Subgroups — C₂×C₄₇×#2325 #26073764

Order 12032.

4150 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#121×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×D₄×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2325	C₂	1	16	yes	maximal, direct product factor
4	C₂×C₄₇×#388	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#387	C₂	1	2	yes	maximal, complemented
6	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#386	C₂	1	2	yes	maximal, complemented
8	C₂×C₄₇×#385	C₂	1	2	yes	maximal, complemented
9	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
12	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
15	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#121×C₄₇	C₄	1	16	yes	complemented
18	C₂×#121×C₄₇	C₂²	1	8	yes	—
19	C₂×C₄×D₄×C₄₇	—	2	16	no	—
20	C₂×C₄×D₄×C₄₇	C₂²	1	16	yes	complemented
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
26	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
27	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
28	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
29	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
30	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
31	C₄₇×#388	C₂²	1	16	yes	complemented
32	C₄₇×#387	C₂²	1	16	yes	complemented
33	C₄₇×#386	C₂²	1	16	yes	complemented
34	C₄₇×#386	C₂²	1	16	yes	complemented
35	C₄₇×#385	C₂²	1	16	yes	complemented
36	C₄₇×#380	C₂²	1	8	yes	complemented
37	C₂×#95×C₄₇	C₂²	1	2	yes	—
38	C₂×#95×C₄₇	C₂²	1	2	yes	—
39	C₂×#95×C₄₇	C₂²	1	2	yes	—
40	C₂×#95×C₄₇	C₂²	1	2	yes	—
41	C₂×#95×C₄₇	C₂²	1	2	yes	—
42	C₂×#95×C₄₇	C₂²	1	8	yes	complemented
43	C₂⁵×C₄₇	C₂³	1	2	yes	—
44	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	—	2	8	no	—
46	C₂²×D₄×C₄₇	—	2	8	no	—
47	C₂²×D₄×C₄₇	—	4	2	no	—
48	C₂²×D₄×C₄₇	—	4	2	no	—
49	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
50	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
51	C₂²×D₄×C₄₇	C₂³	1	8	yes	—
52	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
53	C₂³×C₄×C₄₇	—	2	4	no	—
54	C₂³×C₄×C₄₇	—	2	8	no	—
55	C₂³×C₄×C₄₇	—	4	2	no	—
56	C₂³×C₄×C₄₇	—	4	2	no	—
57	C₂³×C₄×C₄₇	—	4	2	no	—
58	C₂³×C₄×C₄₇	—	4	2	no	—
59	C₂³×C₄×C₄₇	—	4	4	no	—
60	C₂³×C₄×C₄₇	—	4	4	no	—
61	C₂³×C₄×C₄₇	—	4	2	no	—
62	C₂³×C₄×C₄₇	—	4	2	no	—
63	C₂³×C₄×C₄₇	C₂×C₄	1	8	yes	complemented
64	C₂³×C₄×C₄₇	D₄	1	8	yes	complemented
65	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
68	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
72	C₂³×C₄×C₄₇	C₂³	1	8	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
74	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
75	C₂³×C₄×C₄₇	C₂³	1	4	yes	—
76	#121×C₄₇	C₂×C₄	1	64	yes	complemented
77	C₄×D₄×C₄₇	—	2	64	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
79	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
80	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	8	yes	complemented
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
83	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
85	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
86	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
87	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
88	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
