Subgroups — #26377058

Order 12032.

2186 conjugacy classes of subgroups.

The subgroup lattice has 666 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	#20246430	C₂	1	2	yes	maximal
4	#20246419	C₂	1	2	yes	maximal, complemented
5	#20246361	C₂	1	2	yes	maximal, complemented
6	#20246328	C₂	1	2	yes	maximal, complemented
7	#20246273	C₂	1	2	yes	maximal, complemented
8	#20246248	C₂	1	2	yes	maximal, complemented
9	#20246182	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	#126×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	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	2	yes	—
20	C₂×#13093983	C₂²	1	2	yes	—
21	#15689030	C₂²	1	2	yes	—
22	#15689026	C₂²	1	2	yes	—
23	#15689026	C₂²	1	4	yes	—
24	#15689022	C₂²	1	4	yes	—
25	#15689022	C₂²	1	2	yes	—
26	#15689022	C₂²	1	2	yes	—
27	#15689016	C₂²	1	4	yes	—
28	#15689016	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	#15688991	C₂²	1	2	yes	—
40	#15688991	C₂²	1	2	yes	—
41	#15688989	C₂²	1	1	yes	characteristic
42	#15688989	C₂²	1	2	yes	—
43	#15688989	C₂²	1	1	yes	characteristic
44	#15688986	C₂²	1	2	yes	—
45	#15688986	C₂²	1	1	yes	characteristic
46	#15688986	C₂²	1	1	yes	characteristic
47	#15688983	C₂²	1	2	yes	—
48	#15688983	C₂²	1	2	yes	—
49	C₄⋊C₄×Dic₄₇	C₂²	1	4	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	2	yes	—
57	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
58	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
59	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
60	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
61	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
62	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
63	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
65	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
66	#15688969	C₂²	1	2	yes	—
67	#15688969	C₂²	1	2	yes	—
68	#15688969	C₂²	1	1	yes	characteristic
69	#15688969	C₂²	1	1	yes	characteristic
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	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	Q₈×Dic₄₇	—	2	8	no	—
86	D₄×Dic₄₇	—	2	8	no	—
87	#13093983	—	2	8	no	—
88	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
89	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
90	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
91	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
93	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
94	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
95	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊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	4	yes	—
101	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
102	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
103	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
104	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
105	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
106	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
107	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
108	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
109	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
110	C₄₇⋊#95	C₂³	1	1	yes	characteristic
111	C₄₇⋊#95	C₂³	1	2	yes	—
112	C₄₇⋊#95	C₂³	1	4	yes	—
113	C₄₇⋊#95	C₂³	1	1	yes	characteristic
114	C₄₇⋊#95	C₂³	1	1	yes	characteristic
115	C₄₇⋊#95	C₂³	1	2	yes	—
116	C₄₇⋊#95	C₂³	1	4	yes	—
117	C₄₇⋊#95	C₂³	1	2	yes	—
118	C₄₇⋊#95	C₂³	1	1	yes	characteristic
119	C₄₇⋊#95	C₂³	1	2	yes	—
120	C₄₇⋊#95	C₂³	1	4	yes	—
121	C₄₇⋊#95	C₂³	1	2	yes	—
122	C₄₇⋊#95	C₂³	1	2	yes	—
123	C₄₇⋊#95	C₂³	1	2	yes	—
124	C₄₇⋊#95	C₂³	1	4	yes	—
125	C₄₇⋊#95	C₂³	1	4	yes	—
126	C₄₇⋊#95	C₂³	1	2	yes	—
127	C₄₇⋊#95	C₂³	1	4	yes	—
128	C₄₇⋊#95	C₂³	1	4	yes	—
129	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
