Finite Group Databasebeta

← #11867812

Subgroups — #11867812

Order 1152.

1003 conjugacy classes of subgroups.

The subgroup lattice has 617 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5526C211yesmaximal, characteristic, complemented
2#10595044C211yesmaximal, characteristic
3C2×#63827C211yesmaximal, characteristic, complemented
4C2×#63814C211yesmaximal, characteristic, complemented
5#10592694C211yesmaximal, characteristic, complemented
6C3×#5002C211yesmaximal, characteristic, complemented
7C2×#63566C211yesmaximal, characteristic, complemented
8#10590520C212yesmaximal, complemented
9#10590518C212yesmaximal, complemented
10#10590503C212yesmaximal, complemented
11#10590501C212yesmaximal, complemented
12#83400—31nomaximal
13#78841—31nomaximal
14C2×C3×#235C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C32×#117C2211yescharacteristic
18C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
19C2×#3748C2211yescharacteristic
20C22×C3×C3⋊C8C2211yescharacteristic
21C3×#897C2212yes—
22C3×#897C2212yes—
23C3×#886—22no—
24C3×#875—21no—
25C3×#869—21no—
26#63980—22no—
27#63908—21no—
28#63908C2212yes—
29#63856—21no—
30#63856C2212yes—
31C2×#3718C2212yes—
32#63827—24no—
33C2×#3715C2212yes—
34C2×#3711C2212yes—
35#63814—24no—
36C2×D3×C3⋊C8C2212yes—
37#63635C2212yes—
38#63634C2212yes—
39C3×#810C2211yescharacteristic
40C3×#810C2211yescharacteristic
41C3×#809C2211yescharacteristic
42C3×#809C2211yescharacteristic
43#63566C2212yes—
44#63566C2212yes—
45C3×#536—31no—
46#5833—31no—
47#5833—31no—
48C2×#951—31no—
49C2×#948—31no—
50C2×#942—31no—
51C2×#901—31no—
52#5526D311yescharacteristic, complemented
53C3×#416—31no—
54C2×#835—31no—
55C2×#816—31no—
56#5052—32no—
57#5051—32no—
58#5049—32no—
59#5048—32no—
60#5002D311yescharacteristic, complemented
61#4995—31no—
62#4995—31no—
63#4995—61no—
64#4816—32no—
65#4813—32no—
66#4780—32no—
67#4778—32no—
68C22×C32×C4C2311yescharacteristic
69C22×C3⋊Dic3—21no—
70C2×C3×#67—21no—
71C2×C3×#67D412yes—
72C22×C3×Dic3—21no—
73C3×#235—22no—
74C3×#235—22no—
75C3×#235—22no—
76C3×#235—22no—
77C2×C3×D12D411yescharacteristic
78C2×C3×D12C2311yescharacteristic
79C2×C3×C4×D3—21no—
80C2×C3×C4×D3C2312yes—
81C2×C3×Dic6—22no—
82C2×C3×Dic6—22no—
83C2×C3×Dic6—21no—
84C2×C3×Dic6D411yescharacteristic
85C2×C3×Dic6C2312yes—
86C2×C3×Dic6C2311yescharacteristic
87C2×#625—22no—
88C32×C4⋊C4C2311yescharacteristic
89C32×C4⋊C4C2311yescharacteristic
90C32×C22⋊C4—21no—
91C32×C42—21no—
92C4⋊(C3⋊Dic3)—21no—
93C4⋊(C3⋊Dic3)C2312yes—
94#3748D414yescomplemented
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×(C2×D3)⋊C4—22no—
97C3×(C2×D3)⋊C4—22no—
98C3×C4⋊Dic3—22no—
99C3×C4⋊Dic3—22no—
100C2×C3×C3⋊C8—22no—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3724—22no—
104(C2×D3)⋊Dic3—22no—
105(C2×D3)⋊Dic3—22no—
106#3718—24no—
107#3715—24no—
108#3711—24no—
109D3×C3⋊C8—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C2×C3×#41—31no—
113C22×C3×Q8—31no—
114C2×#235C2×D311yescharacteristic
115C2×#235C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C22×C3×C8—31no—
118C3×C4⋊Q8—61no—
119C3×#124—61no—
120C3×#123—62no—
121C3×C22⋊Q8—32no—
122C3×C22⋊Q8—32no—
123C3×#117—21no—
124C3×#117C2×D311yescharacteristic
125C3×#117C2×D311yescharacteristic
126#951—64no—
127#948—64no—
