Subgroups — #26121939

Order 12032.

914 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×#15688885	C₂	1	2	yes	maximal
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×C₄₇⋊#95	—	2	1	no	—
9	C₂×C₄₇⋊#95	—	2	1	no	—
10	#15688885	—	2	4	no	—
11	#15688885	C₄	1	8	yes	complemented
12	#15688878	—	2	2	no	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	—	2	1	no	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄×C₄⋊C₄×C₄₇	—	2	2	no	—
18	C₄×C₄⋊C₄×C₄₇	C₄	1	4	yes	complemented
19	C₂×#95×C₄₇	—	2	1	no	—
20	C₂³×Dic₄₇	—	2	2	no	—
21	C₂²×C₄₇⋊C₈	—	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	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
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	C₂×C₄	1	4	yes	—
34	C₄₇⋊#95	—	4	2	no	—
35	C₄₇⋊#95	—	4	2	no	—
36	C₂³×C₄×C₄₇	—	2	1	no	—
37	C₂³×C₄×C₄₇	—	2	1	no	—
38	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
50	C₂×C₄⋊C₄×C₄₇	Q₈	1	2	yes	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	4	no	—
54	C₂×C₄²×C₄₇	—	4	4	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	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	4	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	—	4	2	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	4	1	no	—
74	C₂²×C₄×C₄₇	—	4	1	no	—
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
77	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
78	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	#41	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×Dic₄₇	—	2	4	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	C₂²×Dic₄₇	—	4	2	no	—
95	C₂²×Dic₄₇	—	4	2	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	2	no	—
98	C₄⋊C₄×C₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	2	no	—
100	C₄⋊C₄×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
102	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	4	no	—
106	C₄²×C₄₇	—	4	8	no	—
107	C₄⋊Dic₄₇	—	2	4	no	—
108	C₄⋊Dic₄₇	—	2	4	no	—
109	C₄⋊Dic₄₇	—	4	2	no	—
110	C₄⋊Dic₄₇	—	4	2	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	—	4	2	no	—
115	C₂×C₄₇⋊C₈	—	4	2	no	—
116	C₂×C₄₇⋊C₈	—	4	2	no	—
117	C₂×C₄₇⋊C₈	—	4	2	no	—
118	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
119	C₂³×C₄₇	C₄×D₄	1	2	yes	—
120	C₂³×C₄₇	#121	1	1	yes	characteristic
121	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
122	C₂³×C₄₇	#123	1	2	yes	—
123	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
125	C₂³×C₄₇	#135	1	2	yes	—
126	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
127	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
128	C₂³×C₄₇	#137	1	1	yes	characteristic
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	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	4	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	#103	1	4	yes	—
149	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	#117	1	2	yes	—
152	C₂×C₄×C₄₇	#117	1	2	yes	—
153	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
154	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
155	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#123	1	2	yes	—
163	C₂×C₄×C₄₇	#124	1	2	yes	—
164	C₂×C₄×C₄₇	#125	1	2	yes	—
165	C₂×C₄×C₄₇	#126	1	2	yes	—
166	C₂×C₄×C₄₇	#126	1	2	yes	—
167	C₂×Dic₄₇	—	4	4	no	—
168	C₂×Dic₄₇	—	4	4	no	—
169	C₂×Dic₄₇	—	4	4	no	—
170	C₂×Dic₄₇	—	8	2	no	—
171	C₂×Dic₄₇	—	8	2	no	—
172	C₂×Dic₄₇	—	8	2	no	—
173	C₂×Dic₄₇	—	8	2	no	—
174	C₄₇⋊C₈	—	4	4	no	—
175	#10807	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₄₇	#380	1	1	yes	characteristic
178	C₂²×C₄₇	#381	1	1	yes	characteristic
179	C₂²×C₄₇	#387	1	2	yes	—
180	C₂²×C₄₇	#388	1	2	yes	—
181	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
182	C₂²×C₄₇	#416	1	1	yes	characteristic
183	C₂²×C₄₇	#417	1	1	yes	characteristic
184	C₂²×C₄₇	#418	1	1	yes	characteristic
