Finite Group Databasebeta

← C2×#20242867 #26198779

Subgroups — C2×#20242867 #26198779

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689500C211yesmaximal, characteristic, complemented
2C2×#15689318C212yesmaximal, complemented
3#20242867C218yesmaximal, direct product factor
4C2×#15688874C211yesmaximal, characteristic, complemented
5C2×#15688866C212yesmaximal, complemented
6C2×C47×#436C211yesmaximal, characteristic, complemented
7C22×D376—21no—
8C22×D376—21no—
9C22×#10625334—22no—
10C2×#13094021C2212yes—
11#15689500—22no—
12#15689500C2214yescomplemented
13#15689318—24no—
14#15689318C2218yescomplemented
15C2×C4⋊(C47⋊C8)C2212yes—
16C2×#13093944—22no—
17#15688874C2214yescomplemented
18#15688866C2218yescomplemented
19C22×M16×C47—21no—
20C2×C4×D4×C47C2211yescharacteristic
21C47×#436—22no—
22C47×#436C2214yescomplemented
23C2×C4⋊C8×C47C2211yescharacteristic
24C2×C22⋊C8×C47—21no—
25C2×C4×C8×C47C2211yescharacteristic
26C22×D188—22no—
27C22×D188—22no—
28C22×D188—22no—
29C2×D376—24no—
30C2×D376—24no—
31C2×D376—44no—
32C2×D376—44no—
33C2×#10625334—28no—
34C2×#10625334—48no—
35C22×C47⋊C8—22no—
36#13094021—22no—
37#13094021—22no—
38#13094021—22no—
39#13094021C2314yes—
40C4⋊(C47⋊C8)—22no—
41C4⋊(C47⋊C8)C2314yes—
42#13093944—28no—
43C22×D4×C47D411yescharacteristic
44C23×C4×C47—21no—
45C2×M16×C47—24no—
46C2×M16×C47—44no—
47C22×C8×C47—21no—
48C22×C8×C47D411yescharacteristic
49C22×C8×C47D411yescharacteristic
50C4×D4×C47—21no—
51C4×D4×C47—21no—
52C4×D4×C47D412yes—
53C4×D4×C47C2312yes—
54C2×C4⋊C4×C47D411yescharacteristic
55C2×C22⋊C4×C47—21no—
56C2×C42×C47C2311yescharacteristic
57C4⋊C8×C47—21no—
58C4⋊C8×C47C2312yes—
59C22⋊C8×C47—24no—
60C4×C8×C47D412yes—
61C4×C8×C47C2312yes—
62C24×C47—21no—
63C23×D47—42no—
64C2×D4×C47—21no—
65C2×D4×C47—24no—
66C2×D4×C47C2×D412yes—
67C22×C4×C47—21no—
68C22×C4×C47—22no—
69C22×C4×C47—22no—
70C22×C4×C47—42no—
71C22×C4×C47—42no—
72C22×C4×C47C2×D411yescharacteristic
73C22×C4×C47C2×D411yescharacteristic
74C22×C4×C47#4111yescharacteristic
75C2×D188—24no—
76C2×D188—24no—
77C2×D188—24no—
78C2×D188—44no—
79C2×D188—44no—
80C2×D188—44no—
81C2×D188—44no—
82C2×D188—42no—
83C2×D188—42no—
84C2×D188—42no—
85C2×D188—84no—
86M16×C47—48no—
87C2×C8×C47—22no—
88C2×C8×C47—22no—
89C2×C8×C47—42no—
90C2×C8×C47D814yescomplemented
91C2×C8×C47C2×D412yes—
92C2×C8×C47C2×D412yes—
93C4⋊C4×C47—21no—
94C4⋊C4×C47C2×D412yes—
95C22⋊C4×C47—22no—
96C22⋊C4×C47—22no—
97C42×C47C2×D411yescharacteristic
98C42×C47C2×D411yescharacteristic
99C42×C47#4111yescharacteristic
100C42×C47C2411yescharacteristic
101#10625334—416no—
102C2×C47⋊C8—24no—
103C2×C47⋊C8—44no—
104D376—48no—
105D376—48no—
106C23×C47—22no—
107C23×C47—42no—
108C23×C47—42no—
109C23×C47—42no—
110C23×C47#12111yescharacteristic
111C22×D47—44no—
112C22×D47—84no—
113C22×D47—84no—
114C22×D47—84no—
115D4×C47—24no—
116D4×C47—42no—
