Subgroups — #26123212

Order 12032.

930 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689147	C₂	1	1	yes	maximal, characteristic
2	C₂²×#13093943	C₂	1	2	yes	maximal
3	C₂×#15688892	C₂	1	2	yes	maximal
4	#20243082	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
6	C₂²×#10625329	C₂²	1	2	yes	—
7	C₂²×#10625329	C₂²	1	2	yes	—
8	#15689147	—	2	4	no	—
9	C₂×C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
10	C₂×#13093943	—	2	4	no	—
11	C₂×#13093943	—	2	4	no	—
12	C₂×#13093943	—	2	4	no	—
13	#15688892	—	2	4	no	—
14	#15688878	—	2	1	no	—
15	#15688878	—	2	1	no	—
16	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#391	—	2	1	no	—
20	C₄₇×#391	—	2	1	no	—
21	C₄₇×#391	—	2	2	no	—
22	C₂×#95×C₄₇	C₄	1	4	yes	—
23	C₂×#10625329	—	2	2	no	—
24	C₂×#10625329	—	2	2	no	—
25	C₂×#10625329	—	2	2	no	—
26	C₂×#10625329	—	2	2	no	—
27	C₂×#10625329	—	2	2	no	—
28	C₂×#10625329	—	2	2	no	—
29	C₂×#10625329	—	2	2	no	—
30	C₂×#10625329	—	2	2	no	—
31	C₂×#10625329	—	2	2	no	—
32	C₂×#10625329	—	2	2	no	—
33	C₂×#10625329	D₄	1	4	yes	—
34	C₂×#10625329	D₄	1	4	yes	—
35	C₂²×C₄₇⋊C₈	—	2	2	no	—
36	C₂²×C₄₇⋊C₈	—	2	2	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
38	#13093943	—	2	16	no	—
39	C₂²×Q₈×C₄₇	—	2	2	no	—
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×Q₈×C₄₇	—	2	1	no	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	—	2	1	no	—
45	C₂²×Q₈×C₄₇	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	2	no	—
47	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
48	C₂²×Q₈×C₄₇	Q₈	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄²×C₄₇	—	2	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄²×C₄₇	D₄	1	2	yes	—
62	#95×C₄₇	—	2	4	no	—
63	#95×C₄₇	—	2	4	no	—
64	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
65	C₂×Q₈×C₄₇	—	2	4	no	—
66	C₂×Q₈×C₄₇	—	2	2	no	—
67	C₂×Q₈×C₄₇	—	2	2	no	—
68	C₂×Q₈×C₄₇	—	2	2	no	—
69	C₂×Q₈×C₄₇	—	2	2	no	—
70	C₂×Q₈×C₄₇	—	2	4	no	—
71	C₂×Q₈×C₄₇	—	2	4	no	—
72	C₂×Q₈×C₄₇	—	2	4	no	—
73	C₂×Q₈×C₄₇	—	4	1	no	—
74	C₂×Q₈×C₄₇	—	4	2	no	—
75	C₂×Q₈×C₄₇	—	4	2	no	—
76	C₂×Q₈×C₄₇	—	4	2	no	—
77	C₂×Q₈×C₄₇	—	4	1	no	—
78	C₂×Q₈×C₄₇	—	4	2	no	—
79	C₂×Q₈×C₄₇	—	4	2	no	—
80	C₂×Q₈×C₄₇	—	4	1	no	—
81	C₂×Q₈×C₄₇	—	4	2	no	—
82	C₂×Q₈×C₄₇	—	4	1	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	4	no	—
87	C₂²×C₄×C₄₇	—	2	4	no	—
88	C₂²×C₄×C₄₇	—	2	4	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	4	2	no	—
92	C₂²×C₄×C₄₇	—	4	4	no	—
93	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
94	C₂²×C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₄⋊C₄	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	#41	1	2	yes	—
104	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	#41	1	2	yes	—
106	C₄⋊C₄×C₄₇	—	4	2	no	—
107	C₄⋊C₄×C₄₇	—	4	1	no	—
108	C₄⋊C₄×C₄₇	—	4	1	no	—
109	C₄²×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	—	2	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	#10625329	—	2	4	no	—
