Finite Group Databasebeta

← #11868132

Subgroups — #11868132

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
1C3×#5748C211yesmaximal, characteristic, complemented
2C2×#63823C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4#10594776C211yesmaximal, characteristic, complemented
5#10592823C211yesmaximal, characteristic, complemented
6C2×C3×#823C211yesmaximal, characteristic, complemented
7#10591076C211yesmaximal, characteristic, complemented
8#10590982C214yesmaximal, complemented
9#10590979C214yesmaximal, complemented
10#84002—31nomaximal
11#78703—31nomaximal
12C2×C3×#235C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C22×C3×D12C2211yescharacteristic
15C2×C32×M16C2211yescharacteristic
16C2×#3748C2211yescharacteristic
17C2×#3748C2211yescharacteristic
18C2×C3×#208C2211yescharacteristic
19C3×#909—21no—
20C3×#909C2212yescomplemented
21C3×#908—21no—
22C3×#908C2212yescomplemented
23C3×#904—22no—
24C2×#3715—21no—
25C2×#3715C2212yescomplemented
26#63823—22no—
27#63823—22no—
28#63823—22no—
29#63823C2214yes—
30C2×#3713—21no—
31C2×#3713C2212yescomplemented
32#63815C2214yescomplemented
33#63814—22no—
34D3×#208—22no—
35#63649C2214yescomplemented
36C3×#823C2214yescomplemented
37#63560C2212yescomplemented
38#63558C2212yescomplemented
39C3×#575—31no—
40C2×#949—31no—
41C2×#949—31no—
42#5819—31no—
43C2×#932—31no—
44C2×#932—31no—
45#5748D311yescharacteristic, complemented
46#5745—31no—
47C2×C3×#100—31no—
48#5237—31no—
49#5203—34no—
50#5199—34no—
51#5132—31no—
52C2×#823D311yescharacteristic, complemented
53#5124—31no—
54#5124—31no—
55#5124—61no—
56#4749—34no—
57#4748—34no—
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×D12C2311yescharacteristic
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—21no—
79C2×C3×C4×D3—21no—
80C2×C3×Dic6D411yescharacteristic
81C2×C3×Dic6C2311yescharacteristic
82C32×M16—21no—
83C32×M16C2312yes—
84C2×C32×C8—21no—
85#3748—21no—
86#3748D412yes—
87#3748D412yes—
88#3748C2312yes—
89C2×C3⋊(C3⋊C8)—21no—
90C2×C3⋊(C3⋊C8)C2312yes—
91C3×#208—21no—
92C3×#208C2312yes—
93C2×C3×C3⋊C8—21no—
94C3×Dic12—22no—
95C3×D24—22no—
96C3×#204—22no—
97C3×#204—22no—
98#3715—24no—
99#3715—24no—
100#3713—24no—
101#3713—24no—
102#3711—24no—
103D3×C3⋊C8—24no—
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×#137—32no—
112C3×#137—61no—
113C3×AGL(1,ℤ/8)—32no—
114C3×AGL(1,ℤ/8)—61no—
115C3×#135—62no—
116C2×C3×M16—21no—
117C2×C3×M16—31no—
118C2×C3×M16C2×D311yescharacteristic
119C2×C3×M16C2×D311yescharacteristic
120#949—34no—
121#949—62no—
122#949—62no—
123#949—62no—
124#948—34no—
125#948—62no—
126C2×#215—32no—
127C2×#215—61no—
128C2×#214—32no—
129C2×#214—61no—
130#932—34no—
131#932—62no—
132#932—62no—
133#932—62no—
134C2×#213—32no—
135C2×#213—32no—
136C2×#213—61no—
137C2×#213—61no—
138C2×#208—31no—
139C2×#208—31no—
140C2×#208—31no—
141C2×#208—31no—
142C2×#208—61no—
143C2×#208—61no—
144C2×#208—62no—
145C2×#208C2×D311yescharacteristic
146#909—21no—
147#909C2×D312yescomplemented
148#908—21no—
149#908C2×D312yescomplemented
150#907—34no—
151D3×M16—62no—
152#904—22no—
153#901—62no—
154C3×#100—34no—
155#836—32no—
156#833—32no—
157#824—32no—
158#823—32no—
159#823C2×D314yescomplemented
160#822—34no—
161#822—34no—
162#822—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—21no—
184C3×D12—22no—
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×C8—22no—
199C3⋊(C3⋊C8)—22no—
200C3⋊(C3⋊C8)C2×D414yes—
201C3×C3⋊C8—22no—
202#575—31no—
203C2×AGL(1,ℤ/8)—91no—
204C2×AGL(1,ℤ/8)—91no—
205#568—91no—
206#472—94no—
207#471—94no—
208#430—91no—
209#413—91no—
210C2×#100—31no—
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#235#6712yes—
247#235C22×D312yes—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12#6711yescharacteristic
254C2×D12C22×D311yescharacteristic
255C2×D12C22×D312yes—
256C2×C4×D3—21no—
257C2×C4×D3—21no—
258C2×Dic6#6711yescharacteristic
259C2×Dic6C22×D311yescharacteristic
260C3×Q16—62no—
261C3×SD16—62no—
262C3×SD16—62no—
263C3×D8—62no—
264C3×M16—21no—
265C3×M16—21no—
266C3×M16—22no—
267C3×M16—32no—
268C3×M16—41no—
269C3×M16—61no—
270C3×M16C22×D312yes—
271C3×M16C22×D312yes—
272C2×C3×C8—21no—
273C2×C3×C8—21no—
274C2×C3×C8—41no—
275C2×C3×C8—61no—
276#215—64no—
277#215—64no—
278#214—64no—
279#214—64no—
280#213—64no—
281#213—64no—
282#213—64no—
283#213—64no—
284#208—21no—
285#208—32no—
286#208—32no—
287#208—32no—
288#208—32no—
289#208—32no—
290#208—32no—
291#208—62no—
292#208—62no—
293#208—62no—
294#208—64no—
295#208—61no—
296#208—61no—
297#208—121no—
