Subgroups — #26230159

Order 12032.

818 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253833	C₂	1	1	yes	maximal, characteristic
2	#20252101	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244221	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244219	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243718	C₂	1	4	yes	maximal, complemented
6	#20243715	C₂	1	4	yes	maximal, complemented
7	#20243528	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243139	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#13094044	C₂²	1	4	yes	—
11	C₂×#13094030	C₂²	1	2	yes	—
12	#15689673	C₂²	1	1	yes	characteristic
13	#15689518	C₄	1	2	yes	complemented
14	#15689515	C₄	1	2	yes	complemented
15	#15689513	C₄	1	2	yes	complemented
16	#15689510	C₄	1	2	yes	complemented
17	#15689202	—	2	1	no	—
18	#15689202	—	2	1	no	—
19	C₈×D₁₈₈	—	2	1	no	—
20	C₈×D₁₈₈	—	2	1	no	—
21	#15689147	C₂²	1	1	yes	characteristic
22	C₂×#13093951	C₂²	1	4	yes	—
23	C₂×#13093950	C₂²	1	4	yes	—
24	#15689089	C₂²	1	2	yes	—
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	#15688969	C₂²	1	1	yes	characteristic
27	#15688887	C₂²	1	4	yes	—
28	#15688877	C₂²	1	2	yes	—
29	#15688877	C₂²	1	2	yes	—
30	C₂×#131×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#532	C₂²	1	1	yes	characteristic
32	C₄₇×#436	—	2	1	no	—
33	C₄₇×#436	—	2	1	no	—
34	C₈×D₄×C₄₇	—	2	1	no	—
35	C₈×D₄×C₄₇	—	2	1	no	—
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₄₇×#408	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#10625350	C₂³	1	2	yes	—
40	#13094044	—	4	4	no	—
41	#13094044	—	4	4	no	—
42	C₂×#10625337	C₂×C₄	1	4	yes	—
43	C₂×#10625335	C₂×C₄	1	4	yes	—
44	C₂×#10625336	C₂×C₄	1	4	yes	—
45	C₂×#10625334	C₂×C₄	1	4	yes	—
46	#13094030	—	4	4	no	—
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂×#10625324	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	#13094024	C₂×C₄	1	1	yes	characteristic
52	#13094021	C₂×C₄	1	1	yes	characteristic
53	#13094012	C₂×C₄	1	2	yes	—
54	#13093998	—	2	1	no	—
55	#13093998	—	2	1	no	—
56	C₄×D₁₈₈	—	2	1	no	—
57	C₄×D₁₈₈	—	2	1	no	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
61	#13093951	—	4	4	no	—
62	#13093950	—	4	4	no	—
63	(C₂×D₄₇)⋊C₈	—	2	2	no	—
64	(C₂×D₄₇)⋊C₈	—	2	2	no	—
65	#13093935	C₂×C₄	1	2	yes	—
66	#13093935	C₂×C₄	1	2	yes	—
67	C₄₇⋊#95	—	2	1	no	—
68	C₄₇⋊#95	—	2	1	no	—
69	C₂×#41×C₄₇	C₂³	1	2	yes	—
70	#131×C₄₇	—	4	4	no	—
71	C₂×M₁₆×C₄₇	—	2	2	no	—
72	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	—	2	2	no	—
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
77	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
78	#124×C₄₇	C₂×C₄	1	2	yes	—
79	#121×C₄₇	—	2	1	no	—
80	#121×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₄⋊C₈×C₄₇	—	2	1	no	—
85	C₄⋊C₈×C₄₇	—	2	1	no	—
86	C₂²⋊C₈×C₄₇	—	2	2	no	—
87	C₂²⋊C₈×C₄₇	—	2	2	no	—
88	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
89	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
90	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
91	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
92	#41×C₄₇	—	2	4	no	—
93	#41×C₄₇	—	2	4	no	—
94	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
103	C₂×C₂²⋊D₄₇	—	2	2	no	—
104	C₂²×Dic₄₇	—	2	2	no	—
105	#10625350	—	2	4	no	—
106	#10625350	—	2	4	no	—
107	C₂×D₁₈₈	—	2	1	no	—
108	C₂×D₁₈₈	—	2	1	no	—
109	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
112	M₁₆×C₄₇	—	2	4	no	—
113	M₁₆×C₄₇	—	4	4	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	4	4	no	—
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₂²⋊C₄×C₄₇	—	2	2	no	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	#10625337	—	4	4	no	—
131	#10625336	—	4	4	no	—
132	#10625335	—	4	4	no	—
133	#10625334	—	4	4	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	(C₂×D₄₇)⋊C₄	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	1	no	—
137	C₄⋊Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	#10625329	—	2	4	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
