Finite Group Databasebeta

← #11868060

Subgroups — #11868060

Order 1152.

954 conjugacy classes of subgroups.

The subgroup lattice has 707 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594712C212yesmaximal, complemented
2C2×#63807C211yesmaximal, characteristic, complemented
3D3×#901C211yesmaximal, characteristic, complemented
4#10592595C211yesmaximal, characteristic, complemented
5C3×#4897C211yesmaximal, characteristic, complemented
6C3×D3×#108C211yesmaximal, characteristic, complemented
7#10591006C212yesmaximal, complemented
8#10590989C212yesmaximal, complemented
9#10590986C212yesmaximal, complemented
10#10590932C211yesmaximal, characteristic, complemented
11#10590929C211yesmaximal, characteristic, complemented
12#80937—31nomaximal
13#79256—31nomaximal
14D3×#235C2211yescharacteristic
15C2×#3795C2212yes—
16#64118C2212yes—
17C2×#3746C2211yescharacteristic, complemented
18#64110C2211yescharacteristic
19C3×#908C2212yes—
20C3×D3×M16C2212yes—
21C2×C3×D24C2211yescharacteristic, complemented
22C3×#901C2211yescharacteristic
23C2×C3×D3×C8C2211yescharacteristic
24#63831C2212yes—
25#63830C2212yes—
26C2×#3716C2212yescomplemented
27#63817C2211yescharacteristic
28#63814C2211yescharacteristic
29D3×#208C2211yescharacteristic
30#63807—22no—
31#63807—21no—
32#63807—21no—
33#63807—21no—
34#63807—21no—
35#63806—22no—
36#63804—21no—
37#63803—21no—
38#63800—22no—
39#63795—22no—
40D3×ΓL(1,𝔽25)—21no—
41D32×C8—21no—
42C32×#108C2211yescharacteristic, complemented
43#63651C2212yescomplemented
44C3×#823C2212yescomplemented
45C3×#822C2212yescomplemented
46C3×#819C2211yescharacteristic, complemented
47#63561C2212yescomplemented
48#63558C2212yescomplemented
49#5773—32no—
50C2×#912—31no—
51D3×#131—31no—
52#5748—32no—
53C2×#904—31no—
54C2×#901—31no—
55C3×#472—31no—
56C2×C3×#108—31no—
57#5200—32no—
58#5160—31no—
59#5143—31no—
60#5132—32no—
61#4898—32no—
62#4898—32no—
63#4897—31no—
64#4897D311yescharacteristic, complemented
65#4896—31no—
66#4896—31no—
67#4896—31no—
68#4896—61no—
69D3×#108D311yescharacteristic, complemented
70#4748—32no—
71#4745—32no—
72#3828C2311yescharacteristic
73C2×#634C2312yes—
74C3×#235C2311yescharacteristic
75C2×C3×D12C2312yes—
76C2×C3×C4×D3C2311yescharacteristic
77D3×#67—21no—
78C2×#625—22no—
79#3804—21no—
80C2×D3×Dic3—22no—
81D3×D12D411yescharacteristic
82C4×D32—21no—
83#3799D411yescharacteristic
84#3798—21no—
85#3795—22no—
86#3795—22no—
87#3795—22no—
88#3795—22no—
89#3795D411yescharacteristic
90D3×Dic6D411yescharacteristic
91C32×M16C2312yes—
92C2×C32×C8C2311yescharacteristic
93#3748C2311yescharacteristic
94#3746—22no—
95#3746—21no—
96#3746—21no—
97#3744—22no—
98#3743—21no—
99C8×C3⋊D3—21no—
100C3×#208C2311yescharacteristic
101C3×#208C2312yes—
102C2×C3×C3⋊C8C2311yescharacteristic
103C3×D24—22no—
104C3×D24—21no—
105C3×D24—21no—
106C3×#204—22no—
107C3×ΓL(1,𝔽25)—22no—
108C3×ΓL(1,𝔽25)—21no—
109C3×D3×C8—22no—
110C3×D3×C8—21no—
111C3×D3×C8D411yescharacteristic
112C3×D3×C8D411yescharacteristic
113C3×D3×C8D411yescharacteristic
114C3×D3×C8D411yescharacteristic
115#3719—22no—
116#3716—22no—
117#3716—22no—
118#3716—22no—
119#3716—22no—
120#3714—22no—
121#3712—21no—
122#3711—21no—
123#3711—21no—
124#3710—21no—
125D3×C3⋊C8—21no—
126D3×C3⋊C8—21no—
127#3067—91noSylow
128D3×#41—31no—
129C2×#237—32no—
130C2×#235—31no—
131C2×#235—32no—
132C3×AGL(1,ℤ/8)—32no—
133C2×C3×D8—31no—
134C3×#131—31no—
135C2×C3×M16—32no—
136C22×C3×C8—31no—
