Subgroups — #26105792

Order 12032.

700 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252016	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic
3	C₄×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20241226	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241225	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241224	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1278	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×#10625324	—	2	1	no	—
9	C₂×M₁₆×D₄₇	C₄	1	2	yes	—
10	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
11	#15689179	C₄	1	2	yes	—
12	#15689177	—	2	1	no	—
13	#15689176	C₂²	1	1	yes	characteristic
14	#15689174	—	2	1	no	—
15	#15689145	C₄	1	2	yes	—
16	#15689085	—	2	1	no	—
17	C₄×#10625329	C₂²	1	1	yes	characteristic
18	#15689075	—	2	1	no	—
19	M₁₆×Dic₄₇	C₄	1	2	yes	—
20	C₄×#10625324	—	2	1	no	—
21	C₄×#10625324	—	2	1	no	—
22	C₄×#10625324	—	2	1	no	—
23	C₄×#10625324	—	2	1	no	—
24	C₄×#10625324	C₄	1	2	yes	—
25	C₄×#10625324	C₄	1	2	yes	—
26	C₂×#13093934	—	2	1	no	—
27	#97×D₄₇	—	2	1	no	—
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₄₇	—	2	1	no	—
30	C₄₇×#431	C₂²	1	1	yes	characteristic
31	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	Q₈	1	1	yes	characteristic
36	C₂×#10625329	C₂×C₄	1	2	yes	—
37	C₂×#10625324	—	2	8	no	—
38	C₂×#10625324	—	2	2	no	—
39	C₂×#10625324	—	2	2	no	—
40	C₂×#10625324	—	2	2	no	—
41	C₂×#10625324	—	2	2	no	—
42	M₁₆×D₄₇	—	2	4	no	—
43	M₁₆×D₄₇	—	2	4	no	—
44	C₂²×C₄₇⋊C₈	—	2	1	no	—
45	C₂×C₈×D₄₇	—	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	Q₈	1	1	yes	characteristic
49	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
51	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄²×D₄₇	D₄	1	1	yes	characteristic
54	C₄²×D₄₇	D₄	1	1	yes	characteristic
55	C₄²×D₄₇	D₄	1	1	yes	characteristic
56	C₄²×D₄₇	D₄	1	1	yes	characteristic
57	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
58	Dic₄₇⋊C₈	—	2	2	no	—
59	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
60	(C₂×D₄₇)⋊C₈	—	2	2	no	—
61	#13093935	—	2	1	no	—
62	#13093934	—	2	2	no	—
63	#13093934	—	2	2	no	—
64	#13093934	—	2	2	no	—
65	#13093934	—	2	2	no	—
66	C₄×C₄₇⋊C₈	—	2	1	no	—
67	C₄×C₄₇⋊C₈	—	2	1	no	—
68	C₄×C₄₇⋊C₈	—	2	1	no	—
69	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
75	C₂²⋊C₈×C₄₇	—	2	1	no	—
76	#97×C₄₇	—	2	1	no	—
77	C₄×C₈×C₄₇	—	2	1	no	—
78	C₄×C₈×C₄₇	—	2	1	no	—
79	C₄×C₈×C₄₇	—	2	1	no	—
80	C₄×C₈×C₄₇	C₂×C₄	1	2	yes	—
81	C₂³×D₄₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂×Q₈	1	1	yes	characteristic
85	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₄₇	—	2	2	no	—
89	C₂×C₄×D₄₇	—	2	2	no	—
90	C₂×C₄×D₄₇	—	2	4	no	—
91	C₂×C₄×D₄₇	—	4	2	no	—
92	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
103	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
104	M₁₆×C₄₇	—	2	2	no	—
105	M₁₆×C₄₇	M₁₆	1	4	yes	complemented
