Subgroups — #26199337

Order 12032.

778 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254506	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689495	C₂	1	1	yes	maximal, characteristic, complemented
3	#20252100	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242851	C₂	1	4	yes	maximal, complemented
5	#20242727	C₂	1	4	yes	maximal, complemented
6	#20242134	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242059	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242056	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#3205	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625335	—	2	1	no	—
11	C₂²×#10625335	—	2	1	no	—
12	C₂×#13094031	—	2	1	no	—
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	#15689526	—	2	1	no	—
15	#15689495	—	2	1	no	—
16	#15689495	—	2	1	no	—
17	#15689495	C₂²	1	2	yes	—
18	#15689495	C₂²	1	2	yes	—
19	#15689469	—	2	1	no	—
20	#15689434	—	2	2	no	—
21	#15689403	C₂²	1	4	yes	complemented
22	#15689201	—	2	1	no	—
23	#15689201	C₂²	1	2	yes	complemented
24	D₄×C₄₇⋊C₈	—	2	1	no	—
25	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
26	#15689176	C₂²	1	1	yes	characteristic
27	#15689147	C₂²	1	1	yes	characteristic
28	#15689090	—	2	1	no	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688875	C₂²	1	2	yes	complemented
31	#15688873	C₂²	1	2	yes	complemented
32	#15688868	C₂²	1	4	yes	complemented
33	#15688867	C₂²	1	4	yes	—
34	C₄₇×#532	C₂²	1	1	yes	characteristic
35	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#493	—	2	1	no	—
37	C₄₇×#486	—	2	1	no	—
38	C₄₇×#459	C₂²	1	4	yes	—
39	C₄₇×#447	—	2	2	no	—
40	C₄₇×#431	C₂²	1	1	yes	characteristic
41	C₂²×Dic₉₄	—	2	1	no	—
42	C₂×#10625335	—	2	2	no	—
43	C₂×#10625335	—	2	2	no	—
44	C₂×#10625335	—	2	2	no	—
45	C₂×#10625335	—	2	2	no	—
46	C₂×#10625335	—	4	4	no	—
47	C₂×#10625335	—	4	4	no	—
48	#13094031	—	4	4	no	—
49	C₂×#10625329	—	2	1	no	—
50	C₂×#10625329	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
53	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
54	#13094024	—	2	1	no	—
55	#13094024	—	2	1	no	—
56	#13094024	—	2	1	no	—
57	#13094024	C₂³	1	2	yes	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	—	2	1	no	—
60	#13093957	—	2	4	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
62	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
63	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
64	#13093945	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
66	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₄×C₄₇⋊C₈	—	2	1	no	—
69	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
70	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
71	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂×#41×C₄₇	—	2	1	no	—
74	C₂²×D₄×C₄₇	—	2	1	no	—
75	C₂²×D₄×C₄₇	—	2	1	no	—
76	C₂²×D₄×C₄₇	—	2	1	no	—
77	C₂×D₈×C₄₇	—	2	4	no	—
78	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
79	#127×C₄₇	—	2	1	no	—
80	#127×C₄₇	—	2	1	no	—
81	#127×C₄₇	—	2	1	no	—
82	#127×C₄₇	D₄	1	1	yes	characteristic
83	#127×C₄₇	C₂³	1	2	yes	—
84	#124×C₄₇	—	2	1	no	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	D₄	1	2	yes	—
87	C₄×D₄×C₄₇	—	2	1	no	—
88	C₄×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
