Subgroups — #17978803

Order 4352.

536 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#14545201	C₂	1	2	yes	maximal, complemented
2	#14545167	C₂	1	2	yes	maximal, complemented
3	#14545166	C₂	1	2	yes	maximal, complemented
4	#14545162	C₂	1	2	yes	maximal, complemented
5	#14545148	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545145	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545144	C₂	1	1	yes	maximal, characteristic, complemented
8	#14545117	C₂	1	1	yes	maximal, characteristic, complemented
9	#14545114	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊#63216	C₂	1	1	yes	maximal, characteristic, complemented
11	#14537740	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587530	C₂²	1	2	yes	—
13	C₂×#10587529	C₂²	1	2	yes	—
14	C₂²×#63216	C₂²	1	2	yes	—
15	#11763730	C₂²	1	2	yes	—
16	#11763730	C₂²	1	2	yes	—
17	C₄⋊#63216	C₂²	1	2	yes	—
18	C₄⋊#63216	C₂²	1	1	yes	characteristic
19	C₄⋊#63216	C₂²	1	1	yes	characteristic
20	C₄⋊#63216	C₂²	1	1	yes	characteristic
21	C₄⋊#63216	C₂²	1	1	yes	characteristic
22	#11763704	C₂²	1	2	yes	—
23	#11763704	C₂²	1	2	yes	—
24	C₂²⋊#63216	C₂²	1	2	yes	—
25	#11763698	C₂²	1	2	yes	—
26	#11763697	C₂²	1	2	yes	—
27	#11763695	C₂²	1	2	yes	—
28	C₄×#63252	C₄	1	1	yes	characteristic
29	#11762933	C₄	1	1	yes	characteristic
30	#11762933	C₂²	1	1	yes	characteristic
31	#11762874	C₄	1	1	yes	characteristic
32	#11762874	C₂²	1	1	yes	characteristic
33	#11762872	C₄	1	1	yes	characteristic
34	#11762872	C₄	1	1	yes	characteristic
35	#11762872	C₂²	1	1	yes	characteristic
36	#11762872	C₂²	1	1	yes	characteristic
37	#11762860	C₄	1	1	yes	characteristic
38	#11762860	C₄	1	1	yes	characteristic
39	C₂×C₄×#3622	C₂²	1	1	yes	characteristic
40	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
41	C₄×C₈×D₁₇	C₂²	1	1	yes	characteristic
42	C₁₇×#431	C₄	1	1	yes	characteristic
43	C₂×#63252	C₈	1	1	yes	characteristic
44	C₂×C₄²×C₁₇	C₂×C₄	1	1	yes	characteristic
45	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
46	C₄×C₂²⋊D₁₇	C₈	1	1	yes	characteristic
47	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
48	C₄×C₂²⋊D₁₇	C₂×C₄	1	1	yes	characteristic
49	#10587612	C₈	1	1	yes	characteristic
50	C₂²×#3622	C₂×C₄	1	1	yes	characteristic
51	C₂²×#3622	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
55	C₂×C₈×D₁₇	C₂³	1	1	yes	characteristic
56	C₄×D₆₈	C₈	1	1	yes	characteristic
57	C₄×D₆₈	C₂×C₄	1	1	yes	characteristic
58	#10587558	C₈	1	1	yes	characteristic
59	#10587558	C₈	1	1	yes	characteristic
60	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
61	C₄²×D₁₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Dic₃₄	C₈	1	1	yes	characteristic
63	C₄×Dic₃₄	C₂×C₄	1	1	yes	characteristic
64	C₂×#63216	—	4	2	no	—
65	C₂×#63216	C₂³	1	2	yes	—
66	C₂×#63216	C₂³	1	2	yes	—
67	C₂×#63216	C₂³	1	2	yes	—
68	C₂×#63216	C₂³	1	2	yes	—
69	#10587530	—	4	2	no	—
70	#10587529	—	4	2	no	—
71	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
