Subgroups — #17968843

Order 4352.

1014 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₁₇⋊#444	C₂	1	1	yes	maximal, characteristic
2	#14545538	C₂	1	1	yes	maximal, characteristic
3	#14545354	C₂	1	2	yes	maximal, complemented
4	#14544605	C₂	1	1	yes	maximal, characteristic, complemented
5	#14544593	C₂	1	1	yes	maximal, characteristic, complemented
6	#14544586	C₂	1	1	yes	maximal, characteristic, complemented
7	#14544562	C₂	1	2	yes	maximal, complemented
8	#14544560	C₂	1	2	yes	maximal, complemented
9	#104×#595	C₂	1	2	yes	maximal, complemented
10	C₄×#10587532	C₂	1	1	yes	maximal, characteristic, complemented
11	D₁₇×#443	C₂	1	1	yes	maximal, characteristic
12	D₁₇⋊#131	C₂²	1	2	yes	—
13	#41×#595	C₂²	1	2	yes	—
14	#11763856	C₄	1	2	yes	complemented
15	#11763855	C₄	1	2	yes	complemented
16	#11763854	C₄	1	4	yes	complemented
17	#11763850	C₄	1	2	yes	complemented
18	#11763849	C₄	1	2	yes	complemented
19	#11763848	C₄	1	4	yes	complemented
20	D₁₇⋊#108	C₂²	1	1	yes	characteristic
21	#11763819	C₂²	1	1	yes	characteristic
22	D₁₇⋊#104	C₂²	1	2	yes	—
23	#11763799	C₂²	1	2	yes	—
24	#11763775	—	2	2	no	—
25	#11763775	C₂²	1	2	yes	—
26	#11763772	—	2	2	no	—
27	#11763772	C₂²	1	2	yes	—
28	M₁₆×#595	—	2	2	no	—
29	M₁₆×#595	C₂²	1	2	yes	—
30	C₂×#10587532	—	2	2	no	—
31	C₂×#10587532	C₂²	1	1	yes	characteristic
32	C₂×#10587532	C₂²	1	1	yes	characteristic
33	C₂×#10587532	C₂²	1	1	yes	characteristic
34	C₂×#10587532	C₂²	1	1	yes	characteristic
35	C₄×#63242	C₂²	1	1	yes	characteristic
36	C₄²×#595	C₂²	1	1	yes	characteristic
37	#11763684	C₂²	1	2	yes	—
38	#11763681	C₂²	1	2	yes	—
39	#11763680	C₂²	1	2	yes	—
40	#135×D₁₇	C₂²	1	1	yes	characteristic
41	#131×D₁₇	C₂²	1	2	yes	—
42	#11762927	C₄	1	1	yes	characteristic, complemented
43	#11762926	C₄	1	1	yes	characteristic, complemented
44	#11762925	C₄	1	1	yes	characteristic, complemented
45	#11762924	C₄	1	2	yes	complemented
46	#11762923	C₄	1	2	yes	complemented
47	#108×D₁₇	C₂²	1	1	yes	characteristic
48	#104×D₁₇	C₂²	1	2	yes	—
49	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
50	C₁₇×#443	C₄	1	1	yes	characteristic, complemented
51	#41×D₁₇	C₂³	1	2	yes	—
52	Q₈×#595	C₂×C₄	1	4	yes	—
53	#10587680	C₂×C₄	1	4	yes	complemented
54	D₄×#595	—	2	4	no	—
55	D₄×#595	C₂×C₄	1	4	yes	—
56	#10587678	—	2	4	no	—
57	#10587678	C₂×C₄	1	4	yes	complemented
