Subgroups — #27080887

Order 12032.

1874 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252393	C₂	1	4	yes	maximal, complemented
2	#20252384	C₂	1	4	yes	maximal, complemented
3	#20252375	C₂	1	4	yes	maximal, complemented
4	#20252364	C₂	1	4	yes	maximal, complemented
5	#20252337	C₂	1	2	yes	maximal, complemented
6	#20252132	C₂	1	2	yes	maximal, complemented
7	#20252115	C₂	1	2	yes	maximal, complemented
8	#20252115	C₂	1	2	yes	maximal, complemented
9	#20252039	C₂	1	1	yes	maximal, characteristic, complemented
10	#20252032	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15689184	C₂	1	1	yes	maximal, characteristic, complemented
12	#20251816	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×#13094031	C₂	1	1	yes	maximal, characteristic, complemented
14	#20251807	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#3455	C₂	1	1	yes	maximal, characteristic
16	C₂×#13094031	C₂²	1	2	yes	—
17	C₂×#13094031	C₂²	1	2	yes	—
18	C₂²×#10625329	C₂²	1	2	yes	—
19	#15689254	C₂²	1	4	yes	complemented
20	#15689254	C₂²	1	4	yes	complemented
21	#15689254	C₂²	1	4	yes	complemented
22	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
23	#15689201	C₂²	1	4	yes	—
24	#15689201	C₂²	1	4	yes	—
25	#15689201	C₂²	1	4	yes	complemented
26	#15689195	C₂²	1	4	yes	—
27	#15689195	C₂²	1	4	yes	—
28	#15689195	C₂²	1	4	yes	—
29	#15689195	C₂²	1	4	yes	—
30	#15689195	C₂²	1	4	yes	complemented
31	#15689195	C₂²	1	4	yes	complemented
32	D₄×C₄₇⋊C₈	C₂²	1	4	yes	—
33	D₄×C₄₇⋊C₈	C₂²	1	4	yes	—
34	D₄×C₄₇⋊C₈	C₂²	1	4	yes	complemented
35	#15689184	C₂²	1	2	yes	—
36	#15689184	C₂²	1	2	yes	—
37	#15689184	C₂²	1	2	yes	—
38	#15689184	C₂²	1	2	yes	—
39	#15689184	C₂²	1	2	yes	complemented
40	#15689184	C₂²	1	2	yes	complemented
41	#15689184	C₂²	1	2	yes	complemented
42	#15689184	C₂²	1	2	yes	complemented
43	#15689180	C₂²	1	4	yes	complemented
44	#15689176	C₂²	1	4	yes	complemented
45	#15689150	C₂²	1	2	yes	—
46	#15689150	C₂²	1	2	yes	—
47	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
48	#15689090	C₂²	1	2	yes	—
49	#15689090	C₂²	1	2	yes	—
50	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
51	#15689079	C₂²	1	4	yes	—
52	#15689079	C₂²	1	4	yes	—
53	#15689079	C₂²	1	2	yes	—
54	#15689079	C₂²	1	2	yes	—
55	#15689079	C₂²	1	4	yes	complemented
56	#15689079	C₂²	1	4	yes	complemented
57	C₄×#10625329	C₂²	1	1	yes	characteristic
58	C₄×#10625329	C₂²	1	1	yes	characteristic
59	C₄×#10625329	C₂²	1	2	yes	—
60	C₄×#10625329	C₂²	1	2	yes	complemented
61	C₄×#10625329	C₂²	1	2	yes	complemented
62	C₂×#13093935	C₂²	1	1	yes	characteristic
63	C₂×#13093935	C₂²	1	2	yes	complemented
64	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
66	C₄₇×#542	C₄	1	2	yes	—
67	C₄₇×#542	C₄	1	2	yes	—
68	C₄₇×#541	C₄	1	2	yes	—
69	C₄₇×#540	C₄	1	2	yes	—
70	C₄₇×#539	C₄	1	4	yes	—
71	C₄₇×#538	C₄	1	4	yes	—
72	C₄₇×#533	C₂²	1	1	yes	characteristic
73	C₄₇×#532	C₂²	1	1	yes	characteristic
74	C₄₇×#529	C₂²	1	4	yes	—
75	C₄₇×#529	C₂²	1	4	yes	—
76	C₄₇×#525	C₂²	1	1	yes	characteristic
77	C₄₇×#525	C₂²	1	1	yes	characteristic
78	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
79	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
80	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
81	#13094031	—	2	8	no	—
82	#13094031	—	2	8	no	—
83	C₂×#10625329	—	2	8	no	—
84	C₂×#10625329	C₂³	1	2	yes	—
85	C₂×#10625329	C₂³	1	4	yes	—
86	C₂×#10625329	C₂³	1	4	yes	—
87	C₂×#10625329	C₂³	1	4	yes	—
88	C₂×#10625329	C₂³	1	2	yes	—
89	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
90	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
91	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
92	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
93	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
94	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
95	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
