Subgroups — #26111619

Order 12032.

610 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13094003	C₂	1	1	yes	maximal, characteristic
2	#20243368	C₂	1	1	yes	maximal, characteristic
3	C₂×#15688855	C₂	1	2	yes	maximal, complemented
4	#20241228	C₂	1	2	yes	maximal, complemented
5	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
6	C₂×#13094003	C₄	1	1	yes	characteristic
7	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
8	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
9	C₂×C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
10	#15689029	C₄	1	1	yes	characteristic
11	#15689021	C₄	1	1	yes	characteristic
12	#15689007	—	2	1	no	—
13	#15688996	—	2	1	no	—
14	#15688983	C₄	1	1	yes	characteristic
15	C₄×Dic₄₇⋊C₄	—	2	1	no	—
16	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₄×C₂²⋊Dic₄₇	—	2	1	no	—
18	#15688878	—	2	1	no	—
19	#15688855	—	2	4	no	—
20	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#431	—	2	4	no	—
22	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
23	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
24	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
25	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
26	C₂²×C₄₇⋊C₈	—	2	2	no	—
27	#13094003	—	2	2	no	—
28	#13094003	C₈	1	4	yes	complemented
29	C₄×Dic₉₄	—	2	2	no	—
30	C₄×Dic₉₄	—	2	2	no	—
31	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
32	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
33	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂×Dic₄₇⋊C₄	—	2	1	no	—
35	C₂×Dic₄₇⋊C₄	—	2	1	no	—
36	C₂×Dic₄₇⋊C₄	—	2	1	no	—
37	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
38	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
39	C₂×C₄×Dic₄₇	—	2	1	no	—
40	C₂×C₄×Dic₄₇	—	2	1	no	—
41	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
42	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
43	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
44	C₄₇⋊#95	—	2	1	no	—
45	C₄₇⋊#95	—	2	1	no	—
46	C₄₇⋊#95	—	2	1	no	—
47	C₄₇⋊#95	—	2	1	no	—
48	C₄₇⋊#95	—	2	1	no	—
49	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₇	—	2	2	no	—
53	C₂×C₄²×C₄₇	—	2	2	no	—
54	C₂×C₄²×C₄₇	—	2	2	no	—
55	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
59	C₄⋊C₈×C₄₇	—	2	4	no	—
60	C₂²⋊C₈×C₄₇	—	2	4	no	—
61	C₄×C₈×C₄₇	—	2	2	no	—
62	C₄×C₈×C₄₇	D₄	1	4	yes	—
63	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₄₇	—	2	2	no	—
65	C₂²×C₄×C₄₇	—	2	2	no	—
66	C₂²×C₄×C₄₇	—	2	1	no	—
67	C₂²×C₄×C₄₇	—	2	2	no	—
68	C₂²×C₄×C₄₇	—	2	1	no	—
69	C₂²×C₄×C₄₇	—	2	1	no	—
70	C₂²×C₄×C₄₇	—	2	1	no	—
71	C₂²×C₄×C₄₇	—	2	2	no	—
72	C₂²×C₄×C₄₇	—	4	1	no	—
73	C₂²×C₄×C₄₇	—	4	1	no	—
74	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	C₂×C₈	1	2	yes	—
78	C₂²×C₄×C₄₇	M₁₆	1	2	yes	—
79	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂²×Dic₄₇	—	2	1	no	—
83	C₂²×Dic₄₇	—	2	1	no	—
84	C₂²×Dic₄₇	—	2	1	no	—
85	C₂²×Dic₄₇	—	2	1	no	—
86	C₂×Dic₉₄	—	2	2	no	—
