Finite Group Databasebeta

← #11868124

Subgroups — #11868124

Order 1152.

1063 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596293C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4#10594780C211yesmaximal, characteristic, complemented
5C3×#5237C211yesmaximal, characteristic, complemented
6#10591542C214yesmaximal, complemented
7#10591406C214yesmaximal, complemented
8#10591141C211yesmaximal, characteristic, complemented
9C2×#63558C211yesmaximal, characteristic, complemented
10#83963—31nomaximal
11#78720—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15#64160—21no—
16#64159—22no—
17#64158—21no—
18#64151C2212yescomplemented
19#64141C2212yescomplemented
20C2×#3748C2211yescharacteristic
21C3×#949—22no—
22C3×#949—22no—
23C2×C3×#215C2212yescomplemented
24C2×C3×#213C2212yescomplemented
25C2×C3×#208C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63830—22no—
29#63830C2214yes—
30C2×#3716—21no—
31C2×#3714—21no—
32#63818—22no—
33#63817—22no—
34#63817C2214yescomplemented
35C3×#836C2212yescomplemented
36C3×#833C2212yescomplemented
37#63577C2214yescomplemented
38#63558C2214yescomplemented
39C2×C3×AGL(1,ℤ/8)—31no—
40#5822—31no—
41#5822—31no—
42#5822—61no—
43C2×#949D311yescharacteristic, complemented
44C2×#932—31no—
45C2×#908—31no—
46#5745—31no—
47#5745—31no—
48C3×#413—31no—
49#5237D311yescharacteristic, complemented
50C2×#833—31no—
51#5177—34no—
52#5160—34no—
53C2×#823—31no—
54#5125—31no—
55#5124—31no—
56#4754—34no—
57#4749—34no—
58C23×C3×D3—21no—
59C32×#41—21no—
60C32×#41—21no—
61C32×#41—21no—
62C32×#41—21no—
63C2×C32×Q8C2311yescharacteristic
64C2×C32×D4—21no—
65C2×C32×D4C2311yescharacteristic
66C22×C32×C4—21no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69#3828—21no—
70#3828—21no—
71#3828D412yes—
72#3828C2312yes—
73C2×C4⋊(C3⋊D3)D411yescharacteristic
74C2×C4×C3⋊D3—21no—
75C2×#634D411yescharacteristic
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12—21no—
80C2×C3×D12—21no—
81C2×C3×D12C2312yes—
82#3756—22no—
83#3755—22no—
84#3754—22no—
85#3753—22no—
86#3748—21no—
87#3748C2312yes—
88C2×C3⋊(C3⋊C8)—21no—
89C3×#215—24no—
90C3×#213—24no—
91C3×#208—21no—
92C3×#208—21no—
93C3×#208D412yes—
94C3×#208D412yes—
95C3×#208C2312yes—
96C3×#208C2312yes—
97C2×C3×C3⋊C8—21no—
98C2×C3×C3⋊C8—21no—
99C2×C3×C3⋊C8C2312yes—
100#3716—24no—
101#3714—24no—
102#3712—24no—
103#3710—24no—
104#3068—91noSylow
105C2×C3×#41—21no—
106C2×C3×#41C2×D311yescharacteristic
107C2×C3×#41C2×D311yescharacteristic
108C22×C3×D4—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C22×D12C2×D311yescharacteristic
113C3×AGL(1,ℤ/8)—62no—
114C3×AGL(1,ℤ/8)—62no—
115C2×C3×SD16—32no—
116C2×C3×D8—32no—
117C2×C3×M16—31no—
118C2×C3×M16—31no—
119C2×C3×M16—31no—
120#951—61no—
121#951—61no—
122#951—62no—
123#950—62no—
124#950—62no—
