Finite Group Databasebeta

← #11867817

Subgroups — #11867817

Order 1152.

1023 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#901C211yesmaximal, characteristic, complemented
2#10595043C211yesmaximal, characteristic
3#10594855C211yesmaximal, characteristic, complemented
4C2×#63833C211yesmaximal, characteristic, complemented
5#10592812C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7#10591130C211yesmaximal, characteristic, complemented
8#10590850C212yesmaximal, complemented
9#10590849C212yesmaximal, complemented
10#10590848C212yesmaximal, complemented
11#10590847C212yesmaximal, complemented
12#83808—31nomaximal
13#78800—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C22×C32×C8C2211yescharacteristic
18#64135C2211yescharacteristic
19C2×C3×C4⋊Dic3C2211yescharacteristic
20C2×C3×#208C2211yescharacteristic
21C3×#901—24no—
22C2×C3×ΓL(1,𝔽25)C2212yes—
23C2×C3×D3×C8C2212yes—
24#63978—22no—
25#63961—22no—
26#63916—21no—
27#63909C2212yes—
28#63873—21no—
29#63871—21no—
30#63863—21no—
31#63857C2212yes—
32#63856C2212yes—
33#63856C2212yes—
34C2×#3719C2212yes—
35#63833—24no—
36C2×#3717C2212yes—
37#63648C2211yescharacteristic
38#63648C2211yescharacteristic
39#63643C2211yescharacteristic
40#63643C2211yescharacteristic
41C3×#816C2212yes—
42C3×#816C2212yes—
43#63575C2212yes—
44#63573C2212yes—
45C2×C3×#131—31no—
46#5833—31no—
47#5825—31no—
48#5816—31no—
49C2×#942—31no—
50C2×#909—31no—
51C2×#901D311yescharacteristic, complemented
52#5510—31no—
53C2×C3×#103—31no—
54#5137—32no—
55#5134—32no—
56#5121—31no—
57#5116—32no—
58#5114—32no—
59#5113—31no—
60#5113—31no—
61#5113—61no—
62C2×#816D311yescharacteristic, complemented
63#4964—31no—
64#4816—32no—
65#4813—32no—
66#4812—32no—
67#4807—32no—
68C22×C32×C4C2311yescharacteristic
69C2×#638—21no—
70#3828—22no—
71#3828—22no—
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×#634C2311yescharacteristic
75C2×C3×#67D412yes—
76C22×C3×Dic3—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235—22no—
80C2×C3×D12D411yescharacteristic
81C2×C3×C4×D3C2312yes—
82C2×C3×Dic6—22no—
83C2×C3×Dic6—22no—
84C2×C3×Dic6—21no—
85C2×C3×Dic6D411yescharacteristic
86C2×C3×Dic6C2312yes—
87C2×#626—22no—
88C2×C32×C8—22no—
89C2×C32×C8C2311yescharacteristic
90C2×C32×C8C2311yescharacteristic
91#3757—21no—
92C4⋊(C3⋊Dic3)C2311yescharacteristic
93C4⋊(C3⋊Dic3)C2311yescharacteristic
94C4×C3⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4⋊Dic3C2312yes—
97C3×#208D414yescomplemented
98C2×C3×C3⋊C8C2312yes—
99C3×ΓL(1,𝔽25)—24no—
100C3×D3×C8—24no—
101#3724—22no—
102#3724—22no—
103Dic3⋊Dic3—22no—
104#3722—22no—
105(C2×D3)⋊Dic3—22no—
