Finite Group Databasebeta

← #11865165

Subgroups — #11865165

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5964C211yesmaximal, characteristic, complemented
2#10596301C211yesmaximal, characteristic, complemented
3C2×#63825C212yesmaximal, complemented
4C3×#5237C211yesmaximal, characteristic, complemented
5#10591646C214yesmaximal, complemented
6#10591510C214yesmaximal, complemented
7#10591110C212yesmaximal, complemented
8#84122—31nomaximal
9#78717—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
12C3×#1010—22no—
13C3×#1009—22no—
14C3×D3×#41—24no—
15C3×#1007C2212yescomplemented
16C3×#1004—22no—
17C3×#1004C2212yescomplemented
18C2×C3×#235—22no—
19C2×C3×#235C2212yes—
20#64156C2212yescomplemented
21#64149C2212yescomplemented
22#64146—22no—
23#64139—22no—
24#64135C2211yescharacteristic, complemented
25C2×C3×#208C2212yescomplemented
26C2×#3717—22no—
27#63825—24no—
28#63825C2218yescomplemented
29C2×#3714—22no—
30C3×#836C2212yescomplemented
31C3×#833C2212yescomplemented
32#63568C2218yescomplemented
33C3×#585—31no—
34#5964D311yescharacteristic, complemented
35#5830—31no—
36#5830—31no—
37#5830—61no—
38C2×#949—32no—
39C2×#908—32no—
40C3×#413—31no—
41#5245—34no—
42#5241—34no—
43#5237D311yescharacteristic, complemented
44#5236—32no—
45#5139—32no—
46#4753—34no—
47#4747—34no—
48C23×C3⋊D3—21no—
49C32×#41—22no—
50C32×#41—22no—
51C2×C32×Q8C2311yescharacteristic
52C2×C32×D4D412yes—
53C2×C32×D4C2311yescharacteristic
54C22×C32×C4D412yes—
55C22×C32×C4C2311yescharacteristic
56C2×#638—24no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)C2312yes—
61C2×C3×#67—24no—
62C2×C3×#67—22no—
63C3×#239—24no—
64C3×D3×Q8—24no—
65C3×#237—28no—
66C3×#237—24no—
67C3×D3×D4—28no—
68C3×D3×D4—24no—
69C3×#235—24no—
70C3×#235—24no—
71C3×#235—22no—
72C3×#235—24no—
73C3×#235—22no—
74C3×#235D414yescomplemented
75C3×#235C2314yes—
76C2×C3×D12—22no—
77C2×C3×D12D412yescomplemented
78C2×C3×C4×D3—24no—
79C2×C3×C4×D3—22no—
80C2×C3×Dic6—22no—
81C2×C3×Dic6D412yescomplemented
82#3757—21no—
83#3752—24no—
84C4⋊(C3⋊Dic3)—21no—
85C4×C3⋊Dic3C2312yes—
86C3×#208—22no—
87C3×#208C2314yes—
88C2×C3×C3⋊C8—22no—
89#3717—28no—
90#3714—28no—
91#3021—91noSylow
92C3×2−1+4—32no—
93C3×2−1+4—62no—
94C3×H(5,𝔽2)—32no—
95C3×H(5,𝔽2)—62no—
96C3×H(5,𝔽2)—62no—
97C2×C3×#41—21no—
98C2×C3×#41—32no—
99C2×C3×#41—64no—
100C2×C3×#41—62no—
101C2×C3×#41C2×D311yescharacteristic
102C2×C3×#41C2×D311yescharacteristic
103#1010—22no—
104#1009—22no—
105D3×#41—24no—
106#1007C2×D312yescomplemented
107#1004—22no—
108#1004C2×D312yescomplemented
