Subgroups — #17978682

Order 4352.

558 conjugacy classes of subgroups.

The subgroup lattice has 432 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	#14545169	C₂	1	2	yes	maximal, complemented
3	#14545167	C₂	1	2	yes	maximal, complemented
4	#14545165	C₂	1	2	yes	maximal, complemented
5	#14545143	C₂	1	1	yes	maximal, characteristic, complemented
6	#14545143	C₂	1	1	yes	maximal, characteristic, complemented
7	#14545141	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#10587530	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#10587538	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#10587529	C₂	1	1	yes	maximal, characteristic, complemented
11	#14537740	C₂	1	1	yes	maximal, characteristic
12	C₂×#10587530	C₂²	1	2	yes	—
13	C₂×#10587538	C₂²	1	2	yes	—
14	C₂×#10587529	C₂²	1	2	yes	—
15	#11763730	C₂²	1	2	yes	—
16	#11763730	C₂²	1	2	yes	—
17	C₄⋊#63216	C₂²	1	2	yes	—
18	#11763704	C₂²	1	2	yes	—
19	#11763704	C₂²	1	2	yes	—
20	C₂²⋊#63216	C₂²	1	2	yes	—
21	#11763698	C₂²	1	2	yes	—
22	#11763697	C₂²	1	2	yes	—
23	#11763695	C₂²	1	2	yes	—
24	C₄×#63216	C₂²	1	1	yes	characteristic
25	C₄×#63216	C₂²	1	1	yes	characteristic
26	C₄×#63216	C₂²	1	1	yes	characteristic
27	C₄×#63216	C₂²	1	1	yes	characteristic
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	#10587538	—	2	4	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	—	2	4	no	—
70	#10587529	—	2	4	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	2	no	—
134	C₂×#3622	—	2	2	no	—
135	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
136	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
137	C₂×#3622	C₂²×C₄	1	1	yes	characteristic
138	C₂×#3622	C₂⁴	1	1	yes	characteristic
139	C₈×D₁₇	—	2	2	no	—
140	C₈×D₁₇	—	2	2	no	—
141	C₈×D₁₇	—	2	2	no	—
142	C₈×D₁₇	—	2	2	no	—
143	#63216	—	2	2	no	—
144	#63216	—	2	2	no	—
145	#63216	—	2	2	no	—
146	#63216	#41	1	4	yes	complemented
147	#33479	—	17	1	no	maximal, Sylow
148	C₂³×C₁₇	C₂²×C₈	1	1	yes	characteristic
149	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
150	C₂²×D₁₇	C₂²×C₈	1	1	yes	characteristic
151	C₂×C₄×C₁₇	—	2	1	no	—
152	C₂×C₄×C₁₇	—	2	1	no	—
153	C₂×C₄×C₁₇	—	2	2	no	—
154	C₂×C₄×C₁₇	—	2	2	no	—
155	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
156	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
157	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
158	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
159	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
160	C₂×C₄×C₁₇	C₂³×C₄	1	1	yes	characteristic
161	C₂²⋊D₁₇	—	2	2	no	—
162	C₂²⋊D₁₇	—	2	2	no	—
