Subgroups — #26226806

Order 12032.

834 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
2	#20245781	C₂	1	1	yes	maximal, characteristic
3	#382×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20244157	C₂	1	2	yes	maximal, complemented
5	#20244153	C₂	1	2	yes	maximal, complemented
6	#20243579	C₂	1	2	yes	maximal
7	#20243574	C₂	1	2	yes	maximal
8	#20243550	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243519	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243518	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
14	#15689174	C₄	1	8	yes	complemented
15	C₂×#13093957	C₂²	1	2	yes	—
16	C₂×#13093955	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	#15688990	—	2	1	no	—
23	#15688989	C₂²	1	1	yes	characteristic
24	#15688989	C₂²	1	1	yes	characteristic
25	#15688988	C₂²	1	2	yes	—
26	#15688987	—	2	1	no	—
27	#15688987	—	2	1	no	—
28	#15688985	—	2	1	no	—
29	#15688980	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
31	#15688970	—	2	1	no	—
32	#15688968	—	2	1	no	—
33	#95×D₄₇	—	2	1	no	—
34	#95×D₄₇	—	2	1	no	—
35	#15688886	C₂²	1	2	yes	—
36	#15688886	C₂²	1	2	yes	—
37	#15688885	C₂²	1	2	yes	—
38	#15688885	C₂²	1	2	yes	—
39	C₂×#107×C₄₇	C₂²	1	2	yes	—
40	C₂×#106×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#382	C₂²	1	1	yes	characteristic
43	C₄₇×#382	C₂²	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	—	2	2	no	—
45	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	D₄	1	1	yes	characteristic
47	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
51	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
52	C₂×Dic₄₇⋊C₄	—	2	2	no	—
53	C₄⋊C₄×D₄₇	—	4	2	no	—
54	C₄⋊C₄×D₄₇	—	4	2	no	—
55	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
60	C₄²×D₄₇	C₂×C₄	1	4	yes	—
61	C₄²×D₄₇	Q₈	1	4	yes	—
62	#13093957	—	4	2	no	—
63	#13093955	—	4	2	no	—
64	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
65	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
66	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
67	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
68	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
69	C₄₇⋊#95	—	2	1	no	—
70	C₄₇⋊#95	—	2	1	no	—
71	C₄₇⋊#95	—	2	1	no	—
72	C₄₇⋊#95	—	2	1	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
81	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
82	#107×C₄₇	—	4	2	no	—
83	#106×C₄₇	—	4	2	no	—
84	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
85	#95×C₄₇	—	2	1	no	—
86	#95×C₄₇	—	2	1	no	—
87	#95×C₄₇	—	2	1	no	—
88	#95×C₄₇	—	2	1	no	—
89	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	2	no	—
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	—	2	4	no	—
101	C₂×C₄×D₄₇	—	2	1	no	—
102	C₂×C₄×D₄₇	—	2	1	no	—
103	C₂×C₄×D₄₇	—	2	1	no	—
104	C₂×C₄×D₄₇	—	2	1	no	—
105	C₂×C₄×D₄₇	—	4	2	no	—
106	C₂×C₄×D₄₇	—	4	4	no	—
107	C₂×C₄×D₄₇	—	4	4	no	—
108	C₂×C₄×D₄₇	—	4	4	no	—
109	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
110	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
111	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
