Subgroups — #26112430

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689329	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20244349	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243389	C₂	1	1	yes	maximal, characteristic
5	C₂×#15688870	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1277	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625325	—	2	1	no	—
9	C₂²×C₈×D₄₇	—	2	1	no	—
10	C₂×#13094024	C₂²	1	1	yes	characteristic
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	#15689329	—	2	2	no	—
13	#15689329	C₄	1	4	yes	complemented
14	C₈×D₁₈₈	—	2	2	no	—
15	C₈×D₁₈₈	—	2	2	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×#13093949	—	2	1	no	—
18	C₂×#13093946	—	2	1	no	—
19	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
20	#15688993	C₂²	1	1	yes	characteristic
21	#15688886	—	2	1	no	—
22	#15688886	—	2	1	no	—
23	#15688886	—	2	1	no	—
24	#15688870	—	2	2	no	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×Dic₉₄	—	2	1	no	—
29	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	—	2	1	no	—
31	C₂×#10625325	—	2	4	no	—
32	C₂×#10625325	—	4	2	no	—
33	C₂×#10625325	—	4	2	no	—
34	C₂²×C₄₇⋊C₈	—	2	1	no	—
35	C₂×C₈×D₄₇	—	2	4	no	—
36	C₂×C₈×D₄₇	—	4	2	no	—
37	C₂×C₈×D₄₇	—	4	2	no	—
38	#13094024	—	2	1	no	—
39	#13094024	—	2	1	no	—
40	#13094024	—	2	1	no	—
41	#13094024	C₂×C₄	1	2	yes	—
42	C₄×D₁₈₈	—	2	1	no	—
43	C₄×D₁₈₈	—	2	1	no	—
44	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
45	C₄×D₁₈₈	D₄	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	—	2	1	no	—
47	C₂×C₄⋊Dic₄₇	—	2	1	no	—
48	C₂×C₄⋊Dic₄₇	—	2	1	no	—
49	C₂×C₄⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄⋊Dic₄₇	—	2	1	no	—
51	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
52	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
55	#13093949	—	2	4	no	—
56	#13093946	—	4	2	no	—
57	(C₂×D₄₇)⋊C₈	—	2	4	no	—
58	C₂²×C₈×C₄₇	—	2	1	no	—
59	C₂²×C₈×C₄₇	—	2	1	no	—
60	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄⋊C₈×C₄₇	—	2	1	no	—
66	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
67	C₄×C₈×C₄₇	—	2	1	no	—
68	C₄×C₈×C₄₇	—	2	1	no	—
69	C₂³×D₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
73	C₂²×Dic₄₇	—	2	1	no	—
74	C₂²×Dic₄₇	—	4	1	no	—
75	C₂²×Dic₄₇	—	4	1	no	—
76	C₂×D₁₈₈	—	2	1	no	—
77	C₂×D₁₈₈	—	2	1	no	—
78	C₂×D₁₈₈	—	2	1	no	—
79	C₂×D₁₈₈	C₂²⋊C₄	1	2	yes	—
80	C₂×D₁₈₈	D₈	1	2	yes	—
81	C₂×D₁₈₈	SD₁₆	1	2	yes	—
82	C₂×C₄×D₄₇	—	2	2	no	—
83	C₂×C₄×D₄₇	—	2	2	no	—
84	C₂×C₄×D₄₇	—	4	1	no	—
85	C₂×C₄×D₄₇	—	4	1	no	—
86	C₂×C₄×D₄₇	—	4	1	no	—
87	C₂×C₄×D₄₇	—	4	1	no	—
88	C₂×Dic₉₄	—	2	2	no	—
89	C₂×Dic₉₄	—	4	1	no	—
90	C₂×Dic₉₄	—	4	1	no	—
91	C₂×Dic₉₄	—	4	1	no	—
92	C₂×Dic₉₄	—	4	1	no	—
93	C₂×Dic₉₄	—	4	1	no	—
94	C₂×C₈×C₄₇	—	2	1	no	—
95	C₂×C₈×C₄₇	—	2	1	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	4	1	no	—
101	C₂×C₈×C₄₇	—	4	1	no	—
102	C₂×C₈×C₄₇	—	4	1	no	—
103	C₂×C₈×C₄₇	—	4	1	no	—
104	C₂×C₈×C₄₇	—	4	1	no	—
105	C₂×C₈×C₄₇	SD₁₆	1	2	yes	complemented
106	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₇	#41	1	1	yes	characteristic
