Subgroups — #26105856

Order 12032.

794 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	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093982	C₂	1	1	yes	maximal, characteristic
4	#20241229	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241228	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	—	2	1	no	—
9	C₂²×#10625324	—	2	1	no	—
10	C₂×#13093982	C₄	1	2	yes	—
11	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
12	#15689145	—	2	2	no	—
13	#15689145	C₄	1	4	yes	complemented
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×Dic₄₇⋊C₈	—	2	1	no	—
16	C₄×#10625324	—	2	2	no	—
17	C₄×#10625324	C₄	1	4	yes	complemented
18	C₂×#13093934	—	2	1	no	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
21	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
22	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
23	#15688970	—	2	1	no	—
24	#15688968	—	2	1	no	—
25	C₄²×Dic₄₇	—	2	1	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
31	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
32	C₂×#10625324	—	2	8	no	—
33	C₂×#10625324	—	2	4	no	—
34	C₂×#10625324	—	2	4	no	—
35	C₂×#10625324	—	4	2	no	—
36	C₂×#10625324	—	4	2	no	—
37	C₂²×C₄₇⋊C₈	—	2	1	no	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	#13093982	—	2	4	no	—
40	#13093982	—	2	4	no	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
43	C₂×C₄×Dic₄₇	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	1	no	—
45	C₂×C₄×Dic₄₇	—	2	2	no	—
46	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
49	C₄²×D₄₇	C₂×C₄	1	2	yes	—
50	C₄²×D₄₇	C₂×C₄	1	2	yes	—
51	C₄²×D₄₇	D₄	1	2	yes	—
52	C₄²×D₄₇	Q₈	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
55	Dic₄₇⋊C₈	—	2	4	no	—
56	#13093934	—	2	4	no	—
57	C₄×C₄₇⋊C₈	—	2	1	no	—
58	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
59	C₄₇⋊#95	—	2	1	no	—
60	C₄₇⋊#95	—	2	2	no	—
61	C₂²×C₈×C₄₇	—	2	1	no	—
62	C₂²×C₈×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
64	C₂×C₄²×C₄₇	—	2	1	no	—
65	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊C₈×C₄₇	—	2	1	no	—
67	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
68	C₄×C₈×C₄₇	—	2	1	no	—
69	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
70	#95×C₄₇	—	2	1	no	—
71	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₄₇	—	2	2	no	—
73	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×Dic₄₇	—	2	2	no	—
77	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂×C₄×D₄₇	—	2	2	no	—
81	C₂×C₄×D₄₇	—	2	2	no	—
82	C₂×C₄×D₄₇	—	2	1	no	—
83	C₂×C₄×D₄₇	—	2	1	no	—
84	C₂×C₄×D₄₇	—	2	1	no	—
85	C₂×C₄×D₄₇	—	2	1	no	—
86	C₂×C₄×D₄₇	—	2	4	no	—
87	C₂×C₄×D₄₇	C₄²	1	2	yes	—
88	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
89	C₂×C₄×D₄₇	C₂²⋊C₄	1	2	yes	—
90	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
91	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
92	C₂×C₄×D₄₇	C₄⋊C₄	1	2	yes	—
93	C₂×C₈×C₄₇	—	2	4	no	—
94	C₂×C₈×C₄₇	—	2	2	no	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	4	1	no	—
97	C₂×C₈×C₄₇	—	4	1	no	—
