Subgroups — C₄₇×#29827 #26069525

Order 12032.

890 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#477	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2858	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2295	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2067	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2055	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1987	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1982	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₇	—	2	2	no	—
14	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#477	—	2	4	no	—
16	C₄₇×#460	—	2	4	no	—
17	C₂×#107×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
21	C₂×#103×C₄₇	C₂²	1	2	yes	—
22	C₂×#102×C₄₇	C₂²	1	2	yes	—
23	C₂×#102×C₄₇	C₂²	1	4	yes	—
24	C₄₇×#391	C₂²	1	2	yes	—
25	C₄₇×#390	—	2	1	no	—
26	C₄₇×#390	—	2	1	no	—
27	C₄₇×#390	C₂²	1	4	yes	—
28	C₄₇×#389	C₂²	1	2	yes	—
29	C₄₇×#387	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#376	—	2	1	no	—
33	C₄³×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#340	C₂²	1	4	yes	—
35	C₂²×Q₈×C₄₇	—	2	1	no	—
36	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₇	—	2	1	no	—
38	C₂²×D₄×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
40	C₂×SD₁₆×C₄₇	—	2	4	no	—
41	C₂×SD₁₆×C₄₇	—	4	4	no	—
42	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₄₇	—	2	2	no	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	#127×C₄₇	—	2	2	no	—
47	#127×C₄₇	—	2	2	no	—
48	#124×C₄₇	—	4	8	no	—
49	C₄×Q₈×C₄₇	—	2	2	no	—
50	C₄×Q₈×C₄₇	D₄	1	4	yes	—
51	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₄²×C₄₇	—	2	1	no	—
60	C₂×C₄²×C₄₇	—	2	1	no	—
61	C₂×C₄²×C₄₇	D₄	1	2	yes	—
62	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
63	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
64	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	#107×C₄₇	—	2	4	no	—
67	C₄⋊C₈×C₄₇	—	2	2	no	—
68	C₄⋊C₈×C₄₇	—	2	2	no	—
69	C₄⋊C₈×C₄₇	—	4	4	no	—
70	#103×C₄₇	—	2	4	no	—
71	#102×C₄₇	—	2	4	no	—
72	#102×C₄₇	—	4	4	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	1	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂×Q₈×C₄₇	—	2	1	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	—	4	4	no	—
82	C₂×Q₈×C₄₇	—	4	2	no	—
83	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	4	4	no	—
89	C₂×D₄×C₄₇	—	4	2	no	—
90	C₂×D₄×C₄₇	—	4	2	no	—
91	C₂×D₄×C₄₇	—	4	2	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
102	SD₁₆×C₄₇	—	4	8	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	4	no	—
106	C₂×C₈×C₄₇	—	2	4	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄⋊C₄×C₄₇	—	2	1	no	—
109	C₄⋊C₄×C₄₇	—	2	2	no	—
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	4	2	no	—
114	C₄⋊C₄×C₄₇	—	4	4	no	—
115	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²⋊C₄×C₄₇	—	4	8	no	—
117	C₂²⋊C₄×C₄₇	—	4	8	no	—
118	C₄²×C₄₇	—	2	4	no	—
119	C₄²×C₄₇	—	2	2	no	—
120	C₄²×C₄₇	—	2	4	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	4	2	no	—
125	C₄²×C₄₇	C₂×D₄	1	2	yes	—
126	C₄²×C₄₇	#41	1	2	yes	—
127	C₂³×C₄₇	—	4	2	no	—
128	C₂³×C₄₇	—	4	4	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	4	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
133	Q₈×C₄₇	—	2	2	no	—
134	Q₈×C₄₇	—	2	2	no	—
135	Q₈×C₄₇	—	4	2	no	—
136	Q₈×C₄₇	—	8	4	no	—
137	D₄×C₄₇	—	4	2	no	—
138	D₄×C₄₇	—	4	2	no	—
139	D₄×C₄₇	—	4	4	no	—
140	D₄×C₄₇	—	8	4	no	—