128#946—32no—
129#946—61no—
130C2×#216—32no—
131C2×#216—32no—
132#942—64no—
133C2×#215—32no—
134#939—62no—
135#939—62no—
136#938—32no—
137#938—61no—
138C2×#214—32no—
139#930—32no—
140#930—61no—
141C2×C4⋊Dic3—31no—
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—61no—
144#924—32no—
145#924—61no—
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—32no—
149C2×#208—61no—
150C22×C3⋊C8—32no—
151C22×C3⋊C8C2×D311yescharacteristic
152#901—64no—
153C2×ΓL(1,𝔽25)—32no—
154C2×D3×C8—32no—
155#897C2×D312yes—
156#897C2×D312yes—
157#886—22no—
158#875—21no—
159#869—21no—
160C3×#103—31no—
161C3×#103—31no—
162C3×#102—31no—
163C3×#102—31no—
164#835—32no—
165#835—32no—
166#816—32no—
167#816—32no—
168#810C2×D311yescharacteristic
169#810C2×D311yescharacteristic
170#809C2×D311yescharacteristic
171#809C2×D311yescharacteristic
172#808—32no—
173#808—32no—
174#808—62no—
175#807—32no—
176#807—32no—
177#807—62no—
178C23×C32C2×D411yescharacteristic
179C22×C3×D3—21no—
180C22×C3×D3C2×D412yes—
181C2×C32×C4—21no—
182C2×C32×C4—21no—
183C2×C32×C4C2×D412yes—
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—81no—
189C3×#67—24no—
190C3×#67—42no—
191C2×C3×Dic3—21no—
192C2×C3×Dic3—22no—
193C2×C3×Dic3—42no—
194C2×C3×Dic3C2×D412yes—
195C3×D12—22no—
196C3×D12—21no—
197C3×D12—21no—
198C3×C4×D3—22no—
199C3×C4×D3—22no—
200C3×C4×D3—42no—
201C3×Dic6—22no—
202C3×Dic6—22no—
203C3×Dic6—21no—
204C3×Dic6—22no—
205C3×Dic6—21no—
206C3×Dic6—42no—
207#625—82no—
208C3⋊(C3⋊C8)C2×D414yes—
209C3×C3⋊C8—21no—
210C3×C3⋊C8—21no—
211C2×#137—91no—
212C2×#131—91no—
213#537—91no—
214#536—31no—
215#470—92no—
216#468—92no—
217#467—92no—
218#465—92no—
219#428—91no—
220#416—31no—
221C2×#103—91no—
222C3×#41—62no—
223C3×#41—62no—
224C3×#41—62no—
225C3×#41—62no—
226C2×C3×Q8—31no—
227C2×C3×Q8—32no—
228C2×C3×Q8—31no—
229C2×C3×Q8—61no—
230C2×C3×Q8—62no—
231C2×C3×Q8—62no—
232C2×C3×D4—32no—
233C2×C3×D4—31no—
234C2×C3×D4—31no—
235C2×C3×D4—61no—
236C22×C3×C4—21no—
237C22×C3×C4—32no—
238C22×C3×C4—61no—
239C22×C3×C4—61no—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—21no—
243C2×#67—62no—
244C2×#67—62no—
245C2×#67#6712yes—
246C22×Dic3—21no—
247C22×Dic3—61no—
248C22×Dic3—61no—
249C22×Dic3—121no—
250#235—22no—
251#235—22no—
252#235—22no—
253#235—22no—
254C2×D12#6711yescharacteristic
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3C22×D312yes—
258C2×Dic6—22no—
259C2×Dic6—22no—
260C2×Dic6—21no—
261C2×Dic6#6711yescharacteristic
262C2×Dic6C22×D311yescharacteristic
263C2×Dic6C22×D312yes—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—62no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—62no—
270C3×C4⋊C4—62no—
271C3×C4⋊C4C22×D311yescharacteristic
272C3×C4⋊C4C22×D311yescharacteristic
273C3×C4⋊C4C22×D311yescharacteristic
274C3×C4⋊C4C22×D311yescharacteristic
275C3×C22⋊C4—21no—
276C3×C22⋊C4—21no—
277C3×C22⋊C4—41no—
278C3×C22⋊C4—62no—
279C3×C22⋊C4—62no—
280C3×C42—21no—
281C3×C42—21no—
282C3×C42—41no—
283#217—62no—
284#217—62no—
285#216—64no—
286#216—64no—
287#215—64no—
288#214—64no—
289(C2×D3)⋊C4—22no—
290(C2×D3)⋊C4—22no—
291(C2×D3)⋊C4—62no—
292(C2×D3)⋊C4—62no—
293C4⋊Dic3—22no—
294C4⋊Dic3—22no—
295C4⋊Dic3—32no—
296C4⋊Dic3—32no—
297C4⋊Dic3—62no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3—121no—
301Dic3⋊C4—62no—
