Subgroups — #26124908

Order 12032.

958 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	C₂²×#13093956	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689022	C₂	1	2	yes	maximal
3	C₂×#15688885	C₂	1	2	yes	maximal
4	C₂×#15688877	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#340	C₂	1	1	yes	maximal, characteristic
6	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
7	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
8	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
9	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
10	C₂×#13093956	—	2	4	no	—
11	C₂×#13093956	—	2	2	no	—
12	#15689022	—	2	4	no	—
13	#15689022	—	2	4	no	—
14	C₂×C₄₇⋊#95	—	2	2	no	—
15	#15688885	—	2	4	no	—
16	#15688877	—	2	2	no	—
17	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#340	C₄	1	4	yes	complemented
20	C₂³×Dic₄₇	—	2	2	no	—
21	C₂³×Dic₄₇	D₄	1	2	yes	—
22	C₂²×C₄₇⋊C₈	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	C₂²×C₄₇⋊C₈	—	2	2	no	—
25	C₂²×C₄₇⋊C₈	—	2	1	no	—
26	C₂²×C₄₇⋊C₈	Q₈	1	2	yes	—
27	C₂×C₄⋊Dic₄₇	—	2	2	no	—
28	C₂×C₄⋊Dic₄₇	—	2	2	no	—
29	C₂×C₄⋊Dic₄₇	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	8	no	—
32	C₂×C₄⋊Dic₄₇	—	2	2	no	—
33	C₂×C₄⋊Dic₄₇	—	4	4	no	—
34	C₂×C₄⋊Dic₄₇	—	4	4	no	—
35	C₂×C₄⋊Dic₄₇	D₄	1	4	yes	—
36	C₂×C₄×Dic₄₇	—	2	2	no	—
37	C₂×C₄×Dic₄₇	—	2	2	no	—
38	C₂×C₄×Dic₄₇	—	2	1	no	—
39	C₂×C₄×Dic₄₇	—	2	1	no	—
40	#13093956	—	2	8	no	—
41	C₄₇⋊#95	—	2	8	no	—
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₇	—	2	2	no	—
45	C₂²×C₈×C₄₇	—	2	2	no	—
46	C₂²×C₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×C₈×C₄₇	D₄	1	2	yes	—
48	C₂²×C₈×C₄₇	Q₈	1	2	yes	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
53	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
54	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
55	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
56	C₂²×C₄×C₄₇	—	2	4	no	—
57	C₂²×C₄×C₄₇	—	2	4	no	—
58	C₂²×C₄×C₄₇	—	2	4	no	—
59	C₂²×C₄×C₄₇	—	4	2	no	—
60	C₂²×C₄×C₄₇	—	4	2	no	—
61	C₂²×C₄×C₄₇	—	4	2	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
65	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
66	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
67	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
69	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
70	C₂²×C₄×C₄₇	#41	1	2	yes	—
71	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
73	C₂²×Dic₄₇	—	2	2	no	—
74	C₂²×Dic₄₇	—	2	2	no	—
75	C₂²×Dic₄₇	—	2	2	no	—
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	—	2	2	no	—
78	C₂²×Dic₄₇	—	2	2	no	—
79	C₂²×Dic₄₇	—	2	4	no	—
80	C₂²×Dic₄₇	—	4	2	no	—
81	C₂²×Dic₄₇	—	4	2	no	—
