Subgroups — #26219575

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	1	yes	maximal, characteristic
2	C₂×#15689146	C₂	1	2	yes	maximal
3	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244111	C₂	1	4	yes	maximal, complemented
5	#20244106	C₂	1	4	yes	maximal, complemented
6	#20243081	C₂	1	2	yes	maximal
7	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	C₂²	1	2	yes	—
9	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
10	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
11	#15689147	—	2	4	no	—
12	#15689146	—	2	8	no	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
15	C₂×Dic₄₇⋊C₈	C₂²	1	8	yes	—
16	C₄×C₄⋊Dic₄₇	C₄	1	2	yes	—
17	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
18	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
19	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
20	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₄₇⋊#95	C₄	1	2	yes	—
22	#15688877	C₂²	1	8	yes	—
23	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
26	C₄×M₁₆×C₄₇	—	2	4	no	—
27	C₂×#97×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
29	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
30	C₂×#10625329	—	2	4	no	—
31	C₂×#10625329	—	2	4	no	—
32	C₂×#10625329	—	2	4	no	—
33	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
34	C₂×C₄⋊Dic₄₇	—	2	8	no	—
35	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
36	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
37	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
38	C₂×C₄×Dic₄₇	—	2	4	no	—
39	C₂×C₄×Dic₄₇	—	2	4	no	—
40	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
43	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
45	Dic₄₇⋊C₈	—	2	16	no	—
46	C₄₇⋊#95	C₂×C₄	1	2	yes	—
47	C₄₇⋊#95	C₂×C₄	1	4	yes	—
48	C₄₇⋊#95	C₂×C₄	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂×M₁₆×C₄₇	—	2	2	no	—
56	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
57	C₂×M₁₆×C₄₇	Q₈	1	4	yes	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄²×C₄₇	D₄	1	4	yes	—
63	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	#97×C₄₇	—	2	4	no	—
67	C₄×C₈×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
72	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
81	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
82	C₂²×C₄×C₄₇	#41	1	2	yes	—
83	C₂²×C₄×C₄₇	#41	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
85	C₂²×Dic₄₇	—	2	8	no	—
86	C₂²×Dic₄₇	—	2	8	no	—
87	C₂²×Dic₄₇	—	4	4	no	—
88	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
89	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
90	M₁₆×C₄₇	—	2	8	no	—
91	M₁₆×C₄₇	—	2	8	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
97	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	—
98	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
99	C₄²×C₄₇	C₄⋊C₄	1	4	yes	—
100	C₄²×C₄₇	C₂×D₄	1	2	yes	—
101	C₄²×C₄₇	C₂×D₄	1	2	yes	—
102	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
103	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
104	C₄⋊Dic₄₇	—	2	4	no	—
105	C₄⋊Dic₄₇	—	2	8	no	—
106	C₄⋊Dic₄₇	M₁₆	1	8	yes	complemented
107	C₄×Dic₄₇	—	2	4	no	—
108	C₄×Dic₄₇	—	2	4	no	—
109	C₄×Dic₄₇	—	2	4	no	—
110	C₄×Dic₄₇	—	2	4	no	—
111	#10625329	—	4	8	no	—
112	C₂×C₄₇⋊C₈	—	2	4	no	—
113	C₂×C₄₇⋊C₈	—	2	4	no	—
114	C₂×C₄₇⋊C₈	—	2	4	no	—
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	2	no	—
122	C₂×C₄×C₄₇	—	2	2	no	—
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	8	no	—
125	C₂×C₄×C₄₇	—	4	4	no	—
