Finite Group Databasebeta

← #11868042

Subgroups — #11868042

Order 1152.

957 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#904C211yesmaximal, characteristic, complemented
2C2×C3×#901C211yesmaximal, characteristic, complemented
3#10594786C212yesmaximal, complemented
4C2×#63646C211yesmaximal, characteristic, complemented
5#10591076C212yesmaximal, complemented
6#10590930C212yesmaximal, complemented
7#10590926C212yesmaximal, complemented
8#10590925C214yesmaximal, complemented
9#83928—31nomaximal
10#83805—31nomaximal
11C2×C3×#235C2211yescharacteristic
12C2×C3×#235C2212yes—
13C22×C32×C8C2211yescharacteristic
14C2×#3748C2212yes—
15C2×C3×#208C2211yescharacteristic
16C2×C3×Dic12C2211yescharacteristic, complemented
17C3×#904—21no—
18C3×#904—21no—
19C3×#904—21no—
20C3×#904—21no—
21C2×C3×D24C2211yescharacteristic, complemented
22C2×C3×#204C2212yescomplemented
23C3×#901—21no—
24C3×#901—21no—
25C3×#901C2212yes—
26C3×#901C2212yes—
27C2×C3×ΓL(1,𝔽25)—21no—
28C2×C3×D3×C8—21no—
29#63827—22no—
30#63827C2214yes—
31#63823—22no—
32#63823C2214yes—
33#63822—24no—
34#63646C2212yescomplemented
35#63646C2212yescomplemented
36#63560C2214yescomplemented
37#63558C2214yescomplemented
38C2×C3×#135—31no—
39C2×C3×#131—31no—
40#5822—32no—
41#5822—32no—
42C2×#904D311yescharacteristic, complemented
43C2×#901D311yescharacteristic, complemented
44#5237—32no—
45#5192—32no—
46#5177—34no—
47#5160—32no—
48#5143—32no—
49#5142—32no—
50#5141—34no—
51#5132—32no—
52C2×#819—31no—
53C2×#819—31no—
54C2×#819—61no—
55C22×C32×C4C2311yescharacteristic
56C2×C3×#67—21no—
57C2×C3×#67—22no—
58C3×#235—21no—
59C3×#235—21no—
60C3×#235—22no—
61C3×#235—22no—
62C3×#235—22no—
63C3×#235—22no—
64C3×#235D412yes—
65C3×#235C2312yes—
66C2×C3×D12D411yescharacteristic
67C2×C3×D12C2312yes—
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—22no—
70C2×C3×Dic6D411yescharacteristic
71C2×C3×Dic6C2312yes—
72C2×C32×C8D411yescharacteristic
73C2×C32×C8D411yescharacteristic
74C2×C32×C8D411yescharacteristic
75C2×C32×C8D411yescharacteristic
76C2×C32×C8C2311yescharacteristic
77C2×C32×C8C2311yescharacteristic
78#3748—22no—
79#3748C2314yes—
80C2×C3⋊(C3⋊C8)—22no—
81C3×#208—21no—
82C3×#208C2312yes—
83C2×C3×C3⋊C8—21no—
84C3×Dic12—21no—
85C3×Dic12—21no—
86C3×D24—21no—
87C3×D24—21no—
88C3×#204—22no—
89C3×#204—22no—
90C3×ΓL(1,𝔽25)—22no—
91C3×ΓL(1,𝔽25)—22no—
92C3×D3×C8—22no—
93C3×D3×C8—22no—
94#3718—24no—
95#3715—24no—
96#3715—24no—
97#3713—24no—
98#3067—91noSylow
99C2×C3×#41—31no—
100C2×C3×#41—32no—
101C2×#235C2×D311yescharacteristic
102C2×#235C2×D312yes—
103C3×#135—61no—
104C3×#135—61no—
105C3×#135—61no—
106C3×#135—61no—
107C2×C3×Q16—31no—
108C2×C3×SD16—32no—
109C2×C3×D8—31no—
110C3×#131—32no—
111C3×#131—32no—
112C3×#131—61no—
113C3×#131—61no—
114C2×C3×M16—31no—
115C2×C3×M16—61no—
116C22×C3×C8—21no—
117C22×C3×C8—61no—
118C22×C3×C8C2×D311yescharacteristic
119C22×C3×C8C2×D311yescharacteristic
120#951—34no—
121#951—62no—
122#950—64no—
123#950—64no—
124#949—34no—
125#949—62no—
126#942—34no—
127#942—62no—
128#932—34no—
129#932—62no—
130C2×#208—32no—
131C2×#208—32no—
132C2×#208—62no—
133C2×#208C2×D311yescharacteristic
134C2×Dic12C2×D311yescharacteristic, complemented
135#904—21no—
136#904—21no—
