Finite Group Databasebeta

← C2×#10595448 #11918894

Subgroups — C2×#10595448 #11918894

Order 1152.

3369 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64366C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10595448C2116yesmaximal, direct product factor
5C2×#63833C213yesmaximal, complemented
6C22×#3717C213yesmaximal, complemented
7C2×#63829C213yesmaximal, complemented
8C2×#63825C213yesmaximal, complemented
9C2×#5837—31nomaximal
10C2×#5751—31nomaximal
11C2×C32×#41C2211yescharacteristic
12#64366—24no—
13#64366C2218yescomplemented
14C2×#3832—21no—
15C2×D4×C3⋊D3—23no—
16C2×#3828C2213yes—
17C22×C4⋊(C3⋊D3)C2213yes—
18C3×#1010—24no—
19C3×#1010C2218yescomplemented
20C2×C3×D3×Q8—21no—
21C2×C3×#237—23no—
22C2×C3×#235C2213yescomplemented
23C22×C3×Dic6C2213yescomplemented
24C3×#948C2218yescomplemented
25C2×C3×#208C2213yescomplemented
26C22×C3×C3⋊C8C2213yescomplemented
27C2×#3719C2213yescomplemented
28#63833C22124yescomplemented
29C2×#3717C2216yescomplemented
30C2×#3717C2213yescomplemented
31C2×#3717C22124yescomplemented
32#63829C22124yescomplemented
33C2×#3716C2211yescharacteristic, complemented
34#63825C22124yescomplemented
35C2×#3714C2213yescomplemented
36C2×C3×2−1+4—31no—
37C2×#1010D311yescharacteristic, complemented
38C2×#1009—31no—
39C2×#1009—31no—
40C2×#1009—61no—
41C2×C3×#131—31no—
42#5837—316no—
43C2×#950—33no—
44C2×#949—33no—
45C2×#948D311yescharacteristic, complemented
46C2×#942—33no—
47C22×#215—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—
60#3832—28no—
61D4×C3⋊D3—224no—
62#3828—26no—
63#3828C23112yes—
64C2×C4⋊(C3⋊D3)—23no—
65C2×C4⋊(C3⋊D3)—26no—
66C2×C4⋊(C3⋊D3)C2313yes—
67C2×C4⋊(C3⋊D3)C23112yes—
68C2×C4×C3⋊D3—23no—
69C2×#634C2311yescharacteristic
70C2×C3×#67—23no—
71C22×C3×Dic3—23no—
72C3×D3×Q8—28no—
73C3×#237—224no—
74C3×#235—26no—
75C3×#235C23112yescomplemented
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—23no—
78C2×C3×Dic6—23no—
79C2×C3×Dic6—26no—
80C2×C3×Dic6C2313yes—
81C2×C3×Dic6C23112yescomplemented
82C3×#208C23112yescomplemented
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2313yes—
85C2×C3×C3⋊C8C23112yescomplemented
86#3719C23112yescomplemented
87#3717C23124yescomplemented
88#3717C23112yescomplemented
89#3716C2314yescomplemented
90#3714C23112yescomplemented
91C2×#577—91noSylow
92C3×2−1+4—38no—
93C3×2−1+4—64no—
94C2×C3×#41—21no—
95C2×C3×#41—33no—
96C2×C3×#41—63no—
97C2×C3×#41C2×D311yescharacteristic
98C2×C3×#41C2×D311yescharacteristic
99C22×C3×Q8—33no—
100C22×C3×Q8—61no—
101#1010—24no—
102#1010C2×D318yescomplemented
103#1009—38no—
104#1009—38no—
105#1009—68no—
106#1009—68no—
107#1009—64no—
108#1009—64no—
109C2×#239—62no—
110C2×#239—61no—
111C2×#239—61no—
112C2×D3×Q8—21no—
113C2×#237—23no—
114C2×D3×D4—66no—
115C2×D3×D4—63no—
116C2×D3×D4—63no—
117C2×#235—33no—
118C2×#235—33no—
119C2×#235—63no—
120C2×#235C2×D313yescomplemented
121C22×D12—33no—
122C22×D12—33no—
123C22×D12—63no—
124C22×Dic6C2×D313yescomplemented
125C3×#131—38no—
126C2×C3×M16—33no—
127C22×C3×C8—33no—
128#950—324no—
