Subgroups — C₁₇×#19409 #16877153

Order 4352.

704 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3208	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3038	C₂	1	1	yes	maximal, characteristic
4	C₁₇×#2988	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1678	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1677	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1666	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1665	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1570	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₁₇×#331	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₁₇×AGL(1,ℤ/8)	—	2	1	no	—
13	C₁₇×#533	C₂²	1	1	yes	characteristic
14	C₂×C₁₇×#127	C₂²	1	1	yes	characteristic
15	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
16	C₁₇×#492	C₂²	1	2	yes	—
17	C₁₇×#486	C₂²	1	2	yes	—
18	C₁₇×#479	—	2	1	no	—
19	C₁₇×#478	—	2	1	no	—
20	C₁₇×#477	C₂²	1	1	yes	characteristic, complemented
21	C₁₇×#476	C₂²	1	1	yes	characteristic, complemented
22	C₁₇×#475	C₂²	1	1	yes	characteristic, complemented
23	C₁₇×#474	C₂²	1	1	yes	characteristic, complemented
24	C₁₇×#460	—	2	1	no	—
25	C₁₇×#460	—	2	1	no	—
26	C₁₇×#460	—	2	1	no	—
27	C₁₇×#460	C₂²	1	2	yes	—
28	C₁₇×#459	—	2	1	no	—
29	C₁₇×#459	C₂²	1	2	yes	—
30	C₁₇×#450	—	2	2	no	—
31	C₈×Q₈×C₁₇	C₂²	1	2	yes	complemented
32	C₈×D₄×C₁₇	—	2	2	no	—
33	C₈×D₄×C₁₇	C₂²	1	2	yes	complemented
34	C₁₇×#431	—	2	1	no	—
35	C₁₇×#431	C₂²	1	1	yes	characteristic
36	C₁₇×#427	—	2	1	no	—
37	C₁₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₁₇×C₄⋊C₈	—	2	1	no	—
39	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₁₇×C₄⋊C₈	C₂²	1	1	yes	characteristic
41	C₁₇×#418	—	2	1	no	—
42	C₁₇×#416	—	2	1	no	—
43	C₁₇×#334	C₂²	1	2	yes	complemented
44	C₁₇×#334	C₂²	1	2	yes	complemented
45	C₁₇×#333	C₂²	1	2	yes	complemented
46	C₁₇×#332	C₂²	1	2	yes	complemented
47	C₁₇×#331	C₂²	1	2	yes	—
48	C₁₇×#331	C₂²	1	2	yes	—
49	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₁₇	—	2	1	no	—
51	C₂²×D₄×C₁₇	—	2	1	no	—
52	C₂²×D₄×C₁₇	—	2	1	no	—
53	C₁₇×AGL(1,ℤ/8)	—	4	4	no	—
54	C₂×SD₁₆×C₁₇	—	2	2	no	—
55	C₂×SD₁₆×C₁₇	—	2	2	no	—
56	C₂×SD₁₆×C₁₇	—	2	2	no	—
57	C₂×D₈×C₁₇	—	2	2	no	—
58	C₂×M₁₆×C₁₇	—	2	1	no	—
59	C₂²×C₈×C₁₇	—	2	1	no	—
60	C₂²×C₈×C₁₇	—	2	1	no	—
61	C₂²×C₈×C₁₇	—	2	2	no	—
62	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
63	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
64	C₁₇×#127	—	2	1	no	—
65	C₁₇×#127	—	2	1	no	—
66	C₁₇×#127	—	2	1	no	—
67	C₁₇×#127	C₂³	1	2	yes	—
68	C₁₇×#125	—	2	1	no	—
69	C₁₇×C₂²⋊Q₈	—	2	1	no	—
70	C₁₇×C₂²⋊Q₈	—	2	1	no	—
71	C₄×Q₈×C₁₇	—	2	1	no	—
72	C₄×Q₈×C₁₇	—	2	1	no	—
73	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
74	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₁₇	—	2	1	no	—