137#951—32no—
138#948—31no—
139C2×#214—32no—
140#932—32no—
141C2×#208—31no—
142#916—62no—
143#915—62no—
144#912—62no—
145#912—61no—
146#912—61no—
147#912—61no—
148#912—61no—
149#911—62no—
150#909—32no—
151#909—32no—
152#909—32no—
153#909—62no—
154#909—62no—
155#908—32no—
156#908—62no—
157#908C2×D312yes—
158#907—31no—
159#907—61no—
160D3×M16—31no—
161D3×M16—61no—
162D3×M16C2×D312yes—
163C2×Dic12—31no—
164C2×Dic12—31no—
165C2×Dic12—61no—
166#904—62no—
167#904—61no—
168#904—61no—
169#904—61no—
170#904—61no—
171#904—62no—
172C2×D24C2×D311yescharacteristic, complemented
173C2×#204—32no—
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—21no—
188C3×#108—32no—
189C3×#108—31no—
190C3×#108C2×D311yescharacteristic, complemented
191C3×#108C2×D311yescharacteristic, complemented
192C3×#100—32no—
193#833—32no—
194#824—32no—
195#824—32no—
196#824—32no—
197#824—32no—
198#824—62no—
199#823—32no—
200#823C2×D312yescomplemented
201#822C2×D312yescomplemented
202#819C2×D311yescharacteristic, complemented
203C22×C3×D3—22no—
204C22×C3×D3#4111yescharacteristic
205C2×D32—21no—
206C2×C32×C4C2411yescharacteristic
207#638—21no—
208C2×C3⋊Dic3—22no—
209C4⋊(C3⋊D3)C2×D411yescharacteristic
210C4×C3⋊D3—21no—
211#634—22no—
212#634—22no—
213#634C2×D411yescharacteristic
214C3×#67—21no—
215C2×C3×Dic3#4111yescharacteristic
216C3×D12—22no—
217C3×D12—22no—
218C3×D12C2×D411yescharacteristic
219C3×C4×D3—21no—
220C3×C4×D3C2×D411yescharacteristic
221C3×C4×D3C2×D411yescharacteristic
222C3×C4×D3C2×D411yescharacteristic
223C3×C4×D3C2×D411yescharacteristic
224C3×Dic6C2×D411yescharacteristic
225#627—21no—
226#626—21no—
227#626—21no—
228#625—21no—
229#625—42no—
230#625—42no—
231#624—21no—
232D3×Dic3—21no—
233D3×Dic3—21no—
234D3×Dic3—42no—
235D3×Dic3—42no—
236C32×C8—22no—
237C32×C8C2×D411yescharacteristic
238C32×C8C2×D411yescharacteristic
239C3⋊(C3⋊C8)—21no—
240C3×C3⋊C8—21no—
241C3×C3⋊C8—22no—
242C3×C3⋊C8C2×D411yescharacteristic
243C3×C3⋊C8C2×D411yescharacteristic
244#575—92no—
245C2×#135—91no—
246C2×#131—91no—
247#473—91no—
248#473—91no—
249#472—31no—
250#472—91no—
251#471—92no—
252#471—92no—
253C2×#108—31no—
254#413—92no—
255C3×#41—31no—
256C2×C3×D4—32no—
257C22×C3×C4—31no—
258C2×#67—61no—
259C2×#67—62no—
260C2×#67—62no—
261C22×Dic3—62no—
262#239—31no—
263D3×Q8—31no—
264#237—31no—
265#237—61no—
266#237—62no—
267#237—62no—
268#237—62no—
269#237—62no—
270D3×D4—31no—
271D3×D4—61no—
272#235—31no—
273#235—31no—
274#235—31no—
275#235—31no—
276#235—61no—
277#235—61no—
278#235—61no—
279#235—61no—
280#235—62no—
281#235—62no—
282#235—62no—
283#235—62no—
284#235C22×D311yescharacteristic
285C2×D12—31no—
286C2×D12C22×D312yes—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×C4×D3—62no—
290C2×C4×D3C22×D311yescharacteristic
291C2×Dic6—31no—
292C2×Dic6—32no—
293C2×Dic6—32no—
294C2×Dic6—62no—
295C3×SD16—62no—
296C3×D8—62no—
297C3×D8—61no—
298C3×D8—61no—
299C3×M16—22no—
300C3×M16—32no—
301C3×M16—31no—
302C3×M16—62no—
303C3×M16—61no—
304C3×M16C22×D312yes—
305C3×M16C22×D312yes—
306C2×C3×C8—21no—
307C2×C3×C8—31no—
308C2×C3×C8—31no—
309C2×C3×C8—31no—
310C2×C3×C8—31no—
311C2×C3×C8—31no—
312C2×C3×C8—62no—
313C2×C3×C8—61no—
314C2×C3×C8C22×D311yescharacteristic
315C2×C3×C8C22×D311yescharacteristic
316#216—62no—
317#214—62no—
318#214—62no—
319#214—62no—
320#214—62no—
321#213—62no—
322#208—31no—
323#208—31no—
324#208—61no—
325#208—61no—
326#208—61no—
327#208C22×D312yes—
328#208C22×D311yescharacteristic
