Finite Group Databasebeta

← #11868119

Subgroups — #11868119

Order 1152.

983 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#908C211yesmaximal, characteristic, complemented
2C3×#5745C211yesmaximal, characteristic, complemented
3#10594786C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592824C211yesmaximal, characteristic, complemented
6#10591076C211yesmaximal, characteristic, complemented
7C2×#63558C211yesmaximal, characteristic, complemented
8#10590926C214yesmaximal, complemented
9#10590925C214yesmaximal, complemented
10#83963—31nomaximal
11#83814—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#908—22no—
20C3×#908—22no—
21C3×#907—22no—
22C3×D3×M16—22no—
23C2×C3×D24C2212yescomplemented
24C2×C3×#204C2212yescomplemented
25C3×#901C2214yescomplemented
26#63827—21no—
27#63827C2212yescomplemented
28C2×#3715—21no—
29#63823—22no—
30#63823—21no—
31#63823C2214yes—
32#63823C2212yescomplemented
33#63822—22no—
34C2×#3713—21no—
35#63646C2214yescomplemented
36#63560C2212yescomplemented
37#63558C2214yescomplemented
38#63558C2212yescomplemented
39C2×C3×AGL(1,ℤ/8)—31no—
40C3×#568—31no—
41#5822—31no—
42#5822—31no—
43C2×#949—31no—
44C2×#932—31no—
45C2×#908D311yescharacteristic, complemented
46#5745D311yescharacteristic, complemented
47#5237—31no—
48C2×#833—31no—
49#5177—34no—
50#5160—34no—
51#5142—34no—
52#5141—34no—
53#5132—31no—
54C2×#823—31no—
55#5125—31no—
56#5125—31no—
57#5125—61no—
58C23×C3×D3—21no—
59C22×C32×C4C2311yescharacteristic
60C2×C3×#67—21no—
61C2×C3×#67—21no—
62C3×#235—21no—
63C3×#235—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235—21no—
67C3×#235—21no—
68C3×#235D412yes—
69C3×#235C2312yes—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12D411yescharacteristic
76C2×C3×D12C2312yes—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C32×M16D412yes—
83C32×M16D412yes—
84C2×C32×C8C2312yes—
85#3748—21no—
86#3748—21no—
87#3748C2312yes—
88#3748C2312yes—
89C2×C3⋊(C3⋊C8)—21no—
90C2×C3⋊(C3⋊C8)—21no—
91C3×#208—21no—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C3×D24—24no—
95C3×#204—24no—
96C3×ΓL(1,𝔽25)—24no—
97C3×D3×C8—24no—
98#3718—22no—
99#3715—22no—
100#3715—22no—
101#3715—24no—
102#3713—24no—
103#3713—22no—
104#3068—91noSylow
105C2×C3×#41—31no—
106C2×C3×#41—31no—
107C22×C3×D4—31no—
108C2×#235C2×D311yescharacteristic
109C2×#235C2×D311yescharacteristic
110C22×D12C2×D311yescharacteristic
111C3×AGL(1,ℤ/8)—62no—
112C3×AGL(1,ℤ/8)—62no—
113C2×C3×SD16—32no—
114C2×C3×D8—32no—
115C3×#131—34no—
116C3×#131—62no—
117C2×C3×M16—21no—
118C2×C3×M16—31no—
119C2×C3×M16—62no—
120C2×C3×M16C2×D311yescharacteristic
121C2×C3×M16C2×D311yescharacteristic
122#951—32no—
123#951—61no—
124#950—62no—
125#950—62no—
126#949—34no—
127#949—32no—
128#949—62no—
129#949—61no—
130#942—32no—
131#942—61no—
132C2×#215—61no—
133C2×#214—61no—
134#932—32no—
135#932—34no—
136#932—61no—
137#932—62no—
138C2×#213—61no—
139C2×#213—61no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—61no—
145C2×#208—61no—
146C2×#208C2×D311yescharacteristic
147#908—22no—
148#908—22no—
149#907—22no—
150D3×M16—22no—
151C2×D24C2×D312yescomplemented