163	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
164	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
165	C₂×Dic₁₇	C₂²×C₈	1	1	yes	characteristic
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	D₆₈	—	2	2	no	—
170	C₄×D₁₇	—	2	1	no	—
171	C₄×D₁₇	—	2	1	no	—
172	C₄×D₁₇	—	2	1	no	—
173	C₄×D₁₇	—	2	1	no	—
174	C₄×D₁₇	—	2	2	no	—
175	C₄×D₁₇	—	2	2	no	—
176	C₄×D₁₇	—	2	2	no	—
177	C₄×D₁₇	M₃₂	1	4	yes	complemented
178	Dic₃₄	—	2	2	no	—
179	C₈×C₁₇	—	2	1	no	—
180	C₈×C₁₇	—	2	1	no	—
181	C₈×C₁₇	—	2	1	no	—
182	C₈×C₁₇	—	2	1	no	—
183	#3622	—	2	1	no	—
184	#3622	—	2	1	no	—
185	#3622	#131	1	2	yes	—
186	#3622	C₂×#41	1	2	yes	—
187	C₈×#41	—	17	1	no	—
188	#2183	—	17	2	no	—
189	#2169	—	17	2	no	—
190	#2168	—	17	2	no	—
191	#2168	—	17	2	no	—
192	#2162	—	17	1	no	—
193	#2162	—	17	1	no	—
194	#2162	—	17	1	no	—
195	C₄×M₃₂	—	17	1	no	—
196	C₄×M₃₂	—	17	1	no	—
197	C₂×C₄×C₁₆	—	17	1	no	—
198	C₂²×C₁₇	—	2	1	no	—
199	C₂²×C₁₇	—	2	1	no	—
200	C₂²×C₁₇	—	2	1	no	—
201	C₂²×C₁₇	C₂³×C₈	1	1	yes	characteristic
202	C₂×D₁₇	—	2	1	no	—
203	C₂×D₁₇	—	2	1	no	—
204	C₂×D₁₇	—	2	1	no	—
205	C₂×D₁₇	—	2	1	no	—
206	C₂×D₁₇	—	2	1	no	—
207	C₂×D₁₇	C₂×M₃₂	1	2	yes	—
208	C₄×C₁₇	—	2	1	no	—
209	C₄×C₁₇	—	2	1	no	—
210	C₄×C₁₇	—	2	1	no	—
211	C₄×C₁₇	C₂×M₃₂	1	2	yes	—
212	C₄×C₁₇	#504	1	2	yes	—
213	C₄×C₁₇	C₄×#41	1	1	yes	characteristic
214	C₄×C₁₇	C₂×#131	1	1	yes	characteristic
215	Dic₁₇	—	2	1	no	—
216	Dic₁₇	—	2	1	no	—
217	Dic₁₇	—	2	1	no	—
218	Dic₁₇	—	2	1	no	—
219	Dic₁₇	—	2	1	no	—
220	Dic₁₇	C₂×M₃₂	1	2	yes	—
221	C₄×#41	—	17	1	no	—
222	C₂×M₃₂	—	17	2	no	—
223	C₂×M₃₂	—	17	2	no	—
224	C₂²×C₁₆	—	17	2	no	—
225	C₈×Q₈	—	17	1	no	—
226	C₈×Q₈	—	17	1	no	—
227	C₈×D₄	—	17	1	no	—
228	C₈×D₄	—	17	1	no	—
229	C₈×D₄	—	17	1	no	—
230	C₈×D₄	—	17	1	no	—
231	C₈×D₄	—	17	1	no	—
232	C₈×D₄	—	17	1	no	—
233	#431	—	17	1	no	—
234	#431	—	17	1	no	—
235	#431	#595	1	1	yes	characteristic
236	C₂×C₄×C₈	—	17	1	no	—
237	C₂×C₄×C₈	—	17	1	no	—
238	C₂×C₄×C₈	—	17	1	no	—
239	C₄⋊C₁₆	—	17	2	no	—
240	C₄⋊C₁₆	—	17	2	no	—
241	C₄⋊C₁₆	—	17	2	no	—
242	C₂²⋊C₁₆	—	17	2	no	—
243	C₂²⋊C₁₆	—	17	2	no	—
244	C₂²⋊C₁₆	—	17	2	no	—
245	#346	—	17	2	no	—
246	#346	—	17	2	no	—
247	C₄×C₁₆	—	17	1	no	—
248	C₄×C₁₆	—	17	1	no	—
249	C₄×C₁₆	—	17	2	no	—
250	C₄×C₁₆	—	17	1	no	—
251	C₄×C₁₆	—	17	1	no	—
252	C₂×C₁₇	—	4	1	no	—
253	C₂×C₁₇	C₈×#41	1	1	yes	characteristic
254	C₂×C₁₇	C₂²×M₃₂	1	1	yes	characteristic
255	C₂×C₁₇	C₂×#504	1	1	yes	characteristic
256	D₁₇	—	2	2	no	—
257	D₁₇	—	4	1	no	—
258	C₂×#41	—	17	1	no	—
259	C₂²×C₈	—	17	1	no	—
260	C₂²×C₈	—	17	1	no	—
261	C₂²×C₈	—	17	1	no	—
262	C₂²×C₈	—	17	1	no	—
263	C₂²×C₈	—	17	1	no	—
264	C₂²×C₈	—	17	1	no	—
265	C₄×Q₈	—	17	1	no	—
