Subgroups — C₁₇×#62153 #16919897

Order 4352.

1696 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3518	C₂	1	1	yes	maximal, characteristic
2	Q₈×#41×C₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×Q₁₆×C₁₇	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×#3357	C₂	1	3	yes	maximal, complemented
8	C₁₇×#3356	C₂	1	3	yes	maximal, complemented
9	C₁₇×#3329	C₂	1	3	yes	maximal, complemented
10	C₁₇×#3328	C₂	1	3	yes	maximal, complemented
11	C₁₇×#3252	C₂	1	3	yes	maximal, complemented
12	C₁₇×#3231	C₂	1	3	yes	maximal, complemented
13	C₁₇×#3108	C₂	1	3	yes	maximal, complemented
14	C₁₇×#3078	C₂	1	3	yes	maximal, complemented
15	C₁₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
17	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
18	C₁₇×#557	—	2	1	no	—
19	C₁₇×#557	C₂²	1	1	yes	characteristic
20	C₁₇×#556	—	2	3	no	—
21	C₁₇×#556	C₂²	1	3	yes	—
22	C₁₇×#555	C₂²	1	3	yes	—
23	C₁₇×#554	—	2	3	no	—
24	C₁₇×#554	C₂²	1	3	yes	—
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×#542	—	2	3	no	—
29	C₁₇×#533	—	2	3	no	—
30	C₁₇×#533	C₂²	1	3	yes	—
31	C₁₇×#533	C₂²	1	3	yes	—
32	C₁₇×#529	C₂²	1	3	yes	—
33	C₁₇×#519	—	2	1	no	—
34	C₄×#41×C₁₇	—	2	1	no	—
35	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×Q₈×C₁₇	C₂²	1	3	yes	—
37	C₁₇×#500	C₂²	1	3	yes	—
38	C₁₇×#498	C₂²	1	3	yes	—
39	C₁₇×#487	C₂²	1	3	yes	—
40	C₁₇×#487	C₂²	1	3	yes	—
41	C₁₇×#485	C₂²	1	6	yes	—
42	C₁₇×#485	C₂²	1	6	yes	—
43	C₁₇×#483	C₂²	1	3	yes	—
44	C₁₇×#480	C₂²	1	3	yes	—
45	C₁₇×#479	C₂²	1	3	yes	—
46	C₁₇×#479	C₂²	1	6	yes	—
47	C₁₇×#479	C₂²	1	3	yes	—
48	C₁₇×#477	C₂²	1	3	yes	—
49	C₁₇×#477	C₂²	1	3	yes	—
50	C₁₇×#477	C₂²	1	3	yes	—
51	C₁₇×#476	C₂²	1	3	yes	—
52	C₁₇×#475	C₂²	1	3	yes	—
53	C₁₇×#475	C₂²	1	3	yes	—
54	C₁₇×#470	C₂²	1	6	yes	—
55	C₁₇×#468	C₂²	1	6	yes	—
56	C₁₇×#464	C₂²	1	3	yes	—
57	C₁₇×#464	C₂²	1	1	yes	characteristic
58	C₁₇×#462	C₂²	1	3	yes	—
59	C₁₇×#461	C₂²	1	3	yes	—
60	C₁₇×#451	C₂²	1	3	yes	—
61	C₁₇×#448	C₂²	1	3	yes	—
62	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
63	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
64	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
65	C₄×Q₁₆×C₁₇	C₂²	1	3	yes	—
66	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
67	C₄×SD₁₆×C₁₇	C₂²	1	3	yes	—
68	C₁₇×#436	C₂²	1	3	yes	—
69	C₁₇×#436	C₂²	1	3	yes	—
70	C₁₇×#431	C₂²	1	3	yes	—
71	C₁₇×#428	C₂²	1	6	yes	—
72	C₁₇×#423	C₂²	1	3	yes	—
73	C₁₇×#419	C₂²	1	6	yes	—
