Subgroups — C₁₇×#19419 #16877163

Order 4352.

616 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3228	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3116	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3106	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1682	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1681	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×#1676	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1672	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1671	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×#1542	C₂	1	1	yes	maximal, characteristic, complemented
16	C₁₇×#533	C₂²	1	1	yes	characteristic
17	C₁₇×#532	C₂²	1	1	yes	characteristic
18	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
19	C₁₇×#500	C₂²	1	1	yes	characteristic
20	C₁₇×#498	C₂²	1	1	yes	characteristic
21	C₁₇×#486	C₂²	1	1	yes	characteristic
22	C₁₇×#486	C₂²	1	1	yes	characteristic
23	C₁₇×#485	—	2	1	no	—
24	C₁₇×#482	—	2	1	no	—
25	C₁₇×#482	—	2	1	no	—
26	C₁₇×#482	—	2	1	no	—
27	C₁₇×#478	—	2	1	no	—
28	C₁₇×#478	—	2	1	no	—
29	C₁₇×#477	C₂²	1	1	yes	characteristic
30	C₁₇×#477	C₂²	1	1	yes	characteristic
31	C₁₇×#476	C₂²	1	1	yes	characteristic
32	C₁₇×#476	C₂²	1	1	yes	characteristic
33	C₁₇×#462	C₂²	1	1	yes	characteristic
34	C₁₇×#461	C₂²	1	1	yes	characteristic
35	C₁₇×#460	C₂²	1	1	yes	characteristic
36	C₁₇×#459	C₂²	1	1	yes	characteristic
37	C₁₇×#452	—	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×#441	—	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×#333	C₂²	1	1	yes	characteristic
62	C₁₇×#333	C₂²	1	1	yes	characteristic
63	C₁₇×#332	C₂²	1	1	yes	characteristic
64	C₁₇×#332	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	D₄	1	1	yes	characteristic
69	C₂×Q₁₆×C₁₇	—	2	1	no	—
70	C₂×SD₁₆×C₁₇	—	2	1	no	—
71	C₂×SD₁₆×C₁₇	—	2	1	no	—
72	C₂×D₈×C₁₇	—	2	1	no	—
73	C₂²×C₈×C₁₇	—	2	1	no	—
74	C₂²×C₈×C₁₇	—	2	1	no	—
75	C₂²×C₈×C₁₇	—	2	1	no	—
76	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
77	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
78	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
79	C₁₇×#127	C₂³	1	1	yes	characteristic
80	C₁₇×#125	—	2	1	no	—
81	C₁₇×#124	—	2	1	no	—
82	C₁₇×C₂²⋊Q₈	—	2	1	no	—
83	C₁₇×C₂²⋊Q₈	—	2	1	no	—
84	C₁₇×#121	—	2	1	no	—
85	C₁₇×#121	—	2	1	no	—
86	C₄×Q₈×C₁₇	—	2	1	no	—
87	C₄×Q₈×C₁₇	—	2	1	no	—
88	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
89	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
90	C₄×D₄×C₁₇	—	2	1	no	—
91	C₄×D₄×C₁₇	—	2	1	no	—
92	C₄×D₄×C₁₇	—	2	1	no	—
93	C₄×D₄×C₁₇	—	2	1	no	—
94	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
95	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
96	C₁₇×#117	—	2	1	no	—
97	C₁₇×#117	—	2	1	no	—
98	C₁₇×#117	D₄	1	1	yes	characteristic
99	C₂×C₄²×C₁₇	—	2	1	no	—
100	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
101	C₁₇×#107	—	2	1	no	—
102	C₁₇×#107	—	2	1	no	—
103	C₁₇×#107	—	2	1	no	—
104	C₁₇×#107	—	2	1	no	—
105	C₁₇×#106	—	2	1	no	—
106	C₁₇×#106	—	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	2	no	—
147	C₂×Q₈×C₁₇	—	2	1	no	—
148	C₂×Q₈×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	2	1	no	—
150	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
156	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
