Subgroups — #26121849

Order 12032.

1370 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093948	C₂	1	2	yes	maximal
2	C₂×#15688885	C₂	1	2	yes	maximal
3	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
4	#20241618	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
8	C₂×#13093948	—	2	4	no	—
9	C₂×#13093948	—	2	4	no	—
10	C₂×#13093948	C₄	1	8	yes	complemented
11	C₂×C₄₇⋊#95	—	2	1	no	—
12	C₂×C₄₇⋊#95	—	2	1	no	—
13	#15688885	—	2	4	no	—
14	#15688878	—	2	2	no	—
15	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
17	C₂×C₄×Q₈×C₄₇	—	2	4	no	—
18	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
19	C₂×C₄×Q₈×C₄₇	C₄	1	4	yes	complemented
20	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	—	2	1	no	—
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₂³×Dic₄₇	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	2	no	—
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	C₂²×C₄₇⋊C₈	—	2	2	no	—
28	C₂²×C₄₇⋊C₈	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂²×C₄₇⋊C₈	—	2	2	no	—
31	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	2	no	—
36	C₂×C₄⋊Dic₄₇	—	2	2	no	—
37	C₂×C₄⋊Dic₄₇	C₂×C₄	1	4	yes	—
38	#13093948	—	2	16	no	—
39	C₄₇⋊#95	—	4	2	no	—
40	C₄₇⋊#95	—	4	2	no	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	—	2	2	no	—
43	C₂²×Q₈×C₄₇	—	2	2	no	—
44	C₂²×Q₈×C₄₇	—	2	1	no	—
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
47	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
48	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
49	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
50	C₂²×Q₈×C₄₇	Q₈	1	2	yes	—
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
56	C₄×Q₈×C₄₇	—	2	16	no	—
57	C₄×Q₈×C₄₇	—	2	8	no	—
58	C₄×Q₈×C₄₇	—	2	8	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
65	C₂×C₄²×C₄₇	—	2	8	no	—
66	C₂×C₄²×C₄₇	—	2	4	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	D₄	1	2	yes	—
71	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
72	C₂×Q₈×C₄₇	—	2	2	no	—
73	C₂×Q₈×C₄₇	—	2	2	no	—
74	C₂×Q₈×C₄₇	—	2	2	no	—
75	C₂×Q₈×C₄₇	—	2	4	no	—
76	C₂×Q₈×C₄₇	—	2	4	no	—
77	C₂×Q₈×C₄₇	—	2	4	no	—
78	C₂×Q₈×C₄₇	—	2	4	no	—
79	C₂×Q₈×C₄₇	—	2	2	no	—
80	C₂×Q₈×C₄₇	—	2	4	no	—
81	C₂×Q₈×C₄₇	—	2	2	no	—
82	C₂×Q₈×C₄₇	—	2	4	no	—
83	C₂×Q₈×C₄₇	—	2	4	no	—
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	C₄²	1	4	yes	—
86	C₂×Q₈×C₄₇	C₂²⋊C₄	1	8	yes	—
87	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
88	C₂×Q₈×C₄₇	C₄⋊C₄	1	8	yes	—
89	C₂×Q₈×C₄₇	C₄⋊C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	4	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	—	4	1	no	—
106	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
109	C₂²×C₄×C₄₇	Q₁₆	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	2	yes	—
120	C₂²×Dic₄₇	—	2	4	no	—
121	C₂²×Dic₄₇	—	4	2	no	—
122	C₂²×Dic₄₇	—	4	2	no	—
123	C₂²×Dic₄₇	—	4	2	no	—
