Subgroups — #26216578

Order 12032.

758 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093981	C₂	1	1	yes	maximal, characteristic
2	#20243532	C₂	1	2	yes	maximal, complemented
3	#20243505	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243455	C₂	1	1	yes	maximal, characteristic
5	#20243455	C₂	1	1	yes	maximal, characteristic
6	#20243369	C₂	1	2	yes	maximal
7	#20243247	C₂	1	2	yes	maximal, complemented
8	#20243153	C₂	1	2	yes	maximal
9	#20243135	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243132	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13093981	C₂²	1	1	yes	characteristic
13	C₂×#13093981	C₂²	1	1	yes	characteristic
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
17	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
18	C₂×#13093934	C₂²	1	2	yes	—
19	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
20	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
21	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
22	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
23	C₄×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
24	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
25	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
26	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
27	C₄×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
28	#15688969	C₂²	1	1	yes	characteristic
29	#15688969	C₂²	1	1	yes	characteristic
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	2	yes	—
32	#15688878	C₂²	1	1	yes	characteristic
33	#15688878	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₄³×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	#13093981	—	2	2	no	—
49	#13093981	—	2	2	no	—
50	#13093981	—	2	4	no	—
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
55	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
58	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
68	C₄²×D₄₇	—	2	4	no	—
69	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
70	(C₂×D₄₇)⋊C₈	—	2	4	no	—
71	(C₂×D₄₇)⋊C₈	—	2	4	no	—
72	#13093934	—	2	4	no	—
73	C₈×Dic₄₇	—	2	4	no	—
74	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
75	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
76	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
77	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
78	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
79	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
80	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
81	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₄⋊C₈×C₄₇	—	2	4	no	—
92	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	—	2	1	no	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	2	2	no	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	—	4	1	no	—
115	C₂×C₄×D₄₇	—	4	1	no	—
116	C₂×C₄×D₄₇	#41	1	4	yes	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	2	2	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	2	no	—
125	C₄²×C₄₇	—	2	2	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	4	1	no	—
128	C₄²×C₄₇	—	4	1	no	—
129	C₄²×C₄₇	#41	1	2	yes	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	(C₂×D₄₇)⋊C₄	—	2	2	no	—
132	(C₂×D₄₇)⋊C₄	—	2	2	no	—
133	(C₂×D₄₇)⋊C₄	—	2	2	no	—
134	(C₂×D₄₇)⋊C₄	—	2	2	no	—
135	Dic₄₇⋊C₄	—	2	2	no	—
136	Dic₄₇⋊C₄	—	2	2	no	—
137	Dic₄₇⋊C₄	—	2	2	no	—
138	Dic₄₇⋊C₄	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	2	no	—
146	C₄×Dic₄₇	—	4	1	no	—
147	C₄×Dic₄₇	—	4	1	no	—
148	C₄×Dic₄₇	#41	1	4	yes	—
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	2	2	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂²×D₄₇	—	2	1	no	—
157	C₂²×D₄₇	—	2	1	no	—
158	C₂²×D₄₇	—	2	1	no	—
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	#117	1	2	yes	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	#117	1	2	yes	—
178	C₂×C₄×C₄₇	#117	1	2	yes	—
179	C₂×C₄×C₄₇	#131	1	2	yes	—
180	C₂×C₄×C₄₇	#131	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
