Subgroups — #26221454

Order 12032.

1238 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic
2	#20245795	C₂	1	1	yes	maximal, characteristic
3	#20244350	C₂	1	2	yes	maximal, complemented
4	#20244191	C₂	1	2	yes	maximal, complemented
5	#20243812	C₂	1	4	yes	maximal
6	C₄×#13093948	C₂	1	4	yes	maximal, complemented
7	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂×#13093983	—	2	1	no	—
10	C₂×#13093948	C₂²	1	8	yes	—
11	C₂×C₄×C₄₇⋊C₈	—	2	4	no	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
13	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15688993	C₂²	1	2	yes	—
15	#15688989	—	2	1	no	—
16	#15688983	—	2	1	no	—
17	#15688983	C₂²	1	2	yes	—
18	C₄×C₄⋊Dic₄₇	—	2	1	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
20	#15688885	C₂²	1	8	yes	—
21	C₄₇×#533	—	2	4	no	—
22	C₄₇×#533	C₄	1	8	yes	complemented
23	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#125×C₄₇	—	2	1	no	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
30	C₂×#117×C₄₇	—	2	1	no	—
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄₇⋊C₈	—	2	4	no	—
33	C₂²×C₄₇⋊C₈	—	2	8	no	—
34	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
35	#13093983	—	4	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	—	2	2	no	—
38	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
39	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	#13093948	—	2	16	no	—
42	C₄×C₄₇⋊C₈	—	2	4	no	—
43	C₄×C₄₇⋊C₈	—	2	4	no	—
44	C₄₇⋊#95	—	2	2	no	—
45	C₄₇⋊#95	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	1	no	—
47	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₄⋊Q₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
55	#125×C₄₇	—	2	8	no	—
56	C₂²⋊Q₈×C₄₇	—	2	8	no	—
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₄₇	—	2	8	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
62	#117×C₄₇	—	2	8	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
72	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	4	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	8	no	—
81	C₂×Q₈×C₄₇	—	4	4	no	—
82	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
90	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
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	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
99	C₂²×Dic₄₇	—	2	4	no	—
100	C₄⋊C₄×C₄₇	—	2	4	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	2	8	no	—
104	C₄⋊C₄×C₄₇	—	2	8	no	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²⋊C₄×C₄₇	—	2	8	no	—
108	C₄²×C₄₇	—	2	8	no	—
109	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
110	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
111	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
113	C₄²×C₄₇	C₂×D₄	1	2	yes	—
114	C₄²×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²⋊Dic₄₇	—	4	4	no	—
116	C₄⋊Dic₄₇	—	2	8	no	—
117	C₄⋊Dic₄₇	—	4	4	no	—
118	C₄⋊Dic₄₇	—	4	4	no	—
119	C₄×Dic₄₇	—	4	4	no	—
120	C₂×C₄₇⋊C₈	—	2	16	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	#41	1	8	yes	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
128	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
129	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
130	Q₈×C₄₇	—	2	8	no	—
131	Q₈×C₄₇	—	4	4	no	—
132	Q₈×C₄₇	—	4	8	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	4	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	#103	1	16	yes	complemented
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
152	C₂×C₄×C₄₇	#135	1	4	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
156	C₂×Dic₄₇	—	4	4	no	—
157	C₂×Dic₄₇	—	4	4	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₄₇⋊C₈	—	2	8	no	—
160	#21400	—	47	1	no	maximal, Sylow
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	—	2	2	no	—
165	C₂²×C₄₇	C₂×#103	1	4	yes	—
166	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
167	C₂²×C₄₇	#532	1	2	yes	—
168	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
169	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×#135	1	2	yes	—
171	C₄×C₄₇	—	2	2	no	—
172	C₄×C₄₇	—	2	2	no	—
173	C₄×C₄₇	—	4	4	no	—
174	C₄×C₄₇	—	4	4	no	—
175	C₄×C₄₇	C₂×#103	1	4	yes	—
176	C₄×C₄₇	C₂×#103	1	4	yes	—
177	C₄×C₄₇	#416	1	4	yes	—
178	C₄×C₄₇	C₄×#41	1	2	yes	—
179	C₄×C₄₇	#525	1	2	yes	—
180	Dic₄₇	—	8	4	no	—
181	C₂×#533	D₄₇	1	1	yes	characteristic
182	C₂²×C₄×C₈	—	47	1	no	—
183	#2285	—	47	1	no	—
184	#1990	—	47	2	no	—
185	#1956	—	47	2	no	—
186	#1892	—	47	4	no	—
187	C₄×#103	—	47	4	no	—
188	C₂×C₄₇	—	2	4	no	—
189	C₂×C₄₇	#2297	1	1	yes	characteristic
190	C₂×C₄₇	C₂²×#103	1	1	yes	characteristic
191	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
192	C₂×C₄₇	#3167	1	2	yes	—
193	C₂×C₄₇	#3170	1	2	yes	—
194	C₂³×C₈	—	47	2	no	—
195	#533	—	2	4	no	—
196	#533	Dic₄₇	1	8	yes	complemented
197	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
198	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
199	C₂×#125	—	2	1	no	—
200	C₂×C₂²⋊Q₈	—	2	1	no	—
201	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
202	C₂×C₄×Q₈	—	2	1	no	—
203	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
204	C₂×#117	—	2	1	no	—
205	C₂×#117	—	94	1	no	—
206	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
207	C₂×#103	—	47	8	no	—
208	C₂×C₄×C₈	—	47	2	no	—
209	C₂×C₄×C₈	—	47	2	no	—
210	C₂×C₄×C₈	—	94	4	no	—
211	#384	—	47	2	no	—
212	#382	—	94	1	no	—
213	#380	—	47	2	no	—
214	#380	—	94	1	no	—
