Subgroups — #26268156

Order 12032.

770 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689405	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic
3	#20248761	C₂	1	1	yes	maximal, characteristic
4	#20248377	C₂	1	1	yes	maximal, characteristic
5	#20244891	C₂	1	2	yes	maximal
6	#20244770	C₂	1	2	yes	maximal
7	#20244149	C₂	1	1	yes	maximal, characteristic
8	#20244115	C₂	1	2	yes	maximal
9	#20244062	C₂	1	2	yes	maximal
10	C₄×#13093949	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1990	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094022	—	2	1	no	—
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
15	#15689405	—	2	4	no	—
16	C₈×Dic₉₄	—	2	4	no	—
17	C₂×#13093955	C₂²	1	2	yes	—
18	C₂×#13093955	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×#13093949	C₂²	1	1	yes	characteristic
22	C₂×#13093949	C₂²	1	1	yes	characteristic
23	C₂×#13093947	C₂²	1	2	yes	—
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	#15689054	—	2	2	no	—
26	#15689053	—	2	2	no	—
27	#15689030	—	2	1	no	—
28	#15689028	—	2	1	no	—
29	#15689028	C₂²	1	2	yes	—
30	#15689022	—	2	1	no	—
31	#15689022	C₂²	1	2	yes	—
32	#15689019	C₂²	1	2	yes	—
33	#15689019	C₂²	1	2	yes	—
34	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688886	C₂²	1	1	yes	characteristic
36	#15688886	C₂²	1	1	yes	characteristic
37	#15688885	C₂²	1	2	yes	—
38	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#384	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₂²×Dic₉₄	D₄	1	1	yes	characteristic
44	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	#13094022	—	4	4	no	—
47	C₄×Dic₉₄	—	2	2	no	—
48	C₄×Dic₉₄	—	2	2	no	—
49	C₄×Dic₉₄	—	2	2	no	—
50	C₄×Dic₉₄	—	2	2	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	—	2	1	no	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	—	2	1	no	—
61	C₂×C₄×Dic₄₇	—	2	1	no	—
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	#13093955	—	2	4	no	—
64	#13093955	—	2	4	no	—
65	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
66	Dic₄₇⋊C₈	—	2	4	no	—
67	#13093949	—	2	2	no	—
68	#13093949	Q₈	1	4	yes	complemented
69	#13093947	—	2	4	no	—
70	C₈×Dic₄₇	—	2	4	no	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×Q₈×C₄₇	—	2	1	no	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊Q₈×C₄₇	—	2	2	no	—
81	C₄⋊Q₈×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	4	2	no	—
90	C₂×Q₈×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂²×Dic₄₇	—	2	1	no	—
98	C₂²×Dic₄₇	—	2	1	no	—
99	C₂²×Dic₄₇	—	2	1	no	—
100	C₂²×Dic₄₇	—	2	1	no	—
101	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
102	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
103	C₂×Dic₉₄	—	2	2	no	—
104	C₂×Dic₉₄	—	2	2	no	—
105	C₂×Dic₉₄	—	2	1	no	—
106	C₂×Dic₉₄	—	2	1	no	—
107	C₂×Dic₉₄	—	2	1	no	—
108	C₂×Dic₉₄	—	2	1	no	—
109	C₂×Dic₉₄	—	2	1	no	—
110	C₂×Dic₉₄	SD₁₆	1	4	yes	—
