Subgroups — #26122270

Order 12032.

926 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	C₂²×#13093935	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688885	C₂	1	2	yes	maximal
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×#13093935	—	2	4	no	—
9	C₂×#13093935	—	2	2	no	—
10	C₂×C₄₇⋊#95	—	2	1	no	—
11	C₂×C₄₇⋊#95	—	2	1	no	—
12	#15688885	—	2	4	no	—
13	#15688885	C₄	1	8	yes	complemented
14	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#389	—	2	2	no	—
19	C₄₇×#389	C₄	1	4	yes	complemented
20	C₂×#95×C₄₇	—	2	1	no	—
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
27	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
28	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
35	#13093935	—	2	8	no	—
36	C₄₇⋊#95	—	4	2	no	—
37	C₄₇⋊#95	—	4	2	no	—
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	—	2	1	no	—
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
49	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
50	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₄²×C₄₇	D₄	1	2	yes	—
57	#95×C₄₇	—	2	4	no	—
58	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
59	C₂²×C₄×C₄₇	—	2	2	no	—
60	C₂²×C₄×C₄₇	—	2	4	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	1	no	—
66	C₂²×C₄×C₄₇	—	2	1	no	—
67	C₂²×C₄×C₄₇	—	2	1	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	2	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	—	4	2	no	—
74	C₂²×C₄×C₄₇	—	4	2	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
84	C₂²×C₄×C₄₇	#41	1	2	yes	—
85	C₂²×C₄×C₄₇	#41	1	2	yes	—
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×Dic₄₇	—	2	4	no	—
88	C₂²×Dic₄₇	—	4	2	no	—
89	C₂²×Dic₄₇	—	4	2	no	—
90	C₂²×Dic₄₇	—	4	2	no	—
91	C₂²×Dic₄₇	—	4	2	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₄⋊C₄×C₄₇	—	2	2	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	2	4	no	—
97	C₄⋊C₄×C₄₇	—	4	8	no	—
98	C₄⋊C₄×C₄₇	—	4	1	no	—
99	C₄⋊C₄×C₄₇	—	4	1	no	—
100	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄⋊Dic₄₇	—	2	4	no	—
106	C₄⋊Dic₄₇	—	4	2	no	—
107	C₄⋊Dic₄₇	—	4	2	no	—
108	C₂×C₄₇⋊C₈	—	2	4	no	—
109	C₂×C₄₇⋊C₈	—	2	4	no	—
110	C₂×C₄₇⋊C₈	—	2	4	no	—
111	C₂×C₄₇⋊C₈	—	2	4	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	C₄⋊C₄	1	8	yes	complemented
115	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
116	C₂³×C₄₇	C₄×D₄	1	2	yes	—
117	C₂³×C₄₇	#121	1	2	yes	—
118	C₂³×C₄₇	#124	1	1	yes	characteristic
119	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
120	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
121	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
122	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
123	C₂³×C₄₇	#137	1	1	yes	characteristic
124	C₂³×C₄₇	#137	1	1	yes	characteristic
125	C₂³×C₄₇	#137	1	2	yes	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	4	2	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	4	2	no	—
141	C₂×C₄×C₄₇	—	4	2	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	8	2	no	—
145	C₂×C₄×C₄₇	—	8	2	no	—
146	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	#117	1	2	yes	—
149	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
157	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
158	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#123	1	2	yes	—
160	C₂×C₄×C₄₇	#125	1	2	yes	—
161	C₂×C₄×C₄₇	#126	1	2	yes	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	4	4	no	—
164	C₂×Dic₄₇	—	4	4	no	—
165	C₂×Dic₄₇	—	8	2	no	—
166	C₂×Dic₄₇	—	8	2	no	—
167	C₂×Dic₄₇	—	8	2	no	—
168	C₂×Dic₄₇	—	8	2	no	—
169	C₄₇⋊C₈	—	2	8	no	—
170	#10881	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
172	C₂²×C₄₇	#386	1	1	yes	characteristic
173	C₂²×C₄₇	#388	1	2	yes	—
