Subgroups — #26235194

Order 12032.

740 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689250	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689247	C₂	1	1	yes	maximal, characteristic
3	#20245865	C₂	1	1	yes	maximal, characteristic
4	#20244110	C₂	1	2	yes	maximal
5	#20244105	C₂	1	2	yes	maximal
6	#20244104	C₂	1	1	yes	maximal, characteristic
7	#20244104	C₂	1	1	yes	maximal, characteristic
8	#20243506	C₂	1	2	yes	maximal
9	#20243244	C₂	1	2	yes	maximal
10	C₄×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
13	#15689250	—	2	4	no	—
14	#15689247	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×#13093934	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	#15689029	C₄	1	1	yes	characteristic
26	#15689029	C₄	1	1	yes	characteristic
27	#15689021	C₄	1	1	yes	characteristic
28	#15689021	C₄	1	1	yes	characteristic
29	#15689007	C₄	1	2	yes	—
30	#15689007	C₄	1	2	yes	—
31	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
32	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688969	C₂²	1	2	yes	—
34	#15688878	C₂²	1	1	yes	characteristic
35	#15688878	C₂²	1	1	yes	characteristic
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄³×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₄×Dic₉₄	D₄	1	4	yes	—
49	C₄×Dic₉₄	Q₈	1	4	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
56	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	Dic₄₇⋊C₈	—	2	4	no	—
64	#13093934	—	2	4	no	—
65	C₄×C₄₇⋊C₈	—	2	2	no	—
66	C₄×C₄₇⋊C₈	—	2	2	no	—
67	C₈×Dic₄₇	—	2	4	no	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₄₇⋊#95	C₂×C₄	1	2	yes	—
73	C₄₇⋊#95	C₂×C₄	1	2	yes	—
74	C₄₇⋊#95	C₂×C₄	1	2	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₇	—	2	2	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
97	C₂×Dic₉₄	—	2	2	no	—
98	C₂×Dic₉₄	—	2	2	no	—
99	C₂×Dic₉₄	C₄⋊C₄	1	4	yes	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	1	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	4	1	no	—
114	C₄²×C₄₇	C₂×D₄	1	2	yes	—
115	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
119	Dic₄₇⋊C₄	—	2	4	no	—
120	Dic₄₇⋊C₄	—	4	2	no	—
121	Dic₄₇⋊C₄	C₄⋊C₄	1	8	yes	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
125	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	#41	1	2	yes	—
137	C₂×C₄₇⋊C₈	#41	1	2	yes	—
138	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
154	C₂×C₄×C₄₇	#131	1	2	yes	—
155	C₂×C₄×C₄₇	#131	1	2	yes	—
156	C₂×C₄×C₄₇	#131	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
162	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
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	C₂×C₄⋊C₄	1	4	yes	—
174	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
175	Dic₉₄	—	2	8	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	—	4	1	no	—
181	C₄₇⋊C₈	—	4	1	no	—
182	#22735	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
184	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
185	C₂²×C₄₇	#519	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
189	C₂²×C₄₇	#568	1	1	yes	characteristic
