Subgroups — C₁₇×#22596 #16880340

Order 4352.

704 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#2283	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#1917	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1916	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1851	C₂	1	1	yes	maximal, characteristic
7	C₁₇×#1851	C₂	1	1	yes	maximal, characteristic
8	C₁₇×#1840	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1832	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1817	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1753	C₂	1	1	yes	maximal, characteristic
13	C₁₇×#1753	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1746	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1728	C₂	1	1	yes	maximal, characteristic
16	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₈×C₁₇	C₂²	1	1	yes	characteristic
29	C₁₇×#383	C₄	1	1	yes	characteristic
30	C₁₇×#383	C₄	1	1	yes	characteristic
31	C₁₇×#382	C₄	1	1	yes	characteristic
32	C₁₇×#382	C₄	1	1	yes	characteristic
33	C₁₇×#381	C₄	1	1	yes	characteristic
34	C₁₇×#381	C₄	1	1	yes	characteristic
35	C₁₇×#380	C₄	1	1	yes	characteristic
36	C₁₇×#380	C₄	1	1	yes	characteristic
37	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#376	C₂²	1	1	yes	characteristic
42	C₁₇×#376	C₂²	1	1	yes	characteristic
43	C₁₇×#336	C₂²	1	1	yes	characteristic
44	C₁₇×#336	C₂²	1	1	yes	characteristic
45	C₁₇×#336	C₂²	1	1	yes	characteristic
46	C₁₇×#336	C₂²	1	1	yes	characteristic
47	C₁₇×#336	C₂²	1	1	yes	characteristic
48	C₁₇×#336	C₂²	1	1	yes	characteristic
49	C₁₇×#336	C₂²	1	1	yes	characteristic
50	C₁₇×#336	C₂²	1	1	yes	characteristic
51	C₁₇×#336	C₂²	1	1	yes	characteristic
52	C₁₇×#336	C₂²	1	1	yes	characteristic
53	C₁₇×#336	C₂²	1	1	yes	characteristic
54	C₁₇×#336	C₂²	1	1	yes	characteristic
55	C₁₇×#336	C₂²	1	1	yes	characteristic
56	C₁₇×#336	C₂²	1	1	yes	characteristic
57	C₁₇×#336	C₂²	1	1	yes	characteristic
58	C₁₇×#336	C₂²	1	1	yes	characteristic
59	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
60	C₂³×C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
61	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₂×M₁₆×C₁₇	—	2	2	no	—
63	C₂×M₁₆×C₁₇	—	2	2	no	—
64	C₂×M₁₆×C₁₇	—	2	2	no	—
65	C₂×M₁₆×C₁₇	—	2	2	no	—
66	C₂×M₁₆×C₁₇	—	4	1	no	—
67	C₂×M₁₆×C₁₇	—	4	1	no	—
68	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊C₄×C₁₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₁₇	—	2	2	no	—
85	C₂×C₄²×C₁₇	—	2	2	no	—
86	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
94	C₁₇×C₄⋊C₈	—	2	2	no	—
95	C₁₇×C₄⋊C₈	—	2	2	no	—
96	C₁₇×C₄⋊C₈	—	4	1	no	—
97	C₁₇×C₄⋊C₈	—	4	1	no	—
98	C₁₇×C₂²⋊C₈	—	2	2	no	—
99	C₁₇×C₂²⋊C₈	—	2	2	no	—
100	C₁₇×#97	—	2	2	no	—
101	C₁₇×#97	—	4	1	no	—
102	C₄×C₈×C₁₇	—	2	2	no	—
103	C₄×C₈×C₁₇	—	4	1	no	—
104	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
106	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
107	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
108	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
109	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
110	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
111	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
112	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
113	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
114	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
115	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
116	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
