Finite Group Databasebeta

← #11868056

Subgroups — #11868056

Order 1152.

958 conjugacy classes of subgroups.

The subgroup lattice has 709 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#912C211yesmaximal, characteristic, complemented
2#10595095C212yesmaximal, complemented
3D3×#901C211yesmaximal, characteristic, complemented
4#10592859C211yesmaximal, characteristic, complemented
5C3×#5160C211yesmaximal, characteristic, complemented
6#10591506C212yesmaximal, complemented
7#10591501C212yesmaximal, complemented
8#10591407C212yesmaximal, complemented
9#10590933C211yesmaximal, characteristic, complemented
10#10590930C211yesmaximal, characteristic, complemented
11D3×#819C211yesmaximal, characteristic, complemented
12#83928—31nomaximal
13#80937—31nomaximal
14C2×C3×#237C2212yes—
15D3×#235C2211yescharacteristic
16C2×C32×D8C2211yescharacteristic, complemented
17#64141C2212yes—
18#64110C2211yescharacteristic
19C2×C3×#214C2212yescomplemented
20C3×#932C2212yes—
21C3×#912—21no—
22C3×#912—21no—
23C3×#912—21no—
24C3×#912—21no—
25C2×C3×Dic12C2211yescharacteristic, complemented
26C3×#901C2211yescharacteristic
27C2×C3×D3×C8C2211yescharacteristic
28#63935—22no—
29#63933—22no—
30#63929—22no—
31#63925—22no—
32#63833C2212yes—
33#63827C2212yes—
34#63817C2211yescharacteristic
35#63814C2211yescharacteristic
36D3×#208C2211yescharacteristic
37D3×#208C2212yes—
38#63804—21no—
39#63803—21no—
40D3×ΓL(1,𝔽25)—21no—
41D32×C8—21no—
42#63660C2212yescomplemented
43#63646C2211yescharacteristic, complemented
44C3×#833C2212yescomplemented
45C3×#819C2211yescharacteristic, complemented
46#63577C2212yescomplemented
47#63560C2212yescomplemented
48#63560C2212yescomplemented
49C2×C3×#135—31no—
50#5822—32no—
51#5773—32no—
52C2×#912D311yescharacteristic, complemented
53D3×#131—31no—
54C2×#901—31no—
55C3×#472—31no—
56#5237—32no—
57#5200—32no—
58#5192—31no—
59#5192—31no—
60#5177—32no—
61#5177—32no—
62#5160—31no—
63#5160—31no—
64#5160—61no—
65#5160D311yescharacteristic, complemented
66#5143—31no—
67C2×#819—31no—
68#4896—31no—
69D3×#108—31no—
70#4748—32no—
71#4745—32no—
72C2×C32×D4C2312yes—
73#3828C2311yescharacteristic
74C2×C3×#67—22no—
75C22×C3×Dic3—22no—
76C3×#237—22no—
77C3×#237—22no—
78C3×#237—22no—
79C3×#237—22no—
80C3×#235C2311yescharacteristic
81C2×C3×C4×D3C2311yescharacteristic
82C2×C3×Dic6C2312yes—
83D3×#67—21no—
84#3804—21no—
85D3×D12D411yescharacteristic
86C4×D32—21no—
87#3799D411yescharacteristic
88#3798—21no—
89#3795D411yescharacteristic
90D3×Dic6D411yescharacteristic
91C32×D8—21no—
92C32×D8—21no—
93C2×C32×C8C2311yescharacteristic
94#3754—22no—
95#3753—22no—
96#3748C2311yescharacteristic
97#3748C2312yes—
98#3743—21no—
99C8×C3⋊D3—21no—
100C3×#214—22no—
101C3×#214—22no—
102C3×#214—22no—
103C3×#213—22no—
104C3×#208C2311yescharacteristic
105C3×#208C2312yes—
106C2×C3×C3⋊C8C2311yescharacteristic
107C3×Dic12—21no—
108C3×Dic12—21no—
109C3×ΓL(1,𝔽25)—21no—
110C3×D3×C8—21no—
111C3×D3×C8D411yescharacteristic
112C3×D3×C8D411yescharacteristic
