Subgroups — C₁₇×#19800 #16877544

Order 4352.

598 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3369	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₇×#3362	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3340	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3305	C₂	1	1	yes	maximal, characteristic
5	C₁₇×#1720	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₇×#1698	C₂	1	1	yes	maximal, characteristic, complemented
7	C₁₇×#1683	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₇×#1677	C₂	1	1	yes	maximal, characteristic, complemented
9	C₁₇×#1672	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1641	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1634	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#1633	C₂	1	1	yes	maximal, characteristic, complemented
13	C₁₇×#1628	C₂	1	1	yes	maximal, characteristic, complemented
14	C₁₇×#1582	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	Q₈²×C₁₇	C₂²	1	1	yes	characteristic
17	C₁₇×#556	C₂²	1	1	yes	characteristic
18	C₁₇×#555	C₂²	1	1	yes	characteristic
19	C₁₇×#550	C₂²	1	1	yes	characteristic
20	C₁₇×#498	C₂²	1	1	yes	characteristic
21	C₁₇×#494	C₂²	1	1	yes	characteristic
22	C₁₇×#489	—	2	1	no	—
23	C₁₇×#487	C₂²	1	1	yes	characteristic
24	C₁₇×#486	—	2	1	no	—
25	C₁₇×#486	C₂²	1	1	yes	characteristic
26	C₁₇×#486	C₂²	1	1	yes	characteristic
27	C₁₇×#486	C₂²	1	1	yes	characteristic
28	C₁₇×#485	—	2	1	no	—
29	C₁₇×#482	—	2	1	no	—
30	C₁₇×#482	—	2	1	no	—
31	C₁₇×#477	C₂²	1	1	yes	characteristic
32	C₁₇×#477	C₂²	1	1	yes	characteristic
33	C₁₇×#476	—	2	1	no	—
34	C₁₇×#476	C₂²	1	1	yes	characteristic
35	C₁₇×#476	C₂²	1	1	yes	characteristic
36	C₁₇×#475	—	2	1	no	—
37	C₁₇×#474	C₂²	1	1	yes	characteristic
38	C₁₇×#466	—	2	1	no	—
39	C₁₇×#465	—	2	1	no	—
40	C₁₇×#464	—	2	1	no	—
41	C₁₇×#462	C₂²	1	1	yes	characteristic
42	C₁₇×#460	—	2	1	no	—
43	C₁₇×#460	C₂²	1	1	yes	characteristic
44	C₁₇×#459	C₂²	1	1	yes	characteristic
45	C₁₇×#449	—	2	1	no	—
46	C₁₇×#446	C₂²	1	1	yes	characteristic
47	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
48	C₁₇×#441	—	2	1	no	—
49	C₄×SD₁₆×C₁₇	—	2	1	no	—
50	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
51	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
52	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
53	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
54	C₁₇×#427	—	2	1	no	—
55	C₁₇×#416	—	2	1	no	—
56	C₁₇×#335	C₂²	1	1	yes	characteristic
57	C₁₇×#334	C₂²	1	1	yes	characteristic
58	C₁₇×#333	C₂²	1	1	yes	characteristic
59	C₁₇×#333	C₂²	1	1	yes	characteristic
60	C₁₇×#332	C₂²	1	1	yes	characteristic
61	C₁₇×#331	C₂²	1	1	yes	characteristic
62	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
63	C₁₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
64	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
65	C₁₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
