Subgroups — C₁₇×#22086 #16879830

Order 4352.

896 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₁₇×#482	C₂	1	1	yes	maximal, characteristic
2	C₄×C₁₇×#121	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2296	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1936	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1920	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1918	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1875	C₂	1	1	yes	maximal, characteristic
11	C₁₇×#1864	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1862	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1854	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1825	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₁₇×#121	C₂²	1	1	yes	characteristic
17	C₂×C₄×D₄×C₁₇	—	2	1	no	—
18	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
20	C₂×C₁₇×#117	C₂²	1	1	yes	characteristic
21	C₂²×C₄²×C₁₇	C₂²	1	1	yes	characteristic
22	C₁₇×#482	C₄	1	8	yes	complemented
23	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×C₂²⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
35	C₁₇×#390	C₂²	1	1	yes	characteristic
36	C₁₇×#389	C₂²	1	1	yes	characteristic
37	C₁₇×#389	C₂²	1	1	yes	characteristic
38	C₁₇×#389	C₂²	1	1	yes	characteristic
39	C₁₇×#389	C₂²	1	1	yes	characteristic
40	C₁₇×#389	C₂²	1	1	yes	characteristic
41	C₁₇×#388	—	2	1	no	—
42	C₁₇×#386	—	2	1	no	—
43	C₁₇×#385	—	2	1	no	—
44	C₁₇×#385	—	2	1	no	—
45	C₁₇×#380	C₂²	1	1	yes	characteristic
46	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
47	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
48	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
49	C₄×C₂²⋊C₄×C₁₇	—	2	1	no	—
50	C₁₇×#340	C₂²	1	1	yes	characteristic
51	C₁₇×#340	C₂²	1	1	yes	characteristic
52	C₁₇×#340	C₂²	1	1	yes	characteristic
53	C₁₇×#340	C₂²	1	1	yes	characteristic
54	C₁₇×#340	C₂²	1	1	yes	characteristic
55	C₁₇×#340	C₂²	1	1	yes	characteristic
56	C₁₇×#340	C₂²	1	1	yes	characteristic
57	C₁₇×#340	C₂²	1	1	yes	characteristic
58	C₁₇×#336	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₂²×D₄×C₁₇	—	2	1	no	—
61	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
62	C₂³×C₄×C₁₇	—	2	1	no	—
63	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
64	C₂³×C₄×C₁₇	D₄	1	1	yes	characteristic
65	C₂³×C₄×C₁₇	C₂³	1	1	yes	characteristic
66	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
67	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
68	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
69	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₁₇×#121	—	2	2	no	—
71	C₁₇×#121	C₂×C₄	1	4	yes	—
72	C₄×D₄×C₁₇	—	4	1	no	—
73	C₄×D₄×C₁₇	—	4	1	no	—
