Subgroups — C₁₇×#18030 #16875774

Order 4352.

606 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3103	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#2984	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#2979	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#1592	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1590	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1588	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1585	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1583	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1582	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1496	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1454	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#481	C₄	1	1	yes	characteristic
19	C₁₇×#481	C₄	1	1	yes	characteristic
20	C₁₇×#475	C₄	1	1	yes	characteristic
21	C₁₇×#475	C₄	1	1	yes	characteristic
22	C₁₇×#460	C₄	1	1	yes	characteristic
23	C₁₇×#460	C₄	1	1	yes	characteristic
24	C₁₇×#448	C₄	1	1	yes	characteristic
25	C₁₇×#448	C₄	1	1	yes	characteristic
26	C₁₇×#446	—	2	1	no	—
27	C₁₇×#446	—	2	1	no	—
28	C₁₇×#446	C₂²	1	1	yes	characteristic
29	C₁₇×#446	C₂²	1	1	yes	characteristic
30	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
31	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
32	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
33	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
34	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
35	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
36	C₁₇×#436	—	2	1	no	—
37	C₁₇×#436	C₂²	1	1	yes	characteristic
38	C₁₇×#436	C₂²	1	1	yes	characteristic
39	C₈×D₄×C₁₇	—	2	1	no	—
40	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#432	—	2	1	no	—
43	C₁₇×#432	C₂²	1	1	yes	characteristic
44	C₁₇×#431	—	2	1	no	—
45	C₁₇×#431	C₂²	1	1	yes	characteristic
46	C₁₇×#431	C₂²	1	1	yes	characteristic
47	C₁₇×#431	C₂²	1	1	yes	characteristic
48	C₁₇×#431	C₂²	1	1	yes	characteristic
49	C₁₇×#408	—	2	1	no	—
50	C₁₇×#408	—	2	1	no	—
51	C₁₇×#335	C₂²	1	1	yes	characteristic
52	C₁₇×#335	C₂²	1	1	yes	characteristic
53	C₁₇×#334	C₂²	1	1	yes	characteristic
54	C₁₇×#334	C₂²	1	1	yes	characteristic
55	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
56	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
57	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
58	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
59	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
60	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
61	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
62	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₇×#322	C₂²	1	1	yes	characteristic
64	C₁₇×#322	C₂²	1	1	yes	characteristic
65	C₁₇×#322	C₂²	1	1	yes	characteristic
66	C₈²×C₁₇	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	—	2	1	no	—
68	C₂²×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
71	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₂×M₁₆×C₁₇	—	2	1	no	—
74	C₂×M₁₆×C₁₇	—	2	1	no	—
75	C₂²×C₈×C₁₇	—	2	1	no	—
76	C₂²×C₈×C₁₇	—	2	1	no	—
77	C₁₇×C₄⋊Q₈	C₂×C₄	1	1	yes	characteristic
78	C₁₇×#127	C₂×C₄	1	1	yes	characteristic
79	C₁₇×#124	—	2	1	no	—
80	C₁₇×#121	—	2	1	no	—
81	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
82	C₁₇×#121	C₂×C₄	1	1	yes	characteristic
83	C₄×Q₈×C₁₇	—	2	1	no	—
84	C₄×Q₈×C₁₇	—	2	1	no	—
85	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
87	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
88	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
89	C₄×D₄×C₁₇	—	2	1	no	—
90	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
91	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄²×C₁₇	—	2	1	no	—
95	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
96	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
97	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
98	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
99	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	—	2	1	no	—
102	C₁₇×C₄⋊C₈	—	2	1	no	—
