Subgroups — #26376940

Order 12032.

2314 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246408	C₂	1	2	yes	maximal
2	#20246397	C₂	1	2	yes	maximal, complemented
3	#20246384	C₂	1	4	yes	maximal, complemented
4	#20246361	C₂	1	1	yes	maximal, characteristic, complemented
5	#20246353	C₂	1	1	yes	maximal, characteristic, complemented
6	#20246309	C₂	1	1	yes	maximal, characteristic, complemented
7	#20246298	C₂	1	1	yes	maximal, characteristic, complemented
8	#20246273	C₂	1	2	yes	maximal, complemented
9	#20246248	C₂	1	2	yes	maximal, complemented
10	#20246167	C₂	1	4	yes	maximal, complemented
11	#20246021	C₂	1	2	yes	maximal, complemented
12	#125×Dic₄₇	C₂	1	2	yes	maximal, complemented
13	#124×Dic₄₇	C₂	1	2	yes	maximal, complemented
14	C₂×#15688989	C₂	1	1	yes	maximal, characteristic, complemented
15	#20245749	C₂	1	2	yes	maximal, complemented
16	C₄×#13093983	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
18	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
19	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
20	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂×#13093983	C₂²	1	2	yes	—
22	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	#15689030	C₂²	1	2	yes	—
24	#15689026	C₂²	1	2	yes	—
25	#15689022	C₂²	1	4	yes	—
26	#15689022	C₂²	1	2	yes	—
27	#15689022	C₂²	1	4	yes	—
28	#15689022	C₂²	1	2	yes	—
29	#15689016	C₂²	1	4	yes	—
30	#15689016	C₂²	1	4	yes	—
31	#15689016	C₂²	1	4	yes	—
32	#15689016	C₂²	1	4	yes	—
33	#15689009	C₂²	1	4	yes	—
34	#15689009	C₂²	1	4	yes	—
35	#15689009	C₂²	1	4	yes	—
36	#15689009	C₂²	1	4	yes	—
37	#15689003	C₂²	1	4	yes	—
38	#15688998	C₂²	1	4	yes	—
39	#15688998	C₂²	1	4	yes	—
40	#15688998	C₂²	1	4	yes	—
41	#15688991	C₂²	1	2	yes	—
42	#15688989	C₂²	1	2	yes	—
43	#15688989	C₂²	1	2	yes	—
44	#15688989	C₂²	1	1	yes	characteristic
45	#15688989	C₂²	1	1	yes	characteristic
46	#15688989	C₂²	1	2	yes	—
47	#15688989	C₂²	1	2	yes	—
48	#15688986	C₂²	1	2	yes	—
49	#15688983	C₂²	1	2	yes	—
50	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
51	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
52	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
53	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
54	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
55	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
56	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
57	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
58	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
59	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
60	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
61	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
62	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
63	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
65	#15688969	C₂²	1	1	yes	characteristic
66	#15688969	C₂²	1	2	yes	—
67	#15688969	C₂²	1	1	yes	characteristic
68	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
69	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
70	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
71	C₄²×Dic₄₇	C₂²	1	2	yes	—
72	C₄₇×#529	C₄	1	16	yes	complemented
73	C₂×#126×C₄₇	C₂²	1	2	yes	—
74	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
75	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
76	C₂×#123×C₄₇	C₂²	1	2	yes	—
77	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
78	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
81	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
82	C₂×#117×C₄₇	C₂²	1	2	yes	—
83	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
