Subgroups — C₂×#20242918 #26198824

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689410	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689315	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689202	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242918	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688876	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688872	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15688867	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×#486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625334	—	2	1	no	—
10	C₂²×#10625324	—	2	1	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	#15689410	—	2	2	no	—
13	#15689410	C₂²	1	4	yes	complemented
14	#15689315	—	2	2	no	—
15	#15689315	C₂²	1	4	yes	—
16	#15689202	—	2	2	no	—
17	#15689202	C₂²	1	4	yes	complemented
18	C₂×#13093955	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×#13093945	—	2	1	no	—
23	C₂×#13093944	—	2	1	no	—
24	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
25	#15688876	C₂²	1	4	yes	complemented
26	#15688872	C₂²	1	4	yes	complemented
27	#15688867	C₂²	1	4	yes	complemented
28	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#486	—	2	2	no	—
31	C₄₇×#486	C₂²	1	4	yes	complemented
32	C₂×#102×C₄₇	—	2	1	no	—
33	C₂×#102×C₄₇	—	2	1	no	—
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂²×D₁₈₈	D₄	1	1	yes	characteristic
36	C₂²×C₄×D₄₇	—	2	1	no	—
37	C₂×#10625334	—	2	4	no	—
38	C₂×#10625334	—	4	4	no	—
39	C₂×#10625324	—	2	4	no	—
40	C₂×#10625324	—	4	4	no	—
41	C₂²×C₄₇⋊C₈	—	2	1	no	—
42	C₂²×C₄₇⋊C₈	—	2	1	no	—
43	C₂²×C₄₇⋊C₈	—	2	1	no	—
44	C₄×D₁₈₈	—	2	1	no	—
45	C₄×D₁₈₈	—	2	1	no	—
46	C₄×D₁₈₈	D₄	1	2	yes	—
47	C₄×D₁₈₈	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
49	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
50	#13093955	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
56	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
57	#13093945	—	2	4	no	—
58	#13093944	—	2	4	no	—
59	(C₂×D₄₇)⋊C₈	—	2	4	no	—
60	C₂²×Q₈×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	1	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	—	2	1	no	—
68	C₄⋊Q₈×C₄₇	—	2	1	no	—
69	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
70	#127×C₄₇	—	2	1	no	—
71	#127×C₄₇	—	2	1	no	—
72	#127×C₄₇	—	2	1	no	—
73	#127×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	#102×C₄₇	—	2	4	no	—
78	#102×C₄₇	—	2	4	no	—
79	C₄×C₈×C₄₇	D₄	1	2	yes	—
80	C₄×C₈×C₄₇	C₂³	1	2	yes	—
81	C₂⁴×C₄₇	—	4	1	no	—
82	C₂³×D₄₇	—	2	1	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	—	8	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	—	4	1	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	2	no	—
93	C₂×D₄×C₄₇	—	4	2	no	—
94	C₂×D₄×C₄₇	—	4	2	no	—
95	C₂×D₄×C₄₇	—	4	2	no	—
96	C₂×D₄×C₄₇	—	8	2	no	—
97	C₂²×C₄×C₄₇	—	4	1	no	—
98	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	C₂²×Dic₄₇	—	2	1	no	—
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×D₁₈₈	—	2	2	no	—
104	C₂×D₁₈₈	—	2	1	no	—
