Finite Group Databasebeta

← C2×#10595450 #11918947

Subgroups — C2×#10595450 #11918947

Order 1152.

3213 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64367C211yesmaximal, characteristic, complemented
2C2×C3×#1010C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4#10595450C2116yesmaximal, direct product factor
5C22×#3719C213yesmaximal, complemented
6C2×#63833C213yesmaximal, complemented
7C2×#63831C213yesmaximal, complemented
8C2×#63829C213yesmaximal, complemented
9C2×#5838—31nomaximal
10C2×#5753—31nomaximal
11C2×C32×#41C2211yescharacteristic
12#64367—24no—
13#64367C2218yescomplemented
14C2×Q8×C3⋊D3—21no—
15C2×#3830—23no—
16C2×#3828C2213yes—
17C22×#634C2213yes—
18C3×#1010—24no—
19C3×#1010C2218yescomplemented
20C2×C3×D3×Q8—21no—
21C2×C3×#237—23no—
22C2×C3×#235C2213yes—
23C22×C3×Dic6C2213yes—
24C3×#948C2218yescomplemented
25C2×C3×#208C2213yes—
26C22×C3×C3⋊C8C2213yes—
27C2×#3719C2213yes—
28C2×#3719C2216yes—
29C2×#3719C22124yescomplemented
30#63833C22124yescomplemented
31C2×#3717C2213yes—
32#63831C22124yescomplemented
33#63829C22124yescomplemented
34C2×#3716C2213yes—
35C2×#3714C2211yescharacteristic
36C2×C3×2−1+4—31no—
37C2×#1010—31no—
38C2×#1010—31no—
39C2×#1010—61no—
40C2×#1010D311yescharacteristic, complemented
41C2×C3×#131—31no—
42#5838—316no—
43C2×#951—33no—
44C2×#950—33no—
45C2×#948D311yescharacteristic, complemented
46C22×#216—33no—
47C2×#942—33no—
48#5753—316no—
49C2×#909—33no—
50C2×#909—33no—
51C22×Dic12—33no—
52C2×#904—33no—
53C32×#41D414yes—
54C32×#41C2314yes—
55C2×C32×Q8D411yescharacteristic
56C2×C32×D4D413yes—
57C22×C32×C4C2313yes—
58C2×#638—23no—
59C22×C3⋊Dic3—23no—
60Q8×C3⋊D3—28no—
61#3830—224no—
62#3828—26no—
63#3828C23112yes—
64C2×C4⋊(C3⋊D3)C2311yescharacteristic
65C2×C4×C3⋊D3—23no—
66C2×#634—23no—
67C2×#634—26no—
68C2×#634C2313yes—
69C2×#634C23112yes—
70C2×C3×#67—23no—
71C22×C3×Dic3—23no—
72C3×D3×Q8—28no—
73C3×#237—224no—
74C3×#235—26no—
75C3×#235C23112yes—
76C2×C3×D12C2311yescharacteristic
77C2×C3×C4×D3—23no—
78C2×C3×Dic6—23no—
79C2×C3×Dic6—26no—
80C2×C3×Dic6C2313yes—
81C2×C3×Dic6C23112yes—
82C3×#208C23112yes—
83C2×C3×C3⋊C8C2311yescharacteristic
84C2×C3×C3⋊C8C2313yes—
85C2×C3×C3⋊C8C23112yes—
86#3719C23112yes—
87#3719C23124yes—
88#3717C23112yes—
89#3716C23112yes—
90#3714C2314yes—
91C2×#578—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#1010—38no—
103#1010—38no—
104#1010—68no—
105#1010—68no—
106#1010—64no—
107#1010—64no—
108#1010C2×D318yescomplemented
109C2×D3×Q8—21no—
110C2×D3×Q8—62no—
111C2×D3×Q8—61no—
112C2×D3×Q8—61no—
113C2×#237—23no—
114C2×#237—66no—
115C2×#237—63no—
116C2×#237—63no—
117C2×#235—33no—
118C2×#235—33no—
119C2×#235—63no—
120C2×#235C2×D313yes—
121C22×Dic6—33no—
122C22×Dic6—33no—
123C22×Dic6—63no—
124C22×Dic6C2×D313yes—
125C3×#131—38no—
126C2×C3×M16—33no—