117	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
118	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
119	C₁₇×#95	C₂×C₄	1	1	yes	characteristic
120	C₂⁴×C₁₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₁₇	—	2	1	no	—
122	C₂²×C₄×C₁₇	—	2	1	no	—
123	C₂²×C₄×C₁₇	—	2	1	no	—
124	C₂²×C₄×C₁₇	—	2	1	no	—
125	C₂²×C₄×C₁₇	—	2	2	no	—
126	C₂²×C₄×C₁₇	—	2	2	no	—
127	C₂²×C₄×C₁₇	—	2	2	no	—
128	C₂²×C₄×C₁₇	—	4	1	no	—
129	C₂²×C₄×C₁₇	—	4	1	no	—
130	C₂²×C₄×C₁₇	—	4	1	no	—
131	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₁₇	#41	1	2	yes	—
145	C₂²×C₄×C₁₇	#41	1	2	yes	—
146	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
147	M₁₆×C₁₇	—	4	4	no	—
148	M₁₆×C₁₇	—	4	4	no	—
149	C₂×C₈×C₁₇	—	2	1	no	—
150	C₂×C₈×C₁₇	—	2	1	no	—
151	C₂×C₈×C₁₇	—	2	1	no	—
152	C₂×C₈×C₁₇	—	2	1	no	—
153	C₂×C₈×C₁₇	—	2	1	no	—
154	C₂×C₈×C₁₇	—	2	1	no	—
155	C₂×C₈×C₁₇	—	2	1	no	—
156	C₂×C₈×C₁₇	—	2	1	no	—
157	C₂×C₈×C₁₇	—	2	1	no	—
158	C₂×C₈×C₁₇	—	2	1	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₂×C₈×C₁₇	—	2	1	no	—
163	C₂×C₈×C₁₇	—	2	1	no	—
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	2	1	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	#41	1	2	yes	—
172	C₂×C₈×C₁₇	#41	1	2	yes	—
173	C₄⋊C₄×C₁₇	—	2	2	no	—
174	C₄⋊C₄×C₁₇	—	2	2	no	—
175	C₄⋊C₄×C₁₇	—	4	1	no	—
176	C₄⋊C₄×C₁₇	—	4	1	no	—
177	C₂²⋊C₄×C₁₇	—	4	1	no	—
178	C₂²⋊C₄×C₁₇	—	4	1	no	—
179	C₂²⋊C₄×C₁₇	—	4	1	no	—
180	C₂²⋊C₄×C₁₇	—	4	1	no	—
181	C₄²×C₁₇	—	2	2	no	—
182	C₄²×C₁₇	—	2	2	no	—
183	C₄²×C₁₇	—	2	1	no	—
184	C₄²×C₁₇	—	2	1	no	—
185	C₄²×C₁₇	—	2	1	no	—
186	C₄²×C₁₇	—	2	1	no	—
187	C₄²×C₁₇	—	2	1	no	—
188	C₄²×C₁₇	—	2	1	no	—
189	C₄²×C₁₇	—	2	1	no	—
190	C₄²×C₁₇	—	2	1	no	—
191	C₄²×C₁₇	—	2	1	no	—
192	C₄²×C₁₇	—	2	1	no	—
193	C₄²×C₁₇	—	2	1	no	—
194	C₄²×C₁₇	—	2	1	no	—
195	#22596	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
196	C₂³×C₁₇	—	2	1	no	—
197	C₂³×C₁₇	—	2	1	no	—
198	C₂³×C₁₇	—	2	1	no	—
199	C₂³×C₁₇	—	2	1	no	—
200	C₂³×C₁₇	—	2	1	no	—
201	C₂³×C₁₇	—	2	1	no	—
202	C₂³×C₁₇	#117	1	2	yes	—
203	C₂³×C₁₇	C₂³×C₄	1	1	yes	characteristic
204	C₂×C₄×C₁₇	—	2	1	no	—
205	C₂×C₄×C₁₇	—	2	1	no	—
206	C₂×C₄×C₁₇	—	2	1	no	—
207	C₂×C₄×C₁₇	—	2	1	no	—
208	C₂×C₄×C₁₇	—	2	2	no	—
209	C₂×C₄×C₁₇	—	2	2	no	—
210	C₂×C₄×C₁₇	—	2	2	no	—
211	C₂×C₄×C₁₇	—	2	2	no	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	1	no	—
214	C₂×C₄×C₁₇	—	2	1	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	2	1	no	—
226	C₂×C₄×C₁₇	—	2	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	—	2	1	no	—
238	C₂×C₄×C₁₇	—	2	1	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	1	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	4	4	no	—
246	C₂×C₄×C₁₇	—	4	4	no	—
247	C₂×C₄×C₁₇	#117	1	2	yes	—
248	C₂×C₄×C₁₇	#131	1	2	yes	—
249	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
250	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
255	C₈×C₁₇	—	2	2	no	—
256	C₈×C₁₇	—	2	2	no	—
257	C₈×C₁₇	—	4	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	#2283	C₂×C₁₇	1	1	yes	characteristic
264	#1917	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1917	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#1916	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#1916	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#1851	C₂×C₁₇	1	1	yes	characteristic
269	#1851	C₂×C₁₇	1	1	yes	characteristic
270	#1840	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1832	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1817	C₂×C₁₇	1	1	yes	characteristic
