Subgroups — #17978487

Order 4352.

600 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545150	C₂	1	2	yes	maximal, complemented
2	#14545149	C₂	1	2	yes	maximal, complemented
3	#14545148	C₂	1	1	yes	maximal, characteristic, complemented
4	#14545147	C₂	1	1	yes	maximal, characteristic, complemented
5	#14545144	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545143	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545120	C₂	1	2	yes	maximal, complemented
8	#14545012	C₂	1	1	yes	maximal, characteristic
9	#14545009	C₂	1	1	yes	maximal, characteristic
10	#14544994	C₂	1	2	yes	maximal, complemented
11	D₁₇×#405	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587530	C₂²	1	2	yes	—
13	C₂×#10587529	C₂²	1	2	yes	—
14	#11763730	C₂²	1	2	yes	complemented
15	#11763730	C₂²	1	2	yes	complemented
16	C₄⋊#63216	C₂²	1	2	yes	complemented
17	C₄⋊#63216	C₂²	1	2	yes	complemented
18	#11763704	C₂²	1	1	yes	characteristic
19	#11763704	C₂²	1	1	yes	characteristic
20	#11763704	C₂²	1	1	yes	characteristic
21	#11763704	C₂²	1	1	yes	characteristic
22	C₂²⋊#63216	C₂²	1	2	yes	—
23	C₂²⋊#63216	C₂²	1	2	yes	—
24	#11763698	C₂²	1	2	yes	complemented
25	#11763697	C₂²	1	2	yes	complemented
26	#11763695	C₂²	1	2	yes	complemented
27	C₄×#63216	C₂²	1	2	yes	complemented
28	C₂×M₁₆×D₁₇	C₄	1	1	yes	characteristic
29	C₂²×C₈×D₁₇	C₂²	1	1	yes	characteristic
30	#117×D₁₇	C₄	1	1	yes	characteristic
31	#11762767	C₂²	1	1	yes	characteristic
32	#11762766	C₂²	1	1	yes	characteristic
33	#11762766	C₂²	1	1	yes	characteristic
34	#11762765	C₂²	1	1	yes	characteristic
35	#11762764	C₄	1	1	yes	characteristic
36	#11762763	C₄	1	1	yes	characteristic
37	#11762763	C₄	1	1	yes	characteristic
38	#97×D₁₇	C₄	1	1	yes	characteristic
39	#97×D₁₇	C₄	1	1	yes	characteristic
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#405	C₄	1	1	yes	characteristic
43	C₂²×C₄×D₁₇	C₂×C₄	1	1	yes	characteristic
44	C₂×M₁₆×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
46	C₁₇×#117	C₂×C₄	1	1	yes	characteristic
47	#10587612	C₂×C₄	1	1	yes	characteristic
48	C₂×#63223	C₂×C₄	1	1	yes	characteristic
49	C₂²×#3622	C₂³	1	1	yes	characteristic
50	M₁₆×D₁₇	—	2	4	no	—
51	C₂×#63218	C₂×C₄	1	1	yes	characteristic
52	C₂×#63218	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	—	2	4	no	—
54	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
60	#10587578	C₈	1	1	yes	characteristic
61	#10587578	C₈	1	1	yes	characteristic
62	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
63	C₄⋊C₄×D₁₇	C₈	1	1	yes	characteristic
64	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
65	C₂²⋊C₄×D₁₇	C₈	1	1	yes	characteristic
66	#10587563	C₈	1	1	yes	characteristic
67	#10587563	C₈	1	1	yes	characteristic
68	#10587558	C₂×C₄	1	1	yes	characteristic
69	#10587558	C₂×C₄	1	1	yes	characteristic
70	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
71	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
