Subgroups — C₁₇×#25405 #16883149

Order 4352.

916 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3152	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₁₇×#471	C₂	1	2	yes	maximal, complemented
3	C₁₇×#3036	C₂	1	1	yes	maximal, characteristic
4	C₂×C₁₇×#461	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2935	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2052	C₂	1	2	yes	maximal, complemented
7	C₁₇×#2019	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1966	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1908	C₂	1	2	yes	maximal, complemented
11	C₄×C₁₇×#100	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×#137	C₂²	1	2	yes	—
13	C₂×C₁₇×#137	C₂²	1	2	yes	—
14	C₂×C₁₇×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₂²×SD₁₆×C₁₇	C₂²	1	2	yes	—
16	C₂×C₁₇×#131	C₂²	1	2	yes	—
17	C₁₇×#532	C₂²	1	1	yes	characteristic
18	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
20	C₁₇×#497	—	2	2	no	—
21	C₁₇×#494	—	2	1	no	—
22	C₁₇×#492	—	2	1	no	—
23	C₁₇×#471	—	2	8	no	—
24	C₁₇×#463	—	2	2	no	—
25	C₁₇×#461	—	2	1	no	—
26	C₁₇×#461	—	2	2	no	—
27	C₁₇×#461	—	2	1	no	—
28	C₁₇×#461	—	2	1	no	—
29	C₁₇×#459	—	2	1	no	—
30	C₁₇×#436	—	2	1	no	—
31	C₁₇×#435	—	2	2	no	—
32	C₈×D₄×C₁₇	—	2	1	no	—
33	C₂×C₁₇×#108	C₂²	1	2	yes	—
34	C₁₇×#423	C₂²	1	1	yes	characteristic
35	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₁₇×#417	C₂²	1	2	yes	—
37	C₂×C₁₇×#103	C₂²	1	2	yes	—
38	C₂×C₁₇×#101	C₂²	1	2	yes	—
39	C₂×C₁₇×#101	C₂²	1	2	yes	—
40	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
41	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
42	C₁₇×#408	C₂²	1	2	yes	—
43	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
44	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
45	C₁₇×#343	C₂²	1	1	yes	characteristic
46	C₁₇×#343	C₂²	1	1	yes	characteristic
47	C₁₇×#341	C₂²	1	2	yes	—
48	C₂×#41×C₁₇	C₂³	1	2	yes	—
49	C₂²×Q₈×C₁₇	C₂³	1	2	yes	—
50	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₁₇	—	2	1	no	—
52	C₁₇×#137	—	2	4	no	—
53	C₁₇×#137	—	2	4	no	—
54	C₁₇×#137	—	4	2	no	—
55	C₁₇×#137	—	4	2	no	—
56	C₁₇×AGL(1,ℤ/8)	—	2	4	no	—
57	C₁₇×AGL(1,ℤ/8)	—	4	2	no	—
58	C₂×Q₁₆×C₁₇	—	2	2	no	—
59	C₂×Q₁₆×C₁₇	—	2	2	no	—
60	C₂×SD₁₆×C₁₇	—	2	2	no	—
61	C₂×SD₁₆×C₁₇	—	2	2	no	—
62	C₂×SD₁₆×C₁₇	—	2	2	no	—
63	C₂×SD₁₆×C₁₇	—	2	4	no	—
64	C₂×SD₁₆×C₁₇	—	2	2	no	—
65	C₂×SD₁₆×C₁₇	—	2	2	no	—
66	C₂×SD₁₆×C₁₇	—	4	2	no	—
67	C₂×D₈×C₁₇	—	2	2	no	—
68	C₁₇×#131	—	2	4	no	—
69	C₁₇×#131	—	4	2	no	—
70	C₂×M₁₆×C₁₇	—	2	2	no	—
71	C₂×M₁₆×C₁₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
73	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
75	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₇	—	2	2	no	—
77	C₂²×C₈×C₁₇	C₂³	1	2	yes	—
78	C₁₇×C₄⋊Q₈	—	2	1	no	—
79	C₁₇×C₄⋊Q₈	—	2	1	no	—
80	C₁₇×C₄⋊Q₈	—	2	1	no	—
81	C₁₇×C₄⋊Q₈	—	2	1	no	—
82	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
83	C₁₇×#127	D₄	1	1	yes	characteristic
