Subgroups — C₁₇×#61470 #16919214

Order 4352.

1812 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	C₁₇×#3482	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3395	C₂	1	1	yes	maximal, characteristic, complemented
4	Q₈×SD₁₆×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#3363	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#3359	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#3356	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3331	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3328	C₂	1	3	yes	maximal, complemented
10	C₁₇×#3276	C₂	1	3	yes	maximal, complemented
11	C₁₇×#3185	C₂	1	3	yes	maximal, complemented
12	C₁₇×#3116	C₂	1	3	yes	maximal, complemented
13	C₁₇×#3113	C₂	1	3	yes	maximal, complemented
14	C₁₇×#2971	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×C₁₇×#137	C₂	1	3	yes	maximal, complemented
16	C₂×C₁₇×#137	C₂²	1	3	yes	—
17	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#557	—	2	1	no	—
19	C₁₇×#557	C₂²	1	1	yes	characteristic
20	C₁₇×#557	C₂²	1	1	yes	characteristic
21	C₁₇×#556	C₂²	1	3	yes	—
22	C₁₇×#554	—	2	3	no	—
23	C₁₇×#554	C₂²	1	3	yes	—
24	C₁₇×#552	—	2	3	no	—
25	D₄×Q₈×C₁₇	C₂²	1	1	yes	characteristic
26	D₄×Q₈×C₁₇	C₂²	1	3	yes	—
27	C₁₇×#548	—	2	1	no	—
28	C₁₇×#547	C₂²	1	3	yes	—
29	C₁₇×#533	—	2	3	no	—
30	C₁₇×#533	C₂²	1	3	yes	—
31	C₁₇×#533	C₂²	1	3	yes	—
32	C₁₇×#529	—	2	3	no	—
33	C₄×#41×C₁₇	—	2	1	no	—
34	C₄×#41×C₁₇	C₂²	1	3	yes	—
35	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₇	—	2	1	no	—
37	C₂×C₄×Q₈×C₁₇	C₂²	1	3	yes	—
38	C₁₇×#498	C₂²	1	3	yes	—
39	C₁₇×#494	C₂²	1	3	yes	—
40	C₁₇×#487	C₂²	1	3	yes	—
41	C₁₇×#487	C₂²	1	3	yes	—
42	C₁₇×#485	C₂²	1	6	yes	—
43	C₁₇×#483	C₂²	1	6	yes	—
44	C₁₇×#477	C₂²	1	3	yes	—
45	C₁₇×#476	C₂²	1	3	yes	—
46	C₁₇×#475	C₂²	1	3	yes	—
47	C₁₇×#475	C₂²	1	3	yes	—
48	C₁₇×#470	C₂²	1	6	yes	—
49	C₁₇×#470	C₂²	1	6	yes	—
50	C₁₇×#462	C₂²	1	3	yes	—
51	C₁₇×#462	C₂²	1	3	yes	—
52	C₁₇×#462	C₂²	1	3	yes	—
53	C₁₇×#461	C₂²	1	3	yes	—
54	C₁₇×#452	C₂²	1	6	yes	—
55	C₁₇×#451	C₂²	1	6	yes	—
56	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
57	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
58	C₁₇×#441	C₂²	1	3	yes	—
59	C₁₇×#441	C₂²	1	6	yes	—
60	C₁₇×#441	C₂²	1	3	yes	—
61	C₁₇×#440	C₂²	1	3	yes	—
62	C₁₇×#440	C₂²	1	1	yes	characteristic
63	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
64	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
65	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
66	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
67	C₁₇×#436	C₂²	1	3	yes	—
68	C₁₇×#436	C₂²	1	3	yes	—
69	C₁₇×#432	C₂²	1	3	yes	—
70	C₁₇×#428	C₂²	1	3	yes	—
71	C₁₇×#419	C₂²	1	3	yes	—
72	C₁₇×#417	C₂²	1	3	yes	—
73	C₄×M₁₆×C₁₇	C₂²	1	3	yes	—
74	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