74	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
75	C₂²×Q₈×C₁₇	—	2	1	no	—
76	C₂²×Q₈×C₁₇	C₂³	1	3	yes	—
77	C₂×Q₁₆×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×Q₁₆×C₁₇	C₂³	1	3	yes	—
79	C₂×SD₁₆×C₁₇	C₂³	1	1	yes	characteristic
80	C₂×SD₁₆×C₁₇	C₂³	1	3	yes	—
81	C₂×M₁₆×C₁₇	C₂³	1	6	yes	—
82	C₁₇×C₄⋊Q₈	—	2	3	no	—
83	C₁₇×C₄⋊Q₈	—	2	3	no	—
84	C₁₇×C₄⋊Q₈	—	2	3	no	—
85	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
86	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
87	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
88	C₁₇×C₄⋊Q₈	C₂³	1	3	yes	—
89	C₁₇×#126	—	2	6	no	—
90	C₁₇×#126	—	2	3	no	—
91	C₁₇×#125	—	2	3	no	—
92	C₁₇×#125	—	2	3	no	—
93	C₁₇×#125	—	2	3	no	—
94	C₁₇×#125	C₂³	1	3	yes	—
95	C₁₇×#124	—	2	3	no	—
96	C₁₇×#124	—	2	6	no	—
97	C₁₇×#124	C₂³	1	1	yes	characteristic
98	C₁₇×#123	—	2	3	no	—
99	C₁₇×C₂²⋊Q₈	—	2	3	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	3	yes	—
106	C₁₇×C₂²⋊Q₈	C₂³	1	6	yes	—
107	C₁₇×#121	—	2	3	no	—
108	C₁₇×#121	C₂³	1	3	yes	—
109	C₄×Q₈×C₁₇	—	2	1	no	—
110	C₄×Q₈×C₁₇	—	2	1	no	—
111	C₄×Q₈×C₁₇	—	2	1	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	—	2	3	no	—
117	C₄×Q₈×C₁₇	—	2	3	no	—
118	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
119	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
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	3	yes	—
124	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
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	3	yes	—
130	C₄×D₄×C₁₇	C₂³	1	3	yes	—
131	C₁₇×#117	—	2	3	no	—
132	C₁₇×#117	—	2	3	no	—
133	C₁₇×#117	—	2	3	no	—
134	C₁₇×#117	D₄	1	3	yes	—
135	C₁₇×#117	C₂³	1	6	yes	—
136	C₂×C₄⋊C₄×C₁₇	—	2	3	no	—
137	C₂×C₄⋊C₄×C₁₇	C₂³	1	3	yes	—
138	C₂×C₄²×C₁₇	—	2	3	no	—
139	C₂×C₄²×C₁₇	C₂³	1	3	yes	—
140	C₁₇×#107	C₂³	1	3	yes	—
141	C₁₇×#107	C₂³	1	6	yes	—
142	C₁₇×#107	C₂³	1	3	yes	—
143	C₁₇×#106	C₂³	1	3	yes	—
144	C₁₇×#106	C₂³	1	6	yes	—
145	C₁₇×#106	C₂³	1	3	yes	—
146	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
147	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
148	C₁₇×C₄⋊C₈	C₂³	1	3	yes	—
149	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
150	C₁₇×#103	C₂³	1	3	yes	—
151	C₁₇×#103	C₂³	1	3	yes	—
152	C₁₇×#103	C₂³	1	6	yes	—
153	C₁₇×#103	C₂³	1	6	yes	—
154	C₁₇×#103	C₂³	1	3	yes	—
155	C₁₇×#103	C₂³	1	1	yes	characteristic
156	C₁₇×#103	C₂³	1	3	yes	—
157	C₁₇×#103	C₂³	1	3	yes	—
158	C₁₇×#102	C₂³	1	1	yes	characteristic