266	C₄×Q₈	—	17	1	no	—
267	C₄×D₄	—	17	1	no	—
268	C₄×D₄	—	17	1	no	—
269	C₄×D₄	—	17	1	no	—
270	C₄×D₄	—	17	1	no	—
271	C₄×D₄	—	17	1	no	—
272	C₄×D₄	—	17	1	no	—
273	#117	—	17	1	no	—
274	#117	—	17	1	no	—
275	#117	—	17	1	no	—
276	C₂×C₄²	—	17	1	no	—
277	C₂×C₄²	—	17	1	no	—
278	C₂×C₄²	C₂×#595	1	1	yes	characteristic
279	M₃₂	—	34	4	no	—
280	M₃₂	—	34	4	no	—
281	C₂×C₁₆	—	17	2	no	—
282	C₂×C₁₆	—	17	2	no	—
283	C₂×C₁₆	—	17	2	no	—
284	C₂×C₁₆	—	17	2	no	—
285	C₂×C₁₆	—	34	4	no	—
286	C₄⋊C₈	—	17	1	no	—
287	C₄⋊C₈	—	17	1	no	—
288	C₄⋊C₈	—	17	1	no	—
289	C₄⋊C₈	—	17	1	no	—
290	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
291	C₄⋊C₈	C₂×#595	1	1	yes	characteristic
292	C₂²⋊C₈	—	17	1	no	—
293	C₂²⋊C₈	—	17	1	no	—
294	C₂²⋊C₈	—	17	1	no	—
295	C₂²⋊C₈	—	17	1	no	—
296	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
297	C₂²⋊C₈	C₂×#595	1	1	yes	characteristic
298	C₄×C₈	—	17	1	no	—
299	C₄×C₈	—	17	1	no	—
300	C₄×C₈	—	17	1	no	—
301	C₄×C₈	—	17	1	no	—
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	C₂×#595	1	1	yes	characteristic
307	C₄×C₈	C₂×#595	1	1	yes	characteristic
308	C₁₇	#33479	1	1	yes	characteristic, complemented, Sylow
309	#41	—	34	4	no	—
310	C₂×Q₈	—	17	1	no	—
311	C₂×D₄	—	17	1	no	—
312	C₂×D₄	—	17	1	no	—
313	C₂×D₄	—	17	1	no	—
314	C₂²×C₄	—	17	1	no	—
315	C₂²×C₄	—	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	#63242	1	1	yes	characteristic
321	C₂²×C₄	#63242	1	1	yes	characteristic
322	C₂²×C₄	C₂²×#595	1	1	yes	characteristic
323	C₂×C₈	—	17	1	no	—
324	C₂×C₈	—	17	1	no	—
325	C₂×C₈	—	17	1	no	—
326	C₂×C₈	—	17	1	no	—
327	C₂×C₈	—	34	2	no	—
328	C₂×C₈	—	34	2	no	—
329	C₂×C₈	—	34	2	no	—
330	C₂×C₈	—	34	2	no	—
331	C₂×C₈	—	34	2	no	—
332	C₂×C₈	—	34	2	no	—
333	C₂×C₈	C₂²×#595	1	1	yes	characteristic
334	C₂×C₈	C₂²×#595	1	1	yes	characteristic
335	C₂×C₈	C₂²×#595	1	1	yes	characteristic
336	C₂×C₈	C₂²×#595	1	1	yes	characteristic
337	C₄⋊C₄	—	17	1	no	—
338	C₄⋊C₄	—	17	1	no	—
339	C₄⋊C₄	—	17	1	no	—
340	C₄⋊C₄	—	17	1	no	—
341	C₄⋊C₄	—	17	1	no	—
342	C₄⋊C₄	—	17	1	no	—
343	C₂²⋊C₄	—	17	1	no	—
344	C₂²⋊C₄	—	17	1	no	—
345	C₂²⋊C₄	—	17	1	no	—
346	C₂²⋊C₄	—	17	1	no	—
347	C₂²⋊C₄	—	17	1	no	—
348	C₂²⋊C₄	—	17	1	no	—
349	C₄²	—	17	1	no	—
350	C₄²	—	17	1	no	—
351	C₄²	—	17	1	no	—
352	C₄²	—	17	1	no	—
353	C₄²	—	17	1	no	—
354	C₄²	—	17	1	no	—
355	C₄²	#63242	1	1	yes	characteristic
356	C₄²	#63242	1	1	yes	characteristic
357	C₄²	C₂²×#595	1	1	yes	characteristic
358	C₄²	C₂²×#595	1	1	yes	characteristic
359	C₁₆	—	17	4	no	—
360	C₁₆	—	34	2	no	—
361	C₁₆	—	34	2	no	—
362	C₁₆	—	34	2	no	—
363	C₂³	—	17	1	no	—
364	C₂³	—	17	1	no	—
365	C₂³	C₂×#63242	1	1	yes	characteristic