117C2×C4×C47—22no—
118C2×C4×C47—22no—
119C2×C4×C47—42no—
120C2×C4×C47—42no—
121C2×C4×C47—42no—
122C2×C4×C47—44no—
123C2×C4×C47#12111yescharacteristic
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47C2×D812yes—
127C2×C4×C47AGL(1,ℤ/8)12yes—
128C2×C4×C47AGL(1,ℤ/8)14yes—
129C2×C4×C47C22×D411yescharacteristic
130C2×C4×C47C22×D411yescharacteristic
131C2×C4×C47C2×#4111yescharacteristic
132D188—44no—
133D188—44no—
134D188—44no—
135D188—44no—
136D188—84no—
137D188—84no—
138D188—84no—
139D188—84no—
140C8×C47—22no—
141C8×C47—42no—
142C8×C47C2×D814yescomplemented
143C47⋊C8—44no—
144C2×#1687—471nomaximal, Sylow
145C22×C47—42no—
146C22×C47—42no—
147C22×C47—42no—
148C22×C47—84no—
149C22×C47#45912yes—
150C22×C47#46912yes—
151C22×C47#47212yes—
152C22×C47C2×#12111yescharacteristic
153C2×D47—84no—
154C2×D47—84no—
155C2×D47—84no—
156C2×D47—168no—
157C4×C47—21no—
158C4×C47—21no—
159C4×C47—42no—
160C4×C47#45912yes—
161C4×C47#46912yes—
162C4×C47C22×D811yescharacteristic
163C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
164C4×C47C2×AGL(1,ℤ/8)12yes—
165C2×#493—471no—
166C2×#459—472no—
167C2×#436D4711yescharacteristic, complemented
168#1687—478no—
169C2×#334—471no—
170C2×#331—472no—
171C2×C47—82no—
172C2×C47#168714yescomplemented
173C2×C47C2×#45911yescharacteristic
174C2×C47C2×#46911yescharacteristic
175C2×C47C2×#47211yescharacteristic
176D47—164no—
177C22×D8—942no—
178C22×D8—941no—
179C22×D8—941no—
180C22×M16—21no—
181C2×#127—472no—
182C2×C4×D4C2×D4711yescharacteristic
183#493—474no—
184#493—942no—
185#459—478no—
186#459—944no—
187#436—22no—
188#436C2×D4714yescomplemented
189C2×C4⋊C8—472no—
190C2×C4⋊C8C2×D4711yescharacteristic
191C2×#102—942no—
192C2×C22⋊C8—21no—
193C2×C4×C8C2×D4711yescharacteristic
194#334—474no—
195#331—478no—
196C47C2×#168711yescharacteristic, complemented, Sylow
197C22×D4—942no—
198C22×D4—942no—
199C22×D4—942no—
200C22×D4D18811yescharacteristic
201C23×C4—21no—
202C2×D8—948no—
203C2×D8—944no—
204C2×D8—944no—
205C2×D8—1884no—
206C2×D8—1888no—
207C2×D8—1884no—
208C2×M16—24no—
209C2×M16—44no—
210C22×C8—21no—
211C22×C8—942no—
212C22×C8C22⋊D4711yescharacteristic
213C22×C8C22⋊D4711yescharacteristic
214#127—474no—
215#127—942no—
216#127—942no—
217#127—942no—
218C4×D4—21no—
219C4×D4—21no—
220C4×D4D18812yes—
221C4×D4C22×D4712yes—
222C2×C4⋊C4D18811yescharacteristic
223C2×C22⋊C4—21no—
224C2×C42C22×D4711yescharacteristic
225C4⋊C8—21no—
226C4⋊C8—474no—
227C4⋊C8—942no—
228C4⋊C8C22×D4712yes—
229#102—948no—
230C22⋊C8—24no—
231C4×C8C22⋊D4712yes—
232C4×C8C22×D4712yes—
233C24—21no—
234C24—1882no—
235C2×D4—21no—
236C2×D4—24no—
237C2×D4—944no—
238C2×D4—944no—
239C2×D4—944no—
240C2×D4—3764no—
241C2×D4—1882no—
242C2×D4—1882no—
243C2×D4—1882no—
244C2×D4—1884no—
245C2×D4—1884no—
246C2×D4—1884no—
247C2×D4—1884no—
248C2×D4C2×D18812yes—
249C22×C4—21no—
