Finite Group Databasebeta

← C2×#20242934 #26198834

Subgroups — C2×#20242934 #26198834

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689473C211yesmaximal, characteristic, complemented
2C2×#15689400C211yesmaximal, characteristic
3C2×#15689329C211yesmaximal, characteristic
4C2×#15689200C211yesmaximal, characteristic
5#20242934C218yesmaximal, direct product factor
6C2×#15688875C211yesmaximal, characteristic, complemented
7C2×#15688868C211yesmaximal, characteristic, complemented
8C2×C47×#332C211yesmaximal, characteristic, complemented
9C22×#10625325—21no—
10C22×#10625324—21no—
11C2×#13094024C2211yescharacteristic
12C2×C4×D188C2211yescharacteristic
13#15689473—22no—
14#15689473C2214yescomplemented
15#15689400—22no—
16#15689400C2214yes—
17#15689329—22no—
18#15689329C2214yes—
19#15689200—22no—
20#15689200C2214yes—
21C2×#13093957—21no—
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×#13093949—21no—
24C2×#13093948—21no—
25C2×#13093948—21no—
26C2×#13093944—21no—
27C2×(C2×D47)⋊C8—21no—
28C2×C4×C47⋊C8C2211yescharacteristic
29#15688875C2214yescomplemented
30#15688868C2214yescomplemented
31C2×C4⋊Q8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4⋊C8×C47C2211yescharacteristic
34C47×#332C2214yescomplemented
35C22×Dic94—21no—
36C22×D188D411yescharacteristic
37C22×C4×D47—21no—
38C2×#10625325—24no—
39C2×#10625325—44no—
40C2×#10625324—24no—
41C2×#10625324—44no—
42C22×C47⋊C8—21no—
43C22×C47⋊C8D411yescharacteristic
44C22×C47⋊C8D411yescharacteristic
45#13094024—21no—
46#13094024—21no—
47#13094024—21no—
48#13094024C2312yes—
49C4×D188—21no—
50C4×D188—21no—
51C4×D188D412yes—
52C4×D188C2312yes—
53C2×C4⋊Dic47—21no—
54C2×C4⋊Dic47—21no—
55C2×C4⋊Dic47D411yescharacteristic
56C2×(C2×D47)⋊C4—21no—
57#13093957—24no—
58C4⋊(C47⋊C8)—21no—
59C4⋊(C47⋊C8)C2312yes—
60#13093949—24no—
61#13093948—24no—
62#13093948—24no—
63#13093944—24no—
64(C2×D47)⋊C8—24no—
65C4×C47⋊C8D412yes—
66C4×C47⋊C8C2312yes—
67C22×Q8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C4⋊Q8×C47—21no—
71C4⋊Q8×C47—21no—
72C4⋊Q8×C47—21no—
73C4⋊Q8×C47C2312yes—
74C2×C4⋊C4×C47—21no—
75C2×C4⋊C4×C47—21no—
76C2×C42×C47C2311yescharacteristic
77C4⋊C8×C47—21no—
78C4⋊C8×C47—21no—
79C4⋊C8×C47C2312yes—
80C4⋊C8×C47C2312yes—
81C23×D47—21no—
82C2×Q8×C47—22no—
83C2×Q8×C47—41no—
84C2×Q8×C47—42no—
85C2×Q8×C47—42no—
86C22×C4×C47—41no—
87C22×C4×C47C2×D411yescharacteristic
88C22×C4×C47C2×D411yescharacteristic
89C22×C4×C47#4111yescharacteristic
90C22×Dic47—21no—
91C22×Dic47—41no—
92C2×D188—22no—
93C2×D188—22no—
94C2×D188—21no—
95C2×D188C2×D412yes—
96C2×C4×D47—22no—
97C2×C4×D47—22no—
98C2×C4×D47—42no—
99C2×C4×D47—42no—
100C2×Dic94—22no—
101C2×Dic94—42no—
102C2×Dic94—42no—
103C2×Dic94—41no—
104C2×C8×C47—22no—
105C2×C8×C47—22no—
106C2×C8×C47—42no—
107C2×C8×C47—42no—
108C4⋊C4×C47—22no—
109C4⋊C4×C47—22no—
110C4⋊C4×C47—41no—
111C4⋊C4×C47—41no—
112C42×C47C2×D411yescharacteristic
113C42×C47C2×D411yescharacteristic
114C42×C47#4111yescharacteristic
115C42×C47C2411yescharacteristic
116(C2×D47)⋊C4—22no—
117(C2×D47)⋊C4—22no—
118C4⋊Dic47—21no—
119C4⋊Dic47—22no—
120C4⋊Dic47—22no—
121C4⋊Dic47—41no—
122C4⋊Dic47—41no—
123C4⋊Dic47C2×D412yes—
124C2×C47⋊C8—22no—
125C2×C47⋊C8—22no—