273	#1768	C₂×C₁₇	1	1	yes	characteristic, complemented
274	#1753	C₂×C₁₇	1	1	yes	characteristic
275	#1753	C₂×C₁₇	1	1	yes	characteristic
276	#1746	C₂×C₁₇	1	1	yes	characteristic, complemented
277	#1728	C₂×C₁₇	1	1	yes	characteristic
278	C₂²×C₁₇	—	2	2	no	—
279	C₂²×C₁₇	—	2	2	no	—
280	C₂²×C₁₇	—	2	2	no	—
281	C₂²×C₁₇	—	4	1	no	—
282	C₂²×C₁₇	—	4	1	no	—
283	C₂²×C₁₇	—	4	1	no	—
284	C₂²×C₁₇	—	4	1	no	—
285	C₂²×C₁₇	C₂×#117	1	1	yes	characteristic
286	C₂²×C₁₇	C₄×#41	1	1	yes	characteristic
287	C₂²×C₁₇	#520	1	1	yes	characteristic
288	C₂²×C₁₇	C₂×#131	1	1	yes	characteristic
289	C₂²×C₁₇	#568	1	1	yes	characteristic
290	C₂²×C₁₇	#568	1	1	yes	characteristic
291	C₂²×C₁₇	#568	1	1	yes	characteristic
292	C₄×C₁₇	—	2	2	no	—
293	C₄×C₁₇	—	2	2	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	—	4	1	no	—
300	C₄×C₁₇	—	4	1	no	—
301	C₄×C₁₇	—	4	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	1	no	—
304	C₄×C₁₇	—	4	1	no	—
305	C₄×C₁₇	#551	1	1	yes	characteristic
306	C₄×C₁₇	#551	1	1	yes	characteristic
307	C₄×C₁₇	#552	1	1	yes	characteristic
308	C₄×C₁₇	#552	1	1	yes	characteristic
309	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
310	C₂²×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
311	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
312	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
313	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
314	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
315	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
317	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
318	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
319	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
320	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
321	C₂×C₄×C₈	C₂²×C₁₇	1	1	yes	characteristic
322	#383	C₄×C₁₇	1	1	yes	characteristic
323	#383	C₄×C₁₇	1	1	yes	characteristic
324	#382	C₄×C₁₇	1	1	yes	characteristic
325	#382	C₄×C₁₇	1	1	yes	characteristic
326	#381	C₄×C₁₇	1	1	yes	characteristic
327	#381	C₄×C₁₇	1	1	yes	characteristic
328	#380	C₄×C₁₇	1	1	yes	characteristic
329	#380	C₄×C₁₇	1	1	yes	characteristic
330	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
331	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
332	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
333	C₄×C₂²⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
334	#376	C₂²×C₁₇	1	1	yes	characteristic
335	#376	C₂²×C₁₇	1	1	yes	characteristic
336	#336	C₂²×C₁₇	1	1	yes	characteristic
337	#336	C₂²×C₁₇	1	1	yes	characteristic
338	#336	C₂²×C₁₇	1	1	yes	characteristic
339	#336	C₂²×C₁₇	1	1	yes	characteristic
340	#336	C₂²×C₁₇	1	1	yes	characteristic
341	#336	C₂²×C₁₇	1	1	yes	characteristic
342	#336	C₂²×C₁₇	1	1	yes	characteristic
343	#336	C₂²×C₁₇	1	1	yes	characteristic
344	#336	C₂²×C₁₇	1	1	yes	characteristic
345	#336	C₂²×C₁₇	1	1	yes	characteristic
346	#336	C₂²×C₁₇	1	1	yes	characteristic
347	#336	C₂²×C₁₇	1	1	yes	characteristic
348	#336	C₂²×C₁₇	1	1	yes	characteristic
349	#336	C₂²×C₁₇	1	1	yes	characteristic
350	#336	C₂²×C₁₇	1	1	yes	characteristic
351	#336	C₂²×C₁₇	1	1	yes	characteristic
352	C₂×C₁₇	—	4	2	no	—
353	C₂×C₁₇	#2343	1	1	yes	characteristic
354	C₂×C₁₇	#2921	1	1	yes	characteristic
355	C₂×C₁₇	#2924	1	1	yes	characteristic
356	C₂×C₁₇	#2967	1	1	yes	characteristic
357	C₂×C₁₇	#2969	1	1	yes	characteristic
358	C₂×C₁₇	#2993	1	1	yes	characteristic
359	C₂×C₁₇	#2995	1	1	yes	characteristic