113C3×D3×C8D411yescharacteristic
114C3×D3×C8D411yescharacteristic
115#3719—22no—
116#3718—22no—
117#3717—22no—
118#3715—22no—
119#3712—21no—
120#3711—21no—
121#3711—22no—
122#3711—21no—
123#3710—21no—
124D3×C3⋊C8—21no—
125D3×C3⋊C8—22no—
126D3×C3⋊C8—21no—
127#3067—91noSylow
128C2×C3×#41—32no—
129D3×#41—31no—
130C2×#237C2×D312yes—
131C2×#235—31no—
132C3×AGL(1,ℤ/8)—32no—
133C3×#135—61no—
134C3×#135—61no—
135C3×#135—61no—
136C3×#135—61no—
137C2×C3×Q16—31no—
138C2×C3×SD16—32no—
139C2×C3×D8—21no—
140C2×C3×D8C2×D311yescharacteristic, complemented
141C2×C3×D8C2×D311yescharacteristic, complemented
142C3×#131—31no—
143C22×C3×C8—31no—
144#951—32no—
145#951—62no—
146#950—62no—
147#950—62no—
148#949—62no—
149#948—31no—
150#942—32no—
151#942—32no—
152C2×#214C2×D312yescomplemented
153#932—32no—
154#932—32no—
155#932—62no—
156#932C2×D312yes—
157C2×#208—31no—
158C2×#208—32no—
159#916—62no—
160#915—62no—
161#912—21no—
162#912—21no—
163#912—21no—
164#912—21no—
165#912—62no—
166#911—62no—
167#909—32no—
168#907—31no—
169#907—61no—
170D3×M16—32no—
171D3×M16—31no—
172D3×M16—61no—
173C2×Dic12C2×D311yescharacteristic, complemented
174#901—31no—
175#901—31no—
176#901—31no—
177#901—31no—
178#901—61no—
179#901—61no—
180#901—61no—
181#901—61no—
182#901C2×D311yescharacteristic
183C2×ΓL(1,𝔽25)—61no—
184C2×D3×C8—61no—
185C2×D3×C8—61no—
186C2×D3×C8C2×D311yescharacteristic
187C3×#108—31no—
188C3×#100—32no—
189#836—32no—
190#836—32no—
191#833—32no—
192#833—32no—
193#833—62no—
194#833C2×D312yescomplemented
195#824—32no—
196#824—32no—
197#822—32no—
198#819—31no—
199#819—31no—
200#819—32no—
201#819—61no—
202#819C2×D311yescharacteristic, complemented
203C23×C32—22no—
204C22×C3×D3#4111yescharacteristic
205C2×D32—21no—
206C32×D4—22no—
207C32×D4—22no—
208C2×C32×C4C2411yescharacteristic
209#638—21no—
210C4⋊(C3⋊D3)C2×D411yescharacteristic
211C4×C3⋊D3—21no—
212#634C2×D411yescharacteristic
213C3×#67—21no—
214C3×#67—42no—
215C3×#67—42no—
216C2×C3×Dic3—22no—
217C2×C3×Dic3—42no—
218C2×C3×Dic3—42no—
219C2×C3×Dic3#4111yescharacteristic
220C3×D12C2×D411yescharacteristic
221C3×C4×D3—21no—
222C3×C4×D3C2×D411yescharacteristic
223C3×C4×D3C2×D411yescharacteristic
224C3×C4×D3C2×D411yescharacteristic
225C3×C4×D3C2×D411yescharacteristic
226C3×Dic6—22no—
227C3×Dic6—22no—
228C3×Dic6C2×D411yescharacteristic
229#627—21no—
230#626—21no—
231#626—21no—
232#625—21no—
233#624—21no—
234D3×Dic3—21no—
235D3×Dic3—21no—
236C32×C8C2×D411yescharacteristic
237C32×C8C2×D411yescharacteristic
238C3⋊(C3⋊C8)—21no—
239C3⋊(C3⋊C8)—22no—
240C3×C3⋊C8—21no—
241C3×C3⋊C8—22no—
242C3×C3⋊C8C2×D411yescharacteristic
243C3×C3⋊C8C2×D411yescharacteristic
244#575—92no—
245C2×#135—31no—
246C2×#131—91no—
247#473—91no—
248#473—91no—
249#472—31no—
250#472—91no—
251#471—92no—
252#471—92no—
253C2×#108—91no—
254#413—92no—
255C3×#41—31no—
256C3×#41—62no—
257C3×#41—62no—
258C3×#41—62no—
259C3×#41—62no—
260C2×C3×Q8—32no—
261C2×C3×D4—22no—
262C2×C3×D4—62no—
263C2×C3×D4C22×D312yes—
264C2×C3×D4C22×D312yes—
265C22×C3×C4—31no—