163	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
164	Q₁₆×C₁₇	—	4	2	no	—
165	SD₁₆×C₁₇	—	4	2	no	—
166	SD₁₆×C₁₇	—	4	2	no	—
167	D₈×C₁₇	—	4	2	no	—
168	C₂×C₈×C₁₇	—	2	1	no	—
169	C₂×C₈×C₁₇	—	2	1	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₂×C₈×C₁₇	—	2	1	no	—
173	C₂×C₈×C₁₇	—	2	1	no	—
174	C₂×C₈×C₁₇	—	8	1	no	—
175	C₂×C₈×C₁₇	—	8	1	no	—
176	C₂×C₈×C₁₇	—	8	1	no	—
177	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
178	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
179	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
180	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
181	C₄⋊C₄×C₁₇	—	2	1	no	—
182	C₄⋊C₄×C₁₇	—	2	1	no	—
183	C₄⋊C₄×C₁₇	—	2	1	no	—
184	C₄⋊C₄×C₁₇	—	2	1	no	—
185	C₄⋊C₄×C₁₇	—	2	1	no	—
186	C₄⋊C₄×C₁₇	—	2	1	no	—
187	C₄⋊C₄×C₁₇	—	2	1	no	—
188	C₄⋊C₄×C₁₇	—	2	1	no	—
189	C₄⋊C₄×C₁₇	—	4	1	no	—
190	C₄⋊C₄×C₁₇	—	4	1	no	—
191	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
192	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
193	C₂²⋊C₄×C₁₇	—	2	1	no	—
194	C₂²⋊C₄×C₁₇	—	2	1	no	—
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₂²⋊C₄×C₁₇	—	4	1	no	—
197	C₂²⋊C₄×C₁₇	—	4	1	no	—
198	C₂²⋊C₄×C₁₇	—	4	1	no	—
199	C₄²×C₁₇	—	2	1	no	—
200	C₄²×C₁₇	—	2	1	no	—
201	C₄²×C₁₇	—	2	1	no	—
202	C₄²×C₁₇	—	4	1	no	—
203	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
204	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₇	#41	1	1	yes	characteristic
206	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
207	#19419	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
208	C₂³×C₁₇	—	2	1	no	—
209	C₂³×C₁₇	—	4	1	no	—
210	C₂³×C₁₇	#121	1	1	yes	characteristic
211	Q₈×C₁₇	—	2	1	no	—
212	Q₈×C₁₇	—	4	1	no	—
213	Q₈×C₁₇	—	4	1	no	—
214	Q₈×C₁₇	—	8	1	no	—
215	Q₈×C₁₇	—	8	1	no	—
216	Q₈×C₁₇	#135	1	2	yes	—
217	D₄×C₁₇	—	2	4	no	—
218	D₄×C₁₇	—	2	1	no	—
219	D₄×C₁₇	—	4	1	no	—
220	D₄×C₁₇	—	4	1	no	—
221	D₄×C₁₇	—	4	1	no	—
222	D₄×C₁₇	—	4	1	no	—
223	D₄×C₁₇	—	8	1	no	—
224	D₄×C₁₇	—	8	2	no	—
225	D₄×C₁₇	#135	1	2	yes	—
226	C₂×C₄×C₁₇	—	2	4	no	—
227	C₂×C₄×C₁₇	—	2	1	no	—
228	C₂×C₄×C₁₇	—	2	1	no	—
229	C₂×C₄×C₁₇	—	2	1	no	—
230	C₂×C₄×C₁₇	—	2	1	no	—
231	C₂×C₄×C₁₇	—	2	1	no	—
232	C₂×C₄×C₁₇	—	2	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	4	1	no	—
235	C₂×C₄×C₁₇	—	4	1	no	—
236	C₂×C₄×C₁₇	—	4	1	no	—
237	C₂×C₄×C₁₇	—	4	1	no	—
238	C₂×C₄×C₁₇	—	4	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	—	8	1	no	—
241	C₂×C₄×C₁₇	—	8	2	no	—
242	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
243	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
244	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
248	C₈×C₁₇	—	2	1	no	—
249	C₈×C₁₇	—	2	1	no	—
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	4	1	no	—
253	C₈×C₁₇	—	4	1	no	—
254	C₈×C₁₇	—	4	1	no	—
255	C₈×C₁₇	—	4	1	no	—
256	C₈×C₁₇	—	4	1	no	—
257	C₈×C₁₇	—	4	1	no	—
258	#3228	C₂×C₁₇	1	1	yes	characteristic, complemented
259	#3116	C₂×C₁₇	1	1	yes	characteristic, complemented
260	#3106	C₂×C₁₇	1	1	yes	characteristic
261	#2988	C₂×C₁₇	1	1	yes	characteristic, complemented
262	#1682	C₂×C₁₇	1	1	yes	characteristic, complemented
263	#1681	C₂×C₁₇	1	1	yes	characteristic, complemented
264	#1678	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1677	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#1676	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#1675	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#1672	C₂×C₁₇	1	1	yes	characteristic, complemented