96	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
97	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
98	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
99	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
100	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
101	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
102	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
103	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
104	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
105	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
106	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
107	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
108	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
109	C₂²⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
110	#13093935	C₂³	1	4	yes	—
111	#13093935	C₂³	1	4	yes	—
112	#13093935	C₂³	1	4	yes	—
113	#13093935	C₂³	1	1	yes	characteristic
114	#13093935	C₂³	1	1	yes	characteristic
115	#13093935	C₂³	1	2	yes	—
116	#13093935	C₂³	1	2	yes	—
117	#13093935	C₂³	1	2	yes	—
118	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
119	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
120	C₄×C₄₇⋊C₈	C₂³	1	4	yes	—
121	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
122	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
123	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
124	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
125	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
126	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
128	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
131	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
132	#126×C₄₇	C₂×C₄	1	4	yes	—
133	#126×C₄₇	C₂×C₄	1	4	yes	—
134	#126×C₄₇	C₂×C₄	1	4	yes	—
135	#126×C₄₇	C₂×C₄	1	4	yes	—
136	#125×C₄₇	C₂×C₄	1	4	yes	—
137	#125×C₄₇	C₂×C₄	1	4	yes	—
138	#125×C₄₇	C₂×C₄	1	2	yes	—
139	#124×C₄₇	C₂×C₄	1	4	yes	—
140	#124×C₄₇	C₂×C₄	1	4	yes	—
141	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
142	#124×C₄₇	C₂×C₄	1	1	yes	characteristic
143	#123×C₄₇	C₂×C₄	1	2	yes	—
144	#123×C₄₇	C₂×C₄	1	2	yes	—
145	#123×C₄₇	C₂×C₄	1	4	yes	—
146	#123×C₄₇	C₂×C₄	1	4	yes	—
147	#123×C₄₇	C₂×C₄	1	4	yes	—
148	#123×C₄₇	C₂×C₄	1	4	yes	—
149	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
150	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
151	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
152	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
153	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
154	#121×C₄₇	C₂×C₄	1	2	yes	—
155	#121×C₄₇	C₂×C₄	1	2	yes	—
156	#121×C₄₇	C₂×C₄	1	4	yes	—
157	#121×C₄₇	C₂×C₄	1	4	yes	—
158	#121×C₄₇	C₂×C₄	1	4	yes	—
159	#120×C₄₇	C₂×C₄	1	2	yes	—
160	#120×C₄₇	C₂×C₄	1	2	yes	—
161	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
162	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
163	C₄×Q₈×C₄₇	C₂³	1	4	yes	—
164	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
165	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
166	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
167	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
168	C₄×D₄×C₄₇	C₂³	1	4	yes	—
169	C₄×D₄×C₄₇	C₂³	1	4	yes	—
170	C₄×D₄×C₄₇	C₂³	1	4	yes	—
171	#117×C₄₇	C₂×C₄	1	2	yes	—
172	#117×C₄₇	C₂×C₄	1	2	yes	—
173	#117×C₄₇	C₂³	1	2	yes	—
174	#117×C₄₇	C₂³	1	2	yes	—
175	#117×C₄₇	C₂³	1	1	yes	characteristic
176	#117×C₄₇	C₂³	1	1	yes	characteristic
177	#117×C₄₇	C₂³	1	2	yes	—
178	#117×C₄₇	C₂³	1	2	yes	—
179	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
180	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
181	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
182	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
183	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
