Subgroups — C₄₇×#10924 #26050622

Order 12032.

1074 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#104×C₄₇	C₂	1	2	yes	maximal
2	C₄₇×#2297	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#376	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#339	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1728	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
8	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
10	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×#104×C₄₇	—	2	4	no	—
12	C₂×#104×C₄₇	—	2	4	no	—
13	C₂×#104×C₄₇	C₄	1	8	yes	complemented
14	C₄₇×#391	C₄	1	2	yes	complemented
15	C₄₇×#390	C₄	1	2	yes	complemented
16	C₄₇×#386	—	2	2	no	—
17	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
18	C₄₇×#376	—	2	4	no	—
19	C₂×#95×C₄₇	—	2	2	no	—
20	C₄₇×#339	—	2	4	no	—
21	C₄₇×#336	—	2	2	no	—
22	C₂×#41×C₄₇	—	2	2	no	—
23	C₂×#41×C₄₇	—	2	2	no	—
24	C₂×#41×C₄₇	—	2	2	no	—
25	C₂×#41×C₄₇	—	2	2	no	—
26	C₂×#41×C₄₇	—	2	2	no	—
27	C₂×#41×C₄₇	C₂×C₄	1	4	yes	—
28	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂²×D₄×C₄₇	—	2	1	no	—
30	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	—	2	2	no	—
32	C₂³×C₄×C₄₇	—	2	1	no	—
33	C₂³×C₄×C₄₇	D₄	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂×M₁₆×C₄₇	—	2	2	no	—
36	C₂×M₁₆×C₄₇	—	2	2	no	—
37	C₂×M₁₆×C₄₇	—	2	2	no	—
38	C₂×M₁₆×C₄₇	—	2	2	no	—
39	C₂×M₁₆×C₄₇	—	2	2	no	—
40	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
41	C₂²×C₈×C₄₇	—	2	2	no	—
42	#117×C₄₇	—	2	2	no	—
43	#117×C₄₇	—	2	2	no	—
44	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄²×C₄₇	—	2	2	no	—
48	C₂×C₄²×C₄₇	—	2	2	no	—
49	C₂×C₄²×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	1	no	—
53	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
54	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
55	C₂×C₄²×C₄₇	D₄	1	2	yes	—
56	C₂×C₄²×C₄₇	D₄	1	4	yes	—
57	C₂×C₄²×C₄₇	D₄	1	4	yes	—
58	#104×C₄₇	—	2	16	no	—
59	#95×C₄₇	—	2	8	no	—
60	#95×C₄₇	—	2	4	no	—
61	C₂⁴×C₄₇	—	2	1	no	—
62	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
63	#41×C₄₇	—	2	4	no	—
64	#41×C₄₇	—	2	4	no	—
65	#41×C₄₇	—	2	4	no	—
66	#41×C₄₇	—	2	4	no	—
67	#41×C₄₇	—	4	2	no	—
68	#41×C₄₇	—	4	2	no	—
69	#41×C₄₇	—	4	2	no	—
70	#41×C₄₇	—	4	2	no	—
71	C₂×Q₈×C₄₇	—	2	1	no	—
72	C₂×Q₈×C₄₇	—	2	2	no	—
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	C₄²	1	2	yes	—
75	C₂×D₄×C₄₇	—	2	4	no	—
76	C₂×D₄×C₄₇	—	2	1	no	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	4	1	no	—
80	C₂×D₄×C₄₇	—	4	2	no	—
81	C₂×D₄×C₄₇	—	4	1	no	—
82	C₂×D₄×C₄₇	C₄²	1	2	yes	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	4	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	4	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	4	no	—
92	C₂²×C₄×C₄₇	—	4	8	no	—
93	C₂²×C₄×C₄₇	—	4	2	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	—	4	1	no	—
96	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	2	yes	—
105	M₁₆×C₄₇	—	2	4	no	—
106	M₁₆×C₄₇	—	2	4	no	—
107	M₁₆×C₄₇	—	4	2	no	—
108	M₁₆×C₄₇	—	4	2	no	—