125#950—64no—
126#949—22no—
127#949—22no—
128#949—61no—
129#949—61no—
130#949—62no—
131#942—32no—
132#942—32no—
133#942—62no—
134C2×#215C2×D312yescomplemented
135C2×#214—61no—
136#932—32no—
137#932—32no—
138#932—34no—
139#932—62no—
140#932—62no—
141C2×#213—61no—
142C2×#213C2×D312yescomplemented
143C2×#208—31no—
144C2×#208—31no—
145C2×#208—61no—
146C2×#208C2×D311yescharacteristic
147C2×#208C2×D311yescharacteristic
148C2×#208C2×D311yescharacteristic
149#908—34no—
150#908—62no—
151#907—34no—
152#907—62no—
153D3×M16—62no—
154D3×M16—62no—
155C2×D24—61no—
156C2×#204—61no—
157#901—34no—
158#901—62no—
159C3×#101—32no—
160C3×#100—32no—
161#836C2×D312yescomplemented
162#833—34no—
163#833C2×D312yescomplemented
164#823—34no—
165#822—34no—
166#819—34no—
167C23×C32—21no—
168C23×C32#4111yescharacteristic
169C22×C3⋊D3—21no—
170C22×C3×D3—22no—
171C22×C3×D3—41no—
172C22×C3×D3—41no—
173C22×C3×D3—82no—
174C32×Q8—21no—
175C32×Q8—21no—
176C32×D4—21no—
177C32×D4—21no—
178C32×D4—41no—
179C32×D4—41no—
180C2×C32×C4—21no—
181C2×C32×C4—41no—
182C2×C32×C4—41no—
183C2×C32×C4C2×D411yescharacteristic
184C2×C32×C4C2×D411yescharacteristic
185C2×C32×C4C2×D411yescharacteristic
186C2×C32×C4C2×D411yescharacteristic
187C2×C32×C4#4111yescharacteristic
188C2×C32×C4C2411yescharacteristic
189#638—22no—
190#638—22no—
191C2×C3⋊Dic3—21no—
192C4⋊(C3⋊D3)—21no—
193C4⋊(C3⋊D3)C2×D412yes—
194C4×C3⋊D3—22no—
195C4×C3⋊D3—22no—
196#634—21no—
197#634C2×D412yes—
198C3×D12—22no—
199C3×D12—22no—
200C3×D12—41no—
201C3×D12—41no—
202C3⋊(C3⋊C8)—22no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C3×C3⋊C8C2×D414yes—
206#575—91no—
207C2×AGL(1,ℤ/8)—31no—
208C2×AGL(1,ℤ/8)—91no—
209#568—91no—
210#472—94no—
211#471—94no—
212#430—91no—
213#413—31no—
214C2×#100—91no—
215C24×C3—61no—
216C23×D3—21no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—21no—
220C3×#41—21no—
221C3×#41—21no—
222C3×#41—21no—
223C3×#41—21no—
224C3×#41—21no—
225C3×#41—21no—
226C3×#41—21no—
227C3×#41—41no—
228C3×#41—41no—
229C2×C3×Q8—21no—
230C2×C3×Q8C22×D311yescharacteristic
231C2×C3×Q8C22×D311yescharacteristic
232C2×C3×D4—21no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—32no—
236C2×C3×D4—41no—
237C2×C3×D4—61no—
238C2×C3×D4—61no—
239C2×C3×D4—61no—
240C2×C3×D4—61no—
241C2×C3×D4—61no—
242C2×C3×D4C22×D311yescharacteristic
243C2×C3×D4C22×D311yescharacteristic
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—41no—
248C22×C3×C4C22×D311yescharacteristic
249C22×C3×C4C22×D311yescharacteristic
250C2×#67—61no—
251C2×#67—61no—
252C2×#67—121no—
253#235—32no—
254#235—32no—
255#235—32no—
256#235—32no—
257#235—62no—
258#235—62no—
259#235—61no—
260#235—61no—
261#235—61no—
262#235—61no—
263#235—121no—
264#235—121no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—21no—
268C2×D12—21no—