91	#102×C₄₇	—	2	4	no	—
92	C₂²⋊C₈×C₄₇	—	2	1	no	—
93	C₄×C₈×C₄₇	—	2	1	no	—
94	C₂⁴×C₄₇	—	4	1	no	—
95	#41×C₄₇	—	4	2	no	—
96	#41×C₄₇	—	4	2	no	—
97	C₂×Q₈×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	1	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	4	1	no	—
105	C₂×D₄×C₄₇	—	4	1	no	—
106	C₂×D₄×C₄₇	—	4	1	no	—
107	C₂×D₄×C₄₇	—	4	2	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	—	8	2	no	—
110	C₂×D₄×C₄₇	—	8	2	no	—
111	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
116	C₂²×Dic₄₇	—	4	1	no	—
117	C₂×Dic₉₄	—	2	2	no	—
118	C₂×Dic₉₄	—	4	2	no	—
119	C₂×Dic₉₄	—	4	2	no	—
120	C₂×Dic₉₄	—	4	1	no	—
121	D₈×C₄₇	—	8	4	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
125	C₂²⋊C₄×C₄₇	—	2	2	no	—
126	C₂²⋊C₄×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₄²×C₄₇	#41	1	1	yes	characteristic
130	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
131	#10625335	—	4	4	no	—
132	#10625335	—	4	4	no	—
133	#10625335	—	4	4	no	—
134	#10625335	—	4	4	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	4	1	no	—
138	C₄⋊Dic₄₇	—	4	1	no	—
139	#10625329	—	4	2	no	—
140	#10625329	—	4	4	no	—
141	C₂×C₄₇⋊C₈	—	2	2	no	—
142	C₂×C₄₇⋊C₈	—	2	2	no	—
143	C₂×C₄₇⋊C₈	—	2	2	no	—
144	C₂×C₄₇⋊C₈	—	4	4	no	—
145	C₂×C₄₇⋊C₈	D₈	1	4	yes	complemented
146	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	8	2	no	—
153	C₂³×C₄₇	—	8	2	no	—
154	C₂³×C₄₇	—	8	2	no	—
155	C₂³×C₄₇	#121	1	1	yes	characteristic
156	Q₈×C₄₇	—	4	2	no	—
157	D₄×C₄₇	—	2	4	no	—
158	D₄×C₄₇	—	4	4	no	—
159	D₄×C₄₇	—	4	2	no	—
160	D₄×C₄₇	—	4	2	no	—
161	D₄×C₄₇	—	4	4	no	—
162	D₄×C₄₇	—	4	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	8	2	no	—
165	D₄×C₄₇	—	8	2	no	—
166	D₄×C₄₇	—	8	2	no	—
167	D₄×C₄₇	—	8	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
177	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	8	2	no	—
183	Dic₉₄	—	4	2	no	—
184	Dic₉₄	—	4	2	no	—
185	Dic₉₄	—	8	2	no	—
186	C₈×C₄₇	—	4	2	no	—
187	C₄₇⋊C₈	—	2	1	no	—
188	C₄₇⋊C₈	—	2	1	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
192	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
193	#19186	—	47	1	no	maximal, Sylow
194	C₂²×C₄₇	—	2	1	no	—
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	4	2	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	8	2	no	—
200	C₂²×C₄₇	—	8	2	no	—
201	C₂²×C₄₇	—	8	2	no	—
202	C₂²×C₄₇	—	16	4	no	—
203	C₂²×C₄₇	#459	1	2	yes	—
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	4	2	no	—
208	C₄×C₄₇	#459	1	2	yes	—
209	C₄×C₄₇	#471	1	2	yes	—
210	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
211	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
212	C₄×C₄₇	#577	1	2	yes	—
213	Dic₄₇	—	8	2	no	—
214	#3226	—	47	1	no	—
215	#3205	D₄₇	1	1	yes	characteristic
216	C₂×#492	—	47	1	no	—
217	#2931	—	47	1	no	—
218	#1685	—	47	4	no	—
219	#1665	—	47	4	no	—
220	#1564	—	47	1	no	—
221	#1546	—	47	1	no	—
222	#1545	—	47	1	no	—
223	C₂×C₄₇	—	2	2	no	—
224	C₂×C₄₇	—	8	2	no	—
225	C₂×C₄₇	—	16	2	no	—
226	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
227	C₂×C₄₇	#3057	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#471	1	1	yes	characteristic
229	C₂²×SD₁₆	—	94	1	no	—
230	C₂²×SD₁₆	—	94	1	no	—
231	C₂×#131	—	94	1	no	—