66	C₁₇×#322	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	—	2	1	no	—
68	C₂×Q₁₆×C₁₇	—	2	1	no	—
69	C₂×Q₁₆×C₁₇	—	4	1	no	—
70	C₂×SD₁₆×C₁₇	—	2	1	no	—
71	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₁₇	D₄	1	1	yes	characteristic
73	C₂×D₈×C₁₇	—	2	1	no	—
74	C₂²×C₈×C₁₇	—	2	1	no	—
75	C₂²×C₈×C₁₇	—	2	1	no	—
76	C₁₇×C₄⋊Q₈	—	2	1	no	—
77	C₁₇×C₄⋊Q₈	—	2	1	no	—
78	C₁₇×C₄⋊Q₈	—	4	1	no	—
79	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
80	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
81	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
82	C₁₇×#127	—	2	1	no	—
83	C₁₇×#127	C₂³	1	1	yes	characteristic
84	C₁₇×#126	—	4	1	no	—
85	C₁₇×#124	—	2	1	no	—
86	C₁₇×#124	—	4	1	no	—
87	C₁₇×C₂²⋊Q₈	—	2	1	no	—
88	C₁₇×#121	—	2	1	no	—
89	C₁₇×#121	—	2	1	no	—
90	C₁₇×#121	—	2	1	no	—
91	C₁₇×#121	—	4	1	no	—
92	C₄×Q₈×C₁₇	—	2	1	no	—
93	C₄×Q₈×C₁₇	—	2	1	no	—
94	C₄×Q₈×C₁₇	—	2	1	no	—
95	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
96	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
97	C₄×D₄×C₁₇	—	2	1	no	—
98	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
99	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
100	C₁₇×#117	—	2	1	no	—
101	C₁₇×#117	—	2	1	no	—
102	C₁₇×#117	—	2	1	no	—
103	C₁₇×#107	—	2	1	no	—
104	C₁₇×#107	—	2	1	no	—
105	C₁₇×#107	—	2	1	no	—
106	C₁₇×#106	—	2	1	no	—
107	C₁₇×#106	—	2	1	no	—
108	C₁₇×#106	—	2	1	no	—
109	C₁₇×#106	—	2	1	no	—
110	C₁₇×#106	D₄	1	1	yes	characteristic
111	C₁₇×#106	D₄	1	1	yes	characteristic
112	C₁₇×C₄⋊C₈	—	2	1	no	—
113	C₁₇×C₄⋊C₈	—	2	1	no	—
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×#103	—	2	1	no	—
119	C₁₇×#103	—	2	1	no	—
120	C₁₇×#103	—	2	1	no	—
121	C₁₇×#103	—	2	1	no	—
122	C₁₇×#103	—	2	1	no	—
123	C₁₇×#103	D₄	1	1	yes	characteristic
124	C₁₇×#103	D₄	1	1	yes	characteristic
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×#102	—	2	1	no	—
133	C₁₇×#102	—	2	1	no	—
134	C₁₇×#102	—	4	1	no	—
135	C₁₇×#102	D₄	1	1	yes	characteristic
136	C₁₇×#102	D₄	1	1	yes	characteristic
137	C₁₇×C₂²⋊C₈	—	2	1	no	—
138	C₁₇×C₂²⋊C₈	—	2	1	no	—
139	C₁₇×#97	—	2	1	no	—
140	C₄×C₈×C₁₇	—	2	1	no	—
141	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
142	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
143	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	4	2	no	—
145	#41×C₁₇	—	8	1	no	—
146	C₂×Q₈×C₁₇	—	2	1	no	—
147	C₂×Q₈×C₁₇	—	2	1	no	—
148	C₂×Q₈×C₁₇	—	2	1	no	—
149	C₂×Q₈×C₁₇	—	4	1	no	—
150	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	—	4	1	no	—
156	C₂×D₄×C₁₇	—	4	1	no	—
157	C₂×D₄×C₁₇	—	4	1	no	—
158	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₁₇	—	2	1	no	—
161	C₂²×C₄×C₁₇	—	2	1	no	—
162	C₂²×C₄×C₁₇	—	4	1	no	—
163	Q₁₆×C₁₇	—	4	2	no	—
164	Q₁₆×C₁₇	—	8	2	no	—
165	SD₁₆×C₁₇	—	2	2	no	—
166	SD₁₆×C₁₇	—	4	1	no	—
167	SD₁₆×C₁₇	—	4	2	no	—
168	D₈×C₁₇	—	8	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	—	4	2	no	—
175	C₂×C₈×C₁₇	—	8	1	no	—
