Subgroups — #17004267

Order 4352.

678 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538813	C₂	1	1	yes	maximal, characteristic
2	C₈×Q₈×D₁₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#14537493	C₂	1	1	yes	maximal, characteristic
4	#14527664	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527662	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527660	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527599	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆⋊#3622	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527595	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527593	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527557	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527211	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527181	C₂	1	1	yes	maximal, characteristic
14	#14527075	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1588	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#10587593	—	2	1	no	—
17	#11763356	C₂²	1	1	yes	characteristic
18	C₄×Q₈×D₁₇	C₂²	1	1	yes	characteristic
19	#11763129	C₄	1	1	yes	characteristic
20	#11763126	C₄	1	1	yes	characteristic
21	#11763093	C₄	1	1	yes	characteristic
22	#11763092	C₄	1	1	yes	characteristic
23	#11763008	C₄	1	1	yes	characteristic
24	#11763007	C₄	1	1	yes	characteristic
25	#11762949	C₄	1	1	yes	characteristic
26	#11762946	C₄	1	1	yes	characteristic
27	Q₈×#3622	C₂²	1	1	yes	characteristic
28	C₈×Dic₃₄	—	2	1	no	—
29	C₈×Dic₃₄	C₂²	1	1	yes	characteristic
30	#11762933	—	2	1	no	—
31	#11762933	C₂²	1	1	yes	characteristic
32	C₄×#63219	C₂²	1	1	yes	characteristic
33	C₄×#63230	C₂²	1	1	yes	characteristic
34	C₄×#63229	C₂²	1	1	yes	characteristic
35	#11762888	C₂²	1	1	yes	characteristic
36	#11762885	—	2	1	no	—
37	D₄×#3622	C₂²	1	1	yes	characteristic
38	#11762874	C₂²	1	1	yes	characteristic
39	#11762872	—	2	1	no	—
40	#11762860	C₂²	1	1	yes	characteristic
41	#11762860	C₂²	1	1	yes	characteristic
42	#11762831	C₂²	1	1	yes	characteristic
43	C₄⋊C₈×D₁₇	—	2	1	no	—
44	C₄⋊C₈×D₁₇	C₂²	1	1	yes	characteristic
45	#11762774	—	2	1	no	—
46	C₄×C₈×D₁₇	—	2	1	no	—
47	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
48	#11762562	C₂²	1	1	yes	characteristic
49	#11762561	C₂²	1	1	yes	characteristic
50	#11762561	C₂²	1	1	yes	characteristic
51	#11762541	C₂²	1	1	yes	characteristic
52	Q₈⋊#3622	C₂²	1	1	yes	characteristic
53	#11762539	C₂²	1	1	yes	characteristic
54	#11762538	C₂²	1	1	yes	characteristic
55	D₄⋊#3622	C₂²	1	1	yes	characteristic
56	#11762536	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	#11762531	C₂²	1	1	yes	characteristic
