Finite Group Databasebeta

← #11868131

Subgroups — #11868131

Order 1152.

1007 conjugacy classes of subgroups.

The subgroup lattice has 649 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5745C211yesmaximal, characteristic, complemented
2#10594795C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592831C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7#10591141C211yesmaximal, characteristic, complemented
8#10590997C214yesmaximal, complemented
9#10590996C214yesmaximal, complemented
10#83814—31nomaximal
11#78703—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×C3×#208C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#907C2214yescomplemented
20C3×D3×M16—22no—
21C3×#901—22no—
22#63833—21no—
23#63831C2212yescomplemented
24#63830—21no—
25#63830—22no—
26#63830—22no—
27#63829—22no—
28C2×#3716C2212yescomplemented
29C2×#3715—21no—
30#63825C2212yescomplemented
31C2×#3714C2212yescomplemented
32#63823—22no—
33#63823C2214yes—
34C2×#3713—21no—
35#63651C2212yescomplemented
36#63650C2212yescomplemented
37C3×#823C2214yescomplemented
38#63577C2214yescomplemented
39C3×#568—31no—
40#5822—31no—
41C2×#949—31no—
42C2×#932—31no—
43C2×#932—31no—
44#5748—31no—
45C2×#908—31no—
46#5745D311yescharacteristic, complemented
47C2×C3×#100—31no—
48#5142—34no—
49#5141—34no—
50#5132—31no—
51#5132—31no—
52#5132—61no—
53C2×#823D311yescharacteristic, complemented
54#5125—31no—
55#5124—31no—
56#4749—34no—
57#4748—34no—
58C23×C3×D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—21no—
61#3828—21no—
62#3828—21no—
63#3828—21no—
64#3828—21no—
65C2×C4⋊(C3⋊D3)C2311yescharacteristic
66C2×C4×C3⋊D3—21no—
67C2×#634C2311yescharacteristic
68C2×C3×#67—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235D412yes—
72C3×#235C2312yes—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12D411yescharacteristic
79C2×C3×D12C2312yes—
80C2×C3×C4×D3—21no—
81C2×C3×Dic6D411yescharacteristic
82C32×M16—21no—
83C32×M16C2312yes—
84C2×C32×C8—21no—
85#3748—21no—
86#3748C2312yes—
87C2×C3⋊(C3⋊C8)—21no—
88C3×#208—21no—
89C3×#208D412yes—
90C3×#208D412yes—
91C3×#208C2312yes—
92C2×C3×C3⋊C8—21no—
93C2×C3×C3⋊C8C2312yes—
94C3×ΓL(1,𝔽25)—24no—
95C3×D3×C8—24no—
96#3719—22no—
97#3717—22no—
98#3716—22no—
99#3716—24no—
100#3715—24no—
101#3714—22no—
102#3714—24no—
103#3713—24no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C22×C3×D4—31no—
107C2×#235—31no—
108C2×#235—31no—
109C2×#235—61no—
110C2×#235C2×D311yescharacteristic
111C22×D12C2×D311yescharacteristic
112C3×#131—34no—
113C3×#131—62no—
114C2×C3×M16—21no—
115C2×C3×M16—31no—
116C2×C3×M16—31no—
117C2×C3×M16—62no—
118C2×C3×M16C2×D311yescharacteristic
119C2×C3×M16C2×D311yescharacteristic
120#951—32no—
121#950—62no—
122#949—34no—
123#949—32no—
124#949—62no—
125#942—61no—
126C2×#215—61no—
127C2×#214—32no—
128C2×#214—61no—
129#932—34no—
130#932—61no—
131#932—62no—
132#932—62no—
133#932—62no—
134C2×#213—32no—
135C2×#213—61no—
136C2×#213—61no—
137C2×#208—31no—
138C2×#208—31no—
139C2×#208—61no—
140C2×#208C2×D311yescharacteristic
141C2×#208C2×D311yescharacteristic
142#909—32no—
143#909—61no—
144#908—32no—
145#908—62no—
146#908—62no—
147#908—61no—
148#907C2×D314yescomplemented
149D3×M16—22no—
150#904—62no—
151C2×D24—32no—