103	C₁₇×C₄⋊C₈	—	2	1	no	—
104	C₁₇×C₄⋊C₈	—	2	1	no	—
105	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
107	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
108	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
109	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
110	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
111	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
112	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
113	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
114	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
115	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
116	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
117	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
118	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
119	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
120	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
121	C₁₇×C₂²⋊C₈	—	2	1	no	—
122	C₁₇×C₂²⋊C₈	—	2	1	no	—
123	C₁₇×C₂²⋊C₈	—	2	1	no	—
124	C₁₇×C₂²⋊C₈	—	2	1	no	—
125	C₁₇×C₂²⋊C₈	—	2	1	no	—
126	C₁₇×C₂²⋊C₈	—	2	1	no	—
127	C₁₇×C₂²⋊C₈	—	2	1	no	—
128	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
129	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
130	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
131	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
132	C₁₇×#97	—	2	1	no	—
133	C₁₇×#97	—	2	1	no	—
134	C₁₇×#97	—	2	1	no	—
135	C₄×C₈×C₁₇	—	2	1	no	—
136	C₄×C₈×C₁₇	—	2	1	no	—
137	C₄×C₈×C₁₇	—	2	1	no	—
138	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
139	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
140	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
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	#41×C₁₇	—	8	1	no	—
145	#41×C₁₇	—	8	1	no	—
146	C₂×Q₈×C₁₇	—	2	1	no	—
147	C₂×Q₈×C₁₇	—	2	1	no	—
148	C₂×Q₈×C₁₇	—	2	2	no	—
149	C₂×Q₈×C₁₇	—	4	1	no	—
150	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×D₄×C₁₇	—	2	1	no	—
153	C₂×D₄×C₁₇	—	2	1	no	—
154	C₂×D₄×C₁₇	—	2	1	no	—
155	C₂×D₄×C₁₇	—	2	1	no	—
156	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	2	1	no	—
160	C₂²×C₄×C₁₇	—	2	1	no	—
161	C₂²×C₄×C₁₇	—	2	1	no	—
162	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
165	SD₁₆×C₁₇	—	2	2	no	—
166	SD₁₆×C₁₇	—	2	2	no	—
167	SD₁₆×C₁₇	—	4	1	no	—
168	SD₁₆×C₁₇	—	4	1	no	—
169	M₁₆×C₁₇	—	8	1	no	—
170	M₁₆×C₁₇	—	8	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	2	1	no	—
173	C₂×C₈×C₁₇	—	2	1	no	—
174	C₂×C₈×C₁₇	—	2	1	no	—
175	C₂×C₈×C₁₇	—	2	1	no	—
176	C₂×C₈×C₁₇	—	2	1	no	—
177	C₂×C₈×C₁₇	—	8	1	no	—
178	C₂×C₈×C₁₇	—	8	1	no	—
179	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
184	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
185	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
186	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
187	C₄⋊C₄×C₁₇	—	2	1	no	—
188	C₄⋊C₄×C₁₇	—	2	1	no	—
189	C₄⋊C₄×C₁₇	—	2	1	no	—
190	C₄⋊C₄×C₁₇	—	2	1	no	—
191	C₄⋊C₄×C₁₇	—	2	1	no	—
192	C₄⋊C₄×C₁₇	—	2	1	no	—
193	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
196	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
197	C₂²⋊C₄×C₁₇	—	2	1	no	—
198	C₂²⋊C₄×C₁₇	—	2	1	no	—
199	C₂²⋊C₄×C₁₇	—	2	1	no	—
200	C₂²⋊C₄×C₁₇	—	2	1	no	—
201	C₄²×C₁₇	—	2	1	no	—
202	C₄²×C₁₇	—	2	1	no	—
203	C₄²×C₁₇	—	2	1	no	—
204	C₄²×C₁₇	—	2	1	no	—
205	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
206	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₇	#41	1	1	yes	characteristic
208	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
209	#18030	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂³×C₁₇	—	2	1	no	—
211	C₂³×C₁₇	—	2	1	no	—
212	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
213	Q₈×C₁₇	—	2	1	no	—
214	Q₈×C₁₇	—	2	1	no	—
215	Q₈×C₁₇	—	2	1	no	—
216	Q₈×C₁₇	—	4	2	no	—
217	Q₈×C₁₇	—	8	1	no	—
218	Q₈×C₁₇	#131	1	2	yes	—
219	D₄×C₁₇	—	2	1	no	—
220	D₄×C₁₇	—	2	1	no	—
221	D₄×C₁₇	—	2	1	no	—
222	D₄×C₁₇	—	2	1	no	—
223	D₄×C₁₇	—	4	2	no	—
224	D₄×C₁₇	—	8	1	no	—
225	D₄×C₁₇	—	8	1	no	—
