Subgroups — #26115061

Order 12032.

582 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094013	C₂	1	1	yes	maximal, characteristic
2	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
3	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×Q₈⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
6	C₂×#15688850	C₂	1	1	yes	maximal, characteristic
7	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#13094013	C₄	1	1	yes	characteristic
9	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×Dic₄₇⋊C₈	—	2	2	no	—
12	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	#15689030	C₄	1	1	yes	characteristic
14	#15689024	C₄	1	1	yes	characteristic
15	#15689013	—	2	2	no	—
16	#15688988	C₄	1	1	yes	characteristic
17	C₄×(C₂×D₄₇)⋊C₄	—	2	2	no	—
18	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
19	#15688877	—	2	2	no	—
20	Q₈⋊(C₄₇⋊C₈)	—	2	2	no	—
21	#15688852	—	2	2	no	—
22	#15688850	—	2	2	no	—
23	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×Q₈⋊C₈	—	2	2	no	—
27	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
28	C₂²×C₄×D₄₇	—	2	1	no	—
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	#13094013	—	2	2	no	—
32	#13094013	C₈	1	4	yes	complemented
33	C₄×D₁₈₈	—	2	1	no	—
34	C₄×D₁₈₈	—	2	1	no	—
35	C₄×D₁₈₈	—	2	1	no	—
36	C₄×D₁₈₈	—	2	1	no	—
37	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
39	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
40	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
41	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
44	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
45	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
47	Dic₄₇⋊C₈	—	4	4	no	—
48	C₄×C₄₇⋊C₈	—	2	1	no	—
49	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
50	C₄₇⋊#95	—	2	2	no	—
51	C₄₇⋊#95	—	2	2	no	—
52	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₈×C₄₇	—	2	1	no	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₄×Q₈×C₄₇	—	2	1	no	—
56	C₄×Q₈×C₄₇	—	2	1	no	—
57	C₄×Q₈×C₄₇	—	2	1	no	—
58	C₄×Q₈×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	—	2	1	no	—
62	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊C₈×C₄₇	—	2	1	no	—
64	C₄⋊C₈×C₄₇	—	2	1	no	—
65	C₄×C₈×C₄₇	—	2	1	no	—
66	C₄×C₈×C₄₇	D₄	1	2	yes	—
67	C₂³×D₄₇	—	2	1	no	—
68	C₂×Q₈×C₄₇	—	2	1	no	—
69	C₂×Q₈×C₄₇	—	2	1	no	—
70	C₂×Q₈×C₄₇	—	2	1	no	—
71	C₂×Q₈×C₄₇	—	2	1	no	—
72	C₂×Q₈×C₄₇	—	2	1	no	—
73	C₂×Q₈×C₄₇	C₂×C₈	1	2	yes	—
74	C₂²×C₄×C₄₇	—	2	1	no	—
75	C₂²×C₄×C₄₇	—	2	1	no	—
76	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	—	2	1	no	—
80	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
81	C₂²×Dic₄₇	C₂²⋊C₄	1	2	yes	—
82	C₂×D₁₈₈	—	2	1	no	—
83	C₂×D₁₈₈	—	2	1	no	—
84	C₂×D₁₈₈	—	2	1	no	—
85	C₂×D₁₈₈	—	2	1	no	—
86	C₂×D₁₈₈	—	2	1	no	—
87	C₂×D₁₈₈	C₂×C₈	1	2	yes	—
88	C₂×C₄×D₄₇	—	4	1	no	—
89	C₂×C₄×D₄₇	—	4	1	no	—
90	C₂×C₄×D₄₇	—	4	2	no	—
91	C₂×C₄×D₄₇	—	4	2	no	—
92	C₂×C₈×C₄₇	—	2	2	no	—