129#949—324no—
130#948C2×D318yescomplemented
131C2×#216—33no—
132#942—324no—
133C2×#215—33no—
134C2×#215—36no—
135C2×#215—324no—
136C2×#214—31no—
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—31no—
146C2×#204—33no—
147C2×#204—36no—
148C2×#204—324no—
149C23×C32C2×D413yes—
150C22×C3⋊D3—23no—
151C22×C3⋊D3—212no—
152C22×C3⋊D3—86no—
153C22×C3×D3—21no—
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—21no—
162C4⋊(C3⋊D3)—23no—
163C4⋊(C3⋊D3)—212no—
164C4⋊(C3⋊D3)C2416yes—
165C4×C3⋊D3—212no—
166#634—21no—
167#634C2412yes—
168C3×#67—212no—
169C2×C3×Dic3—23no—
170C2×C3×Dic3—212no—
171C3×D12—21no—
172C3×D12C2412yes—
173C3×C4×D3—212no—
174C3×Dic6—23no—
175C3×Dic6—212no—
176C3×Dic6C2416yes—
177C3×C3⋊C8C2416yes—
178C3×C3⋊C8C2412yes—
179C2×2−1+4—31no—
180C2×H(5,𝔽2)—91no—
181#577—916no—
182C2×#137—93no—
183C2×AGL(1,ℤ/8)—93no—
184C2×#135—93no—
185C22×SD16—93no—
186C2×#131—31no—
187C23×D3—66no—
188C23×D3—63no—
189C23×D3—63no—
190C3×#41—24no—
191C3×#41—24no—
192C3×#41—312no—
193C3×#41—624no—
194C3×#41—66no—
195C3×#41D1214yes—
196C3×#41#6714yes—
197C3×#41C22×D314yes—
198C3×#41C22×D314yes—
199C2×C3×Q8—21no—
200C2×C3×Q8—33no—
201C2×C3×Q8—312no—
202C2×C3×Q8—68no—
203C2×C3×Q8—63no—
204C2×C3×Q8—66no—
205C2×C3×Q8D1211yescharacteristic
206C2×C3×Q8#6711yescharacteristic
207C2×C3×D4—23no—
208C2×C3×D4—31no—
209C2×C3×D4—63no—
210C2×C3×D4D1213yes—
211C2×C3×D4#6713yes—
212C22×C3×C4—23no—
213C22×C3×C4—63no—
214C22×C3×C4—63no—
215C22×C3×C4C22×D313yes—
216C22×C3×C4C22×D313yes—
217C2×#67—23no—
218C2×#67—66no—
219C2×#67—63no—
220C2×#67—63no—
221C22×Dic3—23no—
222#239—616no—
223#239—68no—
224#239—68no—
225D3×Q8—28no—
226#237—224no—
227D3×D4—648no—
228D3×D4—624no—
229D3×D4—624no—
230#235—26no—
231#235—312no—
232#235—312no—
233#235—612no—
234#235—612no—
235#235—66no—
236#235—66no—
237#235C22×D3112yescomplemented
238C2×D12—33no—
239C2×D12—312no—
240C2×D12—33no—
241C2×D12—312no—
242C2×D12—63no—
243C2×D12—612no—
244C2×D12—66no—
245C2×D12—612no—
246C2×D12—63no—
247C2×D12—66no—
248C2×D12—63no—
249C2×D12—66no—
250C2×D12C22×D311yescharacteristic
251C2×C4×D3—23no—
252C2×C4×D3—66no—
253C2×C4×D3—63no—
254C2×C4×D3—63no—
255C2×Dic6—23no—
256C2×Dic6—26no—
257C2×Dic6—31no—
258C2×Dic6—31no—
259C2×Dic6—61no—
260C2×Dic6C22×D313yes—
261C2×Dic6C22×D3112yescomplemented
262C3×M16—312no—
263C2×C3×C8—31no—
264C2×C3×C8—33no—
265C2×C3×C8—312no—
266#216—312no—
267#215—312no—
268#215—324no—
269#214—34no—
270#213—312no—
271#208C22×D3112yescomplemented
272C2×C3⋊C8C22×D311yescharacteristic
273C2×C3⋊C8C22×D313yes—
274C2×C3⋊C8C22×D3112yescomplemented
275Dic12—312no—
276D24—312no—
277#204—34no—
278#204—312no—
279#204—324no—
280C22×C32—26no—
281C22×C32C22×D416yes—
282C22×C32C22×D411yescharacteristic
283C2×C3⋊D3—26no—
284C2×C3⋊D3—46no—
285C2×C3⋊D3—812no—
286C2×C3×D3—22no—
287C2×C3×D3—42no—
288C32×C4C22×D411yescharacteristic
289C32×C4C22×D416yes—
290C32×C4C2511yescharacteristic
291C3⋊Dic3—22no—
292C3×Dic3—26no—
2932−1+4—38no—
2942−1+4—64no—
295H(5,𝔽2)—98no—
296H(5,𝔽2)—184no—
