Subgroups — #26183930

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20251837	C₂	1	1	yes	maximal, characteristic, complemented
2	#20246218	C₂	1	1	yes	maximal, characteristic, complemented
3	#20241960	C₂	1	1	yes	maximal, characteristic, complemented
4	#20241944	C₂	1	2	yes	maximal, complemented
5	#20241931	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241921	C₂	1	2	yes	maximal, complemented
7	#20241908	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241892	C₂	1	2	yes	maximal, complemented
9	#20241879	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688860	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3489	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	—	2	1	no	—
13	C₂×D₄×Dic₄₇	—	2	1	no	—
14	#15689090	—	2	2	no	—
15	#15689090	—	2	1	no	—
16	#15689087	C₂²	1	2	yes	—
17	#15689087	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	#15689030	—	2	1	no	—
21	#15689003	—	2	2	no	—
22	#15688986	C₂²	1	2	yes	—
23	#15688983	C₂²	1	1	yes	characteristic
24	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
26	#15688860	C₂²	1	1	yes	characteristic
27	#15688860	C₂²	1	2	yes	—
28	#15688860	C₂²	1	2	yes	—
29	#15688860	C₂²	1	2	yes	—
30	#15688860	C₂²	1	2	yes	—
31	#15688860	C₂²	1	1	yes	characteristic
32	#15688860	C₂²	1	2	yes	—
33	#15688857	C₂²	1	2	yes	—
34	#15688857	C₂²	1	1	yes	characteristic
35	#15688857	C₂²	1	1	yes	characteristic
36	C₂×2₋¹⁺⁴×C₄₇	C₄	1	1	yes	characteristic, complemented
37	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
38	D₄×Q₈×C₄₇	—	2	1	no	—
39	C₄₇×#548	—	2	1	no	—
40	C₄₇×#547	—	2	1	no	—
41	C₄₇×#547	—	2	2	no	—
42	C₄₇×#546	—	2	1	no	—
43	C₄₇×#546	—	2	2	no	—
44	C₄₇×#537	C₄	1	2	yes	complemented
45	C₄₇×#537	C₄	1	1	yes	characteristic, complemented
46	C₄₇×#536	C₄	1	1	yes	characteristic, complemented
47	C₄₇×#536	C₄	1	2	yes	complemented
48	C₄₇×#525	C₂²	1	1	yes	characteristic
49	C₄₇×#525	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₄₇×#520	C₄	1	1	yes	characteristic, complemented
53	C₂³×Dic₄₇	—	2	2	no	—
54	#13094031	—	4	4	no	—
55	C₂×#10625329	—	2	2	no	—
56	C₂×#10625329	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	2	no	—
58	C₂²×C₄₇⋊C₈	—	2	1	no	—
59	D₄×Dic₄₇	—	4	4	no	—
60	C₂×C₄⋊Dic₄₇	—	2	1	no	—
61	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
62	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
63	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
64	C₂×C₄×Dic₄₇	—	2	1	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
69	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
70	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
71	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	C₂³	1	1	yes	characteristic
75	C₄₇⋊#95	C₂³	1	2	yes	—
76	C₄₇⋊#95	C₂³	1	1	yes	characteristic
77	2₋¹⁺⁴×C₄₇	—	4	4	no	—
78	C₂×#41×C₄₇	—	2	2	no	—
79	C₂×#41×C₄₇	—	2	1	no	—
80	C₂×#41×C₄₇	—	4	4	no	—
81	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×#41×C₄₇	C₂×C₄	1	2	yes	—
83	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×#41×C₄₇	C₂×C₄	1	2	yes	complemented
85	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
87	C₂×#41×C₄₇	D₄	1	2	yes	—
88	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