89	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
90	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	16	yes	complemented
91	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
93	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
94	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
95	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
96	C₂×C₄²×C₄₇	—	2	8	no	—
97	C₂×C₄²×C₄₇	C₂³	1	8	yes	—
98	#95×C₄₇	C₂³	1	8	yes	—
99	#95×C₄₇	C₂³	1	8	yes	—
100	#95×C₄₇	C₂³	1	8	yes	—
101	#95×C₄₇	C₂³	1	8	yes	—
102	#95×C₄₇	C₂³	1	8	yes	—
103	C₂⁴×C₄₇	—	2	2	no	—
104	C₂⁴×C₄₇	—	2	2	no	—
105	C₂⁴×C₄₇	—	2	2	no	—
106	C₂⁴×C₄₇	—	2	2	no	—
107	C₂⁴×C₄₇	—	2	4	no	—
108	C₂⁴×C₄₇	—	2	4	no	—
109	C₂⁴×C₄₇	—	2	4	no	—
110	C₂⁴×C₄₇	—	2	4	no	—
111	C₂⁴×C₄₇	—	2	4	no	—
112	C₂⁴×C₄₇	—	2	4	no	—
113	C₂⁴×C₄₇	C₂²×C₄	1	8	yes	—
114	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂⁴×C₄₇	C₂×D₄	1	4	yes	—
116	C₂⁴×C₄₇	#41	1	4	yes	—
117	C₂⁴×C₄₇	C₂⁴	1	4	yes	—
118	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
119	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂×D₄×C₄₇	—	2	64	no	—
121	C₂×D₄×C₄₇	—	2	16	no	—
122	C₂×D₄×C₄₇	—	2	16	no	—
123	C₂×D₄×C₄₇	—	4	16	no	—
124	C₂×D₄×C₄₇	—	4	4	no	—
125	C₂×D₄×C₄₇	—	4	4	no	—
126	C₂×D₄×C₄₇	C₂²×C₄	1	32	yes	complemented
127	C₂×D₄×C₄₇	C₂²×C₄	1	16	yes	complemented
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	4	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	4	no	—
133	C₂²×C₄×C₄₇	—	2	4	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	8	no	—
139	C₂²×C₄×C₄₇	—	2	4	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	2	4	no	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	—	2	16	no	—
147	C₂²×C₄×C₄₇	—	4	16	no	—
148	C₂²×C₄×C₄₇	—	4	16	no	—
149	C₂²×C₄×C₄₇	—	4	4	no	—
150	C₂²×C₄×C₄₇	—	4	4	no	—
151	C₂²×C₄×C₄₇	—	4	4	no	—
152	C₂²×C₄×C₄₇	—	4	4	no	—
153	C₂²×C₄×C₄₇	—	4	8	no	—
154	C₂²×C₄×C₄₇	—	4	8	no	—
155	C₂²×C₄×C₄₇	—	4	4	no	—
156	C₂²×C₄×C₄₇	—	4	4	no	—
157	C₂²×C₄×C₄₇	—	4	32	no	—
158	C₂²×C₄×C₄₇	—	4	16	no	—
159	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
160	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
161	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
162	C₂²×C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
163	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
164	C₂²×C₄×C₄₇	C₂×D₄	1	16	yes	complemented
165	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
168	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
169	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
170	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
171	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
172	C₄⋊C₄×C₄₇	—	2	16	no	—
173	C₄⋊C₄×C₄₇	—	4	4	no	—
174	C₄⋊C₄×C₄₇	—	4	4	no	—
175	C₄⋊C₄×C₄₇	C₂²×C₄	1	16	yes	complemented
176	C₂²⋊C₄×C₄₇	—	2	16	no	—
177	C₂²⋊C₄×C₄₇	—	2	16	no	—
178	C₂²⋊C₄×C₄₇	—	4	8	no	—
179	C₂²⋊C₄×C₄₇	—	4	8	no	—
180	C₂²⋊C₄×C₄₇	C₂²×C₄	1	32	yes	complemented
181	C₄²×C₄₇	—	2	16	no	—
182	C₂³×C₄₇	—	2	8	no	—
183	C₂³×C₄₇	—	2	8	no	—
184	C₂³×C₄₇	—	2	8	no	—
185	C₂³×C₄₇	—	2	8	no	—
186	C₂³×C₄₇	—	2	8	no	—
187	C₂³×C₄₇	—	2	8	no	—
188	C₂³×C₄₇	—	2	2	no	—
189	C₂³×C₄₇	—	2	2	no	—
190	C₂³×C₄₇	—	2	2	no	—