297C2×#41—33no—
298C2×#41—63no—
299C2×#41—93no—
300C2×#41—181no—
301C2×#41D3211yescharacteristic
302C22×Q8—33no—
303C22×Q8—61no—
304C22×D4—93no—
305C22×D4—183no—
306#137—924no—
307AGL(1,ℤ/8)—924no—
308#135—924no—
309C2×Q16—93no—
310C2×SD16—91no—
311C2×SD16—93no—
312C2×SD16—96no—
313C2×SD16—924no—
314C2×D8—93no—
315#131—38no—
316C2×M16—33no—
317C22×C8—33no—
318C23×C3—23no—
319C23×C3—61no—
320C23×C3C2×D1213yes—
321C23×C3C2×#6713yes—
322C22×D3—21no—
323C22×D3—66no—
324C22×D3—63no—
325C22×D3—63no—
326C22×D3—624no—
327C22×D3—612no—
328C22×D3—612no—
329C22×D3—246no—
330C22×D3—246no—
331C22×D3—2412no—
332C3×Q8—24no—
333C3×Q8—36no—
334C3×Q8—63no—
335C3×Q8—612no—
336C3×Q8C2×D1214yes—
337C3×Q8C2×#6714yes—
338C3×D4—212no—
339C3×D4—32no—
340C3×D4—612no—
341C3×D4—61no—
342C3×D4C2×D12112yes—
343C3×D4C2×#67112yes—
344C2×C3×C4—21no—
345C2×C3×C4—26no—
346C2×C3×C4—23no—
347C2×C3×C4—26no—
348C2×C3×C4—63no—
349C2×C3×C4—612no—
350C2×C3×C4—612no—
351C2×C3×C4C2×D1213yes—
352C2×C3×C4C2×D1216yes—
353C2×C3×C4C2×#6713yes—
354C2×C3×C4C2×#6716yes—
355C2×C3×C4C23×D311yescharacteristic
356C2×C3×C4C23×D316yes—
357C2×C3×C4C23×D311yescharacteristic
358C2×C3×C4C23×D316yes—
359#67—212no—
360#67—624no—
361#67—612no—
362#67—612no—
363C2×Dic3—23no—
364C2×Dic3—212no—
365C2×Dic3—62no—
366C2×Dic3—61no—
367C2×Dic3—61no—
368D12—21no—
369D12—36no—
370D12—36no—
371D12—66no—
372D12—66no—
373D12—624no—
374D12—63no—
375D12—612no—
376D12—63no—
377D12—612no—
378D12C23×D312yes—
379C4×D3—212no—
380C4×D3—624no—
381C4×D3—612no—
382C4×D3—612no—
383Dic6—23no—
384Dic6—212no—
385Dic6—32no—
386Dic6—32no—
387Dic6—62no—
388Dic6—62no—
389Dic6—61no—
390Dic6—61no—
391Dic6C23×D316yes—
392C3×C8—32no—
393C3×C8—36no—
394C3⋊C8C23×D312yes—
395C3⋊C8C23×D316yes—
396C2×C32—26no—
397C2×C32#57712yescomplemented
398C2×C32C23×D411yescharacteristic
399C3⋊D3—46no—
400C3×D3—42no—
401C24—183no—
402#41—312no—
403#41—624no—
404#41—66no—
405#41—912no—
406#41—188no—
407#41—186no—
408#41#62614yes—
409#41C2×D3214yes—
410C2×Q8—33no—
411C2×Q8—312no—
412C2×Q8—68no—
413C2×Q8—63no—
414C2×Q8—66no—
415C2×Q8—91no—
416C2×Q8#62611yescharacteristic
417C2×D4—31no—
418C2×D4—63no—
419C2×D4—93no—
420C2×D4—912no—
421C2×D4—183no—
422C2×D4—1824no—
423C2×D4—183no—
424C2×D4—186no—
425C2×D4#62613yes—
426C22×C4—63no—
427C22×C4—63no—
428C22×C4—183no—
429C22×C4C2×D3213yes—
430Q16—912no—
431SD16—94no—
432SD16—912no—
433SD16—924no—
434D8—912no—
435M16—312no—
436C2×C8—31no—
437C2×C8—33no—
438C2×C8—312no—
439C22×C3—26no—
440C22×C3—26no—
441C22×C3—26no—
442C22×C3—21no—
443C22×C3—46no—
444C22×C3—62no—
445C22×C3—122no—
446C22×C3C22×D1216yes—
447C22×C3C22×D1211yescharacteristic
448C22×C3C22×#6716yes—
449C22×C3C22×#6711yescharacteristic
450C2×D3—22no—
451C2×D3—42no—
452C2×D3—612no—
453C2×D3—66no—
454C2×D3—66no—
455C2×D3—1212no—
456C2×D3—126no—
457C2×D3—126no—
458C2×D3—2412no—
459C2×D3—2412no—
460C2×D3—2424no—
461C3×C4—21no—
462C3×C4—26no—
463C3×C4—21no—
464C3×C4—66no—
465C3×C4C22×D1211yescharacteristic
466C3×C4C22×D1216yes—
