Subgroups — C₁₇×#25493 #16883237

Order 4352.

648 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3166	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3077	C₂	1	1	yes	maximal, characteristic
3	C₂×C₁₇×#478	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2962	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#2090	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#2089	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#2063	C₂	1	1	yes	maximal, characteristic
8	C₁₇×#2063	C₂	1	1	yes	maximal, characteristic
9	C₁₇×#1998	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1952	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1951	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1931	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#1931	C₂	1	1	yes	maximal, characteristic
15	C₄×C₁₇×#100	C₂	1	1	yes	maximal, characteristic
16	C₁₇×#533	C₂²	1	1	yes	characteristic
17	C₂×C₁₇×#125	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#501	—	2	1	no	—
20	C₁₇×#501	—	2	1	no	—
21	C₁₇×#499	—	2	1	no	—
22	C₁₇×#499	—	2	1	no	—
23	C₁₇×#478	—	2	1	no	—
24	C₁₇×#478	—	2	1	no	—
25	C₁₇×#478	—	2	1	no	—
26	C₁₇×#478	—	2	1	no	—
27	C₁₇×#478	—	2	1	no	—
28	C₁₇×#478	—	2	1	no	—
29	C₁₇×#476	—	2	1	no	—
30	C₁₇×#474	—	2	1	no	—
31	C₁₇×#446	—	2	1	no	—
32	C₁₇×#446	—	2	1	no	—
33	C₁₇×#446	—	2	1	no	—
34	C₈×Q₈×C₁₇	—	2	1	no	—
35	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
36	C₂×C₁₇×#108	C₂²	1	1	yes	characteristic
37	C₁₇×#428	C₂²	1	1	yes	characteristic
38	C₁₇×#428	C₂²	1	1	yes	characteristic
39	C₁₇×#428	C₂²	1	1	yes	characteristic
40	C₁₇×#428	C₂²	1	1	yes	characteristic
41	C₁₇×#428	C₂²	1	1	yes	characteristic
42	C₁₇×#428	C₂²	1	1	yes	characteristic
43	C₂×C₁₇×#107	C₂²	1	1	yes	characteristic
44	C₂×C₁₇×#106	C₂²	1	1	yes	characteristic
45	C₁₇×#424	C₂²	1	1	yes	characteristic
46	C₁₇×#424	C₂²	1	1	yes	characteristic
47	C₁₇×#423	C₂²	1	1	yes	characteristic
48	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
49	C₁₇×#418	C₂²	1	1	yes	characteristic
50	C₁₇×#418	C₂²	1	1	yes	characteristic
51	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
52	C₂×C₁₇×#102	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
54	C₂×C₁₇×#100	C₂²	1	1	yes	characteristic
55	C₁₇×#405	C₂²	1	1	yes	characteristic
56	C₁₇×#405	C₂²	1	1	yes	characteristic
57	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
58	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
59	C₁₇×#343	C₂²	1	1	yes	characteristic
60	C₁₇×#343	C₂²	1	1	yes	characteristic
61	C₁₇×#343	C₂²	1	1	yes	characteristic
62	C₁₇×#343	C₂²	1	1	yes	characteristic
63	C₁₇×#343	C₂²	1	1	yes	characteristic
64	C₁₇×#343	C₂²	1	1	yes	characteristic
65	C₁₇×#341	C₂²	1	1	yes	characteristic
66	C₁₇×#341	C₂²	1	1	yes	characteristic
67	C₂²×D₄×C₁₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₁₇	—	2	1	no	—
69	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
70	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
71	C₂×M₁₆×C₁₇	C₂³	1	1	yes	characteristic
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	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
76	C₂²×C₈×C₁₇	C₂³	1	1	yes	characteristic
77	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
78	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
79	C₁₇×#125	—	2	1	no	—
