Subgroups — C₄₇×#32671 #26072369

Order 12032.

764 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2592	C₂	1	2	yes	maximal, complemented
2	C₄₇×#2056	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2054	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2015	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2012	C₂	1	2	yes	maximal
6	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1968	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1927	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1926	C₂	1	2	yes	maximal, complemented
10	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
12	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#124×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#106×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#103×C₄₇	C₂²	1	2	yes	—
18	C₂×#103×C₄₇	C₂²	1	2	yes	—
19	C₂×#102×C₄₇	C₂²	1	2	yes	—
20	C₂×#102×C₄₇	C₂²	1	2	yes	—
21	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#397	—	2	2	no	—
23	C₄₇×#393	—	2	2	no	—
24	C₄₇×#391	C₂²	1	2	yes	—
25	C₄₇×#391	C₂²	1	2	yes	—
26	C₄₇×#390	C₂²	1	2	yes	—
27	C₄₇×#390	C₂²	1	2	yes	—
28	C₄₇×#388	—	2	2	no	—
29	C₄₇×#388	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#340	C₂²	1	1	yes	characteristic
32	C₄₇×#340	C₂²	1	1	yes	characteristic
33	C₄₇×#336	C₂²	1	2	yes	—
34	C₄₇×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
36	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
37	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
38	C₂×Q₁₆×C₄₇	—	4	1	no	—
39	C₂×Q₁₆×C₄₇	—	4	2	no	—
40	C₂×SD₁₆×C₄₇	—	2	4	no	—
41	C₂×SD₁₆×C₄₇	—	4	2	no	—
42	C₂×SD₁₆×C₄₇	—	4	2	no	—
43	C₂×D₈×C₄₇	—	4	2	no	—
44	C₂×D₈×C₄₇	—	4	1	no	—
45	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
48	#124×C₄₇	—	4	2	no	—
49	#124×C₄₇	—	4	2	no	—
50	C₄×Q₈×C₄₇	—	4	1	no	—
51	C₄×Q₈×C₄₇	—	4	1	no	—
52	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
54	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
55	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
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×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
65	#106×C₄₇	—	4	2	no	—
66	C₄⋊C₈×C₄₇	—	4	1	no	—
67	#103×C₄₇	—	2	4	no	—
68	#103×C₄₇	—	4	2	no	—
69	#102×C₄₇	—	2	4	no	—
70	#102×C₄₇	—	4	2	no	—
71	C₄×C₈×C₄₇	—	4	1	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	#95×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	2	no	—
78	C₂×Q₈×C₄₇	—	2	2	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	4	1	no	—
86	C₂×Q₈×C₄₇	—	4	1	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	2	2	no	—
90	C₂×D₄×C₄₇	—	2	2	no	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
101	Q₁₆×C₄₇	—	4	4	no	—
102	SD₁₆×C₄₇	—	4	8	no	—
103	D₈×C₄₇	—	4	4	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	#41	1	4	yes	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	4	1	no	—
116	C₄⋊C₄×C₄₇	—	4	2	no	—
117	C₂²⋊C₄×C₄₇	—	4	4	no	—
118	C₂²⋊C₄×C₄₇	—	4	4	no	—
119	C₂²⋊C₄×C₄₇	—	4	4	no	—
120	C₂²⋊C₄×C₄₇	—	4	4	no	—
121	C₂²⋊C₄×C₄₇	—	8	2	no	—
122	C₂²⋊C₄×C₄₇	—	8	2	no	—
123	C₄²×C₄₇	—	2	1	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	1	no	—
127	C₄²×C₄₇	—	8	2	no	—
128	C₂³×C₄₇	—	4	2	no	—
129	C₂³×C₄₇	—	4	2	no	—
130	C₂³×C₄₇	—	4	2	no	—
131	C₂³×C₄₇	—	4	2	no	—
132	C₂³×C₄₇	—	4	2	no	—
133	C₂³×C₄₇	—	4	2	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	4	4	no	—
137	Q₈×C₄₇	—	4	2	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	4	2	no	—
140	Q₈×C₄₇	—	4	2	no	—
141	D₄×C₄₇	—	4	2	no	—