72	C₂×#63216	C₂³	1	2	yes	—
73	C₂×#63216	C₂³	1	2	yes	—
74	C₂×#63216	C₂³	1	2	yes	—
75	C₂×#63216	C₂³	1	2	yes	—
76	#10587530	—	2	4	no	—
77	#10587529	—	2	4	no	—
78	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
79	C₁₇×#97	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
82	#10587486	C₂×C₄	1	1	yes	characteristic
83	#10587486	C₂×C₄	1	1	yes	characteristic
84	#10587486	C₂×C₄	1	1	yes	characteristic
85	#10587486	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
88	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
89	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
90	#10587474	C₂×C₄	1	1	yes	characteristic
91	#10587474	C₂×C₄	1	1	yes	characteristic
92	C₄×#3622	C₂³	1	1	yes	characteristic
93	C₄×#3622	C₂³	1	1	yes	characteristic
94	C₂³×D₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₁₇	—	2	2	no	—
98	C₂×C₄×D₁₇	—	2	2	no	—
99	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
100	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
101	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
102	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
103	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
104	C₂×C₄×D₁₇	C₂×C₈	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
107	M₁₆×C₁₇	—	2	2	no	—
108	C₂×C₈×C₁₇	—	2	2	no	—
109	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
113	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
114	C₄⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
115	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
117	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
118	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
120	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
121	#63227	C₂×C₈	1	1	yes	characteristic
122	#63227	C₂×C₈	1	1	yes	characteristic
123	#63227	C₂×C₈	1	1	yes	characteristic
124	#63227	C₂×C₈	1	1	yes	characteristic
125	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
126	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
127	#63225	C₂×C₈	1	1	yes	characteristic
128	#63225	C₂×C₈	1	1	yes	characteristic
129	#63225	C₂×C₈	1	1	yes	characteristic
130	#63225	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
133	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
134	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
135	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
136	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
137	#63223	—	2	2	no	—
138	C₂×#3622	—	2	2	no	—
139	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
140	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
141	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
142	C₂×#3622	C₂⁴	1	1	yes	characteristic
143	#63218	—	2	2	no	—
144	#63218	M₁₆	1	4	yes	—
145	C₈×D₁₇	—	2	2	no	—
146	C₈×D₁₇	—	2	2	no	—
147	C₈×D₁₇	—	2	2	no	—
148	C₈×D₁₇	—	2	2	no	—
149	C₈×D₁₇	—	2	2	no	—