467C3×C4C22×#6711yescharacteristic
468C3×C4C22×#6716yes—
469C3×C4C24×D311yescharacteristic
470C3×C4C24×D311yescharacteristic
471Dic3—26no—
472Dic3—64no—
473Dic3—62no—
474Dic3—62no—
475C32C2×#57711yescharacteristic, complemented, Sylow
476C23—61no—
477C23—183no—
478C23—1812no—
479C23—726no—
480C23C2×#62613yes—
481Q8—36no—
482Q8—612no—
483Q8—63no—
484Q8—92no—
485Q8—181no—
486Q8C2×#62614yes—
487D4—32no—
488D4—612no—
489D4—61no—
490D4—96no—
491D4—1812no—
492D4—1812no—
493D4—183no—
494D4C2×#626112yes—
495C2×C4—612no—
496C2×C4—63no—
497C2×C4—612no—
498C2×C4—181no—
499C2×C4—1812no—
500C2×C4C2×#62616yes—
501C2×C4C2×#62613yes—
502C2×C4C22×D3216yes—
503C2×C4C22×D3211yescharacteristic
504C8—32no—
505C8—36no—
506C2×C3—26no—
507C2×C3—26no—
508C2×C3—21no—
509C2×C3—22no—
510C2×C3—46no—
511C2×C3—122no—
512C2×C3#575112yescomplemented
513C2×C3#583712yescomplemented
514C2×C3C23×D1211yescharacteristic
515C2×C3C23×#6711yescharacteristic
516D3—42no—
517D3—1212no—
518D3—126no—
519D3—126no—
520C22—26no—
521C22—62no—
522C22—122no—
523C22—186no—
524C22—366no—
525C22—7212no—
526C22C22×#62616yes—
527C22C22×#62611yescharacteristic
528C4—66no—
529C4—182no—
530C4C22×#62616yes—
531C4C22×#62611yescharacteristic
532C4C23×D3211yescharacteristic
533C3—21no—
534C3C2×#575111yescharacteristic, complemented
535C3C2×#583711yescharacteristic, complemented
536C2—26no—
537C2—122no—
538C2—366no—
539C2#1059544812yesdirect product factor
540C2C23×#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×#64366C2semidirect
2. C2×C3×#1010C2semidirect
3. C2×C3×#948C2semidirect
4. #10595448C2direct (N × H)
5. C2×#63833C2semidirect
6. C22×#3717C2semidirect
7. C2×#63829C2semidirect
8. C2×#63825C2semidirect
13. #64366C22semidirect
19. C3×#1010C22semidirect
22. C2×C3×#235C22semidirect
23. C22×C3×Dic6C22semidirect
24. C3×#948C22semidirect
25. C2×C3×#208C22semidirect
26. C22×C3×C3⋊C8C22semidirect
27. C2×#3719C22semidirect
28. #63833C22semidirect
29. C2×#3717C22semidirect
30. C2×#3717C22semidirect
31. C2×#3717C22semidirect
32. #63829C22semidirect
33. C2×#3716C22semidirect
34. #63825C22semidirect
35. C2×#3714C22semidirect
37. C2×#1010D3semidirect
45. C2×#948D3semidirect
75. C3×#235C23semidirect
81. C2×C3×Dic6C23semidirect
82. C3×#208C23semidirect
85. C2×C3×C3⋊C8C23semidirect
86. #3719C23semidirect
87. #3717C23semidirect
88. #3717C23semidirect
89. #3716C23semidirect
90. #3714C23semidirect
102. #1010C2×D3semidirect
120. C2×#235C2×D3semidirect
124. C22×Dic6C2×D3semidirect
130. #948C2×D3semidirect
138. C2×#208C2×D3semidirect
139. C22×C3⋊C8C2×D3semidirect
237. #235C22×D3semidirect
261. C2×Dic6C22×D3semidirect
271. #208C22×D3semidirect
274. C2×C3⋊C8C22×D3semidirect
397. C2×C32#577semidirect
475. C32C2×#577semidirect
512. C2×C3#5751semidirect
513. C2×C3#5837semidirect
534. C3C2×#5751semidirect
535. C3C2×#5837semidirect
539. C2#10595448direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#643662
C2×C3×#10102
C2×C3×#9482
#105954482
C2×#638332
C22×#37172
C2×#638292
C2×#638252
C2×#58373
C2×#57513