Finite Group Databasebeta

← #11861230

Subgroups — #11861230

Order 1152.

1033 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596216C211yesmaximal, characteristic, complemented
2C3×#5745C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4C3×#5122C211yesmaximal, characteristic, complemented
5C2×#63577C211yesmaximal, characteristic, complemented
6#10591113C211yesmaximal, characteristic, complemented
7#10591111C211yesmaximal, characteristic, complemented
8#10590924C214yesmaximal, complemented
9#10590923C214yesmaximal, complemented
10#83812—31nomaximal
11#78580—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16#64116—22no—
17M16×C3⋊D3—22no—
18#64110C2214yescomplemented
19C3×#926C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C22×C3×C3⋊C8C2211yescharacteristic
22C3×#907—22no—
23C3×D3×M16—22no—
24C3×#901C2214yescomplemented
25C2×#3719C411yescharacteristic, complemented
26C2×#3717C411yescharacteristic, complemented
27#63829C412yescomplemented
28#63829C412yescomplemented
29#63829C2212yes—
30#63829C2212yes—
31C2×#3716C411yescharacteristic, complemented
32C2×#3714C411yescharacteristic, complemented
33C3×#815C2212yescomplemented
34C3×C8×Dic3C2212yescomplemented
35#63577C2212yescomplemented
36#63577C2212yescomplemented
37#63570C2214yescomplemented
38#63569C2214yescomplemented
39C3×#568—31no—
40C2×#950—31no—
41#5745—31no—
42#5745—31no—
43#5745—61no—
44#5745D311yescharacteristic, complemented
45C2×#904—31no—
46C3×#405—31no—
47#5236—31no—
48#5145—34no—
49#5144—34no—
50#5139—31no—
51C2×#822—31no—
52#5122D311yescharacteristic, complemented
53C2×#819—31no—
54#5005—31no—
55#5005—31no—
56#4717—34no—
57#4700—34no—
58C22×C32×C4C2311yescharacteristic
59C2×#638—21no—
60#3828—21no—
61#3828—21no—
62#3828C2×C412yes—
63#3828C2312yes—
64C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
65C2×C4×C3⋊D3—21no—
66C2×#634C2×C411yescharacteristic
67C2×C3×#67—21no—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235C2×C412yes—
71C3×#235C2312yes—
72C2×C3×D12C2×C411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6C2×C411yescharacteristic
75C32×M16D412yes—
76C32×M16D412yes—
77C2×C32×C8C2312yes—
78#3748—21no—
79#3748C2312yes—
80C2×C3⋊(C3⋊C8)—21no—
81#3743—24no—
82C8×C3⋊D3—24no—
83C3×#217—21no—
84C3×C4⋊Dic3—21no—
85C3×C4×Dic3C2312yes—
86C3×#208—21no—
87C3×#208C2312yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8C2×C411yescharacteristic
90C2×C3×C3⋊C8C2×C411yescharacteristic
91C2×C3×C3⋊C8C2×C411yescharacteristic
92C2×C3×C3⋊C8C2×C411yescharacteristic
93C2×C3×C3⋊C8C2311yescharacteristic
94C2×C3×C3⋊C8C2311yescharacteristic
95C3×ΓL(1,𝔽25)—24no—
96C3×D3×C8—24no—
97#3719C2×C412yes—
98#3719C2×C412yes—
99#3717C2×C412yes—
100#3717C2×C412yes—
101#3716C2×C412yes—
102#3716C2×C412yes—
103#3714C2×C412yes—
104#3714C2×C412yes—
105#2957—91noSylow
106C2×C3×#41—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C2×#235C2×D311yescharacteristic
111C3×#131—34no—
112C3×#131—62no—
113C2×C3×M16—21no—
114C2×C3×M16—31no—
115C2×C3×M16—62no—
116C2×C3×M16C2×D311yescharacteristic
117C2×C3×M16C2×D311yescharacteristic
118C22×C3×C8—31no—
119C3×#117—31no—
120#950—32no—
121#950—32no—
122#950—32no—
123#950—32no—
124C2×#216—31no—
125C2×#215—31no—
126C2×#214—31no—
127C2×#213—31no—
128#926C2×D311yescharacteristic
129C2×#208—31no—
130C2×#208—31no—
131C2×#208—61no—
132C2×#208C2×D311yescharacteristic
133C22×C3⋊C8C2×D311yescharacteristic
134#907—22no—
