Subgroups — #17003752

Order 4352.

714 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#63254	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#10587601	C₂	1	1	yes	maximal, characteristic
4	#14527604	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527601	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527596	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527590	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527588	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527587	C₂	1	1	yes	maximal, characteristic, complemented
10	SD₁₆×#3622	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527535	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527177	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527168	C₂	1	1	yes	maximal, characteristic
14	#14527063	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×SD₁₆⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10587601	C₄	1	1	yes	characteristic
17	C₄×#63254	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₁₇	C₂²	1	1	yes	characteristic
19	Q₈×#3622	C₂²	1	1	yes	characteristic
20	C₈×Dic₃₄	—	2	1	no	—
21	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
22	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
23	#11762933	—	2	1	no	—
24	#11762933	C₂²	1	1	yes	characteristic
25	#11762933	C₂²	1	1	yes	characteristic
26	#11762915	C₄	1	1	yes	characteristic
27	#11762913	C₄	1	1	yes	characteristic
28	#11762910	C₄	1	1	yes	characteristic
29	#11762906	C₄	1	1	yes	characteristic
30	C₄×Dic₆₈	C₂²	1	1	yes	characteristic
31	C₄×#63231	C₂²	1	1	yes	characteristic
32	C₄×#63229	C₂²	1	1	yes	characteristic
33	D₄×#3622	C₂²	1	1	yes	characteristic
34	C₈×C₂²⋊D₁₇	—	2	1	no	—
35	#11762872	—	2	1	no	—
36	#11762861	C₂²	1	1	yes	characteristic
37	#11762860	C₂²	1	1	yes	characteristic
38	#11762859	—	2	1	no	—
39	#11762848	C₄	1	1	yes	characteristic
40	C₄⋊C₈×D₁₇	—	2	1	no	—
41	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
42	#11762816	C₄	1	1	yes	characteristic
43	#11762807	C₄	1	1	yes	characteristic
44	C₄×#63218	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₁₇	—	2	1	no	—
46	C₄×C₈×D₁₇	—	2	1	no	—
47	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11762561	C₂²	1	1	yes	characteristic
49	#11762560	C₂²	1	1	yes	characteristic
50	#11762559	C₂²	1	1	yes	characteristic
51	#11762541	C₂²	1	1	yes	characteristic
52	#11762541	C₂²	1	1	yes	characteristic
53	Q₈⋊#3622	C₂²	1	1	yes	characteristic
54	#11762539	C₂²	1	1	yes	characteristic
55	#11762539	C₂²	1	1	yes	characteristic
56	D₄⋊#3622	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	C₈×#3622	C₂²	1	1	yes	characteristic
59	C₈×#3622	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
62	C₈×D₄×C₁₇	C₂²	1	1	yes	characteristic
