Finite Group Databasebeta

← C2×#10595447 #11918893

Subgroups — C2×#10595447 #11918893

Order 1152.

3317 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C3×#1009C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10595447C2116yesmaximal, direct product factor
5C2×#63831C213yesmaximal, complemented
6C2×#63830C213yesmaximal, complemented
7C2×#63829C213yesmaximal, complemented
8C22×#3716C213yesmaximal, complemented
9C2×#5836—31nomaximal
10C2×#5751—31nomaximal
11C2×C32×#41C2211yescharacteristic
12#64367—24no—
13#64367C2218yescomplemented
14C2×Q8×C3⋊D3—21no—
15C2×#3830—23no—
16C2×#3828C2213yescomplemented
17C22×#634C2213yescomplemented
18C3×#1009—24no—
19C3×#1009C2218yescomplemented
20C2×C3×#239—21no—
21C2×C3×D3×D4—23no—
22C2×C3×#235C2213yes—
23C22×C3×D12C2213yes—
24C3×#948C2218yescomplemented
25C2×C3×#208C2213yescomplemented
26C22×C3×C3⋊C8C2213yescomplemented
27C2×#3719C2213yescomplemented
28C2×#3717C2211yescharacteristic, complemented
29#63831C22124yescomplemented
30#63830C22124yescomplemented
31#63829C22124yescomplemented
32C2×#3716C2213yescomplemented
33C2×#3716C2216yescomplemented
34C2×#3716C22124yescomplemented
35C2×#3714C2213yescomplemented
36C2×C3×H(5,𝔽2)—31no—
37C2×#1010—31no—
38C2×#1010—31no—
39C2×#1010—61no—
40C2×#1009D311yescharacteristic, complemented
41C2×C3×#131—31no—
42#5836—316no—
43C2×#951—33no—
44C2×#950—33no—
45C2×#948D311yescharacteristic, complemented
46C22×#214—33no—
47C2×#932—33no—
48#5751—316no—
49C2×#909—33no—
50C2×#908—33no—
51C2×#904—33no—
52C22×#204—33no—
53C23×C3×D3—23no—
54C32×#41D414yes—
55C32×#41C2314yes—
56C2×C32×Q8D411yescharacteristic
57C2×C32×D4D413yes—
58C22×C32×C4C2313yes—
59C2×#638—23no—
60C22×C3⋊Dic3—23no—
61Q8×C3⋊D3—28no—
62#3830—224no—
63#3828—26no—
64#3828C23112yescomplemented
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×C4×C3⋊D3—23no—
67C2×#634—23no—
68C2×#634—26no—
69C2×#634C2313yes—
70C2×#634C23112yescomplemented
71C2×C3×#67—23no—
72C3×#239—28no—
73C3×D3×D4—224no—
74C3×#235—26no—
75C3×#235C23112yes—
76C2×C3×D12—23no—
77C2×C3×D12—26no—
78C2×C3×D12C2313yes—
79C2×C3×D12C23112yes—
80C2×C3×C4×D3—23no—
81C2×C3×Dic6C2311yescharacteristic
82C3×#208C23112yescomplemented
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2313yes—
85C2×C3×C3⋊C8C23112yescomplemented
86#3719C23112yescomplemented
87#3717C2314yescomplemented
88#3716C23112yescomplemented
89#3716C23124yescomplemented
90#3714C23112yescomplemented
91C2×#577—91noSylow
92C3×H(5,𝔽2)—38no—
93C3×H(5,𝔽2)—64no—
94C2×C3×#41—21no—
95C2×C3×#41—33no—
96C2×C3×#41—61no—
97C2×C3×#41C2×D311yescharacteristic
98C2×C3×#41C2×D311yescharacteristic
99C22×C3×D4—33no—
100C22×C3×D4—63no—
101#1010—38no—
102#1010—38no—
103#1010—68no—
104#1010—68no—
105#1010—64no—
106#1010—64no—
107#1009—24no—
108#1009C2×D318yescomplemented
109C2×#239—21no—
110C2×D3×Q8—62no—
111C2×D3×Q8—61no—
112C2×D3×Q8—61no—
113C2×#237—66no—
114C2×#237—63no—
115C2×#237—63no—
116C2×D3×D4—23no—
117C2×#235—33no—
118C2×#235—33no—
119C2×#235—63no—
120C2×#235C2×D313yes—
121C22×D12C2×D313yes—
122C22×Dic6—33no—
123C22×Dic6—33no—
