Subgroups — C₁₇×#61854 #16919598

Order 4352.

1648 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3550	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3502	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3387	C₂	1	2	yes	maximal, complemented
4	C₁₇×#3386	C₂	1	4	yes	maximal, complemented
5	Q₈×Q₁₆×C₁₇	C₂	1	2	yes	maximal, complemented
6	C₁₇×#3377	C₂	1	4	yes	maximal, complemented
7	C₁₇×#3375	C₂	1	2	yes	maximal, complemented
8	C₁₇×#3365	C₂	1	2	yes	maximal, complemented
9	C₁₇×#3243	C₂	1	4	yes	maximal, complemented
10	C₁₇×#3237	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#3228	C₂	1	1	yes	maximal, characteristic
12	C₁₇×#3121	C₂	1	4	yes	maximal, complemented
13	C₁₇×#3112	C₂	1	1	yes	maximal, characteristic
14	C₁₇×#3104	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#563	—	2	2	no	—
17	C₁₇×#559	C₂²	1	2	yes	—
18	Q₈²×C₁₇	—	2	1	no	—
19	Q₈²×C₁₇	C₂²	1	2	yes	—
20	Q₈²×C₁₇	C₂²	1	2	yes	—
21	C₁₇×#557	—	2	1	no	—
22	C₁₇×#557	—	2	2	no	—
23	C₁₇×#557	C₂²	1	2	yes	—
24	C₁₇×#557	C₂²	1	4	yes	—
25	C₁₇×#556	—	2	1	no	—
26	C₁₇×#556	C₂²	1	2	yes	—
27	D₄×Q₈×C₁₇	—	2	1	no	—
28	D₄×Q₈×C₁₇	C₂²	1	2	yes	—
29	C₁₇×#544	—	2	2	no	—
30	C₁₇×#544	C₂²	1	2	yes	—
31	C₁₇×#542	—	2	2	no	—
32	C₁₇×#542	C₂²	1	4	yes	—
33	C₁₇×#536	—	2	2	no	—
34	C₁₇×#533	—	2	2	no	—
35	C₁₇×#533	C₂²	1	1	yes	characteristic
36	C₁₇×#533	C₂²	1	1	yes	characteristic
37	C₁₇×#533	C₂²	1	1	yes	characteristic
38	C₁₇×#532	C₂²	1	1	yes	characteristic
39	C₁₇×#519	C₂²	1	2	yes	—
40	C₂×C₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#501	C₂²	1	2	yes	—
42	C₁₇×#501	C₂²	1	4	yes	—
43	C₁₇×#500	C₂²	1	1	yes	characteristic
44	C₁₇×#500	C₂²	1	4	yes	—
45	C₁₇×#498	C₂²	1	1	yes	characteristic
46	C₁₇×#491	C₂²	1	2	yes	—
47	C₁₇×#489	C₂²	1	4	yes	—
48	C₁₇×#488	C₂²	1	4	yes	—
49	C₁₇×#486	C₂²	1	1	yes	characteristic
50	C₁₇×#486	C₂²	1	1	yes	characteristic
51	C₁₇×#485	C₂²	1	4	yes	—
52	C₁₇×#484	C₂²	1	2	yes	—
53	C₁₇×#482	C₂²	1	4	yes	—
54	C₁₇×#480	C₂²	1	2	yes	—
55	C₁₇×#479	C₂²	1	4	yes	—
56	C₁₇×#478	C₂²	1	4	yes	—
57	C₁₇×#478	C₂²	1	4	yes	—
58	C₁₇×#477	C₂²	1	2	yes	—
59	C₁₇×#477	C₂²	1	4	yes	—
60	C₁₇×#477	C₂²	1	2	yes	—
61	C₁₇×#477	C₂²	1	2	yes	—
62	C₁₇×#477	C₂²	1	4	yes	—
63	C₁₇×#475	C₂²	1	2	yes	—
64	C₁₇×#475	C₂²	1	4	yes	—
65	C₁₇×#474	C₂²	1	4	yes	—
66	C₁₇×#464	C₂²	1	4	yes	—
67	C₁₇×#464	C₂²	1	4	yes	—
68	C₁₇×#462	C₂²	1	2	yes	—
69	C₁₇×#460	C₂²	1	2	yes	—
70	C₁₇×#451	C₂²	1	2	yes	—
71	C₁₇×#448	C₂²	1	2	yes	—
72	C₁₇×#446	C₂²	1	2	yes	—
73	C₁₇×#446	C₂²	1	4	yes	—
74	C₈×Q₈×C₁₇	C₂²	1	2	yes	—
75	C₁₇×#441	C₂²	1	4	yes	—
76	C₁₇×#440	C₂²	1	4	yes	—
77	C₁₇×#440	C₂²	1	4	yes	—
78	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
79	C₄×Q₁₆×C₁₇	C₂²	1	2	yes	—
80	C₄×Q₁₆×C₁₇	C₂²	1	4	yes	—
81	C₄×SD₁₆×C₁₇	C₂²	1	4	yes	—
82	C₁₇×#433	C₂²	1	4	yes	—
83	C₁₇×#432	C₂²	1	1	yes	characteristic
84	C₁₇×#431	C₂²	1	1	yes	characteristic
85	C₂×#41×C₁₇	—	2	1	no	—
86	C₂²×Q₈×C₁₇	—	2	2	no	—
87	C₂²×Q₈×C₁₇	C₂³	1	1	yes	characteristic
