Subgroups — C₂×C₄₇×#1889 #26060655

Order 12032.

3566 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#120×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#518	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#99×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#379	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1889	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#342	C₂	1	2	yes	maximal, complemented
7	C₂⁶×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	—	2	1	no	—
9	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
10	C₂×#120×C₄₇	—	2	4	no	—
11	C₂×#120×C₄₇	—	2	2	no	—
12	C₂×#120×C₄₇	C₄	1	8	yes	complemented
13	C₂×#120×C₄₇	C₂²	1	4	yes	—
14	C₄₇×#518	—	2	2	no	—
15	C₄₇×#518	—	2	4	no	—
16	C₄₇×#518	C₂²	1	4	yes	complemented
17	C₂×C₄×D₄×C₄₇	—	2	4	no	—
18	C₂×#117×C₄₇	—	2	1	no	—
19	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
20	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
21	C₂²×C₂²⋊C₄×C₄₇	—	2	4	no	—
22	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
23	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
24	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#99×C₄₇	—	2	4	no	—
26	C₂×#99×C₄₇	C₂²	1	4	yes	complemented
27	C₄₇×#379	—	2	4	no	—
28	C₄₇×#379	C₂²	1	8	yes	complemented
29	C₄₇×#342	C₂²	1	8	yes	complemented
30	C₂⁵×C₄₇	—	2	2	no	—
31	C₂⁵×C₄₇	—	2	1	no	—
32	C₂⁵×C₄₇	—	2	2	no	—
33	C₂⁵×C₄₇	—	2	1	no	—
34	C₂⁵×C₄₇	—	2	2	no	—
35	C₂⁵×C₄₇	—	2	4	no	—
36	C₂⁵×C₄₇	—	4	8	no	—
37	C₂⁵×C₄₇	C₂×C₄	1	4	yes	complemented
38	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
39	C₂⁵×C₄₇	C₂³	1	2	yes	—
40	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	—	2	4	no	—
44	C₂²×D₄×C₄₇	—	2	8	no	—
45	C₂²×D₄×C₄₇	—	2	4	no	—
46	C₂²×D₄×C₄₇	—	4	8	no	—
47	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
48	C₂²×D₄×C₄₇	D₄	1	4	yes	—
49	C₂²×D₄×C₄₇	D₄	1	2	yes	—
50	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	—	2	2	no	—
53	C₂³×C₄×C₄₇	—	2	2	no	—
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	D₄	1	4	yes	complemented
56	#120×C₄₇	—	2	16	no	—
57	#120×C₄₇	—	2	8	no	—
58	#120×C₄₇	C₂×C₄	1	16	yes	complemented
59	C₄×D₄×C₄₇	—	2	16	no	—
60	C₄×D₄×C₄₇	—	2	16	no	—
61	#117×C₄₇	—	2	4	no	—
62	#117×C₄₇	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	16	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	4	16	no	—
80	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	complemented
81	C₂×C₂²⋊C₄×C₄₇	D₄	1	4	yes	complemented
82	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
83	C₂×C₂²⋊C₄×C₄₇	C₂³	1	4	yes	—
