Finite Group Databasebeta

← #11904253

Subgroups — #11904253

Order 1152.

2560 conjugacy classes of subgroups.

The subgroup lattice has 567 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596048C211yesmaximal, characteristic, complemented
2C3×C4×#239C211yesmaximal, characteristic, complemented
3C3×Q8×Dic6C211yesmaximal, characteristic, complemented
4#10595410C212yesmaximal, complemented
5#10595386C212yesmaximal, complemented
6#10594564C216yesmaximal, complemented
7#10594518C216yesmaximal, complemented
8#10593987C213yesmaximal, complemented
9#10593970C213yesmaximal, complemented
10C4×#3799C213yesmaximal, complemented
11#10593902C213yesmaximal, complemented
12#87040—31nomaximal
13#85845—31nomaximal
14C2×#3832C2212yes—
15C2×C3×#239C2211yescharacteristic
16C2×#3799C2213yes—
17C2×#3799C2216yes—
18C32×C4×Q8C2211yescharacteristic
19#64104C2216yes—
20#64083C2213yes—
21C4×C4⋊(C3⋊D3)C2213yes—
22C3×Q8×Dic3C2211yescharacteristic
23C3×Q8×Dic3C2212yes—
24C3×#893C2213yes—
25C3×#892C2213yes—
26C3×#888C2216yes—
27C3×C4×D12C2213yes—
28C3×C42×D3C2213yes—
29C3×#869C2213yes—
30C3×C4×Dic6C2213yes—
31#63916C2216yes—
32#63911C2216yes—
33#63910C22112yes—
34#63909C2216yes—
35#63909C2216yes—
36#63907C22112yes—
37#63904C2216yes—
38C4×#626C2216yes—
39#63894C2216yes—
40#63894C2216yes—
41#63894C2213yes—
42C4×#624C2216yes—
43#63864C2216yes—
44#63849C2216yes—
45Dic3×Dic6C2211yescharacteristic
46#63841C2213yes—
47#63836C2216yes—
48C3×Q82—31no—
49C3×C4×#41—31no—
50#5834—32no—
51#5734—36no—
52#5734—33no—
53#5725—36no—
54#5725—33no—
55#5577—32no—
56#5577—31no—
57#5577—31no—
58#5577—33no—
59#5577—61no—
60C4×#239—32no—
61C4×#239—32no—
62C4×#239—33no—
63C4×#239D311yescharacteristic, complemented
64Q8×Dic6D311yescharacteristic, complemented
65#5563—33no—
66#5553—33no—
67#5548—36no—
68#5532—36no—
69#5477—33no—
70C4×#235—33no—
71C2×C32×Q8C2311yescharacteristic
72#3832—28no—
73C2×C4⋊(C3⋊D3)C2313yes—
74C2×C4⋊(C3⋊D3)C2316yes—
75C2×C4⋊(C3⋊D3)C2316yes—
76C2×C4×C3⋊D3C2316yes—
77C3×#239—24no—
78C2×C3×D12C2313yes—
79C2×C3×C4×D3C2313yes—
80C2×C3×C4×D3C2313yes—
81C2×C3×C4×D3C2313yes—
82C2×C3×Dic6C2316yes—
83C2×C3×Dic6C2311yescharacteristic
84C2×#626C2316yes—
85C2×#626C23112yes—
86C2×#624C2316yes—
87C2×#624C2316yes—
88#3799—212no—
89#3799—412no—
90C32×C4⋊C4C2313yes—
91C32×C42C2313yes—
92#3752C2316yes—
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C3×(C2×D3)⋊C4C2316yes—
95C3×C4⋊Dic3C2316yes—
