Subgroups — #26376957

Order 12032.

2330 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20246488	C₂	1	2	yes	maximal, complemented
2	#20246463	C₂	1	2	yes	maximal, complemented
3	#20246408	C₂	1	2	yes	maximal
4	#20246397	C₂	1	2	yes	maximal, complemented
5	#20246328	C₂	1	2	yes	maximal, complemented
6	#20246298	C₂	1	2	yes	maximal, complemented
7	#20246281	C₂	1	2	yes	maximal, complemented
8	#20246248	C₂	1	2	yes	maximal, complemented
9	#20246167	C₂	1	4	yes	maximal, complemented
10	#20246039	C₂	1	1	yes	maximal, characteristic, complemented
11	#20246031	C₂	1	1	yes	maximal, characteristic, complemented
12	#123×Dic₄₇	C₂	1	4	yes	maximal, complemented
13	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
14	#20245753	C₂	1	1	yes	maximal, characteristic, complemented
15	#20245749	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×C₄⋊Dic₄₇	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	2	yes	—
20	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
21	C₂²×C₄⋊Dic₄₇	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	2	yes	—
28	#15689022	C₂²	1	4	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	1	yes	characteristic
42	#15688991	C₂²	1	2	yes	—
43	#15688991	C₂²	1	1	yes	characteristic
44	#15688989	C₂²	1	2	yes	—
45	#15688989	C₂²	1	2	yes	—
46	#15688986	C₂²	1	2	yes	—
47	#15688986	C₂²	1	2	yes	—
48	#15688983	C₂²	1	2	yes	—
49	#15688983	C₂²	1	1	yes	characteristic
50	#15688983	C₂²	1	1	yes	characteristic
51	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
52	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
53	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
54	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
55	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
56	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
57	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
59	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
60	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
61	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
62	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
63	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
64	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
65	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
66	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
67	#15688969	C₂²	1	1	yes	characteristic
68	#15688969	C₂²	1	1	yes	characteristic
69	#15688969	C₂²	1	2	yes	—
70	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
71	C₂×C₄₇⋊#95	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	1	yes	characteristic
81	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
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	—	2	8	no	—
87	D₄×Dic₄₇	—	2	8	no	—
88	D₄×Dic₄₇	—	4	8	no	—
89	C₂×C₄⋊Dic₄₇	—	2	8	no	—
90	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
91	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
93	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
94	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
95	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
96	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
97	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
98	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
99	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
100	C₂×C₂²⋊Dic₄₇	C₂³	1	2	yes	—
101	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
102	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