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	2	2	no	—
192	C₄×C₄₇	—	4	1	no	—
193	C₄×C₄₇	—	4	1	no	—
194	C₄×C₄₇	—	4	1	no	—
195	C₄×C₄₇	#424	1	4	yes	—
196	C₄×C₄₇	#548	1	1	yes	characteristic
197	C₄×C₄₇	#548	1	1	yes	characteristic
198	C₄×C₄₇	#557	1	1	yes	characteristic
199	C₄×C₄₇	#557	1	1	yes	characteristic
200	Dic₄₇	—	2	4	no	—
201	Dic₄₇	—	2	4	no	—
202	Dic₄₇	—	4	2	no	—
203	Dic₄₇	—	4	2	no	—
204	C₂×#446	—	47	1	no	—
205	C₂×C₈×Q₈	—	47	1	no	—
206	#2295	—	47	1	no	—
207	#1940	—	47	2	no	—
208	#1939	—	47	1	no	—
209	#1939	—	47	1	no	—
210	#1939	—	47	2	no	—
211	#1832	—	47	2	no	—
212	#1831	D₄₇	1	1	yes	characteristic
213	#1768	—	47	2	no	—
214	C₄×C₄⋊C₈	—	47	1	no	—
215	C₂×C₄₇	#2351	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
217	C₂×C₄₇	#2906	1	1	yes	characteristic
218	C₂×C₄₇	#2966	1	1	yes	characteristic
219	C₂×C₄₇	#2969	1	1	yes	characteristic
220	C₂×C₄₇	#2985	1	1	yes	characteristic
221	C₂×C₄₇	#2986	1	1	yes	characteristic
222	C₂×C₄×Q₈	—	47	1	no	—
223	#446	—	94	4	no	—
224	C₈×Q₈	—	94	4	no	—
225	C₂×C₄⋊C₈	—	47	2	no	—
226	C₂×C₄⋊C₈	—	47	2	no	—
227	C₂×C₄⋊C₈	—	47	2	no	—
228	C₂×C₄⋊C₈	—	47	2	no	—
229	C₂×C₄⋊C₈	—	47	1	no	—
230	C₂×C₄⋊C₈	—	47	1	no	—
231	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
232	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
233	C₂×#97	—	47	2	no	—
234	C₂×C₄×C₈	—	47	2	no	—
235	C₂×C₄×C₈	—	47	1	no	—
236	C₂×C₄×C₈	—	47	1	no	—
237	#391	—	47	1	no	—
238	#391	—	47	1	no	—
239	#389	—	47	1	no	—
240	#389	—	47	1	no	—
241	#387	—	47	2	no	—
242	#387	—	47	2	no	—
243	C₄×C₄⋊C₄	—	47	1	no	—
244	C₄×C₄⋊C₄	—	47	2	no	—
245	#376	—	47	2	no	—
246	C₄³	C₂×D₄₇	1	1	yes	characteristic
247	#336	—	47	2	no	—
248	#336	—	47	2	no	—
249	#336	—	47	1	no	—
250	#336	—	47	1	no	—
251	#336	C₂×D₄₇	1	2	yes	—
252	#336	C₂×D₄₇	1	2	yes	—
253	C₄₇	#22735	1	1	yes	characteristic, complemented, Sylow
254	C₂²×Q₈	—	47	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	47	1	no	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
260	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
261	C₄×Q₈	—	47	4	no	—
262	C₄×Q₈	—	47	4	no	—
263	C₂×C₄⋊C₄	—	47	2	no	—
264	C₂×C₄⋊C₄	—	47	1	no	—
265	C₂×C₄⋊C₄	—	47	2	no	—
266	C₂×C₄⋊C₄	—	47	1	no	—
267	C₂×C₄⋊C₄	—	47	1	no	—
268	C₂×C₄⋊C₄	—	47	2	no	—
269	C₂×C₄²	—	47	2	no	—
270	C₂×C₄²	—	47	2	no	—
271	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
272	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
273	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
274	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
277	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
278	C₄⋊C₈	—	2	2	no	—
279	C₄⋊C₈	—	2	2	no	—
280	C₄⋊C₈	—	94	2	no	—
281	C₄⋊C₈	—	94	2	no	—
282	C₄⋊C₈	—	94	4	no	—
283	C₄⋊C₈	—	94	4	no	—
284	C₄⋊C₈	—	94	4	no	—
285	C₄⋊C₈	—	94	4	no	—
286	#97	—	94	4	no	—
287	C₄×C₈	—	94	4	no	—
288	C₄×C₈	—	94	2	no	—
289	C₄×C₈	—	94	2	no	—
290	#95	—	47	2	no	—
291	#95	—	47	2	no	—
292	#95	—	47	2	no	—
293	#95	—	47	2	no	—
294	#95	—	47	2	no	—
295	#95	—	47	2	no	—
296	#95	—	47	2	no	—
297	C₂×Q₈	—	47	4	no	—