150	C₈×D₁₇	#41	1	4	yes	—
151	#63216	—	2	2	no	—
152	#63216	—	2	2	no	—
153	#63216	—	2	2	no	—
154	#63216	—	2	2	no	—
155	#33422	—	17	1	no	maximal, Sylow
156	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
157	C₂²×D₁₇	—	2	2	no	—
158	C₂²×D₁₇	—	2	2	no	—
159	C₂²×D₁₇	—	4	1	no	—
160	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
161	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₇	—	2	1	no	—
163	C₂×C₄×C₁₇	—	2	1	no	—
164	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
166	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
168	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
169	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
170	C₂×Dic₁₇	—	2	2	no	—
171	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
172	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
173	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
174	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
175	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
176	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
177	C₄×D₁₇	—	2	2	no	—
178	C₄×D₁₇	—	2	2	no	—
179	C₄×D₁₇	—	2	2	no	—
180	C₄×D₁₇	—	2	1	no	—
181	C₄×D₁₇	—	2	1	no	—
182	C₄×D₁₇	—	2	2	no	—
183	C₄×D₁₇	—	4	1	no	—
184	C₄×D₁₇	—	4	1	no	—
185	C₄×D₁₇	#117	1	2	yes	—
186	C₄×D₁₇	C₂×M₁₆	1	2	yes	—
187	C₈×C₁₇	—	2	1	no	—
188	C₈×C₁₇	—	2	1	no	—
189	C₈×C₁₇	#117	1	2	yes	—
190	C₈×C₁₇	C₂×M₁₆	1	2	yes	—
191	#3622	—	2	1	no	—
192	#3622	—	2	1	no	—
193	#3622	C₂×M₁₆	1	2	yes	—
194	#3622	C₂×#41	1	2	yes	—
195	C₂×#405	—	17	1	no	—
196	#2164	—	17	2	no	—
197	#2164	—	17	2	no	—
198	#2163	—	17	1	no	—
199	#2163	—	17	1	no	—
200	#2162	—	17	1	no	—
201	#2162	—	17	1	no	—
202	#2151	—	17	2	no	—
203	#2112	—	17	1	no	—
204	C₂×C₂²⋊C₁₆	—	17	1	no	—
205	#2108	—	17	2	no	—
206	C₂²×C₁₇	—	2	1	no	—
207	C₂²×C₁₇	—	2	1	no	—
208	C₂²×C₁₇	—	2	1	no	—
209	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
210	C₂×D₁₇	—	2	1	no	—
211	C₂×D₁₇	—	2	1	no	—
212	C₂×D₁₇	—	2	1	no	—
213	C₂×D₁₇	—	2	1	no	—
214	C₂×D₁₇	—	4	4	no	—
215	C₂×D₁₇	#431	1	2	yes	—
216	C₂×D₁₇	#504	1	2	yes	—
217	C₄×C₁₇	—	2	1	no	—
218	C₄×C₁₇	—	2	1	no	—
219	C₄×C₁₇	—	2	1	no	—
220	C₄×C₁₇	—	2	1	no	—
221	C₄×C₁₇	—	2	1	no	—
222	C₄×C₁₇	C₂×#117	1	1	yes	characteristic
223	C₄×C₁₇	C₂²×M₁₆	1	1	yes	characteristic
224	Dic₁₇	—	2	1	no	—
225	Dic₁₇	—	2	1	no	—
226	Dic₁₇	—	2	1	no	—
227	Dic₁₇	—	2	1	no	—
228	Dic₁₇	—	2	1	no	—
229	Dic₁₇	#431	1	2	yes	—
230	C₂²×M₁₆	—	17	1	no	—
231	C₂³×C₈	—	17	1	no	—
232	C₂×#117	—	17	1	no	—
233	C₂×M₃₂	—	17	2	no	—
234	C₂²×C₁₆	—	17	2	no	—
235	#405	—	17	1	no	—
236	#405	—	17	1	no	—
237	#405	—	17	1	no	—
238	#405	—	17	1	no	—
239	#405	—	17	1	no	—
240	#405	—	17	1	no	—
241	#405	—	17	1	no	—
242	#405	#595	1	1	yes	characteristic
243	C₂×#97	—	17	1	no	—
244	C₂×#97	—	17	1	no	—
245	C₂×C₄×C₈	—	17	1	no	—
246	C₂×C₄×C₈	—	17	1	no	—
247	C₄⋊C₁₆	—	17	2	no	—
248	C₄⋊C₁₆	—	17	2	no	—
249	C₄⋊C₁₆	—	17	2	no	—
250	C₄⋊C₁₆	—	17	2	no	—
