Subgroups — C₄₇×#11231 #26050929

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#106×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#340	C₂	1	2	yes	maximal
4	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
5	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
6	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
7	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
8	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#106×C₄₇	—	2	2	no	—
12	C₂×#106×C₄₇	—	2	4	no	—
13	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
14	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
15	C₂×C₄⋊C₈×C₄₇	C₄	1	4	yes	complemented
16	C₂×#95×C₄₇	—	2	2	no	—
17	C₂×#95×C₄₇	—	2	2	no	—
18	C₄₇×#340	—	2	2	no	—
19	C₄₇×#340	—	2	4	no	—
20	C₂³×C₄×C₄₇	—	2	2	no	—
21	C₂³×C₄×C₄₇	—	2	2	no	—
22	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
23	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
24	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂²×C₈×C₄₇	—	2	2	no	—
26	C₂²×C₈×C₄₇	—	2	2	no	—
27	C₂²×C₈×C₄₇	—	2	2	no	—
28	C₂²×C₈×C₄₇	—	2	1	no	—
29	C₂²×C₈×C₄₇	—	2	1	no	—
30	C₂²×C₈×C₄₇	—	2	2	no	—
31	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
32	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
33	C₂²×C₈×C₄₇	D₄	1	2	yes	—
34	C₂²×C₈×C₄₇	D₄	1	2	yes	—
35	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
36	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
37	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
38	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
39	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
40	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
46	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
47	C₂×C₄²×C₄₇	—	2	1	no	—
48	C₂×C₄²×C₄₇	—	2	1	no	—
49	C₂×C₄²×C₄₇	—	2	1	no	—
50	C₂×C₄²×C₄₇	—	2	1	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
53	#106×C₄₇	—	2	8	no	—
54	C₄⋊C₈×C₄₇	—	2	8	no	—
55	#95×C₄₇	—	4	4	no	—
56	#95×C₄₇	—	4	4	no	—
57	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
58	C₂²×C₄×C₄₇	—	2	1	no	—
59	C₂²×C₄×C₄₇	—	2	1	no	—
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	2	no	—
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	4	no	—
66	C₂²×C₄×C₄₇	—	2	4	no	—
67	C₂²×C₄×C₄₇	—	4	2	no	—
68	C₂²×C₄×C₄₇	—	4	2	no	—
69	C₂²×C₄×C₄₇	—	4	2	no	—
70	C₂²×C₄×C₄₇	—	4	2	no	—
71	C₂²×C₄×C₄₇	—	4	2	no	—
72	C₂²×C₄×C₄₇	—	4	2	no	—
73	C₂²×C₄×C₄₇	—	4	2	no	—
74	C₂²×C₄×C₄₇	—	4	2	no	—
75	C₂²×C₄×C₄₇	—	4	2	no	—
76	C₂²×C₄×C₄₇	—	4	2	no	—
77	C₂²×C₄×C₄₇	—	4	2	no	—
78	C₂²×C₄×C₄₇	—	4	2	no	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
81	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂×C₈×C₄₇	—	2	4	no	—
93	C₂×C₈×C₄₇	—	2	2	no	—
94	C₂×C₈×C₄₇	—	2	4	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	2	4	no	—
98	C₂×C₈×C₄₇	—	4	1	no	—
99	C₂×C₈×C₄₇	—	4	2	no	—
100	C₂×C₈×C₄₇	—	4	1	no	—
101	C₂×C₈×C₄₇	C₂²⋊C₄	1	4	yes	—
102	C₄⋊C₄×C₄₇	—	2	4	no	—
103	C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₄⋊C₄×C₄₇	—	2	4	no	—
105	C₄⋊C₄×C₄₇	—	2	4	no	—
106	C₄⋊C₄×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	4	2	no	—