298	C₂×Q₈	—	94	2	no	—
299	C₂×Q₈	—	94	2	no	—
300	C₂²×C₄	—	47	2	no	—
301	C₂²×C₄	—	47	2	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	2	no	—
304	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	47	2	no	—
318	C₂×C₈	—	47	2	no	—
319	C₂×C₈	—	94	1	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	1	no	—
326	C₂×C₈	—	94	1	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	94	1	no	—
329	C₄⋊C₄	—	47	8	no	—
330	C₄⋊C₄	—	47	4	no	—
331	C₄⋊C₄	—	94	2	no	—
332	C₄⋊C₄	—	94	4	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	—	188	2	no	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	2	no	—
338	C₄²	—	2	1	no	—
339	C₄²	—	2	1	no	—
340	C₄²	—	2	1	no	—
341	C₄²	—	2	1	no	—
342	C₄²	—	4	1	no	—
343	C₄²	—	47	4	no	—
344	C₄²	—	47	4	no	—
345	C₄²	—	94	2	no	—
346	C₄²	—	94	2	no	—
347	C₄²	D₄×D₄₇	1	2	yes	—
348	C₄²	Q₈×D₄₇	1	2	yes	—
349	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	Q₈	—	94	8	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	47	4	no	—
365	C₂×C₄	—	47	4	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	—	94	2	no	—
372	C₂×C₄	—	94	2	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
377	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
378	C₂×C₄	#13094030	1	2	yes	—
379	C₂×C₄	#13094032	1	2	yes	—
380	C₂×C₄	#13094032	1	2	yes	—
381	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
383	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
384	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
385	C₂×C₄	#13094071	1	1	yes	characteristic
386	C₂×C₄	#13094071	1	1	yes	characteristic
387	C₈	—	4	2	no	—
388	C₈	—	4	2	no	—
389	C₈	—	94	2	no	—
390	C₈	—	94	2	no	—
391	C₈	—	188	1	no	—
392	C₈	—	188	1	no	—
393	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
394	C₂²	#15689591	1	1	yes	characteristic
395	C₂²	#15689600	1	1	yes	characteristic
396	C₂²	C₂×#13094030	1	1	yes	characteristic
397	C₂²	C₂×#13094032	1	1	yes	characteristic
398	C₂²	C₂×#13094032	1	1	yes	characteristic
399	C₂²	#15689889	1	1	yes	characteristic
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	4	1	no	—
403	C₄	—	4	1	no	—
404	C₄	—	4	1	no	—
405	C₄	—	94	4	no	—
406	C₄	—	94	4	no	—
407	C₄	—	188	2	no	—
408	C₄	—	188	2	no	—
409	C₄	#15689148	1	4	yes	—
410	C₄	#15689781	1	1	yes	characteristic
411	C₄	#15689781	1	1	yes	characteristic
412	C₄	#15689850	1	1	yes	characteristic
413	C₄	#15689850	1	1	yes	characteristic
414	C₂	#20246305	1	1	yes	characteristic
415	C₂	C₂×#15689148	1	1	yes	characteristic
416	C₂	#20251957	1	1	yes	characteristic
417	C₂	#20252357	1	1	yes	characteristic
418	C₂	#20252386	1	1	yes	characteristic
419	C₂	#20252485	1	1	yes	characteristic
420	C₂	#20252489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1831	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#22735
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
253. C₄₇	#22735	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689250	2
C₂×#15689247	2
#20245865	2
#20244110	2
#20244105	2
#20244104	2
#20243506	2
#20243244	2
C₄×C₄⋊(C₄₇⋊C₈)	2
C₄₇×#1831	2
#22735	47