Subgroups — C₄₇×#29728 #26069426

Order 12032.

964 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#451	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#448	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2620	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2310	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2072	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2056	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2055	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2015	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1875	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
14	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
15	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#451	—	2	4	no	—
21	C₄₇×#448	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#396	—	2	2	no	—
30	C₄₇×#394	—	2	2	no	—
31	C₄₇×#391	—	2	2	no	—
32	C₄₇×#391	C₂²	1	2	yes	—
33	C₄₇×#391	C₂²	1	2	yes	—
34	C₄₇×#391	C₂²	1	1	yes	characteristic
35	C₄₇×#390	C₂²	1	1	yes	characteristic
36	C₄₇×#384	C₂²	1	1	yes	characteristic
37	C₄₇×#381	—	2	2	no	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	4	2	no	—
44	C₂²×Q₈×C₄₇	—	4	2	no	—
45	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
46	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
47	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
48	C₂²×D₄×C₄₇	—	2	1	no	—
49	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	—	2	1	no	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×Q₁₆×C₄₇	—	2	4	no	—
53	C₂×Q₁₆×C₄₇	—	4	2	no	—
54	C₂×Q₁₆×C₄₇	—	4	2	no	—
55	C₂×SD₁₆×C₄₇	—	2	4	no	—
56	C₂×SD₁₆×C₄₇	—	4	2	no	—
57	C₂×SD₁₆×C₄₇	—	4	2	no	—
58	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
59	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
60	#124×C₄₇	—	4	2	no	—
61	C₂²⋊Q₈×C₄₇	—	2	2	no	—
62	C₂²⋊Q₈×C₄₇	—	2	2	no	—
63	#121×C₄₇	—	2	2	no	—
64	#121×C₄₇	—	2	2	no	—
65	#117×C₄₇	—	4	2	no	—
66	#117×C₄₇	—	4	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	C₄⋊C₈×C₄₇	—	4	2	no	—
83	#103×C₄₇	—	2	4	no	—
84	#103×C₄₇	—	2	4	no	—
85	#103×C₄₇	—	4	2	no	—
86	#102×C₄₇	—	4	2	no	—
87	C₂²⋊C₈×C₄₇	—	2	2	no	—
88	C₂²⋊C₈×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	4	no	—
90	#95×C₄₇	—	2	4	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	1	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	—	2	4	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	4	8	no	—
105	C₂×Q₈×C₄₇	—	4	2	no	—
106	C₂×Q₈×C₄₇	—	4	2	no	—
107	C₂×Q₈×C₄₇	—	4	8	no	—
108	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	4	2	no	—
114	C₂×D₄×C₄₇	—	8	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	4	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	4	2	no	—
124	C₂²×C₄×C₄₇	—	4	2	no	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₇	#41	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₄₇	—	4	8	no	—
132	SD₁₆×C₄₇	—	4	8	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	4	2	no	—
146	C₄⋊C₄×C₄₇	—	4	2	no	—
147	C₄⋊C₄×C₄₇	—	8	2	no	—
148	C₂²⋊C₄×C₄₇	—	4	2	no	—
149	C₂²⋊C₄×C₄₇	—	4	4	no	—
150	C₂²⋊C₄×C₄₇	—	4	2	no	—
151	C₂²⋊C₄×C₄₇	—	4	2	no	—
152	C₂²⋊C₄×C₄₇	—	4	2	no	—
153	C₂²⋊C₄×C₄₇	—	8	2	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	2	1	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	4	1	no	—
162	C₂³×C₄₇	—	4	1	no	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	#121	1	2	yes	—
167	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	Q₈×C₄₇	—	2	4	no	—
169	Q₈×C₄₇	—	2	4	no	—
170	Q₈×C₄₇	—	4	8	no	—
171	Q₈×C₄₇	—	4	2	no	—
172	Q₈×C₄₇	—	4	2	no	—
173	Q₈×C₄₇	—	4	2	no	—
174	Q₈×C₄₇	—	4	2	no	—
175	D₄×C₄₇	—	4	2	no	—
176	D₄×C₄₇	—	4	2	no	—
177	D₄×C₄₇	—	8	4	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	4	8	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	1	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	1	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	#121	1	2	yes	—
203	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