127C22×C3×C8—33no—
128#951—324no—
129#950—324no—
130#948C2×D318yescomplemented
131C2×#216—36no—
132C2×#216—33no—
133C2×#216—324no—
134#942—324no—
135C2×#215—33no—
136C2×#214—33no—
137C2×#213—31no—
138C2×#208C2×D313yes—
139C22×C3⋊C8C2×D313yes—
140#909—324no—
141#909—324no—
142C2×Dic12—33no—
143C2×Dic12—36no—
144C2×Dic12—324no—
145#904—324no—
146C2×D24—31no—
147C2×#204—33no—
148C2×#204—33no—
149C23×C32C2×D413yes—
150C22×C3⋊D3—21no—
151C22×C3×D3—21no—
152C32×Q8C2×D414yes—
153C32×D4C2×D4112yes—
154C2×C32×C4C2×D413yes—
155C2×C32×C4C2×D416yes—
156C2×C32×C4C2411yescharacteristic
157C2×C32×C4C2416yes—
158#638—212no—
159C2×C3⋊Dic3—23no—
160C2×C3⋊Dic3—212no—
161C4⋊(C3⋊D3)—21no—
162C4⋊(C3⋊D3)C2412yes—
163C4×C3⋊D3—212no—
164#634—23no—
165#634—212no—
166#634C2416yes—
167C3×#67—212no—
168C2×C3×Dic3—23no—
169C2×C3×Dic3—212no—
170C3×D12—21no—
171C3×D12C2412yes—
172C3×C4×D3—212no—
173C3×Dic6—23no—
174C3×Dic6—212no—
175C3×Dic6C2416yes—
176C3×C3⋊C8C2412yes—
177C3×C3⋊C8C2416yes—
178C2×2−1+4—31no—
179C2×2−1+4—91no—
180#578—916no—
181C2×#137—93no—
182C2×#137—93no—
183C2×#135—93no—
184C22×Q16—93no—
185C2×#131—31no—
186C3×#41—24no—
187C3×#41—24no—
188C3×#41—312no—
189C3×#41—624no—
190C3×#41—66no—
191C3×#41D1214yes—
192C3×#41#6714yes—
193C3×#41C22×D314yes—
194C3×#41C22×D314yes—
195C2×C3×Q8—21no—
196C2×C3×Q8—33no—
197C2×C3×Q8—312no—
198C2×C3×Q8—68no—
199C2×C3×Q8—63no—
200C2×C3×Q8—66no—
201C2×C3×Q8D1211yescharacteristic
202C2×C3×Q8#6711yescharacteristic
203C2×C3×D4—23no—
204C2×C3×D4—31no—
205C2×C3×D4—63no—
206C2×C3×D4D1213yes—
207C2×C3×D4#6713yes—
208C22×C3×C4—23no—
209C22×C3×C4—63no—
210C22×C3×C4—63no—
211C22×C3×C4C22×D313yes—
212C22×C3×C4C22×D313yes—
213C2×#67—23no—
214C2×#67—66no—
215C2×#67—63no—
216C2×#67—63no—
217C22×Dic3—23no—
218C22×Dic3—66no—
219C22×Dic3—63no—
220C22×Dic3—63no—
221D3×Q8—28no—
222D3×Q8—616no—
223D3×Q8—68no—
224D3×Q8—68no—
225#237—224no—
226#237—648no—
227#237—624no—
228#237—624no—
229#235—26no—
230#235—312no—
231#235—312no—
232#235—612no—
233#235—612no—
234#235—66no—
235#235—66no—
236#235C22×D3112yes—
237C2×D12—31no—
238C2×D12—31no—
239C2×D12—61no—
240C2×D12C22×D311yescharacteristic
241C2×C4×D3—23no—
242C2×C4×D3—66no—
243C2×C4×D3—63no—
244C2×C4×D3—63no—
245C2×Dic6—23no—
246C2×Dic6—26no—
247C2×Dic6—33no—
248C2×Dic6—312no—
249C2×Dic6—33no—
250C2×Dic6—312no—
251C2×Dic6—63no—
252C2×Dic6—612no—
253C2×Dic6—66no—
254C2×Dic6—612no—
255C2×Dic6—63no—
256C2×Dic6—66no—
257C2×Dic6—63no—
258C2×Dic6—66no—
259C2×Dic6C22×D313yes—
260C2×Dic6C22×D3112yes—
261C3×M16—312no—
262C2×C3×C8—33no—
263C2×C3×C8—31no—
264C2×C3×C8—312no—
265#216—324no—
266#216—312no—
267#215—312no—
268#214—312no—
269#213—34no—
270#208C22×D3112yes—
271C2×C3⋊C8C22×D311yescharacteristic
272C2×C3⋊C8C22×D313yes—
273C2×C3⋊C8C22×D3112yes—
274Dic12—312no—
275Dic12—324no—
