Subgroups — #26115405

Order 12032.

856 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20243368	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15688857	C₂	1	4	yes	maximal, complemented
3	C₄×C₄₇⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2856	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₄×Dic₄₇	—	2	1	no	—
6	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
7	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
8	C₂×C₄₇⋊#95	—	2	1	no	—
9	C₂×C₄₇⋊#95	C₂²	1	2	yes	—
10	#15688878	—	2	1	no	—
11	#15688857	—	2	8	no	—
12	C₂×#127×C₄₇	C₄	1	1	yes	characteristic, complemented
13	C₂×#121×C₄₇	—	2	1	no	—
14	C₂×#121×C₄₇	—	2	1	no	—
15	C₂×#121×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#390	—	2	1	no	—
18	C₄₇×#390	—	2	1	no	—
19	C₄₇×#390	C₄	1	2	yes	complemented
20	C₄₇×#384	C₄	1	1	yes	characteristic, complemented
21	C₂³×Dic₄₇	—	2	2	no	—
22	C₂²×C₄₇⋊C₈	—	2	2	no	—
23	C₂×C₄×Dic₄₇	—	2	4	no	—
24	C₂×C₄×Dic₄₇	—	4	2	no	—
25	C₂×C₄×Dic₄₇	—	4	2	no	—
26	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
27	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
28	C₄₇⋊#95	—	2	4	no	—
29	C₄₇⋊#95	—	2	2	no	—
30	C₄₇⋊#95	D₄	1	4	yes	complemented
31	C₂²×D₄×C₄₇	—	2	2	no	—
32	C₂²×D₄×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	1	no	—
34	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
35	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
38	#127×C₄₇	—	4	2	no	—
39	#121×C₄₇	—	2	4	no	—
40	#121×C₄₇	—	2	4	no	—
41	#121×C₄₇	—	4	4	no	—
42	#121×C₄₇	—	4	2	no	—
43	#121×C₄₇	—	4	2	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
46	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄²×C₄₇	—	4	2	no	—
51	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂⁴×C₄₇	—	2	2	no	—
56	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
57	C₂×D₄×C₄₇	—	2	4	no	—
58	C₂×D₄×C₄₇	—	4	2	no	—
59	C₂×D₄×C₄₇	—	4	2	no	—
60	C₂×D₄×C₄₇	—	4	2	no	—
61	C₂×D₄×C₄₇	—	4	2	no	—
62	C₂×D₄×C₄₇	—	4	4	no	—
63	C₂×D₄×C₄₇	—	4	2	no	—
64	C₂×D₄×C₄₇	—	4	2	no	—
65	C₂×D₄×C₄₇	—	4	4	no	—
66	C₂×D₄×C₄₇	—	4	2	no	—
67	C₂×D₄×C₄₇	—	4	2	no	—
68	C₂×D₄×C₄₇	—	4	2	no	—
69	C₂×D₄×C₄₇	—	4	2	no	—
70	C₂²×C₄×C₄₇	—	2	2	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	4	1	no	—
76	C₂²×C₄×C₄₇	—	4	1	no	—
77	C₂²×C₄×C₄₇	—	4	1	no	—
78	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	D₈	1	2	yes	—
83	C₂²×C₄×C₄₇	SD₁₆	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
87	C₂²×C₄×C₄₇	#41	1	2	yes	—
88	C₂²×Dic₄₇	—	2	4	no	—
89	C₂²×Dic₄₇	—	2	4	no	—
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	4	2	no	—
92	C₂²×Dic₄₇	—	4	2	no	—
93	C₂²×Dic₄₇	—	4	2	no	—
94	C₂²×Dic₄₇	—	4	2	no	—
95	C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₄⋊C₄×C₄₇	—	4	2	no	—
97	C₄⋊C₄×C₄₇	—	4	2	no	—
98	C₂²⋊C₄×C₄₇	—	4	4	no	—
99	C₂²⋊C₄×C₄₇	—	4	4	no	—
100	C₂²⋊C₄×C₄₇	—	4	2	no	—
101	C₂²⋊C₄×C₄₇	—	4	2	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	—	4	1	no	—