152C2×#204—32no—
153#901—22no—
154C3×#100—34no—
155#824—32no—
156#824—32no—
157#824—62no—
158#823—32no—
159#823—32no—
160#823—62no—
161#823C2×D314yescomplemented
162#822—34no—
163#819—34no—
164C23×C32#4111yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—21no—
167C22×C3×D3—22no—
168C22×C3×D3—41no—
169C22×C3×D3—41no—
170C22×C3×D3—82no—
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4#4111yescharacteristic
176C2×C32×C4C2411yescharacteristic
177#638—41no—
178#638—41no—
179C2×C3⋊Dic3—21no—
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)—21no—
182C4×C3⋊D3—41no—
183C4×C3⋊D3—41no—
184#634—21no—
185#634—21no—
186C3×#67—22no—
187C3×#67—22no—
188C2×C3×Dic3—21no—
189C3×D12—21no—
190C3×D12—22no—
191C3×D12—22no—
192C3×D12—41no—
193C3×D12—41no—
194C3×D12C2×D412yes—
195C3×C4×D3—22no—
196C3×C4×D3—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199C32×C8—22no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C3×C3⋊C8C2×D414yes—
203#575—91no—
204C2×AGL(1,ℤ/8)—91no—
205C2×AGL(1,ℤ/8)—91no—
206#568—31no—
207#472—94no—
208#471—94no—
209#430—91no—
210#413—91no—
211C2×#100—31no—
212C24×C3—61no—
213C23×D3—21no—
214C3×#41—32no—
215C3×#41—32no—
216C3×#41—61no—
217C3×#41—61no—
218C2×C3×Q8—31no—
219C2×C3×D4—31no—
220C2×C3×D4—32no—
221C2×C3×D4—61no—
222C2×C3×D4—61no—
223C2×C3×D4—61no—
224C2×C3×D4—61no—
225C2×C3×D4—61no—
226C2×C3×D4—61no—
227C22×C3×C4—21no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—21no—
232C2×#67—62no—
233C2×#67—61no—
234C2×#67—61no—
235#235—21no—
236#235—21no—
237#235—61no—
238#235—61no—
239#235—61no—
240#235—61no—
241#235—61no—
242#235—61no—
243#235—61no—
244#235—61no—
245#235—121no—
246#235—121no—
247#235—121no—
248#235—121no—
249#235D1212yes—
250#235C22×D312yes—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—31no—
257C2×D12—31no—
258C2×D12—61no—
259C2×D12D1211yescharacteristic
260C2×D12C22×D312yes—
261C2×C4×D3—21no—
262C2×C4×D3—62no—
263C2×C4×D3—61no—
264C2×C4×D3—61no—
265C2×Dic6—31no—
266C2×Dic6—31no—
267C2×Dic6—61no—
268C2×Dic6D1211yescharacteristic
269C3×M16—21no—
270C3×M16—21no—
271C3×M16—22no—
272C3×M16—32no—
273C3×M16—32no—
274C3×M16—32no—
275C3×M16—41no—
276C3×M16—64no—
277C3×M16—61no—
278C3×M16C22×D312yes—
279C3×M16C22×D312yes—
280C2×C3×C8—21no—
281C2×C3×C8—21no—
282C2×C3×C8—32no—
283C2×C3×C8—41no—
284C2×C3×C8—64no—
285C2×C3×C8—61no—
286#216—62no—
287#215—62no—
288#215—64no—
289#214—62no—
290#214—64no—
291#214—64no—
292#213—62no—
293#213—64no—
294#213—64no—
295#213—64no—
296#208—21no—
297#208—32no—
298#208—32no—
299#208—62no—
300#208—61no—
301#208—61no—
302#208—121no—
303#208#6712yes—
304#208#6712yes—
305#208C22×D312yes—
306C2×C3⋊C8—21no—
307C2×C3⋊C8—61no—
308C2×C3⋊C8—61no—
309C2×C3⋊C8—121no—
310C2×C3⋊C8C22×D312yes—
311Dic12—62no—
312D24—64no—
313D24—62no—
314#204—64no—
315#204—62no—
316#204—62no—
317ΓL(1,𝔽25)—24no—
318D3×C8—24no—
319C22×C32—41no—
320C22×C32#12111yescharacteristic
321C22×C32#12111yescharacteristic
322C22×C32C2×#4111yescharacteristic
323C2×C3⋊D3—41no—
324C2×C3⋊D3—81no—
325C2×C3×D3—22no—
326C2×C3×D3—42no—
327C2×C3×D3—81no—
328C2×C3×D3—82no—
329C2×C3×D3—82no—
330C2×C3×D3—82no—
331C32×C4#12111yescharacteristic
332C32×C4#12111yescharacteristic
333C32×C4C22×D411yescharacteristic