63	C₁₇×#335	C₂²	1	1	yes	characteristic
64	C₁₇×Q₈⋊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×Q₈×D₁₇	C₂×C₄	1	1	yes	characteristic
68	C₂×#63254	C₂×C₄	1	1	yes	characteristic
69	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₁₇	—	2	1	no	—
71	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
72	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
73	Q₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
74	C₂×#63231	C₂×C₄	1	1	yes	characteristic
75	D₄×Dic₁₇	C₂×C₄	1	1	yes	characteristic
76	C₂×#63229	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₁₇	—	2	1	no	—
78	C₂×C₄×Dic₁₇	—	2	1	no	—
79	C₂²×#3622	—	2	1	no	—
80	#10587601	C₈	1	8	yes	complemented
81	C₂×Dic₆₈	C₂×C₄	1	1	yes	characteristic
82	C₂×#63218	C₂×C₄	1	1	yes	characteristic
83	C₂×#63218	C₂×C₄	1	1	yes	characteristic
84	C₂×C₈×D₁₇	—	2	1	no	—
85	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
86	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
87	#10587578	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₄×D₁₇	—	2	1	no	—
89	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
90	#10587573	—	2	1	no	—
91	#10587573	C₂×C₄	1	1	yes	characteristic
92	#10587573	C₂×C₄	1	1	yes	characteristic
93	#10587567	—	2	1	no	—
94	#10587563	—	2	1	no	—
95	C₄²×D₁₇	—	2	1	no	—
96	C₄²×D₁₇	C₂³	1	1	yes	characteristic
97	C₄×Dic₃₄	—	2	1	no	—
98	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
99	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
100	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
101	C₁₇×C₄⋊C₈	—	2	1	no	—
102	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
103	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
105	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
106	C₁₇×C₂²⋊C₈	—	2	1	no	—
107	C₄×C₈×C₁₇	—	2	1	no	—
108	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
109	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
111	#10587506	C₂×C₄	1	1	yes	characteristic
112	#10587503	C₂×C₄	1	1	yes	characteristic
113	C₂²⋊#3622	—	2	1	no	—
114	#10587491	—	2	1	no	—
115	#10587491	—	2	1	no	—
116	#10587489	C₂×C₄	1	1	yes	characteristic
117	#10587487	C₂×C₄	1	1	yes	characteristic
118	#10587487	C₂×C₄	1	1	yes	characteristic
119	#10587486	C₂×C₄	1	1	yes	characteristic
120	#10587486	C₂×C₄	1	1	yes	characteristic
121	#10587485	—	2	1	no	—
122	#10587485	—	2	1	no	—
123	#10587485	—	2	1	no	—
124	#10587485	—	2	1	no	—
125	#10587485	—	2	1	no	—
126	#10587485	—	2	1	no	—
127	C₈×Dic₁₇	—	2	1	no	—
128	C₈×Dic₁₇	—	2	1	no	—
129	C₈×Dic₁₇	—	2	1	no	—
130	C₈×Dic₁₇	—	2	1	no	—
131	C₈×Dic₁₇	—	2	1	no	—
132	C₈×Dic₁₇	D₄	1	1	yes	characteristic
133	C₈×Dic₁₇	D₄	1	1	yes	characteristic
134	#10587481	C₂×C₄	1	1	yes	characteristic