145	#10625324	—	4	4	no	—
146	C₈×D₄₇	—	4	4	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
149	C₂²×D₄₇	—	2	2	no	—
150	Q₈×C₄₇	—	2	4	no	—
151	D₄×C₄₇	—	2	4	no	—
152	D₄×C₄₇	—	4	2	no	—
153	D₄×C₄₇	—	4	2	no	—
154	D₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	4	1	no	—
157	C₂×C₄×C₄₇	—	4	1	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
167	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
168	C₂²⋊D₄₇	—	4	4	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	D₁₈₈	—	2	4	no	—
174	D₁₈₈	—	4	2	no	—
175	D₁₈₈	—	4	2	no	—
176	C₄×D₄₇	—	4	2	no	—
177	C₄×D₄₇	—	4	2	no	—
178	Dic₉₄	—	2	4	no	—
179	C₈×C₄₇	—	2	1	no	—
180	C₈×C₄₇	—	2	1	no	—
181	C₈×C₄₇	—	2	1	no	—
182	C₈×C₄₇	—	2	1	no	—
183	C₈×C₄₇	—	4	2	no	—
184	C₄₇⋊C₈	—	2	4	no	—
185	C₄₇⋊C₈	—	4	2	no	—
186	#22281	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	2	1	no	—
188	C₂²×C₄₇	—	2	1	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	—	4	2	no	—
191	C₂²×C₄₇	—	4	2	no	—
192	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₂²×C₄₇	#540	1	2	yes	—
194	C₂×D₄₇	—	4	2	no	—
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	—	4	2	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	4	2	no	—
202	C₄×C₄₇	#518	1	2	yes	—
203	C₄×C₄₇	#535	1	1	yes	characteristic
204	C₄×C₄₇	#535	1	1	yes	characteristic
205	Dic₄₇	—	4	2	no	—
206	Dic₄₇	—	8	2	no	—
207	#3150	—	47	1	no	—
208	#2931	—	47	1	no	—
209	#2931	D₄₇	1	1	yes	characteristic, complemented
210	#1963	—	47	1	no	—
211	#1963	—	47	1	no	—
212	#1876	—	47	4	no	—
213	#1876	—	47	4	no	—
214	#1838	—	47	1	no	—
215	#1746	—	47	1	no	—
216	C₂×C₄₇	—	2	2	no	—
217	C₂×C₄₇	—	8	2	no	—
218	C₂×C₄₇	#2328	1	1	yes	characteristic
219	C₂×C₄₇	#2955	1	1	yes	characteristic
220	C₂×C₄₇	#2955	1	1	yes	characteristic
221	D₄₇	—	8	2	no	—
222	C₂×#135	—	47	4	no	—
223	C₂×#131	—	47	2	no	—
224	C₂×#131	C₂×D₄₇	1	2	yes	—
225	#532	—	47	1	no	—
226	#532	C₂×D₄₇	1	1	yes	characteristic
227	#497	—	47	2	no	—
228	#497	—	47	2	no	—
229	#496	—	47	2	no	—
230	#496	—	47	2	no	—
231	#436	—	2	1	no	—
232	#436	—	2	1	no	—
233	#436	—	94	1	no	—
234	#436	—	94	1	no	—
235	C₈×D₄	—	2	1	no	—
236	C₈×D₄	—	2	1	no	—
237	C₈×D₄	—	94	1	no	—
238	C₈×D₄	—	94	1	no	—
239	#423	—	47	1	no	—
240	#423	C₂×D₄₇	1	1	yes	characteristic
241	C₂×#104	—	47	4	no	—
242	C₂×#104	—	47	4	no	—
243	#408	—	47	2	no	—
244	#408	C₂×D₄₇	1	2	yes	—
245	C₂×#97	—	47	1	no	—
246	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
247	#376	—	47	1	no	—
248	#341	—	47	4	no	—
249	#336	—	47	2	no	—
250	#336	—	47	2	no	—
251	C₄₇	#22281	1	1	yes	characteristic, complemented, Sylow
252	C₂×#41	—	47	2	no	—
253	C₂×#41	C₂²×D₄₇	1	2	yes	—
254	#135	—	188	4	no	—
255	#135	—	188	4	no	—
256	C₂×Q₁₆	—	47	4	no	—
257	C₂×SD₁₆	—	47	4	no	—
258	C₂×SD₁₆	—	47	4	no	—
259	C₂×D₈	—	47	4	no	—
260	#131	—	4	4	no	—
261	#131	—	188	4	no	—
262	C₂×M₁₆	—	2	2	no	—
263	C₂×M₁₆	—	47	2	no	—
264	C₂×M₁₆	—	94	2	no	—
265	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	47	2	no	—
268	C₂²×C₈	—	94	2	no	—
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
271	C₄⋊Q₈	—	47	1	no	—
272	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
273	#127	—	47	1	no	—
274	#127	C₄×D₄₇	1	1	yes	characteristic
275	#124	—	47	2	no	—
276	#124	C₄×D₄₇	1	2	yes	—
277	#121	—	2	1	no	—
278	#121	—	2	1	no	—
279	#121	—	94	1	no	—
280	#121	—	94	1	no	—
281	C₄×D₄	—	2	1	no	—
282	C₄×D₄	—	2	1	no	—
283	C₄×D₄	—	94	1	no	—
284	C₄×D₄	—	94	1	no	—
285	C₂×C₄²	—	47	2	no	—
286	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
287	C₄⋊C₈	—	2	1	no	—
288	C₄⋊C₈	—	2	1	no	—
289	C₄⋊C₈	—	94	1	no	—
290	C₄⋊C₈	—	94	1	no	—
291	#104	—	188	4	no	—
292	#104	—	188	4	no	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	2	2	no	—
295	C₂²⋊C₈	—	94	2	no	—
296	C₂²⋊C₈	—	94	2	no	—
297	#97	—	47	2	no	—
298	#97	—	47	2	no	—
299	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
300	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