74	C₄×D₄×C₁₇	—	4	4	no	—
75	C₁₇×#117	—	2	2	no	—
76	C₁₇×#117	—	4	1	no	—
77	C₁₇×#117	—	4	1	no	—
78	C₁₇×#117	C₂×C₄	1	4	yes	complemented
79	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
81	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
82	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
98	C₂×C₄²×C₁₇	—	2	1	no	—
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	—	4	1	no	—
102	C₂×C₄²×C₁₇	—	4	1	no	—
103	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
104	C₂×C₄²×C₁₇	D₄	1	1	yes	characteristic
105	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
106	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
107	C₁₇×#107	—	4	1	no	—
108	C₁₇×#107	C₂×C₄	1	4	yes	complemented
109	C₁₇×#106	—	4	1	no	—
110	C₁₇×#106	C₂×C₄	1	4	yes	complemented
111	C₁₇×#102	—	4	1	no	—
112	C₁₇×#102	—	4	1	no	—
113	C₁₇×#102	C₂×C₄	1	4	yes	complemented
114	C₁₇×#102	C₂×C₄	1	4	yes	complemented
115	C₁₇×C₂²⋊C₈	—	2	2	no	—
116	C₁₇×C₂²⋊C₈	C₂×C₄	1	4	yes	complemented
117	C₁₇×#97	—	4	1	no	—
118	C₁₇×#97	—	4	1	no	—
119	C₁₇×#95	—	2	1	no	—
120	C₁₇×#95	—	2	1	no	—
121	C₁₇×#95	—	2	1	no	—
122	C₁₇×#95	—	2	1	no	—
123	C₁₇×#95	—	2	1	no	—
124	C₁₇×#95	—	2	1	no	—
125	C₁₇×#95	—	2	1	no	—
126	C₂⁴×C₁₇	—	2	1	no	—
127	C₂⁴×C₁₇	C₂×D₄	1	1	yes	characteristic
128	C₂×D₄×C₁₇	—	2	4	no	—
129	C₂×D₄×C₁₇	—	2	1	no	—
130	C₂×D₄×C₁₇	—	2	1	no	—
131	C₂×D₄×C₁₇	—	2	1	no	—
132	C₂×D₄×C₁₇	—	2	1	no	—
133	C₂×D₄×C₁₇	—	2	1	no	—
134	C₂×D₄×C₁₇	—	4	2	no	—
135	C₂×D₄×C₁₇	—	4	2	no	—
136	C₂×D₄×C₁₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₁₇	—	2	1	no	—
138	C₂²×C₄×C₁₇	—	2	1	no	—
139	C₂²×C₄×C₁₇	—	2	1	no	—
140	C₂²×C₄×C₁₇	—	2	1	no	—
141	C₂²×C₄×C₁₇	—	2	1	no	—
142	C₂²×C₄×C₁₇	—	2	1	no	—
143	C₂²×C₄×C₁₇	—	2	1	no	—
144	C₂²×C₄×C₁₇	—	2	2	no	—
145	C₂²×C₄×C₁₇	—	2	1	no	—
146	C₂²×C₄×C₁₇	—	2	1	no	—
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂²×C₄×C₁₇	—	2	1	no	—
149	C₂²×C₄×C₁₇	—	4	1	no	—
150	C₂²×C₄×C₁₇	—	4	1	no	—
151	C₂²×C₄×C₁₇	—	4	1	no	—
152	C₂²×C₄×C₁₇	—	4	1	no	—
153	C₂²×C₄×C₁₇	—	4	1	no	—
154	C₂²×C₄×C₁₇	—	4	2	no	—
155	C₂²×C₄×C₁₇	—	4	2	no	—
156	C₂²×C₄×C₁₇	—	4	2	no	—
157	C₂²×C₄×C₁₇	C₂²×C₄	1	2	yes	—
158	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	#41	1	2	yes	—
164	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	—	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	C₂²×C₄	1	2	yes	—
176	C₂×C₈×C₁₇	C₂²×C₄	1	2	yes	—
177	C₄⋊C₄×C₁₇	—	2	1	no	—
178	C₄⋊C₄×C₁₇	—	2	1	no	—
179	C₄⋊C₄×C₁₇	—	2	1	no	—
180	C₄⋊C₄×C₁₇	—	2	1	no	—
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	2	1	no	—
183	C₄⋊C₄×C₁₇	—	2	1	no	—
184	C₄⋊C₄×C₁₇	—	2	1	no	—
185	C₄⋊C₄×C₁₇	—	2	1	no	—
186	C₄⋊C₄×C₁₇	—	2	1	no	—
187	C₄⋊C₄×C₁₇	—	2	1	no	—
