Finite Group Databasebeta

← C2×#20245604 #26371164

Subgroups — C2×#20245604 #26371164

Order 12032.

604 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689377C211yesmaximal, characteristic
2C2×#15689170C211yesmaximal, characteristic, complemented
3#20245604C218yesmaximal, direct product factor
4C2×#15688945C211yesmaximal, characteristic, complemented
5C2×#15688937C211yesmaximal, characteristic, complemented
6C2×#15688935C211yesmaximal, characteristic, complemented
7C2×#15688904C211yesmaximal, characteristic, complemented
8C2×C47×#365C211yesmaximal, characteristic, complemented
9C22×D376C2211yescharacteristic
10C22×#10625324C2211yescharacteristic
11C2×M16×D47—21no—
12C2×#13093999—21no—
13C2×#13093964C2211yescharacteristic
14#15689377—22no—
15#15689377C2214yes—
16#15689170—22no—
17#15689170C2214yescomplemented
18C2×#13093960C2211yescharacteristic
19C2×#13093959—21no—
20C2×#13093944—21no—
21#15688945C2214yescomplemented
22#15688937C2214yescomplemented
23#15688935C2214yescomplemented
24#15688904C2214yescomplemented
25C2×M32×C47C2211yescharacteristic
26C2×#108×C47C2211yescharacteristic
27C2×#106×C47C2211yescharacteristic
28C47×#365C2214yescomplemented
29C22×D188—21no—
30C22×D188—41no—
31C22×C4×D47D411yescharacteristic
32C2×D376—21no—
33C2×D376—21no—
34C2×D376—21no—
35C2×D376—21no—
36C2×D376—21no—
37C2×D376C2312yes—
38C2×#10625329—21no—
39C2×#10625324—21no—
40C2×#10625324—21no—
41C2×#10625324—21no—
42C2×#10625324—21no—
43C2×#10625324—41no—
44C2×#10625324D412yes—
45C2×#10625324C2312yes—
46M16×D47—24no—
47M16×D47—42no—
48C22×C47⋊C8D411yescharacteristic
49C2×C8×D47—41no—
50#13093999—24no—
51#13093999—42no—
52C2×(C2×D47)⋊C4—41no—
53#13093964—21no—
54#13093964C2312yes—
55C2×C47⋊C16—21no—
56#13093960—21no—
57#13093960C2312yes—
58#13093959—24no—
59#13093944—24no—
60C2×M16×C47—21no—
61C22×C8×C47C2311yescharacteristic
62C2×C4⋊C4×C47—21no—
63M32×C47—21no—
64M32×C47C2312yes—
65C2×C16×C47—21no—
66#108×C47—21no—
67#108×C47C2312yes—
68#106×C47—21no—
69#106×C47C2312yes—
70C23×D47—41no—
71C23×D47SD1611yescharacteristic
72C22×C4×C47—41no—
73C22×C4×C47C2×D411yescharacteristic
74C22×Dic47SD1611yescharacteristic
75C2×D188—22no—
76C2×D188—41no—
77C2×D188—41no—
78C2×D188—41no—
79C2×D188—41no—
80C2×D188—44no—
81C2×D188—41no—
82C2×D188—84no—
83C2×C4×D47—21no—
84C2×C4×D47—21no—
85C2×C4×D47—21no—
86C2×C4×D47—21no—
87C2×C4×D47SD1612yes—
88C2×C4×D47C2×D412yes—
89M16×C47—22no—
90M16×C47—41no—
91C2×C8×C47—41no—
92C2×C8×C47C2×D411yescharacteristic
93C2×C8×C47#4111yescharacteristic
94C2×C8×C47#4111yescharacteristic
95C2×C8×C47#4111yescharacteristic
96C2×C8×C47#4111yescharacteristic
97C2×C8×C47C2411yescharacteristic
98C4⋊C4×C47—22no—
99C4⋊C4×C47—41no—
100(C2×D47)⋊C4—44no—
101#10625329—22no—
102#10625329—41no—
103C2×C47⋊C8—21no—
104C2×C47⋊C8—21no—
105C2×C47⋊C8—41no—
106C2×C47⋊C8C2×D412yes—
107D376—22no—
108D376—22no—
109D376—41no—
110D376—41no—
111#10625324—22no—
112#10625324—22no—
113#10625324—22no—
114#10625324—22no—
115#10625324—44no—
116C8×D47—44no—
117C16×C47—22no—
118C47⋊C16—22no—