226	D₄×C₁₇	—	8	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	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	4	1	no	—
238	C₂×C₄×C₁₇	—	4	2	no	—
239	C₂×C₄×C₁₇	—	4	2	no	—
240	C₂×C₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	4	1	no	—
242	C₂×C₄×C₁₇	—	4	1	no	—
243	C₂×C₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	2	1	no	—
254	C₈×C₁₇	—	2	1	no	—
255	C₈×C₁₇	—	2	1	no	—
256	C₈×C₁₇	—	2	1	no	—
257	C₈×C₁₇	—	2	1	no	—
258	C₈×C₁₇	—	4	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	C₈×C₁₇	—	4	1	no	—
262	C₈×C₁₇	—	4	1	no	—
263	C₈×C₁₇	—	4	1	no	—
264	#3103	C₂×C₁₇	1	1	yes	characteristic
265	#2984	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#2979	C₂×C₁₇	1	1	yes	characteristic
267	#1592	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#1590	C₂×C₁₇	1	1	yes	characteristic, complemented
269	#1588	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1585	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1583	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1582	C₂×C₁₇	1	1	yes	characteristic, complemented
273	SD₁₆⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₈×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
275	#1572	C₂×C₁₇	1	1	yes	characteristic, complemented
276	#1496	C₂×C₁₇	1	1	yes	characteristic
277	#1479	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1454	C₂×C₁₇	1	1	yes	characteristic, complemented
279	C₂²×C₁₇	—	2	1	no	—
280	C₂²×C₁₇	—	2	1	no	—
281	C₂²×C₁₇	—	2	1	no	—
282	C₂²×C₁₇	—	4	1	no	—
283	C₂²×C₁₇	—	4	1	no	—
284	C₂²×C₁₇	—	4	1	no	—
285	C₂²×C₁₇	—	4	1	no	—
286	C₂²×C₁₇	—	4	1	no	—
287	C₂²×C₁₇	—	4	1	no	—
288	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
289	C₄×C₁₇	—	2	1	no	—
290	C₄×C₁₇	—	2	2	no	—
291	C₄×C₁₇	—	2	1	no	—
292	C₄×C₁₇	—	2	1	no	—
293	C₄×C₁₇	—	2	1	no	—
294	C₄×C₁₇	—	4	1	no	—
295	C₄×C₁₇	—	4	1	no	—
296	C₄×C₁₇	—	4	1	no	—
297	C₄×C₁₇	—	4	1	no	—
298	C₄×C₁₇	—	4	1	no	—
299	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
300	C₄×C₁₇	#568	1	1	yes	characteristic
301	C₄×C₁₇	#577	1	1	yes	characteristic
302	C₄×C₁₇	#577	1	1	yes	characteristic
303	#532	C₂²×C₁₇	1	1	yes	characteristic
304	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
305	#481	C₄×C₁₇	1	1	yes	characteristic
306	#481	C₄×C₁₇	1	1	yes	characteristic
307	#475	C₄×C₁₇	1	1	yes	characteristic
308	#475	C₄×C₁₇	1	1	yes	characteristic
309	#460	C₄×C₁₇	1	1	yes	characteristic
310	#460	C₄×C₁₇	1	1	yes	characteristic
311	#448	C₄×C₁₇	1	1	yes	characteristic
312	#448	C₄×C₁₇	1	1	yes	characteristic
313	#446	—	2	1	no	—
314	#446	—	2	1	no	—
315	#446	C₂²×C₁₇	1	1	yes	characteristic
316	#446	C₂²×C₁₇	1	1	yes	characteristic
317	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
318	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
319	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
320	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
321	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
322	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
323	#436	—	2	1	no	—
324	#436	C₂²×C₁₇	1	1	yes	characteristic
325	#436	C₂²×C₁₇	1	1	yes	characteristic
326	C₈×D₄	—	2	1	no	—
327	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
328	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
329	#432	—	2	1	no	—
330	#432	C₂²×C₁₇	1	1	yes	characteristic
331	#431	—	2	1	no	—
332	#431	C₂²×C₁₇	1	1	yes	characteristic
333	#431	C₂²×C₁₇	1	1	yes	characteristic
334	#431	C₂²×C₁₇	1	1	yes	characteristic
335	#431	C₂²×C₁₇	1	1	yes	characteristic
336	#408	—	2	1	no	—
337	#408	—	2	1	no	—
338	#335	C₂²×C₁₇	1	1	yes	characteristic
339	#335	C₂²×C₁₇	1	1	yes	characteristic
340	#334	C₂²×C₁₇	1	1	yes	characteristic
341	#334	C₂²×C₁₇	1	1	yes	characteristic
342	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
343	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
345	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
346	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
347	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
348	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