93	C₂×C₈×C₄₇	—	4	2	no	—
94	C₂×C₈×C₄₇	—	4	1	no	—
95	C₂×C₈×C₄₇	—	4	2	no	—
96	C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₄⋊C₄×C₄₇	—	4	1	no	—
99	C₄⋊C₄×C₄₇	—	4	1	no	—
100	C₄²×C₄₇	—	4	1	no	—
101	C₄²×C₄₇	—	4	1	no	—
102	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₄²×C₄₇	#41	1	1	yes	characteristic
105	C₄²×C₄₇	#41	1	1	yes	characteristic
106	(C₂×D₄₇)⋊C₄	—	2	8	no	—
107	(C₂×D₄₇)⋊C₄	—	4	4	no	—
108	(C₂×D₄₇)⋊C₄	—	4	1	no	—
109	(C₂×D₄₇)⋊C₄	—	4	1	no	—
110	C₄⋊Dic₄₇	—	2	1	no	—
111	C₄⋊Dic₄₇	—	2	1	no	—
112	C₄×Dic₄₇	—	2	1	no	—
113	C₄×Dic₄₇	—	2	1	no	—
114	C₄×Dic₄₇	—	2	2	no	—
115	C₄×Dic₄₇	—	2	2	no	—
116	C₄×Dic₄₇	—	4	2	no	—
117	C₄×Dic₄₇	C₂×C₈	1	2	yes	—
118	C₄×Dic₄₇	M₁₆	1	2	yes	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	4	1	no	—
122	C₂×C₄₇⋊C₈	—	4	2	no	—
123	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
124	C₂²×D₄₇	—	2	2	no	—
125	C₂²×D₄₇	—	4	1	no	—
126	C₂²×D₄₇	—	4	1	no	—
127	C₂²×D₄₇	—	4	2	no	—
128	C₂²×D₄₇	—	4	2	no	—
129	Q₈×C₄₇	—	2	2	no	—
130	Q₈×C₄₇	—	2	2	no	—
131	Q₈×C₄₇	—	4	1	no	—
132	Q₈×C₄₇	—	4	1	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	4	1	no	—
136	C₂×C₄×C₄₇	—	4	1	no	—
137	C₂×C₄×C₄₇	—	4	1	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
143	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
144	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#131	1	1	yes	characteristic
149	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
150	C₂×C₄×C₄₇	#137	1	2	yes	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	4	1	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	C₂²⋊C₈	1	4	yes	—
159	D₁₈₈	—	2	2	no	—
160	D₁₈₈	—	2	2	no	—
161	D₁₈₈	—	4	1	no	—
162	D₁₈₈	—	4	1	no	—
163	C₄×D₄₇	—	8	2	no	—
164	C₄×D₄₇	—	8	1	no	—
165	C₄×D₄₇	—	8	1	no	—
166	C₈×C₄₇	—	4	2	no	—
167	C₈×C₄₇	—	8	1	no	—
168	C₄₇⋊C₈	—	4	2	no	—
169	C₄₇⋊C₈	—	8	1	no	—
170	#9640	—	47	1	no	maximal, Sylow
171	C₂²×C₄₇	#390	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
173	C₂²×C₄₇	#408	1	1	yes	characteristic
174	C₂²×C₄₇	#417	1	2	yes	—
175	C₂²×C₄₇	#421	1	2	yes	—
176	C₂×D₄₇	—	4	2	no	—
177	C₂×D₄₇	—	4	4	no	—
178	C₂×D₄₇	—	8	1	no	—
179	C₂×D₄₇	—	8	1	no	—
180	C₂×D₄₇	—	8	2	no	—
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	4	2	no	—
184	C₄×C₄₇	—	8	1	no	—
185	C₄×C₄₇	C₈×D₄	1	1	yes	characteristic
186	C₄×C₄₇	C₈×D₄	1	1	yes	characteristic
187	C₄×C₄₇	#436	1	1	yes	characteristic
188	C₄×C₄₇	#436	1	1	yes	characteristic
189	C₄×C₄₇	#489	1	2	yes	—
190	C₄×C₄₇	#496	1	1	yes	characteristic
191	C₄×C₄₇	#497	1	1	yes	characteristic
192	Dic₄₇	—	2	4	no	—
193	Dic₄₇	—	4	2	no	—
194	Dic₄₇	—	8	1	no	—
195	C₄×#124	—	47	1	no	—
196	#1842	—	47	1	no	—
197	#1744	—	47	1	no	—
198	C₂×Q₈⋊C₈	—	47	1	no	—
199	C₂×Q₈⋊C₈	D₄₇	1	1	yes	characteristic, complemented
200	C₂×D₄⋊C₈	—	47	1	no	—
201	C₂×D₄⋊C₈	—	47	1	no	—
202	C₂×C₄₇	#1477	1	2	yes	—
203	C₂×C₄₇	#1495	1	2	yes	—
204	C₂×C₄₇	#1954	1	1	yes	characteristic