302Dic3⋊C4—62no—
303#208—34no—
304#208—34no—
305#208—64no—
306#208—64no—
307C2×C3⋊C8—22no—
308C2×C3⋊C8—32no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—62no—
311C2×C3⋊C8—64no—
312C2×C3⋊C8C22×D311yescharacteristic
313C2×C3⋊C8C22×D311yescharacteristic
314ΓL(1,𝔽25)—64no—
315D3×C8—64no—
316C22×C32—21no—
317C22×C32—21no—
318C22×C32#12112yes—
319C22×C32C22×D411yescharacteristic
320C2×C3×D3—22no—
321C2×C3×D3—22no—
322C2×C3×D3—22no—
323C2×C3×D3—41no—
324C2×C3×D3—41no—
325C2×C3×D3—41no—
326C32×C4—41no—
327C32×C4—41no—
328C32×C4#12112yes—
329C32×C4C22×D411yescharacteristic
330C32×C4C2×#4111yescharacteristic
331C3⋊Dic3—42no—
332C3×Dic3—22no—
333C3×Dic3—42no—
334C3×Dic3—41no—
335C2×#41—31no—
336C2×#41—31no—
337C22×Q8—31no—
338#137—184no—
339C2×Q16—92no—
340C2×SD16—92no—
341#131—184no—
342C2×M16—92no—
343C2×M16—91no—
344C22×C8—31no—
345C22×C8—92no—
346C4⋊Q8—61no—
347#124—61no—
348#123—62no—
349C22⋊Q8—32no—
350C22⋊Q8—32no—
351C22⋊Q8—92no—
352C22⋊Q8—181no—
353#121—92no—
354#121—181no—
355#121—182no—
356#117D3211yescharacteristic
357C2×C4⋊C4—91no—
358#107—92no—
359#106—92no—
360#103—31no—
361#103—31no—
362#103—92no—
363#103—92no—
364#102—31no—
365#102—31no—
366C23×C3—21no—
367C23×C3—32no—
368C23×C3—61no—
369C23×C3D3×D411yescharacteristic
370C23×C3C2×#6711yescharacteristic
371C22×D3—21no—
372C22×D3C2×#6712yes—
373C3×Q8—62no—
374C3×Q8—62no—
375C3×Q8—62no—
376C3×Q8—61no—
377C3×Q8—61no—
378C3×Q8—122no—
379C3×D4—64no—
380C3×D4—62no—
381C3×D4—61no—
382C3×D4—61no—
383C3×D4—122no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—21no—
392C2×C3×C4—32no—
393C2×C3×C4—41no—
394C2×C3×C4—41no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—122no—
400C2×C3×C4—122no—
401C2×C3×C4#23512yes—
402C2×C3×C4D3×D412yes—
403C2×C3×C4D3×D412yes—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4#23712yes—
406C2×C3×C4C2×#6711yescharacteristic
407C2×C3×C4C23×D311yescharacteristic
408C2×C3×C4C23×D311yescharacteristic
409#67—24no—
410#67—42no—
411#67—242no—
412#67—242no—
413C2×Dic3—21no—
414C2×Dic3—22no—
415C2×Dic3—42no—
416C2×Dic3—62no—
417C2×Dic3—62no—
418C2×Dic3—122no—
419C2×Dic3—241no—
420C2×Dic3—241no—
421C2×Dic3—242no—
422C2×Dic3C2×#6712yes—
423D12—22no—
424D12—21no—
425D12—21no—
426C4×D3—22no—
427C4×D3—22no—
428C4×D3—42no—
429Dic6—22no—
430Dic6—21no—
431Dic6—22no—
432Dic6—21no—
433Dic6—22no—
434Dic6—42no—
435C3×C8—61no—
436C3×C8—61no—
437C3⋊C8—21no—
438C3⋊C8—21no—
439C3⋊C8—34no—
440C3⋊C8—34no—
441C3⋊C8—64no—
442C2×C32—22no—
443C2×C32C2×#12111yescharacteristic
444C2×C32#57711yescharacteristic
445C2×C32#57811yescharacteristic
446C3×D3—42no—
447C3×D3—81no—
448#41—62no—
449#41—62no—
450#41—62no—
451#41—62no—
452C2×Q8—31no—
453C2×Q8—31no—
454C2×Q8—32no—
455C2×Q8—61no—
456C2×Q8—62no—
457C2×Q8—62no—
458C2×D4—32no—
459C2×D4—31no—
460C2×D4—31no—
461C2×D4—61no—
462C2×D4—182no—
463C22×C4—32no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—181no—
467C22×C4C2×D3211yescharacteristic
468Q16—184no—
469SD16—184no—
470M16—94no—
471M16—184no—
472C2×C8—31no—
473C2×C8—31no—
474C2×C8—62no—
475C2×C8—92no—
476C2×C8—184no—
477C4⋊C4—62no—
478C4⋊C4—62no—
479C4⋊C4—92no—
480C4⋊C4—182no—
481C4⋊C4—181no—
482C4⋊C4C2×D3211yescharacteristic
483C4⋊C4C2×D3211yescharacteristic
484C22⋊C4—21no—