112	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊C₄×C₄₇	—	2	2	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
124	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
125	(C₂×D₄₇)⋊C₄	—	4	4	no	—
126	C₄⋊Dic₄₇	—	2	2	no	—
127	C₄⋊Dic₄₇	—	2	2	no	—
128	C₄⋊Dic₄₇	—	2	2	no	—
129	C₄⋊Dic₄₇	—	2	2	no	—
130	Dic₄₇⋊C₄	—	4	4	no	—
131	C₄×Dic₄₇	—	4	4	no	—
132	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
133	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
134	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
135	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
136	C₂×C₄₇⋊C₈	—	2	1	no	—
137	C₂×C₄₇⋊C₈	—	2	1	no	—
138	C₂×C₄₇⋊C₈	—	2	1	no	—
139	C₂×C₄₇⋊C₈	—	2	1	no	—
140	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
141	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
142	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
143	C₂²×D₄₇	—	2	1	no	—
144	C₂²×D₄₇	—	2	1	no	—
145	C₂²×D₄₇	—	2	2	no	—
146	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
147	C₂²×D₄₇	#135	1	4	yes	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
160	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
162	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
163	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	1	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	—	4	2	no	—
174	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
175	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
176	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
177	C₄×D₄₇	—	2	8	no	—
178	C₄×D₄₇	—	2	2	no	—
179	C₄×D₄₇	—	2	2	no	—
180	C₄×D₄₇	—	2	2	no	—
181	C₄×D₄₇	—	2	2	no	—
182	C₄×D₄₇	—	4	4	no	—
183	C₄×D₄₇	—	8	8	no	—
184	C₈×C₄₇	—	2	2	no	—
185	C₈×C₄₇	—	2	2	no	—
186	C₄₇⋊C₈	—	2	2	no	—
187	C₄₇⋊C₈	—	2	2	no	—
188	#21983	—	47	1	no	maximal, Sylow
189	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
190	C₂²×C₄₇	#535	1	1	yes	characteristic
191	C₂²×C₄₇	#536	1	1	yes	characteristic
192	C₂²×C₄₇	C₂×#135	1	2	yes	—
193	C₂²×C₄₇	#575	1	2	yes	—
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	2	2	no	—
196	C₂×D₄₇	—	2	4	no	—
197	C₂×D₄₇	—	2	4	no	—
198	C₂×D₄₇	#427	1	4	yes	—
199	C₄×C₄₇	—	2	2	no	—
200	C₄×C₄₇	—	2	2	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	#520	1	1	yes	characteristic
204	C₄×C₄₇	#520	1	1	yes	characteristic
205	C₄×C₄₇	#544	1	1	yes	characteristic
206	C₄×C₄₇	#544	1	1	yes	characteristic
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	2	2	no	—
209	Dic₄₇	—	2	2	no	—
210	Dic₄₇	—	8	2	no	—
211	Dic₄₇	—	8	2	no	—
212	C₂×#431	—	47	1	no	—
213	#2283	—	47	1	no	—
214	C₂×#382	—	47	1	no	—
215	#1949	—	47	2	no	—
216	#1949	—	47	2	no	—
217	#1853	—	47	2	no	—
218	#1852	—	47	2	no	—
219	#1846	—	47	1	no	—
220	#1846	D₄₇	1	1	yes	characteristic, complemented
221	#1835	—	47	1	no	—
222	#1835	—	47	1	no	—
223	C₂×C₄₇	#2317	1	1	yes	characteristic
224	C₂×C₄₇	C₂×#427	1	1	yes	characteristic
225	C₂×C₄₇	#2911	1	1	yes	characteristic
226	C₂×C₄₇	#3211	1	2	yes	—
227	C₂×C₄₇	#3232	1	2	yes	—
228	D₄₇	—	2	4	no	—
229	C₂²×C₄⋊C₄	—	47	2	no	—
230	C₂²×C₄²	—	47	1	no	—
231	#431	—	47	8	no	—
232	C₂×#107	—	47	2	no	—
233	C₂×#107	C₂×D₄₇	1	2	yes	—
234	C₂×#106	—	47	2	no	—