130	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
131	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
132	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
133	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
134	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
135	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
136	#126×C₄₇	C₂×C₄	1	16	yes	complemented
137	#125×C₄₇	C₂×C₄	1	8	yes	complemented
138	#124×C₄₇	C₂×C₄	1	8	yes	—
139	#123×C₄₇	C₂×C₄	1	16	yes	complemented
140	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
141	#121×C₄₇	C₂×C₄	1	8	yes	—
142	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
143	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
144	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
145	#117×C₄₇	C₂×C₄	1	16	yes	complemented
146	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
147	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
148	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
149	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
152	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂×C₂²⋊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×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
158	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
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	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
164	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
165	C₂×Q₈×C₄₇	—	2	4	no	—
166	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
167	C₂×D₄×C₄₇	—	2	4	no	—
168	C₂×D₄×C₄₇	—	4	2	no	—
169	C₂×D₄×C₄₇	—	4	2	no	—
170	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
171	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
172	C₂²×C₄×C₄₇	—	2	4	no	—
173	C₂²×C₄×C₄₇	—	4	1	no	—
174	C₂²×C₄×C₄₇	—	4	1	no	—
175	C₂²×C₄×C₄₇	—	4	2	no	—
176	C₂²×C₄×C₄₇	—	4	4	no	—
177	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
178	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
179	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
180	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
181	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	2	yes	—
187	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
188	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂²×Dic₄₇	—	2	8	no	—
191	C₂²×Dic₄₇	—	4	4	no	—
192	C₂²×Dic₄₇	—	4	4	no	—
193	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
194	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
195	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
196	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
197	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
198	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
199	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
200	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
201	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
202	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
203	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
204	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
205	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
206	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
207	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
208	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
209	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
210	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
211	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
212	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
213	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
214	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
215	C₂²⋊Dic₄₇	—	2	8	no	—
216	C₂²⋊Dic₄₇	—	2	8	no	—
217	C₂²⋊Dic₄₇	—	4	2	no	—