88	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
89	C₂×Q₁₆×C₁₇	C₂³	1	2	yes	—
90	C₂×SD₁₆×C₁₇	C₂³	1	4	yes	—
91	C₁₇×C₄⋊Q₈	—	2	2	no	—
92	C₁₇×C₄⋊Q₈	—	2	4	no	—
93	C₁₇×C₄⋊Q₈	—	2	2	no	—
94	C₁₇×C₄⋊Q₈	—	2	4	no	—
95	C₁₇×C₄⋊Q₈	—	2	2	no	—
96	C₁₇×C₄⋊Q₈	—	2	4	no	—
97	C₁₇×C₄⋊Q₈	—	2	2	no	—
98	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
99	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
100	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
101	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
102	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
103	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
104	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
105	C₁₇×C₄⋊Q₈	C₂³	1	4	yes	—
106	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
107	C₁₇×#127	C₂³	1	1	yes	characteristic
108	C₁₇×#126	—	2	4	no	—
109	C₁₇×#126	—	2	4	no	—
110	C₁₇×#125	—	2	4	no	—
111	C₁₇×#125	—	2	4	no	—
112	C₁₇×#125	—	2	4	no	—
113	C₁₇×#125	—	2	2	no	—
114	C₁₇×#125	—	2	1	no	—
115	C₁₇×#125	D₄	1	2	yes	—
116	C₁₇×#125	C₂³	1	2	yes	—
117	C₁₇×#125	C₂³	1	4	yes	—
118	C₁₇×#124	—	2	2	no	—
119	C₁₇×#124	—	2	4	no	—
120	C₁₇×#124	—	2	1	no	—
121	C₁₇×#124	C₂³	1	4	yes	—
122	C₁₇×#123	—	2	4	no	—
123	C₁₇×#123	—	2	4	no	—
124	C₁₇×C₂²⋊Q₈	—	2	2	no	—
125	C₁₇×C₂²⋊Q₈	—	2	1	no	—
126	C₁₇×C₂²⋊Q₈	—	2	1	no	—
127	C₁₇×C₂²⋊Q₈	—	2	1	no	—
128	C₁₇×C₂²⋊Q₈	—	2	2	no	—
129	C₁₇×C₂²⋊Q₈	—	2	4	no	—
130	C₁₇×C₂²⋊Q₈	—	2	4	no	—
131	C₁₇×C₂²⋊Q₈	—	2	4	no	—
132	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
133	C₁₇×C₂²⋊Q₈	D₄	1	2	yes	—
134	C₁₇×C₂²⋊Q₈	C₂³	1	2	yes	—
135	C₁₇×#121	—	2	1	no	—
136	C₁₇×#121	C₂³	1	2	yes	—
137	C₄×Q₈×C₁₇	—	2	2	no	—
138	C₄×Q₈×C₁₇	—	2	2	no	—
139	C₄×Q₈×C₁₇	—	2	2	no	—
140	C₄×Q₈×C₁₇	—	2	2	no	—
141	C₄×Q₈×C₁₇	—	2	4	no	—
142	C₄×Q₈×C₁₇	—	2	2	no	—
143	C₄×Q₈×C₁₇	—	2	1	no	—
144	C₄×Q₈×C₁₇	—	2	1	no	—
145	C₄×Q₈×C₁₇	—	2	1	no	—
146	C₄×Q₈×C₁₇	—	2	1	no	—
147	C₄×Q₈×C₁₇	—	2	1	no	—
148	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
149	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
150	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
151	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
152	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
153	C₄×Q₈×C₁₇	C₂³	1	4	yes	—
154	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
155	C₄×Q₈×C₁₇	C₂³	1	2	yes	—
156	C₄×D₄×C₁₇	—	2	2	no	—
157	C₄×D₄×C₁₇	—	2	1	no	—
158	C₄×D₄×C₁₇	C₂³	1	2	yes	—
159	C₄×D₄×C₁₇	C₂³	1	4	yes	—
160	C₁₇×#117	—	2	1	no	—
161	C₁₇×#117	—	2	2	no	—
162	C₁₇×#117	—	2	4	no	—
163	C₁₇×#117	C₂³	1	2	yes	—
164	C₁₇×#117	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
166	C₂×C₄⋊C₄×C₁₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₁₇	—	2	1	no	—
168	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
169	C₁₇×#107	C₂³	1	4	yes	—
170	C₁₇×#107	C₂³	1	2	yes	—
171	C₁₇×#107	C₂³	1	4	yes	—
172	C₁₇×#107	C₂³	1	4	yes	—
173	C₁₇×#107	C₂³	1	2	yes	—
174	C₁₇×#106	C₂³	1	4	yes	—
175	C₁₇×#106	C₂³	1	4	yes	—
