Finite Group Databasebeta

← #99×C47⋊C8 #26106821

Subgroups — #99×C47⋊C8 #26106821

Order 12032.

614 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D4×C47⋊C8C211yesmaximal, characteristic
2C22⋊C4×C47⋊C8C212yesmaximal, complemented
3#20241706C211yesmaximal, characteristic
4#20241236C212yesmaximal, complemented
5C4×#99×C47C211yesmaximal, characteristic
6C23×C47⋊C8C411yescharacteristic, complemented
7C23×C47⋊C8C2211yescharacteristic
8D4×C47⋊C8—22no—
9D4×C47⋊C8—22no—
10C2×C4⋊(C47⋊C8)C411yescharacteristic, complemented
11C2×C22⋊(C47⋊C8)C411yescharacteristic, complemented
12C2×C22⋊(C47⋊C8)C2211yescharacteristic
13C2×C22⋊(C47⋊C8)C2212yes—
14C2×C4×C47⋊C8—22no—
15C2×C4×C47⋊C8C411yescharacteristic, complemented
16#15688878—22no—
17#15688849C412yescomplemented
18#15688847C412yescomplemented
19C2×C4×D4×C47C2211yescharacteristic
20C2×#99×C47C412yes—
21C4×C22⋊C4×C47C2212yes—
22C47×#342C412yes—
23C22×C47⋊C8—22no—
24C22×C47⋊C8—21no—
25C22×C47⋊C8—21no—
26C22×C47⋊C8—42no—
27C22×C47⋊C8—42no—
28C22×C47⋊C8C2×C411yescharacteristic
29C22×C47⋊C8C2×C411yescharacteristic
30C22×C47⋊C8C2×C411yescharacteristic
31C22×C47⋊C8C2×C411yescharacteristic
32C22×C47⋊C8D412yes—
33C22×C47⋊C8D412yes—
34C4⋊(C47⋊C8)—22no—
35C22⋊(C47⋊C8)—22no—
36C22⋊(C47⋊C8)—22no—
37C22⋊(C47⋊C8)—22no—
38C22⋊(C47⋊C8)C2×C414yes—
39C4×C47⋊C8—21no—
40C4×C47⋊C8—21no—
41C4×C47⋊C8—44no—
42C22×D4×C47C2×C411yescharacteristic
43C23×C4×C47C2×C411yescharacteristic
44C23×C4×C47C2311yescharacteristic
45C4×D4×C47—22no—
46C4×D4×C47—22no—
47C2×C4⋊C4×C47C2×C411yescharacteristic
48C2×C22⋊C4×C47C2×C411yescharacteristic
49C2×C22⋊C4×C47C2×C411yescharacteristic
50C2×C22⋊C4×C47C2×C414yes—
51C2×C42×C47—22no—
52C2×C42×C47C2×C411yescharacteristic
53#99×C47C818yescomplemented
54#95×C47—22no—
55C24×C47C4211yescharacteristic
56C24×C47C22×C411yescharacteristic
57C2×D4×C47—22no—
58C2×D4×C47—22no—
59C2×D4×C47C2×C814yes—
60C22×C4×C47—24no—
61C22×C4×C47—21no—
62C22×C4×C47—21no—
63C22×C4×C47—41no—
64C22×C4×C47—41no—
65C22×C4×C47—41no—
66C22×C4×C47—41no—
67C22×C4×C47C4211yescharacteristic
68C22×C4×C47C4211yescharacteristic
69C22×C4×C47C4211yescharacteristic
70C22×C4×C47C22×C411yescharacteristic
71C22×C4×C47C22×C411yescharacteristic
72C22×C4×C47C2×D412yes—
73C22×C4×C47#4112yes—
74C4⋊C4×C47—22no—
75C22⋊C4×C47—22no—
76C22⋊C4×C47—24no—
77C22⋊C4×C47—22no—
78C22⋊C4×C47C2×C818yescomplemented
79C42×C47—21no—
80C42×C47—21no—
81C42×C47—42no—
82C42×C47—42no—
83C2×C47⋊C8—24no—
84C2×C47⋊C8—22no—
85C2×C47⋊C8—21no—
86C2×C47⋊C8—21no—
87C2×C47⋊C8—24no—
88C2×C47⋊C8—41no—
89C2×C47⋊C8—42no—
90C2×C47⋊C8—42no—
91C2×C47⋊C8—42no—
92C2×C47⋊C8—42no—
93C2×C47⋊C8—42no—
94C2×C47⋊C8—41no—
95C2×C47⋊C8—41no—
96C2×C47⋊C8C22⋊C411yescharacteristic
97C2×C47⋊C8C22⋊C412yes—
98C2×C47⋊C8C22⋊C411yescharacteristic
99C23×C47—21no—
100C23×C47—21no—
101C23×C47—41no—
102C23×C47—41no—
103C23×C47—41no—
104C23×C47—41no—
