Subgroups — #26215303

Order 12032.

1106 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×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689200	C₂	1	1	yes	maximal, characteristic
3	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
4	C₄⋊C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243171	C₂	1	2	yes	maximal, complemented
7	#20243168	C₂	1	2	yes	maximal, complemented
8	C₄×(C₂×D₄₇)⋊C₈	C₂	1	2	yes	maximal, complemented
9	#20243133	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243080	C₂	1	2	yes	maximal, complemented
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×#10625324	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093986	C₄	1	2	yes	—
16	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
17	#15689202	C₄	1	8	yes	complemented
18	#15689200	C₄	1	8	yes	complemented
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	C₂×#13093934	C₂²	1	2	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
24	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
26	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
27	#15688970	C₄	1	4	yes	—
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688878	C₂²	1	2	yes	—
30	#15688877	C₂²	1	2	yes	—
31	#15688877	C₂²	1	1	yes	characteristic
32	#15688877	C₂²	1	1	yes	characteristic
33	#15688877	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
37	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#336	C₂²	1	2	yes	—
40	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₄₇	C₂×C₄	1	4	yes	—
42	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
43	C₂×#10625324	—	4	2	no	—
44	C₂×#10625324	—	4	2	no	—
45	C₂×#10625324	—	4	2	no	—
46	C₂×#10625324	—	4	2	no	—
47	C₂×#10625324	C₂×C₄	1	8	yes	complemented
48	C₂×#10625324	C₂×C₄	1	8	yes	complemented
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
53	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
54	#13093986	—	2	8	no	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₄²×D₄₇	—	4	2	no	—
64	C₄²×D₄₇	—	4	2	no	—
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
66	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	complemented
67	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	complemented
68	#13093934	—	4	2	no	—
69	C₄×C₄₇⋊C₈	—	4	2	no	—
70	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
71	C₄₇⋊#95	C₂×C₄	1	4	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
79	C₄×C₈×C₄₇	—	4	2	no	—
80	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
81	#95×C₄₇	C₂×C₄	1	2	yes	—
82	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	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	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
88	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
90	C₂×D₁₈₈	—	2	4	no	—
91	C₂×D₁₈₈	C₄²	1	4	yes	—
92	C₂×C₄×D₄₇	—	2	2	no	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	2	2	no	—
96	C₂×C₄×D₄₇	—	2	8	no	—
97	C₂×C₄×D₄₇	—	2	8	no	—
98	C₂×C₄×D₄₇	—	4	4	no	—
99	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
100	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
101	C₂×C₈×C₄₇	—	2	2	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	1	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
110	C₄⋊C₄×C₄₇	M₁₆	1	8	yes	complemented
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
114	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
115	(C₂×D₄₇)⋊C₄	—	2	8	no	—
116	(C₂×D₄₇)⋊C₄	C₄²	1	8	yes	—
117	C₄⋊Dic₄₇	C₄²	1	4	yes	—
118	C₄×Dic₄₇	—	2	4	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	2	1	no	—
122	C₄×Dic₄₇	—	2	1	no	—
123	C₄×Dic₄₇	—	2	4	no	—
124	C₄×Dic₄₇	—	4	4	no	—
125	C₂×C₄₇⋊C₈	—	2	1	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
134	#10625324	—	4	8	no	—
135	#10625324	—	4	8	no	—
136	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	—	2	2	no	—
139	C₂²×D₄₇	—	2	4	no	—
140	C₂²×D₄₇	—	2	4	no	—