84	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	#99×C₄₇	—	2	8	no	—
87	C₂⁴×C₄₇	—	2	16	no	—
88	C₂⁴×C₄₇	—	2	8	no	—
89	C₂⁴×C₄₇	—	2	4	no	—
90	C₂⁴×C₄₇	—	2	8	no	—
91	C₂⁴×C₄₇	—	2	1	no	—
92	C₂⁴×C₄₇	—	2	4	no	—
93	C₂⁴×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂⁴×C₄₇	—	2	2	no	—
96	C₂⁴×C₄₇	—	2	4	no	—
97	C₂⁴×C₄₇	—	2	8	no	—
98	C₂⁴×C₄₇	—	2	2	no	—
99	C₂⁴×C₄₇	—	2	4	no	—
100	C₂⁴×C₄₇	—	4	16	no	—
101	C₂⁴×C₄₇	—	4	8	no	—
102	C₂⁴×C₄₇	—	4	4	no	—
103	C₂⁴×C₄₇	—	4	8	no	—
104	C₂⁴×C₄₇	—	4	4	no	—
105	C₂⁴×C₄₇	—	4	16	no	—
106	C₂⁴×C₄₇	—	4	16	no	—
107	C₂⁴×C₄₇	—	4	8	no	—
108	C₂⁴×C₄₇	—	4	32	no	—
109	C₂⁴×C₄₇	—	4	4	no	—
110	C₂⁴×C₄₇	—	4	1	no	—
111	C₂⁴×C₄₇	—	4	2	no	—
112	C₂⁴×C₄₇	—	4	1	no	—
113	C₂⁴×C₄₇	—	4	4	no	—
114	C₂⁴×C₄₇	—	4	4	no	—
115	C₂⁴×C₄₇	—	4	2	no	—
116	C₂⁴×C₄₇	—	4	2	no	—
117	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	complemented
118	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂⁴×C₄₇	C₂²×C₄	1	4	yes	complemented
120	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
122	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
123	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
125	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
126	C₂⁴×C₄₇	#41	1	4	yes	—
127	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂×D₄×C₄₇	—	2	8	no	—
129	C₂×D₄×C₄₇	—	2	8	no	—
130	C₂×D₄×C₄₇	—	2	4	no	—
131	C₂×D₄×C₄₇	—	2	8	no	—
132	C₂×D₄×C₄₇	—	2	8	no	—
133	C₂×D₄×C₄₇	—	2	4	no	—
134	C₂×D₄×C₄₇	—	2	4	no	—
135	C₂×D₄×C₄₇	—	2	4	no	—
136	C₂×D₄×C₄₇	—	2	16	no	—
137	C₂×D₄×C₄₇	—	4	32	no	—
138	C₂×D₄×C₄₇	—	4	16	no	—
139	C₂×D₄×C₄₇	C₂²⋊C₄	1	8	yes	complemented
140	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
141	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
142	C₂²×C₄×C₄₇	—	2	1	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	4	no	—
146	C₂²×C₄×C₄₇	—	2	4	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	8	no	—
149	C₂²×C₄×C₄₇	—	2	4	no	—
150	C₂²×C₄×C₄₇	—	2	4	no	—
151	C₂²×C₄×C₄₇	—	4	4	no	—
152	C₂²×C₄×C₄₇	—	4	8	no	—
153	C₂²×C₄×C₄₇	—	4	8	no	—
154	C₂²×C₄×C₄₇	—	4	4	no	—
155	C₂²×C₄×C₄₇	—	8	4	no	—
156	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	complemented
157	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
158	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	complemented
159	C₄⋊C₄×C₄₇	—	2	8	no	—
160	C₂²⋊C₄×C₄₇	—	2	8	no	—
161	C₂²⋊C₄×C₄₇	—	2	4	no	—
162	C₂²⋊C₄×C₄₇	—	2	4	no	—
163	C₂²⋊C₄×C₄₇	—	2	4	no	—
164	C₂²⋊C₄×C₄₇	—	2	4	no	—
165	C₂²⋊C₄×C₄₇	—	2	4	no	—
166	C₂²⋊C₄×C₄₇	—	2	2	no	—
167	C₂²⋊C₄×C₄₇	—	2	16	no	—
168	C₂²⋊C₄×C₄₇	—	2	4	no	—
