Subgroups — #26224605

Order 12032.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094016	C₂	1	1	yes	maximal, characteristic
2	#20244104	C₂	1	1	yes	maximal, characteristic
3	#20244104	C₂	1	1	yes	maximal, characteristic
4	#20243950	C₂	1	2	yes	maximal
5	#20243950	C₂	1	2	yes	maximal
6	#20243261	C₂	1	2	yes	maximal
7	#20243258	C₂	1	1	yes	maximal, characteristic
8	#20243254	C₂	1	2	yes	maximal
9	#20243253	C₂	1	1	yes	maximal, characteristic
10	C₄×#13093935	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1831	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094016	C₄	1	1	yes	characteristic
13	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×#13093935	C₂²	1	1	yes	characteristic
16	C₂×#13093935	C₂²	1	1	yes	characteristic
17	C₂×#13093935	C₂²	1	1	yes	characteristic
18	C₂×#13093935	C₂²	1	1	yes	characteristic
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
23	#15689021	C₄	1	1	yes	characteristic
24	#15689021	C₄	1	1	yes	characteristic
25	#15689007	C₄	1	2	yes	—
26	#15689007	C₄	1	2	yes	—
27	#15688989	C₄	1	1	yes	characteristic
28	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
29	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
32	#15688877	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⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄³×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	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
45	#13094016	—	2	4	no	—
46	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
51	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
56	Dic₄₇⋊C₈	—	2	4	no	—
57	Dic₄₇⋊C₈	—	2	4	no	—
58	#13093935	—	2	2	no	—
59	#13093935	—	2	2	no	—
60	#13093935	—	2	2	no	—
61	#13093935	—	2	2	no	—
62	#13093934	—	2	4	no	—
63	C₄×C₄₇⋊C₈	—	2	2	no	—
64	C₄×C₄₇⋊C₈	Q₈	1	4	yes	—
65	C₈×Dic₄₇	—	2	4	no	—
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	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	—	2	2	no	—
82	C₄⋊C₈×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	2	no	—
102	C₄²×C₄₇	—	2	1	no	—
103	C₄²×C₄₇	—	2	1	no	—
104	C₄²×C₄₇	—	2	1	no	—
105	C₄²×C₄₇	—	2	1	no	—
106	C₄²×C₄₇	—	4	1	no	—
107	C₄²×C₄₇	—	4	1	no	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₇	#41	1	2	yes	—
110	C₄⋊Dic₄₇	—	2	2	no	—
111	C₄⋊Dic₄₇	—	2	2	no	—
112	C₄⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	M₁₆	1	4	yes	—
114	Dic₄₇⋊C₄	—	2	4	no	—
115	Dic₄₇⋊C₄	—	2	4	no	—
116	Dic₄₇⋊C₄	—	4	2	no	—
117	Dic₄₇⋊C₄	—	4	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	—	2	2	no	—
120	C₄×Dic₄₇	—	2	2	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	1	no	—
123	C₂×C₄₇⋊C₈	—	2	1	no	—
124	C₂×C₄₇⋊C₈	—	2	1	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	1	no	—
128	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
130	C₂×C₄₇⋊C₈	#41	1	2	yes	—
131	C₂×C₄₇⋊C₈	#41	1	2	yes	—
132	C₂×C₄₇⋊C₈	#41	1	2	yes	—
133	C₂×C₄₇⋊C₈	#41	1	2	yes	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	1	no	—
143	C₂×C₄×C₄₇	—	2	1	no	—
144	C₂×C₄×C₄₇	—	2	1	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₄₇	#131	1	2	yes	—
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	2	2	no	—
170	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
171	C₈×C₄₇	—	4	2	no	—
172	C₈×C₄₇	—	4	2	no	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	#125	1	4	yes	complemented
177	#21675	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
180	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
181	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
182	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
183	C₂²×C₄₇	#568	1	1	yes	characteristic
184	C₂²×C₄₇	#568	1	1	yes	characteristic
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	4	1	no	—
187	C₄×C₄₇	—	4	1	no	—
188	C₄×C₄₇	—	4	1	no	—
189	C₄×C₄₇	—	4	1	no	—
190	C₄×C₄₇	#446	1	4	yes	—
191	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
192	C₄×C₄₇	#529	1	1	yes	characteristic
193	C₄×C₄₇	#529	1	1	yes	characteristic
194	C₄×C₄₇	#533	1	1	yes	characteristic
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	4	2	no	—
197	Dic₄₇	—	4	2	no	—
198	Dic₄₇	—	4	2	no	—
199	C₄×#125	—	47	1	no	—
200	#1939	—	47	1	no	—
201	#1939	—	47	1	no	—
202	#1917	—	47	2	no	—
203	#1917	—	47	2	no	—
204	#1831	D₄₇	1	1	yes	characteristic
205	#1771	—	47	2	no	—
206	#1770	—	47	1	no	—
207	#1770	—	47	2	no	—
208	C₈×C₄⋊C₄	—	47	1	no	—
209	C₄×#97	—	47	1	no	—
210	C₂×C₄₇	C₄×#125	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
212	C₂×C₄₇	#2961	1	1	yes	characteristic
213	C₂×C₄₇	#2969	1	1	yes	characteristic
214	C₂×C₄₇	#2969	1	1	yes	characteristic