176	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
177	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
178	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
179	C₁₇×C₄⋊C₈	C₂³	1	4	yes	—
180	C₁₇×#103	C₂³	1	4	yes	—
181	C₁₇×#103	C₂³	1	4	yes	—
182	C₁₇×#103	C₂³	1	2	yes	—
183	C₁₇×#103	C₂³	1	2	yes	—
184	C₁₇×#103	C₂³	1	4	yes	—
185	C₁₇×#103	C₂³	1	2	yes	—
186	C₁₇×#103	C₂³	1	2	yes	—
187	C₁₇×#102	C₂³	1	4	yes	—
188	C₁₇×#102	C₂³	1	4	yes	—
189	C₁₇×#102	C₂³	1	4	yes	—
190	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
191	C₁₇×C₂²⋊C₈	C₂³	1	2	yes	—
192	C₁₇×#97	C₂³	1	2	yes	—
193	C₁₇×#97	C₂³	1	4	yes	—
194	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
195	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
196	C₄×C₈×C₁₇	C₂³	1	4	yes	—
197	#41×C₁₇	—	8	2	no	—
198	C₂×Q₈×C₁₇	—	2	4	no	—
199	C₂×Q₈×C₁₇	—	2	1	no	—
200	C₂×Q₈×C₁₇	—	2	1	no	—
201	C₂×Q₈×C₁₇	—	2	1	no	—
202	C₂×Q₈×C₁₇	—	2	4	no	—
203	C₂×Q₈×C₁₇	—	2	1	no	—
204	C₂×Q₈×C₁₇	—	2	4	no	—
205	C₂×Q₈×C₁₇	—	2	1	no	—
206	C₂×Q₈×C₁₇	—	8	4	no	—
207	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
208	C₂×Q₈×C₁₇	C₂×D₄	1	2	yes	—
209	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
210	C₂×Q₈×C₁₇	C₂⁴	1	2	yes	—
211	C₂×D₄×C₁₇	—	2	2	no	—
212	C₂×D₄×C₁₇	—	2	1	no	—
213	C₂×D₄×C₁₇	—	2	1	no	—
214	C₂×D₄×C₁₇	C₂⁴	1	2	yes	—
215	C₂²×C₄×C₁₇	—	2	1	no	—
216	C₂²×C₄×C₁₇	—	2	1	no	—
217	C₂²×C₄×C₁₇	—	2	2	no	—
218	C₂²×C₄×C₁₇	—	2	4	no	—
219	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
220	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
221	C₂²×C₄×C₁₇	C₂⁴	1	1	yes	characteristic
222	Q₁₆×C₁₇	—	2	4	no	—
223	Q₁₆×C₁₇	—	2	4	no	—
224	SD₁₆×C₁₇	—	2	8	no	—
225	C₂×C₈×C₁₇	C₂⁴	1	4	yes	—
226	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
227	C₂×C₈×C₁₇	C₂⁴	1	2	yes	—
228	C₄⋊C₄×C₁₇	—	2	1	no	—
229	C₄⋊C₄×C₁₇	—	2	1	no	—
230	C₄⋊C₄×C₁₇	—	2	2	no	—
231	C₄⋊C₄×C₁₇	—	2	4	no	—
232	C₄⋊C₄×C₁₇	—	2	4	no	—
233	C₄⋊C₄×C₁₇	—	2	2	no	—
234	C₄⋊C₄×C₁₇	—	2	1	no	—
235	C₄⋊C₄×C₁₇	—	2	4	no	—
236	C₄⋊C₄×C₁₇	—	2	4	no	—
237	C₄⋊C₄×C₁₇	—	2	2	no	—
238	C₄⋊C₄×C₁₇	—	2	4	no	—
239	C₄⋊C₄×C₁₇	—	2	2	no	—
240	C₄⋊C₄×C₁₇	—	2	1	no	—
241	C₄⋊C₄×C₁₇	—	2	4	no	—
242	C₄⋊C₄×C₁₇	—	2	2	no	—
243	C₄⋊C₄×C₁₇	—	2	2	no	—
244	C₄⋊C₄×C₁₇	—	2	1	no	—
245	C₄⋊C₄×C₁₇	—	2	1	no	—
246	C₄⋊C₄×C₁₇	—	2	4	no	—
247	C₄⋊C₄×C₁₇	—	2	1	no	—
248	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
249	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
250	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
251	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
252	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
253	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
254	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
255	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
256	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
257	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
258	C₄⋊C₄×C₁₇	C₂⁴	1	2	yes	—