269C2×D12—21no—
270C2×D12—31no—
271C2×D12—31no—
272C2×D12—61no—
273C2×D12C22×D312yes—
274C2×C4×D3—61no—
275C2×C4×D3—61no—
276C2×C4×D3—121no—
277C2×Dic6—31no—
278C2×Dic6—31no—
279C2×Dic6—61no—
280C3×SD16—64no—
281C3×D8—64no—
282C3×M16—32no—
283C3×M16—32no—
284C3×M16—32no—
285C3×M16—32no—
286C3×M16—61no—
287C3×M16—61no—
288C2×C3×C8—32no—
289C2×C3×C8—61no—
290C2×C3×C8—61no—
291#216—62no—
292#216—62no—
293#216—64no—
294#215—24no—
295#215—62no—
296#215—62no—
297#215—64no—
298#214—64no—
299#214—62no—
300#214—62no—
301#214—64no—
302#213—24no—
303#213—64no—
304#213—62no—
305#213—62no—
306#213—64no—
307#208—21no—
308#208—21no—
309#208—32no—
310#208—32no—
311#208—62no—
312#208—62no—
313#208—61no—
314#208—61no—
315#208#6712yes—
316#208#6712yes—
317#208C22×D312yes—
318#208C22×D312yes—
319C2×C3⋊C8—21no—
320C2×C3⋊C8—21no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8—61no—
323C2×C3⋊C8—61no—
324C2×C3⋊C8C22×D312yes—
325D24—64no—
326#204—64no—
327ΓL(1,𝔽25)—64no—
328ΓL(1,𝔽25)—64no—
329D3×C8—64no—
330D3×C8—64no—
331C22×C32—41no—
332C22×C32—41no—
333C22×C32—81no—
334C22×C32#12111yescharacteristic
335C22×C32#12111yescharacteristic
336C22×C32C2×#4111yescharacteristic
337C2×C3⋊D3—22no—
338C2×C3⋊D3—81no—
339C2×C3×D3—42no—
340C2×C3×D3—82no—
341C2×C3×D3—82no—
342C2×C3×D3—82no—
343C32×C4—41no—
344C32×C4#12111yescharacteristic
345C32×C4#12111yescharacteristic
346C32×C4C22×D411yescharacteristic
347C32×C4C22×D411yescharacteristic
348C3⋊Dic3—22no—
349C2×#41—91no—
350C2×#41D3211yescharacteristic
351C22×D4—31no—
352#137—92no—
353#137—181no—
354AGL(1,ℤ/8)—62no—
355AGL(1,ℤ/8)—62no—
356AGL(1,ℤ/8)—94no—
357AGL(1,ℤ/8)—92no—
358AGL(1,ℤ/8)—182no—
359AGL(1,ℤ/8)—181no—
360#135—182no—
361C2×SD16—32no—
362C2×SD16—181no—
363C2×D8—32no—
364C2×D8—181no—
365#131—94no—
366#131—182no—
367C2×M16—31no—
368C2×M16—31no—
369C2×M16—31no—
370C2×M16—91no—
371C2×M16—182no—
372#108—94no—
373#101—32no—
374#100—32no—
375#100—94no—
376C23×C3—21no—
377C23×C3—21no—
378C23×C3—21no—
379C23×C3—41no—
380C23×C3—62no—
381C23×C3—121no—
382C23×C3—121no—
383C23×C3—242no—
384C23×C3#23511yescharacteristic
385C23×C3#23711yescharacteristic
386C22×D3—22no—
387C22×D3—41no—
388C22×D3—41no—
389C22×D3—61no—
390C22×D3—61no—
391C22×D3—82no—
392C22×D3—121no—
393C3×Q8—22no—
394C3×Q8—21no—
395C3×Q8—21no—
396C3×Q8—21no—
397C3×Q8—21no—
398C3×Q8—41no—
399C3×D4—22no—
400C3×D4—21no—
401C3×D4—21no—
402C3×D4—21no—
403C3×D4—21no—
404C3×D4—41no—
405C3×D4—42no—
406C3×D4—42no—
407C3×D4—41no—
408C3×D4—41no—
409C3×D4—41no—
410C3×D4—41no—
411C3×D4—62no—
412C3×D4—62no—
413C3×D4—121no—
414C3×D4—121no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—21no—
422C2×C3×C4—21no—
423C2×C3×C4—41no—
424C2×C3×C4—42no—
425C2×C3×C4—42no—
426C2×C3×C4—41no—
427C2×C3×C4—41no—
428C2×C3×C4—41no—
429C2×C3×C4—41no—