59	#11762530	C₂²	1	1	yes	characteristic
60	C₈×Q₈×C₁₇	C₂²	1	1	yes	characteristic
61	C₄×SD₁₆×C₁₇	C₂²	1	1	yes	characteristic
62	C₁₇×#436	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×#63252	—	2	1	no	—
69	C₂×SD₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
70	C₂×M₁₆×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×#63230	C₂×C₄	1	1	yes	characteristic
75	#10587626	C₂×C₄	1	1	yes	characteristic
76	#10587624	C₂×C₄	1	1	yes	characteristic
77	C₂×#63229	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₁₇	—	2	1	no	—
79	C₂²×#3622	—	2	1	no	—
80	#10587593	—	4	4	no	—
81	C₂×#63219	C₂×C₄	1	1	yes	characteristic
82	C₂×#63218	—	2	1	no	—
83	C₂×#63218	—	2	1	no	—
84	C₂×C₈×D₁₇	—	2	1	no	—
85	C₂×C₈×D₁₇	—	2	1	no	—
86	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
87	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
88	#10587581	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₄×D₁₇	—	2	1	no	—
90	C₄⋊C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
91	#10587574	C₂×C₄	1	1	yes	characteristic
92	#10587573	—	2	1	no	—
93	#10587573	C₂×C₄	1	1	yes	characteristic
94	#10587571	—	2	1	no	—
95	#10587570	—	2	1	no	—
96	C₄×D₆₈	C₂³	1	1	yes	characteristic
97	C₄²×D₁₇	—	2	1	no	—
98	C₄²×D₁₇	C₂³	1	1	yes	characteristic
99	C₄×Dic₃₄	—	2	1	no	—
100	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
101	C₁₇×#106	C₂×C₄	1	1	yes	characteristic
102	C₁₇×C₄⋊C₈	—	2	1	no	—
103	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
104	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
105	C₁₇×#103	C₂×C₄	1	1	yes	characteristic
106	C₁₇×#102	C₂×C₄	1	1	yes	characteristic
107	C₁₇×C₂²⋊C₈	—	2	1	no	—
108	C₄×C₈×C₁₇	—	2	1	no	—
109	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
110	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
111	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
112	#10587506	C₂×C₄	1	1	yes	characteristic
113	#10587503	C₂×C₄	1	1	yes	characteristic
114	C₂²⋊#3622	—	2	1	no	—
115	#10587492	C₂×C₄	1	1	yes	characteristic
116	#10587491	—	2	1	no	—
117	#10587491	—	2	1	no	—
118	#10587491	—	2	1	no	—
119	#10587491	C₂×C₄	1	1	yes	characteristic
120	#10587491	C₂×C₄	1	1	yes	characteristic
121	#10587488	C₂×C₄	1	1	yes	characteristic
122	#10587487	C₂×C₄	1	1	yes	characteristic
123	#10587485	—	2	1	no	—
124	#10587485	—	2	1	no	—
125	#10587485	—	2	1	no	—
126	#10587485	—	2	1	no	—
127	#10587485	—	2	1	no	—
128	#10587485	C₂×C₄	1	1	yes	characteristic
129	#10587485	C₂×C₄	1	1	yes	characteristic
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	#10587480	C₂×C₄	1	1	yes	characteristic