218	C₂²⋊Dic₄₇	—	4	4	no	—
219	C₂²⋊Dic₄₇	—	4	4	no	—
220	C₂²⋊Dic₄₇	—	4	2	no	—
221	C₄⋊Dic₄₇	—	2	4	no	—
222	C₄⋊Dic₄₇	—	2	8	no	—
223	C₄⋊Dic₄₇	—	4	2	no	—
224	C₄⋊Dic₄₇	—	4	4	no	—
225	C₄⋊Dic₄₇	—	4	4	no	—
226	C₄⋊Dic₄₇	—	4	2	no	—
227	C₄⋊Dic₄₇	#41	1	8	yes	—
228	C₄×Dic₄₇	—	2	4	no	—
229	C₄×Dic₄₇	—	2	4	no	—
230	C₄×Dic₄₇	—	2	8	no	—
231	C₄×Dic₄₇	—	2	8	no	—
232	C₄×Dic₄₇	—	4	2	no	—
233	C₄×Dic₄₇	—	4	4	no	—
234	C₄×Dic₄₇	—	4	4	no	—
235	C₄×Dic₄₇	—	4	4	no	—
236	C₄×Dic₄₇	—	4	2	no	—
237	C₂³×C₄₇	—	2	2	no	—
238	C₂³×C₄₇	—	2	4	no	—
239	C₂³×C₄₇	—	2	2	no	—
240	C₂³×C₄₇	—	2	2	no	—
241	C₂³×C₄₇	—	2	4	no	—
242	C₂³×C₄₇	—	2	2	no	—
243	C₂³×C₄₇	—	2	1	no	—
244	C₂³×C₄₇	—	2	1	no	—
245	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
246	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
247	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
248	Q₈×C₄₇	—	2	8	no	—
249	D₄×C₄₇	—	2	8	no	—
250	D₄×C₄₇	—	4	8	no	—
251	C₂×C₄×C₄₇	—	2	2	no	—
252	C₂×C₄×C₄₇	—	2	4	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	4	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	2	no	—
262	C₂×C₄×C₄₇	—	2	8	no	—
263	C₂×C₄×C₄₇	—	4	4	no	—
264	C₂×C₄×C₄₇	—	4	8	no	—
265	C₂×C₄×C₄₇	—	4	4	no	—
266	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
268	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
269	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
270	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
271	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
273	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
274	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
275	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
276	C₂×Dic₄₇	—	2	4	no	—
277	C₂×Dic₄₇	—	2	4	no	—
278	C₂×Dic₄₇	—	2	2	no	—
279	C₂×Dic₄₇	—	2	2	no	—
280	C₂×Dic₄₇	—	2	4	no	—
281	C₂×Dic₄₇	—	2	2	no	—
282	C₂×Dic₄₇	—	2	2	no	—
283	C₂×Dic₄₇	—	2	2	no	—
284	C₂×Dic₄₇	—	2	2	no	—
285	C₂×Dic₄₇	—	2	4	no	—
286	C₂×Dic₄₇	—	2	4	no	—
287	C₂×Dic₄₇	—	2	2	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	—	8	8	no	—
294	C₂×Dic₄₇	C₂×#41	1	8	yes	—
295	#34237	—	47	1	no	maximal, Sylow
296	C₂²×C₄₇	—	2	2	no	—
297	C₂²×C₄₇	—	2	4	no	—
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	4	no	—
301	C₂²×C₄₇	—	2	4	no	—
302	C₂²×C₄₇	—	4	4	no	—
303	C₂²×C₄₇	—	4	2	no	—
304	C₂²×C₄₇	—	4	2	no	—
305	C₂²×C₄₇	—	4	4	no	—
306	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
307	C₂²×C₄₇	C₂²×#41	1	2	yes	—
308	C₂²×C₄₇	#585	1	1	yes	characteristic
309	C₂²×C₄₇	#585	1	2	yes	—
310	C₂²×C₄₇	#585	1	1	yes	characteristic
311	C₄×C₄₇	—	2	2	no	—
312	C₄×C₄₇	—	2	4	no	—
313	C₄×C₄₇	—	2	2	no	—
314	C₄×C₄₇	—	2	2	no	—
315	C₄×C₄₇	—	2	2	no	—
316	C₄×C₄₇	—	2	4	no	—
317	C₄×C₄₇	—	2	2	no	—
318	C₄×C₄₇	—	2	4	no	—
319	C₄×C₄₇	C₄×#41	1	4	yes	—
320	Dic₄₇	—	2	8	no	—
321	Dic₄₇	—	4	2	no	—
322	Dic₄₇	—	4	2	no	—
323	Dic₄₇	—	4	2	no	—
324	Dic₄₇	—	4	4	no	—
325	Dic₄₇	—	4	2	no	—
326	C₂×#529	D₄₇	1	1	yes	characteristic
327	#2370	—	47	2	no	—
328	#2367	—	47	2	no	—
329	#2363	—	47	2	no	—
330	#2362	—	47	2	no	—
331	#2357	—	47	2	no	—
332	#2353	—	47	2	no	—
333	#2346	—	47	2	no	—
334	#2343	—	47	2	no	—
335	#2335	—	47	4	no	—
336	#2320	—	47	1	no	—
337	#2319	—	47	1	no	—
338	C₄×#126	—	47	4	no	—
339	#2283	—	47	1	no	—
340	#2276	—	47	1	no	—
341	#2275	—	47	1	no	—
342	C₄×#117	—	47	1	no	—
343	C₂×C₄₇	—	4	2	no	—
344	C₂×C₄₇	—	4	4	no	—
345	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
346	C₂×C₄₇	#3428	1	1	yes	characteristic
347	C₂×C₄₇	#3428	1	1	yes	characteristic
348	C₂×C₄₇	#3521	1	2	yes	—
349	C₂×C₄₇	#3524	1	2	yes	—
350	#529	Dic₄₇	1	16	yes	complemented
351	C₂×#126	C₂×D₄₇	1	2	yes	—
352	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
353	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
354	C₂×#123	C₂×D₄₇	1	2	yes	—
355	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