188	C₄⋊C₄×C₁₇	—	4	2	no	—
189	C₄⋊C₄×C₁₇	—	4	2	no	—
190	C₄⋊C₄×C₁₇	—	4	2	no	—
191	C₄⋊C₄×C₁₇	—	4	2	no	—
192	C₄⋊C₄×C₁₇	—	4	2	no	—
193	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
194	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
195	C₄⋊C₄×C₁₇	C₂²×C₄	1	2	yes	—
196	C₂²⋊C₄×C₁₇	—	2	4	no	—
197	C₂²⋊C₄×C₁₇	—	2	4	no	—
198	C₂²⋊C₄×C₁₇	—	4	2	no	—
199	C₂²⋊C₄×C₁₇	—	4	2	no	—
200	C₂²⋊C₄×C₁₇	—	4	2	no	—
201	C₂²⋊C₄×C₁₇	—	4	2	no	—
202	C₂²⋊C₄×C₁₇	—	4	2	no	—
203	C₄²×C₁₇	—	2	4	no	—
204	C₄²×C₁₇	—	2	1	no	—
205	C₄²×C₁₇	—	2	1	no	—
206	C₄²×C₁₇	—	2	1	no	—
207	C₄²×C₁₇	—	2	1	no	—
208	C₄²×C₁₇	—	4	1	no	—
209	C₄²×C₁₇	—	4	1	no	—
210	C₄²×C₁₇	—	4	2	no	—
211	C₄²×C₁₇	—	4	2	no	—
212	#22086	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
213	C₂³×C₁₇	—	2	1	no	—
214	C₂³×C₁₇	—	2	1	no	—
215	C₂³×C₁₇	—	2	1	no	—
216	C₂³×C₁₇	—	2	1	no	—
217	C₂³×C₁₇	—	2	1	no	—
218	C₂³×C₁₇	—	2	1	no	—
219	C₂³×C₁₇	—	2	2	no	—
220	C₂³×C₁₇	—	4	1	no	—
221	C₂³×C₁₇	—	4	1	no	—
222	C₂³×C₁₇	—	4	1	no	—
223	C₂³×C₁₇	—	4	1	no	—
224	C₂³×C₁₇	—	4	1	no	—
225	C₂³×C₁₇	—	4	1	no	—
226	C₂³×C₁₇	C₄×D₄	1	2	yes	—
227	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
228	D₄×C₁₇	—	2	2	no	—
229	D₄×C₁₇	—	2	2	no	—
230	D₄×C₁₇	—	4	8	no	—
231	D₄×C₁₇	—	4	1	no	—
232	D₄×C₁₇	—	4	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	2	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	2	no	—
240	C₂×C₄×C₁₇	—	2	2	no	—
241	C₂×C₄×C₁₇	—	2	2	no	—
242	C₂×C₄×C₁₇	—	2	2	no	—
243	C₂×C₄×C₁₇	—	2	2	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	2	1	no	—
247	C₂×C₄×C₁₇	—	2	1	no	—
248	C₂×C₄×C₁₇	—	2	1	no	—
249	C₂×C₄×C₁₇	—	2	1	no	—
250	C₂×C₄×C₁₇	—	2	1	no	—
251	C₂×C₄×C₁₇	—	2	1	no	—
252	C₂×C₄×C₁₇	—	2	1	no	—
253	C₂×C₄×C₁₇	—	4	4	no	—
254	C₂×C₄×C₁₇	—	4	4	no	—
255	C₂×C₄×C₁₇	—	4	1	no	—
256	C₂×C₄×C₁₇	—	4	1	no	—
257	C₂×C₄×C₁₇	—	4	1	no	—
258	C₂×C₄×C₁₇	—	4	1	no	—
259	C₂×C₄×C₁₇	—	4	1	no	—
260	C₂×C₄×C₁₇	—	4	1	no	—
261	C₂×C₄×C₁₇	—	4	1	no	—
262	C₂×C₄×C₁₇	—	4	1	no	—
263	C₂×C₄×C₁₇	—	4	1	no	—
264	C₂×C₄×C₁₇	—	4	1	no	—
265	C₂×C₄×C₁₇	—	4	1	no	—
266	C₂×C₄×C₁₇	—	4	1	no	—
267	C₂×C₄×C₁₇	—	4	1	no	—
268	C₂×C₄×C₁₇	—	4	1	no	—
269	C₂×C₄×C₁₇	—	4	1	no	—
270	C₂×C₄×C₁₇	—	4	1	no	—
271	C₂×C₄×C₁₇	—	4	1	no	—
272	C₂×C₄×C₁₇	—	4	1	no	—
273	C₂×C₄×C₁₇	—	8	4	no	—
274	C₂×C₄×C₁₇	C₄×D₄	1	2	yes	—
275	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
276	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
278	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
279	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
280	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
281	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
282	C₈×C₁₇	—	2	2	no	—
283	C₈×C₁₇	—	2	2	no	—