135#907—64no—
136#907—62no—
137#907—62no—
138D3×M16—22no—
139D3×M16—64no—
140D3×M16—62no—
141D3×M16—62no—
142C2×Dic12—31no—
143#904—32no—
144#904—32no—
145#904—32no—
146#904—32no—
147C2×D24—31no—
148C2×#204—31no—
149C2×#204—31no—
150#901—34no—
151#901—34no—
152#901—64no—
153#901C2×D314yescomplemented
154C3×#97—32no—
155C3×C4×C8—32no—
156#837—34no—
157#825—34no—
158#822—32no—
159#822—32no—
160#819—32no—
161#819—32no—
162#815C2×D312yescomplemented
163C8×Dic3C2×D312yescomplemented
164#805—34no—
165#805—34no—
166C23×C32#4111yescharacteristic
167C22×C3⋊D3—21no—
168C22×C3×D3—21no—
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C22×C411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4#4111yescharacteristic
174C2×C32×C4C2411yescharacteristic
175#638—22no—
176#638—22no—
177C2×C3⋊Dic3—21no—
178C4⋊(C3⋊D3)—21no—
179C4⋊(C3⋊D3)C22×C412yes—
180C4×C3⋊D3—22no—
181C4×C3⋊D3—22no—
182#634—21no—
183#634C22×C412yes—
184C3×#67—22no—
185C3×#67—22no—
186C2×C3×Dic3—21no—
187C2×C3×Dic3—22no—
188C3×D12—21no—
189C3×D12C22×C412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×Dic6—21no—
193C3×Dic6C22×C412yes—
194C32×C8C2×D414yes—
195C3⋊(C3⋊C8)—22no—
196C3×C3⋊C8—22no—
197C3×C3⋊C8C22×C411yescharacteristic
198C3×C3⋊C8C22×C411yescharacteristic
199C3×C3⋊C8C22×C411yescharacteristic
200C3×C3⋊C8C22×C411yescharacteristic
201C2×#135—91no—
202#568—31no—
203#568—91no—
204#444—94no—
205#443—94no—
206C2×#108—91no—
207#421—91no—
208#421—91no—
209#405—31no—
210C3×#41—32no—
211C3×#41—32no—
212C3×#41—61no—
213C3×#41—61no—
214C2×C3×Q8—31no—
215C2×C3×D4—31no—
216C2×C3×D4—61no—
217C22×C3×C4—21no—
218C22×C3×C4—61no—
219C22×C3×C4C22×D311yescharacteristic
220C22×C3×C4C22×D311yescharacteristic
221C2×#67—21no—
222C2×#67—62no—
223C2×#67—61no—
224C2×#67—61no—
225#235—21no—
226#235—21no—
227#235—32no—
228#235—32no—
229#235—32no—
230#235—32no—
231#235—62no—
232#235—62no—
233#235—62no—
234#235—62no—
235#235—61no—
236#235—61no—
237#235—61no—
238#235—61no—
239#235C4×D312yes—
240#235C22×D312yes—
241C2×D12—31no—
242C2×D12—31no—
243C2×D12—61no—
244C2×D12C4×D311yescharacteristic
245C2×C4×D3—21no—
246C2×C4×D3—62no—
247C2×C4×D3—61no—
248C2×C4×D3—61no—
249C2×Dic6—31no—
250C2×Dic6—31no—
251C2×Dic6—61no—
252C2×Dic6C4×D311yescharacteristic
253C3×M16—22no—
254C3×M16—22no—
255C3×M16—32no—
256C3×M16—61no—
257C3×M16—64no—
258C3×M16D1212yes—
259C3×M16D1212yes—
260C3×M16#6712yes—
261C3×M16#6712yes—
262C2×C3×C8—22no—
263C2×C3×C8—31no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—31no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—61no—
270C2×C3×C8—64no—
271C2×C3×C8C22×D312yes—
272C2×C3×C8C22×D312yes—
273C3×C4⋊C4—61no—
274C3×C22⋊C4—61no—
275C3×C42—32no—
276#217—21no—
277#216—32no—
278#216—32no—
279#215—32no—
280#215—32no—
281#214—32no—
282#214—32no—
283#213—32no—
284#213—32no—
285C4⋊Dic3—21no—
286C4×Dic3C22×D312yes—
287#208—21no—
288#208—32no—
289#208—32no—
290#208—62no—
291#208—62no—
292#208—61no—
293#208—61no—
294#208C22×D312yes—
295C2×C3⋊C8—21no—
296C2×C3⋊C8—62no—
297C2×C3⋊C8—61no—
298C2×C3⋊C8—61no—
299C2×C3⋊C8C4×D311yescharacteristic
300C2×C3⋊C8C4×D311yescharacteristic
301C2×C3⋊C8C4×D311yescharacteristic
302C2×C3⋊C8C4×D311yescharacteristic
303C2×C3⋊C8C22×D311yescharacteristic
304C2×C3⋊C8C22×D311yescharacteristic
305Dic12—32no—
306Dic12—32no—
307D24—32no—
308D24—32no—
309#204—32no—
310#204—32no—
311#204—32no—
312#204—32no—
313ΓL(1,𝔽25)—24no—
314ΓL(1,𝔽25)—68no—