137#904—21no—
138#904—21no—
139C2×D24C2×D311yescharacteristic, complemented
140C2×#204C2×D312yescomplemented
141#901—21no—
142#901—21no—
143#901C2×D312yes—
144#901C2×D312yes—
145C2×ΓL(1,𝔽25)—21no—
146C2×D3×C8—21no—
147#836—34no—
148#833—34no—
149#824—34no—
150#823—34no—
151#819—32no—
152#819—32no—
153#819—32no—
154#819—32no—
155#819—62no—
156#819—62no—
157C23×C32#4111yescharacteristic
158C22×C3×D3—21no—
159C22×C3×D3—22no—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4#4111yescharacteristic
165C2×C32×C4C2411yescharacteristic
166C3×#67—22no—
167C3×#67—22no—
168C3×#67—42no—
169C3×#67—42no—
170C2×C3×Dic3—21no—
171C2×C3×Dic3—22no—
172C3×D12—21no—
173C3×D12—22no—
174C3×D12—22no—
175C3×D12C2×D412yes—
176C3×C4×D3—22no—
177C3×C4×D3—22no—
178C3×C4×D3—42no—
179C3×C4×D3—42no—
180C3×Dic6—21no—
181C3×Dic6—22no—
182C3×Dic6—22no—
183C3×Dic6C2×D412yes—
184C32×C8C2×D411yescharacteristic
185C32×C8C2×D411yescharacteristic
186C32×C8C2×D411yescharacteristic
187C32×C8C2×D411yescharacteristic
188C3⋊(C3⋊C8)—24no—
189C3×C3⋊C8—22no—
190#575—92no—
191C2×#135—31no—
192C2×#131—31no—
193#473—92no—
194#472—92no—
195#471—94no—
196C2×#108—91no—
197#413—92no—
198C3×#41—32no—
199C3×#41—32no—
200C3×#41—61no—
201C3×#41—61no—
202C3×#41—62no—
203C3×#41—62no—
204C3×#41—62no—
205C3×#41—62no—
206C2×C3×Q8—31no—
207C2×C3×Q8—32no—
208C2×C3×D4—31no—
209C2×C3×D4—32no—
210C2×C3×D4—61no—
211C2×C3×D4—62no—
212C22×C3×C4—21no—
213C22×C3×C4—61no—
214C22×C3×C4—62no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C2×#67—21no—
218C2×#67—22no—
219#235—21no—
220#235—21no—
221#235—22no—
222#235—22no—
223#235—22no—
224#235—22no—
225#235D1212yes—
226#235C22×D312yes—
227C2×D12D1211yescharacteristic
228C2×D12C22×D312yes—
229C2×C4×D3—21no—
230C2×C4×D3—22no—
231C2×Dic6D1211yescharacteristic
232C2×Dic6C22×D312yes—
233C3×Q16—61no—
234C3×Q16—61no—
235C3×SD16—62no—
236C3×SD16—62no—
237C3×D8—61no—
238C3×D8—61no—
239C3×M16—32no—
240C3×M16—61no—
241C3×M16—62no—
242C3×M16—62no—
243C2×C3×C8—21no—
244C2×C3×C8—21no—
245C2×C3×C8—21no—
246C2×C3×C8—21no—
247C2×C3×C8—21no—
248C2×C3×C8—21no—
249C2×C3×C8—61no—
250C2×C3×C8—62no—
251C2×C3×C8—62no—
252C2×C3×C8#6711yescharacteristic
253C2×C3×C8#6711yescharacteristic
254C2×C3×C8#6711yescharacteristic
255C2×C3×C8#6711yescharacteristic
256C2×C3×C8#6711yescharacteristic
257C2×C3×C8#6711yescharacteristic
258C2×C3×C8#6711yescharacteristic
259C2×C3×C8#6711yescharacteristic
260C2×C3×C8C22×D311yescharacteristic
261C2×C3×C8C22×D311yescharacteristic
262C2×C3×C8C22×D311yescharacteristic
263C2×C3×C8C22×D311yescharacteristic
264#216—64no—
265#216—64no—
266#215—64no—
267#215—64no—
268#214—64no—
269#214—64no—
270#213—64no—
271#213—64no—
272#208—21no—
273#208—34no—
274#208—34no—
275#208—64no—
276#208—62no—
277#208—62no—
278#208—122no—
279#208C22×D312yes—
280C2×C3⋊C8—21no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—122no—
284Dic12—21no—
285Dic12—21no—
286D24—21no—
287D24—21no—
288#204—22no—
289#204—22no—
290ΓL(1,𝔽25)—22no—
291ΓL(1,𝔽25)—22no—
292D3×C8—22no—
293D3×C8—22no—
294C22×C32—41no—
295C22×C32#12111yescharacteristic
296C22×C32#12111yescharacteristic
297C22×C32C2×#4111yescharacteristic
298C2×C3×D3—22no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—82no—