266C22×C3×C4—62no—
267C2×#67—22no—
268C2×#67—61no—
269C22×Dic3—22no—
270#239—31no—
271D3×Q8—31no—
272#237—22no—
273#237—22no—
274#237—22no—
275#237—22no—
276#237—31no—
277#237—61no—
278D3×D4—31no—
279D3×D4—61no—
280#235—31no—
281#235—31no—
282#235—31no—
283#235—31no—
284#235—61no—
285#235—61no—
286#235—61no—
287#235—61no—
288#235C22×D311yescharacteristic
289C2×D12—31no—
290C2×C4×D3—61no—
291C2×C4×D3—61no—
292C2×C4×D3C22×D311yescharacteristic
293C2×Dic6—31no—
294C2×Dic6C22×D312yes—
295C3×Q16—61no—
296C3×Q16—61no—
297C3×SD16—62no—
298C3×SD16—62no—
299C3×SD16—62no—
300C3×D8—21no—
301C3×D8—21no—
302C3×D8—21no—
303C3×D8—21no—
304C3×D8—41no—
305C3×D8—41no—
306C3×D8—62no—
307C3×M16—32no—
308C3×M16—31no—
309C3×M16—61no—
310C2×C3×C8—21no—
311C2×C3×C8—31no—
312C2×C3×C8—31no—
313C2×C3×C8—31no—
314C2×C3×C8—31no—
315C2×C3×C8—31no—
316C2×C3×C8—61no—
317C2×C3×C8C22×D311yescharacteristic
318C2×C3×C8C22×D311yescharacteristic
319#216—62no—
320#216—62no—
321#216—62no—
322#215—62no—
323#215—62no—
324#214—22no—
325#214—22no—
326#214—22no—
327#214—62no—
328#214—62no—
329#214—62no—
330#214—122no—
331#213—22no—
332#213—62no—
333#213—62no—
334#213—122no—
335#208—32no—
336#208—32no—
337#208—31no—
338#208—31no—
339#208—62no—
340#208—61no—
341#208—61no—
342#208—62no—
343#208—61no—
344#208C22×D312yes—
345#208C22×D311yescharacteristic
346C2×C3⋊C8—61no—
347C2×C3⋊C8—62no—
348C2×C3⋊C8—61no—
349C2×C3⋊C8C22×D311yescharacteristic
350Dic12—21no—
351Dic12—21no—
352Dic12—62no—
353#204—62no—
354ΓL(1,𝔽25)—21no—
355ΓL(1,𝔽25)—61no—
356ΓL(1,𝔽25)—61no—
357ΓL(1,𝔽25)—62no—
358ΓL(1,𝔽25)—61no—
359ΓL(1,𝔽25)—61no—
360ΓL(1,𝔽25)—61no—
361ΓL(1,𝔽25)—61no—
362ΓL(1,𝔽25)—121no—
363D3×C8—21no—
364D3×C8—61no—
365D3×C8—61no—
366D3×C8—62no—
367D3×C8—61no—
368D3×C8—61no—
369D3×C8—61no—
370D3×C8—61no—
371D3×C8—121no—
372D3×C8#6711yescharacteristic
373D3×C8#6711yescharacteristic
374D3×C8#6711yescharacteristic
375D3×C8#6711yescharacteristic
376C22×C32—42no—
377C22×C32—82no—
378C22×C32C2×#4111yescharacteristic
379C2×C3⋊D3—21no—
380C2×C3×D3—21no—
381C2×C3×D3—41no—
382C2×C3×D3#12111yescharacteristic
383C2×C3×D3#12111yescharacteristic
384D32—42no—
385C32×C4C22×D411yescharacteristic
386C32×C4C22×D411yescharacteristic
387C3⋊Dic3—21no—
388C3×Dic3—21no—
389C3×Dic3—42no—
390C3×Dic3#12111yescharacteristic
391C3×Dic3#12111yescharacteristic
392C2×#41—32no—
393C2×#41—91no—
394#137—92no—
395#137—92no—
396#137—182no—
397AGL(1,ℤ/8)—32no—
398AGL(1,ℤ/8)—92no—
399AGL(1,ℤ/8)—182no—
400#135—61no—
401#135—61no—
402#135—61no—
403#135—61no—
404#135—182no—
405#135—182no—
406C2×Q16—31no—
407C2×SD16—32no—
408C2×D8D3211yescharacteristic, complemented
409#131—31no—
410#131—91no—
411#131—91no—
412#131—91no—
413#131—181no—
414#131—181no—
415C2×M16—91no—
416C2×M16—92no—
417C2×M16—181no—
418C22×C8—31no—
419C22×C8—181no—
420#108—31no—
421#108—92no—
422#108—91no—
423#101—92no—
424#101—92no—
425#100—32no—
426#100—92no—
427C23×C3—22no—
428C23×C3—22no—
429C23×C3—31no—
430C23×C3—42no—
431C22×D3—61no—
432C22×D3—61no—