119C23×C47C2×SD1611yescharacteristic
120C22×D47—21no—
121C22×D47—21no—
122C22×D47—42no—
123C22×D47—42no—
124C22×D47—82no—
125C22×D47—82no—
126C22×D47—81no—
127C22×D47—81no—
128C22×D47C2×SD1612yes—
129C2×C4×C47—42no—
130C2×C4×C47—82no—
131C2×C4×C47#12311yescharacteristic
132C2×C4×C47#12311yescharacteristic
133C2×C4×C47C2×SD1611yescharacteristic
134C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
135C2×C4×C47AGL(1,ℤ/8)11yescharacteristic
136C2×C4×C47C22×D411yescharacteristic
137C2×Dic47—21no—
138C2×Dic47—21no—
139C2×Dic47C2×SD1612yes—
140D188—42no—
141D188—42no—
142D188—88no—
143D188—81no—
144D188—81no—
145C4×D47—22no—
146C4×D47—22no—
147C4×D47—22no—
148C4×D47—22no—
149C8×C47—42no—
150C8×C47#12311yescharacteristic
151C8×C47#12311yescharacteristic
152C8×C47C2×#4111yescharacteristic
153C8×C47C2×#4111yescharacteristic
154C47⋊C8—22no—
155C47⋊C8—42no—
156C2×#2238—471nomaximal, Sylow
157C22×C47—22no—
158C22×C47#48111yescharacteristic
159C22×C47#48111yescharacteristic
160C22×C47C22×SD1611yescharacteristic
161C2×D47—22no—
162C2×D47—42no—
163C2×D47—42no—
164C2×D47—81no—
165C2×D47—82no—
166C2×D47—82no—
167C2×D47—82no—
168C2×D47—162no—
169C2×D47—162no—
170C4×C47—82no—
171C4×C47#48111yescharacteristic
172C4×C47#48111yescharacteristic
173C4×C47C2×#12311yescharacteristic
174C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
175Dic47—22no—
176C2×#469—471no—
177C2×#430—471no—
178#2238—478no—
179C2×#365—471no—
180C2×#365D4711yescharacteristic, complemented
181C2×#361—471no—
182C2×#361—471no—
183C2×#349—471no—
184C2×C47—21no—
185C2×C47—21no—
186C2×C47#223812yescomplemented
187C2×C47C2×#48111yescharacteristic
188D47—42no—
189D47—162no—
190C22×D8—471no—
191C22×M16—471no—
192C22×M16—941no—
193C2×#121—941no—
194C2×M32—471no—
195C2×M32C2×D4711yescharacteristic
196#469—474no—
197#469—942no—
198#430—474no—
199#430—942no—
200C2×#108—471no—
201C2×#108—941no—
202C2×#108C2×D4711yescharacteristic
203C2×#106C2×D4711yescharacteristic
204C2×#102—941no—
205#365—474no—
206#365C2×D4714yescomplemented
207#361—474no—
208#361—474no—
209#349—474no—
210C47C2×#223811yescharacteristic, complemented, Sylow
211C22×D4—941no—
212C22×D4—1881no—
213C23×C4—471no—
214C2×D8—472no—
215C2×D8—941no—
216C2×D8—941no—
217C2×D8—941no—
218C2×D8—941no—
219C2×D8—941no—
220C2×M16—21no—
221C2×M16—472no—
222C2×M16—472no—
223C2×M16—941no—
224C2×M16—941no—
225C2×M16—941no—
226C2×M16—941no—
227C2×M16—944no—
228C2×M16—941no—
229C2×M16—1881no—
230C2×M16—1882no—
231C22×C8—471no—
232C22×C8—1881no—
233C22×C8C22×D4711yescharacteristic
234#121—944no—
235#121—1882no—
236C2×C4⋊C4—21no—
237C2×C22⋊C4—1881no—
238M32—21no—
239M32—472no—
240M32—941no—
241M32C22×D4712yes—
242C2×C16—21no—
243C2×C16—941no—
244#108—21no—
245#108—472no—
246#108—944no—
247#108—941no—
248#108C22×D4712yes—
249#106—21no—
250#106C22×D4712yes—
251#102—944no—
252C24—471no—
253C24—1881no—
254C2×D4—942no—
255C2×D4—3764no—
256C2×D4—1884no—
257C2×D4—1881no—
258C2×D4—1881no—
259C2×D4—1881no—
260C2×D4—1881no—
261C2×D4—1881no—
262C22×C4—41no—
263C22×C4—471no—
264C22×C4—472no—