80	C₁₇×#125	—	2	1	no	—
81	C₁₇×#125	—	2	1	no	—
82	C₁₇×#125	—	2	1	no	—
83	C₁₇×#125	D₄	1	1	yes	characteristic
84	C₁₇×#125	D₄	1	1	yes	characteristic
85	C₁₇×C₂²⋊Q₈	—	2	1	no	—
86	C₁₇×C₂²⋊Q₈	—	2	1	no	—
87	C₄×Q₈×C₁₇	—	2	1	no	—
88	C₄×Q₈×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	C₁₇×#117	C₂³	1	1	yes	characteristic
94	C₁₇×#117	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
98	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
99	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
100	C₂×C₂²⋊C₄×C₁₇	—	2	1	no	—
101	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
102	C₁₇×#108	—	2	2	no	—
103	C₁₇×#108	—	2	2	no	—
104	C₁₇×#107	—	2	1	no	—
105	C₁₇×#107	—	2	1	no	—
106	C₁₇×#107	—	2	1	no	—
107	C₁₇×#107	—	2	1	no	—
108	C₁₇×#107	—	2	1	no	—
109	C₁₇×#107	—	2	1	no	—
110	C₁₇×#107	—	2	1	no	—
111	C₁₇×#107	—	2	1	no	—
112	C₁₇×#106	—	2	1	no	—
113	C₁₇×#106	—	2	1	no	—
114	C₁₇×#106	—	2	1	no	—
115	C₁₇×#106	—	2	1	no	—
116	C₁₇×#106	—	2	1	no	—
117	C₁₇×#106	—	2	1	no	—
118	C₁₇×#106	—	2	1	no	—
119	C₁₇×#106	—	2	1	no	—
120	C₁₇×C₄⋊C₈	—	2	1	no	—
121	C₁₇×C₄⋊C₈	—	2	1	no	—
122	C₁₇×C₄⋊C₈	—	2	1	no	—
123	C₁₇×C₄⋊C₈	—	2	1	no	—
124	C₁₇×C₄⋊C₈	—	2	1	no	—
125	C₁₇×C₄⋊C₈	—	2	1	no	—
126	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
127	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
128	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
129	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
130	C₁₇×#102	—	2	1	no	—
131	C₁₇×#102	—	2	1	no	—
132	C₁₇×#102	—	2	1	no	—
133	C₁₇×#102	—	2	1	no	—
134	C₁₇×#102	—	2	1	no	—
135	C₁₇×#102	—	2	1	no	—
136	C₁₇×#102	—	2	1	no	—
137	C₁₇×#102	—	2	1	no	—
138	C₁₇×#100	—	2	2	no	—
139	C₁₇×#100	Q₈	1	4	yes	complemented
140	C₁₇×#97	—	2	1	no	—
141	C₁₇×#97	—	2	1	no	—
142	C₁₇×#97	—	2	1	no	—
143	C₁₇×#97	—	2	1	no	—
144	C₄×C₈×C₁₇	—	2	1	no	—
145	C₄×C₈×C₁₇	—	2	1	no	—
146	C₄×C₈×C₁₇	—	2	1	no	—
147	C₄×C₈×C₁₇	—	2	1	no	—
148	C₂⁴×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	—	2	1	no	—
151	C₂×D₄×C₁₇	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
157	C₂²×C₄×C₁₇	—	2	1	no	—
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	2	1	no	—
160	C₂²×C₄×C₁₇	—	4	1	no	—
161	C₂²×C₄×C₁₇	—	4	1	no	—
162	C₂²×C₄×C₁₇	—	8	2	no	—
163	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
164	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
165	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
166	M₁₆×C₁₇	—	2	1	no	—
167	M₁₆×C₁₇	—	2	1	no	—
168	M₁₆×C₁₇	—	2	1	no	—
169	M₁₆×C₁₇	—	2	1	no	—
170	M₁₆×C₁₇	—	2	1	no	—
171	M₁₆×C₁₇	—	2	1	no	—
172	M₁₆×C₁₇	—	2	1	no	—
173	M₁₆×C₁₇	—	2	1	no	—
174	M₁₆×C₁₇	—	2	1	no	—
175	M₁₆×C₁₇	C₂×Q₈	1	2	yes	—
176	M₁₆×C₁₇	C₂×Q₈	1	2	yes	—
177	M₁₆×C₁₇	#41	1	2	yes	—
178	C₂×C₈×C₁₇	—	2	1	no	—
179	C₂×C₈×C₁₇	—	2	1	no	—
180	C₂×C₈×C₁₇	—	2	1	no	—
181	C₂×C₈×C₁₇	—	2	1	no	—
182	C₂×C₈×C₁₇	—	2	1	no	—
183	C₂×C₈×C₁₇	—	2	1	no	—
184	C₂×C₈×C₁₇	—	2	1	no	—
185	C₂×C₈×C₁₇	—	2	1	no	—
186	C₂×C₈×C₁₇	—	2	1	no	—
187	C₂×C₈×C₁₇	—	2	1	no	—
188	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
189	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
190	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
191	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	—	2	1	no	—
193	C₄⋊C₄×C₁₇	—	2	1	no	—
194	C₄⋊C₄×C₁₇	—	2	1	no	—
195	C₄⋊C₄×C₁₇	—	2	1	no	—