141	D₄×C₄₇	—	8	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	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	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	2	no	—
157	C₂×C₄×C₄₇	#121	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
161	C₂×C₄×C₄₇	#137	1	2	yes	—
162	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
165	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
166	C₈×C₄₇	—	4	2	no	—
167	C₈×C₄₇	—	4	2	no	—
168	#29827	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
169	C₂²×C₄₇	—	8	2	no	—
170	C₂²×C₄₇	—	8	4	no	—
171	C₂²×C₄₇	—	8	4	no	—
172	C₂²×C₄₇	—	8	2	no	—
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
175	C₂²×C₄₇	#537	1	2	yes	—
176	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
178	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
179	C₄×C₄₇	—	2	4	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	4	2	no	—
182	C₄×C₄₇	—	4	2	no	—
183	C₄×C₄₇	—	4	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	#464	1	4	yes	—
187	C₄×C₄₇	#535	1	1	yes	characteristic
188	C₄×C₄₇	#536	1	1	yes	characteristic
189	C₄×C₄₇	#542	1	2	yes	—
190	C₂×#477	C₂×C₄₇	1	1	yes	characteristic, complemented
191	C₂×#460	C₂×C₄₇	1	1	yes	characteristic
192	#2858	C₂×C₄₇	1	1	yes	characteristic
193	#2295	C₂×C₄₇	1	1	yes	characteristic, complemented
194	#2067	C₂×C₄₇	1	4	yes	complemented
195	#2055	C₂×C₄₇	1	4	yes	complemented
196	#1987	C₂×C₄₇	1	1	yes	characteristic, complemented
197	#1982	C₂×C₄₇	1	1	yes	characteristic
198	#1842	C₂×C₄₇	1	1	yes	characteristic, complemented
199	C₂×C₄₇	—	16	2	no	—
200	C₂×C₄₇	#2620	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#464	1	1	yes	characteristic
202	C₂×C₄₇	#3038	1	1	yes	characteristic
203	C₂×C₄₇	#3247	1	2	yes	—
204	C₂×C₄₇	#3254	1	2	yes	—
205	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
206	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
207	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
208	C₂×#124	—	2	2	no	—
209	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
210	#477	—	2	4	no	—
211	#460	—	2	4	no	—
212	C₂×#107	C₂²×C₄₇	1	2	yes	—
213	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	—
216	C₂×#103	C₂²×C₄₇	1	2	yes	—
217	C₂×#102	C₂²×C₄₇	1	2	yes	—
218	C₂×#102	C₂²×C₄₇	1	4	yes	—
219	#391	C₂²×C₄₇	1	2	yes	—
220	#390	—	2	1	no	—
221	#390	—	2	1	no	—
222	#390	C₂²×C₄₇	1	4	yes	—
223	#389	C₂²×C₄₇	1	2	yes	—
224	#387	—	2	2	no	—
225	C₄×C₄⋊C₄	—	2	1	no	—
226	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
227	#376	—	2	1	no	—
228	C₄³	C₂²×C₄₇	1	1	yes	characteristic
229	#340	C₂²×C₄₇	1	4	yes	—
230	C₄₇	#29827	1	1	yes	characteristic, direct product factor, Sylow
231	C₂²×Q₈	—	2	1	no	—
232	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
236	C₂×SD₁₆	—	2	4	no	—
237	C₂×SD₁₆	—	4	4	no	—
238	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
239	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
240	C₄⋊Q₈	—	2	2	no	—
241	C₄⋊Q₈	—	2	2	no	—
242	#127	—	2	2	no	—
243	#127	—	2	2	no	—
244	#124	—	4	8	no	—
245	C₄×Q₈	—	2	2	no	—
246	C₄×Q₈	D₄×C₄₇	1	4	yes	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
252	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
253	C₂×C₂²⋊C₄	—	2	4	no	—
254	C₂×C₂²⋊C₄	—	2	4	no	—
255	C₂×C₄²	—	2	1	no	—
256	C₂×C₄²	—	2	1	no	—
257	C₂×C₄²	D₄×C₄₇	1	2	yes	—
258	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
259	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
261	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
262	#107	—	2	4	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	4	4	no	—