105C23×C47C4×C812yescomplemented
106C23×C47C2×C4211yescharacteristic
107C23×C47C4×D412yes—
108C23×C47C22×C812yes—
109C23×C47#13112yes—
110D4×C47—28no—
111C2×C4×C47—21no—
112C2×C4×C47—21no—
113C2×C4×C47—22no—
114C2×C4×C47—21no—
115C2×C4×C47—22no—
116C2×C4×C47—21no—
117C2×C4×C47—21no—
118C2×C4×C47—21no—
119C2×C4×C47—28no—
120C2×C4×C47—41no—
121C2×C4×C47—42no—
122C2×C4×C47—42no—
123C2×C4×C47—44no—
124C2×C4×C47—44no—
125C2×C4×C47—41no—
126C2×C4×C47—41no—
127C2×C4×C47—41no—
128C2×C4×C47—41no—
129C2×C4×C47C4×C812yescomplemented
130C2×C4×C47C2×C22⋊C411yescharacteristic
131C2×C4×C47#11711yescharacteristic
132C2×C4×C47C4×D412yes—
133C47⋊C8—21no—
134C47⋊C8—22no—
135C47⋊C8—44no—
136C47⋊C8—41no—
137C47⋊C8—41no—
138C47⋊C8#9912yesdirect product factor
139C8×#99—471nomaximal, Sylow
140C22×C47—22no—
141C22×C47—21no—
142C22×C47—22no—
143C22×C47—21no—
144C22×C47—22no—
145C22×C47—42no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47—42no—
149C22×C47—41no—
150C22×C47—41no—
151C22×C47C4×C22⋊C411yescharacteristic
152C22×C47C2×C4×C811yescharacteristic
153C22×C47#40511yescharacteristic
154C22×C47C8×D414yes—
155C4×C47—22no—
156C4×C47—22no—
157C4×C47—21no—
158C4×C47—48no—
159C4×C47—41no—
160C4×C47—41no—
161C4×C47C2×#9911yescharacteristic
162C4×C47#41011yescharacteristic
163C2×C8×D4—471no—
164C4×#99D4711yescharacteristic
165C8×C22⋊C4—472no—
166#1459—471no—
167#1282—472no—
168C2×C47—24no—
169C2×C47—21no—
170C2×C47—21no—
171C2×C47—42no—
172C2×C47C8×C22⋊C411yescharacteristic
173C2×C47C4×#9911yescharacteristic
174C2×C47#175711yescharacteristic
175C23×C8—471no—
176C23×C8—471no—
177C2×C4×D4C2×D4711yescharacteristic
178C8×D4—942no—
179C8×D4—942no—
180C2×C4⋊C8—471no—
181C2×#99Dic4712yes—
182C2×C22⋊C8—472no—
183C2×C22⋊C8—471no—
184C2×C22⋊C8—471no—
185C2×C4×C8—471no—
186C2×C4×C8—942no—
187C4×C22⋊C4C2×D4712yes—
188#342Dic4712yes—
189#336—942no—
190#324—472no—
191#323—472no—
192C47C8×#9911yescharacteristic, complemented, Sylow
193C22×D4C2×Dic4711yescharacteristic
194C23×C4C4×D4711yescharacteristic
195C23×C4C22×D4711yescharacteristic
196C22×C8—471no—
197C22×C8—472no—
198C22×C8—471no—
199C22×C8—472no—
200C22×C8—471no—
201C22×C8—471no—
202C22×C8—941no—
203C22×C8—941no—
204C22×C8—942no—
205C22×C8—1882no—
206C22×C8—1882no—
207C4×D4—22no—
208C4×D4—22no—
209C2×C4⋊C4C4×D4711yescharacteristic
210C2×C22⋊C4C4×D4711yescharacteristic
211C2×C22⋊C4C2×Dic4711yescharacteristic
212C2×C22⋊C4C2×Dic4714yes—
213C2×C42—22no—
214C2×C42C4×D4711yescharacteristic
215C4⋊C8—942no—
216#99C47⋊C818yesdirect product factor
217C22⋊C8—474no—
218C22⋊C8—942no—
219C22⋊C8—942no—
220C22⋊C8—942no—
221C4×C8—941no—
222C4×C8—941no—
223C4×C8—1884no—
224#95—22no—
225C24C4×Dic4711yescharacteristic
226C24C22×Dic4711yescharacteristic
227C2×D4—22no—
228C2×D4—22no—
229C2×D4C2×C47⋊C814yes—
230C22×C4—24no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—41no—
234C22×C4—41no—