58	#10587677	—	2	2	no	—
59	#10587677	C₂³	1	2	yes	—
60	C₂×C₄×#595	—	2	2	no	—
61	C₂×C₄×#595	—	2	2	no	—
62	C₂×C₄×#595	C₂³	1	1	yes	characteristic
63	C₂×C₄×#595	C₂³	1	1	yes	characteristic
64	D₁₇⋊M₁₆	—	2	2	no	—
65	D₁₇⋊M₁₆	C₂³	1	2	yes	—
66	C₂×#63242	—	2	2	no	—
67	C₂×#63242	C₂³	1	1	yes	characteristic
68	C₂×#63242	C₂³	1	1	yes	characteristic
69	C₁₇×#135	C₂×C₄	1	1	yes	characteristic
70	C₁₇×#131	C₂×C₄	1	2	yes	complemented
71	#10587636	C₂×C₄	1	2	yes	—
72	#10587634	C₂×C₄	1	2	yes	complemented
73	#10587605	C₂×C₄	1	1	yes	characteristic
74	Q₁₆×D₁₇	C₂×C₄	1	1	yes	characteristic
75	#10587602	C₂×C₄	1	2	yes	—
76	SD₁₆×D₁₇	C₂×C₄	1	2	yes	—
77	#10587598	C₂×C₄	1	1	yes	characteristic
78	D₈×D₁₇	C₂×C₄	1	1	yes	characteristic
79	#10587593	—	2	2	no	—
80	#10587593	C₂×C₄	1	2	yes	complemented
81	M₁₆×D₁₇	—	2	2	no	—
82	M₁₆×D₁₇	C₂³	1	2	yes	—
83	#10587590	C₂×C₄	1	1	yes	characteristic
84	#10587587	—	2	2	no	—
85	#10587587	C₂×C₄	1	2	yes	complemented
86	C₂×C₈×D₁₇	—	2	2	no	—
87	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
88	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
89	C₄²×D₁₇	C₂³	1	1	yes	characteristic
90	#10587550	C₂×C₄	1	4	yes	complemented
91	#10587549	C₂×C₄	1	4	yes	—
92	#10587548	C₂×C₄	1	4	yes	complemented
93	#10587547	C₂×C₄	1	4	yes	—
94	C₄×#3624	—	2	2	no	—
95	#10587536	C₂×C₄	1	2	yes	complemented
96	#10587535	C₂×C₄	1	2	yes	complemented
97	#10587534	C₂×C₄	1	2	yes	—
98	#10587533	C₂×C₄	1	2	yes	—
99	#10587532	—	2	2	no	—
100	#10587532	—	2	1	no	—
101	#10587532	—	2	1	no	—
102	#10587532	—	2	2	no	—
103	#10587532	—	2	2	no	—
104	#10587532	C₂×C₄	1	2	yes	—
105	#10587532	C₂×C₄	1	2	yes	—
106	#10587532	C₂×C₄	1	2	yes	complemented
107	#10587532	C₂×C₄	1	2	yes	complemented
108	#10587532	D₄	1	2	yes	—
109	#10587532	D₄	1	2	yes	—
110	C₈×#595	—	2	2	no	—
111	C₈×#595	—	2	2	no	—
112	C₈×#595	—	2	2	no	—
113	C₁₇×#108	C₂×C₄	1	1	yes	characteristic, complemented
114	C₁₇×#104	C₂×C₄	1	2	yes	complemented
115	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic, complemented
116	#10587508	C₂×C₄	1	2	yes	complemented
117	#10587496	C₂×C₄	1	2	yes	complemented
118	#10587493	C₂×C₄	1	2	yes	complemented
119	#10587490	C₂×C₄	1	1	yes	characteristic, complemented
120	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
