Subgroups — C₁₇×#18593 #16876337

Order 4352.

916 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₇×#3511	C₂	1	1	yes	maximal, characteristic
2	C₁₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₇×#3165	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₇×#3107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₇×#1654	C₂	1	2	yes	maximal, complemented
6	C₁₇×#1652	C₂	1	2	yes	maximal, complemented
7	C₁₇×#1650	C₂	1	2	yes	maximal, complemented
8	C₁₇×#1647	C₂	1	2	yes	maximal, complemented
9	C₁₇×#1546	C₂	1	1	yes	maximal, characteristic, complemented
10	C₁₇×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₁₇×#1484	C₂	1	1	yes	maximal, characteristic, complemented
12	C₁₇×#556	C₂²	1	2	yes	—
13	C₁₇×#555	—	2	1	no	—
14	C₁₇×#554	—	2	1	no	—
15	C₁₇×#553	—	2	2	no	—
16	C₁₇×#548	—	2	2	no	—
17	C₁₇×#547	C₂²	1	2	yes	—
18	C₁₇×#542	—	2	2	no	—
19	C₁₇×#537	—	2	1	no	—
20	C₁₇×#533	—	2	1	no	—
21	C₁₇×#533	C₂²	1	1	yes	characteristic
22	C₁₇×#532	—	2	1	no	—
23	C₁₇×#532	C₂²	1	1	yes	characteristic
24	C₂×C₁₇×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₁₇×#520	—	2	1	no	—
26	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
27	C₁₇×#501	—	2	2	no	—
28	C₁₇×#500	C₂²	1	2	yes	—
29	C₁₇×#498	C₂²	1	2	yes	—
30	C₁₇×#485	—	2	1	no	—
31	C₁₇×#477	—	2	1	no	—
32	C₁₇×#475	C₂²	1	1	yes	characteristic
33	C₁₇×#474	C₂²	1	2	yes	—
34	C₁₇×#474	C₂²	1	1	yes	characteristic
35	C₁₇×#468	—	2	2	no	—
36	C₁₇×#462	C₂²	1	1	yes	characteristic
37	C₁₇×#461	C₂²	1	2	yes	—
38	C₁₇×#461	C₂²	1	1	yes	characteristic
39	C₁₇×#460	—	2	1	no	—
40	C₁₇×#452	—	2	1	no	—
41	C₄×Q₁₆×C₁₇	—	2	1	no	—
42	C₄×SD₁₆×C₁₇	—	2	1	no	—
43	C₁₇×#431	C₂²	1	1	yes	characteristic
44	C₁₇×#428	—	2	2	no	—
45	C₁₇×#423	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₁₇	C₂²	1	1	yes	characteristic
47	C₁₇×#332	C₂²	1	2	yes	—
48	C₁₇×#332	C₂²	1	2	yes	—
49	C₁₇×Q₈⋊C₈	C₂²	1	2	yes	—
50	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
52	C₁₇×D₄⋊C₈	C₂²	1	2	yes	—
53	C₂×#41×C₁₇	—	2	2	no	—
54	C₂×#41×C₁₇	—	2	1	no	—
55	C₂×#41×C₁₇	D₄	1	1	yes	characteristic
56	C₂²×Q₈×C₁₇	—	2	1	no	—
57	C₂×Q₁₆×C₁₇	—	2	1	no	—
58	C₂×SD₁₆×C₁₇	—	2	1	no	—
59	C₂×SD₁₆×C₁₇	—	2	2	no	—
60	C₂×M₁₆×C₁₇	—	2	1	no	—
61	C₂×M₁₆×C₁₇	—	2	1	no	—
62	C₁₇×C₄⋊Q₈	—	2	1	no	—
63	C₁₇×C₄⋊Q₈	—	2	1	no	—
64	C₁₇×C₄⋊Q₈	D₄	1	2	yes	—
65	C₁₇×C₄⋊Q₈	D₄	1	1	yes	characteristic
66	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
67	C₁₇×C₄⋊Q₈	C₂³	1	1	yes	characteristic
68	C₁₇×C₄⋊Q₈	C₂³	1	2	yes	—