87	C₂×Dic₉₄	—	2	2	no	—
88	C₂×Dic₉₄	—	2	1	no	—
89	C₂×Dic₉₄	C₂×C₈	1	2	yes	—
90	C₂×C₈×C₄₇	—	2	4	no	—
91	C₂×C₈×C₄₇	—	4	2	no	—
92	C₂×C₈×C₄₇	—	4	2	no	—
93	C₄²×C₄₇	—	2	2	no	—
94	C₄²×C₄₇	—	2	1	no	—
95	C₄²×C₄₇	—	2	2	no	—
96	C₄²×C₄₇	—	2	1	no	—
97	C₄²×C₄₇	C₂×D₄	1	2	yes	—
98	C₄²×C₄₇	#41	1	2	yes	—
99	C₂²⋊Dic₄₇	—	2	4	no	—
100	C₂²⋊Dic₄₇	—	4	2	no	—
101	C₄⋊Dic₄₇	—	2	1	no	—
102	C₄⋊Dic₄₇	—	2	2	no	—
103	C₄⋊Dic₄₇	—	2	2	no	—
104	C₄⋊Dic₄₇	C₂×C₈	1	2	yes	—
105	Dic₄₇⋊C₄	—	2	4	no	—
106	Dic₄₇⋊C₄	—	4	2	no	—
107	Dic₄₇⋊C₄	—	4	1	no	—
108	Dic₄₇⋊C₄	—	4	1	no	—
109	C₄×Dic₄₇	—	4	2	no	—
110	C₄×Dic₄₇	—	4	1	no	—
111	C₄×Dic₄₇	—	4	1	no	—
112	C₂×C₄₇⋊C₈	—	4	2	no	—
113	C₂×C₄₇⋊C₈	—	4	2	no	—
114	C₂×C₄₇⋊C₈	—	4	2	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	—	2	1	no	—
120	C₂³×C₄₇	—	2	1	no	—
121	C₂³×C₄₇	C₂²⋊C₈	1	2	yes	—
122	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
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	4	no	—
128	C₂×C₄×C₄₇	—	2	4	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	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	—	2	1	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	—	4	2	no	—
137	C₂×C₄×C₄₇	—	4	2	no	—
138	C₂×C₄×C₄₇	—	4	2	no	—
139	C₂×C₄×C₄₇	C₂²⋊C₈	1	2	yes	—
140	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
141	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
142	C₂×C₄×C₄₇	#121	1	2	yes	—
143	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×M₁₆	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#131	1	2	yes	—
147	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
148	C₂×C₄×C₄₇	#137	1	2	yes	—
149	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	4	1	no	—
153	C₂×Dic₄₇	—	4	1	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	Dic₉₄	—	2	4	no	—
163	Dic₉₄	—	4	2	no	—
164	C₈×C₄₇	—	4	4	no	—
165	C₄₇⋊C₈	—	8	2	no	—
166	#9073	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	4	1	no	—
171	C₂²×C₄₇	—	4	1	no	—
172	C₂²×C₄₇	—	4	1	no	—
173	C₂²×C₄₇	—	4	1	no	—
174	C₂²×C₄₇	#386	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×C₂²⋊C₈	1	1	yes	characteristic
176	C₂²×C₄₇	#408	1	1	yes	characteristic
177	C₂²×C₄₇	#417	1	1	yes	characteristic
178	C₂²×C₄₇	#419	1	1	yes	characteristic
179	C₂²×C₄₇	#421	1	1	yes	characteristic
180	C₂²×C₄₇	#421	1	1	yes	characteristic
181	C₄×C₄₇	—	2	2	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	4	1	no	—
185	C₄×C₄₇	—	4	1	no	—
186	C₄×C₄₇	C₈×D₄	1	2	yes	—
187	C₄×C₄₇	#435	1	2	yes	—
188	C₄×C₄₇	#468	1	2	yes	—
189	C₄×C₄₇	#470	1	2	yes	—
190	Dic₄₇	—	4	2	no	—
191	Dic₄₇	—	4	2	no	—
192	Dic₄₇	—	8	1	no	—
193	Dic₄₇	—	8	1	no	—
194	C₂×#431	D₄₇	1	1	yes	characteristic
195	C₄×C₂²⋊Q₈	—	47	1	no	—
196	#1797	—	47	1	no	—
197	C₂×Q₈⋊C₈	—	47	2	no	—
198	#1279	—	47	2	no	—
199	C₂×C₄₇	—	4	2	no	—
200	C₂×C₄₇	#1477	1	1	yes	characteristic
201	C₂×C₄₇	#1479	1	1	yes	characteristic
202	C₂×C₄₇	#1495	1	1	yes	characteristic
203	C₂×C₄₇	#1497	1	1	yes	characteristic