169	C₂²⋊C₄×C₄₇	—	2	4	no	—
170	C₂²⋊C₄×C₄₇	—	4	32	no	—
171	C₂²⋊C₄×C₄₇	—	4	4	no	—
172	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	complemented
173	C₄²×C₄₇	—	2	8	no	—
174	C₂³×C₄₇	—	2	8	no	—
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	16	no	—
177	C₂³×C₄₇	—	2	16	no	—
178	C₂³×C₄₇	—	2	8	no	—
179	C₂³×C₄₇	—	2	32	no	—
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	8	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	—	2	4	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	—	2	4	no	—
186	C₂³×C₄₇	—	4	4	no	—
187	C₂³×C₄₇	—	4	8	no	—
188	C₂³×C₄₇	—	4	4	no	—
189	C₂³×C₄₇	—	4	4	no	—
190	C₂³×C₄₇	—	4	2	no	—
191	C₂³×C₄₇	—	4	8	no	—
192	C₂³×C₄₇	—	4	2	no	—
193	C₂³×C₄₇	—	4	8	no	—
194	C₂³×C₄₇	—	4	32	no	—
195	C₂³×C₄₇	—	4	16	no	—
196	C₂³×C₄₇	—	4	16	no	—
197	C₂³×C₄₇	—	4	8	no	—
198	C₂³×C₄₇	—	4	4	no	—
199	C₂³×C₄₇	—	4	16	no	—
200	C₂³×C₄₇	—	4	8	no	—
201	C₂³×C₄₇	—	4	16	no	—
202	C₂³×C₄₇	—	4	8	no	—
203	C₂³×C₄₇	—	4	32	no	—
204	C₂³×C₄₇	—	4	16	no	—
205	C₂³×C₄₇	—	4	8	no	—
206	C₂³×C₄₇	—	4	4	no	—
207	C₂³×C₄₇	—	4	32	no	—
208	C₂³×C₄₇	—	4	16	no	—
209	C₂³×C₄₇	—	4	2	no	—
210	C₂³×C₄₇	—	4	4	no	—
211	C₂³×C₄₇	—	4	2	no	—
212	C₂³×C₄₇	—	4	4	no	—
213	C₂³×C₄₇	—	4	8	no	—
214	C₂³×C₄₇	—	4	4	no	—
215	C₂³×C₄₇	—	4	4	no	—
216	C₂³×C₄₇	—	4	8	no	—
217	C₂³×C₄₇	—	8	4	no	—
218	C₂³×C₄₇	—	8	2	no	—
219	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
220	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	complemented
222	C₂³×C₄₇	C₄×D₄	1	4	yes	—
223	C₂³×C₄₇	C₄×D₄	1	4	yes	—
224	C₂³×C₄₇	#120	1	1	yes	characteristic
225	C₂³×C₄₇	#120	1	2	yes	—
226	C₂³×C₄₇	#120	1	1	yes	characteristic
227	C₂³×C₄₇	#121	1	4	yes	—
228	C₂³×C₄₇	#121	1	4	yes	—
229	C₂³×C₄₇	#123	1	2	yes	—
230	C₂³×C₄₇	#123	1	2	yes	—
231	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
232	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
233	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
234	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
235	C₂³×C₄₇	C₂×#41	1	2	yes	—
236	D₄×C₄₇	—	2	8	no	—
237	D₄×C₄₇	—	2	8	no	—
238	D₄×C₄₇	—	2	16	no	—
239	D₄×C₄₇	—	4	32	no	—
240	C₂×C₄×C₄₇	—	2	2	no	—
241	C₂×C₄×C₄₇	—	2	2	no	—
242	C₂×C₄×C₄₇	—	2	4	no	—
243	C₂×C₄×C₄₇	—	2	4	no	—
244	C₂×C₄×C₄₇	—	2	4	no	—
245	C₂×C₄×C₄₇	—	2	8	no	—
246	C₂×C₄×C₄₇	—	4	8	no	—
247	C₂×C₄×C₄₇	—	4	4	no	—
248	C₂×C₄×C₄₇	—	4	8	no	—
249	C₂×C₄×C₄₇	—	4	8	no	—
250	C₂×C₄×C₄₇	—	4	8	no	—
251	C₂×C₄×C₄₇	—	4	4	no	—
252	C₂×C₄×C₄₇	—	8	4	no	—
253	C₂×C₄×C₄₇	—	8	8	no	—
254	C₂×C₄×C₄₇	—	8	8	no	—
255	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	complemented