84	C₂³×Dic₄₇	C₂³	1	4	yes	—
85	C₂³×Dic₄₇	C₂³	1	4	yes	—
86	Q₈×Dic₄₇	—	4	4	no	—
87	D₄×Dic₄₇	—	2	16	no	—
88	D₄×Dic₄₇	—	4	4	no	—
89	#13093983	—	2	8	no	—
90	C₂×C₄⋊Dic₄₇	—	4	4	no	—
91	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
93	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
94	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
95	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
96	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
97	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
98	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
100	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
101	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
103	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
104	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
105	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
107	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
108	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
109	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
110	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
112	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
113	C₄₇⋊#95	C₂³	1	1	yes	characteristic
114	C₄₇⋊#95	C₂³	1	2	yes	—
115	C₄₇⋊#95	C₂³	1	2	yes	—
116	C₄₇⋊#95	C₂³	1	4	yes	—
117	C₄₇⋊#95	C₂³	1	4	yes	—
118	C₄₇⋊#95	C₂³	1	4	yes	—
119	C₄₇⋊#95	C₂³	1	2	yes	—
120	C₄₇⋊#95	C₂³	1	2	yes	—
121	C₄₇⋊#95	C₂³	1	1	yes	characteristic
122	C₄₇⋊#95	C₂³	1	1	yes	characteristic
123	C₄₇⋊#95	C₂³	1	1	yes	characteristic
124	C₄₇⋊#95	C₂³	1	2	yes	—
125	C₄₇⋊#95	C₂³	1	2	yes	—
126	C₄₇⋊#95	C₂³	1	4	yes	—
127	C₄₇⋊#95	C₂³	1	4	yes	—
128	C₄₇⋊#95	C₂³	1	4	yes	—
129	C₄₇⋊#95	C₂³	1	4	yes	—
130	C₄₇⋊#95	C₂³	1	4	yes	—
131	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
132	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
133	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
134	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
136	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
137	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
138	#126×C₄₇	C₂×C₄	1	16	yes	complemented
139	#125×C₄₇	C₂×C₄	1	8	yes	complemented
140	#124×C₄₇	C₂×C₄	1	8	yes	complemented
141	#123×C₄₇	C₂×C₄	1	16	yes	complemented
142	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
143	#121×C₄₇	C₂×C₄	1	8	yes	—
144	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
145	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
146	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
147	#117×C₄₇	C₂×C₄	1	16	yes	complemented
148	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
150	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
152	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
160	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
161	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
164	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
166	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
167	C₂×Q₈×C₄₇	—	2	2	no	—
168	C₂×Q₈×C₄₇	—	2	2	no	—
169	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
170	C₂×D₄×C₄₇	—	2	8	no	—
171	C₂×D₄×C₄₇	—	2	2	no	—
172	C₂×D₄×C₄₇	—	2	2	no	—
173	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
174	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
175	C₂²×C₄×C₄₇	—	2	4	no	—
176	C₂²×C₄×C₄₇	—	2	2	no	—
177	C₂²×C₄×C₄₇	—	2	2	no	—
178	C₂²×C₄×C₄₇	—	4	2	no	—
179	C₂²×C₄×C₄₇	—	4	4	no	—
180	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
181	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
