	—
234	C₄²×C₁₇	C₂⁴	1	3	yes	—
235	#61887	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂³×C₁₇	—	2	1	no	—
237	C₂³×C₁₇	—	2	3	no	—
238	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
239	Q₈×C₁₇	—	2	6	no	—
240	Q₈×C₁₇	—	2	3	no	—
241	Q₈×C₁₇	—	2	3	no	—
242	Q₈×C₁₇	—	2	3	no	—
243	Q₈×C₁₇	—	2	3	no	—
244	Q₈×C₁₇	—	4	6	no	—
245	Q₈×C₁₇	#135	1	4	yes	—
246	D₄×C₁₇	—	2	1	no	—
247	D₄×C₁₇	—	2	3	no	—
248	D₄×C₁₇	—	2	1	no	—
249	D₄×C₁₇	—	2	3	no	—
250	D₄×C₁₇	—	4	2	no	—
251	D₄×C₁₇	—	4	6	no	—
252	D₄×C₁₇	—	4	6	no	—
253	D₄×C₁₇	—	8	3	no	—
254	C₂×C₄×C₁₇	—	2	6	no	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	1	no	—
257	C₂×C₄×C₁₇	—	2	1	no	—
258	C₂×C₄×C₁₇	—	2	1	no	—
259	C₂×C₄×C₁₇	—	2	3	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	3	no	—
262	C₂×C₄×C₁₇	—	2	3	no	—
263	C₂×C₄×C₁₇	—	4	3	no	—
264	C₂×C₄×C₁₇	—	4	6	no	—
265	C₂×C₄×C₁₇	—	4	6	no	—
266	C₂×C₄×C₁₇	—	4	6	no	—
267	C₂×C₄×C₁₇	—	8	3	no	—
268	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
271	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
272	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
273	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
274	C₈×C₁₇	—	2	3	no	—
275	C₈×C₁₇	—	2	1	no	—
276	C₈×C₁₇	—	2	3	no	—
277	C₈×C₁₇	—	2	1	no	—
278	#3523	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#3480	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#3395	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#3394	C₂×C₁₇	1	3	yes	complemented
282	#3393	C₂×C₁₇	1	3	yes	complemented
283	#3392	C₂×C₁₇	1	1	yes	characteristic, complemented
284	#3365	C₂×C₁₇	1	3	yes	complemented
285	#3364	C₂×C₁₇	1	3	yes	complemented
286	#3359	C₂×C₁₇	1	1	yes	characteristic, complemented
287	#3358	C₂×C₁₇	1	1	yes	characteristic, complemented
288	#3212	C₂×C₁₇	1	3	yes	complemented
289	#3210	C₂×C₁₇	1	3	yes	complemented
290	#3107	C₂×C₁₇	1	3	yes	complemented
291	#3102	C₂×C₁₇	1	3	yes	complemented
292	#2982	C₂×C₁₇	1	1	yes	characteristic, complemented
293	C₂²×C₁₇	—	2	1	no	—
294	C₂²×C₁₇	—	2	1	no	—
295	C₂²×C₁₇	—	2	1	no	—
296	C₂²×C₁₇	—	4	3	no	—
297	C₂²×C₁₇	—	4	1	no	—
298	C₂²×C₁₇	—	4	3	no	—
299	C₂²×C₁₇	—	4	1	no	—
300	C₂²×C₁₇	—	4	1	no	—
301	C₂²×C₁₇	—	4	3	no	—
302	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₇	—	2	3	no	—
304	C₄×C₁₇	—	2	3	no	—
305	C₄×C₁₇	—	2	1	no	—
306	C₄×C₁₇	—	2	3	no	—
307	C₄×C₁₇	—	4	1	no	—
308	C₄×C₁₇	—	4	1	no	—
309	C₄×C₁₇	—	4	3	no	—
310	C₄×C₁₇	—	4	3	no	—
311	C₄×C₁₇	—	4	1	no	—
312	C₄×C₁₇	—	4	3	no	—
313	C₄×C₁₇	C₂×#135	1	6	yes	—
314	C₄×C₁₇	#585	1	1	yes	characteristic
315	C₄×C₁₇	#585	1	1	yes	characteristic
316	#559	C₂²×C₁₇	1	3	yes	—
317	#557	C₂²×C₁₇	1	1	yes	characteristic
318	#557	C₂²×C₁₇	1	1	yes	characteristic
319	#557	C₂²×C₁₇	1	3	yes	—
320	#556	C₂²×C₁₇	1	3	yes	—
321	#556	C₂²×C₁₇	1	3	yes	—
322	#553	—	2	3	no	—
323	#552	—	2	3	no	—
324	#550	C₂²×C₁₇	1	1	yes	characteristic
325	D₄×Q₈	—	2	1	no	—
326	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
327	#548	—	2	1	no	—
328	#541	—	2	3	no	—
329	#533	C₂²×C₁₇	1	3	yes	—
330	#532	C₂²×C₁₇	1	3	yes	—
331	#529	—	2	3	no	—
332	#529	C₂²×C₁₇	1	3	yes	—
333	#519	—	2	1	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	C₂²×C₁₇	1	3	yes	—
336	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
337	#495	C₂²×C₁₇	1	6	yes	—