124C22×Dic6—63no—
125C3×#131—38no—
126C2×C3×M16—33no—
127C22×C3×C8—33no—
128#951—324no—
129#950—324no—
130#948C2×D318yescomplemented
131C2×#216—33no—
132C2×#215—31no—
133C2×#214—36no—
134C2×#214—33no—
135C2×#214—324no—
136#932—324no—
137C2×#213—33no—
138C2×#208C2×D313yescomplemented
139C22×C3⋊C8C2×D313yescomplemented
140#909—324no—
141#908—324no—
142C2×Dic12—33no—
143#904—324no—
144C2×D24—33no—
145C2×#204—33no—
146C2×#204—36no—
147C2×#204—324no—
148C2×#204—31no—
149C23×C32C2×D413yes—
150C22×C3⋊D3—21no—
151C22×C3×D3—23no—
152C22×C3×D3—212no—
153C22×C3×D3—86no—
154C32×Q8C2×D414yes—
155C32×D4C2×D4112yes—
156C2×C32×C4C2×D413yes—
157C2×C32×C4C2×D416yes—
158C2×C32×C4C2411yescharacteristic
159C2×C32×C4C2416yes—
160#638—212no—
161C2×C3⋊Dic3—23no—
162C2×C3⋊Dic3—212no—
163C4⋊(C3⋊D3)—21no—
164C4⋊(C3⋊D3)C2412yes—
165C4×C3⋊D3—212no—
166#634—23no—
167#634—212no—
168#634C2416yes—
169C3×#67—212no—
170C2×C3×Dic3—21no—
171C3×D12—23no—
172C3×D12—212no—
173C3×D12C2416yes—
174C3×C4×D3—212no—
175C3×Dic6—21no—
176C3×Dic6C2412yes—
177C3×C3⋊C8C2416yes—
178C3×C3⋊C8C2412yes—
179C2×2−1+4—91no—
180C2×H(5,𝔽2)—31no—
181#577—916no—
182C2×#137—93no—
183C2×AGL(1,ℤ/8)—93no—
184C2×#135—93no—
185C22×SD16—93no—
186C2×#131—31no—
187C24×C3—63no—
188C23×D3—23no—
189C3×#41—24no—
190C3×#41—24no—
191C3×#41—312no—
192C3×#41—68no—
193C3×#41—66no—
194C3×#41D1214yes—
195C3×#41#6714yes—
196C3×#41C22×D314yes—
197C3×#41C22×D314yes—
198C2×C3×Q8—21no—
199C2×C3×Q8—31no—
200C2×C3×Q8D1211yescharacteristic
201C2×C3×Q8#6711yescharacteristic
202C2×C3×D4—23no—
203C2×C3×D4—33no—
204C2×C3×D4—312no—
205C2×C3×D4—63no—
206C2×C3×D4—624no—
207C2×C3×D4—63no—
208C2×C3×D4—66no—
209C2×C3×D4D1213yes—
210C2×C3×D4#6713yes—
211C22×C3×C4—23no—
212C22×C3×C4—63no—
213C22×C3×C4C22×D313yes—
214C22×C3×C4C22×D313yes—
215C2×#67—23no—
216C2×#67—66no—
217C2×#67—63no—
218C2×#67—63no—
219C22×Dic3—66no—
220C22×Dic3—63no—
221C22×Dic3—63no—
222#239—28no—
223D3×Q8—616no—
224D3×Q8—68no—
225D3×Q8—68no—
226#237—648no—
227#237—624no—
228#237—624no—
229D3×D4—224no—
230#235—26no—
231#235—312no—
232#235—312no—
233#235—612no—
234#235—612no—
235#235—66no—
236#235—66no—
237#235C22×D3112yes—
238C2×D12—23no—
239C2×D12—26no—
240C2×D12—31no—
241C2×D12—31no—
242C2×D12—61no—
243C2×D12C22×D313yes—
244C2×D12C22×D3112yes—
245C2×C4×D3—23no—
246C2×C4×D3—66no—
247C2×C4×D3—63no—
248C2×C4×D3—63no—
249C2×Dic6—33no—
250C2×Dic6—312no—
251C2×Dic6—33no—
252C2×Dic6—312no—
253C2×Dic6—63no—
254C2×Dic6—612no—
255C2×Dic6—66no—
256C2×Dic6—612no—
257C2×Dic6—63no—
258C2×Dic6—66no—
259C2×Dic6—63no—
260C2×Dic6—66no—
261C2×Dic6C22×D311yescharacteristic
262C3×M16—312no—
263C2×C3×C8—31no—
264C2×C3×C8—33no—
265C2×C3×C8—312no—
266#216—312no—
267#215—34no—
268#214—324no—
269#214—312no—
270#213—312no—
271#208C22×D3112yescomplemented
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D313yes—
274C2×C3⋊C8C22×D3112yescomplemented
275Dic12—312no—
276D24—312no—
277#204—312no—
278#204—324no—
279#204—34no—
280C22×C32—26no—
281C22×C32C22×D416yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—42no—
285C2×C3×D3—26no—
