Subgroups — C₁₇×#19412 #16877156

Order 4352.

650 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3207	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3115	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3106	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1684	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1683	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1678	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1668	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1667	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1666	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1665	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1572	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1551	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#532	C₂²	1	1	yes	characteristic
17	C₁₇×#532	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#493	C₂²	1	1	yes	characteristic
20	C₁₇×#492	C₂²	1	1	yes	characteristic
21	C₁₇×#487	C₂²	1	1	yes	characteristic
22	C₁₇×#486	C₂²	1	1	yes	characteristic
23	C₁₇×#482	—	2	1	no	—
24	C₁₇×#482	—	2	1	no	—
25	C₁₇×#477	C₂²	1	1	yes	characteristic
26	C₁₇×#476	C₂²	1	1	yes	characteristic
27	C₁₇×#475	C₂²	1	1	yes	characteristic
28	C₁₇×#474	C₂²	1	1	yes	characteristic
29	C₁₇×#463	—	2	1	no	—
30	C₁₇×#463	—	2	1	no	—
31	C₁₇×#460	C₂²	1	1	yes	characteristic
32	C₁₇×#460	C₂²	1	1	yes	characteristic
33	C₁₇×#459	C₂²	1	1	yes	characteristic
34	C₁₇×#459	C₂²	1	1	yes	characteristic
35	C₁₇×#449	—	2	1	no	—
36	C₁₇×#449	—	2	1	no	—
37	C₁₇×#449	—	2	1	no	—
38	C₁₇×#449	—	2	1	no	—
39	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
40	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
41	C₁₇×#442	—	2	1	no	—
42	C₁₇×#440	—	2	1	no	—
43	C₄×SD₁₆×C₁₇	—	2	1	no	—
44	C₄×D₈×C₁₇	—	2	1	no	—
45	C₈×D₄×C₁₇	—	2	1	no	—
46	C₈×D₄×C₁₇	—	2	1	no	—
47	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
48	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
49	C₁₇×#432	C₂²	1	1	yes	characteristic
50	C₁₇×#431	—	2	1	no	—
51	C₁₇×#431	C₂²	1	1	yes	characteristic
52	C₁₇×#431	C₂²	1	1	yes	characteristic
53	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
54	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
55	C₁₇×#335	C₂²	1	1	yes	characteristic
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#334	C₂²	1	1	yes	characteristic
58	C₁₇×#334	C₂²	1	1	yes	characteristic
59	C₁₇×#333	C₂²	1	1	yes	characteristic
60	C₁₇×#333	C₂²	1	1	yes	characteristic
61	C₁₇×#332	C₂²	1	1	yes	characteristic
62	C₁₇×#332	C₂²	1	1	yes	characteristic
63	C₁₇×#331	C₂²	1	1	yes	characteristic
64	C₁₇×#331	C₂²	1	1	yes	characteristic
65	C₁₇×#331	C₂²	1	1	yes	characteristic
66	C₁₇×#331	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	—	2	1	no	—
68	C₂×#41×C₁₇	—	2	1	no	—
69	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
70	C₂×SD₁₆×C₁₇	—	2	1	no	—
71	C₂×SD₁₆×C₁₇	—	2	1	no	—
72	C₂×SD₁₆×C₁₇	—	2	1	no	—
73	C₂×SD₁₆×C₁₇	—	2	1	no	—
74	C₂×D₈×C₁₇	—	2	1	no	—
75	C₂×D₈×C₁₇	—	2	1	no	—
76	C₂×D₈×C₁₇	—	2	1	no	—
77	C₂×D₈×C₁₇	—	2	1	no	—
78	C₂²×C₈×C₁₇	—	2	1	no	—
79	C₂²×C₈×C₁₇	—	2	1	no	—
80	C₂²×C₈×C₁₇	—	2	1	no	—
81	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
83	C₁₇×#127	C₂³	1	1	yes	characteristic
84	C₁₇×#127	C₂³	1	1	yes	characteristic
85	C₁₇×#124	—	2	1	no	—
