Subgroups — #26121545

Order 12032.

1678 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689087	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	4	yes	maximal, complemented
4	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic
5	C₂⁴×Dic₄₇	C₄	1	2	yes	—
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×C₄⋊Dic₄₇	—	2	8	no	—
8	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
9	C₂²×C₄⋊Dic₄₇	—	2	2	no	—
10	C₂²×C₄⋊Dic₄₇	C₄	1	2	yes	—
11	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	#15689087	—	2	2	no	—
13	#15689087	C₄	1	4	yes	complemented
14	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
15	#15688891	—	2	8	no	—
16	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#407	—	2	2	no	—
19	C₄₇×#407	C₄	1	4	yes	complemented
20	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
21	C₂³×Dic₄₇	—	2	4	no	—
22	C₂³×Dic₄₇	—	2	8	no	—
23	C₂³×Dic₄₇	—	4	8	no	—
24	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	4	no	—
27	C₂×#10625329	—	2	4	no	—
28	C₂×#10625329	C₂×C₄	1	4	yes	complemented
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	16	no	—
31	C₂×C₄⋊Dic₄₇	—	2	16	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	2	no	—
35	C₂×C₄⋊Dic₄₇	—	2	4	no	—
36	C₂×C₄⋊Dic₄₇	—	2	8	no	—
37	C₂×C₄⋊Dic₄₇	D₄	1	8	yes	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	8	no	—
39	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	—	2	4	no	—
41	C₂³×C₄×C₄₇	—	2	4	no	—
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
45	C₂³×C₄×C₄₇	D₄	1	2	yes	—
46	C₂³×C₄×C₄₇	D₄	1	2	yes	—
47	C₂³×C₄×C₄₇	D₄	1	2	yes	—
48	C₂³×C₄×C₄₇	Q₈	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	—	2	4	no	—
52	C₂×M₁₆×C₄₇	—	2	4	no	—
53	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
54	C₂²×C₈×C₄₇	—	2	2	no	—
55	C₂²⋊C₈×C₄₇	—	2	8	no	—
56	C₂⁴×C₄₇	—	2	4	no	—
57	C₂⁴×C₄₇	—	2	4	no	—
58	C₂⁴×C₄₇	—	2	2	no	—
59	C₂⁴×C₄₇	—	2	2	no	—
60	C₂⁴×C₄₇	C₄²	1	2	yes	—
61	C₂⁴×C₄₇	C₂²⋊C₄	1	2	yes	—
62	C₂⁴×C₄₇	C₄⋊C₄	1	2	yes	—
63	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	8	no	—
67	C₂²×C₄×C₄₇	—	2	8	no	—
68	C₂²×C₄×C₄₇	—	2	4	no	—
69	C₂²×C₄×C₄₇	—	2	4	no	—
70	C₂²×C₄×C₄₇	—	2	8	no	—
71	C₂²×C₄×C₄₇	—	2	8	no	—
72	C₂²×C₄×C₄₇	—	2	4	no	—
73	C₂²×C₄×C₄₇	—	2	4	no	—
74	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
77	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
78	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
79	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
80	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
87	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	#41	1	4	yes	—
89	C₂²×Dic₄₇	—	2	16	no	—
90	C₂²×Dic₄₇	—	2	4	no	—
91	C₂²×Dic₄₇	—	2	4	no	—
92	C₂²×Dic₄₇	—	4	32	no	—
93	C₂²×Dic₄₇	—	4	8	no	—
94	C₂²×Dic₄₇	—	4	8	no	—
95	C₂²×Dic₄₇	—	4	8	no	—
96	C₂²×Dic₄₇	C₂²⋊C₄	1	8	yes	—
97	M₁₆×C₄₇	—	2	8	no	—
98	M₁₆×C₄₇	—	4	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	4	2	no	—
101	C₂×C₈×C₄₇	—	4	2	no	—
102	C₄⋊Dic₄₇	—	2	16	no	—