72	C₁₇×C₄⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
74	C₁₇×C₂²⋊C₈	C₂×C₄	1	1	yes	characteristic
75	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
76	C₄×C₈×C₁₇	C₂×C₄	1	1	yes	characteristic
77	#10587491	C₂×C₄	1	1	yes	characteristic
78	#10587491	C₂×C₄	1	1	yes	characteristic
79	#10587491	C₂×C₄	1	1	yes	characteristic
80	#10587491	C₂×C₄	1	1	yes	characteristic
81	#10587485	C₂×C₄	1	1	yes	characteristic
82	#10587485	C₂×C₄	1	1	yes	characteristic
83	#10587485	C₂×C₄	1	1	yes	characteristic
84	#10587485	C₂×C₄	1	1	yes	characteristic
85	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
86	C₈×Dic₁₇	C₂×C₄	1	1	yes	characteristic
87	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
88	C₈×Dic₁₇	C₂³	1	1	yes	characteristic
89	C₄×#3622	C₂×C₄	1	1	yes	characteristic
90	C₄×#3622	C₂×C₄	1	1	yes	characteristic
91	C₄×#3622	C₂³	1	1	yes	characteristic
92	C₄×#3622	C₂³	1	1	yes	characteristic
93	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
94	C₂²×C₄×C₁₇	C₂×C₈	1	1	yes	characteristic
95	C₂²×C₄×C₁₇	C₂²×C₄	1	1	yes	characteristic
96	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
97	C₂×C₂²⋊D₁₇	C₂×C₈	1	1	yes	characteristic
98	#63252	—	2	4	no	—
99	C₂×D₆₈	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	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×Dic₃₄	C₂×C₈	1	1	yes	characteristic
107	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₁₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
112	C₄²×C₁₇	C₂×C₈	1	1	yes	characteristic
113	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
114	C₄²×C₁₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
116	C₂²⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
117	#63227	C₂×C₈	1	1	yes	characteristic
118	#63227	C₂×C₈	1	1	yes	characteristic
119	#63227	C₂×C₈	1	1	yes	characteristic
120	#63227	C₂×C₈	1	1	yes	characteristic
121	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
122	C₄⋊Dic₁₇	C₂×C₈	1	1	yes	characteristic
123	#63225	C₂×C₈	1	1	yes	characteristic
124	#63225	C₂×C₈	1	1	yes	characteristic
125	#63225	C₂×C₈	1	1	yes	characteristic
126	#63225	C₂×C₈	1	1	yes	characteristic
127	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
128	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
129	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
130	C₄×Dic₁₇	C₂×C₈	1	1	yes	characteristic
131	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
132	C₄×Dic₁₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×#3622	—	2	1	no	—
134	C₂×#3622	—	2	1	no	—
135	C₂×#3622	—	4	1	no	—
136	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
137	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
138	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
139	C₂×#3622	C₂⁴	1	1	yes	characteristic
140	C₈×D₁₇	—	2	1	no	—
141	C₈×D₁₇	—	2	1	no	—
142	C₈×D₁₇	—	2	1	no	—
143	C₈×D₁₇	—	2	1	no	—
144	C₈×D₁₇	—	4	1	no	—