159	C₁₇×#102	C₂³	1	3	yes	—
160	C₁₇×C₂²⋊C₈	C₂³	1	3	yes	—
161	C₁₇×C₂²⋊C₈	C₂³	1	3	yes	—
162	C₄×C₈×C₁₇	C₂³	1	3	yes	—
163	C₄×C₈×C₁₇	C₂³	1	3	yes	—
164	#41×C₁₇	—	2	4	no	—
165	C₂×Q₈×C₁₇	—	2	3	no	—
166	C₂×Q₈×C₁₇	—	2	3	no	—
167	C₂×Q₈×C₁₇	—	2	3	no	—
168	C₂×Q₈×C₁₇	—	2	3	no	—
169	C₂×Q₈×C₁₇	—	2	6	no	—
170	C₂×Q₈×C₁₇	—	4	3	no	—
171	C₂×Q₈×C₁₇	—	4	4	no	—
172	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
173	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
174	C₂×Q₈×C₁₇	C₂⁴	1	3	yes	—
175	C₂×Q₈×C₁₇	C₂⁴	1	1	yes	characteristic
176	C₂×D₄×C₁₇	—	2	3	no	—
177	C₂×D₄×C₁₇	C₂×D₄	1	3	yes	—
178	C₂×D₄×C₁₇	C₂⁴	1	1	yes	characteristic
179	C₂²×C₄×C₁₇	—	2	3	no	—
180	C₂²×C₄×C₁₇	—	2	3	no	—
181	C₂²×C₄×C₁₇	—	2	3	no	—
182	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
183	C₂²×C₄×C₁₇	C₂×D₄	1	3	yes	—
184	C₂²×C₄×C₁₇	C₂⁴	1	3	yes	—
185	Q₁₆×C₁₇	—	2	2	no	—
186	Q₁₆×C₁₇	—	4	3	no	—
187	SD₁₆×C₁₇	—	2	2	no	—
188	SD₁₆×C₁₇	—	4	3	no	—
189	M₁₆×C₁₇	—	4	6	no	—
190	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
191	C₂×C₈×C₁₇	C₂⁴	1	3	yes	—
192	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
193	C₂×C₈×C₁₇	C₂⁴	1	1	yes	characteristic
194	C₄⋊C₄×C₁₇	—	2	3	no	—
195	C₄⋊C₄×C₁₇	—	2	3	no	—
196	C₄⋊C₄×C₁₇	—	2	6	no	—
197	C₄⋊C₄×C₁₇	—	2	3	no	—
198	C₄⋊C₄×C₁₇	—	2	3	no	—
199	C₄⋊C₄×C₁₇	—	2	3	no	—
200	C₄⋊C₄×C₁₇	—	2	3	no	—
201	C₄⋊C₄×C₁₇	—	2	3	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	1	no	—
209	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
210	C₄⋊C₄×C₁₇	C₂×D₄	1	3	yes	—
211	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
212	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
213	C₄⋊C₄×C₁₇	C₂⁴	1	3	yes	—
214	C₄⋊C₄×C₁₇	C₂⁴	1	1	yes	characteristic
215	C₂²⋊C₄×C₁₇	—	2	6	no	—
216	C₂²⋊C₄×C₁₇	—	2	6	no	—
217	C₂²⋊C₄×C₁₇	—	2	3	no	—
218	C₂²⋊C₄×C₁₇	—	2	3	no	—
219	C₂²⋊C₄×C₁₇	—	2	1	no	—
220	C₂²⋊C₄×C₁₇	—	2	3	no	—
221	C₂²⋊C₄×C₁₇	—	2	1	no	—
222	C₂²⋊C₄×C₁₇	C₂×D₄	1	6	yes	—
223	C₄²×C₁₇	—	2	6	no	—
224	C₄²×C₁₇	—	2	3	no	—
225	C₄²×C₁₇	—	2	3	no	—
226	C₄²×C₁₇	—	2	3	no	—
227	C₄²×C₁₇	—	2	1	no	—
228	C₄²×C₁₇	—	2	3	no	—
229	C₄²×C₁₇	C₂×D₄	1	3	yes	—
230	C₄²×C₁₇	C₂×D₄	1	3	yes	—
231	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
232	C₄²×C₁₇	C₂⁴	1	3	yes	—
233	#62153	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
234	C₂³×C₁₇	—	2	1	no	—
235	C₂³×C₁₇	C₂²×D₄	1	3	yes	—
236	Q₈×C₁₇	—	2	1	no	—
237	Q₈×C₁₇	—	2	1	no	—
238	Q₈×C₁₇	—	2	3	no	—
239	Q₈×C₁₇	—	2	3	no	—