103	C₄⋊Dic₄₇	—	2	8	no	—
104	C₄⋊Dic₄₇	—	2	8	no	—
105	#10625329	—	2	8	no	—
106	#10625329	—	4	4	no	—
107	C₂×C₄₇⋊C₈	—	2	4	no	—
108	C₂×C₄₇⋊C₈	—	4	2	no	—
109	C₂×C₄₇⋊C₈	—	4	2	no	—
110	C₂³×C₄₇	—	2	8	no	—
111	C₂³×C₄₇	—	2	16	no	—
112	C₂³×C₄₇	—	2	8	no	—
113	C₂³×C₄₇	—	2	8	no	—
114	C₂³×C₄₇	—	2	8	no	—
115	C₂³×C₄₇	—	2	4	no	—
116	C₂³×C₄₇	—	2	2	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	2	2	no	—
119	C₂³×C₄₇	—	2	2	no	—
120	C₂³×C₄₇	—	2	2	no	—
121	C₂³×C₄₇	—	2	2	no	—
122	C₂³×C₄₇	—	2	2	no	—
123	C₂³×C₄₇	#95	1	4	yes	—
124	C₂³×C₄₇	#100	1	4	yes	—
125	C₂³×C₄₇	#101	1	4	yes	—
126	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
127	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
128	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	#117	1	2	yes	—
131	C₂×C₄×C₄₇	—	2	4	no	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	8	no	—
136	C₂×C₄×C₄₇	—	2	8	no	—
137	C₂×C₄×C₄₇	—	2	8	no	—
138	C₂×C₄×C₄₇	—	2	8	no	—
139	C₂×C₄×C₄₇	#95	1	4	yes	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
146	C₂×C₄×C₄₇	#120	1	2	yes	—
147	C₂×C₄×C₄₇	#120	1	2	yes	—
148	C₂×C₄×C₄₇	#121	1	4	yes	—
149	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
150	C₂×C₄×C₄₇	#123	1	2	yes	—
151	C₂×C₄×C₄₇	#123	1	2	yes	—
152	C₂×Dic₄₇	—	2	8	no	—
153	C₂×Dic₄₇	—	4	32	no	—
154	C₂×Dic₄₇	—	4	8	no	—
155	C₂×Dic₄₇	—	4	8	no	—
156	C₂×Dic₄₇	—	4	8	no	—
157	C₈×C₄₇	—	4	4	no	—
158	C₄₇⋊C₈	—	4	4	no	—
159	#10727	—	47	1	no	maximal, Sylow
160	C₂²×C₄₇	—	2	16	no	—
161	C₂²×C₄₇	—	2	16	no	—
162	C₂²×C₄₇	—	2	4	no	—
163	C₂²×C₄₇	—	2	4	no	—
164	C₂²×C₄₇	—	2	4	no	—
165	C₂²×C₄₇	—	2	4	no	—
166	C₂²×C₄₇	—	2	4	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	4	no	—
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	2	no	—
173	C₂²×C₄₇	#343	1	8	yes	complemented
174	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
175	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
176	C₂²×C₄₇	#379	1	1	yes	characteristic
177	C₂²×C₄₇	#380	1	2	yes	—
178	C₂²×C₄₇	#381	1	1	yes	characteristic
179	C₂²×C₄₇	C₂×#100	1	2	yes	—
180	C₂²×C₄₇	C₂×#101	1	2	yes	—
181	C₄×C₄₇	—	2	4	no	—
182	C₄×C₄₇	#385	1	2	yes	—
183	C₄×C₄₇	#385	1	2	yes	—
184	C₄×C₄₇	#386	1	2	yes	—
185	C₄×C₄₇	#386	1	2	yes	—
186	Dic₄₇	—	4	8	no	—
187	C₂³×C₄⋊C₄	—	47	1	no	—
188	C₂×#407	—	47	1	no	—
189	C₂×#407	D₄₇	1	1	yes	characteristic
190	C₂×#343	—	47	4	no	—
191	C₂×C₄₇	—	2	8	no	—
192	C₂×C₄₇	—	2	2	no	—
193	C₂×C₄₇	—	2	2	no	—
194	C₂×C₄₇	C₂²⋊#95	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#343	1	2	yes	—
196	C₂×C₄₇	#1783	1	1	yes	characteristic
197	C₂×C₄₇	#1784	1	1	yes	characteristic
198	C₂×C₄₇	#1821	1	2	yes	—
199	C₂⁴×C₄	—	47	2	no	—
200	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
201	C₂²×M₁₆	—	47	2	no	—
202	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
203	C₂²×C₄⋊C₄	—	47	2	no	—
204	C₂²×C₄⋊C₄	—	47	2	no	—
205	C₂²×C₄⋊C₄	—	94	8	no	—
206	C₂²×C₄⋊C₄	—	94	2	no	—
207	C₂²×C₄⋊C₄	—	94	2	no	—
208	#407	—	2	2	no	—
209	#407	—	47	4	no	—
210	#407	—	94	2	no	—
