Subgroups — C₄₇×#13936 #26053634

Order 12032.

1226 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1443	C₂	1	4	yes	maximal
3	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
4	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
5	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#1434	C₂	1	2	yes	maximal
7	C₄₇×#1434	C₂	1	2	yes	maximal
8	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
13	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
15	C₄×C₄⋊C₄×C₄₇	C₄	1	8	yes	complemented
16	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#95×C₄₇	C₂²	1	2	yes	—
18	C₂×#95×C₄₇	C₂²	1	2	yes	—
19	C₂×#95×C₄₇	C₂²	1	4	yes	—
20	C₂×#95×C₄₇	C₂²	1	4	yes	—
21	C₂×#95×C₄₇	C₂²	1	4	yes	—
22	C₂×#95×C₄₇	C₂²	1	4	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
26	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
27	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
28	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
29	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
30	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
31	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
33	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
34	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
35	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
40	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
41	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
42	C₂×C₄²×C₄₇	—	2	4	no	—
43	C₂×C₄²×C₄₇	—	2	4	no	—
44	C₂×C₄²×C₄₇	—	2	4	no	—
45	C₂×C₄²×C₄₇	—	2	4	no	—
46	C₂×C₄²×C₄₇	—	4	4	no	—
47	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
48	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	—
49	#95×C₄₇	—	2	4	no	—
50	#95×C₄₇	—	2	2	no	—
51	#95×C₄₇	—	2	8	no	—
52	#95×C₄₇	—	2	4	no	—
53	#95×C₄₇	—	4	4	no	—
54	#95×C₄₇	—	4	4	no	—
55	#95×C₄₇	—	4	4	no	—
56	#95×C₄₇	—	4	2	no	—
57	#95×C₄₇	C₂×C₄	1	8	yes	—
58	#95×C₄₇	Q₈	1	4	yes	—
59	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	2	2	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	4	no	—
77	C₂²×C₄×C₄₇	—	2	4	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	1	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	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	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
99	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
100	C₂²×C₄×C₄₇	#41	1	4	yes	—
101	C₂²×C₄×C₄₇	#41	1	2	yes	—
102	C₂²×C₄×C₄₇	#41	1	4	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	4	yes	—
105	C₂²×C₄×C₄₇	#41	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	4	8	no	—
109	C₄²×C₄₇	—	2	8	no	—
110	C₄²×C₄₇	—	4	8	no	—
111	C₄²×C₄₇	—	4	8	no	—
112	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
113	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
114	C₂³×C₄₇	C₂×#41	1	2	yes	—
115	C₂³×C₄₇	C₂×#41	1	2	yes	—
116	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
117	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
118	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
119	C₂³×C₄₇	C₂×#41	1	2	yes	—
120	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
121	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
122	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
123	C₂×C₄×C₄₇	—	2	2	no	—
124	C₂×C₄×C₄₇	—	2	2	no	—
125	C₂×C₄×C₄₇	—	2	4	no	—
126	C₂×C₄×C₄₇	—	2	4	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	4	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	4	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	4	2	no	—
143	C₂×C₄×C₄₇	—	4	2	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	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	4	no	—
156	C₂×C₄×C₄₇	—	4	4	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	—	4	4	no	—
163	C₂×C₄×C₄₇	#117	1	4	yes	—
164	C₂×C₄×C₄₇	#117	1	4	yes	—
165	C₂×C₄×C₄₇	#117	1	4	yes	—
166	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
167	C₂×C₄×C₄₇	#126	1	8	yes	—
