Subgroups — #26184893

Order 12032.

1276 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252021	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689147	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242110	C₂	1	4	yes	maximal, complemented
4	#20242073	C₂	1	2	yes	maximal, complemented
5	#20242065	C₂	1	4	yes	maximal, complemented
6	#20242056	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#532	C₂	1	1	yes	maximal, characteristic
8	C₂²×#10625329	—	2	1	no	—
9	#15689180	—	2	1	no	—
10	#15689180	C₂²	1	2	yes	complemented
11	#15689176	—	2	1	no	—
12	#15689176	C₂²	1	2	yes	—
13	#15689147	—	2	1	no	—
14	#15689147	—	2	1	no	—
15	#15689147	C₂²	1	2	yes	—
16	#15689147	C₂²	1	2	yes	complemented
17	#15689147	C₂²	1	2	yes	complemented
18	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
20	#15689087	—	2	1	no	—
21	C₄×#10625329	—	2	1	no	—
22	#15688869	C₂²	1	8	yes	complemented
23	#15688867	C₂²	1	8	yes	complemented
24	C₂²×#41×C₄₇	—	2	1	no	—
25	C₄₇×#532	—	2	1	no	—
26	C₄₇×#532	—	2	1	no	—
27	C₄₇×#532	—	2	1	no	—
28	C₄₇×#532	—	2	1	no	—
29	C₄₇×#532	C₄	1	2	yes	—
30	C₄₇×#532	C₄	1	2	yes	—
31	C₄₇×#532	C₂²	1	2	yes	—
32	C₄₇×#532	C₂²	1	2	yes	—
33	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#124×C₄₇	—	2	1	no	—
36	C₂×#121×C₄₇	—	2	1	no	—
37	C₂×#121×C₄₇	C₄	1	2	yes	—
38	C₂×C₄×D₄×C₄₇	—	2	1	no	—
39	C₂×C₄×D₄×C₄₇	C₄	1	2	yes	—
40	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#10625329	—	2	2	no	—
42	C₂×#10625329	—	2	2	no	—
43	C₂×#10625329	—	2	2	no	—
44	C₂×#10625329	—	4	4	no	—
45	C₂²×C₄₇⋊C₈	—	2	2	no	—
46	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
47	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
48	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
50	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
51	C₄⋊(C₄₇⋊C₈)	C₂³	1	4	yes	—
52	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
53	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
54	#13093935	—	2	2	no	—
55	C₄×C₄₇⋊C₈	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	2	no	—
57	C₂×#41×C₄₇	—	2	2	no	—
58	C₂×#41×C₄₇	—	2	2	no	—
59	C₂×#41×C₄₇	—	2	2	no	—
60	C₂×#41×C₄₇	—	4	8	no	—
61	C₂²×Q₈×C₄₇	—	2	1	no	—
62	C₂²×D₄×C₄₇	—	2	2	no	—
63	C₂²×D₄×C₄₇	—	2	1	no	—
64	C₂²×D₄×C₄₇	—	2	1	no	—
65	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₂³×C₄×C₄₇	—	2	2	no	—
67	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
69	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₄⋊Q₈×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
73	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
74	#127×C₄₇	—	2	1	no	—
75	#127×C₄₇	—	2	1	no	—
76	#127×C₄₇	C₂×C₄	1	2	yes	—
77	#127×C₄₇	C₂³	1	2	yes	—
78	#124×C₄₇	—	2	2	no	—
79	#124×C₄₇	—	2	2	no	—
80	#124×C₄₇	—	2	2	no	—
81	#124×C₄₇	—	2	2	no	—
82	#121×C₄₇	—	2	2	no	—
83	#121×C₄₇	—	2	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	2	no	—
86	#121×C₄₇	—	2	2	no	—
87	#121×C₄₇	—	2	2	no	—
88	#121×C₄₇	C₂×C₄	1	4	yes	—
89	#121×C₄₇	C₂×C₄	1	4	yes	—
90	C₄×D₄×C₄₇	—	2	2	no	—
91	C₄×D₄×C₄₇	—	2	2	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₄×D₄×C₄₇	—	2	2	no	—
95	C₄×D₄×C₄₇	—	2	2	no	—
96	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
97	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
98	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
99	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
100	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
101	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
102	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
106	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
107	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
108	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
110	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
111	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	C₂⁴×C₄₇	—	2	2	no	—
115	C₂⁴×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	#41×C₄₇	—	4	8	no	—
117	#41×C₄₇	—	4	8	no	—
118	#41×C₄₇	—	4	8	no	—
119	#41×C₄₇	—	4	8	no	—
120	C₂×Q₈×C₄₇	—	2	2	no	—
121	C₂×Q₈×C₄₇	—	2	2	no	—
122	C₂×Q₈×C₄₇	—	4	4	no	—
123	C₂×D₄×C₄₇	—	2	4	no	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	4	4	no	—
131	C₂×D₄×C₄₇	—	4	4	no	—
132	C₂×D₄×C₄₇	—	4	8	no	—
