Subgroups — #17960486

Order 4352.

586 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11763865	C₂	1	1	yes	maximal, characteristic
2	C₂×#11763865	C₂	1	1	yes	maximal, characteristic
3	#14543835	C₂	1	2	yes	maximal, complemented
4	#14543834	C₂	1	2	yes	maximal, complemented
5	D₁₇×#405	C₂	1	1	yes	maximal, characteristic
6	C₂×#10587530	—	2	1	no	—
7	C₂×#10587530	C₄	1	2	yes	complemented
8	#11763865	—	2	1	no	—
9	#11763865	—	2	1	no	—
10	#11763865	—	2	1	no	—
11	#11763865	—	2	1	no	—
12	#11763865	—	2	1	no	—
13	#11763865	—	2	1	no	—
14	#11763865	C₄	1	2	yes	complemented
15	#11763865	C₄	1	2	yes	complemented
16	C₂×#10587538	C₂²	1	2	yes	—
17	C₂×#10587538	C₂²	1	2	yes	—
18	C₂×#10587529	—	2	1	no	—
19	C₂×#10587529	C₄	1	2	yes	complemented
20	C₂×M₁₆×D₁₇	C₄	1	1	yes	characteristic
21	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
22	#117×D₁₇	C₄	1	1	yes	characteristic
23	#11762767	C₂²	1	1	yes	characteristic
24	#11762766	—	2	1	no	—
25	#11762765	C₂²	1	1	yes	characteristic
26	#11762764	C₄	1	1	yes	characteristic
27	#11762763	—	2	1	no	—
28	#97×D₁₇	—	2	1	no	—
29	C₄×C₈×D₁₇	—	2	1	no	—
30	C₁₇×#405	C₄	1	1	yes	characteristic
31	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
32	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
33	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
34	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
35	#10587612	C₂×C₄	1	1	yes	characteristic
36	C₂×#63223	C₂×C₄	1	1	yes	characteristic
37	C₂²×#3622	C₂³	1	1	yes	characteristic
38	M₁₆×D₁₇	—	2	1	no	—
39	M₁₆×D₁₇	—	2	1	no	—
40	M₁₆×D₁₇	C₈	1	2	yes	—
41	M₁₆×D₁₇	C₈	1	2	yes	—
42	C₂×#63218	—	2	1	no	—
43	C₂×C₈×D₁₇	—	2	1	no	—
44	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
49	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
50	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
51	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
52	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	D₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
55	C₂×C₈×D₁₇	Q₈	1	1	yes	characteristic
56	#10587578	—	2	1	no	—
57	C₄⋊C₄×D₁₇	—	2	1	no	—
58	C₂²⋊C₄×D₁₇	C₈	1	2	yes	—
59	#10587563	C₈	1	2	yes	—
60	#10587558	—	2	1	no	—
61	C₄²×D₁₇	—	2	1	no	—
62	#10587538	—	2	2	no	—
63	#10587538	—	2	2	no	—
64	#10587538	—	2	2	no	—
65	#10587538	C₂×C₄	1	4	yes	complemented
66	C₂×#63216	—	2	2	no	—
67	C₂×#63216	C₂×C₄	1	4	yes	complemented
68	#10587530	—	2	2	no	—
69	#10587530	—	2	2	no	—
70	#10587530	—	2	2	no	—
71	#10587530	—	2	2	no	—
72	#10587529	—	2	2	no	—
73	#10587529	—	2	2	no	—
74	#10587529	—	2	2	no	—
75	#10587529	—	2	2	no	—
76	C₁₇×#97	—	2	1	no	—
77	C₄×C₈×C₁₇	—	2	1	no	—
78	#10587486	—	2	1	no	—
79	#10587486	—	2	1	no	—
80	C₈×Dic₁₇	—	2	1	no	—
81	C₈×Dic₁₇	—	2	1	no	—
82	#10587474	—	2	1	no	—
83	C₄×#3622	—	2	1	no	—
84	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
85	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
87	C₂×C₄×D₁₇	—	2	2	no	—
88	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
89	C₂×C₄×D₁₇	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₇	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