235	C₂×#106	C₂×D₄₇	1	2	yes	—
236	C₂×C₄⋊C₈	—	47	1	no	—
237	C₂×C₄⋊C₈	—	47	1	no	—
238	C₂×C₂²⋊C₈	—	47	1	no	—
239	C₂×C₂²⋊C₈	—	47	1	no	—
240	C₂×C₄×C₈	—	47	1	no	—
241	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
242	#383	—	94	1	no	—
243	#382	—	47	2	no	—
244	#382	—	47	1	no	—
245	#382	—	47	1	no	—
246	#382	—	94	1	no	—
247	#382	—	94	1	no	—
248	#382	C₂×D₄₇	1	1	yes	characteristic
249	#382	C₂×D₄₇	1	1	yes	characteristic
250	#381	—	94	1	no	—
251	#380	—	47	2	no	—
252	C₄×C₄⋊C₄	—	47	2	no	—
253	C₄×C₂²⋊C₄	—	94	1	no	—
254	#376	—	94	1	no	—
255	C₂×#95	—	94	1	no	—
256	C₂×#95	—	94	1	no	—
257	#340	—	47	2	no	—
258	#340	—	47	2	no	—
259	#340	—	47	2	no	—
260	#340	—	47	2	no	—
261	C₄₇	#21983	1	1	yes	characteristic, complemented, Sylow
262	C₂³×C₄	—	47	1	no	—
263	C₂³×C₄	—	47	1	no	—
264	C₂³×C₄	—	47	1	no	—
265	C₂³×C₄	—	94	2	no	—
266	C₂²×C₈	—	47	1	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
270	C₂×C₄⋊C₄	—	47	2	no	—
271	C₂×C₄⋊C₄	—	47	2	no	—
272	C₂×C₄⋊C₄	—	94	2	no	—
273	C₂×C₄⋊C₄	—	188	2	no	—
274	C₂×C₄⋊C₄	—	188	2	no	—
275	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
276	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
277	C₂×C₂²⋊C₄	—	94	2	no	—
278	C₂×C₄²	—	47	1	no	—
279	C₂×C₄²	—	47	1	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	4	no	—
282	C₂×C₄²	—	47	4	no	—
283	C₂×C₄²	—	94	2	no	—
284	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
285	#107	—	4	2	no	—
286	#107	—	188	2	no	—
287	#106	—	4	2	no	—
288	#106	—	188	2	no	—
289	C₄⋊C₈	—	47	4	no	—
290	C₄⋊C₈	—	47	4	no	—
291	C₂²⋊C₈	—	47	4	no	—
292	C₂²⋊C₈	—	47	4	no	—
293	C₄×C₈	—	47	4	no	—
294	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
295	#95	—	2	1	no	—
296	#95	—	2	1	no	—
297	#95	—	2	1	no	—
298	#95	—	2	1	no	—
299	#95	—	94	2	no	—
300	#95	—	94	2	no	—
301	#95	—	94	2	no	—
302	#95	—	94	2	no	—
303	#95	—	94	1	no	—
304	#95	—	94	1	no	—
305	#95	—	94	1	no	—
306	#95	—	94	1	no	—
307	C₂⁴	—	47	1	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	47	1	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	4	no	—
314	C₂²×C₄	—	47	2	no	—
315	C₂²×C₄	—	47	2	no	—
316	C₂²×C₄	—	47	4	no	—
317	C₂²×C₄	—	94	4	no	—
318	C₂²×C₄	—	94	1	no	—
319	C₂²×C₄	—	94	1	no	—
320	C₂²×C₄	—	94	1	no	—
321	C₂²×C₄	—	94	1	no	—
322	C₂²×C₄	—	94	2	no	—
323	C₂²×C₄	—	94	2	no	—
324	C₂²×C₄	—	188	2	no	—
325	C₂²×C₄	—	188	4	no	—
326	C₂²×C₄	—	188	4	no	—
327	C₂²×C₄	—	188	4	no	—
328	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
329	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
330	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
331	C₂×C₈	—	2	1	no	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	1	no	—
334	C₂×C₈	—	2	1	no	—
335	C₂×C₈	—	47	2	no	—
336	C₂×C₈	—	47	2	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	94	1	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	1	no	—
341	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
342	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
343	C₄⋊C₄	—	2	2	no	—
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	94	2	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	—	94	2	no	—