256	C₂×#1889	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
257	C₂²×C₄₇	—	2	4	no	—
258	C₂²×C₄₇	—	2	8	no	—
259	C₂²×C₄₇	—	2	8	no	—
260	C₂²×C₄₇	—	2	4	no	—
261	C₂²×C₄₇	—	2	4	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	—	2	4	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	2	8	no	—
266	C₂²×C₄₇	—	2	16	no	—
267	C₂²×C₄₇	—	2	4	no	—
268	C₂²×C₄₇	—	4	2	no	—
269	C₂²×C₄₇	—	4	4	no	—
270	C₂²×C₄₇	—	4	4	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	1	no	—
273	C₂²×C₄₇	—	4	1	no	—
274	C₂²×C₄₇	—	4	2	no	—
275	C₂²×C₄₇	—	4	4	no	—
276	C₂²×C₄₇	—	4	4	no	—
277	C₂²×C₄₇	—	4	16	no	—
278	C₂²×C₄₇	—	4	8	no	—
279	C₂²×C₄₇	—	4	8	no	—
280	C₂²×C₄₇	—	4	16	no	—
281	C₂²×C₄₇	—	4	32	no	—
282	C₂²×C₄₇	—	4	16	no	—
283	C₂²×C₄₇	—	4	8	no	—
284	C₂²×C₄₇	—	4	4	no	—
285	C₂²×C₄₇	—	4	8	no	—
286	C₂²×C₄₇	—	4	4	no	—
287	C₂²×C₄₇	—	8	2	no	—
288	C₂²×C₄₇	—	8	4	no	—
289	C₂²×C₄₇	#386	1	2	yes	—
290	C₂²×C₄₇	#386	1	4	yes	—
291	C₂²×C₄₇	#386	1	2	yes	—
292	C₂²×C₄₇	B(4,𝔽₂)	1	4	yes	—
293	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
294	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
295	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
296	C₂²×C₄₇	C₂×#121	1	2	yes	—
297	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
298	C₄×C₄₇	—	2	4	no	—
299	C₄×C₄₇	—	4	4	no	—
300	C₄×C₄₇	—	4	8	no	—
301	C₄×C₄₇	—	8	4	no	—
302	C₂²×#120	C₂×C₄₇	1	1	yes	characteristic
303	C₂×#518	C₂×C₄₇	1	1	yes	characteristic, complemented
304	C₂²×#99	C₂×C₄₇	1	1	yes	characteristic, complemented
305	C₂×#379	C₂×C₄₇	1	2	yes	complemented
306	#1889	C₂×C₄₇	1	8	yes	direct product factor
307	C₂×#342	C₂×C₄₇	1	2	yes	complemented
308	C₂×C₄₇	—	2	1	no	—
309	C₂×C₄₇	—	2	2	no	—
310	C₂×C₄₇	—	2	2	no	—
311	C₂×C₄₇	—	2	1	no	—
312	C₂×C₄₇	—	2	2	no	—
313	C₂×C₄₇	—	2	4	no	—
314	C₂×C₄₇	—	4	8	no	—
315	C₂×C₄₇	—	4	4	no	—
316	C₂×C₄₇	#1889	1	4	yes	direct product factor
317	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
318	C₂×C₄₇	C₂×B(4,𝔽₂)	1	2	yes	—
319	C₂⁶	C₂²×C₄₇	1	1	yes	characteristic
320	C₂³×D₄	—	2	1	no	—
321	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
322	C₂×#120	—	2	4	no	—
323	C₂×#120	—	2	2	no	—
324	C₂×#120	C₄×C₄₇	1	8	yes	complemented
325	C₂×#120	C₂²×C₄₇	1	4	yes	—
326	#518	—	2	2	no	—
327	#518	—	2	4	no	—
328	#518	C₂²×C₄₇	1	4	yes	complemented
329	C₂×C₄×D₄	—	2	4	no	—
330	C₂×#117	—	2	1	no	—
331	C₂²×C₂²⋊C₄	—	2	1	no	—
332	C₂²×C₂²⋊C₄	—	2	1	no	—
333	C₂²×C₂²⋊C₄	—	2	4	no	—
334	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
335	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
336	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
