Subgroups — C₄₇×#15124 #26054822

Order 12032.

3822 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#121×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#392	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#390	C₂	1	2	yes	maximal, complemented
5	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1438	C₂	1	4	yes	maximal, complemented
7	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
9	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
10	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
11	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#127×C₄₇	—	2	8	no	—
13	C₂×#127×C₄₇	—	2	4	no	—
14	C₂×#121×C₄₇	—	2	8	no	—
15	C₂×#121×C₄₇	—	2	8	no	—
16	C₂×#121×C₄₇	—	2	8	no	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	4	yes	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	8	yes	—
20	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#392	—	2	16	no	—
24	C₄₇×#390	—	2	8	no	—
25	C₄×C₂²⋊C₄×C₄₇	—	2	4	no	—
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
28	C₂⁵×C₄₇	C₂³	1	4	yes	—
29	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
30	C₂²×D₄×C₄₇	—	2	8	no	—
31	C₂²×D₄×C₄₇	—	2	8	no	—
32	C₂²×D₄×C₄₇	—	2	16	no	—
33	C₂²×D₄×C₄₇	—	2	16	no	—
34	C₂²×D₄×C₄₇	—	2	8	no	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	—	2	4	no	—
37	C₂²×D₄×C₄₇	—	2	8	no	—
38	C₂²×D₄×C₄₇	—	2	4	no	—
39	C₂²×D₄×C₄₇	—	2	4	no	—
40	C₂²×D₄×C₄₇	—	2	4	no	—
41	C₂²×D₄×C₄₇	—	2	8	no	—
42	C₂²×D₄×C₄₇	—	2	4	no	—
43	C₂²×D₄×C₄₇	—	2	8	no	—
44	C₂²×D₄×C₄₇	—	4	8	no	—
45	C₂²×D₄×C₄₇	—	4	8	no	—
46	C₂²×D₄×C₄₇	D₄	1	8	yes	complemented
47	C₂³×C₄×C₄₇	—	2	4	no	—
48	C₂³×C₄×C₄₇	—	2	4	no	—
49	C₂³×C₄×C₄₇	—	2	2	no	—
50	C₂³×C₄×C₄₇	—	2	2	no	—
51	C₂³×C₄×C₄₇	D₄	1	4	yes	complemented
52	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	#127×C₄₇	—	2	32	no	—
58	#121×C₄₇	—	2	64	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	complemented
62	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	4	8	no	—
70	C₂×C₂²⋊C₄×C₄₇	D₄	1	8	yes	complemented
71	C₂×C₄²×C₄₇	—	2	4	no	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	—	2	4	no	—
74	C₂×C₄²×C₄₇	D₄	1	4	yes	complemented
75	#95×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	2	8	no	—
77	C₂⁴×C₄₇	—	2	1	no	—
78	C₂⁴×C₄₇	—	2	2	no	—
79	C₂⁴×C₄₇	—	2	2	no	—
80	C₂⁴×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	—	2	1	no	—
82	C₂⁴×C₄₇	—	2	4	no	—
83	C₂⁴×C₄₇	—	2	4	no	—
84	C₂⁴×C₄₇	—	2	4	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	8	no	—
87	C₂⁴×C₄₇	—	2	4	no	—
88	C₂⁴×C₄₇	—	2	4	no	—
89	C₂⁴×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	8	no	—
91	C₂⁴×C₄₇	—	2	8	no	—
92	C₂⁴×C₄₇	—	2	8	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	8	yes	—
94	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
95	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