96C3×C4⋊Dic3C2313yes—
97C3×C4⋊Dic3C2313yes—
98C3×Dic3⋊C4C2316yes—
99C3×C4×Dic3C2316yes—
100C3×C4×Dic3C2313yes—
101C3×C4×Dic3C2313yes—
102C3×C4×Dic3C2311yescharacteristic
103Dic3⋊Dic3C2312yes—
104#3722C2316yes—
105#3722C23112yes—
106(C2×D3)⋊Dic3C2316yes—
107Dic32C2316yes—
108Dic32C2312yes—
109#3483—91noSylow
110C2×C3×#41—31no—
111C2×#239—32no—
112C2×#239—32no—
113C2×#239—33no—
114C2×#239—36no—
115C2×#239—62no—
116C2×#239C2×D311yescharacteristic
117C2×#235—33no—
118C2×#235—36no—
119C3×C4⋊Q8—36no—
120C3×C4⋊Q8—33no—
121C3×C4×Q8—21no—
122C3×C4×Q8—32no—
123C3×C4×Q8—31no—
124C3×C4×Q8—33no—
125C3×C4×Q8C2×D311yescharacteristic
126C3×C4×Q8C2×D311yescharacteristic
127C3×C4×D4—33no—
128C3×C4×D4—33no—
129C3×#117—33no—
130C2×C3×C42—33no—
131#947—312no—
132#947—36no—
133Q8×Dic3—31no—
134Q8×Dic3C2×D312yes—
135Q8×Dic3C2×D311yescharacteristic
136#940—36no—
137#938—36no—
138#930—36no—
139#930—36no—
140C4×#67—36no—
141C4×#67—36no—
142#926—33no—
143#895—36no—
144#895—36no—
145#895—36no—
146#895—36no—
147#895—36no—
148#895—312no—
149#895—66no—
150#893—36no—
151#893—36no—
152#893—33no—
153#893—36no—
154#893C2×D313yes—
155#892—33no—
156#892—36no—
157#892—36no—
158#892—36no—
159#892C2×D313yes—
160#888C2×D316yes—
161#885—312no—
162#884—312no—
163#875—36no—
164#874—36no—
165#874—33no—
166#874—33no—
167#874—63no—
168C4×D12—36no—
169C4×D12—33no—
170C4×D12—33no—
171C4×D12—33no—
172C4×D12—36no—
173C4×D12—36no—
174C4×D12—63no—
175C4×D12C2×D313yes—
176#872—36no—
177C42×D3—36no—
178C42×D3—36no—
179C42×D3C2×D313yes—
180#869C2×D313yes—
181C4×Dic6—31no—
182C4×Dic6C2×D313yes—
183C22×C3⋊D3C2416yes—
184C22×C3×D3C2413yes—
185C32×Q8#4114yescomplemented
186C2×C32×C4C2413yes—
187C2×C32×C4C2413yes—
188C2×C32×C4C2411yescharacteristic
189C2×C3⋊Dic3C2412yes—
190C4⋊(C3⋊D3)—26no—
191C4⋊(C3⋊D3)—212no—
192C4⋊(C3⋊D3)—46no—
193C4×C3⋊D3—212no—
194C2×C3×Dic3C2413yes—
195C2×C3×Dic3C2416yes—
196C2×C3×Dic3C2411yescharacteristic
197C2×C3×Dic3C2412yes—
198C2×C3×Dic3C2411yescharacteristic
199C3×D12—26no—
200C3×C4×D3—26no—
201C3×C4×D3—26no—
202C3×C4×D3—26no—
203C3×Dic6—46no—
204C3×Dic6#4114yescomplemented
205#626—212no—
206#626—412no—
207#624—212no—
208#624—212no—
209Q82—31no—
210#555—96no—
211#555—93no—
212#550—93no—
213#550—92no—
214#550—91no—
215#532—93no—
216#532—96no—
217C4×#41—31no—
218C4×#41—93no—
219C4×#41—92no—
220C3×#41—64no—
221C2×C3×Q8—21no—
222C2×C3×Q8—31no—
223C2×C3×Q8—36no—
224C2×C3×Q8C22×D311yescharacteristic
