Subgroups — #26186144

Order 12032.

774 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253384	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242215	C₂	1	4	yes	maximal, complemented
4	C₈×#10625334	C₂	1	4	yes	maximal, complemented
5	#20242164	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241812	C₂	1	1	yes	maximal, characteristic, complemented
7	#20241787	C₂	1	1	yes	maximal, characteristic, complemented
8	#20241671	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₈×D₄₇	—	2	1	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	#15689434	C₄	1	2	yes	—
13	#15689400	C₄	1	2	yes	—
14	#15689315	C₄	1	2	yes	—
15	#15689256	C₄	1	2	yes	—
16	C₄×#10625334	C₂²	1	4	yes	—
17	C₈×D₁₈₈	—	2	1	no	—
18	C₈×D₁₈₈	—	2	1	no	—
19	C₈×D₁₈₈	C₂²	1	2	yes	—
20	C₈×D₁₈₈	C₂²	1	2	yes	—
21	#15689176	C₂²	1	1	yes	characteristic
22	#15689176	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
25	#15688875	C₂²	1	4	yes	complemented
26	D₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	complemented
27	#15688850	C₂²	1	4	yes	—
28	#15688844	C₂²	1	2	yes	complemented
29	C₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
30	C₂×#131×C₄₇	—	2	1	no	—
31	C₄₇×#532	C₂²	1	1	yes	characteristic
32	C₄₇×#436	—	2	1	no	—
33	C₄₇×#436	C₂²	1	2	yes	complemented
34	C₈×D₄×C₄₇	—	2	1	no	—
35	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₄₇×#408	—	2	1	no	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄×D₄₇	—	2	1	no	—
41	C₂×#10625334	C₂×C₄	1	4	yes	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂×C₈×D₄₇	—	2	2	no	—
44	C₂×C₈×D₄₇	—	2	2	no	—
45	C₂×C₈×D₄₇	—	4	4	no	—
46	C₄×D₁₈₈	—	2	1	no	—
47	C₄×D₁₈₈	—	2	1	no	—
48	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
49	C₄×D₁₈₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
52	#13093957	C₂×C₄	1	4	yes	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093945	C₂×C₄	1	4	yes	—
58	#13093944	C₂×C₄	1	4	yes	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
60	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
61	(C₂×D₄₇)⋊C₈	—	2	2	no	—
62	(C₂×D₄₇)⋊C₈	—	2	2	no	—
63	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
64	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
65	C₂×#41×C₄₇	—	2	1	no	—
66	#131×C₄₇	—	4	4	no	—
67	C₂×M₁₆×C₄₇	—	2	1	no	—
68	C₂×M₁₆×C₄₇	—	2	2	no	—
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
73	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
74	#124×C₄₇	—	2	1	no	—
75	#121×C₄₇	—	2	1	no	—
76	#121×C₄₇	C₂×C₄	1	2	yes	—
77	C₄×D₄×C₄₇	—	2	1	no	—
78	C₄×D₄×C₄₇	C₂³	1	2	yes	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	C₂²⋊C₈×C₄₇	—	2	2	no	—
83	C₂²⋊C₈×C₄₇	—	2	2	no	—
84	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
85	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
86	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂³×D₄₇	—	2	1	no	—
89	#41×C₄₇	—	4	2	no	—
90	#41×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
100	C₂²×Dic₄₇	—	2	1	no	—
101	C₂×D₁₈₈	—	2	1	no	—
102	C₂×D₁₈₈	—	2	4	no	—
103	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	4	2	no	—
107	C₂×C₄×D₄₇	—	4	2	no	—
108	M₁₆×C₄₇	—	4	2	no	—
109	M₁₆×C₄₇	—	4	4	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	4	no	—
113	C₂×C₈×C₄₇	D₈	1	4	yes	complemented
114	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₄⋊C₄×C₄₇	—	2	1	no	—
119	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₇	#41	1	1	yes	characteristic
125	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
126	#10625334	—	2	8	no	—
127	(C₂×D₄₇)⋊C₄	—	2	2	no	—
128	(C₂×D₄₇)⋊C₄	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	1	no	—
130	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	4	2	no	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
135	C₈×D₄₇	—	4	4	no	—
136	C₈×D₄₇	—	4	4	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	4	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	4	2	no	—
142	C₂²×D₄₇	—	4	2	no	—
143	Q₈×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	4	no	—
147	D₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	1	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
157	C₂×C₄×C₄₇	#135	1	2	yes	—
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	4	2	no	—
163	D₁₈₈	—	2	4	no	—
164	D₁₈₈	—	2	2	no	—
165	D₁₈₈	#131	1	4	yes	complemented
166	C₄×D₄₇	—	4	2	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	4	no	—
169	C₈×C₄₇	—	2	1	no	—
170	C₈×C₄₇	—	2	1	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₈×C₄₇	C₂×D₈	1	2	yes	—
173	C₈×C₄₇	C₂×D₈	1	2	yes	—
174	C₄₇⋊C₈	—	2	4	no	—
175	C₄₇⋊C₈	—	4	2	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	#17900	—	47	1	no	maximal, Sylow
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	C₄×D₈	1	2	yes	—
184	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
185	C₂×D₄₇	—	2	4	no	—
186	C₂×D₄₇	—	4	8	no	—
187	C₂×D₄₇	—	4	2	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	C₄×D₈	1	2	yes	—
194	C₄×C₄₇	C₂×#131	1	2	yes	—
195	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
196	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
197	Dic₄₇	—	4	2	no	—
198	#3100	—	47	1	no	—
199	#2931	D₄₇	1	1	yes	characteristic, complemented
200	C₂×C₈×D₄	—	47	1	no	—