356	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
357	C₂×C₄×Q₈	—	47	2	no	—
358	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
359	C₂×C₄×D₄	—	47	2	no	—
360	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
361	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
362	C₂×#117	—	47	2	no	—
363	C₂×#117	C₂×D₄₇	1	2	yes	—
364	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
365	#391	—	47	2	no	—
366	#390	—	47	2	no	—
367	#390	—	47	4	no	—
368	#389	—	47	2	no	—
369	#389	—	47	2	no	—
370	#389	—	47	4	no	—
371	#388	—	47	4	no	—
372	#388	—	47	4	no	—
373	#388	—	47	4	no	—
374	#388	—	47	4	no	—
375	#388	—	47	4	no	—
376	#388	—	47	4	no	—
377	#387	—	47	4	no	—
378	#387	—	47	4	no	—
379	#387	—	47	4	no	—
380	#387	—	47	4	no	—
381	#386	—	47	4	no	—
382	#385	—	47	4	no	—
383	#383	—	47	2	no	—
384	#383	—	47	2	no	—
385	#382	—	47	2	no	—
386	#382	—	47	1	no	—
387	#382	—	47	1	no	—
388	#381	—	47	2	no	—
389	#381	—	47	1	no	—
390	#381	—	47	1	no	—
391	#380	—	47	2	no	—
392	#380	—	47	2	no	—
393	C₄×C₄⋊C₄	—	47	4	no	—
394	C₄×C₄⋊C₄	—	47	4	no	—
395	C₄×C₄⋊C₄	—	47	4	no	—
396	C₄×C₄⋊C₄	—	47	2	no	—
397	C₄×C₄⋊C₄	—	47	2	no	—
398	C₄×C₄⋊C₄	—	47	1	no	—
399	C₄×C₄⋊C₄	—	47	2	no	—
400	C₄×C₄⋊C₄	—	47	2	no	—
401	C₄×C₄⋊C₄	—	47	2	no	—
402	C₄×C₄⋊C₄	—	47	1	no	—
403	C₄×C₂²⋊C₄	—	47	2	no	—
404	C₄×C₂²⋊C₄	—	47	2	no	—
405	C₄×C₂²⋊C₄	—	47	2	no	—
406	C₄×C₂²⋊C₄	—	47	2	no	—
407	C₄×C₂²⋊C₄	—	47	4	no	—
408	C₄×C₂²⋊C₄	—	47	4	no	—
409	C₄×C₂²⋊C₄	—	47	4	no	—
410	#376	—	47	1	no	—
411	#376	—	47	1	no	—
412	#376	—	47	2	no	—
413	#376	—	47	2	no	—
414	C₂×#95	—	47	2	no	—
415	C₄³	—	47	2	no	—
416	C₄₇	#34237	1	1	yes	characteristic, complemented, Sylow
417	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
418	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
419	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
420	C₂³×C₄	—	47	4	no	—
421	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
422	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
423	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
424	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
425	#126	C₂×Dic₄₇	1	16	yes	complemented
426	#125	C₂×Dic₄₇	1	8	yes	complemented
427	#124	C₂×Dic₄₇	1	8	yes	—
428	#123	C₂×Dic₄₇	1	16	yes	complemented
429	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
430	#121	C₂×Dic₄₇	1	8	yes	—
431	C₄×Q₈	—	94	8	no	—
432	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
433	C₄×D₄	—	94	8	no	—
434	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
435	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
436	#117	—	94	8	no	—
437	#117	C₂×Dic₄₇	1	16	yes	complemented
438	C₂×C₄⋊C₄	—	47	2	no	—
439	C₂×C₄⋊C₄	—	47	2	no	—
440	C₂×C₄⋊C₄	—	47	4	no	—
441	C₂×C₄⋊C₄	—	47	2	no	—
442	C₂×C₄⋊C₄	—	47	2	no	—
443	C₂×C₄⋊C₄	—	47	4	no	—
444	C₂×C₄⋊C₄	—	47	4	no	—
445	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
446	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
447	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
448	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
449	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
450	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
451	C₂×C₂²⋊C₄	—	47	4	no	—
452	C₂×C₂²⋊C₄	—	47	4	no	—
453	C₂×C₂²⋊C₄	—	47	2	no	—
454	C₂×C₂²⋊C₄	—	47	2	no	—
455	C₂×C₂²⋊C₄	—	47	4	no	—
456	C₂×C₂²⋊C₄	—	47	4	no	—
457	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
458	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
459	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
460	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
461	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
462	C₂×C₄²	—	47	4	no	—
463	C₂×C₄²	—	47	2	no	—
464	C₂×C₄²	—	47	4	no	—
465	C₂×C₄²	—	47	2	no	—
466	C₂×C₄²	—	47	2	no	—
