Subgroups — C₄×#15688891 #26121483

Order 12032.

994 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688891	C₂	1	4	yes	maximal
4	C₂×C₄×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic
5	C₂²×#10625329	C₂²	1	2	yes	—
6	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
7	C₂²×C₄×Dic₄₇	C₄	1	2	yes	—
8	C₄×#10625329	—	2	2	no	—
9	C₄×#10625329	C₄	1	4	yes	complemented
10	C₂×#13093935	—	2	1	no	—
11	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
12	C₄×C₄⋊Dic₄₇	—	2	1	no	—
13	C₄×C₄⋊Dic₄₇	—	2	1	no	—
14	C₄×C₄⋊Dic₄₇	—	2	1	no	—
15	C₄×C₄⋊Dic₄₇	—	2	1	no	—
16	C₂×C₄₇⋊#95	C₄	1	2	yes	—
17	#15688891	C₄	1	16	yes	direct product factor
18	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×M₁₆×C₄₇	—	2	2	no	—
21	C₄×M₁₆×C₄₇	C₄	1	4	yes	complemented
22	C₂×#97×C₄₇	—	2	1	no	—
23	C₂×C₄×C₈×C₄₇	—	2	1	no	—
24	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	4	no	—
27	C₂×#10625329	C₂×C₄	1	4	yes	—
28	C₂×#10625329	C₂×C₄	1	8	yes	—
29	C₂²×C₄₇⋊C₈	—	2	2	no	—
30	C₂×C₄⋊Dic₄₇	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	—	2	2	no	—
32	C₂×C₄⋊Dic₄₇	—	2	4	no	—
33	C₂×C₄⋊Dic₄₇	C₂×C₄	1	8	yes	—
34	C₂×C₄×Dic₄₇	—	2	2	no	—
35	C₂×C₄×Dic₄₇	—	2	2	no	—
36	C₂×C₄×Dic₄₇	—	4	4	no	—
37	#13093935	—	2	4	no	—
38	C₄×C₄₇⋊C₈	—	2	4	no	—
39	C₄₇⋊#95	—	2	2	no	—
40	C₄₇⋊#95	—	2	2	no	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₇	—	2	2	no	—
45	C₂×M₁₆×C₄₇	—	2	4	no	—
46	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	—
47	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
48	C₂²×C₈×C₄₇	—	2	2	no	—
49	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×C₄²×C₄₇	D₄	1	2	yes	—
52	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
54	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	Q₈	1	2	yes	—
57	#97×C₄₇	—	2	4	no	—
58	C₄×C₈×C₄₇	—	2	4	no	—
59	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₄₇	—	2	2	no	—
61	C₂²×C₄×C₄₇	—	2	2	no	—
62	C₂²×C₄×C₄₇	—	4	2	no	—
63	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
64	C₂²×C₄×C₄₇	C₄²	1	2	yes	—
65	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
66	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
67	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
68	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
69	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₇	C₄⋊C₄	1	2	yes	—
71	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	#41	1	4	yes	—
79	C₂²×Dic₄₇	—	2	4	no	—
80	C₂²×Dic₄₇	—	2	4	no	—
81	C₂²×Dic₄₇	—	4	4	no	—
82	C₂²×Dic₄₇	—	4	4	no	—
83	C₂²×Dic₄₇	C₄²	1	8	yes	—
84	M₁₆×C₄₇	—	2	4	no	—
85	M₁₆×C₄₇	—	2	8	no	—
86	M₁₆×C₄₇	C₄²	1	8	yes	complemented
87	C₂×C₈×C₄₇	—	2	4	no	—
88	C₂×C₈×C₄₇	—	2	8	no	—
89	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
90	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
91	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
92	C₄²×C₄₇	C₂²⋊C₄	1	2	yes	—
93	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
94	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
95	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
96	C₄²×C₄₇	C₄⋊C₄	1	2	yes	—
97	C₄⋊Dic₄₇	—	2	8	no	—
98	C₄⋊Dic₄₇	—	2	8	no	—
99	C₄×Dic₄₇	—	4	4	no	—