337	C₂×#99	—	2	4	no	—
338	C₂×#99	C₂²×C₄₇	1	4	yes	complemented
339	#379	—	2	4	no	—
340	#379	C₂²×C₄₇	1	8	yes	complemented
341	#342	C₂²×C₄₇	1	8	yes	complemented
342	C₄₇	C₂×#1889	1	1	yes	characteristic, direct product factor, Sylow
343	C₂⁵	—	2	2	no	—
344	C₂⁵	—	2	1	no	—
345	C₂⁵	—	2	2	no	—
346	C₂⁵	—	2	1	no	—
347	C₂⁵	—	2	2	no	—
348	C₂⁵	—	2	4	no	—
349	C₂⁵	—	4	8	no	—
350	C₂⁵	C₂×C₄×C₄₇	1	4	yes	complemented
351	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
352	C₂⁵	C₂³×C₄₇	1	2	yes	—
353	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
354	C₂²×D₄	—	2	2	no	—
355	C₂²×D₄	—	2	2	no	—
356	C₂²×D₄	—	2	4	no	—
357	C₂²×D₄	—	2	8	no	—
358	C₂²×D₄	—	2	4	no	—
359	C₂²×D₄	—	4	8	no	—
360	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
361	C₂²×D₄	D₄×C₄₇	1	4	yes	—
362	C₂²×D₄	D₄×C₄₇	1	2	yes	—
363	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
364	C₂³×C₄	—	2	1	no	—
365	C₂³×C₄	—	2	2	no	—
366	C₂³×C₄	—	2	2	no	—
367	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
368	C₂³×C₄	D₄×C₄₇	1	4	yes	complemented
369	#120	—	2	16	no	—
370	#120	—	2	8	no	—
371	#120	C₂×C₄×C₄₇	1	16	yes	complemented
372	C₄×D₄	—	2	16	no	—
373	C₄×D₄	—	2	16	no	—
374	#117	—	2	4	no	—
375	#117	—	2	4	no	—
376	C₂×C₄⋊C₄	—	2	2	no	—
377	C₂×C₂²⋊C₄	—	2	2	no	—
378	C₂×C₂²⋊C₄	—	2	4	no	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	4	no	—
381	C₂×C₂²⋊C₄	—	2	2	no	—
382	C₂×C₂²⋊C₄	—	2	2	no	—
383	C₂×C₂²⋊C₄	—	2	2	no	—
384	C₂×C₂²⋊C₄	—	2	1	no	—
385	C₂×C₂²⋊C₄	—	2	2	no	—
386	C₂×C₂²⋊C₄	—	2	8	no	—
387	C₂×C₂²⋊C₄	—	2	4	no	—
388	C₂×C₂²⋊C₄	—	2	4	no	—
389	C₂×C₂²⋊C₄	—	2	4	no	—
390	C₂×C₂²⋊C₄	—	2	2	no	—
391	C₂×C₂²⋊C₄	—	2	16	no	—
392	C₂×C₂²⋊C₄	—	4	16	no	—
393	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	complemented
394	C₂×C₂²⋊C₄	D₄×C₄₇	1	4	yes	complemented
395	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
396	C₂×C₂²⋊C₄	C₂³×C₄₇	1	4	yes	—
397	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
398	C₂×C₄²	—	2	2	no	—
399	#99	—	2	8	no	—
400	C₂⁴	—	2	16	no	—
401	C₂⁴	—	2	8	no	—
402	C₂⁴	—	2	4	no	—
403	C₂⁴	—	2	8	no	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	4	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	2	2	no	—
409	C₂⁴	—	2	4	no	—
410	C₂⁴	—	2	8	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	—	2	4	no	—
413	C₂⁴	—	4	16	no	—
414	C₂⁴	—	4	4	no	—
415	C₂⁴	—	4	8	no	—
416	C₂⁴	—	4	8	no	—
417	C₂⁴	—	4	4	no	—
418	C₂⁴	—	4	16	no	—
419	C₂⁴	—	4	16	no	—
420	C₂⁴	—	4	8	no	—
421	C₂⁴	—	4	32	no	—
422	C₂⁴	—	4	4	no	—
423	C₂⁴	—	4	1	no	—
424	C₂⁴	—	4	2	no	—
425	C₂⁴	—	4	1	no	—
426	C₂⁴	—	4	4	no	—