184	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
185	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	#41×C₄₇	—	2	4	no	—
187	#41×C₄₇	—	2	4	no	—
188	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
189	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
190	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
191	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
192	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
193	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
194	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
195	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
196	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
197	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
198	C₂²×C₄×C₄₇	—	2	4	no	—
199	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
200	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
201	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
202	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
203	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
204	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
205	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
206	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
207	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
208	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
209	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
210	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
211	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
212	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
213	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
214	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
215	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
217	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
218	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
219	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
220	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
221	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
222	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
223	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
224	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
225	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
226	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
227	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
228	C₂²⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
229	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
230	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
231	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
232	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
233	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
234	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
235	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
236	C₂²⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
237	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
238	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
239	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
240	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
241	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
242	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
244	C₄²×C₄₇	C₂⁴	1	2	yes	—
245	C₄²×C₄₇	C₂⁴	1	2	yes	—
246	C₄²×C₄₇	C₂⁴	1	2	yes	—
247	#10625329	—	2	4	no	—
248	#10625329	—	2	8	no	—
249	#10625329	—	2	8	no	—
250	#10625329	—	2	8	no	—
251	#10625329	#41	1	8	yes	—
252	C₂×C₄₇⋊C₈	—	2	4	no	—
253	C₂×C₄₇⋊C₈	—	2	4	no	—
254	C₂×C₄₇⋊C₈	—	2	8	no	—
255	C₂×C₄₇⋊C₈	—	2	8	no	—
256	C₂×C₄₇⋊C₈	—	2	8	no	—
257	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
258	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
