Subgroups — C₂×#20244133 #26219684

Order 12032.

974 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#13093959	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689159	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689149	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic
5	#20244133	C₂	1	8	yes	maximal, direct product factor
6	C₂×#15688884	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688882	C₂	1	1	yes	maximal, characteristic
8	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic
9	C₂²×#10625329	C₂²	1	1	yes	characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂×#13093983	C₂²	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×#13093959	—	2	4	no	—
14	C₂×#13093959	C₂²	1	4	yes	—
15	#15689159	C₄	1	4	yes	complemented
16	#15689159	C₂²	1	4	yes	—
17	C₂×#13093957	C₄	1	2	yes	complemented
18	C₂×#13093955	C₄	1	2	yes	complemented
19	#15689149	—	2	2	no	—
20	#15689149	C₂²	1	4	yes	—
21	C₂×Dic₄₇⋊C₈	—	2	2	no	—
22	C₂×C₈×Dic₄₇	—	2	4	no	—
23	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
24	#15688884	C₂²	1	4	yes	—
25	#15688882	C₂²	1	4	yes	—
26	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
27	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#424	—	2	2	no	—
30	C₄₇×#424	C₂²	1	4	yes	—
31	C₂×C₄⋊C₈×C₄₇	—	2	2	no	—
32	C₂³×Dic₄₇	—	2	1	no	—
33	C₂×#10625329	—	2	1	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	C₂³	1	2	yes	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
41	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
42	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	—
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	#13093983	—	2	1	no	—
45	#13093983	—	2	1	no	—
46	#13093983	C₂×C₄	1	2	yes	—
47	#13093983	C₂³	1	2	yes	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
50	C₂×C₄×Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	1	no	—
52	C₂×C₄×Dic₄₇	—	2	1	no	—
53	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	#13093959	—	2	8	no	—
56	#13093957	C₂×C₄	1	8	yes	complemented
57	#13093955	C₂×C₄	1	8	yes	complemented
58	Dic₄₇⋊C₈	—	2	8	no	—
59	C₈×Dic₄₇	—	2	8	no	—
60	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂×M₁₆×C₄₇	—	2	1	no	—
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	2	no	—
64	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
65	C₂²×C₈×C₄₇	—	2	2	no	—
66	C₂²×C₈×C₄₇	—	2	2	no	—
67	C₂²×C₈×C₄₇	—	2	1	no	—
68	C₂²×C₈×C₄₇	D₄	1	2	yes	—
69	C₂²×C₈×C₄₇	D₄	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
71	#117×C₄₇	—	2	1	no	—
72	#117×C₄₇	—	2	1	no	—
73	#117×C₄₇	C₂×C₄	1	2	yes	—
74	#117×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₄⋊C₈×C₄₇	—	2	8	no	—
79	C₂⁴×C₄₇	#41	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	—	2	2	no	—
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	2	yes	—
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×Q₈	1	2	yes	—
87	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
88	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	#41	1	2	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	—	2	8	no	—
92	C₂²×Dic₄₇	—	2	4	no	—
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	2	no	—
95	M₁₆×C₄₇	—	2	2	no	—
96	M₁₆×C₄₇	—	2	2	no	—
97	M₁₆×C₄₇	—	4	2	no	—
98	C₂×C₈×C₄₇	—	2	4	no	—
99	C₂×C₈×C₄₇	—	2	4	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₂×C₈×C₄₇	—	2	2	no	—
102	C₂×C₈×C₄₇	—	2	2	no	—
103	C₂×C₈×C₄₇	—	4	2	no	—
104	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
105	C₄⋊C₄×C₄₇	—	2	2	no	—
106	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
107	C₂²⋊C₄×C₄₇	—	2	2	no	—
108	C₂²⋊C₄×C₄₇	—	2	2	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₂²⋊Dic₄₇	—	2	2	no	—
112	C₂²⋊Dic₄₇	—	2	2	no	—
113	C₄⋊Dic₄₇	—	2	2	no	—
114	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
115	C₄×Dic₄₇	—	2	2	no	—
116	C₄×Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
120	#10625329	—	2	2	no	—
121	#10625329	—	2	2	no	—
122	#10625329	—	4	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
126	C₂×C₄₇⋊C₈	C₄⋊C₄	1	4	yes	—
127	C₂×C₄₇⋊C₈	C₄⋊C₄	1	8	yes	—
128	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
131	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