89	C₂²×Q₈×C₄₇	—	2	1	no	—
90	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
91	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
92	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
93	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
94	C₂²×D₄×C₄₇	D₄	1	2	yes	—
95	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
96	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
97	C₄⋊Q₈×C₄₇	—	2	1	no	—
98	C₄⋊Q₈×C₄₇	—	2	2	no	—
99	#124×C₄₇	—	2	1	no	—
100	#124×C₄₇	—	2	2	no	—
101	#123×C₄₇	—	2	2	no	—
102	#123×C₄₇	—	2	2	no	—
103	#123×C₄₇	—	2	2	no	—
104	#123×C₄₇	—	2	2	no	—
105	#123×C₄₇	—	2	1	no	—
106	C₂²⋊Q₈×C₄₇	—	2	1	no	—
107	C₂²⋊Q₈×C₄₇	—	2	2	no	—
108	C₂²⋊Q₈×C₄₇	—	2	1	no	—
109	C₂²⋊Q₈×C₄₇	—	2	2	no	—
110	C₂²⋊Q₈×C₄₇	—	2	1	no	—
111	C₂²⋊Q₈×C₄₇	—	2	2	no	—
112	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
113	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
114	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
115	C₂²⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
116	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	complemented
117	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
119	#121×C₄₇	—	2	2	no	—
120	#121×C₄₇	—	2	2	no	—
121	#121×C₄₇	—	2	2	no	—
122	#121×C₄₇	—	2	1	no	—
123	#121×C₄₇	—	2	2	no	—
124	#121×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
125	#121×C₄₇	C₂×C₄	1	2	yes	complemented
126	#121×C₄₇	C₂³	1	1	yes	characteristic
127	#120×C₄₇	—	2	2	no	—
128	#120×C₄₇	—	2	1	no	—
129	C₄×Q₈×C₄₇	—	2	1	no	—
130	C₄×D₄×C₄₇	—	2	2	no	—
131	C₄×D₄×C₄₇	—	2	1	no	—
132	C₄×D₄×C₄₇	—	2	1	no	—
133	C₄×D₄×C₄₇	—	2	2	no	—
134	C₄×D₄×C₄₇	—	2	1	no	—
135	C₄×D₄×C₄₇	—	2	2	no	—
136	#117×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
137	#117×C₄₇	C₂×C₄	1	2	yes	complemented
138	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	complemented
141	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
142	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
143	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
145	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
146	#41×C₄₇	—	2	4	no	—
147	#41×C₄₇	—	2	4	no	—
148	#41×C₄₇	—	4	4	no	—
149	#41×C₄₇	—	4	4	no	—
150	#41×C₄₇	—	4	2	no	—
151	#41×C₄₇	—	4	2	no	—
152	#41×C₄₇	—	4	4	no	—
153	#41×C₄₇	—	4	2	no	—
154	#41×C₄₇	—	4	8	no	—
155	#41×C₄₇	—	4	4	no	—
156	C₂×Q₈×C₄₇	—	2	2	no	—
157	C₂×Q₈×C₄₇	—	2	1	no	—
158	C₂×Q₈×C₄₇	—	4	2	no	—
159	C₂×Q₈×C₄₇	—	4	2	no	—
160	C₂×Q₈×C₄₇	—	4	4	no	—
161	C₂×Q₈×C₄₇	—	4	4	no	—
162	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
163	C₂×Q₈×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
164	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
165	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
166	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂×D₄×C₄₇	—	2	4	no	—
168	C₂×D₄×C₄₇	—	2	1	no	—
169	C₂×D₄×C₄₇	—	2	2	no	—
170	C₂×D₄×C₄₇	—	2	1	no	—
171	C₂×D₄×C₄₇	—	2	1	no	—
172	C₂×D₄×C₄₇	—	2	2	no	—
173	C₂×D₄×C₄₇	—	4	4	no	—
174	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
175	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
176	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