204	C₂×C₄₇	#1869	1	1	yes	characteristic
205	C₂×C₄₇	#1894	1	1	yes	characteristic
206	C₂×C₄₇	#1897	1	1	yes	characteristic
207	C₂×C₂²⋊Q₈	—	47	1	no	—
208	C₂×C₄×Q₈	—	47	1	no	—
209	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
210	#431	—	2	4	no	—
211	C₂×C₄⋊C₈	—	2	1	no	—
212	C₂×C₄⋊C₈	—	47	2	no	—
213	C₂×C₂²⋊C₈	—	2	1	no	—
214	C₂×C₂²⋊C₈	—	94	1	no	—
215	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
216	#391	—	47	1	no	—
217	#389	—	47	1	no	—
218	#387	—	94	1	no	—
219	#385	—	94	1	no	—
220	#380	—	47	1	no	—
221	C₄×C₄⋊C₄	—	47	1	no	—
222	C₄×C₄⋊C₄	—	94	1	no	—
223	C₄×C₂²⋊C₄	—	94	1	no	—
224	#336	—	94	1	no	—
225	Q₈⋊C₈	—	94	4	no	—
226	C₄₇	#9073	1	1	yes	characteristic, complemented, Sylow
227	C₂²×Q₈	—	47	1	no	—
228	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
229	C₂³×C₄	D₁₈₈	1	1	yes	characteristic
230	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
231	C₂²×C₈	—	2	2	no	—
232	C₂²×C₈	—	94	2	no	—
233	C₂²⋊Q₈	—	47	4	no	—
234	C₂²⋊Q₈	—	94	2	no	—
235	C₄×Q₈	—	94	2	no	—
236	C₄×Q₈	—	94	2	no	—
237	C₂×C₄⋊C₄	—	47	1	no	—
238	C₂×C₄⋊C₄	—	47	1	no	—
239	C₂×C₄⋊C₄	—	47	1	no	—
240	C₂×C₄⋊C₄	—	94	1	no	—
241	C₂×C₄⋊C₄	—	94	1	no	—
242	C₂×C₄⋊C₄	—	94	1	no	—
243	C₂×C₂²⋊C₄	—	94	1	no	—
244	C₂×C₂²⋊C₄	—	94	1	no	—
245	C₂×C₄²	—	2	2	no	—
246	C₂×C₄²	—	2	2	no	—
247	C₂×C₄²	—	94	1	no	—
248	C₂×C₄²	—	94	1	no	—
249	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
250	C₂×C₄²	D₁₈₈	1	1	yes	characteristic
251	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
253	C₄⋊C₈	—	2	4	no	—
254	C₄⋊C₈	—	94	2	no	—
255	C₄⋊C₈	—	94	2	no	—
256	C₂²⋊C₈	—	2	4	no	—
257	C₂²⋊C₈	—	188	2	no	—
258	C₄×C₈	—	2	2	no	—
259	C₄×C₈	C₂²⋊D₄₇	1	4	yes	—
260	#95	—	94	1	no	—
261	#95	—	94	1	no	—
262	#95	—	94	1	no	—
263	#95	—	94	1	no	—
264	#95	—	94	1	no	—
265	C₂⁴	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
266	C₂×Q₈	—	47	2	no	—
267	C₂×Q₈	—	94	1	no	—
268	C₂×Q₈	—	94	2	no	—
269	C₂×Q₈	—	94	2	no	—
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	2	no	—
272	C₂²×C₄	—	2	1	no	—
273	C₂²×C₄	—	2	2	no	—
274	C₂²×C₄	—	2	1	no	—
275	C₂²×C₄	—	2	1	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	4	1	no	—
279	C₂²×C₄	—	4	1	no	—
280	C₂²×C₄	—	94	1	no	—
281	C₂²×C₄	—	94	1	no	—
282	C₂²×C₄	—	94	1	no	—
283	C₂²×C₄	—	94	1	no	—
284	C₂²×C₄	C₈×D₄₇	1	2	yes	—
285	C₂²×C₄	#10625324	1	2	yes	—
286	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
287	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
288	C₂²×C₄	(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
291	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
292	C₂×C₈	—	2	4	no	—
293	C₂×C₈	—	4	2	no	—
294	C₂×C₈	—	4	2	no	—
295	C₂×C₈	—	188	2	no	—
296	C₂×C₈	—	188	2	no	—
297	C₂×C₈	—	188	2	no	—
298	C₄⋊C₄	—	47	2	no	—
299	C₄⋊C₄	—	94	4	no	—
300	C₄⋊C₄	—	94	1	no	—
301	C₄⋊C₄	—	94	2	no	—
302	C₄⋊C₄	—	94	2	no	—
303	C₄⋊C₄	—	188	2	no	—
304	C₄⋊C₄	—	188	1	no	—
305	C₄⋊C₄	—	188	1	no	—
306	C₂²⋊C₄	—	94	4	no	—