109C2×#235—22no—
110C2×#235C2×D312yes—
111C22×D12—31no—
112C22×D12—31no—
113C22×D12—61no—
114C2×C3×M16—32no—
115#949—38no—
116#949—64no—
117#947—32no—
118#947—32no—
119#947—62no—
120C2×#215—62no—
121#940—32no—
122#940—32no—
123#940—62no—
124#937—64no—
125#937—62no—
126#937—62no—
127C2×#213—62no—
128#930—64no—
129#930—62no—
130#930—62no—
131#926—31no—
132#926—31no—
133#926—61no—
134C2×#208C2×D312yescomplemented
135#908—38no—
136#908—64no—
137C2×D24—62no—
138C2×#204—62no—
139C3×#101—32no—
140C3×#100—32no—
141#837—38no—
142#836C2×D312yescomplemented
143#833C2×D312yescomplemented
144#825—38no—
145C23×C32C2×D412yes—
146C23×C32C2×D411yescharacteristic
147C22×C3⋊D3—22no—
148C22×C3⋊D3—42no—
149C22×C3⋊D3—82no—
150C22×C3×D3—24no—
151C22×C3×D3—22no—
152C32×Q8—22no—
153C32×D4—24no—
154C32×D4—22no—
155C2×C32×C4—22no—
156C2×C32×C4—22no—
157C2×C32×C4C2×D412yes—
158C2×C32×C4C2×D411yescharacteristic
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4C2411yescharacteristic
162#638—84no—
163C2×C3⋊Dic3—22no—
164C4⋊(C3⋊D3)—24no—
165C4⋊(C3⋊D3)—41no—
166C4⋊(C3⋊D3)—41no—
167C3×#67—28no—
168C3×#67—24no—
169C3×#67—24no—
170C2×C3×Dic3—24no—
171C2×C3×Dic3—22no—
172C3×D12—24no—
173C3×D12—22no—
174C3×D12C2×D414yes—
175C3×C4×D3—28no—
176C3×C4×D3—24no—
177C3×C4×D3—24no—
178C3×Dic6—24no—
179C3×Dic6—22no—
180C3×Dic6C2×D414yes—
181C3×C3⋊C8—24no—
182#585—31no—
183C2×AGL(1,ℤ/8)—92no—
184#535—91no—
185#454—94no—
186#453—94no—
187#421—92no—
188#413—31no—
189C23×D3—62no—
190C23×D3—61no—
191C23×D3—61no—
192C3×#41—22no—
193C3×#41—22no—
194C3×#41—22no—
195C3×#41—22no—
196C3×#41—34no—
197C3×#41—34no—
198C3×#41—42no—
199C3×#41—42no—
200C3×#41—64no—
201C3×#41—64no—
202C3×#41—64no—
203C3×#41—68no—
204C3×#41—64no—
205C3×#41—62no—
206C3×#41—64no—
207C3×#41—62no—
208C2×C3×Q8—21no—
209C2×C3×Q8—32no—
210C2×C3×Q8—62no—
211C2×C3×Q8—64no—
212C2×C3×Q8C22×D311yescharacteristic
213C2×C3×Q8C22×D311yescharacteristic
214C2×C3×D4—22no—
215C2×C3×D4—21no—
216C2×C3×D4—32no—
217C2×C3×D4—62no—
218C2×C3×D4—64no—
219C2×C3×D4—68no—
220C2×C3×D4—62no—
221C2×C3×D4—64no—
222C2×C3×D4D1212yes—
223C2×C3×D4#6712yes—
224C2×C3×D4C22×D311yescharacteristic
225C2×C3×D4C22×D311yescharacteristic
226C22×C3×C4—22no—
227C22×C3×C4—21no—
228C22×C3×C4—64no—
229C22×C3×C4—62no—
230C22×C3×C4D1212yes—
231C22×C3×C4#6712yes—
232C22×C3×C4C22×D311yescharacteristic
233C22×C3×C4C22×D311yescharacteristic
234C2×#67—24no—
235C2×#67—22no—
236C2×#67—68no—
237C2×#67—64no—
238C2×#67—64no—
239#239—24no—
240D3×Q8—24no—
241#237—28no—
242#237—24no—
243D3×D4—28no—
244D3×D4—24no—
