Subgroups — C₄₇×#21812 #26061510

Order 12032.

1354 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1983	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1961	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1960	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1788	C₂	1	4	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₂²	1	2	yes	—
9	C₄₇×#532	—	2	4	no	—
10	C₄₇×#532	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₇	C₂²	1	2	yes	—
14	C₂×#121×C₄₇	—	2	1	no	—
15	C₂×#121×C₄₇	—	2	1	no	—
16	C₂×C₄×D₄×C₄₇	—	2	1	no	—
17	C₂×C₄×D₄×C₄₇	—	2	1	no	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#432	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
21	C₂×#103×C₄₇	C₂²	1	8	yes	—
22	C₂×#102×C₄₇	C₂²	1	8	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×#97×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#383	—	2	1	no	—
26	C₄₇×#382	C₂²	1	2	yes	—
27	C₄₇×#381	—	2	1	no	—
28	C₄₇×#380	C₂²	1	2	yes	—
29	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
30	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
31	C₄₇×#376	—	2	1	no	—
32	C₂×#41×C₄₇	—	2	4	no	—
33	C₂×#41×C₄₇	—	4	8	no	—
34	C₂×#41×C₄₇	C₂×C₄	1	8	yes	—
35	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
47	#127×C₄₇	—	2	2	no	—
48	#127×C₄₇	C₂×C₄	1	4	yes	—
49	#124×C₄₇	—	2	4	no	—
50	#124×C₄₇	C₂×C₄	1	8	yes	—
51	#121×C₄₇	—	2	8	no	—
52	#121×C₄₇	—	2	8	no	—
53	C₄×D₄×C₄₇	—	2	8	no	—
54	C₄×D₄×C₄₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₄⋊C₈×C₄₇	—	2	4	no	—
69	#103×C₄₇	—	4	8	no	—
70	#102×C₄₇	—	4	8	no	—
71	C₂²⋊C₈×C₄₇	—	2	4	no	—
72	#97×C₄₇	—	2	4	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
79	#41×C₄₇	—	4	16	no	—
80	#41×C₄₇	—	4	16	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	8	no	—
83	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
84	C₂×D₄×C₄₇	—	2	8	no	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	8	no	—
89	C₂×D₄×C₄₇	—	4	4	no	—
90	C₂×D₄×C₄₇	—	4	4	no	—
91	C₂×D₄×C₄₇	—	4	8	no	—
92	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	8	no	—
96	C₂²×C₄×C₄₇	—	2	4	no	—
97	C₂²×C₄×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	4	2	no	—
99	C₂²×C₄×C₄₇	—	4	8	no	—
100	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
110	C₂×C₈×C₄₇	—	2	4	no	—
111	C₂×C₈×C₄₇	—	2	4	no	—
112	C₂×C₈×C₄₇	—	2	4	no	—
113	C₄⋊C₄×C₄₇	—	2	4	no	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄⋊C₄×C₄₇	—	2	8	no	—
116	C₂²⋊C₄×C₄₇	—	2	8	no	—
117	C₂²⋊C₄×C₄₇	—	2	8	no	—
118	C₂²⋊C₄×C₄₇	—	4	4	no	—
119	C₄²×C₄₇	—	4	4	no	—
120	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
121	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
122	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	C₂×D₄	1	2	yes	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₂³×C₄₇	—	2	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	—	2	4	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	4	no	—
132	C₂³×C₄₇	—	4	4	no	—
133	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
134	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
135	Q₈×C₄₇	—	2	8	no	—
136	Q₈×C₄₇	—	4	4	no	—
137	D₄×C₄₇	—	2	8	no	—
138	D₄×C₄₇	—	4	8	no	—
139	D₄×C₄₇	—	4	8	no	—
140	D₄×C₄₇	—	4	16	no	—
141	D₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	4	4	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	16	no	—
153	C₂×C₄×C₄₇	—	4	4	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	—	4	4	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
159	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	H(5,𝔽₂)	1	4	yes	—
