Subgroups — #26216709

Order 12032.

1102 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689164	C₂	1	2	yes	maximal
2	C₂×#15689162	C₂	1	2	yes	maximal
3	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
4	#20245794	C₂	1	1	yes	maximal, characteristic
5	#382×D₄₇	C₂	1	1	yes	maximal, characteristic
6	#20243555	C₂	1	2	yes	maximal, complemented
7	#20243553	C₂	1	2	yes	maximal, complemented
8	#20243552	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243550	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243550	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×#10625324	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₂²	1	2	yes	—
15	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	#15689164	—	2	8	no	—
18	#15689162	—	2	8	no	—
19	C₂×#13093958	C₂²	1	2	yes	—
20	C₂×#13093957	C₂²	1	2	yes	—
21	C₂×#13093957	C₂²	1	2	yes	—
22	C₂×#13093956	C₂²	1	2	yes	—
23	C₂×#13093955	C₂²	1	2	yes	—
24	C₂×#13093955	C₂²	1	2	yes	—
25	C₄×#10625324	C₄	1	8	yes	complemented
26	C₂×#13093934	C₂²	1	1	yes	characteristic
27	C₂×#13093934	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	#15688992	C₂²	1	2	yes	—
30	#15688989	C₂²	1	1	yes	characteristic
31	#15688989	C₂²	1	1	yes	characteristic
32	#15688988	C₂²	1	2	yes	—
33	#15688987	—	2	2	no	—
34	#15688982	—	2	2	no	—
35	#15688974	—	2	2	no	—
36	#95×D₄₇	—	2	2	no	—
37	C₂×#107×C₄₇	C₂²	1	2	yes	—
38	C₂×#106×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#382	C₂²	1	1	yes	characteristic
41	C₄₇×#382	C₂²	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	—	2	2	no	—
43	C₂²×C₄×D₄₇	D₄	1	2	yes	—
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	C₂×#10625324	C₂×C₄	1	4	yes	—
46	C₂×#10625324	C₂×C₄	1	4	yes	—
47	C₂×#10625324	D₄	1	4	yes	—
48	C₂×#10625324	D₄	1	4	yes	—
49	C₂×#10625324	Q₈	1	4	yes	—
50	C₂×#10625324	Q₈	1	4	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
53	#13093982	—	2	4	no	—
54	#13093982	—	2	4	no	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	—	2	4	no	—
58	C₂×Dic₄₇⋊C₄	—	2	2	no	—
59	C₄⋊C₄×D₄₇	—	2	4	no	—
60	C₄⋊C₄×D₄₇	—	2	4	no	—
61	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
62	C₂×C₄×Dic₄₇	—	2	2	no	—
63	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
65	C₄²×D₄₇	C₂×C₄	1	4	yes	—
66	C₄²×D₄₇	Q₈	1	4	yes	—
67	#13093958	—	2	4	no	—
68	#13093957	—	2	4	no	—
69	#13093957	—	2	4	no	—
70	#13093956	—	2	4	no	—
71	#13093955	—	2	4	no	—
72	#13093955	—	2	4	no	—
73	#13093934	C₂×C₄	1	4	yes	complemented
74	#13093934	C₂×C₄	1	4	yes	complemented
75	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
76	C₄₇⋊#95	—	2	2	no	—
77	C₄₇⋊#95	—	2	2	no	—
78	C₄₇⋊#95	—	2	4	no	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#107×C₄₇	—	2	4	no	—
85	#106×C₄₇	—	2	4	no	—
86	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
87	#95×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
97	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	—	4	4	no	—
99	C₂×C₄×D₄₇	—	4	8	no	—
100	C₂×C₄×D₄₇	—	4	4	no	—
101	C₂×C₄×D₄₇	C₄⋊C₄	1	8	yes	—
102	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
103	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
104	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
105	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
106	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
107	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
120	(C₂×D₄₇)⋊C₄	—	4	4	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	C₄⋊Dic₄₇	—	2	2	no	—
125	Dic₄₇⋊C₄	—	4	8	no	—
126	Dic₄₇⋊C₄	—	4	4	no	—
127	C₄×Dic₄₇	—	4	4	no	—
128	C₄×Dic₄₇	C₄⋊C₄	1	8	yes	—
129	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
130	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
136	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
137	#10625324	C₄⋊C₄	1	16	yes	complemented
138	#10625324	C₄⋊C₄	1	16	yes	complemented