174	C₂²×C₄₇	#389	1	2	yes	—
175	C₂²×C₄₇	#391	1	1	yes	characteristic
176	C₂²×C₄₇	#417	1	1	yes	characteristic
177	C₂²×C₄₇	#417	1	1	yes	characteristic
178	C₂²×C₄₇	#418	1	1	yes	characteristic
179	C₂²×C₄₇	#419	1	1	yes	characteristic
180	C₂²×C₄₇	#440	1	2	yes	—
181	C₂²×C₄₇	#440	1	2	yes	—
182	C₂²×C₄₇	#441	1	2	yes	—
183	C₂²×C₄₇	#442	1	2	yes	—
184	C₂²×C₄₇	#468	1	2	yes	—
185	C₂²×C₄₇	#468	1	2	yes	—
186	C₂²×C₄₇	#469	1	2	yes	—
187	C₂²×C₄₇	#470	1	2	yes	—
188	C₂²×C₄₇	#489	1	2	yes	—
189	C₂²×C₄₇	#490	1	1	yes	characteristic
190	C₂²×C₄₇	#491	1	1	yes	characteristic
191	C₂²×C₄₇	#501	1	2	yes	—
192	C₂²×C₄₇	#501	1	1	yes	characteristic
193	C₂²×C₄₇	#501	1	1	yes	characteristic
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	8	2	no	—
198	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
199	C₄×C₄₇	#385	1	2	yes	—
200	C₄×C₄₇	#387	1	2	yes	—
201	C₄×C₄₇	#387	1	2	yes	—
202	Dic₄₇	—	8	4	no	—
203	C₂²×#97	—	47	1	no	—
204	C₂×#389	D₄₇	1	1	yes	characteristic
205	C₂×#340	—	47	2	no	—
206	C₂×#340	—	47	2	no	—
207	C₄⋊#95	—	47	1	no	—
208	C₂×C₄₇	#1436	1	1	yes	characteristic
209	C₂×C₄₇	#1762	1	1	yes	characteristic
210	C₂×C₄₇	#1763	1	1	yes	characteristic
211	C₂×C₄₇	#1894	1	1	yes	characteristic
212	C₂×C₄₇	#1895	1	1	yes	characteristic
213	C₂×C₄₇	#1935	1	2	yes	—
214	C₂×C₄₇	#1936	1	2	yes	—
215	C₂×C₄₇	#1943	1	2	yes	—
216	C₂×C₄₇	#1944	1	2	yes	—
217	C₂×C₄₇	#1992	1	1	yes	characteristic
218	C₂×C₄₇	#1993	1	1	yes	characteristic
219	C₂³×C₈	—	47	2	no	—
220	C₂²×C₄⋊C₄	—	2	1	no	—
221	C₂²×C₄⋊C₄	—	47	2	no	—
222	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
223	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
224	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#97	—	94	4	no	—
226	C₂×#97	—	94	2	no	—
227	#389	—	2	2	no	—
228	#389	Dic₄₇	1	4	yes	complemented
229	C₂×#95	—	2	1	no	—
230	C₂×#95	—	94	1	no	—
231	C₂×#95	—	94	1	no	—
232	#340	—	47	8	no	—
233	#340	—	94	4	no	—
234	C₄₇	#10881	1	1	yes	characteristic, complemented, Sylow
235	C₂³×C₄	—	2	1	no	—
236	C₂³×C₄	—	2	1	no	—
237	C₂³×C₄	—	94	2	no	—
238	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
239	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
240	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
241	C₂²×C₈	—	47	4	no	—
242	C₂²×C₈	—	47	4	no	—
243	C₂²×C₈	—	47	4	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	C₂²×C₈	—	94	2	no	—
247	C₂²×C₈	—	94	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	4	no	—
253	C₂×C₄⋊C₄	—	2	1	no	—
254	C₂×C₄⋊C₄	—	4	4	no	—
255	C₂×C₄⋊C₄	—	47	4	no	—
256	C₂×C₄⋊C₄	—	94	2	no	—
257	C₂×C₄⋊C₄	—	94	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
262	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
267	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
268	#97	—	94	8	no	—
269	#95	—	2	4	no	—
270	#95	—	188	2	no	—
271	#95	—	188	2	no	—
272	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	2	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	2	no	—
290	C₂²×C₄	—	4	1	no	—
291	C₂²×C₄	—	94	4	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	—	188	2	no	—
296	C₂²×C₄	—	188	2	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
299	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
301	C₂²×C₄	#10625350	1	2	yes	—
302	C₂²×C₄	D₄×D₄₇	1	2	yes	—
303	C₂²×C₄	#10625352	1	2	yes	—
304	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
305	C₂²×C₄	#10625354	1	2	yes	—
306	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
308	C₂×C₈	—	47	8	no	—
309	C₂×C₈	—	94	4	no	—
310	C₂×C₈	—	94	4	no	—
311	C₂×C₈	—	94	4	no	—
312	C₂×C₈	—	94	4	no	—
313	C₂×C₈	—	94	4	no	—
314	C₂×C₈	—	94	4	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	4	8	no	—