165	C₈×C₄₇	—	4	4	no	—
166	#21812	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	4	4	no	—
171	C₂²×C₄₇	—	4	4	no	—
172	C₂²×C₄₇	—	4	4	no	—
173	C₂²×C₄₇	—	4	4	no	—
174	C₂²×C₄₇	—	8	8	no	—
175	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₇	#535	1	2	yes	—
177	C₂²×C₄₇	#575	1	2	yes	—
178	C₂²×C₄₇	#575	1	2	yes	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	2	2	no	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	—	8	4	no	—
186	C₄×C₄₇	#518	1	2	yes	—
187	C₄×C₄₇	#535	1	2	yes	—
188	C₂×#532	C₂×C₄₇	1	1	yes	characteristic
189	C₂×#432	C₂×C₄₇	1	1	yes	characteristic, complemented
190	#2283	C₂×C₄₇	1	1	yes	characteristic, complemented
191	#1983	C₂×C₄₇	1	4	yes	complemented
192	#1961	C₂×C₄₇	1	2	yes	complemented
193	#1960	C₂×C₄₇	1	2	yes	complemented
194	#1788	C₂×C₄₇	1	4	yes	complemented
195	C₂×C₄₇	—	4	2	no	—
196	C₂×C₄₇	—	8	4	no	—
197	C₂×C₄₇	#2309	1	1	yes	characteristic
198	C₂×C₄₇	#2896	1	1	yes	characteristic
199	C₂×C₄₇	#2896	1	1	yes	characteristic
200	C₂×C₄₇	#3219	1	4	yes	—
201	C₂²×#41	C₂²×C₄₇	1	2	yes	—
202	#532	—	2	4	no	—
203	#532	C₄×C₄₇	1	8	yes	complemented
204	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
205	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
206	C₂×#124	C₂²×C₄₇	1	2	yes	—
207	C₂×#121	—	2	1	no	—
208	C₂×#121	—	2	1	no	—
209	C₂×C₄×D₄	—	2	1	no	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
212	#432	—	2	4	no	—
213	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
214	C₂×#103	C₂²×C₄₇	1	8	yes	—
215	C₂×#102	C₂²×C₄₇	1	8	yes	—
216	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
217	C₂×#97	C₂²×C₄₇	1	2	yes	—
218	#383	—	2	1	no	—
219	#382	C₂²×C₄₇	1	2	yes	—
220	#381	—	2	1	no	—
221	#380	C₂²×C₄₇	1	2	yes	—
222	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
223	C₄×C₂²⋊C₄	—	2	1	no	—
224	#376	—	2	1	no	—
225	C₄₇	#21812	1	1	yes	characteristic, direct product factor, Sylow
226	C₂×#41	—	2	4	no	—
227	C₂×#41	—	4	8	no	—
228	C₂×#41	C₂×C₄×C₄₇	1	8	yes	—
229	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
230	C₂²×D₄	—	2	2	no	—
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
234	C₂³×C₄	—	2	2	no	—
235	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
236	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
238	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
239	C₄⋊Q₈	—	2	2	no	—
240	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
241	#127	—	2	2	no	—
242	#127	C₂×C₄×C₄₇	1	4	yes	—
243	#124	—	2	4	no	—
244	#124	C₂×C₄×C₄₇	1	8	yes	—
245	#121	—	2	8	no	—
246	#121	—	2	8	no	—
247	C₄×D₄	—	2	8	no	—
248	C₄×D₄	—	2	8	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	—	2	1	no	—
251	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
252	C₂×C₂²⋊C₄	—	2	2	no	—
253	C₂×C₂²⋊C₄	—	2	2	no	—
254	C₂×C₂²⋊C₄	—	2	2	no	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
257	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
258	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₄₇	1	4	yes	—
260	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
261	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
262	C₄⋊C₈	—	2	4	no	—
263	#103	—	4	8	no	—
264	#102	—	4	8	no	—
265	C₂²⋊C₈	—	2	4	no	—
266	#97	—	2	4	no	—
267	#95	—	2	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	C₂⁴	—	2	2	no	—
272	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
273	#41	—	4	16	no	—
274	#41	—	4	16	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	8	no	—