121	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic, complemented
122	#10587476	C₂×C₄	1	2	yes	complemented
123	C₄×#3622	C₂×C₄	1	1	yes	characteristic, complemented
124	C₂²×#595	—	2	1	no	—
125	C₂²×#595	—	2	4	no	—
126	C₂²×#595	#41	1	2	yes	—
127	#41×C₁₇	C₂²×C₄	1	2	yes	—
128	#63256	C₂²×C₄	1	2	yes	—
129	Q₈×D₁₇	C₂²×C₄	1	2	yes	—
130	#63254	—	2	2	no	—
131	#63254	C₂²×C₄	1	2	yes	—
132	D₄×D₁₇	—	2	2	no	—
133	D₄×D₁₇	C₂²×C₄	1	2	yes	—
134	#63252	—	2	2	no	—
135	#63252	C₂²×C₄	1	2	yes	—
136	C₂×C₄×D₁₇	—	2	1	no	—
137	C₂×C₄×D₁₇	—	2	2	no	—
138	C₂×C₄×D₁₇	C₂⁴	1	1	yes	characteristic
139	C₂²⋊#595	—	2	2	no	—
140	C₂²⋊#595	—	2	4	no	—
141	#63247	—	2	2	no	—
142	#63247	—	2	4	no	—
143	C₂×#3624	—	2	1	no	—
144	C₂×#3624	—	2	4	no	—
145	C₂×#3624	#41	1	2	yes	—
146	C₄⋊#595	—	2	4	no	—
147	C₄⋊#595	C₂²×C₄	1	4	yes	—
148	C₄×#595	—	2	4	no	—
149	C₄×#595	—	2	2	no	—
150	C₄×#595	—	2	1	no	—
151	C₄×#595	—	4	4	no	—
152	C₄×#595	C₂²×C₄	1	2	yes	—
153	C₄×#595	C₂²×C₄	1	2	yes	—
154	C₄×#595	C₂×D₄	1	2	yes	—
155	#63243	—	2	4	no	—
156	#63243	C₂²×C₄	1	4	yes	—
157	#63242	—	2	2	no	—
158	#63242	—	2	1	no	—
159	#63242	—	2	4	no	—
160	#63242	C₂²×C₄	1	2	yes	—
161	#63242	C₂²×C₄	1	2	yes	—
162	#63242	C₂×D₄	1	2	yes	—
163	Q₁₆×C₁₇	C₄²	1	1	yes	characteristic, complemented
164	SD₁₆×C₁₇	C₄²	1	2	yes	complemented
165	D₈×C₁₇	C₄²	1	1	yes	characteristic, complemented
166	M₁₆×C₁₇	—	2	2	no	—
167	M₁₆×C₁₇	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₁₇	—	2	2	no	—
169	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
170	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
171	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
172	#63231	C₄²	1	2	yes	complemented
173	#63230	C₄²	1	2	yes	complemented
174	#63229	C₄²	1	2	yes	complemented
175	#63228	C₄²	1	2	yes	complemented
176	C₄×Dic₁₇	—	2	1	no	—
177	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
178	#63223	—	2	2	no	—
179	#63223	C₂²×C₄	1	2	yes	—
180	C₂×#3622	—	2	2	no	—
181	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
182	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
183	Dic₆₈	C₄²	1	1	yes	characteristic, complemented
184	D₁₃₆	C₄²	1	1	yes	characteristic, complemented
185	#63219	C₄²	1	2	yes	complemented
186	#63218	—	2	2	no	—
187	#63218	—	2	2	no	—
188	#63218	—	2	2	no	—
189	C₈×D₁₇	—	2	2	no	—
190	C₈×D₁₇	—	2	2	no	—
191	C₈×D₁₇	—	2	2	no	—