259	C₂²⋊C₄×C₁₇	—	2	2	no	—
260	C₂²⋊C₄×C₁₇	—	2	2	no	—
261	C₂²⋊C₄×C₁₇	—	2	4	no	—
262	C₂²⋊C₄×C₁₇	—	2	4	no	—
263	C₂²⋊C₄×C₁₇	—	2	2	no	—
264	C₂²⋊C₄×C₁₇	—	2	2	no	—
265	C₂²⋊C₄×C₁₇	—	2	4	no	—
266	C₂²⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
267	C₄²×C₁₇	—	2	4	no	—
268	C₄²×C₁₇	—	2	2	no	—
269	C₄²×C₁₇	—	2	2	no	—
270	C₄²×C₁₇	—	2	4	no	—
271	C₄²×C₁₇	—	2	4	no	—
272	C₄²×C₁₇	—	2	2	no	—
273	C₄²×C₁₇	—	2	2	no	—
274	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
275	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
276	C₄²×C₁₇	C₂⁴	1	4	yes	—
277	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
278	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
279	#61854	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
280	C₂³×C₁₇	—	2	2	no	—
281	C₂³×C₁₇	C₂²×D₄	1	1	yes	characteristic
282	Q₈×C₁₇	—	2	4	no	—
283	Q₈×C₁₇	—	2	4	no	—
284	Q₈×C₁₇	—	2	2	no	—
285	Q₈×C₁₇	—	2	2	no	—
286	Q₈×C₁₇	—	2	2	no	—
287	Q₈×C₁₇	—	4	2	no	—
288	Q₈×C₁₇	—	4	2	no	—
289	Q₈×C₁₇	—	4	2	no	—
290	Q₈×C₁₇	—	8	1	no	—
291	Q₈×C₁₇	—	8	4	no	—
292	Q₈×C₁₇	—	8	4	no	—
293	Q₈×C₁₇	—	8	1	no	—
294	Q₈×C₁₇	2₋¹⁺⁴	1	4	yes	—
295	D₄×C₁₇	—	2	4	no	—
296	D₄×C₁₇	—	4	2	no	—
297	D₄×C₁₇	—	8	1	no	—
298	D₄×C₁₇	—	8	2	no	—
299	C₂×C₄×C₁₇	—	2	4	no	—
300	C₂×C₄×C₁₇	—	2	2	no	—
301	C₂×C₄×C₁₇	—	2	2	no	—
302	C₂×C₄×C₁₇	—	2	2	no	—
303	C₂×C₄×C₁₇	—	2	2	no	—
304	C₂×C₄×C₁₇	—	2	2	no	—
305	C₂×C₄×C₁₇	—	2	2	no	—
306	C₂×C₄×C₁₇	—	2	2	no	—
307	C₂×C₄×C₁₇	—	2	2	no	—
308	C₂×C₄×C₁₇	—	2	2	no	—
309	C₂×C₄×C₁₇	—	4	1	no	—
310	C₂×C₄×C₁₇	—	4	4	no	—
311	C₂×C₄×C₁₇	—	8	4	no	—
312	C₂×C₄×C₁₇	—	8	1	no	—
313	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
314	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
316	C₂×C₄×C₁₇	C₂²×D₄	1	4	yes	—
317	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
318	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
319	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
320	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
321	C₈×C₁₇	—	2	4	no	—
322	C₈×C₁₇	—	2	2	no	—
323	C₈×C₁₇	—	2	2	no	—
324	#3550	C₂×C₁₇	1	1	yes	characteristic
325	#3502	C₂×C₁₇	1	1	yes	characteristic, complemented
326	#3387	C₂×C₁₇	1	2	yes	complemented
327	#3386	C₂×C₁₇	1	4	yes	complemented
328	Q₈×Q₁₆	C₂×C₁₇	1	2	yes	complemented
329	#3377	C₂×C₁₇	1	4	yes	complemented
330	#3375	C₂×C₁₇	1	2	yes	complemented
331	#3365	C₂×C₁₇	1	2	yes	complemented
332	#3243	C₂×C₁₇	1	4	yes	complemented
333	#3237	C₂×C₁₇	1	1	yes	characteristic, complemented
334	#3228	C₂×C₁₇	1	1	yes	characteristic
335	#3121	C₂×C₁₇	1	4	yes	complemented
336	#3112	C₂×C₁₇	1	1	yes	characteristic
337	#3104	C₂×C₁₇	1	1	yes	characteristic, complemented
338	#2985	C₂×C₁₇	1	1	yes	characteristic, complemented
339	C₂²×C₁₇	—	2	1	no	—
340	C₂²×C₁₇	—	2	1	no	—
341	C₂²×C₁₇	—	2	1	no	—
342	C₂²×C₁₇	—	4	2	no	—
343	C₂²×C₁₇	—	4	2	no	—
344	C₂²×C₁₇	—	4	2	no	—
345	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
346	C₄×C₁₇	—	2	1	no	—
347	C₄×C₁₇	—	2	1	no	—
348	C₄×C₁₇	—	2	4	no	—