84	C₁₇×#124	D₄	1	2	yes	—
85	C₁₇×#121	—	2	1	no	—
86	C₁₇×#121	—	2	1	no	—
87	C₄×D₄×C₁₇	—	2	1	no	—
88	C₄×D₄×C₁₇	—	2	1	no	—
89	C₄×D₄×C₁₇	—	2	1	no	—
90	C₄×D₄×C₁₇	—	2	1	no	—
91	C₄×D₄×C₁₇	—	2	1	no	—
92	C₄×D₄×C₁₇	—	2	1	no	—
93	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
94	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
98	C₁₇×#108	—	2	4	no	—
99	C₁₇×C₄⋊C₈	—	2	1	no	—
100	C₁₇×C₄⋊C₈	—	2	1	no	—
101	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
102	C₁₇×C₄⋊C₈	D₄	1	2	yes	—
103	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
104	C₁₇×#103	—	2	2	no	—
105	C₁₇×#103	—	2	2	no	—
106	C₁₇×#103	—	2	2	no	—
107	C₁₇×#102	—	2	2	no	—
108	C₁₇×#101	—	2	4	no	—
109	C₁₇×#101	—	4	2	no	—
110	C₁₇×#100	—	2	2	no	—
111	C₁₇×#100	D₄	1	4	yes	complemented
112	C₁₇×C₂²⋊C₈	—	2	2	no	—
113	C₁₇×C₂²⋊C₈	—	2	2	no	—
114	C₁₇×#97	—	2	1	no	—
115	C₁₇×#97	—	2	1	no	—
116	C₄×C₈×C₁₇	—	2	1	no	—
117	C₄×C₈×C₁₇	—	2	1	no	—
118	C₂⁴×C₁₇	—	2	1	no	—
119	#41×C₁₇	—	2	2	no	—
120	#41×C₁₇	—	2	2	no	—
121	#41×C₁₇	—	2	2	no	—
122	#41×C₁₇	—	2	2	no	—
123	C₂×Q₈×C₁₇	—	2	2	no	—
124	C₂×Q₈×C₁₇	—	2	2	no	—
125	C₂×Q₈×C₁₇	—	2	2	no	—
126	C₂×Q₈×C₁₇	—	2	2	no	—
127	C₂×Q₈×C₁₇	—	2	2	no	—
128	C₂×Q₈×C₁₇	—	2	2	no	—
129	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
130	C₂×D₄×C₁₇	—	2	2	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	—	2	1	no	—
136	C₂×D₄×C₁₇	—	2	1	no	—
137	C₂×D₄×C₁₇	—	2	1	no	—
138	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
139	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₁₇	—	2	2	no	—
141	C₂²×C₄×C₁₇	—	2	2	no	—
142	C₂²×C₄×C₁₇	—	2	1	no	—
143	C₂²×C₄×C₁₇	—	4	1	no	—
144	C₂²×C₄×C₁₇	—	4	1	no	—
145	C₂²×C₄×C₁₇	—	8	2	no	—
146	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
148	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₁₇	—	4	4	no	—
150	Q₁₆×C₁₇	—	4	4	no	—
151	SD₁₆×C₁₇	—	4	4	no	—
152	SD₁₆×C₁₇	—	4	4	no	—
153	SD₁₆×C₁₇	—	4	4	no	—
154	SD₁₆×C₁₇	—	4	4	no	—
155	SD₁₆×C₁₇	—	4	4	no	—
156	D₈×C₁₇	—	4	4	no	—
157	M₁₆×C₁₇	—	2	1	no	—
158	M₁₆×C₁₇	—	2	1	no	—
159	M₁₆×C₁₇	—	2	1	no	—
160	M₁₆×C₁₇	—	2	2	no	—
161	M₁₆×C₁₇	—	2	1	no	—
162	M₁₆×C₁₇	—	2	2	no	—
163	M₁₆×C₁₇	—	2	1	no	—
164	M₁₆×C₁₇	—	4	4	no	—
165	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
166	M₁₆×C₁₇	C₂×D₄	1	2	yes	—
167	M₁₆×C₁₇	#41	1	2	yes	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	2	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	2	2	no	—
173	C₂×C₈×C₁₇	—	2	2	no	—
174	C₂×C₈×C₁₇	—	2	1	no	—
175	C₂×C₈×C₁₇	—	4	4	no	—
176	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
177	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
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	—	4	1	no	—
183	C₄⋊C₄×C₁₇	—	4	1	no	—
184	C₄⋊C₄×C₁₇	—	4	1	no	—
185	C₄⋊C₄×C₁₇	—	4	1	no	—
186	C₂²⋊C₄×C₁₇	—	2	2	no	—
187	C₂²⋊C₄×C₁₇	—	2	2	no	—
188	C₂²⋊C₄×C₁₇	—	4	1	no	—
189	C₂²⋊C₄×C₁₇	—	4	1	no	—
