Finite Group Databasebeta

← C2×#20244829 #26245169

Subgroups — C2×#20244829 #26245169

Order 12032.

950 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689122C212yesmaximal
2C2×#15689089C211yesmaximal, characteristic
3#20244829C218yesmaximal, direct product factor
4C2×#15688892C212yesmaximal, complemented
5C2×#15688888C211yesmaximal, characteristic, complemented
6C22×#107×C47C211yesmaximal, characteristic, complemented
7C22×#10625350C2211yescharacteristic
8C22×#10625329C2212yes—
9C22×#10625329C2211yescharacteristic
10#15689122—24no—
11#15689122C2218yes—
12C2×#13093947—22no—
13C2×#13093944—22no—
14#15689089—22no—
15#15689089C2214yes—
16C2×(C2×D47)⋊C8—22no—
17#15688892C2218yescomplemented
18#15688888C2214yescomplemented
19C23×C8×C47C2211yescharacteristic
20C22×C4⋊C4×C47C2212yes—
21C2×#107×C47—22no—
22C2×#107×C47—22no—
23C2×#107×C47C2214yescomplemented
24C2×#10625350—21no—
25C2×#10625350—21no—
26C2×#10625350—24no—
27C2×#10625350—24no—
28C2×#10625350D412yes—
29C2×#10625350C2312yes—
30C22×Dic94D411yescharacteristic
31C22×D188D411yescharacteristic
32C22×C22⋊D47—21no—
33C22×C4×D47—21no—
34C2×#10625329—21no—
35C2×#10625329—22no—
36C2×#10625329—24no—
37C2×#10625329—24no—
38C2×#10625329—24no—
39C2×#10625329C2312yes—
40C2×#10625329C2314yes—
41C22×C47⋊C8—21no—
42C22×C47⋊C8—22no—
43#13093947—28no—
44#13093944—28no—
45(C2×D47)⋊C8—28no—
46C23×C4×C47—22no—
47C23×C4×C47C2311yescharacteristic
48C22×C8×C47—24no—
49C22×C8×C47D412yes—
50C22×C8×C47D412yes—
51C22×C8×C47C2312yes—
52C2×C4⋊C4×C47—22no—
53C2×C4⋊C4×C47—22no—
54C2×C4⋊C4×C47—22no—
55C2×C4⋊C4×C47—22no—
56C2×C4⋊C4×C47—22no—
57C2×C4⋊C4×C47C2314yes—
58#107×C47—28no—
59C24×C47#4111yescharacteristic
60C23×D47—21no—
61C22×C4×C47—24no—
62C22×C4×C47—42no—
63C22×C4×C47—42no—
64C22×C4×C47—84no—
65C22×C4×C47C2×D411yescharacteristic
66C22×C4×C47C2×D411yescharacteristic
67C22×C4×C47C2×D411yescharacteristic
68C22×C4×C47C2×D411yescharacteristic
69C22×C4×C47#4111yescharacteristic
70C22×C4×C47#4114yes—
71C22×C4×C47#4114yes—
72C22×C4×C47C2411yescharacteristic
73C2×C22⋊D47—22no—
74C2×C22⋊D47—22no—
75C2×C22⋊D47—44no—
76C22×Dic47—21no—
77#10625350—28no—
78#10625350—24no—
79#10625350—24no—
80#10625350—42no—
81#10625350—42no—
82#10625350—44no—
83C2×D188—24no—
84C2×D188—21no—
85C2×D188C2×D412yes—
86C2×C4×D47—22no—
87C2×C4×D47—22no—
88C2×C4×D47—42no—
89C2×C4×D47—42no—
90C2×Dic94—24no—
91C2×Dic94—21no—
92C2×Dic94C2×D412yes—
93C2×C8×C47—24no—
94C2×C8×C47—24no—
95C2×C8×C47—24no—
96C2×C8×C47C2×D414yes—
97C4⋊C4×C47—24no—
98C4⋊C4×C47—24no—
99C4⋊C4×C47—42no—
100C4⋊C4×C47—42no—
101#10625329—24no—
102#10625329—24no—
103#10625329—24no—
104#10625329—44no—
105#10625329—42no—
106C2×C47⋊C8—22no—
107C2×C47⋊C8—24no—
108C2×C47⋊C8—44no—
109C2×C47⋊C8—42no—
110C23×C47—22no—
111C23×C47—22no—
112C23×C47#12111yescharacteristic
113C23×C47#12111yescharacteristic
114C23×C47#12614yes—
115C23×C47C2×#4111yescharacteristic
116C22×D47—22no—