76	C₄×D₄×C₁₇	—	2	1	no	—
77	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
78	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
79	C₁₇×#117	—	2	1	no	—
80	C₁₇×#117	—	2	1	no	—
81	C₁₇×#117	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₁₇	—	2	1	no	—
83	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
84	C₁₇×#107	—	2	1	no	—
85	C₁₇×#107	—	2	1	no	—
86	C₁₇×#106	—	2	1	no	—
87	C₁₇×#106	—	2	1	no	—
88	C₁₇×C₄⋊C₈	—	2	2	no	—
89	C₁₇×C₄⋊C₈	—	2	1	no	—
90	C₁₇×C₄⋊C₈	—	2	1	no	—
91	C₁₇×C₄⋊C₈	—	2	1	no	—
92	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
93	C₁₇×C₄⋊C₈	D₄	1	1	yes	characteristic
94	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
95	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
96	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
98	C₁₇×#103	—	2	1	no	—
99	C₁₇×#103	—	2	1	no	—
100	C₁₇×#102	—	2	1	no	—
101	C₁₇×#102	—	2	1	no	—
102	C₁₇×#102	—	2	2	no	—
103	C₁₇×#102	—	2	2	no	—
104	C₁₇×#102	—	2	2	no	—
105	C₁₇×#102	—	2	2	no	—
106	C₁₇×C₂²⋊C₈	—	2	2	no	—
107	C₁₇×C₂²⋊C₈	D₄	1	2	yes	—
108	C₄×C₈×C₁₇	—	2	2	no	—
109	C₄×C₈×C₁₇	C₂³	1	2	yes	—
110	C₂⁴×C₁₇	—	4	1	no	—
111	#41×C₁₇	—	2	2	no	—
112	#41×C₁₇	SD₁₆	1	4	yes	complemented
113	C₂×Q₈×C₁₇	—	2	1	no	—
114	C₂×Q₈×C₁₇	—	2	1	no	—
115	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
116	C₂×D₄×C₁₇	—	2	1	no	—
117	C₂×D₄×C₁₇	—	2	2	no	—
118	C₂×D₄×C₁₇	—	2	2	no	—
119	C₂×D₄×C₁₇	—	2	2	no	—
120	C₂×D₄×C₁₇	—	4	1	no	—
121	C₂×D₄×C₁₇	—	4	1	no	—
122	C₂×D₄×C₁₇	—	4	1	no	—
123	C₂×D₄×C₁₇	—	4	2	no	—
124	C₂×D₄×C₁₇	—	4	2	no	—
125	C₂×D₄×C₁₇	—	8	1	no	—
126	C₂×D₄×C₁₇	—	8	1	no	—
127	C₂×D₄×C₁₇	—	8	2	no	—
128	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₁₇	—	2	1	no	—
130	C₂²×C₄×C₁₇	—	2	1	no	—
131	C₂²×C₄×C₁₇	—	2	1	no	—
132	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
133	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
135	SD₁₆×C₁₇	—	4	4	no	—
136	SD₁₆×C₁₇	—	8	2	no	—
137	SD₁₆×C₁₇	—	8	2	no	—
138	D₈×C₁₇	—	4	4	no	—
139	M₁₆×C₁₇	—	4	2	no	—
140	C₂×C₈×C₁₇	—	2	2	no	—
141	C₂×C₈×C₁₇	—	2	1	no	—
142	C₂×C₈×C₁₇	—	2	1	no	—
143	C₂×C₈×C₁₇	—	2	2	no	—
144	C₂×C₈×C₁₇	—	4	2	no	—
145	C₂×C₈×C₁₇	—	8	2	no	—
146	C₂×C₈×C₁₇	—	8	1	no	—
147	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₁₇	C₂×D₄	1	2	yes	—
149	C₄⋊C₄×C₁₇	—	2	1	no	—
150	C₄⋊C₄×C₁₇	—	2	1	no	—
151	C₄⋊C₄×C₁₇	—	2	1	no	—
152	C₄⋊C₄×C₁₇	—	2	1	no	—
153	C₄⋊C₄×C₁₇	—	2	1	no	—
154	C₄⋊C₄×C₁₇	—	2	1	no	—
155	C₄⋊C₄×C₁₇	—	4	1	no	—
156	C₄⋊C₄×C₁₇	—	4	1	no	—
157	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
158	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂²⋊C₄×C₁₇	—	2	1	no	—
160	C₂²⋊C₄×C₁₇	—	2	1	no	—
161	C₂²⋊C₄×C₁₇	—	2	1	no	—
162	C₂²⋊C₄×C₁₇	—	4	1	no	—
163	C₄²×C₁₇	—	2	1	no	—
164	C₄²×C₁₇	—	2	1	no	—