75	C₂×#41×C₁₇	C₂³	1	3	yes	—
76	C₂²×Q₈×C₁₇	—	2	1	no	—
77	C₂²×Q₈×C₁₇	C₂³	1	3	yes	—
78	C₁₇×#137	—	2	12	no	—
79	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
80	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
81	C₂×Q₁₆×C₁₇	C₂³	1	6	yes	—
82	C₂×SD₁₆×C₁₇	C₂³	1	3	yes	—
83	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
84	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
85	C₂×M₁₆×C₁₇	C₂³	1	3	yes	—
86	C₁₇×C₄⋊Q₈	—	2	3	no	—
87	C₁₇×C₄⋊Q₈	—	2	3	no	—
88	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
90	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
91	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
92	C₁₇×#126	—	2	6	no	—
93	C₁₇×#125	—	2	3	no	—
94	C₁₇×#125	—	2	3	no	—
95	C₁₇×#125	—	2	3	no	—
96	C₁₇×#125	—	2	3	no	—
97	C₁₇×#125	—	2	3	no	—
98	C₁₇×#124	—	2	3	no	—
99	C₁₇×#123	—	2	6	no	—
100	C₁₇×C₂²⋊Q₈	—	2	3	no	—
101	C₁₇×C₂²⋊Q₈	—	2	3	no	—
102	C₁₇×C₂²⋊Q₈	—	2	3	no	—
103	C₁₇×C₂²⋊Q₈	—	2	6	no	—
104	C₁₇×C₂²⋊Q₈	—	2	6	no	—
105	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
106	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₇×#121	—	2	3	no	—
108	C₄×Q₈×C₁₇	—	2	1	no	—
109	C₄×Q₈×C₁₇	—	2	1	no	—
110	C₄×Q₈×C₁₇	—	2	1	no	—
111	C₄×Q₈×C₁₇	—	2	3	no	—
112	C₄×Q₈×C₁₇	—	2	3	no	—
113	C₄×Q₈×C₁₇	—	2	3	no	—
114	C₄×Q₈×C₁₇	—	2	3	no	—
115	C₄×Q₈×C₁₇	—	2	3	no	—
116	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
117	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
118	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
119	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
120	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
121	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
122	C₄×Q₈×C₁₇	C₂³	1	3	yes	—
123	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
124	C₄×D₄×C₁₇	—	2	3	no	—
125	C₄×D₄×C₁₇	—	2	3	no	—
126	C₄×D₄×C₁₇	—	2	3	no	—
127	C₄×D₄×C₁₇	—	2	3	no	—
128	C₄×D₄×C₁₇	D₄	1	3	yes	—
129	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
130	C₄×D₄×C₁₇	C₂³	1	3	yes	—
131	C₄×D₄×C₁₇	C₂³	1	3	yes	—
132	C₁₇×#117	—	2	3	no	—
133	C₁₇×#117	—	2	3	no	—
134	C₁₇×#117	—	2	3	no	—
135	C₁₇×#117	D₄	1	3	yes	—
136	C₁₇×#117	C₂³	1	3	yes	—
137	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
138	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
139	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
140	C₂×C₄²×C₁₇	—	2	3	no	—
141	C₂×C₄²×C₁₇	—	2	3	no	—
142	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
143	C₁₇×#107	C₂³	1	1	yes	characteristic
144	C₁₇×#107	C₂³	1	3	yes	—
145	C₁₇×#106	C₂³	1	3	yes	—
146	C₁₇×#106	C₂³	1	6	yes	—
147	C₁₇×#106	C₂³	1	3	yes	—
148	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
150	C₁₇×#103	C₂³	1	3	yes	—
151	C₁₇×#103	C₂³	1	3	yes	—
152	C₁₇×#103	C₂³	1	1	yes	characteristic