215	C₂×C₄₇	#2970	1	1	yes	characteristic
216	C₂×C₄₇	#2971	1	1	yes	characteristic
217	C₂×#125	—	47	1	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	47	2	no	—
220	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
221	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
222	C₂×#97	—	47	2	no	—
223	C₂×#97	—	47	1	no	—
224	C₂×#97	—	47	1	no	—
225	C₂×#97	—	47	1	no	—
226	C₂×#97	—	47	1	no	—
227	C₂×C₄×C₈	—	47	1	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	#389	—	47	1	no	—
231	#389	—	47	1	no	—
232	#387	—	47	2	no	—
233	#387	—	47	2	no	—
234	#382	—	47	1	no	—
235	C₄×C₄⋊C₄	—	47	1	no	—
236	C₄×C₄⋊C₄	—	47	1	no	—
237	C₄×C₄⋊C₄	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	2	no	—
239	C₄³	C₂×D₄₇	1	1	yes	characteristic
240	#336	—	47	2	no	—
241	#336	—	47	2	no	—
242	#336	—	47	2	no	—
243	#336	—	47	2	no	—
244	#336	C₂×D₄₇	1	2	yes	—
245	#336	C₂×D₄₇	1	2	yes	—
246	C₄₇	#21675	1	1	yes	characteristic, complemented, Sylow
247	C₂²×C₈	—	47	1	no	—
248	C₂²×C₈	—	47	1	no	—
249	C₂²×C₈	—	47	1	no	—
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
252	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
253	#125	—	94	4	no	—
254	C₂×C₄⋊C₄	—	47	1	no	—
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	47	1	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×C₄²	—	47	2	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
265	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
266	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	94	4	no	—
274	C₄⋊C₈	—	94	4	no	—
275	#97	—	94	2	no	—
276	#97	—	94	2	no	—
277	#97	—	94	2	no	—
278	#97	—	94	2	no	—
279	#97	—	94	4	no	—
280	C₄×C₈	—	47	4	no	—
281	C₄×C₈	—	94	4	no	—
282	C₄×C₈	—	94	2	no	—
283	#95	—	47	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	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
297	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	47	2	no	—
307	C₂×C₈	—	47	2	no	—
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	47	2	no	—
311	C₂×C₈	—	47	2	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	94	1	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	C₄⋊C₄	—	47	4	no	—
319	C₄⋊C₄	—	94	4	no	—
320	C₄⋊C₄	—	94	4	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	188	2	no	—
325	C₄⋊C₄	—	188	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	2	2	no	—
328	C₄²	—	2	1	no	—
329	C₄²	—	2	1	no	—
330	C₄²	—	2	1	no	—
331	C₄²	—	2	1	no	—
332	C₄²	—	4	1	no	—
333	C₄²	—	4	1	no	—
334	C₄²	—	94	2	no	—
335	C₄²	—	94	2	no	—
336	C₄²	—	94	2	no	—
337	C₄²	—	94	2	no	—
338	C₄²	#10625352	1	2	yes	—
339	C₄²	Q₈×D₄₇	1	2	yes	—
340	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	#13093989	1	2	yes	—
368	C₂×C₄	#13093989	1	2	yes	—
369	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
370	C₂×C₄	#13094030	1	2	yes	—
371	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
372	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
374	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
375	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
376	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
377	C₈	—	4	2	no	—
378	C₈	—	4	2	no	—
379	C₈	—	47	4	no	—
380	C₈	—	94	2	no	—
381	C₈	—	94	2	no	—
382	C₈	—	94	2	no	—
383	C₂²	C₂×#13093989	1	1	yes	characteristic
384	C₂²	#15689591	1	1	yes	characteristic
385	C₂²	#15689591	1	1	yes	characteristic
386	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
387	C₂²	C₂×#13094030	1	1	yes	characteristic
388	C₂²	#15689889	1	1	yes	characteristic
389	C₂²	#15689889	1	1	yes	characteristic
390	C₄	—	2	2	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	94	4	no	—
396	C₄	—	188	2	no	—
397	C₄	—	188	2	no	—
398	C₄	—	188	2	no	—
399	C₄	#15689252	1	4	yes	—
400	C₄	#125×D₄₇	1	1	yes	characteristic
401	C₄	#15689652	1	1	yes	characteristic
402	C₄	#15689652	1	1	yes	characteristic
403	C₄	#15689679	1	1	yes	characteristic
404	C₂	#20245943	1	1	yes	characteristic
405	C₂	C₂×#15689252	1	1	yes	characteristic
406	C₂	#20252325	1	1	yes	characteristic
407	C₂	#20252386	1	1	yes	characteristic
408	C₂	#20252386	1	1	yes	characteristic
409	C₂	#20252400	1	1	yes	characteristic
410	C₂	#20252405	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1831	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1831	D₄₇
hypocenter	C₄₇	#21675
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
176. C₄₇⋊C₈	#125	semidirect
246. C₄₇	#21675	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094016	2
#20244104	2
#20243950	2
#20243261	2
#20243258	2
#20243254	2
#20243253	2
C₄×#13093935	2
C₄₇×#1831	2
#21675	47