302C32×C4#12111yescharacteristic
303C32×C4#12111yescharacteristic
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3×Dic3—22no—
307C3×Dic3—42no—
308C2×#41—31no—
309C2×#41—32no—
310#137—94no—
311#137—182no—
312AGL(1,ℤ/8)—94no—
313AGL(1,ℤ/8)—182no—
314#135—61no—
315#135—61no—
316#135—61no—
317#135—61no—
318#135—184no—
319C2×Q16—31no—
320C2×SD16—32no—
321C2×D8—31no—
322#131—32no—
323#131—32no—
324#131—61no—
325#131—61no—
326C2×M16—31no—
327C2×M16—61no—
328C2×M16—92no—
329C22×C8—61no—
330C22×C8D3211yescharacteristic
331#108—92no—
332#108—92no—
333#101—94no—
334#100—94no—
335C23×C3—21no—
336C23×C3—61no—
337C23×C3—62no—
338C23×C3#23511yescharacteristic
339C23×C3#23711yescharacteristic
340C22×D3—21no—
341C22×D3—22no—
342C3×Q8—32no—
343C3×Q8—61no—
344C3×Q8—62no—
345C3×Q8—62no—
346C3×D4—32no—
347C3×D4—62no—
348C3×D4—62no—
349C3×D4—61no—
350C3×D4—62no—
351C3×D4—62no—
352C3×D4—122no—
353C3×D4—122no—
354C2×C3×C4—21no—
355C2×C3×C4—21no—
356C2×C3×C4—21no—
357C2×C3×C4—21no—
358C2×C3×C4—21no—
359C2×C3×C4—21no—
360C2×C3×C4—61no—
361C2×C3×C4—62no—
362C2×C3×C4—62no—
363C2×C3×C4—62no—
364C2×C3×C4—122no—
365C2×C3×C4—122no—
366C2×C3×C4C2×D1211yescharacteristic
367C2×C3×C4C2×D1211yescharacteristic
368C2×C3×C4#23511yescharacteristic
369C2×C3×C4D3×D411yescharacteristic
370C2×C3×C4D3×D411yescharacteristic
371C2×C3×C4#23711yescharacteristic
372C2×C3×C4C2×#6711yescharacteristic
373C2×C3×C4C2×#6711yescharacteristic
374C2×C3×C4C2×#6711yescharacteristic
375C2×C3×C4C2×#6711yescharacteristic
376C2×C3×C4C23×D311yescharacteristic
377C2×C3×C4C23×D311yescharacteristic
378#67—22no—
379#67—22no—
380#67—42no—
381#67—42no—
382C2×Dic3—21no—
383C2×Dic3—22no—
384D12—21no—
385D12—22no—
386D12—22no—
387D12C2×D1212yes—
388C4×D3—22no—
389C4×D3—22no—
390C4×D3—42no—
391C4×D3—42no—
392Dic6—21no—
393Dic6—22no—
394Dic6—22no—
395Dic6C2×D1212yes—
396C3×C8—21no—
397C3×C8—21no—
398C3×C8—21no—
399C3×C8—21no—
400C3×C8—62no—
401C3×C8C2×#6711yescharacteristic
402C3×C8C2×#6711yescharacteristic
403C3×C8C2×#6711yescharacteristic
404C3×C8C2×#6711yescharacteristic
405C3×C8C2×#6711yescharacteristic
406C3×C8C2×#6711yescharacteristic
407C3×C8C2×#6711yescharacteristic
408C3×C8C2×#6711yescharacteristic
409C3⋊C8—22no—
410C3⋊C8—64no—
411C3⋊C8—64no—
412C3⋊C8—124no—
413C2×C32—21no—
414C2×C32—21no—
415C2×C32—21no—
416C2×C32C2×#12111yescharacteristic
417C3×D3—42no—
418C3×D3—82no—
419#41—32no—
420#41—32no—
421#41—61no—
422#41—61no—
423#41—62no—
424#41—62no—
425#41—62no—
426#41—62no—
427C2×Q8—32no—
428C2×Q8—31no—
429C2×D4—32no—
430C2×D4—31no—
431C2×D4—61no—
432C2×D4—62no—
433C22×C4—61no—
434C22×C4—62no—
435C22×C4C2×D3211yescharacteristic
436Q16—61no—
437Q16—61no—
438Q16—184no—
439SD16—62no—
440SD16—62no—
441SD16—184no—
442SD16—184no—
443D8—61no—
444D8—61no—
445D8—184no—
446M16—32no—
447M16—61no—
448M16—62no—
449M16—62no—
450M16—94no—
451M16—182no—
452C2×C8—61no—
453C2×C8—62no—
454C2×C8—62no—
455C2×C8—182no—
456C2×C8#62511yescharacteristic
457C2×C8#62511yescharacteristic
458C2×C8#62511yescharacteristic
459C2×C8#62511yescharacteristic
460C2×C8C2×D3211yescharacteristic
461C2×C8C2×D3211yescharacteristic
462C22×C3—21no—
463C22×C3—21no—
464C22×C3—21no—