165	C₄²×C₁₇	—	2	1	no	—
166	C₄²×C₁₇	—	4	1	no	—
167	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
168	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
169	C₄²×C₁₇	#41	1	1	yes	characteristic
170	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
171	#19409	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂³×C₁₇	—	2	1	no	—
173	C₂³×C₁₇	—	4	2	no	—
174	C₂³×C₁₇	—	8	2	no	—
175	C₂³×C₁₇	—	8	2	no	—
176	C₂³×C₁₇	—	8	2	no	—
177	C₂³×C₁₇	#121	1	1	yes	characteristic
178	Q₈×C₁₇	—	2	1	no	—
179	Q₈×C₁₇	—	4	1	no	—
180	Q₈×C₁₇	—	4	1	no	—
181	Q₈×C₁₇	—	8	1	no	—
182	Q₈×C₁₇	C₂×SD₁₆	1	2	yes	—
183	D₄×C₁₇	—	2	4	no	—
184	D₄×C₁₇	—	2	1	no	—
185	D₄×C₁₇	—	4	2	no	—
186	D₄×C₁₇	—	4	2	no	—
187	D₄×C₁₇	—	4	2	no	—
188	D₄×C₁₇	—	4	2	no	—
189	D₄×C₁₇	—	8	2	no	—
190	D₄×C₁₇	—	8	2	no	—
191	D₄×C₁₇	—	8	2	no	—
192	D₄×C₁₇	—	8	2	no	—
193	D₄×C₁₇	C₂×SD₁₆	1	2	yes	—
194	C₂×C₄×C₁₇	—	2	1	no	—
195	C₂×C₄×C₁₇	—	2	1	no	—
196	C₂×C₄×C₁₇	—	2	1	no	—
197	C₂×C₄×C₁₇	—	2	4	no	—
198	C₂×C₄×C₁₇	—	2	1	no	—
199	C₂×C₄×C₁₇	—	2	1	no	—
200	C₂×C₄×C₁₇	—	4	1	no	—
201	C₂×C₄×C₁₇	—	4	1	no	—
202	C₂×C₄×C₁₇	—	4	1	no	—
203	C₂×C₄×C₁₇	—	4	1	no	—
204	C₂×C₄×C₁₇	—	4	1	no	—
205	C₂×C₄×C₁₇	—	8	1	no	—
206	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
207	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
208	C₂×C₄×C₁₇	#121	1	1	yes	characteristic
209	C₂×C₄×C₁₇	C₂×SD₁₆	1	2	yes	—
210	C₂×C₄×C₁₇	#135	1	2	yes	—
211	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
213	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
214	C₈×C₁₇	—	2	2	no	—
215	C₈×C₁₇	—	2	2	no	—
216	C₈×C₁₇	—	4	2	no	—
217	C₈×C₁₇	—	4	1	no	—
218	C₈×C₁₇	—	4	1	no	—
219	C₈×C₁₇	—	4	2	no	—
220	#3208	C₂×C₁₇	1	1	yes	characteristic, complemented
221	#3076	C₂×C₁₇	1	1	yes	characteristic, complemented
222	#3038	C₂×C₁₇	1	1	yes	characteristic
223	#2988	C₂×C₁₇	1	1	yes	characteristic, complemented
224	#1678	C₂×C₁₇	1	2	yes	complemented
225	#1677	C₂×C₁₇	1	2	yes	complemented
226	#1666	C₂×C₁₇	1	2	yes	complemented
227	#1665	C₂×C₁₇	1	2	yes	complemented
228	#1570	C₂×C₁₇	1	1	yes	characteristic, complemented
229	#1550	C₂×C₁₇	1	1	yes	characteristic, complemented
230	C₂×#331	C₂×C₁₇	1	1	yes	characteristic, complemented
231	C₂²×C₁₇	—	2	1	no	—
232	C₂²×C₁₇	—	2	1	no	—
233	C₂²×C₁₇	—	2	2	no	—
234	C₂²×C₁₇	—	4	1	no	—
235	C₂²×C₁₇	—	4	1	no	—
236	C₂²×C₁₇	—	8	2	no	—
237	C₂²×C₁₇	—	8	2	no	—
238	C₂²×C₁₇	—	8	2	no	—
239	C₂²×C₁₇	—	16	4	no	—
240	C₂²×C₁₇	#465	1	2	yes	—
241	C₂²×C₁₇	C₂×#121	1	1	yes	characteristic
242	C₄×C₁₇	—	2	1	no	—
243	C₄×C₁₇	—	2	2	no	—
244	C₄×C₁₇	—	2	1	no	—
245	C₄×C₁₇	—	2	1	no	—
246	C₄×C₁₇	—	4	1	no	—
247	C₄×C₁₇	—	4	1	no	—
248	C₄×C₁₇	—	8	1	no	—
249	C₄×C₁₇	—	8	1	no	—
250	C₄×C₁₇	#465	1	2	yes	—
251	C₄×C₁₇	C₂²×SD₁₆	1	1	yes	characteristic