329C2×C3⋊C8—61no—
330C2×C3⋊C8—61no—
331C2×C3⋊C8C22×D311yescharacteristic
332Dic12—62no—
333Dic12—62no—
334Dic12—62no—
335Dic12—61no—
336Dic12—61no—
337Dic12—61no—
338Dic12—61no—
339Dic12—121no—
340Dic12—121no—
341Dic12—122no—
342D24—22no—
343D24—21no—
344D24—21no—
345D24—62no—
346#204—22no—
347#204—62no—
348#204—62no—
349#204—62no—
350#204—62no—
351#204—62no—
352#204—62no—
353#204—122no—
354ΓL(1,𝔽25)—22no—
355ΓL(1,𝔽25)—21no—
356ΓL(1,𝔽25)—61no—
357ΓL(1,𝔽25)—61no—
358ΓL(1,𝔽25)—61no—
359ΓL(1,𝔽25)—61no—
360ΓL(1,𝔽25)—61no—
361ΓL(1,𝔽25)—61no—
362ΓL(1,𝔽25)—121no—
363D3×C8—22no—
364D3×C8—21no—
365D3×C8—61no—
366D3×C8—61no—
367D3×C8—61no—
368D3×C8—61no—
369D3×C8—61no—
370D3×C8—61no—
371D3×C8—121no—
372D3×C8D1211yescharacteristic
373D3×C8D1211yescharacteristic
374D3×C8D1211yescharacteristic
375D3×C8D1211yescharacteristic
376C22×C32C2×#4111yescharacteristic
377C2×C3⋊D3—21no—
378C2×C3×D3—21no—
379C2×C3×D3—41no—
380C2×C3×D3—42no—
381C2×C3×D3—82no—
382C2×C3×D3#12111yescharacteristic
383C2×C3×D3#12111yescharacteristic
384D32—42no—
385C32×C4C22×D411yescharacteristic
386C32×C4C22×D411yescharacteristic
387C3⋊Dic3—21no—
388C3⋊Dic3—42no—
389C3×Dic3—21no—
390C3×Dic3#12111yescharacteristic
391C3×Dic3#12111yescharacteristic
392C2×#41—92no—
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—181no—
401#135—181no—
402#135—181no—
403#135—181no—
404#135—182no—
405#135—182no—
406C2×Q16—91no—
407C2×SD16—92no—
408C2×D8—31no—
409#131—31no—
410#131—91no—
411#131—91no—
412#131—91no—
413#131—181no—
414#131—181no—
415C2×M16—32no—
416C2×M16—91no—
417C2×M16—181no—
418C22×C8—31no—
419C22×C8—181no—
420#108—32no—
421#108—31no—
422#108D3211yescharacteristic, complemented
423#101—92no—
424#101—92no—
425#100—32no—
426#100—92no—
427C23×C3—31no—
428C23×C3—62no—
429C22×D3—22no—
430C22×D3—61no—
431C22×D3—61no—
432C22×D3#23911yescharacteristic
433C3×Q8—31no—
434C3×D4—31no—
435C3×D4—61no—
436C3×D4—62no—
437C3×D4—62no—
438C2×C3×C4—21no—
439C2×C3×C4—31no—
440C2×C3×C4—31no—
441C2×C3×C4—31no—
442C2×C3×C4—31no—
443C2×C3×C4—31no—
444C2×C3×C4—61no—
445C2×C3×C4C23×D311yescharacteristic
446C2×C3×C4C23×D311yescharacteristic
447#67—21no—
448#67—61no—
449#67—61no—
450#67—61no—
451#67—61no—
452#67—61no—
453#67—61no—
454#67—121no—
455#67—122no—
456#67—122no—
457#67—122no—
458#67—122no—
459C2×Dic3—61no—
460C2×Dic3—61no—
461C2×Dic3—62no—
462C2×Dic3—62no—
463C2×Dic3—122no—
464C2×Dic3—122no—
465C2×Dic3—122no—
466C2×Dic3#23911yescharacteristic
467D12—22no—
468D12—22no—
469D12—31no—
470D12—31no—
471D12—61no—
472D12—61no—
473D12—61no—
474D12D3×D411yescharacteristic
475C4×D3—21no—
476C4×D3—61no—
477C4×D3—61no—
478C4×D3—61no—
479C4×D3—61no—
480C4×D3—61no—
481C4×D3—61no—
482C4×D3—121no—
483C4×D3—122no—
484C4×D3—122no—
485C4×D3C2×D1211yescharacteristic
486C4×D3C2×D1211yescharacteristic
487C4×D3D3×D411yescharacteristic
488C4×D3D3×D411yescharacteristic
489Dic6—31no—
490Dic6—31no—
491Dic6—61no—
492Dic6—61no—
493Dic6—61no—
494Dic6—62no—
495Dic6—62no—
496Dic6—62no—
497Dic6—62no—
498Dic6—122no—
499Dic6—122no—
500Dic6D3×D411yescharacteristic
501C3×C8—22no—
502C3×C8—22no—
503C3×C8—21no—
504C3×C8—21no—
505C3×C8—31no—
506C3×C8—31no—
507C3×C8—42no—
508C3×C8—61no—
509C3×C8—62no—
510C3×C8C2×D1211yescharacteristic
511C3×C8C2×D1211yescharacteristic
512C3×C8D3×D411yescharacteristic
513C3×C8D3×D411yescharacteristic
514C3⋊C8—21no—
515C3⋊C8—22no—
516C3⋊C8—61no—
517C3⋊C8—61no—
518C3⋊C8—121no—