126C2×C47⋊C8—22no—
127C2×C47⋊C8—42no—
128C2×C47⋊C8C2×D412yes—
129C2×C47⋊C8C2×D412yes—
130#10625325—48no—
131#10625324—48no—
132C23×C47#12111yescharacteristic
133C22×D47—22no—
134C22×D47—42no—
135C22×D47—42no—
136C22×D47—42no—
137Q8×C47—42no—
138Q8×C47—42no—
139Q8×C47—82no—
140C2×C4×C47—22no—
141C2×C4×C47—42no—
142C2×C4×C47—82no—
143C2×C4×C47#12111yescharacteristic
144C2×C4×C47#12111yescharacteristic
145C2×C4×C47#12111yescharacteristic
146C2×C4×C47#13512yes—
147C2×C4×C47AGL(1,ℤ/8)12yes—
148C2×C4×C47AGL(1,ℤ/8)12yes—
149C2×C4×C47#13712yes—
150C2×C4×C47C22×D411yescharacteristic
151C2×C4×C47C22×D411yescharacteristic
152C2×C4×C47C2×#4111yescharacteristic
153C2×Dic47—22no—
154C2×Dic47—42no—
155C2×Dic47—42no—
156C2×Dic47—82no—
157D188—22no—
158D188—22no—
159D188—42no—
160C4×D47—42no—
161C4×D47—42no—
162C4×D47—44no—
163Dic94—42no—
164Dic94—42no—
165Dic94—82no—
166C8×C47—42no—
167C8×C47—42no—
168C47⋊C8—22no—
169C47⋊C8—22no—
170C47⋊C8—42no—
171C2×#1699—471nomaximal, Sylow
172C22×C47#46312yes—
173C22×C47#46812yes—
174C22×C47#47312yes—
175C22×C47C2×#12111yescharacteristic
176C2×D47—42no—
177C2×D47—42no—
178C2×D47—42no—
179C2×D47—84no—
180C4×C47—21no—
181C4×C47—21no—
182C4×C47—82no—
183C4×C47#46312yes—
184C4×C47#46812yes—
185C4×C47C2×#13511yescharacteristic
186C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
187C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
188C4×C47C2×#13711yescharacteristic
189Dic47—42no—
190Dic47—82no—
191C2×#487—471no—
192C2×#474—471no—
193C2×#461—471no—
194C2×#436—471no—
195#1699—478no—
196C2×#335—471no—
197C2×#332—471no—
198C2×#332D4711yescharacteristic, complemented
199C2×C47#169914yescomplemented
200C2×C47C2×#46311yescharacteristic
201C2×C47C2×#46811yescharacteristic
202C2×C47C2×#47311yescharacteristic
203D47—82no—
204C22×SD16—941no—
205C22×M16—941no—
206C2×C4⋊Q8—471no—
207C2×C4⋊Q8C2×D4711yescharacteristic
208C2×C4×D4—471no—
209#487—474no—
210#487—942no—
211#474—474no—
212#474—942no—
213#461—474no—
214#461—942no—
215#436—474no—
216#436—942no—
217C2×#107—941no—
218C2×C4⋊C8—471no—
219C2×C4⋊C8C2×D4711yescharacteristic
220C2×C4⋊C8C2×D4711yescharacteristic
221C2×#103—941no—
222C2×#103—941no—
223C2×#103—941no—
224C2×#102—941no—
225C2×C22⋊C8—941no—
226C2×C4×C8—471no—
227#335—474no—
228#332—474no—
229#332C2×D4714yescomplemented
230C47C2×#169911yescharacteristic, complemented, Sylow
231C22×Q8—21no—
232C22×Q8—941no—
233C22×D4—471no—
234C23×C4—941no—
235C2×SD16—944no—
236C2×SD16—1884no—
237C2×M16—944no—
238C2×M16—1884no—
239C22×C8—21no—
240C22×C8—21no—
241C22×C8—471no—
242C22×C8—471no—
243C22×C8—941no—
244C4⋊Q8—21no—
245C4⋊Q8—21no—
246C4⋊Q8—21no—
247C4⋊Q8—472no—
248C4⋊Q8—941no—
249C4⋊Q8—941no—
250C4⋊Q8—941no—
251C4⋊Q8C22×D4712yes—
252C4×D4—472no—
253C4×D4—472no—
254C4×D4—941no—
255C4×D4—941no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—471no—
259C2×C4⋊C4—941no—
260C2×C4⋊C4—941no—
261C2×C22⋊C4—941no—
262C2×C42C22×D4711yescharacteristic
263#107—944no—
264C4⋊C8—21no—
265C4⋊C8—21no—
266C4⋊C8—472no—
267C4⋊C8—941no—
268C4⋊C8C22×D4712yes—
269C4⋊C8C22×D4712yes—
270#103—944no—
271#103—944no—
272#103—944no—
273#102—944no—
274C22⋊C8—944no—
275C4×C8—472no—
276C4×C8—472no—
277C24—941no—
