Subgroups — #17004423

Order 4352.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14538855	C₂	1	1	yes	maximal, characteristic
2	#14537895	C₂	1	1	yes	maximal, characteristic
3	#14537881	C₂	1	1	yes	maximal, characteristic, complemented
4	#14527652	C₂	1	1	yes	maximal, characteristic, complemented
5	#14527638	C₂	1	1	yes	maximal, characteristic, complemented
6	#14527631	C₂	1	1	yes	maximal, characteristic, complemented
7	#14527617	C₂	1	1	yes	maximal, characteristic, complemented
8	#14527600	C₂	1	1	yes	maximal, characteristic, complemented
9	#14527593	C₂	1	1	yes	maximal, characteristic, complemented
10	#14527588	C₂	1	1	yes	maximal, characteristic, complemented
11	#14527587	C₂	1	1	yes	maximal, characteristic, complemented
12	#14527570	C₂	1	1	yes	maximal, characteristic, complemented
13	#14527188	C₂	1	1	yes	maximal, characteristic, complemented
14	#14527084	C₂	1	1	yes	maximal, characteristic, complemented
15	C₁₇×#1488	C₂	1	1	yes	maximal, characteristic
16	#11763366	C₂²	1	1	yes	characteristic
17	#11763150	C₄	1	1	yes	characteristic
18	#11763150	C₄	1	1	yes	characteristic
19	#11763094	C₄	1	1	yes	characteristic
20	#11763089	C₄	1	1	yes	characteristic
21	#11763019	C₄	1	1	yes	characteristic
22	#11763014	C₄	1	1	yes	characteristic
23	#11762971	C₄	1	1	yes	characteristic
24	#11762971	C₄	1	1	yes	characteristic
25	#11762937	—	2	1	no	—
26	#11762937	—	2	1	no	—
27	#11762936	C₂²	1	1	yes	characteristic
28	#11762936	C₂²	1	1	yes	characteristic
29	Q₈×#3622	C₂²	1	1	yes	characteristic
30	Q₈×#3622	C₂²	1	1	yes	characteristic
31	#11762933	C₂²	1	1	yes	characteristic
32	#11762933	C₂²	1	1	yes	characteristic
33	C₄×#63231	C₂²	1	1	yes	characteristic
34	C₄×#63231	C₂²	1	1	yes	characteristic
35	C₄×#63229	C₂²	1	1	yes	characteristic
36	C₄×#63229	C₂²	1	1	yes	characteristic
37	D₄×#3622	—	2	1	no	—
38	D₄×#3622	—	2	1	no	—
39	D₄×#3622	C₂²	1	1	yes	characteristic
40	D₄×#3622	C₂²	1	1	yes	characteristic
41	#11762867	—	2	1	no	—
42	#11762867	—	2	1	no	—
43	#11762862	—	2	1	no	—
44	#11762862	C₂²	1	1	yes	characteristic
45	#11762862	C₂²	1	1	yes	characteristic
46	C₂×C₄⋊#3622	—	2	1	no	—
47	C₂×C₄⋊#3622	C₂²	1	1	yes	characteristic
48	#11762561	C₂²	1	1	yes	characteristic
49	#11762561	C₂²	1	1	yes	characteristic
50	#11762559	C₂²	1	1	yes	characteristic
51	#11762559	C₂²	1	1	yes	characteristic
52	#11762541	C₂²	1	1	yes	characteristic
53	#11762541	C₂²	1	1	yes	characteristic
54	#11762541	C₂²	1	1	yes	characteristic
55	#11762541	C₂²	1	1	yes	characteristic
56	#11762531	C₂²	1	1	yes	characteristic
57	#11762531	C₂²	1	1	yes	characteristic
58	#11762530	C₂²	1	1	yes	characteristic
