Subgroups — #26121527

Order 12032.

1646 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×#15688983	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688885	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic
5	C₂³×C₄₇⋊C₈	—	2	8	no	—
6	C₂³×C₄₇⋊C₈	—	2	2	no	—
7	C₂³×C₄₇⋊C₈	—	2	2	no	—
8	C₂³×C₄₇⋊C₈	C₄	1	4	yes	complemented
9	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
10	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
11	C₂²×C₂²⋊Dic₄₇	—	2	1	no	—
12	#15688983	—	2	2	no	—
13	#15688983	C₄	1	4	yes	complemented
14	C₂×C₄₇⋊#95	—	2	1	no	—
15	#15688885	—	2	8	no	—
16	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₄₇×#380	—	2	2	no	—
20	C₄₇×#380	C₄	1	4	yes	complemented
21	C₂×#95×C₄₇	—	2	1	no	—
22	C₂³×Dic₄₇	—	2	2	no	—
23	C₂²×C₄₇⋊C₈	—	2	16	no	—
24	C₂²×C₄₇⋊C₈	—	2	16	no	—
25	C₂²×C₄₇⋊C₈	—	2	8	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	4	no	—
29	C₂²×C₄₇⋊C₈	—	2	16	no	—
30	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
31	C₂²×C₄₇⋊C₈	D₄	1	8	yes	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	2	4	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
36	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
37	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
38	C₂×C₂²⋊Dic₄₇	—	4	2	no	—
39	C₄₇⋊#95	—	2	4	no	—
40	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	4	no	—
42	C₂³×C₄×C₄₇	—	2	4	no	—
43	C₂³×C₄×C₄₇	—	2	2	no	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	D₄	1	2	yes	—
49	C₂³×C₄×C₄₇	D₄	1	2	yes	—
50	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
59	#95×C₄₇	—	2	4	no	—
60	C₂⁴×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	4	no	—
62	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
63	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
64	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
65	C₂⁴×C₄₇	D₈	1	2	yes	—
66	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
67	C₂⁴×C₄₇	SD₁₆	1	2	yes	—
68	C₂⁴×C₄₇	Q₁₆	1	2	yes	—
69	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	—	2	4	no	—
71	C₂²×C₄×C₄₇	—	2	4	no	—
72	C₂²×C₄×C₄₇	—	2	4	no	—
73	C₂²×C₄×C₄₇	—	2	8	no	—
74	C₂²×C₄×C₄₇	—	2	8	no	—
75	C₂²×C₄×C₄₇	—	2	4	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	8	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	4	no	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	4	4	no	—
82	C₂²×C₄×C₄₇	—	4	2	no	—
83	C₂²×C₄×C₄₇	—	4	2	no	—
84	C₂²×C₄×C₄₇	—	4	4	no	—
85	C₂²×C₄×C₄₇	C₄²	1	4	yes	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
90	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	4	yes	—
100	C₂²×Dic₄₇	—	2	4	no	—
101	C₂²×Dic₄₇	—	4	4	no	—
102	C₂²×Dic₄₇	—	4	2	no	—
103	C₂²×Dic₄₇	—	4	2	no	—
104	C₂²×Dic₄₇	—	4	4	no	—
105	C₄⋊C₄×C₄₇	—	2	8	no	—
106	C₄⋊C₄×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	4	2	no	—
108	C₂²⋊C₄×C₄₇	—	4	8	no	—
109	C₂²⋊Dic₄₇	—	4	8	no	—
110	C₄⋊Dic₄₇	—	2	8	no	—
111	C₄⋊Dic₄₇	—	4	2	no	—
112	C₄⋊Dic₄₇	—	4	2	no	—
113	C₂×C₄₇⋊C₈	—	2	32	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
115	C₂×C₄₇⋊C₈	—	2	4	no	—
116	C₂×C₄₇⋊C₈	—	2	8	no	—
117	C₂×C₄₇⋊C₈	—	2	8	no	—
118	C₂×C₄₇⋊C₈	C₂²⋊C₄	1	8	yes	complemented
119	C₂³×C₄₇	—	2	4	no	—
120	C₂³×C₄₇	—	2	4	no	—
121	C₂³×C₄₇	—	2	4	no	—
122	C₂³×C₄₇	—	2	4	no	—
123	C₂³×C₄₇	—	2	4	no	—
124	C₂³×C₄₇	—	2	4	no	—
125	C₂³×C₄₇	—	2	8	no	—
126	C₂³×C₄₇	—	2	8	no	—
127	C₂³×C₄₇	—	2	8	no	—
128	C₂³×C₄₇	—	2	8	no	—
129	C₂³×C₄₇	#95	1	4	yes	—