135	#10587481	C₂×C₄	1	1	yes	characteristic
136	#10587479	C₂×C₄	1	1	yes	characteristic
137	#10587478	C₂×C₄	1	1	yes	characteristic
138	C₄⋊#3622	—	2	1	no	—
139	C₄⋊#3622	C₂³	1	1	yes	characteristic
140	C₄⋊#3622	C₂³	1	1	yes	characteristic
141	C₄×#3622	—	2	1	no	—
142	C₄×#3622	C₂³	1	1	yes	characteristic
143	C₄×#3622	C₂³	1	1	yes	characteristic
144	C₄×#3622	C₂³	1	1	yes	characteristic
145	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₁₇	—	2	1	no	—
148	C₂×C₂²⋊D₁₇	—	2	1	no	—
149	C₂²×Dic₁₇	—	2	1	no	—
150	C₂²×Dic₁₇	—	2	1	no	—
151	Q₈×D₁₇	—	2	2	no	—
152	Q₈×D₁₇	C₂×C₈	1	4	yes	complemented
153	#63254	—	2	2	no	—
154	#63254	C₂×C₈	1	4	yes	—
155	C₂×C₄×D₁₇	—	2	1	no	—
156	C₂×C₄×D₁₇	—	2	1	no	—
157	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
159	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
160	C₂×Dic₃₄	—	2	1	no	—
161	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
162	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
163	SD₁₆×C₁₇	C₂×C₈	1	4	yes	complemented
164	C₂×C₈×C₁₇	—	2	1	no	—
165	C₂×C₈×C₁₇	—	2	1	no	—
166	C₂×C₈×C₁₇	—	2	1	no	—
167	C₂×C₈×C₁₇	—	4	2	no	—
168	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
169	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
171	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
172	C₄⋊C₄×C₁₇	—	2	1	no	—
173	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
174	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
175	C₂²⋊C₄×C₁₇	—	2	1	no	—
176	C₄²×C₁₇	—	2	1	no	—
177	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
178	C₂²⋊Dic₁₇	—	2	1	no	—
179	#63231	C₂×C₈	1	4	yes	complemented
180	#63229	C₂×C₈	1	4	yes	complemented
181	#63227	—	2	1	no	—
182	C₄⋊Dic₁₇	—	2	1	no	—
183	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
184	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
185	#63225	—	2	1	no	—
186	#63225	—	2	1	no	—
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	#63225	—	2	1	no	—
190	C₄×Dic₁₇	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	—	2	1	no	—
193	C₄×Dic₁₇	—	2	1	no	—
194	C₄×Dic₁₇	—	2	1	no	—
195	C₄×Dic₁₇	—	2	1	no	—
196	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
197	C₄×Dic₁₇	C₂×D₄	1	1	yes	characteristic
198	C₄×Dic₁₇	#41	1	1	yes	characteristic
199	C₂×#3622	—	2	1	no	—
200	C₂×#3622	—	2	1	no	—
201	C₂×#3622	—	2	1	no	—
202	C₂×#3622	—	4	2	no	—
203	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
204	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
205	C₂×#3622	C₂×D₄	1	1	yes	characteristic
206	C₂×#3622	C₂×D₄	1	1	yes	characteristic
207	Dic₆₈	C₂×C₈	1	4	yes	complemented
208	#63218	—	2	2	no	—
209	#63218	C₂×C₈	1	4	yes	complemented
210	C₈×D₁₇	—	2	2	no	—
211	C₈×D₁₇	—	4	1	no	—
212	C₈×D₁₇	—	4	2	no	—
213	C₈×#137	—	17	1	no	maximal, Sylow