111	C₂×Dic₉₄	C₂×Q₈	1	2	yes	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
118	C₄⋊C₄×C₄₇	—	2	2	no	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	8	1	no	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	1	no	—
129	C₄⋊Dic₄₇	—	2	1	no	—
130	C₄⋊Dic₄₇	—	2	1	no	—
131	C₄⋊Dic₄₇	—	2	1	no	—
132	C₄⋊Dic₄₇	—	8	2	no	—
133	C₄⋊Dic₄₇	C₂×Q₈	1	2	yes	—
134	C₄⋊Dic₄₇	#41	1	2	yes	—
135	Dic₄₇⋊C₄	—	2	4	no	—
136	Dic₄₇⋊C₄	—	4	2	no	—
137	Dic₄₇⋊C₄	—	4	4	no	—
138	Dic₄₇⋊C₄	—	4	4	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	4	2	no	—
142	C₄×Dic₄₇	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	2	2	no	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	Q₈×C₄₇	—	8	4	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	#121	1	2	yes	—
157	C₂×C₄×C₄₇	#121	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
165	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	—	2	2	no	—
172	C₂×Dic₄₇	—	2	2	no	—
173	C₂×Dic₄₇	—	2	2	no	—
174	C₂×Dic₄₇	—	4	1	no	—
175	C₂×Dic₄₇	—	4	1	no	—
176	C₂×Dic₄₇	—	4	1	no	—
177	C₂×Dic₄₇	—	4	1	no	—
178	C₂×Dic₄₇	—	4	1	no	—
179	C₂×Dic₄₇	—	4	1	no	—
180	C₂×Dic₄₇	—	4	1	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	C₂×SD₁₆	1	4	yes	—
184	Dic₉₄	—	2	8	no	—
185	Dic₉₄	—	2	2	no	—
186	Dic₉₄	—	2	2	no	—
187	Dic₉₄	—	4	1	no	—
188	Dic₉₄	—	4	1	no	—
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₄₇⋊C₈	—	2	4	no	—
192	#25472	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
194	C₂²×C₄₇	#548	1	1	yes	characteristic
195	C₂²×C₄₇	D₄×Q₈	1	1	yes	characteristic
196	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
198	C₂²×C₄₇	#577	1	1	yes	characteristic
199	C₂²×C₄₇	#578	1	1	yes	characteristic
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	#465	1	4	yes	—
204	C₄×C₄₇	#533	1	1	yes	characteristic
205	C₄×C₄₇	#541	1	1	yes	characteristic
206	C₄×C₄₇	#547	1	1	yes	characteristic
207	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
208	Dic₄₇	—	2	4	no	—
209	Dic₄₇	—	4	2	no	—
210	Dic₄₇	—	4	2	no	—
211	Dic₄₇	—	4	2	no	—
212	Dic₄₇	—	4	2	no	—
213	Dic₄₇	—	8	1	no	—
214	C₂×#475	—	47	1	no	—
215	C₂×C₈×Q₈	—	47	1	no	—
216	#2582	—	47	1	no	—
217	#2546	—	47	1	no	—
218	#2088	—	47	2	no	—
219	#2066	—	47	2	no	—
220	#1990	D₄₇	1	1	yes	characteristic
221	#1948	—	47	1	no	—
222	#1941	—	47	2	no	—
223	#1933	—	47	2	no	—
224	C₄×#103	—	47	1	no	—
225	C₂×C₄₇	#2429	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#465	1	1	yes	characteristic
227	C₂×C₄₇	#3063	1	1	yes	characteristic
228	C₂×C₄₇	#3359	1	1	yes	characteristic
229	C₂×C₄₇	#3365	1	1	yes	characteristic
230	C₂×C₄₇	Q₈×SD₁₆	1	1	yes	characteristic
231	C₂×C₄₇	#3383	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	—	94	1	no	—
233	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₄×Q₈	—	47	1	no	—
235	C₂×C₄×Q₈	—	47	1	no	—
236	#475	—	94	4	no	—
237	C₈×Q₈	—	94	4	no	—
238	C₂×#106	—	47	2	no	—
239	C₂×#106	—	47	2	no	—
240	C₂×C₄⋊C₈	—	47	1	no	—
