Subgroups — C₄₇×#29723 #26069421

Order 12032.

1082 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#450	C₂	1	2	yes	maximal
2	C₄₇×#2621	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2309	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2073	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2055	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2013	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1873	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²×SD₁₆×C₄₇	C₂²	1	4	yes	—
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
13	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#450	—	2	8	no	—
16	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
17	C₂×#103×C₄₇	C₂²	1	4	yes	complemented
18	C₂×#102×C₄₇	C₂²	1	4	yes	—
19	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
20	C₄₇×#398	—	2	2	no	—
21	C₄₇×#397	—	2	2	no	—
22	C₄₇×#391	C₂²	1	2	yes	complemented
23	C₄₇×#390	—	2	2	no	—
24	C₄₇×#390	C₂²	1	2	yes	—
25	C₄₇×#390	C₂²	1	2	yes	—
26	C₄₇×#382	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#379	—	2	2	no	—
28	C₄₇×#340	C₂²	1	4	yes	complemented
29	C₄₇×#336	C₂²	1	2	yes	complemented
30	C₂⁵×C₄₇	—	2	1	no	—
31	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
32	C₂²×D₄×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	2	no	—
34	C₂²×D₄×C₄₇	—	4	2	no	—
35	C₂²×D₄×C₄₇	—	4	2	no	—
36	C₂²×D₄×C₄₇	D₄	1	4	yes	—
37	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂×SD₁₆×C₄₇	—	2	8	no	—
40	C₂×SD₁₆×C₄₇	—	4	4	no	—
41	C₂×SD₁₆×C₄₇	—	4	4	no	—
42	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
43	C₄⋊Q₈×C₄₇	—	4	2	no	—
44	C₂²⋊Q₈×C₄₇	—	2	4	no	—
45	C₂²⋊Q₈×C₄₇	—	2	4	no	—
46	#117×C₄₇	—	4	2	no	—
47	#117×C₄₇	—	4	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
51	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
52	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
58	C₂×C₄²×C₄₇	—	2	1	no	—
59	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊C₈×C₄₇	—	4	2	no	—
62	#103×C₄₇	—	4	4	no	—
63	#102×C₄₇	—	2	8	no	—
64	C₂²⋊C₈×C₄₇	—	2	4	no	—
65	#95×C₄₇	—	2	2	no	—
66	#95×C₄₇	—	2	4	no	—
67	C₂⁴×C₄₇	—	2	2	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	4	2	no	—
70	C₂⁴×C₄₇	—	4	2	no	—
71	C₂⁴×C₄₇	—	8	4	no	—
72	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	—	2	4	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×D₄×C₄₇	—	2	4	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	4	no	—
80	C₂×D₄×C₄₇	—	2	4	no	—
81	C₂×D₄×C₄₇	—	4	8	no	—
82	C₂×D₄×C₄₇	—	4	2	no	—
83	C₂×D₄×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	—	4	8	no	—
85	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	#41	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
97	SD₁₆×C₄₇	—	4	16	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	2	4	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₄⋊C₄×C₄₇	—	4	2	no	—
105	C₄⋊C₄×C₄₇	—	4	4	no	—
106	C₄⋊C₄×C₄₇	—	4	4	no	—
107	C₂²⋊C₄×C₄₇	—	4	2	no	—
108	C₂²⋊C₄×C₄₇	—	4	2	no	—
109	C₂²⋊C₄×C₄₇	—	4	4	no	—
110	C₂²⋊C₄×C₄₇	—	8	4	no	—
111	C₂²⋊C₄×C₄₇	—	8	4	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	—	2	2	no	—
114	C₄²×C₄₇	—	4	2	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	2	4	no	—
119	C₂³×C₄₇	—	4	8	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	—	4	2	no	—
122	C₂³×C₄₇	—	4	4	no	—
123	C₂³×C₄₇	—	4	4	no	—
124	C₂³×C₄₇	—	8	8	no	—
125	C₂³×C₄₇	—	8	8	no	—
126	C₂³×C₄₇	—	8	8	no	—
127	C₂³×C₄₇	#121	1	2	yes	—
128	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
129	Q₈×C₄₇	—	4	4	no	—
130	Q₈×C₄₇	—	4	4	no	—
131	D₄×C₄₇	—	2	8	no	—
132	D₄×C₄₇	—	4	8	no	—