338	#494	C₂²×C₁₇	1	3	yes	—
339	#492	C₂²×C₁₇	1	3	yes	—
340	#488	C₂²×C₁₇	1	6	yes	—
341	#487	C₂²×C₁₇	1	3	yes	—
342	#486	C₂²×C₁₇	1	3	yes	—
343	#485	C₂²×C₁₇	1	3	yes	—
344	#482	C₂²×C₁₇	1	1	yes	characteristic
345	#479	C₂²×C₁₇	1	3	yes	—
346	#478	C₂²×C₁₇	1	3	yes	—
347	#475	C₂²×C₁₇	1	3	yes	—
348	#474	C₂²×C₁₇	1	3	yes	—
349	#464	C₂²×C₁₇	1	3	yes	—
350	#464	C₂²×C₁₇	1	6	yes	—
351	#464	C₂²×C₁₇	1	6	yes	—
352	#463	C₂²×C₁₇	1	3	yes	—
353	#462	C₂²×C₁₇	1	3	yes	—
354	#462	C₂²×C₁₇	1	3	yes	—
355	#461	C₂²×C₁₇	1	3	yes	—
356	#461	C₂²×C₁₇	1	3	yes	—
357	#460	C₂²×C₁₇	1	3	yes	—
358	#459	C₂²×C₁₇	1	3	yes	—
359	#452	C₂²×C₁₇	1	3	yes	—
360	#452	C₂²×C₁₇	1	6	yes	—
361	#449	C₂²×C₁₇	1	3	yes	—
362	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
363	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
364	C₈×Q₈	C₂²×C₁₇	1	3	yes	—
365	C₈×Q₈	C₂²×C₁₇	1	3	yes	—
366	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
367	C₄×Q₁₆	C₂²×C₁₇	1	6	yes	—
368	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
369	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
370	C₄×SD₁₆	C₂²×C₁₇	1	6	yes	—
371	C₄×D₈	C₂²×C₁₇	1	3	yes	—
372	#431	C₂²×C₁₇	1	3	yes	—
373	#431	C₂²×C₁₇	1	3	yes	—
374	C₂×C₁₇	—	4	1	no	—
375	C₂×C₁₇	—	8	3	no	—
376	C₂×C₁₇	—	8	1	no	—
377	C₂×C₁₇	#3487	1	1	yes	characteristic
378	C₂×C₁₇	C₂²×#135	1	1	yes	characteristic
379	C₂×C₁₇	#3586	1	1	yes	characteristic
380	C₂×#41	—	2	1	no	—
381	C₂×#41	C₂³×C₁₇	1	3	yes	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	D₄×C₁₇	1	1	yes	characteristic
384	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
385	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
386	C₂×SD₁₆	C₂³×C₁₇	1	3	yes	—
387	C₂×SD₁₆	C₂³×C₁₇	1	6	yes	—
388	C₂×SD₁₆	C₂³×C₁₇	1	3	yes	—
389	C₂×D₈	C₂³×C₁₇	1	3	yes	—
390	C₄⋊Q₈	—	2	3	no	—
391	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
392	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
393	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
394	#127	C₂³×C₁₇	1	3	yes	—
395	#126	—	2	6	no	—
396	#126	—	2	6	no	—
397	#126	—	2	3	no	—
398	#125	—	2	3	no	—
399	#125	—	2	6	no	—
400	#125	—	2	3	no	—
401	#125	—	2	3	no	—
402	#125	C₂³×C₁₇	1	3	yes	—
403	#124	—	2	3	no	—
404	#124	C₂³×C₁₇	1	3	yes	—
405	#124	C₂³×C₁₇	1	6	yes	—
406	#123	—	2	3	no	—
407	#123	—	2	6	no	—
408	C₂²⋊Q₈	—	2	3	no	—
409	C₂²⋊Q₈	—	2	3	no	—
410	C₂²⋊Q₈	—	2	3	no	—
411	C₂²⋊Q₈	—	2	3	no	—
412	C₂²⋊Q₈	C₂³×C₁₇	1	3	yes	—
413	#121	—	2	3	no	—
414	#121	—	2	3	no	—
415	#121	—	2	3	no	—
416	#121	C₂³×C₁₇	1	1	yes	characteristic
417	C₄×Q₈	—	2	1	no	—
418	C₄×Q₈	—	2	1	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	—	2	3	no	—
421	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
422	C₄×Q₈	D₄×C₁₇	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
425	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₇	1	6	yes	—
427	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
428	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
429	C₄×D₄	—	2	3	no	—
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	—	2	3	no	—
435	C₄×D₄	C₂³×C₁₇	1	3	yes	—
436	C₄×D₄	C₂³×C₁₇	1	3	yes	—
437	C₄×D₄	C₂³×C₁₇	1	3	yes	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	#117	—	2	3	no	—
441	#117	—	2	3	no	—
442	#117	—	2	3	no	—
443	#117	C₂³×C₁₇	1	1	yes	characteristic