124	C₂²×Dic₄₇	—	4	2	no	—
125	C₂²×Dic₄₇	—	4	2	no	—
126	C₂²×Dic₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	2	16	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
131	C₄²×C₄₇	—	2	16	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	—	2	2	no	—
134	C₄²×C₄₇	—	2	4	no	—
135	C₄⋊Dic₄₇	—	2	4	no	—
136	C₄⋊Dic₄₇	—	2	4	no	—
137	C₄⋊Dic₄₇	—	4	2	no	—
138	C₄⋊Dic₄₇	—	4	2	no	—
139	C₂×C₄₇⋊C₈	—	2	4	no	—
140	C₂×C₄₇⋊C₈	—	2	4	no	—
141	C₂×C₄₇⋊C₈	—	2	4	no	—
142	C₂×C₄₇⋊C₈	—	4	2	no	—
143	C₂×C₄₇⋊C₈	—	4	2	no	—
144	C₂×C₄₇⋊C₈	—	4	2	no	—
145	C₂×C₄₇⋊C₈	—	4	2	no	—
146	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₄×D₄	1	2	yes	—
148	C₂³×C₄₇	#120	1	2	yes	—
149	C₂³×C₄₇	#121	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
152	C₂³×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
153	C₂³×C₄₇	#135	1	2	yes	—
154	C₂³×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
155	C₂³×C₄₇	#137	1	1	yes	characteristic
156	C₂³×C₄₇	#137	1	2	yes	—
157	Q₈×C₄₇	—	2	4	no	—
158	Q₈×C₄₇	—	2	4	no	—
159	Q₈×C₄₇	—	2	4	no	—
160	Q₈×C₄₇	—	2	8	no	—
161	Q₈×C₄₇	—	2	8	no	—
162	Q₈×C₄₇	#95	1	8	yes	complemented
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	2	8	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	4	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	4	no	—
182	C₂×C₄×C₄₇	#103	1	4	yes	complemented
183	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
190	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
194	C₂×C₄×C₄₇	#120	1	2	yes	—
195	C₂×C₄×C₄₇	#121	1	2	yes	—
196	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
198	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
199	C₂×C₄×C₄₇	#123	1	2	yes	—
200	C₂×C₄×C₄₇	#123	1	2	yes	—
201	C₂×Dic₄₇	—	4	4	no	—
202	C₂×Dic₄₇	—	4	4	no	—
203	C₂×Dic₄₇	—	4	4	no	—
204	C₂×Dic₄₇	—	8	2	no	—
205	C₂×Dic₄₇	—	8	2	no	—
206	C₂×Dic₄₇	—	8	2	no	—
207	C₂×Dic₄₇	—	8	2	no	—
208	C₄₇⋊C₈	—	4	4	no	—
209	#10789	—	47	1	no	maximal, Sylow
210	C₂²×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
211	C₂²×C₄₇	#379	1	1	yes	characteristic
212	C₂²×C₄₇	#380	1	1	yes	characteristic
213	C₂²×C₄₇	#385	1	2	yes	—
214	C₂²×C₄₇	#386	1	2	yes	—
215	C₂²×C₄₇	C₂×#103	1	1	yes	characteristic
216	C₂²×C₄₇	#416	1	1	yes	characteristic
217	C₂²×C₄₇	#417	1	1	yes	characteristic
218	C₂²×C₄₇	#419	1	1	yes	characteristic
219	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
220	C₂²×C₄₇	C₄×Q₁₆	1	2	yes	—
221	C₂²×C₄₇	#440	1	2	yes	—
222	C₂²×C₄₇	#441	1	2	yes	—
223	C₂²×C₄₇	#448	1	2	yes	—
224	C₂²×C₄₇	#449	1	2	yes	—
225	C₂²×C₄₇	#451	1	2	yes	—
226	C₂²×C₄₇	#452	1	2	yes	—
227	C₂²×C₄₇	#460	1	1	yes	characteristic
228	C₂²×C₄₇	#462	1	1	yes	characteristic
229	C₂²×C₄₇	#464	1	2	yes	—
230	C₂²×C₄₇	#475	1	1	yes	characteristic
231	C₂²×C₄₇	#477	1	1	yes	characteristic
232	C₂²×C₄₇	#479	1	2	yes	—
233	C₄×C₄₇	—	2	8	no	—
234	C₄×C₄₇	—	2	4	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	4	no	—