96	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
97	C₂×D₄×C₄₇	—	2	32	no	—
98	C₂×D₄×C₄₇	—	2	32	no	—
99	C₂×D₄×C₄₇	—	2	16	no	—
100	C₂×D₄×C₄₇	—	2	16	no	—
101	C₂×D₄×C₄₇	—	2	16	no	—
102	C₂×D₄×C₄₇	—	4	32	no	—
103	C₂×D₄×C₄₇	—	4	32	no	—
104	C₂×D₄×C₄₇	—	4	32	no	—
105	C₂×D₄×C₄₇	—	4	16	no	—
106	C₂×D₄×C₄₇	—	4	32	no	—
107	C₂×D₄×C₄₇	—	4	16	no	—
108	C₂×D₄×C₄₇	—	4	16	no	—
109	C₂×D₄×C₄₇	—	4	8	no	—
110	C₂×D₄×C₄₇	—	4	8	no	—
111	C₂×D₄×C₄₇	—	4	8	no	—
112	C₂×D₄×C₄₇	—	4	16	no	—
113	C₂×D₄×C₄₇	—	4	8	no	—
114	C₂²×C₄×C₄₇	—	2	4	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	2	4	no	—
122	C₂²×C₄×C₄₇	—	2	8	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	4	no	—
127	C₂²×C₄×C₄₇	—	2	8	no	—
128	C₂²×C₄×C₄₇	—	2	16	no	—
129	C₂²×C₄×C₄₇	—	2	8	no	—
130	C₂²×C₄×C₄₇	—	4	4	no	—
131	C₂²×C₄×C₄₇	—	4	8	no	—
132	C₂²×C₄×C₄₇	—	4	4	no	—
133	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
136	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
138	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
139	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
140	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
141	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₇	#41	1	4	yes	—
143	C₂²×C₄×C₄₇	#41	1	2	yes	—
144	C₄⋊C₄×C₄₇	—	2	16	no	—
145	C₂²⋊C₄×C₄₇	—	2	32	no	—
146	C₂²⋊C₄×C₄₇	—	2	16	no	—
147	C₂²⋊C₄×C₄₇	—	4	32	no	—
148	C₄²×C₄₇	—	2	8	no	—
149	C₄²×C₄₇	—	4	4	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	4	no	—
156	C₂³×C₄₇	—	2	8	no	—
157	C₂³×C₄₇	—	2	8	no	—
158	C₂³×C₄₇	—	2	8	no	—
159	C₂³×C₄₇	—	2	8	no	—
160	C₂³×C₄₇	—	2	8	no	—
161	C₂³×C₄₇	—	2	16	no	—
162	C₂³×C₄₇	—	2	16	no	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	—	4	2	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	4	no	—
169	C₂³×C₄₇	—	4	4	no	—
170	C₂³×C₄₇	—	4	4	no	—
171	C₂³×C₄₇	—	4	4	no	—
172	C₂³×C₄₇	—	4	4	no	—
173	C₂³×C₄₇	—	4	8	no	—
174	C₂³×C₄₇	—	4	4	no	—
175	C₂³×C₄₇	—	4	4	no	—
176	C₂³×C₄₇	—	4	8	no	—
177	C₂³×C₄₇	—	4	4	no	—
178	C₂³×C₄₇	—	4	8	no	—
179	C₂³×C₄₇	—	4	4	no	—
180	C₂³×C₄₇	—	4	4	no	—
181	C₂³×C₄₇	—	4	8	no	—
182	C₂³×C₄₇	—	4	8	no	—
183	C₂³×C₄₇	—	4	8	no	—
184	C₂³×C₄₇	—	4	8	no	—
185	C₂³×C₄₇	—	4	8	no	—
186	C₂³×C₄₇	—	4	8	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	#127	1	4	yes	complemented
189	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
191	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
193	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
194	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂³×C₄₇	C₂×#41	1	2	yes	—
196	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
197	D₄×C₄₇	—	4	64	no	—
198	D₄×C₄₇	—	4	64	no	—
199	D₄×C₄₇	—	4	32	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	2	4	no	—
202	C₂×C₄×C₄₇	—	2	8	no	—
203	C₂×C₄×C₄₇	—	2	8	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	8	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	8	no	—