182	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
183	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
184	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
185	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
186	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
187	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
193	C₂²×Dic₄₇	—	2	8	no	—
194	C₂²×Dic₄₇	—	2	8	no	—
195	C₂²×Dic₄₇	—	4	4	no	—
196	C₂²×Dic₄₇	—	4	4	no	—
197	C₂²×Dic₄₇	—	4	4	no	—
198	C₂²×Dic₄₇	—	4	4	no	—
199	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
200	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
201	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
202	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
203	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
204	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
205	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
206	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
207	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
208	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
209	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
210	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
211	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
212	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
213	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
214	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
215	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
216	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
217	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
218	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
219	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
220	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
221	C₂²⋊Dic₄₇	—	2	4	no	—
222	C₂²⋊Dic₄₇	—	2	8	no	—
223	C₂²⋊Dic₄₇	—	4	4	no	—
224	C₂²⋊Dic₄₇	—	4	4	no	—
225	C₂²⋊Dic₄₇	#41	1	8	yes	—
226	C₄⋊Dic₄₇	—	2	4	no	—
227	C₄⋊Dic₄₇	—	2	4	no	—
228	C₄⋊Dic₄₇	—	2	4	no	—
229	C₄⋊Dic₄₇	—	2	4	no	—
230	C₄⋊Dic₄₇	—	2	8	no	—
231	C₄⋊Dic₄₇	—	4	4	no	—
232	C₄⋊Dic₄₇	—	4	4	no	—
233	C₄⋊Dic₄₇	—	4	4	no	—
234	C₄×Dic₄₇	—	2	4	no	—
235	C₄×Dic₄₇	—	2	4	no	—
236	C₄×Dic₄₇	—	2	4	no	—
237	C₄×Dic₄₇	—	2	4	no	—
238	C₄×Dic₄₇	—	2	8	no	—
239	C₄×Dic₄₇	—	4	2	no	—
240	C₄×Dic₄₇	—	4	4	no	—
241	C₄×Dic₄₇	—	4	2	no	—
242	C₄×Dic₄₇	—	4	4	no	—
243	C₂³×C₄₇	—	2	1	no	—
244	C₂³×C₄₇	—	2	1	no	—
245	C₂³×C₄₇	—	2	2	no	—
246	C₂³×C₄₇	—	2	4	no	—
247	C₂³×C₄₇	—	2	2	no	—
248	C₂³×C₄₇	—	2	2	no	—
249	C₂³×C₄₇	—	2	4	no	—
250	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
251	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
252	C₂³×C₄₇	C₂×#41	1	4	yes	—
253	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
254	Q₈×C₄₇	—	2	8	no	—
255	D₄×C₄₇	—	2	16	no	—
256	D₄×C₄₇	—	2	8	no	—
257	C₂×C₄×C₄₇	—	2	8	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	4	no	—
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	2	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	1	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	4	no	—
267	C₂×C₄×C₄₇	—	2	2	no	—
268	C₂×C₄×C₄₇	—	2	8	no	—
269	C₂×C₄×C₄₇	—	4	4	no	—
270	C₂×C₄×C₄₇	—	4	8	no	—
271	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
272	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
273	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
274	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
276	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
277	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
278	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