519C3⋊C8C2×D1211yescharacteristic
520C3⋊C8C2×D1211yescharacteristic
521C2×C32—21no—
522C2×C32C2×#12111yescharacteristic
523C3⋊D3—41no—
524C3×D3—21no—
525C3×D3—21no—
526C3×D3—41no—
527C3×D3—82no—
528#41—31no—
529#41—91no—
530#41—91no—
531#41—91no—
532#41—181no—
533#41—181no—
534#41—182no—
535#41—182no—
536#41—182no—
537#41—182no—
538C2×Q8—91no—
539C2×Q8—92no—
540C2×D4—32no—
541C2×D4—91no—
542C2×D4—181no—
543C2×D4—182no—
544C22×C4—31no—
545C22×C4—181no—
546C22×C4—182no—
547Q16—182no—
548Q16—182no—
549Q16—181no—
550Q16—181no—
551SD16—62no—
552SD16—182no—
553SD16—182no—
554SD16—182no—
555SD16—182no—
556SD16—182no—
557D8—62no—
558D8—61no—
559D8—61no—
560D8—182no—
561M16—31no—
562M16—32no—
563M16—62no—
564M16—61no—
565M16—91no—
566M16—181no—
567M16—181no—
568M16—181no—
569M16—181no—
570M16C2×D3212yes—
571C2×C8—31no—
572C2×C8—31no—
573C2×C8—31no—
574C2×C8—31no—
575C2×C8—31no—
576C2×C8—62no—
577C2×C8—61no—
578C2×C8—181no—
579C2×C8—181no—
580C2×C8—181no—
581C2×C8—181no—
582C2×C8C2×D3211yescharacteristic
583C22×C3—21no—
584C22×C3—31no—
585C22×C3—31no—
586C22×C3—61no—
587C22×C3—121no—
588C22×C3—122no—
589C22×C3—242no—
590C22×C3C2×#23911yescharacteristic
591C22×C3D3×#4111yescharacteristic
592C2×D3—21no—
593C2×D3—41no—
594C2×D3—42no—
595C2×D3—61no—
596C2×D3—61no—
597C2×D3—82no—
598C2×D3—121no—
599C2×D3—122no—
600C2×D3—122no—
601C2×D3#89511yescharacteristic
602C2×D3#89511yescharacteristic
603C3×C4—21no—
604C3×C4—21no—
605C3×C4—31no—
606C3×C4—31no—
607C3×C4—61no—
608C3×C4C22×D1211yescharacteristic
609C3×C4C2×D3×D411yescharacteristic
610C3×C4C2×D3×D411yescharacteristic
611C3×C4C2×D3×D411yescharacteristic
612Dic3—21no—
613Dic3—61no—
614Dic3—61no—
615Dic3—121no—
616Dic3—122no—
617Dic3—122no—
618Dic3—242no—
619Dic3#89511yescharacteristic
620Dic3#89511yescharacteristic
621C32#306711yescharacteristic, complemented, Sylow
622C23—31no—
623C23—62no—
624C23—181no—
625Q8—31no—
626Q8—91no—
627Q8—181no—
628Q8—182no—
629Q8—182no—
630D4—31no—
631D4—61no—
632D4—62no—
633D4—62no—
634D4—91no—
635D4—181no—
636D4—181no—
637D4—181no—
638D4—181no—
639D4—362no—
640D4—362no—
641C2×C4—31no—
642C2×C4—31no—
643C2×C4—31no—
644C2×C4—31no—
645C2×C4—31no—
646C2×C4—61no—
647C2×C4—181no—
648C2×C4—181no—
649C2×C4—181no—
650C2×C4—181no—
651C2×C4—182no—
652C2×C4—362no—
653C2×C4—362no—
654C2×C4C22×D3211yescharacteristic
655C8—22no—
656C8—31no—
657C8—31no—
658C8—61no—
659C8—62no—
660C8—181no—
661C8D3×D1211yescharacteristic
662C8D3×D1211yescharacteristic
663C2×C3—21no—
664C2×C3—21no—
665C2×C3—21no—
666C2×C3—41no—
667C2×C3—61no—
668C2×C3—61no—
669C2×C3—121no—
670C2×C3—242no—
671C2×C3C2×#89511yescharacteristic
672C2×C3D3×#12111yescharacteristic
673D3—21no—
674D3—21no—
675D3—41no—
676D3—82no—
677D3—121no—
678D3—121no—
679D3—241no—
680C22—31no—
681C22—31no—
682C22—61no—
683C22—121no—
684C22—122no—
685C22—181no—
686C22—242no—
687C22—362no—
688C22D3×#23911yescharacteristic
689C4—31no—
690C4—31no—
691C4—61no—
692C4—181no—
693C4—362no—
694C4C2×D3×D1211yescharacteristic
695C4D32×D411yescharacteristic
696C3—21no—
697C3#7925611yescharacteristic, complemented
698C3#8093711yescharacteristic, complemented
699C2—21no—
700C2—61no—
701C2—61no—
702C2—121no—
703C2—242no—
704C2—361no—
705C2D3×#89511yescharacteristic
subgroupG/H
centerC2D3×#895
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×#108C22
socleC2×C32C2×#121
hypercenter#108D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #108

