Subgroups — C₁₇×#25465 #16883209

Order 4352.

812 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	C₂×C₁₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#478	C₂	1	1	yes	maximal, characteristic
3	C₁₇×#2542	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2370	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2084	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2083	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2067	C₂	1	1	yes	maximal, characteristic
8	C₁₇×#2065	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1947	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1926	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1925	C₂	1	1	yes	maximal, characteristic
15	C₁₇×#1762	C₂	1	1	yes	maximal, characteristic
16	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
19	C₂×C₁₇×C₂²⋊Q₈	—	2	1	no	—
20	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
21	C₁₇×#501	—	2	4	no	—
22	C₁₇×#478	—	2	4	no	—
23	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
25	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
26	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
27	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
28	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
29	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
33	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
34	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#97	C₂²	1	1	yes	characteristic
37	C₁₇×#399	—	2	1	no	—
38	C₁₇×#399	—	2	1	no	—
39	C₁₇×#390	C₂²	1	1	yes	characteristic
40	C₁₇×#390	C₂²	1	1	yes	characteristic
41	C₁₇×#389	—	2	1	no	—
42	C₁₇×#389	C₂²	1	1	yes	characteristic
43	C₁₇×#389	C₂²	1	1	yes	characteristic
44	C₁₇×#387	—	2	1	no	—
45	C₁₇×#387	—	2	1	no	—
46	C₁₇×#384	C₂²	1	1	yes	characteristic
47	C₁₇×#384	C₂²	1	1	yes	characteristic
48	C₄×C₄⋊C₄×C₁₇	—	2	1	no	—
49	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
50	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
51	C₄×C₄⋊C₄×C₁₇	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊C₄×C₁₇	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×#340	C₂²	1	1	yes	characteristic
59	C₁₇×#336	C₂²	1	1	yes	characteristic
60	C₁₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×Q₈×C₁₇	—	2	1	no	—
62	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
63	C₂³×C₄×C₁₇	—	2	1	no	—
64	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×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	C₁₇×C₄⋊Q₈	—	2	2	no	—
69	C₁₇×C₄⋊Q₈	—	2	2	no	—
70	C₁₇×#125	—	2	2	no	—
71	C₁₇×#125	D₄	1	4	yes	—
72	C₁₇×C₂²⋊Q₈	—	4	4	no	—
73	C₁₇×C₂²⋊Q₈	—	4	4	no	—
74	C₄×D₄×C₁₇	—	2	2	no	—
75	C₄×D₄×C₁₇	—	2	2	no	—
76	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
78	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	2	1	no	—
85	C₂×C₄⋊C₄×C₁₇	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₁₇	D₄	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×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
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×C₂²⋊C₄×C₁₇	—	2	1	no	—
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	—	2	1	no	—
102	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
104	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
105	C₁₇×#107	—	2	2	no	—
106	C₁₇×#107	—	2	2	no	—
107	C₁₇×#107	—	2	2	no	—
108	C₁₇×#106	—	2	2	no	—
109	C₁₇×#106	—	2	2	no	—
110	C₁₇×#106	—	2	2	no	—
111	C₁₇×C₄⋊C₈	—	2	2	no	—
112	C₁₇×C₄⋊C₈	—	2	2	no	—
113	C₁₇×C₄⋊C₈	—	2	2	no	—
114	C₁₇×#102	—	2	2	no	—