103	C₂×C₄×Dic₄₇	—	4	4	no	—
104	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
105	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
107	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
108	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
109	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
110	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
112	C₄₇⋊#95	C₂³	1	2	yes	—
113	C₄₇⋊#95	C₂³	1	1	yes	characteristic
114	C₄₇⋊#95	C₂³	1	4	yes	—
115	C₄₇⋊#95	C₂³	1	2	yes	—
116	C₄₇⋊#95	C₂³	1	4	yes	—
117	C₄₇⋊#95	C₂³	1	1	yes	characteristic
118	C₄₇⋊#95	C₂³	1	1	yes	characteristic
119	C₄₇⋊#95	C₂³	1	2	yes	—
120	C₄₇⋊#95	C₂³	1	1	yes	characteristic
121	C₄₇⋊#95	C₂³	1	2	yes	—
122	C₄₇⋊#95	C₂³	1	4	yes	—
123	C₄₇⋊#95	C₂³	1	2	yes	—
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	2	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	2	yes	—
162	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
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	4	no	—
168	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
169	C₂×D₄×C₄₇	—	2	4	no	—
170	C₂×D₄×C₄₇	—	2	4	no	—
171	C₂×D₄×C₄₇	—	2	4	no	—
172	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
173	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
174	C₂²×C₄×C₄₇	—	2	2	no	—
175	C₂²×C₄×C₄₇	—	2	2	no	—
176	C₂²×C₄×C₄₇	—	2	4	no	—
177	C₂²×C₄×C₄₇	—	4	4	no	—
178	C₂²×C₄×C₄₇	—	4	2	no	—
179	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
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	8	yes	—
183	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
189	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
190	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
191	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
192	C₂²×Dic₄₇	—	2	8	no	—
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	C₂⁴	1	2	yes	—
199	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
200	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
201	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
202	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
203	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
204	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
205	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
206	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
207	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
208	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
209	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
210	C₂²⋊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	C₄²×C₄₇	C₂²×C₄	1	4	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	8	yes	—
220	C₂²⋊Dic₄₇	—	2	4	no	—
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	C₄⋊Dic₄₇	—	2	4	no	—
226	C₄⋊Dic₄₇	—	2	8	no	—
227	C₄⋊Dic₄₇	—	2	8	no	—
228	C₄⋊Dic₄₇	—	4	2	no	—
229	C₄⋊Dic₄₇	—	4	4	no	—
230	C₄⋊Dic₄₇	—	4	2	no	—
231	C₄⋊Dic₄₇	—	4	4	no	—
232	C₄⋊Dic₄₇	#41	1	8	yes	—
233	C₄×Dic₄₇	—	2	4	no	—
234	C₄×Dic₄₇	—	2	4	no	—
235	C₄×Dic₄₇	—	2	8	no	—
236	C₄×Dic₄₇	—	4	2	no	—
237	C₄×Dic₄₇	—	4	4	no	—
238	C₄×Dic₄₇	—	4	2	no	—
239	C₄×Dic₄₇	—	4	4	no	—
240	C₄×Dic₄₇	—	4	4	no	—
241	C₂³×C₄₇	—	2	2	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	4	no	—
244	C₂³×C₄₇	—	2	2	no	—
245	C₂³×C₄₇	—	2	2	no	—
246	C₂³×C₄₇	—	2	4	no	—
247	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
248	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
249	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