168	C₂×C₄×C₄₇	#126	1	8	yes	—
169	#13936	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
170	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
171	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
174	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
175	C₂²×C₄₇	#518	1	1	yes	characteristic
176	C₂²×C₄₇	#520	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#126	1	2	yes	—
178	C₂²×C₄₇	C₂×#126	1	2	yes	—
179	C₂²×C₄₇	#529	1	2	yes	—
180	C₂²×C₄₇	#533	1	2	yes	—
181	C₂²×C₄₇	#540	1	2	yes	—
182	C₂²×C₄₇	#542	1	2	yes	—
183	C₂²×C₄₇	#552	1	2	yes	—
184	C₂²×C₄₇	#553	1	2	yes	—
185	C₂²×C₄₇	#553	1	2	yes	—
186	C₂²×C₄₇	#554	1	2	yes	—
187	C₂²×C₄₇	#554	1	1	yes	characteristic
188	C₂²×C₄₇	#555	1	2	yes	—
189	C₂²×C₄₇	#556	1	1	yes	characteristic
190	C₂²×C₄₇	#557	1	1	yes	characteristic
191	C₂²×C₄₇	#559	1	1	yes	characteristic
192	C₂²×C₄₇	#559	1	2	yes	—
193	C₄×C₄₇	—	2	4	no	—
194	C₄×C₄₇	—	4	4	no	—
195	C₄×C₄₇	—	4	2	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	4	4	no	—
198	C₄×C₄₇	—	4	4	no	—
199	C₄×C₄₇	—	8	4	no	—
200	C₄×C₄₇	#383	1	8	yes	—
201	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
202	#1443	C₂×C₄₇	1	4	yes	—
203	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
204	C₄⋊#95	C₂×C₄₇	1	2	yes	—
205	C₄⋊#95	C₂×C₄₇	1	2	yes	—
206	#1434	C₂×C₄₇	1	2	yes	—
207	#1434	C₂×C₄₇	1	2	yes	—
208	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#383	1	1	yes	characteristic
210	C₂×C₄₇	#2295	1	1	yes	characteristic
211	C₂×C₄₇	#2319	1	1	yes	characteristic
212	C₂×C₄₇	#2345	1	1	yes	characteristic
213	C₂×C₄₇	#2346	1	1	yes	characteristic
214	C₂×C₄₇	#2355	1	1	yes	characteristic
215	C₂×C₄₇	#2357	1	1	yes	characteristic
216	C₂×C₄₇	#2494	1	2	yes	—
217	C₂×C₄₇	#2497	1	2	yes	—
218	C₂×C₄₇	#2511	1	2	yes	—
219	C₂×C₄₇	#2513	1	2	yes	—
220	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
221	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
222	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
223	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
224	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
225	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
226	C₄×C₄⋊C₄	C₄×C₄₇	1	8	yes	complemented
227	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
228	C₂×#95	C₂²×C₄₇	1	2	yes	—
229	C₂×#95	C₂²×C₄₇	1	2	yes	—
230	C₂×#95	C₂²×C₄₇	1	4	yes	—
231	C₂×#95	C₂²×C₄₇	1	4	yes	—
232	C₂×#95	C₂²×C₄₇	1	4	yes	—
233	C₂×#95	C₂²×C₄₇	1	4	yes	—
234	C₂×#95	C₂²×C₄₇	1	2	yes	—
235	C₂×#95	C₂²×C₄₇	1	2	yes	—
236	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
237	C₄₇	#13936	1	1	yes	characteristic, direct product factor, Sylow
238	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
239	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
240	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
241	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
242	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
243	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
244	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
245	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	4	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	4	no	—
250	C₂×C₄⋊C₄	—	2	4	no	—
251	C₂×C₄⋊C₄	—	2	4	no	—
252	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
253	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
254	C₂×C₄²	—	2	4	no	—
255	C₂×C₄²	—	2	4	no	—
256	C₂×C₄²	—	2	4	no	—
257	C₂×C₄²	—	2	4	no	—
258	C₂×C₄²	—	4	4	no	—
259	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
260	C₂×C₄²	C₂×C₄×C₄₇	1	8	yes	—
261	#95	—	2	4	no	—
262	#95	—	2	2	no	—
263	#95	—	2	8	no	—
264	#95	—	2	4	no	—
265	#95	—	4	4	no	—
266	#95	—	4	4	no	—
267	#95	—	4	4	no	—
268	#95	—	4	2	no	—
269	#95	C₂×C₄×C₄₇	1	8	yes	—
270	#95	Q₈×C₄₇	1	4	yes	—
271	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	4	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	4	no	—