115	C₁₇×#102	—	2	2	no	—
116	C₁₇×#102	—	2	2	no	—
117	C₁₇×#102	Q₈	1	4	yes	complemented
118	C₁₇×#97	—	2	2	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	D₄	1	1	yes	characteristic
125	C₁₇×#95	D₄	1	1	yes	characteristic
126	C₂⁴×C₁₇	—	2	1	no	—
127	C₂×Q₈×C₁₇	—	4	2	no	—
128	C₂×Q₈×C₁₇	—	4	2	no	—
129	C₂×Q₈×C₁₇	—	4	2	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	—	2	1	no	—
135	C₂×D₄×C₁₇	C₂×Q₈	1	2	yes	—
136	C₂²×C₄×C₁₇	—	2	1	no	—
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	—	4	2	no	—
144	C₂²×C₄×C₁₇	—	4	2	no	—
145	C₂²×C₄×C₁₇	—	4	2	no	—
146	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
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	C₂×Q₈	1	2	yes	—
164	C₂×C₈×C₁₇	#41	1	2	yes	—
165	C₄⋊C₄×C₁₇	—	2	4	no	—
166	C₄⋊C₄×C₁₇	—	2	4	no	—
167	C₄⋊C₄×C₁₇	—	2	2	no	—
168	C₄⋊C₄×C₁₇	—	2	2	no	—
169	C₄⋊C₄×C₁₇	—	2	1	no	—
170	C₄⋊C₄×C₁₇	—	2	1	no	—
171	C₄⋊C₄×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	—	2	1	no	—
174	C₄⋊C₄×C₁₇	—	2	1	no	—
175	C₄⋊C₄×C₁₇	—	2	1	no	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	4	2	no	—
181	C₄⋊C₄×C₁₇	—	4	2	no	—
182	C₄⋊C₄×C₁₇	—	4	2	no	—
183	C₄⋊C₄×C₁₇	—	4	2	no	—
184	C₄⋊C₄×C₁₇	—	4	2	no	—
185	C₄⋊C₄×C₁₇	—	4	2	no	—
186	C₄⋊C₄×C₁₇	—	8	1	no	—
187	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
188	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
189	C₄⋊C₄×C₁₇	C₂×Q₈	1	2	yes	—
190	C₂²⋊C₄×C₁₇	—	4	2	no	—
191	C₂²⋊C₄×C₁₇	—	4	2	no	—
192	C₂²⋊C₄×C₁₇	—	4	2	no	—
193	C₂²⋊C₄×C₁₇	—	4	2	no	—
194	C₂²⋊C₄×C₁₇	—	4	2	no	—
195	C₄²×C₁₇	—	2	1	no	—
196	C₄²×C₁₇	—	2	1	no	—
197	C₄²×C₁₇	—	2	1	no	—
198	C₄²×C₁₇	—	2	1	no	—
199	C₄²×C₁₇	—	4	2	no	—
200	C₄²×C₁₇	—	8	1	no	—
201	C₄²×C₁₇	—	8	1	no	—
202	C₄²×C₁₇	C₂×D₄	1	2	yes	—
203	C₄²×C₁₇	#41	1	2	yes	—
204	#25465	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂³×C₁₇	—	2	2	no	—
206	C₂³×C₁₇	—	4	1	no	—
207	C₂³×C₁₇	—	4	1	no	—
208	C₂³×C₁₇	—	4	1	no	—
209	C₂³×C₁₇	—	4	1	no	—
210	C₂³×C₁₇	—	4	1	no	—
211	C₂³×C₁₇	—	4	1	no	—
212	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
213	Q₈×C₁₇	—	8	4	no	—
214	D₄×C₁₇	—	2	2	no	—
215	D₄×C₁₇	—	2	2	no	—
216	D₄×C₁₇	—	4	1	no	—
217	D₄×C₁₇	—	4	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	2	no	—
227	C₂×C₄×C₁₇	—	2	2	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	2	2	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	—	4	1	no	—
236	C₂×C₄×C₁₇	—	4	1	no	—
237	C₂×C₄×C₁₇	—	4	1	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	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	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	4	1	no	—
247	C₂×C₄×C₁₇	—	4	1	no	—
248	C₂×C₄×C₁₇	—	4	1	no	—
249	C₂×C₄×C₁₇	—	4	1	no	—
250	C₂×C₄×C₁₇	—	4	1	no	—
251	C₂×C₄×C₁₇	—	4	1	no	—
252	C₂×C₄×C₁₇	—	4	1	no	—
253	C₂×C₄×C₁₇	—	8	4	no	—
254	C₂×C₄×C₁₇	#121	1	2	yes	—
255	C₂×C₄×C₁₇	#121	1	2	yes	—
256	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
257	C₂×C₄×C₁₇	AGL(1,ℤ/8)	1	2	yes	—
258	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
260	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
261	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
262	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
263	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
264	C₈×C₁₇	—	2	2	no	—
265	C₈×C₁₇	—	2	2	no	—
266	C₈×C₁₇	—	4	1	no	—
267	C₈×C₁₇	—	4	1	no	—
268	C₂×#501	C₂×C₁₇	1	1	yes	characteristic, complemented
269	C₂×#478	C₂×C₁₇	1	1	yes	characteristic
270	#2542	C₂×C₁₇	1	1	yes	characteristic
271	#2370	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#2084	C₂×C₁₇	1	1	yes	characteristic, complemented
