Subgroups — C₂²×#15689199 #27080122

Order 12032.

3262 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₄×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689199	C₂	1	24	yes	maximal, direct product factor
4	C₂²×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×(C₂×D₄₇)⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×M₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂³×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
10	C₂³×C₄×D₄₇	C₂²	1	1	yes	characteristic
11	C₂²×#10625324	—	2	8	no	—
12	C₂²×#10625324	C₂²	1	12	yes	complemented
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	C₂×C₄×C₂²⋊D₄₇	C₄	1	12	yes	—
16	C₂×C₄×C₂²⋊D₄₇	C₂²	1	12	yes	—
17	C₂²×Dic₄₇⋊C₄	C₄	1	1	yes	characteristic
18	C₂²×C₂²⋊Dic₄₇	C₄	1	1	yes	characteristic
19	C₂²×(C₂×D₄₇)⋊C₄	C₄	1	1	yes	characteristic
20	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
21	#15689199	C₂²	1	64	yes	direct product factor
22	C₂×Dic₄₇⋊C₈	C₂²	1	12	yes	complemented
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	12	yes	complemented
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	12	yes	complemented
25	C₂×C₈×Dic₄₇	C₂²	1	12	yes	complemented
26	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×M₁₆×C₄₇	—	2	8	no	—
28	C₂²×M₁₆×C₄₇	C₂²	1	12	yes	complemented
29	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂⁴×D₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂²×C₂²⋊D₄₇	—	2	8	no	—
33	C₂²×C₂²⋊D₄₇	C₂×C₄	1	12	yes	—
34	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂²×C₄×D₄₇	—	2	4	no	—
38	C₂²×C₄×D₄₇	—	2	4	no	—
39	C₂²×C₄×D₄₇	C₂×C₄	1	6	yes	—
40	C₂²×C₄×D₄₇	C₂³	1	6	yes	—
41	C₂×#10625324	—	2	48	no	—
42	C₂×#10625324	C₂³	1	16	yes	complemented
43	C₂²×C₄₇⋊C₈	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	—	2	4	no	—
45	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
47	C₄×C₂²⋊D₄₇	C₂×C₄	1	48	yes	—
48	C₄×C₂²⋊D₄₇	C₂³	1	16	yes	—
49	C₂×Dic₄₇⋊C₄	C₂×C₄	1	12	yes	—
50	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	12	yes	—
51	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	12	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	6	yes	—
53	C₂×C₄×Dic₄₇	C₂³	1	6	yes	—
54	Dic₄₇⋊C₈	C₂³	1	16	yes	complemented
55	C₂²⋊(C₄₇⋊C₈)	C₂³	1	16	yes	complemented
56	(C₂×D₄₇)⋊C₈	C₂³	1	16	yes	complemented
57	C₈×Dic₄₇	C₂³	1	16	yes	complemented
58	C₂⁵×C₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂³×C₄×C₄₇	—	2	4	no	—
60	C₂³×C₄×C₄₇	—	2	4	no	—
61	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	C₂×C₄	1	6	yes	—
63	C₂³×C₄×C₄₇	C₂³	1	6	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×M₁₆×C₄₇	—	2	48	no	—
66	C₂×M₁₆×C₄₇	C₂³	1	16	yes	complemented
67	C₂²×C₈×C₄₇	—	2	4	no	—
68	C₂²×C₈×C₄₇	D₄	1	8	yes	complemented