349	C₄×C₁₇	—	2	4	no	—
350	C₄×C₁₇	—	2	1	no	—
351	C₄×C₁₇	—	2	1	no	—
352	C₄×C₁₇	—	2	4	no	—
353	C₄×C₁₇	—	4	2	no	—
354	C₄×C₁₇	—	4	2	no	—
355	C₄×C₁₇	—	4	2	no	—
356	C₄×C₁₇	—	4	2	no	—
357	C₄×C₁₇	—	4	2	no	—
358	C₄×C₁₇	—	4	2	no	—
359	C₄×C₁₇	#578	1	2	yes	—
360	C₄×C₁₇	C₂×2₋¹⁺⁴	1	2	yes	—
361	#563	—	2	2	no	—
362	#559	C₂²×C₁₇	1	2	yes	—
363	Q₈²	—	2	1	no	—
364	Q₈²	C₂²×C₁₇	1	2	yes	—
365	Q₈²	C₂²×C₁₇	1	2	yes	—
366	#557	—	2	1	no	—
367	#557	—	2	2	no	—
368	#557	C₂²×C₁₇	1	2	yes	—
369	#557	C₂²×C₁₇	1	4	yes	—
370	#556	—	2	1	no	—
371	#556	C₂²×C₁₇	1	2	yes	—
372	D₄×Q₈	—	2	1	no	—
373	D₄×Q₈	C₂²×C₁₇	1	2	yes	—
374	#544	—	2	2	no	—
375	#544	C₂²×C₁₇	1	2	yes	—
376	#542	—	2	2	no	—
377	#542	C₂²×C₁₇	1	4	yes	—
378	#536	—	2	2	no	—
379	#533	—	2	2	no	—
380	#533	C₂²×C₁₇	1	1	yes	characteristic
381	#533	C₂²×C₁₇	1	1	yes	characteristic
382	#533	C₂²×C₁₇	1	1	yes	characteristic
383	#532	C₂²×C₁₇	1	1	yes	characteristic
384	#519	C₂²×C₁₇	1	2	yes	—
385	C₂×C₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
386	#501	C₂²×C₁₇	1	2	yes	—
387	#501	C₂²×C₁₇	1	4	yes	—
388	#500	C₂²×C₁₇	1	1	yes	characteristic
389	#500	C₂²×C₁₇	1	4	yes	—
390	#498	C₂²×C₁₇	1	1	yes	characteristic
391	#491	C₂²×C₁₇	1	2	yes	—
392	#489	C₂²×C₁₇	1	4	yes	—
393	#488	C₂²×C₁₇	1	4	yes	—
394	#486	C₂²×C₁₇	1	1	yes	characteristic
395	#486	C₂²×C₁₇	1	1	yes	characteristic
396	#485	C₂²×C₁₇	1	4	yes	—
397	#484	C₂²×C₁₇	1	2	yes	—
398	#482	C₂²×C₁₇	1	4	yes	—
399	#480	C₂²×C₁₇	1	2	yes	—
400	#479	C₂²×C₁₇	1	4	yes	—
401	#478	C₂²×C₁₇	1	4	yes	—
402	#478	C₂²×C₁₇	1	4	yes	—
403	#477	C₂²×C₁₇	1	2	yes	—
404	#477	C₂²×C₁₇	1	2	yes	—
405	#477	C₂²×C₁₇	1	2	yes	—
406	#477	C₂²×C₁₇	1	4	yes	—
407	#477	C₂²×C₁₇	1	4	yes	—
408	#475	C₂²×C₁₇	1	2	yes	—
409	#475	C₂²×C₁₇	1	4	yes	—
410	#474	C₂²×C₁₇	1	4	yes	—
411	#464	C₂²×C₁₇	1	4	yes	—
412	#464	C₂²×C₁₇	1	4	yes	—
413	#462	C₂²×C₁₇	1	2	yes	—
414	#460	C₂²×C₁₇	1	2	yes	—
415	#451	C₂²×C₁₇	1	2	yes	—
416	#448	C₂²×C₁₇	1	2	yes	—
417	#446	C₂²×C₁₇	1	2	yes	—
418	#446	C₂²×C₁₇	1	4	yes	—
419	C₈×Q₈	C₂²×C₁₇	1	2	yes	—
420	#441	C₂²×C₁₇	1	4	yes	—
421	#440	C₂²×C₁₇	1	4	yes	—
422	#440	C₂²×C₁₇	1	4	yes	—
423	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
424	C₄×Q₁₆	C₂²×C₁₇	1	2	yes	—
425	C₄×Q₁₆	C₂²×C₁₇	1	4	yes	—
426	C₄×SD₁₆	C₂²×C₁₇	1	4	yes	—
427	#433	C₂²×C₁₇	1	4	yes	—
428	#432	C₂²×C₁₇	1	1	yes	characteristic
429	#431	C₂²×C₁₇	1	1	yes	characteristic
430	C₂×C₁₇	—	4	1	no	—
431	C₂×C₁₇	—	8	2	no	—
432	C₂×C₁₇	#3486	1	1	yes	characteristic
433	C₂×C₁₇	C₂×#578	1	1	yes	characteristic
434	C₂×C₁₇	#3585	1	1	yes	characteristic
435	C₂×#41	—	2	1	no	—
436	C₂²×Q₈	—	2	2	no	—
437	C₂²×Q₈	C₂³×C₁₇	1	1	yes	characteristic
438	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
439	C₂×Q₁₆	C₂³×C₁₇	1	2	yes	—
440	C₂×SD₁₆	C₂³×C₁₇	1	4	yes	—
441	C₄⋊Q₈	—	2	2	no	—
442	C₄⋊Q₈	—	2	4	no	—
443	C₄⋊Q₈	—	2	2	no	—
444	C₄⋊Q₈	—	2	4	no	—
445	C₄⋊Q₈	—	2	2	no	—
446	C₄⋊Q₈	—	2	4	no	—
447	C₄⋊Q₈	—	2	2	no	—
448	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