269	#1671	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1572	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1551	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1542	C₂×C₁₇	1	1	yes	characteristic, complemented
273	C₂²×C₁₇	—	2	1	no	—
274	C₂²×C₁₇	—	2	1	no	—
275	C₂²×C₁₇	—	2	2	no	—
276	C₂²×C₁₇	—	2	1	no	—
277	C₂²×C₁₇	—	4	1	no	—
278	C₂²×C₁₇	—	4	1	no	—
279	C₂²×C₁₇	—	8	1	no	—
280	C₂²×C₁₇	—	8	1	no	—
281	C₂²×C₁₇	—	8	1	no	—
282	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
283	C₄×C₁₇	—	2	1	no	—
284	C₄×C₁₇	—	2	1	no	—
285	C₄×C₁₇	—	2	2	no	—
286	C₄×C₁₇	—	2	1	no	—
287	C₄×C₁₇	—	2	1	no	—
288	C₄×C₁₇	—	4	1	no	—
289	C₄×C₁₇	—	4	1	no	—
290	C₄×C₁₇	—	8	1	no	—
291	C₄×C₁₇	—	8	1	no	—
292	C₄×C₁₇	—	8	1	no	—
293	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
294	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
295	C₄×C₁₇	#577	1	1	yes	characteristic
296	C₄×C₁₇	#578	1	1	yes	characteristic
297	#533	C₂²×C₁₇	1	1	yes	characteristic
298	#532	C₂²×C₁₇	1	1	yes	characteristic
299	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
300	#500	C₂²×C₁₇	1	1	yes	characteristic
301	#498	C₂²×C₁₇	1	1	yes	characteristic
302	#486	C₂²×C₁₇	1	1	yes	characteristic
303	#486	C₂²×C₁₇	1	1	yes	characteristic
304	#485	—	2	1	no	—
305	#482	—	2	1	no	—
306	#482	—	2	1	no	—
307	#482	—	2	1	no	—
308	#478	—	2	1	no	—
309	#478	—	2	1	no	—
310	#477	C₂²×C₁₇	1	1	yes	characteristic
311	#477	C₂²×C₁₇	1	1	yes	characteristic
312	#476	C₂²×C₁₇	1	1	yes	characteristic
313	#476	C₂²×C₁₇	1	1	yes	characteristic
314	#462	C₂²×C₁₇	1	1	yes	characteristic
315	#461	C₂²×C₁₇	1	1	yes	characteristic
316	#460	C₂²×C₁₇	1	1	yes	characteristic
317	#459	C₂²×C₁₇	1	1	yes	characteristic
318	#452	—	2	1	no	—
319	#449	—	2	1	no	—
320	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
321	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
322	#441	—	2	1	no	—
323	#440	—	2	1	no	—
324	C₄×SD₁₆	—	2	1	no	—
325	C₄×D₈	—	2	1	no	—
326	C₈×D₄	—	2	1	no	—
327	C₈×D₄	—	2	1	no	—
328	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
329	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
330	#432	C₂²×C₁₇	1	1	yes	characteristic
331	#431	—	2	1	no	—
332	#431	C₂²×C₁₇	1	1	yes	characteristic
333	#431	C₂²×C₁₇	1	1	yes	characteristic
334	C₂×C₄⋊C₈	—	2	1	no	—
335	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
336	#335	C₂²×C₁₇	1	1	yes	characteristic
337	#335	C₂²×C₁₇	1	1	yes	characteristic
338	#334	C₂²×C₁₇	1	1	yes	characteristic
339	#334	C₂²×C₁₇	1	1	yes	characteristic
340	#333	C₂²×C₁₇	1	1	yes	characteristic
341	#333	C₂²×C₁₇	1	1	yes	characteristic
342	#333	C₂²×C₁₇	1	1	yes	characteristic
343	#333	C₂²×C₁₇	1	1	yes	characteristic
344	#332	C₂²×C₁₇	1	1	yes	characteristic
345	#332	C₂²×C₁₇	1	1	yes	characteristic
346	#331	C₂²×C₁₇	1	1	yes	characteristic
347	#331	C₂²×C₁₇	1	1	yes	characteristic
348	C₂×C₁₇	—	4	1	no	—
349	C₂×C₁₇	—	4	2	no	—
350	C₂×C₁₇	—	16	1	no	—
351	C₂×C₁₇	#3046	1	1	yes	characteristic
352	C₂×C₁₇	#3050	1	1	yes	characteristic
353	C₂×C₁₇	#3068	1	1	yes	characteristic
354	C₂×#41	—	2	1	no	—
355	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×SD₁₆	—	2	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×D₈	—	2	1	no	—
360	C₂²×C₈	—	2	1	no	—