133	D₄×C₄₇	—	4	4	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	4	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	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	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	#121	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
154	C₈×C₄₇	—	4	4	no	—
155	#29723	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
156	C₂²×C₄₇	—	2	2	no	—
157	C₂²×C₄₇	—	2	4	no	—
158	C₂²×C₄₇	—	4	2	no	—
159	C₂²×C₄₇	—	4	2	no	—
160	C₂²×C₄₇	—	4	4	no	—
161	C₂²×C₄₇	—	4	8	no	—
162	C₂²×C₄₇	—	8	16	no	—
163	C₂²×C₄₇	—	8	4	no	—
164	C₂²×C₄₇	—	8	2	no	—
165	C₂²×C₄₇	—	8	2	no	—
166	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
167	C₂²×C₄₇	#534	1	1	yes	characteristic
168	C₂²×C₄₇	#535	1	1	yes	characteristic
169	C₂²×C₄₇	#577	1	4	yes	—
170	C₄×C₄₇	—	2	2	no	—
171	C₄×C₄₇	—	4	2	no	—
172	C₄×C₄₇	—	4	2	no	—
173	C₄×C₄₇	—	8	2	no	—
174	C₄×C₄₇	—	8	2	no	—
175	C₄×C₄₇	—	8	2	no	—
176	C₄×C₄₇	#534	1	2	yes	—
177	C₄×C₄₇	#538	1	2	yes	—
178	C₂×#450	C₂×C₄₇	1	2	yes	—
179	#2621	C₂×C₄₇	1	1	yes	characteristic, complemented
180	#2309	C₂×C₄₇	1	1	yes	characteristic
181	#2073	C₂×C₄₇	1	2	yes	complemented
182	#2055	C₂×C₄₇	1	4	yes	complemented
183	#2013	C₂×C₄₇	1	2	yes	complemented
184	#1873	C₂×C₄₇	1	2	yes	complemented
185	#1798	C₂×C₄₇	1	1	yes	characteristic, complemented
186	C₂×C₄₇	—	4	2	no	—
187	C₂×C₄₇	—	8	4	no	—
188	C₂×C₄₇	#2617	1	1	yes	characteristic
189	C₂×C₄₇	#3042	1	2	yes	—
190	C₂×C₄₇	#3200	1	2	yes	—
191	C₂×C₄₇	#3222	1	2	yes	—
192	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
193	C₂²×SD₁₆	C₂²×C₄₇	1	4	yes	—
194	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
195	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
196	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
197	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
198	#450	—	2	8	no	—
199	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
200	C₂×#103	C₂²×C₄₇	1	4	yes	complemented
201	C₂×#102	C₂²×C₄₇	1	4	yes	—
202	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
203	#398	—	2	2	no	—
204	#397	—	2	2	no	—
205	#391	C₂²×C₄₇	1	2	yes	complemented
206	#390	—	2	2	no	—
207	#390	C₂²×C₄₇	1	2	yes	—
208	#390	C₂²×C₄₇	1	2	yes	—
209	#382	C₂²×C₄₇	1	1	yes	characteristic, complemented
210	#379	—	2	2	no	—
211	#340	C₂²×C₄₇	1	4	yes	complemented
212	#336	C₂²×C₄₇	1	2	yes	complemented
213	C₄₇	#29723	1	1	yes	characteristic, direct product factor, Sylow
214	C₂⁵	—	2	1	no	—
215	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
216	C₂²×D₄	—	2	1	no	—
217	C₂²×D₄	—	2	2	no	—
218	C₂²×D₄	—	4	2	no	—
219	C₂²×D₄	—	4	2	no	—
220	C₂²×D₄	D₄×C₄₇	1	4	yes	—
221	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
222	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
223	C₂×SD₁₆	—	2	8	no	—
224	C₂×SD₁₆	—	4	4	no	—
225	C₂×SD₁₆	—	4	4	no	—
226	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
227	C₄⋊Q₈	—	4	2	no	—
228	C₂²⋊Q₈	—	2	4	no	—
229	C₂²⋊Q₈	—	2	4	no	—
230	#117	—	4	2	no	—
231	#117	—	4	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
235	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
236	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
237	C₂×C₂²⋊C₄	—	2	1	no	—
238	C₂×C₂²⋊C₄	—	2	2	no	—
239	C₂×C₂²⋊C₄	—	2	4	no	—
240	C₂×C₂²⋊C₄	—	2	4	no	—
241	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
242	C₂×C₄²	—	2	1	no	—
243	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
244	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
245	C₄⋊C₈	—	4	2	no	—
246	#103	—	4	4	no	—
247	#102	—	2	8	no	—
248	C₂²⋊C₈	—	2	4	no	—
249	#95	—	2	2	no	—
250	#95	—	2	4	no	—
251	C₂⁴	—	2	2	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	4	2	no	—
254	C₂⁴	—	4	2	no	—
255	C₂⁴	—	8	4	no	—
256	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
257	C₂×Q₈	—	2	2	no	—