206	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
207	C₈×C₄₇	—	4	2	no	—
208	C₈×C₄₇	—	4	2	no	—
209	#29728	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	2	2	no	—
212	C₂²×C₄₇	—	2	2	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	8	1	no	—
216	C₂²×C₄₇	—	8	2	no	—
217	C₂²×C₄₇	—	8	2	no	—
218	C₂²×C₄₇	—	8	1	no	—
219	C₂²×C₄₇	—	8	1	no	—
220	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
221	C₂²×C₄₇	#534	1	1	yes	characteristic
222	C₂²×C₄₇	#535	1	1	yes	characteristic
223	C₂²×C₄₇	#577	1	2	yes	—
224	C₂²×C₄₇	#578	1	2	yes	—
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	4	4	no	—
227	C₄×C₄₇	—	4	2	no	—
228	C₄×C₄₇	—	4	2	no	—
229	C₄×C₄₇	—	8	1	no	—
230	C₄×C₄₇	—	8	2	no	—
231	C₄×C₄₇	—	8	1	no	—
232	C₄×C₄₇	—	8	1	no	—
233	C₄×C₄₇	#534	1	2	yes	—
234	C₄×C₄₇	#538	1	2	yes	—
235	C₂×#451	C₂×C₄₇	1	1	yes	characteristic, complemented
236	C₂×#448	C₂×C₄₇	1	1	yes	characteristic
237	#2620	C₂×C₄₇	1	1	yes	characteristic
238	#2310	C₂×C₄₇	1	1	yes	characteristic, complemented
239	#2072	C₂×C₄₇	1	2	yes	complemented
240	#2056	C₂×C₄₇	1	2	yes	complemented
241	#2055	C₂×C₄₇	1	2	yes	complemented
242	#2015	C₂×C₄₇	1	2	yes	complemented
243	#1875	C₂×C₄₇	1	1	yes	characteristic
244	#1873	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#1798	C₂×C₄₇	1	1	yes	characteristic, complemented
246	C₂×C₄₇	—	4	2	no	—
247	C₂×C₄₇	—	16	1	no	—
248	C₂×C₄₇	#2617	1	1	yes	characteristic
249	C₂×C₄₇	#3043	1	1	yes	characteristic
250	C₂×C₄₇	#3044	1	1	yes	characteristic
251	C₂×C₄₇	#3201	1	2	yes	—
252	C₂×C₄₇	#3225	1	2	yes	—
253	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
254	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
255	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
256	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
261	#451	—	2	4	no	—
262	#448	—	2	4	no	—
263	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
264	C₂×#103	C₂²×C₄₇	1	2	yes	—
265	C₂×#103	C₂²×C₄₇	1	2	yes	—
266	C₂×#103	C₂²×C₄₇	1	2	yes	—
267	C₂×#102	C₂²×C₄₇	1	2	yes	—
268	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
270	#396	—	2	2	no	—
271	#394	—	2	2	no	—
272	#391	—	2	2	no	—
273	#391	C₂²×C₄₇	1	2	yes	—
274	#391	C₂²×C₄₇	1	2	yes	—
275	#391	C₂²×C₄₇	1	1	yes	characteristic
276	#390	C₂²×C₄₇	1	1	yes	characteristic
277	#384	C₂²×C₄₇	1	1	yes	characteristic
278	#381	—	2	2	no	—
279	#340	C₂²×C₄₇	1	2	yes	—
280	#340	C₂²×C₄₇	1	2	yes	—
281	#336	C₂²×C₄₇	1	2	yes	—
282	C₄₇	#29728	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	1	no	—
284	C₂²×Q₈	—	2	2	no	—
285	C₂²×Q₈	—	4	2	no	—
286	C₂²×Q₈	—	4	2	no	—
287	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
288	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
289	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
290	C₂²×D₄	—	2	1	no	—
291	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
292	C₂³×C₄	—	2	1	no	—
293	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×Q₁₆	—	4	2	no	—
296	C₂×Q₁₆	—	4	2	no	—
297	C₂×SD₁₆	—	2	4	no	—
298	C₂×SD₁₆	—	4	2	no	—
299	C₂×SD₁₆	—	4	2	no	—
300	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
301	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
302	#124	—	4	2	no	—
303	C₂²⋊Q₈	—	2	2	no	—
304	C₂²⋊Q₈	—	2	2	no	—
305	#121	—	2	2	no	—
306	#121	—	2	2	no	—
307	#117	—	4	2	no	—
308	#117	—	4	2	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
312	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
313	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
314	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	2	1	no	—
317	C₂×C₂²⋊C₄	—	2	1	no	—
318	C₂×C₂²⋊C₄	—	2	2	no	—
319	C₂×C₂²⋊C₄	—	2	2	no	—
320	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
321	C₂×C₄²	—	2	1	no	—
322	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
323	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
324	C₄⋊C₈	—	4	2	no	—
325	#103	—	2	4	no	—
326	#103	—	2	4	no	—
327	#103	—	4	2	no	—
328	#102	—	4	2	no	—
329	C₂²⋊C₈	—	2	2	no	—
