Subgroups — #26215309

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic
2	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243258	C₂	1	1	yes	maximal, characteristic, complemented
4	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243174	C₂	1	2	yes	maximal, complemented
7	#20243169	C₂	1	2	yes	maximal, complemented
8	#20243152	C₂	1	2	yes	maximal, complemented
9	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243081	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#436	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	2	yes	—
13	C₂×D₄×Dic₄₇	C₄	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
15	#15689201	C₄	1	8	yes	complemented
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×#13093934	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂²⋊C₄×Dic₄₇	C₄	1	4	yes	—
25	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
26	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688877	C₂²	1	2	yes	—
28	#15688877	C₂²	1	2	yes	—
29	#15688877	C₂²	1	2	yes	—
30	#15688877	C₂²	1	1	yes	characteristic
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	1	yes	characteristic
34	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#436	C₄	1	8	yes	complemented
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂³×Dic₄₇	C₂×C₄	1	4	yes	—
41	C₂×#10625329	—	4	2	no	—
42	C₂×#10625329	—	4	2	no	—
43	C₂×#10625329	C₂×C₄	1	8	yes	complemented
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	D₄×Dic₄₇	—	2	8	no	—
48	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	4	yes	—
50	C₂×C₄×Dic₄₇	—	4	2	no	—
51	C₂×C₄×Dic₄₇	—	4	2	no	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
54	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
59	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	8	yes	complemented
60	#13093934	—	4	2	no	—
61	#13093934	—	4	2	no	—
62	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
63	C₈×Dic₄₇	—	4	2	no	—
64	C₄₇⋊#95	C₂×C₄	1	4	yes	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
68	C₂×M₁₆×C₄₇	—	4	2	no	—
69	C₂×M₁₆×C₄₇	—	4	2	no	—
70	C₂×M₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
75	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
76	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
80	C₂²⋊C₈×C₄₇	C₂×C₄	1	8	yes	complemented
81	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
82	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	C₄²	1	4	yes	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
91	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
93	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
95	C₂²×Dic₄₇	—	2	8	no	—
96	C₂²×Dic₄₇	—	4	4	no	—
97	C₂²×Dic₄₇	—	4	4	no	—
98	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
99	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
101	M₁₆×C₄₇	—	4	8	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
111	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
112	C₂²⋊C₄×C₄₇	C₄²	1	8	yes	—
113	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	C₂²⋊Dic₄₇	—	2	8	no	—
116	C₄⋊Dic₄₇	—	2	4	no	—
117	C₄×Dic₄₇	—	2	1	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	—	2	2	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	4	4	no	—
124	C₄×Dic₄₇	—	4	2	no	—
125	C₄×Dic₄₇	M₁₆	1	8	yes	complemented
126	#10625329	—	4	8	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
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	C₂²×C₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
136	C₂³×C₄₇	—	2	2	no	—
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	4	no	—
139	C₂³×C₄₇	—	2	4	no	—
140	C₂³×C₄₇	C₂×C₄²	1	4	yes	—
141	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	8	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	2	4	no	—
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₄₇	C₂×C₄²	1	4	yes	—
152	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
153	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
157	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
158	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
