Subgroups — #26109635

Order 12032.

592 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13093983	C₂	1	1	yes	maximal, characteristic
2	#20243368	C₂	1	1	yes	maximal, characteristic
3	#20241228	C₂	1	2	yes	maximal, complemented
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₄×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×#13093983	C₄	1	1	yes	characteristic
7	C₂×#13093983	C₄	1	1	yes	characteristic
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
10	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
11	C₄×C₄⋊Dic₄₇	C₄	1	1	yes	characteristic
12	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
13	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
14	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
15	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
16	#15688969	—	2	1	no	—
17	C₄²×Dic₄₇	—	2	1	no	—
18	#15688878	—	2	1	no	—
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
21	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
22	C₄₇×#336	—	2	1	no	—
23	C₂²×C₄₇⋊C₈	—	2	2	no	—
24	#13093983	—	2	2	no	—
25	#13093983	—	2	2	no	—
26	#13093983	—	2	2	no	—
27	#13093983	C₈	1	4	yes	complemented
28	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
29	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
31	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
33	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
34	C₂×C₄×Dic₄₇	—	2	1	no	—
35	C₂×C₄×Dic₄₇	—	2	1	no	—
36	C₂×C₄×Dic₄₇	—	2	1	no	—
37	C₂×C₄×Dic₄₇	—	2	1	no	—
38	C₂×C₄×Dic₄₇	—	2	1	no	—
39	C₂×C₄×Dic₄₇	—	2	1	no	—
40	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
41	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
43	C₄₇⋊#95	—	2	1	no	—
44	C₄₇⋊#95	—	2	1	no	—
45	C₄₇⋊#95	—	2	1	no	—
46	C₄₇⋊#95	—	2	1	no	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂×C₄²×C₄₇	—	2	2	no	—
52	C₂×C₄²×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	C₂×C₄	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	C₂³	1	1	yes	characteristic
57	C₂²⋊C₈×C₄₇	—	2	4	no	—
58	C₄×C₈×C₄₇	—	2	2	no	—
59	C₄×C₈×C₄₇	—	2	2	no	—
60	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
61	C₂²×C₄×C₄₇	—	2	1	no	—
62	C₂²×C₄×C₄₇	—	2	1	no	—
63	C₂²×C₄×C₄₇	—	2	1	no	—
64	C₂²×C₄×C₄₇	—	2	1	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	2	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	2	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	4	1	no	—
72	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
76	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
77	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
80	C₂²×Dic₄₇	—	2	1	no	—
81	C₂²×Dic₄₇	—	2	1	no	—
82	C₂²×Dic₄₇	—	2	1	no	—
83	C₂²×Dic₄₇	—	2	1	no	—
84	C₂×C₈×C₄₇	—	2	4	no	—
85	C₂×C₈×C₄₇	—	4	2	no	—
86	C₂×C₈×C₄₇	—	4	2	no	—
87	C₄²×C₄₇	—	2	1	no	—
88	C₄²×C₄₇	—	2	1	no	—
89	C₄²×C₄₇	—	2	2	no	—
90	C₄²×C₄₇	—	2	2	no	—
91	C₄²×C₄₇	#41	1	2	yes	—
92	C₄²×C₄₇	#41	1	2	yes	—
93	C₂²⋊Dic₄₇	—	2	4	no	—
94	C₂²⋊Dic₄₇	—	2	4	no	—
