Subgroups — C₄₇×#15227 #26054925

Order 12032.

3142 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#124×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#390	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1438	C₂	1	8	yes	maximal, complemented
6	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
9	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
10	C₂×#127×C₄₇	—	2	8	no	—
11	C₂×#127×C₄₇	—	2	4	no	—
12	C₂×#124×C₄₇	—	2	8	no	—
13	C₂×#124×C₄₇	—	2	8	no	—
14	C₂×#124×C₄₇	—	2	8	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
17	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#391	—	2	4	no	—
21	C₄₇×#390	—	2	8	no	—
22	C₂×#95×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₂²	1	4	yes	—
24	C₂⁵×C₄₇	C₂³	1	4	yes	—
25	C₂²×Q₈×C₄₇	—	2	4	no	—
26	C₂²×Q₈×C₄₇	—	2	4	no	—
27	C₂²×Q₈×C₄₇	—	2	2	no	—
28	C₂²×Q₈×C₄₇	—	2	2	no	—
29	C₂²×Q₈×C₄₇	D₄	1	4	yes	complemented
30	C₂²×D₄×C₄₇	—	2	16	no	—
31	C₂²×D₄×C₄₇	—	2	4	no	—
32	C₂²×D₄×C₄₇	—	2	4	no	—
33	C₂²×D₄×C₄₇	—	2	8	no	—
34	C₂²×D₄×C₄₇	—	2	4	no	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	—	2	4	no	—
37	C₂²×D₄×C₄₇	—	2	4	no	—
38	C₂²×D₄×C₄₇	—	2	16	no	—
39	C₂²×D₄×C₄₇	—	4	8	no	—
40	C₂²×D₄×C₄₇	D₄	1	8	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	#127×C₄₇	—	2	32	no	—
47	#124×C₄₇	—	2	64	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
51	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
52	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	4	16	no	—
55	C₂×C₄²×C₄₇	—	2	4	no	—
56	C₂×C₄²×C₄₇	—	2	4	no	—
57	C₂×C₄²×C₄₇	—	2	4	no	—
58	C₂×C₄²×C₄₇	D₄	1	4	yes	—
59	C₂×C₄²×C₄₇	D₄	1	8	yes	complemented
60	#95×C₄₇	—	2	8	no	—
61	#95×C₄₇	—	2	8	no	—
62	C₂⁴×C₄₇	—	2	4	no	—
63	C₂⁴×C₄₇	—	2	4	no	—
64	C₂⁴×C₄₇	—	2	4	no	—
65	C₂⁴×C₄₇	—	2	4	no	—
66	C₂⁴×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	16	no	—
69	C₂⁴×C₄₇	—	2	16	no	—
70	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
71	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
72	C₂×Q₈×C₄₇	—	2	16	no	—
73	C₂×Q₈×C₄₇	—	2	8	no	—
74	C₂×Q₈×C₄₇	—	4	4	no	—
75	C₂×Q₈×C₄₇	—	4	8	no	—
76	C₂×Q₈×C₄₇	—	4	4	no	—
77	C₂×D₄×C₄₇	—	2	32	no	—
78	C₂×D₄×C₄₇	—	2	16	no	—
79	C₂×D₄×C₄₇	—	2	16	no	—
80	C₂×D₄×C₄₇	—	2	16	no	—
81	C₂×D₄×C₄₇	—	4	64	no	—
82	C₂×D₄×C₄₇	—	4	16	no	—
83	C₂×D₄×C₄₇	—	4	8	no	—
84	C₂×D₄×C₄₇	—	4	8	no	—
85	C₂×D₄×C₄₇	—	4	8	no	—
86	C₂×D₄×C₄₇	—	4	16	no	—
87	C₂×D₄×C₄₇	—	4	8	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
102	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
108	C₂²×C₄×C₄₇	#41	1	8	yes	—
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₄⋊C₄×C₄₇	—	4	4	no	—
111	C₂²⋊C₄×C₄₇	—	2	64	no	—
112	C₂²⋊C₄×C₄₇	—	4	32	no	—
113	C₄²×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	—	2	16	no	—
115	C₂³×C₄₇	—	2	8	no	—
116	C₂³×C₄₇	—	2	8	no	—
117	C₂³×C₄₇	—	2	8	no	—
118	C₂³×C₄₇	—	2	32	no	—
119	C₂³×C₄₇	—	4	4	no	—
120	C₂³×C₄₇	—	4	4	no	—