159	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	4	no	—
165	C₂×Dic₄₇	—	2	4	no	—
166	C₂×Dic₄₇	—	2	4	no	—
167	C₂×Dic₄₇	—	4	16	no	—
168	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
169	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
170	C₈×C₄₇	—	2	4	no	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₄₇⋊C₈	—	2	4	no	—
174	C₄₇⋊C₈	—	2	2	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	#20568	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	—	2	4	no	—
178	C₂²×C₄₇	—	2	4	no	—
179	C₂²×C₄₇	—	2	4	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
183	C₂²×C₄₇	#518	1	1	yes	characteristic
184	C₂²×C₄₇	#520	1	1	yes	characteristic
185	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
186	C₂²×C₄₇	#568	1	2	yes	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	C₄×M₁₆	1	4	yes	—
190	C₄×C₄₇	#518	1	1	yes	characteristic
191	C₄×C₄₇	#518	1	1	yes	characteristic
192	C₄×C₄₇	#520	1	1	yes	characteristic
193	C₄×C₄₇	#520	1	1	yes	characteristic
194	Dic₄₇	—	2	4	no	—
195	Dic₄₇	—	2	4	no	—
196	Dic₄₇	—	4	4	no	—
197	C₂×#436	—	47	1	no	—
198	C₂×#436	D₄₇	1	1	yes	characteristic
199	C₄²×D₄	—	47	1	no	—
200	#1770	—	47	1	no	—
201	#1770	—	47	1	no	—
202	C₄×C₄⋊C₈	—	47	1	no	—
203	#1753	—	47	2	no	—
204	#1753	—	47	2	no	—
205	#1749	—	47	2	no	—
206	#1744	—	47	1	no	—
207	#1728	—	47	2	no	—
208	C₂×C₄₇	—	4	4	no	—
209	C₂×C₄₇	#2275	1	1	yes	characteristic
210	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
211	C₂×C₄₇	#2875	1	1	yes	characteristic
212	C₂×C₄₇	#2975	1	2	yes	—
213	C₂×C₄₇	#2989	1	2	yes	—
214	C₂²×M₁₆	—	47	2	no	—
215	C₂²×M₁₆	C₂×D₄₇	1	2	yes	—
216	C₂×C₄×D₄	—	47	2	no	—
217	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
218	C₂²×C₄²	—	47	2	no	—
219	#436	—	47	8	no	—
220	#436	Dic₄₇	1	8	yes	complemented
221	C₂×C₄⋊C₈	—	47	1	no	—
222	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
223	C₂×C₂²⋊C₈	—	47	2	no	—
224	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
225	C₂×#97	—	47	2	no	—
226	C₂×#97	—	47	2	no	—
227	C₂×C₄×C₈	—	47	1	no	—
228	C₂×C₄×C₈	—	47	2	no	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₄×C₄⋊C₄	—	47	2	no	—
231	C₄×C₄⋊C₄	—	47	1	no	—
232	C₄×C₂²⋊C₄	—	47	2	no	—
233	C₄×C₂²⋊C₄	—	47	4	no	—
234	C₄³	—	47	1	no	—
235	#336	—	47	1	no	—
236	#336	—	47	2	no	—
237	#336	—	47	2	no	—
238	#336	—	47	2	no	—
239	#336	—	47	1	no	—
240	#336	—	47	1	no	—
241	#336	—	47	1	no	—
242	C₄₇	#20568	1	1	yes	characteristic, complemented, Sylow
243	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
244	C₂³×C₄	—	47	4	no	—
245	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
246	C₂×M₁₆	—	4	2	no	—
247	C₂×M₁₆	—	4	2	no	—
248	C₂×M₁₆	—	47	8	no	—
249	C₂×M₁₆	—	188	2	no	—
250	C₂×M₁₆	—	188	2	no	—
251	C₂×M₁₆	C₂×Dic₄₇	1	8	yes	complemented
252	C₂²×C₈	—	47	1	no	—
253	C₂²×C₈	—	47	2	no	—
254	C₂²×C₈	—	47	1	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	C₄×D₄	—	94	8	no	—
259	C₄×D₄	C₄×D₄₇	1	4	yes	—
260	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	—	47	4	no	—
264	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
265	C₂×C₄²	—	47	2	no	—
266	C₂×C₄²	—	47	1	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	2	no	—
269	C₂×C₄²	—	47	2	no	—
270	C₂×C₄²	—	47	4	no	—
271	C₂×C₄²	—	188	2	no	—
272	C₂×C₄²	—	188	2	no	—
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₄⋊C₈	—	47	4	no	—
275	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
276	C₂²⋊C₈	—	47	8	no	—
277	C₂²⋊C₈	C₂×Dic₄₇	1	8	yes	complemented
278	#97	—	188	2	no	—
279	#97	—	188	2	no	—
280	C₄×C₈	—	47	4	no	—
281	C₄×C₈	—	188	2	no	—
282	C₄×C₈	C₂×Dic₄₇	1	4	yes	complemented
283	#95	—	47	4	no	—
284	#95	—	47	2	no	—
285	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
286	C₂×D₄	—	2	4	no	—
287	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	2	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	4	no	—
295	C₂²×C₄	—	94	8	no	—
296	C₂²×C₄	—	188	4	no	—
297	C₂²×C₄	—	188	4	no	—
298	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
299	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
301	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