108	C₄⋊C₄×C₄₇	—	4	2	no	—
109	C₄⋊C₄×C₄₇	—	4	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
115	C₂³×C₄₇	#121	1	1	yes	characteristic
116	C₂³×C₄₇	#121	1	1	yes	characteristic
117	C₂³×C₄₇	#121	1	2	yes	—
118	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
119	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
120	C₂³×C₄₇	#135	1	2	yes	—
121	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
122	C₂³×C₄₇	#137	1	2	yes	—
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	—	4	2	no	—
130	C₂×C₄×C₄₇	—	4	1	no	—
131	C₂×C₄×C₄₇	—	4	1	no	—
132	C₂×C₄×C₄₇	—	4	4	no	—
133	C₂×C₄×C₄₇	—	4	4	no	—
134	C₂×C₄×C₄₇	—	4	4	no	—
135	C₂×C₄×C₄₇	—	4	4	no	—
136	C₂×C₄×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	—	4	4	no	—
138	C₂×C₄×C₄₇	—	8	2	no	—
139	C₂×C₄×C₄₇	—	8	2	no	—
140	C₂×C₄×C₄₇	—	8	2	no	—
141	C₂×C₄×C₄₇	—	8	2	no	—
142	C₂×C₄×C₄₇	—	8	2	no	—
143	C₂×C₄×C₄₇	—	8	2	no	—
144	C₂×C₄×C₄₇	—	8	2	no	—
145	C₂×C₄×C₄₇	—	8	2	no	—
146	C₂×C₄×C₄₇	#106	1	4	yes	complemented
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
152	C₂×C₄×C₄₇	#121	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
154	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
155	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#123	1	2	yes	—
159	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
160	C₂×C₄×C₄₇	#125	1	2	yes	—
161	C₂×C₄×C₄₇	#125	1	2	yes	—
162	C₂×C₄×C₄₇	#126	1	2	yes	—
163	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
165	C₈×C₄₇	—	2	4	no	—
166	C₈×C₄₇	—	4	2	no	—
167	#11231	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
168	C₂²×C₄₇	#380	1	1	yes	characteristic
169	C₂²×C₄₇	#389	1	2	yes	—
170	C₂²×C₄₇	#394	1	1	yes	characteristic
171	C₂²×C₄₇	#396	1	2	yes	—
172	C₂²×C₄₇	#398	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×#106	1	1	yes	characteristic
174	C₂²×C₄₇	#427	1	1	yes	characteristic
175	C₂²×C₄₇	#428	1	2	yes	—
176	C₂²×C₄₇	#460	1	2	yes	—
177	C₂²×C₄₇	#461	1	2	yes	—
178	C₂²×C₄₇	#463	1	2	yes	—
179	C₂²×C₄₇	#464	1	2	yes	—
180	C₂²×C₄₇	#465	1	2	yes	—
181	C₂²×C₄₇	#465	1	2	yes	—
182	C₂²×C₄₇	#468	1	2	yes	—
183	C₂²×C₄₇	#469	1	1	yes	characteristic
184	C₂²×C₄₇	#470	1	1	yes	characteristic
185	C₂²×C₄₇	#475	1	2	yes	—
186	C₂²×C₄₇	#476	1	2	yes	—
187	C₂²×C₄₇	#478	1	2	yes	—
188	C₂²×C₄₇	#479	1	2	yes	—
189	C₄×C₄₇	—	2	4	no	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	—	8	4	no	—
192	C₄×C₄₇	—	8	4	no	—
193	C₄×C₄₇	#386	1	1	yes	characteristic
194	C₄×C₄₇	#387	1	2	yes	—
195	C₄×C₄₇	#391	1	1	yes	characteristic
196	C₄×C₄₇	#395	1	1	yes	characteristic
197	C₄×C₄₇	#398	1	2	yes	—
198	C₄×C₄₇	#400	1	1	yes	characteristic
199	C₂²×#106	C₂×C₄₇	1	1	yes	characteristic
200	C₂²×C₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic
201	C₂×#340	C₂×C₄₇	1	2	yes	—
202	C₂×#340	C₂×C₄₇	1	1	yes	characteristic
203	C₄⋊#95	C₂×C₄₇	1	2	yes	—
204	C₂×C₄₇	#1441	1	1	yes	characteristic
205	C₂×C₄₇	#1807	1	1	yes	characteristic
206	C₂×C₄₇	#1809	1	1	yes	characteristic
207	C₂×C₄₇	#1948	1	2	yes	—
208	C₂×C₄₇	#1949	1	2	yes	—
209	C₂×C₄₇	#2055	1	2	yes	—
210	C₂×C₄₇	#2065	1	2	yes	—
211	C₂×C₄₇	#2066	1	2	yes	—