176	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
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	C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	4	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	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
194	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₂²⋊C₄×C₁₇	—	2	1	no	—
197	C₂²⋊C₄×C₁₇	—	4	1	no	—
198	C₂²⋊C₄×C₁₇	—	4	1	no	—
199	C₂²⋊C₄×C₁₇	—	4	1	no	—
200	C₂²⋊C₄×C₁₇	—	4	1	no	—
201	C₂²⋊C₄×C₁₇	—	4	1	no	—
202	C₄²×C₁₇	—	2	1	no	—
203	C₄²×C₁₇	—	2	1	no	—
204	C₄²×C₁₇	—	4	1	no	—
205	C₄²×C₁₇	—	4	1	no	—
206	C₄²×C₁₇	—	4	1	no	—
207	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
208	#19800	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	2	1	no	—
211	C₂³×C₁₇	—	4	1	no	—
212	Q₈×C₁₇	—	2	1	no	—
213	Q₈×C₁₇	—	2	1	no	—
214	Q₈×C₁₇	—	2	1	no	—
215	Q₈×C₁₇	—	4	1	no	—
216	Q₈×C₁₇	—	4	1	no	—
217	Q₈×C₁₇	—	8	1	no	—
218	Q₈×C₁₇	—	8	1	no	—
219	Q₈×C₁₇	—	16	1	no	—
220	Q₈×C₁₇	#135	1	2	yes	—
221	D₄×C₁₇	—	2	1	no	—
222	D₄×C₁₇	—	2	1	no	—
223	D₄×C₁₇	—	2	1	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	—	8	2	no	—
230	D₄×C₁₇	—	8	1	no	—
231	D₄×C₁₇	—	16	1	no	—
232	D₄×C₁₇	—	16	1	no	—
233	C₂×C₄×C₁₇	—	2	1	no	—
234	C₂×C₄×C₁₇	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	1	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	1	no	—
238	C₂×C₄×C₁₇	—	2	1	no	—
239	C₂×C₄×C₁₇	—	4	1	no	—
240	C₂×C₄×C₁₇	—	4	1	no	—
241	C₂×C₄×C₁₇	—	4	1	no	—
242	C₂×C₄×C₁₇	—	4	1	no	—
243	C₂×C₄×C₁₇	—	4	1	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	8	2	no	—
247	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₁₇	H(5,𝔽₂)	1	1	yes	characteristic
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	2	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	C₈×C₁₇	—	4	1	no	—
259	#3369	C₂×C₁₇	1	1	yes	characteristic, complemented
260	#3362	C₂×C₁₇	1	1	yes	characteristic, complemented
261	#3340	C₂×C₁₇	1	1	yes	characteristic, complemented
262	#3305	C₂×C₁₇	1	1	yes	characteristic
263	#1720	C₂×C₁₇	1	1	yes	characteristic, complemented
264	#1698	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1683	C₂×C₁₇	1	1	yes	characteristic, complemented
266	#1677	C₂×C₁₇	1	1	yes	characteristic, complemented
267	#1672	C₂×C₁₇	1	1	yes	characteristic, complemented
268	#1641	C₂×C₁₇	1	1	yes	characteristic, complemented
269	#1634	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1633	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1628	C₂×C₁₇	1	1	yes	characteristic, complemented
272	#1582	C₂×C₁₇	1	1	yes	characteristic, complemented
273	SD₁₆⋊C₈	C₂×C₁₇	1	1	yes	characteristic, complemented
274	C₂²×C₁₇	—	4	1	no	—
275	C₂²×C₁₇	—	4	1	no	—
276	C₂²×C₁₇	—	4	1	no	—
277	C₂²×C₁₇	—	4	1	no	—
278	C₂²×C₁₇	—	4	1	no	—
279	C₂²×C₁₇	—	4	1	no	—
280	C₂²×C₁₇	—	8	1	no	—
281	C₂²×C₁₇	—	8	1	no	—
282	C₂²×C₁₇	—	8	1	no	—
283	C₂²×C₁₇	D₄²	1	1	yes	characteristic
284	C₄×C₁₇	—	2	2	no	—
285	C₄×C₁₇	—	2	1	no	—