121	C₂³×C₄₇	—	4	4	no	—
122	C₂³×C₄₇	—	4	8	no	—
123	C₂³×C₄₇	—	4	4	no	—
124	C₂³×C₄₇	—	4	8	no	—
125	C₂³×C₄₇	—	4	8	no	—
126	C₂³×C₄₇	—	4	8	no	—
127	C₂³×C₄₇	—	4	8	no	—
128	C₂³×C₄₇	—	4	8	no	—
129	C₂³×C₄₇	—	4	16	no	—
130	C₂³×C₄₇	—	4	16	no	—
131	C₂³×C₄₇	—	4	16	no	—
132	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
133	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
136	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
137	C₂³×C₄₇	C₂×#41	1	4	yes	—
138	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
139	Q₈×C₄₇	—	4	16	no	—
140	D₄×C₄₇	—	4	64	no	—
141	D₄×C₄₇	—	4	32	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	16	no	—
145	C₂×C₄×C₄₇	—	2	8	no	—
146	C₂×C₄×C₄₇	—	2	8	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	8	no	—
149	C₂×C₄×C₄₇	—	2	8	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	8	no	—
154	C₂×C₄×C₄₇	—	4	8	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	8	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	#120	1	4	yes	—
159	C₂×C₄×C₄₇	#120	1	8	yes	—
160	C₂×C₄×C₄₇	#121	1	8	yes	—
161	C₂×C₄×C₄₇	#121	1	4	yes	—
162	C₂×C₄×C₄₇	#124	1	8	yes	complemented
163	C₂×C₄×C₄₇	#127	1	4	yes	—
164	#15227	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
165	C₂²×C₄₇	—	4	8	no	—
166	C₂²×C₄₇	—	4	16	no	—
167	C₂²×C₄₇	—	4	16	no	—
168	C₂²×C₄₇	—	4	16	no	—
169	C₂²×C₄₇	—	8	4	no	—
170	C₂²×C₄₇	—	8	4	no	—
171	C₂²×C₄₇	—	8	8	no	—
172	C₂²×C₄₇	—	8	8	no	—
173	C₂²×C₄₇	—	8	8	no	—
174	C₂²×C₄₇	C₂×#120	1	2	yes	—
175	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#121	1	2	yes	—
177	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#124	1	2	yes	—
179	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
180	C₂²×C₄₇	#532	1	4	yes	—
181	C₂²×C₄₇	#535	1	4	yes	—
182	C₂²×C₄₇	#535	1	2	yes	—
183	C₂²×C₄₇	#546	1	8	yes	—
184	C₂²×C₄₇	#550	1	4	yes	—
185	C₂²×C₄₇	#559	1	4	yes	—
186	C₄×C₄₇	—	2	8	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	—	4	8	no	—
189	C₄×C₄₇	—	8	2	no	—
190	C₄×C₄₇	#392	1	8	yes	—
191	C₂²×#127	C₂×C₄₇	1	1	yes	characteristic
192	C₂²×#124	C₂×C₄₇	1	2	yes	complemented
193	C₂×#391	C₂×C₄₇	1	1	yes	characteristic, complemented
194	C₂×#390	C₂×C₄₇	1	2	yes	complemented
195	#1438	C₂×C₄₇	1	8	yes	complemented
196	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
197	C₂×C₄₇	—	8	8	no	—
198	C₂×C₄₇	C₂×#392	1	1	yes	characteristic
199	C₂×C₄₇	#2431	1	4	yes	—
200	C₂×C₄₇	#2435	1	2	yes	—
201	C₂×C₄₇	#2544	1	4	yes	—
202	C₂×C₄₇	#2548	1	2	yes	—
203	C₂×C₄₇	#2657	1	1	yes	characteristic
204	C₂×C₄₇	#2858	1	1	yes	characteristic
205	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
206	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
207	C₂³×D₄	C₂²×C₄₇	1	4	yes	—
208	C₂×#127	—	2	8	no	—
209	C₂×#127	—	2	4	no	—
210	C₂×#124	—	2	8	no	—
211	C₂×#124	—	2	8	no	—
212	C₂×#124	—	2	8	no	—
213	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
214	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