273	#2083	C₂×C₁₇	1	1	yes	characteristic, complemented
274	#2067	C₂×C₁₇	1	1	yes	characteristic
275	#2065	C₂×C₁₇	1	1	yes	characteristic
276	#1987	C₂×C₁₇	1	1	yes	characteristic, complemented
277	#1948	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1947	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#1940	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#1926	C₂×C₁₇	1	1	yes	characteristic
281	#1925	C₂×C₁₇	1	1	yes	characteristic
282	#1762	C₂×C₁₇	1	1	yes	characteristic
283	C₂²×C₁₇	—	4	2	no	—
284	C₂²×C₁₇	—	4	2	no	—
285	C₂²×C₁₇	—	4	2	no	—
286	C₂²×C₁₇	—	8	1	no	—
287	C₂²×C₁₇	—	8	1	no	—
288	C₂²×C₁₇	—	8	1	no	—
289	C₂²×C₁₇	—	8	1	no	—
290	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
291	C₂²×C₁₇	#547	1	1	yes	characteristic
292	C₂²×C₁₇	D₄×Q₈	1	1	yes	characteristic
293	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
294	C₂²×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₂²×C₁₇	#577	1	1	yes	characteristic
296	C₂²×C₁₇	#578	1	1	yes	characteristic
297	C₄×C₁₇	—	2	2	no	—
298	C₄×C₁₇	—	2	2	no	—
299	C₄×C₁₇	—	2	2	no	—
300	C₄×C₁₇	—	2	2	no	—
301	C₄×C₁₇	—	4	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	2	no	—
304	C₄×C₁₇	—	4	2	no	—
305	C₄×C₁₇	—	4	2	no	—
306	C₄×C₁₇	—	8	1	no	—
307	C₄×C₁₇	—	8	1	no	—
308	C₄×C₁₇	—	8	1	no	—
309	C₄×C₁₇	—	8	1	no	—
310	C₄×C₁₇	#533	1	1	yes	characteristic
311	C₄×C₁₇	#541	1	1	yes	characteristic
312	C₄×C₁₇	#548	1	1	yes	characteristic
313	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
314	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
315	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
316	C₂×C₂²⋊Q₈	—	2	1	no	—
317	C₂×C₂²⋊Q₈	—	2	1	no	—
318	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
319	#501	—	2	4	no	—
320	#478	—	2	4	no	—
321	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
322	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
323	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
324	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
325	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
326	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
327	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
328	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
329	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
330	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
332	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
333	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
334	C₂×#97	C₂²×C₁₇	1	1	yes	characteristic
335	#399	—	2	1	no	—
336	#399	—	2	1	no	—
337	#390	C₂²×C₁₇	1	1	yes	characteristic
338	#390	C₂²×C₁₇	1	1	yes	characteristic
339	#389	—	2	1	no	—
340	#389	C₂²×C₁₇	1	1	yes	characteristic
341	#389	C₂²×C₁₇	1	1	yes	characteristic
342	#387	—	2	1	no	—
343	#387	—	2	1	no	—
344	#384	C₂²×C₁₇	1	1	yes	characteristic
345	#384	C₂²×C₁₇	1	1	yes	characteristic
346	C₄×C₄⋊C₄	—	2	1	no	—
347	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
348	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
349	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
350	C₄×C₄⋊C₄	C₂²×C₁₇	1	1	yes	characteristic
351	#340	C₂²×C₁₇	1	1	yes	characteristic
352	#340	C₂²×C₁₇	1	1	yes	characteristic
353	#340	C₂²×C₁₇	1	1	yes	characteristic
354	#340	C₂²×C₁₇	1	1	yes	characteristic
355	#340	C₂²×C₁₇	1	1	yes	characteristic
356	#340	C₂²×C₁₇	1	1	yes	characteristic
357	#336	C₂²×C₁₇	1	1	yes	characteristic