69	C₂²×C₈×C₄₇	C₂³	1	6	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	6	yes	—
71	C₂⁴×C₄₇	—	2	4	no	—
72	C₂⁴×C₄₇	—	2	4	no	—
73	C₂⁴×C₄₇	—	2	4	no	—
74	C₂⁴×C₄₇	C₂²×C₄	1	6	yes	—
75	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
76	C₂³×D₄₇	—	2	4	no	—
77	C₂³×D₄₇	—	2	4	no	—
78	C₂³×D₄₇	—	2	4	no	—
79	C₂³×D₄₇	C₂²×C₄	1	6	yes	—
80	C₂²×C₄×C₄₇	—	2	4	no	—
81	C₂²×C₄×C₄₇	—	2	24	no	—
82	C₂²×C₄×C₄₇	—	2	12	no	—
83	C₂²×C₄×C₄₇	—	2	12	no	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	6	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	12	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	3	yes	—
87	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
88	C₂²×C₄×C₄₇	#41	1	4	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
91	C₂×C₂²⋊D₄₇	—	2	48	no	—
92	C₂×C₂²⋊D₄₇	C₂²×C₄	1	16	yes	—
93	C₂²×Dic₄₇	—	2	4	no	—
94	C₂²×Dic₄₇	—	2	4	no	—
95	C₂²×Dic₄₇	M₁₆	1	8	yes	complemented
96	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
97	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
98	C₂²×Dic₄₇	C₂²×C₄	1	6	yes	—
99	C₂×C₄×D₄₇	—	2	24	no	—
100	C₂×C₄×D₄₇	—	2	12	no	—
101	C₂×C₄×D₄₇	—	2	12	no	—
102	C₂×C₄×D₄₇	C₂²×C₄	1	12	yes	—
103	C₂×C₄×D₄₇	C₂⁴	1	4	yes	—
104	M₁₆×C₄₇	—	2	32	no	—
105	C₂×C₈×C₄₇	—	2	12	no	—
106	C₂×C₈×C₄₇	C₂×D₄	1	24	yes	complemented
107	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
108	C₂×C₈×C₄₇	C₂⁴	1	4	yes	—
109	C₂²⋊Dic₄₇	C₂²×C₄	1	16	yes	—
110	(C₂×D₄₇)⋊C₄	C₂²×C₄	1	16	yes	—
111	Dic₄₇⋊C₄	C₂²×C₄	1	16	yes	—
112	C₄×Dic₄₇	C₂²×C₄	1	12	yes	—
113	C₄×Dic₄₇	C₂⁴	1	4	yes	—
114	C₂×C₄₇⋊C₈	—	2	12	no	—
115	C₂×C₄₇⋊C₈	—	2	12	no	—
116	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
117	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
118	#10625324	—	2	32	no	—
119	C₂³×C₄₇	—	2	12	no	—
120	C₂³×C₄₇	—	2	12	no	—
121	C₂³×C₄₇	—	2	12	no	—
122	C₂³×C₄₇	—	4	16	no	—
123	C₂³×C₄₇	C₄×D₄	1	4	yes	—
124	C₂³×C₄₇	C₂×M₁₆	1	4	yes	—
125	C₂³×C₄₇	#131	1	4	yes	—
126	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
127	C₂³×C₄₇	C₂³×C₄	1	3	yes	—
128	C₂²×D₄₇	—	2	12	no	—
129	C₂²×D₄₇	—	2	12	no	—
130	C₂²×D₄₇	—	2	12	no	—
131	C₂²×D₄₇	—	4	16	no	—
132	C₂²×D₄₇	C₂³×C₄	1	4	yes	—
133	C₂×C₄×C₄₇	—	2	12	no	—
134	C₂×C₄×C₄₇	—	2	24	no	—
135	C₂×C₄×C₄₇	—	2	4	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	C₄×D₄	1	12	yes	—
138	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
139	C₂×C₄×C₄₇	C₂³×C₄	1	3	yes	—
140	C₂×C₄×C₄₇	C₂²×D₄	1	6	yes	—
141	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
142	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
143	C₂²⋊D₄₇	—	2	32	no	—
144	C₂×Dic₄₇	—	2	12	no	—
145	C₂×Dic₄₇	—	2	12	no	—
146	C₂×Dic₄₇	C₂×M₁₆	1	24	yes	complemented
147	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