130	C₂³×C₄₇	#102	1	4	yes	—
131	C₂³×C₄₇	#102	1	4	yes	—
132	C₂³×C₄₇	#103	1	4	yes	—
133	C₂³×C₄₇	#103	1	4	yes	—
134	C₂³×C₄₇	#106	1	4	yes	—
135	C₂³×C₄₇	#107	1	4	yes	—
136	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
137	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
139	C₂³×C₄₇	#121	1	4	yes	—
140	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
143	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
144	C₂³×C₄₇	#135	1	4	yes	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	8	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	8	no	—
152	C₂×C₄×C₄₇	—	2	8	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	8	4	no	—
157	C₂×C₄×C₄₇	—	8	4	no	—
158	C₂×C₄×C₄₇	#95	1	4	yes	—
159	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#117	1	2	yes	—
165	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
166	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
167	C₂×C₄×C₄₇	#120	1	2	yes	—
168	C₂×C₄×C₄₇	#120	1	2	yes	—
169	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
170	C₂×C₄×C₄₇	#123	1	2	yes	—
171	C₂×C₄×C₄₇	#123	1	2	yes	—
172	C₂×Dic₄₇	—	4	4	no	—
173	C₂×Dic₄₇	—	4	4	no	—
174	C₂×Dic₄₇	—	4	4	no	—
175	C₂×Dic₄₇	—	8	4	no	—
176	C₂×Dic₄₇	—	8	4	no	—
177	C₄₇⋊C₈	—	2	8	no	—
178	#10721	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	8	no	—
180	C₂²×C₄₇	—	2	8	no	—
181	C₂²×C₄₇	—	2	8	no	—
182	C₂²×C₄₇	—	2	8	no	—
183	C₂²×C₄₇	—	2	8	no	—
184	C₂²×C₄₇	—	2	8	no	—
185	C₂²×C₄₇	—	2	4	no	—
186	C₂²×C₄₇	—	2	4	no	—
187	C₂²×C₄₇	#340	1	8	yes	complemented
188	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
189	C₂²×C₄₇	#380	1	2	yes	—
190	C₂²×C₄₇	#386	1	2	yes	—
191	C₂²×C₄₇	#386	1	2	yes	—
192	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
193	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
194	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
195	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
196	C₂²×C₄₇	#416	1	2	yes	—
197	C₂²×C₄₇	#416	1	2	yes	—
198	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
199	C₂²×C₄₇	C₂×#107	1	1	yes	characteristic
200	C₂²×C₄₇	#427	1	2	yes	—
201	C₂²×C₄₇	#465	1	4	yes	—
202	C₂²×C₄₇	#465	1	4	yes	—
203	C₂²×C₄₇	#466	1	4	yes	—
204	C₂²×C₄₇	#467	1	4	yes	—
205	C₄×C₄₇	—	2	4	no	—
206	C₄×C₄₇	—	8	4	no	—
207	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
208	C₄×C₄₇	#379	1	1	yes	characteristic
209	C₄×C₄₇	#381	1	1	yes	characteristic
210	C₄×C₄₇	#385	1	2	yes	—
211	C₄×C₄₇	#385	1	2	yes	—
212	Dic₄₇	—	8	4	no	—
213	C₂⁴×C₈	—	47	1	no	—
214	C₂×#380	—	47	1	no	—
215	C₂×#380	D₄₇	1	1	yes	characteristic
216	C₂×#340	—	47	4	no	—
217	C₂×C₄₇	—	2	8	no	—
218	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
219	C₂×C₄₇	C₂×#340	1	1	yes	characteristic
220	C₂×C₄₇	#1735	1	1	yes	characteristic
221	C₂×C₄₇	#1807	1	2	yes	—
222	C₂×C₄₇	#1808	1	2	yes	—
223	C₂×C₄₇	#1892	1	2	yes	—
224	C₂×C₄₇	#1892	1	2	yes	—
225	C₂×C₄₇	#1893	1	2	yes	—
226	C₂×C₄₇	#1893	1	2	yes	—
227	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
228	C₂³×C₈	—	47	2	no	—
229	C₂³×C₈	—	47	4	no	—
230	C₂³×C₈	—	94	8	no	—
231	C₂³×C₈	—	94	2	no	—
232	C₂³×C₈	—	94	2	no	—
233	C₂²×C₄⋊C₄	—	47	2	no	—
234	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
235	C₂²×C₂²⋊C₄	—	2	1	no	—
236	C₂²×C₂²⋊C₄	—	94	1	no	—
237	#380	—	2	2	no	—
238	#380	—	47	4	no	—
239	#380	—	94	2	no	—
240	#380	Dic₄₇	1	4	yes	complemented
241	C₂×#95	—	2	1	no	—
242	C₂×#95	—	94	1	no	—
243	#340	—	94	8	no	—