214	C₂³×C₁₇	—	2	1	no	—
215	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
216	Q₈×C₁₇	—	2	1	no	—
217	Q₈×C₁₇	C₂²×C₈	1	2	yes	—
218	D₄×C₁₇	—	2	1	no	—
219	D₄×C₁₇	C₂²×C₈	1	2	yes	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	4	1	no	—
224	C₂×C₄×C₁₇	—	4	1	no	—
225	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
228	C₂²⋊D₁₇	—	2	4	no	—
229	C₂×Dic₁₇	—	2	1	no	—
230	C₂×Dic₁₇	—	2	1	no	—
231	C₂×Dic₁₇	—	2	4	no	—
232	C₂×Dic₁₇	—	2	1	no	—
233	C₂×Dic₁₇	—	2	1	no	—
234	C₂×Dic₁₇	—	4	2	no	—
235	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
236	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
238	C₄×D₁₇	—	2	4	no	—
239	C₄×D₁₇	—	2	1	no	—
240	C₄×D₁₇	—	2	1	no	—
241	C₄×D₁₇	—	4	1	no	—
242	C₄×D₁₇	—	4	2	no	—
243	C₄×D₁₇	C₂²×C₈	1	2	yes	—
244	C₄×D₁₇	#131	1	2	yes	—
245	Dic₃₄	—	2	1	no	—
246	Dic₃₄	—	2	1	no	—
247	Dic₃₄	—	2	4	no	—
248	Dic₃₄	C₂²×C₈	1	2	yes	—
249	Dic₃₄	C₂²×C₈	1	2	yes	—
250	C₈×C₁₇	—	2	1	no	—
251	C₈×C₁₇	—	2	1	no	—
252	C₈×C₁₇	—	2	1	no	—
253	C₈×C₁₇	—	4	1	no	—
254	C₈×C₁₇	—	4	1	no	—
255	C₈×C₁₇	—	4	1	no	—
256	C₈×C₁₇	C₂²×C₈	1	2	yes	—
257	#3622	—	2	1	no	—
258	#3622	—	2	1	no	—
259	#3622	—	4	1	no	—
260	#3622	—	4	1	no	—
261	#3622	—	4	1	no	—
262	#3622	C₂²×C₈	1	2	yes	—
263	#3622	#137	1	2	yes	complemented
264	C₈×#41	—	17	1	no	—
265	C₂×C₈×Q₈	—	17	1	no	—
266	C₄×#137	—	17	1	no	—
267	#1579	—	17	1	no	—
268	#1579	—	17	1	no	—
269	SD₁₆⋊C₈	—	17	1	no	—
270	SD₁₆⋊C₈	D₁₇	1	1	yes	characteristic, complemented
271	C₈×Q₁₆	—	17	1	no	—
272	C₈×Q₁₆	—	17	1	no	—
273	C₈×SD₁₆	—	17	1	no	—
274	C₈×SD₁₆	—	17	1	no	—
275	#1565	—	17	1	no	—
276	#1479	—	17	1	no	—
277	#1477	—	17	1	no	—
278	C₈×M₁₆	—	17	1	no	—
279	C₂²×C₁₇	—	2	2	no	—
280	C₂²×C₁₇	—	4	1	no	—
281	C₂²×C₁₇	—	4	1	no	—
282	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
283	C₂×D₁₇	—	2	1	no	—
284	C₂×D₁₇	—	2	1	no	—
285	C₂×D₁₇	C₈×D₄	1	2	yes	—
286	C₄×C₁₇	—	2	2	no	—
287	C₄×C₁₇	—	2	1	no	—
288	C₄×C₁₇	—	4	1	no	—
289	C₄×C₁₇	—	4	1	no	—
290	C₄×C₁₇	C₂³×C₈	1	1	yes	characteristic
291	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
292	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
293	C₄×C₁₇	#575	1	1	yes	characteristic
294	Dic₁₇	—	2	2	no	—
295	Dic₁₇	—	2	2	no	—
296	Dic₁₇	—	2	1	no	—
297	Dic₁₇	—	2	1	no	—
298	Dic₁₇	—	4	1	no	—
299	Dic₁₇	—	4	1	no	—
300	Dic₁₇	C₈×D₄	1	2	yes	—
301	C₂×#137	—	17	1	no	—
302	C₄×#41	—	17	1	no	—
303	C₂×C₄×Q₈	—	17	1	no	—
304	C₈×Q₈	—	17	1	no	—
305	C₈×Q₈	—	17	1	no	—
306	C₈×Q₈	—	17	1	no	—
307	C₈×Q₈	—	17	1	no	—
308	C₈×Q₈	—	17	1	no	—
309	C₈×Q₈	—	34	1	no	—
310	C₈×Q₈	—	34	1	no	—
311	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
312	#441	—	17	1	no	—
313	#441	—	17	1	no	—
314	#440	—	17	1	no	—
315	#440	—	17	1	no	—
316	C₄×Q₁₆	—	17	1	no	—
317	C₄×Q₁₆	—	17	1	no	—
318	C₄×SD₁₆	—	17	1	no	—