209	C₂×C₄×C₄₇	—	2	16	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	4	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	4	no	—
217	C₂×C₄×C₄₇	—	4	8	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	4	16	no	—
220	C₂×C₄×C₄₇	#120	1	4	yes	—
221	C₂×C₄×C₄₇	#120	1	8	yes	—
222	C₂×C₄×C₄₇	#121	1	4	yes	—
223	C₂×C₄×C₄₇	#121	1	8	yes	—
224	C₂×C₄×C₄₇	#121	1	8	yes	complemented
225	C₂×C₄×C₄₇	#127	1	4	yes	—
226	#15124	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
227	C₂²×C₄₇	—	2	4	no	—
228	C₂²×C₄₇	—	2	8	no	—
229	C₂²×C₄₇	—	4	2	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	4	no	—
232	C₂²×C₄₇	—	4	8	no	—
233	C₂²×C₄₇	—	4	4	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	4	8	no	—
236	C₂²×C₄₇	—	4	16	no	—
237	C₂²×C₄₇	—	4	16	no	—
238	C₂²×C₄₇	—	4	8	no	—
239	C₂²×C₄₇	—	4	8	no	—
240	C₂²×C₄₇	—	8	4	no	—
241	C₂²×C₄₇	—	8	4	no	—
242	C₂²×C₄₇	—	8	8	no	—
243	C₂²×C₄₇	—	8	4	no	—
244	C₂²×C₄₇	—	8	4	no	—
245	C₂²×C₄₇	—	8	8	no	—
246	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
247	C₂²×C₄₇	C₂×#120	1	2	yes	—
248	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
249	C₂²×C₄₇	C₂×#121	1	2	yes	—
250	C₂²×C₄₇	C₂×#121	1	2	yes	—
251	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
252	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
253	C₂²×C₄₇	#532	1	2	yes	—
254	C₂²×C₄₇	#532	1	1	yes	characteristic
255	C₂²×C₄₇	#535	1	2	yes	—
256	C₂²×C₄₇	#535	1	2	yes	—
257	C₂²×C₄₇	#540	1	2	yes	—
258	C₂²×C₄₇	D₄²	1	4	yes	—
259	C₂²×C₄₇	D₄²	1	4	yes	—
260	C₂²×C₄₇	#546	1	4	yes	—
261	C₂²×C₄₇	#550	1	4	yes	—
262	C₄×C₄₇	—	2	8	no	—
263	C₄×C₄₇	—	4	2	no	—
264	C₄×C₄₇	—	4	8	no	—
265	C₄×C₄₇	—	4	4	no	—
266	C₄×C₄₇	#392	1	8	yes	complemented
267	C₂²×#127	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂²×#121	C₂×C₄₇	1	2	yes	complemented
269	C₂×#392	C₂×C₄₇	1	4	yes	complemented
270	C₂×#390	C₂×C₄₇	1	2	yes	complemented
271	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
272	#1438	C₂×C₄₇	1	4	yes	complemented
273	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic, complemented
274	C₂×C₄₇	—	4	4	no	—
275	C₂×C₄₇	—	8	8	no	—
276	C₂×C₄₇	C₂×#392	1	1	yes	characteristic
277	C₂×C₄₇	#2408	1	2	yes	—
278	C₂×C₄₇	#2428	1	4	yes	—
279	C₂×C₄₇	#2431	1	2	yes	—
280	C₂×C₄₇	#2433	1	2	yes	—
281	C₂×C₄₇	#2541	1	2	yes	—
282	C₂×C₄₇	#2619	1	1	yes	characteristic
283	C₂×C₄₇	#2856	1	1	yes	characteristic
284	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
285	C₂³×D₄	C₂²×C₄₇	1	4	yes	—
286	C₂³×D₄	C₂²×C₄₇	1	4	yes	—
287	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
288	C₂×#127	—	2	8	no	—
289	C₂×#127	—	2	4	no	—
290	C₂×#121	—	2	8	no	—
291	C₂×#121	—	2	8	no	—
292	C₂×#121	—	2	8	no	—
293	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
294	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	4	yes	—