110	(C₂×D₄₇)⋊C₄	—	2	2	no	—
111	(C₂×D₄₇)⋊C₄	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	1	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	2	no	—
115	C₄⋊Dic₄₇	—	4	1	no	—
116	C₄⋊Dic₄₇	—	4	1	no	—
117	C₄⋊Dic₄₇	—	4	1	no	—
118	C₄⋊Dic₄₇	—	4	1	no	—
119	C₄⋊Dic₄₇	—	4	1	no	—
120	C₄⋊Dic₄₇	—	4	1	no	—
121	C₄⋊Dic₄₇	—	8	1	no	—
122	C₄⋊Dic₄₇	C₂²⋊C₄	1	2	yes	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	4	1	no	—
125	C₂×C₄₇⋊C₈	—	4	1	no	—
126	#10625325	—	4	8	no	—
127	C₈×D₄₇	—	4	8	no	—
128	C₂³×C₄₇	#121	1	1	yes	characteristic
129	C₂²×D₄₇	—	2	2	no	—
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	—	2	2	no	—
132	C₂²×D₄₇	—	4	1	no	—
133	C₂²×D₄₇	—	4	1	no	—
134	C₂²×D₄₇	—	4	1	no	—
135	C₂²×D₄₇	—	4	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
150	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	4	1	no	—
154	C₂×Dic₄₇	—	4	1	no	—
155	C₂×Dic₄₇	—	4	2	no	—
156	C₂×Dic₄₇	—	8	1	no	—
157	C₂×Dic₄₇	—	8	1	no	—
158	C₂×Dic₄₇	—	8	1	no	—
159	C₂×Dic₄₇	—	8	1	no	—
160	C₂×Dic₄₇	—	8	1	no	—
161	D₁₈₈	—	2	2	no	—
162	D₁₈₈	—	2	2	no	—
163	D₁₈₈	—	2	2	no	—
164	D₁₈₈	#102	1	4	yes	—
165	C₄×D₄₇	—	4	2	no	—
166	C₄×D₄₇	—	4	2	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	Dic₉₄	—	4	2	no	—
170	Dic₉₄	—	4	2	no	—
171	Dic₉₄	—	8	1	no	—
172	Dic₉₄	—	8	1	no	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	—	4	1	no	—
176	C₈×C₄₇	—	8	1	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	#9217	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	#386	1	1	yes	characteristic
180	C₂²×C₄₇	#461	1	1	yes	characteristic
181	C₂²×C₄₇	#463	1	1	yes	characteristic
182	C₂²×C₄₇	#465	1	1	yes	characteristic
183	C₂²×C₄₇	#466	1	1	yes	characteristic
184	C₂²×C₄₇	#471	1	1	yes	characteristic
185	C₂²×C₄₇	#473	1	1	yes	characteristic
186	C₂×D₄₇	—	2	4	no	—
187	C₂×D₄₇	—	4	2	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₂×D₄₇	—	4	2	no	—
192	C₂×D₄₇	—	4	2	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
196	C₄×C₄₇	#416	1	1	yes	characteristic
197	C₄×C₄₇	C₄×SD₁₆	1	1	yes	characteristic
198	C₄×C₄₇	#440	1	1	yes	characteristic
199	C₄×C₄₇	#450	1	1	yes	characteristic
200	C₄×C₄₇	#452	1	1	yes	characteristic
201	C₄×C₄₇	#465	1	1	yes	characteristic
202	C₄×C₄₇	#466	1	1	yes	characteristic
203	Dic₄₇	—	4	2	no	—
204	Dic₄₇	—	8	2	no	—
205	Dic₄₇	—	16	1	no	—
206	C₂×#461	—	47	1	no	—
207	C₂×C₈×D₄	—	47	1	no	—
208	#1990	—	47	1	no	—
209	#1802	—	47	1	no	—
210	C₂×#332	—	47	1	no	—
211	#1296	—	47	1	no	—
212	#1277	D₄₇	1	1	yes	characteristic, complemented
213	C₂×C₄₇	#1671	1	1	yes	characteristic
214	C₂×C₄₇	#1673	1	1	yes	characteristic
215	C₂×C₄₇	#1679	1	1	yes	characteristic
216	C₂×C₄₇	#1681	1	1	yes	characteristic
217	C₂×C₄₇	#1877	1	1	yes	characteristic
218	C₂×C₄₇	#1893	1	1	yes	characteristic
219	C₂×C₄₇	#1908	1	1	yes	characteristic
220	D₄₇	—	4	4	no	—
221	C₂²×SD₁₆	—	94	1	no	—
222	C₂³×C₈	—	94	1	no	—
223	C₂×C₄⋊Q₈	—	47	1	no	—
224	C₂×C₄×D₄	—	47	1	no	—
225	#461	—	47	4	no	—
226	#461	—	94	2	no	—
227	C₈×D₄	—	94	2	no	—
228	C₈×D₄	—	94	2	no	—
229	C₂×C₄⋊C₈	—	47	1	no	—