152C2×#204C2×D312yescomplemented
153#901C2×D314yescomplemented
154#836—32no—
155#833—32no—
156#833—34no—
157#824—32no—
158#823—34no—
159#823—32no—
160#819—34no—
161#819—34no—
162#819—64no—
163C23×C32#4111yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C22×C3×D3—21no—
167C22×C3×D3—41no—
168C22×C3×D3—41no—
169C22×C3×D3—82no—
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4#4111yescharacteristic
175C2×C32×C4C2411yescharacteristic
176C3×#67—22no—
177C3×#67—22no—
178C3×#67—41no—
179C3×#67—41no—
180C2×C3×Dic3—21no—
181C2×C3×Dic3—21no—
182C3×D12—21no—
183C3×D12—22no—
184C3×D12—21no—
185C3×D12—22no—
186C3×D12—21no—
187C3×D12—41no—
188C3×D12—41no—
189C3×D12C2×D412yes—
190C3×C4×D3—22no—
191C3×C4×D3—22no—
192C3×C4×D3—41no—
193C3×C4×D3—41no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6—21no—
197C3×Dic6C2×D412yes—
198C32×C8C2×D414yes—
199C3⋊(C3⋊C8)—22no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202#575—91no—
203C2×AGL(1,ℤ/8)—31no—
204C2×AGL(1,ℤ/8)—91no—
205#568—31no—
206#472—94no—
207#471—94no—
208#430—91no—
209#413—91no—
210C2×#100—91no—
211C24×C3—61no—
212C23×D3—21no—
213C3×#41—32no—
214C3×#41—32no—
215C3×#41—61no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41—61no—
221C2×C3×Q8—31no—
222C2×C3×Q8—31no—
223C2×C3×D4—31no—
224C2×C3×D4—31no—
225C2×C3×D4—32no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C22×C3×C4—21no—
234C22×C3×C4—61no—
235C22×C3×C4—61no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—21no—
239C2×#67—21no—
240#235—21no—
241#235—21no—
242#235—21no—
243#235—21no—
244#235—21no—
245#235—21no—
246#235D1212yes—
247#235C22×D312yes—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12D1211yescharacteristic
254C2×D12C22×D312yes—
255C2×D12C22×D311yescharacteristic
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×Dic6D1211yescharacteristic
259C2×Dic6C22×D311yescharacteristic
260C3×SD16—64no—
261C3×D8—64no—
262C3×M16—22no—
263C3×M16—22no—
264C3×M16—32no—
265C3×M16—61no—
266C3×M16—64no—
267C3×M16#6712yes—
268C3×M16#6712yes—
269C3×M16#6712yes—
270C3×M16#6712yes—
271C2×C3×C8—22no—
272C2×C3×C8—61no—
273C2×C3×C8—64no—
274C2×C3×C8C22×D312yes—
275C2×C3×C8C22×D312yes—
276#216—62no—
277#216—62no—
278#215—64no—
279#215—62no—
280#215—62no—
281#214—62no—
282#214—64no—
283#214—62no—
284#213—64no—
285#213—62no—
286#213—64no—
287#213—62no—
288#208—21no—
289#208—32no—
290#208—32no—
291#208—32no—
292#208—32no—
293#208—62no—
294#208—62no—
295#208—61no—
296#208—61no—
297#208—61no—
298#208—61no—
299#208—121no—
300#208—121no—
301#208C22×D312yes—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—61no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—61no—
307C2×C3⋊C8—121no—
308C2×C3⋊C8—121no—
309D24—24no—
310#204—24no—
311ΓL(1,𝔽25)—24no—
312D3×C8—24no—
313C22×C32—41no—
314C22×C32#12111yescharacteristic
315C22×C32#12111yescharacteristic
316C22×C32C2×#4111yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—41no—
319C2×C3×D3—42no—
320C2×C3×D3—81no—
321C2×C3×D3—82no—
322C2×C3×D3—82no—
323C2×C3×D3—81no—
324C2×C3×D3—82no—
325C32×C4#12111yescharacteristic
326C32×C4#12111yescharacteristic
327C32×C4C22×D411yescharacteristic