215	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
216	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
217	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
218	#391	—	2	4	no	—
219	#390	—	2	8	no	—
220	C₂×#95	C₂²×C₄₇	1	4	yes	—
221	C₂×#95	C₂²×C₄₇	1	4	yes	—
222	C₄₇	#15227	1	1	yes	characteristic, direct product factor, Sylow
223	C₂⁵	C₂³×C₄₇	1	4	yes	—
224	C₂²×Q₈	—	2	4	no	—
225	C₂²×Q₈	—	2	4	no	—
226	C₂²×Q₈	—	2	2	no	—
227	C₂²×Q₈	—	2	2	no	—
228	C₂²×Q₈	D₄×C₄₇	1	4	yes	complemented
229	C₂²×D₄	—	2	16	no	—
230	C₂²×D₄	—	2	4	no	—
231	C₂²×D₄	—	2	4	no	—
232	C₂²×D₄	—	2	8	no	—
233	C₂²×D₄	—	2	4	no	—
234	C₂²×D₄	—	2	4	no	—
235	C₂²×D₄	—	2	4	no	—
236	C₂²×D₄	—	2	4	no	—
237	C₂²×D₄	—	2	16	no	—
238	C₂²×D₄	—	4	8	no	—
239	C₂²×D₄	D₄×C₄₇	1	8	yes	—
240	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
241	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
242	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
243	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
244	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
245	#127	—	2	32	no	—
246	#124	—	2	64	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₂²⋊C₄	—	2	16	no	—
250	C₂×C₂²⋊C₄	—	2	16	no	—
251	C₂×C₂²⋊C₄	—	2	16	no	—
252	C₂×C₂²⋊C₄	—	2	16	no	—
253	C₂×C₂²⋊C₄	—	4	16	no	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	D₄×C₄₇	1	4	yes	—
258	C₂×C₄²	D₄×C₄₇	1	8	yes	complemented
259	#95	—	2	8	no	—
260	#95	—	2	8	no	—
261	C₂⁴	—	2	4	no	—
262	C₂⁴	—	2	4	no	—
263	C₂⁴	—	2	4	no	—
264	C₂⁴	—	2	4	no	—
265	C₂⁴	—	2	4	no	—
266	C₂⁴	—	2	4	no	—
267	C₂⁴	—	2	16	no	—
268	C₂⁴	—	2	16	no	—
269	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
270	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
271	C₂×Q₈	—	2	16	no	—
272	C₂×Q₈	—	2	8	no	—
273	C₂×Q₈	—	4	4	no	—
274	C₂×Q₈	—	4	8	no	—
275	C₂×Q₈	—	4	4	no	—
276	C₂×D₄	—	2	32	no	—
277	C₂×D₄	—	2	16	no	—
278	C₂×D₄	—	2	16	no	—
279	C₂×D₄	—	2	16	no	—
280	C₂×D₄	—	4	64	no	—
281	C₂×D₄	—	4	16	no	—
282	C₂×D₄	—	4	8	no	—
283	C₂×D₄	—	4	8	no	—
284	C₂×D₄	—	4	8	no	—
285	C₂×D₄	—	4	16	no	—
286	C₂×D₄	—	4	8	no	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	8	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	8	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
301	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
303	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
304	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
306	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
307	C₂²×C₄	#41×C₄₇	1	8	yes	—
308	C₂²×C₄	#41×C₄₇	1	2	yes	—
309	C₄⋊C₄	—	4	4	no	—
310	C₂²⋊C₄	—	2	64	no	—
311	C₂²⋊C₄	—	4	32	no	—
312	C₄²	—	2	8	no	—
313	C₄²	—	2	16	no	—
314	C₂³	—	2	8	no	—
315	C₂³	—	2	8	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	32	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	8	no	—
322	C₂³	—	4	4	no	—
323	C₂³	—	4	8	no	—
324	C₂³	—	4	8	no	—