98	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
99	C₂×C₄×D₁₇	M₁₆	1	1	yes	characteristic
100	M₁₆×C₁₇	—	2	1	no	—
101	M₁₆×C₁₇	C₂×C₈	1	2	yes	—
102	C₂×C₈×C₁₇	—	2	1	no	—
103	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
104	C₂×C₈×C₁₇	C₄²	1	1	yes	characteristic
105	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₈×C₁₇	C₂²⋊C₄	1	1	yes	characteristic
107	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄⋊C₄×C₁₇	—	2	1	no	—
110	C₂²⋊C₄×C₁₇	C₂×C₈	1	2	yes	—
111	C₄²×C₁₇	—	2	1	no	—
112	C₂²⋊Dic₁₇	C₂×C₈	1	2	yes	—
113	#63227	—	2	2	no	—
114	C₄⋊Dic₁₇	—	2	1	no	—
115	#63225	—	2	2	no	—
116	C₄×Dic₁₇	—	2	1	no	—
117	C₄×Dic₁₇	—	2	2	no	—
118	#63223	—	2	1	no	—
119	#63223	C₂×C₈	1	2	yes	—
120	C₂×#3622	—	2	1	no	—
121	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
122	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
123	C₂×#3622	C₂×D₄	1	1	yes	characteristic
124	C₂×#3622	C₂×D₄	1	1	yes	characteristic
125	C₂×#3622	C₂×D₄	1	1	yes	characteristic
126	C₂×#3622	C₂×Q₈	1	1	yes	characteristic
127	#63218	—	2	2	no	—
128	#63218	—	2	2	no	—
129	C₈×D₁₇	—	2	2	no	—
130	C₈×D₁₇	—	2	2	no	—
131	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
132	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
133	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
134	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
135	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
136	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
137	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
138	C₈×D₁₇	C₂²⋊C₄	1	1	yes	characteristic
139	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
140	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
141	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
142	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
143	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
144	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
145	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
146	C₈×D₁₇	C₄⋊C₄	1	1	yes	characteristic
147	#63216	—	2	4	no	—
148	#63216	—	2	4	no	—
149	C₂×#1378	—	17	1	no	maximal, Sylow
150	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
151	C₂²×D₁₇	—	4	2	no	—
152	C₂²×D₁₇	C₄×C₈	1	1	yes	characteristic
153	C₂²×D₁₇	C₄×C₈	1	1	yes	characteristic
154	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
155	C₂²×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
156	C₂²×D₁₇	C₄⋊C₈	1	1	yes	characteristic
157	C₂²×D₁₇	C₄⋊C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	—	2	2	no	—
159	C₂×C₄×C₁₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
164	C₂×C₄×C₁₇	C₂×M₁₆	1	1	yes	characteristic
165	C₂×Dic₁₇	—	2	2	no	—
166	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
167	C₂×Dic₁₇	C₄×C₈	1	1	yes	characteristic
168	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
169	C₂×Dic₁₇	C₂²⋊C₈	1	1	yes	characteristic
170	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
171	C₂×Dic₁₇	C₄⋊C₈	1	1	yes	characteristic