196	C₄⋊C₄×C₁₇	—	2	1	no	—
197	C₄⋊C₄×C₁₇	—	2	1	no	—
198	C₄⋊C₄×C₁₇	—	2	1	no	—
199	C₄⋊C₄×C₁₇	—	2	1	no	—
200	C₄⋊C₄×C₁₇	—	2	1	no	—
201	C₄⋊C₄×C₁₇	—	2	1	no	—
202	C₄⋊C₄×C₁₇	—	2	1	no	—
203	C₄⋊C₄×C₁₇	—	2	1	no	—
204	C₄⋊C₄×C₁₇	—	4	1	no	—
205	C₄⋊C₄×C₁₇	—	4	1	no	—
206	C₄⋊C₄×C₁₇	—	4	1	no	—
207	C₄⋊C₄×C₁₇	—	4	1	no	—
208	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
209	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
211	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
212	C₂²⋊C₄×C₁₇	—	2	1	no	—
213	C₂²⋊C₄×C₁₇	—	2	1	no	—
214	C₂²⋊C₄×C₁₇	—	4	1	no	—
215	C₂²⋊C₄×C₁₇	—	4	1	no	—
216	C₄²×C₁₇	—	2	1	no	—
217	C₄²×C₁₇	—	2	1	no	—
218	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
219	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
220	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
221	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
222	#25493	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
223	C₂³×C₁₇	—	2	2	no	—
224	C₂³×C₁₇	—	4	1	no	—
225	C₂³×C₁₇	—	4	1	no	—
226	C₂³×C₁₇	—	8	1	no	—
227	C₂³×C₁₇	—	8	1	no	—
228	C₂³×C₁₇	C₂×#41	1	1	yes	characteristic
229	Q₈×C₁₇	—	4	2	no	—
230	Q₈×C₁₇	—	8	1	no	—
231	D₄×C₁₇	—	2	2	no	—
232	D₄×C₁₇	—	2	2	no	—
233	D₄×C₁₇	—	4	1	no	—
234	D₄×C₁₇	—	4	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	—	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	—	8	2	no	—
245	C₂×C₄×C₁₇	—	8	2	no	—
246	C₂×C₄×C₁₇	—	8	1	no	—
247	C₂×C₄×C₁₇	—	8	1	no	—
248	C₂×C₄×C₁₇	—	8	1	no	—
249	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
250	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
251	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
252	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
253	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₂²×Q₈	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
257	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
258	C₂×C₄×C₁₇	2₋¹⁺⁴	1	1	yes	characteristic
259	C₈×C₁₇	—	2	1	no	—
260	C₈×C₁₇	—	2	1	no	—
261	C₈×C₁₇	—	2	1	no	—
262	C₈×C₁₇	—	2	1	no	—
263	C₈×C₁₇	—	2	2	no	—
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	C₈×C₁₇	—	4	1	no	—
269	#3166	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#3077	C₂×C₁₇	1	1	yes	characteristic
271	C₂×#478	C₂×C₁₇	1	1	yes	characteristic
272	#2962	C₂×C₁₇	1	1	yes	characteristic, complemented
273	#2090	C₂×C₁₇	1	1	yes	characteristic, complemented
274	#2089	C₂×C₁₇	1	1	yes	characteristic, complemented
275	#2063	C₂×C₁₇	1	1	yes	characteristic
276	#2063	C₂×C₁₇	1	1	yes	characteristic
277	#1998	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1952	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#1951	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#1950	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#1931	C₂×C₁₇	1	1	yes	characteristic
282	#1931	C₂×C₁₇	1	1	yes	characteristic
283	C₄×#100	C₂×C₁₇	1	1	yes	characteristic
284	C₂²×C₁₇	—	2	1	no	—
285	C₂²×C₁₇	—	2	1	no	—
286	C₂²×C₁₇	—	4	2	no	—
287	C₂²×C₁₇	—	8	2	no	—
288	C₂²×C₁₇	—	8	2	no	—
289	C₂²×C₁₇	—	8	1	no	—
290	C₂²×C₁₇	—	8	1	no	—
291	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
292	C₂²×C₁₇	#533	1	1	yes	characteristic
293	C₂²×C₁₇	#541	1	1	yes	characteristic
294	C₄×C₁₇	—	2	1	no	—
295	C₄×C₁₇	—	2	1	no	—
296	C₄×C₁₇	—	2	1	no	—