295	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	8	yes	—
296	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
297	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
299	#392	—	2	16	no	—
300	#390	—	2	8	no	—
301	C₄×C₂²⋊C₄	—	2	4	no	—
302	C₂×#95	C₂²×C₄₇	1	4	yes	—
303	C₂×#95	C₂²×C₄₇	1	2	yes	—
304	C₄₇	#15124	1	1	yes	characteristic, direct product factor, Sylow
305	C₂⁵	C₂³×C₄₇	1	4	yes	—
306	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
307	C₂²×D₄	—	2	8	no	—
308	C₂²×D₄	—	2	8	no	—
309	C₂²×D₄	—	2	16	no	—
310	C₂²×D₄	—	2	16	no	—
311	C₂²×D₄	—	2	8	no	—
312	C₂²×D₄	—	2	4	no	—
313	C₂²×D₄	—	2	4	no	—
314	C₂²×D₄	—	2	8	no	—
315	C₂²×D₄	—	2	4	no	—
316	C₂²×D₄	—	2	4	no	—
317	C₂²×D₄	—	2	4	no	—
318	C₂²×D₄	—	2	8	no	—
319	C₂²×D₄	—	2	4	no	—
320	C₂²×D₄	—	2	8	no	—
321	C₂²×D₄	—	4	8	no	—
322	C₂²×D₄	—	4	8	no	—
323	C₂²×D₄	D₄×C₄₇	1	8	yes	complemented
324	C₂³×C₄	—	2	4	no	—
325	C₂³×C₄	—	2	4	no	—
326	C₂³×C₄	—	2	2	no	—
327	C₂³×C₄	—	2	2	no	—
328	C₂³×C₄	D₄×C₄₇	1	4	yes	complemented
329	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
330	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
332	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
333	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
334	#127	—	2	32	no	—
335	#121	—	2	64	no	—
336	C₂×C₄⋊C₄	—	2	4	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	complemented
339	C₂×C₂²⋊C₄	—	2	8	no	—
340	C₂×C₂²⋊C₄	—	2	8	no	—
341	C₂×C₂²⋊C₄	—	2	8	no	—
342	C₂×C₂²⋊C₄	—	2	4	no	—
343	C₂×C₂²⋊C₄	—	2	4	no	—
344	C₂×C₂²⋊C₄	—	2	16	no	—
345	C₂×C₂²⋊C₄	—	2	16	no	—
346	C₂×C₂²⋊C₄	—	4	8	no	—
347	C₂×C₂²⋊C₄	D₄×C₄₇	1	8	yes	complemented
348	C₂×C₄²	—	2	4	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	4	no	—
351	C₂×C₄²	D₄×C₄₇	1	4	yes	complemented
352	#95	—	2	4	no	—
353	#95	—	2	8	no	—
354	C₂⁴	—	2	1	no	—
355	C₂⁴	—	2	2	no	—
356	C₂⁴	—	2	2	no	—
357	C₂⁴	—	2	2	no	—
358	C₂⁴	—	2	1	no	—
359	C₂⁴	—	2	4	no	—
360	C₂⁴	—	2	4	no	—
361	C₂⁴	—	2	4	no	—
362	C₂⁴	—	2	4	no	—
363	C₂⁴	—	2	8	no	—
364	C₂⁴	—	2	4	no	—
365	C₂⁴	—	2	4	no	—
366	C₂⁴	—	2	4	no	—
367	C₂⁴	—	2	8	no	—
368	C₂⁴	—	2	8	no	—
369	C₂⁴	—	2	8	no	—
370	C₂⁴	C₂×D₄×C₄₇	1	8	yes	—
371	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
372	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
373	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
374	C₂×D₄	—	2	32	no	—
375	C₂×D₄	—	2	32	no	—
376	C₂×D₄	—	2	16	no	—
377	C₂×D₄	—	2	16	no	—
378	C₂×D₄	—	2	16	no	—
379	C₂×D₄	—	4	32	no	—
380	C₂×D₄	—	4	32	no	—
381	C₂×D₄	—	4	32	no	—
382	C₂×D₄	—	4	16	no	—
383	C₂×D₄	—	4	32	no	—
384	C₂×D₄	—	4	16	no	—
385	C₂×D₄	—	4	16	no	—
386	C₂×D₄	—	4	8	no	—
387	C₂×D₄	—	4	8	no	—
388	C₂×D₄	—	4	8	no	—
389	C₂×D₄	—	4	16	no	—
390	C₂×D₄	—	4	8	no	—
391	C₂²×C₄	—	2	4	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	2	8	no	—