444	C₂×C₄⋊C₄	D₄×C₁₇	1	3	yes	—
445	C₂×C₄²	—	2	3	no	—
446	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
447	#107	C₂³×C₁₇	1	3	yes	—
448	#107	C₂³×C₁₇	1	1	yes	characteristic
449	#106	C₂³×C₁₇	1	3	yes	—
450	#106	C₂³×C₁₇	1	1	yes	characteristic
451	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
452	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
453	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
454	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
455	#103	C₂³×C₁₇	1	3	yes	—
456	#103	C₂³×C₁₇	1	3	yes	—
457	#103	C₂³×C₁₇	1	3	yes	—
458	#103	C₂³×C₁₇	1	3	yes	—
459	#103	C₂³×C₁₇	1	6	yes	—
460	#102	C₂³×C₁₇	1	1	yes	characteristic
461	#102	C₂³×C₁₇	1	3	yes	—
462	#102	C₂³×C₁₇	1	1	yes	characteristic
463	#102	C₂³×C₁₇	1	3	yes	—
464	#102	C₂³×C₁₇	1	6	yes	—
465	C₂²⋊C₈	C₂³×C₁₇	1	3	yes	—
466	C₂²⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
467	C₄×C₈	C₂³×C₁₇	1	3	yes	—
468	C₄×C₈	C₂³×C₁₇	1	3	yes	—
469	C₄×C₈	C₂³×C₁₇	1	6	yes	—
470	C₁₇	#61887	1	1	yes	characteristic, direct product factor, Sylow
471	#41	—	4	3	no	—
472	#41	—	4	3	no	—
473	#41	—	4	4	no	—
474	C₂×Q₈	—	2	4	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	4	4	no	—
477	C₂×Q₈	C₂×D₄×C₁₇	1	3	yes	—
478	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
479	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
480	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
481	C₂×D₄	—	2	1	no	—
482	C₂×D₄	—	2	3	no	—
483	C₂×D₄	—	2	3	no	—
484	C₂×D₄	—	2	3	no	—
485	C₂×D₄	C₂⁴×C₁₇	1	3	yes	—
486	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
487	C₂²×C₄	—	2	3	no	—
488	C₂²×C₄	—	2	3	no	—
489	C₂²×C₄	—	2	3	no	—
490	C₂²×C₄	—	2	3	no	—
491	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
492	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
493	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
494	Q₁₆	—	4	6	no	—
495	Q₁₆	—	4	3	no	—
496	SD₁₆	—	4	3	no	—
497	SD₁₆	—	4	3	no	—
498	SD₁₆	—	4	6	no	—
499	D₈	—	4	3	no	—
500	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
501	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
502	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
503	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
504	C₄⋊C₄	—	2	3	no	—
505	C₄⋊C₄	—	2	3	no	—
506	C₄⋊C₄	—	2	3	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	3	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	6	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
517	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
518	C₄⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
519	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
520	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
521	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
522	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
523	C₂²⋊C₄	—	2	3	no	—
524	C₂²⋊C₄	—	2	1	no	—
525	C₂²⋊C₄	—	2	1	no	—
526	C₂²⋊C₄	—	2	3	no	—
527	C₂²⋊C₄	—	2	6	no	—
528	C₂²⋊C₄	—	2	3	no	—
529	C₂²⋊C₄	—	2	3	no	—
530	C₂²⋊C₄	—	2	6	no	—
531	C₂²⋊C₄	—	2	3	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₄²	—	2	1	no	—
534	C₄²	—	2	3	no	—
535	C₄²	—	2	3	no	—
536	C₄²	—	2	6	no	—
537	C₄²	—	2	3	no	—
538	C₄²	C₂×D₄×C₁₇	1	3	yes	—
539	C₄²	C₂×D₄×C₁₇	1	3	yes	—
540	C₄²	C₂⁴×C₁₇	1	3	yes	—