259	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
260	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
261	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
262	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
263	C₂³×C₄₇	—	2	2	no	—
264	C₂³×C₄₇	—	4	2	no	—
265	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
266	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
267	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
268	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
269	Q₈×C₄₇	—	2	2	no	—
270	Q₈×C₄₇	—	2	2	no	—
271	Q₈×C₄₇	—	4	4	no	—
272	D₄×C₄₇	—	2	4	no	—
273	D₄×C₄₇	—	2	4	no	—
274	D₄×C₄₇	—	2	2	no	—
275	D₄×C₄₇	—	2	2	no	—
276	D₄×C₄₇	—	4	4	no	—
277	D₄×C₄₇	—	4	4	no	—
278	D₄×C₄₇	—	4	4	no	—
279	C₂×C₄×C₄₇	—	2	2	no	—
280	C₂×C₄×C₄₇	—	2	4	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	4	no	—
283	C₂×C₄×C₄₇	—	2	4	no	—
284	C₂×C₄×C₄₇	—	2	2	no	—
285	C₂×C₄×C₄₇	—	4	2	no	—
286	C₂×C₄×C₄₇	—	4	4	no	—
287	C₂×C₄×C₄₇	—	4	4	no	—
288	C₂×C₄×C₄₇	—	4	2	no	—
289	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
292	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
293	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
294	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
295	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
296	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
297	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
298	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
299	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
300	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
301	C₄₇⋊C₈	—	2	2	no	—
302	C₄₇⋊C₈	—	2	2	no	—
303	C₄₇⋊C₈	—	2	2	no	—
304	C₄₇⋊C₈	—	2	2	no	—
305	C₄₇⋊C₈	—	2	4	no	—
306	C₄₇⋊C₈	C₂×#41	1	8	yes	—
307	#60212	—	47	1	no	maximal, Sylow
308	C₂²×C₄₇	—	2	2	no	—
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	2	no	—
311	C₂²×C₄₇	—	2	2	no	—
312	C₂²×C₄₇	—	2	4	no	—
313	C₂²×C₄₇	—	2	4	no	—
314	C₂²×C₄₇	—	2	2	no	—
315	C₂²×C₄₇	—	2	2	no	—
316	C₂²×C₄₇	—	8	2	no	—
317	C₂²×C₄₇	C₄×#41	1	2	yes	—
318	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
319	C₄×C₄₇	—	2	2	no	—
320	C₄×C₄₇	—	2	2	no	—
321	C₄×C₄₇	—	2	2	no	—
322	C₄×C₄₇	—	2	2	no	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	2	no	—
325	C₄×C₄₇	—	2	4	no	—
326	C₄×C₄₇	—	2	4	no	—
327	C₄×C₄₇	—	2	2	no	—
328	C₄×C₄₇	C₄×#41	1	2	yes	—
329	C₄×C₄₇	C₂²×#41	1	2	yes	—
330	#3455	D₄₇	1	1	yes	characteristic
331	#2969	—	47	4	no	—
332	#2968	—	47	4	no	—
333	#2967	—	47	4	no	—
334	#2966	—	47	4	no	—
335	#2962	—	47	2	no	—
336	#2935	—	47	2	no	—
337	#2933	—	47	2	no	—
338	#2933	—	47	2	no	—
339	#2923	—	47	1	no	—
340	#2922	—	47	1	no	—
341	C₂×#433	—	47	1	no	—
342	#2875	—	47	1	no	—
343	C₄×#131	—	47	1	no	—
344	#2873	—	47	1	no	—
345	C₂×C₄₇	—	2	2	no	—
346	C₂×C₄₇	—	4	2	no	—
347	C₂×C₄₇	—	4	2	no	—
348	C₂×C₄₇	—	4	2	no	—
349	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
350	C₂×C₄₇	#3573	1	2	yes	—
351	C₂×#131	—	47	2	no	—
352	C₂×#131	—	47	2	no	—
353	C₂²×M₁₆	—	47	2	no	—
354	#542	Dic₄₇	1	2	yes	—
355	#542	Dic₄₇	1	2	yes	—
356	#541	Dic₄₇	1	2	yes	—
357	#540	Dic₄₇	1	2	yes	—
358	#539	Dic₄₇	1	4	yes	—
359	#538	Dic₄₇	1	4	yes	—
360	#533	C₂×D₄₇	1	1	yes	characteristic
361	#532	C₂×D₄₇	1	1	yes	characteristic
362	#529	C₂×D₄₇	1	4	yes	—
363	#529	C₂×D₄₇	1	4	yes	—
364	#525	C₂×D₄₇	1	1	yes	characteristic
365	#525	C₂×D₄₇	1	1	yes	characteristic
366	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
367	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
368	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
369	#446	—	47	4	no	—
370	#446	—	47	4	no	—
371	#446	—	47	4	no	—
372	C₈×Q₈	—	47	4	no	—
373	#436	—	47	4	no	—
374	#436	—	47	4	no	—
375	#436	—	47	4	no	—
376	#435	—	47	4	no	—
377	#435	—	47	4	no	—
378	#435	—	47	4	no	—
379	#435	—	47	4	no	—
380	#435	—	47	4	no	—
381	#435	—	47	4	no	—
382	C₈×D₄	—	47	4	no	—