153	C₁₇×#103	C₂³	1	3	yes	—
154	C₁₇×#103	C₂³	1	3	yes	—
155	C₁₇×#103	C₂³	1	3	yes	—
156	C₁₇×#103	C₂³	1	6	yes	—
157	C₁₇×#103	C₂³	1	6	yes	—
158	C₁₇×#102	C₂³	1	1	yes	characteristic
159	C₁₇×#102	C₂³	1	3	yes	—
160	C₁₇×C₂²⋊C₈	C₂³	1	6	yes	—
161	C₁₇×#97	C₂³	1	1	yes	characteristic
162	C₁₇×#97	C₂³	1	3	yes	—
163	C₄×C₈×C₁₇	C₂³	1	3	yes	—
164	C₄×C₈×C₁₇	C₂³	1	3	yes	—
165	#41×C₁₇	—	2	4	no	—
166	#41×C₁₇	—	2	6	no	—
167	#41×C₁₇	—	4	3	no	—
168	C₂×Q₈×C₁₇	—	2	3	no	—
169	C₂×Q₈×C₁₇	—	2	3	no	—
170	C₂×Q₈×C₁₇	—	2	3	no	—
171	C₂×Q₈×C₁₇	—	2	6	no	—
172	C₂×Q₈×C₁₇	—	4	3	no	—
173	C₂×Q₈×C₁₇	—	4	4	no	—
174	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
176	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
177	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
178	C₂×D₄×C₁₇	—	2	3	no	—
179	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
180	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
181	C₂²×C₄×C₁₇	—	2	3	no	—
182	C₂²×C₄×C₁₇	—	2	3	no	—
183	C₂²×C₄×C₁₇	—	2	3	no	—
184	C₂²×C₄×C₁₇	—	2	3	no	—
185	C₂²×C₄×C₁₇	—	2	1	no	—
186	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
187	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
188	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
189	Q₁₆×C₁₇	—	2	6	no	—
190	Q₁₆×C₁₇	—	2	6	no	—
191	Q₁₆×C₁₇	—	4	6	no	—
192	SD₁₆×C₁₇	—	2	6	no	—
193	SD₁₆×C₁₇	#41	1	4	yes	complemented
194	M₁₆×C₁₇	—	2	6	no	—
195	M₁₆×C₁₇	—	4	3	no	—
196	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
197	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
198	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
199	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
200	C₄⋊C₄×C₁₇	—	2	3	no	—
201	C₄⋊C₄×C₁₇	—	2	6	no	—
202	C₄⋊C₄×C₁₇	—	2	3	no	—
203	C₄⋊C₄×C₁₇	—	2	3	no	—
204	C₄⋊C₄×C₁₇	—	2	3	no	—
205	C₄⋊C₄×C₁₇	—	2	3	no	—
206	C₄⋊C₄×C₁₇	—	2	3	no	—
207	C₄⋊C₄×C₁₇	—	2	3	no	—
208	C₄⋊C₄×C₁₇	—	2	3	no	—
209	C₄⋊C₄×C₁₇	—	2	6	no	—
210	C₄⋊C₄×C₁₇	—	2	3	no	—
211	C₄⋊C₄×C₁₇	—	2	3	no	—
212	C₄⋊C₄×C₁₇	—	2	3	no	—
213	C₄⋊C₄×C₁₇	—	2	3	no	—
214	C₄⋊C₄×C₁₇	—	2	1	no	—
215	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
216	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
217	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
218	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
219	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
220	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
221	C₂²⋊C₄×C₁₇	—	2	6	no	—
222	C₂²⋊C₄×C₁₇	—	2	6	no	—
223	C₂²⋊C₄×C₁₇	—	2	3	no	—
224	C₂²⋊C₄×C₁₇	—	2	3	no	—
225	C₂²⋊C₄×C₁₇	—	2	1	no	—
226	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
227	C₄²×C₁₇	—	2	3	no	—
228	C₄²×C₁₇	—	2	3	no	—
229	C₄²×C₁₇	—	2	3	no	—
230	C₄²×C₁₇	—	2	3	no	—
231	C₄²×C₁₇	—	2	1	no	—
232	C₄²×C₁₇	—	2	3	no	—
233	C₄²×C₁₇	—	2	3	no	—
234	C₄²×C₁₇	C₂×D₄	1	3	yes	—
