Subgroups — #26232812

Order 12032.

1292 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689254	C₂	1	2	yes	maximal, complemented
2	#20244329	C₂	1	4	yes	maximal, complemented
3	#20244325	C₂	1	2	yes	maximal, complemented
4	#20243368	C₂	1	1	yes	maximal, characteristic
5	#20243368	C₂	1	2	yes	maximal
6	#20243150	C₂	1	2	yes	maximal
7	C₄×C₂²⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
8	C₂²×C₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
9	#15689254	—	2	8	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
11	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	4	yes	—
12	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
15	C₂×#13093935	C₂²	1	4	yes	—
16	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
17	#15688878	C₂²	1	4	yes	—
18	#15688878	C₂²	1	4	yes	—
19	#15688878	C₂²	1	2	yes	—
20	#15688878	C₂²	1	2	yes	—
21	C₂³×Q₈×C₄₇	C₄	1	1	yes	characteristic
22	C₂×C₄×Q₈×C₄₇	—	2	8	no	—
23	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
24	C₂×C₄×Q₈×C₄₇	C₄	1	2	yes	—
25	C₂×C₄×Q₈×C₄₇	C₄	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
28	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄⋊C₄×C₄₇	C₄	1	2	yes	—
30	C₂²×C₄⋊C₄×C₄₇	C₄	1	1	yes	characteristic
31	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
32	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
33	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
34	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
35	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
36	C₄⋊(C₄₇⋊C₈)	—	2	8	no	—
37	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
38	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
39	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
40	C₂²⋊(C₄₇⋊C₈)	Q₈	1	4	yes	complemented
41	#13093935	—	2	8	no	—
42	C₄×C₄₇⋊C₈	—	2	4	no	—
43	C₂²×Q₈×C₄₇	—	2	4	no	—
44	C₂²×Q₈×C₄₇	—	2	4	no	—
45	C₂²×Q₈×C₄₇	—	2	4	no	—
46	C₂²×Q₈×C₄₇	C₂×C₄	1	2	yes	—
47	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₄×Q₈×C₄₇	—	2	4	no	—
55	C₄×Q₈×C₄₇	—	2	8	no	—
56	C₄×Q₈×C₄₇	—	2	4	no	—
57	C₄×Q₈×C₄₇	—	2	4	no	—
58	C₄×Q₈×C₄₇	—	2	8	no	—
59	C₄×Q₈×C₄₇	D₄	1	8	yes	—
60	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
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	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	—	2	4	no	—
70	C₂×C₄²×C₄₇	—	2	8	no	—
71	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
79	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
80	C₂×Q₈×C₄₇	—	2	32	no	—
81	C₂×Q₈×C₄₇	—	2	4	no	—
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	4	no	—
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	2	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂×Q₈×C₄₇	M₁₆	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	4	no	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	4	no	—
101	C₂²×C₄×C₄₇	—	4	1	no	—
102	C₂²×C₄×C₄₇	—	4	2	no	—
103	C₂²×C₄×C₄₇	M₁₆	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
114	C₂²×C₄×C₄₇	#41	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
116	C₄⋊C₄×C₄₇	—	2	4	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	2	4	no	—
120	C₄⋊C₄×C₄₇	—	2	2	no	—
121	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
122	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
123	C₄²×C₄₇	—	2	2	no	—
124	C₄²×C₄₇	—	2	4	no	—
125	C₄²×C₄₇	—	2	4	no	—
126	C₄²×C₄₇	—	2	2	no	—
127	C₄²×C₄₇	—	2	2	no	—
128	C₄²×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	C₂×D₄	1	4	yes	—
130	C₄²×C₄₇	C₂×D₄	1	8	yes	—
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	4	no	—
135	C₂×C₄₇⋊C₈	—	2	2	no	—
136	C₂×C₄₇⋊C₈	—	2	4	no	—
137	C₂×C₄₇⋊C₈	—	2	2	no	—
138	C₂×C₄₇⋊C₈	—	2	4	no	—
139	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
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	C₂×M₁₆	1	2	yes	—
146	C₂³×C₄₇	#131	1	2	yes	—
147	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	Q₈×C₄₇	—	2	16	no	—
149	Q₈×C₄₇	—	2	8	no	—
150	Q₈×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	16	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	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	2	1	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	8	no	—
175	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
176	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