212	C₂×C₄₇	#2088	1	2	yes	—
213	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
215	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
217	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
218	C₂×#106	—	2	2	no	—
219	C₂×#106	—	2	4	no	—
220	C₂×C₄⋊C₈	—	2	2	no	—
221	C₂×C₄⋊C₈	—	2	2	no	—
222	C₂×C₄⋊C₈	C₄×C₄₇	1	4	yes	complemented
223	C₂×#95	—	2	2	no	—
224	C₂×#95	—	2	2	no	—
225	#340	—	2	2	no	—
226	#340	—	2	4	no	—
227	C₄₇	#11231	1	1	yes	characteristic, direct product factor, Sylow
228	C₂³×C₄	—	2	2	no	—
229	C₂³×C₄	—	2	2	no	—
230	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
231	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
232	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
233	C₂²×C₈	—	2	2	no	—
234	C₂²×C₈	—	2	2	no	—
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	2	no	—
239	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	—
240	C₂²×C₈	C₂×C₄×C₄₇	1	2	yes	—
241	C₂²×C₈	D₄×C₄₇	1	2	yes	—
242	C₂²×C₈	D₄×C₄₇	1	2	yes	—
243	C₂×C₄⋊C₄	—	2	2	no	—
244	C₂×C₄⋊C₄	—	2	2	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	2	no	—
247	C₂×C₄⋊C₄	—	2	2	no	—
248	C₂×C₄⋊C₄	—	2	2	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	—	2	2	no	—
251	C₂×C₄⋊C₄	—	2	2	no	—
252	C₂×C₄⋊C₄	—	2	2	no	—
253	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
254	C₂×C₄⋊C₄	Q₈×C₄₇	1	4	yes	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	—	2	1	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
260	C₂×C₄²	Q₈×C₄₇	1	2	yes	—
261	#106	—	2	8	no	—
262	C₄⋊C₈	—	2	8	no	—
263	#95	—	4	4	no	—
264	#95	—	4	4	no	—
265	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
266	C₂²×C₄	—	2	1	no	—
267	C₂²×C₄	—	2	1	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	1	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	4	no	—
274	C₂²×C₄	—	2	4	no	—
275	C₂²×C₄	—	4	2	no	—
276	C₂²×C₄	—	4	2	no	—
277	C₂²×C₄	—	4	2	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	—	4	2	no	—
280	C₂²×C₄	—	4	2	no	—
281	C₂²×C₄	—	4	2	no	—
282	C₂²×C₄	—	4	2	no	—
283	C₂²×C₄	—	4	2	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	—	4	2	no	—
287	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
288	C₂²×C₄	C₄⋊C₄×C₄₇	1	2	yes	—
289	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
290	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
294	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
295	C₂²×C₄	C₂×Q₈×C₄₇	1	1	yes	characteristic
296	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	#41×C₄₇	1	2	yes	—
299	C₂²×C₄	#41×C₄₇	1	2	yes	—
300	C₂×C₈	—	2	4	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	4	no	—
306	C₂×C₈	—	4	1	no	—
307	C₂×C₈	—	4	2	no	—
308	C₂×C₈	—	4	1	no	—
309	C₂×C₈	C₂²⋊C₄×C₄₇	1	4	yes	—
310	C₄⋊C₄	—	2	4	no	—
311	C₄⋊C₄	—	2	4	no	—
312	C₄⋊C₄	—	2	4	no	—
313	C₄⋊C₄	—	2	4	no	—
314	C₄⋊C₄	—	4	2	no	—
315	C₄⋊C₄	—	4	2	no	—
316	C₄⋊C₄	—	4	2	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	2	2	no	—
322	C₂³	C₂×C₄⋊C₄×C₄₇	1	1	yes	characteristic
323	C₂³	#121×C₄₇	1	2	yes	—
324	C₂³	#121×C₄₇	1	1	yes	characteristic
325	C₂³	#121×C₄₇	1	1	yes	characteristic
326	C₂³	C₂²⋊Q₈×C₄₇	1	2	yes	—