235	C₄²×C₁₇	C₂×D₄	1	3	yes	—
236	C₄²×C₁₇	C₂⁴	1	3	yes	—
237	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
238	#61470	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
239	C₂³×C₁₇	—	2	1	no	—
240	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
241	Q₈×C₁₇	—	2	1	no	—
242	Q₈×C₁₇	—	2	3	no	—
243	Q₈×C₁₇	—	2	3	no	—
244	Q₈×C₁₇	—	2	3	no	—
245	Q₈×C₁₇	—	2	3	no	—
246	Q₈×C₁₇	—	4	6	no	—
247	Q₈×C₁₇	—	4	6	no	—
248	Q₈×C₁₇	—	8	3	no	—
249	Q₈×C₁₇	#137	1	4	yes	complemented
250	Q₈×C₁₇	C₂×#41	1	2	yes	—
251	D₄×C₁₇	—	2	6	no	—
252	D₄×C₁₇	—	2	1	no	—
253	D₄×C₁₇	—	4	6	no	—
254	D₄×C₁₇	C₂×#41	1	2	yes	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	6	no	—
257	C₂×C₄×C₁₇	—	2	3	no	—
258	C₂×C₄×C₁₇	—	2	3	no	—
259	C₂×C₄×C₁₇	—	2	1	no	—
260	C₂×C₄×C₁₇	—	2	1	no	—
261	C₂×C₄×C₁₇	—	2	3	no	—
262	C₂×C₄×C₁₇	—	2	3	no	—
263	C₂×C₄×C₁₇	—	2	3	no	—
264	C₂×C₄×C₁₇	—	2	3	no	—
265	C₂×C₄×C₁₇	—	4	3	no	—
266	C₂×C₄×C₁₇	—	4	6	no	—
267	C₂×C₄×C₁₇	—	4	6	no	—
268	C₂×C₄×C₁₇	—	4	2	no	—
269	C₂×C₄×C₁₇	—	4	6	no	—
270	C₂×C₄×C₁₇	—	8	3	no	—
271	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
272	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
273	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
274	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
275	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
276	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
277	C₈×C₁₇	—	2	3	no	—
278	C₈×C₁₇	—	2	1	no	—
279	C₈×C₁₇	—	2	3	no	—
280	C₈×C₁₇	C₂×#41	1	2	yes	—
281	#3482	C₂×C₁₇	1	1	yes	characteristic
282	Q₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
283	#3395	C₂×C₁₇	1	1	yes	characteristic, complemented
284	Q₈×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
285	#3363	C₂×C₁₇	1	1	yes	characteristic, complemented
286	#3359	C₂×C₁₇	1	1	yes	characteristic, complemented
287	#3356	C₂×C₁₇	1	3	yes	complemented
288	#3331	C₂×C₁₇	1	3	yes	complemented
289	#3328	C₂×C₁₇	1	3	yes	complemented
290	#3276	C₂×C₁₇	1	3	yes	complemented
291	#3185	C₂×C₁₇	1	3	yes	complemented
292	#3116	C₂×C₁₇	1	3	yes	complemented
293	#3113	C₂×C₁₇	1	3	yes	complemented
294	#2971	C₂×C₁₇	1	1	yes	characteristic, complemented
295	C₄×#137	C₂×C₁₇	1	3	yes	complemented
296	C₂²×C₁₇	—	2	3	no	—
297	C₂²×C₁₇	—	2	3	no	—
298	C₂²×C₁₇	—	2	2	no	—
299	C₂²×C₁₇	—	2	3	no	—
300	C₂²×C₁₇	—	4	1	no	—
301	C₂²×C₁₇	—	4	1	no	—
302	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
303	C₄×C₁₇	—	2	1	no	—
304	C₄×C₁₇	—	2	3	no	—
305	C₄×C₁₇	—	2	3	no	—
306	C₄×C₁₇	—	2	2	no	—
307	C₄×C₁₇	—	2	1	no	—
308	C₄×C₁₇	—	4	1	no	—
309	C₄×C₁₇	—	4	1	no	—
310	C₄×C₁₇	—	4	3	no	—
311	C₄×C₁₇	—	4	3	no	—
312	C₄×C₁₇	—	4	3	no	—
313	C₄×C₁₇	—	4	3	no	—
314	C₄×C₁₇	C₂×#137	1	6	yes	—
315	C₄×C₁₇	C₂²×#41	1	1	yes	characteristic
316	C₄×C₁₇	#585	1	1	yes	characteristic
