Subgroups — #26220795

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 366 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	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
3	#20244346	C₂	1	4	yes	maximal, complemented
4	#20244341	C₂	1	2	yes	maximal, complemented
5	#20244337	C₂	1	2	yes	maximal, complemented
6	#20243104	C₂	1	4	yes	maximal
7	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
8	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
9	C₂×#13093983	C₂²	1	2	yes	—
10	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
14	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
15	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
16	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
17	#15688969	—	2	1	no	—
18	C₄²×Dic₄₇	—	2	1	no	—
19	#15688885	C₂²	1	8	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	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
27	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
28	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
29	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
30	C₂×#117×C₄₇	C₂²	1	2	yes	—
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	—	2	4	no	—
36	#13093983	Q₈	1	8	yes	complemented
37	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
38	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
39	C₂×C₄×Dic₄₇	—	2	2	no	—
40	C₂×C₄×Dic₄₇	—	2	2	no	—
41	C₂×C₄×Dic₄₇	—	2	2	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	—	2	1	no	—
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	4	no	—
56	#125×C₄₇	C₂×C₄	1	8	yes	—
57	C₂²⋊Q₈×C₄₇	—	2	8	no	—
58	C₂²⋊Q₈×C₄₇	—	2	8	no	—
59	C₄×Q₈×C₄₇	—	2	8	no	—
60	C₄×Q₈×C₄₇	—	2	8	no	—
61	#117×C₄₇	—	2	4	no	—
62	#117×C₄₇	C₂×C₄	1	8	yes	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
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	4	no	—
80	C₂×Q₈×C₄₇	—	4	4	no	—
81	C₂×Q₈×C₄₇	—	4	4	no	—
82	C₂²×C₄×C₄₇	—	2	4	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	4	2	no	—
86	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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×Q₈	1	4	yes	—
96	C₂²×C₄×C₄₇	#41	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	4	no	—
99	C₄⋊C₄×C₄₇	—	2	8	no	—
100	C₄⋊C₄×C₄₇	—	2	8	no	—
101	C₄⋊C₄×C₄₇	—	2	4	no	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
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	—	2	8	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄⋊Dic₄₇	C₂×Q₈	1	8	yes	—
118	C₄×Dic₄₇	—	2	8	no	—
119	C₄×Dic₄₇	—	4	4	no	—
120	C₄×Dic₄₇	—	4	4	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	8	no	—
123	C₂×C₄₇⋊C₈	—	4	8	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	2	2	no	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂³×C₄₇	C₂²⋊Q₈	1	4	yes	—
128	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₄₇	—	4	8	no	—
130	Q₈×C₄₇	—	4	8	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	8	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	4	4	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
144	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
146	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
147	C₂×C₄×C₄₇	#124	1	4	yes	—
148	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
149	C₂×C₄×C₄₇	#135	1	4	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
154	C₂×Dic₄₇	—	2	8	no	—
155	C₂×Dic₄₇	—	4	4	no	—
156	C₂×Dic₄₇	—	4	4	no	—
157	C₄₇⋊C₈	—	4	4	no	—
158	#21311	—	47	1	no	maximal, Sylow
159	C₂²×C₄₇	—	2	8	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	#391	1	4	yes	—
163	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
165	C₂²×C₄₇	C₂×#135	1	2	yes	—
166	C₂²×C₄₇	#575	1	2	yes	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	4	4	no	—
171	C₄×C₄₇	—	4	4	no	—
172	C₄×C₄₇	#391	1	4	yes	—
173	C₄×C₄₇	#416	1	4	yes	—
174	C₄×C₄₇	C₂×C₄×Q₈	1	2	yes	—
175	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
176	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	Dic₄₇	—	4	8	no	—
178	C₂×#533	D₄₇	1	1	yes	characteristic
179	C₂²×C₄⋊C₈	—	47	1	no	—
180	C₄×#117	—	47	1	no	—
181	#1989	—	47	4	no	—
182	#1988	—	47	2	no	—
183	#1987	—	47	2	no	—
184	#1735	—	47	4	no	—
185	C₂×C₄₇	—	2	4	no	—
186	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
188	C₂×C₄₇	#2896	1	1	yes	characteristic
189	C₂×C₄₇	#3076	1	4	yes	—
190	C₂³×C₈	—	47	2	no	—
191	#533	—	2	4	no	—
192	#533	Dic₄₇	1	8	yes	complemented
193	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
195	C₂×#125	C₂×D₄₇	1	2	yes	—
196	C₂×C₂²⋊Q₈	—	2	1	no	—
197	C₂×C₂²⋊Q₈	—	2	1	no	—
198	C₂×C₄×Q₈	—	2	1	no	—
199	C₂×C₄×Q₈	—	2	1	no	—
200	C₂×#117	—	47	2	no	—
201	C₂×#117	C₂×D₄₇	1	2	yes	—
202	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
203	C₂×C₄⋊C₈	—	47	2	no	—
204	C₂×C₄⋊C₈	—	47	2	no	—
