Subgroups — #26224213

Order 12032.

848 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689254	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689193	C₂	1	1	yes	maximal, characteristic
3	#20246671	C₂	1	1	yes	maximal, characteristic
4	#20244182	C₂	1	1	yes	maximal, characteristic
5	#20244002	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244002	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243995	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243995	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243507	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243170	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243168	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243163	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243074	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
19	#15689254	—	2	4	no	—
20	#15689193	—	2	4	no	—
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×#13093935	C₂²	1	1	yes	characteristic
31	C₂×#13093935	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
37	#15689062	C₄	1	1	yes	characteristic
38	#15689062	C₄	1	1	yes	characteristic
39	#15689049	C₄	1	1	yes	characteristic
40	#15689049	C₄	1	1	yes	characteristic
41	#15689040	C₄	1	1	yes	characteristic
42	#15689040	C₄	1	1	yes	characteristic
43	#15689034	C₄	1	1	yes	characteristic
44	#15689034	C₄	1	1	yes	characteristic
45	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
47	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
48	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
49	#15688969	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
64	C₂×#10625324	—	2	2	no	—
65	C₂×#10625324	—	2	2	no	—
66	C₂×#10625324	—	2	2	no	—
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂×C₈×D₄₇	—	2	2	no	—
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	—	2	2	no	—
74	C₄×D₁₈₈	—	2	2	no	—
75	C₄×D₁₈₈	—	2	2	no	—
76	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
85	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
90	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
91	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
92	(C₂×D₄₇)⋊C₈	—	2	2	no	—
93	(C₂×D₄₇)⋊C₈	—	2	2	no	—
94	(C₂×D₄₇)⋊C₈	—	2	2	no	—
95	(C₂×D₄₇)⋊C₈	—	2	2	no	—
96	(C₂×D₄₇)⋊C₈	—	2	2	no	—
97	(C₂×D₄₇)⋊C₈	—	2	2	no	—
98	#13093935	—	2	2	no	—
99	#13093935	D₄	1	4	yes	—
100	#13093934	—	2	2	no	—
101	#13093934	—	2	2	no	—
102	C₄×C₄₇⋊C₈	—	2	2	no	—
103	C₈×Dic₄₇	—	2	2	no	—
104	C₈×Dic₄₇	—	2	2	no	—
105	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
106	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₄×Q₈×C₄₇	—	2	2	no	—
123	C₄×Q₈×C₄₇	—	2	2	no	—
124	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	C₄⋊C₈×C₄₇	—	2	2	no	—
131	C₄×C₈×C₄₇	—	2	2	no	—
132	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂×Q₈×C₄₇	—	2	2	no	—
135	C₂×Q₈×C₄₇	—	2	2	no	—