117C22×D47—42no—
118C22×D47—42no—
119C22×D47—42no—
120C2×C4×C47—44no—
121C2×C4×C47—84no—
122C2×C4×C47—84no—
123C2×C4×C47—84no—
124C2×C4×C47#12111yescharacteristic
125C2×C4×C47#12111yescharacteristic
126C2×C4×C47#12312yes—
127C2×C4×C47#12312yes—
128C2×C4×C47#12314yes—
129C2×C4×C47#12314yes—
130C2×C4×C47#12412yes—
131C2×C4×C47#12412yes—
132C2×C4×C47#12614yes—
133C2×C4×C47C22×D411yescharacteristic
134C2×C4×C47C22×D411yescharacteristic
135C2×C4×C47C2×#4112yes—
136C2×C4×C47C2×#4112yes—
137C22⋊D47—44no—
138C22⋊D47—44no—
139C2×Dic47—22no—
140C2×Dic47—42no—
141D188—24no—
142D188—42no—
143C4×D47—42no—
144C4×D47—42no—
145C4×D47—44no—
146Dic94—24no—
147Dic94—42no—
148C8×C47—24no—
149C47⋊C8—44no—
150C47⋊C8—42no—
151C2×#2078—471nomaximal, Sylow
152C22×C47—28no—
153C22×C47—21no—
154C22×C47—21no—
155C22×C47—21no—
156C22×C47—21no—
157C22×C47#39712yes—
158C22×C47#39712yes—
159C22×C47#47212yes—
160C22×C47#47312yes—
161C22×C47C2×#12111yescharacteristic
162C22×C47C2×#12612yes—
163C2×D47—42no—
164C2×D47—42no—
165C2×D47—42no—
166C2×D47—84no—
167C4×C47—84no—
168C4×C47#39712yes—
169C4×C47#39712yes—
170C4×C47C2×#12311yescharacteristic
171C4×C47C2×#12312yes—
172C4×C47C2×#12411yescharacteristic
173Dic47—42no—
174C22×#107D4711yescharacteristic, complemented
175C2×#417—472no—
176C2×#408—471no—
177#2078—478no—
178C2×#343—472no—
179C2×#341—471no—
180C2×C47—22no—
181C2×C47—22no—
182C2×C47#207814yescomplemented
183C2×C47C2×#39711yescharacteristic
184C2×C47C2×#47211yescharacteristic
185C2×C47C2×#47311yescharacteristic
186D47—82no—
187C22×#41—471no—
188C22×M16—471no—
189C22×M16—472no—
190C23×C8C2×D4711yescharacteristic
191C22×C4⋊C4C2×D4712yes—
192C2×#107—22no—
193C2×#107—22no—
194C2×#107C2×D4714yescomplemented
195#417—478no—
196#417—944no—
197C2×#103—942no—
198C2×#102—942no—
199#408—474no—
200#408—942no—
201C2×C22⋊C8—942no—
202#343—478no—
203#341—474no—
204C47C2×#207811yescharacteristic, complemented, Sylow
205C2×#41—472no—
206C2×#41—472no—
207C2×#41—941no—
208C2×#41—941no—
209C2×#41—944no—
210C2×#41—944no—
211C22×Q8—471no—
212C22×D4—471no—
213C22×D4—941no—
214C23×C4—22no—
215C23×C4—941no—
216C23×C4C22×D4711yescharacteristic
217C2×M16—474no—
218C2×M16—472no—
219C2×M16—942no—
220C2×M16—941no—
221C2×M16—944no—
222C2×M16—944no—
223C2×M16—944no—
224C22×C8—24no—
225C22×C8—942no—
226C22×C8—941no—
227C22×C8C22⋊D4712yes—
228C22×C8C22⋊D4712yes—
229C22×C8C22×D4712yes—
230C2×C4⋊C4—22no—
231C2×C4⋊C4—22no—
232C2×C4⋊C4—22no—
233C2×C4⋊C4—22no—
234C2×C4⋊C4—22no—
235C2×C4⋊C4C22×D4714yes—
236#107—28no—
237#103—948no—
238#102—948no—
239C22⋊C8—948no—
240C24—941no—
241C24#1062535211yescharacteristic
242#41—948no—
243#41—944no—
244#41—944no—
245#41—1882no—
246#41—1882no—
247#41—1884no—
248C2×Q8—472no—
249C2×Q8—941no—
250C2×Q8—944no—
251C2×D4—472no—
252C2×D4—942no—
253C2×D4—942no—
254C2×D4—941no—
255C2×D4—944no—
256C2×D4—1884no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—84no—
261C22×C4—941no—