133	C₂×D₄×C₄₇	—	4	2	no	—
134	C₂×D₄×C₄₇	—	4	2	no	—
135	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
136	C₂²×C₄×C₄₇	—	2	4	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	4	2	no	—
143	C₂²×C₄×C₄₇	—	4	8	no	—
144	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
160	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
166	C₂²⋊C₄×C₄₇	—	2	4	no	—
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₂²⋊C₄×C₄₇	—	2	4	no	—
169	C₂²⋊C₄×C₄₇	—	2	4	no	—
170	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
171	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
172	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
173	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
175	C₄²×C₄₇	C₂²⋊C₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
180	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
181	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
182	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
183	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
184	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
185	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
186	#10625329	—	4	4	no	—
187	#10625329	—	4	4	no	—
188	#10625329	—	4	4	no	—
189	C₂×C₄₇⋊C₈	—	2	4	no	—
190	C₂×C₄₇⋊C₈	—	2	4	no	—
191	C₂×C₄₇⋊C₈	—	4	4	no	—
192	C₂³×C₄₇	—	2	2	no	—
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	4	1	no	—
196	C₂³×C₄₇	—	4	4	no	—
197	C₂³×C₄₇	—	4	4	no	—
198	C₂³×C₄₇	—	4	4	no	—
199	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
200	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
201	C₂³×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
202	Q₈×C₄₇	—	4	4	no	—
203	Q₈×C₄₇	—	4	4	no	—
204	D₄×C₄₇	—	4	4	no	—
205	D₄×C₄₇	—	4	4	no	—
206	D₄×C₄₇	—	4	8	no	—
207	D₄×C₄₇	—	4	8	no	—
208	D₄×C₄₇	—	4	2	no	—
209	D₄×C₄₇	—	4	4	no	—
210	D₄×C₄₇	—	4	2	no	—
211	D₄×C₄₇	—	4	4	no	—
212	D₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	4	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	8	no	—
233	C₂×C₄×C₄₇	—	4	4	no	—
234	C₂×C₄×C₄₇	—	4	8	no	—
235	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
245	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
246	C₂×C₄×C₄₇	#137	1	2	yes	—
247	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₄₇⋊C₈	—	4	4	no	—
251	C₄₇⋊C₈	—	4	4	no	—
252	#17745	—	47	1	no	maximal, Sylow
253	C₂²×C₄₇	—	2	1	no	—
254	C₂²×C₄₇	—	2	1	no	—
255	C₂²×C₄₇	—	2	1	no	—
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	—	2	1	no	—
260	C₂²×C₄₇	—	4	4	no	—
261	C₂²×C₄₇	—	4	4	no	—
262	C₂²×C₄₇	—	4	4	no	—
263	C₂²×C₄₇	—	4	4	no	—
264	C₂²×C₄₇	—	8	8	no	—
265	C₂²×C₄₇	#417	1	2	yes	—
266	C₂²×C₄₇	#418	1	2	yes	—
267	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
268	C₄×C₄₇	—	2	1	no	—
269	C₄×C₄₇	—	2	1	no	—
270	C₄×C₄₇	—	2	1	no	—
271	C₄×C₄₇	—	2	1	no	—
272	C₄×C₄₇	—	2	1	no	—
273	C₄×C₄₇	—	2	1	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	4	4	no	—
276	C₄×C₄₇	#413	1	2	yes	—
277	C₄×C₄₇	#417	1	2	yes	—
278	C₄×C₄₇	#418	1	2	yes	—
279	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
280	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
281	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
282	C₂×#532	D₄₇	1	1	yes	characteristic
283	#2920	—	47	1	no	—
284	C₂×#423	—	47	1	no	—
285	#1557	—	47	4	no	—
286	#1549	—	47	2	no	—
287	#1547	—	47	4	no	—
288	#1545	—	47	2	no	—
289	C₂×C₄₇	—	2	2	no	—
290	C₂×C₄₇	—	2	2	no	—
291	C₂×C₄₇	—	4	1	no	—
292	C₂×C₄₇	—	8	4	no	—
293	C₂×C₄₇	C₂×#413	1	1	yes	characteristic
294	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
295	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
296	C₂²×#41	—	2	1	no	—
297	C₂²×M₁₆	—	94	1	no	—
298	#532	—	2	1	no	—
299	#532	—	2	1	no	—
300	#532	—	2	1	no	—
301	#532	—	2	1	no	—
302	#532	Dic₄₇	1	2	yes	—
303	#532	Dic₄₇	1	2	yes	—
304	#532	C₂×D₄₇	1	2	yes	—
305	#532	C₂×D₄₇	1	2	yes	—
306	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
307	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
308	C₂×#124	—	2	1	no	—
309	C₂×#121	—	2	1	no	—
310	C₂×#121	Dic₄₇	1	2	yes	—
311	C₂×C₄×D₄	—	2	1	no	—
312	C₂×C₄×D₄	Dic₄₇	1	2	yes	—
313	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
314	#432	—	47	2	no	—
315	#432	—	94	1	no	—
316	#431	—	47	2	no	—