82	C₂²×Dic₄₇	—	4	2	no	—
83	C₂²×Dic₄₇	—	4	2	no	—
84	C₂²×Dic₄₇	—	4	2	no	—
85	C₂²×Dic₄₇	—	4	2	no	—
86	C₂²×Dic₄₇	SD₁₆	1	4	yes	—
87	C₂×C₈×C₄₇	—	2	4	no	—
88	C₂×C₈×C₄₇	—	2	2	no	—
89	C₂×C₈×C₄₇	—	2	4	no	—
90	C₂×C₈×C₄₇	—	2	2	no	—
91	C₂×C₈×C₄₇	C₄⋊C₄	1	4	yes	complemented
92	C₄⋊C₄×C₄₇	—	2	4	no	—
93	C₄⋊C₄×C₄₇	—	2	4	no	—
94	C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₄⋊C₄×C₄₇	C₄⋊C₄	1	8	yes	complemented
96	C₄⋊Dic₄₇	—	2	4	no	—
97	C₄⋊Dic₄₇	—	2	4	no	—
98	C₄⋊Dic₄₇	—	4	16	no	—
99	C₄⋊Dic₄₇	—	4	2	no	—
100	C₄⋊Dic₄₇	—	4	2	no	—
101	C₄×Dic₄₇	—	4	1	no	—
102	C₄×Dic₄₇	—	4	2	no	—
103	C₄×Dic₄₇	—	4	1	no	—
104	C₂×C₄₇⋊C₈	—	2	4	no	—
105	C₂×C₄₇⋊C₈	—	2	2	no	—
106	C₂×C₄₇⋊C₈	—	4	1	no	—
107	C₂×C₄₇⋊C₈	—	4	2	no	—
108	C₂×C₄₇⋊C₈	—	4	1	no	—
109	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
110	C₂³×C₄₇	#120	1	2	yes	—
111	C₂³×C₄₇	#121	1	1	yes	characteristic
112	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
113	C₂³×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
114	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
115	C₂³×C₄₇	#135	1	2	yes	—
116	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
117	C₂³×C₄₇	#137	1	2	yes	—
118	C₂×C₄×C₄₇	—	2	8	no	—
119	C₂×C₄×C₄₇	—	4	4	no	—
120	C₂×C₄×C₄₇	—	4	4	no	—
121	C₂×C₄×C₄₇	—	4	4	no	—
122	C₂×C₄×C₄₇	—	4	4	no	—
123	C₂×C₄×C₄₇	—	4	4	no	—
124	C₂×C₄×C₄₇	—	4	4	no	—
125	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
126	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
127	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
128	C₂×C₄×C₄₇	C₄×Q₈	1	1	yes	characteristic
129	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
130	C₂×C₄×C₄₇	#121	1	2	yes	—
131	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
132	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
133	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
134	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
135	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
136	C₂×C₄×C₄₇	#123	1	2	yes	—
137	C₂×C₄×C₄₇	#125	1	2	yes	—
138	C₂×C₄×C₄₇	#125	1	1	yes	characteristic
139	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₄⋊Q₈	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
143	C₂×Dic₄₇	—	2	4	no	—
144	C₂×Dic₄₇	—	2	4	no	—
145	C₂×Dic₄₇	—	2	4	no	—
146	C₂×Dic₄₇	—	4	2	no	—
147	C₂×Dic₄₇	—	4	2	no	—
148	C₂×Dic₄₇	—	4	2	no	—
149	C₂×Dic₄₇	—	4	2	no	—
150	C₂×Dic₄₇	—	4	4	no	—
151	C₂×Dic₄₇	—	4	4	no	—
152	C₂×Dic₄₇	—	4	4	no	—
153	C₂×Dic₄₇	—	8	2	no	—
154	C₂×Dic₄₇	—	8	2	no	—
155	C₂×Dic₄₇	—	8	2	no	—
156	C₂×Dic₄₇	—	8	2	no	—
157	C₈×C₄₇	—	2	4	no	—
158	C₄₇⋊C₈	—	4	2	no	—
159	#11327	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	#385	1	2	yes	—