278C2×Q8—22no—
279C2×Q8—41no—
280C2×Q8—42no—
281C2×Q8—42no—
282C2×Q8—942no—
283C2×Q8—1882no—
284C2×Q8—1882no—
285C2×Q8—1881no—
286C2×D4—472no—
287C2×D4—941no—
288C2×D4—942no—
289C2×D4—942no—
290C22×C4—41no—
291C22×C4—941no—
292C22×C4—942no—
293C22×C4—942no—
294C22×C4—1881no—
295C22×C4—1882no—
296C22×C4—1882no—
297C22×C4#1062535011yescharacteristic
298C22×C4D4×D4711yescharacteristic
299C22×C4D4×D4711yescharacteristic
300SD16—1888no—
301M16—1888no—
302C2×C8—22no—
303C2×C8—22no—
304C2×C8—42no—
305C2×C8—42no—
306C2×C8—472no—
307C2×C8—472no—
308C2×C8—942no—
309C2×C8—942no—
310C2×C8—942no—
311C2×C8—1882no—
312C4⋊C4—22no—
313C4⋊C4—22no—
314C4⋊C4—41no—
315C4⋊C4—41no—
316C4⋊C4—472no—
317C4⋊C4—941no—
318C4⋊C4—942no—
319C4⋊C4—942no—
320C4⋊C4—1881no—
321C4⋊C4—1881no—
322C22⋊C4—942no—
323C22⋊C4—942no—
324C42#1062535011yescharacteristic
325C42D4×D4711yescharacteristic
326C42D4×D4711yescharacteristic
327C42C23×D4711yescharacteristic
328C23—942no—
329C23—1882no—
330C23—1882no—
331C23—1882no—
332C23#1309399711yescharacteristic
333Q8—42no—
334Q8—42no—
335Q8—82no—
336Q8—3762no—
337Q8—1882no—
338Q8—1882no—
339D4—942no—
340D4—942no—
341D4—1882no—
342C2×C4—22no—
343C2×C4—42no—
344C2×C4—82no—
345C2×C4—942no—
346C2×C4—3762no—
347C2×C4—1882no—
348C2×C4—1882no—
349C2×C4—1884no—
350C2×C4—1882no—
351C2×C4—1882no—
352C2×C4#1309399711yescharacteristic
353C2×C4#1309399711yescharacteristic
354C2×C4#1309399711yescharacteristic
355C2×C4#1309404512yes—
356C2×C4#1309404812yes—
357C2×C4#1309405112yes—
358C2×C4#1309405612yes—
359C2×C4C2×D4×D4711yescharacteristic
360C2×C4C2×D4×D4711yescharacteristic
361C2×C4C2×#1062535011yescharacteristic
362C8—42no—
363C8—42no—
364C8—942no—
365C8—942no—
366C8—1882no—
367C22—3764no—
368C22—1882no—
369C22—1882no—
370C22—1882no—
371C22#1568933712yes—
372C22#1568937212yes—
373C22#1568939712yes—
374C22C2×#1309399711yescharacteristic
375C4—21no—
376C4—21no—
377C4—82no—
378C4—3762no—
379C4—1882no—
380C4#1568933712yes—
381C4#1568937212yes—
382C4C2×#1309404511yescharacteristic
383C4C2×#1309404811yescharacteristic
384C4C2×#1309405111yescharacteristic
385C4C2×#1309405611yescharacteristic
386C2—3762no—
387C2#2024293414yesdirect product factor
388C2C2×#1568933711yescharacteristic
389C2C2×#1568937211yescharacteristic
390C2C2×#1568939711yescharacteristic
subgroupG/H
centerC23#13093997
commutator, cosocleC42×C47C24
FrattiniC42C23×D47
FittingC2×C47×#332C2
socleC23×C47#121
prime radicalC22×D188D4
hypercenterC2×#332D47
hypocenterC47C2×#1699
LCSG ▷ C42×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#332

Complements

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

NH ≅ G/Ntype
1. C2×#15689473C2semidirect
5. #20242934C2direct (N × H)
6. C2×#15688875C2semidirect
7. C2×#15688868C2semidirect
8. C2×C47×#332C2semidirect
14. #15689473C22semidirect
29. #15688875C22semidirect
30. #15688868C22semidirect
34. C47×#332C22semidirect
198. C2×#332D47semidirect
199. C2×C47#1699semidirect
229. #332C2×D47semidirect
230. C47C2×#1699semidirect
387. C2#20242934direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156894732
C2×#156894002
C2×#156893292
C2×#156892002
#202429342
C2×#156888752
C2×#156888682
C2×C47×#3322
C2×#169947