Subgroups — #26215015

Order 12032.

1038 conjugacy classes of subgroups.

The subgroup lattice has 414 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689179	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689174	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243264	C₂	1	2	yes	maximal, complemented
5	#20243261	C₂	1	2	yes	maximal, complemented
6	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243253	C₂	1	1	yes	maximal, characteristic, complemented
8	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243151	C₂	1	2	yes	maximal
10	#20243145	C₂	1	2	yes	maximal
11	C₄₇×#1770	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊C₄×D₄₇	C₄	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
14	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
15	#15689179	C₄	1	8	yes	complemented
16	#15689174	C₄	1	8	yes	complemented
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
18	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
23	C₂×#13093935	C₂²	1	2	yes	—
24	C₂×#13093934	C₂²	1	2	yes	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
27	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
28	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
29	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688974	C₄	1	2	yes	—
32	#95×D₄₇	C₄	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#97×C₄₇	C₂²	1	2	yes	—
38	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
42	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
50	C₄⋊C₄×D₄₇	—	2	8	no	—
51	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₄²×D₄₇	—	4	2	no	—
57	C₄²×D₄₇	—	4	2	no	—
58	C₄²×D₄₇	C₂×C₄	1	4	yes	—
59	C₄²×D₄₇	C₂×C₄	1	4	yes	—
60	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
61	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
62	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
63	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
64	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
65	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
66	#13093935	—	4	2	no	—
67	#13093934	C₂×C₄	1	8	yes	complemented
68	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
69	C₈×Dic₄₇	—	4	2	no	—
70	C₈×Dic₄₇	—	4	2	no	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₄₇⋊#95	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
80	#97×C₄₇	—	4	2	no	—
81	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
82	#95×C₄₇	C₂×C₄	1	2	yes	—
83	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
88	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
92	C₂×C₄×D₄₇	—	2	4	no	—
93	C₂×C₄×D₄₇	—	2	4	no	—
94	C₂×C₄×D₄₇	—	2	1	no	—
95	C₂×C₄×D₄₇	—	2	1	no	—
96	C₂×C₄×D₄₇	—	2	1	no	—
97	C₂×C₄×D₄₇	—	2	1	no	—
98	C₂×C₄×D₄₇	—	2	8	no	—
99	C₂×C₄×D₄₇	—	2	8	no	—
100	C₂×C₄×D₄₇	—	4	4	no	—
101	C₂×C₄×D₄₇	C₄²	1	4	yes	—
102	C₂×C₄×D₄₇	C₄²	1	4	yes	—
103	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	—	2	1	no	—
106	C₂×C₈×C₄₇	—	2	2	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
112	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄⋊C₄×C₄₇	—	2	4	no	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	—	2	2	no	—
117	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
119	C₄⋊Dic₄₇	M₁₆	1	8	yes	—
120	Dic₄₇⋊C₄	—	2	8	no	—
121	C₄×Dic₄₇	—	2	2	no	—
122	C₄×Dic₄₇	—	2	2	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	C₄²	1	4	yes	—
125	C₄×Dic₄₇	C₄²	1	4	yes	—
126	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
127	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
136	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
137	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
138	C₂²×D₄₇	—	2	1	no	—
139	C₂²×D₄₇	—	2	1	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
142	C₂²×D₄₇	#131	1	4	yes	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	4	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	1	no	—
158	C₂×Dic₄₇	—	2	1	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	4	no	—
162	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