225C2×C3×Q8C22×D311yescharacteristic
226C2×C3×D4—33no—
227C22×C3×C4—33no—
228C22×C3×C4—33no—
229C22×C3×C4—33no—
230C2×#67—36no—
231C2×#67—312no—
232#239—24no—
233#239—612no—
234#239—68no—
235#239—68no—
236#239—128no—
237#239—1212no—
238#235—612no—
239#235—1212no—
240C2×D12—36no—
241C2×D12—33no—
242C2×D12—36no—
243C2×D12—33no—
244C2×D12—36no—
245C2×D12—312no—
246C2×D12—36no—
247C2×D12—36no—
248C2×D12—63no—
249C2×D12—66no—
250C2×D12—66no—
251C2×D12C22×D313yes—
252C2×C4×D3—36no—
253C2×C4×D3—36no—
254C2×C4×D3—36no—
255C2×C4×D3—36no—
256C2×C4×D3—36no—
257C2×C4×D3—36no—
258C2×C4×D3—66no—
259C2×C4×D3C22×D313yes—
260C2×C4×D3C22×D313yes—
261C2×C4×D3C22×D313yes—
262C2×Dic6C22×D316yes—
263C2×Dic6C22×D311yescharacteristic
264C3×C4⋊C4—23no—
265C3×C4⋊C4—33no—
266C3×C4⋊C4—36no—
267C3×C4⋊C4—36no—
268C3×C4⋊C4—33no—
269C3×C4⋊C4C22×D313yes—
270C3×C4⋊C4C22×D313yes—
271C3×C22⋊C4—36no—
272C3×C42—23no—
273C3×C42—31no—
274C3×C42—33no—
275C3×C42—36no—
276C3×C42—33no—
277C3×C42C22×D313yes—
278C3×C42C22×D313yes—
279#217—36no—
280(C2×D3)⋊C4—36no—
281(C2×D3)⋊C4—36no—
282(C2×D3)⋊C4—36no—
283(C2×D3)⋊C4—36no—
284(C2×D3)⋊C4—312no—
285(C2×D3)⋊C4—312no—
286(C2×D3)⋊C4—36no—
287(C2×D3)⋊C4—66no—
288(C2×D3)⋊C4C22×D316yes—
289C4⋊Dic3—31no—
290C4⋊Dic3—31no—
291C4⋊Dic3—32no—
292C4⋊Dic3—61no—
293C4⋊Dic3C22×D313yes—
294C4⋊Dic3C22×D316yes—
295C4⋊Dic3C22×D313yes—
296Dic3⋊C4—32no—
297Dic3⋊C4C22×D316yes—
298C4×Dic3—32no—
299C4×Dic3—32no—
300C4×Dic3—36no—
301C4×Dic3—36no—
302C4×Dic3C22×D316yes—
303C4×Dic3C22×D313yes—
304C4×Dic3C22×D311yescharacteristic
305C4×Dic3C22×D313yes—
306C22×C32C2511yescharacteristic
307C2×C3⋊D3—26no—
308C2×C3⋊D3—26no—
309C2×C3⋊D3—26no—
310C2×C3×D3—23no—
311C2×C3×D3—23no—
312C2×C3×D3—23no—
313C32×C4—23no—
314C32×C4C2×#4116yes—
315C32×C4C2×#4112yes—
316C3⋊Dic3—22no—
317C3×Dic3—23no—
318C3×Dic3—21no—
319C3×Dic3—26no—
320C3×Dic3C2×#4114yes—
321C3×Dic3H(5,𝔽2)12yes—
322C2×#41—31no—
323C2×#41—93no—
324C2×#41—96no—
325C2×#41—92no—
326C4⋊Q8—36no—
327C4⋊Q8—33no—
328#127—96no—
329#127—93no—
330#124—96no—
331#124—912no—
332#121—912no—
333#121—96no—
334#121—96no—
335#121—96no—
336#121—96no—
337C4×Q8—31no—
338C4×Q8—32no—
339C4×Q8—33no—
340C4×Q8—91no—
341C4×Q8D3211yescharacteristic
342C4×D4—33no—
343C4×D4—33no—
344C4×D4—93no—
345C4×D4—96no—
346C4×D4—96no—
347C4×D4—96no—
348C4×D4—96no—
349C4×D4—93no—
350#117—33no—
351#117—96no—
352#117—96no—
353#117—93no—
354C2×C42—33no—
355C2×C42—96no—