277	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
278	C₂×D₄	—	2	8	no	—
279	C₂×D₄	—	2	4	no	—
280	C₂×D₄	—	2	4	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	8	no	—
283	C₂×D₄	—	4	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	8	no	—
286	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
287	C₂²×C₄	—	2	4	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	8	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	4	2	no	—
292	C₂²×C₄	—	4	2	no	—
293	C₂²×C₄	—	4	8	no	—
294	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
295	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
296	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
297	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
304	C₂×C₈	—	2	4	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	2	4	no	—
307	C₄⋊C₄	—	2	4	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₂²⋊C₄	—	2	8	no	—
311	C₂²⋊C₄	—	2	8	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₄²	—	4	4	no	—
314	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
315	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
316	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
317	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
318	C₄²	C₂×D₄×C₄₇	1	2	yes	—
319	C₄²	C₂×D₄×C₄₇	1	2	yes	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	—	2	2	no	—
323	C₂³	—	2	4	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	4	no	—
326	C₂³	—	4	4	no	—
327	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
328	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
329	Q₈	—	2	8	no	—
330	Q₈	—	4	4	no	—
331	D₄	—	2	8	no	—
332	D₄	—	4	8	no	—
333	D₄	—	4	8	no	—
334	D₄	—	4	16	no	—
335	D₄	—	4	4	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	4	16	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
352	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
353	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
354	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
356	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
358	C₂×C₄	H(5,𝔽₂)×C₄₇	1	4	yes	—
359	C₈	—	4	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	4	no	—
364	C₂²	—	4	4	no	—
365	C₂²	—	4	4	no	—
366	C₂²	—	4	4	no	—
367	C₂²	—	8	8	no	—
368	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
369	C₂²	C₄₇×#535	1	2	yes	—
370	C₂²	C₄₇×#575	1	2	yes	—
371	C₂²	C₄₇×#575	1	2	yes	—
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	4	no	—
378	C₄	—	8	4	no	—
379	C₄	C₄₇×#518	1	2	yes	—
380	C₄	C₄₇×#535	1	2	yes	—
381	C₂	—	4	2	no	—
382	C₂	—	8	4	no	—
383	C₂	C₄₇×#2309	1	1	yes	characteristic
384	C₂	C₄₇×#2896	1	1	yes	characteristic
385	C₂	C₄₇×#2896	1	1	yes	characteristic
386	C₂	C₄₇×#3219	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#532	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#432	C₂	semidirect
3. C₄₇×#2283	C₂	semidirect
4. C₄₇×#1983	C₂	semidirect
5. C₄₇×#1961	C₂	semidirect
6. C₄₇×#1960	C₂	semidirect
7. C₄₇×#1788	C₂	semidirect
10. C₄₇×#532	C₄	semidirect
166. #21812	C₄₇	direct (N × H)
189. C₂×#432	C₂×C₄₇	semidirect
190. #2283	C₂×C₄₇	semidirect
191. #1983	C₂×C₄₇	semidirect
192. #1961	C₂×C₄₇	semidirect
193. #1960	C₂×C₄₇	semidirect
194. #1788	C₂×C₄₇	semidirect
203. #532	C₄×C₄₇	semidirect
225. C₄₇	#21812	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#532	2
C₂×C₄₇×#432	2
C₄₇×#2283	2
C₄₇×#1983	2
C₄₇×#1961	2
C₄₇×#1960	2
C₄₇×#1788	2
#21812	47

Subgroups — C47×#21812 #26061510

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21812 #26061510