163	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
164	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
165	C₂×Dic₄₇	C₂×M₁₆	1	8	yes	—
166	C₄×D₄₇	—	2	8	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	8	no	—
172	C₄×D₄₇	—	4	16	no	—
173	C₈×C₄₇	—	2	4	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	2	2	no	—
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	2	2	no	—
178	C₄₇⋊C₈	—	2	4	no	—
179	#20535	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
181	C₂²×C₄₇	#518	1	1	yes	characteristic
182	C₂²×C₄₇	#519	1	1	yes	characteristic
183	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
184	C₂²×C₄₇	C₂×#131	1	2	yes	—
185	C₂×D₄₇	—	2	2	no	—
186	C₂×D₄₇	—	2	4	no	—
187	C₂×D₄₇	—	2	4	no	—
188	C₂×D₄₇	—	2	2	no	—
189	C₂×D₄₇	#405	1	4	yes	—
190	C₄×C₄₇	—	2	2	no	—
191	C₄×C₄₇	—	4	4	no	—
192	C₄×C₄₇	C₄×M₁₆	1	4	yes	—
193	C₄×C₄₇	#520	1	1	yes	characteristic
194	C₄×C₄₇	#520	1	1	yes	characteristic
195	C₄×C₄₇	#520	1	1	yes	characteristic
196	C₄×C₄₇	#520	1	1	yes	characteristic
197	Dic₄₇	—	2	2	no	—
198	Dic₄₇	—	2	2	no	—
199	Dic₄₇	—	2	8	no	—
200	Dic₄₇	—	2	2	no	—
201	C₂×#432	—	47	1	no	—
202	C₂×#431	—	47	1	no	—
203	C₂×C₄×C₄⋊C₄	—	47	1	no	—
204	#1771	—	47	2	no	—
205	#1771	—	47	2	no	—
206	#1770	—	47	1	no	—
207	#1770	D₄₇	1	1	yes	characteristic, complemented
208	C₈×C₄⋊C₄	—	47	1	no	—
209	C₈×C₄⋊C₄	—	47	1	no	—
210	#1749	—	47	2	no	—
211	C₄×C₂²⋊C₈	—	47	2	no	—
212	C₂×C₄₇	#2274	1	1	yes	characteristic
213	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
214	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
215	C₂×C₄₇	#2974	1	2	yes	—
216	C₂×C₄₇	#2984	1	2	yes	—
217	D₄₇	—	2	4	no	—
218	C₂²×C₄⋊C₄	—	47	2	no	—
219	C₂²×C₄²	—	47	1	no	—
220	C₂²×C₄²	—	47	2	no	—
221	#432	—	47	8	no	—
222	#431	—	47	8	no	—
223	C₂×C₄⋊C₈	—	47	1	no	—
224	C₂×C₄⋊C₈	—	47	1	no	—
225	C₂×C₄⋊C₈	—	47	1	no	—
226	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
227	C₂×C₂²⋊C₈	—	47	1	no	—
228	C₂×C₂²⋊C₈	—	47	1	no	—
229	C₂×C₂²⋊C₈	—	47	2	no	—
230	C₂×#97	—	47	2	no	—
231	C₂×#97	—	47	2	no	—
232	C₂×#97	C₂×D₄₇	1	2	yes	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	2	no	—
235	C₂×C₄×C₈	—	47	2	no	—
236	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
237	C₄×C₄⋊C₄	—	47	2	no	—
238	C₄×C₄⋊C₄	—	47	1	no	—
239	C₄×C₄⋊C₄	—	47	2	no	—
240	C₄×C₄⋊C₄	—	47	2	no	—
241	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
242	C₂×#95	—	47	2	no	—
243	#336	—	47	2	no	—
244	#336	—	47	2	no	—
245	#336	—	47	2	no	—
246	#336	C₂×D₄₇	1	2	yes	—
247	C₄₇	#20535	1	1	yes	characteristic, complemented, Sylow
248	C₂³×C₄	—	47	1	no	—
249	C₂³×C₄	—	47	1	no	—
250	C₂³×C₄	—	47	1	no	—
251	C₂³×C₄	—	47	4	no	—
252	C₂²×C₈	—	47	1	no	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	47	2	no	—
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
257	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	47	4	no	—
260	C₂×C₄⋊C₄	—	94	8	no	—
261	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
262	C₂×C₄²	—	47	1	no	—
263	C₂×C₄²	—	47	1	no	—
264	C₂×C₄²	—	47	1	no	—
265	C₂×C₄²	—	47	4	no	—
266	C₂×C₄²	—	47	4	no	—
267	C₂×C₄²	—	47	2	no	—
268	C₂×C₄²	—	47	4	no	—
269	C₂×C₄²	—	188	2	no	—
270	C₂×C₄²	—	188	2	no	—
271	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
272	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
273	C₄⋊C₈	—	47	4	no	—
274	C₄⋊C₈	—	47	4	no	—
275	C₄⋊C₈	—	47	4	no	—
276	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
277	C₂²⋊C₈	—	47	4	no	—
278	C₂²⋊C₈	—	47	4	no	—
279	C₂²⋊C₈	—	47	8	no	—
280	#97	—	4	2	no	—
281	#97	—	47	8	no	—
282	#97	—	188	2	no	—
283	C₄×C₈	—	47	4	no	—
284	C₄×C₈	—	188	2	no	—
285	C₄×C₈	—	188	2	no	—
286	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
287	#95	—	47	4	no	—
288	#95	—	47	2	no	—
289	#95	C₄×D₄₇	1	2	yes	—
290	C₂⁴	—	47	1	no	—
291	C₂²×C₄	—	47	1	no	—
292	C₂²×C₄	—	47	4	no	—
293	C₂²×C₄	—	47	1	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	47	4	no	—
296	C₂²×C₄	—	47	4	no	—
297	C₂²×C₄	—	47	2	no	—
298	C₂²×C₄	—	47	2	no	—
299	C₂²×C₄	—	94	8	no	—
300	C₂²×C₄	—	94	4	no	—
301	C₂²×C₄	—	94	8	no	—
302	C₂²×C₄	—	94	4	no	—
303	C₂²×C₄	—	94	1	no	—
