Subgroups — #26220994

Order 12032.

666 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245866	C₂	1	1	yes	maximal, characteristic
2	#20244325	C₂	1	1	yes	maximal, characteristic
3	#20244106	C₂	1	1	yes	maximal, characteristic
4	#20244104	C₂	1	1	yes	maximal, characteristic
5	#20243953	C₂	1	2	yes	maximal
6	#20243951	C₂	1	2	yes	maximal
7	#20243244	C₂	1	2	yes	maximal
8	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
9	#20243138	C₂	1	2	yes	maximal
10	C₄×#13093934	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×#13093934	C₂²	1	1	yes	characteristic
16	C₂×#13093934	C₂²	1	1	yes	characteristic
17	C₂×#13093934	C₂²	1	1	yes	characteristic
18	C₂×#13093934	C₂²	1	1	yes	characteristic
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15689030	C₄	1	1	yes	characteristic
22	#15689030	C₄	1	1	yes	characteristic
23	#15689022	C₄	1	1	yes	characteristic
24	#15689022	C₄	1	1	yes	characteristic
25	#15689009	C₄	1	2	yes	—
26	#15689009	C₄	1	2	yes	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	#15688969	C₂²	1	2	yes	—
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688878	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
56	Dic₄₇⋊C₈	—	2	4	no	—
57	Dic₄₇⋊C₈	—	2	4	no	—
58	#13093934	—	2	2	no	—
59	#13093934	—	2	2	no	—
60	#13093934	—	2	2	no	—
61	#13093934	Q₈	1	4	yes	complemented
62	C₄×C₄₇⋊C₈	—	2	2	no	—
63	C₈×Dic₄₇	—	2	4	no	—
64	C₄₇⋊#95	C₂×C₄	1	2	yes	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×Q₈×C₄₇	—	2	2	no	—
76	C₄×Q₈×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	—	2	2	no	—
82	C₄×C₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	2	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
105	C₂×C₈×C₄₇	#41	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	2	2	no	—
107	C₄⋊C₄×C₄₇	—	2	4	no	—
108	C₄²×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	#41	1	2	yes	—
111	C₄²×C₄₇	#41	1	2	yes	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	—	4	2	no	—
115	C₄⋊Dic₄₇	—	4	2	no	—
116	C₄×Dic₄₇	—	2	2	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	1	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	2	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	4	1	no	—
123	C₄×Dic₄₇	—	4	1	no	—
124	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
125	C₄×Dic₄₇	#41	1	2	yes	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
134	C₂×C₄₇⋊C₈	#41	1	2	yes	—
135	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
136	Q₈×C₄₇	—	4	4	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	#117	1	2	yes	—
146	C₂×C₄×C₄₇	#117	1	2	yes	—
147	C₂×C₄×C₄₇	#131	1	2	yes	—
148	C₂×C₄×C₄₇	#131	1	2	yes	—
149	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	1	no	—
156	C₂×Dic₄₇	—	2	1	no	—
157	C₂×Dic₄₇	—	2	1	no	—
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	1	no	—
160	C₂×Dic₄₇	—	2	1	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	1	no	—
168	C₂×Dic₄₇	—	2	1	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	—	2	2	no	—
171	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
172	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
173	C₈×C₄₇	—	2	2	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	2	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	#21343	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
181	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
182	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
184	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
185	C₂²×C₄₇	#568	1	1	yes	characteristic
186	C₂²×C₄₇	#568	1	1	yes	characteristic
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	4	2	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	#433	1	4	yes	—
191	C₄×C₄₇	#529	1	1	yes	characteristic
192	C₄×C₄₇	#529	1	1	yes	characteristic
193	C₄×C₄₇	#533	1	1	yes	characteristic
194	C₄×C₄₇	#533	1	1	yes	characteristic
195	Dic₄₇	—	2	2	no	—
196	Dic₄₇	—	2	2	no	—
197	Dic₄₇	—	4	1	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	—	4	1	no	—
200	Dic₄₇	—	4	2	no	—
201	#2295	—	47	1	no	—
202	#1984	—	47	1	no	—
203	#1984	D₄₇	1	1	yes	characteristic
204	#1939	—	47	1	no	—
205	#1939	—	47	1	no	—
206	#1917	—	47	2	no	—
207	#1917	—	47	2	no	—
208	#1768	—	47	2	no	—
209	C₄×C₄⋊C₈	—	47	1	no	—
210	#1746	—	47	2	no	—
211	C₄×#97	—	47	1	no	—
212	C₂×C₄₇	#2295	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
214	C₂×C₄₇	#2923	1	1	yes	characteristic
215	C₂×C₄₇	#2962	1	1	yes	characteristic
216	C₂×C₄₇	#2962	1	1	yes	characteristic
217	C₂×C₄₇	#2969	1	1	yes	characteristic
218	C₂×C₄₇	#2969	1	1	yes	characteristic
219	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	47	2	no	—
221	C₂×C₄⋊C₈	—	47	2	no	—
222	C₂×C₄⋊C₈	—	47	1	no	—
223	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×#97	—	47	1	no	—