106(C2×D3)⋊Dic3—22no—
107(C2×D3)⋊Dic3—22no—
108#3719—24no—
109#3717—24no—
110#3063—91noSylow
111C2×C3×#41—31no—
112C22×C3×Q8—31no—
113C2×#235—31no—
114C2×#235—31no—
115C2×#235—61no—
116C2×#235C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C3×#131—64no—
119C2×C3×M16—31no—
120C2×C3×M16—32no—
121C22×C3×C8—21no—
122C22×C3×C8—32no—
123C22×C3×C8C2×D311yescharacteristic
124C22×C3×C8C2×D311yescharacteristic
125C2×C3×C4⋊C4—31no—
126#947—61no—
127#946—32no—
128#946—32no—
129#946—61no—
130#944—61no—
131#944—61no—
132C2×#216—32no—
133#942—64no—
134C2×#215—32no—
135#939—62no—
136#938—61no—
137#936—61no—
138#935—62no—
139#930—32no—
140#930—62no—
141#929—62no—
142#926—31no—
143#926—31no—
144#926—61no—
145C2×C4⋊Dic3C2×D311yescharacteristic
146#924—32no—
147#924—32no—
148#924—32no—
149C2×#208C2×D311yescharacteristic
150#909—64no—
151C2×Dic12—32no—
152C2×#204—32no—
153#901—24no—
154C2×ΓL(1,𝔽25)C2×D312yes—
155C2×D3×C8C2×D312yes—
156#897—32no—
157#897—61no—
158#895—32no—
159#895—61no—
160C3×#103—32no—
161C3×#103—32no—
162#821—31no—
163#821—31no—
164#821—31no—
165#821—31no—
166#821—61no—
167#821—61no—
168#818—32no—
169#817—32no—
170#816—31no—
171#816—31no—
172#816—31no—
173#816—31no—
174#816—61no—
175#816—61no—
176#816C2×D312yes—
177#816C2×D312yes—
178#808—32no—
179#807—32no—
180C23×C32C2×D411yescharacteristic
181C22×C3⋊D3—21no—
182C22×C3×D3C2×D412yes—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D412yes—
185C2×C32×C4#4112yes—
186C2×C32×C4C2411yescharacteristic
187#638—42no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C4⋊(C3⋊D3)—21no—
192C4⋊(C3⋊D3)—21no—
193C4×C3⋊D3—42no—
194#634—21no—
195#634—21no—
196C3×#67—24no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—22no—
199C2×C3×Dic3—42no—
200C2×C3×Dic3—81no—
201C2×C3×Dic3C2×D412yes—
202C3×D12—22no—
203C3×C4×D3—22no—
204C3×C4×D3—22no—
205C3×Dic6—22no—
206C3×Dic6—22no—
207C3×Dic6—22no—
208C3×Dic6—42no—
209#626—82no—
210C32×C8—21no—
211C32×C8—21no—
212C3×C3⋊C8C2×D414yes—
213C2×#137—91no—
214C2×#131—31no—
215#537—91no—
216#536—91no—
217#470—92no—
218#468—92no—
219#467—92no—
220#465—92no—
221#428—91no—
222#416—91no—
223C2×#103—31no—
224C3×#41—62no—
225C3×#41—62no—
226C2×C3×Q8—31no—
227C2×C3×Q8—32no—
228C2×C3×Q8—61no—
229C2×C3×Q8—62no—
230C2×C3×Q8—62no—
231C2×C3×D4—32no—
232C2×C3×D4—31no—
233C22×C3×C4—21no—
234C22×C3×C4—32no—
235C22×C3×C4—61no—
236C22×C3×C4—61no—
237C22×C3×C4C22×D311yescharacteristic
238C22×C3×C4C22×D311yescharacteristic
239C2×#67—62no—
240C2×#67—61no—
241C2×#67—61no—
242C2×#67—121no—
243C2×#67D1212yes—
244C22×Dic3—21no—
245C22×Dic3—21no—
246#235—22no—
247#235—22no—