350	C₄⋊C₄	—	94	2	no	—
351	C₄⋊C₄	—	188	4	no	—
352	C₂²⋊C₄	—	188	4	no	—
353	C₄²	—	47	4	no	—
354	C₄²	—	47	4	no	—
355	C₄²	—	47	2	no	—
356	C₄²	—	47	2	no	—
357	C₄²	—	188	4	no	—
358	C₄²	C₂×C₄×D₄₇	1	2	yes	—
359	C₄²	Q₈×D₄₇	1	2	yes	—
360	C₂³	—	47	2	no	—
361	C₂³	—	47	4	no	—
362	C₂³	—	94	2	no	—
363	C₂³	—	94	1	no	—
364	C₂³	—	94	1	no	—
365	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	4	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	47	2	no	—
375	C₂×C₄	—	47	2	no	—
376	C₂×C₄	—	47	2	no	—
377	C₂×C₄	—	94	8	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	2	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	1	no	—
382	C₂×C₄	—	94	2	no	—
383	C₂×C₄	—	94	2	no	—
384	C₂×C₄	—	94	2	no	—
385	C₂×C₄	—	94	2	no	—
386	C₂×C₄	—	376	8	no	—
387	C₂×C₄	—	188	4	no	—
388	C₂×C₄	—	188	2	no	—
389	C₂×C₄	—	188	2	no	—
390	C₂×C₄	—	188	2	no	—
391	C₂×C₄	—	188	2	no	—
392	C₂×C₄	—	188	2	no	—
393	C₂×C₄	—	188	2	no	—
394	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
395	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
396	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
398	C₂×C₄	#13094069	1	1	yes	characteristic
399	C₂×C₄	#13094069	1	1	yes	characteristic
400	C₂×C₄	#13094072	1	1	yes	characteristic
401	C₂×C₄	#13094072	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	2	no	—
404	C₈	—	94	2	no	—
405	C₈	—	94	2	no	—
406	C₂²	—	47	4	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	94	4	no	—
409	C₂²	—	94	4	no	—
410	C₂²	—	94	2	no	—
411	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
412	C₂²	#15689686	1	1	yes	characteristic
413	C₂²	#15689698	1	1	yes	characteristic
414	C₂²	#135×D₄₇	1	2	yes	—
415	C₂²	#15689920	1	2	yes	—
416	C₄	—	2	2	no	—
417	C₄	—	2	2	no	—
418	C₄	—	8	2	no	—
419	C₄	—	8	2	no	—
420	C₄	—	94	2	no	—
421	C₄	—	94	2	no	—
422	C₄	—	94	2	no	—
423	C₄	—	376	2	no	—
424	C₄	—	376	2	no	—
425	C₄	#15689604	1	1	yes	characteristic
426	C₄	#15689604	1	1	yes	characteristic
427	C₄	#15689750	1	1	yes	characteristic
428	C₄	#15689750	1	1	yes	characteristic
429	C₂	—	94	4	no	—
430	C₂	#20246009	1	1	yes	characteristic
431	C₂	#427×D₄₇	1	1	yes	characteristic
432	C₂	#20251976	1	1	yes	characteristic
433	C₂	#20254348	1	2	yes	—
434	C₂	#20254557	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1846	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1846	D₄₇
hypocenter	C₄₇	#21983
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1846

Complements

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

N	H ≅ G/N	type
4. #20244157	C₂	semidirect
5. #20244153	C₂	semidirect
8. #20243550	C₂	semidirect
9. #20243519	C₂	semidirect
10. #20243518	C₂	semidirect
11. C₄₇×#1846	C₂	semidirect
14. #15689174	C₄	semidirect
64. Dic₄₇⋊C₈	C₂×C₄	semidirect
65. Dic₄₇⋊C₈	C₂×C₄	semidirect
68. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
84. C₄×C₈×C₄₇	C₂×C₄	semidirect
220. #1846	D₄₇	semidirect
261. C₄₇	#21983	semidirect
294. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689174	2
#20245781	2
#382×D₄₇	2
#20244157	2
#20244153	2
#20243579	2
#20243574	2
#20243550	2
#20243519	2
#20243518	2
C₄₇×#1846	2
#21983	47