225	C₂×#97	—	47	1	no	—
226	C₂×#97	—	47	1	no	—
227	C₂×#97	—	47	1	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
231	#391	—	47	1	no	—
232	#391	—	47	1	no	—
233	#389	—	47	1	no	—
234	#389	—	47	1	no	—
235	#387	—	47	2	no	—
236	#387	—	47	2	no	—
237	C₄×C₄⋊C₄	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	1	no	—
239	#376	—	47	2	no	—
240	C₄³	—	47	1	no	—
241	#336	—	47	2	no	—
242	#336	—	47	2	no	—
243	#336	—	47	2	no	—
244	#336	—	47	2	no	—
245	#336	—	47	2	no	—
246	#336	C₂×D₄₇	1	2	yes	—
247	#336	C₂×D₄₇	1	2	yes	—
248	C₄₇	#21343	1	1	yes	characteristic, complemented, Sylow
249	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	—	47	1	no	—
252	C₂²×C₈	—	47	2	no	—
253	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
254	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	C₄×Q₈	—	2	2	no	—
257	C₄×Q₈	—	2	2	no	—
258	C₂×C₄⋊C₄	—	47	1	no	—
259	C₂×C₄⋊C₄	—	47	1	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
263	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	2	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	94	4	no	—
275	C₄⋊C₈	—	94	4	no	—
276	C₄⋊C₈	—	94	2	no	—
277	#97	—	47	4	no	—
278	#97	—	94	2	no	—
279	#97	—	94	2	no	—
280	#97	—	94	2	no	—
281	C₄×C₈	—	2	2	no	—
282	C₄×C₈	—	94	4	no	—
283	C₄×C₈	—	94	2	no	—
284	#95	—	47	2	no	—
285	#95	—	47	2	no	—
286	#95	—	47	2	no	—
287	#95	—	47	2	no	—
288	#95	—	47	2	no	—
289	#95	—	47	2	no	—
290	#95	—	47	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	2	2	no	—
293	C₂×Q₈	—	2	2	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
301	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
302	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	2	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	47	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	94	1	no	—
315	C₂×C₈	—	94	1	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	Q₈×D₄₇	1	2	yes	—
322	C₂×C₈	#10625354	1	2	yes	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	4	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	188	2	no	—
328	C₄⋊C₄	—	188	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	47	2	no	—
332	C₄²	—	47	2	no	—
333	C₄²	—	94	2	no	—
334	C₄²	—	94	2	no	—
335	C₄²	—	94	1	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	1	no	—
338	C₄²	—	94	2	no	—
339	C₄²	—	188	1	no	—
340	C₄²	—	188	1	no	—
341	C₄²	#10625352	1	2	yes	—
342	C₄²	#10625352	1	2	yes	—
343	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
344	Q₈	—	4	4	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	47	2	no	—
354	C₂×C₄	—	47	2	no	—
355	C₂×C₄	—	94	1	no	—
356	C₂×C₄	—	94	1	no	—
357	C₂×C₄	—	94	1	no	—
358	C₂×C₄	—	94	1	no	—
359	C₂×C₄	—	94	1	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	1	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	1	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	1	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	94	2	no	—
371	C₂×C₄	#13093980	1	2	yes	—
372	C₂×C₄	#13093980	1	2	yes	—
373	C₂×C₄	#13094030	1	2	yes	—
374	C₂×C₄	#13094032	1	2	yes	—
375	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
376	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
379	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	4	2	no	—
384	C₈	—	94	2	no	—
385	C₈	—	94	2	no	—
386	C₈	—	188	2	no	—
387	C₂²	C₂×#13093980	1	1	yes	characteristic
388	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
389	C₂²	C₄×#10625354	1	1	yes	characteristic
390	C₂²	C₂×#13094030	1	1	yes	characteristic
391	C₂²	C₂×#13094032	1	1	yes	characteristic
392	C₂²	#15689888	1	1	yes	characteristic
393	C₂²	#15689888	1	1	yes	characteristic
394	C₄	—	2	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	—	94	2	no	—
398	C₄	—	94	2	no	—
399	C₄	—	188	1	no	—
400	C₄	—	188	2	no	—
401	C₄	—	188	1	no	—
402	C₄	—	188	2	no	—
403	C₄	#15689181	1	4	yes	—
404	C₄	#15689652	1	1	yes	characteristic
405	C₄	#15689659	1	1	yes	characteristic
406	C₄	#15689675	1	1	yes	characteristic
407	C₄	#15689678	1	1	yes	characteristic
408	C₂	#20245863	1	1	yes	characteristic
409	C₂	C₂×#15689181	1	1	yes	characteristic
410	C₂	#20252035	1	1	yes	characteristic
411	C₂	#20252330	1	1	yes	characteristic
412	C₂	#20252336	1	1	yes	characteristic
413	C₂	#20252391	1	1	yes	characteristic
414	C₂	#20252394	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1984	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#21343
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
61. #13093934	Q₈	semidirect
248. C₄₇	#21343	semidirect

Maximal subgroups

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

subgroup	index
#20245866	2
#20244325	2
#20244106	2
#20244104	2
#20243953	2
#20243951	2
#20243244	2
C₄⋊C₈×Dic₄₇	2
#20243138	2
C₄×#13093934	2
C₄₇×#1984	2
#21343	47