106	C₂×C₈×C₄₇	—	2	4	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
115	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
116	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
118	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
119	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
122	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
123	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
124	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
126	#10625329	—	2	2	no	—
127	#10625329	M₁₆	1	4	yes	complemented
128	C₂×C₄₇⋊C₈	—	2	4	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	#10625324	—	2	8	no	—
133	#10625324	—	2	8	no	—
134	#10625324	—	2	8	no	—
135	#10625324	—	4	4	no	—
136	C₈×D₄₇	—	2	8	no	—
137	C₂³×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	4	1	no	—
141	C₂²×D₄₇	#95	1	1	yes	characteristic
142	C₂²×D₄₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	C₂×C₄²	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
152	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	4	1	no	—
156	C₂×Dic₄₇	#95	1	1	yes	characteristic
157	C₂×Dic₄₇	#95	1	1	yes	characteristic
158	C₂×Dic₄₇	#95	1	1	yes	characteristic
159	C₂×Dic₄₇	#95	1	1	yes	characteristic
160	C₂×Dic₄₇	#95	1	1	yes	characteristic
161	C₂×Dic₄₇	#95	1	1	yes	characteristic
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	1	no	—
164	C₄×D₄₇	—	2	1	no	—
165	C₄×D₄₇	—	2	1	no	—
166	C₄×D₄₇	—	2	1	no	—
167	C₄×D₄₇	—	2	2	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	2	2	no	—
170	C₄×D₄₇	—	2	2	no	—
171	C₄×D₄₇	—	2	2	no	—
172	C₄×D₄₇	—	2	2	no	—
173	C₄×D₄₇	—	4	1	no	—
174	C₄×D₄₇	—	4	1	no	—
175	C₄×D₄₇	#104	1	4	yes	—
176	C₈×C₄₇	—	2	4	no	—
177	C₈×C₄₇	—	2	4	no	—
178	C₈×C₄₇	—	4	2	no	—
179	C₄₇⋊C₈	—	2	4	no	—
180	C₄₇⋊C₈	—	2	4	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	#7887	—	47	1	no	maximal, Sylow
183	C₂²×C₄₇	—	2	1	no	—
184	C₂²×C₄₇	—	2	1	no	—
185	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
186	C₂²×C₄₇	#423	1	2	yes	—
187	C₂×D₄₇	—	2	1	no	—
188	C₂×D₄₇	—	2	1	no	—
189	C₂×D₄₇	—	2	1	no	—
190	C₂×D₄₇	—	2	1	no	—
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	4	4	no	—
193	C₂×D₄₇	#339	1	2	yes	—
194	C₄×C₄₇	—	2	1	no	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
197	C₄×C₄₇	C₄×M₁₆	1	1	yes	characteristic
198	C₄×C₄₇	#407	1	2	yes	—
199	C₄×C₄₇	C₂×#104	1	2	yes	—
200	C₄×C₄₇	#430	1	2	yes	—
201	Dic₄₇	—	2	1	no	—
202	Dic₄₇	—	2	1	no	—
203	Dic₄₇	—	2	1	no	—
204	Dic₄₇	—	2	1	no	—
205	Dic₄₇	—	2	1	no	—
206	Dic₄₇	#339	1	2	yes	—
207	#2920	—	47	1	no	—
208	C₂×C₄×M₁₆	—	47	1	no	—
209	C₂×C₄×M₁₆	—	47	1	no	—
210	#1278	—	47	1	no	—
211	#1278	—	47	1	no	—
212	#1278	—	47	1	no	—
213	#1278	D₄₇	1	1	yes	characteristic, complemented
214	C₂×C₄₇	—	2	2	no	—
215	C₂×C₄₇	#1728	1	1	yes	characteristic
216	C₂×C₄₇	C₂×#339	1	1	yes	characteristic
217	C₂×C₄₇	#1738	1	1	yes	characteristic
218	D₄₇	—	2	2	no	—
219	D₄₇	—	4	1	no	—