262C22×C4—942no—
263C22×C4—942no—
264C22×C4—1882no—
265C22×C4—1882no—
266C22×C4#1062535014yes—
267C22×C4D4×D4711yescharacteristic
268C22×C4D4×D4711yescharacteristic
269C22×C4#1062535211yescharacteristic
270C22×C4#1062535414yes—
271C22×C4C2×C22⋊D4711yescharacteristic
272C22×C4C2×C22⋊D4711yescharacteristic
273C22×C4C23×D4711yescharacteristic
274M16—944no—
275M16—944no—
276M16—944no—
277M16—1884no—
278M16—1882no—
279C2×C8—24no—
280C2×C8—24no—
281C2×C8—24no—
282C2×C8—944no—
283C2×C8—942no—
284C2×C8—1884no—
285C2×C8—1882no—
286C2×C8C2×C22⋊D4714yes—
287C4⋊C4—24no—
288C4⋊C4—24no—
289C4⋊C4—42no—
290C4⋊C4—42no—
291C23—22no—
292C23—22no—
293C23—942no—
294C23—1882no—
295C23—1882no—
296C23—1882no—
297C23#1309399511yescharacteristic
298C23#1309399511yescharacteristic
299C23#1309401914yes—
300C23C2×#1062535211yescharacteristic
301Q8—944no—
302Q8—1882no—
303D4—944no—
304D4—1884no—
305D4—1884no—
306D4—1882no—
307C2×C4—44no—
308C2×C4—84no—
309C2×C4—84no—
310C2×C4—84no—
311C2×C4—942no—
312C2×C4—1882no—
313C2×C4—1884no—
314C2×C4—1882no—
315C2×C4—1882no—
316C2×C4#1309399511yescharacteristic
317C2×C4#1309399511yescharacteristic
318C2×C4#1309400712yes—
319C2×C4#1309400712yes—
320C2×C4#1309400914yes—
321C2×C4#1309400914yes—
322C2×C4#1309401312yes—
323C2×C4#1309401312yes—
324C2×C4#1309401914yes—
325C2×C4C2×D4×D4711yescharacteristic
326C2×C4C22×C22⋊D4711yescharacteristic
327C2×C4C2×#1062535012yes—
328C2×C4C2×#1062535412yes—
329C8—24no—
330C8—1884no—
331C8—1882no—
332C22—28no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—3764no—
338C22—1882no—
339C22—1882no—
340C22—1882no—
341C22#1568904912yes—
342C22#1568904912yes—
343C22#1568939012yes—
344C22#1568939512yes—
345C22C2×#1309399511yescharacteristic
346C22C2×#1309401912yes—
347C4—84no—
348C4—1882no—
349C4#1568904912yes—
350C4#1568904912yes—
351C4C2×#1309400711yescharacteristic
352C4C2×#1309400912yes—
353C4C2×#1309401311yescharacteristic
354C2—22no—
355C2—22no—
356C2—3762no—
357C2#2024482914yesdirect product factor
358C2C2×#1568904911yescharacteristic
359C2C2×#1568939011yescharacteristic
360C2C2×#1568939511yescharacteristic
subgroupG/H
centerC23#13093995
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC22×#107×C47C2
socleC23×C47#121
prime radicalC22×#10625350C22
hypercenterC22×#107D47
hypocenterC47C2×#2078
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#107

Complements

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

NH ≅ G/Ntype
3. #20244829C2direct (N × H)
4. C2×#15688892C2semidirect
5. C2×#15688888C2semidirect
6. C22×#107×C47C2semidirect
17. #15688892C22semidirect
18. #15688888C22semidirect
23. C2×#107×C47C22semidirect
174. C22×#107D47semidirect
182. C2×C47#2078semidirect
194. C2×#107C2×D47semidirect
204. C47C2×#2078semidirect
357. C2#20244829direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891222
C2×#156890892
#202448292
C2×#156888922
C2×#156888882
C22×#107×C472
C2×#207847