276D24—34no—
277#204—312no—
278#204—312no—
279C22×C32—26no—
280C22×C32C22×D416yes—
281C22×C32C22×D411yescharacteristic
282C2×C3⋊D3—22no—
283C2×C3⋊D3—42no—
284C2×C3×D3—22no—
285C2×C3×D3—42no—
286C32×C4C22×D411yescharacteristic
287C32×C4C22×D416yes—
288C32×C4C2511yescharacteristic
289C3⋊Dic3—26no—
290C3×Dic3—26no—
2912−1+4—38no—
2922−1+4—64no—
2932−1+4—98no—
2942−1+4—184no—
295C2×#41—33no—
296C2×#41—63no—
297C2×#41—93no—
298C2×#41—183no—
299C2×#41D3211yescharacteristic
300C22×Q8—33no—
301C22×Q8—61no—
302C22×Q8—93no—
303C22×Q8—181no—
304#137—924no—
305#137—924no—
306#135—924no—
307C2×Q16—93no—
308C2×Q16—96no—
309C2×Q16—924no—
310C2×SD16—93no—
311C2×SD16—93no—
312C2×D8—91no—
313#131—38no—
314C2×M16—33no—
315C22×C8—33no—
316C23×C3—23no—
317C23×C3—61no—
318C23×C3C2×D1213yes—
319C23×C3C2×#6713yes—
320C22×D3—21no—
321C22×D3—62no—
322C22×D3—61no—
323C22×D3—61no—
324C3×Q8—24no—
325C3×Q8—36no—
326C3×Q8—63no—
327C3×Q8—612no—
328C3×Q8C2×D1214yes—
329C3×Q8C2×#6714yes—
330C3×D4—212no—
331C3×D4—32no—
332C3×D4—612no—
333C3×D4—61no—
334C3×D4C2×D12112yes—
335C3×D4C2×#67112yes—
336C2×C3×C4—21no—
337C2×C3×C4—26no—
338C2×C3×C4—23no—
339C2×C3×C4—26no—
340C2×C3×C4—63no—
341C2×C3×C4—612no—
342C2×C3×C4—612no—
343C2×C3×C4C2×D1213yes—
344C2×C3×C4C2×D1216yes—
345C2×C3×C4C2×#6713yes—
346C2×C3×C4C2×#6716yes—
347C2×C3×C4C23×D311yescharacteristic
348C2×C3×C4C23×D316yes—
349C2×C3×C4C23×D311yescharacteristic
350C2×C3×C4C23×D316yes—
351#67—212no—
352#67—624no—
353#67—612no—
354#67—612no—
355C2×Dic3—23no—
356C2×Dic3—212no—
357C2×Dic3—66no—
358C2×Dic3—624no—
359C2×Dic3—63no—
360C2×Dic3—612no—
361C2×Dic3—63no—
362C2×Dic3—612no—
363D12—21no—
364D12—32no—
365D12—32no—
366D12—62no—
367D12—62no—
368D12—61no—
369D12—61no—
370D12C23×D312yes—
371C4×D3—212no—
372C4×D3—624no—
373C4×D3—612no—
374C4×D3—612no—
375Dic6—23no—
376Dic6—212no—
377Dic6—36no—
378Dic6—36no—
379Dic6—66no—
380Dic6—66no—
381Dic6—624no—
382Dic6—63no—
383Dic6—612no—
384Dic6—63no—
385Dic6—612no—
386Dic6C23×D316yes—
387C3×C8—36no—
388C3×C8—32no—
389C3⋊C8C23×D312yes—
390C3⋊C8C23×D316yes—
391C2×C32—26no—
392C2×C32#57812yescomplemented
393C2×C32C23×D411yescharacteristic
394C3⋊D3—42no—
395C3×D3—42no—
396#41—312no—
397#41—624no—
398#41—66no—
399#41—912no—
400#41—1824no—
401#41—186no—
402#41#62614yes—
403#41C2×D3214yes—
404C2×Q8—33no—
405C2×Q8—312no—
406C2×Q8—68no—
407C2×Q8—63no—
408C2×Q8—66no—
409C2×Q8—93no—
410C2×Q8—912no—
411C2×Q8—188no—
412C2×Q8—183no—
413C2×Q8—186no—
414C2×Q8#62611yescharacteristic
415C2×D4—31no—
416C2×D4—63no—
417C2×D4—91no—
418C2×D4—183no—
419C2×D4#62613yes—
420C22×C4—63no—
421C22×C4—63no—
422C22×C4—183no—
423C22×C4—183no—
424C22×C4C2×D3213yes—
425Q16—912no—
426Q16—924no—
427SD16—912no—
428SD16—912no—
429D8—94no—
430M16—312no—
431C2×C8—31no—
432C2×C8—33no—
433C2×C8—312no—