179	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
180	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
181	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
182	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
188	C₄₇⋊C₈	—	2	4	no	—
189	C₄₇⋊C₈	—	4	2	no	—
190	C₄₇⋊C₈	—	4	4	no	—
191	#22510	—	47	1	no	maximal, Sylow
192	C₂²×C₄₇	—	2	2	no	—
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	#446	1	4	yes	complemented
199	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
200	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
201	C₂²×C₄₇	#519	1	1	yes	characteristic
202	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
203	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
205	C₂²×C₄₇	#568	1	1	yes	characteristic
206	C₄×C₄₇	—	2	2	no	—
207	C₄×C₄₇	—	2	4	no	—
208	C₄×C₄₇	—	2	4	no	—
209	C₄×C₄₇	—	2	2	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	#407	1	4	yes	—
215	C₄×C₄₇	#548	1	2	yes	—
216	C₄×C₄₇	D₄×Q₈	1	2	yes	—
217	C₂²×C₄×Q₈	D₄₇	1	1	yes	characteristic
218	C₂×#446	—	47	2	no	—
219	#1985	—	47	4	no	—
220	#1984	—	47	2	no	—
221	#1797	—	47	2	no	—
222	#1797	—	47	1	no	—
223	#1749	—	47	2	no	—
224	C₄×C₂²⋊C₈	—	47	1	no	—
225	C₂×C₄₇	—	2	4	no	—
226	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#407	1	1	yes	characteristic
228	C₂×C₄₇	#2880	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
230	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
231	C₂×C₄₇	#2983	1	1	yes	characteristic
232	C₂×C₄₇	#2984	1	1	yes	characteristic
233	C₂³×Q₈	Dic₄₇	1	1	yes	characteristic
234	C₂×C₄×Q₈	—	2	8	no	—
235	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
236	C₂×C₄×Q₈	Dic₄₇	1	2	yes	—
237	C₂×C₄×Q₈	Dic₄₇	1	1	yes	characteristic
238	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
239	C₂×C₄×Q₈	C₂×D₄₇	1	2	yes	—
240	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
241	C₂²×C₄⋊C₄	Dic₄₇	1	2	yes	—
242	C₂²×C₄⋊C₄	Dic₄₇	1	1	yes	characteristic
243	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
244	C₂²×C₄²	C₂×D₄₇	1	2	yes	—
245	#446	—	94	8	no	—
246	C₂×C₄⋊C₈	—	47	2	no	—
247	C₂×C₄⋊C₈	—	47	4	no	—
248	C₂×C₂²⋊C₈	—	47	1	no	—
249	C₂×C₂²⋊C₈	—	47	1	no	—
250	C₂×C₂²⋊C₈	—	47	2	no	—
251	C₂×#97	—	47	4	no	—
252	C₂×C₄×C₈	—	47	2	no	—
253	#336	—	47	4	no	—
254	#336	—	47	2	no	—
255	#336	—	47	4	no	—
256	#336	—	47	2	no	—
257	C₄₇	#22510	1	1	yes	characteristic, complemented, Sylow
258	C₂²×Q₈	—	2	4	no	—
259	C₂²×Q₈	—	2	4	no	—
260	C₂²×Q₈	—	2	4	no	—
261	C₂²×Q₈	C₂×Dic₄₇	1	2	yes	—
262	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
263	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
264	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
265	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
266	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
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	2	no	—
271	C₂²×C₈	—	47	4	no	—
272	C₄×Q₈	—	2	4	no	—
273	C₄×Q₈	—	2	8	no	—
274	C₄×Q₈	—	2	4	no	—
275	C₄×Q₈	—	2	4	no	—
276	C₄×Q₈	—	2	8	no	—
277	C₄×Q₈	C₂²⋊D₄₇	1	8	yes	—
278	C₂×C₄⋊C₄	—	2	8	no	—
279	C₂×C₄⋊C₄	—	2	4	no	—
280	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
281	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
283	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
286	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
287	C₂×C₄²	—	2	4	no	—
288	C₂×C₄²	—	2	8	no	—
289	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
290	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
291	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
292	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
293	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
294	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
295	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
296	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
297	C₄⋊C₈	—	94	4	no	—
298	C₄⋊C₈	—	94	8	no	—
299	C₂²⋊C₈	—	47	4	no	—
300	C₂²⋊C₈	—	94	2	no	—
301	C₂²⋊C₈	—	94	4	no	—
302	#97	—	94	8	no	—
303	C₄×C₈	—	94	4	no	—
304	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
305	C₂×Q₈	—	2	32	no	—
306	C₂×Q₈	—	2	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	—	2	2	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	2	no	—
313	C₂×Q₈	#10625329	1	4	yes	—
314	C₂×Q₈	C₂²⋊Dic₄₇	1	4	yes	—