Complements

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

NH ≅ G/Ntype
1. #10594712C2semidirect
2. C2×#63807C2semidirect
3. D3×#901C2semidirect
4. #10592595C2semidirect
5. C3×#4897C2semidirect
6. C3×D3×#108C2semidirect
7. #10591006C2semidirect
8. #10590989C2semidirect
9. #10590986C2semidirect
10. #10590932C2semidirect
11. #10590929C2semidirect
17. C2×#3746C22semidirect
21. C2×C3×D24C22semidirect
26. C2×#3716C22semidirect
42. C32×#108C22semidirect
43. #63651C22semidirect
44. C3×#823C22semidirect
45. C3×#822C22semidirect
46. C3×#819C22semidirect
47. #63561C22semidirect
48. #63558C22semidirect
64. #4897D3semidirect
69. D3×#108D3semidirect
172. C2×D24C2×D3semidirect
190. C3×#108C2×D3semidirect
191. C3×#108C2×D3semidirect
200. #823C2×D3semidirect
201. #822C2×D3semidirect
202. #819C2×D3semidirect
422. #108D32semidirect
621. C32#3067semidirect
697. C3#79256semidirect
698. C3#80937semidirect

Maximal subgroups

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

subgroupindex
#105947122
C2×#638072
D3×#9012
#105925952
C3×#48972
C3×D3×#1082
#105910062
#105909892
#105909862
#105909322
#105909292
#809373
#792563