349	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
350	#322	C₂²×C₁₇	1	1	yes	characteristic
351	#322	C₂²×C₁₇	1	1	yes	characteristic
352	#322	C₂²×C₁₇	1	1	yes	characteristic
353	C₈²	C₂²×C₁₇	1	1	yes	characteristic
354	C₂×C₁₇	—	4	1	no	—
355	C₂×C₁₇	—	8	1	no	—
356	C₂×C₁₇	—	8	1	no	—
357	C₂×C₁₇	#2933	1	1	yes	characteristic
358	C₂×C₁₇	#2949	1	1	yes	characteristic
359	C₂×C₁₇	#2955	1	1	yes	characteristic
360	C₂×#41	—	2	1	no	—
361	C₂²×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
362	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
363	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
364	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
365	C₂×SD₁₆	C₂×C₄×C₁₇	1	1	yes	characteristic
366	C₂×M₁₆	—	2	1	no	—
367	C₂×M₁₆	—	2	1	no	—
368	C₂²×C₈	—	2	1	no	—
369	C₂²×C₈	—	2	1	no	—
370	C₄⋊Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
371	#127	C₂×C₄×C₁₇	1	1	yes	characteristic
372	#124	—	2	1	no	—
373	#121	—	2	1	no	—
374	#121	C₂×C₄×C₁₇	1	1	yes	characteristic
375	#121	C₂×C₄×C₁₇	1	1	yes	characteristic
376	C₄×Q₈	—	2	1	no	—
377	C₄×Q₈	—	2	1	no	—
378	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
379	C₄×Q₈	C₂×C₄×C₁₇	1	1	yes	characteristic
380	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
381	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
384	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
387	C₂×C₄²	—	2	1	no	—
388	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
389	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
390	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
391	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
392	#106	C₂×C₄×C₁₇	1	1	yes	characteristic
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
399	C₄⋊C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
400	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
401	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
406	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
407	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
408	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
409	#103	C₂×C₄×C₁₇	1	1	yes	characteristic
410	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
411	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
412	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
413	#102	C₂×C₄×C₁₇	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	2	1	no	—
416	C₂²⋊C₈	—	2	1	no	—
417	C₂²⋊C₈	—	2	1	no	—
418	C₂²⋊C₈	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
422	C₂²⋊C₈	C₂×C₄×C₁₇	1	1	yes	characteristic
423	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
424	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
425	#97	—	2	1	no	—
426	#97	—	2	1	no	—
427	#97	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	—	2	1	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
433	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
434	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
435	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
436	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
437	C₁₇	#18030	1	1	yes	characteristic, direct product factor, Sylow
438	#41	—	8	1	no	—
439	#41	—	8	1	no	—
440	C₂×Q₈	—	2	1	no	—
441	C₂×Q₈	—	2	1	no	—
442	C₂×Q₈	—	2	2	no	—
443	C₂×Q₈	—	4	1	no	—
444	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
445	C₂×Q₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
446	C₂×D₄	—	2	1	no	—
447	C₂×D₄	—	2	1	no	—
448	C₂×D₄	—	2	1	no	—
449	C₂×D₄	—	2	1	no	—
450	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
451	C₂×D₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
452	C₂²×C₄	—	2	1	no	—
453	C₂²×C₄	—	2	1	no	—
454	C₂²×C₄	—	2	1	no	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
458	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
459	SD₁₆	—	2	2	no	—
460	SD₁₆	—	2	2	no	—
461	SD₁₆	—	4	1	no	—
462	SD₁₆	—	4	1	no	—
463	M₁₆	—	8	1	no	—
464	M₁₆	—	8	1	no	—
465	C₂×C₈	—	2	1	no	—
466	C₂×C₈	—	2	1	no	—
467	C₂×C₈	—	2	1	no	—
468	C₂×C₈	—	2	1	no	—