148	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
149	C₂×Dic₄₇	C₂³×C₄	1	4	yes	—
150	C₄×D₄₇	—	2	24	no	—
151	C₄×D₄₇	—	2	4	no	—
152	C₄×D₄₇	—	2	4	no	—
153	C₈×C₄₇	—	2	4	no	—
154	C₈×C₄₇	C₂²×D₄	1	8	yes	complemented
155	C₄₇⋊C₈	—	2	4	no	—
156	C₄₇⋊C₈	—	2	4	no	—
157	C₂²×#436	—	47	1	no	maximal, Sylow
158	C₂²×C₄₇	—	2	4	no	—
159	C₂²×C₄₇	—	2	4	no	—
160	C₂²×C₄₇	—	2	4	no	—
161	C₂²×C₄₇	—	4	24	no	—
162	C₂²×C₄₇	#436	1	16	yes	complemented
163	C₂²×C₄₇	C₂×C₄×D₄	1	6	yes	—
164	C₂²×C₄₇	C₂²×M₁₆	1	6	yes	—
165	C₂²×C₄₇	C₂×#131	1	6	yes	—
166	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
167	C₂×D₄₇	—	2	4	no	—
168	C₂×D₄₇	—	2	4	no	—
169	C₂×D₄₇	—	2	4	no	—
170	C₂×D₄₇	—	4	24	no	—
171	C₄×C₄₇	—	2	4	no	—
172	C₄×C₄₇	C₂×C₄×D₄	1	6	yes	—
173	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
174	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
175	Dic₄₇	—	2	4	no	—
176	Dic₄₇	—	2	4	no	—
177	Dic₄₇	C₂²×M₁₆	1	8	yes	complemented
178	C₂³×M₁₆	—	47	1	no	—
179	C₂³×M₁₆	D₄₇	1	1	yes	characteristic, complemented
180	C₂²×C₄×D₄	—	47	1	no	—
181	C₂×#436	—	47	24	no	—
182	C₂²×C₄⋊C₈	—	47	1	no	—
183	C₂²×C₂²⋊C₈	—	47	1	no	—
184	C₂²×C₂²⋊C₈	—	47	1	no	—
185	C₂²×C₄×C₈	—	47	1	no	—
186	C₂×C₄₇	—	4	4	no	—
187	C₂×C₄₇	C₂×#436	1	12	yes	complemented
188	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
189	C₂×C₄₇	C₂³×M₁₆	1	1	yes	characteristic
190	C₂×C₄₇	C₂²×#131	1	1	yes	characteristic
191	D₄₇	—	4	4	no	—
192	C₂³×D₄	—	47	1	no	—
193	C₂⁴×C₄	—	47	1	no	—
194	C₂⁴×C₄	C₂×D₄₇	1	1	yes	characteristic
195	C₂²×M₁₆	—	2	8	no	—
196	C₂²×M₁₆	—	47	12	no	—
197	C₂²×M₁₆	—	94	8	no	—
198	C₂²×M₁₆	C₂×D₄₇	1	12	yes	complemented
199	C₂³×C₈	—	47	1	no	—
200	C₂³×C₈	—	47	1	no	—
201	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
202	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
203	C₂×C₄×D₄	—	47	12	no	—
204	C₂×C₄×D₄	—	47	12	no	—
205	C₂²×C₄⋊C₄	—	47	1	no	—
206	C₂²×C₂²⋊C₄	—	47	1	no	—
207	C₂²×C₂²⋊C₄	—	47	1	no	—
208	C₂²×C₄²	—	47	1	no	—
209	#436	—	47	64	no	—
210	C₂×C₄⋊C₈	—	47	12	no	—
211	C₂×C₂²⋊C₈	—	47	12	no	—
212	C₂×C₂²⋊C₈	—	47	12	no	—
213	C₂×C₄×C₈	—	47	12	no	—
214	C₄₇	C₂²×#436	1	1	yes	characteristic, complemented, Sylow
215	C₂⁵	—	47	1	no	—
216	C₂⁵	C₄×D₄₇	1	1	yes	characteristic
217	C₂²×D₄	—	47	12	no	—
218	C₂²×D₄	—	94	8	no	—
219	C₂³×C₄	—	2	4	no	—
220	C₂³×C₄	—	2	4	no	—
221	C₂³×C₄	—	47	1	no	—
222	C₂³×C₄	—	47	1	no	—
223	C₂³×C₄	—	47	1	no	—
224	C₂³×C₄	—	47	6	no	—
225	C₂³×C₄	—	47	6	no	—
226	C₂³×C₄	—	94	4	no	—
227	C₂³×C₄	—	94	4	no	—
228	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
229	C₂³×C₄	C₄×D₄₇	1	6	yes	—
230	C₂³×C₄	C₂²×D₄₇	1	6	yes	—
231	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
232	C₂×M₁₆	—	2	48	no	—
233	C₂×M₁₆	—	47	16	no	—
234	C₂×M₁₆	—	94	48	no	—
235	C₂×M₁₆	C₂²×D₄₇	1	16	yes	complemented