328C32×C4C22×D411yescharacteristic
329C3×Dic3—22no—
330C3×Dic3—41no—
331C2×#41—31no—
332C2×#41—31no—
333C22×D4—31no—
334#137—92no—
335#137—181no—
336AGL(1,ℤ/8)—62no—
337AGL(1,ℤ/8)—62no—
338AGL(1,ℤ/8)—94no—
339AGL(1,ℤ/8)—92no—
340AGL(1,ℤ/8)—181no—
341AGL(1,ℤ/8)—182no—
342#135—182no—
343C2×SD16—32no—
344C2×SD16—181no—
345C2×D8—32no—
346C2×D8—181no—
347#131—34no—
348#131—62no—
349C2×M16—31no—
350C2×M16—62no—
351C2×M16—91no—
352C2×M16—91no—
353C2×M16D3211yescharacteristic
354#108—94no—
355#101—92no—
356#100—94no—
357#100—92no—
358C23×C3—21no—
359C23×C3—61no—
360C23×C3—61no—
361C23×C3—62no—
362C23×C3—121no—
363C23×C3—121no—
364C23×C3—242no—
365C23×C3#23511yescharacteristic
366C23×C3#23711yescharacteristic
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—82no—
373C3×Q8—32no—
374C3×Q8—61no—
375C3×Q8—61no—
376C3×Q8—61no—
377C3×D4—32no—
378C3×D4—62no—
379C3×D4—62no—
380C3×D4—61no—
381C3×D4—62no—
382C3×D4—61no—
383C3×D4—61no—
384C3×D4—62no—
385C3×D4—121no—
386C3×D4—121no—
387C3×D4—121no—
388C3×D4—121no—
389C2×C3×C4—21no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—61no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—61no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4C2×D1211yescharacteristic
402C2×C3×C4C2×D1211yescharacteristic
403C2×C3×C4#23511yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4#23711yescharacteristic
407C2×C3×C4C2×#6711yescharacteristic
408C2×C3×C4C2×#6711yescharacteristic
409C2×C3×C4C2×#6711yescharacteristic
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C23×D311yescharacteristic
412C2×C3×C4C23×D311yescharacteristic
413#67—22no—
414#67—22no—
415#67—41no—
416#67—41no—
417C2×Dic3—21no—
418C2×Dic3—21no—
419D12—21no—
420D12—22no—
421D12—21no—
422D12—22no—
423D12—21no—
424D12—41no—
425D12—41no—
426D12C2×D1212yes—
427C4×D3—22no—
428C4×D3—22no—
429C4×D3—41no—
430C4×D3—41no—
431Dic6—21no—
432Dic6—21no—
433Dic6—21no—
434Dic6C2×D1212yes—
435C3×C8—24no—
436C3×C8—62no—
437C3×C8C2×#6714yes—
438C3×C8C2×#6714yes—
439C3⋊C8—22no—
440C3⋊C8—62no—
441C3⋊C8—62no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8—122no—
445C3⋊C8—122no—
446C2×C32—21no—
447C2×C32—21no—
448C2×C32—21no—
449C2×C32C2×#12111yescharacteristic
450C3×D3—42no—
451C3×D3—81no—
452C3×D3—82no—
453C24—61no—
454#41—32no—
455#41—32no—
456#41—61no—
457#41—61no—
458#41—61no—
459#41—61no—
460#41—61no—
461#41—61no—
462C2×Q8—31no—
463C2×Q8—31no—
464C2×D4—31no—
465C2×D4—32no—
466C2×D4—31no—
467C2×D4—61no—
468C2×D4—61no—
469C2×D4—61no—
470C2×D4—61no—
471C2×D4—61no—
472C2×D4—61no—
473C2×D4—61no—
474C22×C4—61no—
475C22×C4—61no—
476C22×C4C2×D3211yescharacteristic
477Q16—182no—
478SD16—64no—
479SD16—182no—
480SD16—184no—
481SD16—182no—
482D8—64no—
483D8—184no—
484D8—182no—
485M16—32no—
486M16—61no—
487M16—64no—
488M16—92no—
489M16—92no—
490M16—181no—
491M16—181no—
492M16#62512yes—
493M16#62512yes—
494C2×C8—61no—
495C2×C8—64no—
496C2×C8—181no—
497C2×C8—181no—
498C2×C8C2×D3212yes—
499C22×C3—21no—
500C22×C3—21no—
501C22×C3—21no—
502C22×C3—41no—
503C22×C3—41no—
504C22×C3—62no—
505C22×C3—81no—
506C22×C3—121no—
507C22×C3—122no—
508C22×C3—241no—
