Subgroups — #26230221

Order 12032.

814 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20244325	C₂	1	2	yes	maximal, complemented
2	#20244107	C₂	1	2	yes	maximal, complemented
3	#20243947	C₂	1	2	yes	maximal, complemented
4	#20243947	C₂	1	2	yes	maximal, complemented
5	#20243568	C₂	1	2	yes	maximal
6	#20243368	C₂	1	1	yes	maximal, characteristic
7	C₂²⋊C₄×C₄₇⋊C₈	C₂	1	2	yes	maximal
8	C₂×#15688878	C₂	1	1	yes	maximal, characteristic
9	C₄×C₂²⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
11	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
19	#15688878	C₂²	1	2	yes	—
20	#15688878	C₂²	1	2	yes	—
21	#15688878	C₂²	1	2	yes	—
22	#15688878	C₂²	1	2	yes	—
23	#15688878	C₂²	1	2	yes	—
24	#15688878	C₂²	1	2	yes	—
25	#15688878	C₂²	1	2	yes	—
26	C₂×C₂²⋊Q₈×C₄₇	C₄	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
29	C₄₇×#391	C₄	1	1	yes	characteristic
30	C₄₇×#389	C₄	1	1	yes	characteristic
31	C₄₇×#387	C₄	1	2	yes	—
32	C₄₇×#385	C₄	1	2	yes	—
33	C₄₇×#380	C₄	1	1	yes	characteristic
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
36	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
37	C₂²×C₄₇⋊C₈	—	2	2	no	—
38	C₂²×C₄₇⋊C₈	—	4	1	no	—
39	C₂²×C₄₇⋊C₈	—	4	1	no	—
40	C₂²×C₄₇⋊C₈	—	4	1	no	—
41	C₂²×C₄₇⋊C₈	—	4	1	no	—
42	C₂²×C₄₇⋊C₈	Q₈	1	4	yes	complemented
43	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
48	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
49	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
51	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
52	C₄×C₄₇⋊C₈	—	4	2	no	—
53	C₄×C₄₇⋊C₈	—	4	2	no	—
54	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²⋊Q₈×C₄₇	C₈	1	8	yes	complemented
59	C₄×Q₈×C₄₇	—	4	1	no	—
60	C₄×Q₈×C₄₇	—	4	1	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄²×C₄₇	—	4	1	no	—
70	C₂×C₄²×C₄₇	—	4	1	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	#95×C₄₇	C₂×C₄	1	2	yes	—
78	#95×C₄₇	C₂×C₄	1	2	yes	—
79	#95×C₄₇	C₂×C₄	1	2	yes	—
80	#95×C₄₇	C₂×C₄	1	2	yes	—
81	#95×C₄₇	C₂×C₄	1	2	yes	—
82	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂×Q₈×C₄₇	—	4	1	no	—
84	C₂×Q₈×C₄₇	—	4	1	no	—
85	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	4	1	no	—
92	C₂²×C₄×C₄₇	—	4	1	no	—
93	C₂²×C₄×C₄₇	—	4	1	no	—
94	C₂²×C₄×C₄₇	—	4	1	no	—
95	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
106	C₂²×C₄×C₄₇	#41	1	2	yes	—
107	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
108	C₄⋊C₄×C₄₇	—	4	1	no	—
109	C₄⋊C₄×C₄₇	—	4	2	no	—
110	C₄⋊C₄×C₄₇	—	4	1	no	—
111	C₄⋊C₄×C₄₇	—	4	2	no	—
112	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
113	C₄⋊C₄×C₄₇	C₂×C₈	1	8	yes	complemented
114	C₂²⋊C₄×C₄₇	—	2	4	no	—
115	C₂²⋊C₄×C₄₇	C₂×C₈	1	8	yes	—
116	C₄²×C₄₇	—	2	1	no	—
117	C₄²×C₄₇	—	2	1	no	—
118	C₄²×C₄₇	—	2	1	no	—
119	C₄²×C₄₇	—	2	1	no	—
120	C₄²×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	4	1	no	—
125	C₄²×C₄₇	—	4	1	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	—	2	2	no	—
133	C₂×C₄₇⋊C₈	—	2	2	no	—
134	C₂×C₄₇⋊C₈	—	2	2	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	2	no	—
137	C₂×C₄₇⋊C₈	—	4	4	no	—
138	C₂×C₄₇⋊C₈	—	4	4	no	—
139	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	—	2	1	no	—
143	C₂³×C₄₇	—	2	1	no	—
144	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
145	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
146	C₂³×C₄₇	#131	1	2	yes	—
147	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₄₇	—	4	4	no	—
149	C₂×C₄×C₄₇	—	2	1	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	4	4	no	—
177	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
179	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
180	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
181	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
182	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
185	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
186	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
187	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
188	C₄₇⋊C₈	—	2	4	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₄₇⋊C₈	—	4	2	no	—
191	C₄₇⋊C₈	—	4	2	no	—
192	#22287	—	47	1	no	maximal, Sylow