126	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
132	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
133	C₂×C₄×C₄₇	#121	1	4	yes	—
134	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
135	C₂×C₄×C₄₇	#125	1	4	yes	—
136	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
137	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
138	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
144	C₂×Dic₄₇	—	2	4	no	—
145	C₂×Dic₄₇	—	2	4	no	—
146	C₂×Dic₄₇	—	2	4	no	—
147	C₂×Dic₄₇	—	2	4	no	—
148	C₂×Dic₄₇	—	2	4	no	—
149	C₂×Dic₄₇	—	4	16	no	—
150	C₂×Dic₄₇	C₂×M₁₆	1	8	yes	—
151	C₈×C₄₇	—	2	4	no	—
152	C₈×C₄₇	—	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	#389	1	4	yes	—
169	C₄×C₄₇	#423	1	4	yes	complemented
170	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
171	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
172	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
173	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
174	Dic₄₇	—	2	8	no	—
175	Dic₄₇	—	4	4	no	—
176	C₂×#423	—	47	1	no	—
177	C₂×#423	—	47	2	no	—
178	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
179	C₂×C₄×C₄⋊C₄	—	47	1	no	—
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	2	no	—
190	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
191	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
192	C₂²×C₄⋊C₄	—	47	2	no	—
193	C₂²×C₄²	—	47	2	no	—
194	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
195	#423	—	94	8	no	—
196	#423	—	94	4	no	—
197	C₂×C₄⋊C₈	—	47	8	no	—
198	C₂×C₄⋊C₈	—	47	2	no	—
199	C₂×C₄⋊C₈	—	47	2	no	—
200	C₄×M₁₆	—	2	4	no	—
201	C₂×#97	C₂×D₄₇	1	2	yes	—
202	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
203	C₄×C₄⋊C₄	—	47	1	no	—
204	C₄×C₄⋊C₄	—	47	2	no	—
205	C₄×C₄⋊C₄	—	47	1	no	—
206	C₄×C₄⋊C₄	—	47	2	no	—
207	C₄×C₄⋊C₄	—	47	2	no	—
208	C₂×#95	—	47	2	no	—
209	#336	—	47	8	no	—
210	C₄₇	#21146	1	1	yes	characteristic, complemented, Sylow
211	C₂³×C₄	—	47	4	no	—
212	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
213	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
215	C₂×M₁₆	—	2	2	no	—
216	C₂×M₁₆	—	2	2	no	—
217	C₂×M₁₆	—	2	2	no	—
218	C₂×M₁₆	—	2	2	no	—
219	C₂×M₁₆	—	94	4	no	—
220	C₂×M₁₆	—	94	4	no	—
221	C₂×M₁₆	—	94	4	no	—
222	C₂×M₁₆	Dic₉₄	1	4	yes	—
223	C₂×M₁₆	D₁₈₈	1	4	yes	—
224	C₂²×C₈	—	47	4	no	—
225	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
226	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
227	C₂×C₄⋊C₄	—	47	2	no	—
228	C₂×C₄⋊C₄	—	47	4	no	—
229	C₂×C₄⋊C₄	—	47	2	no	—
230	C₂×C₄⋊C₄	—	94	8	no	—
231	C₂×C₄²	—	47	2	no	—
232	C₂×C₄²	—	47	2	no	—
233	C₂×C₄²	—	47	4	no	—
234	C₂×C₄²	—	94	4	no	—
235	C₂×C₄²	—	94	4	no	—
236	C₂×C₄²	Dic₉₄	1	4	yes	—
237	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
238	C₂×C₄²	C₄×D₄₇	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	—	2	4	no	—
246	C₄×C₈	—	2	4	no	—
247	#95	—	47	2	no	—
248	#95	—	47	4	no	—
249	#95	—	47	2	no	—
250	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	47	4	no	—
254	C₂²×C₄	—	47	4	no	—
255	C₂²×C₄	—	94	8	no	—
256	C₂²×C₄	—	94	8	no	—
257	C₂²×C₄	—	188	4	no	—
258	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
259	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
260	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
261	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
262	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
265	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
268	C₂²×C₄	#10625350	1	2	yes	—