191	C₂³×C₄₇	—	2	2	no	—
192	C₂³×C₄₇	—	2	16	no	—
193	C₂³×C₄₇	—	2	16	no	—
194	C₂³×C₄₇	—	2	16	no	—
195	C₂³×C₄₇	—	2	4	no	—
196	C₂³×C₄₇	—	2	4	no	—
197	C₂³×C₄₇	—	2	4	no	—
198	C₂³×C₄₇	—	2	4	no	—
199	C₂³×C₄₇	—	2	4	no	—
200	C₂³×C₄₇	—	2	4	no	—
201	C₂³×C₄₇	—	4	8	no	—
202	C₂³×C₄₇	—	4	8	no	—
203	C₂³×C₄₇	—	4	8	no	—
204	C₂³×C₄₇	—	4	8	no	—
205	C₂³×C₄₇	C₄×D₄	1	16	yes	—
206	C₂³×C₄₇	C₂³×C₄	1	8	yes	—
207	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
208	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
209	C₂³×C₄₇	C₂²×D₄	1	4	yes	—
210	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
211	C₂³×C₄₇	C₂×#41	1	4	yes	—
212	C₂³×C₄₇	C₂×#41	1	2	yes	—
213	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
214	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
215	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
216	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
217	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
218	D₄×C₄₇	—	2	64	no	—
219	D₄×C₄₇	—	4	16	no	—
220	C₂×C₄×C₄₇	—	2	16	no	—
221	C₂×C₄×C₄₇	—	2	8	no	—
222	C₂×C₄×C₄₇	—	2	8	no	—
223	C₂×C₄×C₄₇	—	2	16	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	4	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	2	4	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	4	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	4	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	4	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	4	16	no	—
242	C₂×C₄×C₄₇	—	4	16	no	—
243	C₂×C₄×C₄₇	—	4	32	no	—
244	C₂×C₄×C₄₇	—	4	16	no	—
245	C₂×C₄×C₄₇	—	4	8	no	—
246	C₂×C₄×C₄₇	—	4	8	no	—
247	C₂×C₄×C₄₇	—	4	8	no	—
248	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
249	C₂×C₄×C₄₇	C₂³×C₄	1	8	yes	—
250	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
251	C₂×C₄×C₄₇	C₂²×D₄	1	8	yes	—
252	C₂×#2325	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₇	—	2	32	no	—
254	C₂²×C₄₇	—	2	4	no	—
255	C₂²×C₄₇	—	2	4	no	—
256	C₂²×C₄₇	—	2	4	no	—
257	C₂²×C₄₇	—	2	4	no	—
258	C₂²×C₄₇	—	2	4	no	—
259	C₂²×C₄₇	—	2	4	no	—
260	C₂²×C₄₇	—	2	8	no	—
261	C₂²×C₄₇	—	2	8	no	—
262	C₂²×C₄₇	—	2	8	no	—
263	C₂²×C₄₇	—	4	32	no	—
264	C₂²×C₄₇	—	4	4	no	—
265	C₂²×C₄₇	—	4	4	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	C₂×C₄×D₄	1	8	yes	—
269	C₂²×C₄₇	C₂×C₄×D₄	1	4	yes	—
270	C₂²×C₄₇	#518	1	4	yes	—
271	C₂²×C₄₇	#520	1	4	yes	—
272	C₂²×C₄₇	#534	1	4	yes	—
273	C₂²×C₄₇	#537	1	4	yes	—
274	C₂²×C₄₇	#538	1	4	yes	—
275	C₂²×C₄₇	#539	1	4	yes	—
276	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
277	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
278	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
279	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
280	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
281	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
282	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
283	C₄×C₄₇	—	2	8	no	—
284	C₄×C₄₇	—	2	4	no	—
285	C₄×C₄₇	—	2	4	no	—
286	C₄×C₄₇	—	2	8	no	—
287	C₄×C₄₇	—	4	4	no	—
288	C₄×C₄₇	—	4	4	no	—
289	C₄×C₄₇	—	4	4	no	—
290	C₂²×#121	C₂×C₄₇	1	1	yes	characteristic
291	C₂²×C₄×D₄	C₂×C₄₇	1	2	yes	complemented
292	#2325	C₂×C₄₇	1	16	yes	direct product factor
293	C₂×#388	C₂×C₄₇	1	2	yes	complemented