358	#336	C₂²×C₁₇	1	1	yes	characteristic
359	C₂×C₁₇	—	8	2	no	—
360	C₂×C₁₇	#2429	1	1	yes	characteristic
361	C₂×C₁₇	#3038	1	1	yes	characteristic
362	C₂×C₁₇	#3046	1	1	yes	characteristic
363	C₂×C₁₇	#3343	1	1	yes	characteristic
364	C₂×C₁₇	#3345	1	1	yes	characteristic
365	C₂×C₁₇	#3384	1	1	yes	characteristic
366	C₂×C₁₇	#3386	1	1	yes	characteristic
367	C₂²×Q₈	—	2	1	no	—
368	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
369	C₂³×C₄	—	2	1	no	—
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	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	—	2	2	no	—
376	#125	—	2	2	no	—
377	#125	D₄×C₁₇	1	4	yes	—
378	C₂²⋊Q₈	—	4	4	no	—
379	C₂²⋊Q₈	—	4	4	no	—
380	C₄×D₄	—	2	2	no	—
381	C₄×D₄	—	2	2	no	—
382	C₂×C₄⋊C₄	—	2	1	no	—
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	—	2	1	no	—
385	C₂×C₄⋊C₄	—	2	1	no	—
386	C₂×C₄⋊C₄	—	2	1	no	—
387	C₂×C₄⋊C₄	—	2	1	no	—
388	C₂×C₄⋊C₄	—	2	1	no	—
389	C₂×C₄⋊C₄	—	2	1	no	—
390	C₂×C₄⋊C₄	—	2	1	no	—
391	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	D₄×C₁₇	1	1	yes	characteristic
393	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
396	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
398	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
400	C₂×C₂²⋊C₄	—	2	1	no	—
401	C₂×C₂²⋊C₄	—	2	1	no	—
402	C₂×C₂²⋊C₄	—	2	1	no	—
403	C₂×C₂²⋊C₄	—	2	1	no	—
404	C₂×C₂²⋊C₄	—	2	1	no	—
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	—	2	1	no	—
407	C₂×C₄²	—	2	1	no	—
408	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
409	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
410	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
411	#107	—	2	2	no	—
412	#107	—	2	2	no	—
413	#107	—	2	2	no	—
414	#106	—	2	2	no	—
415	#106	—	2	2	no	—
416	#106	—	2	2	no	—
417	C₄⋊C₈	—	2	2	no	—
418	C₄⋊C₈	—	2	2	no	—
419	C₄⋊C₈	—	2	2	no	—
420	#102	—	2	2	no	—
421	#102	—	2	2	no	—
422	#102	—	2	2	no	—
423	#102	Q₈×C₁₇	1	4	yes	complemented
424	#97	—	2	2	no	—
425	#95	—	2	1	no	—
426	#95	—	2	1	no	—
427	#95	—	2	1	no	—
428	#95	—	2	1	no	—
429	#95	—	2	1	no	—
430	#95	D₄×C₁₇	1	1	yes	characteristic
431	#95	D₄×C₁₇	1	1	yes	characteristic
432	C₁₇	#25465	1	1	yes	characteristic, direct product factor, Sylow
433	C₂⁴	—	2	1	no	—
434	C₂×Q₈	—	4	2	no	—
435	C₂×Q₈	—	4	2	no	—
436	C₂×Q₈	—	4	2	no	—
437	C₂×D₄	—	2	1	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	C₂×Q₈×C₁₇	1	2	yes	—
443	C₂²×C₄	—	2	1	no	—
444	C₂²×C₄	—	2	1	no	—
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	4	2	no	—
451	C₂²×C₄	—	4	2	no	—
452	C₂²×C₄	—	4	2	no	—
453	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
456	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
457	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
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	C₂×Q₈×C₁₇	1	2	yes	—
471	C₂×C₈	#41×C₁₇	1	2	yes	—
472	C₄⋊C₄	—	2	2	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	2	4	no	—
478	C₄⋊C₄	—	2	4	no	—
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	2	1	no	—
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	—	4	2	no	—
488	C₄⋊C₄	—	4	2	no	—
489	C₄⋊C₄	—	4	2	no	—
490	C₄⋊C₄	—	4	2	no	—
491	C₄⋊C₄	—	4	2	no	—
492	C₄⋊C₄	—	4	2	no	—
493	C₄⋊C₄	—	8	1	no	—
494	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
495	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
496	C₄⋊C₄	C₂×Q₈×C₁₇	1	2	yes	—
497	C₂²⋊C₄	—	4	2	no	—
498	C₂²⋊C₄	—	4	2	no	—
499	C₂²⋊C₄	—	4	2	no	—
500	C₂²⋊C₄	—	4	2	no	—
501	C₂²⋊C₄	—	4	2	no	—
502	C₄²	—	2	1	no	—
503	C₄²	—	2	1	no	—
504	C₄²	—	2	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	4	2	no	—