244	C₄₇	#10721	1	1	yes	characteristic, complemented, Sylow
245	C₂⁵	C₂²⋊D₄₇	1	1	yes	characteristic
246	C₂³×C₄	—	2	4	no	—
247	C₂³×C₄	—	2	4	no	—
248	C₂³×C₄	—	2	2	no	—
249	C₂³×C₄	—	94	2	no	—
250	C₂³×C₄	Dic₉₄	1	2	yes	—
251	C₂³×C₄	C₄×D₄₇	1	2	yes	—
252	C₂³×C₄	C₄×D₄₇	1	2	yes	—
253	C₂³×C₄	D₁₈₈	1	2	yes	—
254	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
255	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
257	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
258	C₂²×C₈	—	47	4	no	—
259	C₂²×C₈	—	47	8	no	—
260	C₂²×C₈	—	94	16	no	—
261	C₂²×C₈	—	94	16	no	—
262	C₂²×C₈	—	94	16	no	—
263	C₂²×C₈	—	94	8	no	—
264	C₂²×C₈	—	94	2	no	—
265	C₂²×C₈	—	94	4	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂×C₄⋊C₄	—	2	4	no	—
268	C₂×C₄⋊C₄	—	2	4	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	47	4	no	—
271	C₂×C₄⋊C₄	—	94	4	no	—
272	C₂×C₄⋊C₄	—	94	4	no	—
273	C₂×C₄⋊C₄	—	94	2	no	—
274	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
275	C₂×C₂²⋊C₄	—	2	4	no	—
276	C₂×C₂²⋊C₄	—	4	2	no	—
277	C₂×C₂²⋊C₄	—	4	2	no	—
278	C₂×C₂²⋊C₄	—	94	4	no	—
279	C₂×C₂²⋊C₄	—	188	2	no	—
280	C₂×C₂²⋊C₄	—	188	2	no	—
281	#95	—	2	4	no	—
282	#95	—	94	4	no	—
283	C₂⁴	—	2	4	no	—
284	C₂⁴	—	2	4	no	—
285	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
286	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
287	C₂⁴	#10625334	1	2	yes	—
288	C₂⁴	#10625335	1	2	yes	—
289	C₂⁴	#10625336	1	2	yes	—
290	C₂⁴	#10625337	1	2	yes	—
291	C₂⁴	C₂²⋊Dic₄₇	1	2	yes	—
292	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	8	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	4	4	no	—
305	C₂²×C₄	—	4	2	no	—
306	C₂²×C₄	—	4	2	no	—
307	C₂²×C₄	—	4	4	no	—
308	C₂²×C₄	—	94	4	no	—
309	C₂²×C₄	—	188	4	no	—
310	C₂²×C₄	—	188	2	no	—
311	C₂²×C₄	—	188	2	no	—
312	C₂²×C₄	—	188	4	no	—
313	C₂²×C₄	C₄×Dic₄₇	1	4	yes	—
314	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
315	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
316	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
317	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
318	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
319	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
320	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
321	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
324	C₂²×C₄	D₄×D₄₇	1	4	yes	—
325	C₂²×C₄	#10625352	1	4	yes	—
326	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
327	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂×C₈	—	47	8	no	—
329	C₂×C₈	—	94	32	no	—
330	C₂×C₈	—	94	4	no	—
331	C₂×C₈	—	94	4	no	—
332	C₂×C₈	—	94	8	no	—
333	C₂×C₈	—	94	8	no	—
334	C₄⋊C₄	—	2	8	no	—
335	C₄⋊C₄	—	4	2	no	—
336	C₄⋊C₄	—	4	2	no	—
337	C₄⋊C₄	—	94	8	no	—
338	C₄⋊C₄	—	188	2	no	—
339	C₄⋊C₄	—	188	2	no	—
340	C₂²⋊C₄	—	4	8	no	—
341	C₂²⋊C₄	—	188	8	no	—
342	C₂³	—	2	4	no	—
343	C₂³	—	2	4	no	—
344	C₂³	—	2	4	no	—
345	C₂³	—	2	8	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	8	no	—
348	C₂³	—	2	8	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	4	no	—
351	C₂³	—	2	4	no	—
352	C₂³	C₄₇⋊#95	1	4	yes	—
353	C₂³	#13093944	1	4	yes	—
354	C₂³	#13093945	1	4	yes	—
355	C₂³	#13093947	1	4	yes	—
356	C₂³	#13093948	1	4	yes	—
357	C₂³	#13093955	1	4	yes	—
358	C₂³	#13093957	1	4	yes	—
359	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
360	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
361	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