334C32×C4C22×D411yescharacteristic
335C3⋊Dic3—41no—
336C3×Dic3—22no—
337C2×#41—31no—
338C2×#41—91no—
339C22×D4—31no—
340#137—92no—
341#137—181no—
342AGL(1,ℤ/8)—92no—
343AGL(1,ℤ/8)—94no—
344AGL(1,ℤ/8)—182no—
345AGL(1,ℤ/8)—182no—
346AGL(1,ℤ/8)—181no—
347AGL(1,ℤ/8)—182no—
348#135—182no—
349C2×SD16—92no—
350C2×SD16—181no—
351C2×D8—92no—
352C2×D8—181no—
353#131—34no—
354#131—62no—
355C2×M16—31no—
356C2×M16—31no—
357C2×M16—62no—
358C2×M16—91no—
359C2×M16D3211yescharacteristic
360#108—94no—
361#101—92no—
362#100—34no—
363#100—92no—
364C23×C3—21no—
365C23×C3—61no—
366C23×C3—62no—
367C23×C3—121no—
368C23×C3—121no—
369C23×C3—242no—
370C23×C3#23511yescharacteristic
371C23×C3#23511yescharacteristic
372C22×D3—21no—
373C22×D3—22no—
374C22×D3—41no—
375C22×D3—41no—
376C22×D3—62no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—82no—
380C3×Q8—32no—
381C3×Q8—61no—
382C3×D4—32no—
383C3×D4—62no—
384C3×D4—62no—
385C3×D4—61no—
386C3×D4—62no—
387C3×D4—62no—
388C3×D4—121no—
389C3×D4—121no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4C2×D1211yescharacteristic
400C2×C3×C4C2×D1211yescharacteristic
401C2×C3×C4#23511yescharacteristic
402C2×C3×C4#23511yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C23×D311yescharacteristic
410C2×C3×C4C23×D311yescharacteristic
411#67—22no—
412#67—22no—
413#67—122no—
414#67—122no—
415#67—121no—
416#67—121no—
417#67—121no—
418#67—121no—
419C2×Dic3—21no—
420C2×Dic3—62no—
421C2×Dic3—61no—
422C2×Dic3—61no—
423D12—21no—
424D12—22no—
425D12—22no—
426D12—41no—
427D12—41no—
428D12—61no—
429D12—61no—
430D12—61no—
431D12—61no—
432D12—121no—
433D12—121no—
434D12C2×D1212yes—
435C4×D3—22no—
436C4×D3—22no—
437C4×D3—122no—
438C4×D3—122no—
439C4×D3—121no—
440C4×D3—121no—
441C4×D3—121no—
442C4×D3—121no—
443Dic6—21no—
444Dic6—61no—
445Dic6—61no—
446Dic6—61no—
447Dic6—61no—
448Dic6—121no—
449Dic6—121no—
450Dic6C2×D1212yes—
451C3×C8—22no—
452C3×C8—22no—
453C3×C8—34no—
454C3×C8—42no—
455C3×C8—62no—
456C3⋊C8—22no—
457C3⋊C8—62no—
458C3⋊C8—62no—
459C3⋊C8—122no—
460C3⋊C8C2×#6714yes—
461C2×C32—21no—
462C2×C32—21no—
463C2×C32—21no—
464C2×C32C2×#12111yescharacteristic
465C3⋊D3—81no—
466C3×D3—42no—
467C3×D3—82no—
468C24—61no—
469#41—32no—
470#41—32no—
471#41—61no—
472#41—61no—
473#41—181no—
474#41—181no—
475#41—181no—
476#41—181no—
477C2×Q8—31no—
478C2×Q8—91no—
479C2×D4—32no—
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—61no—
486C2×D4—61no—
487C2×D4—91no—
488C2×D4—181no—
489C22×C4—61no—
490C22×C4—181no—
491C22×C4C2×D3211yescharacteristic
492Q16—182no—
493SD16—184no—
494SD16—182no—
495SD16—182no—
496SD16—184no—
497D8—184no—
498D8—182no—
499D8—184no—
500M16—21no—
501M16—32no—
502M16—32no—
503M16—32no—
504M16—64no—
505M16—61no—
506M16—92no—
507M16—181no—
508M16C2×D3212yes—
509C2×C8—21no—
510C2×C8—32no—
511C2×C8—64no—
512C2×C8—61no—
513C2×C8—181no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—62no—
520C22×C3—81no—
521C22×C3—122no—
522C22×C3—241no—
523C22×C3—242no—
524C22×C3—242no—
525C22×C3—242no—
526C22×C3#88411yescharacteristic
527C22×C3#88411yescharacteristic
528C22×C3#93011yescharacteristic
529C22×C3#93011yescharacteristic
530C22×C3C2×#23511yescharacteristic
531C22×C3C2×#23511yescharacteristic
532C2×D3—22no—