361	C₂²×C₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
364	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
365	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
366	#127	C₂³×C₁₇	1	1	yes	characteristic
367	#125	—	2	1	no	—
368	#124	—	2	1	no	—
369	C₂²⋊Q₈	—	2	1	no	—
370	C₂²⋊Q₈	—	2	1	no	—
371	#121	—	2	1	no	—
372	#121	—	2	1	no	—
373	C₄×Q₈	—	2	1	no	—
374	C₄×Q₈	—	2	1	no	—
375	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
376	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
382	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
383	#117	—	2	1	no	—
384	#117	—	2	1	no	—
385	#117	D₄×C₁₇	1	1	yes	characteristic
386	C₂×C₄²	—	2	1	no	—
387	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
388	#107	—	2	1	no	—
389	#107	—	2	1	no	—
390	#107	—	2	1	no	—
391	#107	—	2	1	no	—
392	#106	—	2	1	no	—
393	#106	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	C₄⋊C₈	—	2	1	no	—
397	C₄⋊C₈	—	2	1	no	—
398	C₄⋊C₈	—	2	1	no	—
399	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
400	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
401	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
402	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
403	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
404	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
405	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
406	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#102	—	2	1	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	1	no	—
415	#102	—	2	1	no	—
416	#102	—	2	1	no	—
417	#102	—	2	1	no	—
418	#102	—	2	1	no	—
419	C₂²⋊C₈	—	2	1	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	C₂²⋊C₈	—	2	1	no	—
422	C₂²⋊C₈	—	2	1	no	—
423	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
424	C₂²⋊C₈	D₄×C₁₇	1	1	yes	characteristic
425	#97	—	2	1	no	—
426	C₄×C₈	—	2	1	no	—
427	C₄×C₈	—	2	1	no	—
428	C₄×C₈	—	2	1	no	—
429	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
430	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
431	C₁₇	#19419	1	1	yes	characteristic, direct product factor, Sylow
432	#41	—	2	2	no	—
433	#41	—	2	2	no	—
434	#41	—	8	2	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	1	no	—
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
445	C₂²×C₄	—	2	1	no	—
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	4	1	no	—
449	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
451	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
452	Q₁₆	—	4	2	no	—
453	SD₁₆	—	4	2	no	—
454	SD₁₆	—	4	2	no	—
455	D₈	—	4	2	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	2	1	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	8	1	no	—
463	C₂×C₈	—	8	1	no	—
464	C₂×C₈	—	8	1	no	—
465	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
466	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
467	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
468	C₂×C₈	C₂×D₄×C₁₇	1	1	yes	characteristic
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	—	2	1	no	—
473	C₄⋊C₄	—	2	1	no	—
474	C₄⋊C₄	—	2	1	no	—
475	C₄⋊C₄	—	2	1	no	—
476	C₄⋊C₄	—	2	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	—	4	1	no	—
479	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₂²⋊C₄	—	2	1	no	—
482	C₂²⋊C₄	—	2	1	no	—
483	C₂²⋊C₄	—	2	1	no	—
484	C₂²⋊C₄	—	4	1	no	—