465C22×C3—41no—
466C22×C3—41no—
467C22×C3—42no—
468C22×C3—62no—
469C22×C3—122no—
470C22×C3—122no—
471C22×C3—242no—
472C22×C3#93011yescharacteristic
473C22×C3#93011yescharacteristic
474C22×C3#93811yescharacteristic
475C22×C3#93811yescharacteristic
476C22×C3C2×#23511yescharacteristic
477C22×C3C2×#23711yescharacteristic
478C2×D3—22no—
479C2×D3—42no—
480C2×D3—42no—
481C2×D3—82no—
482C3×C4—21no—
483C3×C4—21no—
484C3×C4—21no—
485C3×C4—21no—
486C3×C4—62no—
487C3×C4—122no—
488C3×C4#93011yescharacteristic
489C3×C4#93011yescharacteristic
490C3×C4#93811yescharacteristic
491C3×C4#93811yescharacteristic
492C3×C4C22×D1211yescharacteristic
493C3×C4C2×D3×D411yescharacteristic
494C3×C4C22×#6711yescharacteristic
495C3×C4C22×#6711yescharacteristic
496Dic3—22no—
497Dic3—42no—
498C32#306711yescharacteristic, complemented, Sylow
499C23—61no—
500C23—62no—
501C23#379511yescharacteristic
502Q8—32no—
503Q8—61no—
504Q8—62no—
505Q8—62no—
506D4—32no—
507D4—62no—
508D4—62no—
509D4—62no—
510D4—62no—
511D4—61no—
512D4—122no—
513D4—122no—
514C2×C4—61no—
515C2×C4—62no—
516C2×C4—62no—
517C2×C4—62no—
518C2×C4—122no—
519C2×C4—122no—
520C2×C4#379511yescharacteristic
521C2×C4D3×D1211yescharacteristic
522C2×C4D3×D1211yescharacteristic
523C2×C4C2×#62511yescharacteristic
524C2×C4C2×#62511yescharacteristic
525C2×C4C22×D3211yescharacteristic
526C8—62no—
527C8—184no—
528C8C2×#62511yescharacteristic
529C8C2×#62511yescharacteristic
530C8C2×#62511yescharacteristic
531C8C2×#62511yescharacteristic
532C2×C3—22no—
533C2×C3—21no—
534C2×C3—21no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—21no—
539C2×C3—21no—
540C2×C3—41no—
541C2×C3—41no—
542C2×C3—122no—
543C2×C3—242no—
544C2×C3C2×#93011yescharacteristic
545C2×C3C2×#93811yescharacteristic
546D3—42no—
547D3—82no—
548C22—41no—
549C22—62no—
550C22—122no—
551C22—122no—
552C22—242no—
553C22#6390811yescharacteristic
554C22#6390811yescharacteristic
555C22C2×#379511yescharacteristic
556C4—62no—
557C4—122no—
558C4#6390811yescharacteristic
559C4#6390811yescharacteristic
560C4C2×D3×D1211yescharacteristic
561C4C22×#62511yescharacteristic
562C3—21no—
563C3#8380511yescharacteristic, complemented
564C3#8392811yescharacteristic, complemented
565C2—21no—
566C2—21no—
567C2—21no—
568C2—122no—
569C2—242no—
570C2C2×#6390811yescharacteristic
subgroupG/H
centerC4#63908
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC2×C32C2×#121
hypercenterC22×C8D32
hypocenterC32#3067
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#904C2semidirect
2. C2×C3×#901C2semidirect
3. #10594786C2semidirect
4. C2×#63646C2semidirect
5. #10591076C2semidirect
6. #10590930C2semidirect
7. #10590926C2semidirect
8. #10590925C2semidirect
16. C2×C3×Dic12C22semidirect
21. C2×C3×D24C22semidirect
22. C2×C3×#204C22semidirect
34. #63646C22semidirect
35. #63646C22semidirect
36. #63560C22semidirect
37. #63558C22semidirect
42. C2×#904D3semidirect
43. C2×#901D3semidirect
134. C2×Dic12C2×D3semidirect
139. C2×D24C2×D3semidirect
140. C2×#204C2×D3semidirect
498. C32#3067semidirect
563. C3#83805semidirect
564. C3#83928semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9042
C2×C3×#9012
#105947862
C2×#636462
#105910762
#105909302
#105909262
#105909252
#839283
#838053