106	C₄×Dic₄₇	—	4	8	no	—
107	C₂×C₄₇⋊C₈	—	4	2	no	—
108	C₂×C₄₇⋊C₈	—	4	2	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂³×C₄₇	—	2	1	no	—
111	C₂³×C₄₇	—	2	1	no	—
112	C₂³×C₄₇	—	2	1	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	4	2	no	—
115	C₂³×C₄₇	—	4	2	no	—
116	C₂³×C₄₇	—	4	2	no	—
117	C₂³×C₄₇	—	4	2	no	—
118	C₂³×C₄₇	—	4	2	no	—
119	C₂³×C₄₇	—	4	2	no	—
120	C₂³×C₄₇	—	4	2	no	—
121	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
122	C₂³×C₄₇	#121	1	2	yes	—
123	C₂³×C₄₇	C₂×D₈	1	1	yes	characteristic
124	C₂³×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
125	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
126	D₄×C₄₇	—	8	4	no	—
127	D₄×C₄₇	—	8	4	no	—
128	D₄×C₄₇	—	8	4	no	—
129	D₄×C₄₇	—	8	4	no	—
130	D₄×C₄₇	—	8	4	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
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	4	no	—
140	C₂×C₄×C₄₇	—	2	4	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	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	#99	1	2	yes	—
151	C₂×C₄×C₄₇	#102	1	2	yes	—
152	C₂×C₄×C₄₇	#102	1	2	yes	—
153	C₂×C₄×C₄₇	#104	1	2	yes	—
154	C₂×C₄×C₄₇	#104	1	2	yes	—
155	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
156	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	8	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	—	4	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₂×Dic₄₇	—	4	4	no	—
164	C₂×Dic₄₇	—	4	4	no	—
165	C₄₇⋊C₈	—	8	2	no	—
166	#9712	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	1	no	—
170	C₂²×C₄₇	—	2	1	no	—
171	C₂²×C₄₇	—	2	1	no	—
172	C₂²×C₄₇	—	2	1	no	—
173	C₂²×C₄₇	—	2	2	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	8	2	no	—
176	C₂²×C₄₇	—	8	2	no	—
177	C₂²×C₄₇	—	8	2	no	—
178	C₂²×C₄₇	—	8	2	no	—
179	C₂²×C₄₇	—	8	2	no	—
180	C₂²×C₄₇	—	8	2	no	—
181	C₂²×C₄₇	—	8	2	no	—
182	C₂²×C₄₇	#390	1	1	yes	characteristic
183	C₂²×C₄₇	C₂×#99	1	1	yes	characteristic
184	C₂²×C₄₇	#410	1	1	yes	characteristic
185	C₂²×C₄₇	C₂×#102	1	1	yes	characteristic
186	C₂²×C₄₇	#418	1	1	yes	characteristic
187	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
188	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
189	C₂²×C₄₇	#459	1	2	yes	—
190	C₂²×C₄₇	#460	1	2	yes	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	2	2	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	2	2	no	—
195	C₄×C₄₇	—	2	2	no	—
196	C₄×C₄₇	—	4	1	no	—
197	C₄×C₄₇	—	8	2	no	—
198	C₄×C₄₇	#327	1	4	yes	complemented
199	Dic₄₇	—	4	8	no	—
200	#2856	D₄₇	1	1	yes	characteristic
201	#1797	—	47	1	no	—
202	C₂×#327	—	47	4	no	—
203	C₄×#95	—	47	1	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	—	2	2	no	—
206	C₂×C₄₇	—	16	2	no	—
207	C₂×C₄₇	C₂×#327	1	1	yes	characteristic
208	C₂×C₄₇	#1502	1	1	yes	characteristic
209	C₂×C₄₇	#1505	1	1	yes	characteristic
210	C₂×C₄₇	#1507	1	1	yes	characteristic
211	C₂×C₄₇	#1962	1	1	yes	characteristic