467	C₂×C₄²	—	47	4	no	—
468	C₂×C₄²	—	47	2	no	—
469	C₂×C₄²	—	47	4	no	—
470	C₂×C₄²	—	47	4	no	—
471	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
472	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
473	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
474	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
475	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
476	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
477	#95	—	47	1	no	—
478	#95	—	47	2	no	—
479	#95	—	47	4	no	—
480	#95	—	47	1	no	—
481	#95	—	47	2	no	—
482	#95	—	47	1	no	—
483	#95	—	47	2	no	—
484	#95	—	47	4	no	—
485	#95	—	47	2	no	—
486	#95	—	47	1	no	—
487	#95	—	47	4	no	—
488	#95	—	47	2	no	—
489	#95	—	47	2	no	—
490	#95	—	47	2	no	—
491	#95	—	47	4	no	—
492	#95	—	47	4	no	—
493	#95	—	47	2	no	—
494	#95	—	47	4	no	—
495	#95	—	47	4	no	—
496	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
497	C₂⁴	C₂³×D₄₇	1	2	yes	—
498	C₂×Q₈	—	2	4	no	—
499	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
500	C₂×D₄	—	2	4	no	—
501	C₂×D₄	—	4	2	no	—
502	C₂×D₄	—	4	2	no	—
503	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
504	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
505	C₂²×C₄	—	2	4	no	—
506	C₂²×C₄	—	4	1	no	—
507	C₂²×C₄	—	4	1	no	—
508	C₂²×C₄	—	4	2	no	—
509	C₂²×C₄	—	4	4	no	—
510	C₂²×C₄	—	47	4	no	—
511	C₂²×C₄	—	47	2	no	—
512	C₂²×C₄	—	47	2	no	—
513	C₂²×C₄	—	47	2	no	—
514	C₂²×C₄	—	47	4	no	—
515	C₂²×C₄	—	47	2	no	—
516	C₂²×C₄	—	94	8	no	—
517	C₂²×C₄	—	188	4	no	—
518	C₂²×C₄	—	188	4	no	—
519	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
520	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
521	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
522	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
523	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
524	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
525	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
526	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
527	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
528	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
529	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
530	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
531	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
532	C₄⋊C₄	—	47	8	no	—
533	C₄⋊C₄	—	94	8	no	—
534	C₄⋊C₄	—	94	4	no	—
535	C₄⋊C₄	—	188	4	no	—
536	C₄⋊C₄	—	188	2	no	—
537	C₄⋊C₄	—	188	2	no	—
538	C₄⋊C₄	—	188	4	no	—
539	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
540	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
541	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
542	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
543	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
544	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
545	C₂²⋊C₄	—	94	8	no	—
546	C₂²⋊C₄	—	94	8	no	—
547	C₂²⋊C₄	—	188	2	no	—
548	C₂²⋊C₄	—	188	4	no	—
549	C₂²⋊C₄	—	188	4	no	—
550	C₂²⋊C₄	—	188	2	no	—
551	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
552	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
553	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
554	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
555	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
556	C₄²	—	94	8	no	—
557	C₄²	—	94	8	no	—
558	C₄²	—	94	4	no	—
559	C₄²	—	94	4	no	—
560	C₄²	—	188	2	no	—
561	C₄²	—	188	4	no	—
562	C₄²	—	188	2	no	—
563	C₄²	—	188	4	no	—
564	C₄²	—	188	4	no	—
565	C₄²	C₂²×Dic₄₇	1	4	yes	—
566	C₄²	C₂²×Dic₄₇	1	4	yes	—
567	C₄²	C₂²×Dic₄₇	1	4	yes	—
568	C₄²	C₂²×Dic₄₇	1	4	yes	—
569	C₄²	C₂²×Dic₄₇	1	8	yes	—
570	C₂³	—	2	2	no	—
571	C₂³	—	2	4	no	—
572	C₂³	—	2	2	no	—
573	C₂³	—	2	2	no	—
574	C₂³	—	2	4	no	—
575	C₂³	—	2	1	no	—
576	C₂³	—	2	1	no	—
577	C₂³	—	2	2	no	—