383	C₈×D₄	—	47	4	no	—
384	C₈×D₄	—	47	4	no	—
385	#433	—	47	2	no	—
386	#433	—	47	2	no	—
387	#433	—	47	2	no	—
388	#433	—	47	2	no	—
389	#433	—	47	2	no	—
390	#433	—	47	2	no	—
391	#433	—	47	2	no	—
392	#433	—	47	2	no	—
393	#432	—	47	4	no	—
394	#431	—	47	4	no	—
395	#424	—	47	2	no	—
396	#424	—	47	2	no	—
397	C₂×C₄⋊C₈	—	47	2	no	—
398	#408	—	47	2	no	—
399	#408	—	47	2	no	—
400	C₂×C₂²⋊C₈	—	47	2	no	—
401	#405	—	47	4	no	—
402	#405	—	47	4	no	—
403	#405	—	47	2	no	—
404	#405	—	47	4	no	—
405	#405	—	47	2	no	—
406	#405	—	47	4	no	—
407	C₄×M₁₆	—	47	1	no	—
408	C₄×M₁₆	—	47	1	no	—
409	C₄×M₁₆	—	47	2	no	—
410	C₄×M₁₆	—	47	2	no	—
411	C₄×M₁₆	—	47	2	no	—
412	C₂×#97	—	47	1	no	—
413	C₂×#97	—	47	2	no	—
414	C₂×C₄×C₈	—	47	1	no	—
415	C₂×C₄×C₈	—	47	2	no	—
416	C₄₇	#60212	1	1	yes	characteristic, complemented, Sylow
417	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
418	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
419	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
420	#131	—	94	8	no	—
421	#131	—	94	8	no	—
422	C₂×M₁₆	—	47	2	no	—
423	C₂×M₁₆	—	47	2	no	—
424	C₂×M₁₆	—	47	4	no	—
425	C₂×M₁₆	—	47	4	no	—
426	C₂×M₁₆	—	47	4	no	—
427	C₂×M₁₆	—	94	8	no	—
428	C₂²×C₈	—	47	4	no	—
429	C₂²×C₈	—	47	2	no	—
430	C₂²×C₈	—	47	4	no	—
431	C₂²×C₈	—	47	2	no	—
432	C₂²×C₈	—	47	4	no	—
433	C₄⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic
434	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
435	#127	C₂×Dic₄₇	1	1	yes	characteristic
436	#126	C₂×Dic₄₇	1	4	yes	—
437	#126	C₂×Dic₄₇	1	4	yes	—
438	#126	C₂×Dic₄₇	1	4	yes	—
439	#126	C₂×Dic₄₇	1	4	yes	—
440	#125	C₂×Dic₄₇	1	4	yes	—
441	#125	C₂×Dic₄₇	1	4	yes	—
442	#125	C₂×Dic₄₇	1	2	yes	—
443	#124	C₂×Dic₄₇	1	4	yes	—
444	#124	C₂×Dic₄₇	1	4	yes	—
445	#124	C₂×Dic₄₇	1	1	yes	characteristic
446	#124	C₂×Dic₄₇	1	1	yes	characteristic
447	#123	C₂×Dic₄₇	1	2	yes	—
448	#123	C₂×Dic₄₇	1	2	yes	—
449	#123	C₂×Dic₄₇	1	4	yes	—
450	#123	C₂×Dic₄₇	1	4	yes	—
451	#123	C₂×Dic₄₇	1	4	yes	—
452	#123	C₂×Dic₄₇	1	4	yes	—
453	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
454	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
455	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
456	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
457	C₂²⋊Q₈	C₂×Dic₄₇	1	4	yes	—
458	#121	C₂×Dic₄₇	1	2	yes	—
459	#121	C₂×Dic₄₇	1	2	yes	—
460	#121	C₂×Dic₄₇	1	4	yes	—
461	#121	C₂×Dic₄₇	1	4	yes	—
462	#121	C₂×Dic₄₇	1	4	yes	—
463	#120	C₂×Dic₄₇	1	2	yes	—
464	#120	C₂×Dic₄₇	1	2	yes	—
465	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
466	C₄×Q₈	C₂×Dic₄₇	1	2	yes	—
467	C₄×Q₈	C₂²×D₄₇	1	4	yes	—
468	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
469	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
470	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
471	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
472	C₄×D₄	C₂²×D₄₇	1	4	yes	—
473	C₄×D₄	C₂²×D₄₇	1	4	yes	—
474	C₄×D₄	C₂²×D₄₇	1	4	yes	—
475	#117	C₂×Dic₄₇	1	2	yes	—
476	#117	C₂×Dic₄₇	1	2	yes	—
477	#117	C₂²×D₄₇	1	2	yes	—
478	#117	C₂²×D₄₇	1	2	yes	—
479	#117	C₂²×D₄₇	1	1	yes	characteristic
480	#117	C₂²×D₄₇	1	1	yes	characteristic
481	#117	C₂²×D₄₇	1	2	yes	—
482	#117	C₂²×D₄₇	1	2	yes	—
483	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
484	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
485	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
486	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
487	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
488	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
489	C₄⋊C₈	—	47	2	no	—
490	C₄⋊C₈	—	47	2	no	—
491	C₄⋊C₈	—	47	2	no	—
492	C₄⋊C₈	—	47	2	no	—
493	C₄⋊C₈	—	47	4	no	—
494	C₄⋊C₈	—	47	4	no	—
495	C₄⋊C₈	—	47	4	no	—
496	C₄⋊C₈	—	47	4	no	—
497	C₂²⋊C₈	—	47	2	no	—
498	C₂²⋊C₈	—	47	2	no	—
499	C₂²⋊C₈	—	47	2	no	—
500	C₂²⋊C₈	—	47	2	no	—
501	C₂²⋊C₈	—	47	4	no	—
502	C₂²⋊C₈	—	47	4	no	—