212	C₂×C₄₇	#1964	1	1	yes	characteristic
213	C₂×C₄₇	#1982	1	1	yes	characteristic
214	C₂×#127	Dic₄₇	1	1	yes	characteristic, complemented
215	C₂×#121	—	2	1	no	—
216	C₂×#121	—	2	1	no	—
217	C₂×#121	C₂×D₄₇	1	2	yes	—
218	C₂²×C₄²	—	94	1	no	—
219	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄⋊C₈	—	94	1	no	—
221	C₂×C₂²⋊C₈	—	47	2	no	—
222	#390	—	2	1	no	—
223	#390	—	2	1	no	—
224	#390	Dic₄₇	1	2	yes	complemented
225	#384	Dic₄₇	1	1	yes	characteristic, complemented
226	C₂×#95	—	47	2	no	—
227	C₂×#95	—	94	1	no	—
228	#336	—	94	1	no	—
229	#327	—	94	8	no	—
230	C₄₇	#9712	1	1	yes	characteristic, complemented, Sylow
231	C₂²×D₄	—	2	2	no	—
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
235	C₂³×C₄	—	94	2	no	—
236	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
237	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
238	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
239	C₂²×C₈	—	94	2	no	—
240	#127	—	4	2	no	—
241	#121	—	2	4	no	—
242	#121	—	2	4	no	—
243	#121	—	4	4	no	—
244	#121	—	4	2	no	—
245	#121	—	4	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
249	C₂×C₂²⋊C₄	—	2	2	no	—
250	C₂×C₂²⋊C₄	—	2	2	no	—
251	C₂×C₂²⋊C₄	—	2	2	no	—
252	C₂×C₄²	—	4	2	no	—
253	C₂×C₄²	—	94	4	no	—
254	C₂×C₄²	—	188	2	no	—
255	C₂×C₄²	—	188	2	no	—
256	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
257	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
260	C₄⋊C₈	—	188	2	no	—
261	C₂²⋊C₈	—	94	4	no	—
262	#95	—	47	4	no	—
263	#95	—	94	4	no	—
264	#95	—	94	2	no	—
265	C₂⁴	—	2	2	no	—
266	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	4	2	no	—
269	C₂×D₄	—	4	2	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	4	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂×D₄	—	4	2	no	—
275	C₂×D₄	—	4	4	no	—
276	C₂×D₄	—	4	2	no	—
277	C₂×D₄	—	4	2	no	—
278	C₂×D₄	—	4	2	no	—
279	C₂×D₄	—	4	2	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	2	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	94	4	no	—
289	C₂²×C₄	—	94	4	no	—
290	C₂²×C₄	—	94	4	no	—
291	C₂²×C₄	—	188	2	no	—
292	C₂²×C₄	—	188	2	no	—
293	C₂²×C₄	—	188	2	no	—
294	C₂²×C₄	—	188	2	no	—
295	C₂²×C₄	#10625334	1	2	yes	—
296	C₂²×C₄	#10625335	1	2	yes	—
297	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
298	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
300	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
301	C₂²×C₄	D₄×D₄₇	1	2	yes	—
302	C₂²×C₄	#10625352	1	2	yes	—
303	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
305	C₂×C₈	—	188	2	no	—
306	C₂×C₈	—	188	2	no	—
307	C₂×C₈	—	188	2	no	—
308	C₄⋊C₄	—	2	4	no	—
309	C₄⋊C₄	—	4	2	no	—
310	C₄⋊C₄	—	4	2	no	—
311	C₂²⋊C₄	—	4	4	no	—
312	C₂²⋊C₄	—	4	4	no	—
313	C₂²⋊C₄	—	4	2	no	—
314	C₂²⋊C₄	—	4	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	4	1	no	—
318	C₄²	—	4	1	no	—
319	C₄²	—	188	8	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	—	2	1	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	2	no	—