136	C₂×Q₈×C₄₇	—	4	1	no	—
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×D₁₈₈	—	2	2	no	—
151	C₂×D₁₈₈	—	2	2	no	—
152	C₂×D₁₈₈	—	4	1	no	—
153	C₂×C₄×D₄₇	—	2	1	no	—
154	C₂×C₄×D₄₇	—	2	1	no	—
155	C₂×C₄×D₄₇	—	2	1	no	—
156	C₂×C₄×D₄₇	—	2	1	no	—
157	C₂×C₄×D₄₇	—	2	1	no	—
158	C₂×C₄×D₄₇	—	2	1	no	—
159	C₂×C₄×D₄₇	—	2	1	no	—
160	C₂×C₄×D₄₇	—	2	1	no	—
161	C₂×C₄×D₄₇	—	2	1	no	—
162	C₂×C₄×D₄₇	—	2	1	no	—
163	C₂×C₄×D₄₇	—	2	1	no	—
164	C₂×C₄×D₄₇	—	2	1	no	—
165	C₂×C₈×C₄₇	—	2	1	no	—
166	C₂×C₈×C₄₇	—	2	1	no	—
167	C₂×C₈×C₄₇	—	2	1	no	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	1	no	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	#41	1	2	yes	—
176	C₂×C₈×C₄₇	#41	1	2	yes	—
177	C₄⋊C₄×C₄₇	—	2	2	no	—
178	C₄⋊C₄×C₄₇	—	2	2	no	—
179	C₄⋊C₄×C₄₇	—	2	2	no	—
180	C₄²×C₄₇	—	2	1	no	—
181	C₄²×C₄₇	—	2	1	no	—
182	C₄²×C₄₇	—	2	1	no	—
183	C₄²×C₄₇	—	2	1	no	—
184	C₄²×C₄₇	C₂×D₄	1	2	yes	—
185	C₄²×C₄₇	#41	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	—	2	2	no	—
187	(C₂×D₄₇)⋊C₄	—	2	2	no	—
188	(C₂×D₄₇)⋊C₄	—	2	2	no	—
189	(C₂×D₄₇)⋊C₄	—	2	2	no	—
190	(C₂×D₄₇)⋊C₄	—	2	2	no	—
191	(C₂×D₄₇)⋊C₄	—	2	2	no	—
192	(C₂×D₄₇)⋊C₄	—	4	1	no	—
193	(C₂×D₄₇)⋊C₄	—	4	1	no	—
194	(C₂×D₄₇)⋊C₄	—	4	1	no	—
195	(C₂×D₄₇)⋊C₄	—	4	1	no	—
196	C₄⋊Dic₄₇	—	2	2	no	—
197	C₄×Dic₄₇	—	2	1	no	—
198	C₄×Dic₄₇	—	2	1	no	—
199	C₄×Dic₄₇	—	2	1	no	—
200	C₄×Dic₄₇	—	2	1	no	—
201	C₂×C₄₇⋊C₈	—	2	1	no	—
202	C₂×C₄₇⋊C₈	—	2	1	no	—
203	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	1	no	—
206	C₂×C₄₇⋊C₈	—	2	1	no	—
207	C₂×C₄₇⋊C₈	—	2	1	no	—
208	C₂×C₄₇⋊C₈	—	2	1	no	—
209	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
210	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
211	C₂×C₄₇⋊C₈	#41	1	2	yes	—
212	C₂×C₄₇⋊C₈	#41	1	2	yes	—
213	#10625324	—	4	4	no	—
214	C₈×D₄₇	—	4	4	no	—
215	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
216	C₂²×D₄₇	—	2	1	no	—
217	C₂²×D₄₇	—	2	1	no	—
218	C₂²×D₄₇	—	2	1	no	—
219	C₂²×D₄₇	—	2	1	no	—
220	C₂²×D₄₇	—	2	1	no	—
221	C₂²×D₄₇	—	2	1	no	—
222	C₂²×D₄₇	—	2	1	no	—
223	C₂²×D₄₇	—	2	1	no	—
224	C₂²×D₄₇	—	2	1	no	—
225	C₂²×D₄₇	—	2	1	no	—
226	C₂²×D₄₇	—	2	1	no	—
227	C₂²×D₄₇	—	2	1	no	—
228	C₂²×D₄₇	—	2	1	no	—
229	C₂²×D₄₇	#131	1	2	yes	—
230	Q₈×C₄₇	—	4	4	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
247	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
248	C₂×C₄×C₄₇	#131	1	2	yes	—
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
255	C₂×Dic₄₇	—	2	1	no	—
256	C₂×Dic₄₇	—	2	1	no	—
257	C₂×Dic₄₇	—	2	1	no	—
258	C₂×Dic₄₇	—	2	1	no	—
259	C₂×Dic₄₇	—	2	1	no	—
260	C₂×Dic₄₇	—	2	1	no	—
261	C₂×Dic₄₇	—	2	1	no	—
262	C₂×Dic₄₇	—	2	1	no	—
263	C₂×Dic₄₇	—	2	1	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	2	1	no	—
267	C₂×Dic₄₇	—	2	1	no	—
268	C₂×Dic₄₇	—	2	1	no	—
269	C₂×Dic₄₇	—	2	1	no	—
270	C₂×Dic₄₇	—	2	1	no	—
271	C₂×Dic₄₇	—	2	1	no	—
272	C₂×Dic₄₇	—	2	1	no	—
273	D₁₈₈	—	4	4	no	—
274	C₄×D₄₇	—	4	1	no	—
275	C₄×D₄₇	—	4	1	no	—