279	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
280	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
281	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
282	C₂×Dic₄₇	—	2	2	no	—
283	C₂×Dic₄₇	—	2	2	no	—
284	C₂×Dic₄₇	—	2	2	no	—
285	C₂×Dic₄₇	—	2	2	no	—
286	C₂×Dic₄₇	—	2	2	no	—
287	C₂×Dic₄₇	—	2	2	no	—
288	C₂×Dic₄₇	—	2	4	no	—
289	C₂×Dic₄₇	—	2	4	no	—
290	C₂×Dic₄₇	—	2	2	no	—
291	C₂×Dic₄₇	—	2	4	no	—
292	C₂×Dic₄₇	—	2	4	no	—
293	C₂×Dic₄₇	—	2	2	no	—
294	C₂×Dic₄₇	—	2	2	no	—
295	C₂×Dic₄₇	—	2	2	no	—
296	C₂×Dic₄₇	—	2	4	no	—
297	C₂×Dic₄₇	—	2	4	no	—
298	C₂×Dic₄₇	—	8	8	no	—
299	C₂×Dic₄₇	—	8	8	no	—
300	C₂×Dic₄₇	C₂×#41	1	4	yes	—
301	C₂×Dic₄₇	C₂×#41	1	4	yes	—
302	#34229	—	47	1	no	maximal, Sylow
303	C₂²×C₄₇	—	2	2	no	—
304	C₂²×C₄₇	—	2	2	no	—
305	C₂²×C₄₇	—	2	4	no	—
306	C₂²×C₄₇	—	2	4	no	—
307	C₂²×C₄₇	—	2	4	no	—
308	C₂²×C₄₇	—	2	4	no	—
309	C₂²×C₄₇	—	2	4	no	—
310	C₂²×C₄₇	—	4	4	no	—
311	C₂²×C₄₇	—	4	4	no	—
312	C₂²×C₄₇	C₄×#41	1	4	yes	—
313	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
314	C₂²×C₄₇	C₂²×#41	1	2	yes	—
315	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
316	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
317	C₂²×C₄₇	#585	1	2	yes	—
318	C₄×C₄₇	—	2	2	no	—
319	C₄×C₄₇	—	2	2	no	—
320	C₄×C₄₇	—	2	4	no	—
321	C₄×C₄₇	—	2	2	no	—
322	C₄×C₄₇	—	2	4	no	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	2	no	—
325	C₄×C₄₇	—	2	4	no	—
326	C₄×C₄₇	#520	1	4	yes	—
327	Dic₄₇	—	2	4	no	—
328	Dic₄₇	—	2	4	no	—
329	Dic₄₇	—	4	2	no	—
330	Dic₄₇	—	4	4	no	—
331	Dic₄₇	—	4	4	no	—
332	Dic₄₇	—	4	2	no	—
333	C₂×#529	D₄₇	1	1	yes	characteristic
334	#2361	—	47	2	no	—
335	#2360	—	47	2	no	—
336	#2359	—	47	4	no	—
337	#2357	—	47	1	no	—
338	#2356	—	47	1	no	—
339	#2351	—	47	1	no	—
340	#2349	—	47	1	no	—
341	#2346	—	47	2	no	—
342	#2343	—	47	2	no	—
343	#2334	—	47	4	no	—
344	#2318	—	47	2	no	—
345	C₄×#125	—	47	2	no	—
346	C₄×#124	—	47	2	no	—
347	C₂×#382	—	47	1	no	—
348	#2275	—	47	2	no	—
349	C₄×#117	—	47	1	no	—
350	C₂×C₄₇	—	2	4	no	—
351	C₂×C₄₇	—	4	4	no	—
352	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
353	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
354	C₂×C₄₇	#3428	1	1	yes	characteristic
355	C₂×C₄₇	#3514	1	2	yes	—
356	C₂×C₄₇	#3515	1	2	yes	—
357	#529	Dic₄₇	1	16	yes	complemented
358	C₂×#126	C₂×D₄₇	1	2	yes	—
359	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
360	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
361	C₂×#123	C₂×D₄₇	1	2	yes	—
362	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
363	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
364	C₂×C₄×Q₈	—	47	2	no	—
365	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
366	C₂×C₄×D₄	—	47	4	no	—
367	C₂×C₄×D₄	—	47	2	no	—
368	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
369	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
370	C₂×#117	—	47	2	no	—
371	C₂×#117	C₂×D₄₇	1	2	yes	—
372	C₂²×C₄⋊C₄	—	47	2	no	—
373	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
374	#391	—	47	2	no	—
375	#390	—	47	2	no	—
376	#389	—	47	2	no	—
377	#389	—	47	2	no	—
378	#389	—	47	4	no	—
379	#389	—	47	4	no	—
380	#388	—	47	4	no	—
381	#388	—	47	4	no	—
382	#388	—	47	4	no	—
383	#388	—	47	4	no	—
384	#387	—	47	4	no	—
385	#387	—	47	4	no	—
386	#387	—	47	4	no	—
387	#387	—	47	4	no	—
388	#386	—	47	4	no	—
389	#385	—	47	4	no	—
390	#385	—	47	4	no	—
391	#385	—	47	4	no	—
392	#383	—	47	2	no	—
393	#382	—	47	2	no	—
394	#382	—	47	2	no	—
395	#382	—	47	2	no	—
396	#382	—	47	2	no	—
397	#382	—	47	1	no	—
398	#382	—	47	1	no	—
399	#381	—	47	2	no	—
400	#380	—	47	2	no	—
