Subgroups — #26219576

Order 12032.

1114 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	2	yes	maximal
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
4	#20244112	C₂	1	4	yes	maximal, complemented
5	#20244107	C₂	1	4	yes	maximal, complemented
6	#20243082	C₂	1	2	yes	maximal
7	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	2	yes	—
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	#15689147	—	2	8	no	—
12	#15689147	—	2	4	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	8	yes	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₄×#10625329	—	2	4	no	—
17	C₂×#13093935	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	#15688878	C₂²	1	8	yes	—
20	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
24	C₄×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
25	C₄×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
27	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂×#95×C₄₇	C₄	1	2	yes	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	—	2	4	no	—
34	C₂×#10625329	—	2	4	no	—
35	C₂×#10625329	—	2	4	no	—
36	C₂×#10625329	D₄	1	4	yes	—
37	C₂×#10625329	Q₈	1	4	yes	—
38	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
42	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	16	no	—
44	#13093935	—	2	4	no	—
45	C₄×C₄₇⋊C₈	—	2	4	no	—
46	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
51	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₇	—	2	4	no	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	4	yes	—
61	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
62	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
63	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	#95×C₄₇	C₂×C₄	1	2	yes	—
66	#95×C₄₇	C₂×C₄	1	4	yes	—
67	#95×C₄₇	C₂×C₄	1	2	yes	—
68	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	8	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	4	4	no	—
74	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
75	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₄⋊C₄×C₄₇	—	2	8	no	—
91	C₄⋊C₄×C₄₇	—	2	4	no	—
92	C₄⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
93	C₄²×C₄₇	—	2	4	no	—
94	C₄²×C₄₇	—	2	4	no	—
95	C₄²×C₄₇	—	2	4	no	—
96	C₄²×C₄₇	—	2	4	no	—
97	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
98	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
99	C₄²×C₄₇	C₂×D₄	1	2	yes	—
100	C₄²×C₄₇	C₂×D₄	1	2	yes	—
101	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
102	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
103	#10625329	—	2	8	no	—
104	#10625329	—	2	8	no	—
105	#10625329	—	4	8	no	—
106	C₂×C₄₇⋊C₈	—	2	2	no	—
107	C₂×C₄₇⋊C₈	—	2	2	no	—
108	C₂×C₄₇⋊C₈	—	2	2	no	—
109	C₂×C₄₇⋊C₈	—	2	2	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	C₂×D₄	1	4	yes	—
114	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
115	C₂³×C₄₇	—	2	2	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
118	C₂³×C₄₇	C₄×D₄	1	2	yes	—
119	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
120	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	4	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	8	no	—
127	C₂×C₄×C₄₇	—	2	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	4	4	no	—
131	C₂×C₄×C₄₇	—	4	16	no	—
132	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
134	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
136	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
137	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
138	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₄₇	#121	1	4	yes	—
140	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
141	C₂×C₄×C₄₇	#125	1	4	yes	—
142	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
143	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
144	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₄₇⋊C₈	—	2	4	no	—
152	C₄₇⋊C₈	—	2	4	no	—
153	C₄₇⋊C₈	—	4	4	no	—
154	#21146	—	47	1	no	maximal, Sylow
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	#389	1	4	yes	—
160	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
161	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
163	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
164	C₂²×C₄₇	#568	1	2	yes	—
165	C₄×C₄₇	—	2	2	no	—
166	C₄×C₄₇	—	2	2	no	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	8	no	—
169	C₄×C₄₇	—	4	4	no	—
170	C₄×C₄₇	#389	1	4	yes	—
171	C₄×C₄₇	#423	1	4	yes	complemented
172	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
173	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
174	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
175	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
176	C₂×#423	—	47	2	no	—
177	C₂×#423	—	47	1	no	—
178	C₂×C₄×M₁₆	—	47	1	no	—
179	C₂×C₄×C₄⋊C₄	D₄₇	1	1	yes	characteristic
180	#1940	—	47	4	no	—
181	#1939	—	47	4	no	—
182	#1728	—	47	2	no	—
183	C₂×C₄₇	—	2	4	no	—
184	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
185	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
186	C₂×C₄₇	#2905	1	1	yes	characteristic
187	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
188	C₂×C₄₇	Q₈×M₁₆	1	2	yes	—
189	C₂²×M₁₆	—	47	1	no	—
190	C₂²×M₁₆	—	47	1	no	—
191	C₂²×M₁₆	—	47	2	no	—
192	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
193	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
194	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
195	#423	—	94	8	no	—
196	#423	—	94	4	no	—
197	C₂×C₄⋊C₈	—	47	2	no	—
198	C₂×C₄⋊C₈	—	47	8	no	—
199	C₂×C₄⋊C₈	—	47	2	no	—
200	C₄×M₁₆	—	94	4	no	—
201	C₂×#97	—	47	2	no	—
202	C₂×C₄×C₈	—	47	2	no	—
203	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
204	C₄×C₄⋊C₄	Dic₄₇	1	2	yes	—
205	C₄×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