161	C₂²×C₄₇	#389	1	1	yes	characteristic
162	C₂²×C₄₇	#392	1	1	yes	characteristic
163	C₂²×C₄₇	#395	1	2	yes	—
164	C₂²×C₄₇	#398	1	1	yes	characteristic
165	C₂²×C₄₇	C₄×SD₁₆	1	2	yes	—
166	C₂²×C₄₇	#441	1	1	yes	characteristic
167	C₂²×C₄₇	#442	1	1	yes	characteristic
168	C₂²×C₄₇	#448	1	2	yes	—
169	C₂²×C₄₇	#449	1	2	yes	—
170	C₂²×C₄₇	#450	1	2	yes	—
171	C₂²×C₄₇	#452	1	2	yes	—
172	C₂²×C₄₇	#465	1	2	yes	—
173	C₂²×C₄₇	#468	1	2	yes	—
174	C₂²×C₄₇	#475	1	2	yes	—
175	C₂²×C₄₇	#476	1	2	yes	—
176	C₂²×C₄₇	#478	1	2	yes	—
177	C₂²×C₄₇	#479	1	2	yes	—
178	C₂²×C₄₇	#498	1	1	yes	characteristic
179	C₂²×C₄₇	#499	1	1	yes	characteristic
180	C₂²×C₄₇	#501	1	2	yes	—
181	C₄×C₄₇	—	4	8	no	—
182	C₄×C₄₇	#384	1	1	yes	characteristic
183	C₄×C₄₇	#385	1	1	yes	characteristic
184	C₄×C₄₇	#389	1	2	yes	—
185	C₄×C₄₇	#395	1	1	yes	characteristic
186	C₄×C₄₇	#398	1	2	yes	—
187	C₄×C₄₇	#399	1	1	yes	characteristic
188	Dic₄₇	—	4	4	no	—
189	Dic₄₇	—	8	4	no	—
190	C₂²×#106	—	47	1	no	—
191	C₂×#389	—	47	2	no	—
192	C₂×#340	—	47	2	no	—
193	C₂×#340	D₄₇	1	1	yes	characteristic
194	C₂×#336	—	47	1	no	—
195	C₂×C₄₇	#1444	1	1	yes	characteristic
196	C₂×C₄₇	#1864	1	2	yes	—
197	C₂×C₄₇	#1865	1	2	yes	—
198	C₂×C₄₇	#1941	1	1	yes	characteristic
199	C₂×C₄₇	#1943	1	1	yes	characteristic
200	C₂×C₄₇	#2000	1	2	yes	—
201	C₂×C₄₇	#2058	1	2	yes	—
202	C₂×C₄₇	#2059	1	2	yes	—
203	C₂×C₄₇	#2088	1	2	yes	—
204	C₂³×C₈	—	47	1	no	—
205	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂²×C₄⋊C₄	—	47	2	no	—
207	C₂²×C₄⋊C₄	—	94	2	no	—
208	C₂²×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
209	C₂²×C₄²	—	47	1	no	—
210	C₂×#106	—	94	4	no	—
211	C₂×#106	—	94	2	no	—
212	#389	—	94	4	no	—
213	#389	—	94	4	no	—
214	C₂×#95	—	94	2	no	—
215	#340	—	94	4	no	—
216	#340	Dic₄₇	1	4	yes	complemented
217	#336	—	94	2	no	—
218	C₄₇	#11327	1	1	yes	characteristic, complemented, Sylow
219	C₂³×C₄	—	2	2	no	—
220	C₂³×C₄	—	47	2	no	—
221	C₂³×C₄	—	94	2	no	—
222	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
223	C₂²×C₈	—	2	2	no	—
224	C₂²×C₈	—	2	2	no	—
225	C₂²×C₈	—	47	2	no	—
226	C₂²×C₈	—	94	1	no	—
227	C₂²×C₈	—	94	2	no	—
228	C₂²×C₈	—	94	2	no	—
229	C₂²×C₈	—	94	1	no	—
230	C₂²×C₈	Dic₉₄	1	2	yes	—
231	C₂²×C₈	D₁₈₈	1	2	yes	—
232	C₂²×C₈	C₂×Dic₄₇	1	2	yes	—
233	C₂×C₄⋊C₄	—	2	2	no	—
234	C₂×C₄⋊C₄	—	2	2	no	—
235	C₂×C₄⋊C₄	—	2	2	no	—
236	C₂×C₄⋊C₄	—	47	4	no	—
237	C₂×C₄⋊C₄	—	94	2	no	—
238	C₂×C₄⋊C₄	—	94	2	no	—
239	C₂×C₄⋊C₄	—	94	2	no	—
240	C₂×C₄⋊C₄	—	94	2	no	—
241	C₂×C₄⋊C₄	—	94	8	no	—
242	C₂×C₄⋊C₄	—	94	2	no	—
243	C₂×C₄⋊C₄	—	188	4	no	—
244	C₂×C₄⋊C₄	—	188	4	no	—
245	C₂×C₄⋊C₄	Dic₉₄	1	4	yes	—
246	C₂×C₄⋊C₄	D₁₈₈	1	4	yes	—
247	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