329	C₂³	—	4	2	no	—
330	C₂³	—	4	2	no	—
331	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
332	C₂³	#13093995	1	2	yes	—
333	C₂³	C₂×#10625334	1	1	yes	characteristic
334	C₂³	C₂×#10625335	1	1	yes	characteristic
335	C₂³	#13094050	1	2	yes	—
336	D₄	—	8	4	no	—
337	D₄	—	8	4	no	—
338	D₄	—	8	4	no	—
339	D₄	—	8	4	no	—
340	D₄	—	8	4	no	—
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	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	94	8	no	—
361	C₂×C₄	—	188	4	no	—
362	C₂×C₄	—	188	4	no	—
363	C₂×C₄	—	188	4	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	4	no	—
366	C₂×C₄	—	188	4	no	—
367	C₂×C₄	#13093939	1	2	yes	—
368	C₂×C₄	#13093945	1	2	yes	—
369	C₂×C₄	#13093945	1	2	yes	—
370	C₂×C₄	#13093951	1	2	yes	—
371	C₂×C₄	#13093951	1	2	yes	—
372	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
373	C₂×C₄	#13094011	1	1	yes	characteristic
374	C₂×C₄	#13094020	1	1	yes	characteristic
375	C₈	—	376	2	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	8	2	no	—
386	C₂²	—	8	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	#15689026	1	1	yes	characteristic
392	C₂²	C₂×#13093939	1	1	yes	characteristic
393	C₂²	#15689097	1	1	yes	characteristic
394	C₂²	C₂×#13093945	1	1	yes	characteristic
395	C₂²	#15689128	1	1	yes	characteristic
396	C₂²	C₂×#13093951	1	1	yes	characteristic
397	C₂²	C₂×#13093951	1	1	yes	characteristic
398	C₂²	#15689315	1	2	yes	—
399	C₂²	#15689320	1	2	yes	—
400	C₄	—	2	1	no	—
401	C₄	—	2	2	no	—
402	C₄	—	2	1	no	—
403	C₄	—	2	2	no	—
404	C₄	—	2	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	8	2	no	—
407	C₄	—	188	8	no	—
408	C₄	#15688857	1	4	yes	complemented
409	C₂	—	2	2	no	—
410	C₂	—	2	2	no	—
411	C₂	—	16	2	no	—
412	C₂	C₂×#15688857	1	1	yes	characteristic
413	C₂	#20241883	1	1	yes	characteristic
414	C₂	#20241896	1	1	yes	characteristic
415	C₂	#20241904	1	1	yes	characteristic
416	C₂	#20244217	1	1	yes	characteristic
417	C₂	#20244225	1	1	yes	characteristic
418	C₂	#20244316	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator	C₂²×C₄×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting, prime radical	C₄₇×#2856	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	#2856	D₄₇
hypocenter	C₄₇	#9712
LCS	G ▷ C₂²×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ #2856

Complements

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

N	H ≅ G/N	type
1. #20243368	C₂	semidirect
2. C₂×#15688857	C₂	semidirect
3. C₄×C₄₇⋊#95	C₂	semidirect
12. C₂×#127×C₄₇	C₄	semidirect
19. C₄₇×#390	C₄	semidirect
20. C₄₇×#384	C₄	semidirect
30. C₄₇⋊#95	D₄	semidirect
198. C₄×C₄₇	#327	semidirect
214. C₂×#127	Dic₄₇	semidirect
224. #390	Dic₄₇	semidirect
225. #384	Dic₄₇	semidirect
230. C₄₇	#9712	semidirect
408. C₄	#15688857	semidirect

Maximal subgroups

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

subgroup	index
#20243368	2
C₂×#15688857	2
C₄×C₄₇⋊#95	2
C₄₇×#2856	2
#9712	47