294	C₂×#387	C₂×C₄₇	1	2	yes	complemented
295	C₂×#386	C₂×C₄₇	1	2	yes	complemented
296	C₂×#386	C₂×C₄₇	1	2	yes	complemented
297	C₂×#385	C₂×C₄₇	1	2	yes	complemented
298	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
299	C₂²×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
300	C₂×C₄₇	—	2	8	no	—
301	C₂×C₄₇	—	4	8	no	—
302	C₂×C₄₇	#2325	1	8	yes	direct product factor
303	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
304	C₂×C₄₇	C₂×#518	1	1	yes	characteristic
305	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
306	C₂×C₄₇	C₂×#534	1	1	yes	characteristic
307	C₂×C₄₇	C₂×#537	1	1	yes	characteristic
308	C₂×C₄₇	C₂×#538	1	1	yes	characteristic
309	C₂×C₄₇	C₂×#539	1	1	yes	characteristic
310	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
311	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
312	C₂⁴×C₄	C₂²×C₄₇	1	2	yes	—
313	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
314	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
315	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×#121	C₄×C₄₇	1	16	yes	complemented
317	C₂×#121	C₂²×C₄₇	1	8	yes	—
318	C₂×C₄×D₄	—	2	16	no	—
319	C₂×C₄×D₄	C₂²×C₄₇	1	16	yes	complemented
320	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
322	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
324	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
325	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
326	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
327	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
328	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
329	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
330	#388	C₂²×C₄₇	1	16	yes	complemented
331	#387	C₂²×C₄₇	1	16	yes	complemented
332	#386	C₂²×C₄₇	1	16	yes	complemented
333	#386	C₂²×C₄₇	1	16	yes	complemented
334	#385	C₂²×C₄₇	1	16	yes	complemented
335	#380	C₂²×C₄₇	1	8	yes	complemented
336	C₂×#95	C₂²×C₄₇	1	2	yes	—
337	C₂×#95	C₂²×C₄₇	1	2	yes	—
338	C₂×#95	C₂²×C₄₇	1	2	yes	—
339	C₂×#95	C₂²×C₄₇	1	2	yes	—
340	C₂×#95	C₂²×C₄₇	1	2	yes	—
341	C₂×#95	C₂²×C₄₇	1	8	yes	complemented
342	C₄₇	C₂×#2325	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁵	C₂³×C₄₇	1	2	yes	—
344	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
345	C₂²×D₄	—	2	8	no	—
346	C₂²×D₄	—	2	8	no	—
347	C₂²×D₄	—	4	2	no	—
348	C₂²×D₄	—	4	2	no	—
349	C₂²×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
350	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	complemented
351	C₂²×D₄	C₂³×C₄₇	1	8	yes	—
352	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
353	C₂³×C₄	—	2	4	no	—
354	C₂³×C₄	—	2	8	no	—
355	C₂³×C₄	—	4	2	no	—
356	C₂³×C₄	—	4	2	no	—
357	C₂³×C₄	—	4	2	no	—
358	C₂³×C₄	—	4	2	no	—
359	C₂³×C₄	—	4	4	no	—
360	C₂³×C₄	—	4	4	no	—
361	C₂³×C₄	—	4	2	no	—
362	C₂³×C₄	—	4	2	no	—
363	C₂³×C₄	C₂×C₄×C₄₇	1	8	yes	complemented
364	C₂³×C₄	D₄×C₄₇	1	8	yes	complemented
365	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
366	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
367	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
368	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
370	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