145	C₈×D₁₇	—	4	1	no	—
146	#63216	—	2	2	no	—
147	#63216	—	2	2	no	—
148	#63216	—	2	2	no	—
149	#63216	—	2	2	no	—
150	#33504	—	17	1	no	maximal, Sylow
151	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
152	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
153	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
154	C₂×C₄×C₁₇	—	2	2	no	—
155	C₂×C₄×C₁₇	—	2	1	no	—
156	C₂×C₄×C₁₇	—	2	1	no	—
157	C₂×C₄×C₁₇	—	2	2	no	—
158	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
161	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
162	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
163	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
164	C₂²⋊D₁₇	—	2	2	no	—
165	C₂²⋊D₁₇	M₃₂	1	4	yes	complemented
166	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
167	C₂×Dic₁₇	C₂²×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	C₂²×C₈	1	1	yes	characteristic
171	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
172	D₆₈	—	2	2	no	—
173	C₄×D₁₇	—	2	2	no	—
174	C₄×D₁₇	—	2	1	no	—
175	C₄×D₁₇	—	2	1	no	—
176	C₄×D₁₇	—	2	1	no	—
177	C₄×D₁₇	—	2	1	no	—
178	C₄×D₁₇	—	2	2	no	—
179	C₄×D₁₇	—	2	2	no	—
180	C₄×D₁₇	—	2	2	no	—
181	Dic₃₄	—	2	2	no	—
182	C₈×C₁₇	—	2	1	no	—
183	C₈×C₁₇	—	2	1	no	—
184	C₈×C₁₇	—	2	1	no	—
185	C₈×C₁₇	—	2	1	no	—
186	#3622	—	2	1	no	—
187	#3622	—	2	1	no	—
188	#3622	—	2	1	no	—
189	#3622	H(5,𝔽₂)	1	1	yes	characteristic
190	#3622	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×#41	—	17	1	no	—
192	#2183	—	17	2	no	—
193	#2168	—	17	2	no	—
194	#2168	—	17	2	no	—
195	D₄×C₁₆	—	17	2	no	—
196	#2163	—	17	1	no	—
197	#2163	—	17	1	no	—
198	#2162	—	17	1	no	—
199	#2150	—	17	1	no	—
200	C₂×C₄⋊C₁₆	—	17	1	no	—
201	C₂×C₄⋊C₁₆	—	17	1	no	—
202	C₂²×C₁₇	—	2	1	no	—
203	C₂²×C₁₇	—	2	1	no	—
204	C₂²×C₁₇	C₂×M₃₂	1	2	yes	—
205	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
206	C₂×D₁₇	—	2	1	no	—
207	C₂×D₁₇	—	2	1	no	—
208	C₂×D₁₇	—	2	1	no	—
209	C₂×D₁₇	—	2	1	no	—
210	C₂×D₁₇	—	2	1	no	—
211	C₂×D₁₇	C₂×M₃₂	1	2	yes	—
212	C₄×C₁₇	—	2	1	no	—
213	C₄×C₁₇	—	2	1	no	—
214	C₄×C₁₇	—	2	1	no	—
215	C₄×C₁₇	—	2	1	no	—
216	C₄×C₁₇	#504	1	2	yes	—
217	C₄×C₁₇	#520	1	1	yes	characteristic
218	C₄×C₁₇	#568	1	1	yes	characteristic
219	Dic₁₇	—	2	1	no	—
220	Dic₁₇	—	2	1	no	—
221	Dic₁₇	—	2	1	no	—
222	Dic₁₇	—	2	1	no	—
223	Dic₁₇	—	2	1	no	—
224	Dic₁₇	C₂×M₃₂	1	2	yes	—
225	C₄×#41	—	17	1	no	—
226	C₂×M₃₂	—	17	2	no	—
227	C₂²×C₁₆	—	17	2	no	—
228	C₂²×C₁₆	—	17	2	no	—
229	C₈×Q₈	—	17	1	no	—
230	C₈×Q₈	—	17	1	no	—
231	C₈×D₄	—	17	1	no	—
232	C₈×D₄	—	17	1	no	—
233	C₈×D₄	—	17	1	no	—
234	C₈×D₄	—	17	1	no	—
235	C₈×D₄	—	17	1	no	—
236	C₈×D₄	—	17	1	no	—
237	#431	—	17	1	no	—
238	#431	—	17	1	no	—
239	#431	#595	1	1	yes	characteristic
240	C₂×C₄×C₈	—	17	1	no	—
241	C₂×C₄×C₈	—	17	1	no	—
242	C₂×C₄×C₈	—	17	1	no	—
243	C₄⋊C₁₆	—	17	1	no	—
244	C₄⋊C₁₆	—	17	1	no	—
245	C₄⋊C₁₆	—	17	1	no	—
246	C₄⋊C₁₆	—	17	2	no	—
247	C₄⋊C₁₆	—	17	1	no	—
248	C₄⋊C₁₆	—	17	2	no	—
249	C₄⋊C₁₆	—	17	2	no	—