325	C₂³	—	4	8	no	—
326	C₂³	—	4	8	no	—
327	C₂³	—	4	8	no	—
328	C₂³	—	4	16	no	—
329	C₂³	—	4	16	no	—
330	C₂³	—	4	16	no	—
331	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
332	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
333	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
334	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
335	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
336	C₂³	C₂×#41×C₄₇	1	4	yes	—
337	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
338	Q₈	—	4	16	no	—
339	D₄	—	4	64	no	—
340	D₄	—	4	32	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	16	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	8	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	8	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	8	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	#120×C₄₇	1	4	yes	—
358	C₂×C₄	#120×C₄₇	1	8	yes	—
359	C₂×C₄	#121×C₄₇	1	8	yes	—
360	C₂×C₄	#121×C₄₇	1	4	yes	—
361	C₂×C₄	#124×C₄₇	1	8	yes	complemented
362	C₂×C₄	#127×C₄₇	1	4	yes	—
363	C₂²	—	4	16	no	—
364	C₂²	—	4	8	no	—
365	C₂²	—	4	16	no	—
366	C₂²	—	4	16	no	—
367	C₂²	—	8	8	no	—
368	C₂²	—	8	8	no	—
369	C₂²	—	8	4	no	—
370	C₂²	—	8	4	no	—
371	C₂²	—	8	8	no	—
372	C₂²	C₂×#120×C₄₇	1	2	yes	—
373	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
374	C₂²	C₂×#121×C₄₇	1	2	yes	—
375	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
376	C₂²	C₂×#124×C₄₇	1	2	yes	—
377	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
378	C₂²	C₄₇×#532	1	4	yes	—
379	C₂²	C₄₇×#535	1	4	yes	—
380	C₂²	C₄₇×#535	1	2	yes	—
381	C₂²	C₄₇×#546	1	8	yes	—
382	C₂²	C₄₇×#550	1	4	yes	—
383	C₂²	C₄₇×#559	1	4	yes	—
384	C₄	—	2	8	no	—
385	C₄	—	4	4	no	—
386	C₄	—	4	8	no	—
387	C₄	—	8	2	no	—
388	C₄	C₄₇×#392	1	8	yes	—
389	C₂	—	8	8	no	—
390	C₂	C₂×C₄₇×#392	1	1	yes	characteristic
391	C₂	C₄₇×#2431	1	4	yes	—
392	C₂	C₄₇×#2435	1	2	yes	—
393	C₂	C₄₇×#2544	1	4	yes	—
394	C₂	C₄₇×#2548	1	2	yes	—
395	C₂	C₄₇×#2657	1	1	yes	characteristic
396	C₂	C₄₇×#2858	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂²×#127×C₄₇	C₂
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#124×C₄₇	C₂	semidirect
3. C₂×C₄₇×#391	C₂	semidirect
4. C₂×C₄₇×#390	C₂	semidirect
5. C₄₇×#1438	C₂	semidirect
6. C₄×#95×C₄₇	C₂	semidirect
29. C₂²×Q₈×C₄₇	D₄	semidirect
59. C₂×C₄²×C₄₇	D₄	semidirect
162. C₂×C₄×C₄₇	#124	semidirect
164. #15227	C₄₇	direct (N × H)
192. C₂²×#124	C₂×C₄₇	semidirect
193. C₂×#391	C₂×C₄₇	semidirect
194. C₂×#390	C₂×C₄₇	semidirect
195. #1438	C₂×C₄₇	semidirect
196. C₄×#95	C₂×C₄₇	semidirect
222. C₄₇	#15227	direct (N × H)
228. C₂²×Q₈	D₄×C₄₇	semidirect
258. C₂×C₄²	D₄×C₄₇	semidirect
361. C₂×C₄	#124×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₄₇	2
C₂²×#124×C₄₇	2
C₂×C₄₇×#391	2
C₂×C₄₇×#390	2
C₄₇×#1438	2
C₄×#95×C₄₇	2
#15227	47

Subgroups — C47×#15227 #26054925

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15227 #26054925