69	C₁₇×#127	D₄	1	1	yes	characteristic
70	C₁₇×#126	—	2	4	no	—
71	C₁₇×#125	—	2	2	no	—
72	C₁₇×#125	—	2	1	no	—
73	C₁₇×#124	—	2	4	no	—
74	C₁₇×#124	—	2	2	no	—
75	C₁₇×#124	—	2	1	no	—
76	C₁₇×#123	—	2	4	no	—
77	C₁₇×C₂²⋊Q₈	—	2	2	no	—
78	C₁₇×C₂²⋊Q₈	—	2	4	no	—
79	C₁₇×C₂²⋊Q₈	—	2	2	no	—
80	C₁₇×C₂²⋊Q₈	—	2	2	no	—
81	C₁₇×C₂²⋊Q₈	—	2	1	no	—
82	C₁₇×C₂²⋊Q₈	—	2	1	no	—
83	C₁₇×#121	—	2	2	no	—
84	C₁₇×#121	—	2	2	no	—
85	C₁₇×#121	—	2	4	no	—
86	C₁₇×#121	—	2	2	no	—
87	C₁₇×#121	—	2	1	no	—
88	C₁₇×#121	D₄	1	2	yes	—
89	C₄×Q₈×C₁₇	—	2	2	no	—
90	C₄×Q₈×C₁₇	—	2	2	no	—
91	C₄×Q₈×C₁₇	—	2	1	no	—
92	C₄×Q₈×C₁₇	—	2	1	no	—
93	C₄×Q₈×C₁₇	D₄	1	1	yes	characteristic
94	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
95	C₄×D₄×C₁₇	—	2	2	no	—
96	C₄×D₄×C₁₇	—	2	4	no	—
97	C₄×D₄×C₁₇	—	2	2	no	—
98	C₄×D₄×C₁₇	—	2	1	no	—
99	C₄×D₄×C₁₇	—	2	1	no	—
100	C₄×D₄×C₁₇	—	2	1	no	—
101	C₄×D₄×C₁₇	D₄	1	1	yes	characteristic
102	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
103	C₄×D₄×C₁₇	C₂³	1	2	yes	—
104	C₁₇×#117	—	2	2	no	—
105	C₁₇×#117	—	2	2	no	—
106	C₁₇×#117	—	2	1	no	—
107	C₁₇×#117	—	2	1	no	—
108	C₁₇×#117	D₄	1	1	yes	characteristic
109	C₂×C₄⋊C₄×C₁₇	—	2	1	no	—
110	C₂×C₄⋊C₄×C₁₇	—	2	2	no	—
111	C₂×C₄⋊C₄×C₁₇	D₄	1	2	yes	—
112	C₂×C₄²×C₁₇	—	2	1	no	—
113	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
114	C₁₇×#107	—	2	4	no	—
115	C₁₇×#107	—	2	1	no	—
116	C₁₇×#107	—	2	2	no	—
117	C₁₇×#106	—	2	4	no	—
118	C₁₇×#106	—	2	1	no	—
119	C₁₇×C₄⋊C₈	—	2	1	no	—
120	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
121	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
122	C₁₇×C₄⋊C₈	C₂³	1	2	yes	—
123	C₁₇×#103	—	2	1	no	—
124	C₁₇×#103	—	2	1	no	—
125	C₁₇×#103	—	2	1	no	—
126	C₁₇×#103	—	2	2	no	—
127	C₁₇×#102	—	2	1	no	—
128	C₁₇×#102	—	2	2	no	—
129	C₁₇×C₂²⋊C₈	—	2	1	no	—
130	C₁₇×#97	—	2	1	no	—
131	C₄×C₈×C₁₇	—	2	1	no	—
132	C₄×C₈×C₁₇	C₂³	1	2	yes	—
133	#41×C₁₇	—	4	1	no	—
134	#41×C₁₇	—	4	1	no	—
135	#41×C₁₇	—	4	2	no	—
136	#41×C₁₇	—	4	2	no	—
137	#41×C₁₇	—	8	2	no	—
138	#41×C₁₇	—	8	2	no	—
139	C₂×Q₈×C₁₇	—	2	1	no	—
140	C₂×Q₈×C₁₇	—	2	2	no	—
141	C₂×Q₈×C₁₇	—	2	2	no	—
142	C₂×Q₈×C₁₇	—	2	1	no	—
143	C₂×Q₈×C₁₇	—	2	1	no	—
144	C₂×Q₈×C₁₇	—	8	1	no	—
145	C₂×Q₈×C₁₇	—	8	1	no	—
146	C₂×Q₈×C₁₇	C₂×D₄	1	1	yes	characteristic
147	C₂×D₄×C₁₇	—	2	2	no	—
148	C₂×D₄×C₁₇	—	2	1	no	—
149	C₂×D₄×C₁₇	—	2	4	no	—
150	C₂×D₄×C₁₇	—	2	1	no	—
151	C₂×D₄×C₁₇	—	2	1	no	—
152	C₂×D₄×C₁₇	C₂×D₄	1	2	yes	—
153	C₂×D₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	—	2	4	no	—