430C2×C3×C4#23511yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4D3×D411yescharacteristic
434C2×C3×C4D3×D411yescharacteristic
435C2×C3×C4D3×D411yescharacteristic
436C2×C3×C4D3×D411yescharacteristic
437C2×C3×C4#23711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C2×#6711yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C23×D311yescharacteristic
442#67—62no—
443#67—62no—
444#67—62no—
445#67—62no—
446#67—122no—
447#67—122no—
448C2×Dic3—61no—
449C2×Dic3—61no—
450C2×Dic3—121no—
451D12—22no—
452D12—22no—
453D12—32no—
454D12—32no—
455D12—41no—
456D12—41no—
457D12—62no—
458D12—61no—
459D12—61no—
460D12—121no—
461C4×D3—62no—
462C4×D3—62no—
463C4×D3—62no—
464C4×D3—62no—
465C4×D3—122no—
466C4×D3—122no—
467Dic6—32no—
468Dic6—32no—
469Dic6—62no—
470Dic6—61no—
471Dic6—61no—
472Dic6—121no—
473C3×C8—34no—
474C3×C8—62no—
475C3×C8—62no—
476C3⋊C8—22no—
477C3⋊C8—22no—
478C3⋊C8—64no—
479C3⋊C8—62no—
480C3⋊C8—62no—
481C3⋊C8C2×#6714yes—
482C2×C32—21no—
483C2×C32—21no—
484C2×C32—21no—
485C2×C32—81no—
486C2×C32C2×#12111yescharacteristic
487C3⋊D3—42no—
488C3×D3—82no—
489C24—61no—
490#41—21no—
491#41—21no—
492#41—21no—
493#41—21no—
494#41—92no—
495#41—92no—
496#41—181no—
497#41—181no—
498C2×Q8—91no—
499C2×Q8C2×D3211yescharacteristic
500C2×D4—21no—
501C2×D4—32no—
502C2×D4—61no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4—61no—
507C2×D4—91no—
508C2×D4—181no—
509C2×D4C2×D3211yescharacteristic
510C22×C4—21no—
511C22×C4—181no—
512C22×C4C2×D3211yescharacteristic
513Q16—182no—
514SD16—64no—
515SD16—184no—
516SD16—182no—
517SD16—182no—
518D8—64no—
519D8—184no—
520D8—182no—
521M16—32no—
522M16—32no—
523M16—32no—
524M16—32no—
525M16—61no—
526M16—61no—
527M16—92no—
528M16—184no—
529M16—181no—
530C2×C8—32no—
531C2×C8—61no—
532C2×C8—61no—
533C2×C8—184no—
534C2×C8—181no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—41no—
539C22×C3—41no—
540C22×C3—42no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—81no—
544C22×C3—81no—
545C22×C3—81no—
546C22×C3—82no—
547C22×C3—122no—
548C22×C3—242no—
549C22×C3—242no—
550C22×C3—242no—
551C22×C3#88411yescharacteristic
552C22×C3#88411yescharacteristic
553C22×C3#93811yescharacteristic
554C22×C3#93811yescharacteristic
555C22×C3C2×#23511yescharacteristic
556C22×C3C2×#23711yescharacteristic
557C2×D3—42no—
558C2×D3—62no—
559C2×D3—62no—
560C2×D3—82no—
561C2×D3—82no—
562C2×D3—82no—
563C2×D3—122no—
564C2×D3—241no—
565C2×D3—241no—
566C2×D3—242no—
567C3×C4—21no—
568C3×C4—21no—
569C3×C4—21no—
570C3×C4—21no—
571C3×C4—42no—
572C3×C4—41no—
573C3×C4—41no—
574C3×C4#88411yescharacteristic
575C3×C4#88411yescharacteristic
576C3×C4#93811yescharacteristic
577C3×C4#93811yescharacteristic
578C3×C4C2×D3×D411yescharacteristic
579C3×C4C2×D3×D411yescharacteristic
580C3×C4C2×D3×D411yescharacteristic