59	C₈×#3622	C₂²	1	1	yes	characteristic
60	C₄×#41×C₁₇	C₂²	1	1	yes	characteristic
61	C₁₇×#432	C₂²	1	1	yes	characteristic
62	C₁₇×#431	C₂²	1	1	yes	characteristic
63	C₁₇×Q₈⋊C₈	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×D₄⋊C₈	C₂²	1	1	yes	characteristic
67	C₂×#41×C₁₇	C₂×C₄	1	1	yes	characteristic
68	C₄×Q₈×C₁₇	C₂×C₄	1	1	yes	characteristic
69	C₄×Q₈×C₁₇	C₂³	1	1	yes	characteristic
70	C₄×D₄×C₁₇	—	2	1	no	—
71	C₄×D₄×C₁₇	—	2	1	no	—
72	C₄×D₄×C₁₇	C₂×C₄	1	1	yes	characteristic
73	C₄×D₄×C₁₇	C₂³	1	1	yes	characteristic
74	C₁₇×#117	—	2	1	no	—
75	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₁₇	—	2	1	no	—
77	C₂×C₄²×C₁₇	C₂³	1	1	yes	characteristic
78	C₂×#63231	C₂×C₄	1	1	yes	characteristic
79	C₂×#63231	C₂×C₄	1	1	yes	characteristic
80	C₂×#63229	C₂×C₄	1	1	yes	characteristic
81	C₂×#63229	C₂×C₄	1	1	yes	characteristic
82	#10587612	—	2	1	no	—
83	#10587610	—	2	1	no	—
84	#10587610	C₂×C₄	1	1	yes	characteristic
85	#10587610	C₂×C₄	1	1	yes	characteristic
86	C₂²×#3622	—	2	1	no	—
87	C₂²×#3622	—	2	1	no	—
88	C₂²×#3622	—	2	1	no	—
89	#10587556	—	2	1	no	—
90	#10587555	C₂×C₄	1	1	yes	characteristic
91	#10587555	C₂×C₄	1	1	yes	characteristic
92	C₄×Dic₃₄	—	2	1	no	—
93	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
94	C₄×Dic₃₄	C₂³	1	1	yes	characteristic
95	C₁₇×C₄⋊C₈	—	2	1	no	—
96	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
97	C₁₇×C₄⋊C₈	C₂³	1	1	yes	characteristic
98	C₁₇×C₂²⋊C₈	—	2	1	no	—
99	C₁₇×C₂²⋊C₈	—	2	1	no	—
100	C₁₇×#97	—	2	1	no	—
101	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
102	C₄×C₈×C₁₇	C₂³	1	1	yes	characteristic
103	#10587506	C₂×C₄	1	1	yes	characteristic
104	#10587506	C₂×C₄	1	1	yes	characteristic
105	#10587503	C₂×C₄	1	1	yes	characteristic
106	#10587503	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊#3622	—	2	1	no	—
108	C₂²⋊#3622	—	2	1	no	—
109	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊#3622	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊#3622	D₄	1	1	yes	characteristic
112	C₂²⋊#3622	D₄	1	1	yes	characteristic
113	#10587486	—	2	1	no	—
114	#10587486	—	2	1	no	—
115	#10587485	—	2	1	no	—
116	#10587485	—	2	1	no	—
117	#10587485	—	2	1	no	—
118	#10587485	—	2	1	no	—
119	C₈×Dic₁₇	—	2	1	no	—
120	C₈×Dic₁₇	—	2	1	no	—
121	#10587481	C₂×C₄	1	1	yes	characteristic
122	#10587481	C₂×C₄	1	1	yes	characteristic
123	#10587481	C₂×C₄	1	1	yes	characteristic
124	#10587481	C₂×C₄	1	1	yes	characteristic
125	#10587479	C₂×C₄	1	1	yes	characteristic
126	#10587479	C₂×C₄	1	1	yes	characteristic
127	#10587478	C₂×C₄	1	1	yes	characteristic
128	#10587478	C₂×C₄	1	1	yes	characteristic
129	C₄⋊#3622	—	2	1	no	—