485C22⋊C4—62no—
486C22⋊C4—62no—
487C22⋊C4—182no—
488C22⋊C4—182no—
489C42—21no—
490C22×C3—21no—
491C22×C3—21no—
492C22×C3—21no—
493C22×C3—21no—
494C22×C3—21no—
495C22×C3—22no—
496C22×C3—41no—
497C22×C3—41no—
498C22×C3—62no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—121no—
502C22×C3—121no—
503C22×C3—121no—
504C22×C3#88412yes—
505C22×C3#93912yes—
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C22×#6711yescharacteristic
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—41no—
512C2×D3—41no—
513C2×D3—41no—
514C3×C4—21no—
515C3×C4—21no—
516C3×C4—22no—
517C3×C4—41no—
518C3×C4—41no—
519C3×C4—41no—
520C3×C4—41no—
521C3×C4—62no—
522C3×C4—81no—
523C3×C4—81no—
524C3×C4—122no—
525C3×C4—121no—
526C3×C4#88412yes—
527C3×C4#93912yes—
528C3×C4C2×#23511yescharacteristic
529C3×C4C2×D3×D411yescharacteristic
530C3×C4C2×D3×D411yescharacteristic
531C3×C4C2×#23711yescharacteristic
532Dic3—22no—
533Dic3—41no—
534Dic3—42no—
535Dic3—122no—
536Dic3—122no—
537Dic3—242no—
538C32#306311yescharacteristic, complemented, Sylow
539C23—32no—
540C23—61no—
541C23D3×#6711yescharacteristic
542Q8—62no—
543Q8—62no—
544Q8—61no—
545Q8—62no—
546Q8—61no—
547Q8—122no—
548D4—64no—
549D4—61no—
550D4—61no—
551D4—62no—
552D4—122no—
553D4—722no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—32no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—61no—
561C2×C4—122no—
562C2×C4—122no—
563C2×C4—182no—
564C2×C4—721no—
565C2×C4#379512yes—
566C2×C4#380212yes—
567C2×C4D3×#6711yescharacteristic
568C2×C4C22×D3211yescharacteristic
569C8—61no—
570C8—61no—
571C8—94no—
572C2×C3—22no—
573C2×C3—22no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—21no—
577C2×C3—42no—
578C2×C3—122no—
579C2×C3—241no—
580C2×C3C2×#88411yescharacteristic
581C2×C3#577011yescharacteristic
582C2×C3#577111yescharacteristic
583C2×C3C2×#93911yescharacteristic
584C2×C3#583711yescharacteristic
585C2×C3#583811yescharacteristic
586D3—42no—
587D3—81no—
588C22—21no—
589C22—21no—
590C22—62no—
591C22—62no—
592C22—62no—
593C22—121no—
594C22—121no—
595C22—121no—
596C22#6388512yes—
597C22C2×D3×#6711yescharacteristic
598C4—41no—
599C4—41no—
600C4—62no—
601C4—121no—
602C4—122no—
603C4—362no—
604C4#6388512yes—
605C4C2×#379511yescharacteristic
606C4C2×#380211yescharacteristic
607C3—21no—
608C3#7884111yescharacteristic, complemented
609C3#8340011yescharacteristic, complemented
610C2—22no—
611C2—122no—
612C2—241no—
613C2C2×#6388511yescharacteristic
614C2#1059545711yescharacteristic
615C2#1059546711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radical#10595044C2
hypercenter#117D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
1. C3×#5526C2semidirect
3. C2×#63827C2semidirect
4. C2×#63814C2semidirect
5. #10592694C2semidirect
6. C3×#5002C2semidirect
7. C2×#63566C2semidirect
8. #10590520C2semidirect
9. #10590518C2semidirect
10. #10590503C2semidirect
11. #10590501C2semidirect
52. #5526D3semidirect
60. #5002D3semidirect
94. #3748D4semidirect
538. C32#3063semidirect
608. C3#78841semidirect
609. C3#83400semidirect

Maximal subgroups

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

subgroupindex
C3×#55262
#105950442
C2×#638272
C2×#638142
#105926942
C3×#50022
C2×#635662
#105905202
#105905182
#105905032
#105905012
#834003
#788413