362	C₂³	#13093996	1	4	yes	—
363	C₂³	C₂×#10625334	1	1	yes	characteristic
364	C₂³	C₂×#10625336	1	1	yes	characteristic
365	C₂³	C₂×#10625335	1	1	yes	characteristic
366	C₂³	C₂×#10625337	1	1	yes	characteristic
367	C₂³	#13094044	1	4	yes	—
368	C₂×C₄	—	2	4	no	—
369	C₂×C₄	—	2	4	no	—
370	C₂×C₄	—	2	4	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	4	no	—
373	C₂×C₄	—	2	4	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	8	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	4	no	—
378	C₂×C₄	—	4	4	no	—
379	C₂×C₄	—	8	4	no	—
380	C₂×C₄	—	8	4	no	—
381	C₂×C₄	—	376	4	no	—
382	C₂×C₄	—	376	4	no	—
383	C₂×C₄	—	188	4	no	—
384	C₂×C₄	—	188	4	no	—
385	C₂×C₄	—	188	4	no	—
386	C₂×C₄	C₄₇⋊#95	1	4	yes	—
387	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
389	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
390	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
391	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
392	C₂×C₄	#13093980	1	2	yes	—
393	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
394	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
395	C₂×C₄	#13093992	1	2	yes	—
396	C₂×C₄	#13093994	1	2	yes	—
397	C₂×C₄	#13094001	1	4	yes	—
398	C₂×C₄	#13094005	1	2	yes	—
399	C₂×C₄	#13094008	1	2	yes	—
400	C₈	—	94	8	no	—
401	C₂²	—	2	8	no	—
402	C₂²	—	2	8	no	—
403	C₂²	—	2	8	no	—
404	C₂²	—	2	8	no	—
405	C₂²	—	2	4	no	—
406	C₂²	—	2	4	no	—
407	C₂²	—	2	8	no	—
408	C₂²	—	2	8	no	—
409	C₂²	#15688885	1	8	yes	complemented
410	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
411	C₂²	#15688981	1	2	yes	—
412	C₂²	#15689000	1	2	yes	—
413	C₂²	#15689003	1	2	yes	—
414	C₂²	C₂×#13093944	1	1	yes	characteristic
415	C₂²	C₂×#13093945	1	1	yes	characteristic
416	C₂²	C₂×#13093947	1	1	yes	characteristic
417	C₂²	C₂×#13093948	1	1	yes	characteristic
418	C₂²	#15689117	1	2	yes	—
419	C₂²	#15689119	1	2	yes	—
420	C₂²	C₂×#13093955	1	1	yes	characteristic
421	C₂²	C₂×#13093957	1	1	yes	characteristic
422	C₂²	#15689159	1	2	yes	—
423	C₂²	#15689350	1	4	yes	—
424	C₂²	#15689354	1	4	yes	—
425	C₂²	#15689357	1	4	yes	—
426	C₂²	#15689362	1	4	yes	—
427	C₄	—	2	4	no	—
428	C₄	—	8	4	no	—
429	C₄	—	376	4	no	—
430	C₄	C₂²⋊C₄×Dic₄₇	1	2	yes	—
431	C₄	#15688978	1	1	yes	characteristic
432	C₄	#15688984	1	1	yes	characteristic
433	C₄	#15688995	1	2	yes	—
434	C₄	#15688998	1	2	yes	—
435	C₂	—	2	8	no	—
436	C₂	#20241610	1	1	yes	characteristic
437	C₂	C₂×#15688885	1	1	yes	characteristic
438	C₂	#20243104	1	1	yes	characteristic
439	C₂	#20243411	1	2	yes	—
440	C₂	#20243415	1	2	yes	—
441	C₂	#20243809	1	2	yes	—
442	C₂	#20243812	1	2	yes	—
443	C₂	#20243814	1	2	yes	—
444	C₂	#20243817	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#380	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂⁵×C₄₇	D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#380	D₄₇
hypocenter	C₄₇	#10721
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂⁴×C₄ ◁ C₂×#380

Complements

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

N	H ≅ G/N	type
3. C₂×#15688885	C₂	semidirect
8. C₂³×C₄₇⋊C₈	C₄	semidirect
13. #15688983	C₄	semidirect
20. C₄₇×#380	C₄	semidirect
118. C₂×C₄₇⋊C₈	C₂²⋊C₄	semidirect
187. C₂²×C₄₇	#340	semidirect
240. #380	Dic₄₇	semidirect
244. C₄₇	#10721	semidirect
409. C₂²	#15688885	semidirect

Maximal subgroups

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

subgroup	index
C₂⁴×C₄₇⋊C₈	2
C₂×#15688983	2
C₂×#15688885	2
C₂×C₄₇×#380	2
#10721	47