245#235—24no—
246#235—24no—
247#235—22no—
248#235—24no—
249#235—22no—
250#235#6714yescomplemented
251#235C22×D314yes—
252C2×D12—22no—
253C2×D12—32no—
254C2×D12—32no—
255C2×D12—62no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—62no—
260C2×D12—62no—
261C2×D12—61no—
262C2×D12—61no—
263C2×D12—122no—
264C2×D12—122no—
265C2×D12#6712yescomplemented
266C2×C4×D3—24no—
267C2×C4×D3—22no—
268C2×Dic6—22no—
269C2×Dic6#6712yescomplemented
270C3×M16—34no—
271C3×M16—62no—
272C2×C3×C8—62no—
273#217—62no—
274#217—61no—
275#217—61no—
276#215—68no—
277#213—68no—
278(C2×D3)⋊C4—68no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281C4⋊Dic3—62no—
282C4⋊Dic3—61no—
283C4⋊Dic3—61no—
284C4×Dic3—32no—
285C4×Dic3—32no—
286C4×Dic3—62no—
287#208—22no—
288#208C22×D314yes—
289C2×C3⋊C8—22no—
290D24—68no—
291#204—68no—
292C22×C32—22no—
293C22×C32—41no—
294C22×C32—42no—
295C22×C32#12012yes—
296C22×C32C22×D411yescharacteristic
297C2×C3⋊D3—44no—
298C2×C3⋊D3—42no—
299C2×C3⋊D3—84no—
300C2×C3×D3—24no—
301C2×C3×D3—82no—
302C2×C3×D3—84no—
303C32×C4—22no—
304C32×C4#12011yescharacteristic
305C32×C4#12011yescharacteristic
306C32×C4C22×D412yes—
307C3⋊Dic3—42no—
308C3×Dic3—24no—
3092−1+4—32no—
3102−1+4—62no—
311H(5,𝔽2)—32no—
312H(5,𝔽2)—62no—
313H(5,𝔽2)—62no—
314C2×#41—32no—
315C2×#41—64no—
316C2×#41—62no—
317C2×#41D3211yescharacteristic
318C22×D4—91no—
319AGL(1,ℤ/8)—98no—
320AGL(1,ℤ/8)—184no—
321C2×SD16—182no—
322C2×D8—182no—
323C2×M16—32no—
324#127—92no—
325#124—92no—
326#121—182no—
327#120—182no—
328#117—91no—
329#104—98no—
330#101—32no—
331#100—32no—
332C23×C3—21no—
333C23×C3—22no—
334C23×C3—64no—
335C23×C3—62no—
336C23×C3C2×D1212yes—
337C23×C3C2×D1211yescharacteristic
338C23×C3C2×#6712yes—
339C23×C3C2×#6711yescharacteristic
340C22×D3—24no—
341C22×D3—22no—
342C22×D3—64no—
343C22×D3—62no—
344C22×D3—62no—
345C22×D3—124no—
346C22×D3—122no—
347C22×D3—122no—
348C22×D3—242no—
349C22×D3—242no—
350C22×D3—244no—
351C3×Q8—22no—
352C3×Q8—22no—
353C3×Q8—34no—
354C3×Q8—42no—
355C3×Q8—64no—
356C3×Q8—62no—
357C3×D4—24no—
358C3×D4—24no—
359C3×D4—22no—
360C3×D4—22no—
361C3×D4—34no—
362C3×D4—42no—
363C3×D4—44no—
364C3×D4—64no—
365C3×D4—68no—
366C3×D4—64no—
367C3×D4—64no—
368C3×D4—62no—
369C2×C3×C4—22no—
370C2×C3×C4—22no—
371C2×C3×C4—22no—
372C2×C3×C4—22no—
373C2×C3×C4—21no—
374C2×C3×C4—21no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—22no—
378C2×C3×C4—42no—
379C2×C3×C4—42no—
380C2×C3×C4—68no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4—64no—
384C2×C3×C4—64no—
385C2×C3×C4C2×D1212yes—