190	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
194	#25405	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂³×C₁₇	—	2	2	no	—
196	C₂³×C₁₇	—	2	2	no	—
197	C₂³×C₁₇	—	4	1	no	—
198	C₂³×C₁₇	—	4	1	no	—
199	C₂³×C₁₇	—	8	1	no	—
200	C₂³×C₁₇	—	8	1	no	—
201	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
202	Q₈×C₁₇	—	2	2	no	—
203	Q₈×C₁₇	—	2	2	no	—
204	Q₈×C₁₇	—	4	2	no	—
205	Q₈×C₁₇	—	4	2	no	—
206	Q₈×C₁₇	—	4	2	no	—
207	Q₈×C₁₇	—	4	2	no	—
208	D₄×C₁₇	—	2	2	no	—
209	D₄×C₁₇	—	2	2	no	—
210	D₄×C₁₇	—	2	2	no	—
211	D₄×C₁₇	—	2	2	no	—
212	D₄×C₁₇	—	4	2	no	—
213	D₄×C₁₇	—	4	2	no	—
214	D₄×C₁₇	—	4	1	no	—
215	D₄×C₁₇	—	4	1	no	—
216	D₄×C₁₇	—	4	2	no	—
217	D₄×C₁₇	—	8	1	no	—
218	C₂×C₄×C₁₇	—	2	2	no	—
219	C₂×C₄×C₁₇	—	2	2	no	—
220	C₂×C₄×C₁₇	—	4	1	no	—
221	C₂×C₄×C₁₇	—	4	2	no	—
222	C₂×C₄×C₁₇	—	4	2	no	—
223	C₂×C₄×C₁₇	—	4	1	no	—
224	C₂×C₄×C₁₇	—	4	2	no	—
225	C₂×C₄×C₁₇	—	4	2	no	—
226	C₂×C₄×C₁₇	—	4	2	no	—
227	C₂×C₄×C₁₇	—	8	2	no	—
228	C₂×C₄×C₁₇	—	8	2	no	—
229	C₂×C₄×C₁₇	—	8	1	no	—
230	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
231	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
232	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
233	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
234	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
235	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
236	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
238	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
240	C₈×C₁₇	—	2	2	no	—
241	C₈×C₁₇	—	2	2	no	—
242	C₈×C₁₇	—	2	2	no	—
243	C₈×C₁₇	—	2	2	no	—
244	C₈×C₁₇	—	2	2	no	—
245	C₈×C₁₇	—	4	2	no	—
246	C₈×C₁₇	—	4	1	no	—
247	#3152	C₂×C₁₇	1	1	yes	characteristic, complemented
248	C₂×#471	C₂×C₁₇	1	2	yes	complemented
249	#3036	C₂×C₁₇	1	1	yes	characteristic
250	C₂×#461	C₂×C₁₇	1	1	yes	characteristic, complemented
251	#2935	C₂×C₁₇	1	1	yes	characteristic, complemented
252	#2052	C₂×C₁₇	1	2	yes	complemented
253	#2019	C₂×C₁₇	1	2	yes	complemented
254	#1966	C₂×C₁₇	1	1	yes	characteristic, complemented
255	#1950	C₂×C₁₇	1	1	yes	characteristic, complemented
256	#1908	C₂×C₁₇	1	2	yes	complemented
257	C₄×#100	C₂×C₁₇	1	1	yes	characteristic, complemented
258	C₂²×C₁₇	—	2	1	no	—
259	C₂²×C₁₇	—	2	1	no	—
260	C₂²×C₁₇	—	4	2	no	—
261	C₂²×C₁₇	—	4	2	no	—
262	C₂²×C₁₇	—	4	2	no	—
263	C₂²×C₁₇	—	4	2	no	—
264	C₂²×C₁₇	—	8	2	no	—
265	C₂²×C₁₇	—	8	2	no	—
266	C₂²×C₁₇	—	8	1	no	—
267	C₂²×C₁₇	—	8	1	no	—
268	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
269	C₂²×C₁₇	#532	1	1	yes	characteristic
270	C₂²×C₁₇	#540	1	1	yes	characteristic
271	C₄×C₁₇	—	2	1	no	—
272	C₄×C₁₇	—	2	1	no	—
273	C₄×C₁₇	—	2	1	no	—
274	C₄×C₁₇	—	4	2	no	—
275	C₄×C₁₇	—	8	2	no	—
276	C₄×C₁₇	—	8	1	no	—
277	C₄×C₁₇	#471	1	2	yes	complemented
278	C₄×C₁₇	D₄²	1	1	yes	characteristic
279	C₄×C₁₇	D₄²	1	1	yes	characteristic
280	C₄×C₁₇	#546	1	1	yes	characteristic
281	C₄×C₁₇	#550	1	1	yes	characteristic
282	C₂×#137	C₂²×C₁₇	1	2	yes	—