105	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	—	4	2	no	—
109	C₂×C₄×D₄₇	—	4	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
113	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	4	1	no	—
117	C₄⋊C₄×C₄₇	—	4	1	no	—
118	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₄²×C₄₇	#41	1	1	yes	characteristic
121	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
122	#10625334	—	4	8	no	—
123	(C₂×D₄₇)⋊C₄	—	2	2	no	—
124	(C₂×D₄₇)⋊C₄	—	2	2	no	—
125	C₄⋊Dic₄₇	—	2	1	no	—
126	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	4	2	no	—
131	C₂×C₄₇⋊C₈	—	4	2	no	—
132	C₂×C₄₇⋊C₈	—	4	2	no	—
133	#10625324	—	4	8	no	—
134	C₂³×C₄₇	—	4	2	no	—
135	C₂³×C₄₇	—	8	2	no	—
136	C₂³×C₄₇	—	8	2	no	—
137	C₂³×C₄₇	—	8	2	no	—
138	C₂³×C₄₇	#121	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	4	2	no	—
141	C₂²×D₄₇	—	4	2	no	—
142	C₂²×D₄₇	—	4	2	no	—
143	Q₈×C₄₇	—	8	2	no	—
144	Q₈×C₄₇	—	8	2	no	—
145	D₄×C₄₇	—	4	2	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	8	2	no	—
150	D₄×C₄₇	—	8	2	no	—
151	D₄×C₄₇	—	8	2	no	—
152	D₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	8	2	no	—
156	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
157	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
158	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₄₇	#135	1	2	yes	—
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
161	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
162	C₂×C₄×C₄₇	#137	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	D₁₈₈	—	2	2	no	—
169	D₁₈₈	—	2	2	no	—
170	D₁₈₈	—	4	2	no	—
171	C₄×D₄₇	—	4	2	no	—
172	C₄×D₄₇	—	4	2	no	—
173	C₄×D₄₇	—	4	4	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	2	2	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	—	4	2	no	—
179	C₂×#1697	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	8	2	no	—
181	C₂²×C₄₇	—	8	2	no	—
182	C₂²×C₄₇	—	8	2	no	—
183	C₂²×C₄₇	—	16	4	no	—
184	C₂²×C₄₇	#463	1	2	yes	—
185	C₂²×C₄₇	#468	1	2	yes	—
186	C₂²×C₄₇	#472	1	2	yes	—
187	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₂×D₄₇	—	8	4	no	—
192	C₄×C₄₇	—	2	1	no	—
193	C₄×C₄₇	—	2	1	no	—
194	C₄×C₄₇	—	8	2	no	—
195	C₄×C₄₇	#463	1	2	yes	—
196	C₄×C₄₇	#468	1	2	yes	—
197	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
198	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
199	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
201	Dic₄₇	—	4	2	no	—
202	C₂×#486	D₄₇	1	1	yes	characteristic, complemented
203	C₂×#476	—	47	1	no	—
204	C₂×#459	—	47	1	no	—
205	C₂×#436	—	47	1	no	—
206	#1697	—	47	8	no	—
207	C₂×#335	—	47	1	no	—
208	C₂×#333	—	47	1	no	—
209	C₂×#331	—	47	1	no	—
210	C₂×C₄₇	—	16	2	no	—
211	C₂×C₄₇	#1697	1	4	yes	complemented
212	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
213	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
215	D₄₇	—	8	2	no	—
216	C₂²×D₈	—	94	1	no	—
217	C₂²×M₁₆	—	94	1	no	—
218	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
219	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄×D₄	—	47	1	no	—
221	#486	—	2	2	no	—
222	#486	C₂×D₄₇	1	4	yes	complemented
223	#476	—	47	4	no	—