114	#10625329	—	2	4	no	—
115	#10625329	—	2	4	no	—
116	#10625329	—	2	4	no	—
117	#10625329	—	4	2	no	—
118	#10625329	—	4	2	no	—
119	#10625329	—	4	2	no	—
120	#10625329	—	4	2	no	—
121	C₂×C₄₇⋊C₈	—	2	4	no	—
122	C₂×C₄₇⋊C₈	—	2	4	no	—
123	C₂×C₄₇⋊C₈	—	4	2	no	—
124	C₂×C₄₇⋊C₈	—	4	2	no	—
125	C₂×C₄₇⋊C₈	—	4	2	no	—
126	C₂×C₄₇⋊C₈	—	4	2	no	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
130	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂³×C₄₇	#117	1	1	yes	characteristic
132	C₂³×C₄₇	C₄×D₄	1	2	yes	—
133	C₂³×C₄₇	C₄×D₄	1	2	yes	—
134	Q₈×C₄₇	—	4	2	no	—
135	Q₈×C₄₇	—	4	2	no	—
136	Q₈×C₄₇	—	4	4	no	—
137	Q₈×C₄₇	—	4	4	no	—
138	Q₈×C₄₇	—	4	2	no	—
139	Q₈×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	8	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	4	8	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	4	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	4	no	—
153	C₂×C₄×C₄₇	—	8	4	no	—
154	C₂×C₄×C₄₇	#101	1	4	yes	complemented
155	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
156	C₂×C₄×C₄₇	#120	1	2	yes	—
157	C₂×C₄×C₄₇	#121	1	2	yes	—
158	C₂×C₄×C₄₇	#121	1	2	yes	—
159	C₂×C₄×C₄₇	#121	1	2	yes	—
160	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
163	C₂×C₄×C₄₇	C₂²⋊Q₈	1	2	yes	—
164	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂²⋊Q₈	1	1	yes	characteristic
166	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
167	C₂×C₄×C₄₇	#123	1	2	yes	—
168	C₂×C₄×C₄₇	#123	1	2	yes	—
169	C₂×C₄×C₄₇	#124	1	2	yes	—
170	C₂×C₄×C₄₇	#124	1	1	yes	characteristic
171	C₂×C₄×C₄₇	#126	1	2	yes	—
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₄₇⋊C₈	—	4	4	no	—
174	C₄₇⋊C₈	—	4	4	no	—
175	#11045	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	—	2	2	no	—
177	C₂²×C₄₇	—	2	2	no	—
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	2	no	—
180	C₂²×C₄₇	—	2	2	no	—
181	C₂²×C₄₇	#380	1	1	yes	characteristic
182	C₂²×C₄₇	#385	1	2	yes	—
183	C₂²×C₄₇	#386	1	1	yes	characteristic
184	C₂²×C₄₇	#388	1	2	yes	—
185	C₂²×C₄₇	#390	1	1	yes	characteristic
186	C₂²×C₄₇	C₂×#101	1	2	yes	—
187	C₂²×C₄₇	#413	1	2	yes	—
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	—	8	2	no	—
192	C₄×C₄₇	#392	1	1	yes	characteristic
193	C₄×C₄₇	#393	1	1	yes	characteristic
194	C₄×C₄₇	#394	1	2	yes	—
195	C₄×C₄₇	#396	1	2	yes	—
196	C₄×C₄₇	#397	1	1	yes	characteristic
197	C₄×C₄₇	#399	1	1	yes	characteristic
198	C₂×#423	—	47	1	no	—
199	C₂²×#101	—	47	2	no	—
200	C₂×#391	D₄₇	1	1	yes	characteristic
201	C₂×#343	—	47	2	no	—
202	#1728	—	47	1	no	—
203	C₂×C₄₇	—	2	2	no	—
204	C₂×C₄₇	—	2	2	no	—
205	C₂×C₄₇	#1439	1	1	yes	characteristic
206	C₂×C₄₇	#1801	1	2	yes	—
207	C₂×C₄₇	#1901	1	2	yes	—
208	C₂×C₄₇	#1966	1	1	yes	characteristic
209	C₂×C₄₇	#1967	1	1	yes	characteristic
210	C₂³×Q₈	C₂×D₄₇	1	1	yes	characteristic
211	C₂²×M₁₆	—	47	2	no	—
212	C₂²×M₁₆	—	47	2	no	—