230	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×#103	—	94	1	no	—
233	C₂×#102	—	94	1	no	—
234	C₂×C₂²⋊C₈	—	94	1	no	—
235	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
236	#384	—	47	1	no	—
237	#340	—	94	1	no	—
238	#340	—	94	1	no	—
239	#340	—	94	1	no	—
240	#332	—	94	2	no	—
241	C₄₇	#9217	1	1	yes	characteristic, complemented, Sylow
242	C₂²×Q₈	—	94	1	no	—
243	C₂²×D₄	—	47	1	no	—
244	C₂³×C₄	—	94	1	no	—
245	C₂×SD₁₆	—	94	4	no	—
246	C₂×SD₁₆	—	188	2	no	—
247	C₂×SD₁₆	—	188	2	no	—
248	C₂²×C₈	—	2	1	no	—
249	C₂²×C₈	—	2	1	no	—
250	C₂²×C₈	—	94	4	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₂²×C₈	—	188	2	no	—
253	C₂²×C₈	—	188	2	no	—
254	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
255	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
256	C₄⋊Q₈	—	47	2	no	—
257	C₄⋊Q₈	—	94	1	no	—
258	C₄⋊Q₈	—	94	1	no	—
259	C₄⋊Q₈	—	94	1	no	—
260	C₄×D₄	—	47	2	no	—
261	C₄×D₄	—	47	2	no	—
262	C₄×D₄	—	94	1	no	—
263	C₄×D₄	—	94	1	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	94	1	no	—
266	C₂×C₄⋊C₄	—	94	1	no	—
267	C₂×C₄⋊C₄	—	94	1	no	—
268	C₂×C₄⋊C₄	—	94	1	no	—
269	C₂×C₄⋊C₄	—	94	1	no	—
270	C₂×C₂²⋊C₄	—	94	1	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
278	#103	—	94	4	no	—
279	#102	—	188	2	no	—
280	C₂²⋊C₈	—	94	4	no	—
281	C₄×C₈	—	2	1	no	—
282	C₄×C₈	—	2	1	no	—
283	C₂⁴	—	94	1	no	—
284	C₂×Q₈	—	94	2	no	—
285	C₂×Q₈	—	188	1	no	—
286	C₂×Q₈	—	188	1	no	—
287	C₂×Q₈	—	188	1	no	—
288	C₂×Q₈	—	188	1	no	—
289	C₂×Q₈	—	188	1	no	—
290	C₂×D₄	—	47	2	no	—
291	C₂×D₄	—	47	2	no	—
292	C₂×D₄	—	47	2	no	—
293	C₂×D₄	—	94	1	no	—
294	C₂×D₄	—	94	1	no	—
295	C₂×D₄	—	94	1	no	—
296	C₂²×C₄	—	94	1	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	188	1	no	—
300	C₂²×C₄	—	188	1	no	—
301	C₂²×C₄	—	188	1	no	—
302	C₂²×C₄	—	188	1	no	—
303	C₂²×C₄	—	188	1	no	—
304	C₂²×C₄	—	188	1	no	—
305	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
306	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	#10625354	1	1	yes	characteristic
308	SD₁₆	—	188	8	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	—	4	1	no	—
318	C₂×C₈	—	4	1	no	—
319	C₂×C₈	—	4	1	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	188	8	no	—
322	C₂×C₈	—	188	1	no	—
323	C₂×C₈	—	188	1	no	—
324	C₂×C₈	#10625325	1	2	yes	complemented
325	C₄⋊C₄	—	47	2	no	—
326	C₄⋊C₄	—	94	1	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	376	1	no	—
330	C₄⋊C₄	—	188	1	no	—
331	C₄⋊C₄	—	188	1	no	—
332	C₄⋊C₄	—	188	1	no	—
333	C₄⋊C₄	—	188	1	no	—
334	C₄⋊C₄	—	188	1	no	—
335	C₄⋊C₄	—	188	1	no	—
336	C₂²⋊C₄	—	94	2	no	—
337	C₂²⋊C₄	—	94	2	no	—
338	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
339	C₄²	#10625350	1	1	yes	characteristic
340	C₄²	D₄×D₄₇	1	1	yes	characteristic
341	C₄²	D₄×D₄₇	1	1	yes	characteristic
342	C₂³	—	94	2	no	—
343	C₂³	—	94	2	no	—
344	C₂³	—	94	2	no	—
345	C₂³	—	188	1	no	—
346	C₂³	—	188	1	no	—
347	C₂³	—	188	1	no	—
348	C₂³	—	188	1	no	—
349	C₂³	#13093999	1	1	yes	characteristic
350	Q₈	—	376	1	no	—
351	Q₈	—	376	1	no	—
352	Q₈	—	188	2	no	—
353	Q₈	—	188	2	no	—
354	D₄	—	47	4	no	—
355	D₄	—	94	2	no	—
