Subgroups — C₄₇×#21892 #26061590

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#423	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1987	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1981	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1894	C₂	1	4	yes	maximal
7	C₄₇×#1805	C₂	1	4	yes	maximal, complemented
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₄₇×#533	—	2	4	no	—
10	C₄₇×#533	C₄	1	8	yes	complemented
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
17	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
18	C₂×#117×C₄₇	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#423	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	8	yes	—
24	C₄₇×#383	—	2	1	no	—
25	C₄₇×#382	C₂²	1	2	yes	—
26	C₄₇×#381	—	2	1	no	—
27	C₄₇×#380	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₄₇×#376	—	2	1	no	—
31	C₄₇×#340	C₂²	1	8	yes	—
32	C₂²×Q₈×C₄₇	—	2	1	no	—
33	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂×M₁₆×C₄₇	—	2	4	no	—
38	C₂×M₁₆×C₄₇	—	4	4	no	—
39	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
40	C₄⋊Q₈×C₄₇	—	2	2	no	—
41	C₄⋊Q₈×C₄₇	—	2	2	no	—
42	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
43	C₄⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
44	#125×C₄₇	—	2	8	no	—
45	C₂²⋊Q₈×C₄₇	—	2	8	no	—
46	C₂²⋊Q₈×C₄₇	—	2	4	no	—
47	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
48	C₄×Q₈×C₄₇	—	2	8	no	—
49	C₄×Q₈×C₄₇	—	2	4	no	—
50	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
51	#117×C₄₇	—	2	8	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
58	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
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	—	2	2	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	D₄	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	—	2	4	no	—
70	C₄⋊C₈×C₄₇	—	2	4	no	—
71	#103×C₄₇	—	4	8	no	—
72	#95×C₄₇	—	2	2	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	2	2	no	—
79	C₂×Q₈×C₄₇	—	2	4	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	4	4	no	—
82	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	—	2	4	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	4	2	no	—
90	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
91	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	M₁₆×C₄₇	—	4	8	no	—
101	C₂×C₈×C₄₇	—	2	4	no	—
102	C₂×C₈×C₄₇	—	2	8	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	—	2	8	no	—
107	C₄⋊C₄×C₄₇	—	2	8	no	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	—	2	4	no	—
110	C₄⋊C₄×C₄₇	—	2	4	no	—
111	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂²⋊C₄×C₄₇	—	2	8	no	—
113	C₂²⋊C₄×C₄₇	—	4	4	no	—
114	C₄²×C₄₇	—	2	8	no	—
115	C₄²×C₄₇	—	4	4	no	—
116	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
117	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
120	C₄²×C₄₇	C₂×D₄	1	2	yes	—
121	C₄²×C₄₇	C₂×D₄	1	2	yes	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	—	2	2	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
126	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₄₇	—	2	8	no	—
128	Q₈×C₄₇	—	4	8	no	—
129	Q₈×C₄₇	—	4	2	no	—
130	Q₈×C₄₇	—	4	2	no	—
131	C₂×C₄×C₄₇	—	2	2	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	2	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	—	2	4	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	4	4	no	—
142	C₂×C₄×C₄₇	—	4	4	no	—
143	C₂×C₄×C₄₇	—	4	4	no	—
144	C₂×C₄×C₄₇	—	4	4	no	—
145	C₂×C₄×C₄₇	—	4	4	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
152	C₂×C₄×C₄₇	#137	1	4	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
157	C₈×C₄₇	—	4	4	no	—