192	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
193	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
194	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
195	C₈×D₁₇	C₂²×C₄	1	1	yes	characteristic
196	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
197	C₈×D₁₇	C₂×D₄	1	1	yes	characteristic
198	C₈×D₁₇	#41	1	1	yes	characteristic
199	C₈×D₁₇	#41	1	1	yes	characteristic
200	#20512	—	17	1	no	maximal, Sylow
201	C₂²×D₁₇	—	2	2	no	—
202	C₂²×D₁₇	C₂×#41	1	1	yes	characteristic
203	C₂×#595	—	2	4	no	—
204	C₂×#595	—	2	2	no	—
205	C₂×#595	—	4	2	no	—
206	C₂×#595	—	4	2	no	—
207	C₂×#595	—	8	4	no	—
208	C₂×#595	C₄×D₄	1	4	yes	—
209	Q₈×C₁₇	C₂×C₄²	1	2	yes	—
210	D₄×C₁₇	—	2	2	no	—
211	D₄×C₁₇	C₂×C₄²	1	2	yes	—
212	C₂×C₄×C₁₇	—	2	1	no	—
213	C₂×C₄×C₁₇	—	2	2	no	—
214	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
215	C₂²⋊D₁₇	—	2	2	no	—
216	C₂²⋊D₁₇	—	2	2	no	—
217	C₂²⋊D₁₇	—	2	2	no	—
218	C₂×Dic₁₇	—	2	1	no	—
219	C₂×Dic₁₇	—	2	2	no	—
220	C₂×Dic₁₇	C₂×#41	1	1	yes	characteristic
221	D₆₈	—	2	2	no	—
222	D₆₈	C₂×C₄²	1	2	yes	—
223	C₄×D₁₇	—	2	4	no	—
224	C₄×D₁₇	—	2	2	no	—
225	C₄×D₁₇	—	2	2	no	—
226	C₄×D₁₇	—	2	2	no	—
227	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
228	C₄×D₁₇	C₂³×C₄	1	1	yes	characteristic
229	C₄×D₁₇	C₂²×D₄	1	1	yes	characteristic
230	C₄×D₁₇	C₂×#41	1	1	yes	characteristic
231	Dic₃₄	—	2	2	no	—
232	Dic₃₄	C₂×C₄²	1	2	yes	—
233	#3624	—	2	4	no	—
234	#3624	—	2	2	no	—
235	#3624	C₄×D₄	1	4	yes	—
236	C₈×C₁₇	—	2	2	no	—
237	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
238	C₈×C₁₇	C₂×C₄²	1	1	yes	characteristic
239	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
240	C₈×C₁₇	C₄×D₄	1	1	yes	characteristic
241	#3622	—	2	2	no	—
242	#3622	C₂×C₄²	1	1	yes	characteristic
243	#3622	C₂×C₄²	1	1	yes	characteristic
244	#3622	C₄×D₄	1	1	yes	characteristic
245	#3622	C₄×D₄	1	1	yes	characteristic
246	C₂×#444	—	17	1	no	—
247	C₂×#443	—	17	1	no	—
248	#2943	—	17	1	no	—
249	#2875	—	17	2	no	—
250	#1778	—	17	1	no	—
251	#1773	—	17	1	no	—
252	#1772	—	17	1	no	—
253	#1765	—	17	2	no	—
254	#1764	—	17	2	no	—
255	C₄×#104	—	17	2	no	—
256	C₄×#97	—	17	1	no	—
257	C₂²×C₁₇	—	2	2	no	—
258	C₂²×C₁₇	C₄×#41	1	1	yes	characteristic
259	C₂×D₁₇	—	2	2	no	—
260	C₂×D₁₇	—	2	2	no	—
261	C₂×D₁₇	—	4	4	no	—
262	C₂×D₁₇	C₂×C₄×D₄	1	1	yes	characteristic