213	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
214	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
215	#423	—	94	4	no	—
216	C₂×C₄⋊C₈	—	94	2	no	—
217	C₂×#101	—	94	4	no	—
218	C₂×#101	—	94	4	no	—
219	C₂×#101	—	94	4	no	—
220	#391	—	2	1	no	—
221	#391	—	2	1	no	—
222	#391	—	2	2	no	—
223	C₂×#95	Dic₄₇	1	4	yes	—
224	#343	—	94	4	no	—
225	#336	—	94	1	no	—
226	#336	—	94	1	no	—
227	C₄₇	#11045	1	1	yes	characteristic, complemented, Sylow
228	C₂²×Q₈	—	2	1	no	—
229	C₂²×Q₈	—	2	1	no	—
230	C₂²×Q₈	—	2	2	no	—
231	C₂²×Q₈	—	2	2	no	—
232	C₂²×Q₈	—	2	2	no	—
233	C₂²×Q₈	—	2	2	no	—
234	C₂²×Q₈	—	2	1	no	—
235	C₂²×Q₈	—	2	1	no	—
236	C₂²×Q₈	Dic₉₄	1	2	yes	—
237	C₂²×Q₈	D₁₈₈	1	2	yes	—
238	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
239	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
240	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	47	4	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	94	2	no	—
246	C₂×M₁₆	—	94	2	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂×M₁₆	—	94	2	no	—
249	C₂×M₁₆	—	94	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	2	no	—
254	C₂²×C₈	—	94	2	no	—
255	C₂²×C₈	—	94	2	no	—
256	C₂×C₄⋊C₄	—	2	2	no	—
257	C₂×C₄⋊C₄	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	1	no	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₄²	—	2	2	no	—
261	C₂×C₄²	—	2	2	no	—
262	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
264	C₂×C₄²	C₂²⋊D₄₇	1	2	yes	—
265	C₄⋊C₈	—	94	8	no	—
266	#101	—	94	16	no	—
267	#95	—	2	4	no	—
268	#95	—	2	4	no	—
269	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
270	C₂×Q₈	—	2	4	no	—
271	C₂×Q₈	—	2	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	2	2	no	—
276	C₂×Q₈	—	2	2	no	—
277	C₂×Q₈	—	2	4	no	—
278	C₂×Q₈	—	4	1	no	—
279	C₂×Q₈	—	4	2	no	—
280	C₂×Q₈	—	4	2	no	—
281	C₂×Q₈	—	4	2	no	—
282	C₂×Q₈	—	4	1	no	—
283	C₂×Q₈	—	4	2	no	—
284	C₂×Q₈	—	4	2	no	—
285	C₂×Q₈	—	4	1	no	—
286	C₂×Q₈	—	4	2	no	—
287	C₂×Q₈	—	4	1	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	4	no	—
291	C₂²×C₄	—	2	4	no	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	4	2	no	—
297	C₂²×C₄	—	4	4	no	—
298	C₂²×C₄	C₄⋊Dic₄₇	1	4	yes	—
299	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
300	C₂²×C₄	C₂²⋊Dic₄₇	1	2	yes	—
301	C₂²×C₄	C₂×Dic₉₄	1	1	yes	characteristic
302	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
303	C₂²×C₄	#10625350	1	1	yes	characteristic
304	C₂²×C₄	#10625350	1	1	yes	characteristic
305	C₂²×C₄	D₄×D₄₇	1	2	yes	—
306	C₂²×C₄	D₄×D₄₇	1	2	yes	—
307	C₂²×C₄	#10625352	1	2	yes	—
308	C₂²×C₄	#10625352	1	2	yes	—
309	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
311	M₁₆	—	94	4	no	—
312	M₁₆	—	94	4	no	—
313	M₁₆	—	94	4	no	—
314	M₁₆	—	94	4	no	—
315	M₁₆	—	188	2	no	—
316	M₁₆	—	188	2	no	—
317	M₁₆	—	188	2	no	—
318	M₁₆	—	188	2	no	—
319	C₂×C₈	—	94	4	no	—
320	C₂×C₈	—	94	4	no	—
321	C₂×C₈	—	188	2	no	—
322	C₂×C₈	—	188	2	no	—
323	C₂×C₈	—	188	2	no	—