286	C₄×C₁₇	—	4	1	no	—
287	C₄×C₁₇	—	4	1	no	—
288	C₄×C₁₇	—	4	1	no	—
289	C₄×C₁₇	—	4	1	no	—
290	C₄×C₁₇	—	4	1	no	—
291	C₄×C₁₇	—	8	1	no	—
292	C₄×C₁₇	—	8	1	no	—
293	C₄×C₁₇	—	8	1	no	—
294	C₄×C₁₇	C₂×#135	1	1	yes	characteristic
295	C₄×C₁₇	#575	1	1	yes	characteristic
296	C₄×C₁₇	#577	1	1	yes	characteristic
297	C₄×C₁₇	#578	1	1	yes	characteristic
298	Q₈²	C₂²×C₁₇	1	1	yes	characteristic
299	#556	C₂²×C₁₇	1	1	yes	characteristic
300	#555	C₂²×C₁₇	1	1	yes	characteristic
301	#550	C₂²×C₁₇	1	1	yes	characteristic
302	#498	C₂²×C₁₇	1	1	yes	characteristic
303	#494	C₂²×C₁₇	1	1	yes	characteristic
304	#489	—	2	1	no	—
305	#487	C₂²×C₁₇	1	1	yes	characteristic
306	#486	—	2	1	no	—
307	#486	C₂²×C₁₇	1	1	yes	characteristic
308	#486	C₂²×C₁₇	1	1	yes	characteristic
309	#486	C₂²×C₁₇	1	1	yes	characteristic
310	#485	—	2	1	no	—
311	#482	—	2	1	no	—
312	#482	—	2	1	no	—
313	#477	C₂²×C₁₇	1	1	yes	characteristic
314	#477	C₂²×C₁₇	1	1	yes	characteristic
315	#476	—	2	1	no	—
316	#476	C₂²×C₁₇	1	1	yes	characteristic
317	#476	C₂²×C₁₇	1	1	yes	characteristic
318	#475	—	2	1	no	—
319	#474	C₂²×C₁₇	1	1	yes	characteristic
320	#466	—	2	1	no	—
321	#465	—	2	1	no	—
322	#464	—	2	1	no	—
323	#462	C₂²×C₁₇	1	1	yes	characteristic
324	#460	—	2	1	no	—
325	#460	C₂²×C₁₇	1	1	yes	characteristic
326	#459	C₂²×C₁₇	1	1	yes	characteristic
327	#449	—	2	1	no	—
328	#446	C₂²×C₁₇	1	1	yes	characteristic
329	C₈×Q₈	C₂²×C₁₇	1	1	yes	characteristic
330	#441	—	2	1	no	—
331	C₄×SD₁₆	—	2	1	no	—
332	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
333	C₄×SD₁₆	C₂²×C₁₇	1	1	yes	characteristic
334	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
335	C₈×D₄	C₂²×C₁₇	1	1	yes	characteristic
336	#427	—	2	1	no	—
337	#416	—	2	1	no	—
338	#335	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	#332	C₂²×C₁₇	1	1	yes	characteristic
343	#331	C₂²×C₁₇	1	1	yes	characteristic
344	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
345	Q₈⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
346	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
347	D₄⋊C₈	C₂²×C₁₇	1	1	yes	characteristic
348	#322	C₂²×C₁₇	1	1	yes	characteristic
349	C₂×C₁₇	—	8	1	no	—
350	C₂×C₁₇	—	8	1	no	—
351	C₂×C₁₇	—	16	1	no	—
352	C₂×C₁₇	#3269	1	1	yes	characteristic
353	C₂×C₁₇	#3282	1	1	yes	characteristic
354	C₂×C₁₇	#3288	1	1	yes	characteristic
355	C₂×#41	—	2	1	no	—
356	C₂×Q₁₆	—	2	1	no	—
357	C₂×Q₁₆	—	4	1	no	—
358	C₂×SD₁₆	—	2	1	no	—
359	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
360	C₂×SD₁₆	D₄×C₁₇	1	1	yes	characteristic
361	C₂×D₈	—	2	1	no	—
362	C₂²×C₈	—	2	1	no	—
363	C₂²×C₈	—	2	1	no	—
364	C₄⋊Q₈	—	2	1	no	—
365	C₄⋊Q₈	—	2	1	no	—
366	C₄⋊Q₈	—	4	1	no	—
367	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
368	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
369	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
370	#127	—	2	1	no	—
371	#127	C₂³×C₁₇	1	1	yes	characteristic
