Subgroups — #26123267

Order 12032.

942 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251952	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689140	C₂	1	2	yes	maximal
3	#20243121	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15688883	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2297	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂×#13093983	C₂²	1	2	yes	—
8	#15689150	—	2	4	no	—
9	#15689147	—	2	2	no	—
10	#15689140	—	2	4	no	—
11	#15689140	—	2	4	no	—
12	C₂×#13093951	—	2	4	no	—
13	#15688890	—	2	2	no	—
14	#15688883	—	2	4	no	—
15	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#391	C₄	1	2	yes	complemented
19	C₄₇×#390	C₄	1	2	yes	complemented
20	C₄₇×#386	—	2	2	no	—
21	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
22	C₂×#10625329	—	2	2	no	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	D₄	1	4	yes	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	#13093983	—	2	2	no	—
30	#13093983	—	2	2	no	—
31	#13093983	—	2	2	no	—
32	#13093983	D₄	1	4	yes	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	#13093951	—	2	16	no	—
38	C₂×#41×C₄₇	—	2	1	no	—
39	C₂×#41×C₄₇	—	2	1	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	—	2	2	no	—
43	C₂×#41×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	D₄	1	2	yes	—
45	C₂×#41×C₄₇	Q₈	1	2	yes	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	—	2	1	no	—
50	C₂³×C₄×C₄₇	—	2	1	no	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	#117×C₄₇	—	2	2	no	—
53	#117×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	1	no	—
60	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
61	C₂×C₄²×C₄₇	D₄	1	2	yes	—
62	#95×C₄₇	—	2	4	no	—
63	C₂⁴×C₄₇	—	2	1	no	—
64	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
65	#41×C₄₇	—	2	4	no	—
66	#41×C₄₇	—	2	4	no	—
67	#41×C₄₇	—	2	4	no	—
68	#41×C₄₇	—	2	4	no	—
69	#41×C₄₇	—	4	2	no	—
70	#41×C₄₇	—	4	2	no	—
71	#41×C₄₇	—	4	2	no	—
72	#41×C₄₇	—	4	2	no	—
73	C₂×Q₈×C₄₇	—	2	1	no	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	—	2	2	no	—
76	C₂×Q₈×C₄₇	C₄⋊C₄	1	2	yes	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	1	no	—
80	C₂×D₄×C₄₇	—	2	2	no	—
81	C₂×D₄×C₄₇	—	2	2	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	C₄⋊C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	—	4	2	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	1	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	C₂²×C₄×C₄₇	#41	1	2	yes	—
106	C₂²×Dic₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₂²⋊C₄×C₄₇	—	2	4	no	—
109	C₂²⋊C₄×C₄₇	—	4	8	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	4	no	—
113	C₄²×C₄₇	—	4	1	no	—
114	C₄²×C₄₇	—	4	1	no	—
115	C₂²⋊Dic₄₇	—	2	4	no	—
116	C₂²⋊Dic₄₇	—	4	2	no	—
117	C₄⋊Dic₄₇	—	2	4	no	—
118	C₄⋊Dic₄₇	—	4	2	no	—
119	C₄×Dic₄₇	—	2	4	no	—
120	C₄×Dic₄₇	—	4	2	no	—
121	#10625329	—	2	4	no	—
122	#10625329	—	2	4	no	—
123	#10625329	—	4	2	no	—
124	#10625329	—	4	2	no	—
125	C₂×C₄₇⋊C₈	—	2	4	no	—
126	C₂×C₄₇⋊C₈	—	4	2	no	—
127	C₂×C₄₇⋊C₈	—	4	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	1	no	—
132	C₂³×C₄₇	—	4	1	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
134	C₂³×C₄₇	#121	1	2	yes	—
135	C₂³×C₄₇	#121	1	2	yes	—
136	C₂³×C₄₇	#121	1	1	yes	characteristic
137	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
138	Q₈×C₄₇	—	2	4	no	—
139	Q₈×C₄₇	—	4	2	no	—
140	D₄×C₄₇	—	2	4	no	—
141	D₄×C₄₇	—	4	4	no	—
142	D₄×C₄₇	—	4	4	no	—
143	D₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	8	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	1	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#120	1	2	yes	—
163	C₂×C₄×C₄₇	#121	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
166	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
167	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#123	1	2	yes	—