240	Q₈×C₁₇	—	2	1	no	—
241	Q₈×C₁₇	—	4	6	no	—
242	Q₈×C₁₇	—	4	6	no	—
243	Q₈×C₁₇	—	8	3	no	—
244	Q₈×C₁₇	—	8	3	no	—
245	Q₈×C₁₇	#137	1	4	yes	—
246	Q₈×C₁₇	2₋¹⁺⁴	1	2	yes	—
247	D₄×C₁₇	—	2	6	no	—
248	D₄×C₁₇	—	2	1	no	—
249	D₄×C₁₇	—	2	1	no	—
250	D₄×C₁₇	—	8	3	no	—
251	C₂×C₄×C₁₇	—	2	1	no	—
252	C₂×C₄×C₁₇	—	2	6	no	—
253	C₂×C₄×C₁₇	—	2	3	no	—
254	C₂×C₄×C₁₇	—	2	3	no	—
255	C₂×C₄×C₁₇	—	2	1	no	—
256	C₂×C₄×C₁₇	—	2	1	no	—
257	C₂×C₄×C₁₇	—	2	3	no	—
258	C₂×C₄×C₁₇	—	2	3	no	—
259	C₂×C₄×C₁₇	—	2	3	no	—
260	C₂×C₄×C₁₇	—	2	3	no	—
261	C₂×C₄×C₁₇	—	4	3	no	—
262	C₂×C₄×C₁₇	—	4	6	no	—
263	C₂×C₄×C₁₇	—	4	6	no	—
264	C₂×C₄×C₁₇	—	8	3	no	—
265	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
267	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
269	C₂×C₄×C₁₇	C₂²×D₄	1	3	yes	—
270	C₂×C₄×C₁₇	C₂⁵	1	1	yes	characteristic
271	C₈×C₁₇	—	2	1	no	—
272	C₈×C₁₇	—	2	1	no	—
273	C₈×C₁₇	—	2	3	no	—
274	C₈×C₁₇	—	2	3	no	—
275	#3518	C₂×C₁₇	1	1	yes	characteristic
276	Q₈×#41	C₂×C₁₇	1	1	yes	characteristic, complemented
277	Q₈×Q₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
278	Q₈×SD₁₆	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#3363	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#3359	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#3357	C₂×C₁₇	1	3	yes	complemented
282	#3356	C₂×C₁₇	1	3	yes	complemented
283	#3329	C₂×C₁₇	1	3	yes	complemented
284	#3328	C₂×C₁₇	1	3	yes	complemented
285	#3252	C₂×C₁₇	1	3	yes	complemented
286	#3231	C₂×C₁₇	1	3	yes	complemented
287	#3108	C₂×C₁₇	1	3	yes	complemented
288	#3078	C₂×C₁₇	1	3	yes	complemented
289	#2991	C₂×C₁₇	1	1	yes	characteristic, complemented
290	C₂²×C₁₇	—	2	3	no	—
291	C₂²×C₁₇	—	2	3	no	—
292	C₂²×C₁₇	—	2	3	no	—
293	C₂²×C₁₇	—	4	1	no	—
294	C₂²×C₁₇	—	4	1	no	—
295	C₂²×C₁₇	—	4	1	no	—
296	C₂²×C₁₇	C₂³×D₄	1	1	yes	characteristic
297	C₄×C₁₇	—	2	1	no	—
298	C₄×C₁₇	—	2	3	no	—
299	C₄×C₁₇	—	2	3	no	—
300	C₄×C₁₇	—	2	2	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	4	1	no	—
303	C₄×C₁₇	—	4	3	no	—
304	C₄×C₁₇	—	4	3	no	—
305	C₄×C₁₇	—	4	3	no	—
306	C₄×C₁₇	—	4	1	no	—
307	C₄×C₁₇	—	4	3	no	—
308	C₄×C₁₇	C₂×#137	1	6	yes	—
309	C₄×C₁₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
310	C₄×C₁₇	#585	1	1	yes	characteristic
311	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
312	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
313	#557	—	2	1	no	—
314	#557	C₂²×C₁₇	1	1	yes	characteristic
315	#556	—	2	3	no	—