95	C₄⋊Dic₄₇	—	2	1	no	—
96	C₄⋊Dic₄₇	—	2	1	no	—
97	C₄⋊Dic₄₇	—	2	1	no	—
98	C₄⋊Dic₄₇	—	2	1	no	—
99	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
100	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
101	C₄⋊Dic₄₇	M₁₆	1	2	yes	—
102	C₄⋊Dic₄₇	M₁₆	1	2	yes	—
103	C₄×Dic₄₇	—	2	4	no	—
104	C₄×Dic₄₇	—	2	4	no	—
105	C₄×Dic₄₇	—	4	2	no	—
106	C₄×Dic₄₇	—	4	2	no	—
107	C₄×Dic₄₇	—	4	2	no	—
108	C₄×Dic₄₇	—	4	1	no	—
109	C₄×Dic₄₇	—	4	1	no	—
110	C₂×C₄₇⋊C₈	—	4	2	no	—
111	C₂×C₄₇⋊C₈	—	4	2	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂³×C₄₇	—	2	1	no	—
114	C₂³×C₄₇	—	2	1	no	—
115	C₂³×C₄₇	—	2	1	no	—
116	C₂³×C₄₇	—	2	1	no	—
117	C₂³×C₄₇	—	2	1	no	—
118	C₂³×C₄₇	—	2	1	no	—
119	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
120	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂×C₄×C₄₇	—	2	1	no	—
122	C₂×C₄×C₄₇	—	2	1	no	—
123	C₂×C₄×C₄₇	—	2	1	no	—
124	C₂×C₄×C₄₇	—	2	1	no	—
125	C₂×C₄×C₄₇	—	2	1	no	—
126	C₂×C₄×C₄₇	—	2	1	no	—
127	C₂×C₄×C₄₇	—	2	2	no	—
128	C₂×C₄×C₄₇	—	2	2	no	—
129	C₂×C₄×C₄₇	—	2	2	no	—
130	C₂×C₄×C₄₇	—	2	2	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	4	4	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
138	C₂×C₄×C₄₇	#104	1	2	yes	—
139	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
140	C₂×C₄×C₄₇	#117	1	1	yes	characteristic
141	C₂×C₄×C₄₇	#123	1	2	yes	—
142	C₂×C₄×C₄₇	#123	1	2	yes	—
143	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#135	1	2	yes	—
148	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	4	1	no	—
155	C₂×Dic₄₇	—	4	1	no	—
156	C₂×Dic₄₇	—	4	1	no	—
157	C₂×Dic₄₇	—	4	1	no	—
158	C₂×Dic₄₇	—	4	1	no	—
159	C₂×Dic₄₇	—	4	1	no	—
160	C₂×Dic₄₇	—	4	1	no	—
161	C₂×Dic₄₇	—	4	1	no	—
162	C₈×C₄₇	—	4	4	no	—
163	C₄₇⋊C₈	—	8	2	no	—
164	#8708	—	47	1	no	maximal, Sylow
165	C₂²×C₄₇	—	2	2	no	—
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	4	1	no	—
169	C₂²×C₄₇	—	4	1	no	—
170	C₂²×C₄₇	—	4	1	no	—
171	C₂²×C₄₇	—	4	1	no	—
172	C₂²×C₄₇	#381	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
174	C₂²×C₄₇	#407	1	1	yes	characteristic
175	C₂²×C₄₇	#416	1	1	yes	characteristic
176	C₂²×C₄₇	#417	1	1	yes	characteristic
177	C₂²×C₄₇	C₂×#104	1	1	yes	characteristic
178	C₂²×C₄₇	#421	1	1	yes	characteristic
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	4	1	no	—
183	C₄×C₄₇	#431	1	1	yes	characteristic
184	C₄×C₄₇	#431	1	1	yes	characteristic
185	C₄×C₄₇	#432	1	1	yes	characteristic
186	C₄×C₄₇	#432	1	1	yes	characteristic
187	C₄×C₄₇	#482	1	2	yes	—
188	C₄×C₄₇	#485	1	2	yes	—
189	Dic₄₇	—	4	2	no	—
190	Dic₄₇	—	4	2	no	—
191	Dic₄₇	—	4	2	no	—
192	Dic₄₇	—	4	2	no	—
193	C₄×#117	—	47	1	no	—
194	#1797	—	47	1	no	—
195	C₄×C₂²⋊C₈	D₄₇	1	1	yes	characteristic
196	#1279	—	47	2	no	—
197	#1279	—	47	2	no	—
198	C₂×C₄₇	—	4	2	no	—
199	C₂×C₄₇	#1476	1	1	yes	characteristic
200	C₂×C₄₇	#1477	1	1	yes	characteristic
201	C₂×C₄₇	#1488	1	1	yes	characteristic
202	C₂×C₄₇	#1489	1	1	yes	characteristic
203	C₂×C₄₇	#1817	1	1	yes	characteristic
204	C₂×C₄₇	#1825	1	1	yes	characteristic