136	#10587479	C₂×C₄	1	1	yes	characteristic
137	#10587479	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	C₂×C₂²⋊D₁₇	—	2	1	no	—
150	C₂×C₂²⋊D₁₇	—	2	1	no	—
151	Q₈×D₁₇	—	2	2	no	—
152	Q₈×D₁₇	—	2	2	no	—
153	#63252	—	4	2	no	—
154	#63252	—	4	2	no	—
155	C₂×D₆₈	—	2	1	no	—
156	C₂×D₆₈	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₄×D₁₇	—	2	1	no	—
158	C₂×C₄×D₁₇	—	2	1	no	—
159	C₂×C₄×D₁₇	—	2	1	no	—
160	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
161	C₂×C₄×D₁₇	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄×D₁₇	#41	1	1	yes	characteristic
163	C₂×Dic₃₄	—	2	1	no	—
164	C₂×Dic₃₄	—	2	1	no	—
165	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
166	SD₁₆×C₁₇	—	2	2	no	—
167	M₁₆×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	C₂²×C₄	1	1	yes	characteristic
172	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₂×C₈×C₁₇	C₂×D₄	1	1	yes	characteristic
175	C₄⋊C₄×C₁₇	—	2	1	no	—
176	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
177	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²⋊C₄×C₁₇	—	2	1	no	—
179	C₄²×C₁₇	—	2	1	no	—
180	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
181	C₂²⋊Dic₁₇	—	2	1	no	—
182	#63230	—	2	2	no	—
183	#63229	—	2	2	no	—
184	#63227	—	2	1	no	—
185	#63227	—	2	1	no	—
186	C₄⋊Dic₁₇	—	2	1	no	—
187	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
188	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
189	#63225	—	2	1	no	—
190	#63225	—	2	1	no	—
191	#63225	—	2	1	no	—
192	#63225	—	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	#63219	—	2	2	no	—
208	#63218	—	4	2	no	—
209	#63218	—	4	2	no	—
210	C₈×D₁₇	—	2	2	no	—
211	C₈×D₁₇	—	2	2	no	—
212	C₈×D₁₇	—	4	2	no	—
213	C₈×D₁₇	—	4	2	no	—
214	#17908	—	17	1	no	maximal, Sylow
215	C₂³×C₁₇	—	2	1	no	—
216	C₂²×D₁₇	—	2	1	no	—
217	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
218	Q₈×C₁₇	—	2	1	no	—
219	Q₈×C₁₇	#131	1	2	yes	complemented
220	D₄×C₁₇	—	2	1	no	—
221	D₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	2	1	no	—
223	C₂×C₄×C₁₇	—	2	1	no	—
224	C₂×C₄×C₁₇	—	2	1	no	—
225	C₂×C₄×C₁₇	—	4	1	no	—
226	C₂×C₄×C₁₇	—	4	1	no	—
227	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
230	C₂²⋊D₁₇	—	4	2	no	—
231	C₂²⋊D₁₇	—	4	2	no	—
232	C₂²⋊D₁₇	—	4	2	no	—
233	C₂×Dic₁₇	—	2	1	no	—
234	C₂×Dic₁₇	—	2	1	no	—
235	C₂×Dic₁₇	—	2	1	no	—
236	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
237	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
238	C₂×Dic₁₇	C₄×D₄	1	1	yes	characteristic
239	D₆₈	—	2	1	no	—
240	D₆₈	—	2	1	no	—
241	D₆₈	—	4	2	no	—
242	C₄×D₁₇	—	2	4	no	—