86	C₁₇×#124	—	2	1	no	—
87	C₁₇×#121	—	2	1	no	—
88	C₁₇×#121	—	2	1	no	—
89	C₁₇×#121	—	2	1	no	—
90	C₁₇×#121	—	2	1	no	—
91	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
92	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
93	C₄×D₄×C₁₇	—	2	1	no	—
94	C₄×D₄×C₁₇	—	2	1	no	—
95	C₄×D₄×C₁₇	—	2	1	no	—
96	C₄×D₄×C₁₇	—	2	1	no	—
97	C₄×D₄×C₁₇	—	2	1	no	—
98	C₄×D₄×C₁₇	—	2	1	no	—
99	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
100	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
101	C₁₇×#117	—	2	1	no	—
102	C₁₇×#117	D₄	1	1	yes	characteristic
103	C₂×C₄²×C₁₇	—	2	1	no	—
104	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
105	C₁₇×#107	—	2	1	no	—
106	C₁₇×#107	—	2	1	no	—
107	C₁₇×#106	—	2	1	no	—
108	C₁₇×#106	—	2	1	no	—
109	C₁₇×C₄⋊C₈	—	2	1	no	—
110	C₁₇×C₄⋊C₈	—	2	1	no	—
111	C₁₇×C₄⋊C₈	—	2	1	no	—
112	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
113	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
114	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
115	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
116	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
117	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
118	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
119	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
120	C₁₇×#103	—	2	1	no	—
121	C₁₇×#103	—	2	1	no	—
122	C₁₇×#103	—	2	1	no	—
123	C₁₇×#103	—	2	1	no	—
124	C₁₇×#102	—	2	1	no	—
125	C₁₇×#102	—	2	1	no	—
126	C₁₇×#102	—	2	1	no	—
127	C₁₇×#102	—	2	1	no	—
128	C₁₇×#102	—	2	1	no	—
129	C₁₇×#102	—	2	1	no	—
130	C₁₇×#102	—	2	1	no	—
131	C₁₇×#102	—	2	1	no	—
132	C₁₇×C₂²⋊C₈	—	2	1	no	—
133	C₁₇×C₂²⋊C₈	—	2	1	no	—
134	C₁₇×C₂²⋊C₈	—	2	1	no	—
135	C₁₇×C₂²⋊C₈	—	2	1	no	—
136	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
137	C₁₇×C₂²⋊C₈	D₄	1	1	yes	characteristic
138	C₁₇×#97	—	2	1	no	—
139	C₄×C₈×C₁₇	—	2	1	no	—
140	C₄×C₈×C₁₇	—	2	1	no	—
141	C₄×C₈×C₁₇	—	2	1	no	—
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	2	2	no	—
145	#41×C₁₇	—	2	2	no	—
146	#41×C₁₇	—	8	1	no	—
147	#41×C₁₇	—	8	1	no	—
148	#41×C₁₇	—	8	2	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	—	2	1	no	—
151	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	2	1	no	—
157	C₂×D₄×C₁₇	—	2	1	no	—
158	C₂×D₄×C₁₇	—	2	1	no	—
159	C₂×D₄×C₁₇	—	4	1	no	—
160	C₂×D₄×C₁₇	—	4	1	no	—
161	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	—	2	1	no	—
163	C₂²×C₄×C₁₇	—	2	1	no	—
164	C₂²×C₄×C₁₇	—	2	1	no	—
165	C₂²×C₄×C₁₇	—	4	1	no	—
166	C₂²×C₄×C₁₇	—	4	1	no	—
167	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
170	SD₁₆×C₁₇	—	4	2	no	—
171	SD₁₆×C₁₇	—	4	2	no	—
172	SD₁₆×C₁₇	—	8	1	no	—
173	SD₁₆×C₁₇	—	8	1	no	—
174	D₈×C₁₇	—	4	2	no	—
175	D₈×C₁₇	—	4	2	no	—
176	D₈×C₁₇	—	8	1	no	—
177	D₈×C₁₇	—	8	1	no	—
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	—	8	1	no	—
185	C₂×C₈×C₁₇	—	8	1	no	—
186	C₂×C₈×C₁₇	—	8	1	no	—
187	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₁₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
198	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
199	C₂²⋊C₄×C₁₇	—	2	1	no	—
200	C₂²⋊C₄×C₁₇	—	2	1	no	—
201	C₂²⋊C₄×C₁₇	—	2	1	no	—
202	C₂²⋊C₄×C₁₇	—	4	1	no	—
203	C₂²⋊C₄×C₁₇	—	4	1	no	—
204	C₂²⋊C₄×C₁₇	—	4	1	no	—
205	C₂²⋊C₄×C₁₇	—	4	1	no	—
206	C₄²×C₁₇	—	2	1	no	—
207	C₄²×C₁₇	—	2	1	no	—
208	C₄²×C₁₇	—	2	1	no	—