201	#1581	—	47	4	no	—
202	C₈×D₈	—	47	4	no	—
203	#1571	—	47	1	no	—
204	#1486	—	47	1	no	—
205	#1480	—	47	1	no	—
206	#1450	—	47	1	no	—
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	8	2	no	—
209	C₂×C₄₇	#2929	1	1	yes	characteristic
210	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
211	C₂×C₄₇	#2955	1	1	yes	characteristic
212	D₄₇	—	4	4	no	—
213	C₂×#131	—	2	1	no	—
214	C₂³×C₈	—	94	1	no	—
215	#532	C₂×D₄₇	1	1	yes	characteristic
216	C₂×C₄×D₄	—	47	1	no	—
217	#480	—	47	2	no	—
218	#474	—	47	2	no	—
219	#459	—	47	2	no	—
220	#447	—	47	2	no	—
221	C₄×D₈	—	47	4	no	—
222	#436	—	2	1	no	—
223	#436	C₂×D₄₇	1	2	yes	complemented
224	C₈×D₄	—	2	1	no	—
225	C₈×D₄	—	47	2	no	—
226	C₈×D₄	—	47	2	no	—
227	C₈×D₄	—	94	1	no	—
228	C₈×D₄	—	94	1	no	—
229	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
230	#431	—	47	1	no	—
231	#431	—	47	1	no	—
232	#423	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	—	47	1	no	—
234	#408	—	2	1	no	—
235	C₂×C₂²⋊C₈	—	94	1	no	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	#335	—	47	4	no	—
238	D₄⋊C₈	—	47	4	no	—
239	D₄⋊C₈	—	47	4	no	—
240	#322	—	47	2	no	—
241	C₈²	—	47	2	no	—
242	C₄₇	#17900	1	1	yes	characteristic, complemented, Sylow
243	C₂×#41	—	2	1	no	—
244	C₂²×D₄	—	47	1	no	—
245	C₂³×C₄	—	94	1	no	—
246	C₂×D₈	—	47	4	no	—
247	#131	—	4	4	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	—	94	1	no	—
252	C₂²×C₈	—	94	2	no	—
253	C₂²×C₈	—	94	2	no	—
254	C₂²×C₈	—	188	4	no	—
255	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
257	C₄⋊Q₈	C₄×D₄₇	1	1	yes	characteristic
258	#127	C₄×D₄₇	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	C₄×D₄₇	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	47	2	no	—
264	C₄×D₄	—	47	2	no	—
265	C₄×D₄	—	94	1	no	—
266	C₄×D₄	—	94	1	no	—
267	C₄×D₄	C₂²×D₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	—	47	1	no	—
269	C₂×C₂²⋊C₄	—	94	1	no	—
270	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
271	#107	—	47	4	no	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	94	1	no	—
276	C₄⋊C₈	—	94	1	no	—
277	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
278	#102	—	47	4	no	—
279	#102	—	47	4	no	—
280	C₂²⋊C₈	—	2	2	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	47	2	no	—
283	C₂²⋊C₈	—	94	1	no	—
284	C₂²⋊C₈	—	94	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₄×C₈	—	47	2	no	—
287	C₄×C₈	—	47	2	no	—
288	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
289	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂⁴	—	94	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	47	2	no	—
300	C₂×D₄	—	94	4	no	—
301	C₂×D₄	—	94	1	no	—
302	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	2	no	—
307	C₂²×C₄	—	188	2	no	—
308	C₂²×C₄	—	188	2	no	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	#10625350	1	1	yes	characteristic
311	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
312	D₈	—	94	8	no	—
313	M₁₆	—	4	2	no	—
314	M₁₆	—	4	4	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	4	4	no	—
318	C₂×C₈	—	47	4	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	188	2	no	—
322	C₂×C₈	—	188	4	no	—
323	C₂×C₈	—	188	4	no	—
324	C₂×C₈	#10625334	1	4	yes	complemented
325	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
326	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
327	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	47	2	no	—
331	C₄⋊C₄	—	94	1	no	—
332	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
333	C₂²⋊C₄	—	2	2	no	—
334	C₂²⋊C₄	—	2	2	no	—
335	C₂²⋊C₄	—	94	2	no	—
336	C₂²⋊C₄	—	94	2	no	—
337	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₄²	#10625350	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
340	C₄²	C₂³×D₄₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	—	94	4	no	—
343	C₂³	—	94	2	no	—
344	C₂³	—	188	2	no	—
345	C₂³	—	188	2	no	—
346	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
347	Q₈	—	4	2	no	—
348	D₄	—	2	4	no	—
349	D₄	—	4	2	no	—
350	D₄	—	4	4	no	—
351	D₄	—	4	2	no	—
352	D₄	—	47	4	no	—
353	D₄	—	94	4	no	—
354	D₄	—	94	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#10625334	1	2	yes	—
369	C₂×C₄	#13094044	1	2	yes	—
370	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
373	C₈	—	2	1	no	—
374	C₈	—	2	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	94	4	no	—
377	C₈	—	188	2	no	—
378	C₈	—	188	2	no	—
379	C₈	C₂×#10625334	1	2	yes	—
380	C₈	C₂×#10625334	1	2	yes	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	94	4	no	—
387	C₂²	—	188	8	no	—
388	C₂²	—	188	2	no	—
389	C₂²	—	188	2	no	—
390	C₂²	C₄×#10625334	1	2	yes	—
391	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	188	2	no	—
397	C₄	C₄×#10625334	1	2	yes	—
398	C₄	#131×D₄₇	1	2	yes	—
399	C₄	C₂²×#10625334	1	1	yes	characteristic
400	C₄	C₂×#13094044	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	188	4	no	—
404	C₂	#20252080	1	1	yes	characteristic
405	C₂	C₂×C₄×#10625334	1	1	yes	characteristic
406	C₂	#20252289	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#2931	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253384	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#2931	D₄₇
hypocenter	C₄₇	#17900
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₄×C₈ ◁ #2931