232	#532	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	—	47	1	no	—
234	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
235	#500	—	94	1	no	—
236	#493	—	2	1	no	—
237	#492	—	47	2	no	—
238	#492	—	47	2	no	—
239	#492	—	94	1	no	—
240	#492	—	94	1	no	—
241	#486	—	2	1	no	—
242	#486	—	94	1	no	—
243	#480	—	94	2	no	—
244	#474	—	47	4	no	—
245	#459	C₂×D₄₇	1	4	yes	—
246	#447	—	2	2	no	—
247	#436	—	47	2	no	—
248	#436	—	94	1	no	—
249	C₈×D₄	—	47	2	no	—
250	C₈×D₄	—	94	1	no	—
251	#431	—	47	1	no	—
252	#431	C₂×D₄₇	1	1	yes	characteristic
253	#423	—	47	1	no	—
254	#408	—	94	1	no	—
255	C₂×C₄×C₈	—	47	1	no	—
256	#335	—	47	2	no	—
257	#334	—	47	2	no	—
258	#332	—	47	4	no	—
259	#331	—	47	4	no	—
260	C₄₇	#19186	1	1	yes	characteristic, complemented, Sylow
261	C₂×#41	—	2	1	no	—
262	C₂²×Q₈	—	94	1	no	—
263	C₂²×D₄	—	2	1	no	—
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	1	no	—
266	C₂×SD₁₆	—	94	2	no	—
267	C₂×SD₁₆	—	94	2	no	—
268	C₂×SD₁₆	—	94	2	no	—
269	C₂×SD₁₆	—	94	2	no	—
270	C₂×SD₁₆	—	188	4	no	—
271	C₂×SD₁₆	—	188	4	no	—
272	C₂×D₈	—	2	4	no	—
273	#131	—	188	4	no	—
274	C₂×M₁₆	—	94	2	no	—
275	C₂×M₁₆	—	94	1	no	—
276	C₂²×C₈	—	47	1	no	—
277	C₂²×C₈	—	47	1	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₄⋊Q₈	—	47	2	no	—
280	C₄⋊Q₈	—	94	1	no	—
281	C₄⋊Q₈	—	94	1	no	—
282	C₄⋊Q₈	—	94	1	no	—
283	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
284	#127	—	2	1	no	—
285	#127	—	2	1	no	—
286	#127	—	2	1	no	—
287	#127	C₂²⋊D₄₇	1	1	yes	characteristic
288	#127	C₂²×D₄₇	1	2	yes	—
289	#124	—	2	1	no	—
290	#121	—	2	1	no	—
291	#121	C₂²⋊D₄₇	1	2	yes	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂²×D₄₇	1	2	yes	—
294	C₂×C₄⋊C₄	—	94	1	no	—
295	C₂×C₄⋊C₄	—	94	1	no	—
296	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
297	#107	—	94	4	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	47	2	no	—
300	C₄⋊C₈	—	94	1	no	—
301	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
302	#102	—	2	4	no	—
303	#102	—	94	4	no	—
304	C₂²⋊C₈	—	2	1	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	2	no	—
307	C₂²⋊C₈	—	94	1	no	—
308	C₄×C₈	—	2	1	no	—
309	C₄×C₈	—	47	1	no	—
310	C₄×C₈	—	47	1	no	—
311	C₄×C₈	—	47	1	no	—
312	C₄×C₈	—	47	1	no	—
313	C₄×C₈	—	94	1	no	—
314	C₂⁴	—	4	1	no	—
315	#41	—	4	2	no	—
316	#41	—	4	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	94	2	no	—
319	C₂×Q₈	—	188	2	no	—
320	C₂×Q₈	—	188	2	no	—
321	C₂×Q₈	—	188	1	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	1	no	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	—	2	2	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	1	no	—
329	C₂×D₄	—	4	1	no	—
330	C₂×D₄	—	4	1	no	—
331	C₂×D₄	—	4	2	no	—
332	C₂×D₄	—	4	2	no	—
333	C₂×D₄	—	8	2	no	—
334	C₂×D₄	—	8	2	no	—
335	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	188	1	no	—
338	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	#10625352	1	1	yes	characteristic
340	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	SD₁₆	—	188	4	no	—
342	SD₁₆	—	188	4	no	—
343	SD₁₆	—	188	4	no	—
344	SD₁₆	—	188	4	no	—
345	D₈	—	8	4	no	—
346	M₁₆	—	188	4	no	—
347	M₁₆	—	188	2	no	—
348	C₂×C₈	—	2	2	no	—
349	C₂×C₈	—	47	4	no	—
350	C₂×C₈	—	47	1	no	—
351	C₂×C₈	—	47	1	no	—