205	C₂×C₄₇	#1826	1	1	yes	characteristic
206	C₂×#117	—	47	1	no	—
207	C₂×#117	—	47	1	no	—
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	47	2	no	—
210	C₂×C₂²⋊C₈	—	2	1	no	—
211	C₂×C₂²⋊C₈	—	94	1	no	—
212	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
213	C₄×C₄⋊C₄	—	47	1	no	—
214	C₄×C₄⋊C₄	—	47	1	no	—
215	C₄×C₄⋊C₄	—	47	1	no	—
216	C₄×C₄⋊C₄	—	47	1	no	—
217	C₄×C₂²⋊C₄	—	94	1	no	—
218	C₄×C₂²⋊C₄	—	94	1	no	—
219	#376	—	94	1	no	—
220	C₄³	—	94	1	no	—
221	#336	—	2	1	no	—
222	#336	—	94	1	no	—
223	C₄₇	#8708	1	1	yes	characteristic, complemented, Sylow
224	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
225	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
226	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
227	C₂²×C₈	—	2	2	no	—
228	C₂²×C₈	—	94	2	no	—
229	#117	—	47	4	no	—
230	#117	—	94	2	no	—
231	#117	—	94	2	no	—
232	#117	—	94	2	no	—
233	C₂×C₄⋊C₄	—	47	1	no	—
234	C₂×C₄⋊C₄	—	47	1	no	—
235	C₂×C₄⋊C₄	—	47	1	no	—
236	C₂×C₄⋊C₄	—	47	1	no	—
237	C₂×C₂²⋊C₄	—	94	1	no	—
238	C₂×C₂²⋊C₄	—	94	1	no	—
239	C₂×C₄²	—	2	2	no	—
240	C₂×C₄²	—	2	2	no	—
241	C₂×C₄²	—	94	1	no	—
242	C₂×C₄²	—	94	1	no	—
243	C₂×C₄²	—	94	1	no	—
244	C₂×C₄²	—	94	1	no	—
245	C₂×C₄²	—	94	1	no	—
246	C₂×C₄²	—	94	1	no	—
247	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
248	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
249	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
250	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
251	C₄⋊C₈	—	94	2	no	—
252	C₄⋊C₈	—	94	2	no	—
253	C₂²⋊C₈	—	2	4	no	—
254	C₂²⋊C₈	—	188	2	no	—
255	C₄×C₈	—	2	2	no	—
256	C₄×C₈	—	2	2	no	—
257	#95	—	94	1	no	—
258	#95	—	94	1	no	—
259	#95	—	94	1	no	—
260	#95	—	94	1	no	—
261	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
262	C₂²×C₄	—	2	1	no	—
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	2	1	no	—
265	C₂²×C₄	—	2	1	no	—
266	C₂²×C₄	—	2	2	no	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	2	2	no	—
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	—	2	1	no	—
271	C₂²×C₄	—	2	1	no	—
272	C₂²×C₄	—	4	1	no	—
273	C₂²×C₄	—	94	1	no	—
274	C₂²×C₄	—	94	1	no	—
275	C₂²×C₄	—	94	1	no	—
276	C₂²×C₄	—	94	1	no	—
277	C₂²×C₄	C₈×D₄₇	1	2	yes	—
278	C₂²×C₄	#10625324	1	2	yes	—
279	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
280	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
281	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
282	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
283	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
284	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
285	C₂×C₈	—	2	4	no	—
286	C₂×C₈	—	4	2	no	—
287	C₂×C₈	—	4	2	no	—
288	C₂×C₈	—	188	2	no	—
289	C₂×C₈	—	188	2	no	—
290	C₂×C₈	—	188	2	no	—
291	C₄⋊C₄	—	47	2	no	—
292	C₄⋊C₄	—	47	2	no	—
293	C₄⋊C₄	—	47	2	no	—
294	C₄⋊C₄	—	47	2	no	—
295	C₄⋊C₄	—	94	1	no	—
296	C₄⋊C₄	—	94	1	no	—
297	C₄⋊C₄	—	94	1	no	—
298	C₄⋊C₄	—	94	1	no	—
299	C₂²⋊C₄	—	94	4	no	—
300	C₂²⋊C₄	—	94	4	no	—
301	C₄²	—	2	1	no	—