284	C₈×C₁₇	—	4	1	no	—
285	C₈×C₁₇	—	4	1	no	—
286	C₂×#482	C₂×C₁₇	1	1	yes	characteristic
287	C₄×#121	C₂×C₁₇	1	1	yes	characteristic
288	#2296	C₂×C₁₇	1	1	yes	characteristic, complemented
289	#1944	C₂×C₁₇	1	1	yes	characteristic, complemented
290	#1943	C₂×C₁₇	1	1	yes	characteristic, complemented
291	#1936	C₂×C₁₇	1	1	yes	characteristic, complemented
292	#1936	C₂×C₁₇	1	1	yes	characteristic, complemented
293	#1920	C₂×C₁₇	1	1	yes	characteristic, complemented
294	#1918	C₂×C₁₇	1	1	yes	characteristic, complemented
295	#1875	C₂×C₁₇	1	1	yes	characteristic
296	#1864	C₂×C₁₇	1	1	yes	characteristic, complemented
297	#1862	C₂×C₁₇	1	1	yes	characteristic, complemented
298	#1854	C₂×C₁₇	1	1	yes	characteristic, complemented
299	#1825	C₂×C₁₇	1	1	yes	characteristic, complemented
300	#1749	C₂×C₁₇	1	1	yes	characteristic, complemented
301	C₂²×C₁₇	—	2	2	no	—
302	C₂²×C₁₇	—	2	2	no	—
303	C₂²×C₁₇	—	2	2	no	—
304	C₂²×C₁₇	—	4	1	no	—
305	C₂²×C₁₇	—	4	1	no	—
306	C₂²×C₁₇	—	4	1	no	—
307	C₂²×C₁₇	—	4	1	no	—
308	C₂²×C₁₇	—	4	2	no	—
309	C₂²×C₁₇	—	4	2	no	—
310	C₂²×C₁₇	—	4	2	no	—
311	C₂²×C₁₇	—	8	1	no	—
312	C₂²×C₁₇	—	8	1	no	—
313	C₂²×C₁₇	—	8	1	no	—
314	C₂²×C₁₇	—	8	1	no	—
315	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
316	C₂²×C₁₇	#534	1	1	yes	characteristic
317	C₂²×C₁₇	#536	1	1	yes	characteristic
318	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₁₇	#575	1	1	yes	characteristic
320	C₂²×C₁₇	#575	1	1	yes	characteristic
321	C₂²×C₁₇	#575	1	1	yes	characteristic
322	C₄×C₁₇	—	2	2	no	—
323	C₄×C₁₇	—	2	2	no	—
324	C₄×C₁₇	—	4	1	no	—
325	C₄×C₁₇	—	4	1	no	—
326	C₄×C₁₇	—	4	1	no	—
327	C₄×C₁₇	—	4	2	no	—
328	C₄×C₁₇	—	4	2	no	—
329	C₄×C₁₇	—	4	2	no	—
330	C₄×C₁₇	—	8	1	no	—
331	C₄×C₁₇	—	8	1	no	—
332	C₄×C₁₇	—	8	1	no	—
333	C₄×C₁₇	—	8	1	no	—
334	C₄×C₁₇	#520	1	1	yes	characteristic
335	C₄×C₁₇	#520	1	1	yes	characteristic
336	C₄×C₁₇	#539	1	1	yes	characteristic
337	C₄×C₁₇	#539	1	1	yes	characteristic
338	C₂×#121	C₂²×C₁₇	1	1	yes	characteristic
339	C₂×C₄×D₄	—	2	1	no	—
340	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
341	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
342	C₂×#117	C₂²×C₁₇	1	1	yes	characteristic
343	C₂²×C₄²	C₂²×C₁₇	1	1	yes	characteristic
344	#482	C₄×C₁₇	1	8	yes	complemented
345	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
346	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
347	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
348	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
350	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
351	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
352	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