141	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
146	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×M₁₆	1	8	yes	—
148	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	H(5,𝔽₂)	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×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
163	C₂×Dic₄₇	#131	1	4	yes	—
164	D₁₈₈	—	2	8	no	—
165	C₄×D₄₇	—	2	4	no	—
166	C₄×D₄₇	—	2	4	no	—
167	C₄×D₄₇	—	2	4	no	—
168	C₄×D₄₇	—	2	4	no	—
169	C₄×D₄₇	—	4	16	no	—
170	C₈×C₄₇	—	2	2	no	—
171	C₈×C₄₇	—	2	4	no	—
172	C₈×C₄₇	—	2	2	no	—
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	2	4	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	#20567	—	47	1	no	maximal, Sylow
177	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
178	C₂²×C₄₇	#518	1	1	yes	characteristic
179	C₂²×C₄₇	#520	1	1	yes	characteristic
180	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
181	C₂²×C₄₇	C₂×#131	1	2	yes	—
182	C₂×D₄₇	—	2	4	no	—
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	—	2	4	no	—
185	C₂×D₄₇	—	4	4	no	—
186	C₂×D₄₇	—	4	4	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	8	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	2	no	—
197	C₂×#436	—	47	1	no	—
198	C₂×#436	—	47	1	no	—
199	C₄²×D₄	—	47	1	no	—
200	C₈×C₄⋊C₄	—	47	1	no	—
201	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
202	#1767	—	47	1	no	—
203	#1753	—	47	2	no	—
204	#1753	—	47	2	no	—
205	C₄×C₂²⋊C₈	—	47	2	no	—
206	#1744	—	47	1	no	—
207	#1728	—	47	2	no	—
208	C₂×C₄₇	#2275	1	1	yes	characteristic
209	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
210	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
211	C₂×C₄₇	#2974	1	2	yes	—
212	C₂×C₄₇	#2991	1	2	yes	—
213	D₄₇	—	4	4	no	—
214	C₂²×M₁₆	—	47	2	no	—
215	C₂²×M₁₆	—	47	2	no	—
216	C₂×C₄×D₄	—	47	2	no	—
217	C₂×C₄×D₄	—	47	1	no	—
218	C₂²×C₄²	—	47	2	no	—
219	#436	—	47	8	no	—
220	#436	—	47	8	no	—
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	—	47	2	no	—
225	C₂×#97	—	47	2	no	—
226	C₂×C₄×C₈	—	47	1	no	—
227	C₂×C₄×C₈	—	47	2	no	—
228	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	C₄×C₄⋊C₄	—	47	2	no	—
231	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
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	1	no	—
238	#336	—	47	1	no	—
239	#336	—	47	1	no	—
240	#336	—	47	2	no	—
241	#336	C₂×D₄₇	1	2	yes	—
242	C₄₇	#20567	1	1	yes	characteristic, complemented, Sylow
243	C₂²×D₄	—	47	1	no	—
244	C₂³×C₄	—	47	2	no	—
245	C₂³×C₄	—	47	4	no	—
246	C₂×M₁₆	—	47	8	no	—
247	C₂×M₁₆	—	47	8	no	—
248	C₂×M₁₆	—	188	2	no	—
249	C₂×M₁₆	—	188	2	no	—
250	C₂×M₁₆	—	188	2	no	—
251	C₂×M₁₆	—	188	2	no	—
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	—	47	4	no	—
259	C₄×D₄	—	47	4	no	—
260	C₄×D₄	—	94	8	no	—
261	C₂×C₄⋊C₄	—	47	1	no	—
262	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
263	C₂×C₂²⋊C₄	—	47	2	no	—
264	C₂×C₂²⋊C₄	—	47	4	no	—
265	C₂×C₄²	—	47	2	no	—
266	C₂×C₄²	—	47	2	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	47	4	no	—
270	C₂×C₄²	—	188	2	no	—
271	C₂×C₄²	—	188	2	no	—
272	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
273	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
274	C₄⋊C₈	—	47	4	no	—
275	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
276	C₂²⋊C₈	—	47	8	no	—
277	C₂²⋊C₈	—	47	8	no	—
278	#97	—	188	2	no	—
279	C₄×C₈	—	4	2	no	—
280	C₄×C₈	—	47	4	no	—
281	C₄×C₈	—	188	2	no	—
282	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
283	#95	—	47	4	no	—
284	#95	C₄×D₄₇	1	2	yes	—
285	C₂⁴	—	47	2	no	—
286	C₂×D₄	—	47	4	no	—
287	C₂×D₄	—	94	4	no	—
288	C₂²×C₄	—	47	2	no	—
289	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	—	47	4	no	—
291	C₂²×C₄	—	47	4	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	94	8	no	—
294	C₂²×C₄	—	94	2	no	—
295	C₂²×C₄	—	94	2	no	—
296	C₂²×C₄	—	94	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	8	no	—