327	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
328	C₂³	#135×C₄₇	1	2	yes	—
329	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
330	C₂³	#137×C₄₇	1	2	yes	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	1	no	—
340	C₂×C₄	—	4	4	no	—
341	C₂×C₄	—	4	4	no	—
342	C₂×C₄	—	4	4	no	—
343	C₂×C₄	—	4	4	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	8	2	no	—
347	C₂×C₄	—	8	2	no	—
348	C₂×C₄	—	8	2	no	—
349	C₂×C₄	—	8	2	no	—
350	C₂×C₄	—	8	2	no	—
351	C₂×C₄	—	8	2	no	—
352	C₂×C₄	—	8	2	no	—
353	C₂×C₄	—	8	2	no	—
354	C₂×C₄	#106×C₄₇	1	4	yes	complemented
355	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
356	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
357	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
358	C₂×C₄	C₄×Q₈×C₄₇	1	2	yes	—
359	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
360	C₂×C₄	#121×C₄₇	1	2	yes	—
361	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
362	C₂×C₄	C₂²⋊Q₈×C₄₇	1	2	yes	—
363	C₂×C₄	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
365	C₂×C₄	#123×C₄₇	1	1	yes	characteristic
366	C₂×C₄	#123×C₄₇	1	2	yes	—
367	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
368	C₂×C₄	#125×C₄₇	1	2	yes	—
369	C₂×C₄	#125×C₄₇	1	2	yes	—
370	C₂×C₄	#126×C₄₇	1	2	yes	—
371	C₂×C₄	C₄⋊Q₈×C₄₇	1	1	yes	characteristic
372	C₂×C₄	C₄⋊Q₈×C₄₇	1	2	yes	—
373	C₈	—	2	4	no	—
374	C₈	—	4	2	no	—
375	C₂²	C₄₇×#380	1	1	yes	characteristic
376	C₂²	C₄₇×#389	1	2	yes	—
377	C₂²	C₄₇×#394	1	1	yes	characteristic
378	C₂²	C₄₇×#396	1	2	yes	—
379	C₂²	C₄₇×#398	1	1	yes	characteristic
380	C₂²	C₂×#106×C₄₇	1	1	yes	characteristic
381	C₂²	C₄₇×#427	1	1	yes	characteristic
382	C₂²	C₄₇×#428	1	2	yes	—
383	C₂²	C₄₇×#460	1	2	yes	—
384	C₂²	C₄₇×#461	1	2	yes	—
385	C₂²	C₄₇×#463	1	2	yes	—
386	C₂²	C₄₇×#464	1	2	yes	—
387	C₂²	C₄₇×#465	1	2	yes	—
388	C₂²	C₄₇×#465	1	2	yes	—
389	C₂²	C₄₇×#468	1	2	yes	—
390	C₂²	C₄₇×#469	1	1	yes	characteristic
391	C₂²	C₄₇×#470	1	1	yes	characteristic
392	C₂²	C₄₇×#475	1	2	yes	—
393	C₂²	C₄₇×#476	1	2	yes	—
394	C₂²	C₄₇×#478	1	2	yes	—
395	C₂²	C₄₇×#479	1	2	yes	—
396	C₄	—	2	4	no	—
397	C₄	—	4	2	no	—
398	C₄	—	8	4	no	—
399	C₄	—	8	4	no	—
400	C₄	C₄₇×#386	1	1	yes	characteristic
401	C₄	C₄₇×#387	1	2	yes	—
402	C₄	C₄₇×#391	1	1	yes	characteristic
403	C₄	C₄₇×#395	1	1	yes	characteristic
404	C₄	C₄₇×#398	1	2	yes	—
405	C₄	C₄₇×#400	1	1	yes	characteristic
406	C₂	C₄₇×#1441	1	1	yes	characteristic
407	C₂	C₄₇×#1807	1	1	yes	characteristic
408	C₂	C₄₇×#1809	1	1	yes	characteristic
409	C₂	C₄₇×#1948	1	2	yes	—
410	C₂	C₄₇×#1949	1	2	yes	—
411	C₂	C₄₇×#2055	1	2	yes	—
412	C₂	C₄₇×#2065	1	2	yes	—
413	C₂	C₄₇×#2066	1	2	yes	—
414	C₂	C₄₇×#2088	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
15. C₂×C₄⋊C₈×C₄₇	C₄	semidirect
146. C₂×C₄×C₄₇	#106	semidirect
167. #11231	C₄₇	direct (N × H)
222. C₂×C₄⋊C₈	C₄×C₄₇	semidirect
227. C₄₇	#11231	direct (N × H)
354. C₂×C₄	#106×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#106×C₄₇	2
C₂²×C₄⋊C₈×C₄₇	2
C₂×C₄₇×#340	2
C₄₇×C₄⋊#95	2
#11231	47

Subgroups — C47×#11231 #26050929

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#11231 #26050929