Subgroups — #26106572

Order 12032.

608 conjugacy classes of subgroups.

The subgroup lattice has 466 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	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20241291	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241290	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241289	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1303	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₇	—	2	1	no	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	#15689179	C₄	1	2	yes	complemented
11	#15689177	—	2	1	no	—
12	#15689176	C₂²	1	1	yes	characteristic
13	#15689174	—	2	1	no	—
14	#15689147	C₂²	1	1	yes	characteristic
15	#15689146	—	2	1	no	—
16	#15689145	—	2	1	no	—
17	#15689145	C₄	1	2	yes	complemented
18	#15689145	C₄	1	2	yes	complemented
19	C₄⋊C₈×D₄₇	—	2	1	no	—
20	C₄⋊C₈×D₄₇	C₄	1	2	yes	complemented
21	#15689085	—	2	1	no	—
22	C₄×#10625324	—	2	1	no	—
23	#15688990	C₄	1	2	yes	—
24	#15688988	—	2	1	no	—
25	#15688985	C₄	1	2	yes	—
26	#15688980	—	2	1	no	—
27	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄×(C₂×D₄₇)⋊C₄	—	2	1	no	—
29	#15688969	—	2	1	no	—
30	C₄₇×#431	C₂²	1	1	yes	characteristic
31	C₄₇×#423	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊C₄×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	D₄	1	1	yes	characteristic
36	C₂×#10625329	—	2	1	no	—
37	C₂×#10625324	—	2	2	no	—
38	C₂×#10625324	—	2	2	no	—
39	M₁₆×D₄₇	—	4	2	no	—
40	M₁₆×D₄₇	—	4	2	no	—
41	C₂×C₈×D₄₇	—	2	2	no	—
42	C₂×C₄⋊Dic₄₇	—	2	1	no	—
43	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
44	C₂×C₄×Dic₄₇	—	2	1	no	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
48	C₄²×D₄₇	C₂×C₄	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	D₄	1	1	yes	characteristic
53	C₄²×D₄₇	D₄	1	1	yes	characteristic
54	C₄²×D₄₇	Q₈	1	1	yes	characteristic
55	C₄²×D₄₇	Q₈	1	1	yes	characteristic
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
59	Dic₄₇⋊C₈	—	2	2	no	—
60	Dic₄₇⋊C₈	—	2	2	no	—
61	Dic₄₇⋊C₈	—	2	2	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
63	(C₂×D₄₇)⋊C₈	—	2	2	no	—
64	#13093934	—	2	2	no	—
65	C₄×C₄₇⋊C₈	—	2	1	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₄₇⋊#95	—	2	2	no	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂×M₁₆×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	—	2	1	no	—
75	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
76	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
77	C₂²⋊C₈×C₄₇	—	2	1	no	—
78	C₄×C₈×C₄₇	—	2	1	no	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	C₂³×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	—	2	2	no	—
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×D₄	1	1	yes	characteristic
85	C₂²×Dic₄₇	—	2	2	no	—
86	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₄₇	—	2	1	no	—
90	C₂×C₄×D₄₇	—	2	1	no	—
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	2	1	no	—
93	C₂×C₄×D₄₇	—	4	2	no	—
94	C₂×C₄×D₄₇	—	4	2	no	—
95	C₂×C₄×D₄₇	C₄²	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₄²	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	C₂²⋊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	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
107	M₁₆×C₄₇	—	4	1	no	—
108	M₁₆×C₄₇	—	4	1	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	4	2	no	—
112	C₄²×C₄₇	—	4	1	no	—