177	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
178	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
179	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
180	C₂×D₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
181	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	—	2	1	no	—
183	C₂²×C₄×C₄₇	—	2	2	no	—
184	C₂²×C₄×C₄₇	—	2	1	no	—
185	C₂²×C₄×C₄₇	—	2	2	no	—
186	C₂²×C₄×C₄₇	—	2	2	no	—
187	C₂²×C₄×C₄₇	—	2	1	no	—
188	C₂²×C₄×C₄₇	—	4	2	no	—
189	C₂²×C₄×C₄₇	—	4	4	no	—
190	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
192	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
193	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
194	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
196	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
198	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
200	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
201	C₂²×Dic₄₇	—	2	1	no	—
202	C₂²×Dic₄₇	—	2	1	no	—
203	C₂²×Dic₄₇	—	2	2	no	—
204	C₂²×Dic₄₇	—	4	4	no	—
205	C₂²×Dic₄₇	—	4	4	no	—
206	C₂²×Dic₄₇	—	8	2	no	—
207	C₄⋊C₄×C₄₇	—	2	2	no	—
208	C₄⋊C₄×C₄₇	—	2	2	no	—
209	C₄⋊C₄×C₄₇	—	2	2	no	—
210	C₄⋊C₄×C₄₇	—	2	2	no	—
211	C₄⋊C₄×C₄₇	—	2	1	no	—
212	C₄⋊C₄×C₄₇	—	2	1	no	—
213	C₄⋊C₄×C₄₇	—	2	2	no	—
214	C₄⋊C₄×C₄₇	—	2	1	no	—
215	C₄⋊C₄×C₄₇	—	2	2	no	—
216	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
217	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
219	C₂²⋊C₄×C₄₇	—	2	2	no	—
220	C₂²⋊C₄×C₄₇	—	2	2	no	—
221	C₂²⋊C₄×C₄₇	—	2	2	no	—
222	C₂²⋊C₄×C₄₇	—	2	1	no	—
223	C₂²⋊C₄×C₄₇	—	2	2	no	—
224	C₂²⋊C₄×C₄₇	—	2	1	no	—
225	C₂²⋊C₄×C₄₇	—	2	2	no	—
226	C₂²⋊C₄×C₄₇	—	2	1	no	—
227	C₂²⋊C₄×C₄₇	—	2	2	no	—
228	C₂²⋊C₄×C₄₇	—	2	1	no	—
229	C₂²⋊C₄×C₄₇	—	2	2	no	—
230	C₂²⋊C₄×C₄₇	—	2	1	no	—
231	C₄²×C₄₇	—	2	2	no	—
232	C₄²×C₄₇	—	2	1	no	—
233	C₂²⋊Dic₄₇	—	4	2	no	—
234	C₂²⋊Dic₄₇	—	4	4	no	—
235	C₂²⋊Dic₄₇	—	8	1	no	—
236	C₄⋊Dic₄₇	—	4	2	no	—
237	C₄×Dic₄₇	—	4	2	no	—
238	#10625329	—	4	4	no	—
239	#10625329	—	4	2	no	—
240	C₂×C₄₇⋊C₈	—	2	1	no	—
241	C₂×C₄₇⋊C₈	—	2	1	no	—
242	C₂×C₄₇⋊C₈	—	2	2	no	—
243	C₂×C₄₇⋊C₈	—	4	4	no	—
244	C₂×C₄₇⋊C₈	—	4	2	no	—
245	C₂³×C₄₇	—	2	2	no	—
246	C₂³×C₄₇	—	2	2	no	—
247	C₂³×C₄₇	—	2	4	no	—
248	C₂³×C₄₇	—	2	1	no	—
249	C₂³×C₄₇	—	2	1	no	—
250	C₂³×C₄₇	—	2	1	no	—
251	C₂³×C₄₇	—	4	2	no	—
252	C₂³×C₄₇	—	4	1	no	—
253	C₂³×C₄₇	—	4	1	no	—
254	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
255	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
256	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
257	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
258	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
259	Q₈×C₄₇	—	2	2	no	—
260	Q₈×C₄₇	—	2	2	no	—
261	Q₈×C₄₇	—	4	2	no	—
262	Q₈×C₄₇	—	4	2	no	—
263	Q₈×C₄₇	—	4	1	no	—
264	Q₈×C₄₇	—	4	4	no	—
265	Q₈×C₄₇	—	4	2	no	—
266	D₄×C₄₇	—	2	4	no	—
267	D₄×C₄₇	—	2	4	no	—
268	D₄×C₄₇	—	2	4	no	—
269	D₄×C₄₇	—	2	2	no	—
270	D₄×C₄₇	—	4	2	no	—
271	D₄×C₄₇	—	4	2	no	—
272	D₄×C₄₇	—	4	1	no	—
273	D₄×C₄₇	—	4	2	no	—
274	D₄×C₄₇	—	4	1	no	—
275	D₄×C₄₇	—	4	1	no	—
276	D₄×C₄₇	—	4	4	no	—
277	D₄×C₄₇	—	8	2	no	—
278	D₄×C₄₇	—	8	1	no	—
279	D₄×C₄₇	#99	1	4	yes	—
280	C₂×C₄×C₄₇	—	2	4	no	—