401	C₄×C₄⋊C₄	—	47	4	no	—
402	C₄×C₄⋊C₄	—	47	4	no	—
403	C₄×C₄⋊C₄	—	47	2	no	—
404	C₄×C₄⋊C₄	—	47	2	no	—
405	C₄×C₄⋊C₄	—	47	2	no	—
406	C₄×C₄⋊C₄	—	47	2	no	—
407	C₄×C₄⋊C₄	—	47	1	no	—
408	C₄×C₄⋊C₄	—	47	1	no	—
409	C₄×C₂²⋊C₄	—	47	1	no	—
410	C₄×C₂²⋊C₄	—	47	2	no	—
411	C₄×C₂²⋊C₄	—	47	2	no	—
412	C₄×C₂²⋊C₄	—	47	1	no	—
413	C₄×C₂²⋊C₄	—	47	4	no	—
414	C₄×C₂²⋊C₄	—	47	4	no	—
415	C₄×C₂²⋊C₄	—	47	4	no	—
416	#376	—	47	1	no	—
417	#376	—	47	1	no	—
418	#376	—	47	2	no	—
419	C₂×#95	—	47	2	no	—
420	C₂×#95	—	47	2	no	—
421	C₂×#95	—	47	2	no	—
422	C₄³	—	47	2	no	—
423	C₄₇	#34229	1	1	yes	characteristic, complemented, Sylow
424	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
425	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
426	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
427	C₂³×C₄	—	47	4	no	—
428	C₂³×C₄	—	47	4	no	—
429	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
430	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
431	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
432	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
433	#126	C₂×Dic₄₇	1	16	yes	complemented
434	#125	C₂×Dic₄₇	1	8	yes	complemented
435	#124	C₂×Dic₄₇	1	8	yes	complemented
436	#123	C₂×Dic₄₇	1	16	yes	complemented
437	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
438	#121	C₂×Dic₄₇	1	8	yes	—
439	C₄×Q₈	—	188	4	no	—
440	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
441	C₄×D₄	—	94	16	no	—
442	C₄×D₄	—	188	4	no	—
443	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
444	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
445	#117	—	94	8	no	—
446	#117	C₂×Dic₄₇	1	16	yes	complemented
447	C₂×C₄⋊C₄	—	47	2	no	—
448	C₂×C₄⋊C₄	—	47	2	no	—
449	C₂×C₄⋊C₄	—	47	2	no	—
450	C₂×C₄⋊C₄	—	47	2	no	—
451	C₂×C₄⋊C₄	—	47	4	no	—
452	C₂×C₄⋊C₄	—	47	4	no	—
453	C₂×C₄⋊C₄	—	47	4	no	—
454	C₂×C₄⋊C₄	—	47	4	no	—
455	C₂×C₄⋊C₄	—	188	4	no	—
456	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
458	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
459	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
460	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
461	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
462	C₂×C₂²⋊C₄	—	47	2	no	—
463	C₂×C₂²⋊C₄	—	47	2	no	—
464	C₂×C₂²⋊C₄	—	47	4	no	—
465	C₂×C₂²⋊C₄	—	47	4	no	—
466	C₂×C₂²⋊C₄	—	47	4	no	—
467	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
469	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
470	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
471	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
472	C₂×C₄²	—	47	2	no	—
473	C₂×C₄²	—	47	2	no	—
474	C₂×C₄²	—	47	2	no	—
475	C₂×C₄²	—	47	4	no	—
476	C₂×C₄²	—	47	2	no	—
477	C₂×C₄²	—	47	4	no	—
478	C₂×C₄²	—	47	2	no	—
479	C₂×C₄²	—	47	2	no	—
480	C₂×C₄²	—	47	4	no	—
481	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
482	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
483	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
484	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
485	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
486	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
487	#95	—	47	1	no	—
488	#95	—	47	2	no	—
489	#95	—	47	2	no	—
490	#95	—	47	4	no	—
491	#95	—	47	4	no	—
492	#95	—	47	4	no	—
493	#95	—	47	2	no	—
494	#95	—	47	2	no	—
495	#95	—	47	1	no	—
496	#95	—	47	4	no	—
497	#95	—	47	1	no	—
498	#95	—	47	1	no	—
499	#95	—	47	2	no	—
500	#95	—	47	2	no	—
501	#95	—	47	4	no	—
502	#95	—	47	4	no	—
503	#95	—	47	4	no	—
504	#95	—	47	4	no	—
505	C₂⁴	C₂³×D₄₇	1	2	yes	—
506	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