449	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
450	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
451	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
452	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
453	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
454	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
455	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
456	C₄⋊Q₈	C₂³×C₁₇	1	4	yes	—
457	#127	C₂³×C₁₇	1	1	yes	characteristic
458	#126	—	2	4	no	—
459	#126	—	2	4	no	—
460	#125	—	2	4	no	—
461	#125	—	2	4	no	—
462	#125	—	2	4	no	—
463	#125	—	2	2	no	—
464	#125	—	2	1	no	—
465	#125	D₄×C₁₇	1	2	yes	—
466	#125	C₂³×C₁₇	1	2	yes	—
467	#125	C₂³×C₁₇	1	4	yes	—
468	#124	—	2	2	no	—
469	#124	—	2	4	no	—
470	#124	—	2	1	no	—
471	#124	C₂³×C₁₇	1	4	yes	—
472	#123	—	2	4	no	—
473	#123	—	2	4	no	—
474	C₂²⋊Q₈	—	2	2	no	—
475	C₂²⋊Q₈	—	2	1	no	—
476	C₂²⋊Q₈	—	2	1	no	—
477	C₂²⋊Q₈	—	2	1	no	—
478	C₂²⋊Q₈	—	2	2	no	—
479	C₂²⋊Q₈	—	2	4	no	—
480	C₂²⋊Q₈	—	2	4	no	—
481	C₂²⋊Q₈	—	2	4	no	—
482	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
483	C₂²⋊Q₈	D₄×C₁₇	1	2	yes	—
484	C₂²⋊Q₈	C₂³×C₁₇	1	2	yes	—
485	#121	—	2	1	no	—
486	#121	C₂³×C₁₇	1	2	yes	—
487	C₄×Q₈	—	2	2	no	—
488	C₄×Q₈	—	2	2	no	—
489	C₄×Q₈	—	2	2	no	—
490	C₄×Q₈	—	2	2	no	—
491	C₄×Q₈	—	2	4	no	—
492	C₄×Q₈	—	2	2	no	—
493	C₄×Q₈	—	2	1	no	—
494	C₄×Q₈	—	2	1	no	—
495	C₄×Q₈	—	2	1	no	—
496	C₄×Q₈	—	2	1	no	—
497	C₄×Q₈	—	2	1	no	—
498	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
499	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
500	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
501	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
502	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
503	C₄×Q₈	C₂³×C₁₇	1	4	yes	—
504	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
505	C₄×Q₈	C₂³×C₁₇	1	2	yes	—
506	C₄×D₄	—	2	2	no	—
507	C₄×D₄	—	2	1	no	—
508	C₄×D₄	C₂³×C₁₇	1	2	yes	—
509	C₄×D₄	C₂³×C₁₇	1	4	yes	—
510	#117	—	2	1	no	—
511	#117	—	2	2	no	—
512	#117	—	2	4	no	—
513	#117	C₂³×C₁₇	1	2	yes	—
514	#117	C₂³×C₁₇	1	2	yes	—
515	C₂×C₄⋊C₄	—	2	1	no	—
516	C₂×C₄⋊C₄	C₂³×C₁₇	1	1	yes	characteristic
517	C₂×C₄²	—	2	1	no	—
518	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
519	#107	C₂³×C₁₇	1	2	yes	—
520	#107	C₂³×C₁₇	1	4	yes	—
521	#107	C₂³×C₁₇	1	2	yes	—
522	#107	C₂³×C₁₇	1	4	yes	—
523	#107	C₂³×C₁₇	1	4	yes	—
524	#106	C₂³×C₁₇	1	4	yes	—
525	#106	C₂³×C₁₇	1	4	yes	—
526	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
527	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
528	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
529	C₄⋊C₈	C₂³×C₁₇	1	4	yes	—
530	#103	C₂³×C₁₇	1	2	yes	—
531	#103	C₂³×C₁₇	1	2	yes	—
532	#103	C₂³×C₁₇	1	4	yes	—
533	#103	C₂³×C₁₇	1	2	yes	—
534	#103	C₂³×C₁₇	1	2	yes	—
535	#103	C₂³×C₁₇	1	4	yes	—
536	#103	C₂³×C₁₇	1	4	yes	—
537	#102	C₂³×C₁₇	1	4	yes	—
538	#102	C₂³×C₁₇	1	4	yes	—
539	#102	C₂³×C₁₇	1	4	yes	—