360	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
361	C₂³×C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
363	C₂×M₁₆	—	2	2	no	—
364	C₂×M₁₆	—	2	2	no	—
365	C₂×M₁₆	—	2	2	no	—
366	C₂×M₁₆	—	2	2	no	—
367	C₂×M₁₆	—	4	1	no	—
368	C₂×M₁₆	—	4	1	no	—
369	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
370	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
371	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
372	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
373	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
374	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
375	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
376	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
377	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
378	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
379	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
380	C₂×C₄⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
381	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
384	C₂×C₂²⋊C₄	C₂×C₄×C₁₇	1	1	yes	characteristic
385	C₂×C₄²	—	2	2	no	—
386	C₂×C₄²	—	2	2	no	—
387	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
388	C₂×C₄²	C₂×C₄×C₁₇	1	1	yes	characteristic
389	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
390	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
391	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
392	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
395	C₄⋊C₈	—	2	2	no	—
396	C₄⋊C₈	—	2	2	no	—
397	C₄⋊C₈	—	4	1	no	—
398	C₄⋊C₈	—	4	1	no	—
399	C₂²⋊C₈	—	2	2	no	—
400	C₂²⋊C₈	—	2	2	no	—
401	#97	—	2	2	no	—
402	#97	—	4	1	no	—
403	C₄×C₈	—	2	2	no	—
404	C₄×C₈	—	4	1	no	—
405	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
406	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
407	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
408	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
409	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
410	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
411	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
412	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
413	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
414	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
415	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
416	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
417	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
418	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
419	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
420	#95	C₂×C₄×C₁₇	1	1	yes	characteristic
421	C₁₇	#22596	1	1	yes	characteristic, direct product factor, Sylow
422	C₂⁴	C₂²×C₄×C₁₇	1	1	yes	characteristic
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	4	1	no	—
431	C₂²×C₄	—	4	1	no	—
432	C₂²×C₄	—	4	1	no	—
433	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
436	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
437	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
438	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
440	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
441	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²×C₄×C₁₇	1	1	yes	characteristic
446	C₂²×C₄	#41×C₁₇	1	2	yes	—
447	C₂²×C₄	#41×C₁₇	1	2	yes	—
448	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
449	M₁₆	—	4	4	no	—