134	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
135	C₂³×C₄₇	C₂²⋊Q₈	1	2	yes	—
136	C₂³×C₄₇	#125	1	2	yes	—
137	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
138	C₂×C₄×C₄₇	—	2	4	no	—
139	C₂×C₄×C₄₇	—	4	4	no	—
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
145	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
146	C₂×C₄×C₄₇	#121	1	2	yes	—
147	C₂×C₄×C₄₇	#121	1	2	yes	—
148	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
149	C₂×C₄×C₄₇	#125	1	2	yes	—
150	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
151	C₂×C₄×C₄₇	C₄⋊Q₈	1	2	yes	—
152	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×Dic₄₇	—	2	8	no	—
159	C₂×Dic₄₇	—	2	16	no	—
160	C₂×Dic₄₇	—	2	4	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	—	4	4	no	—
163	C₈×C₄₇	—	2	4	no	—
164	C₈×C₄₇	—	4	2	no	—
165	C₄₇⋊C₈	—	4	2	no	—
166	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
167	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
168	C₂×#1945	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	2	no	—
171	C₂²×C₄₇	—	2	4	no	—
172	C₂²×C₄₇	—	2	4	no	—
173	C₂²×C₄₇	#389	1	2	yes	—
174	C₂²×C₄₇	#389	1	2	yes	—
175	C₂²×C₄₇	#443	1	4	yes	—
176	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₂²×C₄₇	C₂×#125	1	1	yes	characteristic
179	C₄×C₄₇	—	4	4	no	—
180	C₄×C₄₇	#389	1	2	yes	—
181	C₄×C₄₇	#389	1	2	yes	—
182	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
183	C₄×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
185	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
186	Dic₄₇	—	2	8	no	—
187	Dic₄₇	—	4	4	no	—
188	C₂²×#108	—	47	1	no	—
189	C₂×#427	—	47	1	no	—
190	C₂×#424	—	47	1	no	—
191	C₂×#424	D₄₇	1	1	yes	characteristic
192	C₂²×C₄×C₈	—	47	1	no	—
193	#1945	—	47	8	no	—
194	C₂×#339	—	47	1	no	—
195	C₂×#339	—	47	1	no	—
196	C₂×C₄₇	—	2	1	no	—
197	C₂×C₄₇	—	2	1	no	—
198	C₂×C₄₇	—	2	2	no	—
199	C₂×C₄₇	#1945	1	4	yes	complemented
200	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
201	C₂×C₄₇	C₂×#443	1	2	yes	—
202	C₂²×M₁₆	—	47	1	no	—
203	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
204	C₂³×C₈	—	47	1	no	—
205	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
206	C₂×#117	—	47	1	no	—
207	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
208	C₂²×C₄²	—	47	1	no	—
209	C₂×#108	—	47	4	no	—
210	C₂×#108	—	94	4	no	—
211	#427	—	47	4	no	—
212	#427	—	47	4	no	—
213	C₂×#107	—	47	2	no	—
214	C₂×#106	—	47	2	no	—
215	#424	—	2	2	no	—
216	#424	—	47	4	no	—
217	#424	—	94	2	no	—
218	#424	C₂×D₄₇	1	4	yes	—
219	C₂×C₄⋊C₈	—	2	2	no	—
220	C₂×C₄⋊C₈	—	94	2	no	—
221	C₂×C₄×C₈	—	47	4	no	—
222	C₂×C₄×C₈	—	94	4	no	—
223	#339	—	47	4	no	—
224	#339	—	47	4	no	—
225	C₄₇	C₂×#1945	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	—	94	1	no	—
227	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
228	C₂×M₁₆	—	2	1	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	2	no	—
231	C₂×M₁₆	—	47	2	no	—
232	C₂×M₁₆	—	94	1	no	—
233	C₂×M₁₆	—	94	2	no	—
234	C₂×M₁₆	—	94	2	no	—
235	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
236	C₂²×C₈	—	2	2	no	—
237	C₂²×C₈	—	2	2	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₂²×C₈	—	47	1	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	47	2	no	—
242	C₂²×C₈	—	47	4	no	—
243	C₂²×C₈	—	47	4	no	—
244	C₂²×C₈	—	47	2	no	—
245	C₂²×C₈	—	94	1	no	—
246	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
247	C₂²×C₈	C₂²⋊D₄₇	1	2	yes	—
248	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
249	#117	—	2	1	no	—
250	#117	—	2	1	no	—
251	#117	—	47	2	no	—
252	#117	—	47	2	no	—
253	#117	—	94	1	no	—
254	#117	—	94	1	no	—
255	#117	C₄×D₄₇	1	2	yes	—
256	#117	C₂²×D₄₇	1	2	yes	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	94	1	no	—
261	C₂×C₄²	—	2	1	no	—
262	C₂×C₄²	—	47	4	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	—	94	1	no	—
265	C₂×C₄²	—	94	2	no	—
266	C₂×C₄²	—	94	1	no	—
267	#108	—	94	8	no	—
268	#107	—	47	8	no	—
269	#106	—	47	8	no	—
270	C₄⋊C₈	—	2	8	no	—
271	C₄⋊C₈	—	94	8	no	—
272	C₄×C₈	—	94	8	no	—
273	C₂⁴	#10625350	1	1	yes	characteristic
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	94	8	no	—
276	C₂²×C₄	—	94	4	no	—
277	C₂²×C₄	—	94	2	no	—