170	C₂×C₄×C₄₇	#123	1	2	yes	—
171	C₂×C₄×C₄₇	#124	1	2	yes	—
172	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#126	1	2	yes	—
174	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
175	C₂×Dic₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	8	4	no	—
177	C₄₇⋊C₈	—	4	4	no	—
178	#11056	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	1	no	—
183	C₂²×C₄₇	—	4	1	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	8	2	no	—
187	C₂²×C₄₇	—	8	2	no	—
188	C₂²×C₄₇	#380	1	1	yes	characteristic
189	C₂²×C₄₇	#386	1	1	yes	characteristic
190	C₂²×C₄₇	#390	1	1	yes	characteristic
191	C₂²×C₄₇	#394	1	2	yes	—
192	C₂²×C₄₇	#396	1	2	yes	—
193	C₄×C₄₇	—	4	4	no	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	#385	1	2	yes	—
197	C₄×C₄₇	#388	1	2	yes	—
198	C₄×C₄₇	#392	1	1	yes	characteristic
199	C₄×C₄₇	#393	1	1	yes	characteristic
200	C₄×C₄₇	#397	1	1	yes	characteristic
201	C₄×C₄₇	#399	1	1	yes	characteristic
202	Dic₄₇	—	8	4	no	—
203	#2905	—	47	1	no	—
204	C₂×#421	—	47	2	no	—
205	#2297	D₄₇	1	1	yes	characteristic
206	#1740	—	47	1	no	—
207	C₂×#339	—	47	2	no	—
208	C₂×C₄₇	—	2	2	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	2	1	no	—
211	C₂×C₄₇	—	2	2	no	—
212	C₂×C₄₇	—	8	2	no	—
213	C₂×C₄₇	#1439	1	1	yes	characteristic
214	C₂×C₄₇	#1884	1	2	yes	—
215	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
216	C₂²×M₁₆	—	47	2	no	—
217	C₂×#117	—	47	2	no	—
218	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
219	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
220	#424	—	94	4	no	—
221	#423	—	94	2	no	—
222	#421	—	94	4	no	—
223	#421	—	94	4	no	—
224	C₂×#104	—	94	4	no	—
225	#391	Dic₄₇	1	2	yes	complemented
226	#390	Dic₄₇	1	2	yes	complemented
227	#386	—	2	2	no	—
228	C₄×C₂²⋊C₄	—	2	2	no	—
229	#342	—	94	2	no	—
230	#339	—	94	4	no	—
231	C₄₇	#11056	1	1	yes	characteristic, complemented, Sylow
232	C₂×#41	—	2	1	no	—
233	C₂×#41	—	2	1	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	2	no	—
237	C₂×#41	—	2	2	no	—
238	C₂×#41	Dic₉₄	1	2	yes	—
239	C₂×#41	D₁₈₈	1	2	yes	—
240	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
241	C₂²×D₄	—	2	1	no	—
242	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂³×C₄	—	2	1	no	—
244	C₂³×C₄	—	2	1	no	—
245	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
246	C₂×M₁₆	—	47	4	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂×M₁₆	—	94	2	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂²×C₈	—	94	2	no	—
253	#117	—	2	2	no	—
254	#117	—	2	2	no	—
255	#117	—	47	4	no	—
256	#117	—	94	2	no	—
257	#117	—	94	2	no	—
258	#117	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
261	C₂×C₂²⋊C₄	—	2	4	no	—
262	C₂×C₂²⋊C₄	—	94	2	no	—
263	C₂×C₂²⋊C₄	C₂²⋊D₄₇	1	2	yes	—
264	C₂×C₄²	—	2	2	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	1	no	—
267	C₂×C₄²	—	94	2	no	—
268	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
269	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
270	C₄⋊C₈	—	94	8	no	—
271	#104	—	94	16	no	—
272	#95	—	2	4	no	—
273	C₂⁴	—	2	1	no	—
274	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
275	#41	—	2	4	no	—
276	#41	—	2	4	no	—
277	#41	—	2	4	no	—
278	#41	—	2	4	no	—
279	#41	—	4	2	no	—
280	#41	—	4	2	no	—
281	#41	—	4	2	no	—
282	#41	—	4	2	no	—
283	C₂×Q₈	—	2	1	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	C₄⋊Dic₄₇	1	2	yes	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	1	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	4	2	no	—
294	C₂×D₄	C₄⋊Dic₄₇	1	2	yes	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	4	4	no	—
300	C₂²×C₄	—	4	2	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	1	no	—
303	C₂²×C₄	—	4	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	188	2	no	—
306	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