241	C₂×C₄⋊C₈	—	47	2	no	—
242	C₂×#103	—	47	1	no	—
243	C₂×#103	—	47	1	no	—
244	C₂×#103	—	47	2	no	—
245	C₂×C₄×C₈	—	47	2	no	—
246	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
247	#398	—	94	2	no	—
248	#398	—	94	2	no	—
249	#391	—	47	2	no	—
250	#391	—	94	1	no	—
251	#391	—	94	1	no	—
252	#389	—	47	2	no	—
253	#389	—	47	2	no	—
254	#389	—	47	2	no	—
255	#389	—	94	1	no	—
256	#384	C₂×D₄₇	1	1	yes	characteristic
257	C₄×C₄⋊C₄	—	47	1	no	—
258	#340	—	47	1	no	—
259	#340	—	47	1	no	—
260	#340	—	47	2	no	—
261	#340	C₂×D₄₇	1	2	yes	—
262	#340	C₂×D₄₇	1	2	yes	—
263	C₄₇	#25472	1	1	yes	characteristic, complemented, Sylow
264	C₂²×Q₈	—	2	1	no	—
265	C₂²×Q₈	—	47	1	no	—
266	C₂²×Q₈	—	47	1	no	—
267	C₂²×C₈	—	47	2	no	—
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₄⋊Q₈	—	2	2	no	—
271	C₄⋊Q₈	—	2	2	no	—
272	C₄⋊Q₈	—	188	4	no	—
273	C₄×Q₈	—	94	2	no	—
274	C₄×Q₈	—	94	2	no	—
275	C₄×Q₈	—	94	2	no	—
276	C₄×Q₈	—	94	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	1	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	47	1	no	—
281	C₂×C₄⋊C₄	—	47	1	no	—
282	C₂×C₄⋊C₄	—	47	2	no	—
283	C₂×C₄⋊C₄	—	47	1	no	—
284	C₂×C₄⋊C₄	—	47	1	no	—
285	C₂×C₄⋊C₄	—	94	2	no	—
286	C₂×C₄⋊C₄	—	94	2	no	—
287	C₂×C₄⋊C₄	—	94	2	no	—
288	C₂×C₄⋊C₄	—	94	1	no	—
289	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
290	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
291	C₂×C₄²	—	47	2	no	—
292	C₂×C₄²	—	94	1	no	—
293	C₂×C₄²	—	94	1	no	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	#106	—	94	4	no	—
296	#106	—	94	4	no	—
297	C₄⋊C₈	—	47	4	no	—
298	C₄⋊C₈	—	94	4	no	—
299	#103	—	47	4	no	—
300	#103	—	94	4	no	—
301	#103	—	94	2	no	—
302	C₄×C₈	—	2	2	no	—
303	C₄×C₈	—	94	4	no	—
304	#95	—	94	2	no	—
305	#95	—	94	2	no	—
306	#95	—	94	2	no	—
307	#95	—	94	2	no	—
308	#95	—	94	2	no	—
309	#95	—	94	1	no	—
310	C₂×Q₈	—	4	2	no	—
311	C₂×Q₈	—	4	2	no	—
312	C₂×Q₈	—	4	2	no	—
313	C₂×Q₈	—	47	4	no	—
314	C₂×Q₈	—	47	2	no	—
315	C₂×Q₈	—	94	2	no	—
316	C₂×Q₈	—	94	2	no	—
317	C₂×Q₈	—	94	1	no	—
318	C₂×Q₈	—	94	1	no	—
319	C₂×Q₈	—	94	1	no	—
320	C₂×Q₈	—	94	1	no	—
321	C₂×Q₈	—	94	1	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	47	2	no	—
325	C₂²×C₄	—	47	2	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	—	94	1	no	—
328	C₂²×C₄	—	94	1	no	—
329	C₂²×C₄	—	94	1	no	—
330	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
331	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	2	1	no	—
336	C₂×C₈	—	2	1	no	—
337	C₂×C₈	—	2	1	no	—
338	C₂×C₈	—	47	4	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	Q₈×D₄₇	1	2	yes	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	4	2	no	—
347	C₄⋊C₄	—	4	2	no	—
348	C₄⋊C₄	—	8	1	no	—
349	C₄⋊C₄	—	47	2	no	—
350	C₄⋊C₄	—	47	2	no	—
351	C₄⋊C₄	—	94	4	no	—
352	C₄⋊C₄	—	94	2	no	—
353	C₄⋊C₄	—	94	1	no	—
354	C₄⋊C₄	—	94	1	no	—
355	C₄⋊C₄	—	94	1	no	—
356	C₄⋊C₄	—	94	1	no	—
357	C₄⋊C₄	—	376	2	no	—
358	C₄⋊C₄	—	188	4	no	—