252	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
253	C₄×C₁₇	#576	1	1	yes	characteristic
254	C₄×C₁₇	#577	1	1	yes	characteristic
255	C₂×AGL(1,ℤ/8)	—	2	1	no	—
256	#533	C₂²×C₁₇	1	1	yes	characteristic
257	C₂×#127	C₂²×C₁₇	1	1	yes	characteristic
258	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
259	#492	C₂²×C₁₇	1	2	yes	—
260	#486	C₂²×C₁₇	1	2	yes	—
261	#479	—	2	1	no	—
262	#478	—	2	1	no	—
263	#477	C₂²×C₁₇	1	1	yes	characteristic, complemented
264	#476	C₂²×C₁₇	1	1	yes	characteristic, complemented
265	#475	C₂²×C₁₇	1	1	yes	characteristic, complemented
266	#474	C₂²×C₁₇	1	1	yes	characteristic, complemented
267	#460	—	2	1	no	—
268	#460	—	2	1	no	—
269	#460	—	2	1	no	—
270	#460	C₂²×C₁₇	1	2	yes	—
271	#459	—	2	1	no	—
272	#459	C₂²×C₁₇	1	2	yes	—
273	#450	—	2	2	no	—
274	C₈×Q₈	C₂²×C₁₇	1	2	yes	complemented
275	C₈×D₄	—	2	2	no	—
276	C₈×D₄	C₂²×C₁₇	1	2	yes	complemented
277	#431	—	2	1	no	—
278	#431	C₂²×C₁₇	1	1	yes	characteristic
279	#427	—	2	1	no	—
280	#423	C₂²×C₁₇	1	1	yes	characteristic
281	C₂×C₄⋊C₈	—	2	1	no	—
282	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
284	#418	—	2	1	no	—
285	#416	—	2	1	no	—
286	#334	C₂²×C₁₇	1	2	yes	complemented
287	#334	C₂²×C₁₇	1	2	yes	complemented
288	#333	C₂²×C₁₇	1	2	yes	complemented
289	#332	C₂²×C₁₇	1	2	yes	complemented
290	#331	C₂²×C₁₇	1	2	yes	—
291	#331	C₂²×C₁₇	1	2	yes	—
292	C₂×C₁₇	—	2	2	no	—
293	C₂×C₁₇	—	4	2	no	—
294	C₂×C₁₇	—	16	2	no	—
295	C₂×C₁₇	#3045	1	1	yes	characteristic
296	C₂×C₁₇	C₂×#465	1	1	yes	characteristic
297	C₂×C₁₇	#3068	1	1	yes	characteristic
298	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
299	C₂²×D₄	—	2	1	no	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	—	2	1	no	—
302	AGL(1,ℤ/8)	—	4	4	no	—
303	C₂×SD₁₆	—	2	2	no	—
304	C₂×SD₁₆	—	2	2	no	—
305	C₂×SD₁₆	—	2	2	no	—
306	C₂×D₈	—	2	2	no	—
307	C₂×M₁₆	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₂²×C₈	—	2	2	no	—
311	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
312	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
313	#127	—	2	1	no	—
314	#127	—	2	1	no	—
315	#127	—	2	1	no	—
316	#127	C₂³×C₁₇	1	2	yes	—
317	#125	—	2	1	no	—
318	C₂²⋊Q₈	—	2	1	no	—
319	C₂²⋊Q₈	—	2	1	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
323	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
327	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
328	#117	—	2	1	no	—
329	#117	—	2	1	no	—
330	#117	D₄×C₁₇	1	1	yes	characteristic
331	C₂×C₄²	—	2	1	no	—
332	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
333	#107	—	2	1	no	—
334	#107	—	2	1	no	—
335	#106	—	2	1	no	—
336	#106	—	2	1	no	—
337	C₄⋊C₈	—	2	2	no	—
338	C₄⋊C₈	—	2	1	no	—
339	C₄⋊C₈	—	2	1	no	—
340	C₄⋊C₈	—	2	1	no	—
341	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