297	C₄×C₁₇	—	2	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	—	8	1	no	—
303	C₄×C₁₇	—	8	1	no	—
304	C₄×C₁₇	—	8	1	no	—
305	C₄×C₁₇	#547	1	1	yes	characteristic
306	C₄×C₁₇	#548	1	1	yes	characteristic
307	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
308	C₄×C₁₇	D₄×Q₈	1	1	yes	characteristic
309	#533	C₂²×C₁₇	1	1	yes	characteristic
310	C₂×#125	C₂²×C₁₇	1	1	yes	characteristic
311	C₂×C₄×D₄	C₂²×C₁₇	1	1	yes	characteristic
312	#501	—	2	1	no	—
313	#501	—	2	1	no	—
314	#499	—	2	1	no	—
315	#499	—	2	1	no	—
316	#478	—	2	1	no	—
317	#478	—	2	1	no	—
318	#478	—	2	1	no	—
319	#478	—	2	1	no	—
320	#478	—	2	1	no	—
321	#478	—	2	1	no	—
322	#476	—	2	1	no	—
323	#474	—	2	1	no	—
324	#446	—	2	1	no	—
325	#446	—	2	1	no	—
326	#446	—	2	1	no	—
327	C₈×Q₈	—	2	1	no	—
328	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
329	C₂×#108	C₂²×C₁₇	1	1	yes	characteristic
330	#428	C₂²×C₁₇	1	1	yes	characteristic
331	#428	C₂²×C₁₇	1	1	yes	characteristic
332	#428	C₂²×C₁₇	1	1	yes	characteristic
333	#428	C₂²×C₁₇	1	1	yes	characteristic
334	#428	C₂²×C₁₇	1	1	yes	characteristic
335	#428	C₂²×C₁₇	1	1	yes	characteristic
336	C₂×#107	C₂²×C₁₇	1	1	yes	characteristic
337	C₂×#106	C₂²×C₁₇	1	1	yes	characteristic
338	#424	C₂²×C₁₇	1	1	yes	characteristic
339	#424	C₂²×C₁₇	1	1	yes	characteristic
340	#423	C₂²×C₁₇	1	1	yes	characteristic
341	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
342	#418	C₂²×C₁₇	1	1	yes	characteristic
343	#418	C₂²×C₁₇	1	1	yes	characteristic
344	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
345	C₂×#102	C₂²×C₁₇	1	1	yes	characteristic
346	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
347	C₂×#100	C₂²×C₁₇	1	1	yes	characteristic
348	#405	C₂²×C₁₇	1	1	yes	characteristic
349	#405	C₂²×C₁₇	1	1	yes	characteristic
350	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
351	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
352	#343	C₂²×C₁₇	1	1	yes	characteristic
353	#343	C₂²×C₁₇	1	1	yes	characteristic
354	#343	C₂²×C₁₇	1	1	yes	characteristic
355	#343	C₂²×C₁₇	1	1	yes	characteristic
356	#343	C₂²×C₁₇	1	1	yes	characteristic
357	#343	C₂²×C₁₇	1	1	yes	characteristic
358	#341	C₂²×C₁₇	1	1	yes	characteristic
359	#341	C₂²×C₁₇	1	1	yes	characteristic
360	C₂×C₁₇	—	2	1	no	—
361	C₂×C₁₇	—	2	1	no	—
362	C₂×C₁₇	—	8	2	no	—
363	C₂×C₁₇	#2429	1	1	yes	characteristic
364	C₂×C₁₇	#3067	1	1	yes	characteristic
365	C₂×C₁₇	#3068	1	1	yes	characteristic
366	C₂²×D₄	C₂³×C₁₇	1	1	yes	characteristic
367	C₂³×C₄	—	2	1	no	—
368	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
369	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
370	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
371	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
372	C₂×M₁₆	C₂³×C₁₇	1	1	yes	characteristic
373	C₂×M₁₆	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	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
377	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
378	#125	—	2	1	no	—
379	#125	—	2	1	no	—
380	#125	—	2	1	no	—
381	#125	—	2	1	no	—
382	#125	D₄×C₁₇	1	1	yes	characteristic
383	#125	D₄×C₁₇	1	1	yes	characteristic
384	C₂²⋊Q₈	—	2	1	no	—
385	C₂²⋊Q₈	—	2	1	no	—
386	C₄×Q₈	—	2	1	no	—
387	C₄×Q₈	—	2	1	no	—
388	C₄×D₄	—	2	1	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	#117	C₂³×C₁₇	1	1	yes	characteristic
393	#117	C₂³×C₁₇	1	1	yes	characteristic