263	C₂×D₁₇	C₄×#41	1	1	yes	characteristic
264	#595	—	2	4	no	—
265	#595	—	4	2	no	—
266	#595	—	4	4	no	—
267	C₄×C₁₇	—	2	2	no	—
268	C₄×C₁₇	—	2	2	no	—
269	C₄×C₁₇	C₂²×C₄²	1	1	yes	characteristic
270	C₄×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
271	Dic₁₇	—	2	2	no	—
272	Dic₁₇	—	2	2	no	—
273	Dic₁₇	C₂×C₄×D₄	1	1	yes	characteristic
274	Dic₁₇	C₄×#41	1	1	yes	characteristic
275	C₂×#135	—	17	1	no	—
276	C₂×#131	—	17	2	no	—
277	C₂×#131	—	17	2	no	—
278	C₄×#41	—	17	2	no	—
279	#444	—	17	4	no	—
280	#444	—	17	2	no	—
281	#444	—	17	2	no	—
282	#443	—	17	1	no	—
283	#443	—	17	2	no	—
284	#443	—	17	1	no	—
285	#443	—	17	2	no	—
286	#443	—	17	1	no	—
287	#443	#595	1	1	yes	characteristic, complemented
288	#442	—	17	2	no	—
289	#441	—	17	2	no	—
290	#440	—	17	4	no	—
291	C₂×#108	—	17	1	no	—
292	C₂×#108	—	17	1	no	—
293	#427	—	17	1	no	—
294	C₂×#104	—	17	2	no	—
295	C₂×#104	—	17	2	no	—
296	#416	—	17	2	no	—
297	#405	—	17	2	no	—
298	#405	—	17	2	no	—
299	#405	—	34	2	no	—
300	#405	—	34	2	no	—
301	C₄×M₁₆	—	17	2	no	—
302	C₄×M₁₆	—	34	2	no	—
303	C₂×#97	—	17	1	no	—
304	C₂×#97	—	17	1	no	—
305	C₂×#97	—	17	1	no	—
306	C₂×#97	—	17	1	no	—
307	C₂×#97	—	34	2	no	—
308	C₂×C₄×C₈	—	17	1	no	—
309	C₂×C₄×C₈	—	17	1	no	—
310	C₄³	—	17	1	no	—
311	#341	—	17	2	no	—
312	#339	—	17	2	no	—
313	#339	—	17	2	no	—
314	C₂×C₁₇	—	2	1	no	—
315	C₂×C₁₇	—	4	2	no	—
316	C₂×C₁₇	C₄²×D₄	1	1	yes	characteristic
317	D₁₇	—	2	1	no	—
318	D₁₇	—	4	2	no	—
319	D₁₇	#2956	1	2	yes	—
320	C₂×#41	—	17	2	no	—
321	#135	—	17	2	no	—
322	#135	—	17	1	no	—
323	#135	—	17	2	no	—
324	#135	—	17	1	no	—
325	#135	—	17	1	no	—
326	#135	C₂×#595	1	1	yes	characteristic
327	C₂×Q₁₆	—	17	1	no	—
328	C₂×SD₁₆	—	17	2	no	—
329	C₂×D₈	—	17	1	no	—
330	#131	—	17	4	no	—
331	#131	—	17	4	no	—
332	#131	—	17	2	no	—
333	#131	—	17	2	no	—
334	#131	—	17	2	no	—
335	#131	—	34	2	no	—
336	#131	—	34	2	no	—
337	#131	—	34	4	no	—
338	#131	C₂×#595	1	2	yes	complemented
339	C₂×M₁₆	—	17	2	no	—
340	C₂×M₁₆	—	17	2	no	—
341	C₂×M₁₆	—	34	2	no	—
342	C₂×M₁₆	—	34	2	no	—
343	C₂²×C₈	—	17	1	no	—
344	C₂²×C₈	—	17	1	no	—
345	C₂²×C₈	—	17	1	no	—
346	C₂²×C₈	—	17	1	no	—
347	C₂²×C₈	—	34	2	no	—
348	C₂²×C₈	—	34	2	no	—
349	C₄×Q₈	—	17	4	no	—
350	C₄×D₄	—	17	4	no	—
351	C₄×D₄	—	34	4	no	—
352	#117	—	17	2	no	—
353	#117	—	34	2	no	—
354	C₂×C₄²	—	17	1	no	—
355	C₂×C₄²	—	17	1	no	—