450	M₁₆	—	4	4	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	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	—	2	1	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	#41×C₁₇	1	2	yes	—
474	C₂×C₈	#41×C₁₇	1	2	yes	—
475	C₄⋊C₄	—	2	2	no	—
476	C₄⋊C₄	—	2	2	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₂²⋊C₄	—	4	1	no	—
482	C₂²⋊C₄	—	4	1	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	2	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	2	no	—
496	C₄²	—	2	2	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	2	1	no	—
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	C₁₇×#117	1	2	yes	—
504	C₂³	C₂³×C₄×C₁₇	1	1	yes	characteristic
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	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	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	1	no	—
538	C₂×C₄	—	2	1	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	4	4	no	—
547	C₂×C₄	—	4	4	no	—
548	C₂×C₄	C₁₇×#117	1	2	yes	—
549	C₂×C₄	C₁₇×#131	1	2	yes	—
550	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
551	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
552	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
553	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
554	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
555	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	4	1	no	—
561	C₈	—	4	1	no	—
562	C₈	—	4	1	no	—
563	C₈	—	4	1	no	—
564	C₂²	—	2	2	no	—
565	C₂²	—	2	2	no	—
566	C₂²	—	2	2	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	4	1	no	—
571	C₂²	C₂×C₁₇×#117	1	1	yes	characteristic
572	C₂²	C₄×#41×C₁₇	1	1	yes	characteristic
573	C₂²	C₁₇×#520	1	1	yes	characteristic
574	C₂²	C₂×C₁₇×#131	1	1	yes	characteristic
575	C₂²	C₁₇×#568	1	1	yes	characteristic
576	C₂²	C₁₇×#568	1	1	yes	characteristic
577	C₂²	C₁₇×#568	1	1	yes	characteristic
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	4	1	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	4	1	no	—
587	C₄	—	4	1	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	1	no	—
590	C₄	—	4	1	no	—
591	C₄	C₁₇×#551	1	1	yes	characteristic
592	C₄	C₁₇×#551	1	1	yes	characteristic
593	C₄	C₁₇×#552	1	1	yes	characteristic
594	C₄	C₁₇×#552	1	1	yes	characteristic
595	C₂	—	4	2	no	—
596	C₂	C₁₇×#2343	1	1	yes	characteristic
597	C₂	C₁₇×#2921	1	1	yes	characteristic
598	C₂	C₁₇×#2924	1	1	yes	characteristic
599	C₂	C₁₇×#2967	1	1	yes	characteristic
600	C₂	C₁₇×#2969	1	1	yes	characteristic
601	C₂	C₁₇×#2993	1	1	yes	characteristic
602	C₂	C₁₇×#2995	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
socle	C₂³×C₁₇	C₂³×C₄
prime radical	C₂⁴×C₁₇	C₂²×C₄
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#1917	C₂	semidirect
3. C₁₇×#1917	C₂	semidirect
4. C₁₇×#1916	C₂	semidirect
5. C₁₇×#1916	C₂	semidirect
8. C₁₇×#1840	C₂	semidirect
9. C₁₇×#1832	C₂	semidirect
11. C₁₇×#1768	C₂	semidirect
14. C₁₇×#1746	C₂	semidirect
195. #22596	C₁₇	direct (N × H)
264. #1917	C₂×C₁₇	semidirect
265. #1917	C₂×C₁₇	semidirect
266. #1916	C₂×C₁₇	semidirect
267. #1916	C₂×C₁₇	semidirect
270. #1840	C₂×C₁₇	semidirect
271. #1832	C₂×C₁₇	semidirect
273. #1768	C₂×C₁₇	semidirect
276. #1746	C₂×C₁₇	semidirect
421. C₁₇	#22596	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×#2283	2
C₁₇×#1917	2
C₁₇×#1916	2
C₁₇×#1851	2
C₁₇×#1840	2
C₁₇×#1832	2
C₁₇×#1817	2
C₁₇×#1768	2
C₁₇×#1753	2
C₁₇×#1746	2
C₁₇×#1728	2
#22596	17

Subgroups — C17×#22596 #16880340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22596 #16880340