356C23×C3—33no—
357C22×D3—36no—
358C22×D3—36no—
359C22×D3—66no—
360C22×D3C23×D313yes—
361C3×Q8—24no—
362C3×Q8—34no—
363C3×Q8—126no—
364C3×Q8#23514yescomplemented
365C3×Q8#23914yescomplemented
366C3×D4—66no—
367C2×C3×C4—21no—
368C2×C3×C4—23no—
369C2×C3×C4—23no—
370C2×C3×C4—31no—
371C2×C3×C4—32no—
372C2×C3×C4—33no—
373C2×C3×C4—36no—
374C2×C3×C4—31no—
375C2×C3×C4—66no—
376C2×C3×C4—66no—
377C2×C3×C4—66no—
378C2×C3×C4C23×D313yes—
379C2×C3×C4C23×D313yes—
380C2×C3×C4C23×D313yes—
381C2×C3×C4C23×D313yes—
382C2×C3×C4C23×D311yescharacteristic
383C2×C3×C4C23×D311yescharacteristic
384#67—612no—
385#67—1212no—
386C2×Dic3—32no—
387C2×Dic3—32no—
388C2×Dic3—62no—
389C2×Dic3C23×D313yes—
390C2×Dic3C23×D316yes—
391C2×Dic3C23×D311yescharacteristic
392C2×Dic3C23×D312yes—
393C2×Dic3C23×D311yescharacteristic
394D12—26no—
395D12—612no—
396D12—612no—
397D12—66no—
398D12—612no—
399D12—66no—
400D12—126no—
401D12—1212no—
402D12—126no—
403D12—126no—
404D12—1212no—
405D12—246no—
406C4×D3—26no—
407C4×D3—26no—
408C4×D3—26no—
409C4×D3—612no—
410C4×D3—612no—
411C4×D3—612no—
412C4×D3—612no—
413C4×D3—612no—
414C4×D3—612no—
415C4×D3—1212no—
416Dic6—46no—
417Dic6#23914yescomplemented
418C2×C32C22×#4111yescharacteristic
419C2×C32C22×#4111yescharacteristic
420C2×C32C2×H(5,𝔽2)11yescharacteristic
421C3⋊D3—46no—
422C3×D3—43no—
423#41—64no—
424#41—1812no—
425#41—188no—
426#41—3612no—
427C2×Q8—31no—
428C2×Q8—36no—
429C2×Q8C2×D3211yescharacteristic
430C2×D4—33no—
431C2×D4—96no—
432C2×D4—912no—
433C2×D4—96no—
434C2×D4—93no—
435C2×D4—96no—
436C22×C4—33no—
437C22×C4—33no—
438C22×C4—33no—
439C22×C4—96no—
440C22×C4—96no—
441C22×C4—96no—
442C4⋊C4—33no—
443C4⋊C4—36no—
444C4⋊C4—36no—
445C4⋊C4—33no—
446C4⋊C4—92no—
447C4⋊C4—91no—
448C4⋊C4C2×D3213yes—
449C22⋊C4—36no—
450C22⋊C4—96no—
451C22⋊C4—912no—
452C22⋊C4—96no—
453C22⋊C4—96no—
454C42—31no—
455C42—33no—
456C42—33no—
457C42—36no—
458C42—92no—
459C42—96no—
460C42C2×D3213yes—
461C22×C3—21no—
462C22×C3—63no—
463C22×C3—63no—
464C22×C3—63no—
465C22×C3C24×D311yescharacteristic
466C22×C3C24×D311yescharacteristic
467C2×D3—23no—
468C2×D3—23no—
469C2×D3—23no—
470C2×D3—66no—
471C2×D3—66no—
472C2×D3—66no—
473C2×D3—66no—
474C2×D3—66no—
475C2×D3—66no—
476C2×D3—126no—
477C2×D3—126no—
478C2×D3—126no—
479C3×C4—23no—
480C3×C4—23no—
481C3×C4—26no—
482C3×C4—22no—
483C3×C4—34no—
484C3×C4—32no—
485C3×C4—43no—
486C3×C4—63no—
487C3×C4—61no—
488C3×C4—66no—
489C3×C4C2×#23516yes—