353	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
354	C₂×C₂²⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
355	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
356	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
357	#390	C₂²×C₁₇	1	1	yes	characteristic
358	#389	C₂²×C₁₇	1	1	yes	characteristic
359	#389	C₂²×C₁₇	1	1	yes	characteristic
360	#389	C₂²×C₁₇	1	1	yes	characteristic
361	#389	C₂²×C₁₇	1	1	yes	characteristic
362	#389	C₂²×C₁₇	1	1	yes	characteristic
363	#388	—	2	1	no	—
364	#386	—	2	1	no	—
365	#385	—	2	1	no	—
366	#385	—	2	1	no	—
367	#380	C₂²×C₁₇	1	1	yes	characteristic
368	C₄×C₄⋊C₄	—	2	1	no	—
369	C₄×C₄⋊C₄	—	2	1	no	—
370	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
371	C₄×C₂²⋊C₄	—	2	1	no	—
372	#340	C₂²×C₁₇	1	1	yes	characteristic
373	#340	C₂²×C₁₇	1	1	yes	characteristic
374	#340	C₂²×C₁₇	1	1	yes	characteristic
375	#340	C₂²×C₁₇	1	1	yes	characteristic
376	#340	C₂²×C₁₇	1	1	yes	characteristic
377	#340	C₂²×C₁₇	1	1	yes	characteristic
378	#340	C₂²×C₁₇	1	1	yes	characteristic
379	#340	C₂²×C₁₇	1	1	yes	characteristic
380	#336	C₂²×C₁₇	1	1	yes	characteristic
381	#336	C₂²×C₁₇	1	1	yes	characteristic
382	C₂×C₁₇	—	4	2	no	—
383	C₂×C₁₇	—	8	2	no	—
384	C₂×C₁₇	#2322	1	1	yes	characteristic
385	C₂×C₁₇	#2943	1	1	yes	characteristic
386	C₂×C₁₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
387	C₂×C₁₇	#3194	1	1	yes	characteristic
388	C₂×C₁₇	#3197	1	1	yes	characteristic
389	C₂×C₁₇	#3235	1	1	yes	characteristic
390	C₂×C₁₇	#3240	1	1	yes	characteristic
391	C₂²×D₄	—	2	1	no	—
392	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
393	C₂³×C₄	—	2	1	no	—
394	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
395	C₂³×C₄	D₄×C₁₇	1	1	yes	characteristic
396	C₂³×C₄	C₂³×C₁₇	1	1	yes	characteristic
397	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
398	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
399	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
400	C₂²×C₈	C₂³×C₁₇	1	1	yes	characteristic
401	#121	—	2	2	no	—
402	#121	C₂×C₄×C₁₇	1	4	yes	—
403	C₄×D₄	—	4	1	no	—
404	C₄×D₄	—	4	1	no	—
405	C₄×D₄	—	4	4	no	—
406	#117	—	2	2	no	—
407	#117	—	4	1	no	—
408	#117	—	4	1	no	—
409	#117	C₂×C₄×C₁₇	1	4	yes	complemented
410	C₂×C₄⋊C₄	—	2	1	no	—
411	C₂×C₄⋊C₄	—	2	1	no	—
412	C₂×C₄⋊C₄	—	2	1	no	—
413	C₂×C₄⋊C₄	—	2	1	no	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
416	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
417	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
418	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
419	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
420	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