266	#103	—	2	4	no	—
267	#102	—	2	4	no	—
268	#102	—	4	4	no	—
269	#95	—	2	2	no	—
270	#95	—	2	2	no	—
271	#95	—	2	2	no	—
272	#95	—	2	1	no	—
273	C₂⁴	—	2	2	no	—
274	C₂×Q₈	—	2	1	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	4	4	no	—
278	C₂×Q₈	—	4	2	no	—
279	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	4	no	—
283	C₂×D₄	—	2	4	no	—
284	C₂×D₄	—	4	4	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
294	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
298	SD₁₆	—	4	8	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₄⋊C₄	—	2	4	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	2	2	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
312	C₂²⋊C₄	—	4	8	no	—
313	C₂²⋊C₄	—	4	8	no	—
314	C₄²	—	2	4	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	4	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	4	2	no	—
321	C₄²	C₂×D₄×C₄₇	1	2	yes	—
322	C₄²	#41×C₄₇	1	2	yes	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	4	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	2	no	—
328	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
329	Q₈	—	2	2	no	—
330	Q₈	—	2	2	no	—
331	Q₈	—	4	2	no	—
332	Q₈	—	8	4	no	—
333	D₄	—	4	2	no	—
334	D₄	—	4	2	no	—
335	D₄	—	4	4	no	—
336	D₄	—	8	4	no	—
337	D₄	—	8	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	4	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	#121×C₄₇	1	2	yes	—
354	C₂×C₄	#121×C₄₇	1	2	yes	—
355	C₂×C₄	#135×C₄₇	1	2	yes	—
356	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
357	C₂×C₄	#137×C₄₇	1	2	yes	—
358	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
360	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
361	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
362	C₈	—	4	2	no	—
363	C₈	—	4	2	no	—
364	C₂²	—	8	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	4	no	—
368	C₂²	—	8	4	no	—
369	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
370	C₂²	C₄₇×#537	1	2	yes	—
371	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
372	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
373	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
374	C₄	—	2	2	no	—
375	C₄	—	2	4	no	—
376	C₄	—	4	2	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	2	no	—
379	C₄	—	8	2	no	—
380	C₄	—	8	2	no	—
381	C₄	C₄₇×#464	1	4	yes	—
382	C₄	C₄₇×#535	1	1	yes	characteristic
383	C₄	C₄₇×#536	1	1	yes	characteristic
384	C₄	C₄₇×#542	1	2	yes	—
385	C₂	—	16	2	no	—
386	C₂	C₄₇×#2620	1	1	yes	characteristic
387	C₂	C₂×C₄₇×#464	1	1	yes	characteristic
388	C₂	C₄₇×#3038	1	1	yes	characteristic
389	C₂	C₄₇×#3247	1	2	yes	—
390	C₂	C₄₇×#3254	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#127×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₄³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#477	C₂	semidirect
4. C₄₇×#2295	C₂	semidirect
5. C₄₇×#2067	C₂	semidirect
6. C₄₇×#2055	C₂	semidirect
7. C₄₇×#1987	C₂	semidirect
9. C₄₇×#1842	C₂	semidirect
168. #29827	C₄₇	direct (N × H)
190. C₂×#477	C₂×C₄₇	semidirect
193. #2295	C₂×C₄₇	semidirect
194. #2067	C₂×C₄₇	semidirect
195. #2055	C₂×C₄₇	semidirect
196. #1987	C₂×C₄₇	semidirect
198. #1842	C₂×C₄₇	semidirect
230. C₄₇	#29827	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×#477	2
C₂×C₄₇×#460	2
C₄₇×#2858	2
C₄₇×#2295	2
C₄₇×#2067	2
C₄₇×#2055	2
C₄₇×#1987	2
C₄₇×#1982	2
C₄₇×#1842	2
#29827	47

Subgroups — C47×#29827 #26069525

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29827 #26069525