243	C₄×D₁₇	—	2	1	no	—
244	C₄×D₁₇	—	2	1	no	—
245	C₄×D₁₇	—	4	1	no	—
246	C₄×D₁₇	—	4	2	no	—
247	C₄×D₁₇	—	4	1	no	—
248	C₄×D₁₇	—	4	1	no	—
249	C₄×D₁₇	AGL(1,ℤ/8)	1	2	yes	—
250	C₄×D₁₇	#137	1	2	yes	—
251	Dic₃₄	—	2	4	no	—
252	Dic₃₄	—	2	1	no	—
253	Dic₃₄	—	4	2	no	—
254	Dic₃₄	#131	1	2	yes	complemented
255	C₈×C₁₇	—	2	1	no	—
256	C₈×C₁₇	—	2	1	no	—
257	C₈×C₁₇	—	2	1	no	—
258	C₈×C₁₇	—	2	1	no	—
259	C₈×C₁₇	—	4	1	no	—
260	C₈×C₁₇	—	4	1	no	—
261	C₈×C₁₇	—	4	1	no	—
262	#3622	—	2	1	no	—
263	#3622	—	2	1	no	—
264	#3622	—	2	1	no	—
265	#3622	—	2	1	no	—
266	#3622	—	4	1	no	—
267	#3622	—	4	1	no	—
268	#3622	—	4	1	no	—
269	#3103	—	17	1	no	—
270	C₂×C₈×Q₈	—	17	1	no	—
271	#2931	—	17	1	no	—
272	#1588	—	17	1	no	—
273	#1588	—	17	1	no	—
274	#1588	—	17	1	no	—
275	#1588	D₁₇	1	1	yes	characteristic, complemented
276	SD₁₆⋊C₈	—	17	1	no	—
277	SD₁₆⋊C₈	—	17	1	no	—
278	SD₁₆⋊C₈	—	17	1	no	—
279	SD₁₆⋊C₈	—	17	1	no	—
280	#1571	—	17	1	no	—
281	#1487	—	17	1	no	—
282	#1480	—	17	1	no	—
283	#1452	—	17	1	no	—
284	C₂²×C₁₇	—	4	1	no	—
285	C₂²×C₁₇	—	4	1	no	—
286	C₂²×C₁₇	—	4	1	no	—
287	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
288	C₂×D₁₇	—	2	1	no	—
289	C₂×D₁₇	—	2	1	no	—
290	C₂×D₁₇	—	4	1	no	—
291	C₂×D₁₇	—	4	1	no	—
292	C₂×D₁₇	—	4	1	no	—
293	C₂×D₁₇	#440	1	2	yes	—
294	C₄×C₁₇	—	2	2	no	—
295	C₄×C₁₇	—	2	1	no	—
296	C₄×C₁₇	—	4	1	no	—
297	C₄×C₁₇	—	4	1	no	—
298	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
299	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
300	C₄×C₁₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
301	C₄×C₁₇	C₂×#137	1	1	yes	characteristic
302	Dic₁₇	—	2	1	no	—
303	Dic₁₇	—	2	2	no	—
304	Dic₁₇	—	2	1	no	—
305	Dic₁₇	—	4	1	no	—
306	Dic₁₇	—	4	1	no	—
307	Dic₁₇	#440	1	2	yes	—
308	C₂×#131	—	34	1	no	—
309	#532	—	17	1	no	—
310	C₂×C₄×Q₈	—	17	1	no	—
311	#481	—	17	1	no	—
312	#481	—	17	1	no	—
313	#475	—	17	1	no	—
314	#475	—	17	1	no	—
315	#460	—	17	1	no	—
316	#460	—	17	1	no	—
317	#448	—	17	1	no	—
318	#448	—	17	1	no	—
319	C₈×Q₈	—	17	1	no	—
320	C₈×Q₈	—	17	1	no	—
321	C₈×Q₈	—	17	1	no	—
322	C₈×Q₈	—	34	1	no	—
323	C₈×Q₈	—	34	1	no	—
324	C₈×Q₈	C₂×D₁₇	1	1	yes	characteristic
325	C₄×SD₁₆	—	17	1	no	—
326	C₄×SD₁₆	—	17	1	no	—
327	C₄×SD₁₆	—	17	1	no	—
328	C₄×SD₁₆	C₂×D₁₇	1	1	yes	characteristic
329	#436	—	17	1	no	—
330	#436	—	34	1	no	—
331	#436	C₂×D₁₇	1	1	yes	characteristic
332	C₈×D₄	—	17	1	no	—
333	C₈×D₄	—	17	1	no	—
334	C₈×D₄	—	34	1	no	—
335	#431	—	17	1	no	—
336	#431	—	17	1	no	—
337	#423	—	17	1	no	—
338	C₂×C₄⋊C₈	—	17	1	no	—
339	C₂×C₄⋊C₈	—	34	1	no	—
340	#408	—	34	1	no	—
341	C₂×C₄×C₈	—	17	1	no	—
342	C₂×C₄×C₈	—	34	1	no	—