507	C₂×Q₈	—	2	2	no	—
508	C₂×Q₈	—	2	2	no	—
509	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
510	C₂×D₄	—	2	8	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	2	2	no	—
513	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
514	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
515	C₂²×C₄	—	2	4	no	—
516	C₂²×C₄	—	2	2	no	—
517	C₂²×C₄	—	2	2	no	—
518	C₂²×C₄	—	4	2	no	—
519	C₂²×C₄	—	4	4	no	—
520	C₂²×C₄	—	47	2	no	—
521	C₂²×C₄	—	47	2	no	—
522	C₂²×C₄	—	47	2	no	—
523	C₂²×C₄	—	47	4	no	—
524	C₂²×C₄	—	47	4	no	—
525	C₂²×C₄	—	47	2	no	—
526	C₂²×C₄	—	94	8	no	—
527	C₂²×C₄	—	94	8	no	—
528	C₂²×C₄	—	188	4	no	—
529	C₂²×C₄	—	188	4	no	—
530	C₂²×C₄	—	188	4	no	—
531	C₂²×C₄	—	188	4	no	—
532	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
533	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
534	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
535	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
536	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
537	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
538	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
539	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
540	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
541	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
542	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
543	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
544	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
545	C₄⋊C₄	—	94	4	no	—
546	C₄⋊C₄	—	94	4	no	—
547	C₄⋊C₄	—	94	8	no	—
548	C₄⋊C₄	—	94	4	no	—
549	C₄⋊C₄	—	94	4	no	—
550	C₄⋊C₄	—	188	4	no	—
551	C₄⋊C₄	—	188	4	no	—
552	C₄⋊C₄	—	188	4	no	—
553	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
554	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
555	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
556	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
557	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
558	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
559	C₂²⋊C₄	—	47	8	no	—
560	C₂²⋊C₄	—	94	8	no	—
561	C₂²⋊C₄	—	94	4	no	—
562	C₂²⋊C₄	—	188	4	no	—
563	C₂²⋊C₄	—	188	4	no	—
564	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
565	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
566	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
567	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
568	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
569	C₄²	—	94	4	no	—
570	C₄²	—	94	4	no	—
571	C₄²	—	94	8	no	—
572	C₄²	—	94	4	no	—
573	C₄²	—	94	4	no	—
574	C₄²	—	188	2	no	—
575	C₄²	—	188	2	no	—
576	C₄²	—	188	4	no	—
577	C₄²	—	188	4	no	—
578	C₄²	C₂²×Dic₄₇	1	4	yes	—
579	C₄²	C₂²×Dic₄₇	1	4	yes	—
580	C₄²	C₂²×Dic₄₇	1	4	yes	—
581	C₄²	C₂²×Dic₄₇	1	4	yes	—
582	C₄²	C₂²×Dic₄₇	1	8	yes	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	2	no	—
586	C₂³	—	2	4	no	—
587	C₂³	—	2	2	no	—
588	C₂³	—	2	2	no	—
589	C₂³	—	2	4	no	—
590	C₂³	C₂³×Dic₄₇	1	4	yes	—
591	C₂³	C₂³×Dic₄₇	1	2	yes	—
592	C₂³	#41×D₄₇	1	4	yes	—
593	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
594	Q₈	—	2	8	no	—
595	D₄	—	2	16	no	—
596	D₄	—	2	8	no	—
597	C₂×C₄	—	2	8	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	4	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	4	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	8	no	—
609	C₂×C₄	—	4	4	no	—
610	C₂×C₄	—	4	8	no	—
611	C₂×C₄	—	47	4	no	—
612	C₂×C₄	—	47	4	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	94	2	no	—
615	C₂×C₄	—	94	2	no	—
616	C₂×C₄	—	94	2	no	—
617	C₂×C₄	—	94	2	no	—
618	C₂×C₄	—	94	2	no	—
619	C₂×C₄	—	94	4	no	—