315ΓL(1,𝔽25)—64no—
316ΓL(1,𝔽25)—64no—
317D3×C8—24no—
318D3×C8—68no—
319D3×C8—64no—
320D3×C8—64no—
321C22×C32—41no—
322C22×C32C4×D411yescharacteristic
323C22×C32C4×D411yescharacteristic
324C22×C32C2×#4111yescharacteristic
325C2×C3⋊D3—22no—
326C2×C3⋊D3—81no—
327C2×C3×D3—22no—
328C2×C3×D3—81no—
329C32×C4C4×D411yescharacteristic
330C32×C4C4×D411yescharacteristic
331C32×C4C23×C411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—31no—
337C2×#41—91no—
338#135—92no—
339#135—92no—
340#135—92no—
341#135—92no—
342C2×Q16—91no—
343C2×SD16—91no—
344C2×SD16—91no—
345C2×D8—91no—
346#131—34no—
347#131—62no—
348#131—94no—
349#131—182no—
350C2×M16—31no—
351C2×M16—62no—
352C2×M16—91no—
353C2×M16—182no—
354C2×M16D3211yescharacteristic
355C22×C8—31no—
356#117—31no—
357#108—92no—
358#108—92no—
359#104—94no—
360#104—94no—
361#97—32no—
362C4×C8—32no—
363C23×C3—21no—
364C23×C3—61no—
365C23×C3#23511yescharacteristic
366C23×C3#23511yescharacteristic
367C22×D3—21no—
368C22×D3—62no—
369C22×D3—61no—
370C22×D3—61no—
371C3×Q8—32no—
372C3×Q8—61no—
373C3×D4—32no—
374C3×D4—62no—
375C3×D4—62no—
376C3×D4—61no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—21no—
383C2×C3×C4—61no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4C2×C4×D311yescharacteristic
388C2×C3×C4C2×C4×D311yescharacteristic
389C2×C3×C4C2×C4×D311yescharacteristic
390C2×C3×C4C2×C4×D311yescharacteristic
391C2×C3×C4C2×D1211yescharacteristic
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4#23511yescharacteristic
394C2×C3×C4#23511yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C23×D311yescharacteristic
398C2×C3×C4C23×D311yescharacteristic
399#67—22no—
400#67—22no—
401#67—64no—
402#67—64no—
403#67—62no—
404#67—62no—
405#67—62no—
406#67—62no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—62no—
410C2×Dic3—61no—
411C2×Dic3—61no—
412D12—21no—
413D12—32no—
414D12—32no—
415D12—62no—
416D12—62no—
417D12—61no—
418D12—61no—
419D12C2×C4×D312yes—
420C4×D3—22no—
421C4×D3—22no—
422C4×D3—64no—
423C4×D3—64no—
424C4×D3—62no—
425C4×D3—62no—
426C4×D3—62no—
427C4×D3—62no—
428Dic6—21no—
429Dic6—32no—
430Dic6—32no—
431Dic6—62no—
432Dic6—62no—
433Dic6—61no—
434Dic6—61no—
435Dic6C2×C4×D312yes—
436C3×C8—24no—
437C3×C8—31no—
438C3×C8—31no—
439C3×C8—31no—
440C3×C8—31no—
441C3×C8—62no—
442C3×C8C2×D1214yes—
443C3×C8C2×#6714yes—
444C3⋊C8—22no—
445C3⋊C8—64no—
446C3⋊C8—62no—
447C3⋊C8—62no—
448C3⋊C8C2×C4×D311yescharacteristic
449C3⋊C8C2×C4×D311yescharacteristic
450C3⋊C8C2×C4×D311yescharacteristic
451C3⋊C8C2×C4×D311yescharacteristic
452C2×C32—21no—
453C2×C32—21no—
454C2×C32—21no—
455C2×C32C2×C4×D411yescharacteristic
456C3⋊D3—42no—
457C3×D3—42no—
458#41—32no—
459#41—32no—
460#41—61no—
461#41—61no—
462#41—92no—
463#41—92no—
464#41—181no—
465#41—181no—
466C2×Q8—31no—
467C2×Q8—91no—
468C2×D4—31no—
469C2×D4—61no—
470C2×D4—91no—
471C2×D4—181no—
472C22×C4—61no—
473C22×C4—181no—
474C22×C4C2×D3211yescharacteristic
475Q16—92no—
476Q16—92no—
477SD16—92no—
478SD16—92no—
479SD16—92no—
480SD16—92no—
481D8—92no—
482D8—92no—
483M16—32no—
484M16—61no—
485M16—64no—
486M16—92no—
487M16—181no—
488M16—184no—
489M16#62612yes—
490M16#62612yes—
491C2×C8—31no—
492C2×C8—31no—
493C2×C8—31no—
494C2×C8—31no—
495C2×C8—31no—
496C2×C8—31no—
497C2×C8—61no—
498C2×C8—64no—
499C2×C8—181no—
500C2×C8—184no—
501C2×C8C2×D3212yes—
502C4⋊C4—61no—
503C22⋊C4—61no—
504C42—32no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—41no—