503	C₂²⋊C₈	—	47	4	no	—
504	C₂²⋊C₈	—	47	4	no	—
505	#97	—	47	1	no	—
506	#97	—	47	2	no	—
507	#97	—	47	1	no	—
508	#97	—	47	2	no	—
509	#97	—	47	4	no	—
510	#97	—	47	2	no	—
511	#97	—	47	4	no	—
512	#97	—	47	4	no	—
513	C₄×C₈	—	47	1	no	—
514	C₄×C₈	—	47	2	no	—
515	C₄×C₈	—	47	1	no	—
516	C₄×C₈	—	47	2	no	—
517	C₄×C₈	—	47	4	no	—
518	C₄×C₈	—	47	2	no	—
519	C₄×C₈	—	47	4	no	—
520	C₄×C₈	—	47	4	no	—
521	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
522	#41	—	2	4	no	—
523	#41	—	2	4	no	—
524	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
525	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
526	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
527	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
528	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
529	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
530	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
531	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
532	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
533	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
536	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
537	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
538	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
539	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
540	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
541	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
542	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
543	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
544	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
545	M₁₆	—	47	8	no	—
546	M₁₆	—	94	8	no	—
547	M₁₆	—	94	8	no	—
548	M₁₆	—	94	8	no	—
549	M₁₆	—	94	4	no	—
550	C₂×C₈	—	47	4	no	—
551	C₂×C₈	—	47	2	no	—
552	C₂×C₈	—	47	2	no	—
553	C₂×C₈	—	47	4	no	—
554	C₂×C₈	—	47	2	no	—
555	C₂×C₈	—	47	2	no	—
556	C₂×C₈	—	94	8	no	—
557	C₂×C₈	—	94	8	no	—
558	C₂×C₈	—	94	8	no	—
559	C₂×C₈	—	94	4	no	—
560	C₂×C₈	—	94	4	no	—
561	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
562	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
563	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
564	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
565	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
566	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
567	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
568	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
569	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
570	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
571	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
572	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
573	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
574	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
575	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
576	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
577	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
578	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
579	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
580	C₂²⋊C₄	C₂²×Dic₄₇	1	2	yes	—
581	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
582	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
583	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
584	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
585	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
586	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
587	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
588	C₂²⋊C₄	C₂²×Dic₄₇	1	4	yes	—
589	C₄²	C₂²×Dic₄₇	1	2	yes	—
590	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
591	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
592	C₄²	C₂²×Dic₄₇	1	4	yes	—
593	C₄²	C₂²×Dic₄₇	1	4	yes	—
594	C₄²	C₂³×D₄₇	1	1	yes	characteristic