396	C₂²×C₄	—	2	4	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	4	no	—
400	C₂²×C₄	—	2	4	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	2	8	no	—
405	C₂²×C₄	—	2	16	no	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	4	4	no	—
408	C₂²×C₄	—	4	8	no	—
409	C₂²×C₄	—	4	4	no	—
410	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
411	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
413	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
414	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
415	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
416	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
417	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
418	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
419	C₂²×C₄	#41×C₄₇	1	4	yes	—
420	C₂²×C₄	#41×C₄₇	1	2	yes	—
421	C₄⋊C₄	—	2	16	no	—
422	C₂²⋊C₄	—	2	32	no	—
423	C₂²⋊C₄	—	2	16	no	—
424	C₂²⋊C₄	—	4	32	no	—
425	C₄²	—	2	8	no	—
426	C₄²	—	4	4	no	—
427	C₂³	—	2	4	no	—
428	C₂³	—	2	4	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	4	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	4	no	—
433	C₂³	—	2	8	no	—
434	C₂³	—	2	8	no	—
435	C₂³	—	2	8	no	—
436	C₂³	—	2	8	no	—
437	C₂³	—	2	8	no	—
438	C₂³	—	2	16	no	—
439	C₂³	—	2	16	no	—
440	C₂³	—	4	1	no	—
441	C₂³	—	4	2	no	—
442	C₂³	—	4	1	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	2	no	—
445	C₂³	—	4	4	no	—
446	C₂³	—	4	4	no	—
447	C₂³	—	4	4	no	—
448	C₂³	—	4	4	no	—
449	C₂³	—	4	4	no	—
450	C₂³	—	4	8	no	—
451	C₂³	—	4	4	no	—
452	C₂³	—	4	4	no	—
453	C₂³	—	4	8	no	—
454	C₂³	—	4	4	no	—
455	C₂³	—	4	8	no	—
456	C₂³	—	4	4	no	—
457	C₂³	—	4	4	no	—
458	C₂³	—	4	8	no	—
459	C₂³	—	4	8	no	—
460	C₂³	—	4	8	no	—
461	C₂³	—	4	8	no	—
462	C₂³	—	4	8	no	—
463	C₂³	—	4	8	no	—
464	C₂³	—	4	8	no	—
465	C₂³	#127×C₄₇	1	4	yes	complemented
466	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
467	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
468	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
469	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
470	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
471	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
472	C₂³	C₂×#41×C₄₇	1	2	yes	—
473	C₂³	H(5,𝔽₂)×C₄₇	1	4	yes	—
474	D₄	—	4	64	no	—
475	D₄	—	4	64	no	—
476	D₄	—	4	32	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	8	no	—
480	C₂×C₄	—	2	8	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	2	4	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	8	no	—
486	C₂×C₄	—	2	16	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	4	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	—	4	4	no	—
494	C₂×C₄	—	4	8	no	—
495	C₂×C₄	—	4	4	no	—
496	C₂×C₄	—	4	16	no	—
497	C₂×C₄	#120×C₄₇	1	4	yes	—
498	C₂×C₄	#120×C₄₇	1	8	yes	—
499	C₂×C₄	#121×C₄₇	1	4	yes	—
500	C₂×C₄	#121×C₄₇	1	8	yes	—