316	#556	C₂²×C₁₇	1	3	yes	—
317	#555	C₂²×C₁₇	1	3	yes	—
318	#554	—	2	3	no	—
319	#554	C₂²×C₁₇	1	3	yes	—
320	D₄×Q₈	C₂²×C₁₇	1	3	yes	—
321	D₄×Q₈	C₂²×C₁₇	1	1	yes	characteristic
322	#548	—	2	1	no	—
323	#542	—	2	3	no	—
324	#533	—	2	3	no	—
325	#533	C₂²×C₁₇	1	3	yes	—
326	#533	C₂²×C₁₇	1	3	yes	—
327	#529	C₂²×C₁₇	1	3	yes	—
328	#519	—	2	1	no	—
329	C₄×#41	—	2	1	no	—
330	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
331	C₂×C₄×Q₈	C₂²×C₁₇	1	3	yes	—
332	#500	C₂²×C₁₇	1	3	yes	—
333	#498	C₂²×C₁₇	1	3	yes	—
334	#487	C₂²×C₁₇	1	3	yes	—
335	#487	C₂²×C₁₇	1	3	yes	—
336	#485	C₂²×C₁₇	1	6	yes	—
337	#485	C₂²×C₁₇	1	6	yes	—
338	#483	C₂²×C₁₇	1	3	yes	—
339	#480	C₂²×C₁₇	1	3	yes	—
340	#479	C₂²×C₁₇	1	3	yes	—
341	#479	C₂²×C₁₇	1	6	yes	—
342	#479	C₂²×C₁₇	1	3	yes	—
343	#477	C₂²×C₁₇	1	3	yes	—
344	#477	C₂²×C₁₇	1	3	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	#468	C₂²×C₁₇	1	6	yes	—
351	#464	C₂²×C₁₇	1	1	yes	characteristic
352	#464	C₂²×C₁₇	1	3	yes	—
353	#462	C₂²×C₁₇	1	3	yes	—
354	#461	C₂²×C₁₇	1	3	yes	—
355	#451	C₂²×C₁₇	1	3	yes	—
356	#448	C₂²×C₁₇	1	3	yes	—
357	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
358	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
359	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
360	C₄×Q₁₆	C₂²×C₁₇	1	3	yes	—
361	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
362	C₄×SD₁₆	C₂²×C₁₇	1	3	yes	—
363	#436	C₂²×C₁₇	1	3	yes	—
364	#436	C₂²×C₁₇	1	3	yes	—
365	#431	C₂²×C₁₇	1	3	yes	—
366	#428	C₂²×C₁₇	1	6	yes	—
367	#423	C₂²×C₁₇	1	3	yes	—
368	#419	C₂²×C₁₇	1	6	yes	—
369	C₂×C₁₇	—	4	3	no	—
370	C₂×C₁₇	—	8	1	no	—
371	C₂×C₁₇	#3489	1	1	yes	characteristic
372	C₂×C₁₇	C₂²×#137	1	1	yes	characteristic
373	C₂×C₁₇	#3584	1	1	yes	characteristic
374	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
375	C₂²×Q₈	—	2	1	no	—
376	C₂²×Q₈	C₂³×C₁₇	1	3	yes	—
377	C₂×Q₁₆	C₂³×C₁₇	1	1	yes	characteristic
378	C₂×Q₁₆	C₂³×C₁₇	1	3	yes	—
379	C₂×SD₁₆	C₂³×C₁₇	1	1	yes	characteristic
380	C₂×SD₁₆	C₂³×C₁₇	1	3	yes	—
381	C₂×M₁₆	C₂³×C₁₇	1	6	yes	—
382	C₄⋊Q₈	—	2	3	no	—
383	C₄⋊Q₈	—	2	3	no	—
384	C₄⋊Q₈	—	2	3	no	—
385	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
386	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
387	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
388	C₄⋊Q₈	C₂³×C₁₇	1	3	yes	—
389	#126	—	2	6	no	—
390	#126	—	2	3	no	—
391	#125	—	2	3	no	—
392	#125	—	2	3	no	—
393	#125	—	2	3	no	—
394	#125	C₂³×C₁₇	1	3	yes	—
395	#124	—	2	3	no	—