283	C₂×#137	C₂²×C₁₇	1	2	yes	—
284	C₂×AGL(1,ℤ/8)	C₂²×C₁₇	1	2	yes	—
285	C₂²×SD₁₆	C₂²×C₁₇	1	2	yes	—
286	C₂×#131	C₂²×C₁₇	1	2	yes	—
287	#532	C₂²×C₁₇	1	1	yes	characteristic
288	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
289	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
290	#497	—	2	2	no	—
291	#494	—	2	1	no	—
292	#492	—	2	1	no	—
293	#471	—	2	8	no	—
294	#463	—	2	2	no	—
295	#461	—	2	1	no	—
296	#461	—	2	1	no	—
297	#461	—	2	2	no	—
298	#461	—	2	1	no	—
299	#459	—	2	1	no	—
300	#436	—	2	1	no	—
301	#435	—	2	2	no	—
302	C₈×D₄	—	2	1	no	—
303	C₂×#108	C₂²×C₁₇	1	2	yes	—
304	#423	C₂²×C₁₇	1	1	yes	characteristic
305	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
306	#417	C₂²×C₁₇	1	2	yes	—
307	C₂×#103	C₂²×C₁₇	1	2	yes	—
308	C₂×#101	C₂²×C₁₇	1	2	yes	—
309	C₂×#101	C₂²×C₁₇	1	2	yes	—
310	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
311	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
312	#408	C₂²×C₁₇	1	2	yes	—
313	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
314	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
315	#343	C₂²×C₁₇	1	1	yes	characteristic
316	#343	C₂²×C₁₇	1	1	yes	characteristic
317	#341	C₂²×C₁₇	1	2	yes	—
318	C₂×C₁₇	—	2	1	no	—
319	C₂×C₁₇	—	2	1	no	—
320	C₂×C₁₇	—	8	2	no	—
321	C₂×C₁₇	—	8	2	no	—
322	C₂×C₁₇	#2428	1	1	yes	characteristic
323	C₂×C₁₇	C₂×#471	1	1	yes	characteristic
324	C₂×C₁₇	#3069	1	1	yes	characteristic
325	C₂×#41	C₂³×C₁₇	1	2	yes	—
326	C₂²×Q₈	C₂³×C₁₇	1	2	yes	—
327	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
328	C₂³×C₄	—	2	1	no	—
329	#137	—	2	4	no	—
330	#137	—	2	4	no	—
331	#137	—	4	2	no	—
332	#137	—	4	2	no	—
333	AGL(1,ℤ/8)	—	2	4	no	—
334	AGL(1,ℤ/8)	—	4	2	no	—
335	C₂×Q₁₆	—	2	2	no	—
336	C₂×Q₁₆	—	2	2	no	—
337	C₂×SD₁₆	—	2	2	no	—
338	C₂×SD₁₆	—	2	4	no	—
339	C₂×SD₁₆	—	2	2	no	—
340	C₂×SD₁₆	—	2	2	no	—
341	C₂×SD₁₆	—	2	2	no	—
342	C₂×SD₁₆	—	2	2	no	—
343	C₂×SD₁₆	—	4	2	no	—
344	C₂×D₈	—	2	2	no	—
345	#131	—	2	4	no	—
346	#131	—	4	2	no	—
347	C₂×M₁₆	—	2	2	no	—
348	C₂×M₁₆	C₂³×C₁₇	1	2	yes	—
349	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
350	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
351	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
352	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
353	C₂²×C₈	—	2	2	no	—
354	C₂²×C₈	C₂³×C₁₇	1	2	yes	—
355	C₄⋊Q₈	—	2	1	no	—
356	C₄⋊Q₈	—	2	1	no	—
357	C₄⋊Q₈	—	2	1	no	—
358	C₄⋊Q₈	—	2	1	no	—
359	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
360	#127	D₄×C₁₇	1	1	yes	characteristic
361	#124	D₄×C₁₇	1	2	yes	—
362	#121	—	2	1	no	—
363	#121	—	2	1	no	—
364	C₄×D₄	—	2	1	no	—
365	C₄×D₄	—	2	1	no	—
366	C₄×D₄	—	2	1	no	—
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	—	2	1	no	—
370	C₂×C₄⋊C₄	—	2	1	no	—
371	C₂×C₄⋊C₄	—	2	1	no	—
372	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
373	C₂×C₂²⋊C₄	—	2	1	no	—
374	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