224	#476	—	94	2	no	—
225	#459	—	47	4	no	—
226	#459	—	94	2	no	—
227	#436	—	47	4	no	—
228	#436	—	94	2	no	—
229	C₂×#106	—	94	1	no	—
230	C₂×C₄⋊C₈	—	47	1	no	—
231	C₂×C₄⋊C₈	—	47	1	no	—
232	C₂×C₄⋊C₈	—	47	1	no	—
233	C₂×#102	—	2	1	no	—
234	C₂×#102	—	2	1	no	—
235	C₂×#102	—	94	1	no	—
236	C₂×#102	—	94	1	no	—
237	C₂×C₂²⋊C₈	—	94	1	no	—
238	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
239	#335	—	47	4	no	—
240	#333	—	47	4	no	—
241	#331	—	47	4	no	—
242	C₄₇	C₂×#1697	1	1	yes	characteristic, complemented, Sylow
243	C₂²×Q₈	—	2	1	no	—
244	C₂²×D₄	—	2	1	no	—
245	C₂²×D₄	—	2	1	no	—
246	C₂²×D₄	—	2	1	no	—
247	C₂²×D₄	—	47	1	no	—
248	C₂³×C₄	—	94	1	no	—
249	C₂×D₈	—	94	4	no	—
250	C₂×D₈	—	188	4	no	—
251	C₂×M₁₆	—	94	4	no	—
252	C₂×M₁₆	—	188	4	no	—
253	C₂²×C₈	—	94	1	no	—
254	C₂²×C₈	—	94	1	no	—
255	C₂²×C₈	—	94	1	no	—
256	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
257	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
258	C₄⋊Q₈	—	2	1	no	—
259	C₄⋊Q₈	—	2	1	no	—
260	C₄⋊Q₈	—	2	1	no	—
261	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
262	#127	—	2	1	no	—
263	#127	—	2	1	no	—
264	#127	—	2	1	no	—
265	#127	C₂²×D₄₇	1	2	yes	—
266	C₄×D₄	—	47	2	no	—
267	C₄×D₄	—	47	2	no	—
268	C₄×D₄	—	94	1	no	—
269	C₄×D₄	—	94	1	no	—
270	C₂×C₄⋊C₄	—	2	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	47	1	no	—
273	C₂×C₂²⋊C₄	—	94	1	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#106	—	94	4	no	—
276	C₄⋊C₈	—	47	2	no	—
277	C₄⋊C₈	—	47	2	no	—
278	C₄⋊C₈	—	47	2	no	—
279	C₄⋊C₈	—	94	1	no	—
280	C₄⋊C₈	—	94	1	no	—
281	C₄⋊C₈	—	94	1	no	—
282	#102	—	2	4	no	—
283	#102	—	2	4	no	—
284	#102	—	94	4	no	—
285	#102	—	94	4	no	—
286	C₂²⋊C₈	—	94	4	no	—
287	C₄×C₈	C₂²⋊D₄₇	1	2	yes	—
288	C₄×C₈	C₂²×D₄₇	1	2	yes	—
289	C₂⁴	—	4	1	no	—
290	C₂⁴	—	94	1	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂×Q₈	—	4	1	no	—
293	C₂×Q₈	—	8	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	1	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	4	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂×D₄	—	4	2	no	—
303	C₂×D₄	—	4	2	no	—
304	C₂×D₄	—	8	2	no	—
305	C₂×D₄	—	47	2	no	—
306	C₂×D₄	—	94	1	no	—
307	C₂×D₄	—	94	2	no	—
308	C₂×D₄	—	94	2	no	—
309	C₂²×C₄	—	4	1	no	—
310	C₂²×C₄	—	94	1	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	—	188	2	no	—
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	#10625352	1	1	yes	characteristic
317	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
318	D₈	—	188	8	no	—
319	M₁₆	—	188	8	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	188	2	no	—
326	C₂×C₈	—	188	2	no	—
327	C₂×C₈	—	188	2	no	—
328	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
329	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
330	C₄⋊C₄	—	2	2	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	4	1	no	—
333	C₄⋊C₄	—	4	1	no	—
334	C₄⋊C₄	—	47	2	no	—
335	C₄⋊C₄	—	94	1	no	—
336	C₂²⋊C₄	—	94	2	no	—
337	C₂²⋊C₄	—	94	2	no	—
338	C₄²	D₄×D₄₇	1	1	yes	characteristic
339	C₄²	#10625352	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₄²	C₂³×D₄₇	1	1	yes	characteristic