248	C₂×C₄²	—	94	1	no	—
249	C₂×C₄²	—	94	2	no	—
250	C₂×C₄²	—	94	2	no	—
251	C₂×C₄²	—	94	1	no	—
252	#106	—	94	8	no	—
253	#95	—	94	8	no	—
254	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
255	C₂²×C₄	—	2	4	no	—
256	C₂²×C₄	—	2	4	no	—
257	C₂²×C₄	—	2	4	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	—	4	2	no	—
260	C₂²×C₄	—	4	2	no	—
261	C₂²×C₄	—	4	2	no	—
262	C₂²×C₄	—	47	4	no	—
263	C₂²×C₄	—	94	2	no	—
264	C₂²×C₄	—	94	2	no	—
265	C₂²×C₄	—	94	2	no	—
266	C₂²×C₄	—	94	2	no	—
267	C₂²×C₄	—	94	2	no	—
268	C₂²×C₄	—	94	2	no	—
269	C₂²×C₄	—	94	4	no	—
270	C₂²×C₄	—	188	2	no	—
271	C₂²×C₄	—	188	2	no	—
272	C₂²×C₄	—	188	2	no	—
273	C₂²×C₄	—	188	2	no	—
274	C₂²×C₄	—	188	2	no	—
275	C₂²×C₄	—	188	2	no	—
276	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
277	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
278	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
279	C₂²×C₄	C₂×D₁₈₈	1	2	yes	—
280	C₂²×C₄	D₄×D₄₇	1	2	yes	—
281	C₂²×C₄	#10625352	1	2	yes	—
282	C₂²×C₄	#10625352	1	1	yes	characteristic
283	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
284	C₂²×C₄	#10625354	1	1	yes	characteristic
285	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
286	C₂×C₈	—	2	4	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	4	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	94	4	no	—
291	C₂×C₈	—	94	2	no	—
292	C₂×C₈	—	188	1	no	—
293	C₂×C₈	—	188	2	no	—
294	C₂×C₈	—	188	1	no	—
295	C₂×C₈	C₄⋊Dic₄₇	1	4	yes	complemented
296	C₄⋊C₄	—	2	4	no	—
297	C₄⋊C₄	—	2	4	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	94	4	no	—
300	C₄⋊C₄	—	94	4	no	—
301	C₄⋊C₄	—	188	16	no	—
302	C₄⋊C₄	—	188	2	no	—
303	C₄⋊C₄	—	188	2	no	—
304	C₄⋊C₄	C₄⋊Dic₄₇	1	8	yes	complemented
305	C₄²	—	188	1	no	—
306	C₄²	—	188	2	no	—
307	C₄²	—	188	1	no	—
308	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
309	C₂³	#13093994	1	2	yes	—
310	C₂³	#13093999	1	1	yes	characteristic
311	C₂³	#13094001	1	2	yes	—
312	C₂³	#13094023	1	1	yes	characteristic
313	C₂³	SD₁₆×D₄₇	1	2	yes	—
314	C₂³	#13094045	1	2	yes	—
315	C₂³	#13094048	1	2	yes	—
316	C₂³	#13094056	1	2	yes	—
317	C₂×C₄	—	2	8	no	—
318	C₂×C₄	—	4	4	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	4	4	no	—
321	C₂×C₄	—	4	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	94	4	no	—
325	C₂×C₄	—	94	4	no	—
326	C₂×C₄	—	94	4	no	—
327	C₂×C₄	—	376	2	no	—
328	C₂×C₄	—	376	2	no	—
329	C₂×C₄	—	376	2	no	—
330	C₂×C₄	—	376	2	no	—
331	C₂×C₄	—	188	4	no	—
332	C₂×C₄	—	188	4	no	—
333	C₂×C₄	—	188	4	no	—
334	C₂×C₄	—	188	2	no	—
335	C₂×C₄	—	188	2	no	—
336	C₂×C₄	—	188	2	no	—
337	C₂×C₄	—	188	2	no	—
338	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