427	C₂⁴	—	4	4	no	—
428	C₂⁴	—	4	2	no	—
429	C₂⁴	—	4	2	no	—
430	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	complemented
431	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
432	C₂⁴	C₂²×C₄×C₄₇	1	4	yes	complemented
433	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
434	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
435	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
436	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
437	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
438	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
439	C₂⁴	#41×C₄₇	1	4	yes	—
440	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
441	C₂×D₄	—	2	8	no	—
442	C₂×D₄	—	2	8	no	—
443	C₂×D₄	—	2	4	no	—
444	C₂×D₄	—	2	8	no	—
445	C₂×D₄	—	2	8	no	—
446	C₂×D₄	—	2	4	no	—
447	C₂×D₄	—	2	4	no	—
448	C₂×D₄	—	2	4	no	—
449	C₂×D₄	—	2	16	no	—
450	C₂×D₄	—	4	32	no	—
451	C₂×D₄	—	4	16	no	—
452	C₂×D₄	C₂²⋊C₄×C₄₇	1	8	yes	complemented
453	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
454	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
455	C₂²×C₄	—	2	1	no	—
456	C₂²×C₄	—	2	1	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	4	no	—
459	C₂²×C₄	—	2	4	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	8	no	—
462	C₂²×C₄	—	2	4	no	—
463	C₂²×C₄	—	2	4	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	8	no	—
466	C₂²×C₄	—	4	8	no	—
467	C₂²×C₄	—	4	4	no	—
468	C₂²×C₄	—	8	4	no	—
469	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	complemented
470	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
471	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	complemented
472	C₄⋊C₄	—	2	8	no	—
473	C₂²⋊C₄	—	2	8	no	—
474	C₂²⋊C₄	—	2	4	no	—
475	C₂²⋊C₄	—	2	4	no	—
476	C₂²⋊C₄	—	2	4	no	—
477	C₂²⋊C₄	—	2	4	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	2	no	—
480	C₂²⋊C₄	—	2	16	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	4	32	no	—
484	C₂²⋊C₄	—	4	4	no	—
485	C₂²⋊C₄	C₂²×C₄×C₄₇	1	4	yes	complemented
486	C₄²	—	2	8	no	—
487	C₂³	—	2	8	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	16	no	—
490	C₂³	—	2	16	no	—
491	C₂³	—	2	8	no	—
492	C₂³	—	2	32	no	—
493	C₂³	—	2	4	no	—
494	C₂³	—	2	8	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	4	4	no	—
500	C₂³	—	4	8	no	—
501	C₂³	—	4	4	no	—
502	C₂³	—	4	4	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	8	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	8	no	—
507	C₂³	—	4	32	no	—
508	C₂³	—	4	16	no	—
509	C₂³	—	4	16	no	—
510	C₂³	—	4	8	no	—
511	C₂³	—	4	4	no	—
512	C₂³	—	4	16	no	—
513	C₂³	—	4	8	no	—