485	C₂²⋊C₄	—	4	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	—	4	1	no	—
491	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
492	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
493	C₄²	#41×C₁₇	1	1	yes	characteristic
494	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
495	C₂³	—	2	1	no	—
496	C₂³	—	4	1	no	—
497	C₂³	C₁₇×#121	1	1	yes	characteristic
498	Q₈	—	2	1	no	—
499	Q₈	—	4	1	no	—
500	Q₈	—	4	1	no	—
501	Q₈	—	8	1	no	—
502	Q₈	—	8	1	no	—
503	Q₈	C₁₇×#135	1	2	yes	—
504	D₄	—	2	4	no	—
505	D₄	—	2	1	no	—
506	D₄	—	4	1	no	—
507	D₄	—	4	1	no	—
508	D₄	—	4	1	no	—
509	D₄	—	4	1	no	—
510	D₄	—	8	1	no	—
511	D₄	—	8	2	no	—
512	D₄	C₁₇×#135	1	2	yes	—
513	C₂×C₄	—	2	4	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	1	no	—
524	C₂×C₄	—	4	1	no	—
525	C₂×C₄	—	4	1	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	8	1	no	—
528	C₂×C₄	—	8	2	no	—
529	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
530	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
531	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
532	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
533	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
534	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	2	1	no	—
539	C₈	—	4	1	no	—
540	C₈	—	4	1	no	—
541	C₈	—	4	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	2	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	8	1	no	—
552	C₂²	—	8	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
555	C₄	—	2	1	no	—
556	C₄	—	2	1	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	8	1	no	—
563	C₄	—	8	1	no	—
564	C₄	—	8	1	no	—
565	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
566	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
567	C₄	C₁₇×#577	1	1	yes	characteristic
568	C₄	C₁₇×#578	1	1	yes	characteristic
569	C₂	—	4	1	no	—
570	C₂	—	4	2	no	—
571	C₂	—	16	1	no	—
572	C₂	C₁₇×#3046	1	1	yes	characteristic
573	C₂	C₁₇×#3050	1	1	yes	characteristic
574	C₂	C₁₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3106	C₂
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×#3228	C₂	semidirect
2. C₁₇×#3116	C₂	semidirect
4. C₁₇×#2988	C₂	semidirect
5. C₁₇×#1682	C₂	semidirect
6. C₁₇×#1681	C₂	semidirect
7. C₁₇×#1678	C₂	semidirect
8. C₁₇×#1677	C₂	semidirect
9. C₁₇×#1676	C₂	semidirect
10. C₁₇×#1675	C₂	semidirect
11. C₁₇×#1672	C₂	semidirect
12. C₁₇×#1671	C₂	semidirect
13. C₁₇×#1572	C₂	semidirect
14. C₁₇×#1551	C₂	semidirect
15. C₁₇×#1542	C₂	semidirect
207. #19419	C₁₇	direct (N × H)
258. #3228	C₂×C₁₇	semidirect
259. #3116	C₂×C₁₇	semidirect
261. #2988	C₂×C₁₇	semidirect
262. #1682	C₂×C₁₇	semidirect
263. #1681	C₂×C₁₇	semidirect
264. #1678	C₂×C₁₇	semidirect
265. #1677	C₂×C₁₇	semidirect
266. #1676	C₂×C₁₇	semidirect
267. #1675	C₂×C₁₇	semidirect
268. #1672	C₂×C₁₇	semidirect
269. #1671	C₂×C₁₇	semidirect
270. #1572	C₂×C₁₇	semidirect
271. #1551	C₂×C₁₇	semidirect
272. #1542	C₂×C₁₇	semidirect
431. C₁₇	#19419	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×#3228	2
C₁₇×#3116	2
C₁₇×#3106	2
C₁₇×#2988	2
C₁₇×#1682	2
C₁₇×#1681	2
C₁₇×#1678	2
C₁₇×#1677	2
C₁₇×#1676	2
C₁₇×#1675	2
C₁₇×#1672	2
C₁₇×#1671	2
C₁₇×#1572	2
C₁₇×#1551	2
C₁₇×#1542	2
#19419	17

Subgroups — C17×#19419 #16877163

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19419 #16877163