319	C₄×SD₁₆	C₂×D₁₇	1	1	yes	characteristic
320	C₈×D₄	—	17	1	no	—
321	C₈×D₄	—	34	1	no	—
322	C₈×D₄	—	34	1	no	—
323	C₈×D₄	C₂×D₁₇	1	1	yes	characteristic
324	#431	—	17	1	no	—
325	#431	—	17	1	no	—
326	#431	—	34	1	no	—
327	#428	—	17	1	no	—
328	C₂×C₄⋊C₈	—	17	1	no	—
329	C₂×C₄⋊C₈	—	34	1	no	—
330	#419	—	17	1	no	—
331	#417	—	17	1	no	—
332	C₄×M₁₆	—	17	1	no	—
333	C₂×C₄×C₈	—	17	1	no	—
334	C₂×C₄×C₈	—	34	1	no	—
335	C₂×C₄×C₈	—	34	1	no	—
336	#335	—	17	1	no	—
337	#335	C₂×D₁₇	1	1	yes	characteristic
338	#334	—	17	1	no	—
339	#334	—	17	1	no	—
340	Q₈⋊C₈	—	17	1	no	—
341	Q₈⋊C₈	—	17	1	no	—
342	Q₈⋊C₈	—	17	1	no	—
343	Q₈⋊C₈	—	17	1	no	—
344	Q₈⋊C₈	—	17	1	no	—
345	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
346	D₄⋊C₈	—	17	1	no	—
347	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
348	#322	—	17	1	no	—
349	#322	C₂×D₁₇	1	1	yes	characteristic
350	C₈²	—	17	1	no	—
351	C₈²	—	17	1	no	—
352	C₂×C₁₇	—	4	2	no	—
353	C₂×C₁₇	C₂×C₈×D₄	1	1	yes	characteristic
354	C₂×C₁₇	C₄×#137	1	1	yes	characteristic
355	C₂×C₁₇	#2955	1	1	yes	characteristic
356	D₁₇	—	2	2	no	—
357	C₂×#41	—	17	1	no	—
358	C₂²×Q₈	—	17	1	no	—
359	#137	—	17	8	no	—
360	C₂×Q₁₆	—	17	1	no	—
361	C₂×Q₁₆	—	17	1	no	—
362	C₂×SD₁₆	—	17	1	no	—
363	C₂×SD₁₆	C₄×D₁₇	1	1	yes	characteristic
364	C₂×M₁₆	—	17	1	no	—
365	C₂×M₁₆	—	17	1	no	—
366	C₂²×C₈	—	2	1	no	—
367	C₂²×C₈	—	17	1	no	—
368	C₂²×C₈	—	17	1	no	—
369	C₂²×C₈	—	34	1	no	—
370	C₂²×C₈	—	34	1	no	—
371	C₄×Q₈	—	17	1	no	—
372	C₄×Q₈	—	17	1	no	—
373	C₄×Q₈	—	17	1	no	—
374	C₄×Q₈	—	17	1	no	—
375	C₄×Q₈	—	17	1	no	—
376	C₄×Q₈	—	34	1	no	—
377	C₄×Q₈	—	34	1	no	—
378	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
379	C₄×D₄	—	17	1	no	—
380	C₄×D₄	—	34	1	no	—
381	C₄×D₄	—	34	1	no	—
382	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
383	#117	—	17	1	no	—
384	#117	—	34	1	no	—
385	C₂×C₄⋊C₄	—	17	1	no	—
386	C₂×C₄⋊C₄	—	34	1	no	—
387	C₂×C₄²	—	17	1	no	—
388	C₂×C₄²	—	34	1	no	—
389	C₂×C₄²	—	34	1	no	—
390	#107	—	17	1	no	—
391	#107	—	17	1	no	—
392	#106	—	17	1	no	—
393	#106	C₄×D₁₇	1	1	yes	characteristic
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	—	17	1	no	—
396	C₄⋊C₈	—	17	1	no	—
397	C₄⋊C₈	—	34	1	no	—
398	C₄⋊C₈	—	34	1	no	—
399	C₄⋊C₈	—	34	1	no	—
400	C₄⋊C₈	—	34	1	no	—
401	C₄⋊C₈	—	34	1	no	—
402	C₄⋊C₈	—	34	1	no	—
403	C₄⋊C₈	—	34	1	no	—
404	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
405	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
406	#103	—	17	1	no	—
407	#103	—	17	1	no	—
408	#103	—	17	1	no	—
409	#103	—	17	1	no	—
410	#103	—	17	1	no	—
411	#103	C₄×D₁₇	1	1	yes	characteristic
412	#102	—	17	1	no	—
413	#102	C₄×D₁₇	1	1	yes	characteristic
414	C₂²⋊C₈	—	2	1	no	—
415	C₂²⋊C₈	—	34	1	no	—
416	C₂²⋊C₈	—	34	1	no	—
417	C₂²⋊C₈	—	34	1	no	—
418	#97	—	17	1	no	—