248#235—64no—
249#235—62no—
250#235—62no—
251#235—62no—
252#235—62no—
253#235—122no—
254C2×D12—31no—
255C2×D12—31no—
256C2×D12—61no—
257C2×D12—62no—
258C2×D12D1211yescharacteristic
259C2×C4×D3—61no—
260C2×C4×D3—61no—
261C2×C4×D3—121no—
262C2×C4×D3C22×D312yes—
263C2×Dic6—22no—
264C2×Dic6—22no—
265C2×Dic6—21no—
266C2×Dic6—31no—
267C2×Dic6—31no—
268C2×Dic6—61no—
269C2×Dic6D1211yescharacteristic
270C2×Dic6C22×D312yes—
271C3×M16—34no—
272C3×M16—64no—
273C2×C3×C8—22no—
274C2×C3×C8—22no—
275C2×C3×C8—21no—
276C2×C3×C8—21no—
277C2×C3×C8—32no—
278C2×C3×C8—42no—
279C2×C3×C8—64no—
280C2×C3×C8C22×D311yescharacteristic
281C2×C3×C8C22×D311yescharacteristic
282C2×C3×C8C22×D311yescharacteristic
283C2×C3×C8C22×D311yescharacteristic
284C3×C4⋊C4—32no—
285C3×C4⋊C4—61no—
286#217—62no—
287#217—62no—
288#217—62no—
289#217—61no—
290#217—61no—
291#217—121no—
292#216—64no—
293#215—64no—
294(C2×D3)⋊C4—62no—
295(C2×D3)⋊C4—62no—
296(C2×D3)⋊C4—62no—
297(C2×D3)⋊C4—62no—
298(C2×D3)⋊C4—62no—
299C4⋊Dic3—21no—
300C4⋊Dic3—31no—
301C4⋊Dic3—31no—
302C4⋊Dic3—31no—
303C4⋊Dic3—31no—
304C4⋊Dic3—61no—
305C4⋊Dic3—61no—
306C4⋊Dic3—62no—
307C4⋊Dic3C22×D312yes—
308Dic3⋊C4—62no—
309Dic3⋊C4—62no—
310Dic3⋊C4—62no—
311Dic3⋊C4—62no—
312Dic3⋊C4—62no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3—121no—
316#208#6714yescomplemented
317C2×C3⋊C8C22×D312yes—
318Dic12—64no—
319#204—64no—
320ΓL(1,𝔽25)—24no—
321D3×C8—24no—
322C22×C32—21no—
323C22×C32—21no—
324C22×C32#12112yes—
325C22×C32C22×D411yescharacteristic
326C2×C3⋊D3—41no—
327C2×C3⋊D3—41no—
328C2×C3⋊D3—41no—
329C2×C3×D3—22no—
330C2×C3×D3—22no—
331C2×C3×D3—22no—
332C32×C4#12112yes—
333C32×C4C22×D411yescharacteristic
334C32×C4C2×#4111yescharacteristic
335C3⋊Dic3—41no—
336C3⋊Dic3—41no—
337C3⋊Dic3—41no—
338C3×Dic3—22no—
339C3×Dic3—42no—
340C3×Dic3—42no—
341C2×#41—31no—
342C2×#41—91no—
343C22×Q8—31no—
344#137—184no—
345C2×Q16—92no—
346C2×SD16—92no—
347#131—64no—
348C2×M16—31no—
349C2×M16—32no—
350C22×C8—32no—
351C22×C8D3211yescharacteristic
352C4⋊Q8—181no—
353#124—181no—
354#123—182no—
355C22⋊Q8—92no—
356C22⋊Q8—92no—
357C22⋊Q8—92no—
358C22⋊Q8—181no—
359#121—92no—
360#121—181no—
361#121—182no—
362#117—91no—
363C2×C4⋊C4—31no—
364#107—92no—
365#106—92no—
366#103—32no—
367#103—32no—
368#103—91no—
369#103—91no—
370#102—91no—
371#102—91no—
372C23×C3—21no—
373C23×C3—32no—
374C23×C3C2×D1211yescharacteristic
375C23×C3D3×D411yescharacteristic
376C22×D3—61no—
377C22×D3—61no—
378C22×D3—121no—
379C22×D3C2×D1212yes—
380C3×Q8—62no—
381C3×Q8—62no—
382C3×Q8—62no—
383C3×Q8—122no—
384C3×D4—64no—
385C3×D4—62no—
386C2×C3×C4—21no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—22no—