541	C₄²	C₂⁴×C₁₇	1	3	yes	—
542	C₂³	—	2	1	no	—
543	C₂³	—	2	3	no	—
544	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
545	Q₈	—	2	6	no	—
546	Q₈	—	2	3	no	—
547	Q₈	—	2	3	no	—
548	Q₈	—	2	3	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	4	6	no	—
551	Q₈	C₁₇×#135	1	4	yes	—
552	D₄	—	2	1	no	—
553	D₄	—	2	3	no	—
554	D₄	—	2	1	no	—
555	D₄	—	2	3	no	—
556	D₄	—	4	6	no	—
557	D₄	—	4	2	no	—
558	D₄	—	4	6	no	—
559	D₄	—	8	3	no	—
560	C₂×C₄	—	2	6	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	1	no	—
563	C₂×C₄	—	2	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	3	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	3	no	—
569	C₂×C₄	—	4	3	no	—
570	C₂×C₄	—	4	6	no	—
571	C₂×C₄	—	4	6	no	—
572	C₂×C₄	—	4	6	no	—
573	C₂×C₄	—	8	3	no	—
574	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
575	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
576	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
577	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
578	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
579	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
580	C₈	—	2	3	no	—
581	C₈	—	2	1	no	—
582	C₈	—	2	3	no	—
583	C₈	—	2	1	no	—
584	C₂²	—	2	1	no	—
585	C₂²	—	2	1	no	—
586	C₂²	—	2	1	no	—
587	C₂²	—	4	3	no	—
588	C₂²	—	4	1	no	—
589	C₂²	—	4	1	no	—
590	C₂²	—	4	3	no	—
591	C₂²	—	4	3	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
594	C₄	—	2	1	no	—
595	C₄	—	2	3	no	—
596	C₄	—	2	3	no	—
597	C₄	—	2	3	no	—
598	C₄	—	4	3	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	1	no	—
601	C₄	—	4	3	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	C₂×C₁₇×#135	1	6	yes	—
605	C₄	C₁₇×#585	1	1	yes	characteristic
606	C₄	C₁₇×#585	1	1	yes	characteristic
607	C₂	—	4	1	no	—
608	C₂	—	8	3	no	—
609	C₂	—	8	1	no	—
610	C₂	C₁₇×#3487	1	1	yes	characteristic
611	C₂	C₂²×C₁₇×#135	1	1	yes	characteristic
612	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄×Q₈×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3523	C₂	semidirect
2. C₁₇×#3480	C₂	semidirect
3. C₁₇×#3395	C₂	semidirect
4. C₁₇×#3394	C₂	semidirect
5. C₁₇×#3393	C₂	semidirect
6. C₁₇×#3392	C₂	semidirect
7. C₁₇×#3365	C₂	semidirect
8. C₁₇×#3364	C₂	semidirect
9. C₁₇×#3359	C₂	semidirect
10. C₁₇×#3358	C₂	semidirect
11. C₁₇×#3212	C₂	semidirect
12. C₁₇×#3210	C₂	semidirect
13. C₁₇×#3107	C₂	semidirect
14. C₁₇×#3102	C₂	semidirect
15. C₁₇×#2982	C₂	semidirect
235. #61887	C₁₇	direct (N × H)
278. #3523	C₂×C₁₇	semidirect
279. #3480	C₂×C₁₇	semidirect
280. #3395	C₂×C₁₇	semidirect
281. #3394	C₂×C₁₇	semidirect
282. #3393	C₂×C₁₇	semidirect
283. #3392	C₂×C₁₇	semidirect
284. #3365	C₂×C₁₇	semidirect
285. #3364	C₂×C₁₇	semidirect
286. #3359	C₂×C₁₇	semidirect
287. #3358	C₂×C₁₇	semidirect
288. #3212	C₂×C₁₇	semidirect
289. #3210	C₂×C₁₇	semidirect
290. #3107	C₂×C₁₇	semidirect
291. #3102	C₂×C₁₇	semidirect
292. #2982	C₂×C₁₇	semidirect
470. C₁₇	#61887	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×#3523	2
C₁₇×#3480	2
C₁₇×#3395	2
C₁₇×#3394	2
C₁₇×#3393	2
C₁₇×#3392	2
C₁₇×#3365	2
C₁₇×#3364	2
C₁₇×#3359	2
C₁₇×#3358	2
C₁₇×#3212	2
C₁₇×#3210	2
C₁₇×#3107	2
C₁₇×#3102	2
C₁₇×#2982	2
#61887	17

Subgroups — C17×#61887 #16919631

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61887 #16919631