250	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
251	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
252	Q₈×C₄₇	—	2	8	no	—
253	D₄×C₄₇	—	2	16	no	—
254	D₄×C₄₇	—	2	8	no	—
255	C₂×C₄×C₄₇	—	2	8	no	—
256	C₂×C₄×C₄₇	—	2	4	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	1	no	—
259	C₂×C₄×C₄₇	—	2	1	no	—
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	4	no	—
265	C₂×C₄×C₄₇	—	2	2	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	8	no	—
268	C₂×C₄×C₄₇	—	4	4	no	—
269	C₂×C₄×C₄₇	—	4	8	no	—
270	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
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	4	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	2	yes	—
279	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
280	C₂×Dic₄₇	—	2	4	no	—
281	C₂×Dic₄₇	—	2	4	no	—
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	4	no	—
287	C₂×Dic₄₇	—	2	4	no	—
288	C₂×Dic₄₇	—	2	2	no	—
289	C₂×Dic₄₇	—	2	2	no	—
290	C₂×Dic₄₇	—	2	2	no	—
291	C₂×Dic₄₇	—	2	2	no	—
292	C₂×Dic₄₇	—	2	2	no	—
293	C₂×Dic₄₇	—	2	2	no	—
294	C₂×Dic₄₇	—	2	2	no	—
295	C₂×Dic₄₇	—	2	4	no	—
296	C₂×Dic₄₇	—	2	2	no	—
297	C₂×Dic₄₇	—	4	16	no	—
298	C₂×Dic₄₇	—	8	8	no	—
299	C₂×Dic₄₇	C₂×#41	1	8	yes	—
300	#34230	—	47	1	no	maximal, Sylow
301	C₂²×C₄₇	—	2	2	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	4	no	—
304	C₂²×C₄₇	—	2	4	no	—
305	C₂²×C₄₇	—	2	4	no	—
306	C₂²×C₄₇	—	2	4	no	—
307	C₂²×C₄₇	—	2	4	no	—
308	C₂²×C₄₇	—	4	4	no	—
309	C₂²×C₄₇	—	4	4	no	—
310	C₂²×C₄₇	#520	1	4	yes	—
311	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
312	C₂²×C₄₇	C₂²×#41	1	2	yes	—
313	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
314	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
315	C₂²×C₄₇	#585	1	2	yes	—
316	C₄×C₄₇	—	2	2	no	—
317	C₄×C₄₇	—	2	4	no	—
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	C₄×#41	1	4	yes	—
325	Dic₄₇	—	2	8	no	—
326	Dic₄₇	—	4	2	no	—
327	Dic₄₇	—	4	4	no	—
328	Dic₄₇	—	4	2	no	—
329	Dic₄₇	—	4	2	no	—
330	Dic₄₇	—	4	2	no	—
331	C₂×#529	D₄₇	1	1	yes	characteristic
332	#2370	—	47	2	no	—
333	#2367	—	47	2	no	—
334	#2361	—	47	2	no	—
335	#2360	—	47	2	no	—
336	#2353	—	47	2	no	—
337	#2349	—	47	2	no	—
338	#2347	—	47	2	no	—
339	#2343	—	47	2	no	—
340	#2334	—	47	4	no	—
341	#2320	—	47	1	no	—
342	#2319	—	47	1	no	—
343	C₄×#123	—	47	4	no	—
344	#2283	—	47	1	no	—
345	#2276	—	47	1	no	—
346	#2275	—	47	1	no	—
347	C₂×C₄×C₄⋊C₄	—	47	1	no	—
348	C₂×C₄₇	—	2	4	no	—
349	C₂×C₄₇	—	4	4	no	—
350	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
351	C₂×C₄₇	C₂×#520	1	1	yes	characteristic
352	C₂×C₄₇	#3428	1	1	yes	characteristic
353	C₂×C₄₇	#3513	1	2	yes	—
354	C₂×C₄₇	#3516	1	2	yes	—
355	#529	Dic₄₇	1	16	yes	complemented
356	C₂×#126	C₂×D₄₇	1	2	yes	—
357	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
358	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
359	C₂×#123	C₂×D₄₇	1	2	yes	—
360	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
361	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
362	C₂×C₄×Q₈	—	47	2	no	—
363	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
364	C₂×C₄×D₄	—	47	2	no	—
365	C₂×C₄×D₄	—	47	4	no	—
366	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
367	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
368	C₂×#117	C₂×D₄₇	1	2	yes	—
369	C₂²×C₄⋊C₄	—	47	2	no	—
370	C₂²×C₄²	—	47	2	no	—
371	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
372	#391	—	47	2	no	—
373	#390	—	47	2	no	—
374	#389	—	47	2	no	—
375	#389	—	47	2	no	—
376	#389	—	47	4	no	—