371	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
372	C₂³×C₄	C₂³×C₄₇	1	8	yes	—
373	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
374	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
375	C₂³×C₄	C₂³×C₄₇	1	4	yes	—
376	#121	C₂×C₄×C₄₇	1	64	yes	complemented
377	C₄×D₄	—	2	64	no	—
378	C₂×C₄⋊C₄	—	2	8	no	—
379	C₂×C₄⋊C₄	—	4	2	no	—
380	C₂×C₄⋊C₄	—	4	2	no	—
381	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	8	yes	complemented
382	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
383	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
384	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
385	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
386	C₂×C₂²⋊C₄	—	2	8	no	—
387	C₂×C₂²⋊C₄	—	2	8	no	—
388	C₂×C₂²⋊C₄	—	4	4	no	—
389	C₂×C₂²⋊C₄	—	4	4	no	—
390	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	16	yes	complemented
391	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
392	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
393	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
394	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
395	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
396	C₂×C₄²	—	2	8	no	—
397	C₂×C₄²	C₂³×C₄₇	1	8	yes	—
398	#95	C₂³×C₄₇	1	8	yes	—
399	#95	C₂³×C₄₇	1	8	yes	—
400	#95	C₂³×C₄₇	1	8	yes	—
401	#95	C₂³×C₄₇	1	8	yes	—
402	#95	C₂³×C₄₇	1	8	yes	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	—	2	2	no	—
405	C₂⁴	—	2	2	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	4	no	—
408	C₂⁴	—	2	4	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	4	no	—
411	C₂⁴	—	2	4	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	C₂²×C₄×C₄₇	1	8	yes	—
414	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	—
415	C₂⁴	C₂×D₄×C₄₇	1	4	yes	—
416	C₂⁴	#41×C₄₇	1	4	yes	—
417	C₂⁴	C₂⁴×C₄₇	1	4	yes	—
418	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
419	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
420	C₂×D₄	—	2	64	no	—
421	C₂×D₄	—	2	16	no	—
422	C₂×D₄	—	2	16	no	—
423	C₂×D₄	—	4	16	no	—
424	C₂×D₄	—	4	4	no	—
425	C₂×D₄	—	4	4	no	—
426	C₂×D₄	C₂²×C₄×C₄₇	1	32	yes	complemented
427	C₂×D₄	C₂²×C₄×C₄₇	1	16	yes	complemented
428	C₂²×C₄	—	2	4	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	—	2	2	no	—
432	C₂²×C₄	—	2	4	no	—
433	C₂²×C₄	—	2	4	no	—
434	C₂²×C₄	—	2	2	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	8	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	2	4	no	—
445	C₂²×C₄	—	2	4	no	—
446	C₂²×C₄	—	2	16	no	—
447	C₂²×C₄	—	4	16	no	—
448	C₂²×C₄	—	4	16	no	—
449	C₂²×C₄	—	4	4	no	—
450	C₂²×C₄	—	4	4	no	—
451	C₂²×C₄	—	4	4	no	—
452	C₂²×C₄	—	4	4	no	—
453	C₂²×C₄	—	4	8	no	—
454	C₂²×C₄	—	4	8	no	—
455	C₂²×C₄	—	4	4	no	—
456	C₂²×C₄	—	4	4	no	—
457	C₂²×C₄	—	4	32	no	—
458	C₂²×C₄	—	4	16	no	—
459	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
460	C₂²×C₄	C₂²×C₄×C₄₇	1	8	yes	—
461	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
462	C₂²×C₄	C₂²×C₄×C₄₇	1	16	yes	complemented
463	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
464	C₂²×C₄	C₂×D₄×C₄₇	1	16	yes	complemented
465	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
466	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