258	C₂×Q₈	—	2	2	no	—
259	C₂×Q₈	—	2	4	no	—
260	C₂×Q₈	—	2	4	no	—
261	C₂×D₄	—	2	4	no	—
262	C₂×D₄	—	2	2	no	—
263	C₂×D₄	—	2	4	no	—
264	C₂×D₄	—	2	4	no	—
265	C₂×D₄	—	4	8	no	—
266	C₂×D₄	—	4	2	no	—
267	C₂×D₄	—	4	2	no	—
268	C₂×D₄	—	4	8	no	—
269	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
276	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
277	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
279	C₂²×C₄	#41×C₄₇	1	2	yes	—
280	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
281	SD₁₆	—	4	16	no	—
282	C₂×C₈	—	2	4	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₄⋊C₄	—	2	2	no	—
286	C₄⋊C₄	—	2	2	no	—
287	C₄⋊C₄	—	2	4	no	—
288	C₄⋊C₄	—	4	2	no	—
289	C₄⋊C₄	—	4	4	no	—
290	C₄⋊C₄	—	4	4	no	—
291	C₂²⋊C₄	—	4	2	no	—
292	C₂²⋊C₄	—	4	2	no	—
293	C₂²⋊C₄	—	4	4	no	—
294	C₂²⋊C₄	—	8	4	no	—
295	C₂²⋊C₄	—	8	4	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	4	2	no	—
299	C₂³	—	2	1	no	—
300	C₂³	—	2	1	no	—
301	C₂³	—	2	4	no	—
302	C₂³	—	2	4	no	—
303	C₂³	—	4	8	no	—
304	C₂³	—	4	2	no	—
305	C₂³	—	4	2	no	—
306	C₂³	—	4	4	no	—
307	C₂³	—	4	4	no	—
308	C₂³	—	8	8	no	—
309	C₂³	—	8	8	no	—
310	C₂³	—	8	8	no	—
311	C₂³	#121×C₄₇	1	2	yes	—
312	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
313	Q₈	—	4	4	no	—
314	Q₈	—	4	4	no	—
315	D₄	—	2	8	no	—
316	D₄	—	4	8	no	—
317	D₄	—	4	4	no	—
318	C₂×C₄	—	2	1	no	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	4	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	4	2	no	—
328	C₂×C₄	—	4	2	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	4	4	no	—
332	C₂×C₄	—	4	4	no	—
333	C₂×C₄	#121×C₄₇	1	2	yes	—
334	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
336	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
337	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
338	C₈	—	4	4	no	—
339	C₂²	—	2	4	no	—
340	C₂²	—	2	2	no	—
341	C₂²	—	4	2	no	—
342	C₂²	—	4	2	no	—
343	C₂²	—	4	8	no	—
344	C₂²	—	4	4	no	—
345	C₂²	—	8	16	no	—
346	C₂²	—	8	4	no	—
347	C₂²	—	8	2	no	—
348	C₂²	—	8	2	no	—
349	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
350	C₂²	C₄₇×#534	1	1	yes	characteristic
351	C₂²	C₄₇×#535	1	1	yes	characteristic
352	C₂²	C₄₇×#577	1	4	yes	—
353	C₄	—	2	2	no	—
354	C₄	—	4	2	no	—
355	C₄	—	4	2	no	—
356	C₄	—	8	2	no	—
357	C₄	—	8	2	no	—
358	C₄	—	8	2	no	—
359	C₄	C₄₇×#534	1	2	yes	—
360	C₄	C₄₇×#538	1	2	yes	—
361	C₂	—	4	2	no	—
362	C₂	—	8	4	no	—
363	C₂	C₄₇×#2617	1	1	yes	characteristic
364	C₂	C₄₇×#3042	1	2	yes	—
365	C₂	C₄₇×#3200	1	2	yes	—
366	C₂	C₄₇×#3222	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2621	C₂	semidirect
4. C₄₇×#2073	C₂	semidirect
5. C₄₇×#2055	C₂	semidirect
6. C₄₇×#2013	C₂	semidirect
7. C₄₇×#1873	C₂	semidirect
8. C₄₇×#1798	C₂	semidirect
11. C₂×C₄⋊Q₈×C₄₇	C₂²	semidirect
16. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
17. C₂×#103×C₄₇	C₂²	semidirect
22. C₄₇×#391	C₂²	semidirect
26. C₄₇×#382	C₂²	semidirect
28. C₄₇×#340	C₂²	semidirect
29. C₄₇×#336	C₂²	semidirect
155. #29723	C₄₇	direct (N × H)
179. #2621	C₂×C₄₇	semidirect
181. #2073	C₂×C₄₇	semidirect
182. #2055	C₂×C₄₇	semidirect
183. #2013	C₂×C₄₇	semidirect
184. #1873	C₂×C₄₇	semidirect
185. #1798	C₂×C₄₇	semidirect
194. C₂×C₄⋊Q₈	C₂²×C₄₇	semidirect
199. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
200. C₂×#103	C₂²×C₄₇	semidirect
205. #391	C₂²×C₄₇	semidirect
209. #382	C₂²×C₄₇	semidirect
211. #340	C₂²×C₄₇	semidirect
212. #336	C₂²×C₄₇	semidirect
213. C₄₇	#29723	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×#450	2
C₄₇×#2621	2
C₄₇×#2309	2
C₄₇×#2073	2
C₄₇×#2055	2
C₄₇×#2013	2
C₄₇×#1873	2
C₄₇×#1798	2
#29723	47

Subgroups — C47×#29723 #26069421

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29723 #26069421