130	C₄⋊#3622	—	2	1	no	—
131	C₄⋊#3622	—	2	1	no	—
132	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
133	C₄⋊#3622	C₂×C₄	1	1	yes	characteristic
134	C₄⋊#3622	D₄	1	1	yes	characteristic
135	C₄⋊#3622	D₄	1	1	yes	characteristic
136	C₄⋊#3622	C₂³	1	1	yes	characteristic
137	C₄⋊#3622	C₂³	1	1	yes	characteristic
138	C₄×#3622	—	2	1	no	—
139	C₄×#3622	—	2	1	no	—
140	C₄×#3622	C₂³	1	1	yes	characteristic
141	C₄×#3622	C₂³	1	1	yes	characteristic
142	C₄×#3622	C₂³	1	1	yes	characteristic
143	C₄×#3622	C₂³	1	1	yes	characteristic
144	#41×C₁₇	—	2	2	no	—
145	#41×C₁₇	—	2	2	no	—
146	C₂×Q₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×D₄×C₁₇	—	2	1	no	—
148	C₂×D₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₁₇	—	2	1	no	—
150	C₂²×C₄×C₁₇	—	2	1	no	—
151	C₂²×C₄×C₁₇	—	2	1	no	—
152	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₁₇	C₂×D₄	1	1	yes	characteristic
154	C₂²×C₄×C₁₇	#41	1	1	yes	characteristic
155	C₂×Dic₃₄	—	2	1	no	—
156	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
157	C₂×Dic₃₄	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₁₇	—	2	1	no	—
159	C₂×C₈×C₁₇	—	2	1	no	—
160	C₂×C₈×C₁₇	—	2	1	no	—
161	C₂×C₈×C₁₇	—	2	1	no	—
162	C₄⋊C₄×C₁₇	—	2	1	no	—
163	C₄⋊C₄×C₁₇	—	2	1	no	—
164	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
165	C₄⋊C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²⋊C₄×C₁₇	—	2	1	no	—
167	C₂²⋊C₄×C₁₇	—	2	1	no	—
168	C₂²⋊C₄×C₁₇	—	2	1	no	—
169	C₄²×C₁₇	—	2	1	no	—
170	C₄²×C₁₇	—	2	1	no	—
171	C₄²×C₁₇	—	2	1	no	—
172	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
173	C₄²×C₁₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₁₇	#41	1	1	yes	characteristic
175	C₄²×C₁₇	C₂⁴	1	1	yes	characteristic
176	C₂²⋊Dic₁₇	—	2	1	no	—
177	C₂²⋊Dic₁₇	—	2	1	no	—
178	#63231	—	2	2	no	—
179	#63231	—	2	2	no	—
180	#63229	—	2	2	no	—
181	#63229	—	2	2	no	—
182	C₄⋊Dic₁₇	—	2	1	no	—
183	C₄⋊Dic₁₇	—	2	1	no	—
184	C₄⋊Dic₁₇	—	2	1	no	—
185	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
186	C₄⋊Dic₁₇	C₂²×C₄	1	1	yes	characteristic
187	#63225	—	2	1	no	—
188	#63225	—	2	1	no	—
189	#63225	—	2	1	no	—
190	#63225	—	2	1	no	—
191	C₄×Dic₁₇	—	2	1	no	—
192	C₄×Dic₁₇	—	2	1	no	—
193	C₂×#3622	—	2	1	no	—
194	C₂×#3622	—	2	1	no	—
195	C₂×#3622	—	8	1	no	—
196	C₂×#3622	—	8	1	no	—
197	C₂×#3622	—	8	1	no	—
198	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
199	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
200	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
201	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
202	C₂×#3622	C₂×D₄	1	1	yes	characteristic
203	C₂×#3622	C₂×D₄	1	1	yes	characteristic