359	C₄⋊C₄	—	188	4	no	—
360	C₄⋊C₄	—	188	2	no	—
361	C₄²	—	94	2	no	—
362	C₄²	—	94	2	no	—
363	C₄²	—	188	2	no	—
364	C₄²	—	188	2	no	—
365	C₄²	#10625350	1	2	yes	—
366	C₄²	D₄×D₄₇	1	2	yes	—
367	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
368	Q₈	—	8	4	no	—
369	Q₈	—	94	8	no	—
370	Q₈	—	94	2	no	—
371	Q₈	—	94	2	no	—
372	Q₈	—	188	1	no	—
373	Q₈	—	188	1	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	47	4	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	94	2	no	—
387	C₂×C₄	—	94	2	no	—
388	C₂×C₄	—	94	2	no	—
389	C₂×C₄	—	94	2	no	—
390	C₂×C₄	—	94	2	no	—
391	C₂×C₄	—	188	1	no	—
392	C₂×C₄	—	188	1	no	—
393	C₂×C₄	—	188	1	no	—
394	C₂×C₄	—	188	1	no	—
395	C₂×C₄	—	188	1	no	—
396	C₂×C₄	—	188	1	no	—
397	C₂×C₄	—	188	1	no	—
398	C₂×C₄	—	188	1	no	—
399	C₂×C₄	—	188	1	no	—
400	C₂×C₄	#13093997	1	2	yes	—
401	C₂×C₄	#13093997	1	2	yes	—
402	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
403	C₂×C₄	#13094043	1	2	yes	—
404	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
406	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
407	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
408	C₂×C₄	#13094071	1	1	yes	characteristic
409	C₂×C₄	#13094072	1	1	yes	characteristic
410	C₈	—	2	2	no	—
411	C₈	—	4	1	no	—
412	C₈	—	94	4	no	—
413	C₂²	C₂×#13093997	1	1	yes	characteristic
414	C₂²	#15689781	1	1	yes	characteristic
415	C₂²	#15689788	1	1	yes	characteristic
416	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
417	C₂²	C₂×#13094043	1	1	yes	characteristic
418	C₂²	#15689929	1	1	yes	characteristic
419	C₂²	#15689936	1	1	yes	characteristic
420	C₄	—	2	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	—	94	4	no	—
424	C₄	—	376	1	no	—
425	C₄	—	188	2	no	—
426	C₄	—	188	2	no	—
427	C₄	—	188	2	no	—
428	C₄	—	188	2	no	—
429	C₄	#15689351	1	4	yes	—
430	C₄	#15689677	1	1	yes	characteristic
431	C₄	#15689731	1	1	yes	characteristic
432	C₄	#15689775	1	1	yes	characteristic
433	C₄	#15689786	1	1	yes	characteristic
434	C₂	#20246988	1	1	yes	characteristic
435	C₂	C₂×#15689351	1	1	yes	characteristic
436	C₂	#20253077	1	1	yes	characteristic
437	C₂	#20256027	1	1	yes	characteristic
438	C₂	#20256089	1	1	yes	characteristic
439	C₂	#20256245	1	1	yes	characteristic
440	C₂	#20256281	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator, cosocle	C₂²×C₄×C₄₇	C₂⁴
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1990	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
hypercenter	#1990	D₄₇
hypocenter	C₄₇	#25472
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1990

Complements

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

N	H ≅ G/N	type
68. #13093949	Q₈	semidirect
263. C₄₇	#25472	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689405	2
C₂×C₈×Dic₉₄	2
#20248761	2
#20248377	2
#20244891	2
#20244770	2
#20244149	2
#20244115	2
#20244062	2
C₄×#13093949	2
C₄₇×#1990	2
#25472	47