205	C₂×C₄₇	#1959	1	1	yes	characteristic
206	C₂×C₄₇	#1963	1	1	yes	characteristic
207	D₄₇	—	8	2	no	—
208	C₂×#124	—	47	1	no	—
209	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
210	C₂×C₄×D₄	—	47	1	no	—
211	C₂×C₄⋊C₈	—	47	1	no	—
212	C₂×C₄⋊C₈	—	94	2	no	—
213	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
214	C₂×C₄×C₈	—	47	1	no	—
215	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
216	#391	—	47	1	no	—
217	#390	—	47	1	no	—
218	#388	—	94	2	no	—
219	#382	—	47	1	no	—
220	C₄×C₂²⋊C₄	—	94	2	no	—
221	C₄³	—	47	1	no	—
222	#336	—	94	2	no	—
223	Q₈⋊C₈	—	2	2	no	—
224	Q₈⋊C₈	—	94	2	no	—
225	D₄⋊C₈	—	94	2	no	—
226	D₄⋊C₈	—	94	2	no	—
227	C₄₇	#9640	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
229	C₂²×D₄	—	47	1	no	—
230	C₂³×C₄	—	94	1	no	—
231	C₂²×C₈	—	2	1	no	—
232	C₂²×C₈	—	2	1	no	—
233	C₂²×C₈	—	94	1	no	—
234	C₂²×C₈	—	94	1	no	—
235	#124	—	47	4	no	—
236	#124	—	94	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	—	2	1	no	—
241	C₄×D₄	—	94	1	no	—
242	C₄×D₄	—	94	1	no	—
243	C₄×D₄	—	94	1	no	—
244	C₄×D₄	—	94	1	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	47	1	no	—
247	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
248	C₂×C₂²⋊C₄	—	94	2	no	—
249	C₂×C₂²⋊C₄	—	94	2	no	—
250	C₂×C₂²⋊C₄	—	94	1	no	—
251	C₂×C₄²	—	2	1	no	—
252	C₂×C₄²	—	47	1	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	47	2	no	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	C₄⋊C₈	—	2	1	no	—
258	C₄⋊C₈	—	2	1	no	—
259	C₄⋊C₈	—	94	1	no	—
260	C₄⋊C₈	—	94	1	no	—
261	C₄⋊C₈	—	188	4	no	—
262	C₄×C₈	—	2	1	no	—
263	C₄×C₈	—	47	2	no	—
264	C₄×C₈	—	94	1	no	—
265	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
266	#95	—	94	2	no	—
267	#95	—	94	2	no	—
268	C₂⁴	—	94	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	1	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	1	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	C₈×D₄₇	1	2	yes	—
275	C₂×D₄	—	47	2	no	—
276	C₂×D₄	—	94	1	no	—
277	C₂×D₄	—	94	1	no	—
278	C₂×D₄	—	94	1	no	—
279	C₂×D₄	—	94	1	no	—
280	C₂×D₄	—	94	1	no	—
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	47	2	no	—
285	C₂²×C₄	—	94	1	no	—
286	C₂²×C₄	—	188	1	no	—
287	C₂²×C₄	—	188	1	no	—
288	C₂²×C₄	—	188	2	no	—
289	C₂²×C₄	—	188	2	no	—
290	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
291	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	188	1	no	—
299	C₂×C₈	—	188	2	no	—
300	C₂×C₈	—	188	2	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	4	1	no	—
304	C₄⋊C₄	—	4	1	no	—
305	C₄⋊C₄	—	94	1	no	—
306	C₄⋊C₄	—	94	1	no	—
307	C₂²⋊C₄	—	94	8	no	—
308	C₂²⋊C₄	—	188	4	no	—
309	C₂²⋊C₄	—	188	1	no	—
310	C₂²⋊C₄	—	188	1	no	—
311	C₄²	—	4	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	47	2	no	—
314	C₄²	—	47	2	no	—
315	C₄²	—	94	1	no	—
316	C₄²	—	94	1	no	—
317	C₄²	—	94	2	no	—
318	C₄²	—	94	2	no	—
319	C₄²	—	188	2	no	—
320	C₄²	#10625350	1	1	yes	characteristic
321	C₄²	D₄×D₄₇	1	1	yes	characteristic