172	C₄×D₁₇	—	4	4	no	—
173	C₄×D₁₇	#95	1	1	yes	characteristic
174	C₄×D₁₇	#95	1	1	yes	characteristic
175	C₄×D₁₇	#95	1	1	yes	characteristic
176	C₄×D₁₇	#95	1	1	yes	characteristic
177	C₄×D₁₇	#97	1	1	yes	characteristic
178	C₄×D₁₇	#97	1	1	yes	characteristic
179	C₄×D₁₇	#97	1	1	yes	characteristic
180	C₄×D₁₇	#97	1	1	yes	characteristic
181	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
182	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
183	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
184	C₄×D₁₇	C₂²⋊C₈	1	1	yes	characteristic
185	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
186	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
187	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
188	C₄×D₁₇	C₄⋊C₈	1	1	yes	characteristic
189	C₈×C₁₇	—	2	2	no	—
190	C₈×C₁₇	#95	1	1	yes	characteristic
191	C₈×C₁₇	#95	1	1	yes	characteristic
192	C₈×C₁₇	#95	1	1	yes	characteristic
193	C₈×C₁₇	#95	1	1	yes	characteristic
194	#3622	—	2	2	no	—
195	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
196	#3622	C₂×C₂²⋊C₄	1	1	yes	characteristic
197	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
198	#3622	C₂×C₄⋊C₄	1	1	yes	characteristic
199	C₂²×M₃₂	—	17	1	no	—
200	C₂²×M₃₂	—	17	1	no	—
201	C₂×#405	—	17	1	no	—
202	#1378	—	17	2	no	—
203	#1378	—	17	2	no	—
204	C₂²×C₁₇	—	4	1	no	—
205	C₂²×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
206	C₂²×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
207	C₂²×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
208	C₂×D₁₇	—	2	2	no	—
209	C₂×D₁₇	—	2	2	no	—
210	C₂×D₁₇	—	2	2	no	—
211	C₂×D₁₇	—	4	1	no	—
212	C₂×D₁₇	—	4	1	no	—
213	C₂×D₁₇	—	4	1	no	—
214	C₂×D₁₇	#336	1	1	yes	characteristic
215	C₂×D₁₇	#336	1	1	yes	characteristic
216	C₂×D₁₇	#336	1	1	yes	characteristic
217	C₂×D₁₇	#336	1	1	yes	characteristic
218	C₄×C₁₇	—	4	2	no	—
219	C₄×C₁₇	C₂×#95	1	1	yes	characteristic
220	C₄×C₁₇	C₂×#97	1	1	yes	characteristic
221	C₄×C₁₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
222	C₄×C₁₇	C₂×C₄⋊C₈	1	1	yes	characteristic
223	Dic₁₇	—	4	2	no	—
224	Dic₁₇	#336	1	1	yes	characteristic
225	Dic₁₇	#336	1	1	yes	characteristic
226	Dic₁₇	#336	1	1	yes	characteristic
227	Dic₁₇	#336	1	1	yes	characteristic
228	C₂²×M₁₆	—	17	1	no	—
229	C₂³×C₈	—	17	1	no	—
230	C₂×#117	—	17	1	no	—
231	C₂×M₃₂	—	17	2	no	—
232	C₂×M₃₂	—	17	2	no	—
233	C₂×M₃₂	—	17	2	no	—
234	C₂×M₃₂	—	17	2	no	—
235	C₂×M₃₂	—	17	2	no	—
236	C₂×M₃₂	—	34	1	no	—
237	C₂×M₃₂	—	34	1	no	—
238	C₂×M₃₂	—	34	1	no	—
239	C₂×M₃₂	—	34	1	no	—
240	C₂×M₃₂	—	34	1	no	—
241	C₂×M₃₂	—	34	1	no	—
242	C₂×M₃₂	—	34	1	no	—
243	C₂²×C₁₆	—	17	2	no	—
244	C₂²×C₁₆	—	34	1	no	—
245	#405	—	17	1	no	—
246	#405	—	17	1	no	—
247	#405	—	17	1	no	—
248	#405	—	34	1	no	—
249	#405	—	34	1	no	—
250	#405	#595	1	1	yes	characteristic
251	C₂×#97	—	34	1	no	—
252	C₂×C₄×C₈	—	34	1	no	—
253	C₂×C₁₇	—	2	1	no	—
254	C₂×C₁₇	—	2	1	no	—
255	C₂×C₁₇	—	2	1	no	—
256	C₂×C₁₇	C₂×#336	1	1	yes	characteristic
257	D₁₇	—	2	1	no	—
258	D₁₇	—	2	1	no	—
259	D₁₇	—	2	1	no	—
260	D₁₇	#1378	1	2	yes	complemented