421	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
422	C₂×C₂²⋊C₄	—	2	1	no	—
423	C₂×C₂²⋊C₄	—	2	1	no	—
424	C₂×C₂²⋊C₄	—	2	1	no	—
425	C₂×C₂²⋊C₄	—	2	1	no	—
426	C₂×C₂²⋊C₄	—	2	1	no	—
427	C₂×C₂²⋊C₄	—	2	1	no	—
428	C₂×C₂²⋊C₄	—	2	1	no	—
429	C₂×C₄²	—	2	1	no	—
430	C₂×C₄²	—	2	1	no	—
431	C₂×C₄²	—	2	1	no	—
432	C₂×C₄²	—	4	1	no	—
433	C₂×C₄²	—	4	1	no	—
434	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
435	C₂×C₄²	D₄×C₁₇	1	1	yes	characteristic
436	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
437	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
438	#107	—	4	1	no	—
439	#107	C₂×C₄×C₁₇	1	4	yes	complemented
440	#106	—	4	1	no	—
441	#106	C₂×C₄×C₁₇	1	4	yes	complemented
442	#102	—	4	1	no	—
443	#102	—	4	1	no	—
444	#102	C₂×C₄×C₁₇	1	4	yes	complemented
445	#102	C₂×C₄×C₁₇	1	4	yes	complemented
446	C₂²⋊C₈	—	2	2	no	—
447	C₂²⋊C₈	C₂×C₄×C₁₇	1	4	yes	complemented
448	#97	—	4	1	no	—
449	#97	—	4	1	no	—
450	#95	—	2	1	no	—
451	#95	—	2	1	no	—
452	#95	—	2	1	no	—
453	#95	—	2	1	no	—
454	#95	—	2	1	no	—
455	#95	—	2	1	no	—
456	#95	—	2	1	no	—
457	C₁₇	#22086	1	1	yes	characteristic, direct product factor, Sylow
458	C₂⁴	—	2	1	no	—
459	C₂⁴	C₂×D₄×C₁₇	1	1	yes	characteristic
460	C₂×D₄	—	2	4	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	2	1	no	—
466	C₂×D₄	—	4	2	no	—
467	C₂×D₄	—	4	2	no	—
468	C₂×D₄	C₂²×C₄×C₁₇	1	2	yes	—
469	C₂²×C₄	—	2	1	no	—
470	C₂²×C₄	—	2	1	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	1	no	—
473	C₂²×C₄	—	2	1	no	—
474	C₂²×C₄	—	2	1	no	—
475	C₂²×C₄	—	2	1	no	—
476	C₂²×C₄	—	2	2	no	—
477	C₂²×C₄	—	2	1	no	—
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	—	4	1	no	—
482	C₂²×C₄	—	4	1	no	—
483	C₂²×C₄	—	4	1	no	—
484	C₂²×C₄	—	4	1	no	—
485	C₂²×C₄	—	4	1	no	—
486	C₂²×C₄	—	4	2	no	—
487	C₂²×C₄	—	4	2	no	—
488	C₂²×C₄	—	4	2	no	—
489	C₂²×C₄	C₂²×C₄×C₁₇	1	2	yes	—
490	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
491	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
493	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
494	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
495	C₂²×C₄	#41×C₁₇	1	2	yes	—
496	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
497	C₂×C₈	—	2	1	no	—
498	C₂×C₈	—	2	1	no	—
499	C₂×C₈	—	2	1	no	—
500	C₂×C₈	—	2	1	no	—
501	C₂×C₈	—	2	1	no	—
502	C₂×C₈	—	2	1	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
508	C₂×C₈	C₂²×C₄×C₁₇	1	2	yes	—
509	C₄⋊C₄	—	2	1	no	—
510	C₄⋊C₄	—	2	1	no	—
511	C₄⋊C₄	—	2	1	no	—
512	C₄⋊C₄	—	2	1	no	—
513	C₄⋊C₄	—	2	1	no	—
514	C₄⋊C₄	—	2	1	no	—
515	C₄⋊C₄	—	2	1	no	—
516	C₄⋊C₄	—	2	1	no	—
517	C₄⋊C₄	—	2	1	no	—
518	C₄⋊C₄	—	2	1	no	—
519	C₄⋊C₄	—	2	1	no	—
520	C₄⋊C₄	—	4	2	no	—
521	C₄⋊C₄	—	4	2	no	—
522	C₄⋊C₄	—	4	2	no	—