372	#126	—	4	1	no	—
373	#124	—	2	1	no	—
374	#124	—	4	1	no	—
375	C₂²⋊Q₈	—	2	1	no	—
376	#121	—	2	1	no	—
377	#121	—	2	1	no	—
378	#121	—	2	1	no	—
379	#121	—	4	1	no	—
380	C₄×Q₈	—	2	1	no	—
381	C₄×Q₈	—	2	1	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
384	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
387	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
388	#117	—	2	1	no	—
389	#117	—	2	1	no	—
390	#117	—	2	1	no	—
391	#107	—	2	1	no	—
392	#107	—	2	1	no	—
393	#107	—	2	1	no	—
394	#106	—	2	1	no	—
395	#106	—	2	1	no	—
396	#106	—	2	1	no	—
397	#106	—	2	1	no	—
398	#106	D₄×C₁₇	1	1	yes	characteristic
399	#106	D₄×C₁₇	1	1	yes	characteristic
400	C₄⋊C₈	—	2	1	no	—
401	C₄⋊C₈	—	2	1	no	—
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	#103	—	2	1	no	—
407	#103	—	2	1	no	—
408	#103	—	2	1	no	—
409	#103	—	2	1	no	—
410	#103	—	2	1	no	—
411	#103	D₄×C₁₇	1	1	yes	characteristic
412	#103	D₄×C₁₇	1	1	yes	characteristic
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	#102	—	2	1	no	—
420	#102	—	2	1	no	—
421	#102	—	2	1	no	—
422	#102	—	4	1	no	—
423	#102	D₄×C₁₇	1	1	yes	characteristic
424	#102	D₄×C₁₇	1	1	yes	characteristic
425	C₂²⋊C₈	—	2	1	no	—
426	C₂²⋊C₈	—	2	1	no	—
427	#97	—	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	C₄×C₈	C₂³×C₁₇	1	1	yes	characteristic
432	C₁₇	#19800	1	1	yes	characteristic, direct product factor, Sylow
433	#41	—	4	2	no	—
434	#41	—	8	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	2	1	no	—
437	C₂×Q₈	—	2	1	no	—
438	C₂×Q₈	—	4	1	no	—
439	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
440	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
441	C₂×D₄	—	2	1	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	—	4	1	no	—
445	C₂×D₄	—	4	1	no	—
446	C₂×D₄	—	4	1	no	—
447	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
448	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	4	1	no	—
452	Q₁₆	—	4	2	no	—
453	Q₁₆	—	8	2	no	—
454	SD₁₆	—	2	2	no	—
455	SD₁₆	—	4	1	no	—
456	SD₁₆	—	4	2	no	—
457	D₈	—	8	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	—	2	1	no	—
463	C₂×C₈	—	4	2	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	—	4	1	no	—
480	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
481	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
482	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
483	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
484	C₂²⋊C₄	—	2	1	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	4	1	no	—
487	C₂²⋊C₄	—	4	1	no	—
488	C₂²⋊C₄	—	4	1	no	—
489	C₂²⋊C₄	—	4	1	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	4	1	no	—
494	C₄²	—	4	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
497	C₂³	—	2	1	no	—
498	C₂³	—	2	1	no	—
499	C₂³	—	4	1	no	—
500	Q₈	—	2	1	no	—
501	Q₈	—	2	1	no	—
502	Q₈	—	2	1	no	—
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	Q₈	—	8	1	no	—
506	Q₈	—	8	1	no	—
507	Q₈	—	16	1	no	—