278	C₂²×C₄	—	94	2	no	—
279	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
280	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
281	C₂²×C₄	#10625350	1	1	yes	characteristic
282	C₂²×C₄	D₄×D₄₇	1	2	yes	—
283	C₂²×C₄	#10625352	1	2	yes	—
284	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
285	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
286	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	2	no	—
291	M₁₆	—	4	2	no	—
292	M₁₆	—	94	2	no	—
293	M₁₆	—	94	2	no	—
294	M₁₆	—	188	2	no	—
295	C₂×C₈	—	2	4	no	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	2	no	—
301	C₂×C₈	—	47	4	no	—
302	C₂×C₈	—	47	4	no	—
303	C₂×C₈	—	47	8	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	47	4	no	—
307	C₂×C₈	—	47	4	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	188	2	no	—
310	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	47	4	no	—
313	C₄⋊C₄	—	94	2	no	—
314	C₄⋊C₄	C₂×C₄×D₄₇	1	4	yes	—
315	C₂²⋊C₄	—	2	2	no	—
316	C₂²⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	94	2	no	—
318	C₂²⋊C₄	—	94	2	no	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	—	47	4	no	—
322	C₄²	—	94	2	no	—
323	C₄²	—	94	4	no	—
324	C₄²	—	94	2	no	—
325	C₄²	—	94	2	no	—
326	C₂³	—	2	4	no	—
327	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
328	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
329	C₂³	#13094002	1	2	yes	—
330	C₂³	#13094014	1	2	yes	—
331	C₂³	C₂×#10625350	1	1	yes	characteristic
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	4	4	no	—
334	C₂×C₄	—	94	8	no	—
335	C₂×C₄	—	94	16	no	—
336	C₂×C₄	—	94	4	no	—
337	C₂×C₄	—	94	4	no	—
338	C₂×C₄	—	188	4	no	—
339	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
340	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
341	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂×C₄	#13093989	1	2	yes	—
344	C₂×C₄	#13093989	1	2	yes	—
345	C₂×C₄	#13093996	1	2	yes	—
346	C₂×C₄	#13093996	1	2	yes	—
347	C₂×C₄	#13094002	1	2	yes	—
348	C₂×C₄	#13094014	1	2	yes	—
349	C₂×C₄	#13094022	1	2	yes	—
350	C₂×C₄	#13094022	1	2	yes	—
351	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
352	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
353	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
354	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
357	C₈	—	2	4	no	—
358	C₈	—	4	2	no	—
359	C₈	—	47	4	no	—
360	C₈	—	47	4	no	—
361	C₈	—	188	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	2	2	no	—
364	C₂²	—	2	4	no	—
365	C₂²	—	2	4	no	—
366	C₂²	#15689018	1	2	yes	—
367	C₂²	#15689018	1	2	yes	—
368	C₂²	#15689238	1	4	yes	—
369	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
370	C₂²	C₂×#13094002	1	1	yes	characteristic
371	C₂²	C₂×#13094014	1	1	yes	characteristic
372	C₄	—	4	4	no	—
373	C₄	—	94	8	no	—
374	C₄	—	188	4	no	—
375	C₄	#15689018	1	2	yes	—
376	C₄	#15689018	1	2	yes	—
377	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
378	C₄	C₂×#13093989	1	1	yes	characteristic
379	C₄	C₂×#13093996	1	1	yes	characteristic
380	C₄	C₂×#13094022	1	1	yes	characteristic
381	C₂	—	2	1	no	—
382	C₂	—	2	2	no	—
383	C₂	—	2	1	no	—
384	C₂	#20244133	1	4	yes	direct product factor
385	C₂	C₂×#15689018	1	1	yes	characteristic
386	C₂	C₂×#15689238	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#424	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂⁴×C₄₇	#41
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#424	D₄₇
hypocenter	C₄₇	C₂×#1945
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂³×C₈ ◁ C₂×#424

Complements

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

N	H ≅ G/N	type
5. #20244133	C₂	direct (N × H)
15. #15689159	C₄	semidirect
17. C₂×#13093957	C₄	semidirect
18. C₂×#13093955	C₄	semidirect
56. #13093957	C₂×C₄	semidirect
57. #13093955	C₂×C₄	semidirect
199. C₂×C₄₇	#1945	semidirect
225. C₄₇	C₂×#1945	semidirect
384. C₂	#20244133	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#13093959	2
C₂×#15689159	2
C₂×#15689149	2
C₂²×C₈×Dic₄₇	2
#20244133	2
C₂×#15688884	2
C₂×#15688882	2
C₂×C₄₇×#424	2
C₂×#1945	47

Subgroups — C2×#20244133 #26219684

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20244133 #26219684