236	C₂²×C₈	—	2	4	no	—
237	C₂²×C₈	—	47	6	no	—
238	C₂²×C₈	—	47	6	no	—
239	C₂²×C₈	—	94	4	no	—
240	C₂²×C₈	—	94	4	no	—
241	C₂²×C₈	C₂²⋊D₄₇	1	8	yes	complemented
242	C₂²×C₈	C₂²×D₄₇	1	6	yes	—
243	C₂²×C₈	C₂²×D₄₇	1	6	yes	—
244	C₄×D₄	—	47	48	no	—
245	C₄×D₄	—	47	16	no	—
246	C₂×C₄⋊C₄	—	47	12	no	—
247	C₂×C₂²⋊C₄	—	47	12	no	—
248	C₂×C₂²⋊C₄	—	47	12	no	—
249	C₂×C₄²	—	47	6	no	—
250	C₂×C₄²	—	47	6	no	—
251	C₄⋊C₈	—	47	16	no	—
252	C₂²⋊C₈	—	47	16	no	—
253	C₂²⋊C₈	—	47	16	no	—
254	C₄×C₈	—	47	16	no	—
255	C₂⁴	—	2	4	no	—
256	C₂⁴	—	2	4	no	—
257	C₂⁴	—	2	4	no	—
258	C₂⁴	—	47	6	no	—
259	C₂⁴	—	94	4	no	—
260	C₂⁴	—	94	4	no	—
261	C₂⁴	—	94	4	no	—
262	C₂⁴	C₂×C₄×D₄₇	1	6	yes	—
263	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
264	C₂×D₄	—	47	16	no	—
265	C₂×D₄	—	94	48	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	24	no	—
268	C₂²×C₄	—	2	12	no	—
269	C₂²×C₄	—	2	12	no	—
270	C₂²×C₄	—	47	8	no	—
271	C₂²×C₄	—	47	6	no	—
272	C₂²×C₄	—	47	6	no	—
273	C₂²×C₄	—	47	6	no	—
274	C₂²×C₄	—	47	12	no	—
275	C₂²×C₄	—	47	4	no	—
276	C₂²×C₄	—	94	4	no	—
277	C₂²×C₄	—	94	4	no	—
278	C₂²×C₄	—	94	24	no	—
279	C₂²×C₄	—	94	12	no	—
280	C₂²×C₄	—	94	12	no	—
281	C₂²×C₄	C₂×C₄×D₄₇	1	6	yes	—
282	C₂²×C₄	C₂×C₄×D₄₇	1	12	yes	—
283	C₂²×C₄	C₂×C₄×D₄₇	1	3	yes	—
284	C₂²×C₄	#10625350	1	4	yes	—
285	C₂²×C₄	C₂×C₂²⋊D₄₇	1	4	yes	—
286	C₂²×C₄	C₂³×D₄₇	1	4	yes	—
287	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
288	M₁₆	—	2	32	no	—
289	M₁₆	—	94	32	no	—
290	C₂×C₈	—	2	12	no	—
291	C₂×C₈	—	47	4	no	—
292	C₂×C₈	—	47	4	no	—
293	C₂×C₈	—	94	12	no	—
294	C₂×C₈	—	94	12	no	—
295	C₂×C₈	C₂×C₂²⋊D₄₇	1	24	yes	complemented
296	C₂×C₈	C₂³×D₄₇	1	4	yes	—
297	C₂×C₈	C₂³×D₄₇	1	4	yes	—
298	C₄⋊C₄	—	47	16	no	—
299	C₂²⋊C₄	—	47	16	no	—
300	C₂²⋊C₄	—	47	16	no	—
301	C₄²	—	47	12	no	—
302	C₄²	—	47	4	no	—
303	C₂³	—	2	12	no	—
304	C₂³	—	2	12	no	—
305	C₂³	—	2	12	no	—
306	C₂³	—	4	16	no	—
307	C₂³	—	47	4	no	—
308	C₂³	—	94	12	no	—
309	C₂³	—	94	12	no	—
310	C₂³	—	94	12	no	—
311	C₂³	—	188	16	no	—
312	C₂³	C₄×C₂²⋊D₄₇	1	4	yes	—
313	C₂³	M₁₆×D₄₇	1	4	yes	—
314	C₂³	#13094032	1	4	yes	—
315	C₂³	C₂²×C₄×D₄₇	1	4	yes	—
316	C₂³	C₂²×C₄×D₄₇	1	3	yes	—
317	D₄	—	94	32	no	—
318	C₂×C₄	—	2	12	no	—
319	C₂×C₄	—	2	24	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	47	24	no	—
323	C₂×C₄	—	47	4	no	—
324	C₂×C₄	—	47	4	no	—
325	C₂×C₄	—	47	4	no	—
326	C₂×C₄	—	94	12	no	—
327	C₂×C₄	—	94	12	no	—
328	C₂×C₄	—	94	24	no	—
329	C₂×C₄	—	94	4	no	—
330	C₂×C₄	—	94	4	no	—
331	C₂×C₄	C₄×C₂²⋊D₄₇	1	12	yes	—
332	C₂×C₄	C₂²×C₄×D₄₇	1	4	yes	—
333	C₂×C₄	C₂²×C₄×D₄₇	1	3	yes	—
334	C₂×C₄	C₂²×C₂²⋊D₄₇	1	6	yes	—
335	C₂×C₄	C₂×#10625350	1	6	yes	—
336	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
337	C₈	—	2	4	no	—
338	C₈	—	94	4	no	—
339	C₈	—	94	4	no	—
340	C₈	C₂²×C₂²⋊D₄₇	1	8	yes	complemented