307	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
309	C₂²×C₄	#10625350	1	1	yes	characteristic
310	C₂²×C₄	#10625350	1	1	yes	characteristic
311	C₂²×C₄	D₄×D₄₇	1	2	yes	—
312	C₂²×C₄	D₄×D₄₇	1	2	yes	—
313	C₂²×C₄	#10625352	1	2	yes	—
314	C₂²×C₄	#10625352	1	2	yes	—
315	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
317	M₁₆	—	94	4	no	—
318	M₁₆	—	94	4	no	—
319	M₁₆	—	188	2	no	—
320	M₁₆	—	188	2	no	—
321	C₂×C₈	—	94	4	no	—
322	C₂×C₈	—	188	2	no	—
323	C₂×C₈	—	188	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	94	4	no	—
326	C₄⋊C₄	—	188	2	no	—
327	C₂²⋊C₄	—	2	4	no	—
328	C₂²⋊C₄	—	4	8	no	—
329	C₂²⋊C₄	—	94	4	no	—
330	C₂²⋊C₄	—	188	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	4	no	—
334	C₄²	—	4	1	no	—
335	C₄²	—	4	1	no	—
336	C₄²	—	94	4	no	—
337	C₄²	—	188	2	no	—
338	C₂³	—	2	2	no	—
339	C₂³	—	4	2	no	—
340	C₂³	—	4	4	no	—
341	C₂³	—	4	1	no	—
342	C₂³	—	4	1	no	—
343	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
344	C₂³	#13093995	1	2	yes	—
345	C₂³	#13093996	1	2	yes	—
346	C₂³	#13093998	1	1	yes	characteristic
347	C₂³	#13094003	1	1	yes	characteristic
348	Q₈	—	2	4	no	—
349	Q₈	—	4	2	no	—
350	D₄	—	2	4	no	—
351	D₄	—	4	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	8	no	—
359	C₂×C₄	—	4	1	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	1	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	4	no	—
367	C₂×C₄	—	376	4	no	—
368	C₂×C₄	—	188	4	no	—
369	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
370	C₂×C₄	#13093983	1	1	yes	characteristic
371	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
372	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
373	C₂×C₄	#13093992	1	1	yes	characteristic
374	C₂×C₄	#13093994	1	2	yes	—
375	C₂×C₄	#13093997	1	2	yes	—
376	C₂×C₄	#13093998	1	1	yes	characteristic
377	C₂×C₄	#13094001	1	2	yes	—
378	C₂×C₄	#13094001	1	2	yes	—
379	C₂×C₄	#13094003	1	1	yes	characteristic
380	C₂×C₄	#13094005	1	1	yes	characteristic
381	C₂×C₄	#13094006	1	2	yes	—
382	C₂×C₄	#13094008	1	2	yes	—
383	C₂×C₄	#13094010	1	2	yes	—
384	C₂×C₄	#13094011	1	1	yes	characteristic
385	C₂×C₄	#13094017	1	2	yes	—
386	C₂×C₄	#13094020	1	1	yes	characteristic
387	C₈	—	188	4	no	—
388	C₂²	—	2	2	no	—
389	C₂²	—	2	4	no	—
390	C₂²	—	4	2	no	—
391	C₂²	—	4	1	no	—
392	C₂²	—	4	1	no	—
393	C₂²	—	4	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	#15688983	1	1	yes	characteristic
398	C₂²	#15689003	1	1	yes	characteristic
399	C₂²	#15689026	1	1	yes	characteristic
400	C₂²	#15689039	1	2	yes	—
401	C₂²	#15689046	1	2	yes	—
402	C₄	—	4	4	no	—
403	C₄	—	4	4	no	—
404	C₄	—	4	2	no	—
405	C₄	—	376	4	no	—
406	C₄	#15688998	1	2	yes	—
407	C₄	#15689016	1	2	yes	—
408	C₄	#15689032	1	1	yes	characteristic
409	C₄	#15689035	1	1	yes	characteristic
410	C₄	#15689048	1	1	yes	characteristic
411	C₄	#15689059	1	1	yes	characteristic
412	C₂	—	2	1	no	—
413	C₂	—	2	2	no	—
414	C₂	—	2	1	no	—
415	C₂	—	2	2	no	—
416	C₂	—	8	2	no	—
417	C₂	#20241633	1	1	yes	characteristic
418	C₂	#20243772	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	#13093992
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₄₇×#2297	C₂
socle	C₂²×C₄₇	#386
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2297	D₄₇
hypocenter	C₄₇	#11056
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #2297

Complements

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

N	H ≅ G/N	type
1. #20251952	C₂	semidirect
3. #20243121	C₂	semidirect
4. C₂×#15688883	C₂	semidirect
18. C₄₇×#391	C₄	semidirect
19. C₄₇×#390	C₄	semidirect
225. #391	Dic₄₇	semidirect
226. #390	Dic₄₇	semidirect
231. C₄₇	#11056	semidirect

Maximal subgroups

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

subgroup	index
#20251952	2
C₂×#15689140	2
#20243121	2
C₂×#15688883	2
C₄₇×#2297	2
#11056	47