315	C₂²×C₄	—	2	4	no	—
316	C₂²×C₄	—	2	4	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	4	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	—	2	2	no	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	4	no	—
326	C₂²×C₄	—	4	1	no	—
327	C₂²×C₄	—	4	2	no	—
328	C₂²×C₄	#10625329	1	4	yes	—
329	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
330	C₂²×C₄	#10625354	1	2	yes	—
331	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
332	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
333	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
334	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
335	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
336	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
337	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
338	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
340	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
341	C₂×C₈	—	47	4	no	—
342	C₂×C₈	—	94	2	no	—
343	C₂×C₈	—	94	2	no	—
344	C₂×C₈	—	94	2	no	—
345	C₂×C₈	—	94	4	no	—
346	C₂×C₈	—	94	2	no	—
347	C₂×C₈	—	94	4	no	—
348	C₂×C₈	—	94	2	no	—
349	C₂×C₈	—	94	4	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	C₂²⋊Dic₄₇	1	8	yes	—
356	C₄⋊C₄	C₂²⋊Dic₄₇	1	4	yes	—
357	C₄²	—	2	2	no	—
358	C₄²	—	2	4	no	—
359	C₄²	—	2	4	no	—
360	C₄²	—	2	2	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₂×C₂²⋊D₄₇	1	4	yes	—
364	C₄²	C₂×C₂²⋊D₄₇	1	8	yes	—
365	C₂³	—	2	1	no	—
366	C₂³	—	2	1	no	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	Q₈×Dic₄₇	1	2	yes	—
370	C₂³	C₂×#10625329	1	2	yes	—
371	C₂³	#13094031	1	2	yes	—
372	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
373	Q₈	—	2	16	no	—
374	Q₈	—	2	8	no	—
375	Q₈	—	2	8	no	—
376	C₂×C₄	—	2	16	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	2	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	4	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	8	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	4	8	no	—
400	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
401	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
402	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	4	yes	—
403	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	2	yes	—
404	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
405	C₂×C₄	C₂×#10625329	1	4	yes	—
406	C₂×C₄	C₂×#10625329	1	2	yes	—
407	C₂×C₄	C₂×#10625329	1	2	yes	—
408	C₂×C₄	C₂×#10625329	1	2	yes	—
409	C₂×C₄	C₂²×C₂²⋊D₄₇	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	#13094072	1	2	yes	—
413	C₈	—	94	4	no	—
414	C₈	—	188	2	no	—
415	C₈	—	188	4	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	2	no	—
422	C₂²	#15689254	1	4	yes	complemented
423	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
424	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
425	C₂²	#15689601	1	1	yes	characteristic
426	C₂²	C₂²×#10625329	1	1	yes	characteristic
427	C₂²	C₂²×#10625329	1	1	yes	characteristic
428	C₂²	C₂×#13094031	1	1	yes	characteristic
429	C₂²	#15689890	1	1	yes	characteristic
430	C₄	—	2	4	no	—
431	C₄	—	2	4	no	—
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	2	no	—
436	C₄	—	4	2	no	—
437	C₄	—	4	1	no	—
438	C₄	#15689087	1	4	yes	—
439	C₄	#15689784	1	2	yes	—
440	C₄	Q₈×C₂²⋊D₄₇	1	2	yes	—
441	C₂	—	2	4	no	—
442	C₂	Q₈×C₂²⋊Dic₄₇	1	1	yes	characteristic
443	C₂	C₂×#15689087	1	1	yes	characteristic
444	C₂	#20251837	1	1	yes	characteristic
445	C₂	C₂×#15689254	1	1	yes	characteristic
446	C₂	Q₈×#10625329	1	1	yes	characteristic
447	C₂	#20252473	1	1	yes	characteristic
448	C₂	#20252477	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂²×C₄×Q₈×C₄₇	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂²×C₄×Q₈	D₄₇
hypocenter	C₄₇	#22510
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄×Q₈

Complements

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

N	H ≅ G/N	type
1. C₂×#15689254	C₂	semidirect
2. #20244329	C₂	semidirect
3. #20244325	C₂	semidirect
40. C₂²⋊(C₄₇⋊C₈)	Q₈	semidirect
139. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
198. C₂²×C₄₇	#446	semidirect
257. C₄₇	#22510	semidirect
422. C₂²	#15689254	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689254	2
#20244329	2
#20244325	2
#20243368	2
#20243150	2
C₄×C₂²⋊(C₄₇⋊C₈)	2
C₂²×C₄×Q₈×C₄₇	2
#22510	47