301	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
302	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
303	#95	—	94	1	no	—
304	#95	—	94	1	no	—
305	#41	—	2	4	no	—
306	#41	—	2	4	no	—
307	#41	—	94	4	no	—
308	#41	—	94	4	no	—
309	C₂×Q₈	—	47	2	no	—
310	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	2	1	no	—
313	C₂×D₄	—	2	1	no	—
314	C₂×D₄	—	47	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	—	94	1	no	—
317	C₂×D₄	—	94	1	no	—
318	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	94	2	no	—
321	C₂²×C₄	—	94	2	no	—
322	C₂²×C₄	#10625350	1	1	yes	characteristic
323	C₂²×C₄	#10625350	1	1	yes	characteristic
324	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
325	Q₁₆	—	188	4	no	—
326	SD₁₆	—	188	4	no	—
327	SD₁₆	—	188	4	no	—
328	D₈	—	188	4	no	—
329	M₁₆	—	2	4	no	—
330	M₁₆	—	4	4	no	—
331	M₁₆	—	94	4	no	—
332	M₁₆	—	188	4	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₂×C₈	—	4	4	no	—
337	C₂×C₈	—	47	4	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	188	4	no	—
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
345	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
346	C₄⋊C₄	—	2	1	no	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	94	1	no	—
349	C₄⋊C₄	—	94	1	no	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	2	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₂²⋊C₄	—	94	2	no	—
354	C₄²	—	94	2	no	—
355	C₄²	—	94	2	no	—
356	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
357	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
358	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
359	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₂³	—	2	2	no	—
361	C₂³	—	94	2	no	—
362	C₂³	C₂×#10625350	1	1	yes	characteristic
363	Q₈	—	2	4	no	—
364	Q₈	—	94	4	no	—
365	D₄	—	2	4	no	—
366	D₄	—	4	2	no	—
367	D₄	—	4	2	no	—
368	D₄	—	4	4	no	—
369	D₄	—	94	4	no	—
370	D₄	—	188	2	no	—
371	D₄	—	188	2	no	—
372	D₄	—	188	4	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	—	188	2	no	—
381	C₂×C₄	—	188	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
388	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
389	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂×C₄	#13094069	1	2	yes	—
391	C₂×C₄	#13094070	1	2	yes	—
392	C₈	—	2	1	no	—
393	C₈	—	2	1	no	—
394	C₈	—	2	1	no	—
395	C₈	—	2	1	no	—
396	C₈	—	4	2	no	—
397	C₈	—	94	4	no	—
398	C₈	—	188	2	no	—
399	C₂²	—	2	1	no	—
400	C₂²	—	2	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	188	2	no	—
405	C₂²	—	188	2	no	—
406	C₂²	—	188	2	no	—
407	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
408	C₂²	#15689724	1	2	yes	—
409	C₄	—	2	1	no	—
410	C₄	—	2	1	no	—
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	4	2	no	—
414	C₄	—	376	2	no	—
415	C₄	—	188	2	no	—
416	C₄	#15689595	1	2	yes	—
417	C₄	#15689687	1	1	yes	characteristic
418	C₄	#15689690	1	1	yes	characteristic
419	C₂	—	2	2	no	—
420	C₂	—	8	2	no	—
421	C₂	—	376	2	no	—
422	C₂	#20246110	1	1	yes	characteristic
423	C₂	#20252289	1	1	yes	characteristic
424	C₂	#20252289	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#2931	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253833	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2931	D₄₇
hypocenter	C₄₇	#22281
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. #20252101	C₂	semidirect
3. #20244221	C₂	semidirect
4. #20244219	C₂	semidirect
5. #20243718	C₂	semidirect
6. #20243715	C₂	semidirect
7. #20243528	C₂	semidirect
8. #20243139	C₂	semidirect
9. C₄₇×#2931	C₂	semidirect
13. #15689518	C₄	semidirect
14. #15689515	C₄	semidirect
15. #15689513	C₄	semidirect
16. #15689510	C₄	semidirect
209. #2931	D₄₇	semidirect
251. C₄₇	#22281	semidirect

Maximal subgroups

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

subgroup	index
#20253833	2
#20252101	2
#20244221	2
#20244219	2
#20243718	2
#20243715	2
#20243528	2
#20243139	2
C₄₇×#2931	2
#22281	47