113	C₄²×C₄₇	—	4	1	no	—
114	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
118	(C₂×D₄₇)⋊C₄	—	4	4	no	—
119	C₄⋊Dic₄₇	—	4	2	no	—
120	C₄×Dic₄₇	—	4	1	no	—
121	C₄×Dic₄₇	—	4	1	no	—
122	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
123	C₄×Dic₄₇	C₄²	1	1	yes	characteristic
124	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
125	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
128	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
129	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
130	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
131	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
132	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
133	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
134	#10625329	—	4	1	no	—
135	#10625329	—	4	1	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	#10625324	—	4	4	no	—
139	#10625324	—	4	4	no	—
140	C₈×D₄₇	—	4	4	no	—
141	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂²×D₄₇	—	2	1	no	—
143	C₂²×D₄₇	—	2	1	no	—
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	4	1	no	—
146	C₂²×D₄₇	#95	1	1	yes	characteristic
147	C₂²×D₄₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	4	1	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	C₂×C₄²	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
160	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
161	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
162	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	4	1	no	—
166	C₂×Dic₄₇	—	4	1	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	#95	1	1	yes	characteristic
171	C₂×Dic₄₇	#95	1	1	yes	characteristic
172	C₂×Dic₄₇	#95	1	1	yes	characteristic
173	C₂×Dic₄₇	#95	1	1	yes	characteristic
174	C₂×Dic₄₇	#95	1	1	yes	characteristic
175	C₂×Dic₄₇	#95	1	1	yes	characteristic
176	C₄×D₄₇	—	2	2	no	—
177	C₄×D₄₇	—	2	2	no	—
178	C₄×D₄₇	—	2	1	no	—
179	C₄×D₄₇	—	2	1	no	—
180	C₄×D₄₇	—	2	1	no	—
181	C₄×D₄₇	—	2	1	no	—
182	C₄×D₄₇	—	2	2	no	—
183	C₄×D₄₇	—	2	2	no	—
184	C₄×D₄₇	—	2	1	no	—
185	C₄×D₄₇	—	2	1	no	—
186	C₄×D₄₇	—	2	1	no	—
187	C₄×D₄₇	—	2	1	no	—
188	C₄×D₄₇	—	4	1	no	—
189	C₄×D₄₇	—	4	1	no	—
190	C₄×D₄₇	—	4	1	no	—
191	C₄×D₄₇	—	4	1	no	—
192	C₈×C₄₇	—	4	2	no	—
193	C₈×C₄₇	—	4	2	no	—
194	C₄₇⋊C₈	—	4	2	no	—
195	C₄₇⋊C₈	—	4	2	no	—
196	#8093	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
200	C₂²×C₄₇	#417	1	1	yes	characteristic
201	C₂²×C₄₇	#417	1	1	yes	characteristic
202	C₂×D₄₇	—	2	1	no	—
203	C₂×D₄₇	—	2	1	no	—
204	C₂×D₄₇	—	2	1	no	—
205	C₂×D₄₇	—	2	1	no	—
206	C₂×D₄₇	—	2	1	no	—
207	C₂×D₄₇	—	4	2	no	—
208	C₂×D₄₇	—	4	2	no	—
209	C₂×D₄₇	#344	1	2	yes	—
210	C₄×C₄₇	—	2	1	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	8	2	no	—
214	C₄×C₄₇	#418	1	1	yes	characteristic
215	C₄×C₄₇	#419	1	1	yes	characteristic
216	C₄×C₄₇	#421	1	2	yes	—
217	C₄×C₄₇	#428	1	1	yes	characteristic
218	C₄×C₄₇	#428	1	1	yes	characteristic
219	Dic₄₇	—	2	1	no	—
220	Dic₄₇	—	2	1	no	—
221	Dic₄₇	—	2	1	no	—
222	Dic₄₇	—	2	1	no	—
223	Dic₄₇	—	2	1	no	—
224	Dic₄₇	—	2	1	no	—
225	Dic₄₇	—	8	2	no	—
226	#2920	—	47	1	no	—
227	C₂×#423	—	47	1	no	—
228	#2283	—	47	1	no	—
229	#1303	—	47	1	no	—
230	#1303	—	47	1	no	—
231	#1303	—	47	1	no	—
232	#1303	D₄₇	1	1	yes	characteristic, complemented
233	C₂×C₄₇	—	2	1	no	—
234	C₂×C₄₇	—	2	1	no	—
235	C₂×C₄₇	#1733	1	1	yes	characteristic