98	C₄⋊C₄×C₄₇	—	2	2	no	—
99	C₄⋊C₄×C₄₇	M₁₆	1	4	yes	complemented
100	C₄²×C₄₇	—	4	1	no	—
101	C₄²×C₄₇	—	4	1	no	—
102	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
106	(C₂×D₄₇)⋊C₄	—	2	8	no	—
107	C₄⋊Dic₄₇	—	2	2	no	—
108	C₄⋊Dic₄₇	M₁₆	1	4	yes	complemented
109	C₄×Dic₄₇	—	2	8	no	—
110	C₄×Dic₄₇	—	4	1	no	—
111	C₄×Dic₄₇	—	4	1	no	—
112	C₄×Dic₄₇	—	4	4	no	—
113	C₄×Dic₄₇	C₄²	1	2	yes	—
114	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
115	C₄×Dic₄₇	C₂²⋊C₄	1	2	yes	—
116	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
117	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
118	C₄×Dic₄₇	C₄⋊C₄	1	2	yes	—
119	C₂×C₄₇⋊C₈	—	2	4	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	4	1	no	—
123	C₂×C₄₇⋊C₈	—	4	1	no	—
124	#10625324	—	2	16	no	—
125	#10625324	—	4	8	no	—
126	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
127	C₂²×D₄₇	—	2	2	no	—
128	C₂²×D₄₇	—	2	1	no	—
129	C₂²×D₄₇	—	2	1	no	—
130	C₂²×D₄₇	—	2	2	no	—
131	C₂²×D₄₇	#95	1	2	yes	—
132	C₂×C₄×C₄₇	—	2	2	no	—
133	C₂×C₄×C₄₇	—	2	4	no	—
134	C₂×C₄×C₄₇	—	4	2	no	—
135	C₂×C₄×C₄₇	—	4	2	no	—
136	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
137	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
138	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
139	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
143	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
144	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
145	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
146	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
147	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
148	C₂×Dic₄₇	—	2	2	no	—
149	C₂×Dic₄₇	—	2	1	no	—
150	C₂×Dic₄₇	—	2	1	no	—
151	C₂×Dic₄₇	—	2	4	no	—
152	C₂×Dic₄₇	—	4	2	no	—
153	C₂×Dic₄₇	—	4	2	no	—
154	C₂×Dic₄₇	#95	1	2	yes	—
155	C₂×Dic₄₇	#95	1	2	yes	—
156	C₂×Dic₄₇	#95	1	2	yes	—
157	C₂×Dic₄₇	#104	1	4	yes	—
158	C₄×D₄₇	—	2	2	no	—
159	C₄×D₄₇	—	2	2	no	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	4	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	4	no	—
166	C₄×D₄₇	—	2	4	no	—
167	C₈×C₄₇	—	2	4	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₄₇⋊C₈	—	2	4	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	#7903	—	47	1	no	maximal, Sylow
172	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
173	C₂²×C₄₇	#407	1	2	yes	—
174	C₂²×C₄₇	#417	1	1	yes	characteristic
175	C₂²×C₄₇	#417	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#104	1	2	yes	—
177	C₂×D₄₇	—	2	2	no	—
178	C₂×D₄₇	—	2	2	no	—
179	C₂×D₄₇	—	2	2	no	—
180	C₂×D₄₇	—	4	2	no	—
181	C₂×D₄₇	—	4	2	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	4	4	no	—
185	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
186	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
187	C₄×C₄₇	#418	1	1	yes	characteristic
188	C₄×C₄₇	#419	1	1	yes	characteristic
189	C₄×C₄₇	#423	1	2	yes	—
190	C₄×C₄₇	#428	1	1	yes	characteristic
191	C₄×C₄₇	#428	1	1	yes	characteristic
192	Dic₄₇	—	2	2	no	—
193	Dic₄₇	—	2	2	no	—