261	C₂³×C₄	—	17	1	no	—
262	C₂×M₁₆	—	17	1	no	—
263	C₂×M₁₆	—	17	2	no	—
264	C₂×M₁₆	—	17	2	no	—
265	C₂×M₁₆	—	34	1	no	—
266	C₂×M₁₆	—	34	1	no	—
267	C₂×M₁₆	—	34	1	no	—
268	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
269	C₂²×C₈	—	17	1	no	—
270	C₂²×C₈	—	17	1	no	—
271	C₂²×C₈	—	17	1	no	—
272	C₂²×C₈	—	17	1	no	—
273	C₂²×C₈	—	17	1	no	—
274	C₂²×C₈	—	17	1	no	—
275	C₂²×C₈	—	17	1	no	—
276	C₂²×C₈	—	17	1	no	—
277	C₂²×C₈	—	17	1	no	—
278	C₂²×C₈	—	17	1	no	—
279	C₂²×C₈	—	17	1	no	—
280	C₂²×C₈	—	17	1	no	—
281	C₂²×C₈	—	17	1	no	—
282	C₂²×C₈	—	34	1	no	—
283	C₂²×C₈	C₂×#595	1	1	yes	characteristic
284	#117	—	17	1	no	—
285	#117	—	17	2	no	—
286	#117	—	34	1	no	—
287	#117	—	34	1	no	—
288	#117	C₂×#595	1	1	yes	characteristic
289	C₂×C₄⋊C₄	—	34	1	no	—
290	C₂×C₂²⋊C₄	—	17	2	no	—
291	C₂×C₄²	—	34	1	no	—
292	M₃₂	—	17	4	no	—
293	M₃₂	—	34	2	no	—
294	M₃₂	—	34	2	no	—
295	M₃₂	—	34	2	no	—
296	M₃₂	—	34	2	no	—
297	M₃₂	—	34	2	no	—
298	M₃₂	—	34	2	no	—
299	M₃₂	—	34	2	no	—
300	C₂×C₁₆	—	17	4	no	—
301	C₂×C₁₆	—	34	2	no	—
302	C₂×C₁₆	—	34	2	no	—
303	C₂×C₁₆	—	34	2	no	—
304	C₂×C₁₆	—	34	2	no	—
305	C₂×C₁₆	—	34	2	no	—
306	#97	—	2	1	no	—
307	#97	—	34	1	no	—
308	#97	—	34	1	no	—
309	#97	—	34	1	no	—
310	C₄×C₈	—	2	1	no	—
311	C₄×C₈	—	34	1	no	—
312	C₄×C₈	—	34	1	no	—
313	C₄×C₈	—	34	1	no	—
314	C₁₇	C₂×#1378	1	1	yes	characteristic, complemented, Sylow
315	C₂⁴	—	17	1	no	—
316	C₂²×C₄	—	17	1	no	—
317	C₂²×C₄	—	17	1	no	—
318	C₂²×C₄	—	17	1	no	—
319	C₂²×C₄	—	17	1	no	—
320	C₂²×C₄	—	17	1	no	—
321	C₂²×C₄	—	17	1	no	—
322	C₂²×C₄	—	17	1	no	—
323	C₂²×C₄	—	17	1	no	—
324	C₂²×C₄	—	17	1	no	—
325	C₂²×C₄	—	17	1	no	—
326	C₂²×C₄	—	17	1	no	—
327	C₂²×C₄	—	17	1	no	—
328	C₂²×C₄	—	17	1	no	—
329	C₂²×C₄	—	34	2	no	—
330	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
331	M₁₆	—	2	1	no	—
332	M₁₆	—	17	2	no	—
333	M₁₆	—	34	2	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	1	no	—
336	M₁₆	#63242	1	2	yes	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	17	1	no	—
339	C₂×C₈	—	17	1	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	17	1	no	—
343	C₂×C₈	—	17	1	no	—
344	C₂×C₈	—	17	1	no	—
345	C₂×C₈	—	17	1	no	—
346	C₂×C₈	—	17	1	no	—
347	C₂×C₈	—	17	1	no	—
348	C₂×C₈	—	17	1	no	—
349	C₂×C₈	—	17	1	no	—
350	C₂×C₈	—	17	1	no	—
351	C₂×C₈	—	17	1	no	—
352	C₂×C₈	—	17	1	no	—
353	C₂×C₈	—	17	1	no	—
354	C₂×C₈	—	17	1	no	—
355	C₂×C₈	—	17	1	no	—
356	C₂×C₈	—	17	1	no	—
357	C₂×C₈	—	17	1	no	—
358	C₂×C₈	—	17	1	no	—
359	C₂×C₈	—	17	1	no	—
360	C₂×C₈	—	34	2	no	—
361	C₂×C₈	—	34	2	no	—
362	C₂×C₈	—	34	1	no	—
363	C₂×C₈	C₄×#595	1	1	yes	characteristic
364	C₂×C₈	C₄×#595	1	1	yes	characteristic
365	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
366	C₂×C₈	C₄⋊#595	1	1	yes	characteristic
367	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
368	C₂×C₈	C₂²⋊#595	1	1	yes	characteristic
369	C₄⋊C₄	—	2	1	no	—
370	C₄⋊C₄	—	34	2	no	—
371	C₄⋊C₄	—	34	1	no	—
372	C₂²⋊C₄	—	17	2	no	—
373	C₂²⋊C₄	—	34	2	no	—
374	C₂²⋊C₄	#63242	1	2	yes	—
375	C₄²	—	2	1	no	—
376	C₄²	—	34	2	no	—
377	C₄²	—	34	1	no	—
378	C₁₆	—	34	4	no	—
379	C₁₆	—	34	4	no	—