211	#407	Dic₄₇	1	4	yes	complemented
212	C₂×C₂²⋊C₈	—	2	2	no	—
213	C₂×C₂²⋊C₈	—	94	2	no	—
214	#343	—	94	8	no	—
215	C₄₇	#10727	1	1	yes	characteristic, complemented, Sylow
216	C₂⁵	C₄×D₄₇	1	1	yes	characteristic
217	C₂³×C₄	—	2	4	no	—
218	C₂³×C₄	—	2	4	no	—
219	C₂³×C₄	—	47	4	no	—
220	C₂³×C₄	—	94	8	no	—
221	C₂³×C₄	—	94	4	no	—
222	C₂³×C₄	—	188	8	no	—
223	C₂³×C₄	Dic₉₄	1	2	yes	—
224	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
225	C₂³×C₄	C₄×D₄₇	1	2	yes	—
226	C₂³×C₄	D₁₈₈	1	2	yes	—
227	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
228	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
229	C₂³×C₄	C₂²⋊D₄₇	1	2	yes	—
230	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
231	C₂×M₁₆	—	2	2	no	—
232	C₂×M₁₆	—	2	4	no	—
233	C₂×M₁₆	—	2	4	no	—
234	C₂×M₁₆	—	47	4	no	—
235	C₂×M₁₆	—	94	2	no	—
236	C₂×M₁₆	—	94	4	no	—
237	C₂×M₁₆	—	94	4	no	—
238	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	complemented
239	C₂²×C₈	—	2	2	no	—
240	C₂²×C₈	—	94	2	no	—
241	C₂×C₄⋊C₄	—	47	8	no	—
242	C₂×C₄⋊C₄	—	94	8	no	—
243	C₂×C₄⋊C₄	—	94	16	no	—
244	C₂×C₄⋊C₄	—	94	16	no	—
245	C₂×C₄⋊C₄	—	94	4	no	—
246	C₂×C₄⋊C₄	—	94	2	no	—
247	C₂×C₄⋊C₄	—	94	4	no	—
248	C₂×C₄⋊C₄	—	94	2	no	—
249	C₂²⋊C₈	—	2	8	no	—
250	C₂²⋊C₈	—	94	8	no	—
251	C₂⁴	—	2	4	no	—
252	C₂⁴	—	2	4	no	—
253	C₂⁴	—	2	2	no	—
254	C₂⁴	—	2	2	no	—
255	C₂⁴	C₄×Dic₄₇	1	2	yes	—
256	C₂⁴	Dic₄₇⋊C₄	1	2	yes	—
257	C₂⁴	(C₂×D₄₇)⋊C₄	1	2	yes	—
258	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
259	C₂²×C₄	—	2	2	no	—
260	C₂²×C₄	—	2	2	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	8	no	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	4	no	—
268	C₂²×C₄	—	2	4	no	—
269	C₂²×C₄	—	47	8	no	—
270	C₂²×C₄	—	94	16	no	—
271	C₂²×C₄	—	94	4	no	—
272	C₂²×C₄	—	94	4	no	—
273	C₂²×C₄	—	188	32	no	—
274	C₂²×C₄	—	188	8	no	—
275	C₂²×C₄	—	188	8	no	—
276	C₂²×C₄	—	188	8	no	—
277	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
278	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
279	C₂²×C₄	Dic₄₇⋊C₄	1	4	yes	—
280	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
281	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	2	yes	—
282	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	4	yes	—
283	C₂²×C₄	C₂²⋊Dic₄₇	1	4	yes	—
284	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
287	C₂²×C₄	D₄×D₄₇	1	4	yes	—
288	C₂²×C₄	#10625352	1	4	yes	—
289	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
292	M₁₆	—	2	8	no	—
293	M₁₆	—	4	4	no	—
294	M₁₆	—	94	8	no	—
295	M₁₆	—	188	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	94	4	no	—
300	C₂×C₈	—	188	2	no	—
301	C₂×C₈	—	188	2	no	—
302	C₄⋊C₄	—	94	16	no	—
303	C₄⋊C₄	—	94	8	no	—
304	C₄⋊C₄	—	94	8	no	—
305	C₂³	—	2	8	no	—
306	C₂³	—	2	16	no	—
307	C₂³	—	2	8	no	—
308	C₂³	—	2	4	no	—
309	C₂³	—	2	2	no	—
310	C₂³	—	2	4	no	—
311	C₂³	—	2	2	no	—
312	C₂³	—	2	2	no	—
313	C₂³	—	2	2	no	—
314	C₂³	—	2	2	no	—
315	C₂³	—	2	2	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	2	8	no	—
318	C₂³	C₄₇⋊#95	1	4	yes	—