194	Dic₄₇	—	4	4	no	—
195	Dic₄₇	#339	1	4	yes	—
196	C₂×#423	—	47	1	no	—
197	C₂×C₄×M₁₆	—	47	1	no	—
198	C₄×#117	—	47	1	no	—
199	#1279	—	47	1	no	—
200	#1279	—	47	1	no	—
201	#1279	—	47	1	no	—
202	#1279	D₄₇	1	1	yes	characteristic, complemented
203	C₂×C₄₇	#1489	1	2	yes	—
204	C₂×C₄₇	#1489	1	2	yes	—
205	C₂×C₄₇	#1728	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
207	C₂×C₄₇	#1736	1	1	yes	characteristic
208	D₄₇	—	4	2	no	—
209	C₂²×M₁₆	—	94	1	no	—
210	C₂²×M₁₆	—	94	1	no	—
211	C₂×#117	—	47	2	no	—
212	C₂²×C₄²	—	47	1	no	—
213	#423	—	47	4	no	—
214	#423	—	94	2	no	—
215	C₂×C₄⋊C₈	—	47	1	no	—
216	C₂×C₄⋊C₈	—	94	1	no	—
217	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₄×M₁₆	—	47	4	no	—
219	C₄×M₁₆	—	94	2	no	—
220	C₂×#97	—	94	1	no	—
221	C₂×C₄×C₈	—	47	1	no	—
222	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₄×C₄⋊C₄	—	47	2	no	—
224	C₄×C₄⋊C₄	—	47	1	no	—
225	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
226	C₄×C₂²⋊C₄	—	94	1	no	—
227	C₄×C₂²⋊C₄	—	94	1	no	—
228	#376	—	94	1	no	—
229	C₄³	—	94	1	no	—
230	C₄₇	#7903	1	1	yes	characteristic, complemented, Sylow
231	C₂³×C₄	—	47	1	no	—
232	C₂³×C₄	—	47	1	no	—
233	C₂³×C₄	—	47	1	no	—
234	C₂×M₁₆	—	94	4	no	—
235	C₂×M₁₆	—	94	8	no	—
236	C₂×M₁₆	—	94	4	no	—
237	C₂×M₁₆	—	188	2	no	—
238	C₂×M₁₆	—	188	2	no	—
239	C₂²×C₈	—	2	1	no	—
240	C₂²×C₈	—	2	1	no	—
241	C₂²×C₈	—	94	1	no	—
242	C₂²×C₈	—	94	1	no	—
243	#117	—	94	4	no	—
244	#117	—	94	4	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
247	C₂×C₂²⋊C₄	—	94	2	no	—
248	C₂×C₄²	—	2	1	no	—
249	C₂×C₄²	—	47	1	no	—
250	C₂×C₄²	—	47	1	no	—
251	C₂×C₄²	—	47	1	no	—
252	C₂×C₄²	—	47	2	no	—
253	C₂×C₄²	—	47	2	no	—
254	C₂×C₄²	—	47	2	no	—
255	C₂×C₄²	—	47	2	no	—
256	C₂×C₄²	—	94	2	no	—
257	C₂×C₄²	—	94	2	no	—
258	C₂×C₄²	—	94	1	no	—
259	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
260	C₄⋊C₈	—	2	1	no	—
261	C₄⋊C₈	—	47	2	no	—
262	C₄⋊C₈	—	94	4	no	—
263	C₄⋊C₈	—	94	1	no	—
264	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
265	#97	—	94	4	no	—
266	C₄×C₈	—	2	1	no	—
267	C₄×C₈	—	47	2	no	—
268	C₄×C₈	—	94	1	no	—
269	C₄×C₈	C₄×D₄₇	1	2	yes	—
270	#95	—	2	1	no	—
271	#95	—	94	2	no	—
272	#95	—	94	1	no	—
273	C₂⁴	—	47	1	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	47	1	no	—
276	C₂²×C₄	—	47	1	no	—
277	C₂²×C₄	—	47	1	no	—
278	C₂²×C₄	—	47	2	no	—
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	94	4	no	—
285	C₂²×C₄	—	94	2	no	—
286	C₂²×C₄	—	94	2	no	—
287	C₂²×C₄	—	94	1	no	—
288	C₂²×C₄	—	94	1	no	—
289	C₂²×C₄	—	94	1	no	—
290	C₂²×C₄	—	94	1	no	—
291	C₂²×C₄	—	94	2	no	—
292	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
295	M₁₆	—	94	16	no	—
296	M₁₆	—	188	8	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	4	1	no	—
301	C₂×C₈	—	4	1	no	—
302	C₂×C₈	—	94	4	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	188	1	no	—
306	C₂×C₈	—	188	1	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	47	4	no	—
309	C₄⋊C₄	—	94	2	no	—
310	C₄⋊C₄	#10625324	1	4	yes	complemented