286C2×C3×D3—46no—
287C2×C3×D3—812no—
288C32×C4C22×D411yescharacteristic
289C32×C4C22×D416yes—
290C32×C4C2511yescharacteristic
291C3⋊Dic3—26no—
292C3×Dic3—22no—
2932−1+4—98no—
2942−1+4—184no—
295H(5,𝔽2)—38no—
296H(5,𝔽2)—64no—
297C2×#41—33no—
298C2×#41—61no—
299C2×#41—93no—
300C2×#41—183no—
301C2×#41D3211yescharacteristic
302C22×Q8—93no—
303C22×Q8—181no—
304C22×D4—33no—
305C22×D4—63no—
306#137—924no—
307AGL(1,ℤ/8)—924no—
308#135—924no—
309C2×Q16—93no—
310C2×SD16—93no—
311C2×SD16—96no—
312C2×SD16—924no—
313C2×SD16—91no—
314C2×D8—93no—
315#131—38no—
316C2×M16—33no—
317C22×C8—33no—
318C23×C3—23no—
319C23×C3—63no—
320C23×C3—612no—
321C23×C3—246no—
322C23×C3C2×D1213yes—
323C23×C3C2×#6713yes—
324C22×D3—23no—
325C22×D3—212no—
326C22×D3—62no—
327C22×D3—61no—
328C22×D3—61no—
329C22×D3—86no—
330C3×Q8—24no—
331C3×Q8—32no—
332C3×Q8—61no—
333C3×Q8C2×D1214yes—
334C3×Q8C2×#6714yes—
335C3×D4—212no—
336C3×D4—36no—
337C3×D4—612no—
338C3×D4—63no—
339C3×D4—612no—
340C3×D4C2×D12112yes—
341C3×D4C2×#67112yes—
342C2×C3×C4—21no—
343C2×C3×C4—26no—
344C2×C3×C4—23no—
345C2×C3×C4—26no—
346C2×C3×C4—61no—
347C2×C3×C4—612no—
348C2×C3×C4C2×D1213yes—
349C2×C3×C4C2×D1216yes—
350C2×C3×C4C2×#6713yes—
351C2×C3×C4C2×#6716yes—
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D316yes—
354C2×C3×C4C23×D311yescharacteristic
355C2×C3×C4C23×D316yes—
356#67—212no—
357#67—624no—
358#67—612no—
359#67—612no—
360C2×Dic3—21no—
361C2×Dic3—66no—
362C2×Dic3—624no—
363C2×Dic3—63no—
364C2×Dic3—612no—
365C2×Dic3—63no—
366C2×Dic3—612no—
367D12—23no—
368D12—212no—
369D12—32no—
370D12—32no—
371D12—62no—
372D12—62no—
373D12—61no—
374D12—61no—
375D12C23×D316yes—
376C4×D3—212no—
377C4×D3—624no—
378C4×D3—612no—
379C4×D3—612no—
380Dic6—21no—
381Dic6—36no—
382Dic6—36no—
383Dic6—66no—
384Dic6—66no—
385Dic6—624no—
386Dic6—63no—
387Dic6—612no—
388Dic6—63no—
389Dic6—612no—
390Dic6C23×D312yes—
391C3×C8—32no—
392C3×C8—36no—
393C3⋊C8C23×D312yes—
394C3⋊C8C23×D316yes—
395C2×C32—26no—
396C2×C32#57712yescomplemented
397C2×C32C23×D411yescharacteristic
398C3⋊D3—42no—
399C3×D3—46no—
400C24—63no—
401#41—312no—
402#41—68no—
403#41—66no—
404#41—912no—
405#41—1824no—
406#41—186no—
407#41#62614yes—
408#41C2×D3214yes—
409C2×Q8—31no—
410C2×Q8—93no—
411C2×Q8—912no—
412C2×Q8—188no—
413C2×Q8—183no—
414C2×Q8—186no—
415C2×Q8#62611yescharacteristic
416C2×D4—33no—
417C2×D4—312no—
418C2×D4—63no—
419C2×D4—624no—
420C2×D4—63no—
421C2×D4—66no—
422C2×D4—91no—
423C2×D4—183no—
424C2×D4#62613yes—
425C22×C4—63no—
426C22×C4—183no—
427C22×C4—183no—
428C22×C4C2×D3213yes—
429Q16—912no—
430SD16—912no—
431SD16—924no—
432SD16—94no—
433D8—912no—
434M16—312no—
435C2×C8—31no—
436C2×C8—33no—
437C2×C8—312no—
438C22×C3—26no—
439C22×C3—26no—
440C22×C3—26no—
441C22×C3—21no—
442C22×C3—46no—
443C22×C3—66no—
444C22×C3—126no—
445C22×C3—2412no—
446C22×C3C22×D1216yes—
447C22×C3C22×D1211yescharacteristic
448C22×C3C22×#6716yes—
449C22×C3C22×#6711yescharacteristic
450C2×D3—26no—
451C2×D3—46no—
452C2×D3—64no—
453C2×D3—62no—
454C2×D3—62no—
455C2×D3—812no—
456C2×D3—124no—
457C2×D3—122no—
458C2×D3—122no—