215	C₄×C₄⋊C₄	—	47	2	no	—
216	C₄×C₄⋊C₄	—	94	1	no	—
217	#340	—	47	8	no	—
218	C₄₇	#21400	1	1	yes	characteristic, complemented, Sylow
219	C₂²×Q₈	—	2	1	no	—
220	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
221	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
223	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
224	C₂²×C₈	—	47	4	no	—
225	C₂²×C₈	—	94	8	no	—
226	C₂²×C₈	—	94	4	no	—
227	C₄⋊Q₈	—	2	2	no	—
228	C₄⋊Q₈	—	2	2	no	—
229	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
230	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
231	#125	—	2	8	no	—
232	C₂²⋊Q₈	—	2	8	no	—
233	C₂²⋊Q₈	—	2	4	no	—
234	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
235	C₄×Q₈	—	2	8	no	—
236	C₄×Q₈	—	2	4	no	—
237	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
238	#117	—	2	8	no	—
239	#117	—	188	4	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	2	1	no	—
242	C₂×C₄⋊C₄	—	2	1	no	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	47	4	no	—
246	C₂×C₄⋊C₄	—	94	2	no	—
247	C₂×C₄⋊C₄	—	94	2	no	—
248	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	94	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	94	2	no	—
253	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
254	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
257	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
259	#103	—	94	16	no	—
260	C₄×C₈	—	94	4	no	—
261	C₄×C₈	—	94	4	no	—
262	#95	—	94	2	no	—
263	#95	—	94	2	no	—
264	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
265	C₂×Q₈	—	2	4	no	—
266	C₂×Q₈	—	2	2	no	—
267	C₂×Q₈	—	2	8	no	—
268	C₂×Q₈	—	4	4	no	—
269	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
270	C₂²×C₄	—	2	4	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	94	4	no	—
275	C₂²×C₄	#10625336	1	4	yes	—
276	C₂²×C₄	#10625337	1	4	yes	—
277	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
278	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
279	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
280	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
283	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
287	C₂×C₈	—	47	8	no	—
288	C₂×C₈	—	94	16	no	—
289	C₂×C₈	—	94	4	no	—
290	C₂×C₈	—	94	4	no	—
291	C₄⋊C₄	—	2	4	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	—	2	8	no	—
295	C₄⋊C₄	—	2	8	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	94	8	no	—
298	C₄⋊C₄	—	188	4	no	—
299	C₄⋊C₄	—	188	4	no	—
300	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
301	C₂²⋊C₄	—	2	8	no	—
302	C₂²⋊C₄	—	188	4	no	—
303	C₄²	—	2	8	no	—
304	C₄²	—	188	4	no	—
305	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
306	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
307	C₄²	C₂²×Dic₄₇	1	2	yes	—
308	C₄²	C₂²×Dic₄₇	1	2	yes	—
309	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
310	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
314	C₂³	C₂×#10625336	1	2	yes	—
315	C₂³	C₂×#10625337	1	2	yes	—
316	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
317	Q₈	—	2	8	no	—
318	Q₈	—	4	4	no	—
319	Q₈	—	4	8	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	2	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	2	8	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	188	4	no	—
330	C₂×C₄	—	188	4	no	—
331	C₂×C₄	—	188	4	no	—
332	C₂×C₄	#13093948	1	16	yes	complemented
333	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
335	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
336	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
337	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
338	C₂×C₄	C₂×#10625336	1	2	yes	—
339	C₂×C₄	C₂×#10625336	1	2	yes	—
340	C₂×C₄	C₂×#10625337	1	2	yes	—
341	C₂×C₄	C₂×#10625337	1	2	yes	—
342	C₂×C₄	#13094044	1	4	yes	—
343	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
344	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂×C₄	#41×D₄₇	1	4	yes	—
346	C₈	—	94	8	no	—
347	C₂²	—	2	4	no	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	2	no	—
350	C₂²	—	2	4	no	—
351	C₂²	C₂×#13093948	1	4	yes	—
352	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
353	C₂²	#15689669	1	2	yes	—
354	C₂²	C₂²×#10625336	1	1	yes	characteristic
355	C₂²	C₂²×#10625337	1	1	yes	characteristic
356	C₂²	C₂×#13094044	1	2	yes	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	4	4	no	—
360	C₄	—	4	4	no	—
361	C₄	—	376	4	no	—
362	C₄	C₂×#13093948	1	4	yes	—
363	C₄	C₂×#13093948	1	4	yes	—
364	C₄	#15689119	1	4	yes	—
365	C₄	#41×Dic₄₇	1	2	yes	—
366	C₄	#15689630	1	2	yes	—
367	C₂	—	2	4	no	—
368	C₂	#20245879	1	1	yes	characteristic
369	C₂	C₂²×#13093948	1	1	yes	characteristic
370	C₂	C₂×#15689119	1	1	yes	characteristic
371	C₂	#20253948	1	2	yes	—
372	C₂	#20253970	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#533	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#533	D₄₇
hypocenter	C₄₇	#21400
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#533

Complements

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

N	H ≅ G/N	type
3. #20244350	C₂	semidirect
4. #20244191	C₂	semidirect
6. C₄×#13093948	C₂	semidirect
22. C₄₇×#533	C₄	semidirect
142. C₂×C₄×C₄₇	#103	semidirect
196. #533	Dic₄₇	semidirect
218. C₄₇	#21400	semidirect
332. C₂×C₄	#13093948	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₄₇⋊C₈	2
#20245795	2
#20244350	2
#20244191	2
#20243812	2
C₄×#13093948	2
C₂×C₄₇×#533	2
#21400	47