142	D₄×C₄₇	—	4	2	no	—
143	D₄×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	#135	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
166	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
167	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
168	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
169	C₈×C₄₇	—	2	4	no	—
170	C₈×C₄₇	—	4	1	no	—
171	C₈×C₄₇	—	4	1	no	—
172	#32671	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	8	2	no	—
174	C₂²×C₄₇	—	8	2	no	—
175	C₂²×C₄₇	—	8	2	no	—
176	C₂²×C₄₇	—	8	2	no	—
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	#534	1	1	yes	characteristic
181	C₂²×C₄₇	#550	1	2	yes	—
182	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
183	C₂²×C₄₇	#575	1	1	yes	characteristic
184	C₂²×C₄₇	#577	1	2	yes	—
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	—	4	2	no	—
188	C₄×C₄₇	—	4	1	no	—
189	C₄×C₄₇	—	8	2	no	—
190	C₄×C₄₇	—	8	2	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#538	1	2	yes	—
193	C₄×C₄₇	#555	1	1	yes	characteristic
194	C₄×C₄₇	H(3,𝔽₄)	1	1	yes	characteristic
195	#2592	C₂×C₄₇	1	2	yes	complemented
196	#2056	C₂×C₄₇	1	1	yes	characteristic, complemented
197	#2054	C₂×C₄₇	1	1	yes	characteristic
198	#2015	C₂×C₄₇	1	2	yes	complemented
199	#2012	C₂×C₄₇	1	2	yes	—
200	#1984	C₂×C₄₇	1	1	yes	characteristic, complemented
201	#1968	C₂×C₄₇	1	2	yes	complemented
202	#1927	C₂×C₄₇	1	2	yes	complemented
203	#1926	C₂×C₄₇	1	2	yes	complemented
204	C₂×C₄₇	—	16	2	no	—
205	C₂×C₄₇	#2733	1	1	yes	characteristic
206	C₂×C₄₇	#3191	1	1	yes	characteristic
207	C₂×C₄₇	#3204	1	1	yes	characteristic
208	C₂×C₄₇	#3394	1	2	yes	—
209	C₂×C₄₇	#3401	1	2	yes	—
210	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
211	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
212	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
213	C₂×#124	C₂²×C₄₇	1	2	yes	—
214	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
215	C₂×#106	C₂²×C₄₇	1	2	yes	—
216	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
217	C₂×#103	C₂²×C₄₇	1	2	yes	—
218	C₂×#103	C₂²×C₄₇	1	2	yes	—
219	C₂×#102	C₂²×C₄₇	1	2	yes	—
220	C₂×#102	C₂²×C₄₇	1	2	yes	—
221	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
222	#397	—	2	2	no	—
223	#393	—	2	2	no	—
224	#391	C₂²×C₄₇	1	2	yes	—
225	#391	C₂²×C₄₇	1	2	yes	—
226	#390	C₂²×C₄₇	1	2	yes	—
227	#390	C₂²×C₄₇	1	2	yes	—
228	#388	—	2	2	no	—
229	#388	—	2	2	no	—
230	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
231	#340	C₂²×C₄₇	1	1	yes	characteristic
232	#340	C₂²×C₄₇	1	1	yes	characteristic
233	#336	C₂²×C₄₇	1	2	yes	—
234	#336	C₂²×C₄₇	1	2	yes	—
235	C₄₇	#32671	1	1	yes	characteristic, direct product factor, Sylow
236	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
237	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
238	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
239	C₂×Q₁₆	—	4	2	no	—
240	C₂×Q₁₆	—	4	1	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	4	2	no	—
243	C₂×SD₁₆	—	4	2	no	—
244	C₂×D₈	—	4	2	no	—
245	C₂×D₈	—	4	1	no	—
246	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
248	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
249	#124	—	4	2	no	—
250	#124	—	4	2	no	—
251	C₄×Q₈	—	4	1	no	—
252	C₄×Q₈	—	4	1	no	—
253	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
254	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
255	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
256	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
257	C₂×C₂²⋊C₄	—	2	2	no	—
258	C₂×C₂²⋊C₄	—	2	2	no	—