298#208C22×D312yes—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—32no—
301C2×C3⋊C8—32no—
302C2×C3⋊C8—62no—
303C2×C3⋊C8—64no—
304C2×C3⋊C8—61no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—121no—
307Dic12—22no—
308D24—22no—
309#204—22no—
310#204—22no—
311ΓL(1,𝔽25)—64no—
312D3×C8—64no—
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—32no—
335#137—61no—
336AGL(1,ℤ/8)—32no—
337AGL(1,ℤ/8)—61no—
338AGL(1,ℤ/8)—94no—
339AGL(1,ℤ/8)—182no—
340AGL(1,ℤ/8)—182no—
341AGL(1,ℤ/8)—182no—
342#135—62no—
343C2×SD16—92no—
344C2×SD16—181no—
345C2×D8—92no—
346C2×D8—181no—
347#131—94no—
348#131—182no—
349C2×M16—31no—
350C2×M16—91no—
351C2×M16—91no—
352C2×M16—182no—
353C2×M16D3211yescharacteristic
354#108—94no—
355#101—92no—
356#100—34no—
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—22no—
369C22×D3—21no—
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—61no—
382C3×D4—62no—
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×C4#23511yescharacteristic
402C2×C3×C4D3×D411yescharacteristic
403C2×C3×C4D3×D411yescharacteristic
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4#23711yescharacteristic
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—21no—
421D12—22no—
422D12—22no—
423D12—21no—
424D12—41no—
425D12—41no—
426D12C2×#6712yes—
427C4×D3—22no—
428C4×D3—22no—
429C4×D3—41no—
430C4×D3—41no—
431Dic6—21no—
432Dic6—21no—
433Dic6—21no—
434Dic6C2×#6712yes—
435C3×C8—22no—
436C3×C8—22no—
437C3×C8—42no—
438C3×C8—62no—
439C3⋊C8—22no—
440C3⋊C8—34no—
441C3⋊C8—34no—
442C3⋊C8—64no—
443C3⋊C8—62no—
444C3⋊C8—62no—
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—32no—
465C2×D4—31no—
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—62no—
478SD16—62no—
479SD16—62no—
480SD16—184no—
481SD16—184no—
482D8—62no—
483D8—184no—
484D8—184no—
485M16—21no—
486M16—32no—
487M16—61no—
488M16—92no—
489M16—92no—
490M16—92no—
491M16—184no—
492M16—181no—
493M16C2×D3212yes—
494C2×C8—21no—
495C2×C8—61no—
496C2×C8—92no—
497C2×C8—184no—
498C2×C8—181no—
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#88411yescharacteristic
514C22×C3#88411yescharacteristic
515C22×C3#93911yescharacteristic
516C22×C3#93911yescharacteristic
517C22×C3C2×#23511yescharacteristic
518C22×C3C2×#23711yescharacteristic
519C2×D3—22no—
520C2×D3—42no—
521C2×D3—41no—
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#88411yescharacteristic
534C3×C4#88411yescharacteristic
535C3×C4#93911yescharacteristic
536C3×C4#93911yescharacteristic
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
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—61no—
559D4—62no—
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×C4#380211yescharacteristic
575C2×C4#380211yescharacteristic
576C2×C4D3×#6711yescharacteristic
577C2×C4D3×#6711yescharacteristic
578C2×C4C22×D3211yescharacteristic
579C8—22no—
580C8—62no—
581C8—94no—
582C8—182no—
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×#88411yescharacteristic
597C2×C3C2×#93911yescharacteristic
598D3—42no—
599D3—81no—
600D3—82no—
601C22—41no—
602C22—62no—
603C22—121no—
604C22—122no—
605C22—241no—
606C22—242no—
607C22—241no—
608C22—242no—
609C22—242no—
610C22#6388511yescharacteristic
611C22#6388511yescharacteristic
612C22C2×#379511yescharacteristic
613C4—62no—
614C4—121no—
615C4#6388511yescharacteristic
616C4#6388511yescharacteristic
617C4C2×#380211yescharacteristic
618C4C2×D3×#6711yescharacteristic
619C3—21no—
620C3#7870311yescharacteristic, complemented
621C3#8400211yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—21no—
625C2—122no—
626C2—242no—
627C2—241no—
628C2C2×#6388511yescharacteristic
subgroupG/H
centerC2C2×#63885
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×#5748C2semidirect
2. C2×#63823C2semidirect
3. C2×#63823C2semidirect
4. #10594776C2semidirect
5. #10592823C2semidirect
6. C2×C3×#823C2semidirect
7. #10591076C2semidirect
8. #10590982C2semidirect
9. #10590979C2semidirect
20. C3×#909C22semidirect
22. C3×#908C22semidirect
25. C2×#3715C22semidirect
31. C2×#3713C22semidirect
32. #63815C22semidirect
35. #63649C22semidirect
36. C3×#823C22semidirect
37. #63560C22semidirect
38. #63558C22semidirect
45. #5748D3semidirect
52. C2×#823D3semidirect
147. #909C2×D3semidirect
149. #908C2×D3semidirect
159. #823C2×D3semidirect
543. C32#3068semidirect
620. C3#78703semidirect
621. C3#84002semidirect

Maximal subgroups

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

subgroupindex
C3×#57482
C2×#638232
#105947762
#105928232
C2×C3×#8232
#105910762
#105909822
#105909792
#840023
#787033