377	#389	—	47	4	no	—
378	#388	—	47	4	no	—
379	#388	—	47	4	no	—
380	#388	—	47	4	no	—
381	#388	—	47	4	no	—
382	#387	—	47	4	no	—
383	#387	—	47	4	no	—
384	#387	—	47	4	no	—
385	#387	—	47	4	no	—
386	#386	—	47	4	no	—
387	#385	—	47	4	no	—
388	#385	—	47	4	no	—
389	#385	—	47	4	no	—
390	#383	—	47	2	no	—
391	#383	—	47	1	no	—
392	#383	—	47	1	no	—
393	#382	—	47	2	no	—
394	#382	—	47	2	no	—
395	#381	—	47	2	no	—
396	#381	—	47	2	no	—
397	#380	—	47	2	no	—
398	#380	—	47	1	no	—
399	#380	—	47	1	no	—
400	C₄×C₄⋊C₄	—	47	4	no	—
401	C₄×C₄⋊C₄	—	47	4	no	—
402	C₄×C₄⋊C₄	—	47	2	no	—
403	C₄×C₄⋊C₄	—	47	2	no	—
404	C₄×C₄⋊C₄	—	47	1	no	—
405	C₄×C₄⋊C₄	—	47	2	no	—
406	C₄×C₄⋊C₄	—	47	2	no	—
407	C₄×C₄⋊C₄	—	47	2	no	—
408	C₄×C₄⋊C₄	—	47	2	no	—
409	C₄×C₄⋊C₄	—	47	2	no	—
410	C₄×C₄⋊C₄	—	47	1	no	—
411	C₄×C₂²⋊C₄	—	47	2	no	—
412	C₄×C₂²⋊C₄	—	47	2	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	C₄₇	#34230	1	1	yes	characteristic, complemented, Sylow
422	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
423	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
424	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
425	C₂³×C₄	—	47	4	no	—
426	C₂³×C₄	—	47	4	no	—
427	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
428	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
429	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
430	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
431	#126	C₂×Dic₄₇	1	16	yes	complemented
432	#125	C₂×Dic₄₇	1	8	yes	complemented
433	#124	C₂×Dic₄₇	1	8	yes	complemented
434	#123	C₂×Dic₄₇	1	16	yes	complemented
435	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
436	#121	C₂×Dic₄₇	1	8	yes	—
437	C₄×Q₈	—	94	8	no	—
438	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
439	C₄×D₄	—	94	8	no	—
440	C₄×D₄	—	188	8	no	—
441	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
442	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
443	#117	C₂×Dic₄₇	1	16	yes	complemented
444	C₂×C₄⋊C₄	—	47	2	no	—
445	C₂×C₄⋊C₄	—	47	4	no	—
446	C₂×C₄⋊C₄	—	47	2	no	—
447	C₂×C₄⋊C₄	—	47	4	no	—
448	C₂×C₄⋊C₄	—	47	4	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	—	94	8	no	—
453	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
454	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
455	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
456	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
457	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
459	C₂×C₂²⋊C₄	—	47	2	no	—
460	C₂×C₂²⋊C₄	—	47	4	no	—
461	C₂×C₂²⋊C₄	—	47	2	no	—
462	C₂×C₂²⋊C₄	—	47	4	no	—
463	C₂×C₂²⋊C₄	—	47	4	no	—
464	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
465	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
466	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
467	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
468	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
469	C₂×C₄²	—	47	2	no	—
470	C₂×C₄²	—	47	4	no	—
471	C₂×C₄²	—	47	2	no	—
472	C₂×C₄²	—	47	4	no	—
473	C₂×C₄²	—	47	4	no	—
474	C₂×C₄²	—	47	2	no	—
475	C₂×C₄²	—	47	4	no	—
476	C₂×C₄²	—	47	2	no	—
477	C₂×C₄²	—	188	4	no	—
478	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
479	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
480	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
481	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
482	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
483	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
484	#95	—	47	2	no	—