339	C₂×C₄	C₂×C₄⋊Dic₄₇	1	2	yes	—
340	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
341	C₂×C₄	Q₈×Dic₄₇	1	1	yes	characteristic
342	C₂×C₄	#13093994	1	1	yes	characteristic
343	C₂×C₄	#13093999	1	2	yes	—
344	C₂×C₄	#13094001	1	2	yes	—
345	C₂×C₄	#13094001	1	2	yes	—
346	C₂×C₄	#13094004	1	2	yes	—
347	C₂×C₄	#13094004	1	1	yes	characteristic
348	C₂×C₄	#13094008	1	1	yes	characteristic
349	C₂×C₄	#13094008	1	2	yes	—
350	C₂×C₄	#13094015	1	2	yes	—
351	C₂×C₄	#13094015	1	1	yes	characteristic
352	C₂×C₄	#13094021	1	1	yes	characteristic
353	C₂×C₄	#13094023	1	2	yes	—
354	C₂×C₄	#13094024	1	1	yes	characteristic
355	C₂×C₄	#13094024	1	2	yes	—
356	C₈	—	2	4	no	—
357	C₈	—	188	2	no	—
358	C₂²	#15688998	1	2	yes	—
359	C₂²	#15689022	1	1	yes	characteristic
360	C₂²	#15689033	1	1	yes	characteristic
361	C₂²	#15689044	1	2	yes	—
362	C₂²	#15689055	1	1	yes	characteristic
363	C₂²	SD₁₆×Dic₄₇	1	2	yes	—
364	C₂²	#15689230	1	1	yes	characteristic
365	C₂²	#15689235	1	1	yes	characteristic
366	C₂²	#15689263	1	2	yes	—
367	C₂²	#15689269	1	2	yes	—
368	C₂²	#15689275	1	2	yes	—
369	C₂²	#15689288	1	2	yes	—
370	C₂²	#15689353	1	2	yes	—
371	C₂²	#15689370	1	2	yes	—
372	C₂²	#15689406	1	2	yes	—
373	C₂²	#15689411	1	2	yes	—
374	C₂²	#15689425	1	2	yes	—
375	C₂²	#15689428	1	2	yes	—
376	C₂²	#15689520	1	1	yes	characteristic
377	C₂²	#15689523	1	1	yes	characteristic
378	C₂²	#15689531	1	2	yes	—
379	C₄	—	4	8	no	—
380	C₄	—	376	4	no	—
381	C₄	—	188	4	no	—
382	C₄	#15688993	1	1	yes	characteristic
383	C₄	#15688998	1	1	yes	characteristic
384	C₄	#15689022	1	2	yes	—
385	C₄	#15689044	1	1	yes	characteristic
386	C₄	#15689055	1	2	yes	—
387	C₄	#15689060	1	1	yes	characteristic
388	C₂	#20241653	1	1	yes	characteristic
389	C₂	#20243651	1	2	yes	—
390	C₂	#20243658	1	2	yes	—
391	C₂	#20244117	1	1	yes	characteristic
392	C₂	#20244127	1	1	yes	characteristic
393	C₂	#20244394	1	2	yes	—
394	C₂	#20244720	1	2	yes	—
395	C₂	#20244725	1	2	yes	—
396	C₂	#20244888	1	2	yes	—

	subgroup	G/H
center	C₂⁴	D₄×D₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#340	C₂
socle, prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#340	D₄₇
hypocenter	C₄₇	#11327
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂×#340

Complements

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

N	H ≅ G/N	type
19. C₄₇×#340	C₄	semidirect
91. C₂×C₈×C₄₇	C₄⋊C₄	semidirect
95. C₄⋊C₄×C₄₇	C₄⋊C₄	semidirect
216. #340	Dic₄₇	semidirect
218. C₄₇	#11327	semidirect
295. C₂×C₈	C₄⋊Dic₄₇	semidirect
304. C₄⋊C₄	C₄⋊Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#13093956	2
C₂×#15689022	2
C₂×#15688885	2
C₂×#15688877	2
C₂×C₄₇×#340	2
#11327	47