396	#124	—	2	6	no	—
397	#124	C₂³×C₁₇	1	1	yes	characteristic
398	#123	—	2	3	no	—
399	C₂²⋊Q₈	—	2	3	no	—
400	C₂²⋊Q₈	—	2	3	no	—
401	C₂²⋊Q₈	—	2	3	no	—
402	C₂²⋊Q₈	—	2	3	no	—
403	C₂²⋊Q₈	—	2	6	no	—
404	C₂²⋊Q₈	—	2	6	no	—
405	C₂²⋊Q₈	C₂³×C₁₇	1	3	yes	—
406	C₂²⋊Q₈	C₂³×C₁₇	1	6	yes	—
407	#121	—	2	3	no	—
408	#121	C₂³×C₁₇	1	3	yes	—
409	C₄×Q₈	—	2	1	no	—
410	C₄×Q₈	—	2	1	no	—
411	C₄×Q₈	—	2	1	no	—
412	C₄×Q₈	—	2	3	no	—
413	C₄×Q₈	—	2	3	no	—
414	C₄×Q₈	—	2	3	no	—
415	C₄×Q₈	—	2	3	no	—
416	C₄×Q₈	—	2	3	no	—
417	C₄×Q₈	—	2	3	no	—
418	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
419	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
420	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
421	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
422	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
423	C₄×Q₈	C₂³×C₁₇	1	3	yes	—
424	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
425	C₄×D₄	—	2	3	no	—
426	C₄×D₄	—	2	3	no	—
427	C₄×D₄	—	2	3	no	—
428	C₄×D₄	D₄×C₁₇	1	3	yes	—
429	C₄×D₄	C₂³×C₁₇	1	3	yes	—
430	C₄×D₄	C₂³×C₁₇	1	3	yes	—
431	#117	—	2	3	no	—
432	#117	—	2	3	no	—
433	#117	—	2	3	no	—
434	#117	D₄×C₁₇	1	3	yes	—
435	#117	C₂³×C₁₇	1	6	yes	—
436	C₂×C₄⋊C₄	—	2	3	no	—
437	C₂×C₄⋊C₄	C₂³×C₁₇	1	3	yes	—
438	C₂×C₄²	—	2	3	no	—
439	C₂×C₄²	C₂³×C₁₇	1	3	yes	—
440	#107	C₂³×C₁₇	1	3	yes	—
441	#107	C₂³×C₁₇	1	6	yes	—
442	#107	C₂³×C₁₇	1	3	yes	—
443	#106	C₂³×C₁₇	1	3	yes	—
444	#106	C₂³×C₁₇	1	6	yes	—
445	#106	C₂³×C₁₇	1	3	yes	—
446	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
447	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
448	C₄⋊C₈	C₂³×C₁₇	1	3	yes	—
449	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
450	#103	C₂³×C₁₇	1	3	yes	—
451	#103	C₂³×C₁₇	1	3	yes	—
452	#103	C₂³×C₁₇	1	6	yes	—
453	#103	C₂³×C₁₇	1	6	yes	—
454	#103	C₂³×C₁₇	1	3	yes	—
455	#103	C₂³×C₁₇	1	1	yes	characteristic
456	#103	C₂³×C₁₇	1	3	yes	—
457	#103	C₂³×C₁₇	1	3	yes	—
458	#102	C₂³×C₁₇	1	1	yes	characteristic
459	#102	C₂³×C₁₇	1	3	yes	—
460	C₂²⋊C₈	C₂³×C₁₇	1	3	yes	—
461	C₂²⋊C₈	C₂³×C₁₇	1	3	yes	—
462	C₄×C₈	C₂³×C₁₇	1	3	yes	—
463	C₄×C₈	C₂³×C₁₇	1	3	yes	—
464	C₁₇	#62153	1	1	yes	characteristic, direct product factor, Sylow
465	#41	—	2	4	no	—
466	C₂×Q₈	—	2	3	no	—
467	C₂×Q₈	—	2	3	no	—
468	C₂×Q₈	—	2	3	no	—
469	C₂×Q₈	—	2	3	no	—
470	C₂×Q₈	—	2	6	no	—
471	C₂×Q₈	—	4	3	no	—
472	C₂×Q₈	—	4	4	no	—
473	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
474	C₂×Q₈	C₂⁴×C₁₇	1	3	yes	—