158	#21892	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
159	C₂²×C₄₇	—	2	2	no	—
160	C₂²×C₄₇	—	2	2	no	—
161	C₂²×C₄₇	—	2	2	no	—
162	C₂²×C₄₇	—	4	4	no	—
163	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
164	C₂²×C₄₇	#537	1	2	yes	—
165	C₂²×C₄₇	C₂×#137	1	2	yes	—
166	C₂²×C₄₇	#575	1	2	yes	—
167	C₄×C₄₇	—	2	2	no	—
168	C₄×C₄₇	—	2	2	no	—
169	C₄×C₄₇	—	2	2	no	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	4	4	no	—
172	C₄×C₄₇	—	4	4	no	—
173	C₄×C₄₇	—	8	4	no	—
174	C₄×C₄₇	#419	1	4	yes	—
175	C₄×C₄₇	#520	1	2	yes	—
176	C₄×C₄₇	#535	1	1	yes	characteristic
177	C₄×C₄₇	#536	1	1	yes	characteristic
178	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
179	C₂×#423	C₂×C₄₇	1	1	yes	characteristic
180	#2283	C₂×C₄₇	1	1	yes	characteristic
181	#1987	C₂×C₄₇	1	2	yes	complemented
182	#1981	C₂×C₄₇	1	2	yes	complemented
183	#1894	C₂×C₄₇	1	4	yes	—
184	#1805	C₂×C₄₇	1	4	yes	complemented
185	C₂×C₄₇	—	4	2	no	—
186	C₂×C₄₇	#2311	1	1	yes	characteristic
187	C₂×C₄₇	C₂×#419	1	1	yes	characteristic
188	C₂×C₄₇	#2896	1	1	yes	characteristic
189	C₂×C₄₇	#3252	1	4	yes	—
190	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
191	#533	—	2	4	no	—
192	#533	C₄×C₄₇	1	8	yes	complemented
193	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
194	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
195	C₂×#125	—	2	1	no	—
196	C₂×C₂²⋊Q₈	—	2	1	no	—
197	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
198	C₂×C₄×Q₈	—	2	1	no	—
199	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
200	C₂×#117	—	2	1	no	—
201	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
202	#423	—	2	4	no	—
203	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
204	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
205	C₂×#103	C₂²×C₄₇	1	8	yes	—
206	#383	—	2	1	no	—
207	#382	C₂²×C₄₇	1	2	yes	—
208	#381	—	2	1	no	—
209	#380	C₂²×C₄₇	1	2	yes	—
210	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
211	C₄×C₂²⋊C₄	—	2	1	no	—
212	#376	—	2	1	no	—
213	#340	C₂²×C₄₇	1	8	yes	—
214	C₄₇	#21892	1	1	yes	characteristic, direct product factor, Sylow
215	C₂²×Q₈	—	2	1	no	—
216	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
217	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
218	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
220	C₂×M₁₆	—	2	4	no	—
221	C₂×M₁₆	—	4	4	no	—
222	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
223	C₄⋊Q₈	—	2	2	no	—
224	C₄⋊Q₈	—	2	2	no	—
225	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
226	C₄⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
227	#125	—	2	8	no	—
228	C₂²⋊Q₈	—	2	8	no	—
229	C₂²⋊Q₈	—	2	4	no	—
230	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	—
231	C₄×Q₈	—	2	8	no	—
232	C₄×Q₈	—	2	4	no	—
233	C₄×Q₈	C₂×C₄×C₄₇	1	8	yes	—
234	#117	—	2	8	no	—
235	C₂×C₄⋊C₄	—	2	1	no	—
236	C₂×C₄⋊C₄	—	2	1	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	2	no	—
239	C₂×C₄⋊C₄	—	2	2	no	—
240	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
241	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
242	C₂×C₂²⋊C₄	—	2	2	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₄²	—	2	2	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
247	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
248	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₄₇	1	4	yes	—
250	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
252	C₄⋊C₈	—	2	4	no	—
253	C₄⋊C₈	—	2	4	no	—
254	#103	—	4	8	no	—
255	#95	—	2	2	no	—
256	#95	—	2	2	no	—
257	#95	—	2	2	no	—
258	#95	—	2	2	no	—
259	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
260	C₂×Q₈	—	2	4	no	—
261	C₂×Q₈	—	2	2	no	—
262	C₂×Q₈	—	2	4	no	—
