Subgroups — #441×Dic₄₇ #26214781

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689230	C₂	1	1	yes	maximal, characteristic
2	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×Dic₄₇	C₂	1	2	yes	maximal
4	#20243288	C₂	1	1	yes	maximal, characteristic
5	#20243285	C₂	1	1	yes	maximal, characteristic
6	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic
7	#20243220	C₂	1	2	yes	maximal
8	#20243218	C₂	1	2	yes	maximal
9	#103×Dic₄₇	C₂	1	2	yes	maximal
10	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic
11	C₂×C₄₇×#441	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	#15689230	C₄	1	8	yes	complemented
15	Q₁₆×Dic₄₇	C₄	1	8	yes	complemented
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	C₂×#13093935	C₂²	1	1	yes	characteristic
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄⋊C₄×Dic₄₇	—	2	2	no	—
26	C₄⋊C₄×Dic₄₇	—	2	2	no	—
27	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
29	C₄×C₄⋊Dic₄₇	—	2	2	no	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
31	C₄²×Dic₄₇	—	2	2	no	—
32	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#441	C₄	1	8	yes	complemented
39	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×#103×C₄₇	C₂²	1	2	yes	—
41	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
43	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
44	Q₈×Dic₄₇	—	2	4	no	—
45	Q₈×Dic₄₇	—	2	4	no	—
46	Q₈×Dic₄₇	C₂×C₄	1	8	yes	—
47	Q₈×Dic₄₇	C₂×C₄	1	8	yes	—
48	C₂×C₄⋊Dic₄₇	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	—	2	2	no	—
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×C₄×Dic₄₇	—	2	2	no	—
53	C₂×C₄×Dic₄₇	—	2	2	no	—
54	C₂×C₄×Dic₄₇	—	2	2	no	—
55	C₂×C₄×Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
61	#13093958	C₂×C₄	1	4	yes	—
62	#13093956	C₂×C₄	1	4	yes	—
63	#13093948	C₂×C₄	1	8	yes	—
64	#13093948	C₂×C₄	1	8	yes	—
65	#13093935	—	2	2	no	—
66	#13093934	—	2	2	no	—
67	#13093934	C₂×C₄	1	4	yes	—
68	C₈×Dic₄₇	—	2	2	no	—
69	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
70	C₄₇⋊#95	—	2	2	no	—
71	C₄₇⋊#95	—	2	2	no	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
74	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
75	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₄×Q₈×C₄₇	—	2	4	no	—
80	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#106×C₄₇	C₂×C₄	1	4	yes	—
86	#103×C₄₇	C₂×C₄	1	8	yes	—
87	#97×C₄₇	C₂×C₄	1	4	yes	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×Dic₄₇	—	2	2	no	—
99	C₂²×Dic₄₇	—	2	2	no	—
100	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
102	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
103	Q₁₆×C₄₇	C₄²	1	16	yes	complemented
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₄₇	—	2	8	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
113	C₄²×C₄₇	—	2	8	no	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	#41	1	2	yes	—
116	C₄⋊Dic₄₇	—	2	2	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	8	no	—
119	C₄⋊Dic₄₇	—	2	8	no	—
120	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
121	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
122	C₄×Dic₄₇	—	2	8	no	—
123	C₄×Dic₄₇	—	2	8	no	—
124	C₄×Dic₄₇	—	2	4	no	—
125	C₄×Dic₄₇	—	4	2	no	—
126	C₄×Dic₄₇	—	4	4	no	—
127	C₄×Dic₄₇	—	4	4	no	—
128	C₄×Dic₄₇	—	4	4	no	—
129	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
130	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
131	C₄×Dic₄₇	#41	1	2	yes	—
132	C₄×Dic₄₇	#41	1	2	yes	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	—	2	1	no	—
135	C₂×C₄₇⋊C₈	—	2	1	no	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
138	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
139	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₇	—	2	4	no	—