317	C₂×#137	C₂²×C₁₇	1	3	yes	—
318	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
319	#557	—	2	1	no	—
320	#557	C₂²×C₁₇	1	1	yes	characteristic
321	#557	C₂²×C₁₇	1	1	yes	characteristic
322	#556	C₂²×C₁₇	1	3	yes	—
323	#554	—	2	3	no	—
324	#554	C₂²×C₁₇	1	3	yes	—
325	#552	—	2	3	no	—
326	D₄×Q₈	C₂²×C₁₇	1	3	yes	—
327	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
328	#548	—	2	1	no	—
329	#547	C₂²×C₁₇	1	3	yes	—
330	#533	—	2	3	no	—
331	#533	C₂²×C₁₇	1	3	yes	—
332	#533	C₂²×C₁₇	1	3	yes	—
333	#529	—	2	3	no	—
334	C₄×#41	—	2	1	no	—
335	C₄×#41	C₂²×C₁₇	1	3	yes	—
336	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
337	C₂×C₄×Q₈	—	2	1	no	—
338	C₂×C₄×Q₈	C₂²×C₁₇	1	3	yes	—
339	#498	C₂²×C₁₇	1	3	yes	—
340	#494	C₂²×C₁₇	1	3	yes	—
341	#487	C₂²×C₁₇	1	3	yes	—
342	#487	C₂²×C₁₇	1	3	yes	—
343	#485	C₂²×C₁₇	1	6	yes	—
344	#483	C₂²×C₁₇	1	6	yes	—
345	#477	C₂²×C₁₇	1	3	yes	—
346	#476	C₂²×C₁₇	1	3	yes	—
347	#475	C₂²×C₁₇	1	3	yes	—
348	#475	C₂²×C₁₇	1	3	yes	—
349	#470	C₂²×C₁₇	1	6	yes	—
350	#470	C₂²×C₁₇	1	6	yes	—
351	#462	C₂²×C₁₇	1	3	yes	—
352	#462	C₂²×C₁₇	1	3	yes	—
353	#462	C₂²×C₁₇	1	3	yes	—
354	#461	C₂²×C₁₇	1	3	yes	—
355	#452	C₂²×C₁₇	1	6	yes	—
356	#451	C₂²×C₁₇	1	6	yes	—
357	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
358	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
359	#441	C₂²×C₁₇	1	3	yes	—
360	#441	C₂²×C₁₇	1	6	yes	—
361	#441	C₂²×C₁₇	1	3	yes	—
362	#440	C₂²×C₁₇	1	3	yes	—
363	#440	C₂²×C₁₇	1	1	yes	characteristic
364	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
365	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
366	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
367	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
368	#436	C₂²×C₁₇	1	3	yes	—
369	#436	C₂²×C₁₇	1	3	yes	—
370	#432	C₂²×C₁₇	1	3	yes	—
371	#428	C₂²×C₁₇	1	3	yes	—
372	#419	C₂²×C₁₇	1	3	yes	—
373	#417	C₂²×C₁₇	1	3	yes	—
374	C₄×M₁₆	C₂²×C₁₇	1	3	yes	—
375	C₂×C₁₇	—	4	3	no	—
376	C₂×C₁₇	—	4	2	no	—
377	C₂×C₁₇	D₄×#41	1	1	yes	characteristic
378	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
379	C₂×C₁₇	#3586	1	1	yes	characteristic
380	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
381	C₂×#41	C₂³×C₁₇	1	3	yes	—
382	C₂²×Q₈	—	2	1	no	—
383	C₂²×Q₈	C₂³×C₁₇	1	3	yes	—
384	#137	—	2	12	no	—
385	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
386	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
387	C₂×Q₁₆	C₂³×C₁₇	1	6	yes	—
388	C₂×SD₁₆	C₂³×C₁₇	1	3	yes	—
389	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
390	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
391	C₂×M₁₆	C₂³×C₁₇	1	3	yes	—
392	C₄⋊Q₈	—	2	3	no	—
393	C₄⋊Q₈	—	2	3	no	—
394	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
395	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