250	C₂²⋊C₁₆	—	17	2	no	—
251	C₂²⋊C₁₆	—	17	2	no	—
252	C₂²⋊C₁₆	—	17	2	no	—
253	#346	—	17	2	no	—
254	#346	—	17	2	no	—
255	C₄×C₁₆	—	17	2	no	—
256	C₂×C₁₇	—	2	2	no	—
257	C₂×C₁₇	#2988	1	1	yes	characteristic
258	C₂×C₁₇	C₂²×M₃₂	1	1	yes	characteristic
259	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
260	D₁₇	—	2	2	no	—
261	D₁₇	—	4	1	no	—
262	C₂×#41	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	1	no	—
265	C₂²×C₈	—	17	1	no	—
266	C₂²×C₈	—	17	1	no	—
267	C₂²×C₈	—	17	1	no	—
268	C₂²×C₈	—	17	1	no	—
269	C₄×Q₈	—	17	1	no	—
270	C₄×Q₈	—	17	1	no	—
271	C₄×D₄	—	17	1	no	—
272	C₄×D₄	—	17	1	no	—
273	C₄×D₄	—	17	1	no	—
274	C₄×D₄	—	17	1	no	—
275	C₄×D₄	—	17	1	no	—
276	C₄×D₄	—	17	1	no	—
277	#117	—	17	1	no	—
278	#117	—	17	1	no	—
279	#117	—	17	1	no	—
280	C₂×C₄²	—	17	1	no	—
281	C₂×C₄²	—	17	1	no	—
282	C₂×C₄²	C₂×#595	1	1	yes	characteristic
283	M₃₂	—	68	2	no	—
284	C₂×C₁₆	—	17	2	no	—
285	C₂×C₁₆	—	17	2	no	—
286	C₂×C₁₆	—	17	2	no	—
287	C₂×C₁₆	—	17	2	no	—
288	C₂×C₁₆	—	68	2	no	—
289	C₂×C₁₆	—	68	2	no	—
290	C₄⋊C₈	—	17	1	no	—
291	C₄⋊C₈	—	17	1	no	—
292	C₄⋊C₈	—	17	1	no	—
293	C₄⋊C₈	—	17	1	no	—
294	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
295	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
296	C₂²⋊C₈	—	17	1	no	—
297	C₂²⋊C₈	—	17	1	no	—
298	C₂²⋊C₈	—	17	1	no	—
299	C₂²⋊C₈	—	17	1	no	—
300	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
301	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
302	C₄×C₈	—	17	1	no	—
303	C₄×C₈	—	17	1	no	—
304	C₄×C₈	—	17	1	no	—
305	C₄×C₈	—	17	1	no	—
306	C₄×C₈	—	17	1	no	—
307	C₄×C₈	—	17	1	no	—
308	C₄×C₈	—	17	1	no	—
309	C₄×C₈	—	17	1	no	—
310	C₄×C₈	C₂×#595	1	1	yes	characteristic
311	C₄×C₈	C₂×#595	1	1	yes	characteristic
312	C₁₇	#33504	1	1	yes	characteristic, complemented, Sylow
313	#41	—	34	4	no	—
314	C₂×Q₈	—	17	1	no	—
315	C₂×D₄	—	17	1	no	—
316	C₂×D₄	—	17	1	no	—
317	C₂×D₄	—	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	#63242	1	1	yes	characteristic
325	C₂²×C₄	#63242	1	1	yes	characteristic
326	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
327	C₂×C₈	—	17	1	no	—
328	C₂×C₈	—	17	1	no	—
329	C₂×C₈	—	17	1	no	—
330	C₂×C₈	—	17	1	no	—
331	C₂×C₈	—	34	1	no	—
332	C₂×C₈	—	34	1	no	—
333	C₂×C₈	—	34	1	no	—
334	C₂×C₈	—	34	1	no	—
335	C₂×C₈	—	34	1	no	—
336	C₂×C₈	—	34	1	no	—
337	C₂×C₈	—	68	1	no	—
338	C₂×C₈	—	68	1	no	—
339	C₂×C₈	—	68	1	no	—
340	C₂×C₈	C₂²×#595	1	1	yes	characteristic
341	C₂×C₈	C₂²×#595	1	1	yes	characteristic
342	C₂×C₈	C₂²×#595	1	1	yes	characteristic
343	C₂×C₈	C₂²×#595	1	1	yes	characteristic
344	C₄⋊C₄	—	17	1	no	—
345	C₄⋊C₄	—	17	1	no	—
346	C₄⋊C₄	—	17	1	no	—
347	C₄⋊C₄	—	17	1	no	—
348	C₄⋊C₄	—	17	1	no	—
349	C₄⋊C₄	—	17	1	no	—
350	C₂²⋊C₄	—	17	1	no	—
351	C₂²⋊C₄	—	17	1	no	—
352	C₂²⋊C₄	—	17	1	no	—
353	C₂²⋊C₄	—	17	1	no	—
354	C₂²⋊C₄	—	17	1	no	—
355	C₂²⋊C₄	—	17	1	no	—
356	C₄²	—	17	1	no	—
357	C₄²	—	17	1	no	—
358	C₄²	—	17	1	no	—
359	C₄²	—	17	1	no	—
360	C₄²	—	17	1	no	—