141	Q₈×C₄₇	—	2	4	no	—
142	Q₈×C₄₇	—	2	4	no	—
143	Q₈×C₄₇	C₂×C₄²	1	8	yes	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂³×C₄	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	4	no	—
163	C₂×Dic₄₇	—	2	4	no	—
164	C₂×Dic₄₇	—	4	2	no	—
165	C₂×Dic₄₇	—	4	2	no	—
166	C₂×Dic₄₇	—	4	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
169	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
170	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
171	C₂×Dic₄₇	#137	1	4	yes	—
172	C₈×C₄₇	—	2	2	no	—
173	C₈×C₄₇	C₂×C₄²	1	4	yes	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄×#441	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂²×C₄₇	C₂×#137	1	2	yes	—
181	C₂²×C₄₇	#575	1	2	yes	—
182	C₄×C₄₇	—	2	4	no	—
183	C₄×C₄₇	—	2	8	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
186	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
187	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
188	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
189	Dic₄₇	—	2	2	no	—
190	Dic₄₇	—	2	4	no	—
191	Dic₄₇	—	4	4	no	—
192	Dic₄₇	—	4	4	no	—
193	Dic₄₇	#441	1	4	yes	direct product factor
194	C₂×#441	—	47	1	no	—
195	C₂×#441	D₄₇	1	1	yes	characteristic
196	C₂×C₄×Q₁₆	—	47	1	no	—
197	C₄²×Q₈	—	47	2	no	—
198	#1776	—	47	1	no	—
199	#1776	—	47	1	no	—
200	C₄×#106	—	47	1	no	—
201	#1763	—	47	2	no	—
202	#1763	—	47	2	no	—
203	C₄×#103	—	47	2	no	—
204	C₄×#97	—	47	1	no	—
205	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#441	1	1	yes	characteristic
207	C₂×C₄₇	#2943	1	1	yes	characteristic
208	C₂×C₄₇	C₄×#137	1	2	yes	—
209	C₂×C₄₇	C₄×#137	1	2	yes	—
210	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
211	C₂×C₄×Q₈	—	47	2	no	—
212	C₂×C₄×Q₈	—	47	2	no	—
213	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
214	#441	—	47	8	no	—
215	#441	Dic₄₇	1	8	yes	direct product factor
216	C₄×Q₁₆	—	47	8	no	—
217	C₂×#107	—	47	1	no	—
218	C₂×#106	—	47	1	no	—
219	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
220	C₂×#103	—	47	2	no	—
221	C₂×#103	—	47	2	no	—
222	C₂×#103	C₂×D₄₇	1	2	yes	—
223	C₂×#97	—	47	1	no	—
224	C₂×#97	—	47	1	no	—
225	C₂×#97	—	47	1	no	—
226	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₄×C₈	—	47	1	no	—
228	C₂×C₄×C₈	—	47	1	no	—
229	C₄×C₄⋊C₄	—	47	2	no	—
230	C₄×C₄⋊C₄	—	47	2	no	—
231	C₄×C₄⋊C₄	—	47	2	no	—
232	C₄×C₄⋊C₄	—	94	2	no	—
233	C₄×C₄⋊C₄	—	94	2	no	—
234	C₄×C₄⋊C₄	—	94	2	no	—
235	C₄³	—	47	1	no	—
236	C₄³	—	94	2	no	—
237	#340	—	47	2	no	—
238	#340	—	47	2	no	—
239	#340	—	47	2	no	—
240	C₄₇	C₄×#441	1	1	yes	characteristic, complemented, Sylow
241	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
242	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
243	C₂×Q₁₆	C₄×D₄₇	1	4	yes	—
244	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	—
245	C₂²×C₈	—	47	1	no	—
246	C₂²×C₈	—	47	1	no	—
247	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
248	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
249	C₄×Q₈	—	2	4	no	—
250	C₄×Q₈	—	47	8	no	—
251	C₄×Q₈	—	47	8	no	—
252	C₄×Q₈	—	94	4	no	—
253	C₄×Q₈	—	94	4	no	—
254	C₄×Q₈	C₂×Dic₄₇	1	8	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	94	2	no	—
259	C₂×C₄⋊C₄	—	94	2	no	—
260	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	2	no	—
265	C₂×C₄²	—	47	2	no	—
266	C₂×C₄²	—	94	2	no	—
267	C₂×C₄²	—	94	2	no	—
268	C₂×C₄²	—	94	2	no	—
269	C₂×C₄²	—	94	2	no	—
270	C₂×C₄²	—	94	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#107	—	47	4	no	—
273	#106	—	47	4	no	—
274	#106	C₂×Dic₄₇	1	4	yes	—
275	#103	—	47	8	no	—
276	#103	—	47	8	no	—
277	#103	C₂×Dic₄₇	1	8	yes	—
278	#97	—	47	4	no	—
279	#97	—	94	2	no	—
280	#97	—	94	2	no	—
281	#97	C₂×Dic₄₇	1	4	yes	—
282	C₄×C₈	—	47	4	no	—