185	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
186	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
187	C₂²×C₄₇	#440	1	2	yes	—
188	C₂²×C₄₇	#442	1	2	yes	—
189	C₂²×C₄₇	#460	1	1	yes	characteristic
190	C₂²×C₄₇	#462	1	1	yes	characteristic
191	C₂²×C₄₇	#463	1	2	yes	—
192	C₂²×C₄₇	#475	1	1	yes	characteristic
193	C₂²×C₄₇	#477	1	1	yes	characteristic
194	C₂²×C₄₇	#478	1	2	yes	—
195	C₂²×C₄₇	#481	1	2	yes	—
196	C₂²×C₄₇	#482	1	2	yes	—
197	C₂²×C₄₇	#484	1	2	yes	—
198	C₂²×C₄₇	#485	1	2	yes	—
199	C₄×C₄₇	—	2	4	no	—
200	C₄×C₄₇	—	4	4	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	—	4	4	no	—
203	C₄×C₄₇	#376	1	1	yes	characteristic
204	C₄×C₄₇	C₄×C₄⋊C₄	1	1	yes	characteristic
205	C₄×C₄₇	#382	1	1	yes	characteristic
206	C₄×C₄₇	#383	1	1	yes	characteristic
207	C₄×C₄₇	#387	1	2	yes	—
208	C₄×C₄₇	#388	1	2	yes	—
209	Dic₄₇	—	8	4	no	—
210	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
211	C₂×#340	—	47	2	no	—
212	C₂×#340	—	47	2	no	—
213	C₂×#336	—	47	1	no	—
214	C₄⋊#95	—	47	1	no	—
215	C₂×C₄₇	#1434	1	1	yes	characteristic
216	C₂×C₄₇	C₄×#103	1	1	yes	characteristic
217	C₂×C₄₇	#1762	1	1	yes	characteristic
218	C₂×C₄₇	#1803	1	1	yes	characteristic
219	C₂×C₄₇	#1804	1	1	yes	characteristic
220	C₂×C₄₇	#1824	1	1	yes	characteristic
221	C₂×C₄₇	#1825	1	1	yes	characteristic
222	C₂×C₄₇	#1919	1	2	yes	—
223	C₂×C₄₇	#1921	1	2	yes	—
224	C₂×C₄₇	#1926	1	2	yes	—
225	C₂×C₄₇	#1928	1	2	yes	—
226	C₂³×C₈	—	47	2	no	—
227	C₂²×C₄⋊C₄	—	47	2	no	—
228	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
230	C₂²×C₄²	—	2	1	no	—
231	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
232	C₄×C₄⋊C₄	—	2	2	no	—
233	C₄×C₄⋊C₄	Dic₄₇	1	4	yes	complemented
234	C₂×#95	—	2	1	no	—
235	C₂×#95	—	94	1	no	—
236	C₂×#95	—	94	1	no	—
237	#340	—	47	8	no	—
238	#340	—	94	4	no	—
239	#336	—	94	2	no	—
240	C₄₇	#10807	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	—	2	1	no	—
242	C₂³×C₄	—	2	1	no	—
243	C₂³×C₄	—	94	2	no	—
244	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
245	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
247	C₂²×C₈	—	47	4	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	—	94	2	no	—
250	C₂²×C₈	—	94	2	no	—
251	C₂²×C₈	—	94	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂×C₄⋊C₄	—	2	2	no	—
255	C₂×C₄⋊C₄	—	2	1	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	47	4	no	—
260	C₂×C₄⋊C₄	—	94	2	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	—	94	2	no	—
265	C₂×C₄⋊C₄	Dic₉₄	1	2	yes	—
266	C₂×C₄⋊C₄	C₄×D₄₇	1	4	yes	—
267	C₂×C₄⋊C₄	D₁₈₈	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
270	C₂×C₄²	—	2	2	no	—
271	C₂×C₄²	—	2	2	no	—
272	C₂×C₄²	—	2	4	no	—
273	C₂×C₄²	—	4	4	no	—
274	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
275	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
276	#95	—	2	4	no	—
277	#95	—	188	2	no	—
278	#95	—	188	2	no	—
279	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	4	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	1	no	—
293	C₂²×C₄	—	4	2	no	—
294	C₂²×C₄	—	4	2	no	—
295	C₂²×C₄	—	4	1	no	—
296	C₂²×C₄	—	94	4	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	—	188	2	no	—
299	C₂²×C₄	—	188	2	no	—
300	C₂²×C₄	—	188	2	no	—
301	C₂²×C₄	—	188	2	no	—
302	C₂²×C₄	—	188	2	no	—
303	C₂²×C₄	#10625336	1	2	yes	—
304	C₂²×C₄	#10625337	1	2	yes	—
305	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
306	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
307	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
310	C₂²×C₄	#10625350	1	1	yes	characteristic
311	C₂²×C₄	#10625350	1	1	yes	characteristic
312	C₂²×C₄	#10625350	1	2	yes	—
313	C₂²×C₄	#10625350	1	2	yes	—
314	C₂²×C₄	#10625350	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	C₂×C₈	—	94	4	no	—
318	C₂×C₈	—	94	4	no	—
319	C₂×C₈	—	94	4	no	—
320	C₂×C₈	—	188	2	no	—
321	C₂×C₈	—	188	2	no	—
322	C₂×C₈	—	188	2	no	—