269	C₂²×C₄	#10625350	1	2	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
271	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
272	M₁₆	—	2	8	no	—
273	M₁₆	—	2	8	no	—
274	M₁₆	—	188	8	no	—
275	C₂×C₈	—	2	2	no	—
276	C₂×C₈	—	2	2	no	—
277	C₂×C₈	—	2	2	no	—
278	C₂×C₈	—	2	2	no	—
279	C₂×C₈	—	94	4	no	—
280	C₂×C₈	—	94	4	no	—
281	C₂×C₈	—	94	4	no	—
282	C₂×C₈	C₂×Dic₉₄	1	4	yes	—
283	C₂×C₈	C₂×D₁₈₈	1	4	yes	—
284	C₄⋊C₄	—	47	8	no	—
285	C₄⋊C₄	—	94	8	no	—
286	C₄⋊C₄	—	94	4	no	—
287	C₄²	—	94	4	no	—
288	C₄²	—	94	4	no	—
289	C₄²	—	94	4	no	—
290	C₄²	—	94	4	no	—
291	C₄²	Dic₄₇⋊C₄	1	4	yes	—
292	C₄²	Dic₄₇⋊C₄	1	4	yes	—
293	C₄²	C₂×Dic₉₄	1	2	yes	—
294	C₄²	C₂×Dic₉₄	1	2	yes	—
295	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
296	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
297	C₂³	—	2	2	no	—
298	C₂³	—	2	2	no	—
299	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
300	C₂³	C₄×D₁₈₈	1	2	yes	—
301	C₂³	C₄×Dic₉₄	1	2	yes	—
302	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
303	C₂×C₄	—	2	2	no	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	8	no	—
307	C₂×C₄	—	4	4	no	—
308	C₂×C₄	—	47	8	no	—
309	C₂×C₄	—	94	4	no	—
310	C₂×C₄	—	94	4	no	—
311	C₂×C₄	—	94	4	no	—
312	C₂×C₄	—	94	4	no	—
313	C₂×C₄	—	94	4	no	—
314	C₂×C₄	—	188	16	no	—
315	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
316	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
317	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
318	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
319	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
320	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
321	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
322	C₂×C₄	#13093998	1	4	yes	—
323	C₂×C₄	#13094003	1	4	yes	—
324	C₂×C₄	#13094016	1	4	yes	—
325	C₂×C₄	#13094024	1	4	yes	—
326	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
327	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
329	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
330	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
331	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
332	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
333	C₈	—	2	4	no	—
334	C₈	—	2	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	#15689021	1	4	yes	—
341	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
342	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
343	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
344	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
345	C₂²	#15689889	1	2	yes	—
346	C₄	—	2	2	no	—
347	C₄	—	2	2	no	—
348	C₄	—	2	2	no	—
349	C₄	—	94	8	no	—
350	C₄	—	188	4	no	—
351	C₄	#15689021	1	4	yes	—
352	C₄	#15689146	1	4	yes	complemented
353	C₄	C₂×#13093998	1	1	yes	characteristic
354	C₄	C₂×#13094003	1	1	yes	characteristic
355	C₄	C₂×#13094016	1	1	yes	characteristic
356	C₄	C₂×#13094024	1	1	yes	characteristic
357	C₂	—	2	4	no	—
358	C₂	C₂×#15689021	1	1	yes	characteristic
359	C₂	C₂×#15689146	1	1	yes	characteristic
360	C₂	#20251951	1	1	yes	characteristic
361	C₂	M₁₆×D₁₈₈	1	2	yes	—
362	C₂	M₁₆×Dic₉₄	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	#21146
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
4. #20244111	C₂	semidirect
5. #20244106	C₂	semidirect
106. C₄⋊Dic₄₇	M₁₆	semidirect
169. C₄×C₄₇	#423	semidirect
210. C₄₇	#21146	semidirect
352. C₄	#15689146	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×#15689146	2
C₂×C₄×C₄⋊Dic₄₇	2
#20244111	2
#20244106	2
#20243081	2
C₂×C₄×M₁₆×C₄₇	2
#21146	47