251	C₂²⋊C₁₆	—	17	1	no	—
252	C₂²⋊C₁₆	—	17	1	no	—
253	C₂²⋊C₁₆	—	17	2	no	—
254	C₂²⋊C₁₆	—	17	1	no	—
255	C₂²⋊C₁₆	—	17	1	no	—
256	C₂²⋊C₁₆	—	17	2	no	—
257	#346	—	17	2	no	—
258	#346	—	17	2	no	—
259	C₄×C₁₆	—	17	2	no	—
260	C₄×C₁₆	—	17	2	no	—
261	C₂×C₁₇	—	4	1	no	—
262	C₂×C₁₇	C₂×#431	1	1	yes	characteristic
263	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
264	C₂×C₁₇	#3407	1	1	yes	characteristic
265	D₁₇	—	2	2	no	—
266	D₁₇	—	2	2	no	—
267	C₂³×C₄	—	17	1	no	—
268	C₂×M₁₆	—	17	1	no	—
269	C₂×M₁₆	—	17	1	no	—
270	C₂×M₁₆	—	17	1	no	—
271	C₂×M₁₆	—	34	4	no	—
272	C₂×M₁₆	C₂×#595	1	1	yes	characteristic
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	—	34	4	no	—
281	C₂²×C₈	C₂×#595	1	1	yes	characteristic
282	#117	—	17	1	no	—
283	#117	—	17	1	no	—
284	#117	—	17	1	no	—
285	#117	—	17	1	no	—
286	#117	—	17	1	no	—
287	#117	—	17	1	no	—
288	#117	—	17	1	no	—
289	#117	C₂×#595	1	1	yes	characteristic
290	C₂×C₄⋊C₄	—	17	1	no	—
291	C₂×C₄⋊C₄	—	17	1	no	—
292	C₂×C₂²⋊C₄	—	17	1	no	—
293	C₂×C₂²⋊C₄	—	17	1	no	—
294	C₂×C₄²	—	17	1	no	—
295	C₂×C₄²	—	17	1	no	—
296	M₃₂	—	34	4	no	—
297	C₂×C₁₆	—	17	2	no	—
298	C₂×C₁₆	—	17	2	no	—
299	C₂×C₁₆	—	17	2	no	—
300	C₂×C₁₆	—	17	2	no	—
301	C₂×C₁₆	—	34	4	no	—
302	#97	—	17	1	no	—
303	#97	—	17	1	no	—
304	#97	—	17	1	no	—
305	#97	—	17	1	no	—
306	#97	—	17	1	no	—
307	#97	—	17	1	no	—
308	#97	C₂×#595	1	1	yes	characteristic
309	#97	C₂×#595	1	1	yes	characteristic
310	C₄×C₈	—	17	1	no	—
311	C₄×C₈	—	17	1	no	—
312	C₄×C₈	—	17	1	no	—
313	C₄×C₈	—	17	1	no	—
314	C₄×C₈	—	17	1	no	—
315	C₄×C₈	—	17	1	no	—
316	C₄×C₈	C₂×#595	1	1	yes	characteristic
317	C₄×C₈	C₂×#595	1	1	yes	characteristic
318	C₁₇	#33422	1	1	yes	characteristic, complemented, Sylow
319	C₂⁴	—	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	—	34	2	no	—
331	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
332	M₁₆	—	2	2	no	—
333	M₁₆	—	17	4	no	—
334	M₁₆	—	34	2	no	—
335	M₁₆	—	34	2	no	—
336	C₂×C₈	—	2	2	no	—
337	C₂×C₈	—	17	1	no	—
338	C₂×C₈	—	17	1	no	—
339	C₂×C₈	—	17	4	no	—
340	C₂×C₈	—	17	1	no	—
341	C₂×C₈	—	17	1	no	—
342	C₂×C₈	—	34	2	no	—
343	C₂×C₈	—	34	2	no	—
344	C₂×C₈	—	34	2	no	—
345	C₂×C₈	—	34	2	no	—
346	C₂×C₈	—	34	2	no	—
347	C₂×C₈	—	34	2	no	—
348	C₂×C₈	C₂²×#595	1	1	yes	characteristic
349	C₂×C₈	C₂²×#595	1	1	yes	characteristic
350	C₂×C₈	C₂²×#595	1	1	yes	characteristic
351	C₂×C₈	C₂²×#595	1	1	yes	characteristic
352	C₄⋊C₄	—	17	1	no	—
353	C₄⋊C₄	—	17	1	no	—
354	C₄⋊C₄	—	17	1	no	—
355	C₄⋊C₄	—	17	1	no	—
356	C₄⋊C₄	—	17	1	no	—
357	C₄⋊C₄	—	17	1	no	—
358	C₄⋊C₄	#63242	1	1	yes	characteristic
359	C₄⋊C₄	#63242	1	1	yes	characteristic
360	C₂²⋊C₄	—	17	1	no	—
361	C₂²⋊C₄	—	17	1	no	—
362	C₂²⋊C₄	—	17	1	no	—
363	C₂²⋊C₄	—	17	1	no	—
364	C₂²⋊C₄	—	17	1	no	—
365	C₂²⋊C₄	—	17	1	no	—
366	C₂²⋊C₄	#63242	1	1	yes	characteristic
367	C₂²⋊C₄	#63242	1	1	yes	characteristic
368	C₄²	—	17	1	no	—
369	C₄²	—	17	1	no	—
370	C₄²	—	17	1	no	—
371	C₄²	—	17	1	no	—