356	C₂×C₄²	—	17	1	no	—
357	C₂×C₄²	—	34	2	no	—
358	C₂×C₄²	—	34	2	no	—
359	#108	—	17	2	no	—
360	#108	—	17	2	no	—
361	#108	—	17	2	no	—
362	#108	—	17	1	no	—
363	#108	C₂×#595	1	1	yes	characteristic, complemented
364	#107	—	17	2	no	—
365	#106	—	17	2	no	—
366	#104	—	17	4	no	—
367	#104	—	17	4	no	—
368	#104	—	17	2	no	—
369	#104	—	17	2	no	—
370	#104	—	17	2	no	—
371	#104	C₂×#595	1	2	yes	complemented
372	#103	—	17	4	no	—
373	#102	—	17	4	no	—
374	#97	—	17	2	no	—
375	#97	—	17	2	no	—
376	#97	—	17	2	no	—
377	#97	—	17	2	no	—
378	#97	—	17	2	no	—
379	#97	—	17	2	no	—
380	#97	—	34	2	no	—
381	#97	—	34	1	no	—
382	#97	—	34	1	no	—
383	#97	—	34	2	no	—
384	#97	—	34	2	no	—
385	C₄×C₈	—	17	1	no	—
386	C₄×C₈	—	17	1	no	—
387	C₄×C₈	—	17	1	no	—
388	C₄×C₈	—	34	2	no	—
389	C₄×C₈	—	34	2	no	—
390	C₄×C₈	—	34	2	no	—
391	C₄×C₈	—	34	2	no	—
392	C₄×C₈	C₂×#595	1	1	yes	characteristic, complemented
393	C₁₇	#20512	1	1	yes	characteristic, complemented, Sylow
394	#41	—	17	2	no	—
395	#41	—	17	2	no	—
396	#41	—	17	2	no	—
397	#41	—	34	2	no	—
398	#41	—	34	2	no	—
399	#41	C₂²×#595	1	2	yes	—
400	C₂×Q₈	—	17	2	no	—
401	C₂×D₄	—	17	2	no	—
402	C₂×D₄	—	34	2	no	—
403	C₂²×C₄	—	17	1	no	—
404	C₂²×C₄	—	17	2	no	—
405	C₂²×C₄	—	34	2	no	—
406	C₂²×C₄	—	34	1	no	—
407	C₂²×C₄	—	34	4	no	—
408	C₂²×C₄	—	34	1	no	—
409	Q₁₆	—	17	2	no	—
410	Q₁₆	—	17	1	no	—
411	Q₁₆	C₄×#595	1	1	yes	characteristic, complemented
412	SD₁₆	—	17	2	no	—
413	SD₁₆	—	17	2	no	—
414	SD₁₆	—	17	2	no	—
415	SD₁₆	C₄×#595	1	2	yes	complemented
416	D₈	—	17	2	no	—
417	D₈	—	17	1	no	—
418	D₈	C₄×#595	1	1	yes	characteristic, complemented
419	M₁₆	—	2	2	no	—
420	M₁₆	—	17	4	no	—
421	M₁₆	—	17	2	no	—
422	M₁₆	—	34	2	no	—
423	M₁₆	—	34	2	no	—
424	M₁₆	—	34	2	no	—
425	M₁₆	—	34	4	no	—
426	M₁₆	—	34	4	no	—
427	M₁₆	—	34	2	no	—
428	M₁₆	—	34	2	no	—
429	M₁₆	C₂²×#595	1	2	yes	—
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	17	2	no	—
432	C₂×C₈	—	17	2	no	—
433	C₂×C₈	—	17	2	no	—
434	C₂×C₈	—	17	1	no	—
435	C₂×C₈	—	17	1	no	—
436	C₂×C₈	—	17	1	no	—
437	C₂×C₈	—	17	1	no	—
438	C₂×C₈	—	17	1	no	—
439	C₂×C₈	—	17	1	no	—
440	C₂×C₈	—	17	1	no	—
441	C₂×C₈	—	17	1	no	—
442	C₂×C₈	—	17	1	no	—
443	C₂×C₈	—	17	1	no	—
444	C₂×C₈	—	17	2	no	—
445	C₂×C₈	—	34	2	no	—
446	C₂×C₈	—	34	2	no	—
447	C₂×C₈	—	34	2	no	—
448	C₂×C₈	—	34	4	no	—
449	C₂×C₈	—	34	4	no	—
450	C₂×C₈	—	34	2	no	—