209	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
210	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
211	C₄²×C₁₇	#41	1	1	yes	characteristic
212	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
213	#19412	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂³×C₁₇	—	2	1	no	—
215	C₂³×C₁₇	—	4	1	no	—
216	C₂³×C₁₇	—	4	1	no	—
217	C₂³×C₁₇	#121	1	1	yes	characteristic
218	Q₈×C₁₇	—	2	1	no	—
219	Q₈×C₁₇	—	4	1	no	—
220	Q₈×C₁₇	—	4	1	no	—
221	Q₈×C₁₇	—	8	1	no	—
222	Q₈×C₁₇	#135	1	2	yes	—
223	D₄×C₁₇	—	2	4	no	—
224	D₄×C₁₇	—	2	1	no	—
225	D₄×C₁₇	—	4	1	no	—
226	D₄×C₁₇	—	4	1	no	—
227	D₄×C₁₇	—	4	1	no	—
228	D₄×C₁₇	—	4	1	no	—
229	D₄×C₁₇	—	4	1	no	—
230	D₄×C₁₇	—	4	1	no	—
231	D₄×C₁₇	—	4	1	no	—
232	D₄×C₁₇	—	4	1	no	—
233	D₄×C₁₇	—	8	1	no	—
234	D₄×C₁₇	—	8	1	no	—
235	D₄×C₁₇	—	8	2	no	—
236	D₄×C₁₇	—	8	2	no	—
237	D₄×C₁₇	#135	1	2	yes	—
238	C₂×C₄×C₁₇	—	2	4	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	1	no	—
241	C₂×C₄×C₁₇	—	2	1	no	—
242	C₂×C₄×C₁₇	—	2	1	no	—
243	C₂×C₄×C₁₇	—	2	1	no	—
244	C₂×C₄×C₁₇	—	2	1	no	—
245	C₂×C₄×C₁₇	—	2	1	no	—
246	C₂×C₄×C₁₇	—	4	1	no	—
247	C₂×C₄×C₁₇	—	4	1	no	—
248	C₂×C₄×C₁₇	—	4	1	no	—
249	C₂×C₄×C₁₇	—	4	1	no	—
250	C₂×C₄×C₁₇	—	4	1	no	—
251	C₂×C₄×C₁₇	—	8	1	no	—
252	C₂×C₄×C₁₇	—	8	2	no	—
253	C₂×C₄×C₁₇	—	8	2	no	—
254	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
255	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
256	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
257	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
258	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
259	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
260	C₈×C₁₇	—	2	1	no	—
261	C₈×C₁₇	—	2	1	no	—
262	C₈×C₁₇	—	2	1	no	—
263	C₈×C₁₇	—	2	1	no	—
264	C₈×C₁₇	—	4	1	no	—
265	C₈×C₁₇	—	4	1	no	—
266	C₈×C₁₇	—	4	1	no	—
267	C₈×C₁₇	—	4	1	no	—
268	C₈×C₁₇	—	4	1	no	—
269	C₈×C₁₇	—	4	1	no	—
270	#3207	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#3115	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#3106	C₂×C₁₇	1	1	yes	characteristic, complemented
273	#2988	C₂×C₁₇	1	1	yes	characteristic, complemented
274	#1684	C₂×C₁₇	1	1	yes	characteristic, complemented
275	#1683	C₂×C₁₇	1	1	yes	characteristic, complemented
276	#1678	C₂×C₁₇	1	1	yes	characteristic, complemented
277	#1677	C₂×C₁₇	1	1	yes	characteristic, complemented
278	#1668	C₂×C₁₇	1	1	yes	characteristic, complemented
279	#1667	C₂×C₁₇	1	1	yes	characteristic, complemented
280	#1666	C₂×C₁₇	1	1	yes	characteristic, complemented
281	#1665	C₂×C₁₇	1	1	yes	characteristic, complemented
282	#1572	C₂×C₁₇	1	1	yes	characteristic, complemented
283	#1551	C₂×C₁₇	1	1	yes	characteristic, complemented
284	#1540	C₂×C₁₇	1	1	yes	characteristic, complemented
285	C₂²×C₁₇	—	2	1	no	—
286	C₂²×C₁₇	—	2	1	no	—
287	C₂²×C₁₇	—	2	2	no	—
288	C₂²×C₁₇	—	2	1	no	—
289	C₂²×C₁₇	—	4	1	no	—
290	C₂²×C₁₇	—	4	1	no	—
291	C₂²×C₁₇	—	8	1	no	—
292	C₂²×C₁₇	—	8	1	no	—
293	C₂²×C₁₇	—	8	1	no	—
294	C₂²×C₁₇	—	8	1	no	—
295	C₂²×C₁₇	—	8	1	no	—
296	C₂²×C₁₇	—	8	1	no	—
297	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
298	C₄×C₁₇	—	2	1	no	—
299	C₄×C₁₇	—	2	1	no	—
300	C₄×C₁₇	—	2	2	no	—
301	C₄×C₁₇	—	2	1	no	—
302	C₄×C₁₇	—	2	1	no	—
303	C₄×C₁₇	—	4	1	no	—
304	C₄×C₁₇	—	4	1	no	—
305	C₄×C₁₇	—	8	1	no	—
306	C₄×C₁₇	—	8	1	no	—
307	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