508	Q₈	C₁₇×#135	1	2	yes	—
509	D₄	—	2	1	no	—
510	D₄	—	2	1	no	—
511	D₄	—	2	1	no	—
512	D₄	—	2	1	no	—
513	D₄	—	4	1	no	—
514	D₄	—	4	1	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	1	no	—
517	D₄	—	8	2	no	—
518	D₄	—	8	1	no	—
519	D₄	—	16	1	no	—
520	D₄	—	16	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	4	1	no	—
532	C₂×C₄	—	4	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	8	2	no	—
535	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
536	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
537	C₂×C₄	C₁₇×H(5,𝔽₂)	1	1	yes	characteristic
538	C₈	—	2	1	no	—
539	C₈	—	2	1	no	—
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	4	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	4	1	no	—
547	C₂²	—	4	1	no	—
548	C₂²	—	4	1	no	—
549	C₂²	—	4	1	no	—
550	C₂²	—	4	1	no	—
551	C₂²	—	4	1	no	—
552	C₂²	—	4	1	no	—
553	C₂²	—	8	1	no	—
554	C₂²	—	8	1	no	—
555	C₂²	—	8	1	no	—
556	C₂²	D₄²×C₁₇	1	1	yes	characteristic
557	C₄	—	2	2	no	—
558	C₄	—	2	1	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	1	no	—
561	C₄	—	4	1	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	1	no	—
564	C₄	—	8	1	no	—
565	C₄	—	8	1	no	—
566	C₄	—	8	1	no	—
567	C₄	C₂×C₁₇×#135	1	1	yes	characteristic
568	C₄	C₁₇×#575	1	1	yes	characteristic
569	C₄	C₁₇×#577	1	1	yes	characteristic
570	C₄	C₁₇×#578	1	1	yes	characteristic
571	C₂	—	8	1	no	—
572	C₂	—	8	1	no	—
573	C₂	—	16	1	no	—
574	C₂	C₁₇×#3269	1	1	yes	characteristic
575	C₂	C₁₇×#3282	1	1	yes	characteristic
576	C₂	C₁₇×#3288	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3305	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₇ ◁ C₄²×C₁₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₁₇×#3369	C₂	semidirect
2. C₁₇×#3362	C₂	semidirect
3. C₁₇×#3340	C₂	semidirect
5. C₁₇×#1720	C₂	semidirect
6. C₁₇×#1698	C₂	semidirect
7. C₁₇×#1683	C₂	semidirect
8. C₁₇×#1677	C₂	semidirect
9. C₁₇×#1672	C₂	semidirect
10. C₁₇×#1641	C₂	semidirect
11. C₁₇×#1634	C₂	semidirect
12. C₁₇×#1633	C₂	semidirect
13. C₁₇×#1628	C₂	semidirect
14. C₁₇×#1582	C₂	semidirect
15. C₁₇×SD₁₆⋊C₈	C₂	semidirect
208. #19800	C₁₇	direct (N × H)
259. #3369	C₂×C₁₇	semidirect
260. #3362	C₂×C₁₇	semidirect
261. #3340	C₂×C₁₇	semidirect
263. #1720	C₂×C₁₇	semidirect
264. #1698	C₂×C₁₇	semidirect
265. #1683	C₂×C₁₇	semidirect
266. #1677	C₂×C₁₇	semidirect
267. #1672	C₂×C₁₇	semidirect
268. #1641	C₂×C₁₇	semidirect
269. #1634	C₂×C₁₇	semidirect
270. #1633	C₂×C₁₇	semidirect
271. #1628	C₂×C₁₇	semidirect
272. #1582	C₂×C₁₇	semidirect
273. SD₁₆⋊C₈	C₂×C₁₇	semidirect
432. C₁₇	#19800	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×#3369	2
C₁₇×#3362	2
C₁₇×#3340	2
C₁₇×#3305	2
C₁₇×#1720	2
C₁₇×#1698	2
C₁₇×#1683	2
C₁₇×#1677	2
C₁₇×#1672	2
C₁₇×#1641	2
C₁₇×#1634	2
C₁₇×#1633	2
C₁₇×#1628	2
C₁₇×#1582	2
C₁₇×SD₁₆⋊C₈	2
#19800	17

Subgroups — C17×#19800 #16877544

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#19800 #16877544