155	C₂²×C₄×C₁₇	—	2	2	no	—
156	C₂²×C₄×C₁₇	—	2	1	no	—
157	C₂²×C₄×C₁₇	—	2	1	no	—
158	C₂²×C₄×C₁₇	—	2	1	no	—
159	C₂²×C₄×C₁₇	—	2	2	no	—
160	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
163	Q₁₆×C₁₇	—	4	2	no	—
164	SD₁₆×C₁₇	—	4	2	no	—
165	SD₁₆×C₁₇	—	8	2	no	—
166	M₁₆×C₁₇	—	2	4	no	—
167	M₁₆×C₁₇	—	8	1	no	—
168	C₂×C₈×C₁₇	—	2	2	no	—
169	C₂×C₈×C₁₇	—	2	2	no	—
170	C₂×C₈×C₁₇	—	2	1	no	—
171	C₂×C₈×C₁₇	—	2	1	no	—
172	C₄⋊C₄×C₁₇	—	2	4	no	—
173	C₄⋊C₄×C₁₇	—	2	4	no	—
174	C₄⋊C₄×C₁₇	—	2	1	no	—
175	C₄⋊C₄×C₁₇	—	2	2	no	—
176	C₄⋊C₄×C₁₇	—	2	1	no	—
177	C₄⋊C₄×C₁₇	—	2	2	no	—
178	C₄⋊C₄×C₁₇	—	2	2	no	—
179	C₄⋊C₄×C₁₇	—	2	1	no	—
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	—	4	1	no	—
185	C₄⋊C₄×C₁₇	—	4	1	no	—
186	C₄⋊C₄×C₁₇	C₂×D₄	1	2	yes	—
187	C₄⋊C₄×C₁₇	C₂×D₄	1	4	yes	—
188	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
189	C₄⋊C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
190	C₂²⋊C₄×C₁₇	—	2	4	no	—
191	C₂²⋊C₄×C₁₇	—	2	4	no	—
192	C₂²⋊C₄×C₁₇	—	2	4	no	—
193	C₂²⋊C₄×C₁₇	—	2	1	no	—
194	C₂²⋊C₄×C₁₇	—	2	2	no	—
195	C₂²⋊C₄×C₁₇	—	2	1	no	—
196	C₂²⋊C₄×C₁₇	—	2	1	no	—
197	C₂²⋊C₄×C₁₇	—	2	2	no	—
198	C₂²⋊C₄×C₁₇	—	4	1	no	—
199	C₄²×C₁₇	—	2	4	no	—
200	C₄²×C₁₇	—	2	1	no	—
201	C₄²×C₁₇	—	2	1	no	—
202	C₄²×C₁₇	—	2	1	no	—
203	C₄²×C₁₇	—	4	1	no	—
204	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
205	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
206	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
208	#18593	C₁₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂³×C₁₇	—	2	1	no	—
210	C₂³×C₁₇	—	2	2	no	—
211	C₂³×C₁₇	#120	1	1	yes	characteristic
212	Q₈×C₁₇	—	2	1	no	—
213	Q₈×C₁₇	—	2	1	no	—
214	Q₈×C₁₇	—	4	2	no	—
215	Q₈×C₁₇	—	4	2	no	—
216	Q₈×C₁₇	—	4	2	no	—
217	Q₈×C₁₇	—	4	1	no	—
218	Q₈×C₁₇	—	4	1	no	—
219	Q₈×C₁₇	—	4	1	no	—
220	Q₈×C₁₇	—	4	1	no	—
221	Q₈×C₁₇	—	8	2	no	—
222	D₄×C₁₇	—	2	1	no	—
223	D₄×C₁₇	—	2	1	no	—
224	D₄×C₁₇	—	2	2	no	—
225	D₄×C₁₇	—	2	2	no	—
226	D₄×C₁₇	—	4	2	no	—
227	D₄×C₁₇	—	4	2	no	—
228	D₄×C₁₇	—	4	4	no	—
229	D₄×C₁₇	—	4	2	no	—
230	D₄×C₁₇	—	8	4	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	—	2	1	no	—
235	C₂×C₄×C₁₇	—	2	2	no	—
236	C₂×C₄×C₁₇	—	2	1	no	—
237	C₂×C₄×C₁₇	—	2	1	no	—
238	C₂×C₄×C₁₇	—	2	2	no	—
239	C₂×C₄×C₁₇	—	2	1	no	—
240	C₂×C₄×C₁₇	—	2	4	no	—
241	C₂×C₄×C₁₇	—	4	2	no	—
242	C₂×C₄×C₁₇	—	4	2	no	—
243	C₂×C₄×C₁₇	—	4	2	no	—
244	C₂×C₄×C₁₇	—	4	1	no	—
245	C₂×C₄×C₁₇	—	4	1	no	—
246	C₂×C₄×C₁₇	—	4	2	no	—
247	C₂×C₄×C₁₇	—	4	1	no	—
248	C₂×C₄×C₁₇	—	4	1	no	—