304	C₂²×C₄	—	94	1	no	—
305	C₂²×C₄	—	94	1	no	—
306	C₂²×C₄	—	94	1	no	—
307	C₂²×C₄	—	188	4	no	—
308	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
309	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	1	no	—
314	C₂×C₈	—	2	1	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	1	no	—
317	C₂×C₈	—	2	1	no	—
318	C₂×C₈	—	47	2	no	—
319	C₂×C₈	—	47	2	no	—
320	C₂×C₈	—	47	4	no	—
321	C₂×C₈	—	94	1	no	—
322	C₂×C₈	—	94	2	no	—
323	C₂×C₈	—	94	1	no	—
324	C₂×C₈	—	94	1	no	—
325	C₂×C₈	—	94	1	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
328	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
329	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	47	8	no	—
332	C₄⋊C₄	—	94	8	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	2	no	—
335	C₄²	—	47	4	no	—
336	C₄²	—	47	4	no	—
337	C₄²	—	47	2	no	—
338	C₄²	—	47	2	no	—
339	C₄²	—	94	2	no	—
340	C₄²	—	94	2	no	—
341	C₄²	—	188	4	no	—
342	C₄²	C₂×C₄×D₄₇	1	2	yes	—
343	C₄²	C₂×C₄×D₄₇	1	2	yes	—
344	C₂³	—	47	2	no	—
345	C₂³	—	47	4	no	—
346	C₂³	—	94	1	no	—
347	C₂³	—	94	1	no	—
348	C₂³	—	94	2	no	—
349	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	47	2	no	—
355	C₂×C₄	—	47	2	no	—
356	C₂×C₄	—	47	2	no	—
357	C₂×C₄	—	47	8	no	—
358	C₂×C₄	—	94	8	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	1	no	—
361	C₂×C₄	—	94	1	no	—
362	C₂×C₄	—	94	2	no	—
363	C₂×C₄	—	94	4	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	8	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	2	no	—
368	C₂×C₄	—	94	2	no	—
369	C₂×C₄	—	94	2	no	—
370	C₂×C₄	—	188	16	no	—
371	C₂×C₄	C₄²×D₄₇	1	2	yes	—
372	C₂×C₄	C₄²×D₄₇	1	2	yes	—
373	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
374	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
375	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
376	C₂×C₄	#13094069	1	1	yes	characteristic
377	C₂×C₄	#13094070	1	1	yes	characteristic
378	C₂×C₄	#13094071	1	1	yes	characteristic
379	C₂×C₄	#13094072	1	1	yes	characteristic
380	C₈	—	2	4	no	—
381	C₈	—	2	2	no	—
382	C₈	—	2	2	no	—
383	C₈	—	94	2	no	—
384	C₈	—	94	2	no	—
385	C₈	—	94	4	no	—
386	C₂²	—	47	4	no	—
387	C₂²	—	94	4	no	—
388	C₂²	—	94	4	no	—
389	C₂²	—	94	2	no	—
390	C₂²	—	94	2	no	—
391	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
392	C₂²	#15689595	1	1	yes	characteristic
393	C₂²	#15689599	1	1	yes	characteristic
394	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
395	C₂²	#131×D₄₇	1	2	yes	—
396	C₄	—	2	2	no	—
397	C₄	—	4	4	no	—
398	C₄	—	94	8	no	—
399	C₄	—	94	2	no	—
400	C₄	—	94	2	no	—
401	C₄	—	94	2	no	—
402	C₄	#15689075	1	4	yes	—
403	C₄	#15689602	1	1	yes	characteristic
404	C₄	#15689603	1	1	yes	characteristic
405	C₄	#15689604	1	1	yes	characteristic
406	C₄	#15689605	1	1	yes	characteristic
407	C₂	—	94	4	no	—
408	C₂	#20245742	1	1	yes	characteristic
409	C₂	C₂×#15689075	1	1	yes	characteristic
410	C₂	#405×D₄₇	1	1	yes	characteristic
411	C₂	#20252420	1	2	yes	—
412	C₂	#20252474	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1770	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1770	D₄₇
hypocenter	C₄₇	#20535
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1770

Complements

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

N	H ≅ G/N	type
4. #20243264	C₂	semidirect
5. #20243261	C₂	semidirect
6. #20243257	C₂	semidirect
7. #20243253	C₂	semidirect
8. C₈×C₄⋊Dic₄₇	C₂	semidirect
11. C₄₇×#1770	C₂	semidirect
15. #15689179	C₄	semidirect
16. #15689174	C₄	semidirect
60. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
61. Dic₄₇⋊C₈	C₂×C₄	semidirect
62. Dic₄₇⋊C₈	C₂×C₄	semidirect
67. #13093934	C₂×C₄	semidirect
68. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
79. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
81. C₄×C₈×C₄₇	C₂×C₄	semidirect
207. #1770	D₄₇	semidirect
247. C₄₇	#20535	semidirect
276. C₄⋊C₈	C₄×D₄₇	semidirect
286. 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×#15689179	2
C₂×#15689174	2
C₄×C₄⋊C₄×D₄₇	2
#20243264	2
#20243261	2
#20243257	2
#20243253	2
C₈×C₄⋊Dic₄₇	2
#20243151	2
#20243145	2
C₄₇×#1770	2
#20535	47