342	C₄⋊C₈	D₄×C₁₇	1	1	yes	characteristic
343	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
344	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
345	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
346	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
347	#103	—	2	1	no	—
348	#103	—	2	1	no	—
349	#102	—	2	1	no	—
350	#102	—	2	1	no	—
351	#102	—	2	2	no	—
352	#102	—	2	2	no	—
353	#102	—	2	2	no	—
354	#102	—	2	2	no	—
355	C₂²⋊C₈	—	2	2	no	—
356	C₂²⋊C₈	D₄×C₁₇	1	2	yes	—
357	C₄×C₈	—	2	2	no	—
358	C₄×C₈	C₂³×C₁₇	1	2	yes	—
359	C₁₇	#19409	1	1	yes	characteristic, direct product factor, Sylow
360	C₂⁴	—	4	1	no	—
361	#41	—	2	2	no	—
362	#41	SD₁₆×C₁₇	1	4	yes	complemented
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	1	no	—
365	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
366	C₂×D₄	—	2	1	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	4	2	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	—	4	1	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	8	1	no	—
376	C₂×D₄	—	8	1	no	—
377	C₂×D₄	—	8	2	no	—
378	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
384	C₂²×C₄	#41×C₁₇	1	1	yes	characteristic
385	SD₁₆	—	4	4	no	—
386	SD₁₆	—	8	2	no	—
387	SD₁₆	—	8	2	no	—
388	D₈	—	4	4	no	—
389	M₁₆	—	4	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	4	2	no	—
395	C₂×C₈	—	8	2	no	—
396	C₂×C₈	—	8	1	no	—
397	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
398	C₂×C₈	C₂×D₄×C₁₇	1	2	yes	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	1	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
408	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
409	C₂²⋊C₄	—	2	1	no	—
410	C₂²⋊C₄	—	2	1	no	—
411	C₂²⋊C₄	—	2	1	no	—
412	C₂²⋊C₄	—	4	1	no	—
413	C₄²	—	2	1	no	—
414	C₄²	—	2	1	no	—
415	C₄²	—	2	1	no	—
416	C₄²	—	4	1	no	—
417	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
419	C₄²	#41×C₁₇	1	1	yes	characteristic
420	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
421	C₂³	—	2	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	8	2	no	—
424	C₂³	—	8	2	no	—
425	C₂³	—	8	2	no	—
426	C₂³	C₁₇×#121	1	1	yes	characteristic
427	Q₈	—	2	1	no	—
428	Q₈	—	4	1	no	—
429	Q₈	—	4	1	no	—
430	Q₈	—	8	1	no	—
431	Q₈	C₂×SD₁₆×C₁₇	1	2	yes	—
432	D₄	—	2	4	no	—
433	D₄	—	2	1	no	—
434	D₄	—	4	2	no	—
435	D₄	—	4	2	no	—
436	D₄	—	4	2	no	—
437	D₄	—	4	2	no	—
438	D₄	—	8	2	no	—
439	D₄	—	8	2	no	—
440	D₄	—	8	2	no	—
441	D₄	—	8	2	no	—
442	D₄	C₂×SD₁₆×C₁₇	1	2	yes	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	4	no	—
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	8	1	no	—
455	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
456	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
457	C₂×C₄	C₁₇×#121	1	1	yes	characteristic
458	C₂×C₄	C₂×SD₁₆×C₁₇	1	2	yes	—