485	#95	—	47	1	no	—
486	#95	—	47	4	no	—
487	#95	—	47	2	no	—
488	#95	—	47	4	no	—
489	#95	—	47	1	no	—
490	#95	—	47	1	no	—
491	#95	—	47	2	no	—
492	#95	—	47	1	no	—
493	#95	—	47	2	no	—
494	#95	—	47	4	no	—
495	#95	—	47	2	no	—
496	#95	—	47	4	no	—
497	#95	—	47	2	no	—
498	#95	—	47	2	no	—
499	#95	—	47	4	no	—
500	#95	—	47	4	no	—
501	#95	—	47	2	no	—
502	#95	—	47	4	no	—
503	C₂⁴	C₂³×D₄₇	1	2	yes	—
504	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
505	C₂×Q₈	—	2	4	no	—
506	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
507	C₂×D₄	—	2	4	no	—
508	C₂×D₄	—	2	4	no	—
509	C₂×D₄	—	2	4	no	—
510	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
511	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
512	C₂²×C₄	—	2	2	no	—
513	C₂²×C₄	—	2	2	no	—
514	C₂²×C₄	—	2	4	no	—
515	C₂²×C₄	—	4	4	no	—
516	C₂²×C₄	—	4	2	no	—
517	C₂²×C₄	—	47	4	no	—
518	C₂²×C₄	—	47	2	no	—
519	C₂²×C₄	—	47	2	no	—
520	C₂²×C₄	—	47	2	no	—
521	C₂²×C₄	—	47	4	no	—
522	C₂²×C₄	—	47	2	no	—
523	C₂²×C₄	—	94	8	no	—
524	C₂²×C₄	—	94	8	no	—
525	C₂²×C₄	—	94	8	no	—
526	C₂²×C₄	—	188	4	no	—
527	C₂²×C₄	—	188	4	no	—
528	C₂²×C₄	—	188	4	no	—
529	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
530	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
531	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
532	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
533	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
535	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
536	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
537	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
538	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
539	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
540	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
541	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
542	C₄⋊C₄	—	47	8	no	—
543	C₄⋊C₄	—	94	8	no	—
544	C₄⋊C₄	—	94	8	no	—
545	C₄⋊C₄	—	94	4	no	—
546	C₄⋊C₄	—	188	4	no	—
547	C₄⋊C₄	—	188	2	no	—
548	C₄⋊C₄	—	188	2	no	—
549	C₄⋊C₄	—	188	4	no	—
550	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
551	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
552	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
553	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
554	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
555	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
556	C₂²⋊C₄	—	94	8	no	—
557	C₂²⋊C₄	—	94	4	no	—
558	C₂²⋊C₄	—	94	4	no	—
559	C₂²⋊C₄	—	188	4	no	—
560	C₂²⋊C₄	—	188	4	no	—
561	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
562	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
563	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
564	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
565	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
566	C₄²	—	94	8	no	—
567	C₄²	—	94	4	no	—
568	C₄²	—	94	4	no	—
569	C₄²	—	188	4	no	—
570	C₄²	—	188	2	no	—
571	C₄²	—	188	4	no	—
572	C₄²	—	188	2	no	—
573	C₄²	—	188	4	no	—
574	C₄²	C₂²×Dic₄₇	1	4	yes	—
575	C₄²	C₂²×Dic₄₇	1	4	yes	—
576	C₄²	C₂²×Dic₄₇	1	4	yes	—
577	C₄²	C₂²×Dic₄₇	1	4	yes	—
578	C₄²	C₂²×Dic₄₇	1	8	yes	—
579	C₂³	—	2	2	no	—
580	C₂³	—	2	2	no	—
581	C₂³	—	2	4	no	—
582	C₂³	—	2	2	no	—
583	C₂³	—	2	2	no	—
584	C₂³	—	2	4	no	—
585	C₂³	C₂³×Dic₄₇	1	4	yes	—
586	C₂³	C₂³×Dic₄₇	1	2	yes	—
587	C₂³	#13094070	1	2	yes	—
588	C₂³	#13094071	1	2	yes	—
589	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
590	Q₈	—	2	8	no	—
591	D₄	—	2	16	no	—
592	D₄	—	2	8	no	—