299	C₂²×C₄	—	188	4	no	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
302	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
304	M₁₆	—	188	8	no	—
305	M₁₆	—	188	8	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	2	2	no	—
308	C₂×C₈	—	2	2	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	1	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	2	no	—
319	C₂×C₈	—	94	1	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
322	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
323	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	—
324	C₄⋊C₄	—	47	4	no	—
325	C₄⋊C₄	#10625324	1	8	yes	complemented
326	C₂²⋊C₄	—	47	8	no	—
327	C₂²⋊C₄	—	94	8	no	—
328	C₄²	—	2	2	no	—
329	C₄²	—	2	2	no	—
330	C₄²	—	94	4	no	—
331	C₄²	—	94	4	no	—
332	C₄²	—	94	1	no	—
333	C₄²	—	94	1	no	—
334	C₄²	—	94	1	no	—
335	C₄²	—	94	1	no	—
336	C₄²	—	188	4	no	—
337	C₄²	C₂×C₄×D₄₇	1	2	yes	—
338	C₄²	C₂×C₄×D₄₇	1	2	yes	—
339	C₂³	—	47	4	no	—
340	C₂³	—	94	2	no	—
341	C₂³	—	94	2	no	—
342	C₂³	—	94	4	no	—
343	C₂³	—	94	4	no	—
344	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
345	D₄	—	94	8	no	—
346	C₂×C₄	—	2	4	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	47	4	no	—
350	C₂×C₄	—	47	4	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	—	94	4	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	—	188	16	no	—
363	C₂×C₄	C₄²×D₄₇	1	2	yes	—
364	C₂×C₄	C₄²×D₄₇	1	2	yes	—
365	C₂×C₄	C₂×#10625324	1	8	yes	—
366	C₂×C₄	C₂×#10625324	1	4	yes	—
367	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	#13094069	1	1	yes	characteristic
370	C₂×C₄	#13094070	1	1	yes	characteristic
371	C₂×C₄	#13094070	1	1	yes	characteristic
372	C₂×C₄	#13094072	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	2	no	—
375	C₈	—	2	2	no	—
376	C₈	—	94	2	no	—
377	C₈	—	94	4	no	—
378	C₈	—	94	2	no	—
379	C₂²	—	94	4	no	—
380	C₂²	—	94	4	no	—
381	C₂²	—	94	4	no	—
382	C₂²	—	188	4	no	—
383	C₂²	—	188	4	no	—
384	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
385	C₂²	#15689595	1	1	yes	characteristic
386	C₂²	#15689605	1	1	yes	characteristic
387	C₂²	C₂²×#10625324	1	2	yes	—
388	C₂²	#131×D₄₇	1	2	yes	—
389	C₄	—	2	8	no	—
390	C₄	—	2	2	no	—
391	C₄	—	94	4	no	—
392	C₄	—	94	4	no	—
393	C₄	—	188	2	no	—
394	C₄	C₄×#10625324	1	4	yes	—
395	C₄	#15689595	1	1	yes	characteristic
396	C₄	#15689597	1	1	yes	characteristic
397	C₄	#15689604	1	1	yes	characteristic
398	C₄	#15689605	1	1	yes	characteristic
399	C₂	—	188	4	no	—
400	C₂	#20245748	1	1	yes	characteristic
401	C₂	C₂×C₄×#10625324	1	1	yes	characteristic
402	C₂	#20251810	1	1	yes	characteristic
403	C₂	#20252421	1	2	yes	—
404	C₂	#20252519	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₈×C₄⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₄₇
hypocenter	C₄₇	#20567
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₄⋊C₄×C₄₇⋊C₈	C₂	semidirect
5. #20243243	C₂	semidirect
6. #20243171	C₂	semidirect
7. #20243168	C₂	semidirect
8. C₄×(C₂×D₄₇)⋊C₈	C₂	semidirect
9. #20243133	C₂	semidirect
10. #20243080	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
17. #15689202	C₄	semidirect
18. #15689200	C₄	semidirect
47. C₂×#10625324	C₂×C₄	semidirect
48. C₂×#10625324	C₂×C₄	semidirect
65. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
66. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
67. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
70. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
78. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
80. C₄×C₈×C₄₇	C₂×C₄	semidirect
110. C₄⋊C₄×C₄₇	M₁₆	semidirect
201. C₈×C₄⋊C₄	D₄₇	semidirect
242. C₄₇	#20567	semidirect
275. C₄⋊C₈	C₄×D₄₇	semidirect
282. C₄×C₈	C₄×D₄₇	semidirect
325. C₄⋊C₄	#10625324	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×#15689200	2
C₄×#13093986	2
C₄⋊C₄×C₄₇⋊C₈	2
#20243243	2
#20243171	2
#20243168	2
C₄×(C₂×D₄₇)⋊C₈	2
#20243133	2
#20243080	2
C₈×C₄⋊C₄×C₄₇	2
#20567	47