394	C₂×C₄⋊C₄	—	2	1	no	—
395	C₂×C₄⋊C₄	—	2	1	no	—
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×C₂²⋊C₄	—	2	1	no	—
400	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
401	#108	—	2	2	no	—
402	#108	—	2	2	no	—
403	#107	—	2	1	no	—
404	#107	—	2	1	no	—
405	#107	—	2	1	no	—
406	#107	—	2	1	no	—
407	#107	—	2	1	no	—
408	#107	—	2	1	no	—
409	#107	—	2	1	no	—
410	#107	—	2	1	no	—
411	#106	—	2	1	no	—
412	#106	—	2	1	no	—
413	#106	—	2	1	no	—
414	#106	—	2	1	no	—
415	#106	—	2	1	no	—
416	#106	—	2	1	no	—
417	#106	—	2	1	no	—
418	#106	—	2	1	no	—
419	C₄⋊C₈	—	2	1	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	—	2	1	no	—
423	C₄⋊C₈	—	2	1	no	—
424	C₄⋊C₈	—	2	1	no	—
425	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
426	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
427	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
428	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
429	#102	—	2	1	no	—
430	#102	—	2	1	no	—
431	#102	—	2	1	no	—
432	#102	—	2	1	no	—
433	#102	—	2	1	no	—
434	#102	—	2	1	no	—
435	#102	—	2	1	no	—
436	#102	—	2	1	no	—
437	#100	—	2	2	no	—
438	#100	Q₈×C₁₇	1	4	yes	complemented
439	#97	—	2	1	no	—
440	#97	—	2	1	no	—
441	#97	—	2	1	no	—
442	#97	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	—	2	1	no	—
445	C₄×C₈	—	2	1	no	—
446	C₄×C₈	—	2	1	no	—
447	C₁₇	#25493	1	1	yes	characteristic, direct product factor, Sylow
448	C₂⁴	—	2	1	no	—
449	C₂×Q₈	—	2	1	no	—
450	C₂×Q₈	—	2	1	no	—
451	C₂×D₄	—	2	1	no	—
452	C₂×D₄	—	2	1	no	—
453	C₂×D₄	—	2	1	no	—
454	C₂×D₄	—	2	1	no	—
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	C₂×Q₈×C₁₇	1	2	yes	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	4	1	no	—
461	C₂²×C₄	—	4	1	no	—
462	C₂²×C₄	—	8	2	no	—
463	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
464	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
465	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
466	M₁₆	—	2	1	no	—
467	M₁₆	—	2	1	no	—
468	M₁₆	—	2	1	no	—
469	M₁₆	—	2	1	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	2	1	no	—
472	M₁₆	—	2	1	no	—
473	M₁₆	—	2	1	no	—
474	M₁₆	—	2	1	no	—
475	M₁₆	C₂×Q₈×C₁₇	1	2	yes	—
476	M₁₆	C₂×Q₈×C₁₇	1	2	yes	—
477	M₁₆	#41×C₁₇	1	2	yes	—
478	C₂×C₈	—	2	1	no	—
479	C₂×C₈	—	2	1	no	—
480	C₂×C₈	—	2	1	no	—
481	C₂×C₈	—	2	1	no	—
482	C₂×C₈	—	2	1	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
489	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
490	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	1	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	—	2	1	no	—
498	C₄⋊C₄	—	2	1	no	—
499	C₄⋊C₄	—	2	1	no	—
500	C₄⋊C₄	—	2	1	no	—
501	C₄⋊C₄	—	2	1	no	—
502	C₄⋊C₄	—	2	1	no	—
503	C₄⋊C₄	—	2	1	no	—
504	C₄⋊C₄	—	4	1	no	—
505	C₄⋊C₄	—	4	1	no	—
506	C₄⋊C₄	—	4	1	no	—
507	C₄⋊C₄	—	4	1	no	—
508	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
509	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
510	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
511	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
512	C₂²⋊C₄	—	2	1	no	—
513	C₂²⋊C₄	—	2	1	no	—
514	C₂²⋊C₄	—	4	1	no	—
515	C₂²⋊C₄	—	4	1	no	—
516	C₄²	—	2	1	no	—
517	C₄²	—	2	1	no	—
518	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
519	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
520	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