386C2×C3×C4C2×D1211yescharacteristic
387C2×C3×C4D3×D412yes—
388C2×C3×C4D3×D412yes—
389C2×C3×C4C2×#6712yes—
390C2×C3×C4C2×#6711yescharacteristic
391C2×C3×C4C2×#6712yes—
392C2×C3×C4C2×#6712yes—
393C2×C3×C4C23×D311yescharacteristic
394C2×C3×C4C23×D311yescharacteristic
395#67—28no—
396#67—24no—
397#67—24no—
398#67—244no—
399#67—244no—
400#67—248no—
401C2×Dic3—24no—
402C2×Dic3—22no—
403C2×Dic3—64no—
404C2×Dic3—62no—
405C2×Dic3—62no—
406D12—24no—
407D12—22no—
408D12—64no—
409D12—64no—
410D12—124no—
411D12—122no—
412D12—122no—
413D12—121no—
414D12—121no—
415D12—121no—
416D12—121no—
417D12C2×#6714yes—
418C4×D3—28no—
419C4×D3—24no—
420C4×D3—24no—
421Dic6—24no—
422Dic6—22no—
423Dic6C2×#6714yes—
424C3×C8—64no—
425C3⋊C8—24no—
426C2×C32—21no—
427C2×C32—22no—
428C2×C32—42no—
429C2×C32C2×#12011yescharacteristic
430C3⋊D3—82no—
431C3×D3—44no—
432C24—181no—
433#41—22no—
434#41—22no—
435#41—34no—
436#41—34no—
437#41—64no—
438#41—64no—
439#41—64no—
440#41—68no—
441#41—64no—
442#41—62no—
443#41—64no—
444#41—62no—
445C2×Q8—32no—
446C2×Q8—62no—
447C2×Q8—64no—
448C2×Q8C2×D3211yescharacteristic
449C2×D4—32no—
450C2×D4—62no—
451C2×D4—64no—
452C2×D4—68no—
453C2×D4—62no—
454C2×D4—64no—
455C2×D4—92no—
456C2×D4—184no—
457C2×D4—181no—
458C2×D4—182no—
459C2×D4—182no—
460C2×D4#62612yes—
461C2×D4C2×D3211yescharacteristic
462C22×C4—64no—
463C22×C4—62no—
464C22×C4#62612yes—
465C22×C4C2×D3211yescharacteristic
466SD16—188no—
467D8—188no—
468M16—34no—
469M16—62no—
470C2×C8—62no—
471C4⋊C4—181no—
472C22⋊C4—181no—
473C22⋊C4—184no—
474C42—92no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—21no—
478C22×C3—22no—
479C22×C3—42no—
480C22×C3—41no—
481C22×C3—41no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—44no—
486C22×C3—64no—
487C22×C3—242no—
488C22×C3—244no—
489C22×C3#88212yes—
490C22×C3#95312yes—
491C22×C3C22×D1211yescharacteristic
492C22×C3C22×#6711yescharacteristic
493C2×D3—24no—
494C2×D3—82no—
495C2×D3—84no—
496C2×D3—124no—
497C2×D3—128no—
498C2×D3—124no—
499C2×D3—124no—
500C2×D3—122no—
501C2×D3—122no—
502C2×D3—244no—
503C2×D3—244no—
504C2×D3—248no—
505C3×C4—22no—
506C3×C4—22no—
507C3×C4—22no—
508C3×C4—21no—
509C3×C4—21no—
510C3×C4—42no—
511C3×C4—64no—
512C3×C4#88211yescharacteristic
513C3×C4#88211yescharacteristic
514C3×C4#95311yescharacteristic
515C3×C4#95311yescharacteristic
516C3×C4C2×D3×D412yes—
517C3×C4C22×#6712yes—
518Dic3—24no—
519Dic3—124no—
520Dic3—122no—
521Dic3—122no—
522C32#302111yescharacteristic, complemented, Sylow
523C23—64no—
524C23—62no—
525C23—182no—
526C23—362no—
527C23—722no—