467	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
468	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
469	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
470	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
471	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
472	C₄⋊C₄	—	2	16	no	—
473	C₄⋊C₄	—	4	4	no	—
474	C₄⋊C₄	—	4	4	no	—
475	C₄⋊C₄	C₂²×C₄×C₄₇	1	16	yes	complemented
476	C₂²⋊C₄	—	2	16	no	—
477	C₂²⋊C₄	—	2	16	no	—
478	C₂²⋊C₄	—	4	8	no	—
479	C₂²⋊C₄	—	4	8	no	—
480	C₂²⋊C₄	C₂²×C₄×C₄₇	1	32	yes	complemented
481	C₄²	—	2	16	no	—
482	C₂³	—	2	8	no	—
483	C₂³	—	2	8	no	—
484	C₂³	—	2	8	no	—
485	C₂³	—	2	8	no	—
486	C₂³	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	16	no	—
493	C₂³	—	2	16	no	—
494	C₂³	—	2	16	no	—
495	C₂³	—	2	4	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	4	8	no	—
502	C₂³	—	4	8	no	—
503	C₂³	—	4	8	no	—
504	C₂³	—	4	8	no	—
505	C₂³	C₄×D₄×C₄₇	1	16	yes	—
506	C₂³	C₂³×C₄×C₄₇	1	8	yes	—
507	C₂³	C₂³×C₄×C₄₇	1	4	yes	—
508	C₂³	C₂³×C₄×C₄₇	1	2	yes	—
509	C₂³	C₂²×D₄×C₄₇	1	4	yes	—
510	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
511	C₂³	C₂×#41×C₄₇	1	4	yes	—
512	C₂³	C₂×#41×C₄₇	1	2	yes	—
513	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
514	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
515	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
516	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
517	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
518	D₄	—	2	64	no	—
519	D₄	—	4	16	no	—
520	C₂×C₄	—	2	16	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	8	no	—
523	C₂×C₄	—	2	16	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	4	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	4	no	—
533	C₂×C₄	—	2	4	no	—
534	C₂×C₄	—	2	4	no	—
535	C₂×C₄	—	2	4	no	—
536	C₂×C₄	—	2	4	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	4	no	—
539	C₂×C₄	—	2	4	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	4	16	no	—
542	C₂×C₄	—	4	16	no	—
543	C₂×C₄	—	4	32	no	—
544	C₂×C₄	—	4	16	no	—
545	C₂×C₄	—	4	8	no	—
546	C₂×C₄	—	4	8	no	—
547	C₂×C₄	—	4	8	no	—
548	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
549	C₂×C₄	C₂³×C₄×C₄₇	1	8	yes	—
550	C₂×C₄	C₂³×C₄×C₄₇	1	4	yes	—
551	C₂×C₄	C₂²×D₄×C₄₇	1	8	yes	—
552	C₂²	—	2	32	no	—
553	C₂²	—	2	4	no	—
554	C₂²	—	2	4	no	—
555	C₂²	—	2	4	no	—
556	C₂²	—	2	4	no	—
557	C₂²	—	2	4	no	—
558	C₂²	—	2	4	no	—
559	C₂²	—	2	8	no	—
560	C₂²	—	2	8	no	—
561	C₂²	—	2	8	no	—
562	C₂²	—	4	32	no	—
563	C₂²	—	4	4	no	—
564	C₂²	—	4	4	no	—
565	C₂²	—	4	4	no	—
566	C₂²	—	4	4	no	—
567	C₂²	C₂×C₄×D₄×C₄₇	1	8	yes	—
568	C₂²	C₂×C₄×D₄×C₄₇	1	4	yes	—
569	C₂²	C₄₇×#518	1	4	yes	—
570	C₂²	C₄₇×#520	1	4	yes	—
571	C₂²	C₄₇×#534	1	4	yes	—
572	C₂²	C₄₇×#537	1	4	yes	—
573	C₂²	C₄₇×#538	1	4	yes	—
574	C₂²	C₄₇×#539	1	4	yes	—
575	C₂²	C₂⁴×C₄×C₄₇	1	1	yes	characteristic
576	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
577	C₂²	C₂²×#41×C₄₇	1	1	yes	characteristic
578	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
579	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
580	C₂²	C₂×H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
581	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
582	C₄	—	2	8	no	—