205	C₂×C₄⋊C₈	—	94	4	no	—
206	C₄×C₄⋊C₄	—	47	2	no	—
207	C₄×C₄⋊C₄	—	47	2	no	—
208	C₄×C₂²⋊C₄	—	94	1	no	—
209	C₄×C₂²⋊C₄	—	94	1	no	—
210	#376	—	94	1	no	—
211	C₄³	—	94	1	no	—
212	#340	—	47	8	no	—
213	#340	—	47	8	no	—
214	C₄₇	#21311	1	1	yes	characteristic, complemented, Sylow
215	C₂²×Q₈	—	2	1	no	—
216	C₂²×Q₈	—	2	1	no	—
217	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
220	C₂²×C₈	—	47	4	no	—
221	C₂²×C₈	—	94	8	no	—
222	C₂²×C₈	—	94	4	no	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
226	C₄⋊Q₈	C₂×Dic₄₇	1	4	yes	—
227	#125	—	2	4	no	—
228	#125	C₂×Dic₄₇	1	8	yes	—
229	C₂²⋊Q₈	—	2	8	no	—
230	C₂²⋊Q₈	—	2	8	no	—
231	C₄×Q₈	—	2	8	no	—
232	C₄×Q₈	—	2	8	no	—
233	#117	—	2	4	no	—
234	#117	—	47	8	no	—
235	#117	—	94	4	no	—
236	#117	C₂×Dic₄₇	1	8	yes	—
237	C₂×C₄⋊C₄	—	2	2	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	1	no	—
240	C₂×C₄⋊C₄	—	2	1	no	—
241	C₂×C₄⋊C₄	—	47	4	no	—
242	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
243	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	94	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	94	2	no	—
248	C₂×C₄²	—	94	2	no	—
249	C₂×C₄²	—	94	2	no	—
250	C₂×C₄²	C₂×Dic₄₇	1	4	yes	—
251	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₂²⋊D₄₇	1	4	yes	—
254	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₄⋊C₈	—	94	4	no	—
257	C₄⋊C₈	—	94	4	no	—
258	#95	—	94	2	no	—
259	#95	—	94	2	no	—
260	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
261	C₂×Q₈	—	2	4	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	4	4	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	4	2	no	—
269	C₂²×C₄	—	94	4	no	—
270	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
271	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
272	C₂²×C₄	Q₈×D₄₇	1	4	yes	—
273	C₂²×C₄	#10625354	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
275	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
280	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
281	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
282	C₂×C₈	—	94	4	no	—
283	C₂×C₈	—	94	8	no	—
284	C₂×C₈	—	188	8	no	—
285	C₄⋊C₄	—	2	8	no	—
286	C₄⋊C₄	—	2	8	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	2	no	—
290	C₄⋊C₄	—	2	2	no	—
291	C₄⋊C₄	—	47	8	no	—
292	C₄⋊C₄	—	94	4	no	—
293	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
294	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	94	8	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	94	8	no	—
299	C₄²	—	188	4	no	—
300	C₄²	—	188	4	no	—
301	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
302	C₄²	C₂²⋊Dic₄₇	1	4	yes	—
303	C₄²	C₂²×Dic₄₇	1	2	yes	—
304	C₄²	C₂²×Dic₄₇	1	2	yes	—
305	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
306	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
310	C₂³	#13094000	1	4	yes	—
311	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
312	Q₈	—	4	8	no	—
313	Q₈	—	4	8	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	94	8	no	—
324	C₂×C₄	—	188	4	no	—
325	C₂×C₄	—	188	4	no	—
326	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
327	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
328	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
329	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
330	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
331	C₂×C₄	Q₈×Dic₄₇	1	8	yes	—
332	C₂×C₄	#13094000	1	4	yes	—
333	C₂×C₄	#13094013	1	4	yes	—
334	C₂×C₄	#13094022	1	4	yes	—
335	C₂×C₄	#13094044	1	4	yes	—
336	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
338	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
339	C₂×C₄	C₂×#10625354	1	2	yes	—
340	C₈	—	188	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	8	no	—
344	C₂²	#15689030	1	4	yes	—
345	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
346	C₂²	C₂×#13094000	1	2	yes	—
347	C₂²	C₂×#13094044	1	2	yes	—
348	C₂²	#15689921	1	2	yes	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	4	4	no	—
353	C₄	—	4	4	no	—
354	C₄	—	188	8	no	—
355	C₄	#15689030	1	4	yes	—
356	C₄	#15689119	1	4	yes	—
357	C₄	C₂×Q₈×Dic₄₇	1	2	yes	—
358	C₄	C₂×#13094013	1	1	yes	characteristic
359	C₄	C₂×#13094022	1	1	yes	characteristic
360	C₂	—	2	4	no	—
361	C₂	C₂×#15689030	1	1	yes	characteristic
362	C₂	C₂×#15689119	1	1	yes	characteristic
363	C₂	#20251907	1	1	yes	characteristic
364	C₂	#20253170	1	4	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	#21311
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. #20244346	C₂	semidirect
4. #20244341	C₂	semidirect
5. #20244337	C₂	semidirect
22. C₄₇×#533	C₄	semidirect
36. #13093983	Q₈	semidirect
192. #533	Dic₄₇	semidirect
214. C₄₇	#21311	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
C₄×#13093983	2
#20244346	2
#20244341	2
#20244337	2
#20243104	2
C₂×C₄₇×#533	2
#21311	47