396	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
397	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
398	#126	—	2	6	no	—
399	#125	—	2	3	no	—
400	#125	—	2	3	no	—
401	#125	—	2	3	no	—
402	#125	—	2	3	no	—
403	#125	—	2	3	no	—
404	#124	—	2	3	no	—
405	#123	—	2	6	no	—
406	C₂²⋊Q₈	—	2	3	no	—
407	C₂²⋊Q₈	—	2	3	no	—
408	C₂²⋊Q₈	—	2	3	no	—
409	C₂²⋊Q₈	—	2	6	no	—
410	C₂²⋊Q₈	—	2	6	no	—
411	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
412	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
413	#121	—	2	3	no	—
414	C₄×Q₈	—	2	1	no	—
415	C₄×Q₈	—	2	1	no	—
416	C₄×Q₈	—	2	1	no	—
417	C₄×Q₈	—	2	3	no	—
418	C₄×Q₈	—	2	3	no	—
419	C₄×Q₈	—	2	3	no	—
420	C₄×Q₈	—	2	3	no	—
421	C₄×Q₈	—	2	3	no	—
422	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
423	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
424	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
425	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
426	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
427	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
428	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
429	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
430	C₄×D₄	—	2	3	no	—
431	C₄×D₄	—	2	3	no	—
432	C₄×D₄	—	2	3	no	—
433	C₄×D₄	—	2	3	no	—
434	C₄×D₄	D₄×C₁₇	1	3	yes	—
435	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
436	C₄×D₄	C₂³×C₁₇	1	3	yes	—
437	C₄×D₄	C₂³×C₁₇	1	3	yes	—
438	#117	—	2	3	no	—
439	#117	—	2	3	no	—
440	#117	—	2	3	no	—
441	#117	D₄×C₁₇	1	3	yes	—
442	#117	C₂³×C₁₇	1	3	yes	—
443	C₂×C₄⋊C₄	—	2	3	no	—
444	C₂×C₄⋊C₄	—	2	3	no	—
445	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
446	C₂×C₄²	—	2	3	no	—
447	C₂×C₄²	—	2	3	no	—
448	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
449	#107	C₂³×C₁₇	1	1	yes	characteristic
450	#107	C₂³×C₁₇	1	3	yes	—
451	#106	C₂³×C₁₇	1	3	yes	—
452	#106	C₂³×C₁₇	1	3	yes	—
453	#106	C₂³×C₁₇	1	6	yes	—
454	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
455	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
456	#103	C₂³×C₁₇	1	3	yes	—
457	#103	C₂³×C₁₇	1	3	yes	—
458	#103	C₂³×C₁₇	1	1	yes	characteristic
459	#103	C₂³×C₁₇	1	3	yes	—
460	#103	C₂³×C₁₇	1	3	yes	—
461	#103	C₂³×C₁₇	1	3	yes	—
462	#103	C₂³×C₁₇	1	6	yes	—
463	#103	C₂³×C₁₇	1	6	yes	—
464	#102	C₂³×C₁₇	1	1	yes	characteristic
465	#102	C₂³×C₁₇	1	3	yes	—
466	C₂²⋊C₈	C₂³×C₁₇	1	6	yes	—
467	#97	C₂³×C₁₇	1	1	yes	characteristic
468	#97	C₂³×C₁₇	1	3	yes	—
469	C₄×C₈	C₂³×C₁₇	1	3	yes	—
470	C₄×C₈	C₂³×C₁₇	1	3	yes	—
471	C₁₇	#61470	1	1	yes	characteristic, direct product factor, Sylow
472	#41	—	2	4	no	—
473	#41	—	2	6	no	—
474	#41	—	4	3	no	—
475	C₂×Q₈	—	2	3	no	—
476	C₂×Q₈	—	2	3	no	—
477	C₂×Q₈	—	2	3	no	—
478	C₂×Q₈	—	2	6	no	—
479	C₂×Q₈	—	4	3	no	—
480	C₂×Q₈	—	4	4	no	—
481	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