250C22×C4—22no—
251C22×C4—22no—
252C22×C4—42no—
253C22×C4—42no—
254C22×C4C2×D18811yescharacteristic
255C22×C4#1062535011yescharacteristic
256C22×C4C2×C22⋊D4711yescharacteristic
257D8—1888no—
258D8—18816no—
259D8—1888no—
260M16—48no—
261C2×C8—22no—
262C2×C8—22no—
263C2×C8—42no—
264C2×C8—944no—
265C2×C8—1884no—
266C2×C8#1062533414yescomplemented
267C2×C8C2×C22⋊D4712yes—
268C2×C8C2×C22⋊D4712yes—
269C4⋊C4—21no—
270C4⋊C4C2×D18812yes—
271C22⋊C4—22no—
272C22⋊C4—22no—
273C42C2×D18811yescharacteristic
274C42#1062535011yescharacteristic
275C42C2×C22⋊D4711yescharacteristic
276C42C23×D4711yescharacteristic
277C23—22no—
278C23—42no—
279C23—42no—
280C23—42no—
281C23—3764no—
282C23—3764no—
283C23—3764no—
284C23—1884no—
285C23#1309399811yescharacteristic
286D4—24no—
287D4—42no—
288D4—3764no—
289D4—3764no—
290D4—3764no—
291D4—3764no—
292D4—1884no—
293D4—1884no—
294D4—1884no—
295D4—1884no—
296C2×C4—22no—
297C2×C4—22no—
298C2×C4—42no—
299C2×C4—44no—
300C2×C4—42no—
301C2×C4—42no—
302C2×C4#1309399811yescharacteristic
303C2×C4#1309399811yescharacteristic
304C2×C4#1309399811yescharacteristic
305C2×C4C2×#1062533412yes—
306C2×C4#1309404912yes—
307C2×C4#1309405214yes—
308C2×C4C22×C22⋊D4711yescharacteristic
309C2×C4C22×D18811yescharacteristic
310C2×C4C2×#1062535011yescharacteristic
311C8—22no—
312C8—42no—
313C8—1884no—
314C8C2×#1062533414yescomplemented
315C22—42no—
316C22—42no—
317C22—42no—
318C22—84no—
319C22—3764no—
320C22—3764no—
321C22—3764no—
322C22—7528no—
323C22#1568931812yes—
324C22#1568937612yes—
325C22#1568939312yes—
326C22C2×#1309399811yescharacteristic
327C4—21no—
328C4—21no—
329C4—42no—
330C4#1568931812yes—
331C4#1568937612yes—
332C4C22×#1062533411yescharacteristic
333C4C2×#1309404911yescharacteristic
334C4C2×#1309405212yes—
335C2—82no—
336C2—7524no—
337C2#2024286714yesdirect product factor
338C2C2×#1568931811yescharacteristic
339C2C2×#1568937611yescharacteristic
340C2C2×#1568939311yescharacteristic
subgroupG/H
centerC23#13093998
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#436C2
socleC23×C47#121
hypercenterC2×#436D47
hypocenterC47C2×#1687
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
1. C2×#15689500C2semidirect
2. C2×#15689318C2semidirect
3. #20242867C2direct (N × H)
4. C2×#15688874C2semidirect
5. C2×#15688866C2semidirect
6. C2×C47×#436C2semidirect
12. #15689500C22semidirect
14. #15689318C22semidirect
17. #15688874C22semidirect
18. #15688866C22semidirect
22. C47×#436C22semidirect
90. C2×C8×C47D8semidirect
142. C8×C47C2×D8semidirect
167. C2×#436D47semidirect
172. C2×C47#1687semidirect
188. #436C2×D47semidirect
196. C47C2×#1687semidirect
266. C2×C8#10625334semidirect
314. C8C2×#10625334semidirect
337. C2#20242867direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156895002
C2×#156893182
#202428672
C2×#156888742
C2×#156888662
C2×C47×#4362
C2×#168747