139	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
140	C₂²×D₄₇	—	2	4	no	—
141	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂²×D₄₇	#127	1	2	yes	—
143	C₂²×D₄₇	C₄⋊Q₈	1	2	yes	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	2	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	2	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	—	4	4	no	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
163	C₂×Dic₄₇	#127	1	2	yes	—
164	C₂×Dic₄₇	C₄⋊Q₈	1	2	yes	—
165	C₄×D₄₇	—	4	8	no	—
166	C₄×D₄₇	—	8	8	no	—
167	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
168	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
169	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
170	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
171	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
172	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
173	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
174	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
175	#20801	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
179	C₂²×C₄₇	#575	1	4	yes	—
180	C₂×D₄₇	—	2	4	no	—
181	C₂×D₄₇	—	2	4	no	—
182	C₂×D₄₇	—	2	4	no	—
183	C₂×D₄₇	#384	1	4	yes	—
184	C₄×C₄₇	—	2	4	no	—
185	C₄×C₄₇	—	8	2	no	—
186	C₄×C₄₇	—	8	2	no	—
187	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
188	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
189	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
190	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
191	Dic₄₇	—	2	4	no	—
192	Dic₄₇	—	8	2	no	—
193	Dic₄₇	—	8	2	no	—
194	Dic₄₇	#384	1	4	yes	—
195	C₂×#428	—	47	2	no	—
196	C₂×#428	—	47	2	no	—
197	C₂×C₄×M₁₆	—	47	1	no	—
198	#2285	—	47	1	no	—
199	C₂×#382	—	47	1	no	—
200	#1847	—	47	2	no	—
201	#1847	—	47	2	no	—
202	#1846	—	47	1	no	—
203	#1846	—	47	1	no	—
204	#1846	—	47	1	no	—
205	#1846	D₄₇	1	1	yes	characteristic, complemented
206	C₂×C₄₇	C₂×#384	1	1	yes	characteristic
207	C₂×C₄₇	#2911	1	2	yes	—
208	C₂×C₄₇	#3153	1	2	yes	—
209	C₂×C₄₇	#3166	1	2	yes	—
210	D₄₇	—	2	4	no	—
211	C₂²×M₁₆	—	47	1	no	—
212	C₂²×M₁₆	—	47	1	no	—
213	C₂×#117	—	47	2	no	—
214	C₂²×C₄⋊C₄	—	47	2	no	—
215	C₂²×C₄²	—	47	1	no	—
216	#428	—	94	8	no	—
217	#428	—	94	8	no	—
218	C₂×#107	—	47	2	no	—
219	C₂×#107	—	47	2	no	—
220	C₂×#107	—	47	2	no	—
221	C₂×#107	C₂×D₄₇	1	2	yes	—
222	C₂×#106	—	47	2	no	—
223	C₂×#106	—	47	2	no	—
224	C₂×#106	—	47	2	no	—
225	C₂×#106	C₂×D₄₇	1	2	yes	—
226	C₄×M₁₆	—	47	8	no	—
227	C₂×#97	—	47	1	no	—
228	C₂×#97	—	47	1	no	—
229	C₂×C₄×C₈	—	47	1	no	—
230	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
231	#384	—	47	2	no	—
232	#382	—	47	2	no	—
233	#382	—	47	1	no	—
234	#382	—	47	1	no	—
235	#382	—	94	2	no	—
236	#382	C₂×D₄₇	1	1	yes	characteristic
237	#382	C₂×D₄₇	1	1	yes	characteristic
238	#380	—	94	2	no	—
239	C₄×C₄⋊C₄	—	94	2	no	—
240	C₂×#95	—	94	2	no	—
241	C₄₇	#20801	1	1	yes	characteristic, complemented, Sylow
242	C₂³×C₄	—	47	1	no	—
243	C₂³×C₄	—	47	2	no	—
244	C₂³×C₄	—	94	2	no	—
245	C₂×M₁₆	—	47	4	no	—
246	C₂×M₁₆	—	47	4	no	—
247	C₂×M₁₆	—	47	4	no	—
248	C₂×M₁₆	—	47	4	no	—
249	C₂×M₁₆	—	47	4	no	—
250	C₂×M₁₆	—	47	4	no	—
251	C₂²×C₈	—	47	1	no	—
252	C₂²×C₈	—	47	1	no	—
253	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
255	#117	—	94	4	no	—
256	#117	—	94	4	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	94	4	no	—
260	C₂×C₄⋊C₄	—	94	4	no	—
261	C₂×C₄⋊C₄	—	94	2	no	—
262	C₂×C₄⋊C₄	—	94	4	no	—
263	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	94	2	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	4	no	—
269	C₂×C₄²	—	47	4	no	—
270	C₂×C₄²	—	94	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
272	#107	—	2	4	no	—
273	#107	—	94	4	no	—
274	#107	—	94	4	no	—
275	#107	—	94	4	no	—
276	#106	—	2	4	no	—
277	#106	—	94	4	no	—
278	#106	—	94	4	no	—
279	#106	—	94	4	no	—
280	#97	—	47	4	no	—
281	#97	—	47	4	no	—
282	C₄×C₈	—	47	4	no	—