Complements

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

N	H ≅ G/N	type
2. C₂×C₈×D₁₈₈	C₂	semidirect
3. #20242215	C₂	semidirect
4. C₈×#10625334	C₂	semidirect
5. #20242164	C₂	semidirect
6. #20241812	C₂	semidirect
7. #20241787	C₂	semidirect
8. #20241671	C₂	semidirect
9. C₄₇×#2931	C₂	semidirect
25. #15688875	C₂²	semidirect
26. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
28. #15688844	C₂²	semidirect
29. C₈×C₄₇⋊C₈	C₂²	semidirect
33. C₄₇×#436	C₂²	semidirect
35. C₈×D₄×C₄₇	C₂²	semidirect
113. C₂×C₈×C₄₇	D₈	semidirect
165. D₁₈₈	#131	semidirect
199. #2931	D₄₇	semidirect
223. #436	C₂×D₄₇	semidirect
229. C₈×D₄	C₂×D₄₇	semidirect
242. C₄₇	#17900	semidirect
324. C₂×C₈	#10625334	semidirect

Maximal subgroups

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

subgroup	index
#20253384	2
C₂×C₈×D₁₈₈	2
#20242215	2
C₈×#10625334	2
#20242164	2
#20241812	2
#20241787	2
#20241671	2
C₄₇×#2931	2
#17900	47