308	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
309	C₄×C₁₇	#576	1	1	yes	characteristic
310	C₄×C₁₇	#577	1	1	yes	characteristic
311	#532	C₂²×C₁₇	1	1	yes	characteristic
312	#532	C₂²×C₁₇	1	1	yes	characteristic
313	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
314	#493	C₂²×C₁₇	1	1	yes	characteristic
315	#492	C₂²×C₁₇	1	1	yes	characteristic
316	#487	C₂²×C₁₇	1	1	yes	characteristic
317	#486	C₂²×C₁₇	1	1	yes	characteristic
318	#482	—	2	1	no	—
319	#482	—	2	1	no	—
320	#477	C₂²×C₁₇	1	1	yes	characteristic
321	#476	C₂²×C₁₇	1	1	yes	characteristic
322	#475	C₂²×C₁₇	1	1	yes	characteristic
323	#474	C₂²×C₁₇	1	1	yes	characteristic
324	#463	—	2	1	no	—
325	#463	—	2	1	no	—
326	#460	C₂²×C₁₇	1	1	yes	characteristic
327	#460	C₂²×C₁₇	1	1	yes	characteristic
328	#459	C₂²×C₁₇	1	1	yes	characteristic
329	#459	C₂²×C₁₇	1	1	yes	characteristic
330	#449	—	2	1	no	—
331	#449	—	2	1	no	—
332	#449	—	2	1	no	—
333	#449	—	2	1	no	—
334	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
335	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
336	#442	—	2	1	no	—
337	#440	—	2	1	no	—
338	C₄×SD₁₆	—	2	1	no	—
339	C₄×D₈	—	2	1	no	—
340	C₈×D₄	—	2	1	no	—
341	C₈×D₄	—	2	1	no	—
342	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
343	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
344	#432	C₂²×C₁₇	1	1	yes	characteristic
345	#431	—	2	1	no	—
346	#431	C₂²×C₁₇	1	1	yes	characteristic
347	#431	C₂²×C₁₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	—	2	1	no	—
349	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
350	#335	C₂²×C₁₇	1	1	yes	characteristic
351	#335	C₂²×C₁₇	1	1	yes	characteristic
352	#334	C₂²×C₁₇	1	1	yes	characteristic
353	#334	C₂²×C₁₇	1	1	yes	characteristic
354	#333	C₂²×C₁₇	1	1	yes	characteristic
355	#333	C₂²×C₁₇	1	1	yes	characteristic
356	#332	C₂²×C₁₇	1	1	yes	characteristic
357	#332	C₂²×C₁₇	1	1	yes	characteristic
358	#331	C₂²×C₁₇	1	1	yes	characteristic
359	#331	C₂²×C₁₇	1	1	yes	characteristic
360	#331	C₂²×C₁₇	1	1	yes	characteristic
361	#331	C₂²×C₁₇	1	1	yes	characteristic
362	C₂×C₁₇	—	4	1	no	—
363	C₂×C₁₇	—	4	2	no	—
364	C₂×C₁₇	—	16	1	no	—
365	C₂×C₁₇	—	16	1	no	—
366	C₂×C₁₇	#3045	1	1	yes	characteristic
367	C₂×C₁₇	#3050	1	1	yes	characteristic
368	C₂×C₁₇	#3068	1	1	yes	characteristic
369	C₂×#41	—	2	1	no	—
370	C₂×#41	—	2	1	no	—
371	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
372	C₂×SD₁₆	—	2	1	no	—
373	C₂×SD₁₆	—	2	1	no	—
374	C₂×SD₁₆	—	2	1	no	—
375	C₂×SD₁₆	—	2	1	no	—
376	C₂×D₈	—	2	1	no	—
377	C₂×D₈	—	2	1	no	—
378	C₂×D₈	—	2	1	no	—
379	C₂×D₈	—	2	1	no	—
380	C₂²×C₈	—	2	1	no	—
381	C₂²×C₈	—	2	1	no	—
382	C₂²×C₈	—	2	1	no	—
383	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
384	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
385	#127	C₂³×C₁₇	1	1	yes	characteristic
386	#127	C₂³×C₁₇	1	1	yes	characteristic
387	#124	—	2	1	no	—
388	#124	—	2	1	no	—
389	#121	—	2	1	no	—
390	#121	—	2	1	no	—
391	#121	—	2	1	no	—
392	#121	—	2	1	no	—
393	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
394	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
395	C₄×D₄	—	2	1	no	—
396	C₄×D₄	—	2	1	no	—
397	C₄×D₄	—	2	1	no	—
398	C₄×D₄	—	2	1	no	—
399	C₄×D₄	—	2	1	no	—
400	C₄×D₄	—	2	1	no	—
401	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