514	C₂³	—	4	16	no	—
515	C₂³	—	4	8	no	—
516	C₂³	—	4	32	no	—
517	C₂³	—	4	16	no	—
518	C₂³	—	4	8	no	—
519	C₂³	—	4	4	no	—
520	C₂³	—	4	32	no	—
521	C₂³	—	4	16	no	—
522	C₂³	—	4	4	no	—
523	C₂³	—	4	8	no	—
524	C₂³	—	4	2	no	—
525	C₂³	—	4	4	no	—
526	C₂³	—	4	2	no	—
527	C₂³	—	4	4	no	—
528	C₂³	—	4	8	no	—
529	C₂³	—	4	4	no	—
530	C₂³	—	8	4	no	—
531	C₂³	—	8	2	no	—
532	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
533	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
534	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	complemented
535	C₂³	C₄×D₄×C₄₇	1	4	yes	—
536	C₂³	C₄×D₄×C₄₇	1	4	yes	—
537	C₂³	#120×C₄₇	1	1	yes	characteristic
538	C₂³	#120×C₄₇	1	2	yes	—
539	C₂³	#120×C₄₇	1	1	yes	characteristic
540	C₂³	#121×C₄₇	1	4	yes	—
541	C₂³	#121×C₄₇	1	4	yes	—
542	C₂³	#123×C₄₇	1	2	yes	—
543	C₂³	#123×C₄₇	1	2	yes	—
544	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
545	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
546	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
547	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
548	C₂³	C₂×#41×C₄₇	1	2	yes	—
549	D₄	—	2	8	no	—
550	D₄	—	2	8	no	—
551	D₄	—	2	16	no	—
552	D₄	—	4	32	no	—
553	C₂×C₄	—	2	2	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	4	no	—
556	C₂×C₄	—	2	4	no	—
557	C₂×C₄	—	2	4	no	—
558	C₂×C₄	—	2	8	no	—
559	C₂×C₄	—	4	8	no	—
560	C₂×C₄	—	4	4	no	—
561	C₂×C₄	—	4	8	no	—
562	C₂×C₄	—	4	8	no	—
563	C₂×C₄	—	4	8	no	—
564	C₂×C₄	—	4	4	no	—
565	C₂×C₄	—	8	4	no	—
566	C₂×C₄	—	8	8	no	—
567	C₂×C₄	—	8	8	no	—
568	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	complemented
569	C₂²	—	2	4	no	—
570	C₂²	—	2	8	no	—
571	C₂²	—	2	8	no	—
572	C₂²	—	2	4	no	—
573	C₂²	—	2	4	no	—
574	C₂²	—	2	2	no	—
575	C₂²	—	2	4	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	8	no	—
578	C₂²	—	2	16	no	—
579	C₂²	—	2	4	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	4	no	—
582	C₂²	—	4	4	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	1	no	—
585	C₂²	—	4	1	no	—
586	C₂²	—	4	2	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	4	no	—
589	C₂²	—	4	16	no	—
590	C₂²	—	4	8	no	—
591	C₂²	—	4	8	no	—
592	C₂²	—	4	16	no	—
593	C₂²	—	4	32	no	—
594	C₂²	—	4	4	no	—
595	C₂²	—	4	16	no	—
596	C₂²	—	4	8	no	—
597	C₂²	—	4	4	no	—
598	C₂²	—	4	8	no	—
599	C₂²	—	8	2	no	—
600	C₂²	—	8	4	no	—
601	C₂²	C₄₇×#386	1	2	yes	—
602	C₂²	C₄₇×#386	1	4	yes	—
603	C₂²	C₄₇×#386	1	2	yes	—
604	C₂²	C₄₇×B(4,𝔽₂)	1	4	yes	—
605	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
606	C₂²	C₂×C₄×D₄×C₄₇	1	2	yes	—
607	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