237	C₄×C₄₇	C₂×#95	1	1	yes	characteristic
238	C₄×C₄₇	C₄×C₂²⋊C₄	1	1	yes	characteristic
239	C₄×C₄₇	#380	1	1	yes	characteristic
240	C₄×C₄₇	#381	1	1	yes	characteristic
241	C₄×C₄₇	#385	1	2	yes	—
242	C₄×C₄₇	#386	1	2	yes	—
243	Dic₄₇	—	8	4	no	—
244	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
245	C₂²×#103	—	47	2	no	—
246	C₂×#340	—	47	2	no	—
247	C₂×#336	—	47	1	no	—
248	C₄⋊#95	—	47	1	no	—
249	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
250	C₂×C₄₇	C₄×#103	1	1	yes	characteristic
251	C₂×C₄₇	#1763	1	1	yes	characteristic
252	C₂×C₄₇	#1787	1	1	yes	characteristic
253	C₂×C₄₇	#1788	1	1	yes	characteristic
254	C₂×C₄₇	#1803	1	1	yes	characteristic
255	C₂×C₄₇	#1805	1	1	yes	characteristic
256	C₂×C₄₇	#1863	1	2	yes	—
257	C₂×C₄₇	#1865	1	2	yes	—
258	C₂×C₄₇	#1878	1	2	yes	—
259	C₂×C₄₇	#1880	1	2	yes	—
260	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂³×C₈	—	47	2	no	—
262	C₂×C₄×Q₈	—	2	4	no	—
263	C₂×C₄×Q₈	—	2	4	no	—
264	C₂×C₄×Q₈	—	2	2	no	—
265	C₂×C₄×Q₈	Dic₄₇	1	4	yes	complemented
266	C₂²×C₄⋊C₄	—	2	1	no	—
267	C₂²×C₄⋊C₄	—	47	2	no	—
268	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
269	C₂²×C₄²	—	2	1	no	—
270	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
271	C₂×#103	—	47	8	no	—
272	C₂×#103	—	94	4	no	—
273	C₂×#103	—	94	4	no	—
274	C₂×#95	—	94	1	no	—
275	C₂×#95	—	94	1	no	—
276	#340	—	94	4	no	—
277	#336	—	94	2	no	—
278	C₄₇	#10789	1	1	yes	characteristic, complemented, Sylow
279	C₂²×Q₈	—	2	2	no	—
280	C₂²×Q₈	—	2	1	no	—
281	C₂²×Q₈	—	2	1	no	—
282	C₂²×Q₈	—	2	1	no	—
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	Dic₉₄	1	2	yes	—
285	C₂²×Q₈	C₄×D₄₇	1	4	yes	—
286	C₂²×Q₈	D₁₈₈	1	2	yes	—
287	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
288	C₂²×Q₈	C₂²⋊D₄₇	1	4	yes	—
289	C₂³×C₄	—	2	1	no	—
290	C₂³×C₄	—	2	1	no	—
291	C₂³×C₄	—	94	2	no	—
292	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
293	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	47	4	no	—
296	C₂²×C₈	—	94	2	no	—
297	C₂²×C₈	—	94	2	no	—
298	C₂²×C₈	—	94	2	no	—
299	C₂²×C₈	—	94	2	no	—
300	C₂²×C₈	—	94	2	no	—
301	C₂²×C₈	—	94	2	no	—
302	C₄×Q₈	—	2	16	no	—
303	C₄×Q₈	—	2	8	no	—
304	C₄×Q₈	—	2	8	no	—
305	C₂×C₄⋊C₄	—	2	8	no	—
306	C₂×C₄⋊C₄	—	2	4	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	1	no	—
309	C₂×C₄⋊C₄	—	47	4	no	—
310	C₂×C₄⋊C₄	—	94	2	no	—
311	C₂×C₄⋊C₄	—	94	2	no	—
312	C₂×C₄⋊C₄	—	94	2	no	—
313	C₂×C₄⋊C₄	—	94	2	no	—
314	C₂×C₄⋊C₄	—	94	2	no	—
315	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
316	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	4	yes	—
317	C₂×C₄²	—	2	8	no	—
318	C₂×C₄²	—	2	4	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
322	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
323	#103	—	94	16	no	—
324	#95	—	188	2	no	—
325	#95	—	188	2	no	—
326	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	4	no	—