509C22×C3—41no—
510C22×C3—62no—
511C22×C3—81no—
512C22×C3—241no—
513C22×C3C4×D1211yescharacteristic
514C22×C3C4×D1211yescharacteristic
515C22×C3C4×#6711yescharacteristic
516C22×C3C4×#6711yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3C2×#23511yescharacteristic
519C2×D3—22no—
520C2×D3—64no—
521C2×D3—62no—
522C2×D3—62no—
523C2×D3—81no—
524C2×D3—241no—
525C2×D3—241no—
526C2×D3—242no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—62no—
532C3×C4—122no—
533C3×C4C4×D1211yescharacteristic
534C3×C4C4×D1211yescharacteristic
535C3×C4C4×#6711yescharacteristic
536C3×C4C4×#6711yescharacteristic
537C3×C4C22×C4×D311yescharacteristic
538C3×C4C22×C4×D311yescharacteristic
539C3×C4C22×D1211yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—22no—
542Dic3—42no—
543Dic3—64no—
544Dic3—62no—
545Dic3—62no—
546C32#295711yescharacteristic, complemented, Sylow
547C23—61no—
548C23—181no—
549C23#379811yescharacteristic
550Q8—32no—
551Q8—61no—
552Q8—92no—
553Q8—181no—
554D4—32no—
555D4—62no—
556D4—62no—
557D4—61no—
558D4—92no—
559D4—182no—
560D4—182no—
561D4—181no—
562C2×C4—61no—
563C2×C4—62no—
564C2×C4—62no—
565C2×C4—62no—
566C2×C4—181no—
567C2×C4—182no—
568C2×C4—182no—
569C2×C4#379811yescharacteristic
570C2×C4C4×D3211yescharacteristic
571C2×C4C4×D3211yescharacteristic
572C2×C4C2×#62611yescharacteristic
573C2×C4C2×#62611yescharacteristic
574C2×C4C22×D3211yescharacteristic
575C8—31no—
576C8—31no—
577C8—31no—
578C8—31no—
579C8—62no—
580C8—182no—
581C8C2×#62614yes—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—41no—
590C2×C3—41no—
591C2×C3—41no—
592C2×C3—122no—
593C2×C3C2×C4×D1211yescharacteristic
594C2×C3C2×C4×#6711yescharacteristic
595D3—42no—
596D3—124no—
597D3—122no—
598D3—122no—
599C22—41no—
600C22—62no—
601C22—182no—
602C22—241no—
603C22—721no—
604C22C4×#62611yescharacteristic
605C22C4×#62611yescharacteristic
606C22C2×#379811yescharacteristic
607C4—62no—
608C4—122no—
609C4—182no—
610C4C4×#62611yescharacteristic
611C4C4×#62611yescharacteristic
612C4C2×C4×D3211yescharacteristic
613C4C22×#62611yescharacteristic
614C3—21no—
615C3#7858011yescharacteristic, complemented
616C3#8381211yescharacteristic, complemented
617C2—21no—
618C2—21no—
619C2—21no—
620C2—122no—
621C2—362no—
622C2C2×C4×#62611yescharacteristic
subgroupG/H
centerC4C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×C4×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2957
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. #10596216C2semidirect
2. C3×#5745C2semidirect
4. C3×#5122C2semidirect
5. C2×#63577C2semidirect
6. #10591113C2semidirect
7. #10591111C2semidirect
8. #10590924C2semidirect
9. #10590923C2semidirect
18. #64110C22semidirect
24. C3×#901C22semidirect
25. C2×#3719C4semidirect
26. C2×#3717C4semidirect
27. #63829C4semidirect
28. #63829C4semidirect
31. C2×#3716C4semidirect
32. C2×#3714C4semidirect
33. C3×#815C22semidirect
34. C3×C8×Dic3C22semidirect
35. #63577C22semidirect
36. #63577C22semidirect
37. #63570C22semidirect
38. #63569C22semidirect
44. #5745D3semidirect
52. #5122D3semidirect
153. #901C2×D3semidirect
162. #815C2×D3semidirect
163. C8×Dic3C2×D3semidirect
546. C32#2957semidirect
615. C3#78580semidirect
616. C3#83812semidirect

Maximal subgroups

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

subgroupindex
#105962162
C3×#57452
C2×#638292
C3×#51222
C2×#635772
#105911132
#105911112
#105909242
#105909232
#838123
#785803