521	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
522	C₂³	—	2	2	no	—
523	C₂³	—	4	1	no	—
524	C₂³	—	4	1	no	—
525	C₂³	—	8	1	no	—
526	C₂³	—	8	1	no	—
527	C₂³	C₂×#41×C₁₇	1	1	yes	characteristic
528	Q₈	—	4	2	no	—
529	Q₈	—	8	1	no	—
530	D₄	—	2	2	no	—
531	D₄	—	2	2	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	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	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	4	1	no	—
541	C₂×C₄	—	4	1	no	—
542	C₂×C₄	—	4	1	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	2	no	—
545	C₂×C₄	—	8	1	no	—
546	C₂×C₄	—	8	1	no	—
547	C₂×C₄	—	8	1	no	—
548	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
549	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
550	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
551	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
552	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
553	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
554	C₂×C₄	C₂²×Q₈×C₁₇	1	1	yes	characteristic
555	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
556	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
557	C₂×C₄	C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
558	C₈	—	2	1	no	—
559	C₈	—	2	1	no	—
560	C₈	—	2	1	no	—
561	C₈	—	2	1	no	—
562	C₈	—	2	2	no	—
563	C₈	—	2	2	no	—
564	C₈	—	2	2	no	—
565	C₈	—	4	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₂²	—	2	1	no	—
569	C₂²	—	2	1	no	—
570	C₂²	—	4	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	8	2	no	—
573	C₂²	—	8	1	no	—
574	C₂²	—	8	1	no	—
575	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
576	C₂²	C₁₇×#533	1	1	yes	characteristic
577	C₂²	C₁₇×#541	1	1	yes	characteristic
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	1	no	—
581	C₄	—	2	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	1	no	—
585	C₄	—	4	1	no	—
586	C₄	—	8	1	no	—
587	C₄	—	8	1	no	—
588	C₄	—	8	1	no	—
589	C₄	C₁₇×#547	1	1	yes	characteristic
590	C₄	C₁₇×#548	1	1	yes	characteristic
591	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
592	C₄	D₄×Q₈×C₁₇	1	1	yes	characteristic
593	C₂	—	2	1	no	—
594	C₂	—	2	1	no	—
595	C₂	—	8	2	no	—
596	C₂	C₁₇×#2429	1	1	yes	characteristic
597	C₂	C₁₇×#3067	1	1	yes	characteristic
598	C₂	C₁₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₇
prime radical	C₂²×D₄×C₁₇	C₂³
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×#3166	C₂	semidirect
4. C₁₇×#2962	C₂	semidirect
5. C₁₇×#2090	C₂	semidirect
6. C₁₇×#2089	C₂	semidirect
9. C₁₇×#1998	C₂	semidirect
10. C₁₇×#1952	C₂	semidirect
11. C₁₇×#1951	C₂	semidirect
12. C₁₇×#1950	C₂	semidirect
139. C₁₇×#100	Q₈	semidirect
222. #25493	C₁₇	direct (N × H)
269. #3166	C₂×C₁₇	semidirect
272. #2962	C₂×C₁₇	semidirect
273. #2090	C₂×C₁₇	semidirect
274. #2089	C₂×C₁₇	semidirect
277. #1998	C₂×C₁₇	semidirect
278. #1952	C₂×C₁₇	semidirect
279. #1951	C₂×C₁₇	semidirect
280. #1950	C₂×C₁₇	semidirect
438. #100	Q₈×C₁₇	semidirect
447. C₁₇	#25493	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×#3166	2
C₁₇×#3077	2
C₂×C₁₇×#478	2
C₁₇×#2962	2
C₁₇×#2090	2
C₁₇×#2089	2
C₁₇×#2063	2
C₁₇×#1998	2
C₁₇×#1952	2
C₁₇×#1951	2
C₁₇×#1950	2
C₁₇×#1931	2
C₄×C₁₇×#100	2
#25493	17

Subgroups — C17×#25493 #16883237

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#25493 #16883237