380	C₂³	—	17	1	no	—
381	C₂³	—	17	1	no	—
382	C₂³	—	17	1	no	—
383	C₂³	—	17	1	no	—
384	C₂³	—	17	1	no	—
385	C₂³	—	17	1	no	—
386	C₂³	—	68	2	no	—
387	C₂³	C₂×#63242	1	1	yes	characteristic
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	17	1	no	—
390	C₂×C₄	—	17	1	no	—
391	C₂×C₄	—	17	1	no	—
392	C₂×C₄	—	17	1	no	—
393	C₂×C₄	—	17	1	no	—
394	C₂×C₄	—	17	1	no	—
395	C₂×C₄	—	17	1	no	—
396	C₂×C₄	—	17	1	no	—
397	C₂×C₄	—	17	1	no	—
398	C₂×C₄	—	17	1	no	—
399	C₂×C₄	—	17	1	no	—
400	C₂×C₄	—	17	1	no	—
401	C₂×C₄	—	17	1	no	—
402	C₂×C₄	—	17	1	no	—
403	C₂×C₄	—	17	1	no	—
404	C₂×C₄	—	17	1	no	—
405	C₂×C₄	—	17	1	no	—
406	C₂×C₄	—	17	1	no	—
407	C₂×C₄	—	17	1	no	—
408	C₂×C₄	—	17	1	no	—
409	C₂×C₄	—	17	1	no	—
410	C₂×C₄	—	17	1	no	—
411	C₂×C₄	—	34	2	no	—
412	C₂×C₄	—	68	4	no	—
413	C₂×C₄	C₂×#63242	1	1	yes	characteristic
414	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
415	C₂×C₄	D₁₇⋊M₁₆	1	1	yes	characteristic
416	C₂×C₄	C₂×C₄×#595	1	1	yes	characteristic
417	C₂×C₄	C₂×C₄⋊#595	1	1	yes	characteristic
418	C₂×C₄	C₂×C₂²⋊#595	1	1	yes	characteristic
419	C₈	—	2	2	no	—
420	C₈	—	17	1	no	—
421	C₈	—	17	1	no	—
422	C₈	—	17	1	no	—
423	C₈	—	17	1	no	—
424	C₈	—	34	2	no	—
425	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
426	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
427	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
428	C₈	(C₂×#595)⋊C₄	1	1	yes	characteristic
429	C₂²	—	4	1	no	—
430	C₂²	—	17	1	no	—
431	C₂²	—	17	1	no	—
432	C₂²	—	17	1	no	—
433	C₂²	—	17	1	no	—
434	C₂²	—	34	2	no	—
435	C₂²	—	34	2	no	—
436	C₂²	—	34	2	no	—
437	C₂²	—	68	1	no	—
438	C₂²	—	68	1	no	—
439	C₂²	—	68	1	no	—
440	C₂²	C₄×#63242	1	1	yes	characteristic
441	C₂²	#11763777	1	1	yes	characteristic
442	C₂²	#11763810	1	1	yes	characteristic
443	C₄	—	4	2	no	—
444	C₄	—	17	1	no	—
445	C₄	—	17	1	no	—
446	C₄	—	17	1	no	—
447	C₄	—	17	1	no	—
448	C₄	—	68	2	no	—
449	C₄	C₂×(C₂×#595)⋊C₄	1	1	yes	characteristic
450	C₄	#11763768	1	1	yes	characteristic
451	C₄	#11763777	1	1	yes	characteristic
452	C₄	#11763810	1	1	yes	characteristic
453	C₂	—	2	1	no	—
454	C₂	—	2	1	no	—
455	C₂	—	2	1	no	—
456	C₂	—	17	2	no	—
457	C₂	—	34	1	no	—
458	C₂	—	34	1	no	—
459	C₂	—	34	1	no	—
460	C₂	#14544445	1	1	yes	characteristic

	subgroup	G/H
center	C₈	(C₂×#595)⋊C₄
commutator	C₂²×C₁₇	C₂×C₄×C₈
Frattini	C₂²×C₄	C₂²×#595
Fitting	C₁₇×#405	C₄
socle	C₂×C₁₇	C₂×#336
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	C₂²×#3622	C₂³
hypercenter	#405	#595
hypocenter	C₁₇	C₂×#1378
LCS	G ▷ C₂²×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₈ ◁ C₂²×C₈ ◁ #405

Complements

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

N	H ≅ G/N	type
3. #14543835	C₂	semidirect
4. #14543834	C₂	semidirect
7. C₂×#10587530	C₄	semidirect
14. #11763865	C₄	semidirect
15. #11763865	C₄	semidirect
19. C₂×#10587529	C₄	semidirect
65. #10587538	C₂×C₄	semidirect
67. C₂×#63216	C₂×C₄	semidirect
260. D₁₇	#1378	semidirect
314. C₁₇	C₂×#1378	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11763865	2
#14543835	2
#14543834	2
D₁₇×#405	2
C₂×#1378	17