286	C₂²×C₄	—	2	2	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	4	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	2	4	no	—
301	C₂²×C₄	—	2	4	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	4	no	—
304	C₂²×C₄	—	2	4	no	—
305	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
306	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
307	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
308	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
309	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
310	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
311	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
312	C₂²×C₄	#41×C₄₇	1	4	yes	—
313	C₂²×C₄	#41×C₄₇	1	2	yes	—
314	C₂²×C₄	#41×C₄₇	1	4	yes	—
315	C₂²×C₄	#41×C₄₇	1	2	yes	—
316	C₂²×C₄	#41×C₄₇	1	4	yes	—
317	C₂²×C₄	#41×C₄₇	1	2	yes	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	—	2	8	no	—
320	C₄⋊C₄	—	4	8	no	—
321	C₄²	—	2	8	no	—
322	C₄²	—	4	8	no	—
323	C₄²	—	4	8	no	—
324	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
325	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
326	C₂³	C₂×#41×C₄₇	1	2	yes	—
327	C₂³	C₂×#41×C₄₇	1	2	yes	—
328	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
329	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
330	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
331	C₂³	C₂×#41×C₄₇	1	2	yes	—
332	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
333	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
334	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	4	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	4	no	—
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	4	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	2	no	—
367	C₂×C₄	—	4	4	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	4	no	—
370	C₂×C₄	—	4	4	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	4	no	—
373	C₂×C₄	—	4	4	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	#117×C₄₇	1	4	yes	—
376	C₂×C₄	#117×C₄₇	1	4	yes	—
377	C₂×C₄	#117×C₄₇	1	4	yes	—
378	C₂×C₄	C₄×Q₈×C₄₇	1	4	yes	—
379	C₂×C₄	#126×C₄₇	1	8	yes	—
380	C₂×C₄	#126×C₄₇	1	8	yes	—
381	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
382	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
383	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
384	C₂²	C₂×C₄×Q₈×C₄₇	1	1	yes	characteristic
385	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
386	C₂²	C₄₇×#518	1	1	yes	characteristic
387	C₂²	C₄₇×#520	1	1	yes	characteristic
388	C₂²	C₂×#126×C₄₇	1	2	yes	—
389	C₂²	C₂×#126×C₄₇	1	2	yes	—
390	C₂²	C₄₇×#529	1	2	yes	—
391	C₂²	C₄₇×#533	1	2	yes	—
392	C₂²	C₄₇×#540	1	2	yes	—
393	C₂²	C₄₇×#542	1	2	yes	—
394	C₂²	C₄₇×#552	1	2	yes	—
395	C₂²	C₄₇×#553	1	2	yes	—
396	C₂²	C₄₇×#553	1	2	yes	—
397	C₂²	C₄₇×#554	1	2	yes	—
398	C₂²	C₄₇×#554	1	1	yes	characteristic
399	C₂²	C₄₇×#555	1	2	yes	—
400	C₂²	C₄₇×#556	1	1	yes	characteristic
401	C₂²	C₄₇×#557	1	1	yes	characteristic
402	C₂²	C₄₇×#559	1	1	yes	characteristic
403	C₂²	C₄₇×#559	1	2	yes	—
404	C₄	—	2	4	no	—
405	C₄	—	4	4	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	4	no	—
411	C₄	C₄₇×#383	1	8	yes	—
412	C₂	C₂×C₄₇×#383	1	1	yes	characteristic
413	C₂	C₄₇×#2295	1	1	yes	characteristic
414	C₂	C₄₇×#2319	1	1	yes	characteristic
415	C₂	C₄₇×#2345	1	1	yes	characteristic
416	C₂	C₄₇×#2346	1	1	yes	characteristic
417	C₂	C₄₇×#2355	1	1	yes	characteristic
418	C₂	C₄₇×#2357	1	1	yes	characteristic
419	C₂	C₄₇×#2494	1	2	yes	—
420	C₂	C₄₇×#2497	1	2	yes	—
421	C₂	C₄₇×#2511	1	2	yes	—
422	C₂	C₄₇×#2513	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
15. C₄×C₄⋊C₄×C₄₇	C₄	semidirect
169. #13936	C₄₇	direct (N × H)
226. C₄×C₄⋊C₄	C₄×C₄₇	semidirect
237. C₄₇	#13936	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×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1443	2
C₄₇×C₄⋊#95	2
C₄₇×#1434	2
C₄×#95×C₄₇	2
#13936	47

Subgroups — C47×#13936 #26053634

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13936 #26053634