451	C₂×C₈	—	34	1	no	—
452	C₂×C₈	—	34	1	no	—
453	C₂×C₈	—	34	2	no	—
454	C₂×C₈	C₂²×#595	1	1	yes	characteristic
455	C₂×C₈	C₂²×#595	1	1	yes	characteristic
456	C₄⋊C₄	—	17	4	no	—
457	C₄⋊C₄	—	34	4	no	—
458	C₂²⋊C₄	—	34	4	no	—
459	C₂²⋊C₄	—	34	2	no	—
460	C₄²	—	17	2	no	—
461	C₄²	—	17	2	no	—
462	C₄²	—	17	2	no	—
463	C₄²	—	17	1	no	—
464	C₄²	—	34	1	no	—
465	C₄²	—	34	2	no	—
466	C₄²	—	34	1	no	—
467	C₄²	—	34	4	no	—
468	C₄²	—	68	4	no	—
469	C₄²	C₂²×#595	1	1	yes	characteristic
470	C₂³	—	17	1	no	—
471	C₂³	—	34	2	no	—
472	Q₈	—	17	2	no	—
473	Q₈	—	34	2	no	—
474	Q₈	C₂×C₄×#595	1	2	yes	—
475	D₄	—	2	2	no	—
476	D₄	—	17	2	no	—
477	D₄	—	34	2	no	—
478	D₄	—	34	2	no	—
479	D₄	—	34	2	no	—
480	D₄	—	34	2	no	—
481	D₄	C₂×C₄×#595	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	17	1	no	—
485	C₂×C₄	—	17	1	no	—
486	C₂×C₄	—	17	1	no	—
487	C₂×C₄	—	17	1	no	—
488	C₂×C₄	—	17	1	no	—
489	C₂×C₄	—	17	4	no	—
490	C₂×C₄	—	34	2	no	—
491	C₂×C₄	—	34	2	no	—
492	C₂×C₄	—	34	4	no	—
493	C₂×C₄	—	34	2	no	—
494	C₂×C₄	—	34	1	no	—
495	C₂×C₄	—	34	2	no	—
496	C₂×C₄	—	34	2	no	—
497	C₂×C₄	—	34	4	no	—
498	C₂×C₄	—	68	2	no	—
499	C₂×C₄	—	68	2	no	—
500	C₂×C₄	—	136	4	no	—
501	C₂×C₄	C₂³×#595	1	1	yes	characteristic
502	C₈	—	2	2	no	—
503	C₈	—	17	4	no	—
504	C₈	—	17	1	no	—
505	C₈	—	17	1	no	—
506	C₈	—	17	1	no	—
507	C₈	—	17	1	no	—
508	C₈	—	34	2	no	—
509	C₈	—	34	4	no	—
510	C₈	—	34	2	no	—
511	C₈	C₂×C₄×#595	1	1	yes	characteristic
512	C₈	C₂×C₄×#595	1	1	yes	characteristic
513	C₈	D₄×#595	1	1	yes	characteristic
514	C₈	D₄×#595	1	1	yes	characteristic
515	C₂²	—	2	2	no	—
516	C₂²	—	17	1	no	—
517	C₂²	—	17	1	no	—
518	C₂²	—	34	2	no	—
519	C₂²	—	34	2	no	—
520	C₂²	—	68	4	no	—
521	C₂²	#41×#595	1	1	yes	characteristic
522	C₄	—	2	2	no	—
523	C₄	—	2	2	no	—
524	C₄	—	17	1	no	—
525	C₄	—	17	1	no	—
526	C₄	—	34	2	no	—
527	C₄	—	34	4	no	—
528	C₄	—	34	2	no	—
529	C₄	—	68	4	no	—
530	C₄	—	68	2	no	—
531	C₄	C₂²×C₄×#595	1	1	yes	characteristic
532	C₄	C₂×D₄×#595	1	1	yes	characteristic
533	C₂	—	2	1	no	—
534	C₂	—	4	2	no	—
535	C₂	—	17	2	no	—
536	C₂	—	34	1	no	—
537	C₂	—	68	2	no	—
538	C₂	C₄×D₄×#595	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂×D₄×#595
commutator	C₄×C₁₇	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#595
Fitting	C₁₇×#443	C₄
socle	C₂×C₁₇	C₄²×D₄
prime radical	#135×D₁₇	C₂²
cosocle	C₂×C₄×D₁₇	C₂⁴