459	C₂×C₄	C₁₇×#135	1	2	yes	—
460	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₁₇	1	1	yes	characteristic
463	C₈	—	2	2	no	—
464	C₈	—	2	2	no	—
465	C₈	—	4	2	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	1	no	—
468	C₈	—	4	2	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	2	1	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	4	1	no	—
473	C₂²	—	4	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	16	4	no	—
478	C₂²	C₁₇×#465	1	2	yes	—
479	C₂²	C₂×C₁₇×#121	1	1	yes	characteristic
480	C₄	—	2	1	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	1	no	—
483	C₄	—	2	1	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	1	no	—
488	C₄	C₁₇×#465	1	2	yes	—
489	C₄	C₂²×SD₁₆×C₁₇	1	1	yes	characteristic
490	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
491	C₄	C₁₇×#576	1	1	yes	characteristic
492	C₄	C₁₇×#577	1	1	yes	characteristic
493	C₂	—	2	2	no	—
494	C₂	—	4	2	no	—
495	C₂	—	16	2	no	—
496	C₂	C₁₇×#3045	1	1	yes	characteristic
497	C₂	C₂×C₁₇×#465	1	1	yes	characteristic
498	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×#3038	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×#3208	C₂	semidirect
2. C₁₇×#3076	C₂	semidirect
4. C₁₇×#2988	C₂	semidirect
5. C₁₇×#1678	C₂	semidirect
6. C₁₇×#1677	C₂	semidirect
7. C₁₇×#1666	C₂	semidirect
8. C₁₇×#1665	C₂	semidirect
9. C₁₇×#1570	C₂	semidirect
10. C₁₇×#1550	C₂	semidirect
11. C₂×C₁₇×#331	C₂	semidirect
20. C₁₇×#477	C₂²	semidirect
21. C₁₇×#476	C₂²	semidirect
22. C₁₇×#475	C₂²	semidirect
23. C₁₇×#474	C₂²	semidirect
31. C₈×Q₈×C₁₇	C₂²	semidirect
33. C₈×D₄×C₁₇	C₂²	semidirect
43. C₁₇×#334	C₂²	semidirect
44. C₁₇×#334	C₂²	semidirect
45. C₁₇×#333	C₂²	semidirect
46. C₁₇×#332	C₂²	semidirect
112. #41×C₁₇	SD₁₆	semidirect
171. #19409	C₁₇	direct (N × H)
220. #3208	C₂×C₁₇	semidirect
221. #3076	C₂×C₁₇	semidirect
223. #2988	C₂×C₁₇	semidirect
224. #1678	C₂×C₁₇	semidirect
225. #1677	C₂×C₁₇	semidirect
226. #1666	C₂×C₁₇	semidirect
227. #1665	C₂×C₁₇	semidirect
228. #1570	C₂×C₁₇	semidirect
229. #1550	C₂×C₁₇	semidirect
230. C₂×#331	C₂×C₁₇	semidirect
263. #477	C₂²×C₁₇	semidirect
264. #476	C₂²×C₁₇	semidirect
265. #475	C₂²×C₁₇	semidirect
266. #474	C₂²×C₁₇	semidirect
274. C₈×Q₈	C₂²×C₁₇	semidirect
276. C₈×D₄	C₂²×C₁₇	semidirect
286. #334	C₂²×C₁₇	semidirect
287. #334	C₂²×C₁₇	semidirect
288. #333	C₂²×C₁₇	semidirect
289. #332	C₂²×C₁₇	semidirect
359. C₁₇	#19409	direct (N × H)
362. #41	SD₁₆×C₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₁₇×#3208	2
C₁₇×#3076	2
C₁₇×#3038	2
C₁₇×#2988	2
C₁₇×#1678	2
C₁₇×#1677	2
C₁₇×#1666	2
C₁₇×#1665	2
C₁₇×#1570	2
C₁₇×#1550	2
C₂×C₁₇×#331	2
#19409	17

Subgroups — C17×#19409 #16877153

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19409 #16877153