361	C₄²	—	17	1	no	—
362	C₄²	#63242	1	1	yes	characteristic
363	C₄²	#63242	1	1	yes	characteristic
364	C₄²	C₂²×#595	1	1	yes	characteristic
365	C₄²	C₂²×#595	1	1	yes	characteristic
366	C₁₆	—	34	2	no	—
367	C₁₆	—	34	2	no	—
368	C₁₆	—	34	2	no	—
369	C₁₆	—	34	2	no	—
370	C₂³	—	17	1	no	—
371	C₂³	—	17	1	no	—
372	C₂³	C₂×#63242	1	1	yes	characteristic
373	Q₈	—	34	2	no	—
374	D₄	—	17	4	no	—
375	D₄	—	34	2	no	—
376	D₄	—	34	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	17	1	no	—
382	C₂×C₄	—	17	1	no	—
383	C₂×C₄	—	17	1	no	—
384	C₂×C₄	—	17	1	no	—
385	C₂×C₄	—	17	1	no	—
386	C₂×C₄	—	17	1	no	—
387	C₂×C₄	—	34	2	no	—
388	C₂×C₄	—	34	2	no	—
389	C₂×C₄	—	34	2	no	—
390	C₂×C₄	—	34	2	no	—
391	C₂×C₄	—	34	1	no	—
392	C₂×C₄	—	34	1	no	—
393	C₂×C₄	—	34	1	no	—
394	C₂×C₄	—	34	1	no	—
395	C₂×C₄	C₂×#63242	1	1	yes	characteristic
396	C₂×C₄	C₂×#63242	1	1	yes	characteristic
397	C₂×C₄	C₂×#63242	1	1	yes	characteristic
398	C₂×C₄	C₂×#63242	1	1	yes	characteristic
399	C₂×C₄	C₂×#63242	1	1	yes	characteristic
400	C₂×C₄	C₂³×#595	1	1	yes	characteristic
401	C₈	—	2	1	no	—
402	C₈	—	2	1	no	—
403	C₈	—	2	1	no	—
404	C₈	—	2	1	no	—
405	C₈	—	17	1	no	—
406	C₈	—	17	1	no	—
407	C₈	—	34	1	no	—
408	C₈	—	34	1	no	—
409	C₈	—	34	1	no	—
410	C₂²	—	2	1	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	17	2	no	—
413	C₂²	—	34	1	no	—
414	C₂²	—	34	1	no	—
415	C₂²	—	34	1	no	—
416	C₂²	—	34	1	no	—
417	C₂²	—	34	1	no	—
418	C₂²	#11763865	1	2	yes	—
419	C₂²	C₂²×#63242	1	1	yes	characteristic
420	C₄	—	2	1	no	—
421	C₄	—	2	1	no	—
422	C₄	—	2	1	no	—
423	C₄	—	2	1	no	—
424	C₄	—	17	2	no	—
425	C₄	—	34	1	no	—
426	C₄	—	34	1	no	—
427	C₄	—	34	1	no	—
428	C₄	—	34	1	no	—
429	C₄	—	34	1	no	—
430	C₄	#11763868	1	2	yes	—
431	C₄	#11763878	1	1	yes	characteristic
432	C₄	#11763888	1	1	yes	characteristic
433	C₂	—	2	2	no	—
434	C₂	—	34	2	no	—
435	C₂	—	68	1	no	—
436	C₂	#14545701	1	1	yes	characteristic
437	C₂	C₂×#11763865	1	1	yes	characteristic
438	C₂	C₂×#11763868	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂³×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Fitting	C₁₇×#431	C₄
prime radical	C₂×#63252	C₈
cosocle	C₂×#3622	C₂⁴
hypercenter	#431	#595
hypocenter	C₁₇	#33504
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂×C₄ ◁ #431

Complements

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

N	H ≅ G/N	type
1. #14545201	C₂	semidirect
2. #14545167	C₂	semidirect
3. #14545166	C₂	semidirect
4. #14545162	C₂	semidirect
5. #14545148	C₂	semidirect
6. #14545145	C₂	semidirect
7. #14545144	C₂	semidirect
8. #14545117	C₂	semidirect
9. #14545114	C₂	semidirect
10. C₂×C₄⋊#63216	C₂	semidirect
165. C₂²⋊D₁₇	M₃₂	semidirect
312. C₁₇	#33504	semidirect

Maximal subgroups

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

subgroup	index
#14545201	2
#14545167	2
#14545166	2
#14545162	2
#14545148	2
#14545145	2
#14545144	2
#14545117	2
#14545114	2
C₂×C₄⋊#63216	2
#14537740	2
#33504	17