276	C₄×D₄₇	—	4	1	no	—
277	C₄×D₄₇	—	4	1	no	—
278	C₄×D₄₇	—	4	1	no	—
279	C₄×D₄₇	—	4	1	no	—
280	C₄×D₄₇	—	4	1	no	—
281	C₄×D₄₇	—	4	1	no	—
282	C₈×C₄₇	—	2	2	no	—
283	C₈×C₄₇	—	2	2	no	—
284	C₈×C₄₇	—	4	1	no	—
285	C₈×C₄₇	—	4	1	no	—
286	C₄₇⋊C₈	—	2	2	no	—
287	C₄₇⋊C₈	—	4	1	no	—
288	C₄₇⋊C₈	—	4	1	no	—
289	C₄₇⋊C₈	#124	1	4	yes	—
290	#21637	—	47	1	no	maximal, Sylow
291	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
292	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
293	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
294	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
295	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
296	C₂²×C₄₇	#568	1	1	yes	characteristic
297	C₂²×C₄₇	#568	1	1	yes	characteristic
298	C₂×D₄₇	—	2	2	no	—
299	C₂×D₄₇	—	2	2	no	—
300	C₂×D₄₇	—	2	2	no	—
301	C₂×D₄₇	—	4	1	no	—
302	C₂×D₄₇	—	4	1	no	—
303	C₂×D₄₇	—	4	1	no	—
304	C₂×D₄₇	—	4	1	no	—
305	C₂×D₄₇	—	4	1	no	—
306	C₂×D₄₇	—	4	1	no	—
307	C₂×D₄₇	—	4	1	no	—
308	C₂×D₄₇	—	4	1	no	—
309	C₂×D₄₇	—	4	1	no	—
310	C₂×D₄₇	—	4	1	no	—
311	C₂×D₄₇	—	4	1	no	—
312	C₄×C₄₇	—	2	2	no	—
313	C₄×C₄₇	—	2	2	no	—
314	C₄×C₄₇	—	2	2	no	—
315	C₄×C₄₇	—	4	1	no	—
316	C₄×C₄₇	—	4	1	no	—
317	C₄×C₄₇	—	4	1	no	—
318	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
319	C₄×C₄₇	#529	1	1	yes	characteristic
320	C₄×C₄₇	#529	1	1	yes	characteristic
321	C₄×C₄₇	#532	1	1	yes	characteristic
322	Dic₄₇	—	4	1	no	—
323	Dic₄₇	—	4	1	no	—
324	Dic₄₇	—	4	1	no	—
325	Dic₄₇	—	4	1	no	—
326	Dic₄₇	—	4	1	no	—
327	Dic₄₇	—	4	1	no	—
328	C₂×#446	—	47	1	no	—
329	C₂×#435	—	47	1	no	—
330	#2398	—	47	1	no	—
331	#1984	D₄₇	1	1	yes	characteristic, complemented
332	#1954	—	47	1	no	—
333	#1924	—	47	1	no	—
334	#1924	—	47	1	no	—
335	#1923	—	47	1	no	—
336	#1923	—	47	1	no	—
337	#1832	—	47	1	no	—
338	#1753	—	47	1	no	—
339	#1753	—	47	1	no	—
340	#1752	—	47	1	no	—
341	C₈×C₂²⋊C₄	—	47	1	no	—
342	#1726	—	47	1	no	—
343	C₂×C₄₇	C₄×#124	1	1	yes	characteristic
344	C₂×C₄₇	#2933	1	1	yes	characteristic
345	C₂×C₄₇	#2933	1	1	yes	characteristic
346	C₂×C₄₇	#2966	1	1	yes	characteristic
347	C₂×C₄₇	#2967	1	1	yes	characteristic
348	C₂×C₄₇	#2968	1	1	yes	characteristic
349	C₂×C₄₇	#2969	1	1	yes	characteristic
350	D₄₇	—	4	2	no	—
351	D₄₇	—	8	1	no	—
352	C₂²×M₁₆	—	47	1	no	—
353	C₂³×C₈	—	47	1	no	—
354	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
355	C₂×C₄×D₄	—	47	1	no	—
356	#446	—	94	4	no	—
357	#435	—	94	4	no	—
358	C₂×C₄⋊C₈	—	47	1	no	—
359	C₂×C₄⋊C₈	—	47	1	no	—
360	C₂×C₄⋊C₈	—	47	1	no	—
361	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
362	C₂×C₂²⋊C₈	—	47	1	no	—
363	C₂×C₂²⋊C₈	—	47	1	no	—
364	C₂×C₂²⋊C₈	—	47	1	no	—
365	C₂×C₂²⋊C₈	—	47	1	no	—
366	C₂×C₂²⋊C₈	—	47	1	no	—
367	C₂×C₂²⋊C₈	—	47	1	no	—
368	C₂×#97	—	47	1	no	—
369	C₂×#97	—	47	1	no	—
370	C₂×#97	—	47	1	no	—
371	C₂×#97	—	47	1	no	—
372	C₂×C₄×C₈	—	47	1	no	—
373	C₂×C₄×C₈	—	47	1	no	—
374	C₂×C₄×C₈	—	47	1	no	—