249	C₂×C₄×C₁₇	—	8	2	no	—
250	C₂×C₄×C₁₇	—	8	4	no	—
251	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
252	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
253	C₂×C₄×C₁₇	#120	1	1	yes	characteristic
254	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
255	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
256	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
257	C₈×C₁₇	—	2	4	no	—
258	C₈×C₁₇	—	4	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	2	no	—
261	#3511	C₂×C₁₇	1	1	yes	characteristic
262	#3254	C₂×C₁₇	1	1	yes	characteristic, complemented
263	#3165	C₂×C₁₇	1	1	yes	characteristic, complemented
264	#3107	C₂×C₁₇	1	1	yes	characteristic, complemented
265	#1654	C₂×C₁₇	1	2	yes	complemented
266	#1652	C₂×C₁₇	1	2	yes	complemented
267	#1650	C₂×C₁₇	1	2	yes	complemented
268	#1647	C₂×C₁₇	1	2	yes	complemented
269	#1546	C₂×C₁₇	1	1	yes	characteristic, complemented
270	#1489	C₂×C₁₇	1	1	yes	characteristic, complemented
271	#1484	C₂×C₁₇	1	1	yes	characteristic, complemented
272	C₂²×C₁₇	—	2	1	no	—
273	C₂²×C₁₇	—	2	1	no	—
274	C₂²×C₁₇	—	2	1	no	—
275	C₂²×C₁₇	—	4	1	no	—
276	C₂²×C₁₇	—	4	2	no	—
277	C₂²×C₁₇	—	4	1	no	—
278	C₂²×C₁₇	—	4	2	no	—
279	C₂²×C₁₇	—	4	1	no	—
280	C₂²×C₁₇	—	4	2	no	—
281	C₂²×C₁₇	C₂×#120	1	1	yes	characteristic
282	C₄×C₁₇	—	2	1	no	—
283	C₄×C₁₇	—	2	1	no	—
284	C₄×C₁₇	—	2	1	no	—
285	C₄×C₁₇	—	4	1	no	—
286	C₄×C₁₇	—	4	2	no	—
287	C₄×C₁₇	—	4	1	no	—
288	C₄×C₁₇	—	4	4	no	—
289	C₄×C₁₇	—	4	1	no	—
290	C₄×C₁₇	—	8	1	no	—
291	C₄×C₁₇	—	8	1	no	—
292	C₄×C₁₇	#456	1	2	yes	—
293	C₄×C₁₇	#575	1	1	yes	characteristic
294	C₄×C₁₇	#575	1	1	yes	characteristic
295	C₄×C₁₇	#576	1	1	yes	characteristic
296	C₄×C₁₇	#577	1	1	yes	characteristic
297	#556	C₂²×C₁₇	1	2	yes	—
298	#555	—	2	1	no	—
299	#554	—	2	1	no	—
300	#553	—	2	2	no	—
301	#548	—	2	2	no	—
302	#547	C₂²×C₁₇	1	2	yes	—
303	#542	—	2	2	no	—
304	#537	—	2	1	no	—
305	#533	—	2	1	no	—
306	#533	C₂²×C₁₇	1	1	yes	characteristic
307	#532	—	2	1	no	—
308	#532	C₂²×C₁₇	1	1	yes	characteristic
309	C₂×C₄⋊Q₈	C₂²×C₁₇	1	1	yes	characteristic
310	#520	—	2	1	no	—
311	C₄×#41	C₂²×C₁₇	1	1	yes	characteristic
312	#501	—	2	2	no	—
313	#500	C₂²×C₁₇	1	2	yes	—
314	#498	C₂²×C₁₇	1	2	yes	—
315	#485	—	2	1	no	—
316	#477	—	2	1	no	—
317	#475	C₂²×C₁₇	1	1	yes	characteristic
318	#474	C₂²×C₁₇	1	1	yes	characteristic
319	#474	C₂²×C₁₇	1	2	yes	—
320	#468	—	2	2	no	—
321	#462	C₂²×C₁₇	1	1	yes	characteristic
322	#461	C₂²×C₁₇	1	1	yes	characteristic