281	C₂×C₄×C₄₇	—	2	4	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	2	no	—
284	C₂×C₄×C₄₇	—	2	2	no	—
285	C₂×C₄×C₄₇	—	2	1	no	—
286	C₂×C₄×C₄₇	—	2	2	no	—
287	C₂×C₄×C₄₇	—	2	1	no	—
288	C₂×C₄×C₄₇	—	2	2	no	—
289	C₂×C₄×C₄₇	—	2	1	no	—
290	C₂×C₄×C₄₇	—	4	1	no	—
291	C₂×C₄×C₄₇	—	4	1	no	—
292	C₂×C₄×C₄₇	—	4	2	no	—
293	C₂×C₄×C₄₇	—	4	2	no	—
294	C₂×C₄×C₄₇	—	4	2	no	—
295	C₂×C₄×C₄₇	—	4	1	no	—
296	C₂×C₄×C₄₇	—	4	4	no	—
297	C₂×C₄×C₄₇	—	4	2	no	—
298	C₂×C₄×C₄₇	—	4	4	no	—
299	C₂×C₄×C₄₇	—	4	2	no	—
300	C₂×C₄×C₄₇	—	8	2	no	—
301	C₂×C₄×C₄₇	—	8	1	no	—
302	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
303	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
304	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
305	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
306	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
307	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×Dic₄₇	—	2	2	no	—
309	C₂×Dic₄₇	—	4	1	no	—
310	C₂×Dic₄₇	—	4	1	no	—
311	C₂×Dic₄₇	—	4	1	no	—
312	C₂×Dic₄₇	—	4	2	no	—
313	C₂×Dic₄₇	—	4	1	no	—
314	C₂×Dic₄₇	—	4	2	no	—
315	C₂×Dic₄₇	—	4	2	no	—
316	C₂×Dic₄₇	—	4	1	no	—
317	C₂×Dic₄₇	—	8	8	no	—
318	C₄₇⋊C₈	—	4	1	no	—
319	C₄₇⋊C₈	—	4	2	no	—
320	C₄₇⋊C₈	—	4	1	no	—
321	#17608	—	47	1	no	maximal, Sylow
322	C₂²×C₄₇	—	2	1	no	—
323	C₂²×C₄₇	—	2	2	no	—
324	C₂²×C₄₇	—	2	1	no	—
325	C₂²×C₄₇	—	2	2	no	—
326	C₂²×C₄₇	—	2	1	no	—
327	C₂²×C₄₇	—	2	1	no	—
328	C₂²×C₄₇	—	2	2	no	—
329	C₂²×C₄₇	—	2	2	no	—
330	C₂²×C₄₇	—	2	1	no	—
331	C₂²×C₄₇	—	2	1	no	—
332	C₂²×C₄₇	—	2	1	no	—
333	C₂²×C₄₇	—	2	2	no	—
334	C₂²×C₄₇	—	2	1	no	—
335	C₂²×C₄₇	—	4	4	no	—
336	C₂²×C₄₇	—	4	4	no	—
337	C₂²×C₄₇	—	4	1	no	—
338	C₂²×C₄₇	—	4	1	no	—
339	C₂²×C₄₇	—	4	1	no	—
340	C₂²×C₄₇	—	8	1	no	—
341	C₂²×C₄₇	—	8	1	no	—
342	C₂²×C₄₇	C₂×#99	1	4	yes	—
343	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
344	C₂²×C₄₇	#577	1	1	yes	characteristic
345	C₂²×C₄₇	#578	1	1	yes	characteristic
346	C₄×C₄₇	—	2	1	no	—
347	C₄×C₄₇	—	2	1	no	—
348	C₄×C₄₇	—	2	2	no	—
349	C₄×C₄₇	—	2	1	no	—
350	C₄×C₄₇	—	2	2	no	—
351	C₄×C₄₇	—	4	2	no	—
352	C₄×C₄₇	—	4	1	no	—
353	C₄×C₄₇	—	4	1	no	—
354	C₄×C₄₇	—	4	1	no	—
355	C₄×C₄₇	—	4	2	no	—
356	C₄×C₄₇	C₂×#99	1	2	yes	—
357	Dic₄₇	—	4	2	no	—
358	Dic₄₇	—	8	1	no	—
359	Dic₄₇	—	8	2	no	—
360	#3489	D₄₇	1	1	yes	characteristic
361	#2880	—	47	1	no	—
362	#2339	—	47	1	no	—
363	#1520	—	47	1	no	—
364	#1516	—	47	2	no	—
365	#1513	—	47	1	no	—
366	#1511	—	47	2	no	—
367	#1508	—	47	1	no	—
368	#1504	—	47	2	no	—
369	#1501	—	47	1	no	—
370	C₂×#328	—	47	2	no	—
371	C₂×C₄₇	—	2	1	no	—
372	C₂×C₄₇	—	2	1	no	—
373	C₂×C₄₇	—	2	4	no	—
374	C₂×C₄₇	—	4	2	no	—
375	C₂×C₄₇	—	4	1	no	—
376	C₂×C₄₇	—	4	1	no	—
377	C₂×C₄₇	—	8	1	no	—
378	C₂×C₄₇	C₂²×#99	1	1	yes	characteristic
379	C₂×C₄₇	#2898	1	1	yes	characteristic
380	C₂×C₄₇	#2901	1	1	yes	characteristic
381	C₂×2₋¹⁺⁴	Dic₄₇	1	1	yes	characteristic, complemented
382	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
383	C₂×#131	—	94	1	no	—
384	D₄×Q₈	—	2	1	no	—
385	#548	—	2	1	no	—
386	#547	—	2	1	no	—
387	#547	—	2	2	no	—
388	#546	—	2	1	no	—
389	#546	—	2	2	no	—
390	#537	Dic₄₇	1	2	yes	complemented
391	#537	Dic₄₇	1	1	yes	characteristic, complemented
392	#536	Dic₄₇	1	1	yes	characteristic, complemented