235C22×C4—41no—
236C22×C4—41no—
237C22×C4C4×Dic4711yescharacteristic
238C22×C4C4×Dic4711yescharacteristic
239C22×C4C4×Dic4711yescharacteristic
240C22×C4C2×C4×D4711yescharacteristic
241C22×C4C2×C4×D4711yescharacteristic
242C22×C4D4×D4712yes—
243C22×C4#1062535212yes—
244C2×C8—471no—
245C2×C8—471no—
246C2×C8—472no—
247C2×C8—944no—
248C2×C8—942no—
249C2×C8—941no—
250C2×C8—941no—
251C2×C8—944no—
252C2×C8—1882no—
253C2×C8—1881no—
254C2×C8—1882no—
255C2×C8—1882no—
256C2×C8—1882no—
257C2×C8—1882no—
258C2×C8—1881no—
259C2×C8—1881no—
260C4⋊C4—22no—
261C22⋊C4—22no—
262C22⋊C4—24no—
263C22⋊C4—22no—
264C22⋊C4C2×C47⋊C818yescomplemented
265C42—21no—
266C42—21no—
267C42—42no—
268C42—42no—
269C23—21no—
270C23—21no—
271C23—41no—
272C23—41no—
273C23—41no—
274C23—41no—
275C23C4×C47⋊C812yescomplemented
276C23C2×C4×Dic4711yescharacteristic
277C23D4×Dic4712yes—
278C23C22×C47⋊C812yes—
279C23#1309403112yes—
280D4—28no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—22no—
284C2×C4—21no—
285C2×C4—22no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—28no—
290C2×C4—41no—
291C2×C4—42no—
292C2×C4—42no—
293C2×C4—44no—
294C2×C4—44no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4C4×C47⋊C812yescomplemented
300C2×C4C22⋊C4×D4711yescharacteristic
301C2×C4#1309398011yescharacteristic
302C2×C4(C22⋊D47)⋊C412yes—
303C8—472no—
304C8—942no—
305C8—941no—
306C8—1884no—
307C8—1881no—
308C8—1881no—
309C22—22no—
310C22—21no—
311C22—22no—
312C22—21no—
313C22—22no—
314C22—42no—
315C22—42no—
316C22—42no—
317C22—42no—
318C22—41no—
319C22—41no—
320C22C22⋊C4×Dic4711yescharacteristic
321C22C2×C4×C47⋊C811yescharacteristic
322C22#1568907911yescharacteristic
323C22D4×C47⋊C814yes—
324C4—22no—
325C4—22no—
326C4—21no—
327C4—48no—
328C4—41no—
329C4—41no—
330C4#99×D4711yescharacteristic
331C4#1568909511yescharacteristic
332C2—24no—
333C2—21no—
334C2—21no—
335C2—42no—
336C2C22⋊C4×C47⋊C811yescharacteristic
337C2#99×Dic4711yescharacteristic
338C2#2024319011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D47
commutatorC22×C47C2×C4×C8
FrattiniC23×C4C22×D47
FittingC4×#99×C47C2
socleC22×C47C4×C22⋊C4
prime radicalC22×D4×C47C2×C4
cosocleC23×C4×C47C23
hypercenterC4×#99D47
hypocenterC47C8×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
2. C22⋊C4×C47⋊C8C2semidirect
4. #20241236C2semidirect
6. C23×C47⋊C8C4semidirect
10. C2×C4⋊(C47⋊C8)C4semidirect
11. C2×C22⋊(C47⋊C8)C4semidirect
15. C2×C4×C47⋊C8C4semidirect
17. #15688849C4semidirect
18. #15688847C4semidirect
53. #99×C47C8semidirect
78. C22⋊C4×C47C2×C8semidirect
105. C23×C47C4×C8semidirect
129. C2×C4×C47C4×C8semidirect
138. C47⋊C8#99direct (N × H)
192. C47C8×#99semidirect
216. #99C47⋊C8direct (N × H)
264. C22⋊C4C2×C47⋊C8semidirect
275. C23C4×C47⋊C8semidirect
299. C2×C4C4×C47⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×D4×C47⋊C82
C22⋊C4×C47⋊C82
#202417062
#202412362
C4×#99×C472
C8×#9947