433C22×D3#23711yescharacteristic
434C3×Q8—31no—
435C3×Q8—62no—
436C3×Q8—62no—
437C3×D4—22no—
438C3×D4—22no—
439C3×D4—22no—
440C3×D4—22no—
441C3×D4—31no—
442C3×D4—42no—
443C3×D4—42no—
444C3×D4—61no—
445C3×D4—122no—
446C3×D4—122no—
447C2×C3×C4—21no—
448C2×C3×C4—31no—
449C2×C3×C4—31no—
450C2×C3×C4—31no—
451C2×C3×C4—31no—
452C2×C3×C4—31no—
453C2×C3×C4—61no—
454C2×C3×C4—62no—
455C2×C3×C4—122no—
456C2×C3×C4—122no—
457C2×C3×C4C23×D311yescharacteristic
458C2×C3×C4C23×D311yescharacteristic
459#67—21no—
460#67—42no—
461#67—42no—
462#67—61no—
463#67—61no—
464#67—61no—
465#67—61no—
466#67—61no—
467#67—61no—
468#67—121no—
469C2×Dic3—22no—
470C2×Dic3—42no—
471C2×Dic3—42no—
472C2×Dic3—61no—
473C2×Dic3—61no—
474C2×Dic3#23711yescharacteristic
475D12—31no—
476D12—31no—
477D12—61no—
478D12—61no—
479D12—61no—
480D12D3×D411yescharacteristic
481C4×D3—21no—
482C4×D3—61no—
483C4×D3—61no—
484C4×D3—61no—
485C4×D3—61no—
486C4×D3—61no—
487C4×D3—61no—
488C4×D3—121no—
489C4×D3D3×D411yescharacteristic
490C4×D3D3×D411yescharacteristic
491C4×D3C2×#6711yescharacteristic
492C4×D3C2×#6711yescharacteristic
493Dic6—22no—
494Dic6—22no—
495Dic6—31no—
496Dic6—31no—
497Dic6—61no—
498Dic6—61no—
499Dic6—61no—
500Dic6D3×D411yescharacteristic
501C3×C8—21no—
502C3×C8—21no—
503C3×C8—31no—
504C3×C8—31no—
505C3×C8—62no—
506C3×C8—61no—
507C3×C8D3×D411yescharacteristic
508C3×C8D3×D411yescharacteristic
509C3×C8C2×#6711yescharacteristic
510C3×C8C2×#6711yescharacteristic
511C3⋊C8—21no—
512C3⋊C8—22no—
513C3⋊C8—61no—
514C3⋊C8—62no—
515C3⋊C8—62no—
516C3⋊C8—61no—
517C3⋊C8—121no—
518C3⋊C8—122no—
519C3⋊C8C2×#6711yescharacteristic
520C3⋊C8C2×#6711yescharacteristic
521C2×C32—21no—
522C2×C32—82no—
523C2×C32C2×#12111yescharacteristic
524C3⋊D3—41no—
525C3×D3—21no—
526C3×D3—21no—
527C3×D3—41no—
528#41—31no—
529#41—62no—
530#41—62no—
531#41—62no—
532#41—62no—
533#41—91no—
534#41—91no—
535#41—91no—
536#41—181no—
537#41—181no—
538C2×Q8—32no—
539C2×Q8—91no—
540C2×D4—62no—
541C2×D4—91no—
542C2×D4—181no—
543C2×D4C2×D3212yes—
544C22×C4—31no—
545C22×C4—62no—
546C22×C4—181no—
547Q16—61no—
548Q16—61no—
549Q16—182no—
550Q16—182no—
551SD16—62no—
552SD16—62no—
553SD16—62no—
554SD16—182no—
555SD16—182no—
556SD16—182no—
557D8—21no—
558D8—21no—
559D8—62no—
560D8—182no—
561M16—31no—
562M16—32no—
563M16—61no—
564M16—91no—
565M16—92no—
566M16—181no—
567M16—181no—
568M16—181no—
569M16—182no—
570M16—181no—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—61no—
577C2×C8—181no—
578C2×C8—181no—
579C2×C8—181no—
580C2×C8—182no—
581C2×C8—181no—
582C2×C8C2×D3211yescharacteristic
583C22×C3—21no—
584C22×C3—31no—
585C22×C3—31no—
586C22×C3—42no—
587C22×C3—42no—
588C22×C3—61no—
589C22×C3—82no—
590C22×C3—82no—
591C22×C3—82no—
592C22×C3—121no—
593C22×C3—162no—
594C22×C3C2×#23711yescharacteristic
595C22×C3D3×#4111yescharacteristic
596C2×D3—21no—
597C2×D3—41no—
598C2×D3—61no—
599C2×D3—61no—
600C2×D3—121no—
601C2×D3—122no—
602C2×D3—122no—
603C2×D3#93811yescharacteristic
604C2×D3#93811yescharacteristic