302	C₄²	—	2	1	no	—
303	C₄²	—	2	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	94	4	no	—
306	C₄²	—	94	4	no	—
307	C₄²	—	188	2	no	—
308	C₄²	—	188	2	no	—
309	C₄²	—	188	2	no	—
310	C₄²	—	188	1	no	—
311	C₄²	—	188	1	no	—
312	C₄²	#10625352	1	2	yes	—
313	C₄²	#10625352	1	2	yes	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	1	no	—
316	C₂³	—	2	1	no	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
321	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
322	C₂×C₄	—	2	1	no	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	4	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	—	94	2	no	—
340	C₂×C₄	—	94	2	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	188	1	no	—
343	C₂×C₄	—	188	1	no	—
344	C₂×C₄	—	188	1	no	—
345	C₂×C₄	—	188	1	no	—
346	C₂×C₄	—	188	1	no	—
347	C₂×C₄	—	188	1	no	—
348	C₂×C₄	—	188	1	no	—
349	C₂×C₄	—	188	1	no	—
350	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
351	C₂×C₄	#13093952	1	2	yes	—
352	C₂×C₄	#13093980	1	1	yes	characteristic
353	C₂×C₄	#13093980	1	1	yes	characteristic
354	C₂×C₄	#13094005	1	2	yes	—
355	C₂×C₄	#13094008	1	2	yes	—
356	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
358	C₂×C₄	M₁₆×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
360	C₂×C₄	#13094046	1	2	yes	—
361	C₂×C₄	#13094052	1	1	yes	characteristic
362	C₂×C₄	#13094057	1	1	yes	characteristic
363	C₈	—	4	4	no	—
364	C₈	—	376	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	1	no	—
372	C₂²	#15688984	1	1	yes	characteristic
373	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
374	C₂²	#15689086	1	1	yes	characteristic
375	C₂²	#15689120	1	1	yes	characteristic
376	C₂²	#15689125	1	1	yes	characteristic
377	C₂²	C₂×#13093952	1	1	yes	characteristic
378	C₂²	#15689141	1	1	yes	characteristic
379	C₄	—	2	2	no	—
380	C₄	—	2	2	no	—
381	C₄	—	2	2	no	—
382	C₄	—	4	1	no	—
383	C₄	—	188	2	no	—
384	C₄	—	188	2	no	—
385	C₄	—	188	2	no	—
386	C₄	—	188	2	no	—
387	C₄	#15689173	1	1	yes	characteristic
388	C₄	#15689173	1	1	yes	characteristic
389	C₄	#15689177	1	1	yes	characteristic
390	C₄	#15689177	1	1	yes	characteristic
391	C₄	#15689448	1	2	yes	—
392	C₄	#15689465	1	2	yes	—
393	C₂	—	4	2	no	—
394	C₂	#20241771	1	1	yes	characteristic
395	C₂	#20241776	1	1	yes	characteristic
396	C₂	#20241823	1	1	yes	characteristic
397	C₂	#20241828	1	1	yes	characteristic
398	C₂	#20243454	1	1	yes	characteristic
399	C₂	#20243484	1	1	yes	characteristic
400	C₂	#20243488	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄×C₂²⋊C₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₄×C₂²⋊C₈	D₄₇
hypocenter	C₄₇	#8708
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₄×C₂²⋊C₈

Complements

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

N	H ≅ G/N	type
3. #20241228	C₂	semidirect
4. #20241228	C₂	semidirect
27. #13093983	C₈	semidirect
223. C₄₇	#8708	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13093983	2
#20243368	2
#20241228	2
C₄×C₂²⋊C₈×C₄₇	2
#8708	47