343	#335	—	17	1	no	—
344	#335	—	17	1	no	—
345	#335	—	17	1	no	—
346	#335	C₂×D₁₇	1	1	yes	characteristic
347	Q₈⋊C₈	—	17	1	no	—
348	Q₈⋊C₈	—	17	1	no	—
349	Q₈⋊C₈	—	17	1	no	—
350	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
351	D₄⋊C₈	—	17	1	no	—
352	D₄⋊C₈	—	17	1	no	—
353	D₄⋊C₈	—	17	1	no	—
354	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
355	#322	—	17	1	no	—
356	#322	—	17	1	no	—
357	#322	—	17	1	no	—
358	#322	C₂×D₁₇	1	1	yes	characteristic
359	C₂×C₁₇	—	8	1	no	—
360	C₂×C₁₇	#2929	1	1	yes	characteristic
361	C₂×C₁₇	C₂×#440	1	1	yes	characteristic
362	C₂×C₁₇	#2955	1	1	yes	characteristic
363	D₁₇	—	2	2	no	—
364	D₁₇	—	8	1	no	—
365	C₂×#41	—	34	1	no	—
366	C₂²×Q₈	—	17	1	no	—
367	C₂×SD₁₆	—	17	1	no	—
368	C₂×SD₁₆	—	17	1	no	—
369	C₂×SD₁₆	—	17	1	no	—
370	C₂×SD₁₆	C₄×D₁₇	1	1	yes	characteristic
371	#131	—	68	4	no	—
372	C₂×M₁₆	—	2	1	no	—
373	C₂×M₁₆	—	34	1	no	—
374	C₂×M₁₆	—	34	1	no	—
375	C₂²×C₈	—	17	1	no	—
376	C₂²×C₈	—	17	1	no	—
377	C₂²×C₈	—	34	1	no	—
378	C₂²×C₈	—	34	1	no	—
379	C₂²×C₈	—	34	1	no	—
380	C₄⋊Q₈	—	17	1	no	—
381	#127	—	17	1	no	—
382	#124	—	34	1	no	—
383	#121	—	17	1	no	—
384	#121	—	17	1	no	—
385	#121	—	34	1	no	—
386	C₄×Q₈	—	17	1	no	—
387	C₄×Q₈	—	17	1	no	—
388	C₄×Q₈	—	17	1	no	—
389	C₄×Q₈	—	34	1	no	—
390	C₄×Q₈	—	34	1	no	—
391	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
392	C₄×D₄	—	17	1	no	—
393	C₄×D₄	—	34	1	no	—
394	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
395	C₂×C₄⋊C₄	—	17	1	no	—
396	C₂×C₄⋊C₄	—	34	1	no	—
397	C₂×C₄²	—	17	1	no	—
398	C₂×C₄²	—	34	1	no	—
399	#106	—	17	1	no	—
400	#106	—	17	1	no	—
401	#106	—	17	1	no	—
402	#106	C₄×D₁₇	1	1	yes	characteristic
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	17	1	no	—
405	C₄⋊C₈	—	17	1	no	—
406	C₄⋊C₈	—	17	1	no	—
407	C₄⋊C₈	—	17	1	no	—
408	C₄⋊C₈	—	34	1	no	—
409	C₄⋊C₈	—	34	1	no	—
410	C₄⋊C₈	—	34	1	no	—
411	C₄⋊C₈	—	34	1	no	—
412	C₄⋊C₈	—	34	1	no	—
413	C₄⋊C₈	—	34	1	no	—
414	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
415	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
416	#103	—	17	1	no	—
417	#103	—	17	1	no	—
418	#103	—	17	1	no	—
419	#103	C₄×D₁₇	1	1	yes	characteristic
420	#102	—	17	1	no	—
421	#102	—	17	1	no	—
422	#102	—	17	1	no	—
423	#102	C₄×D₁₇	1	1	yes	characteristic
424	C₂²⋊C₈	—	2	1	no	—
425	C₂²⋊C₈	—	17	1	no	—
426	C₂²⋊C₈	—	17	1	no	—
427	C₂²⋊C₈	—	34	1	no	—
428	C₂²⋊C₈	—	34	1	no	—
429	C₂²⋊C₈	—	34	1	no	—
430	C₂²⋊C₈	—	34	1	no	—
431	C₄×C₈	—	2	1	no	—
432	C₄×C₈	—	17	1	no	—
433	C₄×C₈	—	17	1	no	—
434	C₄×C₈	—	17	1	no	—
435	C₄×C₈	—	17	1	no	—
436	C₄×C₈	—	17	1	no	—
437	C₄×C₈	—	34	1	no	—
438	C₄×C₈	—	34	1	no	—