393	#536	Dic₄₇	1	2	yes	complemented
394	#525	C₂×D₄₇	1	1	yes	characteristic
395	#525	C₂×D₄₇	1	2	yes	—
396	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
397	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
398	#520	Dic₄₇	1	1	yes	characteristic, complemented
399	C₂×C₄×D₄	—	94	1	no	—
400	#408	—	94	2	no	—
401	#408	—	94	1	no	—
402	#407	—	47	2	no	—
403	#407	—	47	1	no	—
404	C₂×C₂²⋊C₈	—	47	2	no	—
405	C₂×C₂²⋊C₈	—	47	1	no	—
406	#391	—	94	1	no	—
407	#386	—	94	2	no	—
408	#381	—	47	2	no	—
409	#380	—	47	1	no	—
410	C₄×C₂²⋊C₄	—	47	1	no	—
411	C₂×#95	—	47	2	no	—
412	#328	—	47	1	no	—
413	#328	—	47	2	no	—
414	#328	—	47	2	no	—
415	#328	—	47	2	no	—
416	#328	—	47	1	no	—
417	#328	—	47	2	no	—
418	#328	—	47	2	no	—
419	#327	—	47	1	no	—
420	#327	—	47	1	no	—
421	#327	—	47	2	no	—
422	C₄₇	#17608	1	1	yes	characteristic, complemented, Sylow
423	2₋¹⁺⁴	—	4	4	no	—
424	C₂×#41	—	2	2	no	—
425	C₂×#41	—	2	1	no	—
426	C₂×#41	—	4	4	no	—
427	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
428	C₂×#41	C₂×Dic₄₇	1	2	yes	—
429	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic
430	C₂×#41	C₂×Dic₄₇	1	2	yes	complemented
431	C₂×#41	C₂×Dic₄₇	1	1	yes	characteristic, complemented
432	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
433	C₂×#41	C₂²⋊D₄₇	1	2	yes	—
434	C₂×#41	C₂²⋊D₄₇	1	1	yes	characteristic
435	C₂²×Q₈	—	2	1	no	—
436	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
437	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	complemented
438	C₂²×Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
439	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
440	C₂²×D₄	C₂²⋊D₄₇	1	2	yes	—
441	C₂³×C₄	—	94	2	no	—
442	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
443	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
444	#131	—	188	4	no	—
445	C₂×M₁₆	—	94	2	no	—
446	C₂×M₁₆	—	94	1	no	—
447	C₂²×C₈	—	94	2	no	—
448	C₂²×C₈	—	94	1	no	—
449	C₄⋊Q₈	—	2	1	no	—
450	C₄⋊Q₈	—	2	2	no	—
451	#124	—	2	1	no	—
452	#124	—	2	2	no	—
453	#123	—	2	2	no	—
454	#123	—	2	2	no	—
455	#123	—	2	2	no	—
456	#123	—	2	2	no	—
457	#123	—	2	1	no	—
458	C₂²⋊Q₈	—	2	1	no	—
459	C₂²⋊Q₈	—	2	2	no	—
460	C₂²⋊Q₈	—	2	1	no	—
461	C₂²⋊Q₈	—	2	2	no	—
462	C₂²⋊Q₈	—	2	1	no	—
463	C₂²⋊Q₈	—	2	2	no	—
464	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
465	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
466	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
467	C₂²⋊Q₈	C₂×Dic₄₇	1	1	yes	characteristic, complemented
468	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	complemented
469	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
470	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
471	#121	—	2	2	no	—
472	#121	—	2	2	no	—
473	#121	—	2	2	no	—
474	#121	—	2	1	no	—
475	#121	—	2	2	no	—
476	#121	C₂×Dic₄₇	1	1	yes	characteristic, complemented
477	#121	C₂×Dic₄₇	1	2	yes	complemented
478	#121	C₂²×D₄₇	1	1	yes	characteristic
479	#120	—	2	2	no	—
480	#120	—	2	1	no	—
481	C₄×Q₈	—	2	1	no	—
482	C₄×D₄	—	2	2	no	—
483	C₄×D₄	—	2	1	no	—
484	C₄×D₄	—	2	1	no	—
485	C₄×D₄	—	2	2	no	—
486	C₄×D₄	—	2	1	no	—
487	C₄×D₄	—	2	2	no	—
488	C₄×D₄	—	188	4	no	—
489	#117	C₂×Dic₄₇	1	1	yes	characteristic, complemented