317	#431	—	94	1	no	—
318	#423	—	47	2	no	—
319	#423	—	47	2	no	—
320	#423	—	47	2	no	—
321	#423	—	94	1	no	—
322	#423	—	94	1	no	—
323	C₂×C₄⋊C₈	—	47	2	no	—
324	C₂×C₄⋊C₈	—	94	1	no	—
325	#407	—	94	1	no	—
326	C₄×M₁₆	—	94	1	no	—
327	#332	—	47	8	no	—
328	#331	—	47	8	no	—
329	C₄₇	#17745	1	1	yes	characteristic, complemented, Sylow
330	C₂×#41	—	2	2	no	—
331	C₂×#41	—	2	2	no	—
332	C₂×#41	—	2	2	no	—
333	C₂×#41	—	2	2	no	—
334	C₂×#41	—	4	8	no	—
335	C₂²×Q₈	—	2	1	no	—
336	C₂²×D₄	—	2	2	no	—
337	C₂²×D₄	—	2	1	no	—
338	C₂²×D₄	—	2	1	no	—
339	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
340	C₂³×C₄	—	2	2	no	—
341	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
342	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
344	C₂×M₁₆	—	94	2	no	—
345	C₂×M₁₆	—	94	2	no	—
346	C₂×M₁₆	—	94	2	no	—
347	C₂×M₁₆	—	188	4	no	—
348	C₂²×C₈	—	94	2	no	—
349	C₄⋊Q₈	—	2	1	no	—
350	C₄⋊Q₈	—	2	1	no	—
351	C₄⋊Q₈	C₂×Dic₄₇	1	2	yes	—
352	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
353	#127	—	2	1	no	—
354	#127	—	2	1	no	—
355	#127	C₂×Dic₄₇	1	2	yes	—
356	#127	C₂²×D₄₇	1	2	yes	—
357	#124	—	2	2	no	—
358	#124	—	2	2	no	—
359	#124	—	2	2	no	—
360	#124	—	2	2	no	—
361	#121	—	2	2	no	—
362	#121	—	2	2	no	—
363	#121	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	2	no	—
366	#121	—	2	2	no	—
367	#121	C₂×Dic₄₇	1	4	yes	—
368	#121	C₂×Dic₄₇	1	4	yes	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	2	no	—
372	C₄×D₄	—	2	2	no	—
373	C₄×D₄	—	2	2	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
376	C₄×D₄	C₂×Dic₄₇	1	4	yes	—
377	C₂×C₄⋊C₄	—	2	1	no	—
378	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
379	C₂×C₂²⋊C₄	—	2	2	no	—
380	C₂×C₂²⋊C₄	—	2	2	no	—
381	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
382	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
383	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
384	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
385	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
386	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
387	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
388	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
389	C₂×C₄²	C₂²⋊D₄₇	1	1	yes	characteristic
390	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
391	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
393	C₄⋊C₈	—	47	4	no	—
394	C₄⋊C₈	—	47	4	no	—
395	C₄⋊C₈	—	94	2	no	—
396	C₄⋊C₈	—	94	2	no	—
397	C₄⋊C₈	—	94	2	no	—
398	C₄⋊C₈	—	94	2	no	—
399	C₂²⋊C₈	—	94	2	no	—
400	C₂²⋊C₈	—	94	2	no	—
401	#97	—	94	2	no	—
402	C₄×C₈	—	94	2	no	—
403	C₂⁴	—	2	2	no	—
404	C₂⁴	C₂²⋊Dic₄₇	1	1	yes	characteristic
405	#41	—	4	8	no	—
406	#41	—	4	8	no	—
407	#41	—	4	8	no	—
408	#41	—	4	8	no	—
409	C₂×Q₈	—	2	2	no	—
410	C₂×Q₈	—	2	2	no	—
411	C₂×Q₈	—	4	4	no	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	4	no	—
414	C₂×D₄	—	2	2	no	—
415	C₂×D₄	—	2	2	no	—
416	C₂×D₄	—	2	2	no	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	4	4	no	—
420	C₂×D₄	—	4	4	no	—
421	C₂×D₄	—	4	8	no	—
422	C₂×D₄	—	4	2	no	—
423	C₂×D₄	—	4	2	no	—
424	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	4	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	4	no	—
430	C₂²×C₄	—	2	4	no	—
431	C₂²×C₄	—	4	2	no	—
432	C₂²×C₄	—	4	8	no	—
433	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
434	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
435	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
436	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
437	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
438	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
439	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
440	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
441	C₂²×C₄	C₂²⋊Dic₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
446	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
449	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
450	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
451	M₁₆	—	188	4	no	—
452	M₁₆	—	188	4	no	—
453	M₁₆	—	188	4	no	—
454	C₂×C₈	—	94	4	no	—
455	C₂×C₈	—	94	4	no	—
456	C₂×C₈	—	188	4	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	2	no	—
460	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
461	C₂²⋊C₄	—	2	4	no	—