523	C₄⋊C₄	—	4	2	no	—
524	C₄⋊C₄	—	4	2	no	—
525	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
526	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
527	C₄⋊C₄	C₂²×C₄×C₁₇	1	2	yes	—
528	C₂²⋊C₄	—	2	4	no	—
529	C₂²⋊C₄	—	2	4	no	—
530	C₂²⋊C₄	—	4	2	no	—
531	C₂²⋊C₄	—	4	2	no	—
532	C₂²⋊C₄	—	4	2	no	—
533	C₂²⋊C₄	—	4	2	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₄²	—	2	1	no	—
536	C₄²	—	2	1	no	—
537	C₄²	—	2	1	no	—
538	C₄²	—	2	1	no	—
539	C₄²	—	2	4	no	—
540	C₄²	—	4	1	no	—
541	C₄²	—	4	1	no	—
542	C₄²	—	4	2	no	—
543	C₄²	—	4	2	no	—
544	C₂³	—	2	1	no	—
545	C₂³	—	2	1	no	—
546	C₂³	—	2	1	no	—
547	C₂³	—	2	1	no	—
548	C₂³	—	2	1	no	—
549	C₂³	—	2	1	no	—
550	C₂³	—	2	2	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	1	no	—
553	C₂³	—	4	1	no	—
554	C₂³	—	4	1	no	—
555	C₂³	—	4	1	no	—
556	C₂³	—	4	1	no	—
557	C₂³	C₄×D₄×C₁₇	1	2	yes	—
558	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
559	D₄	—	2	2	no	—
560	D₄	—	2	2	no	—
561	D₄	—	4	8	no	—
562	D₄	—	4	1	no	—
563	D₄	—	4	1	no	—
564	C₂×C₄	—	2	1	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	1	no	—
568	C₂×C₄	—	2	2	no	—
569	C₂×C₄	—	2	2	no	—
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	2	no	—
574	C₂×C₄	—	2	2	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	4	4	no	—
585	C₂×C₄	—	4	4	no	—
586	C₂×C₄	—	4	1	no	—
587	C₂×C₄	—	4	1	no	—
588	C₂×C₄	—	4	1	no	—
589	C₂×C₄	—	4	1	no	—
590	C₂×C₄	—	4	1	no	—
591	C₂×C₄	—	4	1	no	—
592	C₂×C₄	—	4	1	no	—
593	C₂×C₄	—	4	1	no	—
594	C₂×C₄	—	4	1	no	—
595	C₂×C₄	—	4	1	no	—
596	C₂×C₄	—	4	1	no	—
597	C₂×C₄	—	4	1	no	—
598	C₂×C₄	—	4	1	no	—
599	C₂×C₄	—	4	1	no	—
600	C₂×C₄	—	4	1	no	—
601	C₂×C₄	—	4	1	no	—
602	C₂×C₄	—	4	1	no	—
603	C₂×C₄	—	4	1	no	—
604	C₂×C₄	—	8	4	no	—
605	C₂×C₄	C₄×D₄×C₁₇	1	2	yes	—
606	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
607	C₂×C₄	C₂³×C₄×C₁₇	1	1	yes	characteristic
608	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
609	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
610	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
611	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
612	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
613	C₈	—	2	2	no	—
614	C₈	—	2	2	no	—
615	C₈	—	4	1	no	—
616	C₈	—	4	1	no	—
617	C₂²	—	2	2	no	—
618	C₂²	—	2	2	no	—
619	C₂²	—	2	2	no	—
620	C₂²	—	4	1	no	—
621	C₂²	—	4	1	no	—
622	C₂²	—	4	1	no	—
623	C₂²	—	4	1	no	—
624	C₂²	—	4	2	no	—
625	C₂²	—	4	2	no	—
626	C₂²	—	4	2	no	—
627	C₂²	—	8	1	no	—
628	C₂²	—	8	1	no	—
629	C₂²	—	8	1	no	—
630	C₂²	—	8	1	no	—
631	C₂²	C₂×C₄×D₄×C₁₇	1	1	yes	characteristic
632	C₂²	C₁₇×#534	1	1	yes	characteristic
633	C₂²	C₁₇×#536	1	1	yes	characteristic
634	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