490	#117	C₂×Dic₄₇	1	2	yes	complemented
491	C₂×C₄⋊C₄	—	2	2	no	—
492	C₂×C₄⋊C₄	—	2	1	no	—
493	C₂×C₄⋊C₄	—	94	1	no	—
494	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	complemented
495	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic, complemented
496	C₂×C₂²⋊C₄	—	2	2	no	—
497	C₂×C₂²⋊C₄	—	2	1	no	—
498	C₂×C₂²⋊C₄	—	94	1	no	—
499	C₂×C₂²⋊C₄	—	94	2	no	—
500	C₂×C₂²⋊C₄	—	94	1	no	—
501	C₂×C₄²	—	94	1	no	—
502	C₂²⋊C₈	—	47	1	no	—
503	C₂²⋊C₈	—	47	1	no	—
504	C₂²⋊C₈	—	47	2	no	—
505	C₂²⋊C₈	—	94	1	no	—
506	C₂²⋊C₈	—	94	2	no	—
507	C₂²⋊C₈	—	94	1	no	—
508	C₂²⋊C₈	—	94	2	no	—
509	#95	—	47	1	no	—
510	#95	—	47	2	no	—
511	#95	—	47	1	no	—
512	#95	—	94	2	no	—
513	#95	—	94	2	no	—
514	C₂⁴	C₂×C₂²⋊D₄₇	1	2	yes	—
515	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
516	#41	—	2	4	no	—
517	#41	—	2	4	no	—
518	#41	—	4	4	no	—
519	#41	—	4	4	no	—
520	#41	—	4	2	no	—
521	#41	—	4	2	no	—
522	#41	—	4	4	no	—
523	#41	—	4	2	no	—
524	#41	—	4	8	no	—
525	#41	—	4	4	no	—
526	C₂×Q₈	—	2	2	no	—
527	C₂×Q₈	—	2	1	no	—
528	C₂×Q₈	—	4	2	no	—
529	C₂×Q₈	—	4	2	no	—
530	C₂×Q₈	—	4	4	no	—
531	C₂×Q₈	—	4	4	no	—
532	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
533	C₂×Q₈	C₂²⋊Dic₄₇	1	1	yes	characteristic
534	C₂×Q₈	C₂²⋊Dic₄₇	1	2	yes	—
535	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
536	C₂×Q₈	C₂²×Dic₄₇	1	1	yes	characteristic
537	C₂×D₄	—	2	4	no	—
538	C₂×D₄	—	2	1	no	—
539	C₂×D₄	—	2	2	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	1	no	—
542	C₂×D₄	—	2	2	no	—
543	C₂×D₄	—	4	4	no	—
544	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
545	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
546	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
547	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
548	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
549	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
550	C₂×D₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
551	C₂×D₄	C₂²×Dic₄₇	1	1	yes	characteristic
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	2	no	—
554	C₂²×C₄	—	2	1	no	—
555	C₂²×C₄	—	2	2	no	—
556	C₂²×C₄	—	2	2	no	—
557	C₂²×C₄	—	2	1	no	—
558	C₂²×C₄	—	4	2	no	—
559	C₂²×C₄	—	4	4	no	—
560	C₂²×C₄	—	94	1	no	—
561	C₂²×C₄	—	94	1	no	—
562	C₂²×C₄	—	94	2	no	—
563	C₂²×C₄	—	376	2	no	—
564	C₂²×C₄	—	188	4	no	—
565	C₂²×C₄	—	188	4	no	—
566	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
567	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
569	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
570	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
571	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
572	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
573	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
574	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
575	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
576	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
577	M₁₆	—	188	4	no	—
578	M₁₆	—	188	2	no	—
579	C₂×C₈	—	94	1	no	—
580	C₂×C₈	—	94	1	no	—
581	C₂×C₈	—	94	2	no	—
582	C₂×C₈	—	188	4	no	—
583	C₂×C₈	—	188	2	no	—
584	C₄⋊C₄	—	2	2	no	—
585	C₄⋊C₄	—	2	2	no	—
586	C₄⋊C₄	—	2	2	no	—
587	C₄⋊C₄	—	2	2	no	—