323	#461	C₂²×C₁₇	1	2	yes	—
324	#460	—	2	1	no	—
325	#452	—	2	1	no	—
326	C₄×Q₁₆	—	2	1	no	—
327	C₄×SD₁₆	—	2	1	no	—
328	#431	C₂²×C₁₇	1	1	yes	characteristic
329	#428	—	2	2	no	—
330	#423	C₂²×C₁₇	1	1	yes	characteristic
331	C₄×M₁₆	C₂²×C₁₇	1	1	yes	characteristic
332	#332	C₂²×C₁₇	1	2	yes	—
333	#332	C₂²×C₁₇	1	2	yes	—
334	Q₈⋊C₈	C₂²×C₁₇	1	2	yes	—
335	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
336	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
337	D₄⋊C₈	C₂²×C₁₇	1	2	yes	—
338	C₂×C₁₇	—	4	1	no	—
339	C₂×C₁₇	—	8	1	no	—
340	C₂×C₁₇	—	8	2	no	—
341	C₂×C₁₇	#3005	1	1	yes	characteristic
342	C₂×C₁₇	#3012	1	1	yes	characteristic
343	C₂×C₁₇	C₂×#456	1	1	yes	characteristic
344	C₂×#41	—	2	2	no	—
345	C₂×#41	—	2	1	no	—
346	C₂×#41	D₄×C₁₇	1	1	yes	characteristic
347	C₂²×Q₈	—	2	1	no	—
348	C₂×Q₁₆	—	2	1	no	—
349	C₂×SD₁₆	—	2	1	no	—
350	C₂×SD₁₆	—	2	2	no	—
351	C₂×M₁₆	—	2	1	no	—
352	C₂×M₁₆	—	2	1	no	—
353	C₄⋊Q₈	—	2	1	no	—
354	C₄⋊Q₈	—	2	1	no	—
355	C₄⋊Q₈	D₄×C₁₇	1	2	yes	—
356	C₄⋊Q₈	D₄×C₁₇	1	1	yes	characteristic
357	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
358	C₄⋊Q₈	C₂³×C₁₇	1	1	yes	characteristic
359	C₄⋊Q₈	C₂³×C₁₇	1	2	yes	—
360	#127	D₄×C₁₇	1	1	yes	characteristic
361	#126	—	2	4	no	—
362	#125	—	2	2	no	—
363	#125	—	2	1	no	—
364	#124	—	2	4	no	—
365	#124	—	2	2	no	—
366	#124	—	2	1	no	—
367	#123	—	2	4	no	—
368	C₂²⋊Q₈	—	2	2	no	—
369	C₂²⋊Q₈	—	2	4	no	—
370	C₂²⋊Q₈	—	2	2	no	—
371	C₂²⋊Q₈	—	2	2	no	—
372	C₂²⋊Q₈	—	2	1	no	—
373	C₂²⋊Q₈	—	2	1	no	—
374	#121	—	2	2	no	—
375	#121	—	2	2	no	—
376	#121	—	2	4	no	—
377	#121	—	2	2	no	—
378	#121	—	2	1	no	—
379	#121	D₄×C₁₇	1	2	yes	—
380	C₄×Q₈	—	2	2	no	—
381	C₄×Q₈	—	2	2	no	—
382	C₄×Q₈	—	2	1	no	—
383	C₄×Q₈	—	2	1	no	—
384	C₄×Q₈	D₄×C₁₇	1	1	yes	characteristic
385	C₄×Q₈	C₂³×C₁₇	1	1	yes	characteristic
386	C₄×D₄	—	2	2	no	—
387	C₄×D₄	—	2	4	no	—
388	C₄×D₄	—	2	2	no	—
389	C₄×D₄	—	2	1	no	—
390	C₄×D₄	—	2	1	no	—
391	C₄×D₄	—	2	1	no	—
392	C₄×D₄	D₄×C₁₇	1	1	yes	characteristic
393	C₄×D₄	C₂³×C₁₇	1	1	yes	characteristic
394	C₄×D₄	C₂³×C₁₇	1	2	yes	—
395	#117	—	2	2	no	—
396	#117	—	2	2	no	—
397	#117	—	2	1	no	—
398	#117	—	2	1	no	—
399	#117	D₄×C₁₇	1	1	yes	characteristic
400	C₂×C₄⋊C₄	—	2	1	no	—
401	C₂×C₄⋊C₄	—	2	2	no	—
402	C₂×C₄⋊C₄	D₄×C₁₇	1	2	yes	—
403	C₂×C₄²	—	2	1	no	—
404	C₂×C₄²	C₂³×C₁₇	1	1	yes	characteristic
405	#107	—	2	4	no	—
406	#107	—	2	1	no	—
407	#107	—	2	2	no	—
408	#106	—	2	4	no	—
409	#106	—	2	1	no	—
410	C₄⋊C₈	—	2	1	no	—
411	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