311	C₂²⋊C₄	—	94	8	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	47	2	no	—
315	C₄²	—	47	2	no	—
316	C₄²	—	47	2	no	—
317	C₄²	—	47	2	no	—
318	C₄²	—	47	2	no	—
319	C₄²	—	47	2	no	—
320	C₄²	—	94	8	no	—
321	C₄²	—	188	4	no	—
322	C₄²	—	188	1	no	—
323	C₄²	—	188	1	no	—
324	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
325	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
326	C₄²	D₄×D₄₇	1	1	yes	characteristic
327	C₄²	Q₈×D₄₇	1	1	yes	characteristic
328	C₂³	—	47	2	no	—
329	C₂³	—	94	2	no	—
330	C₂³	—	94	1	no	—
331	C₂³	—	94	1	no	—
332	C₂³	—	94	2	no	—
333	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	47	2	no	—
339	C₂×C₄	—	47	4	no	—
340	C₂×C₄	—	47	2	no	—
341	C₂×C₄	—	47	2	no	—
342	C₂×C₄	—	94	4	no	—
343	C₂×C₄	—	94	4	no	—
344	C₂×C₄	—	94	2	no	—
345	C₂×C₄	—	94	1	no	—
346	C₂×C₄	—	94	1	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	—	94	2	no	—
351	C₂×C₄	—	94	4	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	188	2	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
359	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
364	C₂×C₄	C₂×#10625324	1	2	yes	—
365	C₂×C₄	#13094048	1	1	yes	characteristic
366	C₂×C₄	#13094051	1	1	yes	characteristic
367	C₂×C₄	#13094053	1	1	yes	characteristic
368	C₂×C₄	#13094056	1	1	yes	characteristic
369	C₈	—	2	4	no	—
370	C₈	—	4	2	no	—
371	C₈	—	94	4	no	—
372	C₈	—	188	2	no	—
373	C₂²	—	94	2	no	—
374	C₂²	—	94	2	no	—
375	C₂²	—	94	2	no	—
376	C₂²	—	188	2	no	—
377	C₂²	—	188	2	no	—
378	C₂²	#95×D₄₇	1	1	yes	characteristic
379	C₂²	#15689085	1	2	yes	—
380	C₂²	#15689121	1	1	yes	characteristic
381	C₂²	#15689123	1	1	yes	characteristic
382	C₂²	#104×D₄₇	1	2	yes	—
383	C₄	—	2	1	no	—
384	C₄	—	2	1	no	—
385	C₄	—	4	4	no	—
386	C₄	—	47	4	no	—
387	C₄	—	94	2	no	—
388	C₄	—	94	2	no	—
389	C₄	—	188	4	no	—
390	C₄	C₄×#10625324	1	1	yes	characteristic
391	C₄	#15689075	1	1	yes	characteristic
392	C₄	#15689126	1	1	yes	characteristic
393	C₄	#15689130	1	1	yes	characteristic
394	C₄	#15689145	1	2	yes	—
395	C₄	#15689162	1	1	yes	characteristic
396	C₄	#15689164	1	1	yes	characteristic
397	C₂	—	188	2	no	—
398	C₂	#20241824	1	2	yes	—
399	C₂	#20241826	1	2	yes	—
400	C₂	#20243080	1	1	yes	characteristic
401	C₂	#339×D₄₇	1	1	yes	characteristic
402	C₂	#20243106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1279	C₂
socle	C₂³×C₄₇	C₂×C₂²⋊C₄
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1279	D₄₇
hypocenter	C₄₇	#7903
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ #1279

Complements

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

N	H ≅ G/N	type
4. #20241229	C₂	semidirect
5. #20241228	C₂	semidirect
6. #20241227	C₂	semidirect
7. C₄₇×#1279	C₂	semidirect
13. #15689145	C₄	semidirect
17. C₄×#10625324	C₄	semidirect
99. C₄⋊C₄×C₄₇	M₁₆	semidirect
108. C₄⋊Dic₄₇	M₁₆	semidirect
202. #1279	D₄₇	semidirect
230. C₄₇	#7903	semidirect
310. C₄⋊C₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689145	2
C₂×C₄×#10625324	2
C₄×#13093982	2
#20241229	2
#20241228	2
#20241227	2
C₄₇×#1279	2
#7903	47