342	C₂³	—	4	2	no	—
343	C₂³	—	8	2	no	—
344	C₂³	—	8	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	94	2	no	—
347	C₂³	—	188	2	no	—
348	C₂³	—	188	2	no	—
349	C₂³	—	188	2	no	—
350	C₂³	#13093995	1	1	yes	characteristic
351	Q₈	—	8	2	no	—
352	Q₈	—	8	2	no	—
353	D₄	—	4	2	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	D₄	—	4	2	no	—
357	D₄	—	8	2	no	—
358	D₄	—	8	2	no	—
359	D₄	—	8	2	no	—
360	D₄	—	8	2	no	—
361	D₄	—	94	2	no	—
362	D₄	—	94	2	no	—
363	D₄	—	188	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	8	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	—	188	4	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	#13093995	1	1	yes	characteristic
373	C₂×C₄	#13093995	1	1	yes	characteristic
374	C₂×C₄	#13093995	1	1	yes	characteristic
375	C₂×C₄	#13094044	1	2	yes	—
376	C₂×C₄	#13094049	1	2	yes	—
377	C₂×C₄	#13094051	1	2	yes	—
378	C₂×C₄	#13094053	1	2	yes	—
379	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
380	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	2	2	no	—
384	C₈	—	188	2	no	—
385	C₈	—	188	2	no	—
386	C₈	—	188	2	no	—
387	C₂²	—	8	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	16	4	no	—
391	C₂²	—	376	4	no	—
392	C₂²	—	188	2	no	—
393	C₂²	—	188	2	no	—
394	C₂²	—	188	2	no	—
395	C₂²	#15689335	1	2	yes	—
396	C₂²	#15689366	1	2	yes	—
397	C₂²	#15689390	1	2	yes	—
398	C₂²	C₂×#13093995	1	1	yes	characteristic
399	C₄	—	2	1	no	—
400	C₄	—	2	1	no	—
401	C₄	—	8	2	no	—
402	C₄	—	188	2	no	—
403	C₄	#15689335	1	2	yes	—
404	C₄	#15689366	1	2	yes	—
405	C₄	C₂×#13094044	1	1	yes	characteristic
406	C₄	C₂×#13094049	1	1	yes	characteristic
407	C₄	C₂×#13094051	1	1	yes	characteristic
408	C₄	C₂×#13094053	1	1	yes	characteristic
409	C₂	—	16	2	no	—
410	C₂	—	376	2	no	—
411	C₂	#20242918	1	4	yes	direct product factor
412	C₂	C₂×#15689335	1	1	yes	characteristic
413	C₂	C₂×#15689366	1	1	yes	characteristic
414	C₂	C₂×#15689390	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×#486	C₂
socle	C₂³×C₄₇	#121
prime radical	C₂×#15689315	C₂
hypercenter	C₂×#486	D₄₇
hypocenter	C₄₇	C₂×#1697
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#486

Complements

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

N	H ≅ G/N	type
1. C₂×#15689410	C₂	semidirect
3. C₂×#15689202	C₂	semidirect
4. #20242918	C₂	direct (N × H)
5. C₂×#15688876	C₂	semidirect
6. C₂×#15688872	C₂	semidirect
7. C₂×#15688867	C₂	semidirect
8. C₂×C₄₇×#486	C₂	semidirect
13. #15689410	C₂²	semidirect
17. #15689202	C₂²	semidirect
25. #15688876	C₂²	semidirect
26. #15688872	C₂²	semidirect
27. #15688867	C₂²	semidirect
31. C₄₇×#486	C₂²	semidirect
202. C₂×#486	D₄₇	semidirect
211. C₂×C₄₇	#1697	semidirect
222. #486	C₂×D₄₇	semidirect
242. C₄₇	C₂×#1697	semidirect
411. C₂	#20242918	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×#15689410	2
C₂×#15689315	2
C₂×#15689202	2
#20242918	2
C₂×#15688876	2
C₂×#15688872	2
C₂×#15688867	2
C₂×C₄₇×#486	2
C₂×#1697	47

Subgroups — C2×#20242918 #26198824

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242918 #26198824