419	#97	—	17	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₄×C₈	—	17	1	no	—
422	C₄×C₈	—	17	1	no	—
423	C₄×C₈	—	17	1	no	—
424	C₄×C₈	—	17	1	no	—
425	C₄×C₈	—	17	1	no	—
426	C₄×C₈	—	34	1	no	—
427	C₄×C₈	—	34	1	no	—
428	C₄×C₈	—	34	1	no	—
429	C₄×C₈	—	34	1	no	—
430	C₄×C₈	—	34	1	no	—
431	C₄×C₈	—	34	1	no	—
432	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
433	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
434	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
435	C₁₇	C₈×#137	1	1	yes	characteristic, complemented, Sylow
436	#41	—	17	4	no	—
437	#41	—	34	2	no	—
438	C₂×Q₈	—	17	4	no	—
439	C₂×Q₈	—	17	1	no	—
440	C₂×Q₈	—	17	1	no	—
441	C₂×Q₈	—	34	1	no	—
442	C₂×Q₈	—	34	2	no	—
443	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
444	C₂×D₄	—	34	1	no	—
445	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
446	C₂²×C₄	—	2	1	no	—
447	C₂²×C₄	—	17	1	no	—
448	C₂²×C₄	—	17	1	no	—
449	C₂²×C₄	—	17	1	no	—
450	C₂²×C₄	—	34	1	no	—
451	C₂²×C₄	—	34	1	no	—
452	C₂²×C₄	—	34	1	no	—
453	C₂²×C₄	—	34	1	no	—
454	Q₁₆	—	17	4	no	—
455	Q₁₆	—	17	4	no	—
456	SD₁₆	—	17	4	no	—
457	SD₁₆	C₈×D₁₇	1	4	yes	complemented
458	M₁₆	—	17	4	no	—
459	M₁₆	—	34	2	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	—	17	1	no	—
465	C₂×C₈	—	17	1	no	—
466	C₂×C₈	—	17	1	no	—
467	C₂×C₈	—	17	1	no	—
468	C₂×C₈	—	34	2	no	—
469	C₂×C₈	—	34	1	no	—
470	C₂×C₈	—	34	1	no	—
471	C₂×C₈	—	34	1	no	—
472	C₂×C₈	—	68	1	no	—
473	C₂×C₈	—	68	2	no	—
474	C₂×C₈	—	68	2	no	—
475	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
476	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
477	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
478	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
479	C₄⋊C₄	—	2	1	no	—
480	C₄⋊C₄	—	17	1	no	—
481	C₄⋊C₄	—	17	1	no	—
482	C₄⋊C₄	—	34	1	no	—
483	C₄⋊C₄	—	34	1	no	—
484	C₄⋊C₄	—	34	1	no	—
485	C₄⋊C₄	—	34	1	no	—
486	C₄⋊C₄	—	34	1	no	—
487	C₄⋊C₄	—	34	1	no	—
488	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
489	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	34	1	no	—
492	C₂²⋊C₄	—	34	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	17	1	no	—
495	C₄²	—	17	1	no	—
496	C₄²	—	17	1	no	—
497	C₄²	—	34	1	no	—
498	C₄²	—	34	1	no	—
499	C₄²	—	34	1	no	—
500	C₄²	—	34	1	no	—
501	C₄²	—	34	1	no	—
502	C₄²	—	34	1	no	—
503	C₄²	C₂³×D₁₇	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	17	1	no	—
506	Q₈	—	2	1	no	—
507	Q₈	—	17	2	no	—
508	Q₈	—	17	2	no	—
509	Q₈	—	34	4	no	—
510	Q₈	—	34	1	no	—
511	Q₈	—	34	1	no	—
512	Q₈	C₂×C₈×D₁₇	1	2	yes	—
513	D₄	—	2	1	no	—
514	D₄	—	34	4	no	—
515	D₄	C₂×C₈×D₁₇	1	2	yes	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	17	1	no	—
522	C₂×C₄	—	17	2	no	—
523	C₂×C₄	—	17	2	no	—
524	C₂×C₄	—	17	1	no	—
525	C₂×C₄	—	17	1	no	—