331	C₂×Q₈	—	2	4	no	—
332	C₂×Q₈	—	2	4	no	—
333	C₂×Q₈	—	2	4	no	—
334	C₂×Q₈	—	2	2	no	—
335	C₂×Q₈	—	2	4	no	—
336	C₂×Q₈	—	2	2	no	—
337	C₂×Q₈	—	2	4	no	—
338	C₂×Q₈	—	2	4	no	—
339	C₂×Q₈	—	2	4	no	—
340	C₂×Q₈	C₄×Dic₄₇	1	4	yes	—
341	C₂×Q₈	Dic₄₇⋊C₄	1	8	yes	—
342	C₂×Q₈	C₄⋊Dic₄₇	1	4	yes	—
343	C₂×Q₈	(C₂×D₄₇)⋊C₄	1	8	yes	—
344	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	4	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	4	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	4	2	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	94	4	no	—
362	C₂²×C₄	—	188	2	no	—
363	C₂²×C₄	—	188	2	no	—
364	C₂²×C₄	—	188	2	no	—
365	C₂²×C₄	—	188	2	no	—
366	C₂²×C₄	—	188	2	no	—
367	C₂²×C₄	—	188	2	no	—
368	C₂²×C₄	#10625336	1	2	yes	—
369	C₂²×C₄	#10625337	1	2	yes	—
370	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
371	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
372	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
373	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
374	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
375	C₂²×C₄	#10625350	1	1	yes	characteristic
376	C₂²×C₄	#10625350	1	1	yes	characteristic
377	C₂²×C₄	#10625350	1	2	yes	—
378	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
380	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
381	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
382	C₂×C₈	—	94	4	no	—
383	C₂×C₈	—	94	4	no	—
384	C₂×C₈	—	94	4	no	—
385	C₂×C₈	—	188	2	no	—
386	C₂×C₈	—	188	2	no	—
387	C₂×C₈	—	188	2	no	—
388	C₂×C₈	—	188	2	no	—
389	C₄⋊C₄	—	2	16	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	4	no	—
392	C₄⋊C₄	—	94	4	no	—
393	C₄⋊C₄	—	94	4	no	—
394	C₄⋊C₄	—	188	2	no	—
395	C₄⋊C₄	—	188	2	no	—
396	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
397	C₄²	—	2	16	no	—
398	C₄²	—	2	2	no	—
399	C₄²	—	2	2	no	—
400	C₄²	—	2	4	no	—
401	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
402	C₂³	C₄×C₂²⋊D₄₇	1	2	yes	—
403	C₂³	#13093993	1	2	yes	—
404	C₂³	#13093998	1	1	yes	characteristic
405	C₂³	#13094003	1	1	yes	characteristic
406	C₂³	C₂×#10625336	1	1	yes	characteristic
407	C₂³	C₂×#10625337	1	1	yes	characteristic
408	C₂³	#13094044	1	2	yes	—
409	C₂³	#13094049	1	1	yes	characteristic
410	C₂³	#13094054	1	1	yes	characteristic
411	C₂³	#13094055	1	2	yes	—
412	Q₈	—	2	4	no	—
413	Q₈	—	2	4	no	—
414	Q₈	—	2	4	no	—
415	Q₈	—	2	8	no	—
416	Q₈	—	2	8	no	—
417	Q₈	C₄₇⋊#95	1	8	yes	complemented
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	8	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	4	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	4	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	376	2	no	—
438	C₂×C₄	—	376	2	no	—
439	C₂×C₄	—	376	2	no	—
440	C₂×C₄	—	376	2	no	—
441	C₂×C₄	—	188	4	no	—
442	C₂×C₄	—	188	4	no	—
443	C₂×C₄	—	188	4	no	—