263	C₂×Q₈	—	2	4	no	—
264	C₂×Q₈	—	4	4	no	—
265	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	4	2	no	—
273	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
274	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
275	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
281	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
282	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
283	M₁₆	—	4	8	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	2	8	no	—
286	C₄⋊C₄	—	2	4	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	2	4	no	—
289	C₄⋊C₄	—	2	8	no	—
290	C₄⋊C₄	—	2	8	no	—
291	C₄⋊C₄	—	2	2	no	—
292	C₄⋊C₄	—	2	4	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
295	C₂²⋊C₄	—	2	8	no	—
296	C₂²⋊C₄	—	4	4	no	—
297	C₄²	—	2	8	no	—
298	C₄²	—	4	4	no	—
299	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
300	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
301	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
302	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
303	C₄²	C₂×D₄×C₄₇	1	2	yes	—
304	C₄²	C₂×D₄×C₄₇	1	2	yes	—
305	C₂³	—	2	2	no	—
306	C₂³	—	2	2	no	—
307	C₂³	—	2	2	no	—
308	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
309	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
310	Q₈	—	2	8	no	—
311	Q₈	—	4	8	no	—
312	Q₈	—	4	2	no	—
313	Q₈	—	4	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	2	no	—
318	C₂×C₄	—	2	4	no	—
319	C₂×C₄	—	2	2	no	—
320	C₂×C₄	—	2	2	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	4	no	—
323	C₂×C₄	—	2	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	—	4	4	no	—
326	C₂×C₄	—	4	4	no	—
327	C₂×C₄	—	4	4	no	—
328	C₂×C₄	—	4	4	no	—
329	C₂×C₄	—	4	4	no	—
330	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
331	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
332	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
333	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
334	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
335	C₂×C₄	#137×C₄₇	1	4	yes	—
336	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
337	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
338	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
339	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
340	C₈	—	4	4	no	—
341	C₂²	—	2	2	no	—
342	C₂²	—	2	2	no	—
343	C₂²	—	2	2	no	—
344	C₂²	—	4	4	no	—
345	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
346	C₂²	C₄₇×#537	1	2	yes	—
347	C₂²	C₂×#137×C₄₇	1	2	yes	—
348	C₂²	C₄₇×#575	1	2	yes	—
349	C₄	—	2	2	no	—
350	C₄	—	2	2	no	—
351	C₄	—	2	2	no	—
352	C₄	—	2	2	no	—
353	C₄	—	4	4	no	—
354	C₄	—	4	4	no	—
355	C₄	—	8	4	no	—
356	C₄	C₄₇×#419	1	4	yes	—
357	C₄	C₄₇×#520	1	2	yes	—
358	C₄	C₄₇×#535	1	1	yes	characteristic
359	C₄	C₄₇×#536	1	1	yes	characteristic
360	C₂	—	4	2	no	—
361	C₂	C₄₇×#2311	1	1	yes	characteristic
362	C₂	C₂×C₄₇×#419	1	1	yes	characteristic
363	C₂	C₄₇×#2896	1	1	yes	characteristic
364	C₂	C₄₇×#3252	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	C₂⁴×C₄₇	C₂×D₄
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
4. C₄₇×#1987	C₂	semidirect
5. C₄₇×#1981	C₂	semidirect
7. C₄₇×#1805	C₂	semidirect
10. C₄₇×#533	C₄	semidirect
158. #21892	C₄₇	direct (N × H)
181. #1987	C₂×C₄₇	semidirect
182. #1981	C₂×C₄₇	semidirect
184. #1805	C₂×C₄₇	semidirect
192. #533	C₄×C₄₇	semidirect
214. C₄₇	#21892	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×#533	2
C₂×C₄₇×#423	2
C₄₇×#2283	2
C₄₇×#1987	2
C₄₇×#1981	2
C₄₇×#1894	2
C₄₇×#1805	2
#21892	47

Subgroups — C47×#21892 #26061590

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21892 #26061590