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	2	2	no	—
196	C₂²×C₄₇	—	2	2	no	—
197	C₂²×C₄₇	—	2	2	no	—
198	C₂²×C₄₇	—	2	2	no	—
199	C₂²×C₄₇	C₈×Q₈	1	4	yes	—
200	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
201	C₂²×C₄₇	#518	1	1	yes	characteristic
202	C₂²×C₄₇	#520	1	1	yes	characteristic
203	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
205	C₂²×C₄₇	#568	1	1	yes	characteristic
206	C₂²×C₄₇	#568	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	2	2	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	—	4	1	no	—
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	#538	1	1	yes	characteristic
217	C₄×C₄₇	#539	1	1	yes	characteristic
218	C₄×C₄₇	#543	1	1	yes	characteristic
219	C₄×C₄₇	#544	1	1	yes	characteristic
220	C₄×C₂²⋊Q₈	D₄₇	1	1	yes	characteristic
221	#1984	—	47	2	no	—
222	#1939	—	47	2	no	—
223	#1916	—	47	2	no	—
224	#1916	—	47	2	no	—
225	#1850	—	47	2	no	—
226	#1797	—	47	1	no	—
227	C₈×C₂²⋊C₄	—	47	2	no	—
228	C₂×#336	—	47	1	no	—
229	C₂×C₄₇	—	2	4	no	—
230	C₂×C₄₇	#2329	1	1	yes	characteristic
231	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
232	C₂×C₄₇	#2961	1	1	yes	characteristic
233	C₂×C₄₇	#2972	1	1	yes	characteristic
234	C₂×C₄₇	#2976	1	1	yes	characteristic
235	C₂×C₄₇	#2988	1	1	yes	characteristic
236	C₂×C₄₇	#2992	1	1	yes	characteristic
237	C₂³×C₈	—	47	1	no	—
238	C₂³×C₈	—	47	1	no	—
239	C₂×C₂²⋊Q₈	Dic₄₇	1	1	yes	characteristic
240	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
242	C₂×C₄⋊C₈	—	47	1	no	—
243	C₂×C₄⋊C₈	—	47	1	no	—
244	C₂×C₄⋊C₈	—	47	2	no	—
245	C₂×C₄⋊C₈	—	47	2	no	—
246	C₂×C₂²⋊C₈	—	47	2	no	—
247	C₂×C₄×C₈	—	47	2	no	—
248	C₂×C₄×C₈	—	47	2	no	—
249	#391	Dic₄₇	1	1	yes	characteristic
250	#389	Dic₄₇	1	1	yes	characteristic
251	#387	Dic₄₇	1	2	yes	—
252	#385	Dic₄₇	1	2	yes	—
253	#380	Dic₄₇	1	1	yes	characteristic
254	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
255	C₄×C₄⋊C₄	C₂×D₄₇	1	2	yes	—
256	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
257	#336	—	47	2	no	—
258	#336	—	47	2	no	—
259	#336	—	47	2	no	—
260	#336	—	47	2	no	—
261	#336	—	47	2	no	—
262	#336	—	47	2	no	—
263	#336	—	47	2	no	—
264	C₄₇	#22287	1	1	yes	characteristic, complemented, Sylow
265	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
266	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
267	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
268	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
269	C₂²×C₈	—	47	2	no	—
270	C₂²×C₈	—	47	4	no	—
271	C₂²×C₈	—	47	2	no	—
272	C₂²×C₈	—	47	2	no	—
273	C₂²×C₈	—	47	2	no	—
274	C₂²×C₈	—	94	2	no	—
275	C₂²×C₈	—	188	1	no	—
276	C₂²×C₈	—	188	1	no	—
277	C₂²×C₈	—	188	1	no	—
278	C₂²×C₈	—	188	1	no	—
279	C₂²⋊Q₈	C₄₇⋊C₈	1	8	yes	complemented
280	C₄×Q₈	—	4	1	no	—
281	C₄×Q₈	—	4	1	no	—
282	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
287	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
288	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
289	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
290	C₂×C₄²	—	4	1	no	—
291	C₂×C₄²	—	4	1	no	—
292	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
293	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
296	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
297	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
298	C₄⋊C₈	—	188	1	no	—
299	C₄⋊C₈	—	188	1	no	—
300	C₄⋊C₈	—	188	2	no	—
301	C₄⋊C₈	—	188	2	no	—
302	C₂²⋊C₈	—	94	4	no	—
303	C₄×C₈	—	188	2	no	—
304	C₄×C₈	—	188	2	no	—
305	#95	C₂×Dic₄₇	1	2	yes	—
306	#95	C₂×Dic₄₇	1	2	yes	—
307	#95	C₂×Dic₄₇	1	2	yes	—
308	#95	C₂×Dic₄₇	1	2	yes	—
309	#95	C₂×Dic₄₇	1	2	yes	—
310	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
311	C₂×Q₈	—	4	1	no	—
312	C₂×Q₈	—	4	1	no	—
313	C₂×Q₈	C₂×C₄₇⋊C₈	1	4	yes	complemented
314	C₂²×C₄	—	2	1	no	—
315	C₂²×C₄	—	2	1	no	—
316	C₂²×C₄	—	2	1	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	4	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	4	1	no	—
322	C₂²×C₄	—	4	1	no	—
323	C₂²×C₄	C₂×C₄₇⋊C₈	1	4	yes	—
324	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
325	C₂²×C₄	#10625354	1	2	yes	—
326	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