412	C₄⋊C₈	C₂³×C₁₇	1	1	yes	characteristic
413	C₄⋊C₈	C₂³×C₁₇	1	2	yes	—
414	#103	—	2	1	no	—
415	#103	—	2	1	no	—
416	#103	—	2	1	no	—
417	#103	—	2	2	no	—
418	#102	—	2	1	no	—
419	#102	—	2	2	no	—
420	C₂²⋊C₈	—	2	1	no	—
421	#97	—	2	1	no	—
422	C₄×C₈	—	2	1	no	—
423	C₄×C₈	C₂³×C₁₇	1	2	yes	—
424	C₁₇	#18593	1	1	yes	characteristic, direct product factor, Sylow
425	#41	—	4	1	no	—
426	#41	—	4	1	no	—
427	#41	—	4	2	no	—
428	#41	—	4	2	no	—
429	#41	—	8	2	no	—
430	#41	—	8	2	no	—
431	C₂×Q₈	—	2	2	no	—
432	C₂×Q₈	—	2	1	no	—
433	C₂×Q₈	—	2	2	no	—
434	C₂×Q₈	—	2	1	no	—
435	C₂×Q₈	—	2	1	no	—
436	C₂×Q₈	—	8	1	no	—
437	C₂×Q₈	—	8	1	no	—
438	C₂×Q₈	C₂×D₄×C₁₇	1	1	yes	characteristic
439	C₂×D₄	—	2	1	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	4	no	—
442	C₂×D₄	—	2	1	no	—
443	C₂×D₄	—	2	1	no	—
444	C₂×D₄	C₂×D₄×C₁₇	1	1	yes	characteristic
445	C₂×D₄	C₂×D₄×C₁₇	1	2	yes	—
446	C₂²×C₄	—	2	4	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
453	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
455	Q₁₆	—	4	2	no	—
456	SD₁₆	—	4	2	no	—
457	SD₁₆	—	8	2	no	—
458	M₁₆	—	2	4	no	—
459	M₁₆	—	8	1	no	—
460	C₂×C₈	—	2	2	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	2	no	—
464	C₄⋊C₄	—	2	4	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	2	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	2	no	—
469	C₄⋊C₄	—	2	2	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	—	4	1	no	—
477	C₄⋊C₄	—	4	1	no	—
478	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
479	C₄⋊C₄	C₂×D₄×C₁₇	1	1	yes	characteristic
480	C₄⋊C₄	C₂×D₄×C₁₇	1	2	yes	—
481	C₄⋊C₄	C₂×D₄×C₁₇	1	4	yes	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	4	no	—
485	C₂²⋊C₄	—	2	1	no	—
486	C₂²⋊C₄	—	2	1	no	—
487	C₂²⋊C₄	—	2	2	no	—
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	4	1	no	—
491	C₄²	—	2	4	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	4	1	no	—
496	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₁₇	1	1	yes	characteristic
499	C₄²	C₂⁴×C₁₇	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₁₇×#120	1	1	yes	characteristic
503	Q₈	—	2	1	no	—
504	Q₈	—	2	1	no	—
505	Q₈	—	4	2	no	—
506	Q₈	—	4	2	no	—
507	Q₈	—	4	2	no	—
508	Q₈	—	4	1	no	—
509	Q₈	—	4	1	no	—
510	Q₈	—	4	1	no	—
511	Q₈	—	4	1	no	—
512	Q₈	—	8	2	no	—
513	D₄	—	2	1	no	—
514	D₄	—	2	1	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	4	2	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	4	no	—
520	D₄	—	4	2	no	—