375	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
376	#400	—	47	1	no	—
377	#400	—	47	1	no	—
378	#397	—	47	1	no	—
379	#397	—	47	1	no	—
380	#394	—	47	1	no	—
381	#394	—	47	1	no	—
382	#393	—	47	1	no	—
383	#393	—	47	1	no	—
384	C₄×C₂²⋊C₄	—	47	1	no	—
385	C₄×C₂²⋊C₄	—	47	1	no	—
386	C₄×C₂²⋊C₄	—	47	1	no	—
387	C₄×C₂²⋊C₄	—	47	1	no	—
388	#376	—	47	1	no	—
389	#336	—	47	1	no	—
390	#336	—	47	1	no	—
391	#336	—	47	1	no	—
392	#336	—	47	1	no	—
393	#336	C₂×D₄₇	1	1	yes	characteristic
394	#336	C₂×D₄₇	1	1	yes	characteristic
395	#336	C₂×D₄₇	1	1	yes	characteristic
396	#336	C₂×D₄₇	1	1	yes	characteristic
397	C₄₇	#21637	1	1	yes	characteristic, complemented, Sylow
398	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
399	C₂²×D₄	—	47	1	no	—
400	C₂³×C₄	—	47	1	no	—
401	C₂³×C₄	—	47	1	no	—
402	C₂×M₁₆	—	94	2	no	—
403	C₂×M₁₆	—	94	2	no	—
404	C₂×M₁₆	—	94	2	no	—
405	C₂²×C₈	—	47	1	no	—
406	C₂²×C₈	—	47	1	no	—
407	C₂²×C₈	—	47	1	no	—
408	C₂²×C₈	—	47	1	no	—
409	C₂²×C₈	—	94	2	no	—
410	C₂²×C₈	—	94	2	no	—
411	C₂²×C₈	—	94	2	no	—
412	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
413	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
414	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
415	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
416	C₄×Q₈	—	2	2	no	—
417	C₄×Q₈	—	2	2	no	—
418	C₄×D₄	—	94	2	no	—
419	C₄×D₄	—	94	2	no	—
420	C₂×C₄⋊C₄	—	47	1	no	—
421	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
422	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
423	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
424	C₂×C₂²⋊C₄	—	47	1	no	—
425	C₂×C₂²⋊C₄	—	47	1	no	—
426	C₂×C₂²⋊C₄	—	47	1	no	—
427	C₂×C₂²⋊C₄	—	47	1	no	—
428	C₂×C₂²⋊C₄	—	47	1	no	—
429	C₂×C₂²⋊C₄	—	47	1	no	—
430	C₂×C₂²⋊C₄	—	47	1	no	—
431	C₂×C₂²⋊C₄	—	47	1	no	—
432	C₂×C₂²⋊C₄	—	47	1	no	—
433	C₂×C₂²⋊C₄	—	47	1	no	—
434	C₂×C₄²	—	47	1	no	—
435	C₂×C₄²	—	47	1	no	—
436	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
437	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
438	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
439	C₄⋊C₈	—	2	2	no	—
440	C₄⋊C₈	—	94	2	no	—
441	C₄⋊C₈	—	94	2	no	—
442	C₄⋊C₈	—	94	2	no	—
443	C₂²⋊C₈	—	94	2	no	—
444	C₂²⋊C₈	—	94	2	no	—
445	C₂²⋊C₈	—	94	2	no	—
446	C₂²⋊C₈	—	94	2	no	—
447	C₂²⋊C₈	—	94	2	no	—
448	C₂²⋊C₈	—	94	2	no	—
449	#97	—	47	4	no	—
450	#97	—	94	2	no	—
451	#97	—	94	2	no	—
452	#97	—	94	2	no	—
453	C₄×C₈	—	2	2	no	—
454	C₄×C₈	—	94	2	no	—
455	C₄×C₈	—	94	2	no	—
456	C₄×C₈	—	94	2	no	—
457	#95	—	47	1	no	—
458	#95	—	47	1	no	—
459	#95	—	47	1	no	—
460	#95	—	47	1	no	—
461	#95	—	47	1	no	—
462	#95	—	47	1	no	—
463	#95	—	47	1	no	—
464	#95	—	47	1	no	—
465	#95	—	47	1	no	—
466	#95	—	47	1	no	—
467	#95	—	47	1	no	—
468	#95	—	47	1	no	—
469	C₂⁴	—	47	1	no	—
470	C₂⁴	—	47	1	no	—
471	C₂×Q₈	—	2	2	no	—
472	C₂×Q₈	—	2	2	no	—
473	C₂×Q₈	—	4	1	no	—
474	C₂×D₄	—	94	2	no	—
475	C₂×D₄	—	94	2	no	—
476	C₂×D₄	—	188	1	no	—