307	C₂²⋊C₄	—	188	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	2	1	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	188	2	no	—
313	C₄²	—	188	1	no	—
314	C₄²	—	188	1	no	—
315	C₄²	#10625350	1	2	yes	—
316	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
317	C₂³	—	2	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	2	1	no	—
323	C₂³	(C₂×D₄₇)⋊C₈	1	2	yes	—
324	C₂³	C₂×(C₂×D₄₇)⋊C₄	1	1	yes	characteristic
325	Q₈	—	94	4	no	—
326	Q₈	—	188	2	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	4	no	—
332	C₂×C₄	—	2	4	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	2	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	94	2	no	—
344	C₂×C₄	—	94	2	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	—	188	1	no	—
351	C₂×C₄	—	188	1	no	—
352	C₂×C₄	—	188	1	no	—
353	C₂×C₄	—	188	1	no	—
354	C₂×C₄	—	188	1	no	—
355	C₂×C₄	(C₂×D₄₇)⋊C₈	1	2	yes	—
356	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
357	C₂×C₄	#13093993	1	1	yes	characteristic
358	C₂×C₄	#13093998	1	2	yes	—
359	C₂×C₄	#13094007	1	1	yes	characteristic
360	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₂×#10625324	1	1	yes	characteristic
362	C₂×C₄	#13094030	1	2	yes	—
363	C₂×C₄	#13094052	1	1	yes	characteristic
364	C₂×C₄	#13094057	1	2	yes	—
365	C₂×C₄	#13094057	1	1	yes	characteristic
366	C₈	—	4	4	no	—
367	C₈	—	376	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	4	1	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	#15689002	1	1	yes	characteristic
376	C₂²	C₂×(C₂×D₄₇)⋊C₈	1	1	yes	characteristic
377	C₂²	#15689089	1	1	yes	characteristic
378	C₂²	#15689125	1	1	yes	characteristic
379	C₂²	#15689133	1	1	yes	characteristic
380	C₂²	#15689141	1	1	yes	characteristic
381	C₂²	#15689141	1	1	yes	characteristic
382	C₄	—	2	1	no	—
383	C₄	—	2	1	no	—
384	C₄	—	2	2	no	—
385	C₄	—	4	1	no	—
386	C₄	—	4	1	no	—
387	C₄	—	376	1	no	—
388	C₄	—	376	1	no	—
389	C₄	—	188	2	no	—
390	C₄	—	188	2	no	—
391	C₄	C₈×C₂²⋊D₄₇	1	2	yes	—
392	C₄	#15689194	1	2	yes	—
393	C₄	#15689369	1	2	yes	—
394	C₄	#15689381	1	2	yes	—
395	C₂	—	4	2	no	—
396	C₂	#20241776	1	1	yes	characteristic
397	C₂	#20241784	1	1	yes	characteristic
398	C₂	#20241854	1	1	yes	characteristic
399	C₂	#20241862	1	1	yes	characteristic
400	C₂	#20243680	1	1	yes	characteristic
401	C₂	#20243821	1	1	yes	characteristic
402	C₂	#20243836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂²×C₈
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₂×C₄₇×#431	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#431	D₄₇
hypocenter	C₄₇	#9073
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×#431

Complements

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

N	H ≅ G/N	type
3. C₂×#15688855	C₂	semidirect
4. #20241228	C₂	semidirect
28. #13094003	C₈	semidirect
226. C₄₇	#9073	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13094003	2
#20243368	2
C₂×#15688855	2
#20241228	2
C₂×C₄₇×#431	2
#9073	47