303	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
304	M₁₆	—	4	8	no	—
305	M₁₆	—	188	8	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	47	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	47	4	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	1	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
322	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
323	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
324	C₄⋊C₄	—	94	4	no	—
325	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
326	C₂²⋊C₄	—	94	8	no	—
327	C₂²⋊C₄	C₄×Dic₄₇	1	8	yes	—
328	C₄²	—	47	8	no	—
329	C₄²	—	94	1	no	—
330	C₄²	—	94	2	no	—
331	C₄²	—	94	1	no	—
332	C₄²	—	94	2	no	—
333	C₄²	—	94	1	no	—
334	C₄²	—	94	1	no	—
335	C₄²	—	188	2	no	—
336	C₄²	—	188	4	no	—
337	C₄²	C₂×C₄×D₄₇	1	2	yes	—
338	C₄²	C₂²×Dic₄₇	1	2	yes	—
339	C₂³	—	2	2	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	4	no	—
343	C₂³	C₂×C₄×Dic₄₇	1	4	yes	—
344	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
345	D₄	—	2	8	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	4	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	4	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	47	4	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	94	4	no	—
361	C₂×C₄	—	94	4	no	—
362	C₂×C₄	—	188	16	no	—
363	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
364	C₂×C₄	C₂×C₄×Dic₄₇	1	4	yes	—
365	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
366	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
367	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
369	C₂×C₄	#13094069	1	1	yes	characteristic
370	C₂×C₄	#13094069	1	1	yes	characteristic
371	C₂×C₄	#13094070	1	1	yes	characteristic
372	C₂×C₄	#13094071	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	94	4	no	—
377	C₈	—	94	2	no	—
378	C₈	—	94	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	2	4	no	—
381	C₂²	—	2	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	—	4	4	no	—
384	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
385	C₂²	#15689595	1	1	yes	characteristic
386	C₂²	#15689602	1	1	yes	characteristic
387	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
388	C₂²	#15689888	1	2	yes	—
389	C₄	—	2	2	no	—
390	C₄	—	2	4	no	—
391	C₄	—	94	4	no	—
392	C₄	—	94	4	no	—
393	C₄	—	188	4	no	—
394	C₄	M₁₆×Dic₄₇	1	4	yes	—
395	C₄	#15689595	1	1	yes	characteristic
396	C₄	#15689598	1	1	yes	characteristic
397	C₄	#15689602	1	1	yes	characteristic
398	C₄	#15689606	1	1	yes	characteristic
399	C₂	—	4	4	no	—
400	C₂	#20245749	1	1	yes	characteristic
401	C₂	C₂×M₁₆×Dic₄₇	1	1	yes	characteristic
402	C₂	#20251814	1	1	yes	characteristic
403	C₂	#20252426	1	2	yes	—
404	C₂	#20252503	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₂×C₄₇×#436	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#436	D₄₇
hypocenter	C₄₇	#20568
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#436

Complements

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

N	H ≅ G/N	type
3. #20243258	C₂	semidirect
4. #20243255	C₂	semidirect
5. C₄⋊C₈×Dic₄₇	C₂	semidirect
6. #20243174	C₂	semidirect
7. #20243169	C₂	semidirect
8. #20243152	C₂	semidirect
9. #20243133	C₂	semidirect
10. #20243081	C₂	semidirect
15. #15689201	C₄	semidirect
36. C₄₇×#436	C₄	semidirect
43. C₂×#10625329	C₂×C₄	semidirect
58. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
59. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
62. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
70. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
79. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
80. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
81. C₄×C₈×C₄₇	C₂×C₄	semidirect
125. C₄×Dic₄₇	M₁₆	semidirect
220. #436	Dic₄₇	semidirect
242. C₄₇	#20568	semidirect
251. C₂×M₁₆	C₂×Dic₄₇	semidirect
275. C₄⋊C₈	C₂×Dic₄₇	semidirect
277. C₂²⋊C₈	C₂×Dic₄₇	semidirect
282. C₄×C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689201	2
C₄×D₄×Dic₄₇	2
#20243258	2
#20243255	2
C₄⋊C₈×Dic₄₇	2
#20243174	2
#20243169	2
#20243152	2
#20243133	2
#20243081	2
C₂×C₄₇×#436	2
#20568	47