477	C₂²×C₄	—	47	1	no	—
478	C₂²×C₄	—	47	1	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	1	no	—
481	C₂²×C₄	—	47	1	no	—
482	C₂²×C₄	—	47	1	no	—
483	C₂²×C₄	—	94	1	no	—
484	C₂²×C₄	—	94	1	no	—
485	C₂²×C₄	—	94	1	no	—
486	C₂²×C₄	—	94	1	no	—
487	C₂²×C₄	—	94	1	no	—
488	C₂²×C₄	—	94	1	no	—
489	C₂²×C₄	—	94	1	no	—
490	C₂²×C₄	—	94	1	no	—
491	C₂²×C₄	—	94	1	no	—
492	C₂²×C₄	—	94	1	no	—
493	C₂²×C₄	—	94	1	no	—
494	C₂²×C₄	—	94	1	no	—
495	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
496	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
497	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
498	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
499	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
500	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
501	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
502	M₁₆	—	188	4	no	—
503	C₂×C₈	—	2	1	no	—
504	C₂×C₈	—	2	1	no	—
505	C₂×C₈	—	2	1	no	—
506	C₂×C₈	—	2	1	no	—
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	47	2	no	—
514	C₂×C₈	—	47	2	no	—
515	C₂×C₈	—	47	2	no	—
516	C₂×C₈	—	47	2	no	—
517	C₂×C₈	—	94	1	no	—
518	C₂×C₈	—	94	1	no	—
519	C₂×C₈	—	94	1	no	—
520	C₂×C₈	—	94	1	no	—
521	C₂×C₈	—	94	1	no	—
522	C₂×C₈	—	94	1	no	—
523	C₂×C₈	—	94	1	no	—
524	C₂×C₈	—	94	1	no	—
525	C₂×C₈	—	188	4	no	—
526	C₂×C₈	#10625354	1	2	yes	—
527	C₂×C₈	#10625354	1	2	yes	—
528	C₄⋊C₄	—	2	2	no	—
529	C₄⋊C₄	—	2	2	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₄⋊C₄	—	94	2	no	—
532	C₂²⋊C₄	—	94	2	no	—
533	C₂²⋊C₄	—	94	2	no	—
534	C₂²⋊C₄	—	94	2	no	—
535	C₂²⋊C₄	—	94	2	no	—
536	C₂²⋊C₄	—	94	2	no	—
537	C₂²⋊C₄	—	94	2	no	—
538	C₂²⋊C₄	—	188	1	no	—
539	C₂²⋊C₄	—	188	1	no	—
540	C₂²⋊C₄	—	188	1	no	—
541	C₂²⋊C₄	—	188	1	no	—
542	C₄²	—	2	1	no	—
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	94	1	no	—
547	C₄²	—	94	1	no	—
548	C₄²	—	94	1	no	—
549	C₄²	—	94	1	no	—
550	C₄²	D₄×D₄₇	1	2	yes	—
551	C₄²	#10625352	1	2	yes	—
552	C₂³	—	47	2	no	—
553	C₂³	—	94	1	no	—
554	C₂³	—	94	1	no	—
555	C₂³	—	94	1	no	—
556	C₂³	—	94	1	no	—
557	C₂³	—	94	1	no	—
558	C₂³	—	94	1	no	—
559	C₂³	—	94	1	no	—
560	C₂³	—	94	1	no	—
561	C₂³	—	94	1	no	—
562	C₂³	—	94	1	no	—
563	C₂³	—	94	1	no	—
564	C₂³	—	94	1	no	—
565	C₂³	—	94	1	no	—
566	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
567	Q₈	—	4	4	no	—
568	D₄	—	188	4	no	—
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	2	1	no	—
584	C₂×C₄	—	94	1	no	—
585	C₂×C₄	—	94	1	no	—
586	C₂×C₄	—	94	1	no	—
587	C₂×C₄	—	94	1	no	—
588	C₂×C₄	—	94	1	no	—
589	C₂×C₄	—	94	1	no	—
590	C₂×C₄	—	94	1	no	—
591	C₂×C₄	—	94	1	no	—
592	C₂×C₄	—	94	1	no	—
593	C₂×C₄	—	94	1	no	—
594	C₂×C₄	—	94	1	no	—
595	C₂×C₄	—	94	1	no	—
596	C₂×C₄	—	94	1	no	—
597	C₂×C₄	—	94	1	no	—
598	C₂×C₄	—	94	1	no	—
599	C₂×C₄	—	94	1	no	—
600	C₂×C₄	—	94	1	no	—
601	C₂×C₄	—	94	1	no	—
602	C₂×C₄	—	188	1	no	—
603	C₂×C₄	—	188	1	no	—
604	C₂×C₄	—	188	1	no	—
605	C₂×C₄	—	188	1	no	—
606	C₂×C₄	—	188	1	no	—