507	C₄²	—	8	1	no	—
508	C₄²	—	8	1	no	—
509	C₄²	C₂×D₄×C₁₇	1	2	yes	—
510	C₄²	#41×C₁₇	1	2	yes	—
511	C₂³	—	2	2	no	—
512	C₂³	—	4	1	no	—
513	C₂³	—	4	1	no	—
514	C₂³	—	4	1	no	—
515	C₂³	—	4	1	no	—
516	C₂³	—	4	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
519	Q₈	—	8	4	no	—
520	D₄	—	2	2	no	—
521	D₄	—	2	2	no	—
522	D₄	—	4	1	no	—
523	D₄	—	4	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	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	2	2	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	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	4	1	no	—
544	C₂×C₄	—	4	1	no	—
545	C₂×C₄	—	4	1	no	—
546	C₂×C₄	—	4	1	no	—
547	C₂×C₄	—	4	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	1	no	—
555	C₂×C₄	—	4	1	no	—
556	C₂×C₄	—	4	1	no	—
557	C₂×C₄	—	4	1	no	—
558	C₂×C₄	—	4	1	no	—
559	C₂×C₄	—	8	4	no	—
560	C₂×C₄	C₁₇×#121	1	2	yes	—
561	C₂×C₄	C₁₇×#121	1	2	yes	—
562	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
563	C₂×C₄	C₁₇×AGL(1,ℤ/8)	1	2	yes	—
564	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
565	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
566	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
567	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
568	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
569	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	2	2	no	—
572	C₈	—	4	1	no	—
573	C₈	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	8	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
582	C₂²	C₁₇×#547	1	1	yes	characteristic
583	C₂²	D₄×Q₈×C₁₇	1	1	yes	characteristic
584	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
585	C₂²	C₂×C₁₇×AGL(1,ℤ/8)	1	1	yes	characteristic
586	C₂²	C₁₇×#577	1	1	yes	characteristic
587	C₂²	C₁₇×#578	1	1	yes	characteristic
588	C₄	—	2	2	no	—
589	C₄	—	2	2	no	—
590	C₄	—	2	2	no	—
591	C₄	—	2	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	4	1	no	—
595	C₄	—	4	1	no	—
596	C₄	—	4	2	no	—
597	C₄	—	8	1	no	—
598	C₄	—	8	1	no	—
599	C₄	—	8	1	no	—
600	C₄	—	8	1	no	—
601	C₄	C₁₇×#533	1	1	yes	characteristic
602	C₄	C₁₇×#541	1	1	yes	characteristic
603	C₄	C₁₇×#548	1	1	yes	characteristic
604	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
605	C₂	—	8	2	no	—
606	C₂	C₁₇×#2429	1	1	yes	characteristic
607	C₂	C₁₇×#3038	1	1	yes	characteristic
608	C₂	C₁₇×#3046	1	1	yes	characteristic
609	C₂	C₁₇×#3343	1	1	yes	characteristic
610	C₂	C₁₇×#3345	1	1	yes	characteristic
611	C₂	C₁₇×#3384	1	1	yes	characteristic
612	C₂	C₁₇×#3386	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₁₇×#501	C₂	semidirect
4. C₁₇×#2370	C₂	semidirect
5. C₁₇×#2084	C₂	semidirect
6. C₁₇×#2083	C₂	semidirect
9. C₁₇×#1987	C₂	semidirect
10. C₁₇×#1948	C₂	semidirect
11. C₁₇×#1947	C₂	semidirect
12. C₁₇×#1940	C₂	semidirect
117. C₁₇×#102	Q₈	semidirect
204. #25465	C₁₇	direct (N × H)
268. C₂×#501	C₂×C₁₇	semidirect
271. #2370	C₂×C₁₇	semidirect
272. #2084	C₂×C₁₇	semidirect
273. #2083	C₂×C₁₇	semidirect
276. #1987	C₂×C₁₇	semidirect
277. #1948	C₂×C₁₇	semidirect
278. #1947	C₂×C₁₇	semidirect
279. #1940	C₂×C₁₇	semidirect
423. #102	Q₈×C₁₇	semidirect
432. C₁₇	#25465	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×#501	2
C₂×C₁₇×#478	2
C₁₇×#2542	2
C₁₇×#2370	2
C₁₇×#2084	2
C₁₇×#2083	2
C₁₇×#2067	2
C₁₇×#2065	2
C₁₇×#1987	2
C₁₇×#1948	2
C₁₇×#1947	2
C₁₇×#1940	2
C₁₇×#1926	2
C₁₇×#1925	2
C₁₇×#1762	2
#25465	17

Subgroups — C17×#25465 #16883209

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25465 #16883209