341	C₂²	—	2	4	no	—
342	C₂²	—	2	4	no	—
343	C₂²	—	2	4	no	—
344	C₂²	—	4	24	no	—
345	C₂²	—	94	4	no	—
346	C₂²	—	94	4	no	—
347	C₂²	—	94	4	no	—
348	C₂²	—	188	24	no	—
349	C₂²	#15689199	1	16	yes	direct product factor
350	C₂²	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
351	C₂²	C₂×M₁₆×D₄₇	1	6	yes	—
352	C₂²	C₂×#13094032	1	6	yes	—
353	C₂²	C₂³×C₄×D₄₇	1	1	yes	characteristic
354	C₄	—	2	4	no	—
355	C₄	—	47	8	no	—
356	C₄	—	94	4	no	—
357	C₄	—	94	4	no	—
358	C₄	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
359	C₄	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
360	C₄	C₂²×#10625350	1	1	yes	characteristic
361	C₂	—	4	4	no	—
362	C₂	—	188	4	no	—
363	C₂	C₂×#15689199	1	12	yes	direct product factor
364	C₂	C₂²×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₂	C₂²×M₁₆×D₄₇	1	1	yes	characteristic
366	C₂	C₂²×#13094032	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂³×M₁₆×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂²×C₄
prime radical	C₂³×C₂²⋊D₄₇	C₄
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂³×M₁₆	D₄₇
hypocenter	C₄₇	C₂²×#436
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂³×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂³×#10625324	C₂	semidirect
3. C₂×#15689199	C₂	direct (N × H)
4. C₂²×Dic₄₇⋊C₈	C₂	semidirect
5. C₂²×C₂²⋊(C₄₇⋊C₈)	C₂	semidirect
6. C₂²×(C₂×D₄₇)⋊C₈	C₂	semidirect
7. C₂²×C₈×Dic₄₇	C₂	semidirect
8. C₂³×M₁₆×C₄₇	C₂	semidirect
12. C₂²×#10625324	C₂²	semidirect
21. #15689199	C₂²	direct (N × H)
22. C₂×Dic₄₇⋊C₈	C₂²	semidirect
23. C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	semidirect
24. C₂×(C₂×D₄₇)⋊C₈	C₂²	semidirect
25. C₂×C₈×Dic₄₇	C₂²	semidirect
28. C₂²×M₁₆×C₄₇	C₂²	semidirect
42. C₂×#10625324	C₂³	semidirect
54. Dic₄₇⋊C₈	C₂³	semidirect
55. C₂²⋊(C₄₇⋊C₈)	C₂³	semidirect
56. (C₂×D₄₇)⋊C₈	C₂³	semidirect
57. C₈×Dic₄₇	C₂³	semidirect
66. C₂×M₁₆×C₄₇	C₂³	semidirect
68. C₂²×C₈×C₄₇	D₄	semidirect
95. C₂²×Dic₄₇	M₁₆	semidirect
106. C₂×C₈×C₄₇	C₂×D₄	semidirect
146. C₂×Dic₄₇	C₂×M₁₆	semidirect
154. C₈×C₄₇	C₂²×D₄	semidirect
162. C₂²×C₄₇	#436	semidirect
177. Dic₄₇	C₂²×M₁₆	semidirect
179. C₂³×M₁₆	D₄₇	semidirect
187. C₂×C₄₇	C₂×#436	semidirect
198. C₂²×M₁₆	C₂×D₄₇	semidirect
214. C₄₇	C₂²×#436	semidirect
235. C₂×M₁₆	C₂²×D₄₇	semidirect
241. C₂²×C₈	C₂²⋊D₄₇	semidirect
295. C₂×C₈	C₂×C₂²⋊D₄₇	semidirect
340. C₈	C₂²×C₂²⋊D₄₇	semidirect
349. C₂²	#15689199	direct (N × H)
363. C₂	C₂×#15689199	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625324	2
C₂²×C₄×C₂²⋊D₄₇	2
C₂×#15689199	2
C₂²×Dic₄₇⋊C₈	2
C₂²×C₂²⋊(C₄₇⋊C₈)	2
C₂²×(C₂×D₄₇)⋊C₈	2
C₂²×C₈×Dic₄₇	2
C₂³×M₁₆×C₄₇	2
C₂²×#436	47

Subgroups — C22×#15689199 #27080122

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689199 #27080122