265C22×C4—472no—
266C22×C4—941no—
267C22×C4—941no—
268C22×C4—941no—
269C22×C4—941no—
270C22×C4D4×D4711yescharacteristic
271D8—942no—
272D8—942no—
273D8—1881no—
274D8—1881no—
275M16—22no—
276M16—41no—
277M16—942no—
278M16—942no—
279M16—942no—
280M16—942no—
281M16—942no—
282M16—1884no—
283M16—1881no—
284C2×C8—41no—
285C2×C8—472no—
286C2×C8—941no—
287C2×C8—941no—
288C2×C8—1884no—
289C2×C8—1881no—
290C2×C8#1062535011yescharacteristic
291C2×C8#1062535011yescharacteristic
292C2×C8D4×D4711yescharacteristic
293C2×C8#1062535411yescharacteristic
294C2×C8#1062535411yescharacteristic
295C2×C8C23×D4711yescharacteristic
296C4⋊C4—22no—
297C4⋊C4—41no—
298C22⋊C4—1884no—
299C16—22no—
300C16—942no—
301C23—472no—
302C23—941no—
303C23—941no—
304C23—3762no—
305C23—3762no—
306C23—3761no—
307C23—3761no—
308C23—1882no—
309C23—1882no—
310C23SD16×D4711yescharacteristic
311D4—3768no—
312D4—3761no—
313D4—3761no—
314D4—1882no—
315D4—1882no—
316C2×C4—42no—
317C2×C4—82no—
318C2×C4—472no—
319C2×C4—941no—
320C2×C4—941no—
321C2×C4—942no—
322C2×C4—942no—
323C2×C4—942no—
324C2×C4—942no—
325C2×C4#1309400911yescharacteristic
326C2×C4#1309400911yescharacteristic
327C2×C4SD16×D4711yescharacteristic
328C2×C4#1309405111yescharacteristic
329C2×C4#1309405111yescharacteristic
330C2×C4C2×D4×D4711yescharacteristic
331C8—42no—
332C8—942no—
333C8—1882no—
334C8#1309400911yescharacteristic
335C8#1309400911yescharacteristic
336C8C2×#1062535011yescharacteristic
337C8C2×#1062535411yescharacteristic
338C22—22no—
339C22—942no—
340C22—3761no—
341C22—3762no—
342C22—3762no—
343C22—3762no—
344C22—1882no—
345C22—1882no—
346C22—7522no—
347C22—7522no—
348C22#1568944311yescharacteristic
349C22#1568944311yescharacteristic
350C22C2×SD16×D4711yescharacteristic
351C4—82no—
352C4—942no—
353C4#1568944311yescharacteristic
354C4#1568944311yescharacteristic
355C4C2×#1309400911yescharacteristic
356C4C2×#1309405111yescharacteristic
357C2—21no—
358C2—21no—
359C2—1882no—
360C2—7522no—
361C2#2024560412yesdirect product factor
362C2C2×#1568944311yescharacteristic
subgroupG/H
centerC22#15689443
commutator, cosocleC2×C8×C47C24
FrattiniC2×C8C23×D47
FittingC2×C47×#365C2
socleC22×C47#481
prime radicalC2×#15689377C2
hypercenterC2×#365D47
hypocenterC47C2×#2238
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#365

Complements

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

NH ≅ G/Ntype
2. C2×#15689170C2semidirect
3. #20245604C2direct (N × H)
4. C2×#15688945C2semidirect
5. C2×#15688937C2semidirect
6. C2×#15688935C2semidirect
7. C2×#15688904C2semidirect
8. C2×C47×#365C2semidirect
17. #15689170C22semidirect
21. #15688945C22semidirect
22. #15688937C22semidirect
23. #15688935C22semidirect
24. #15688904C22semidirect
28. C47×#365C22semidirect
180. C2×#365D47semidirect
186. C2×C47#2238semidirect
206. #365C2×D47semidirect
210. C47C2×#2238semidirect
361. C2#20245604direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156893772
C2×#156891702
#202456042
C2×#156889452
C2×#156889372
C2×#156889352
C2×#156889042
C2×C47×#3652
C2×#223847