540	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
541	C₂²⋊C₈	C₂³×C₁₇	1	2	yes	—
542	#97	C₂³×C₁₇	1	2	yes	—
543	#97	C₂³×C₁₇	1	4	yes	—
544	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
545	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
546	C₄×C₈	C₂³×C₁₇	1	4	yes	—
547	C₁₇	#61854	1	1	yes	characteristic, direct product factor, Sylow
548	#41	—	8	2	no	—
549	C₂×Q₈	—	2	4	no	—
550	C₂×Q₈	—	2	1	no	—
551	C₂×Q₈	—	2	1	no	—
552	C₂×Q₈	—	2	1	no	—
553	C₂×Q₈	—	2	1	no	—
554	C₂×Q₈	—	2	4	no	—
555	C₂×Q₈	—	2	4	no	—
556	C₂×Q₈	—	2	1	no	—
557	C₂×Q₈	—	8	4	no	—
558	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
559	C₂×Q₈	C₂×D₄×C₁₇	1	2	yes	—
560	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
561	C₂×Q₈	C₂⁴×C₁₇	1	2	yes	—
562	C₂×D₄	—	2	2	no	—
563	C₂×D₄	—	2	1	no	—
564	C₂×D₄	—	2	1	no	—
565	C₂×D₄	C₂⁴×C₁₇	1	2	yes	—
566	C₂²×C₄	—	2	1	no	—
567	C₂²×C₄	—	2	1	no	—
568	C₂²×C₄	—	2	2	no	—
569	C₂²×C₄	—	2	4	no	—
570	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
571	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
572	C₂²×C₄	C₂⁴×C₁₇	1	1	yes	characteristic
573	Q₁₆	—	2	4	no	—
574	Q₁₆	—	2	4	no	—
575	SD₁₆	—	2	8	no	—
576	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
577	C₂×C₈	C₂⁴×C₁₇	1	2	yes	—
578	C₂×C₈	C₂⁴×C₁₇	1	4	yes	—
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	2	no	—
581	C₄⋊C₄	—	2	1	no	—
582	C₄⋊C₄	—	2	1	no	—
583	C₄⋊C₄	—	2	4	no	—
584	C₄⋊C₄	—	2	4	no	—
585	C₄⋊C₄	—	2	1	no	—
586	C₄⋊C₄	—	2	1	no	—
587	C₄⋊C₄	—	2	1	no	—
588	C₄⋊C₄	—	2	2	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	4	no	—
592	C₄⋊C₄	—	2	1	no	—
593	C₄⋊C₄	—	2	4	no	—
594	C₄⋊C₄	—	2	4	no	—
595	C₄⋊C₄	—	2	2	no	—
596	C₄⋊C₄	—	2	4	no	—
597	C₄⋊C₄	—	2	4	no	—
598	C₄⋊C₄	—	2	2	no	—
599	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
600	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
601	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
602	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
603	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
604	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
605	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
606	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
607	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
608	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
609	C₄⋊C₄	C₂⁴×C₁₇	1	2	yes	—
610	C₂²⋊C₄	—	2	2	no	—
611	C₂²⋊C₄	—	2	2	no	—
612	C₂²⋊C₄	—	2	4	no	—
613	C₂²⋊C₄	—	2	2	no	—
614	C₂²⋊C₄	—	2	4	no	—
615	C₂²⋊C₄	—	2	2	no	—
616	C₂²⋊C₄	—	2	4	no	—
617	C₂²⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
618	C₄²	—	2	2	no	—
619	C₄²	—	2	2	no	—
620	C₄²	—	2	2	no	—
621	C₄²	—	2	4	no	—
622	C₄²	—	2	4	no	—
623	C₄²	—	2	4	no	—
624	C₄²	—	2	2	no	—
625	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
626	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
627	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
628	C₄²	C₂⁴×C₁₇	1	4	yes	—
629	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