434C22×C3—26no—
435C22×C3—26no—
436C22×C3—26no—
437C22×C3—21no—
438C22×C3—46no—
439C22×C3—62no—
440C22×C3—122no—
441C22×C3C22×D1216yes—
442C22×C3C22×D1211yescharacteristic
443C22×C3C22×#6716yes—
444C22×C3C22×#6711yescharacteristic
445C2×D3—22no—
446C2×D3—42no—
447C2×D3—64no—
448C2×D3—62no—
449C2×D3—62no—
450C2×D3—124no—
451C2×D3—122no—
452C2×D3—122no—
453C3×C4—21no—
454C3×C4—26no—
455C3×C4—21no—
456C3×C4—66no—
457C3×C4C22×D1211yescharacteristic
458C3×C4C22×D1216yes—
459C3×C4C22×#6711yescharacteristic
460C3×C4C22×#6716yes—
461C3×C4C24×D311yescharacteristic
462C3×C4C24×D311yescharacteristic
463Dic3—26no—
464Dic3—612no—
465Dic3—66no—
466Dic3—66no—
467C32C2×#57811yescharacteristic, complemented, Sylow
468C23—61no—
469C23—181no—
470C23C2×#62613yes—
471Q8—36no—
472Q8—612no—
473Q8—63no—
474Q8—96no—
475Q8—1812no—
476Q8—183no—
477Q8C2×#62614yes—
478D4—32no—
479D4—612no—
480D4—61no—
481D4—92no—
482D4—1812no—
483D4—181no—
484D4C2×#626112yes—
485C2×C4—612no—
486C2×C4—63no—
487C2×C4—612no—
488C2×C4—1812no—
489C2×C4—183no—
490C2×C4—1812no—
491C2×C4C2×#62616yes—
492C2×C4C2×#62613yes—
493C2×C4C22×D3216yes—
494C2×C4C22×D3211yescharacteristic
495C8—32no—
496C8—36no—
497C2×C3—26no—
498C2×C3—26no—
499C2×C3—21no—
500C2×C3—22no—
501C2×C3—46no—
502C2×C3—122no—
503C2×C3#575312yescomplemented
504C2×C3#583812yescomplemented
505C2×C3C23×D1211yescharacteristic
506C2×C3C23×#6711yescharacteristic
507D3—42no—
508D3—124no—
509D3—122no—
510D3—122no—
511C22—26no—
512C22—62no—
513C22—122no—
514C22—182no—
515C22—362no—
516C22C22×#62616yes—
517C22C22×#62611yescharacteristic
518C4—66no—
519C4—186no—
520C4C22×#62616yes—
521C4C22×#62611yescharacteristic
522C4C23×D3211yescharacteristic
523C3—21no—
524C3C2×#575311yescharacteristic, complemented
525C3C2×#583811yescharacteristic, complemented
526C2—26no—
527C2—122no—
528C2—362no—
529C2#1059545012yesdirect product factor
530C2C23×#62611yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32C2×#578
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×#1010C2semidirect
3. C2×C3×#948C2semidirect
4. #10595450C2direct (N × H)
5. C22×#3719C2semidirect
6. C2×#63833C2semidirect
7. C2×#63831C2semidirect
8. C2×#63829C2semidirect
13. #64367C22semidirect
19. C3×#1010C22semidirect
24. C3×#948C22semidirect
29. C2×#3719C22semidirect
30. #63833C22semidirect
32. #63831C22semidirect
33. #63829C22semidirect
40. C2×#1010D3semidirect
45. C2×#948D3semidirect
108. #1010C2×D3semidirect
130. #948C2×D3semidirect
392. C2×C32#578semidirect
467. C32C2×#578semidirect
503. C2×C3#5753semidirect
504. C2×C3#5838semidirect
524. C3C2×#5753semidirect
525. C3C2×#5838semidirect
529. C2#10595450direct (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×#10102
C2×C3×#9482
#105954502
C22×#37192
C2×#638332
C2×#638312
C2×#638292
C2×#58383
C2×#57533