533C2×D3—42no—
534C2×D3—81no—
535C2×D3—82no—
536C2×D3—82no—
537C2×D3—82no—
538C2×D3—122no—
539C2×D3—121no—
540C2×D3—121no—
541C2×D3—241no—
542C2×D3—241no—
543C2×D3—242no—
544C3×C4—21no—
545C3×C4—21no—
546C3×C4—21no—
547C3×C4—21no—
548C3×C4—62no—
549C3×C4#88411yescharacteristic
550C3×C4#88411yescharacteristic
551C3×C4#93011yescharacteristic
552C3×C4#93011yescharacteristic
553C3×C4C22×D1211yescharacteristic
554C3×C4C2×D3×D411yescharacteristic
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C22×#6711yescharacteristic
557Dic3—22no—
558Dic3—122no—
559Dic3—121no—
560Dic3—121no—
561C32#306811yescharacteristic, complemented, Sylow
562C23—61no—
563C23—62no—
564C23—121no—
565C23—121no—
566C23—181no—
567C23—242no—
568C23#379811yescharacteristic
569Q8—32no—
570Q8—61no—
571Q8—181no—
572Q8—181no—
573D4—32no—
574D4—62no—
575D4—62no—
576D4—62no—
577D4—62no—
578D4—61no—
579D4—121no—
580D4—121no—
581D4—181no—
582D4—181no—
583D4—361no—
584D4—361no—
585C2×C4—61no—
586C2×C4—62no—
587C2×C4—62no—
588C2×C4—181no—
589C2×C4—361no—
590C2×C4—361no—
591C2×C4#379811yescharacteristic
592C2×C4D3×D1211yescharacteristic
593C2×C4D3×D1211yescharacteristic
594C2×C4D3×#6711yescharacteristic
595C2×C4D3×#6711yescharacteristic
596C2×C4C22×D3211yescharacteristic
597C8—22no—
598C8—34no—
599C8—62no—
600C8—182no—
601C2×C3—21no—
602C2×C3—21no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—41no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—122no—
612C2×C3—242no—
613C2×C3C2×#88411yescharacteristic
614C2×C3C2×#93011yescharacteristic
615D3—42no—
616D3—82no—
617D3—242no—
618D3—241no—
619D3—241no—
620C22—41no—
621C22—62no—
622C22—122no—
623C22—241no—
624C22—242no—
625C22—242no—
626C22—242no—
627C22—361no—
628C22—721no—
629C22#6390611yescharacteristic
630C22#6390611yescharacteristic
631C22C2×#379811yescharacteristic
632C4—62no—
633C4—361no—
634C4#6390611yescharacteristic
635C4#6390611yescharacteristic
636C4C2×D3×D1211yescharacteristic
637C4C2×D3×#6711yescharacteristic
638C3—21no—
639C3#7870311yescharacteristic, complemented
640C3#8381411yescharacteristic, complemented
641C2—21no—
642C2—21no—
643C2—21no—
644C2—122no—
645C2—242no—
646C2—721no—
647C2C2×#6390611yescharacteristic
subgroupG/H
centerC2C2×#63906
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C2×#121
hypercenterC2×M16D32
hypocenterC32#3068
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C3×#5745C2semidirect
2. #10594795C2semidirect
3. C2×#63830C2semidirect
4. C2×#63823C2semidirect
5. #10592831C2semidirect
6. C2×C3×#823C2semidirect
7. #10591141C2semidirect
8. #10590997C2semidirect
9. #10590996C2semidirect
19. C3×#907C22semidirect
23. #63831C22semidirect
28. C2×#3716C22semidirect
30. #63825C22semidirect
31. C2×#3714C22semidirect
35. #63651C22semidirect
36. #63650C22semidirect
37. C3×#823C22semidirect
38. #63577C22semidirect
46. #5745D3semidirect
53. C2×#823D3semidirect
148. #907C2×D3semidirect
161. #823C2×D3semidirect
561. C32#3068semidirect
639. C3#78703semidirect
640. C3#83814semidirect

Maximal subgroups

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

subgroupindex
C3×#57452
#105947952
C2×#638302
C2×#638232
#105928312
C2×C3×#8232
#105911412
#105909972
#105909962
#838143
#787033