462	C₂²⋊C₄	—	2	4	no	—
463	C₂²⋊C₄	—	2	4	no	—
464	C₂²⋊C₄	—	2	4	no	—
465	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
466	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
467	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
468	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
469	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
470	C₄²	C₂²⋊Dic₄₇	1	1	yes	characteristic
471	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
472	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
473	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
474	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
475	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
476	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
477	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
478	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
479	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
480	C₄²	C₂³×D₄₇	1	1	yes	characteristic
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	4	no	—
484	C₂³	—	4	1	no	—
485	C₂³	—	4	4	no	—
486	C₂³	—	4	4	no	—
487	C₂³	—	4	4	no	—
488	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
489	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
490	C₂³	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
491	Q₈	—	4	4	no	—
492	Q₈	—	4	4	no	—
493	D₄	—	4	4	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	8	no	—
496	D₄	—	4	8	no	—
497	D₄	—	4	4	no	—
498	D₄	—	4	4	no	—
499	D₄	—	4	2	no	—
500	D₄	—	4	4	no	—
501	D₄	—	4	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	4	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	1	no	—
520	C₂×C₄	—	4	1	no	—
521	C₂×C₄	—	4	8	no	—
522	C₂×C₄	—	4	4	no	—
523	C₂×C₄	—	4	8	no	—
524	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
525	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
526	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
527	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
528	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
529	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
530	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
531	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
532	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
533	C₂×C₄	#13094049	1	2	yes	—
534	C₂×C₄	#13094050	1	4	yes	—
535	C₂×C₄	#13094054	1	2	yes	—
536	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
539	C₈	—	188	4	no	—
540	C₈	—	188	4	no	—
541	C₂²	—	2	1	no	—
542	C₂²	—	2	1	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	4	4	no	—
549	C₂²	—	4	4	no	—
550	C₂²	—	4	4	no	—
551	C₂²	—	4	4	no	—
552	C₂²	—	8	8	no	—
553	C₂²	#15689124	1	2	yes	—
554	C₂²	#15689128	1	2	yes	—
555	C₂²	C₂²×C₂²⋊Dic₄₇	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	2	1	no	—
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	4	no	—
564	C₄	#15689107	1	2	yes	—
565	C₄	#15689124	1	2	yes	—
566	C₄	#15689128	1	2	yes	—
567	C₄	C₂×#13094049	1	1	yes	characteristic
568	C₄	C₂×#13094050	1	2	yes	—
569	C₄	C₂×#13094054	1	1	yes	characteristic
570	C₂	—	2	2	no	—
571	C₂	—	2	2	no	—
572	C₂	—	4	1	no	—
573	C₂	—	8	4	no	—
574	C₂	C₂×#15689107	1	1	yes	characteristic
575	C₂	C₂×#15689128	1	1	yes	characteristic
576	C₂	C₂×#15689124	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₂²⋊Dic₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#532	C₂
socle	C₂²×C₄₇	C₂²×C₂²⋊C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×#532	D₄₇
hypocenter	C₄₇	#17745
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄² ◁ C₂×#532

Complements

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

N	H ≅ G/N	type
1. #20252021	C₂	semidirect
2. C₂×#15689147	C₂	semidirect
3. #20242110	C₂	semidirect
4. #20242073	C₂	semidirect
5. #20242065	C₂	semidirect
6. #20242056	C₂	semidirect
10. #15689180	C₂²	semidirect
16. #15689147	C₂²	semidirect
17. #15689147	C₂²	semidirect
19. C₂×C₄⋊(C₄₇⋊C₈)	C₂²	semidirect
22. #15688869	C₂²	semidirect
23. #15688867	C₂²	semidirect
329. C₄₇	#17745	semidirect

Maximal subgroups

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

subgroup	index
#20252021	2
C₂×#15689147	2
#20242110	2
#20242073	2
#20242065	2
#20242056	2
C₂×C₄₇×#532	2
#17745	47