390C2×C3×C4—32no—
391C2×C3×C4—62no—
392C2×C3×C4—62no—
393C2×C3×C4—62no—
394C2×C3×C4—62no—
395C2×C3×C4—122no—
396C2×C3×C4—241no—
397C2×C3×C4C2×D1211yescharacteristic
398C2×C3×C4#23512yes—
399C2×C3×C4#23512yes—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403C2×C3×C4C23×D311yescharacteristic
404C2×C3×C4C23×D311yescharacteristic
405#67—24no—
406#67—124no—
407#67—122no—
408#67—122no—
409#67—242no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—42no—
413C2×Dic3—61no—
414C2×Dic3—61no—
415C2×Dic3—61no—
416C2×Dic3—61no—
417C2×Dic3—61no—
418C2×Dic3—61no—
419C2×Dic3—81no—
420C2×Dic3—121no—
421C2×Dic3—121no—
422C2×Dic3—121no—
423C2×Dic3C2×D1212yes—
424D12—22no—
425D12—62no—
426D12—61no—
427D12—61no—
428D12—61no—
429D12—61no—
430D12—121no—
431D12—242no—
432C4×D3—22no—
433C4×D3—22no—
434C4×D3—124no—
435C4×D3—122no—
436C4×D3—122no—
437Dic6—22no—
438Dic6—22no—
439Dic6—22no—
440Dic6—42no—
441Dic6—62no—
442Dic6—61no—
443Dic6—61no—
444Dic6—61no—
445Dic6—61no—
446Dic6—121no—
447C3×C8—21no—
448C3×C8—21no—
449C3×C8—21no—
450C3×C8—21no—
451C3×C8—34no—
452C3×C8—41no—
453C3×C8—41no—
454C3⋊C8C2×#6714yes—
455C2×C32—22no—
456C2×C32C2×#12111yescharacteristic
457C2×C32#57711yescharacteristic
458C2×C32#57811yescharacteristic
459C3⋊D3—81no—
460C3×D3—42no—
461#41—62no—
462#41—62no—
463#41—182no—
464#41—182no—
465C2×Q8—31no—
466C2×Q8—32no—
467C2×Q8—61no—
468C2×Q8—62no—
469C2×Q8—62no—
470C2×Q8—91no—
471C2×D4—32no—
472C2×D4—31no—
473C2×D4—91no—
474C2×D4—182no—
475C2×D4—181no—
476C22×C4—32no—
477C22×C4—61no—
478C22×C4—61no—
479C22×C4—181no—
480C22×C4C2×D3211yescharacteristic
481Q16—184no—
482SD16—184no—
483M16—34no—
484M16—64no—
485C2×C8—22no—
486C2×C8—32no—
487C2×C8—64no—
488C2×C8C2×D3211yescharacteristic
489C2×C8C2×D3211yescharacteristic
490C4⋊C4—32no—
491C4⋊C4—61no—
492C4⋊C4—91no—
493C4⋊C4—91no—
494C4⋊C4—182no—
495C4⋊C4—182no—
496C4⋊C4—182no—
497C22⋊C4—182no—
498C22⋊C4—182no—
499C22⋊C4—182no—
500C22⋊C4—182no—
501C22⋊C4—181no—
502C42—181no—
503C22×C3—21no—
504C22×C3—21no—
505C22×C3—21no—
506C22×C3—21no—
507C22×C3—21no—
508C22×C3—22no—
509C22×C3—41no—
510C22×C3—41no—
511C22×C3—62no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3#88412yes—
515C22×C3#93012yes—
516C22×C3C22×D1211yescharacteristic
517C22×C3C2×D3×D411yescharacteristic
518C2×D3—22no—
519C2×D3—22no—
520C2×D3—22no—
521C2×D3—122no—
522C2×D3—121no—
523C2×D3—121no—
524C2×D3—121no—
525C2×D3—121no—
526C2×D3—121no—
527C2×D3—121no—
528C2×D3—241no—
529C2×D3—241no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—22no—
533C3×C4—62no—
534C3×C4—122no—
535C3×C4—122no—