630	C₂³	—	2	2	no	—
631	C₂³	C₂²×D₄×C₁₇	1	1	yes	characteristic
632	Q₈	—	2	4	no	—
633	Q₈	—	2	4	no	—
634	Q₈	—	2	2	no	—
635	Q₈	—	2	2	no	—
636	Q₈	—	2	2	no	—
637	Q₈	—	4	2	no	—
638	Q₈	—	4	2	no	—
639	Q₈	—	4	2	no	—
640	Q₈	—	8	4	no	—
641	Q₈	—	8	1	no	—
642	Q₈	—	8	1	no	—
643	Q₈	—	8	4	no	—
644	Q₈	C₁₇×2₋¹⁺⁴	1	4	yes	—
645	D₄	—	2	4	no	—
646	D₄	—	4	2	no	—
647	D₄	—	8	1	no	—
648	D₄	—	8	2	no	—
649	C₂×C₄	—	2	4	no	—
650	C₂×C₄	—	2	2	no	—
651	C₂×C₄	—	2	2	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	4	1	no	—
660	C₂×C₄	—	4	4	no	—
661	C₂×C₄	—	8	4	no	—
662	C₂×C₄	—	8	1	no	—
663	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
664	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
665	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
666	C₂×C₄	C₂²×D₄×C₁₇	1	4	yes	—
667	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
668	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
669	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
670	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
671	C₈	—	2	4	no	—
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₂²	—	2	1	no	—
675	C₂²	—	2	1	no	—
676	C₂²	—	2	1	no	—
677	C₂²	—	4	2	no	—
678	C₂²	—	4	2	no	—
679	C₂²	—	4	2	no	—
680	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
681	C₄	—	2	4	no	—
682	C₄	—	2	1	no	—
683	C₄	—	2	1	no	—
684	C₄	—	2	4	no	—
685	C₄	—	2	1	no	—
686	C₄	—	2	1	no	—
687	C₄	—	2	4	no	—
688	C₄	—	4	2	no	—
689	C₄	—	4	2	no	—
690	C₄	—	4	2	no	—
691	C₄	—	4	2	no	—
692	C₄	—	4	2	no	—
693	C₄	—	4	2	no	—
694	C₄	C₁₇×#578	1	2	yes	—
695	C₄	C₂×C₁₇×2₋¹⁺⁴	1	2	yes	—
696	C₂	—	4	1	no	—
697	C₂	—	8	2	no	—
698	C₂	C₁₇×#3486	1	1	yes	characteristic
699	C₂	C₂×C₁₇×#578	1	1	yes	characteristic
700	C₂	C₁₇×#3585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₁₇×#533 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₇×#3502	C₂	semidirect
3. C₁₇×#3387	C₂	semidirect
4. C₁₇×#3386	C₂	semidirect
5. Q₈×Q₁₆×C₁₇	C₂	semidirect
6. C₁₇×#3377	C₂	semidirect
7. C₁₇×#3375	C₂	semidirect
8. C₁₇×#3365	C₂	semidirect
9. C₁₇×#3243	C₂	semidirect
10. C₁₇×#3237	C₂	semidirect
12. C₁₇×#3121	C₂	semidirect
14. C₁₇×#3104	C₂	semidirect
15. C₁₇×#2985	C₂	semidirect
279. #61854	C₁₇	direct (N × H)
325. #3502	C₂×C₁₇	semidirect
326. #3387	C₂×C₁₇	semidirect
327. #3386	C₂×C₁₇	semidirect
328. Q₈×Q₁₆	C₂×C₁₇	semidirect
329. #3377	C₂×C₁₇	semidirect
330. #3375	C₂×C₁₇	semidirect
331. #3365	C₂×C₁₇	semidirect
332. #3243	C₂×C₁₇	semidirect
333. #3237	C₂×C₁₇	semidirect
335. #3121	C₂×C₁₇	semidirect
337. #3104	C₂×C₁₇	semidirect
338. #2985	C₂×C₁₇	semidirect
547. C₁₇	#61854	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×#3550	2
C₁₇×#3502	2
C₁₇×#3387	2
C₁₇×#3386	2
Q₈×Q₁₆×C₁₇	2
C₁₇×#3377	2
C₁₇×#3375	2
C₁₇×#3365	2
C₁₇×#3243	2
C₁₇×#3237	2
C₁₇×#3228	2
C₁₇×#3121	2
C₁₇×#3112	2
C₁₇×#3104	2
C₁₇×#2985	2
#61854	17

Subgroups — C17×#61854 #16919598

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61854 #16919598