578	C₂³	C₂³×Dic₄₇	1	4	yes	—
579	C₂³	C₂³×Dic₄₇	1	2	yes	—
580	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
581	Q₈	—	2	8	no	—
582	D₄	—	2	8	no	—
583	D₄	—	4	8	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	1	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	1	no	—
589	C₂×C₄	—	2	2	no	—
590	C₂×C₄	—	2	4	no	—
591	C₂×C₄	—	2	1	no	—
592	C₂×C₄	—	2	1	no	—
593	C₂×C₄	—	2	2	no	—
594	C₂×C₄	—	2	2	no	—
595	C₂×C₄	—	2	8	no	—
596	C₂×C₄	—	4	4	no	—
597	C₂×C₄	—	4	8	no	—
598	C₂×C₄	—	4	4	no	—
599	C₂×C₄	—	47	8	no	—
600	C₂×C₄	—	94	4	no	—
601	C₂×C₄	—	94	4	no	—
602	C₂×C₄	—	94	2	no	—
603	C₂×C₄	—	94	2	no	—
604	C₂×C₄	—	94	4	no	—
605	C₂×C₄	—	94	2	no	—
606	C₂×C₄	—	94	2	no	—
607	C₂×C₄	—	94	2	no	—
608	C₂×C₄	—	94	2	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	2	no	—
616	C₂×C₄	—	94	2	no	—
617	C₂×C₄	—	376	8	no	—
618	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
619	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
620	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
621	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
622	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
623	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
624	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
625	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
626	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
627	C₂×C₄	#41×D₄₇	1	4	yes	—
628	C₂²	—	2	2	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	2	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	2	4	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	2	no	—
636	C₂²	—	4	2	no	—
637	C₂²	—	4	4	no	—
638	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
639	C₂²	C₂×#41×D₄₇	1	2	yes	—
640	C₂²	#15689959	1	1	yes	characteristic
641	C₂²	#15689959	1	2	yes	—
642	C₂²	#15689959	1	1	yes	characteristic
643	C₄	—	2	2	no	—
644	C₄	—	2	4	no	—
645	C₄	—	2	2	no	—
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	4	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	4	no	—
651	C₄	—	94	8	no	—
652	C₄	—	188	2	no	—
653	C₄	—	188	2	no	—
654	C₄	—	188	2	no	—
655	C₄	—	188	2	no	—
656	C₄	—	188	4	no	—
657	C₄	#41×Dic₄₇	1	4	yes	—
658	C₂	—	4	2	no	—
659	C₂	—	4	4	no	—
660	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
661	C₂	#20256591	1	1	yes	characteristic
662	C₂	#20256591	1	1	yes	characteristic
663	C₂	#20257450	1	2	yes	—
664	C₂	#20257487	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	#34237
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. #20246419	C₂	semidirect
5. #20246361	C₂	semidirect
6. #20246328	C₂	semidirect
7. #20246273	C₂	semidirect
8. #20246248	C₂	semidirect
9. #20246182	C₂	semidirect
10. #20246039	C₂	semidirect
11. #20246031	C₂	semidirect
12. #126×Dic₄₇	C₂	semidirect
13. #20245786	C₂	semidirect
14. #20245753	C₂	semidirect
15. #20245749	C₂	semidirect
16. C₄×#13093983	C₂	semidirect
72. C₄₇×#529	C₄	semidirect
136. #126×C₄₇	C₂×C₄	semidirect
137. #125×C₄₇	C₂×C₄	semidirect
139. #123×C₄₇	C₂×C₄	semidirect
140. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
142. C₄×Q₈×C₄₇	C₂×C₄	semidirect
144. C₄×D₄×C₄₇	C₂×C₄	semidirect
145. #117×C₄₇	C₂×C₄	semidirect
157. C₂×C₄²×C₄₇	C₂×C₄	semidirect
350. #529	Dic₄₇	semidirect
416. C₄₇	#34237	semidirect
425. #126	C₂×Dic₄₇	semidirect
426. #125	C₂×Dic₄₇	semidirect
428. #123	C₂×Dic₄₇	semidirect
429. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
432. C₄×Q₈	C₂×Dic₄₇	semidirect
435. C₄×D₄	C₂×Dic₄₇	semidirect
437. #117	C₂×Dic₄₇	semidirect
471. 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
#20246430	2
#20246419	2
#20246361	2
#20246328	2
#20246273	2
#20246248	2
#20246182	2
#20246039	2
#20246031	2
#126×Dic₄₇	2
#20245786	2
#20245753	2
#20245749	2
C₄×#13093983	2
C₂×C₄₇×#529	2
#34237	47