204	C₂×#3622	C₂×D₄	1	1	yes	characteristic
205	C₂×#3622	C₂×D₄	1	1	yes	characteristic
206	#17921	—	17	1	no	maximal, Sylow
207	C₂³×C₁₇	—	2	1	no	—
208	C₂³×C₁₇	C₄×D₄	1	1	yes	characteristic
209	Q₈×C₁₇	—	2	1	no	—
210	Q₈×C₁₇	#131	1	2	yes	—
211	D₄×C₁₇	—	2	4	no	—
212	D₄×C₁₇	—	2	1	no	—
213	D₄×C₁₇	#131	1	2	yes	—
214	C₂×C₄×C₁₇	—	2	4	no	—
215	C₂×C₄×C₁₇	—	2	1	no	—
216	C₂×C₄×C₁₇	—	2	1	no	—
217	C₂×C₄×C₁₇	—	2	1	no	—
218	C₂×C₄×C₁₇	—	2	1	no	—
219	C₂×C₄×C₁₇	—	2	1	no	—
220	C₂×C₄×C₁₇	—	2	1	no	—
221	C₂×C₄×C₁₇	—	2	1	no	—
222	C₂×C₄×C₁₇	—	4	1	no	—
223	C₂×C₄×C₁₇	—	4	1	no	—
224	C₂×C₄×C₁₇	—	4	1	no	—
225	C₂×C₄×C₁₇	—	8	1	no	—
226	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
227	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
228	C₂×C₄×C₁₇	C₄×D₄	1	1	yes	characteristic
229	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
230	C₂×C₄×C₁₇	C₂²×D₄	1	1	yes	characteristic
231	C₂×C₄×C₁₇	C₂×#41	1	1	yes	characteristic
232	C₂×Dic₁₇	—	2	1	no	—
233	C₂×Dic₁₇	—	2	1	no	—
234	C₂×Dic₁₇	—	2	1	no	—
235	C₂×Dic₁₇	—	2	1	no	—
236	Dic₃₄	—	2	1	no	—
237	Dic₃₄	—	2	1	no	—
238	Dic₃₄	—	2	1	no	—
239	Dic₃₄	—	2	1	no	—
240	Dic₃₄	—	8	1	no	—
241	C₈×C₁₇	—	4	1	no	—
242	C₈×C₁₇	—	4	1	no	—
243	C₈×C₁₇	—	4	1	no	—
244	C₈×C₁₇	—	4	1	no	—
245	#3622	—	2	1	no	—
246	#3622	—	2	1	no	—
247	#3622	—	2	1	no	—
248	#3622	—	2	1	no	—
249	#3622	—	2	1	no	—
250	#3622	—	2	1	no	—
251	#3622	—	2	1	no	—
252	#3622	—	2	1	no	—
253	#3622	—	4	1	no	—
254	#3622	—	4	1	no	—
255	#3107	—	17	1	no	—
256	#2988	—	17	1	no	—
257	#2985	—	17	1	no	—
258	#1587	—	17	1	no	—
259	#1585	—	17	1	no	—
260	#1584	—	17	1	no	—
261	#1582	—	17	1	no	—
262	#1579	—	17	1	no	—
263	SD₁₆⋊C₈	—	17	1	no	—
264	C₈×Q₁₆	—	17	1	no	—
265	C₈×SD₁₆	—	17	1	no	—
266	#1573	—	17	1	no	—
267	#1488	D₁₇	1	1	yes	characteristic
268	#1481	—	17	1	no	—
269	#1454	—	17	1	no	—
270	C₂²×C₁₇	—	2	1	no	—
271	C₂²×C₁₇	—	2	2	no	—
272	C₂²×C₁₇	—	2	1	no	—
273	C₂²×C₁₇	—	2	1	no	—
274	C₂²×C₁₇	—	4	1	no	—
275	C₂²×C₁₇	—	4	1	no	—
276	C₂²×C₁₇	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₁₇	—	2	1	no	—
278	C₄×C₁₇	—	2	2	no	—
279	C₄×C₁₇	—	2	1	no	—
280	C₄×C₁₇	—	2	1	no	—
281	C₄×C₁₇	—	2	1	no	—
282	C₄×C₁₇	—	4	1	no	—
283	C₄×C₁₇	—	4	1	no	—
284	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
285	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
286	C₄×C₁₇	#577	1	1	yes	characteristic
287	C₄×C₁₇	#578	1	1	yes	characteristic
288	Dic₁₇	—	4	1	no	—
289	Dic₁₇	—	4	1	no	—
290	Dic₁₇	—	4	1	no	—
291	Dic₁₇	—	4	1	no	—
292	#533	—	17	1	no	—
293	C₄×#41	C₂×D₁₇	1	1	yes	characteristic
294	#485	—	17	1	no	—
295	#485	—	17	1	no	—
296	#475	—	17	1	no	—
297	#474	—	17	1	no	—
298	#462	—	17	1	no	—