635	C₂²	C₁₇×#575	1	1	yes	characteristic
636	C₂²	C₁₇×#575	1	1	yes	characteristic
637	C₂²	C₁₇×#575	1	1	yes	characteristic
638	C₄	—	2	2	no	—
639	C₄	—	2	2	no	—
640	C₄	—	4	1	no	—
641	C₄	—	4	1	no	—
642	C₄	—	4	1	no	—
643	C₄	—	4	2	no	—
644	C₄	—	4	2	no	—
645	C₄	—	4	2	no	—
646	C₄	—	8	1	no	—
647	C₄	—	8	1	no	—
648	C₄	—	8	1	no	—
649	C₄	—	8	1	no	—
650	C₄	C₁₇×#520	1	1	yes	characteristic
651	C₄	C₁₇×#520	1	1	yes	characteristic
652	C₄	C₁₇×#539	1	1	yes	characteristic
653	C₄	C₁₇×#539	1	1	yes	characteristic
654	C₂	—	4	2	no	—
655	C₂	—	8	2	no	—
656	C₂	C₁₇×#2322	1	1	yes	characteristic
657	C₂	C₁₇×#2943	1	1	yes	characteristic
658	C₂	C₄×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
659	C₂	C₁₇×#3194	1	1	yes	characteristic
660	C₂	C₁₇×#3197	1	1	yes	characteristic
661	C₂	C₁₇×#3235	1	1	yes	characteristic
662	C₂	C₁₇×#3240	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₁₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₁₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂×C₁₇×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₇ ◁ C₂²×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₁₇×#2296	C₂	semidirect
4. C₁₇×#1944	C₂	semidirect
5. C₁₇×#1943	C₂	semidirect
6. C₁₇×#1936	C₂	semidirect
7. C₁₇×#1936	C₂	semidirect
8. C₁₇×#1920	C₂	semidirect
9. C₁₇×#1918	C₂	semidirect
11. C₁₇×#1864	C₂	semidirect
12. C₁₇×#1862	C₂	semidirect
13. C₁₇×#1854	C₂	semidirect
14. C₁₇×#1825	C₂	semidirect
15. C₁₇×#1749	C₂	semidirect
22. C₁₇×#482	C₄	semidirect
78. C₁₇×#117	C₂×C₄	semidirect
108. C₁₇×#107	C₂×C₄	semidirect
110. C₁₇×#106	C₂×C₄	semidirect
113. C₁₇×#102	C₂×C₄	semidirect
114. C₁₇×#102	C₂×C₄	semidirect
116. C₁₇×C₂²⋊C₈	C₂×C₄	semidirect
212. #22086	C₁₇	direct (N × H)
288. #2296	C₂×C₁₇	semidirect
289. #1944	C₂×C₁₇	semidirect
290. #1943	C₂×C₁₇	semidirect
291. #1936	C₂×C₁₇	semidirect
292. #1936	C₂×C₁₇	semidirect
293. #1920	C₂×C₁₇	semidirect
294. #1918	C₂×C₁₇	semidirect
296. #1864	C₂×C₁₇	semidirect
297. #1862	C₂×C₁₇	semidirect
298. #1854	C₂×C₁₇	semidirect
299. #1825	C₂×C₁₇	semidirect
300. #1749	C₂×C₁₇	semidirect
344. #482	C₄×C₁₇	semidirect
409. #117	C₂×C₄×C₁₇	semidirect
439. #107	C₂×C₄×C₁₇	semidirect
441. #106	C₂×C₄×C₁₇	semidirect
444. #102	C₂×C₄×C₁₇	semidirect
445. #102	C₂×C₄×C₁₇	semidirect
447. C₂²⋊C₈	C₂×C₄×C₁₇	semidirect
457. C₁₇	#22086	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₁₇×#482	2
C₄×C₁₇×#121	2
C₁₇×#2296	2
C₁₇×#1944	2
C₁₇×#1943	2
C₁₇×#1936	2
C₁₇×#1920	2
C₁₇×#1918	2
C₁₇×#1875	2
C₁₇×#1864	2
C₁₇×#1862	2
C₁₇×#1854	2
C₁₇×#1825	2
C₁₇×#1749	2
#22086	17

Subgroups — C17×#22086 #16879830

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#22086 #16879830