595	C₄²	C₂³×D₄₇	1	1	yes	characteristic
596	C₄²	C₂³×D₄₇	1	2	yes	—
597	C₄²	C₂³×D₄₇	1	2	yes	—
598	C₄²	C₂³×D₄₇	1	2	yes	—
599	C₂³	—	2	2	no	—
600	C₂³	—	4	2	no	—
601	C₂³	C₂³×Dic₄₇	1	2	yes	—
602	C₂³	C₂³×Dic₄₇	1	2	yes	—
603	C₂³	C₂³×Dic₄₇	1	2	yes	—
604	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
605	Q₈	—	2	2	no	—
606	Q₈	—	2	2	no	—
607	Q₈	—	4	4	no	—
608	D₄	—	2	4	no	—
609	D₄	—	2	4	no	—
610	D₄	—	2	2	no	—
611	D₄	—	2	2	no	—
612	D₄	—	4	4	no	—
613	D₄	—	4	4	no	—
614	D₄	—	4	4	no	—
615	C₂×C₄	—	2	2	no	—
616	C₂×C₄	—	2	4	no	—
617	C₂×C₄	—	2	2	no	—
618	C₂×C₄	—	2	4	no	—
619	C₂×C₄	—	2	4	no	—
620	C₂×C₄	—	2	2	no	—
621	C₂×C₄	—	4	2	no	—
622	C₂×C₄	—	4	4	no	—
623	C₂×C₄	—	4	4	no	—
624	C₂×C₄	—	4	2	no	—
625	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
626	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
627	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
628	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
629	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
630	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
631	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
632	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
633	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
634	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
635	C₂×C₄	#41×D₄₇	1	4	yes	—
636	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
637	C₈	—	47	8	no	—
638	C₈	—	94	2	no	—
639	C₈	—	94	2	no	—
640	C₈	—	94	4	no	—
641	C₈	—	94	2	no	—
642	C₈	—	94	2	no	—
643	C₂²	—	2	2	no	—
644	C₂²	—	2	4	no	—
645	C₂²	—	2	4	no	—
646	C₂²	—	2	2	no	—
647	C₂²	—	2	2	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	2	2	no	—
650	C₂²	—	2	2	no	—
651	C₂²	—	8	2	no	—
652	C₂²	#41×Dic₄₇	1	2	yes	—
653	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	2	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	4	no	—
659	C₄	—	2	2	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	2	no	—
663	C₄	#41×Dic₄₇	1	2	yes	—
664	C₄	C₂×#41×D₄₇	1	2	yes	—
665	C₂	—	2	2	no	—
666	C₂	—	4	2	no	—
667	C₂	—	4	2	no	—
668	C₂	—	4	2	no	—
669	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
670	C₂	#20258100	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁴×C₄
Fitting, prime radical	C₄₇×#3455	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#3455	D₄₇
hypocenter	C₄₇	#60212
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ #3455

Complements

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

N	H ≅ G/N	type
1. #20252393	C₂	semidirect
2. #20252384	C₂	semidirect
3. #20252375	C₂	semidirect
4. #20252364	C₂	semidirect
5. #20252337	C₂	semidirect
6. #20252132	C₂	semidirect
7. #20252115	C₂	semidirect
8. #20252115	C₂	semidirect
9. #20252039	C₂	semidirect
10. #20252032	C₂	semidirect
11. C₂×#15689184	C₂	semidirect
12. #20251816	C₂	semidirect
13. C₄×#13094031	C₂	semidirect
14. #20251807	C₂	semidirect
19. #15689254	C₂²	semidirect
20. #15689254	C₂²	semidirect
21. #15689254	C₂²	semidirect
22. Q₈×C₄₇⋊C₈	C₂²	semidirect
25. #15689201	C₂²	semidirect
30. #15689195	C₂²	semidirect
31. #15689195	C₂²	semidirect
34. D₄×C₄₇⋊C₈	C₂²	semidirect
39. #15689184	C₂²	semidirect
40. #15689184	C₂²	semidirect
41. #15689184	C₂²	semidirect
42. #15689184	C₂²	semidirect
43. #15689180	C₂²	semidirect
44. #15689176	C₂²	semidirect
55. #15689079	C₂²	semidirect
56. #15689079	C₂²	semidirect
60. C₄×#10625329	C₂²	semidirect
61. C₄×#10625329	C₂²	semidirect
63. C₂×#13093935	C₂²	semidirect
65. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
416. C₄₇	#60212	semidirect

Maximal subgroups

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

subgroup	index
#20252393	2
#20252384	2
#20252375	2
#20252364	2
#20252337	2
#20252132	2
#20252115	2
#20252039	2
#20252032	2
C₂×#15689184	2
#20251816	2
C₄×#13094031	2
#20251807	2
C₄₇×#3455	2
#60212	47