439	C₄×C₈	—	34	1	no	—
440	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
441	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
442	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
443	C₁₇	#17908	1	1	yes	characteristic, complemented, Sylow
444	#41	—	68	2	no	—
445	#41	—	68	2	no	—
446	C₂×Q₈	—	17	1	no	—
447	C₂×Q₈	—	34	1	no	—
448	C₂×Q₈	—	34	1	no	—
449	C₂×Q₈	—	34	2	no	—
450	C₂×Q₈	—	34	2	no	—
451	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
452	C₂×D₄	—	17	1	no	—
453	C₂×D₄	—	34	1	no	—
454	C₂×D₄	—	34	1	no	—
455	C₂×D₄	—	34	1	no	—
456	C₂×D₄	—	34	1	no	—
457	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	17	1	no	—
460	C₂²×C₄	—	17	1	no	—
461	C₂²×C₄	—	17	1	no	—
462	C₂²×C₄	—	34	1	no	—
463	C₂²×C₄	—	34	1	no	—
464	C₂²×C₄	—	34	1	no	—
465	SD₁₆	—	2	2	no	—
466	SD₁₆	—	34	2	no	—
467	SD₁₆	—	34	2	no	—
468	SD₁₆	—	34	2	no	—
469	M₁₆	—	4	2	no	—
470	M₁₆	—	68	2	no	—
471	M₁₆	—	68	2	no	—
472	C₂×C₈	—	2	1	no	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	1	no	—
475	C₂×C₈	—	17	1	no	—
476	C₂×C₈	—	17	1	no	—
477	C₂×C₈	—	17	1	no	—
478	C₂×C₈	—	17	1	no	—
479	C₂×C₈	—	34	2	no	—
480	C₂×C₈	—	34	2	no	—
481	C₂×C₈	—	34	1	no	—
482	C₂×C₈	—	34	1	no	—
483	C₂×C₈	—	34	1	no	—
484	C₂×C₈	—	68	2	no	—
485	C₂×C₈	—	68	2	no	—
486	C₂×C₈	—	68	2	no	—
487	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
488	C₂×C₈	C₂×C₄×D₁₇	1	1	yes	characteristic
489	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
490	C₂×C₈	D₄×D₁₇	1	1	yes	characteristic
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	17	1	no	—
493	C₄⋊C₄	—	17	1	no	—
494	C₄⋊C₄	—	34	1	no	—
495	C₄⋊C₄	—	34	1	no	—
496	C₄⋊C₄	—	34	1	no	—
497	C₄⋊C₄	—	34	1	no	—
498	C₄⋊C₄	—	34	1	no	—
499	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
501	C₂²⋊C₄	—	2	1	no	—
502	C₂²⋊C₄	—	34	1	no	—
503	C₂²⋊C₄	—	34	1	no	—
504	C₂²⋊C₄	—	34	1	no	—
505	C₄²	—	2	1	no	—
506	C₄²	—	17	1	no	—
507	C₄²	—	17	1	no	—
508	C₄²	—	17	1	no	—
509	C₄²	—	34	1	no	—
510	C₄²	—	34	1	no	—
511	C₄²	—	34	1	no	—
512	C₄²	C₂³×D₁₇	1	1	yes	characteristic
513	C₂³	—	2	1	no	—
514	C₂³	—	17	1	no	—
515	C₂³	—	34	1	no	—
516	Q₈	—	2	1	no	—
517	Q₈	—	17	2	no	—
518	Q₈	—	34	4	no	—
519	Q₈	—	34	1	no	—
520	Q₈	—	68	2	no	—
521	Q₈	#10587593	1	2	yes	complemented
522	D₄	—	2	1	no	—
523	D₄	—	2	1	no	—
524	D₄	—	34	1	no	—
525	D₄	—	34	1	no	—
526	D₄	—	68	2	no	—
527	D₄	—	68	2	no	—
528	D₄	—	68	2	no	—
529	D₄	—	68	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	1	no	—
532	C₂×C₄	—	2	1	no	—
533	C₂×C₄	—	4	1	no	—
534	C₂×C₄	—	4	1	no	—
535	C₂×C₄	—	17	1	no	—
536	C₂×C₄	—	17	2	no	—
537	C₂×C₄	—	17	2	no	—
538	C₂×C₄	—	17	1	no	—