182	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	1	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	1	no	—
202	C₂×Dic₄₇	—	2	1	no	—
203	C₂×Dic₄₇	#117	1	2	yes	—
204	C₂×Dic₄₇	#117	1	2	yes	—
205	C₂×Dic₄₇	#117	1	2	yes	—
206	C₄×D₄₇	—	2	4	no	—
207	C₄×D₄₇	—	2	4	no	—
208	C₄×D₄₇	—	4	4	no	—
209	C₄×D₄₇	—	4	4	no	—
210	C₈×C₄₇	—	4	2	no	—
211	C₈×C₄₇	—	4	2	no	—
212	C₄₇⋊C₈	—	4	2	no	—
213	C₄₇⋊C₈	—	4	2	no	—
214	#20780	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
220	C₂²×C₄₇	#568	1	1	yes	characteristic
221	C₂²×C₄₇	#568	1	1	yes	characteristic
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	2	2	no	—
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	4	1	no	—
226	C₂×D₄₇	—	4	1	no	—
227	C₂×D₄₇	—	4	1	no	—
228	C₂×D₄₇	—	4	1	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	2	2	no	—
233	C₄×C₄₇	—	4	1	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	#529	1	2	yes	—
236	C₄×C₄₇	#529	1	2	yes	—
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	2	2	no	—
240	Dic₄₇	—	4	1	no	—
241	Dic₄₇	—	4	1	no	—
242	Dic₄₇	—	4	1	no	—
243	Dic₄₇	—	4	1	no	—
244	C₄×#117	—	47	1	no	—
245	#1840	—	47	2	no	—
246	#1831	—	47	1	no	—
247	#1831	D₄₇	1	1	yes	characteristic, complemented
248	#1817	—	47	1	no	—
249	#1817	—	47	1	no	—
250	#1798	—	47	2	no	—
251	#1768	—	47	2	no	—
252	#1750	—	47	2	no	—
253	#1745	—	47	1	no	—
254	#1744	—	47	1	no	—
255	C₂×C₄₇	#2283	1	1	yes	characteristic
256	C₂×C₄₇	#2922	1	1	yes	characteristic
257	C₂×C₄₇	#2923	1	1	yes	characteristic
258	C₂×C₄₇	#2924	1	1	yes	characteristic
259	C₂×C₄₇	#2924	1	1	yes	characteristic
260	C₂×C₄₇	#2925	1	1	yes	characteristic
261	C₂×C₄₇	#2925	1	1	yes	characteristic
262	D₄₇	—	4	2	no	—
263	C₂×#117	—	47	1	no	—
264	C₂×#117	—	47	1	no	—
265	C₂²×C₄²	—	47	1	no	—
266	C₂×C₄⋊C₈	—	47	2	no	—
267	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
268	C₂×C₂²⋊C₈	—	47	2	no	—
269	C₂×C₂²⋊C₈	—	47	2	no	—
270	C₂×#97	—	47	2	no	—
271	C₂×C₄×C₈	—	47	2	no	—
272	C₄×C₄⋊C₄	—	47	1	no	—
273	C₄×C₄⋊C₄	—	47	1	no	—
274	C₄×C₄⋊C₄	—	47	1	no	—
275	C₄×C₄⋊C₄	—	47	1	no	—
276	C₄×C₂²⋊C₄	—	47	1	no	—
277	C₄×C₂²⋊C₄	—	47	1	no	—
278	C₄×C₂²⋊C₄	—	47	1	no	—
279	C₄×C₂²⋊C₄	—	47	1	no	—
280	#376	—	47	1	no	—
281	#376	—	47	1	no	—
282	C₄³	—	47	1	no	—
283	C₄³	C₂×D₄₇	1	1	yes	characteristic
284	#336	—	47	2	no	—
285	#336	—	47	2	no	—
286	#336	—	47	2	no	—
287	#336	—	47	2	no	—
288	#336	—	47	1	no	—
289	#336	—	47	1	no	—
290	#336	—	47	2	no	—
291	#336	C₂×D₄₇	1	1	yes	characteristic
292	#336	C₂×D₄₇	1	1	yes	characteristic
293	#336	C₂×D₄₇	1	2	yes	—
294	C₄₇	#20780	1	1	yes	characteristic, complemented, Sylow
295	C₂³×C₄	—	47	1	no	—
296	C₂³×C₄	—	47	1	no	—
297	C₂³×C₄	—	47	1	no	—
298	C₂²×C₈	—	47	2	no	—
299	C₂²×C₈	—	47	2	no	—
300	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
301	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
302	#117	—	94	4	no	—
303	#117	—	94	2	no	—
304	#117	—	94	2	no	—
305	C₂×C₄⋊C₄	—	47	1	no	—
306	C₂×C₄⋊C₄	—	47	1	no	—
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₄⋊C₄	—	47	1	no	—
309	C₂×C₂²⋊C₄	—	47	1	no	—
310	C₂×C₂²⋊C₄	—	47	1	no	—
311	C₂×C₂²⋊C₄	—	47	1	no	—
312	C₂×C₂²⋊C₄	—	47	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	47	1	no	—
316	C₂×C₄²	—	47	1	no	—
317	C₂×C₄²	—	47	1	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	94	4	no	—
323	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
324	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
325	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
326	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
329	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
330	C₄⋊C₈	—	2	4	no	—
331	C₄⋊C₈	—	94	4	no	—
332	C₂²⋊C₈	—	94	4	no	—
333	C₂²⋊C₈	—	94	4	no	—
334	#97	—	94	4	no	—
335	C₄×C₈	—	94	4	no	—
336	#95	—	47	1	no	—
337	#95	—	47	1	no	—
338	#95	—	47	1	no	—
339	#95	—	47	1	no	—
340	#95	—	47	1	no	—
341	#95	—	47	1	no	—
342	#95	—	47	1	no	—
343	#95	—	47	1	no	—
344	C₂⁴	—	47	1	no	—