482	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
483	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
484	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
485	C₂×D₄	—	2	3	no	—
486	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
487	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
488	C₂²×C₄	—	2	3	no	—
489	C₂²×C₄	—	2	3	no	—
490	C₂²×C₄	—	2	1	no	—
491	C₂²×C₄	—	2	3	no	—
492	C₂²×C₄	—	2	3	no	—
493	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
494	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
495	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
496	Q₁₆	—	2	6	no	—
497	Q₁₆	—	2	6	no	—
498	Q₁₆	—	4	6	no	—
499	SD₁₆	—	2	6	no	—
500	SD₁₆	#41×C₁₇	1	4	yes	complemented
501	M₁₆	—	2	6	no	—
502	M₁₆	—	4	3	no	—
503	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
504	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
505	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
506	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
507	C₄⋊C₄	—	2	1	no	—
508	C₄⋊C₄	—	2	3	no	—
509	C₄⋊C₄	—	2	6	no	—
510	C₄⋊C₄	—	2	3	no	—
511	C₄⋊C₄	—	2	3	no	—
512	C₄⋊C₄	—	2	3	no	—
513	C₄⋊C₄	—	2	3	no	—
514	C₄⋊C₄	—	2	3	no	—
515	C₄⋊C₄	—	2	3	no	—
516	C₄⋊C₄	—	2	3	no	—
517	C₄⋊C₄	—	2	3	no	—
518	C₄⋊C₄	—	2	3	no	—
519	C₄⋊C₄	—	2	3	no	—
520	C₄⋊C₄	—	2	3	no	—
521	C₄⋊C₄	—	2	6	no	—
522	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
523	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
524	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
525	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
526	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
527	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
528	C₂²⋊C₄	—	2	6	no	—
529	C₂²⋊C₄	—	2	6	no	—
530	C₂²⋊C₄	—	2	3	no	—
531	C₂²⋊C₄	—	2	1	no	—
532	C₂²⋊C₄	—	2	3	no	—
533	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
534	C₄²	—	2	1	no	—
535	C₄²	—	2	3	no	—
536	C₄²	—	2	3	no	—
537	C₄²	—	2	3	no	—
538	C₄²	—	2	3	no	—
539	C₄²	—	2	3	no	—
540	C₄²	—	2	3	no	—
541	C₄²	C₂×D₄×C₁₇	1	3	yes	—
542	C₄²	C₂×D₄×C₁₇	1	3	yes	—
543	C₄²	C₂⁴×C₁₇	1	3	yes	—
544	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
545	C₂³	—	2	1	no	—
546	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
547	Q₈	—	2	1	no	—
548	Q₈	—	2	3	no	—
549	Q₈	—	2	3	no	—
550	Q₈	—	2	3	no	—
551	Q₈	—	2	3	no	—
552	Q₈	—	4	6	no	—
553	Q₈	—	4	6	no	—
554	Q₈	—	8	3	no	—
555	Q₈	C₁₇×#137	1	4	yes	complemented
556	Q₈	C₂×#41×C₁₇	1	2	yes	—
557	D₄	—	2	6	no	—
558	D₄	—	2	1	no	—
559	D₄	—	4	6	no	—
560	D₄	C₂×#41×C₁₇	1	2	yes	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	2	6	no	—
563	C₂×C₄	—	2	3	no	—
564	C₂×C₄	—	2	3	no	—
565	C₂×C₄	—	2	1	no	—
566	C₂×C₄	—	2	1	no	—
567	C₂×C₄	—	2	3	no	—
568	C₂×C₄	—	2	3	no	—
569	C₂×C₄	—	2	3	no	—
570	C₂×C₄	—	2	3	no	—