109	C₂×C₈×C₄₇	—	2	4	no	—
110	C₂×C₈×C₄₇	—	4	2	no	—
111	C₂×C₈×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	—	2	4	no	—
113	C₂²⋊C₄×C₄₇	—	4	8	no	—
114	C₂²⋊C₄×C₄₇	—	4	2	no	—
115	C₄²×C₄₇	—	2	4	no	—
116	C₄²×C₄₇	—	2	4	no	—
117	C₄²×C₄₇	—	2	4	no	—
118	C₄²×C₄₇	—	2	4	no	—
119	C₄²×C₄₇	—	2	4	no	—
120	C₄²×C₄₇	—	4	1	no	—
121	C₄²×C₄₇	—	4	1	no	—
122	C₄²×C₄₇	C₂²⋊C₄	1	8	yes	complemented
123	C₂³×C₄₇	—	2	4	no	—
124	C₂³×C₄₇	—	2	2	no	—
125	C₂³×C₄₇	—	4	1	no	—
126	C₂³×C₄₇	—	4	1	no	—
127	C₂³×C₄₇	—	4	4	no	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₄×D₄	1	2	yes	—
130	C₂³×C₄₇	#120	1	1	yes	characteristic
131	C₂³×C₄₇	#121	1	2	yes	—
132	C₂³×C₄₇	#123	1	1	yes	characteristic
133	Q₈×C₄₇	—	2	4	no	—
134	Q₈×C₄₇	—	4	2	no	—
135	D₄×C₄₇	—	2	4	no	—
136	D₄×C₄₇	—	4	4	no	—
137	D₄×C₄₇	—	4	4	no	—
138	D₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	8	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	8	no	—
145	C₂×C₄×C₄₇	—	4	8	no	—
146	C₂×C₄×C₄₇	—	4	8	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	4	1	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	4	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	4	no	—
155	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	#117	1	2	yes	—
158	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
160	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
161	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
162	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
164	C₂×C₄×C₄₇	#121	1	2	yes	—
165	C₂×C₄×C₄₇	#121	1	2	yes	—
166	C₂×C₄×C₄₇	#123	1	2	yes	—
167	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#124	1	2	yes	—
169	C₂×C₄×C₄₇	#126	1	2	yes	—
170	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
171	C₈×C₄₇	—	4	4	no	—
172	#10924	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	4	no	—
176	C₂²×C₄₇	—	2	4	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	4	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	8	2	no	—
181	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
182	C₂²×C₄₇	#386	1	2	yes	—
183	C₂²×C₄₇	#386	1	1	yes	characteristic
184	C₂²×C₄₇	#388	1	2	yes	—
185	C₂²×C₄₇	#390	1	1	yes	characteristic
186	C₂²×C₄₇	#421	1	4	yes	—
187	C₄×C₄₇	—	4	8	no	—
188	C₄×C₄₇	—	4	4	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	—	8	2	no	—
191	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
192	C₄×C₄₇	#388	1	2	yes	—
193	C₄×C₄₇	#388	1	2	yes	—
194	C₄×C₄₇	#390	1	2	yes	—
195	C₂²×#104	C₂×C₄₇	1	2	yes	—
196	#2297	C₂×C₄₇	1	1	yes	characteristic
197	C₂×#376	C₂×C₄₇	1	1	yes	characteristic, complemented
198	C₂×#339	C₂×C₄₇	1	2	yes	complemented
199	#1728	C₂×C₄₇	1	1	yes	characteristic, complemented
200	C₂×C₄₇	—	2	2	no	—
201	C₂×C₄₇	—	2	2	no	—
202	C₂×C₄₇	—	8	2	no	—
203	C₂×C₄₇	#1437	1	1	yes	characteristic
204	C₂×C₄₇	#1759	1	2	yes	—
205	C₂×C₄₇	#1897	1	2	yes	—
206	C₂×C₄₇	#1963	1	2	yes	—
207	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
209	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