607	C₂×C₄	—	188	1	no	—
608	C₂×C₄	—	188	1	no	—
609	C₂×C₄	—	188	1	no	—
610	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
611	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
612	C₂×C₄	#13094030	1	2	yes	—
613	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
614	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
615	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
616	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
617	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
618	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
619	C₈	—	2	2	no	—
620	C₈	—	2	2	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₈	—	47	4	no	—
624	C₈	—	94	2	no	—
625	C₈	—	188	1	no	—
626	C₈	—	188	1	no	—
627	C₂²	—	94	2	no	—
628	C₂²	—	94	2	no	—
629	C₂²	—	94	2	no	—
630	C₂²	—	188	1	no	—
631	C₂²	—	188	1	no	—
632	C₂²	—	188	1	no	—
633	C₂²	—	188	1	no	—
634	C₂²	—	188	1	no	—
635	C₂²	—	188	1	no	—
636	C₂²	—	188	1	no	—
637	C₂²	—	188	1	no	—
638	C₂²	—	188	1	no	—
639	C₂²	—	188	1	no	—
640	C₂²	—	188	1	no	—
641	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
642	C₂²	C₄×#10625354	1	1	yes	characteristic
643	C₂²	C₄×#10625354	1	1	yes	characteristic
644	C₂²	#131×D₄₇	1	1	yes	characteristic
645	C₂²	C₂×#13094030	1	1	yes	characteristic
646	C₂²	#15689888	1	1	yes	characteristic
647	C₂²	#15689889	1	1	yes	characteristic
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	2	2	no	—
651	C₄	—	4	1	no	—
652	C₄	—	4	1	no	—
653	C₄	—	4	1	no	—
654	C₄	—	188	1	no	—
655	C₄	—	188	1	no	—
656	C₄	—	188	1	no	—
657	C₄	—	188	1	no	—
658	C₄	—	188	1	no	—
659	C₄	—	188	1	no	—
660	C₄	#124×D₄₇	1	1	yes	characteristic
661	C₄	#15689659	1	1	yes	characteristic
662	C₄	#15689659	1	1	yes	characteristic
663	C₄	#15689674	1	1	yes	characteristic
664	C₂	—	376	1	no	—
665	C₂	—	188	2	no	—
666	C₂	#20245931	1	1	yes	characteristic
667	C₂	#20252109	1	1	yes	characteristic
668	C₂	#20252118	1	1	yes	characteristic
669	C₂	#20252365	1	1	yes	characteristic
670	C₂	#20252372	1	1	yes	characteristic
671	C₂	#20252381	1	1	yes	characteristic
672	C₂	#20252391	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1984	C₂
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#21637
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
1. C₂×#15689254	C₂	semidirect
5. #20244002	C₂	semidirect
6. #20244002	C₂	semidirect
7. #20243995	C₂	semidirect
8. #20243995	C₂	semidirect
9. #20243507	C₂	semidirect
10. #20243170	C₂	semidirect
11. #20243168	C₂	semidirect
12. #20243163	C₂	semidirect
13. #20243158	C₂	semidirect
14. #20243074	C₂	semidirect
15. C₄₇×#1984	C₂	semidirect
331. #1984	D₄₇	semidirect
397. C₄₇	#21637	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689254	2
C₂×#15689193	2
#20246671	2
#20244182	2
#20244002	2
#20243995	2
#20243507	2
#20243170	2
#20243168	2
#20243163	2
#20243158	2
#20243074	2
C₄₇×#1984	2
#21637	47