283	C₄×C₈	—	94	2	no	—
284	#95	—	94	2	no	—
285	#95	—	94	2	no	—
286	#95	—	94	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
291	C₂×Q₈	C₂×C₄×D₄₇	1	4	yes	—
292	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	94	2	no	—
300	C₂²×C₄	D₄×D₄₇	1	2	yes	—
301	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
302	Q₁₆	C₄×Dic₄₇	1	16	yes	complemented
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	47	2	no	—
307	C₂×C₈	—	94	1	no	—
308	C₂×C₈	—	94	1	no	—
309	C₂×C₈	—	94	1	no	—
310	C₂×C₈	—	94	1	no	—
311	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
312	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
313	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
314	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
315	C₄⋊C₄	—	2	8	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	47	4	no	—
318	C₄⋊C₄	—	47	4	no	—
319	C₄⋊C₄	—	94	8	no	—
320	C₄⋊C₄	—	94	8	no	—
321	C₄⋊C₄	—	94	2	no	—
322	C₄⋊C₄	—	94	2	no	—
323	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
324	C₄²	—	2	8	no	—
325	C₄²	—	47	2	no	—
326	C₄²	—	47	2	no	—
327	C₄²	—	47	2	no	—
328	C₄²	—	47	2	no	—
329	C₄²	—	94	4	no	—
330	C₄²	—	94	8	no	—
331	C₄²	—	94	8	no	—
332	C₄²	—	188	2	no	—
333	C₄²	—	188	4	no	—
334	C₄²	—	188	4	no	—
335	C₄²	—	188	4	no	—
336	C₄²	#10625352	1	2	yes	—
337	C₄²	C₂²×Dic₄₇	1	2	yes	—
338	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
339	Q₈	—	2	4	no	—
340	Q₈	—	2	4	no	—
341	Q₈	—	2	4	no	—
342	Q₈	C₂×C₄×Dic₄₇	1	8	yes	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	47	2	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	47	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	2	no	—
363	C₂×C₄	—	188	2	no	—
364	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
365	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
368	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
369	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
371	C₈	—	2	2	no	—
372	C₈	—	94	2	no	—
373	C₈	—	94	2	no	—
374	C₈	C₂×C₄×Dic₄₇	1	4	yes	—
375	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
376	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
377	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
378	C₂²	#137×D₄₇	1	2	yes	—
379	C₂²	#15689922	1	2	yes	—
380	C₄	—	2	4	no	—
381	C₄	—	2	8	no	—
382	C₄	—	4	4	no	—
383	C₄	—	47	4	no	—
384	C₄	—	94	2	no	—
385	C₄	—	94	4	no	—
386	C₄	—	188	4	no	—
387	C₄	—	188	4	no	—
388	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
389	C₄	C₄×#10625352	1	1	yes	characteristic
390	C₄	C₄×#10625352	1	1	yes	characteristic
391	C₄	#41×Dic₄₇	1	1	yes	characteristic
392	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
393	C₂	#441×D₄₇	1	1	yes	characteristic
394	C₂	#20252187	1	1	yes	characteristic
395	C₂	#20252204	1	2	yes	—
396	C₂	#137×Dic₄₇	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#441	C₂
socle, prime radical	C₂³×C₄₇	C₂²×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#441	D₄₇
hypocenter	C₄₇	C₄×#441
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#441

Complements

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

N	H ≅ G/N	type
14. #15689230	C₄	semidirect
15. Q₁₆×Dic₄₇	C₄	semidirect
38. C₄₇×#441	C₄	semidirect
103. Q₁₆×C₄₇	C₄²	semidirect
193. Dic₄₇	#441	direct (N × H)
215. #441	Dic₄₇	direct (N × H)
240. C₄₇	C₄×#441	semidirect
302. Q₁₆	C₄×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689230	2
C₂×Q₁₆×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
#20243288	2
#20243285	2
#106×Dic₄₇	2
#20243220	2
#20243218	2
#103×Dic₄₇	2
#97×Dic₄₇	2
C₂×C₄₇×#441	2
C₄×#441	47

Subgroups — #441×Dic47 #26214781

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #441×Dic₄₇ #26214781