459C3×C4—21no—
460C3×C4—26no—
461C3×C4—21no—
462C3×C4—62no—
463C3×C4C22×D1211yescharacteristic
464C3×C4C22×D1216yes—
465C3×C4C22×#6711yescharacteristic
466C3×C4C22×#6716yes—
467C3×C4C24×D311yescharacteristic
468C3×C4C24×D311yescharacteristic
469Dic3—22no—
470Dic3—612no—
471Dic3—66no—
472Dic3—66no—
473C32C2×#57711yescharacteristic, complemented, Sylow
474C23—63no—
475C23—612no—
476C23—181no—
477C23—246no—
478C23C2×#62613yes—
479Q8—32no—
480Q8—61no—
481Q8—96no—
482Q8—1812no—
483Q8—183no—
484Q8C2×#62614yes—
485D4—36no—
486D4—612no—
487D4—612no—
488D4—63no—
489D4—92no—
490D4—1812no—
491D4—181no—
492D4C2×#626112yes—
493C2×C4—61no—
494C2×C4—612no—
495C2×C4—1812no—
496C2×C4—183no—
497C2×C4—1812no—
498C2×C4C2×#62616yes—
499C2×C4C2×#62613yes—
500C2×C4C22×D3216yes—
501C2×C4C22×D3211yescharacteristic
502C8—32no—
503C8—36no—
504C2×C3—26no—
505C2×C3—26no—
506C2×C3—21no—
507C2×C3—22no—
508C2×C3—46no—
509C2×C3—126no—
510C2×C3#575112yescomplemented
511C2×C3#583612yescomplemented
512C2×C3C23×D1211yescharacteristic
513C2×C3C23×#6711yescharacteristic
514D3—46no—
515D3—124no—
516D3—122no—
517D3—122no—
518C22—26no—
519C22—66no—
520C22—126no—
521C22—182no—
522C22—2412no—
523C22—362no—
524C22C22×#62616yes—
525C22C22×#62611yescharacteristic
526C4—62no—
527C4—186no—
528C4C22×#62616yes—
529C4C22×#62611yescharacteristic
530C4C23×D3211yescharacteristic
531C3—21no—
532C3C2×#575111yescharacteristic, complemented
533C3C2×#583611yescharacteristic, complemented
534C2—26no—
535C2—126no—
536C2—362no—
537C2#1059544712yesdirect product factor
538C2C23×#62611yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#577
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64367C2semidirect
2. C2×C3×#1009C2semidirect
3. C2×C3×#948C2semidirect
4. #10595447C2direct (N × H)
5. C2×#63831C2semidirect
6. C2×#63830C2semidirect
7. C2×#63829C2semidirect
8. C22×#3716C2semidirect
13. #64367C22semidirect
16. C2×#3828C22semidirect
17. C22×#634C22semidirect
19. C3×#1009C22semidirect
24. C3×#948C22semidirect
25. C2×C3×#208C22semidirect
26. C22×C3×C3⋊C8C22semidirect
27. C2×#3719C22semidirect
28. C2×#3717C22semidirect
29. #63831C22semidirect
30. #63830C22semidirect
31. #63829C22semidirect
32. C2×#3716C22semidirect
33. C2×#3716C22semidirect
34. C2×#3716C22semidirect
35. C2×#3714C22semidirect
40. C2×#1009D3semidirect
45. C2×#948D3semidirect
64. #3828C23semidirect
70. C2×#634C23semidirect
82. C3×#208C23semidirect
85. C2×C3×C3⋊C8C23semidirect
86. #3719C23semidirect
87. #3717C23semidirect
88. #3716C23semidirect
89. #3716C23semidirect
90. #3714C23semidirect
108. #1009C2×D3semidirect
130. #948C2×D3semidirect
138. C2×#208C2×D3semidirect
139. C22×C3⋊C8C2×D3semidirect
271. #208C22×D3semidirect
274. C2×C3⋊C8C22×D3semidirect
396. C2×C32#577semidirect
473. C32C2×#577semidirect
510. C2×C3#5751semidirect
511. C2×C3#5836semidirect
532. C3C2×#5751semidirect
533. C3C2×#5836semidirect
537. C2#10595447direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643672
C2×C3×#10092
C2×C3×#9482
#105954472
C2×#638312
C2×#638302
C2×#638292
C22×#37162
C2×#58363
C2×#57513