581C3×C4C22×#6711yescharacteristic
582Dic3—62no—
583Dic3—62no—
584Dic3—122no—
585C32#306811yescharacteristic, complemented, Sylow
586C23—21no—
587C23—62no—
588C23—121no—
589C23—121no—
590C23—181no—
591C23—242no—
592C23#380411yescharacteristic
593Q8—21no—
594Q8—21no—
595Q8—92no—
596Q8—181no—
597D4—21no—
598D4—21no—
599D4—41no—
600D4—41no—
601D4—62no—
602D4—62no—
603D4—92no—
604D4—121no—
605D4—121no—
606D4—182no—
607D4—182no—
608D4—181no—
609C2×C4—21no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—181no—
613C2×C4—182no—
614C2×C4—182no—
615C2×C4#380411yescharacteristic
616C2×C4D3×#6711yescharacteristic
617C2×C4D3×#6711yescharacteristic
618C2×C4#381111yescharacteristic
619C2×C4#381111yescharacteristic
620C2×C4C22×D3211yescharacteristic
621C8—34no—
622C8—62no—
623C8—62no—
624C8—182no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—21no—
630C2×C3—21no—
631C2×C3—21no—
632C2×C3—41no—
633C2×C3—41no—
634C2×C3—41no—
635C2×C3—82no—
636C2×C3—81no—
637C2×C3—81no—
638C2×C3—242no—
639C2×C3C2×#88411yescharacteristic
640C2×C3C2×#93811yescharacteristic
641D3—82no—
642D3—122no—
643D3—122no—
644D3—242no—
645C22—41no—
646C22—41no—
647C22—81no—
648C22—122no—
649C22—182no—
650C22—242no—
651C22—242no—
652C22—242no—
653C22—721no—
654C22#6395811yescharacteristic
655C22#6395811yescharacteristic
656C22C2×#380411yescharacteristic
657C4—41no—
658C4—182no—
659C4#6395811yescharacteristic
660C4#6395811yescharacteristic
661C4C2×D3×#6711yescharacteristic
662C4C2×#381111yescharacteristic
663C3—21no—
664C3#7872011yescharacteristic, complemented
665C3#8396311yescharacteristic, complemented
666C2—21no—
667C2—21no—
668C2—21no—
669C2—81no—
670C2—242no—
671C2—362no—
672C2C2×#6395811yescharacteristic
subgroupG/H
centerC2C2×#63958
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC2×C32C2×#121
hypercenterC2×#41D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. #10596293C2semidirect
2. C2×C3×#949C2semidirect
3. C2×#63830C2semidirect
4. #10594780C2semidirect
5. C3×#5237C2semidirect
6. #10591542C2semidirect
7. #10591406C2semidirect
8. #10591141C2semidirect
9. C2×#63558C2semidirect
18. #64151C22semidirect
19. #64141C22semidirect
23. C2×C3×#215C22semidirect
24. C2×C3×#213C22semidirect
34. #63817C22semidirect
35. C3×#836C22semidirect
36. C3×#833C22semidirect
37. #63577C22semidirect
38. #63558C22semidirect
43. C2×#949D3semidirect
49. #5237D3semidirect
134. C2×#215C2×D3semidirect
142. C2×#213C2×D3semidirect
161. #836C2×D3semidirect
163. #833C2×D3semidirect
585. C32#3068semidirect
664. C3#78720semidirect
665. C3#83963semidirect

Maximal subgroups

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

subgroupindex
#105962932
C2×C3×#9492
C2×#638302
#105947802
C3×#52372
#105915422
#105914062
#105911412
C2×#635582
#839633
#787203