206	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
207	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
208	C₂×#95	Dic₄₇	1	2	yes	—
209	#336	—	47	8	no	—
210	C₄₇	#21146	1	1	yes	characteristic, complemented, Sylow
211	C₂³×C₄	C₂×Dic₄₇	1	4	yes	—
212	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
213	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
215	C₂×M₁₆	—	47	4	no	—
216	C₂×M₁₆	—	47	4	no	—
217	C₂×M₁₆	—	94	2	no	—
218	C₂×M₁₆	—	94	2	no	—
219	C₂×M₁₆	—	94	2	no	—
220	C₂×M₁₆	—	94	2	no	—
221	C₂×M₁₆	—	94	4	no	—
222	C₂×M₁₆	—	94	4	no	—
223	C₂×M₁₆	—	94	4	no	—
224	C₂²×C₈	—	47	2	no	—
225	C₂²×C₈	—	47	2	no	—
226	C₂²×C₈	—	47	4	no	—
227	C₂×C₄⋊C₄	—	2	8	no	—
228	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
229	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
230	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
231	C₂×C₄²	—	2	4	no	—
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	Dic₉₄	1	4	yes	—
234	C₂×C₄²	D₁₈₈	1	4	yes	—
235	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
236	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
237	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₄₇	1	4	yes	—
240	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
241	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
242	C₄⋊C₈	—	94	16	no	—
243	C₄⋊C₈	—	94	4	no	—
244	C₄⋊C₈	—	94	4	no	—
245	#97	—	94	4	no	—
246	C₄×C₈	—	94	4	no	—
247	#95	C₂×Dic₄₇	1	2	yes	—
248	#95	C₂×Dic₄₇	1	4	yes	—
249	#95	C₂×Dic₄₇	1	2	yes	—
250	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	8	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
257	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
258	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
259	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
260	C₂²×C₄	D₄×D₄₇	1	2	yes	—
261	C₂²×C₄	#10625352	1	2	yes	—
262	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
263	C₂²×C₄	#10625354	1	2	yes	—
264	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
265	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
266	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
268	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
269	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
270	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
271	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
272	M₁₆	—	94	8	no	—
273	M₁₆	—	94	8	no	—
274	M₁₆	—	188	8	no	—
275	C₂×C₈	—	47	4	no	—
276	C₂×C₈	—	47	4	no	—
277	C₂×C₈	—	94	2	no	—
278	C₂×C₈	—	94	2	no	—
279	C₂×C₈	—	94	2	no	—
280	C₂×C₈	—	94	2	no	—
281	C₂×C₈	—	94	4	no	—
282	C₂×C₈	—	94	4	no	—
283	C₂×C₈	—	94	4	no	—
284	C₄⋊C₄	—	2	8	no	—
285	C₄⋊C₄	—	2	4	no	—
286	C₄⋊C₄	#10625329	1	8	yes	complemented
287	C₄²	—	2	4	no	—
288	C₄²	—	2	4	no	—
289	C₄²	—	2	4	no	—
290	C₄²	—	2	4	no	—
291	C₄²	C₄⋊Dic₄₇	1	4	yes	—
292	C₄²	C₄⋊Dic₄₇	1	4	yes	—
293	C₄²	C₂×Dic₉₄	1	2	yes	—
294	C₄²	C₂×Dic₉₄	1	2	yes	—
295	C₄²	C₂×D₁₈₈	1	2	yes	—
296	C₄²	C₂×D₁₈₈	1	2	yes	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	C₂×C₄⋊Dic₄₇	1	2	yes	—
300	C₂³	D₄×Dic₄₇	1	2	yes	—
301	C₂³	Q₈×Dic₄₇	1	2	yes	—
302	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
303	C₂×C₄	—	2	4	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	4	no	—
308	C₂×C₄	—	2	8	no	—
309	C₂×C₄	—	2	4	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	4	16	no	—
314	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
315	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
316	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
318	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
319	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
320	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
321	C₂×C₄	#13093999	1	4	yes	—
322	C₂×C₄	#13094004	1	4	yes	—
323	C₂×C₄	#13094015	1	4	yes	—
324	C₂×C₄	#13094023	1	4	yes	—
325	C₂×C₄	C₂×#10625329	1	8	yes	—
326	C₂×C₄	C₂×#10625329	1	4	yes	—
327	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
329	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
330	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
331	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
332	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
333	C₈	—	94	4	no	—
334	C₈	—	94	4	no	—
335	C₈	—	188	4	no	—
336	C₂²	—	2	2	no	—
337	C₂²	—	2	2	no	—
338	C₂²	—	2	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	#15689022	1	4	yes	—
341	C₂²	C₂²×C₄⋊Dic₄₇	1	1	yes	characteristic
342	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
343	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
344	C₂²	C₂²×#10625329	1	2	yes	—
345	C₂²	#15689890	1	2	yes	—
346	C₄	—	2	2	no	—
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	2	8	no	—
350	C₄	—	4	4	no	—
351	C₄	#15689022	1	4	yes	—
352	C₄	#15689147	1	4	yes	complemented
353	C₄	C₂×#13093999	1	1	yes	characteristic
354	C₄	C₂×#13094004	1	1	yes	characteristic
355	C₄	C₂×#13094015	1	1	yes	characteristic
356	C₄	C₂×#13094023	1	1	yes	characteristic
357	C₂	—	2	4	no	—
358	C₂	C₂×#15689022	1	1	yes	characteristic
359	C₂	C₂×#15689147	1	1	yes	characteristic
360	C₂	#20251952	1	1	yes	characteristic
361	C₂	D₄×#10625329	1	2	yes	—
362	C₂	Q₈×#10625329	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄×C₄⋊C₄×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#21146
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20244112	C₂	semidirect
5. #20244107	C₂	semidirect
92. C₄⋊C₄×C₄₇	M₁₆	semidirect
171. C₄×C₄₇	#423	semidirect
210. C₄₇	#21146	semidirect
286. C₄⋊C₄	#10625329	semidirect
352. C₄	#15689147	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂×C₄×#10625329	2
#20244112	2
#20244107	2
#20243082	2
C₂×C₄×C₄⋊C₄×C₄₇	2
#21146	47