220	C₂²×M₁₆	—	47	2	no	—
221	C₂²×M₁₆	—	94	1	no	—
222	C₂²×C₄²	—	47	1	no	—
223	#432	—	47	2	no	—
224	#432	—	94	1	no	—
225	#431	—	47	1	no	—
226	#431	—	94	1	no	—
227	#431	C₂×D₄₇	1	1	yes	characteristic
228	#423	—	47	2	no	—
229	#407	—	94	1	no	—
230	C₄×M₁₆	—	47	2	no	—
231	C₄×M₁₆	—	47	2	no	—
232	C₄×M₁₆	—	47	2	no	—
233	C₄×M₁₆	—	47	1	no	—
234	C₄×M₁₆	—	94	1	no	—
235	C₄×M₁₆	—	94	1	no	—
236	C₄×M₁₆	—	94	1	no	—
237	C₄×M₁₆	—	94	1	no	—
238	C₄×M₁₆	—	94	1	no	—
239	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
240	C₂×#97	—	94	1	no	—
241	C₂×#97	—	94	1	no	—
242	C₂×C₄×C₈	—	47	1	no	—
243	C₂×C₄×C₈	—	94	1	no	—
244	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
245	C₄₇	#7887	1	1	yes	characteristic, complemented, Sylow
246	C₂³×C₄	—	47	1	no	—
247	C₂³×C₄	—	47	1	no	—
248	C₂³×C₄	—	47	1	no	—
249	C₂×M₁₆	—	47	2	no	—
250	C₂×M₁₆	—	94	2	no	—
251	C₂×M₁₆	—	94	2	no	—
252	C₂×M₁₆	—	94	2	no	—
253	C₂×M₁₆	—	94	8	no	—
254	C₂×M₁₆	—	94	2	no	—
255	C₂×M₁₆	—	94	4	no	—
256	C₂×M₁₆	—	94	4	no	—
257	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
258	C₂²×C₈	—	2	1	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₂²×C₈	—	94	1	no	—
261	C₂×C₄²	—	47	1	no	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	1	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	1	no	—
270	C₂×C₄²	—	47	1	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₄⋊C₈	—	47	2	no	—
274	C₄⋊C₈	—	94	2	no	—
275	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
276	C₂²⋊C₈	—	2	1	no	—
277	C₂²⋊C₈	—	94	2	no	—
278	C₂²⋊C₈	—	94	1	no	—
279	#97	—	2	1	no	—
280	#97	—	94	2	no	—
281	#97	—	94	2	no	—
282	#97	—	94	2	no	—
283	#97	—	94	2	no	—
284	#97	—	94	1	no	—
285	C₄×C₈	—	2	1	no	—
286	C₄×C₈	—	2	1	no	—
287	C₄×C₈	—	2	1	no	—
288	C₄×C₈	—	47	2	no	—
289	C₄×C₈	—	94	2	no	—
290	C₄×C₈	—	94	1	no	—
291	C₄×C₈	—	94	1	no	—
292	C₄×C₈	—	94	1	no	—
293	C₄×C₈	C₄×D₄₇	1	2	yes	—
294	C₂⁴	—	47	1	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	1	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	47	1	no	—
302	C₂²×C₄	—	47	1	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	47	1	no	—
310	C₂²×C₄	—	94	4	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	188	2	no	—
314	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
315	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
316	C₂²×C₄	Q₈×D₄₇	1	1	yes	characteristic
317	M₁₆	—	2	2	no	—
318	M₁₆	—	47	4	no	—
319	M₁₆	—	94	8	no	—
320	M₁₆	—	94	8	no	—
321	M₁₆	—	94	8	no	—
322	M₁₆	—	94	2	no	—
323	M₁₆	—	188	4	no	—
324	M₁₆	#10625324	1	4	yes	complemented
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	2	no	—
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	94	8	no	—
330	C₂×C₈	—	94	4	no	—
331	C₂×C₈	—	94	2	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	2	no	—
334	C₄²	—	47	1	no	—
335	C₄²	—	47	1	no	—
336	C₄²	—	47	1	no	—
337	C₄²	—	47	1	no	—