356	D₄	—	94	2	no	—
357	D₄	—	94	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	376	1	no	—
362	C₂×C₄	—	376	1	no	—
363	C₂×C₄	—	376	1	no	—
364	C₂×C₄	—	376	1	no	—
365	C₂×C₄	—	376	1	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	1	no	—
368	C₂×C₄	—	188	1	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
374	C₂×C₄	#13093986	1	1	yes	characteristic
375	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
376	C₂×C₄	#13093994	1	1	yes	characteristic
377	C₂×C₄	#13093997	1	1	yes	characteristic
378	C₂×C₄	#13094009	1	1	yes	characteristic
379	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
380	C₂×C₄	SD₁₆×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625325	1	1	yes	characteristic
382	C₂×C₄	#13094045	1	1	yes	characteristic
383	C₂×C₄	#13094046	1	1	yes	characteristic
384	C₂×C₄	#13094047	1	1	yes	characteristic
385	C₂×C₄	#13094052	1	1	yes	characteristic
386	C₂×C₄	#13094057	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	4	1	no	—
389	C₈	—	4	2	no	—
390	C₈	—	8	1	no	—
391	C₈	—	188	2	no	—
392	C₂²	—	94	4	no	—
393	C₂²	—	188	2	no	—
394	C₂²	—	188	2	no	—
395	C₂²	—	188	2	no	—
396	C₂²	—	188	2	no	—
397	C₂²	—	188	2	no	—
398	C₂²	—	188	2	no	—
399	C₂²	#15689001	1	1	yes	characteristic
400	C₂²	#15689329	1	1	yes	characteristic
401	C₂²	#15689339	1	1	yes	characteristic
402	C₂²	#15689353	1	1	yes	characteristic
403	C₂²	#15689360	1	1	yes	characteristic
404	C₂²	#15689387	1	1	yes	characteristic
405	C₂²	#15689399	1	1	yes	characteristic
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	376	2	no	—
409	C₄	—	188	2	no	—
410	C₄	—	752	1	no	—
411	C₄	#102×D₄₇	1	1	yes	characteristic
412	C₄	#15689118	1	1	yes	characteristic
413	C₄	C₄×#10625325	1	1	yes	characteristic
414	C₄	#15689225	1	1	yes	characteristic
415	C₄	#15689276	1	1	yes	characteristic
416	C₄	#15689287	1	1	yes	characteristic
417	C₄	#15689355	1	1	yes	characteristic
418	C₄	#15689358	1	1	yes	characteristic
419	C₂	—	188	4	no	—
420	C₂	#20242764	1	1	yes	characteristic
421	C₂	#20242778	1	1	yes	characteristic
422	C₂	#20242812	1	1	yes	characteristic
423	C₂	#20242826	1	1	yes	characteristic
424	C₂	#20243721	1	1	yes	characteristic
425	C₂	#20243815	1	1	yes	characteristic
426	C₂	#20243902	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093999
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1277	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂²×D₁₈₈	D₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1277	D₄₇
hypocenter	C₄₇	#9217
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1277

Complements

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

N	H ≅ G/N	type
3. #20244349	C₂	semidirect
5. C₂×#15688870	C₂	semidirect
6. #20241272	C₂	semidirect
7. C₄₇×#1277	C₂	semidirect
13. #15689329	C₄	semidirect
105. C₂×C₈×C₄₇	SD₁₆	semidirect
212. #1277	D₄₇	semidirect
241. C₄₇	#9217	semidirect
324. C₂×C₈	#10625325	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689329	2
C₂×C₈×D₁₈₈	2
#20244349	2
#20243389	2
C₂×#15688870	2
#20241272	2
C₄₇×#1277	2
#9217	47