330	C₂²⋊C₈	—	2	2	no	—
331	#95	—	2	4	no	—
332	#95	—	2	4	no	—
333	#95	—	2	2	no	—
334	C₂⁴	—	2	1	no	—
335	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
336	C₂×Q₈	—	2	4	no	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	1	no	—
339	C₂×Q₈	—	2	1	no	—
340	C₂×Q₈	—	2	2	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	—	2	2	no	—
346	C₂×Q₈	—	4	8	no	—
347	C₂×Q₈	—	4	2	no	—
348	C₂×Q₈	—	4	2	no	—
349	C₂×Q₈	—	4	8	no	—
350	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	2	1	no	—
353	C₂×D₄	—	2	2	no	—
354	C₂×D₄	—	2	2	no	—
355	C₂×D₄	—	4	2	no	—
356	C₂×D₄	—	8	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	4	2	no	—
366	C₂²×C₄	—	4	2	no	—
367	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
369	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
371	C₂²×C₄	#41×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
373	Q₁₆	—	4	8	no	—
374	SD₁₆	—	4	8	no	—
375	C₂×C₈	—	2	2	no	—
376	C₂×C₈	—	2	2	no	—
377	C₂×C₈	—	2	2	no	—
378	C₂×C₈	—	2	2	no	—
379	C₂×C₈	—	2	2	no	—
380	C₂×C₈	—	2	2	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	1	no	—
383	C₄⋊C₄	—	2	1	no	—
384	C₄⋊C₄	—	2	1	no	—
385	C₄⋊C₄	—	2	2	no	—
386	C₄⋊C₄	—	2	2	no	—
387	C₄⋊C₄	—	4	2	no	—
388	C₄⋊C₄	—	4	2	no	—
389	C₄⋊C₄	—	8	2	no	—
390	C₂²⋊C₄	—	4	2	no	—
391	C₂²⋊C₄	—	4	4	no	—
392	C₂²⋊C₄	—	4	2	no	—
393	C₂²⋊C₄	—	4	2	no	—
394	C₂²⋊C₄	—	4	2	no	—
395	C₂²⋊C₄	—	8	2	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	4	2	no	—
399	C₂³	—	2	1	no	—
400	C₂³	—	2	1	no	—
401	C₂³	—	2	2	no	—
402	C₂³	—	2	2	no	—
403	C₂³	—	4	1	no	—
404	C₂³	—	4	1	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	2	no	—
408	C₂³	#121×C₄₇	1	2	yes	—
409	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
410	Q₈	—	2	4	no	—
411	Q₈	—	2	4	no	—
412	Q₈	—	4	8	no	—
413	Q₈	—	4	2	no	—
414	Q₈	—	4	2	no	—
415	Q₈	—	4	2	no	—
416	Q₈	—	4	2	no	—
417	D₄	—	4	2	no	—
418	D₄	—	4	2	no	—
419	D₄	—	8	4	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	8	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	#121×C₄₇	1	2	yes	—
445	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
447	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
448	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
449	C₈	—	4	2	no	—
450	C₈	—	4	2	no	—
451	C₂²	—	2	2	no	—
452	C₂²	—	2	2	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	—	4	2	no	—
456	C₂²	—	8	1	no	—
457	C₂²	—	8	1	no	—
458	C₂²	—	8	1	no	—
459	C₂²	—	8	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
462	C₂²	C₄₇×#534	1	1	yes	characteristic
463	C₂²	C₄₇×#535	1	1	yes	characteristic
464	C₂²	C₄₇×#577	1	2	yes	—
465	C₂²	C₄₇×#578	1	2	yes	—
466	C₄	—	2	2	no	—
467	C₄	—	4	4	no	—
468	C₄	—	4	2	no	—
469	C₄	—	4	2	no	—
470	C₄	—	8	1	no	—
471	C₄	—	8	1	no	—
472	C₄	—	8	1	no	—
473	C₄	—	8	2	no	—
474	C₄	C₄₇×#534	1	2	yes	—
475	C₄	C₄₇×#538	1	2	yes	—
476	C₂	—	4	2	no	—
477	C₂	—	16	1	no	—
478	C₂	C₄₇×#2617	1	1	yes	characteristic
479	C₂	C₄₇×#3043	1	1	yes	characteristic
480	C₂	C₄₇×#3044	1	1	yes	characteristic
481	C₂	C₄₇×#3201	1	2	yes	—
482	C₂	C₄₇×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#121×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
1. C₂×C₄₇×#451	C₂	semidirect
4. C₄₇×#2310	C₂	semidirect
5. C₄₇×#2072	C₂	semidirect
6. C₄₇×#2056	C₂	semidirect
7. C₄₇×#2055	C₂	semidirect
8. C₄₇×#2015	C₂	semidirect
10. C₄₇×#1873	C₂	semidirect
11. C₄₇×#1798	C₂	semidirect
209. #29728	C₄₇	direct (N × H)
235. C₂×#451	C₂×C₄₇	semidirect
238. #2310	C₂×C₄₇	semidirect
239. #2072	C₂×C₄₇	semidirect
240. #2056	C₂×C₄₇	semidirect
241. #2055	C₂×C₄₇	semidirect
242. #2015	C₂×C₄₇	semidirect
244. #1873	C₂×C₄₇	semidirect
245. #1798	C₂×C₄₇	semidirect
282. C₄₇	#29728	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×#451	2
C₂×C₄₇×#448	2
C₄₇×#2620	2
C₄₇×#2310	2
C₄₇×#2072	2
C₄₇×#2056	2
C₄₇×#2055	2
C₄₇×#2015	2
C₄₇×#1875	2
C₄₇×#1873	2
C₄₇×#1798	2
#29728	47

Subgroups — C47×#29728 #26069426

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29728 #26069426