366	Q₈	—	34	2	no	—
367	D₄	—	34	2	no	—
368	D₄	—	34	2	no	—
369	D₄	—	34	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	2	2	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	17	1	no	—
375	C₂×C₄	—	17	4	no	—
376	C₂×C₄	—	17	1	no	—
377	C₂×C₄	—	17	1	no	—
378	C₂×C₄	—	17	1	no	—
379	C₂×C₄	—	17	1	no	—
380	C₂×C₄	—	17	1	no	—
381	C₂×C₄	—	34	2	no	—
382	C₂×C₄	—	34	2	no	—
383	C₂×C₄	—	34	2	no	—
384	C₂×C₄	—	34	1	no	—
385	C₂×C₄	—	34	1	no	—
386	C₂×C₄	—	34	1	no	—
387	C₂×C₄	—	34	1	no	—
388	C₂×C₄	C₂×#63242	1	1	yes	characteristic
389	C₂×C₄	C₂×#63242	1	1	yes	characteristic
390	C₂×C₄	C₂×#63242	1	1	yes	characteristic
391	C₂×C₄	C₂×#63242	1	1	yes	characteristic
392	C₂×C₄	C₂×#63242	1	1	yes	characteristic
393	C₂×C₄	C₂³×#595	1	1	yes	characteristic
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	17	2	no	—
399	C₈	—	17	2	no	—
400	C₈	—	34	1	no	—
401	C₈	—	34	1	no	—
402	C₂²	—	2	1	no	—
403	C₂²	—	2	1	no	—
404	C₂²	—	2	1	no	—
405	C₂²	—	17	2	no	—
406	C₂²	—	34	1	no	—
407	C₂²	—	34	1	no	—
408	C₂²	—	34	1	no	—
409	C₂²	—	34	1	no	—
410	C₂²	—	34	1	no	—
411	C₂²	C₂²×#63242	1	1	yes	characteristic
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	17	2	no	—
416	C₄	—	34	1	no	—
417	C₄	—	34	1	no	—
418	C₄	—	34	1	no	—
419	C₄	—	34	1	no	—
420	C₄	—	34	1	no	—
421	C₄	#11763865	1	2	yes	—
422	C₄	#11763868	1	2	yes	—
423	C₄	#41×#595	1	1	yes	characteristic
424	C₄	D₁₇⋊#131	1	1	yes	characteristic
425	C₂	—	4	1	no	—
426	C₂	—	34	2	no	—
427	C₂	—	68	1	no	—
428	C₂	#14545588	1	1	yes	characteristic
429	C₂	C₂×#11763865	1	1	yes	characteristic
430	C₂	C₂×#11763868	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	C₂²×#595
commutator, socle	C₂²×C₁₇	C₂³×C₈
Frattini	C₂×C₄	C₂³×#595
Fitting	C₁₇×#431	C₄
prime radical	C₂×#63252	C₈
cosocle	C₂×#3622	C₂⁴
hypercenter	#431	#595
hypocenter	C₁₇	#33479
LCS	G ▷ C₂²×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₄² ◁ #431

Complements

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

N	H ≅ G/N	type
1. #14545201	C₂	semidirect
2. #14545169	C₂	semidirect
3. #14545167	C₂	semidirect
4. #14545165	C₂	semidirect
5. #14545143	C₂	semidirect
6. #14545143	C₂	semidirect
7. #14545141	C₂	semidirect
8. C₄×#10587530	C₂	semidirect
9. C₄×#10587538	C₂	semidirect
10. C₄×#10587529	C₂	semidirect
146. #63216	#41	semidirect
177. C₄×D₁₇	M₃₂	semidirect
308. C₁₇	#33479	semidirect

Maximal subgroups

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

subgroup	index
#14545201	2
#14545169	2
#14545167	2
#14545165	2
#14545143	2
#14545141	2
C₄×#10587530	2
C₄×#10587538	2
C₄×#10587529	2
#14537740	2
#33479	17