100	C₄×Dic₄₇	—	4	4	no	—
101	#10625329	—	2	4	no	—
102	#10625329	—	2	8	no	—
103	#10625329	C₄²	1	8	yes	complemented
104	C₂×C₄₇⋊C₈	—	2	4	no	—
105	C₂×C₄₇⋊C₈	—	2	8	no	—
106	C₂³×C₄₇	—	2	1	no	—
107	C₂³×C₄₇	—	2	1	no	—
108	C₂³×C₄₇	—	2	2	no	—
109	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
110	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
111	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
112	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂³×C₄₇	#117	1	2	yes	—
114	C₂×C₄×C₄₇	—	2	1	no	—
115	C₂×C₄×C₄₇	—	2	1	no	—
116	C₂×C₄×C₄₇	—	2	2	no	—
117	C₂×C₄×C₄₇	—	2	2	no	—
118	C₂×C₄×C₄₇	—	2	4	no	—
119	C₂×C₄×C₄₇	—	2	4	no	—
120	C₂×C₄×C₄₇	—	4	2	no	—
121	C₂×C₄×C₄₇	—	4	2	no	—
122	C₂×C₄×C₄₇	#95	1	2	yes	—
123	C₂×C₄×C₄₇	#95	1	2	yes	—
124	C₂×C₄×C₄₇	#95	1	2	yes	—
125	C₂×C₄×C₄₇	#95	1	2	yes	—
126	C₂×C₄×C₄₇	#100	1	2	yes	—
127	C₂×C₄×C₄₇	#101	1	2	yes	—
128	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
129	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
130	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
131	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
132	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₄₇	#117	1	2	yes	—
135	C₂×C₄×C₄₇	#117	1	2	yes	—
136	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
137	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
138	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
139	C₂×C₄×C₄₇	C₄×Q₈	1	4	yes	—
140	C₂×Dic₄₇	—	2	8	no	—
141	C₂×Dic₄₇	—	4	8	no	—
142	C₂×Dic₄₇	—	4	4	no	—
143	C₂×Dic₄₇	—	4	4	no	—
144	C₂×Dic₄₇	—	4	8	no	—
145	C₈×C₄₇	—	2	8	no	—
146	C₄₇⋊C₈	—	2	8	no	—
147	C₄×#343	—	47	1	no	maximal, Sylow
148	C₂²×C₄₇	—	2	1	no	—
149	C₂²×C₄₇	—	2	1	no	—
150	C₂²×C₄₇	—	2	1	no	—
151	C₂²×C₄₇	—	2	1	no	—
152	C₂²×C₄₇	—	2	2	no	—
153	C₂²×C₄₇	—	2	2	no	—
154	C₂²×C₄₇	—	2	2	no	—
155	C₂²×C₄₇	—	2	2	no	—
156	C₂²×C₄₇	C₄³	1	1	yes	characteristic
157	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
158	C₂²×C₄₇	#376	1	1	yes	characteristic
159	C₂²×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
160	C₂²×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
161	C₂²×C₄₇	C₂×#100	1	1	yes	characteristic
162	C₂²×C₄₇	C₂×#101	1	1	yes	characteristic
163	C₂²×C₄₇	#413	1	2	yes	—
164	C₄×C₄₇	—	2	2	no	—
165	C₄×C₄₇	—	2	2	no	—
166	C₄×C₄₇	—	2	2	no	—
167	C₄×C₄₇	#343	1	4	yes	complemented
168	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
169	C₄×C₄₇	C₄×C₂²⋊C₄	1	2	yes	—
170	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
171	C₄×C₄₇	C₄×C₄⋊C₄	1	2	yes	—
172	Dic₄₇	—	4	8	no	—
173	C₂×C₄×M₁₆	—	47	1	no	—
174	C₂×C₄×M₁₆	D₄₇	1	1	yes	characteristic
175	C₂×C₄×C₄⋊C₄	—	47	1	no	—
176	C₂×#343	—	47	4	no	—
177	C₂×C₄₇	—	2	1	no	—
178	C₂×C₄₇	—	2	1	no	—
179	C₂×C₄₇	—	2	2	no	—
180	C₂×C₄₇	C₄×#95	1	1	yes	characteristic
181	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
182	C₂×C₄₇	#1742	1	1	yes	characteristic
183	C₂×C₄₇	C₄×#100	1	2	yes	—
184	C₂×C₄₇	C₄×#101	1	2	yes	—
185	C₂²×M₁₆	—	47	2	no	—
186	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
187	C₂²×C₄⋊C₄	—	47	2	no	—
188	C₂²×C₄²	—	47	2	no	—
189	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
190	C₄×M₁₆	—	2	2	no	—