490C3×C4C2×#23916yes—
491C3×C4C2×#23912yes—
492C3×C4D3×#4112yes—
493Dic3—21no—
494Dic3—23no—
495Dic3—26no—
496Dic3—62no—
497Dic3—62no—
498Dic3—122no—
499Dic3C2×#23914yes—
500Dic3#100912yes—
501C32#348311yescharacteristic, complemented, Sylow
502C23—33no—
503C23—96no—
504Q8—34no—
505Q8—126no—
506Q8#379914yescomplemented
507D4—66no—
508D4—1812no—
509D4—1812no—
510D4—186no—
511D4—366no—
512D4—3612no—
513C2×C4—31no—
514C2×C4—32no—
515C2×C4—31no—
516C2×C4—33no—
517C2×C4—36no—
518C2×C4—66no—
519C2×C4—66no—
520C2×C4—66no—
521C2×C4—92no—
522C2×C4—1812no—
523C2×C4—1812no—
524C2×C4—1812no—
525C2×C4C22×D3213yes—
526C2×C4C22×D3213yes—
527C2×C4C22×D3211yescharacteristic
528C2×C3—21no—
529C2×C3—21no—
530C2×C3—21no—
531C2×C3—123no—
532C2×C3C22×#23511yescharacteristic
533C2×C3C22×#23911yescharacteristic
534C2×C3C22×#23911yescharacteristic
535C2×C3C2×D3×#4111yescharacteristic
536C2×C3C2×#100911yescharacteristic
537C2×C3D3×H(5,𝔽2)11yescharacteristic
538D3—43no—
539D3—126no—
540D3—126no—
541D3—246no—
542C22—63no—
543C22—63no—
544C22—63no—
545C22—186no—
546C22—186no—
547C22—186no—
548C22C23×D3211yescharacteristic
549C4—23no—
550C4—34no—
551C4—32no—
552C4—61no—
553C4—63no—
554C4—66no—
555C4—182no—
556C4C2×#379916yes—
557C4D3×#23912yes—
558C3—21no—
559C3#8584511yescharacteristic, complemented
560C3#8704011yescharacteristic, complemented
561C2—123no—
562C2—366no—
563C2C22×#379911yescharacteristic
564C2C2×D3×#23911yescharacteristic
565C2D3×#100911yescharacteristic
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC32×C4×Q8C22
hypercenterC4×Q8D32
hypocenterC32#3483
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #10596048C2semidirect
2. C3×C4×#239C2semidirect
3. C3×Q8×Dic6C2semidirect
4. #10595410C2semidirect
5. #10595386C2semidirect
6. #10594564C2semidirect
7. #10594518C2semidirect
8. #10593987C2semidirect
9. #10593970C2semidirect
10. C4×#3799C2semidirect
11. #10593902C2semidirect
63. C4×#239D3semidirect
64. Q8×Dic6D3semidirect
185. C32×Q8#41semidirect
204. C3×Dic6#41semidirect
364. C3×Q8#235semidirect
365. C3×Q8#239semidirect
417. Dic6#239semidirect
501. C32#3483semidirect
506. Q8#3799semidirect
559. C3#85845semidirect
560. C3#87040semidirect

Maximal subgroups

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

subgroupindex
#105960482
C3×C4×#2392
C3×Q8×Dic62
#105954102
#105953862
#105945642
#105945182
#105939872
#105939702
C4×#37992
#105939022
#870403
#858453