528C23C2×#62612yes—
529C23C2×#62611yescharacteristic
530Q8—22no—
531Q8—34no—
532Q8—64no—
533Q8—62no—
534D4—24no—
535D4—22no—
536D4—34no—
537D4—64no—
538D4—68no—
539D4—64no—
540D4—64no—
541D4—62no—
542D4—184no—
543D4—361no—
544D4—361no—
545D4—724no—
546C2×C4—22no—
547C2×C4—22no—
548C2×C4—68no—
549C2×C4—64no—
550C2×C4—62no—
551C2×C4—64no—
552C2×C4—64no—
553C2×C4—182no—
554C2×C4C2×#62612yes—
555C2×C4C2×#62611yescharacteristic
556C2×C4D3×#6712yes—
557C2×C4D3×#6712yes—
558C2×C4C22×D3211yescharacteristic
559C8—64no—
560C2×C3—22no—
561C2×C3—21no—
562C2×C3—22no—
563C2×C3—21no—
564C2×C3—22no—
565C2×C3—21no—
566C2×C3—42no—
567C2×C3—42no—
568C2×C3—42no—
569C2×C3—82no—
570C2×C3—124no—
571C2×C3C2×#88211yescharacteristic
572C2×C3C2×#95311yescharacteristic
573D3—44no—
574D3—244no—
575D3—242no—
576D3—242no—
577C22—22no—
578C22—41no—
579C22—42no—
580C22—64no—
581C22—242no—
582C22—244no—
583C22—364no—
584C22—362no—
585C22—724no—
586C22#6397712yes—
587C22C22×#62611yescharacteristic
588C4—22no—
589C4—64no—
590C4—362no—
591C4#6397711yescharacteristic
592C4#6397711yescharacteristic
593C4C2×D3×#6712yes—
594C3—21no—
595C3#7871711yescharacteristic, complemented
596C3#8412211yescharacteristic, complemented
597C2—21no—
598C2—22no—
599C2—42no—
600C2—124no—
601C2—722no—
602C2C2×#6397711yescharacteristic
subgroupG/H
centerC2C2×#63977
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#120
hypercenterC2×#41D32
hypocenterC32#3021
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C3×#5964C2semidirect
2. #10596301C2semidirect
3. C2×#63825C2semidirect
4. C3×#5237C2semidirect
5. #10591646C2semidirect
6. #10591510C2semidirect
7. #10591110C2semidirect
11. C22×C4⋊(C3⋊D3)C22semidirect
15. C3×#1007C22semidirect
17. C3×#1004C22semidirect
20. #64156C22semidirect
21. #64149C22semidirect
24. #64135C22semidirect
25. C2×C3×#208C22semidirect
28. #63825C22semidirect
30. C3×#836C22semidirect
31. C3×#833C22semidirect
32. #63568C22semidirect
34. #5964D3semidirect
43. #5237D3semidirect
74. C3×#235D4semidirect
77. C2×C3×D12D4semidirect
81. C2×C3×Dic6D4semidirect
106. #1007C2×D3semidirect
108. #1004C2×D3semidirect
134. C2×#208C2×D3semidirect
142. #836C2×D3semidirect
143. #833C2×D3semidirect
250. #235#67semidirect
265. C2×D12#67semidirect
269. C2×Dic6#67semidirect
522. C32#3021semidirect
595. C3#78717semidirect
596. C3#84122semidirect

Maximal subgroups

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

subgroupindex
C3×#59642
#105963012
C2×#638252
C3×#52372
#105916462
#105915102
#105911102
#841223
#787173