259	C₂×C₂²⋊C₄	—	2	2	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
265	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
266	#106	—	4	2	no	—
267	C₄⋊C₈	—	4	1	no	—
268	#103	—	2	4	no	—
269	#103	—	4	2	no	—
270	#102	—	2	4	no	—
271	#102	—	4	2	no	—
272	C₄×C₈	—	4	1	no	—
273	#95	—	2	2	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₂⁴	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	—	2	2	no	—
281	C₂×Q₈	—	2	2	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	2	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	2	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
299	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
302	Q₁₆	—	4	4	no	—
303	SD₁₆	—	4	8	no	—
304	D₈	—	4	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	#41×C₄₇	1	4	yes	—
312	C₄⋊C₄	—	2	2	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	2	2	no	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	4	1	no	—
317	C₄⋊C₄	—	4	2	no	—
318	C₂²⋊C₄	—	4	4	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	4	4	no	—
321	C₂²⋊C₄	—	4	4	no	—
322	C₂²⋊C₄	—	8	2	no	—
323	C₂²⋊C₄	—	8	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	8	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	—	4	2	no	—
332	C₂³	—	4	2	no	—
333	C₂³	—	4	2	no	—
334	C₂³	—	4	2	no	—
335	C₂³	—	4	2	no	—
336	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
337	Q₈	—	4	4	no	—
338	Q₈	—	4	2	no	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	4	2	no	—
345	D₄	—	4	2	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	#135×C₄₇	1	2	yes	—
366	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
367	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
368	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
369	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
370	C₈	—	2	4	no	—
371	C₈	—	4	1	no	—
372	C₈	—	4	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	8	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	C₄₇×#534	1	1	yes	characteristic
381	C₂²	C₄₇×#550	1	2	yes	—
382	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
383	C₂²	C₄₇×#575	1	1	yes	characteristic
384	C₂²	C₄₇×#577	1	2	yes	—
385	C₄	—	2	2	no	—
386	C₄	—	4	2	no	—
387	C₄	—	4	2	no	—
388	C₄	—	4	1	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	2	no	—
392	C₄	C₄₇×#538	1	2	yes	—
393	C₄	C₄₇×#555	1	1	yes	characteristic
394	C₄	C₄₇×H(3,𝔽₄)	1	1	yes	characteristic
395	C₂	—	16	2	no	—
396	C₂	C₄₇×#2733	1	1	yes	characteristic
397	C₂	C₄₇×#3191	1	1	yes	characteristic
398	C₂	C₄₇×#3204	1	1	yes	characteristic
399	C₂	C₄₇×#3394	1	2	yes	—
400	C₂	C₄₇×#3401	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×D₈×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×Q₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#2592	C₂	semidirect
2. C₄₇×#2056	C₂	semidirect
4. C₄₇×#2015	C₂	semidirect
6. C₄₇×#1984	C₂	semidirect
7. C₄₇×#1968	C₂	semidirect
8. C₄₇×#1927	C₂	semidirect
9. C₄₇×#1926	C₂	semidirect
172. #32671	C₄₇	direct (N × H)
195. #2592	C₂×C₄₇	semidirect
196. #2056	C₂×C₄₇	semidirect
198. #2015	C₂×C₄₇	semidirect
200. #1984	C₂×C₄₇	semidirect
201. #1968	C₂×C₄₇	semidirect
202. #1927	C₂×C₄₇	semidirect
203. #1926	C₂×C₄₇	semidirect
235. C₄₇	#32671	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2592	2
C₄₇×#2056	2
C₄₇×#2054	2
C₄₇×#2015	2
C₄₇×#2012	2
C₄₇×#1984	2
C₄₇×#1968	2
C₄₇×#1927	2
C₄₇×#1926	2
#32671	47

Subgroups — C47×#32671 #26072369

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#32671 #26072369