hypercenter	#443	#595
hypocenter	C₁₇	#20512
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄ ◁ C₂×C₈ ◁ #443

Complements

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

N	H ≅ G/N	type
3. #14545354	C₂	semidirect
4. #14544605	C₂	semidirect
5. #14544593	C₂	semidirect
6. #14544586	C₂	semidirect
7. #14544562	C₂	semidirect
8. #14544560	C₂	semidirect
9. #104×#595	C₂	semidirect
10. C₄×#10587532	C₂	semidirect
14. #11763856	C₄	semidirect
15. #11763855	C₄	semidirect
16. #11763854	C₄	semidirect
17. #11763850	C₄	semidirect
18. #11763849	C₄	semidirect
19. #11763848	C₄	semidirect
42. #11762927	C₄	semidirect
43. #11762926	C₄	semidirect
44. #11762925	C₄	semidirect
45. #11762924	C₄	semidirect
46. #11762923	C₄	semidirect
50. C₁₇×#443	C₄	semidirect
53. #10587680	C₂×C₄	semidirect
57. #10587678	C₂×C₄	semidirect
70. C₁₇×#131	C₂×C₄	semidirect
72. #10587634	C₂×C₄	semidirect
80. #10587593	C₂×C₄	semidirect
85. #10587587	C₂×C₄	semidirect
90. #10587550	C₂×C₄	semidirect
92. #10587548	C₂×C₄	semidirect
95. #10587536	C₂×C₄	semidirect
96. #10587535	C₂×C₄	semidirect
106. #10587532	C₂×C₄	semidirect
107. #10587532	C₂×C₄	semidirect
113. C₁₇×#108	C₂×C₄	semidirect
114. C₁₇×#104	C₂×C₄	semidirect
115. C₄×C₈×C₁₇	C₂×C₄	semidirect
116. #10587508	C₂×C₄	semidirect
117. #10587496	C₂×C₄	semidirect
118. #10587493	C₂×C₄	semidirect
119. #10587490	C₂×C₄	semidirect
120. C₈×Dic₁₇	C₂×C₄	semidirect
121. C₈×Dic₁₇	C₂×C₄	semidirect
122. #10587476	C₂×C₄	semidirect
123. C₄×#3622	C₂×C₄	semidirect
163. Q₁₆×C₁₇	C₄²	semidirect
164. SD₁₆×C₁₇	C₄²	semidirect
165. D₈×C₁₇	C₄²	semidirect
172. #63231	C₄²	semidirect
173. #63230	C₄²	semidirect
174. #63229	C₄²	semidirect
175. #63228	C₄²	semidirect
183. Dic₆₈	C₄²	semidirect
184. D₁₃₆	C₄²	semidirect
185. #63219	C₄²	semidirect
287. #443	#595	semidirect
338. #131	C₂×#595	semidirect
363. #108	C₂×#595	semidirect
371. #104	C₂×#595	semidirect
392. C₄×C₈	C₂×#595	semidirect
393. C₁₇	#20512	semidirect
411. Q₁₆	C₄×#595	semidirect
415. SD₁₆	C₄×#595	semidirect
418. D₈	C₄×#595	semidirect

Maximal subgroups

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

subgroup	index
D₁₇⋊#444	2
#14545538	2
#14545354	2
#14544605	2
#14544593	2
#14544586	2
#14544562	2
#14544560	2
#104×#595	2
C₄×#10587532	2
D₁₇×#443	2
#20512	17