345	C₂²×C₄	—	47	1	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	—	47	1	no	—
348	C₂²×C₄	—	47	4	no	—
349	C₂²×C₄	—	47	1	no	—
350	C₂²×C₄	—	47	1	no	—
351	C₂²×C₄	—	47	1	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	94	2	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	1	no	—
357	C₂²×C₄	—	94	1	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	2	no	—
360	C₂²×C₄	—	188	1	no	—
361	C₂²×C₄	—	188	1	no	—
362	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	2	2	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	94	2	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₄⋊C₄	—	94	2	no	—
382	C₄⋊C₄	—	94	2	no	—
383	C₄⋊C₄	—	94	2	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₂²⋊C₄	—	94	2	no	—
386	C₂²⋊C₄	—	94	2	no	—
387	C₂²⋊C₄	—	94	2	no	—
388	C₂²⋊C₄	—	94	2	no	—
389	C₄²	—	2	2	no	—
390	C₄²	—	2	2	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	4	1	no	—
394	C₄²	—	4	1	no	—
395	C₄²	—	47	4	no	—
396	C₄²	—	94	2	no	—
397	C₄²	—	94	2	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	94	2	no	—
401	C₄²	—	94	1	no	—
402	C₄²	—	94	1	no	—
403	C₄²	—	188	1	no	—
404	C₄²	—	188	1	no	—
405	C₄²	#10625352	1	2	yes	—
406	C₄²	#10625354	1	2	yes	—
407	C₂³	—	47	2	no	—
408	C₂³	—	94	1	no	—
409	C₂³	—	94	1	no	—
410	C₂³	—	94	1	no	—
411	C₂³	—	94	1	no	—
412	C₂³	—	94	1	no	—
413	C₂³	—	94	1	no	—
414	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
415	C₂×C₄	—	2	1	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	47	2	no	—
430	C₂×C₄	—	47	2	no	—
431	C₂×C₄	—	47	2	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	1	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	4	no	—
439	C₂×C₄	—	94	4	no	—
440	C₂×C₄	—	94	1	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	94	1	no	—
446	C₂×C₄	—	94	1	no	—
447	C₂×C₄	—	94	1	no	—
448	C₂×C₄	—	94	1	no	—
449	C₂×C₄	—	94	1	no	—
450	C₂×C₄	—	94	1	no	—
451	C₂×C₄	—	94	1	no	—
452	C₂×C₄	—	188	4	no	—
453	C₂×C₄	—	188	4	no	—
454	C₂×C₄	#13093982	1	2	yes	—
455	C₂×C₄	#13093982	1	2	yes	—
456	C₂×C₄	#13094030	1	2	yes	—
457	C₂×C₄	#13094032	1	2	yes	—
458	C₂×C₄	#41×D₄₇	1	2	yes	—
459	C₂×C₄	#41×D₄₇	1	2	yes	—
460	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
461	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	188	2	no	—
465	C₈	—	188	2	no	—
466	C₂²	—	94	2	no	—
467	C₂²	—	94	2	no	—
468	C₂²	—	94	2	no	—
469	C₂²	—	188	1	no	—
470	C₂²	—	188	1	no	—
471	C₂²	—	188	1	no	—
472	C₂²	—	188	1	no	—
473	C₂²	#117×D₄₇	1	1	yes	characteristic
474	C₂²	#117×D₄₇	1	1	yes	characteristic
475	C₂²	C₂×#13093982	1	1	yes	characteristic
476	C₂²	C₂×#13094030	1	1	yes	characteristic
477	C₂²	C₂×#13094032	1	1	yes	characteristic
478	C₂²	#15689889	1	1	yes	characteristic
479	C₂²	#15689889	1	1	yes	characteristic
480	C₄	—	2	2	no	—
481	C₄	—	2	2	no	—
482	C₄	—	2	2	no	—
483	C₄	—	2	2	no	—
484	C₄	—	4	1	no	—
485	C₄	—	4	1	no	—
486	C₄	—	94	2	no	—
487	C₄	—	94	2	no	—
488	C₄	—	94	2	no	—
489	C₄	—	188	1	no	—
490	C₄	—	188	1	no	—
491	C₄	—	188	1	no	—
492	C₄	—	188	1	no	—
493	C₄	#15689652	1	2	yes	—
494	C₄	#15689658	1	2	yes	—
495	C₂	—	188	2	no	—
496	C₂	#20245781	1	1	yes	characteristic
497	C₂	#20252027	1	1	yes	characteristic
498	C₂	#20252034	1	1	yes	characteristic
499	C₂	#20252041	1	1	yes	characteristic
500	C₂	#20252047	1	1	yes	characteristic
501	C₂	#20252053	1	1	yes	characteristic
502	C₂	#20252056	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1831	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#20780
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1831

Complements

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

N	H ≅ G/N	type
2. #20243532	C₂	semidirect
3. #20243505	C₂	semidirect
7. #20243247	C₂	semidirect
9. #20243135	C₂	semidirect
10. #20243132	C₂	semidirect
11. C₄₇×#1831	C₂	semidirect
247. #1831	D₄₇	semidirect
294. C₄₇	#20780	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093981	2
#20243532	2
#20243505	2
#20243455	2
#20243369	2
#20243247	2
#20243153	2
#20243135	2
#20243132	2
C₄₇×#1831	2
#20780	47