509C22×C3—242no—
510C22×C3—241no—
511C22×C3—242no—
512C22×C3—242no—
513C22×C3#93011yescharacteristic
514C22×C3#93011yescharacteristic
515C22×C3#93811yescharacteristic
516C22×C3#93811yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3C2×#23711yescharacteristic
519C2×D3—22no—
520C2×D3—41no—
521C2×D3—42no—
522C2×D3—81no—
523C2×D3—82no—
524C2×D3—82no—
525C2×D3—82no—
526C2×D3—81no—
527C3×C4—21no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—62no—
532C3×C4—121no—
533C3×C4#93011yescharacteristic
534C3×C4#93011yescharacteristic
535C3×C4#93811yescharacteristic
536C3×C4#93811yescharacteristic
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—22no—
542Dic3—41no—
543C32#306811yescharacteristic, complemented, Sylow
544C23—61no—
545C23—61no—
546C23—62no—
547C23—121no—
548C23—121no—
549C23—242no—
550C23#379511yescharacteristic
551Q8—32no—
552Q8—61no—
553Q8—61no—
554Q8—61no—
555D4—32no—
556D4—62no—
557D4—62no—
558D4—62no—
559D4—61no—
560D4—61no—
561D4—62no—
562D4—61no—
563D4—121no—
564D4—121no—
565D4—121no—
566D4—121no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—61no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4#379511yescharacteristic
574C2×C4D3×D1211yescharacteristic
575C2×C4D3×D1211yescharacteristic
576C2×C4C2×#62511yescharacteristic
577C2×C4C2×#62511yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—62no—
580C8—182no—
581C8—182no—
582C8C2×#62514yes—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—41no—
591C2×C3—41no—
592C2×C3—41no—
593C2×C3—122no—
594C2×C3—242no—
595C2×C3—241no—
596C2×C3C2×#93011yescharacteristic
597C2×C3C2×#93811yescharacteristic
598D3—42no—
599D3—82no—
600D3—81no—
601C22—41no—
602C22—62no—
603C22—121no—
604C22—122no—
605C22—241no—
606C22—242no—
607C22—241no—
608C22—242no—
609C22—242no—
610C22#6390811yescharacteristic
611C22#6390811yescharacteristic
612C22C2×#379511yescharacteristic
613C4—62no—
614C4—121no—
615C4#6390811yescharacteristic
616C4#6390811yescharacteristic
617C4C2×D3×D1211yescharacteristic
618C4C22×#62511yescharacteristic
619C3—21no—
620C3#8381411yescharacteristic, complemented
621C3#8396311yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—122no—
626C2—242no—
627C2—241no—
628C2C2×#6390811yescharacteristic
subgroupG/H
centerC2C2×#63908
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. C2×C3×#908C2semidirect
2. C3×#5745C2semidirect
3. #10594786C2semidirect
4. C2×#63823C2semidirect
5. #10592824C2semidirect
6. #10591076C2semidirect
7. C2×#63558C2semidirect
8. #10590926C2semidirect
9. #10590925C2semidirect
23. C2×C3×D24C22semidirect
24. C2×C3×#204C22semidirect
25. C3×#901C22semidirect
27. #63827C22semidirect
32. #63823C22semidirect
35. #63646C22semidirect
36. #63560C22semidirect
37. #63558C22semidirect
38. #63558C22semidirect
45. C2×#908D3semidirect
46. #5745D3semidirect
151. C2×D24C2×D3semidirect
152. C2×#204C2×D3semidirect
153. #901C2×D3semidirect
543. C32#3068semidirect
620. C3#83814semidirect
621. C3#83963semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C3×#57452
#105947862
C2×#638232
#105928242
#105910762
C2×#635582
#105909262
#105909252
#839633
#838143