299	#461	—	17	1	no	—
300	#452	—	17	1	no	—
301	#452	—	17	1	no	—
302	#446	—	17	1	no	—
303	#446	—	17	1	no	—
304	#446	—	34	1	no	—
305	#446	—	34	1	no	—
306	C₈×Q₈	—	17	1	no	—
307	C₈×Q₈	—	17	1	no	—
308	C₈×Q₈	—	17	1	no	—
309	C₈×Q₈	—	17	1	no	—
310	C₄×Q₁₆	—	17	1	no	—
311	C₄×Q₁₆	—	17	1	no	—
312	C₄×SD₁₆	—	17	1	no	—
313	C₄×SD₁₆	—	17	1	no	—
314	C₈×D₄	—	17	1	no	—
315	C₈×D₄	—	17	1	no	—
316	C₈×D₄	—	34	1	no	—
317	C₈×D₄	—	34	1	no	—
318	#433	—	34	1	no	—
319	#433	—	34	1	no	—
320	#432	C₂×D₁₇	1	1	yes	characteristic
321	#431	—	17	1	no	—
322	#431	—	17	1	no	—
323	#431	—	34	1	no	—
324	#431	C₂×D₁₇	1	1	yes	characteristic
325	C₂×C₄⋊C₈	—	17	1	no	—
326	C₂×C₄⋊C₈	—	34	1	no	—
327	#335	—	17	1	no	—
328	#335	—	17	1	no	—
329	#334	—	17	1	no	—
330	#334	—	17	1	no	—
331	Q₈⋊C₈	—	17	1	no	—
332	Q₈⋊C₈	—	17	1	no	—
333	Q₈⋊C₈	—	17	1	no	—
334	Q₈⋊C₈	—	17	1	no	—
335	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
336	Q₈⋊C₈	C₂×D₁₇	1	1	yes	characteristic
337	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
338	D₄⋊C₈	C₂×D₁₇	1	1	yes	characteristic
339	#322	—	17	1	no	—
340	#322	—	17	1	no	—
341	#322	—	17	1	no	—
342	C₈²	—	17	1	no	—
343	C₂×C₁₇	—	4	1	no	—
344	C₂×C₁₇	—	4	2	no	—
345	C₂×C₁₇	#2929	1	1	yes	characteristic
346	C₂×C₁₇	#2947	1	1	yes	characteristic
347	C₂×C₁₇	#2957	1	1	yes	characteristic
348	C₂×#41	C₄×D₁₇	1	1	yes	characteristic
349	C₂×Q₁₆	—	17	1	no	—
350	C₂×Q₁₆	—	17	1	no	—
351	C₂×SD₁₆	—	17	1	no	—
352	C₂×SD₁₆	—	17	1	no	—
353	C₂²×C₈	—	34	1	no	—
354	C₂²×C₈	—	34	1	no	—
355	C₂²×C₈	—	34	1	no	—
356	C₄⋊Q₈	—	17	1	no	—
357	C₄⋊Q₈	—	17	1	no	—
358	#125	—	34	1	no	—
359	C₂²⋊Q₈	—	17	1	no	—
360	C₂²⋊Q₈	—	17	1	no	—
361	C₂²⋊Q₈	—	34	1	no	—
362	C₄×Q₈	—	17	1	no	—
363	C₄×Q₈	—	17	1	no	—
364	C₄×Q₈	—	34	1	no	—
365	C₄×Q₈	C₄×D₁₇	1	1	yes	characteristic
366	C₄×Q₈	C₂²×D₁₇	1	1	yes	characteristic
367	C₄×D₄	—	2	1	no	—
368	C₄×D₄	—	2	1	no	—
369	C₄×D₄	C₄×D₁₇	1	1	yes	characteristic
370	C₄×D₄	C₂²×D₁₇	1	1	yes	characteristic
371	#117	—	2	1	no	—
372	#117	—	34	1	no	—
373	#117	C₄×D₁₇	1	1	yes	characteristic
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂²×D₁₇	1	1	yes	characteristic
376	#107	—	17	1	no	—
377	#107	—	17	1	no	—
378	#106	—	17	1	no	—
379	#106	—	17	1	no	—
380	C₄⋊C₈	—	2	1	no	—
381	C₄⋊C₈	—	17	1	no	—
382	C₄⋊C₈	—	17	1	no	—
383	C₄⋊C₈	—	17	1	no	—
384	C₄⋊C₈	—	17	1	no	—
385	C₄⋊C₈	—	17	1	no	—
386	C₄⋊C₈	—	17	1	no	—
387	C₄⋊C₈	—	34	1	no	—
388	C₄⋊C₈	—	34	1	no	—
389	C₄⋊C₈	—	34	1	no	—
390	C₄⋊C₈	—	34	1	no	—
391	C₄⋊C₈	—	34	1	no	—
392	C₄⋊C₈	—	34	1	no	—
393	C₄⋊C₈	—	34	1	no	—
394	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
395	C₄⋊C₈	C₂²×D₁₇	1	1	yes	characteristic