319	C₄⋊C₄	—	4	1	no	—
320	C₄⋊C₄	—	4	1	no	—
321	C₄⋊C₄	—	94	4	no	—
322	C₄⋊C₄	—	94	4	no	—
323	C₄⋊C₄	—	188	2	no	—
324	C₄⋊C₄	—	188	2	no	—
325	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
326	C₄²	—	2	4	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	2	no	—
329	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
330	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
331	C₂³	#13093996	1	2	yes	—
332	C₂³	#13094013	1	1	yes	characteristic
333	C₂³	#13094022	1	1	yes	characteristic
334	C₂³	#13094049	1	1	yes	characteristic
335	C₂³	#13094049	1	1	yes	characteristic
336	C₂³	#13094050	1	2	yes	—
337	C₂³	#13094054	1	1	yes	characteristic
338	C₂³	#13094054	1	1	yes	characteristic
339	C₂³	#13094055	1	2	yes	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	2	no	—
359	C₂×C₄	—	8	2	no	—
360	C₂×C₄	—	376	2	no	—
361	C₂×C₄	—	376	2	no	—
362	C₂×C₄	—	376	2	no	—
363	C₂×C₄	—	376	2	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	4	no	—
366	C₂×C₄	—	188	4	no	—
367	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
368	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
369	C₂×C₄	#13093982	1	2	yes	—
370	C₂×C₄	#13093983	1	1	yes	characteristic
371	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
372	C₂×C₄	#13093986	1	2	yes	—
373	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
374	C₂×C₄	#13093989	1	2	yes	—
375	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
376	C₂×C₄	#13093992	1	1	yes	characteristic
377	C₂×C₄	#13094000	1	2	yes	—
378	C₂×C₄	#13094002	1	2	yes	—
379	C₂×C₄	#13094005	1	1	yes	characteristic
380	C₂×C₄	#13094009	1	2	yes	—
381	C₂×C₄	#13094014	1	2	yes	—
382	C₂×C₄	#13094019	1	2	yes	—
383	C₈	—	94	8	no	—
384	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
385	C₂²	#15689003	1	1	yes	characteristic
386	C₂²	#15689013	1	2	yes	—
387	C₂²	#15689018	1	2	yes	—
388	C₂²	#15689030	1	1	yes	characteristic
389	C₂²	#15689124	1	1	yes	characteristic
390	C₂²	#15689124	1	1	yes	characteristic
391	C₂²	#15689128	1	1	yes	characteristic
392	C₂²	#15689132	1	1	yes	characteristic
393	C₂²	#15689221	1	2	yes	—
394	C₂²	#15689223	1	2	yes	—
395	C₂²	#15689228	1	2	yes	—
396	C₂²	#15689233	1	2	yes	—
397	C₂²	#15689367	1	2	yes	—
398	C₂²	#15689371	1	2	yes	—
399	C₂²	#15689374	1	2	yes	—
400	C₂²	#15689379	1	2	yes	—
401	C₂²	#15689485	1	2	yes	—
402	C₂²	#15689489	1	1	yes	characteristic
403	C₂²	#15689493	1	1	yes	characteristic
404	C₂²	#15689529	1	2	yes	—
405	C₂²	#15689533	1	1	yes	characteristic
406	C₂²	#15689533	1	1	yes	characteristic
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	2	no	—
410	C₄	—	8	2	no	—
411	C₄	—	376	4	no	—
412	C₄	C₄⋊C₄×Dic₄₇	1	2	yes	—
413	C₄	#15688994	1	2	yes	—
414	C₄	#15689004	1	2	yes	—
415	C₄	#15689009	1	2	yes	—
416	C₂	#20241620	1	1	yes	characteristic
417	C₂	#20243213	1	1	yes	characteristic
418	C₂	#20243218	1	1	yes	characteristic
419	C₂	#20243822	1	1	yes	characteristic
420	C₂	#20243827	1	1	yes	characteristic
421	C₂	#20244077	1	2	yes	—
422	C₂	#20244084	1	2	yes	—
423	C₂	#20244123	1	2	yes	—
424	C₂	#20244128	1	2	yes	—
425	C₂	#20244358	1	1	yes	characteristic
426	C₂	#20244362	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#389	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#389	D₄₇
hypocenter	C₄₇	#10881
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×#389

Complements

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

N	H ≅ G/N	type
13. #15688885	C₄	semidirect
19. C₄₇×#389	C₄	semidirect
114. C₂×C₄₇⋊C₈	C₄⋊C₄	semidirect
228. #389	Dic₄₇	semidirect
234. C₄₇	#10881	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093935	2
C₂×#15688885	2
#20241618	2
C₂×C₄₇×#389	2
#10881	47