605C3×C4—21no—
606C3×C4—21no—
607C3×C4—31no—
608C3×C4—31no—
609C3×C4—61no—
610C3×C4—122no—
611C3×C4C2×D3×D411yescharacteristic
612C3×C4C2×D3×D411yescharacteristic
613C3×C4C2×D3×D411yescharacteristic
614C3×C4C22×#6711yescharacteristic
615Dic3—21no—
616Dic3—42no—
617Dic3—61no—
618Dic3—61no—
619Dic3—121no—
620Dic3#93811yescharacteristic
621Dic3#93811yescharacteristic
622C32#306711yescharacteristic, complemented, Sylow
623C23—22no—
624C23—31no—
625C23—181no—
626Q8—31no—
627Q8—62no—
628Q8—62no—
629Q8—91no—
630Q8—181no—
631D4—22no—
632D4—22no—
633D4—31no—
634D4—61no—
635D4—91no—
636D4—122no—
637D4—122no—
638D4—181no—
639D4—181no—
640D4—181no—
641D4—181no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—31no—
647C2×C4—61no—
648C2×C4—62no—
649C2×C4—122no—
650C2×C4—122no—
651C2×C4—181no—
652C2×C4—181no—
653C2×C4—181no—
654C2×C4—181no—
655C2×C4C22×D3211yescharacteristic
656C8—31no—
657C8—31no—
658C8—62no—
659C8—61no—
660C8—182no—
661C8—181no—
662C8D3×#6711yescharacteristic
663C8D3×#6711yescharacteristic
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—21no—
667C2×C3—41no—
668C2×C3—61no—
669C2×C3—61no—
670C2×C3—82no—
671C2×C3—82no—
672C2×C3—121no—
673C2×C3—162no—
674C2×C3D3×#12111yescharacteristic
675C2×C3C2×#93811yescharacteristic
676D3—21no—
677D3—21no—
678D3—41no—
679D3—121no—
680D3—121no—
681D3—241no—
682C22—31no—
683C22—31no—
684C22—42no—
685C22—61no—
686C22—82no—
687C22—121no—
688C22—181no—
689C22—362no—
690C22D3×#23711yescharacteristic
691C4—31no—
692C4—31no—
693C4—61no—
694C4—122no—
695C4—181no—
696C4D32×D411yescharacteristic
697C4C2×D3×#6711yescharacteristic
698C3—21no—
699C3#8093711yescharacteristic, complemented
700C3#8392811yescharacteristic, complemented
701C2—21no—
702C2—61no—
703C2—61no—
704C2—82no—
705C2—121no—
706C2—361no—
707C2D3×#93811yescharacteristic
subgroupG/H
centerC2D3×#938
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC2×C32C2×#121
hypercenterC2×D8D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#912C2semidirect
2. #10595095C2semidirect
3. D3×#901C2semidirect
4. #10592859C2semidirect
5. C3×#5160C2semidirect
6. #10591506C2semidirect
7. #10591501C2semidirect
8. #10591407C2semidirect
9. #10590933C2semidirect
10. #10590930C2semidirect
11. D3×#819C2semidirect
16. C2×C32×D8C22semidirect
19. C2×C3×#214C22semidirect
25. C2×C3×Dic12C22semidirect
42. #63660C22semidirect
43. #63646C22semidirect
44. C3×#833C22semidirect
45. C3×#819C22semidirect
46. #63577C22semidirect
47. #63560C22semidirect
48. #63560C22semidirect
52. C2×#912D3semidirect
65. #5160D3semidirect
140. C2×C3×D8C2×D3semidirect
141. C2×C3×D8C2×D3semidirect
152. C2×#214C2×D3semidirect
173. C2×Dic12C2×D3semidirect
194. #833C2×D3semidirect
202. #819C2×D3semidirect
408. C2×D8D32semidirect
622. C32#3067semidirect
699. C3#80937semidirect
700. C3#83928semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9122
#105950952
D3×#9012
#105928592
C3×#51602
#105915062
#105915012
#105914072
#105909332
#105909302
D3×#8192
#839283
#809373