501	C₂×C₄	#121×C₄₇	1	8	yes	complemented
502	C₂×C₄	#127×C₄₇	1	4	yes	—
503	C₂²	—	2	4	no	—
504	C₂²	—	2	8	no	—
505	C₂²	—	4	4	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	4	no	—
509	C₂²	—	4	8	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	8	no	—
512	C₂²	—	4	16	no	—
513	C₂²	—	4	16	no	—
514	C₂²	—	4	8	no	—
515	C₂²	—	4	8	no	—
516	C₂²	—	8	8	no	—
517	C₂²	—	8	4	no	—
518	C₂²	—	8	4	no	—
519	C₂²	—	8	8	no	—
520	C₂²	—	8	4	no	—
521	C₂²	—	8	4	no	—
522	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
523	C₂²	C₂×#120×C₄₇	1	2	yes	—
524	C₂²	C₂×#121×C₄₇	1	2	yes	—
525	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
526	C₂²	C₂×#121×C₄₇	1	2	yes	—
527	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
528	C₂²	C₂×#127×C₄₇	1	1	yes	characteristic
529	C₂²	C₄₇×#532	1	2	yes	—
530	C₂²	C₄₇×#532	1	1	yes	characteristic
531	C₂²	C₄₇×#535	1	2	yes	—
532	C₂²	C₄₇×#535	1	2	yes	—
533	C₂²	C₄₇×#540	1	2	yes	—
534	C₂²	D₄²×C₄₇	1	4	yes	—
535	C₂²	D₄²×C₄₇	1	4	yes	—
536	C₂²	C₄₇×#546	1	4	yes	—
537	C₂²	C₄₇×#550	1	4	yes	—
538	C₄	—	2	8	no	—
539	C₄	—	4	4	no	—
540	C₄	—	4	2	no	—
541	C₄	—	4	8	no	—
542	C₄	C₄₇×#392	1	8	yes	complemented
543	C₂	—	4	4	no	—
544	C₂	—	8	8	no	—
545	C₂	C₂×C₄₇×#392	1	1	yes	characteristic
546	C₂	C₄₇×#2408	1	2	yes	—
547	C₂	C₄₇×#2428	1	4	yes	—
548	C₂	C₄₇×#2431	1	2	yes	—
549	C₂	C₄₇×#2433	1	2	yes	—
550	C₂	C₄₇×#2541	1	2	yes	—
551	C₂	C₄₇×#2619	1	1	yes	characteristic
552	C₂	C₄₇×#2856	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#127×C₄₇	C₂	semidirect
2. C₂²×#121×C₄₇	C₂	semidirect
3. C₂×C₄₇×#392	C₂	semidirect
4. C₂×C₄₇×#390	C₂	semidirect
5. C₂×C₄×C₂²⋊C₄×C₄₇	C₂	semidirect
6. C₄₇×#1438	C₂	semidirect
7. C₄₇×C₄⋊#95	C₂	semidirect
46. C₂²×D₄×C₄₇	D₄	semidirect
51. C₂³×C₄×C₄₇	D₄	semidirect
61. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
70. C₂×C₂²⋊C₄×C₄₇	D₄	semidirect
74. C₂×C₄²×C₄₇	D₄	semidirect
188. C₂³×C₄₇	#127	semidirect
224. C₂×C₄×C₄₇	#121	semidirect
226. #15124	C₄₇	direct (N × H)
266. C₄×C₄₇	#392	semidirect
267. C₂²×#127	C₂×C₄₇	semidirect
268. C₂²×#121	C₂×C₄₇	semidirect
269. C₂×#392	C₂×C₄₇	semidirect
270. C₂×#390	C₂×C₄₇	semidirect
271. C₂×C₄×C₂²⋊C₄	C₂×C₄₇	semidirect
272. #1438	C₂×C₄₇	semidirect
273. C₄⋊#95	C₂×C₄₇	semidirect
304. C₄₇	#15124	direct (N × H)
323. C₂²×D₄	D₄×C₄₇	semidirect
328. C₂³×C₄	D₄×C₄₇	semidirect
338. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
347. C₂×C₂²⋊C₄	D₄×C₄₇	semidirect
351. C₂×C₄²	D₄×C₄₇	semidirect
465. C₂³	#127×C₄₇	semidirect
501. C₂×C₄	#121×C₄₇	semidirect
542. C₄	C₄₇×#392	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#127×C₄₇	2
C₂²×#121×C₄₇	2
C₂×C₄₇×#392	2
C₂×C₄₇×#390	2
C₂×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1438	2
C₄₇×C₄⋊#95	2
#15124	47

Subgroups — C47×#15124 #26054822

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15124 #26054822