375	#108	—	2	4	no	—
376	C₄⋊C₈	—	2	1	no	—
377	C₄⋊C₈	—	2	1	no	—
378	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
379	C₄⋊C₈	D₄×C₁₇	1	2	yes	—
380	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
381	#103	—	2	2	no	—
382	#103	—	2	2	no	—
383	#103	—	2	2	no	—
384	#102	—	2	2	no	—
385	#101	—	2	4	no	—
386	#101	—	4	2	no	—
387	#100	—	2	2	no	—
388	#100	D₄×C₁₇	1	4	yes	complemented
389	C₂²⋊C₈	—	2	2	no	—
390	C₂²⋊C₈	—	2	2	no	—
391	#97	—	2	1	no	—
392	#97	—	2	1	no	—
393	C₄×C₈	—	2	1	no	—
394	C₄×C₈	—	2	1	no	—
395	C₁₇	#25405	1	1	yes	characteristic, direct product factor, Sylow
396	C₂⁴	—	2	1	no	—
397	#41	—	2	2	no	—
398	#41	—	2	2	no	—
399	#41	—	2	2	no	—
400	#41	—	2	2	no	—
401	C₂×Q₈	—	2	2	no	—
402	C₂×Q₈	—	2	2	no	—
403	C₂×Q₈	—	2	2	no	—
404	C₂×Q₈	—	2	2	no	—
405	C₂×Q₈	—	2	2	no	—
406	C₂×Q₈	—	2	2	no	—
407	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	2	1	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
417	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	1	no	—
421	C₂²×C₄	—	4	1	no	—
422	C₂²×C₄	—	4	1	no	—
423	C₂²×C₄	—	8	2	no	—
424	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
425	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
426	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
427	Q₁₆	—	4	4	no	—
428	Q₁₆	—	4	4	no	—
429	SD₁₆	—	4	4	no	—
430	SD₁₆	—	4	4	no	—
431	SD₁₆	—	4	4	no	—
432	SD₁₆	—	4	4	no	—
433	SD₁₆	—	4	4	no	—
434	D₈	—	4	4	no	—
435	M₁₆	—	2	1	no	—
436	M₁₆	—	2	1	no	—
437	M₁₆	—	2	1	no	—
438	M₁₆	—	2	2	no	—
439	M₁₆	—	2	1	no	—
440	M₁₆	—	2	1	no	—
441	M₁₆	—	2	2	no	—
442	M₁₆	—	4	4	no	—
443	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
444	M₁₆	C₂×D₄×C₁₇	1	2	yes	—
445	M₁₆	#41×C₁₇	1	2	yes	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	2	1	no	—
449	C₂×C₈	—	2	2	no	—
450	C₂×C₈	—	2	2	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	2	no	—
453	C₂×C₈	—	4	4	no	—
454	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
455	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
456	C₄⋊C₄	—	2	1	no	—
457	C₄⋊C₄	—	2	1	no	—
458	C₄⋊C₄	—	2	1	no	—
459	C₄⋊C₄	—	2	1	no	—
460	C₄⋊C₄	—	4	1	no	—
461	C₄⋊C₄	—	4	1	no	—
462	C₄⋊C₄	—	4	1	no	—
463	C₄⋊C₄	—	4	1	no	—
464	C₂²⋊C₄	—	2	2	no	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	4	1	no	—
467	C₂²⋊C₄	—	4	1	no	—
468	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
471	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
472	C₂³	—	2	2	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	4	1	no	—
476	C₂³	—	8	1	no	—
477	C₂³	—	8	1	no	—
478	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	2	no	—
483	Q₈	—	4	2	no	—
484	Q₈	—	4	2	no	—
485	D₄	—	2	2	no	—
486	D₄	—	2	2	no	—
487	D₄	—	2	2	no	—
488	D₄	—	2	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	2	no	—
491	D₄	—	4	1	no	—
492	D₄	—	4	1	no	—
493	D₄	—	4	2	no	—