402	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
403	#117	—	2	1	no	—
404	#117	D₄×C₁₇	1	1	yes	characteristic
405	C₂×C₄²	—	2	1	no	—
406	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
407	#107	—	2	1	no	—
408	#107	—	2	1	no	—
409	#106	—	2	1	no	—
410	#106	—	2	1	no	—
411	C₄⋊C₈	—	2	1	no	—
412	C₄⋊C₈	—	2	1	no	—
413	C₄⋊C₈	—	2	1	no	—
414	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
415	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
416	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
417	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
418	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
419	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
420	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
421	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
422	#103	—	2	1	no	—
423	#103	—	2	1	no	—
424	#103	—	2	1	no	—
425	#103	—	2	1	no	—
426	#102	—	2	1	no	—
427	#102	—	2	1	no	—
428	#102	—	2	1	no	—
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	C₂²⋊C₈	—	2	1	no	—
435	C₂²⋊C₈	—	2	1	no	—
436	C₂²⋊C₈	—	2	1	no	—
437	C₂²⋊C₈	—	2	1	no	—
438	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
439	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
440	#97	—	2	1	no	—
441	C₄×C₈	—	2	1	no	—
442	C₄×C₈	—	2	1	no	—
443	C₄×C₈	—	2	1	no	—
444	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
445	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
446	C₁₇	#19412	1	1	yes	characteristic, direct product factor, Sylow
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	8	1	no	—
450	#41	—	8	1	no	—
451	#41	—	8	2	no	—
452	C₂×Q₈	—	2	1	no	—
453	C₂×Q₈	—	2	1	no	—
454	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
455	C₂×D₄	—	2	1	no	—
456	C₂×D₄	—	2	1	no	—
457	C₂×D₄	—	2	1	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	4	1	no	—
463	C₂×D₄	—	4	1	no	—
464	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	4	1	no	—
469	C₂²×C₄	—	4	1	no	—
470	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
471	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
472	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
473	SD₁₆	—	4	2	no	—
474	SD₁₆	—	4	2	no	—
475	SD₁₆	—	8	1	no	—
476	SD₁₆	—	8	1	no	—
477	D₈	—	4	2	no	—
478	D₈	—	4	2	no	—
479	D₈	—	8	1	no	—
480	D₈	—	8	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	—	8	1	no	—
488	C₂×C₈	—	8	1	no	—
489	C₂×C₈	—	8	1	no	—
490	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
491	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
493	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
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	C₂×D₄×C₁₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
502	C₂²⋊C₄	—	2	1	no	—
503	C₂²⋊C₄	—	2	1	no	—
504	C₂²⋊C₄	—	2	1	no	—
505	C₂²⋊C₄	—	4	1	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₂²⋊C₄	—	4	1	no	—
509	C₄²	—	2	1	no	—
510	C₄²	—	2	1	no	—
511	C₄²	—	2	1	no	—
512	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
513	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
514	C₄²	#41×C₁₇	1	1	yes	characteristic
515	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
516	C₂³	—	2	1	no	—
517	C₂³	—	4	1	no	—
518	C₂³	—	4	1	no	—
519	C₂³	C₁₇×#121	1	1	yes	characteristic
520	Q₈	—	2	1	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	8	1	no	—