324	C₂×C₈	—	188	2	no	—
325	C₄⋊C₄	—	4	2	no	—
326	C₄⋊C₄	—	4	1	no	—
327	C₄⋊C₄	—	4	1	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
335	C₂³	C₂×C₄⋊Dic₄₇	1	1	yes	characteristic
336	C₂³	#13093983	1	1	yes	characteristic
337	C₂³	D₄×Dic₄₇	1	2	yes	—
338	C₂³	D₄×Dic₄₇	1	2	yes	—
339	Q₈	—	4	2	no	—
340	Q₈	—	4	2	no	—
341	Q₈	—	4	4	no	—
342	Q₈	—	4	4	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	4	no	—
348	C₂×C₄	—	2	8	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	4	8	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	4	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	#13093943	1	4	yes	complemented
360	C₂×C₄	#13093992	1	1	yes	characteristic
361	C₂×C₄	#13093994	1	2	yes	—
362	C₂×C₄	#13093995	1	2	yes	—
363	C₂×C₄	#13093996	1	2	yes	—
364	C₂×C₄	#13093997	1	2	yes	—
365	C₂×C₄	#13093998	1	1	yes	characteristic
366	C₂×C₄	#13093998	1	1	yes	characteristic
367	C₂×C₄	#13094001	1	2	yes	—
368	C₂×C₄	#13094001	1	2	yes	—
369	C₂×C₄	#13094003	1	1	yes	characteristic
370	C₂×C₄	#13094003	1	1	yes	characteristic
371	C₂×C₄	#13094005	1	1	yes	characteristic
372	C₂×C₄	#13094006	1	2	yes	—
373	C₂×C₄	#13094008	1	2	yes	—
374	C₂×C₄	#13094010	1	2	yes	—
375	C₂×C₄	#13094011	1	1	yes	characteristic
376	C₂×C₄	#13094017	1	2	yes	—
377	C₂×C₄	#13094020	1	1	yes	characteristic
378	C₈	—	188	4	no	—
379	C₈	—	188	4	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	4	no	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	2	no	—
385	C₂²	#15688983	1	1	yes	characteristic
386	C₂²	#15688998	1	2	yes	—
387	C₂²	#15689003	1	1	yes	characteristic
388	C₂²	#15689016	1	2	yes	—
389	C₂²	#15689026	1	1	yes	characteristic
390	C₂²	C₂×#13093943	1	2	yes	—
391	C₂²	#15689107	1	2	yes	—
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	4	4	no	—
395	C₄	—	8	2	no	—
396	C₄	#15689032	1	1	yes	characteristic
397	C₄	#15689035	1	1	yes	characteristic
398	C₄	#15689039	1	2	yes	—
399	C₄	#15689046	1	2	yes	—
400	C₄	#15689048	1	1	yes	characteristic
401	C₄	#15689059	1	1	yes	characteristic
402	C₂	—	2	2	no	—
403	C₂	—	2	2	no	—
404	C₂	#20241633	1	1	yes	characteristic
405	C₂	#20243384	1	2	yes	—
406	C₂	#20243857	1	2	yes	—
407	C₂	#20244233	1	1	yes	characteristic
408	C₂	#20244238	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×C₂²⋊Dic₄₇
commutator, prime radical	C₂⁴×C₄₇	C₂²×C₄
Frattini	C₂³×C₄	C₂²×D₄₇
Fitting	C₂×C₄₇×#391	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
cosocle	C₂³×C₄×C₄₇	C₂³
hypercenter	C₂×#391	D₄₇
hypocenter	C₄₇	#11045
LCS	G ▷ C₂⁴×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂²×C₄² ◁ C₂×#391

Complements

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

N	H ≅ G/N	type
154. C₂×C₄×C₄₇	#101	semidirect
227. C₄₇	#11045	semidirect
359. C₂×C₄	#13093943	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689147	2
C₂²×#13093943	2
C₂×#15688892	2
#20243082	2
C₂×C₄₇×#391	2
#11045	47