620	C₂×C₄	—	94	4	no	—
621	C₂×C₄	—	94	2	no	—
622	C₂×C₄	—	94	4	no	—
623	C₂×C₄	—	94	4	no	—
624	C₂×C₄	—	94	2	no	—
625	C₂×C₄	—	94	2	no	—
626	C₂×C₄	—	94	4	no	—
627	C₂×C₄	—	94	2	no	—
628	C₂×C₄	—	94	4	no	—
629	C₂×C₄	—	376	8	no	—
630	C₂×C₄	—	376	8	no	—
631	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
632	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
633	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
634	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
635	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
636	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
637	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
638	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
639	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
640	C₂×C₄	#13094070	1	2	yes	—
641	C₂×C₄	#13094071	1	2	yes	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	2	no	—
646	C₂²	—	2	4	no	—
647	C₂²	—	2	4	no	—
648	C₂²	—	2	4	no	—
649	C₂²	—	4	4	no	—
650	C₂²	—	4	4	no	—
651	C₂²	#41×Dic₄₇	1	4	yes	—
652	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
653	C₂²	C₂×#41×D₄₇	1	2	yes	—
654	C₂²	C₂×#13094070	1	1	yes	characteristic
655	C₂²	C₂×#13094071	1	1	yes	characteristic
656	C₂²	#15689959	1	2	yes	—
657	C₄	—	2	2	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	4	no	—
662	C₄	—	2	2	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	4	no	—
665	C₄	—	94	4	no	—
666	C₄	—	94	4	no	—
667	C₄	—	188	4	no	—
668	C₄	—	188	4	no	—
669	C₄	—	188	2	no	—
670	C₄	—	188	2	no	—
671	C₄	#15689606	1	4	yes	—
672	C₂	—	2	4	no	—
673	C₂	—	4	4	no	—
674	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
675	C₂	C₂×#15689606	1	1	yes	characteristic
676	C₂	#20256591	1	1	yes	characteristic
677	C₂	#20257337	1	2	yes	—
678	C₂	#20257354	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂³	C₂⁴×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Fitting	C₂×C₄₇×#529	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#121×C₄₇	C₂²
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	#34229
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
2. #20246397	C₂	semidirect
3. #20246384	C₂	semidirect
4. #20246361	C₂	semidirect
5. #20246353	C₂	semidirect
6. #20246309	C₂	semidirect
7. #20246298	C₂	semidirect
8. #20246273	C₂	semidirect
9. #20246248	C₂	semidirect
10. #20246167	C₂	semidirect
11. #20246021	C₂	semidirect
12. #125×Dic₄₇	C₂	semidirect
13. #124×Dic₄₇	C₂	semidirect
14. C₂×#15688989	C₂	semidirect
15. #20245749	C₂	semidirect
16. C₄×#13093983	C₂	semidirect
72. C₄₇×#529	C₄	semidirect
138. #126×C₄₇	C₂×C₄	semidirect
139. #125×C₄₇	C₂×C₄	semidirect
140. #124×C₄₇	C₂×C₄	semidirect
141. #123×C₄₇	C₂×C₄	semidirect
142. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
144. C₄×Q₈×C₄₇	C₂×C₄	semidirect
145. C₄×D₄×C₄₇	C₂×C₄	semidirect
146. C₄×D₄×C₄₇	C₂×C₄	semidirect
147. #117×C₄₇	C₂×C₄	semidirect
159. C₂×C₄²×C₄₇	C₂×C₄	semidirect
357. #529	Dic₄₇	semidirect
423. C₄₇	#34229	semidirect
433. #126	C₂×Dic₄₇	semidirect
434. #125	C₂×Dic₄₇	semidirect
435. #124	C₂×Dic₄₇	semidirect
436. #123	C₂×Dic₄₇	semidirect
437. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
440. C₄×Q₈	C₂×Dic₄₇	semidirect
443. C₄×D₄	C₂×Dic₄₇	semidirect
444. C₄×D₄	C₂×Dic₄₇	semidirect
446. #117	C₂×Dic₄₇	semidirect
481. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20246408	2
#20246397	2
#20246384	2
#20246361	2
#20246353	2
#20246309	2
#20246298	2
#20246273	2
#20246248	2
#20246167	2
#20246021	2
#125×Dic₄₇	2
#124×Dic₄₇	2
C₂×#15688989	2
#20245749	2
C₄×#13093983	2
C₂×C₄₇×#529	2
#34229	47