396	#103	—	17	1	no	—
397	#103	—	17	1	no	—
398	#103	—	17	1	no	—
399	#103	—	17	1	no	—
400	#103	—	17	1	no	—
401	#103	—	17	1	no	—
402	#102	—	17	1	no	—
403	#102	—	17	1	no	—
404	C₂²⋊C₈	—	2	1	no	—
405	C₂²⋊C₈	—	2	1	no	—
406	C₂²⋊C₈	—	17	1	no	—
407	C₂²⋊C₈	—	17	1	no	—
408	C₂²⋊C₈	—	17	1	no	—
409	C₂²⋊C₈	—	17	1	no	—
410	C₂²⋊C₈	—	34	1	no	—
411	C₂²⋊C₈	—	34	1	no	—
412	#97	—	2	1	no	—
413	#97	—	34	1	no	—
414	#97	—	34	1	no	—
415	C₄×C₈	—	17	1	no	—
416	C₄×C₈	—	17	1	no	—
417	C₄×C₈	—	17	1	no	—
418	C₄×C₈	—	17	1	no	—
419	C₄×C₈	—	34	1	no	—
420	C₄×C₈	—	34	1	no	—
421	C₄×C₈	—	34	1	no	—
422	C₄×C₈	—	34	1	no	—
423	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
424	C₄×C₈	C₂²×D₁₇	1	1	yes	characteristic
425	C₁₇	#17921	1	1	yes	characteristic, complemented, Sylow
426	#41	—	2	2	no	—
427	#41	—	2	2	no	—
428	C₂×Q₈	—	17	1	no	—
429	C₂×Q₈	—	17	1	no	—
430	C₂×Q₈	—	34	1	no	—
431	C₂×Q₈	C₂×C₄×D₁₇	1	1	yes	characteristic
432	C₂×D₄	—	2	1	no	—
433	C₂×D₄	C₂×C₄×D₁₇	1	1	yes	characteristic
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	1	no	—
436	C₂²×C₄	—	2	1	no	—
437	C₂²×C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
438	C₂²×C₄	D₄×D₁₇	1	1	yes	characteristic
439	C₂²×C₄	#63254	1	1	yes	characteristic
440	Q₁₆	—	34	2	no	—
441	Q₁₆	—	34	2	no	—
442	SD₁₆	—	34	2	no	—
443	SD₁₆	—	34	2	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	2	1	no	—
448	C₂×C₈	—	17	1	no	—
449	C₂×C₈	—	17	1	no	—
450	C₂×C₈	—	17	1	no	—
451	C₂×C₈	—	17	1	no	—
452	C₂×C₈	—	17	1	no	—
453	C₂×C₈	—	17	1	no	—
454	C₂×C₈	—	17	1	no	—
455	C₂×C₈	—	17	1	no	—
456	C₂×C₈	—	34	1	no	—
457	C₂×C₈	—	34	1	no	—
458	C₂×C₈	—	136	1	no	—
459	C₂×C₈	—	136	1	no	—
460	C₂×C₈	—	136	1	no	—
461	C₄⋊C₄	—	2	1	no	—
462	C₄⋊C₄	—	2	1	no	—
463	C₄⋊C₄	—	17	1	no	—
464	C₄⋊C₄	—	17	1	no	—
465	C₄⋊C₄	—	34	1	no	—
466	C₄⋊C₄	—	34	1	no	—
467	C₄⋊C₄	—	34	1	no	—
468	C₄⋊C₄	—	34	1	no	—
469	C₄⋊C₄	—	34	1	no	—
470	C₄⋊C₄	—	34	1	no	—
471	C₄⋊C₄	—	34	1	no	—
472	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
473	C₄⋊C₄	C₂×C₄×D₁₇	1	1	yes	characteristic
474	C₂²⋊C₄	—	2	1	no	—
475	C₂²⋊C₄	—	2	1	no	—
476	C₂²⋊C₄	—	2	1	no	—
477	C₂²⋊C₄	—	34	1	no	—
478	C₂²⋊C₄	—	34	1	no	—
479	C₄²	—	2	1	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	1	no	—
482	C₄²	—	34	1	no	—
483	C₄²	—	34	1	no	—
484	C₄²	C₂×C₄×D₁₇	1	1	yes	characteristic
485	C₄²	D₄×D₁₇	1	1	yes	characteristic
486	C₄²	#63254	1	1	yes	characteristic
487	C₄²	C₂³×D₁₇	1	1	yes	characteristic
488	C₂³	—	2	1	no	—
489	C₂³	#10587567	1	1	yes	characteristic
490	Q₈	—	2	1	no	—
491	Q₈	—	34	1	no	—
492	Q₈	—	34	1	no	—
493	Q₈	—	34	1	no	—
494	Q₈	—	34	1	no	—
495	Q₈	—	136	1	no	—
496	Q₈	#10587593	1	2	yes	—