327	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
328	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
329	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
330	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
331	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
332	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
333	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
334	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
335	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
336	C₂×C₈	—	47	4	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	2	no	—
339	C₂×C₈	—	94	2	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	2	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	2	no	—
348	C₂×C₈	—	188	4	no	—
349	C₂×C₈	—	188	4	no	—
350	C₄⋊C₄	—	4	1	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	1	no	—
353	C₄⋊C₄	—	4	2	no	—
354	C₄⋊C₄	C₂×C₄₇⋊C₈	1	4	yes	complemented
355	C₄⋊C₄	C₂×C₄₇⋊C₈	1	8	yes	complemented
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	C₂×C₄₇⋊C₈	1	8	yes	—
358	C₄²	—	2	2	no	—
359	C₄²	—	2	1	no	—
360	C₄²	—	2	1	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	1	no	—
363	C₄²	—	2	1	no	—
364	C₄²	—	2	2	no	—
365	C₄²	—	2	2	no	—
366	C₄²	—	4	1	no	—
367	C₄²	—	4	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	Q₈×Dic₄₇	1	2	yes	—
373	C₂³	C₂²×C₄₇⋊C₈	1	2	yes	—
374	C₂³	#13094031	1	2	yes	—
375	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
376	Q₈	—	4	4	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	4	4	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
406	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
407	C₂×C₄	C₂²×C₄₇⋊C₈	1	4	yes	—
408	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
409	C₂×C₄	C₂²×C₄₇⋊C₈	1	2	yes	—
410	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
412	C₂×C₄	#13094069	1	1	yes	characteristic
413	C₂×C₄	#13094069	1	1	yes	characteristic
414	C₂×C₄	#13094070	1	1	yes	characteristic
415	C₂×C₄	#13094071	1	1	yes	characteristic
416	C₈	—	94	4	no	—
417	C₈	—	188	2	no	—
418	C₈	—	188	2	no	—
419	C₈	—	188	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	—	2	2	no	—
423	C₂²	—	2	2	no	—
424	C₂²	—	2	2	no	—
425	C₂²	—	2	2	no	—
426	C₂²	Q₈×C₄₇⋊C₈	1	4	yes	—
427	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
428	C₂²	#15689598	1	1	yes	characteristic
429	C₂²	#15689606	1	1	yes	characteristic
430	C₂²	C₂³×C₄₇⋊C₈	1	1	yes	characteristic
431	C₂²	C₂×#13094031	1	1	yes	characteristic
432	C₂²	#15689890	1	1	yes	characteristic
433	C₂²	#15689890	1	1	yes	characteristic
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	1	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	2	no	—
443	C₄	#15689713	1	1	yes	characteristic
444	C₄	#15689722	1	1	yes	characteristic
445	C₄	#15689748	1	1	yes	characteristic
446	C₄	#15689752	1	1	yes	characteristic
447	C₂	—	2	4	no	—
448	C₂	#20246123	1	1	yes	characteristic
449	C₂	C₂×Q₈×C₄₇⋊C₈	1	1	yes	characteristic
450	C₂	#20252329	1	1	yes	characteristic
451	C₂	#20252412	1	1	yes	characteristic
452	C₂	#20252436	1	1	yes	characteristic
453	C₂	#20252499	1	1	yes	characteristic
454	C₂	#20252527	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄×C₂²⋊Q₈×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₄×C₂²⋊Q₈	D₄₇
hypocenter	C₄₇	#22287
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₄×C₂²⋊Q₈

Complements

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

N	H ≅ G/N	type
1. #20244325	C₂	semidirect
2. #20244107	C₂	semidirect
3. #20243947	C₂	semidirect
4. #20243947	C₂	semidirect
42. C₂²×C₄₇⋊C₈	Q₈	semidirect
58. C₂²⋊Q₈×C₄₇	C₈	semidirect
85. C₂×Q₈×C₄₇	C₂×C₈	semidirect
112. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
113. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
264. C₄₇	#22287	semidirect
279. C₂²⋊Q₈	C₄₇⋊C₈	semidirect
313. C₂×Q₈	C₂×C₄₇⋊C₈	semidirect
354. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect
355. C₄⋊C₄	C₂×C₄₇⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
#20244325	2
#20244107	2
#20243947	2
#20243568	2
#20243368	2
C₂²⋊C₄×C₄₇⋊C₈	2
C₂×#15688878	2
C₄×C₂²⋊Q₈×C₄₇	2
#22287	47