588	C₄⋊C₄	—	2	1	no	—
589	C₄⋊C₄	—	2	1	no	—
590	C₄⋊C₄	—	2	2	no	—
591	C₄⋊C₄	—	2	1	no	—
592	C₄⋊C₄	—	2	2	no	—
593	C₄⋊C₄	—	188	2	no	—
594	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
595	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
596	C₄⋊C₄	C₂²×Dic₄₇	1	1	yes	characteristic
597	C₂²⋊C₄	—	2	2	no	—
598	C₂²⋊C₄	—	2	2	no	—
599	C₂²⋊C₄	—	2	2	no	—
600	C₂²⋊C₄	—	2	1	no	—
601	C₂²⋊C₄	—	2	2	no	—
602	C₂²⋊C₄	—	2	1	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	1	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	1	no	—
607	C₂²⋊C₄	—	2	2	no	—
608	C₂²⋊C₄	—	2	1	no	—
609	C₂²⋊C₄	—	376	1	no	—
610	C₂²⋊C₄	—	188	2	no	—
611	C₂²⋊C₄	—	188	4	no	—
612	C₄²	—	2	2	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	188	2	no	—
615	C₂³	—	2	4	no	—
616	C₂³	—	2	2	no	—
617	C₂³	—	2	2	no	—
618	C₂³	—	2	1	no	—
619	C₂³	—	2	1	no	—
620	C₂³	—	2	1	no	—
621	C₂³	—	4	2	no	—
622	C₂³	—	4	1	no	—
623	C₂³	—	4	1	no	—
624	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
625	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
626	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
627	C₂³	C₂×C₂²⋊Dic₄₇	1	2	yes	—
628	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
629	Q₈	—	2	2	no	—
630	Q₈	—	2	2	no	—
631	Q₈	—	4	2	no	—
632	Q₈	—	4	2	no	—
633	Q₈	—	4	1	no	—
634	Q₈	—	4	4	no	—
635	Q₈	—	4	2	no	—
636	D₄	—	2	4	no	—
637	D₄	—	2	4	no	—
638	D₄	—	2	4	no	—
639	D₄	—	2	2	no	—
640	D₄	—	4	2	no	—
641	D₄	—	4	2	no	—
642	D₄	—	4	1	no	—
643	D₄	—	4	2	no	—
644	D₄	—	4	4	no	—
645	D₄	—	4	1	no	—
646	D₄	—	4	1	no	—
647	D₄	—	8	2	no	—
648	D₄	—	8	1	no	—
649	D₄	#13093939	1	4	yes	—
650	C₂×C₄	—	2	4	no	—
651	C₂×C₄	—	2	4	no	—
652	C₂×C₄	—	2	2	no	—
653	C₂×C₄	—	2	2	no	—
654	C₂×C₄	—	2	2	no	—
655	C₂×C₄	—	2	1	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	1	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	1	no	—
660	C₂×C₄	—	4	1	no	—
661	C₂×C₄	—	4	1	no	—
662	C₂×C₄	—	4	2	no	—
663	C₂×C₄	—	4	2	no	—
664	C₂×C₄	—	4	2	no	—
665	C₂×C₄	—	4	1	no	—
666	C₂×C₄	—	4	4	no	—
667	C₂×C₄	—	4	2	no	—
668	C₂×C₄	—	4	4	no	—
669	C₂×C₄	—	4	2	no	—
670	C₂×C₄	—	8	2	no	—
671	C₂×C₄	—	8	1	no	—
672	C₂×C₄	—	94	2	no	—
673	C₂×C₄	—	376	8	no	—
674	C₂×C₄	—	188	1	no	—
675	C₂×C₄	—	188	2	no	—
676	C₂×C₄	—	188	1	no	—
677	C₂×C₄	—	188	2	no	—
678	C₂×C₄	—	188	2	no	—
679	C₂×C₄	—	188	1	no	—
680	C₂×C₄	—	188	1	no	—
681	C₂×C₄	—	188	1	no	—
682	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
683	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
684	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
685	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
686	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
687	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
688	C₈	—	188	1	no	—
689	C₈	—	188	2	no	—
690	C₈	—	188	1	no	—
691	C₂²	—	2	2	no	—
692	C₂²	—	2	2	no	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	2	2	no	—
696	C₂²	—	2	1	no	—
697	C₂²	—	2	1	no	—
698	C₂²	—	2	1	no	—
699	C₂²	—	2	2	no	—
700	C₂²	—	2	1	no	—
701	C₂²	—	2	1	no	—
702	C₂²	—	2	1	no	—
703	C₂²	—	2	2	no	—
704	C₂²	—	4	4	no	—
705	C₂²	—	4	4	no	—
706	C₂²	—	4	1	no	—
707	C₂²	—	4	1	no	—
708	C₂²	—	4	1	no	—
709	C₂²	—	8	1	no	—
710	C₂²	—	8	1	no	—