526	C₂×C₄	—	34	4	no	—
527	C₂×C₄	—	34	4	no	—
528	C₂×C₄	—	34	1	no	—
529	C₂×C₄	—	34	1	no	—
530	C₂×C₄	—	34	1	no	—
531	C₂×C₄	—	34	1	no	—
532	C₂×C₄	—	34	1	no	—
533	C₂×C₄	—	34	1	no	—
534	C₂×C₄	—	68	1	no	—
535	C₂×C₄	—	68	2	no	—
536	C₂×C₄	—	68	2	no	—
537	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
538	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
539	C₂×C₄	#41×D₁₇	1	1	yes	characteristic
540	C₈	—	2	1	no	—
541	C₈	—	2	1	no	—
542	C₈	—	2	1	no	—
543	C₈	—	4	1	no	—
544	C₈	—	4	1	no	—
545	C₈	—	4	1	no	—
546	C₈	—	17	2	no	—
547	C₈	—	17	2	no	—
548	C₈	—	34	1	no	—
549	C₈	—	34	1	no	—
550	C₈	—	68	1	no	—
551	C₈	—	68	1	no	—
552	C₈	—	68	1	no	—
553	C₈	C₂×C₈×D₁₇	1	2	yes	—
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	1	no	—
557	C₂²	—	17	2	no	—
558	C₂²	—	34	1	no	—
559	C₂²	—	34	1	no	—
560	C₂²	C₄×D₄×D₁₇	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	2	no	—
563	C₄	—	4	1	no	—
564	C₄	—	4	1	no	—
565	C₄	—	17	2	no	—
566	C₄	—	34	1	no	—
567	C₄	—	34	1	no	—
568	C₄	—	34	2	no	—
569	C₄	—	34	2	no	—
570	C₄	—	68	1	no	—
571	C₄	—	68	1	no	—
572	C₄	C₂²×C₈×D₁₇	1	1	yes	characteristic
573	C₄	#131×D₁₇	1	1	yes	characteristic
574	C₄	#137×D₁₇	1	1	yes	characteristic
575	C₄	#11763605	1	1	yes	characteristic
576	C₂	—	4	2	no	—
577	C₂	—	34	2	no	—
578	C₂	C₈×D₄×D₁₇	1	1	yes	characteristic
579	C₂	#14537606	1	1	yes	characteristic
580	C₂	#14537684	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₄×C₁₇	C₂³×C₈
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×SD₁₆⋊C₈	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#63254	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	SD₁₆⋊C₈	D₁₇
hypocenter	C₁₇	C₈×#137
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ SD₁₆⋊C₈

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₁₇	C₂	semidirect
4. #14527604	C₂	semidirect
5. #14527601	C₂	semidirect
6. #14527596	C₂	semidirect
7. #14527590	C₂	semidirect
8. #14527588	C₂	semidirect
9. #14527587	C₂	semidirect
10. SD₁₆×#3622	C₂	semidirect
11. #14527535	C₂	semidirect
12. #14527177	C₂	semidirect
14. #14527063	C₂	semidirect
15. C₁₇×SD₁₆⋊C₈	C₂	semidirect
80. #10587601	C₈	semidirect
152. Q₈×D₁₇	C₂×C₈	semidirect
163. SD₁₆×C₁₇	C₂×C₈	semidirect
179. #63231	C₂×C₈	semidirect
180. #63229	C₂×C₈	semidirect
207. Dic₆₈	C₂×C₈	semidirect
209. #63218	C₂×C₈	semidirect
263. #3622	#137	semidirect
270. SD₁₆⋊C₈	D₁₇	semidirect
435. C₁₇	C₈×#137	semidirect
457. SD₁₆	C₈×D₁₇	semidirect

Maximal subgroups

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

subgroup	index
C₈×#63254	2
C₈×Q₈×D₁₇	2
C₄×#10587601	2
#14527604	2
#14527601	2
#14527596	2
#14527590	2
#14527588	2
#14527587	2
SD₁₆×#3622	2
#14527535	2
#14527177	2
#14527168	2
#14527063	2
C₁₇×SD₁₆⋊C₈	2
C₈×#137	17