338	C₄²	—	47	1	no	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	1	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	47	1	no	—
343	C₄²	—	47	1	no	—
344	C₄²	—	47	1	no	—
345	C₄²	—	47	1	no	—
346	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
347	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
348	C₄²	D₄×D₄₇	1	1	yes	characteristic
349	C₄²	D₄×D₄₇	1	1	yes	characteristic
350	C₂³	—	47	1	no	—
351	C₂³	—	47	1	no	—
352	C₂³	—	94	2	no	—
353	C₂³	—	94	2	no	—
354	C₂³	—	188	1	no	—
355	C₂³	C₄⋊C₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	47	1	no	—
359	C₂×C₄	—	47	4	no	—
360	C₂×C₄	—	47	1	no	—
361	C₂×C₄	—	47	1	no	—
362	C₂×C₄	—	47	1	no	—
363	C₂×C₄	—	47	1	no	—
364	C₂×C₄	—	47	1	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	1	no	—
370	C₂×C₄	—	94	1	no	—
371	C₂×C₄	—	94	1	no	—
372	C₂×C₄	—	94	1	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	94	2	no	—
376	C₂×C₄	—	94	2	no	—
377	C₂×C₄	—	94	2	no	—
378	C₂×C₄	—	188	1	no	—
379	C₂×C₄	—	188	1	no	—
380	C₂×C₄	—	188	1	no	—
381	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
382	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
383	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
384	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
388	C₂×C₄	C₂×#10625324	1	2	yes	—
389	C₈	—	2	4	no	—
390	C₈	—	2	4	no	—
391	C₈	—	4	2	no	—
392	C₈	—	94	4	no	—
393	C₈	—	94	4	no	—
394	C₈	—	188	2	no	—
395	C₂²	—	2	1	no	—
396	C₂²	—	2	1	no	—
397	C₂²	—	47	2	no	—
398	C₂²	—	94	1	no	—
399	C₂²	—	94	1	no	—
400	C₂²	—	94	1	no	—
401	C₂²	—	94	1	no	—
402	C₂²	—	94	1	no	—
403	C₂²	—	188	4	no	—
404	C₂²	#95×D₄₇	1	1	yes	characteristic
405	C₂²	#15689145	1	2	yes	—
406	C₄	—	2	1	no	—
407	C₄	—	2	1	no	—
408	C₄	—	47	2	no	—
409	C₄	—	94	1	no	—
410	C₄	—	94	1	no	—
411	C₄	—	94	1	no	—
412	C₄	—	94	1	no	—
413	C₄	—	94	1	no	—
414	C₄	C₄×#10625324	1	1	yes	characteristic
415	C₄	#15689075	1	1	yes	characteristic
416	C₄	#15689085	1	2	yes	—
417	C₄	#104×D₄₇	1	2	yes	—
418	C₄	#15689170	1	2	yes	—
419	C₂	—	2	2	no	—
420	C₂	—	94	2	no	—
421	C₂	—	188	1	no	—
422	C₂	#20243080	1	1	yes	characteristic
423	C₂	#339×D₄₇	1	1	yes	characteristic
424	C₂	#20243113	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1278	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₄⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1278	D₄₇
hypocenter	C₄₇	#7887
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ #1278

Complements

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

N	H ≅ G/N	type
4. #20241226	C₂	semidirect
5. #20241225	C₂	semidirect
6. #20241224	C₂	semidirect
7. C₄₇×#1278	C₂	semidirect
105. M₁₆×C₄₇	M₁₆	semidirect
127. #10625329	M₁₆	semidirect
213. #1278	D₄₇	semidirect
245. C₄₇	#7887	semidirect
324. M₁₆	#10625324	semidirect

Maximal subgroups

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

subgroup	index
#20252016	2
C₂×C₄×#10625324	2
C₄×M₁₆×D₄₇	2
#20241226	2
#20241225	2
#20241224	2
C₄₇×#1278	2
#7887	47