475	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
476	C₂×Q₈	C₂⁴×C₁₇	1	1	yes	characteristic
477	C₂×D₄	—	2	3	no	—
478	C₂×D₄	C₂×D₄×C₁₇	1	3	yes	—
479	C₂×D₄	C₂⁴×C₁₇	1	1	yes	characteristic
480	C₂²×C₄	—	2	3	no	—
481	C₂²×C₄	—	2	3	no	—
482	C₂²×C₄	—	2	3	no	—
483	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
484	C₂²×C₄	C₂×D₄×C₁₇	1	3	yes	—
485	C₂²×C₄	C₂⁴×C₁₇	1	3	yes	—
486	Q₁₆	—	2	2	no	—
487	Q₁₆	—	4	3	no	—
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	4	3	no	—
490	M₁₆	—	4	6	no	—
491	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
492	C₂×C₈	C₂⁴×C₁₇	1	1	yes	characteristic
493	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
494	C₂×C₈	C₂⁴×C₁₇	1	3	yes	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	3	no	—
497	C₄⋊C₄	—	2	3	no	—
498	C₄⋊C₄	—	2	3	no	—
499	C₄⋊C₄	—	2	3	no	—
500	C₄⋊C₄	—	2	3	no	—
501	C₄⋊C₄	—	2	3	no	—
502	C₄⋊C₄	—	2	3	no	—
503	C₄⋊C₄	—	2	3	no	—
504	C₄⋊C₄	—	2	3	no	—
505	C₄⋊C₄	—	2	3	no	—
506	C₄⋊C₄	—	2	3	no	—
507	C₄⋊C₄	—	2	3	no	—
508	C₄⋊C₄	—	2	6	no	—
509	C₄⋊C₄	—	2	3	no	—
510	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
511	C₄⋊C₄	C₂×D₄×C₁₇	1	3	yes	—
512	C₄⋊C₄	C₂⁴×C₁₇	1	1	yes	characteristic
513	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
514	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
515	C₄⋊C₄	C₂⁴×C₁₇	1	3	yes	—
516	C₂²⋊C₄	—	2	6	no	—
517	C₂²⋊C₄	—	2	6	no	—
518	C₂²⋊C₄	—	2	3	no	—
519	C₂²⋊C₄	—	2	3	no	—
520	C₂²⋊C₄	—	2	1	no	—
521	C₂²⋊C₄	—	2	1	no	—
522	C₂²⋊C₄	—	2	3	no	—
523	C₂²⋊C₄	C₂×D₄×C₁₇	1	6	yes	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	3	no	—
526	C₄²	—	2	3	no	—
527	C₄²	—	2	3	no	—
528	C₄²	—	2	6	no	—
529	C₄²	—	2	3	no	—
530	C₄²	C₂×D₄×C₁₇	1	3	yes	—
531	C₄²	C₂×D₄×C₁₇	1	3	yes	—
532	C₄²	C₂⁴×C₁₇	1	3	yes	—
533	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
534	C₂³	—	2	1	no	—
535	C₂³	C₂²×D₄×C₁₇	1	3	yes	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	2	3	no	—
539	Q₈	—	2	3	no	—
540	Q₈	—	2	1	no	—
541	Q₈	—	4	6	no	—
542	Q₈	—	4	6	no	—
543	Q₈	—	8	3	no	—
544	Q₈	—	8	3	no	—
545	Q₈	C₁₇×#137	1	4	yes	—
546	Q₈	C₁₇×2₋¹⁺⁴	1	2	yes	—
547	D₄	—	2	6	no	—
548	D₄	—	2	1	no	—
549	D₄	—	2	1	no	—
550	D₄	—	8	3	no	—
551	C₂×C₄	—	2	1	no	—
552	C₂×C₄	—	2	6	no	—
553	C₂×C₄	—	2	3	no	—
554	C₂×C₄	—	2	3	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	3	no	—
558	C₂×C₄	—	2	3	no	—
559	C₂×C₄	—	2	3	no	—
560	C₂×C₄	—	2	3	no	—
561	C₂×C₄	—	4	3	no	—
562	C₂×C₄	—	4	6	no	—