608	C₂²	C₂×#121×C₄₇	1	2	yes	—
609	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
610	C₄	—	2	4	no	—
611	C₄	—	4	4	no	—
612	C₄	—	4	8	no	—
613	C₄	—	8	4	no	—
614	C₂	—	2	1	no	—
615	C₂	—	2	2	no	—
616	C₂	—	2	2	no	—
617	C₂	—	2	1	no	—
618	C₂	—	2	2	no	—
619	C₂	—	2	4	no	—
620	C₂	—	4	8	no	—
621	C₂	—	4	4	no	—
622	C₂	C₄₇×#1889	1	4	yes	direct product factor
623	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
624	C₂	C₂×C₄₇×B(4,𝔽₂)	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	#120
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂²×#120×C₄₇	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁵×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#518	C₂	semidirect
3. C₂²×#99×C₄₇	C₂	semidirect
4. C₂×C₄₇×#379	C₂	semidirect
5. C₄₇×#1889	C₂	direct (N × H)
6. C₂×C₄₇×#342	C₂	semidirect
12. C₂×#120×C₄₇	C₄	semidirect
16. C₄₇×#518	C₂²	semidirect
26. C₂×#99×C₄₇	C₂²	semidirect
28. C₄₇×#379	C₂²	semidirect
29. C₄₇×#342	C₂²	semidirect
37. C₂⁵×C₄₇	C₂×C₄	semidirect
55. C₂³×C₄×C₄₇	D₄	semidirect
58. #120×C₄₇	C₂×C₄	semidirect
80. C₂×C₂²⋊C₄×C₄₇	C₂×C₄	semidirect
81. C₂×C₂²⋊C₄×C₄₇	D₄	semidirect
117. C₂⁴×C₄₇	C₂²⋊C₄	semidirect
119. C₂⁴×C₄₇	C₂²×C₄	semidirect
139. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
156. C₂²×C₄×C₄₇	C₂²⋊C₄	semidirect
158. C₂²×C₄×C₄₇	C₂×D₄	semidirect
172. C₂²⋊C₄×C₄₇	C₂²×C₄	semidirect
221. C₂³×C₄₇	C₂×C₂²⋊C₄	semidirect
255. C₂×C₄×C₄₇	C₂×C₂²⋊C₄	semidirect
256. C₂×#1889	C₄₇	direct (N × H)
303. C₂×#518	C₂×C₄₇	semidirect
304. C₂²×#99	C₂×C₄₇	semidirect
305. C₂×#379	C₂×C₄₇	semidirect
306. #1889	C₂×C₄₇	direct (N × H)
307. C₂×#342	C₂×C₄₇	semidirect
316. C₂×C₄₇	#1889	direct (N × H)
324. C₂×#120	C₄×C₄₇	semidirect
328. #518	C₂²×C₄₇	semidirect
338. C₂×#99	C₂²×C₄₇	semidirect
340. #379	C₂²×C₄₇	semidirect
341. #342	C₂²×C₄₇	semidirect
342. C₄₇	C₂×#1889	direct (N × H)
350. C₂⁵	C₂×C₄×C₄₇	semidirect
368. C₂³×C₄	D₄×C₄₇	semidirect
371. #120	C₂×C₄×C₄₇	semidirect
393. C₂×C₂²⋊C₄	C₂×C₄×C₄₇	semidirect
394. C₂×C₂²⋊C₄	D₄×C₄₇	semidirect
430. C₂⁴	C₂²⋊C₄×C₄₇	semidirect
432. C₂⁴	C₂²×C₄×C₄₇	semidirect
452. C₂×D₄	C₂²⋊C₄×C₄₇	semidirect
469. C₂²×C₄	C₂²⋊C₄×C₄₇	semidirect
471. C₂²×C₄	C₂×D₄×C₄₇	semidirect
485. C₂²⋊C₄	C₂²×C₄×C₄₇	semidirect
534. C₂³	C₂×C₂²⋊C₄×C₄₇	semidirect
568. C₂×C₄	C₂×C₂²⋊C₄×C₄₇	semidirect
622. C₂	C₄₇×#1889	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×#120×C₄₇	2
C₂×C₄₇×#518	2
C₂²×#99×C₄₇	2
C₂×C₄₇×#379	2
C₄₇×#1889	2
C₂×C₄₇×#342	2
C₂×#1889	47

Subgroups — C2×C47×#1889 #26060655

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1889 #26060655