711	C₂²	C₂×#13093939	1	4	yes	—
712	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
713	C₂²	#15689931	1	1	yes	characteristic
714	C₂²	#15689938	1	1	yes	characteristic
715	C₄	—	2	1	no	—
716	C₄	—	2	1	no	—
717	C₄	—	2	2	no	—
718	C₄	—	2	1	no	—
719	C₄	—	2	2	no	—
720	C₄	—	4	1	no	—
721	C₄	—	4	1	no	—
722	C₄	—	4	2	no	—
723	C₄	—	4	2	no	—
724	C₄	—	4	1	no	—
725	C₄	—	376	2	no	—
726	C₄	—	376	1	no	—
727	C₄	—	188	2	no	—
728	C₄	C₂×#13093939	1	2	yes	—
729	C₂	—	2	1	no	—
730	C₂	—	2	1	no	—
731	C₂	—	2	4	no	—
732	C₂	—	4	2	no	—
733	C₂	—	4	1	no	—
734	C₂	—	4	1	no	—
735	C₂	—	8	1	no	—
736	C₂	C₂²×#13093939	1	1	yes	characteristic
737	C₂	#20251921	1	1	yes	characteristic
738	C₂	#20251935	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3489	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#3489	D₄₇
hypocenter	C₄₇	#17608
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×#41 ◁ #3489

Complements

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

N	H ≅ G/N	type
1. #20251837	C₂	semidirect
2. #20246218	C₂	semidirect
3. #20241960	C₂	semidirect
4. #20241944	C₂	semidirect
5. #20241931	C₂	semidirect
6. #20241921	C₂	semidirect
7. #20241908	C₂	semidirect
8. #20241892	C₂	semidirect
9. #20241879	C₂	semidirect
10. C₂×#15688860	C₂	semidirect
36. C₂×2₋¹⁺⁴×C₄₇	C₄	semidirect
44. C₄₇×#537	C₄	semidirect
45. C₄₇×#537	C₄	semidirect
46. C₄₇×#536	C₄	semidirect
47. C₄₇×#536	C₄	semidirect
52. C₄₇×#520	C₄	semidirect
84. C₂×#41×C₄₇	C₂×C₄	semidirect
85. C₂×#41×C₄₇	C₂×C₄	semidirect
90. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
91. C₂²×Q₈×C₄₇	C₂×C₄	semidirect
112. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
113. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
114. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
115. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
116. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
124. #121×C₄₇	C₂×C₄	semidirect
125. #121×C₄₇	C₂×C₄	semidirect
136. #117×C₄₇	C₂×C₄	semidirect
137. #117×C₄₇	C₂×C₄	semidirect
140. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
141. C₂×C₄⋊C₄×C₄₇	C₂×C₄	semidirect
381. C₂×2₋¹⁺⁴	Dic₄₇	semidirect
390. #537	Dic₄₇	semidirect
391. #537	Dic₄₇	semidirect
392. #536	Dic₄₇	semidirect
393. #536	Dic₄₇	semidirect
398. #520	Dic₄₇	semidirect
422. C₄₇	#17608	semidirect
430. C₂×#41	C₂×Dic₄₇	semidirect
431. C₂×#41	C₂×Dic₄₇	semidirect
436. C₂²×Q₈	C₂×Dic₄₇	semidirect
437. C₂²×Q₈	C₂×Dic₄₇	semidirect
464. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
465. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
466. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
467. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
468. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
476. #121	C₂×Dic₄₇	semidirect
477. #121	C₂×Dic₄₇	semidirect
489. #117	C₂×Dic₄₇	semidirect
490. #117	C₂×Dic₄₇	semidirect
494. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect
495. C₂×C₄⋊C₄	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20251837	2
#20246218	2
#20241960	2
#20241944	2
#20241931	2
#20241921	2
#20241908	2
#20241892	2
#20241879	2
C₂×#15688860	2
C₄₇×#3489	2
#17608	47