352	C₂×C₈	—	47	1	no	—
353	C₂×C₈	—	47	1	no	—
354	C₂×C₈	—	94	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	94	2	no	—
357	C₂×C₈	—	188	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	94	2	no	—
360	C₄⋊C₄	—	94	2	no	—
361	C₄⋊C₄	—	188	1	no	—
362	C₄⋊C₄	—	188	1	no	—
363	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
364	C₂²⋊C₄	—	2	2	no	—
365	C₂²⋊C₄	—	2	2	no	—
366	C₄²	D₄×D₄₇	1	1	yes	characteristic
367	C₄²	#10625352	1	1	yes	characteristic
368	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
369	C₄²	C₂³×D₄₇	1	1	yes	characteristic
370	C₂³	—	2	2	no	—
371	C₂³	—	4	2	no	—
372	C₂³	—	8	2	no	—
373	C₂³	—	8	2	no	—
374	C₂³	—	8	2	no	—
375	C₂³	#13093996	1	1	yes	characteristic
376	Q₈	—	4	2	no	—
377	Q₈	—	376	2	no	—
378	Q₈	—	188	2	no	—
379	Q₈	—	188	2	no	—
380	D₄	—	2	4	no	—
381	D₄	—	4	4	no	—
382	D₄	—	4	2	no	—
383	D₄	—	4	2	no	—
384	D₄	—	4	2	no	—
385	D₄	—	4	2	no	—
386	D₄	—	4	4	no	—
387	D₄	—	8	2	no	—
388	D₄	—	8	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	8	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	376	2	no	—
397	C₂×C₄	—	188	2	no	—
398	C₂×C₄	#13093996	1	1	yes	characteristic
399	C₂×C₄	#13093996	1	1	yes	characteristic
400	C₂×C₄	#13093996	1	1	yes	characteristic
401	C₂×C₄	D₈×D₄₇	1	2	yes	—
402	C₂×C₄	#13094048	1	2	yes	—
403	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
404	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
406	C₈	—	4	2	no	—
407	C₈	—	47	2	no	—
408	C₈	—	47	2	no	—
409	C₈	—	94	1	no	—
410	C₈	—	94	1	no	—
411	C₈	—	188	2	no	—
412	C₈	—	188	2	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	2	no	—
418	C₂²	—	8	2	no	—
419	C₂²	—	8	2	no	—
420	C₂²	—	8	2	no	—
421	C₂²	—	16	4	no	—
422	C₂²	#15689316	1	2	yes	—
423	C₂²	C₂×#13093996	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	4	2	no	—
427	C₄	—	376	2	no	—
428	C₄	#15689316	1	2	yes	—
429	C₄	#15689384	1	2	yes	—
430	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
431	C₄	C₂×#13094048	1	1	yes	characteristic
432	C₄	#15689934	1	2	yes	—
433	C₂	—	2	2	no	—
434	C₂	—	8	2	no	—
435	C₂	—	16	2	no	—
436	C₂	C₂×#15689316	1	1	yes	characteristic
437	C₂	#20253024	1	1	yes	characteristic
438	C₂	C₂×#15689384	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093996
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₄₇×#3205	C₂
socle	C₂²×C₄₇	C₂×#121
hypercenter	#3205	D₄₇
hypocenter	C₄₇	#19186
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3205

Complements

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

N	H ≅ G/N	type
1. #20254506	C₂	semidirect
2. C₂×#15689495	C₂	semidirect
3. #20252100	C₂	semidirect
4. #20242851	C₂	semidirect
5. #20242727	C₂	semidirect
6. #20242134	C₂	semidirect
7. #20242059	C₂	semidirect
8. #20242056	C₂	semidirect
21. #15689403	C₂²	semidirect
23. #15689201	C₂²	semidirect
25. D₄×C₄₇⋊C₈	C₂²	semidirect
30. #15688875	C₂²	semidirect
31. #15688873	C₂²	semidirect
32. #15688868	C₂²	semidirect
145. C₂×C₄₇⋊C₈	D₈	semidirect
260. C₄₇	#19186	semidirect

Maximal subgroups

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

subgroup	index
#20254506	2
C₂×#15689495	2
#20252100	2
#20242851	2
#20242727	2
#20242134	2
#20242059	2
#20242056	2
C₄₇×#3205	2
#19186	47