444	C₂×C₄	#13093948	1	4	yes	complemented
445	C₂×C₄	C₂×C₄×Dic₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	2	yes	—
447	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
448	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
450	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
451	C₂×C₄	#13093983	1	1	yes	characteristic
452	C₂×C₄	#13093983	1	1	yes	characteristic
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	2	yes	—
456	C₂×C₄	#13093993	1	2	yes	—
457	C₂×C₄	#13093998	1	2	yes	—
458	C₂×C₄	#13093998	1	1	yes	characteristic
459	C₂×C₄	#13094003	1	2	yes	—
460	C₂×C₄	#13094003	1	1	yes	characteristic
461	C₂×C₄	#13094007	1	2	yes	—
462	C₂×C₄	#13094007	1	2	yes	—
463	C₈	—	188	4	no	—
464	C₂²	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
465	C₂²	#15688979	1	1	yes	characteristic
466	C₂²	#15688983	1	1	yes	characteristic
467	C₂²	#15688996	1	2	yes	—
468	C₂²	#15689002	1	2	yes	—
469	C₂²	C₂×#13093948	1	1	yes	characteristic
470	C₂²	#15689119	1	1	yes	characteristic
471	C₂²	#15689124	1	1	yes	characteristic
472	C₂²	#15689132	1	1	yes	characteristic
473	C₂²	C₄×#10625336	1	2	yes	—
474	C₂²	C₄×#10625337	1	2	yes	—
475	C₂²	#15689221	1	2	yes	—
476	C₂²	#15689228	1	2	yes	—
477	C₂²	#15689262	1	2	yes	—
478	C₂²	#15689268	1	2	yes	—
479	C₂²	#15689279	1	2	yes	—
480	C₂²	#15689285	1	2	yes	—
481	C₂²	#15689323	1	1	yes	characteristic
482	C₂²	#15689333	1	1	yes	characteristic
483	C₂²	#15689345	1	2	yes	—
484	C₂²	#15689408	1	1	yes	characteristic
485	C₂²	#15689418	1	1	yes	characteristic
486	C₂²	#15689430	1	2	yes	—
487	C₄	—	2	4	no	—
488	C₄	—	2	8	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	376	4	no	—
492	C₄	C₂×C₄₇⋊#95	1	1	yes	characteristic
493	C₄	C₄×C₂²⋊Dic₄₇	1	1	yes	characteristic
494	C₄	#15688983	1	1	yes	characteristic
495	C₄	#15688986	1	1	yes	characteristic
496	C₄	#15688996	1	2	yes	—
497	C₄	#15689002	1	2	yes	—
498	C₂	#20241611	1	1	yes	characteristic
499	C₂	C₄×#13093948	1	1	yes	characteristic
500	C₂	#20243218	1	1	yes	characteristic
501	C₂	#20243323	1	1	yes	characteristic
502	C₂	#20243328	1	1	yes	characteristic
503	C₂	#20243393	1	1	yes	characteristic
504	C₂	#20243403	1	1	yes	characteristic
505	C₂	#20243642	1	2	yes	—
506	C₂	#20243656	1	2	yes	—
507	C₂	#20243729	1	2	yes	—
508	C₂	#20243743	1	2	yes	—

	subgroup	G/H
center	C₂⁴	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	#10789
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄² ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
10. C₂×#13093948	C₄	semidirect
19. C₂×C₄×Q₈×C₄₇	C₄	semidirect
162. Q₈×C₄₇	#95	semidirect
182. C₂×C₄×C₄₇	#103	semidirect
265. C₂×C₄×Q₈	Dic₄₇	semidirect
278. C₄₇	#10789	semidirect
417. Q₈	C₄₇⋊#95	semidirect
444. C₂×C₄	#13093948	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093948	2
C₂×#15688885	2
C₂×#15688878	2
#20241618	2
C₂²×C₄×Q₈×C₄₇	2
#10789	47