593	C₂×C₄	—	2	8	no	—
594	C₂×C₄	—	2	4	no	—
595	C₂×C₄	—	2	2	no	—
596	C₂×C₄	—	2	1	no	—
597	C₂×C₄	—	2	1	no	—
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	4	no	—
603	C₂×C₄	—	2	2	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	8	no	—
606	C₂×C₄	—	4	4	no	—
607	C₂×C₄	—	4	8	no	—
608	C₂×C₄	—	47	8	no	—
609	C₂×C₄	—	94	4	no	—
610	C₂×C₄	—	94	4	no	—
611	C₂×C₄	—	94	2	no	—
612	C₂×C₄	—	94	2	no	—
613	C₂×C₄	—	94	2	no	—
614	C₂×C₄	—	94	2	no	—
615	C₂×C₄	—	94	4	no	—
616	C₂×C₄	—	94	2	no	—
617	C₂×C₄	—	94	4	no	—
618	C₂×C₄	—	94	2	no	—
619	C₂×C₄	—	94	2	no	—
620	C₂×C₄	—	94	2	no	—
621	C₂×C₄	—	94	2	no	—
622	C₂×C₄	—	94	2	no	—
623	C₂×C₄	—	94	4	no	—
624	C₂×C₄	—	94	2	no	—
625	C₂×C₄	—	94	2	no	—
626	C₂×C₄	—	376	8	no	—
627	C₂×C₄	—	188	16	no	—
628	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
629	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
630	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
631	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
632	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
633	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
634	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
635	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
636	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
637	C₂×C₄	#41×D₄₇	1	4	yes	—
638	C₂²	—	2	4	no	—
639	C₂²	—	2	2	no	—
640	C₂²	—	2	2	no	—
641	C₂²	—	2	4	no	—
642	C₂²	—	2	4	no	—
643	C₂²	—	2	4	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	4	4	no	—
646	C₂²	—	4	4	no	—
647	C₂²	#15689606	1	4	yes	—
648	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
649	C₂²	C₂×#41×D₄₇	1	2	yes	—
650	C₂²	C₂×#13094070	1	1	yes	characteristic
651	C₂²	C₂×#13094071	1	1	yes	characteristic
652	C₂²	#15689959	1	2	yes	—
653	C₄	—	2	2	no	—
654	C₄	—	2	4	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	94	8	no	—
662	C₄	—	188	2	no	—
663	C₄	—	188	4	no	—
664	C₄	—	188	2	no	—
665	C₄	—	188	2	no	—
666	C₄	—	188	2	no	—
667	C₄	#41×Dic₄₇	1	4	yes	—
668	C₂	—	2	4	no	—
669	C₂	—	4	4	no	—
670	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
671	C₂	C₂×#15689606	1	1	yes	characteristic
672	C₂	#20256591	1	1	yes	characteristic
673	C₂	#20257322	1	2	yes	—
674	C₂	#20257371	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	#34230
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
1. #20246488	C₂	semidirect
2. #20246463	C₂	semidirect
4. #20246397	C₂	semidirect
5. #20246328	C₂	semidirect
6. #20246298	C₂	semidirect
7. #20246281	C₂	semidirect
8. #20246248	C₂	semidirect
9. #20246167	C₂	semidirect
10. #20246039	C₂	semidirect
11. #20246031	C₂	semidirect
12. #123×Dic₄₇	C₂	semidirect
13. #20245786	C₂	semidirect
14. #20245753	C₂	semidirect
15. #20245749	C₂	semidirect
16. C₂×C₄×C₄⋊Dic₄₇	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
355. #529	Dic₄₇	semidirect
421. C₄₇	#34230	semidirect
431. #126	C₂×Dic₄₇	semidirect
432. #125	C₂×Dic₄₇	semidirect
433. #124	C₂×Dic₄₇	semidirect
434. #123	C₂×Dic₄₇	semidirect
435. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
438. C₄×Q₈	C₂×Dic₄₇	semidirect
441. C₄×D₄	C₂×Dic₄₇	semidirect
442. C₄×D₄	C₂×Dic₄₇	semidirect
443. #117	C₂×Dic₄₇	semidirect
478. 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
#20246488	2
#20246463	2
#20246408	2
#20246397	2
#20246328	2
#20246298	2
#20246281	2
#20246248	2
#20246167	2
#20246039	2
#20246031	2
#123×Dic₄₇	2
#20245786	2
#20245753	2
#20245749	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×C₄₇×#529	2
#34230	47