191	C₄×M₁₆	—	47	4	no	—
192	C₄×M₁₆	—	94	2	no	—
193	C₄×M₁₆	Dic₄₇	1	4	yes	complemented
194	C₂×#97	—	2	1	no	—
195	C₂×#97	—	94	1	no	—
196	C₂×C₄×C₈	—	2	1	no	—
197	C₂×C₄×C₈	—	94	1	no	—
198	C₄×C₄⋊C₄	—	94	1	no	—
199	C₄×C₄⋊C₄	—	94	1	no	—
200	C₄×C₄⋊C₄	—	94	1	no	—
201	C₄×C₄⋊C₄	—	94	1	no	—
202	C₂×#95	—	47	2	no	—
203	#343	—	47	16	no	—
204	C₄₇	C₄×#343	1	1	yes	characteristic, complemented, Sylow
205	C₂³×C₄	—	47	4	no	—
206	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
207	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
208	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
209	C₂×M₁₆	—	2	4	no	—
210	C₂×M₁₆	—	2	2	no	—
211	C₂×M₁₆	—	47	8	no	—
212	C₂×M₁₆	—	47	4	no	—
213	C₂×M₁₆	—	94	4	no	—
214	C₂×M₁₆	—	94	2	no	—
215	C₂×M₁₆	C₄×D₄₇	1	8	yes	—
216	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	—	94	2	no	—
219	C₂×C₄⋊C₄	—	47	8	no	—
220	C₂×C₄⋊C₄	—	94	2	no	—
221	C₂×C₄⋊C₄	—	94	4	no	—
222	C₂×C₄⋊C₄	—	94	2	no	—
223	C₂×C₄²	—	94	2	no	—
224	C₂×C₄²	—	94	2	no	—
225	C₂×C₄²	—	188	4	no	—
226	C₂×C₄²	Dic₉₄	1	2	yes	—
227	C₂×C₄²	C₄×D₄₇	1	2	yes	—
228	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
229	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
230	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
231	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
234	#97	—	2	4	no	—
235	#97	—	94	4	no	—
236	C₄×C₈	—	2	4	no	—
237	C₄×C₈	—	94	4	no	—
238	#95	—	94	2	no	—
239	#95	—	94	2	no	—
240	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
241	C₂²×C₄	—	2	2	no	—
242	C₂²×C₄	—	2	2	no	—
243	C₂²×C₄	—	4	2	no	—
244	C₂²×C₄	—	47	8	no	—
245	C₂²×C₄	—	94	4	no	—
246	C₂²×C₄	—	94	4	no	—
247	C₂²×C₄	—	188	4	no	—
248	C₂²×C₄	—	188	4	no	—
249	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
250	C₂²×C₄	C₄×Dic₄₇	1	2	yes	—
251	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
252	C₂²×C₄	Dic₄₇⋊C₄	1	2	yes	—
253	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
254	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
255	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
256	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
257	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
258	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
259	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
260	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
261	C₂²×C₄	#10625350	1	4	yes	—
262	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
263	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
265	M₁₆	—	2	4	no	—
266	M₁₆	—	2	8	no	—
267	M₁₆	—	47	8	no	—
268	M₁₆	—	94	4	no	—
269	M₁₆	—	94	8	no	—
270	M₁₆	C₄×Dic₄₇	1	8	yes	complemented
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	—	2	8	no	—
273	C₂×C₈	—	94	4	no	—
274	C₂×C₈	—	94	8	no	—
275	C₄⋊C₄	—	94	8	no	—
276	C₄⋊C₄	—	94	8	no	—
277	C₄²	—	188	4	no	—
278	C₄²	—	188	4	no	—
279	C₄²	Dic₄₇⋊C₄	1	2	yes	—
280	C₄²	Dic₄₇⋊C₄	1	2	yes	—
281	C₄²	C₄⋊Dic₄₇	1	2	yes	—
282	C₄²	C₄⋊Dic₄₇	1	2	yes	—
283	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
284	C₄²	(C₂×D₄₇)⋊C₄	1	2	yes	—
285	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
286	C₄²	C₂²⋊Dic₄₇	1	2	yes	—