236	C₂×C₄₇	#1736	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
238	D₄₇	—	2	2	no	—
239	D₄₇	—	4	1	no	—
240	C₂²×M₁₆	—	94	1	no	—
241	C₂²×C₄²	—	47	1	no	—
242	#432	—	47	2	no	—
243	#432	—	94	1	no	—
244	#431	—	47	1	no	—
245	#431	—	94	1	no	—
246	#431	C₂×D₄₇	1	1	yes	characteristic
247	#423	—	47	1	no	—
248	#423	—	47	2	no	—
249	#423	—	47	2	no	—
250	#423	—	94	1	no	—
251	#423	—	94	1	no	—
252	#423	C₂×D₄₇	1	1	yes	characteristic
253	C₂×C₄⋊C₈	—	47	2	no	—
254	C₂×C₄⋊C₈	—	94	1	no	—
255	#407	—	94	1	no	—
256	C₄×M₁₆	—	94	1	no	—
257	#383	—	47	2	no	—
258	#382	—	94	1	no	—
259	#381	—	47	2	no	—
260	#380	—	94	1	no	—
261	C₄×C₄⋊C₄	—	47	1	no	—
262	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
263	C₄×C₂²⋊C₄	—	94	1	no	—
264	#376	—	94	1	no	—
265	C₄₇	#8093	1	1	yes	characteristic, complemented, Sylow
266	C₂³×C₄	—	47	1	no	—
267	C₂³×C₄	—	47	1	no	—
268	C₂³×C₄	—	47	1	no	—
269	C₂×M₁₆	—	2	1	no	—
270	C₂×M₁₆	—	94	2	no	—
271	C₂×M₁₆	—	94	2	no	—
272	C₂×M₁₆	—	94	1	no	—
273	C₂×M₁₆	—	188	2	no	—
274	C₂×M₁₆	—	188	2	no	—
275	C₂²×C₈	—	94	2	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	—	94	1	no	—
278	C₂×C₂²⋊C₄	—	94	2	no	—
279	C₂×C₄²	—	2	1	no	—
280	C₂×C₄²	—	47	1	no	—
281	C₂×C₄²	—	47	1	no	—
282	C₂×C₄²	—	47	1	no	—
283	C₂×C₄²	—	47	1	no	—
284	C₂×C₄²	—	47	1	no	—
285	C₂×C₄²	—	47	1	no	—
286	C₂×C₄²	—	47	1	no	—
287	C₂×C₄²	—	47	1	no	—
288	C₂×C₄²	—	47	1	no	—
289	C₂×C₄²	—	47	1	no	—
290	C₂×C₄²	—	47	1	no	—
291	C₂×C₄²	—	94	1	no	—
292	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
293	C₄⋊C₈	—	2	1	no	—
294	C₄⋊C₈	—	47	2	no	—
295	C₄⋊C₈	—	47	2	no	—
296	C₄⋊C₈	—	94	2	no	—
297	C₄⋊C₈	—	94	2	no	—
298	C₄⋊C₈	—	94	2	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
301	C₄⋊C₈	C₄×D₄₇	1	2	yes	—
302	C₂²⋊C₈	—	2	1	no	—
303	C₂²⋊C₈	—	94	2	no	—
304	C₂²⋊C₈	—	94	1	no	—
305	#97	—	94	2	no	—
306	C₄×C₈	—	2	1	no	—
307	C₄×C₈	—	94	1	no	—
308	#95	—	47	2	no	—
309	#95	—	94	2	no	—
310	#95	—	94	2	no	—
311	#95	—	94	2	no	—
312	#95	C₄×D₄₇	1	2	yes	—
313	C₂⁴	—	47	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	47	1	no	—
316	C₂²×C₄	—	47	1	no	—
317	C₂²×C₄	—	47	1	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	47	1	no	—
322	C₂²×C₄	—	47	1	no	—
323	C₂²×C₄	—	47	1	no	—
324	C₂²×C₄	—	47	1	no	—
325	C₂²×C₄	—	47	1	no	—
326	C₂²×C₄	—	47	1	no	—
327	C₂²×C₄	—	47	1	no	—
328	C₂²×C₄	—	47	1	no	—
329	C₂²×C₄	—	47	1	no	—
330	C₂²×C₄	—	94	1	no	—
331	C₂²×C₄	—	94	1	no	—
332	C₂²×C₄	—	94	1	no	—
333	C₂²×C₄	—	94	1	no	—
334	C₂²×C₄	—	94	2	no	—
335	C₂²×C₄	—	188	2	no	—
336	C₂²×C₄	—	188	2	no	—
337	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
338	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
339	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	1	no	—
342	M₁₆	—	188	4	no	—
343	M₁₆	—	188	4	no	—
344	M₁₆	—	188	1	no	—
345	M₁₆	—	188	1	no	—
346	C₂×C₈	—	2	2	no	—
347	C₂×C₈	—	2	2	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	2	no	—
350	C₂×C₈	—	188	4	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	188	2	no	—
353	C₂²⋊C₄	—	188	4	no	—
354	C₄²	—	4	1	no	—
355	C₄²	—	4	1	no	—
356	C₄²	—	47	1	no	—
357	C₄²	—	47	1	no	—
358	C₄²	—	47	1	no	—
359	C₄²	—	47	1	no	—
360	C₄²	—	47	1	no	—
361	C₄²	—	47	1	no	—
362	C₄²	—	47	1	no	—
363	C₄²	—	47	1	no	—
364	C₄²	—	47	1	no	—
365	C₄²	—	47	1	no	—
366	C₄²	—	47	1	no	—
367	C₄²	—	47	1	no	—
368	C₄²	—	188	1	no	—
369	C₄²	—	188	1	no	—