563	C₂×C₄	—	4	6	no	—
564	C₂×C₄	—	8	3	no	—
565	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
566	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
567	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
569	C₂×C₄	C₂²×D₄×C₁₇	1	3	yes	—
570	C₂×C₄	C₂⁵×C₁₇	1	1	yes	characteristic
571	C₈	—	2	1	no	—
572	C₈	—	2	1	no	—
573	C₈	—	2	3	no	—
574	C₈	—	2	3	no	—
575	C₂²	—	2	3	no	—
576	C₂²	—	2	3	no	—
577	C₂²	—	2	3	no	—
578	C₂²	—	4	1	no	—
579	C₂²	—	4	1	no	—
580	C₂²	—	4	1	no	—
581	C₂²	C₂³×D₄×C₁₇	1	1	yes	characteristic
582	C₄	—	2	3	no	—
583	C₄	—	2	2	no	—
584	C₄	—	2	1	no	—
585	C₄	—	2	1	no	—
586	C₄	—	2	3	no	—
587	C₄	—	4	3	no	—
588	C₄	—	4	1	no	—
589	C₄	—	4	3	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	3	no	—
592	C₄	—	4	3	no	—
593	C₄	C₂×C₁₇×#137	1	6	yes	—
594	C₄	C₂×C₁₇×2₋¹⁺⁴	1	1	yes	characteristic
595	C₄	C₁₇×#585	1	1	yes	characteristic
596	C₂	—	4	3	no	—
597	C₂	—	8	1	no	—
598	C₂	C₁₇×#3489	1	1	yes	characteristic
599	C₂	C₂²×C₁₇×#137	1	1	yes	characteristic
600	C₂	C₁₇×#3584	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂³×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁵×C₁₇
prime radical	C₁₇×#3518	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. Q₈×Q₁₆×C₁₇	C₂	semidirect
4. Q₈×SD₁₆×C₁₇	C₂	semidirect
5. C₁₇×#3363	C₂	semidirect
6. C₁₇×#3359	C₂	semidirect
7. C₁₇×#3357	C₂	semidirect
8. C₁₇×#3356	C₂	semidirect
9. C₁₇×#3329	C₂	semidirect
10. C₁₇×#3328	C₂	semidirect
11. C₁₇×#3252	C₂	semidirect
12. C₁₇×#3231	C₂	semidirect
13. C₁₇×#3108	C₂	semidirect
14. C₁₇×#3078	C₂	semidirect
15. C₁₇×#2991	C₂	semidirect
233. #62153	C₁₇	direct (N × H)
276. Q₈×#41	C₂×C₁₇	semidirect
277. Q₈×Q₁₆	C₂×C₁₇	semidirect
278. Q₈×SD₁₆	C₂×C₁₇	semidirect
279. #3363	C₂×C₁₇	semidirect
280. #3359	C₂×C₁₇	semidirect
281. #3357	C₂×C₁₇	semidirect
282. #3356	C₂×C₁₇	semidirect
283. #3329	C₂×C₁₇	semidirect
284. #3328	C₂×C₁₇	semidirect
285. #3252	C₂×C₁₇	semidirect
286. #3231	C₂×C₁₇	semidirect
287. #3108	C₂×C₁₇	semidirect
288. #3078	C₂×C₁₇	semidirect
289. #2991	C₂×C₁₇	semidirect
464. C₁₇	#62153	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×#3518	2
Q₈×#41×C₁₇	2
Q₈×Q₁₆×C₁₇	2
Q₈×SD₁₆×C₁₇	2
C₁₇×#3363	2
C₁₇×#3359	2
C₁₇×#3357	2
C₁₇×#3356	2
C₁₇×#3329	2
C₁₇×#3328	2
C₁₇×#3252	2
C₁₇×#3231	2
C₁₇×#3108	2
C₁₇×#3078	2
C₁₇×#2991	2
#62153	17

Subgroups — C17×#62153 #16919897

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#62153 #16919897