287	C₂³	—	2	1	no	—
288	C₂³	—	2	1	no	—
289	C₂³	—	2	2	no	—
290	C₂³	C₄²×D₄₇	1	2	yes	—
291	C₂³	C₂×C₄×Dic₄₇	1	1	yes	characteristic
292	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
293	C₂³	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
294	C₂³	#13093981	1	2	yes	—
295	C₂×C₄	—	2	1	no	—
296	C₂×C₄	—	2	1	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	4	no	—
300	C₂×C₄	—	2	4	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	2	no	—
303	C₂×C₄	—	94	8	no	—
304	C₂×C₄	—	188	8	no	—
305	C₂×C₄	—	188	4	no	—
306	C₂×C₄	—	188	4	no	—
307	C₂×C₄	—	188	8	no	—
308	C₂×C₄	C₄₇⋊#95	1	2	yes	—
309	C₂×C₄	C₄₇⋊#95	1	2	yes	—
310	C₂×C₄	C₄₇⋊#95	1	2	yes	—
311	C₂×C₄	C₄₇⋊#95	1	2	yes	—
312	C₂×C₄	#13093940	1	2	yes	—
313	C₂×C₄	#13093942	1	2	yes	—
314	C₂×C₄	C₄²×D₄₇	1	2	yes	—
315	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
316	C₂×C₄	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
317	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
318	C₂×C₄	C₂×Dic₄₇⋊C₄	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
320	C₂×C₄	#13093981	1	2	yes	—
321	C₂×C₄	#13093983	1	2	yes	—
322	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
323	C₂×C₄	C₄×C₂²⋊D₄₇	1	4	yes	—
324	C₂×C₄	C₄×D₁₈₈	1	4	yes	—
325	C₂×C₄	C₄×Dic₉₄	1	4	yes	—
326	C₈	—	2	8	no	—
327	C₈	—	94	8	no	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	2	no	—
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	C₄²×Dic₄₇	1	1	yes	characteristic
337	C₂²	C₂×C₄₇⋊#95	1	1	yes	characteristic
338	C₂²	#15688969	1	1	yes	characteristic
339	C₂²	C₄×(C₂×D₄₇)⋊C₄	1	2	yes	—
340	C₂²	C₄×Dic₄₇⋊C₄	1	2	yes	—
341	C₂²	C₂×#13093940	1	1	yes	characteristic
342	C₂²	C₂×#13093942	1	1	yes	characteristic
343	C₂²	#15689105	1	2	yes	—
344	C₄	—	2	2	no	—
345	C₄	—	2	2	no	—
346	C₄	—	2	2	no	—
347	C₄	—	188	8	no	—
348	C₄	#15688891	1	4	yes	direct product factor
349	C₄	C₄×C₂²⋊Dic₄₇	1	2	yes	—
350	C₄	C₄×(C₂×D₄₇)⋊C₄	1	2	yes	—
351	C₄	C₄×C₄⋊Dic₄₇	1	2	yes	—
352	C₄	C₄×Dic₄₇⋊C₄	1	2	yes	—
353	C₂	—	2	1	no	—
354	C₂	—	2	1	no	—
355	C₂	—	2	2	no	—
356	C₂	C₄×C₄₇⋊#95	1	1	yes	characteristic
357	C₂	C₂×#15688891	1	1	yes	characteristic
358	C₂	#20243126	1	1	yes	characteristic
359	C₂	C₄×#13093940	1	2	yes	—
360	C₂	C₄×#13093942	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	(C₂×D₄₇)⋊C₄
commutator	C₂²×C₄₇	C₄³
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄×M₁₆×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×C₄×M₁₆	D₄₇
hypocenter	C₄₇	C₄×#343
LCS	G ▷ C₂²×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×M₁₆

Complements

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

N	H ≅ G/N	type
9. C₄×#10625329	C₄	semidirect
17. #15688891	C₄	direct (N × H)
21. C₄×M₁₆×C₄₇	C₄	semidirect
86. M₁₆×C₄₇	C₄²	semidirect
103. #10625329	C₄²	semidirect
167. C₄×C₄₇	#343	semidirect
193. C₄×M₁₆	Dic₄₇	semidirect
204. C₄₇	C₄×#343	semidirect
270. M₁₆	C₄×Dic₄₇	semidirect
348. C₄	#15688891	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄×#10625329	2
C₂×C₄×C₄⋊Dic₄₇	2
C₂×#15688891	2
C₂×C₄×M₁₆×C₄₇	2
C₄×#343	47

Subgroups — C4×#15688891 #26121483

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#15688891 #26121483