539	C₂×C₄	—	17	1	no	—
540	C₂×C₄	—	34	4	no	—
541	C₂×C₄	—	34	1	no	—
542	C₂×C₄	—	34	1	no	—
543	C₂×C₄	—	34	1	no	—
544	C₂×C₄	—	34	1	no	—
545	C₂×C₄	—	34	1	no	—
546	C₂×C₄	—	68	1	no	—
547	C₂×C₄	—	68	2	no	—
548	C₂×C₄	—	68	1	no	—
549	C₂×C₄	—	68	1	no	—
550	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
552	C₂×C₄	#41×D₁₇	1	1	yes	characteristic
553	C₈	—	2	1	no	—
554	C₈	—	2	1	no	—
555	C₈	—	2	1	no	—
556	C₈	—	2	1	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	1	no	—
559	C₈	—	4	1	no	—
560	C₈	—	34	1	no	—
561	C₈	—	34	1	no	—
562	C₈	—	34	1	no	—
563	C₈	—	34	1	no	—
564	C₈	—	68	1	no	—
565	C₈	—	68	1	no	—
566	C₈	—	68	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	—	4	1	no	—
570	C₂²	—	17	2	no	—
571	C₂²	—	34	1	no	—
572	C₂²	—	34	1	no	—
573	C₂²	—	68	1	no	—
574	C₂²	—	68	1	no	—
575	C₂²	—	68	1	no	—
576	C₂²	C₄×D₄×D₁₇	1	1	yes	characteristic
577	C₄	—	2	2	no	—
578	C₄	—	2	1	no	—
579	C₄	—	4	1	no	—
580	C₄	—	4	1	no	—
581	C₄	—	17	2	no	—
582	C₄	—	34	1	no	—
583	C₄	—	34	2	no	—
584	C₄	—	34	1	no	—
585	C₄	—	68	1	no	—
586	C₄	—	68	1	no	—
587	C₄	#131×D₁₇	1	1	yes	characteristic
588	C₄	C₂×#10587593	1	1	yes	characteristic
589	C₄	AGL(1,ℤ/8)×D₁₇	1	1	yes	characteristic
590	C₄	#137×D₁₇	1	1	yes	characteristic
591	C₂	—	8	1	no	—
592	C₂	—	34	2	no	—
593	C₂	—	136	1	no	—
594	C₂	#14537475	1	1	yes	characteristic
595	C₂	D₁₇×#440	1	1	yes	characteristic
596	C₂	#14537682	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₁₇
commutator	C₂×C₄×C₁₇	C₂³×C₄
Frattini	C₄²	C₂³×D₁₇
Fitting	C₁₇×#1588	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	#11763356	C₂²
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1588	D₁₇
hypocenter	C₁₇	#17908
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1588

Complements

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

N	H ≅ G/N	type
2. C₈×Q₈×D₁₇	C₂	semidirect
4. #14527664	C₂	semidirect
5. #14527662	C₂	semidirect
6. #14527660	C₂	semidirect
7. #14527599	C₂	semidirect
8. SD₁₆⋊#3622	C₂	semidirect
9. #14527595	C₂	semidirect
10. #14527593	C₂	semidirect
11. #14527557	C₂	semidirect
12. #14527211	C₂	semidirect
14. #14527075	C₂	semidirect
15. C₁₇×#1588	C₂	semidirect
219. Q₈×C₁₇	#131	semidirect
254. Dic₃₄	#131	semidirect
275. #1588	D₁₇	semidirect
443. C₁₇	#17908	semidirect
521. Q₈	#10587593	semidirect

Maximal subgroups

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

subgroup	index
#14538813	2
C₈×Q₈×D₁₇	2
#14537493	2
#14527664	2
#14527662	2
#14527660	2
#14527599	2
SD₁₆⋊#3622	2
#14527595	2
#14527593	2
#14527557	2
#14527211	2
#14527181	2
#14527075	2
C₁₇×#1588	2
#17908	17