370	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
371	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
372	C₄²	D₄×D₄₇	1	1	yes	characteristic
373	C₄²	Q₈×D₄₇	1	1	yes	characteristic
374	C₂³	—	47	1	no	—
375	C₂³	—	47	1	no	—
376	C₂³	—	94	2	no	—
377	C₂³	—	94	1	no	—
378	C₂³	—	94	1	no	—
379	C₂³	—	188	1	no	—
380	C₂³	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	47	1	no	—
387	C₂×C₄	—	47	1	no	—
388	C₂×C₄	—	47	1	no	—
389	C₂×C₄	—	47	1	no	—
390	C₂×C₄	—	47	1	no	—
391	C₂×C₄	—	47	1	no	—
392	C₂×C₄	—	94	2	no	—
393	C₂×C₄	—	94	2	no	—
394	C₂×C₄	—	94	1	no	—
395	C₂×C₄	—	94	1	no	—
396	C₂×C₄	—	94	1	no	—
397	C₂×C₄	—	94	1	no	—
398	C₂×C₄	—	94	1	no	—
399	C₂×C₄	—	94	1	no	—
400	C₂×C₄	—	94	2	no	—
401	C₂×C₄	—	94	2	no	—
402	C₂×C₄	—	94	1	no	—
403	C₂×C₄	—	94	1	no	—
404	C₂×C₄	—	94	1	no	—
405	C₂×C₄	—	94	1	no	—
406	C₂×C₄	—	188	1	no	—
407	C₂×C₄	—	188	1	no	—
408	C₂×C₄	—	188	1	no	—
409	C₂×C₄	—	188	1	no	—
410	C₂×C₄	—	188	1	no	—
411	C₂×C₄	—	188	1	no	—
412	C₂×C₄	—	188	2	no	—
413	C₂×C₄	—	188	2	no	—
414	C₂×C₄	—	188	2	no	—
415	C₂×C₄	C₄²×D₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
418	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
419	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
420	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
421	C₂×C₄	#13094048	1	1	yes	characteristic
422	C₂×C₄	#13094051	1	1	yes	characteristic
423	C₂×C₄	#13094053	1	1	yes	characteristic
424	C₂×C₄	#13094056	1	1	yes	characteristic
425	C₈	—	4	2	no	—
426	C₈	—	4	2	no	—
427	C₈	—	188	2	no	—
428	C₈	—	188	2	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	47	2	no	—
432	C₂²	—	94	1	no	—
433	C₂²	—	94	1	no	—
434	C₂²	—	94	1	no	—
435	C₂²	—	94	1	no	—
436	C₂²	—	94	1	no	—
437	C₂²	—	188	2	no	—
438	C₂²	—	188	2	no	—
439	C₂²	#95×D₄₇	1	1	yes	characteristic
440	C₂²	#15689121	1	1	yes	characteristic
441	C₂²	#15689123	1	1	yes	characteristic
442	C₄	—	2	1	no	—
443	C₄	—	2	1	no	—
444	C₄	—	2	1	no	—
445	C₄	—	8	2	no	—
446	C₄	—	94	1	no	—
447	C₄	—	94	1	no	—
448	C₄	—	94	1	no	—
449	C₄	—	94	1	no	—
450	C₄	—	94	1	no	—
451	C₄	—	94	1	no	—
452	C₄	—	376	2	no	—
453	C₄	#15689126	1	1	yes	characteristic
454	C₄	#15689130	1	1	yes	characteristic
455	C₄	#15689138	1	2	yes	—
456	C₄	#15689162	1	1	yes	characteristic
457	C₄	#15689164	1	1	yes	characteristic
458	C₂	—	2	1	no	—
459	C₂	—	2	1	no	—
460	C₂	—	94	2	no	—
461	C₂	—	188	1	no	—
462	C₂	#20243096	1	1	yes	characteristic
463	C₂	#20243106	1	1	yes	characteristic
464	C₂	#344×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²⋊C₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1303	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₂²⋊C₄
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1303	D₄₇
hypocenter	C₄₇	#8093
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1303

Complements

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

N	H ≅ G/N	type
4. #20241291	C₂	semidirect
5. #20241290	C₂	semidirect
6. #20241289	C₂	semidirect
7. C₄₇×#1303	C₂	semidirect
10. #15689179	C₄	semidirect
17. #15689145	C₄	semidirect
18. #15689145	C₄	semidirect
20. C₄⋊C₈×D₄₇	C₄	semidirect
232. #1303	D₄₇	semidirect
265. C₄₇	#8093	semidirect

Maximal subgroups

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

subgroup	index
#20252016	2
#423×D₄₇	2
#20245784	2
#20241291	2
#20241290	2
#20241289	2
C₄₇×#1303	2
#8093	47