524	Q₈	C₁₇×#135	1	2	yes	—
525	D₄	—	2	4	no	—
526	D₄	—	2	1	no	—
527	D₄	—	4	1	no	—
528	D₄	—	4	1	no	—
529	D₄	—	4	1	no	—
530	D₄	—	4	1	no	—
531	D₄	—	4	1	no	—
532	D₄	—	4	1	no	—
533	D₄	—	4	1	no	—
534	D₄	—	4	1	no	—
535	D₄	—	8	1	no	—
536	D₄	—	8	1	no	—
537	D₄	—	8	2	no	—
538	D₄	—	8	2	no	—
539	D₄	C₁₇×#135	1	2	yes	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	1	no	—
543	C₂×C₄	—	2	1	no	—
544	C₂×C₄	—	2	1	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	4	1	no	—
549	C₂×C₄	—	4	1	no	—
550	C₂×C₄	—	4	1	no	—
551	C₂×C₄	—	4	1	no	—
552	C₂×C₄	—	4	1	no	—
553	C₂×C₄	—	8	1	no	—
554	C₂×C₄	—	8	2	no	—
555	C₂×C₄	—	8	2	no	—
556	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
557	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
558	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
559	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
560	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
561	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
562	C₈	—	2	1	no	—
563	C₈	—	2	1	no	—
564	C₈	—	2	1	no	—
565	C₈	—	2	1	no	—
566	C₈	—	4	1	no	—
567	C₈	—	4	1	no	—
568	C₈	—	4	1	no	—
569	C₈	—	4	1	no	—
570	C₈	—	4	1	no	—
571	C₈	—	4	1	no	—
572	C₂²	—	2	1	no	—
573	C₂²	—	2	1	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	1	no	—
577	C₂²	—	4	1	no	—
578	C₂²	—	8	1	no	—
579	C₂²	—	8	1	no	—
580	C₂²	—	8	1	no	—
581	C₂²	—	8	1	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
585	C₄	—	2	1	no	—
586	C₄	—	2	1	no	—
587	C₄	—	2	2	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	4	1	no	—
591	C₄	—	4	1	no	—
592	C₄	—	8	1	no	—
593	C₄	—	8	1	no	—
594	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
595	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
596	C₄	C₁₇×#576	1	1	yes	characteristic
597	C₄	C₁₇×#577	1	1	yes	characteristic
598	C₂	—	4	1	no	—
599	C₂	—	4	2	no	—
600	C₂	—	16	1	no	—
601	C₂	—	16	1	no	—
602	C₂	C₁₇×#3045	1	1	yes	characteristic
603	C₂	C₁₇×#3050	1	1	yes	characteristic
604	C₂	C₁₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3207	C₂	semidirect
2. C₁₇×#3115	C₂	semidirect
3. C₁₇×#3106	C₂	semidirect
4. C₁₇×#2988	C₂	semidirect
5. C₁₇×#1684	C₂	semidirect
6. C₁₇×#1683	C₂	semidirect
7. C₁₇×#1678	C₂	semidirect
8. C₁₇×#1677	C₂	semidirect
9. C₁₇×#1668	C₂	semidirect
10. C₁₇×#1667	C₂	semidirect
11. C₁₇×#1666	C₂	semidirect
12. C₁₇×#1665	C₂	semidirect
13. C₁₇×#1572	C₂	semidirect
14. C₁₇×#1551	C₂	semidirect
15. C₁₇×#1540	C₂	semidirect
213. #19412	C₁₇	direct (N × H)
270. #3207	C₂×C₁₇	semidirect
271. #3115	C₂×C₁₇	semidirect
272. #3106	C₂×C₁₇	semidirect
273. #2988	C₂×C₁₇	semidirect
274. #1684	C₂×C₁₇	semidirect
275. #1683	C₂×C₁₇	semidirect
276. #1678	C₂×C₁₇	semidirect
277. #1677	C₂×C₁₇	semidirect
278. #1668	C₂×C₁₇	semidirect
279. #1667	C₂×C₁₇	semidirect
280. #1666	C₂×C₁₇	semidirect
281. #1665	C₂×C₁₇	semidirect
282. #1572	C₂×C₁₇	semidirect
283. #1551	C₂×C₁₇	semidirect
284. #1540	C₂×C₁₇	semidirect
446. C₁₇	#19412	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×#3207	2
C₁₇×#3115	2
C₁₇×#3106	2
C₁₇×#2988	2
C₁₇×#1684	2
C₁₇×#1683	2
C₁₇×#1678	2
C₁₇×#1677	2
C₁₇×#1668	2
C₁₇×#1667	2
C₁₇×#1666	2
C₁₇×#1665	2
C₁₇×#1572	2
C₁₇×#1551	2
C₁₇×#1540	2
#19412	17

Subgroups — C17×#19412 #16877156

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19412 #16877156