571	C₂×C₄	—	4	3	no	—
572	C₂×C₄	—	4	6	no	—
573	C₂×C₄	—	4	6	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	6	no	—
576	C₂×C₄	—	8	3	no	—
577	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
578	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
579	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
580	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
581	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
582	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
583	C₈	—	2	3	no	—
584	C₈	—	2	1	no	—
585	C₈	—	2	3	no	—
586	C₈	C₂×#41×C₁₇	1	2	yes	—
587	C₂²	—	2	3	no	—
588	C₂²	—	2	2	no	—
589	C₂²	—	2	3	no	—
590	C₂²	—	2	3	no	—
591	C₂²	—	4	1	no	—
592	C₂²	—	4	1	no	—
593	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
594	C₄	—	2	3	no	—
595	C₄	—	2	2	no	—
596	C₄	—	2	1	no	—
597	C₄	—	2	1	no	—
598	C₄	—	2	3	no	—
599	C₄	—	4	3	no	—
600	C₄	—	4	3	no	—
601	C₄	—	4	3	no	—
602	C₄	—	4	1	no	—
603	C₄	—	4	1	no	—
604	C₄	—	4	3	no	—
605	C₄	C₂×C₁₇×#137	1	6	yes	—
606	C₄	C₂²×#41×C₁₇	1	1	yes	characteristic
607	C₄	C₁₇×#585	1	1	yes	characteristic
608	C₂	—	4	3	no	—
609	C₂	—	4	2	no	—
610	C₂	D₄×#41×C₁₇	1	1	yes	characteristic
611	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
612	C₂	C₁₇×#3586	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3482	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄×#41×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. Q₈×#41×C₁₇	C₂	semidirect
3. C₁₇×#3395	C₂	semidirect
4. Q₈×SD₁₆×C₁₇	C₂	semidirect
5. C₁₇×#3363	C₂	semidirect
6. C₁₇×#3359	C₂	semidirect
7. C₁₇×#3356	C₂	semidirect
8. C₁₇×#3331	C₂	semidirect
9. C₁₇×#3328	C₂	semidirect
10. C₁₇×#3276	C₂	semidirect
11. C₁₇×#3185	C₂	semidirect
12. C₁₇×#3116	C₂	semidirect
13. C₁₇×#3113	C₂	semidirect
14. C₁₇×#2971	C₂	semidirect
15. C₄×C₁₇×#137	C₂	semidirect
193. SD₁₆×C₁₇	#41	semidirect
238. #61470	C₁₇	direct (N × H)
249. Q₈×C₁₇	#137	semidirect
282. Q₈×#41	C₂×C₁₇	semidirect
283. #3395	C₂×C₁₇	semidirect
284. Q₈×SD₁₆	C₂×C₁₇	semidirect
285. #3363	C₂×C₁₇	semidirect
286. #3359	C₂×C₁₇	semidirect
287. #3356	C₂×C₁₇	semidirect
288. #3331	C₂×C₁₇	semidirect
289. #3328	C₂×C₁₇	semidirect
290. #3276	C₂×C₁₇	semidirect
291. #3185	C₂×C₁₇	semidirect
292. #3116	C₂×C₁₇	semidirect
293. #3113	C₂×C₁₇	semidirect
294. #2971	C₂×C₁₇	semidirect
295. C₄×#137	C₂×C₁₇	semidirect
471. C₁₇	#61470	direct (N × H)
500. SD₁₆	#41×C₁₇	semidirect
555. Q₈	C₁₇×#137	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3482	2
Q₈×#41×C₁₇	2
C₁₇×#3395	2
Q₈×SD₁₆×C₁₇	2
C₁₇×#3363	2
C₁₇×#3359	2
C₁₇×#3356	2
C₁₇×#3331	2
C₁₇×#3328	2
C₁₇×#3276	2
C₁₇×#3185	2
C₁₇×#3116	2
C₁₇×#3113	2
C₁₇×#2971	2
C₄×C₁₇×#137	2
#61470	17

Subgroups — C17×#61470 #16919214

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#61470 #16919214