319	C₂³	#13093940	1	4	yes	—
320	C₂³	#13093942	1	4	yes	—
321	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
322	C₂³	C₂²⋊C₄×D₄₇	1	2	yes	—
323	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
324	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
325	C₂³	#13093980	1	2	yes	—
326	C₂×C₄	—	2	4	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	4	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	2	8	no	—
332	C₂×C₄	—	2	8	no	—
333	C₂×C₄	—	2	8	no	—
334	C₂×C₄	—	94	8	no	—
335	C₂×C₄	—	188	32	no	—
336	C₂×C₄	—	188	8	no	—
337	C₂×C₄	—	188	8	no	—
338	C₂×C₄	—	188	8	no	—
339	C₂×C₄	C₄₇⋊#95	1	4	yes	—
340	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
342	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
344	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
345	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
346	C₂×C₄	#13093992	1	2	yes	—
347	C₂×C₄	#13093994	1	2	yes	—
348	C₂×C₄	#13093996	1	4	yes	—
349	C₂×C₄	#13094001	1	4	yes	—
350	C₂×C₄	#13094005	1	2	yes	—
351	C₂×C₄	#13094008	1	2	yes	—
352	C₈	—	4	4	no	—
353	C₈	—	188	4	no	—
354	C₂²	—	2	16	no	—
355	C₂²	—	2	16	no	—
356	C₂²	—	2	4	no	—
357	C₂²	—	2	4	no	—
358	C₂²	—	2	4	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	2	no	—
361	C₂²	—	2	4	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	4	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	4	no	—
367	C₂²	#15688891	1	8	yes	complemented
368	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
369	C₂²	C₂²⋊C₄×Dic₄₇	1	2	yes	—
370	C₂²	#15688978	1	1	yes	characteristic
371	C₂²	#15688981	1	2	yes	—
372	C₂²	#15688984	1	1	yes	characteristic
373	C₂²	C₂×#13093940	1	2	yes	—
374	C₂²	C₂×#13093942	1	2	yes	—
375	C₄	—	2	4	no	—
376	C₄	—	188	8	no	—
377	C₄	#15688995	1	2	yes	—
378	C₄	#15688998	1	2	yes	—
379	C₄	#15689000	1	2	yes	—
380	C₄	#15689003	1	2	yes	—
381	C₂	—	2	2	no	—
382	C₂	—	2	2	no	—
383	C₂	—	2	8	no	—
384	C₂	#20241610	1	1	yes	characteristic
385	C₂	C₂×#15688891	1	2	yes	—
386	C₂	#20243308	1	1	yes	characteristic
387	C₂	#20243311	1	1	yes	characteristic
388	C₂	#20243466	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×(C₂×D₄₇)⋊C₄
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#407	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁵×C₄₇	C₂×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#407	D₄₇
hypocenter	C₄₇	#10727
LCS	G ▷ C₂³×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂⁴×C₄ ◁ C₂×#407

Complements

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

N	H ≅ G/N	type
3. C₂×#15688891	C₂	semidirect
13. #15689087	C₄	semidirect
19. C₄₇×#407	C₄	semidirect
28. C₂×#10625329	C₂×C₄	semidirect
53. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
173. C₂²×C₄₇	#343	semidirect
211. #407	Dic₄₇	semidirect
215. C₄₇	#10727	semidirect
238. C₂×M₁₆	C₂×Dic₄₇	semidirect
367. C₂²	#15688891	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄⋊Dic₄₇	2
C₂×#15689087	2
C₂×#15688891	2
C₂×C₄₇×#407	2
#10727	47