372	C₄²	—	17	1	no	—
373	C₄²	—	17	1	no	—
374	C₄²	C₂²×#595	1	1	yes	characteristic
375	C₄²	C₂²×#595	1	1	yes	characteristic
376	C₁₆	—	34	2	no	—
377	C₁₆	—	34	2	no	—
378	C₁₆	—	34	2	no	—
379	C₁₆	—	34	2	no	—
380	C₂³	—	17	1	no	—
381	C₂³	—	17	1	no	—
382	C₂³	—	34	2	no	—
383	C₂³	—	34	2	no	—
384	C₂³	—	68	1	no	—
385	C₂³	C₂×#63242	1	1	yes	characteristic
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	17	1	no	—
389	C₂×C₄	—	17	2	no	—
390	C₂×C₄	—	17	2	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	—	34	2	no	—
397	C₂×C₄	—	34	2	no	—
398	C₂×C₄	—	34	2	no	—
399	C₂×C₄	—	34	2	no	—
400	C₂×C₄	—	34	2	no	—
401	C₂×C₄	—	34	1	no	—
402	C₂×C₄	—	34	1	no	—
403	C₂×C₄	—	68	1	no	—
404	C₂×C₄	—	68	1	no	—
405	C₂×C₄	C₂×#63242	1	1	yes	characteristic
406	C₂×C₄	C₂×#63242	1	1	yes	characteristic
407	C₂×C₄	C₂×#63242	1	1	yes	characteristic
408	C₂×C₄	C₂×#63242	1	1	yes	characteristic
409	C₂×C₄	C₂×#63242	1	1	yes	characteristic
410	C₂×C₄	C₂³×#595	1	1	yes	characteristic
411	C₈	—	2	1	no	—
412	C₈	—	2	1	no	—
413	C₈	—	17	2	no	—
414	C₈	—	17	2	no	—
415	C₈	—	34	1	no	—
416	C₈	—	34	1	no	—
417	C₈	D₁₇⋊M₁₆	1	2	yes	—
418	C₈	#10587677	1	2	yes	—
419	C₂²	—	2	1	no	—
420	C₂²	—	2	1	no	—
421	C₂²	—	2	1	no	—
422	C₂²	—	17	2	no	—
423	C₂²	—	17	2	no	—
424	C₂²	—	34	1	no	—
425	C₂²	—	34	1	no	—
426	C₂²	—	34	1	no	—
427	C₂²	—	34	1	no	—
428	C₂²	—	68	4	no	—
429	C₂²	C₂²×#63242	1	1	yes	characteristic
430	C₄	—	2	1	no	—
431	C₄	—	2	1	no	—
432	C₄	—	2	1	no	—
433	C₄	—	2	1	no	—
434	C₄	—	2	1	no	—
435	C₄	—	17	2	no	—
436	C₄	—	34	1	no	—
437	C₄	—	34	1	no	—
438	C₄	—	34	1	no	—
439	C₄	—	34	1	no	—
440	C₄	—	34	1	no	—
441	C₄	C₂×#10587677	1	1	yes	characteristic
442	C₄	C₂×D₁₇⋊M₁₆	1	1	yes	characteristic
443	C₂	—	4	1	no	—
444	C₂	—	34	2	no	—
445	C₂	—	34	2	no	—
446	C₂	#14545448	1	1	yes	characteristic
447	C₂	#14545749	1	1	yes	characteristic
448	C₂	#14545752	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#405	C₄
prime radical	C₂³×D₁₇	C₂×C₈
cosocle	C₂×#3622	C₂⁴
hypercenter	#405	#595
hypocenter	C₁₇	#33422
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #405

Complements

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

N	H ≅ G/N	type
1. #14545150	C₂	semidirect
2. #14545149	C₂	semidirect
3. #14545148	C₂	semidirect
4. #14545147	C₂	semidirect
5. #14545144	C₂	semidirect
6. #14545143	C₂	semidirect
7. #14545120	C₂	semidirect
10. #14544994	C₂	semidirect
14. #11763730	C₂²	semidirect
15. #11763730	C₂²	semidirect
16. C₄⋊#63216	C₂²	semidirect
17. C₄⋊#63216	C₂²	semidirect
24. #11763698	C₂²	semidirect
25. #11763697	C₂²	semidirect
26. #11763695	C₂²	semidirect
27. C₄×#63216	C₂²	semidirect
318. C₁₇	#33422	semidirect

Maximal subgroups

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

subgroup	index
#14545150	2
#14545149	2
#14545148	2
#14545147	2
#14545144	2
#14545143	2
#14545120	2
#14545012	2
#14545009	2
#14544994	2
D₁₇×#405	2
#33422	17