497	D₄	—	2	4	no	—
498	D₄	—	2	1	no	—
499	D₄	#10587593	1	2	yes	—
500	C₂×C₄	—	2	4	no	—
501	C₂×C₄	—	2	1	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	1	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	4	1	no	—
509	C₂×C₄	—	4	1	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	8	1	no	—
512	C₂×C₄	—	34	1	no	—
513	C₂×C₄	—	34	1	no	—
514	C₂×C₄	—	34	1	no	—
515	C₂×C₄	—	34	1	no	—
516	C₂×C₄	#10587567	1	1	yes	characteristic
517	C₂×C₄	#10587567	1	1	yes	characteristic
518	C₂×C₄	#10587567	1	1	yes	characteristic
519	C₂×C₄	C₂²×C₄×D₁₇	1	1	yes	characteristic
520	C₂×C₄	C₂×D₄×D₁₇	1	1	yes	characteristic
521	C₂×C₄	C₂×#63254	1	1	yes	characteristic
522	C₈	—	4	1	no	—
523	C₈	—	4	1	no	—
524	C₈	—	4	1	no	—
525	C₈	—	4	1	no	—
526	C₈	—	34	1	no	—
527	C₈	—	34	1	no	—
528	C₈	—	34	1	no	—
529	C₈	—	34	1	no	—
530	C₈	—	34	1	no	—
531	C₈	—	34	1	no	—
532	C₈	—	34	1	no	—
533	C₈	—	34	1	no	—
534	C₈	—	68	1	no	—
535	C₈	—	68	1	no	—
536	C₂²	—	2	1	no	—
537	C₂²	—	2	2	no	—
538	C₂²	—	2	1	no	—
539	C₂²	—	2	1	no	—
540	C₂²	—	4	1	no	—
541	C₂²	—	4	1	no	—
542	C₂²	C₂×#10587567	1	1	yes	characteristic
543	C₄	—	2	1	no	—
544	C₄	—	2	2	no	—
545	C₄	—	2	1	no	—
546	C₄	—	2	1	no	—
547	C₄	—	2	1	no	—
548	C₄	—	4	1	no	—
549	C₄	—	4	1	no	—
550	C₄	—	68	1	no	—
551	C₄	—	68	1	no	—
552	C₄	—	68	1	no	—
553	C₄	—	68	1	no	—
554	C₄	C₂×#10587593	1	1	yes	characteristic
555	C₄	C₂×#10587593	1	1	yes	characteristic
556	C₄	#11763616	1	1	yes	characteristic
557	C₄	#11763623	1	1	yes	characteristic
558	C₂	—	4	1	no	—
559	C₂	—	4	2	no	—
560	C₂	#14537474	1	1	yes	characteristic
561	C₂	#14537630	1	1	yes	characteristic
562	C₂	#14537697	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×#1488	C₂
socle	C₂²×C₁₇	C₂×C₄×D₄
prime radical	C₂×#41×C₁₇	C₂×C₄
cosocle	C₄²×C₁₇	C₂⁴
hypercenter	#1488	D₁₇
hypocenter	C₁₇	#17921
LCS	G ▷ C₂×C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1488

Complements

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

N	H ≅ G/N	type
3. #14537881	C₂	semidirect
4. #14527652	C₂	semidirect
5. #14527638	C₂	semidirect
6. #14527631	C₂	semidirect
7. #14527617	C₂	semidirect
8. #14527600	C₂	semidirect
9. #14527593	C₂	semidirect
10. #14527588	C₂	semidirect
11. #14527587	C₂	semidirect
12. #14527570	C₂	semidirect
13. #14527188	C₂	semidirect
14. #14527084	C₂	semidirect
425. C₁₇	#17921	semidirect

Maximal subgroups

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

subgroup	index
#14538855	2
#14537895	2
#14537881	2
#14527652	2
#14527638	2
#14527631	2
#14527617	2
#14527600	2
#14527593	2
#14527588	2
#14527587	2
#14527570	2
#14527188	2
#14527084	2
C₁₇×#1488	2
#17921	17