210	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
211	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
212	C₂×#104	—	2	4	no	—
213	C₂×#104	—	2	4	no	—
214	C₂×#104	C₄×C₄₇	1	8	yes	complemented
215	#391	C₄×C₄₇	1	2	yes	complemented
216	#390	C₄×C₄₇	1	2	yes	complemented
217	#386	—	2	2	no	—
218	C₄×C₂²⋊C₄	—	2	2	no	—
219	#376	—	2	4	no	—
220	C₂×#95	—	2	2	no	—
221	#339	—	2	4	no	—
222	#336	—	2	2	no	—
223	C₄₇	#10924	1	1	yes	characteristic, direct product factor, Sylow
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	—	2	2	no	—
228	C₂×#41	—	2	2	no	—
229	C₂×#41	C₂×C₄×C₄₇	1	4	yes	—
230	C₂²×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
231	C₂²×D₄	—	2	1	no	—
232	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
233	C₂³×C₄	—	2	2	no	—
234	C₂³×C₄	—	2	1	no	—
235	C₂³×C₄	D₄×C₄₇	1	2	yes	—
236	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
243	C₂²×C₈	—	2	2	no	—
244	#117	—	2	2	no	—
245	#117	—	2	2	no	—
246	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	2	yes	—
247	C₂×C₂²⋊C₄	—	2	1	no	—
248	C₂×C₂²⋊C₄	—	2	4	no	—
249	C₂×C₄²	—	2	2	no	—
250	C₂×C₄²	—	2	2	no	—
251	C₂×C₄²	—	2	2	no	—
252	C₂×C₄²	—	2	2	no	—
253	C₂×C₄²	—	2	2	no	—
254	C₂×C₄²	—	2	1	no	—
255	C₂×C₄²	C₂×C₄×C₄₇	1	2	yes	—
256	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
257	C₂×C₄²	D₄×C₄₇	1	2	yes	—
258	C₂×C₄²	D₄×C₄₇	1	4	yes	—
259	C₂×C₄²	D₄×C₄₇	1	4	yes	—
260	#104	—	2	16	no	—
261	#95	—	2	8	no	—
262	#95	—	2	4	no	—
263	C₂⁴	—	2	1	no	—
264	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
265	#41	—	2	4	no	—
266	#41	—	2	4	no	—
267	#41	—	2	4	no	—
268	#41	—	2	4	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	#41	—	4	2	no	—
272	#41	—	4	2	no	—
273	C₂×Q₈	—	2	1	no	—
274	C₂×Q₈	—	2	2	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	C₄²×C₄₇	1	2	yes	—
277	C₂×D₄	—	2	4	no	—
278	C₂×D₄	—	2	1	no	—
279	C₂×D₄	—	2	2	no	—
280	C₂×D₄	—	2	2	no	—
281	C₂×D₄	—	4	1	no	—
282	C₂×D₄	—	4	2	no	—
283	C₂×D₄	—	4	1	no	—
284	C₂×D₄	C₄²×C₄₇	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	4	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	4	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	4	4	no	—
294	C₂²×C₄	—	4	8	no	—
295	C₂²×C₄	—	4	2	no	—
296	C₂²×C₄	—	4	1	no	—
297	C₂²×C₄	—	4	1	no	—
298	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
299	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
300	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
304	C₂²×C₄	#41×C₄₇	1	2	yes	—
305	C₂²×C₄	#41×C₄₇	1	2	yes	—
306	C₂²×C₄	#41×C₄₇	1	2	yes	—
307	M₁₆	—	2	4	no	—
308	M₁₆	—	2	4	no	—
309	M₁₆	—	4	2	no	—
310	M₁₆	—	4	2	no	—
311	C₂×C₈	—	2	4	no	—
312	C₂×C₈	—	4	2	no	—
313	C₂×C₈	—	4	2	no	—
314	C₄⋊C₄	—	2	4	no	—
315	C₂²⋊C₄	—	4	8	no	—
316	C₂²⋊C₄	—	4	2	no	—
317	C₄²	—	2	4	no	—
318	C₄²	—	2	4	no	—
319	C₄²	—	2	4	no	—
320	C₄²	—	2	4	no	—
321	C₄²	—	2	4	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂²⋊C₄×C₄₇	1	8	yes	complemented
325	C₂³	—	2	4	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	4	4	no	—