521	D₄	—	8	4	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	2	no	—
527	C₂×C₄	—	2	1	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	4	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	4	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	4	no	—
542	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
543	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
544	C₂×C₄	C₁₇×#120	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
546	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₁₇	1	1	yes	characteristic
548	C₈	—	2	4	no	—
549	C₈	—	4	1	no	—
550	C₈	—	4	1	no	—
551	C₈	—	4	2	no	—
552	C₂²	—	2	1	no	—
553	C₂²	—	2	1	no	—
554	C₂²	—	2	1	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	1	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	1	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂×C₁₇×#120	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	4	1	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	1	no	—
568	C₄	—	4	4	no	—
569	C₄	—	4	1	no	—
570	C₄	—	8	1	no	—
571	C₄	—	8	1	no	—
572	C₄	C₁₇×#456	1	2	yes	—
573	C₄	C₁₇×#575	1	1	yes	characteristic
574	C₄	C₁₇×#575	1	1	yes	characteristic
575	C₄	C₁₇×#576	1	1	yes	characteristic
576	C₄	C₁₇×#577	1	1	yes	characteristic
577	C₂	—	4	1	no	—
578	C₂	—	8	1	no	—
579	C₂	—	8	2	no	—
580	C₂	C₁₇×#3005	1	1	yes	characteristic
581	C₂	C₁₇×#3012	1	1	yes	characteristic
582	C₂	C₂×C₁₇×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₇
prime radical	C₁₇×#3511	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
2. C₁₇×#3254	C₂	semidirect
3. C₁₇×#3165	C₂	semidirect
4. C₁₇×#3107	C₂	semidirect
5. C₁₇×#1654	C₂	semidirect
6. C₁₇×#1652	C₂	semidirect
7. C₁₇×#1650	C₂	semidirect
8. C₁₇×#1647	C₂	semidirect
9. C₁₇×#1546	C₂	semidirect
10. C₁₇×#1489	C₂	semidirect
11. C₁₇×#1484	C₂	semidirect
208. #18593	C₁₇	direct (N × H)
262. #3254	C₂×C₁₇	semidirect
263. #3165	C₂×C₁₇	semidirect
264. #3107	C₂×C₁₇	semidirect
265. #1654	C₂×C₁₇	semidirect
266. #1652	C₂×C₁₇	semidirect
267. #1650	C₂×C₁₇	semidirect
268. #1647	C₂×C₁₇	semidirect
269. #1546	C₂×C₁₇	semidirect
270. #1489	C₂×C₁₇	semidirect
271. #1484	C₂×C₁₇	semidirect
424. C₁₇	#18593	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×#3511	2
C₁₇×#3254	2
C₁₇×#3165	2
C₁₇×#3107	2
C₁₇×#1654	2
C₁₇×#1652	2
C₁₇×#1650	2
C₁₇×#1647	2
C₁₇×#1546	2
C₁₇×#1489	2
C₁₇×#1484	2
#18593	17

Subgroups — C17×#18593 #16876337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₇×#18593 #16876337