494	D₄	—	8	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	4	1	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	1	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	8	2	no	—
505	C₂×C₄	—	8	2	no	—
506	C₂×C₄	—	8	1	no	—
507	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
508	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
509	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
510	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
511	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
512	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
513	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
514	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
515	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
516	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
517	C₈	—	2	2	no	—
518	C₈	—	2	2	no	—
519	C₈	—	2	2	no	—
520	C₈	—	2	2	no	—
521	C₈	—	2	2	no	—
522	C₈	—	4	2	no	—
523	C₈	—	4	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	8	2	no	—
531	C₂²	—	8	2	no	—
532	C₂²	—	8	1	no	—
533	C₂²	—	8	1	no	—
534	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
535	C₂²	C₁₇×#532	1	1	yes	characteristic
536	C₂²	C₁₇×#540	1	1	yes	characteristic
537	C₄	—	2	1	no	—
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	4	2	no	—
541	C₄	—	8	1	no	—
542	C₄	—	8	2	no	—
543	C₄	C₁₇×#471	1	2	yes	complemented
544	C₄	D₄²×C₁₇	1	1	yes	characteristic
545	C₄	D₄²×C₁₇	1	1	yes	characteristic
546	C₄	C₁₇×#546	1	1	yes	characteristic
547	C₄	C₁₇×#550	1	1	yes	characteristic
548	C₂	—	2	1	no	—
549	C₂	—	2	1	no	—
550	C₂	—	8	2	no	—
551	C₂	—	8	2	no	—
552	C₂	C₁₇×#2428	1	1	yes	characteristic
553	C₂	C₂×C₁₇×#471	1	1	yes	characteristic
554	C₂	C₁₇×#3069	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₁₇×#3036	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₂×C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3152	C₂	semidirect
2. C₂×C₁₇×#471	C₂	semidirect
4. C₂×C₁₇×#461	C₂	semidirect
5. C₁₇×#2935	C₂	semidirect
6. C₁₇×#2052	C₂	semidirect
7. C₁₇×#2019	C₂	semidirect
8. C₁₇×#1966	C₂	semidirect
9. C₁₇×#1950	C₂	semidirect
10. C₁₇×#1908	C₂	semidirect
11. C₄×C₁₇×#100	C₂	semidirect
111. C₁₇×#100	D₄	semidirect
194. #25405	C₁₇	direct (N × H)
247. #3152	C₂×C₁₇	semidirect
248. C₂×#471	C₂×C₁₇	semidirect
250. C₂×#461	C₂×C₁₇	semidirect
251. #2935	C₂×C₁₇	semidirect
252. #2052	C₂×C₁₇	semidirect
253. #2019	C₂×C₁₇	semidirect
254. #1966	C₂×C₁₇	semidirect
255. #1950	C₂×C₁₇	semidirect
256. #1908	C₂×C₁₇	semidirect
257. C₄×#100	C₂×C₁₇	semidirect
277. C₄×C₁₇	#471	semidirect
388. #100	D₄×C₁₇	semidirect
395. C₁₇	#25405	direct (N × H)
543. C₄	C₁₇×#471	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3152	2
C₂×C₁₇×#471	2
C₁₇×#3036	2
C₂×C₁₇×#461	2
C₁₇×#2935	2
C₁₇×#2052	2
C₁₇×#2019	2
C₁₇×#1966	2
C₁₇×#1950	2
C₁₇×#1908	2
C₄×C₁₇×#100	2
#25405	17

Subgroups — C17×#25405 #16883149

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25405 #16883149