469	C₂×C₈	—	2	1	no	—
470	C₂×C₈	—	2	1	no	—
471	C₂×C₈	—	8	1	no	—
472	C₂×C₈	—	8	1	no	—
473	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
474	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
475	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
476	C₂×C₈	C₂²×C₄×C₁₇	1	1	yes	characteristic
477	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
478	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
479	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
480	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	—	2	1	no	—
487	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
488	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
490	C₄⋊C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
491	C₂²⋊C₄	—	2	1	no	—
492	C₂²⋊C₄	—	2	1	no	—
493	C₂²⋊C₄	—	2	1	no	—
494	C₂²⋊C₄	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	—	2	1	no	—
497	C₄²	—	2	1	no	—
498	C₄²	—	2	1	no	—
499	C₄²	C₂²×C₄×C₁₇	1	1	yes	characteristic
500	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
501	C₄²	#41×C₁₇	1	1	yes	characteristic
502	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
503	C₂³	—	2	1	no	—
504	C₂³	—	2	1	no	—
505	C₂³	C₄×D₄×C₁₇	1	1	yes	characteristic
506	Q₈	—	2	1	no	—
507	Q₈	—	2	1	no	—
508	Q₈	—	2	1	no	—
509	Q₈	—	4	2	no	—
510	Q₈	—	8	1	no	—
511	Q₈	C₁₇×#131	1	2	yes	—
512	D₄	—	2	1	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	8	1	no	—
518	D₄	—	8	1	no	—
519	D₄	—	8	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
538	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
539	C₂×C₄	C₄×D₄×C₁₇	1	1	yes	characteristic
540	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
541	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
542	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
543	C₈	—	2	1	no	—
544	C₈	—	2	1	no	—
545	C₈	—	2	1	no	—
546	C₈	—	2	1	no	—
547	C₈	—	2	1	no	—
548	C₈	—	2	1	no	—
549	C₈	—	2	1	no	—
550	C₈	—	2	1	no	—
551	C₈	—	4	1	no	—
552	C₈	—	4	1	no	—
553	C₈	—	4	1	no	—
554	C₈	—	4	1	no	—
555	C₈	—	4	1	no	—
556	C₈	—	4	1	no	—
557	C₂²	—	2	1	no	—
558	C₂²	—	2	1	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	4	1	no	—
561	C₂²	—	4	1	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
567	C₄	—	2	1	no	—
568	C₄	—	2	1	no	—
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	2	no	—
572	C₄	—	4	1	no	—
573	C₄	—	4	1	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	1	no	—
576	C₄	—	4	1	no	—
577	C₄	C₂×C₁₇×#131	1	1	yes	characteristic
578	C₄	C₁₇×#568	1	1	yes	characteristic
579	C₄	C₁₇×#577	1	1	yes	characteristic
580	C₄	C₁₇×#577	1	1	yes	characteristic
581	C₂	—	4	1	no	—
582	C₂	—	8	1	no	—
583	C₂	—	8	1	no	—
584	C₂	C₁₇×#2933	1	1	yes	characteristic
585	C₂	C₁₇×#2949	1	1	yes	characteristic
586	C₂	C₁₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₄²	C₂⁴×C₁₇
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₁₇ ◁ C₁₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#2984	C₂	semidirect
4. C₁₇×#1592	C₂	semidirect
5. C₁₇×#1590	C₂	semidirect
6. C₁₇×#1588	C₂	semidirect
7. C₁₇×#1585	C₂	semidirect
8. C₁₇×#1583	C₂	semidirect
9. C₁₇×#1582	C₂	semidirect
10. C₁₇×SD₁₆⋊C₈	C₂	semidirect
11. C₈×SD₁₆×C₁₇	C₂	semidirect
12. C₁₇×#1572	C₂	semidirect
14. C₁₇×#1479	C₂	semidirect
15. C₁₇×#1454	C₂	semidirect
209. #18030	C₁₇	direct (N × H)
265. #2984	C₂×C₁₇	semidirect
267. #1592	C₂×C₁₇	semidirect
268. #1590	C₂×C₁₇	semidirect
269. #1588	C₂×C₁₇	semidirect
270. #1585	C₂×C₁₇	semidirect
271. #1583	C₂×C₁₇	semidirect
272. #1582	C₂×C₁₇	semidirect
273. SD₁₆⋊C₈	C₂×C₁₇	semidirect
274. C₈×SD₁₆	C₂×C₁₇	semidirect
275. #1572	C₂×C₁₇	semidirect
277. #1479	C₂×C₁₇	semidirect
278. #1454	C₂×C₁₇	semidirect
437. C₁₇	#18030	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×#3103	2
C₁₇×#2984	2
C₁₇×#2979	2
C₁₇×#1592	2
C₁₇×#1590	2
C₁₇×#1588	2
C₁₇×#1585	2
C₁₇×#1583	2
C₁₇×#1582	2
C₁₇×SD₁₆⋊C₈	2
C₈×SD₁₆×C₁₇	2
C₁₇×#1572	2
C₁₇×#1496	2
C₁₇×#1479	2
C₁₇×#1454	2
#18030	17

Subgroups — C17×#18030 #16875774

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18030 #16875774