583	C₄	—	2	4	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	8	no	—
586	C₄	—	4	4	no	—
587	C₄	—	4	4	no	—
588	C₄	—	4	4	no	—
589	C₂	—	2	8	no	—
590	C₂	—	4	8	no	—
591	C₂	C₄₇×#2325	1	8	yes	direct product factor
592	C₂	C₂²×C₄×D₄×C₄₇	1	1	yes	characteristic
593	C₂	C₂×C₄₇×#518	1	1	yes	characteristic
594	C₂	C₂×C₄₇×#520	1	1	yes	characteristic
595	C₂	C₂×C₄₇×#534	1	1	yes	characteristic
596	C₂	C₂×C₄₇×#537	1	1	yes	characteristic
597	C₂	C₂×C₄₇×#538	1	1	yes	characteristic
598	C₂	C₂×C₄₇×#539	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂²	C₂⁴×C₄×C₄₇
Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂²×#121×C₄₇	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×D₄×C₄₇	C₂	semidirect
3. C₄₇×#2325	C₂	direct (N × H)
4. C₂×C₄₇×#388	C₂	semidirect
5. C₂×C₄₇×#387	C₂	semidirect
6. C₂×C₄₇×#386	C₂	semidirect
7. C₂×C₄₇×#386	C₂	semidirect
8. C₂×C₄₇×#385	C₂	semidirect
9. C₂×C₄₇×#380	C₂	semidirect
10. C₂²×#95×C₄₇	C₂	semidirect
17. C₂×#121×C₄₇	C₄	semidirect
20. C₂×C₄×D₄×C₄₇	C₂²	semidirect
31. C₄₇×#388	C₂²	semidirect
32. C₄₇×#387	C₂²	semidirect
33. C₄₇×#386	C₂²	semidirect
34. C₄₇×#386	C₂²	semidirect
35. C₄₇×#385	C₂²	semidirect
36. C₄₇×#380	C₂²	semidirect
42. C₂×#95×C₄₇	C₂²	semidirect
49. C₂²×D₄×C₄₇	C₂×C₄	semidirect
50. C₂²×D₄×C₄₇	C₂×C₄	semidirect
63. C₂³×C₄×C₄₇	C₂×C₄	semidirect
64. C₂³×C₄×C₄₇	D₄	semidirect
76. #121×C₄₇	C₂×C₄	semidirect
81. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
90. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
126. C₂×D₄×C₄₇	C₂²×C₄	semidirect
127. C₂×D₄×C₄₇	C₂²×C₄	semidirect
162. C₂²×C₄×C₄₇	C₂²×C₄	semidirect
164. C₂²×C₄×C₄₇	C₂×D₄	semidirect
175. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
180. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
252. C₂×#2325	C₄₇	direct (N × H)
291. C₂²×C₄×D₄	C₂×C₄₇	semidirect
292. #2325	C₂×C₄₇	direct (N × H)
293. C₂×#388	C₂×C₄₇	semidirect
294. C₂×#387	C₂×C₄₇	semidirect
295. C₂×#386	C₂×C₄₇	semidirect
296. C₂×#386	C₂×C₄₇	semidirect
297. C₂×#385	C₂×C₄₇	semidirect
298. C₂×#380	C₂×C₄₇	semidirect
299. C₂²×#95	C₂×C₄₇	semidirect
302. C₂×C₄₇	#2325	direct (N × H)
316. C₂×#121	C₄×C₄₇	semidirect
319. C₂×C₄×D₄	C₂²×C₄₇	semidirect
330. #388	C₂²×C₄₇	semidirect
331. #387	C₂²×C₄₇	semidirect
332. #386	C₂²×C₄₇	semidirect
333. #386	C₂²×C₄₇	semidirect
334. #385	C₂²×C₄₇	semidirect
335. #380	C₂²×C₄₇	semidirect
341. C₂×#95	C₂²×C₄₇	semidirect
342. C₄₇	C₂×#2325	direct (N × H)
349. C₂²×D₄	C₂×C₄×C₄₇	semidirect
350. C₂²×D₄	C₂×C₄×C₄₇	semidirect
363. C₂³×C₄	C₂×C₄×C₄₇	semidirect
364. C₂³×C₄	D₄×C₄₇	semidirect
376. #121	C₂×C₄×C₄₇	semidirect
381. C₂×C₄⋊C₄	C₂×C₄×C₄₇	semidirect
390. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
426. C₂×D₄	C₂²×C₄×C₄₇	semidirect
427. C₂×D₄	C₂²×C₄×C₄₇	semidirect
462. C₂²×C₄	C₂²×C₄×C₄₇	semidirect
464. C₂²×C₄	C₂×D₄×C₄₇	semidirect
475. C₄⋊C₄	C₂²×C₄×C₄₇	semidirect
480. C₂²⋊C₄	C₂²×C₄×C₄₇	semidirect
591. C₂	C₄₇×#2325	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#121×C₄₇	2
C₂²×C₄×D₄×C₄₇	2
C₄₇×#2325	2
C₂×C₄₇×#388	2
C₂×C₄₇×#387	2
C₂×C₄₇×#386	2
C₂×C₄₇×#385	2
C₂×C₄₇×#380	2
C₂²×#95×C₄₇	2
C₂×#2325	47

Subgroups — C2×C47×#2325 #26073764

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2325 #26073764