322	C₄²	#10625352	1	1	yes	characteristic
323	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂³	—	94	2	no	—
325	C₂³	—	188	1	no	—
326	C₂³	—	188	1	no	—
327	C₂³	—	188	2	no	—
328	C₂³	—	188	2	no	—
329	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
330	Q₈	—	2	2	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	4	1	no	—
333	Q₈	—	4	1	no	—
334	D₄	—	94	2	no	—
335	D₄	—	94	2	no	—
336	D₄	—	188	1	no	—
337	D₄	—	188	1	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	4	1	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	47	4	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	376	2	no	—
351	C₂×C₄	—	376	1	no	—
352	C₂×C₄	—	376	1	no	—
353	C₂×C₄	—	188	1	no	—
354	C₂×C₄	—	188	2	no	—
355	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
356	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
357	C₂×C₄	#13093996	1	1	yes	characteristic
358	C₂×C₄	#13093997	1	1	yes	characteristic
359	C₂×C₄	#13094010	1	1	yes	characteristic
360	C₂×C₄	#13094020	1	1	yes	characteristic
361	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
362	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
363	C₂×C₄	#13094030	1	1	yes	characteristic
364	C₂×C₄	#13094032	1	1	yes	characteristic
365	C₂×C₄	#13094051	1	2	yes	—
366	C₂×C₄	#13094056	1	2	yes	—
367	C₈	—	4	2	no	—
368	C₈	—	8	1	no	—
369	C₈	—	376	1	no	—
370	C₈	—	188	2	no	—
371	C₂²	—	376	2	no	—
372	C₂²	—	376	1	no	—
373	C₂²	—	376	1	no	—
374	C₂²	—	188	4	no	—
375	C₂²	—	188	2	no	—
376	C₂²	#15689023	1	1	yes	characteristic
377	C₂²	C₂²⋊C₈×D₄₇	1	1	yes	characteristic
378	C₂²	#15689088	1	1	yes	characteristic
379	C₂²	#15689123	1	2	yes	—
380	C₂²	#15689138	1	2	yes	—
381	C₄	—	2	1	no	—
382	C₄	—	2	1	no	—
383	C₄	—	4	2	no	—
384	C₄	—	8	1	no	—
385	C₄	—	94	4	no	—
386	C₄	—	376	1	no	—
387	C₄	—	188	2	no	—
388	C₄	(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
389	C₄	C₈×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₄	#15689198	1	1	yes	characteristic
391	C₄	#15689199	1	1	yes	characteristic
392	C₄	#15689484	1	2	yes	—
393	C₄	#15689509	1	1	yes	characteristic
394	C₄	#15689516	1	1	yes	characteristic
395	C₂	—	376	2	no	—
396	C₂	#20241774	1	2	yes	—
397	C₂	#20241852	1	2	yes	—
398	C₂	#20244180	1	1	yes	characteristic
399	C₂	#20244201	1	1	yes	characteristic
400	C₂	#20244218	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×Q₈⋊C₈	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×Q₈⋊C₈	D₄₇
hypocenter	C₄₇	#9640
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
2. #20243539	C₂	semidirect
3. #20243133	C₂	semidirect
4. C₂×Q₈⋊(C₄₇⋊C₈)	C₂	semidirect
7. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
32. #13094013	C₈	semidirect
199. C₂×Q₈⋊C₈	D₄₇	semidirect
227. C₄₇	#9640	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094013	2
#20243539	2
#20243133	2
C₂×Q₈⋊(C₄₇⋊C₈)	2
C₂×#15688852	2
C₂×#15688850	2
C₂×C₄₇×Q₈⋊C₈	2
#9640	47