323	C₂×C₈	—	188	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	2	4	no	—
327	C₄⋊C₄	—	2	2	no	—
328	C₄⋊C₄	—	2	2	no	—
329	C₄⋊C₄	—	94	4	no	—
330	C₄⋊C₄	—	94	4	no	—
331	C₄⋊C₄	—	188	2	no	—
332	C₄⋊C₄	—	188	2	no	—
333	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
334	C₄⋊C₄	C₄⋊Dic₄₇	1	4	yes	—
335	C₄²	—	2	2	no	—
336	C₄²	—	2	2	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	4	8	no	—
339	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
340	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
341	C₂³	#13093998	1	1	yes	characteristic
342	C₂³	#13094003	1	1	yes	characteristic
343	C₂³	#13094007	1	2	yes	—
344	C₂³	C₂×#10625336	1	1	yes	characteristic
345	C₂³	C₂×#10625337	1	1	yes	characteristic
346	C₂³	#13094044	1	2	yes	—
347	C₂³	#13094049	1	1	yes	characteristic
348	C₂³	#13094050	1	2	yes	—
349	C₂³	#13094054	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	4	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	376	2	no	—
370	C₂×C₄	—	376	2	no	—
371	C₂×C₄	—	376	2	no	—
372	C₂×C₄	—	376	2	no	—
373	C₂×C₄	—	188	4	no	—
374	C₂×C₄	—	188	4	no	—
375	C₂×C₄	—	188	4	no	—
376	C₂×C₄	#13093948	1	4	yes	—
377	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
379	C₂×C₄	#13093981	1	2	yes	—
380	C₂×C₄	#13093981	1	2	yes	—
381	C₂×C₄	#13093983	1	1	yes	characteristic
382	C₂×C₄	#13093983	1	1	yes	characteristic
383	C₂×C₄	#13093983	1	1	yes	characteristic
384	C₂×C₄	#13093983	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
386	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
387	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
388	C₂×C₄	#13093998	1	1	yes	characteristic
389	C₂×C₄	#13094003	1	1	yes	characteristic
390	C₂×C₄	#13094007	1	2	yes	—
391	C₂×C₄	#13094012	1	2	yes	—
392	C₂×C₄	#13094016	1	2	yes	—
393	C₂×C₄	#13094018	1	2	yes	—
394	C₂×C₄	#13094018	1	2	yes	—
395	C₈	—	188	4	no	—
396	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
397	C₂²	#15688983	1	1	yes	characteristic
398	C₂²	#15688986	1	1	yes	characteristic
399	C₂²	#15689007	1	2	yes	—
400	C₂²	#15689014	1	2	yes	—
401	C₂²	C₂×#13093948	1	1	yes	characteristic
402	C₂²	#15689119	1	1	yes	characteristic
403	C₂²	#15689124	1	1	yes	characteristic
404	C₂²	#15689128	1	1	yes	characteristic
405	C₂²	C₄×#10625336	1	2	yes	—
406	C₂²	C₄×#10625337	1	2	yes	—
407	C₂²	#15689223	1	2	yes	—
408	C₂²	#15689233	1	2	yes	—
409	C₂²	#15689323	1	1	yes	characteristic
410	C₂²	#15689333	1	1	yes	characteristic
411	C₂²	#15689338	1	2	yes	—
412	C₂²	#15689408	1	1	yes	characteristic
413	C₂²	#15689418	1	1	yes	characteristic
414	C₂²	#15689423	1	2	yes	—
415	C₂²	#15689441	1	2	yes	—
416	C₂²	#15689447	1	2	yes	—
417	C₂²	#15689458	1	2	yes	—
418	C₂²	#15689464	1	2	yes	—
419	C₄	—	2	4	no	—
420	C₄	—	4	4	no	—
421	C₄	—	4	2	no	—
422	C₄	—	4	4	no	—
423	C₄	—	376	4	no	—
424	C₄	#15688969	1	1	yes	characteristic
425	C₄	C₄×C₄⋊Dic₄₇	1	1	yes	characteristic
426	C₄	#15688989	1	1	yes	characteristic
427	C₄	#15688991	1	1	yes	characteristic
428	C₄	#15689007	1	2	yes	—
429	C₄	#15689014	1	2	yes	—
430	C₂	#20241615	1	1	yes	characteristic
431	C₂	C₄×#13093948	1	1	yes	characteristic
432	C₂	#20243213	1	1	yes	characteristic
433	C₂	#20243393	1	1	yes	characteristic
434	C₂	#20243398	1	1	yes	characteristic
435	C₂	#20243478	1	1	yes	characteristic
436	C₂	#20243483	1	1	yes	characteristic
437	C₂	#20243966	1	2	yes	—
438	C₂	#20243980	1	2	yes	—
439	C₂	#20244015	1	2	yes	—
440	C₂	#20244029	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#10807
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. #15688885	C₄	semidirect
18. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
233. C₄×C₄⋊C₄	Dic₄₇	semidirect
240. C₄₇	#10807	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15688885	2
C₂×#15688878	2
#20241618	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#10807	47