330	C₂³	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
331	C₂³	C₄×D₄×C₄₇	1	2	yes	—
332	C₂³	#120×C₄₇	1	1	yes	characteristic
333	C₂³	#121×C₄₇	1	2	yes	—
334	C₂³	#123×C₄₇	1	1	yes	characteristic
335	Q₈	—	2	4	no	—
336	Q₈	—	4	2	no	—
337	D₄	—	2	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	4	no	—
340	D₄	—	4	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	4	no	—
343	C₂×C₄	—	2	8	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	4	8	no	—
347	C₂×C₄	—	4	8	no	—
348	C₂×C₄	—	4	8	no	—
349	C₂×C₄	—	4	4	no	—
350	C₂×C₄	—	4	4	no	—
351	C₂×C₄	—	4	1	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	4	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	C₂×C₄²×C₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
359	C₂×C₄	#117×C₄₇	1	2	yes	—
360	C₂×C₄	#117×C₄₇	1	1	yes	characteristic
361	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
362	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
363	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
364	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
365	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
366	C₂×C₄	#121×C₄₇	1	2	yes	—
367	C₂×C₄	#121×C₄₇	1	2	yes	—
368	C₂×C₄	#123×C₄₇	1	2	yes	—
369	C₂×C₄	#124×C₄₇	1	1	yes	characteristic
370	C₂×C₄	#124×C₄₇	1	2	yes	—
371	C₂×C₄	#126×C₄₇	1	2	yes	—
372	C₂×C₄	#127×C₄₇	1	1	yes	characteristic
373	C₈	—	4	4	no	—
374	C₂²	—	2	4	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	4	no	—
378	C₂²	—	4	4	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₄×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
383	C₂²	C₄₇×#386	1	2	yes	—
384	C₂²	C₄₇×#386	1	1	yes	characteristic
385	C₂²	C₄₇×#388	1	2	yes	—
386	C₂²	C₄₇×#390	1	1	yes	characteristic
387	C₂²	C₄₇×#421	1	4	yes	—
388	C₄	—	4	8	no	—
389	C₄	—	4	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	C₄×C₂²⋊C₄×C₄₇	1	2	yes	—
393	C₄	C₄₇×#388	1	2	yes	—
394	C₄	C₄₇×#388	1	2	yes	—
395	C₄	C₄₇×#390	1	2	yes	—
396	C₂	—	2	2	no	—
397	C₂	—	2	2	no	—
398	C₂	—	8	2	no	—
399	C₂	C₄₇×#1437	1	1	yes	characteristic
400	C₂	C₄₇×#1759	1	2	yes	—
401	C₂	C₄₇×#1897	1	2	yes	—
402	C₂	C₄₇×#1963	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂×C₄²×C₄₇
Frattini, cosocle	C₂³×C₄	C₂³×C₄₇
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄₇×#376	C₂	semidirect
4. C₂×C₄₇×#339	C₂	semidirect
5. C₄₇×#1728	C₂	semidirect
13. C₂×#104×C₄₇	C₄	semidirect
14. C₄₇×#391	C₄	semidirect
15. C₄₇×#390	C₄	semidirect
122. C₄²×C₄₇	C₂²⋊C₄	semidirect
172. #10924	C₄₇	direct (N × H)
197. C₂×#376	C₂×C₄₇	semidirect
198. C₂×#339	C₂×C₄₇	semidirect
199. #1728	C₂×C₄₇	semidirect
214. C₂×#104	C₄×C₄₇	semidirect
215. #391	C₄×C₄₇	semidirect
216. #390	C₄×C₄₇	semidirect
223. C₄₇	#10924	direct (N × H)
324. C₄²	C₂²⋊C₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#104×C₄₇	2
C₄₇×#2297	2
C₂×C₄₇×#376	2
C₂×C₄₇×#339	2
C₄₇×#1728	2
#10924	47

Subgroups — C47×#10924 #26050622

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#10924 #26050622