283	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
284	#95	—	2	2	no	—
285	#95	—	2	2	no	—
286	#95	—	94	4	no	—
287	#95	—	94	2	no	—
288	#95	—	94	2	no	—
289	C₂⁴	—	47	1	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	47	1	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	47	2	no	—
300	C₂²×C₄	—	47	8	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	—	188	4	no	—
304	C₂²×C₄	—	188	4	no	—
305	C₂²×C₄	—	188	8	no	—
306	C₂²×C₄	D₄×D₄₇	1	2	yes	—
307	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
308	M₁₆	—	47	16	no	—
309	M₁₆	—	47	16	no	—
310	C₂×C₈	—	47	2	no	—
311	C₂×C₈	—	47	2	no	—
312	C₂×C₈	—	47	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	2	no	—
315	C₂×C₈	—	47	2	no	—
316	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
317	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
318	C₂×C₈	D₄×D₄₇	1	2	yes	—
319	C₂×C₈	D₄×D₄₇	1	2	yes	—
320	C₂×C₈	Q₈×D₄₇	1	2	yes	—
321	C₂×C₈	Q₈×D₄₇	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	94	2	no	—
328	C₄⋊C₄	—	94	2	no	—
329	C₄⋊C₄	—	94	2	no	—
330	C₄⋊C₄	—	188	4	no	—
331	C₄⋊C₄	—	188	8	no	—
332	C₂²⋊C₄	—	188	4	no	—
333	C₄²	—	47	8	no	—
334	C₄²	—	47	2	no	—
335	C₄²	—	47	2	no	—
336	C₄²	—	188	4	no	—
337	C₄²	C₂×C₄×D₄₇	1	2	yes	—
338	C₄²	Q₈×D₄₇	1	2	yes	—
339	C₂³	—	47	2	no	—
340	C₂³	—	47	2	no	—
341	C₂³	—	47	2	no	—
342	C₂³	—	94	4	no	—
343	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	4	4	no	—
349	C₂×C₄	—	47	2	no	—
350	C₂×C₄	—	47	2	no	—
351	C₂×C₄	—	47	2	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	47	4	no	—
356	C₂×C₄	—	47	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	376	8	no	—
359	C₂×C₄	—	188	8	no	—
360	C₂×C₄	—	188	2	no	—
361	C₂×C₄	—	188	2	no	—
362	C₂×C₄	—	188	4	no	—
363	C₂×C₄	—	188	4	no	—
364	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
365	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
369	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
371	C₈	—	47	4	no	—
372	C₈	—	47	4	no	—
373	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
374	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
375	C₂²	—	47	4	no	—
376	C₂²	—	94	4	no	—
377	C₂²	—	94	4	no	—
378	C₂²	—	94	4	no	—
379	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
380	C₂²	#127×D₄₇	1	1	yes	characteristic
381	C₂²	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
382	C₂²	#15689920	1	4	yes	—
383	C₄	—	2	4	no	—
384	C₄	—	8	2	no	—
385	C₄	—	8	2	no	—
386	C₄	—	47	4	no	—
387	C₄	—	94	4	no	—
388	C₄	—	376	2	no	—
389	C₄	—	376	2	no	—
390	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
391	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
392	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
393	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
394	C₂	—	94	4	no	—
395	C₂	#384×D₄₇	1	1	yes	characteristic
396	C₂	#20251976	1	2	yes	—
397	C₂	#20253849	1	2	yes	—
398	C₂	#20253936	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1846	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1846	D₄₇
hypocenter	C₄₇	#20801
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1846

Complements

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

N	H ≅ G/N	type
6. #20243555	C₂	semidirect
7. #20243553	C₂	semidirect
8. #20243552	C₂	semidirect
9. #20243550	C₂	semidirect
10. #20243550	C₂	semidirect
11. C₄₇×#1846	C₂	semidirect
25. C₄×#10625324	C₄	semidirect
73. #13093934	C₂×C₄	semidirect
74. #13093934	C₂×C₄	semidirect
75. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
86. C₄×C₈×C₄₇	C₂×C₄	semidirect
137. #10625324	C₄⋊C₄	semidirect
138. #10625324	C₄⋊C₄	semidirect
205. #1846	D₄₇	semidirect
241. C₄₇	#20801	semidirect
283. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689164	2
C₂×#15689162	2
C₂×C₄×#10625324	2
#20245794	2
#382×D₄₇	2
#20243555	2
#20243553	2
#20243552	2
#20243550	2
C₄₇×#1846	2
#20801	47