536C3×C4#88412yes—
537C3×C4#93012yes—
538C3×C4C2×#23511yescharacteristic
539C3×C4C2×#23511yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541C3×C4C22×#6711yescharacteristic
542Dic3—22no—
543Dic3—42no—
544Dic3—42no—
545Dic3—122no—
546Dic3—121no—
547Dic3—121no—
548Dic3—121no—
549Dic3—121no—
550Dic3—121no—
551Dic3—121no—
552Dic3—241no—
553Dic3—241no—
554C32#306311yescharacteristic, complemented, Sylow
555C23—32no—
556C23—181no—
557C23D3×D1211yescharacteristic
558Q8—62no—
559Q8—62no—
560Q8—62no—
561Q8—122no—
562Q8—181no—
563Q8—181no—
564D4—64no—
565D4—62no—
566D4—181no—
567D4—181no—
568D4—362no—
569D4—722no—
570C2×C4—32no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—122no—
576C2×C4—181no—
577C2×C4—181no—
578C2×C4—181no—
579C2×C4—241no—
580C2×C4—362no—
581C2×C4#379812yes—
582C2×C4D3×D1211yescharacteristic
583C2×C4D3×#6712yes—
584C2×C4C22×D3211yescharacteristic
585C8—21no—
586C8—21no—
587C8—34no—
588C2×C3—22no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—42no—
594C2×C3—122no—
595C2×C3C2×#88411yescharacteristic
596C2×C3#575111yescharacteristic
597C2×C3#575311yescharacteristic
598C2×C3#576211yescharacteristic
599C2×C3#576611yescharacteristic
600C2×C3C2×#93011yescharacteristic
601D3—42no—
602D3—242no—
603D3—241no—
604D3—241no—
605C22—21no—
606C22—21no—
607C22—62no—
608C22—62no—
609C22—62no—
610C22—361no—
611C22—361no—
612C22—361no—
613C22#6390612yes—
614C22C2×D3×D1211yescharacteristic
615C4—62no—
616C4—122no—
617C4—122no—
618C4—361no—
619C4—361no—
620C4—361no—
621C4#6390612yes—
622C4C2×#379811yescharacteristic
623C4C2×D3×#6711yescharacteristic
624C3—21no—
625C3#7880011yescharacteristic, complemented
626C3#8380811yescharacteristic, complemented
627C2—22no—
628C2—122no—
629C2—721no—
630C2#1059467711yescharacteristic
631C2#1059469111yescharacteristic
632C2C2×#6390611yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC22×C32C22×D4
prime radical#10595043C2
hypercenterC22×C8D32
hypocenterC32#3063
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#901C2semidirect
3. #10594855C2semidirect
4. C2×#63833C2semidirect
5. #10592812C2semidirect
6. C2×C3×#816C2semidirect
7. #10591130C2semidirect
8. #10590850C2semidirect
9. #10590849C2semidirect
10. #10590848C2semidirect
11. #10590847C2semidirect
51. C2×#901D3semidirect
62. C2×#816D3semidirect
97. C3×#208D4semidirect
316. #208#67semidirect
554. C32#3063semidirect
625. C3#78800semidirect
626. C3#83808semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9012
#105950432
#105948552
C2×#638332
#105928122
C2×C3×#8162
#105911302
#105908502
#105908492
#105908482
#105908472
#838083
#788003