Finite Group Databasebeta

← C2×#10591505 #11867932

Subgroups — C2×#10591505 #11867932

Order 1152.

1069 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×#932C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63823C211yesmaximal, characteristic, complemented
4C2×#63814C211yesmaximal, characteristic, complemented
5C2×#63660C211yesmaximal, characteristic, complemented
6#10591505C218yesmaximal, direct product factor
7C2×#63577C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5199—31nomaximal
10C2×#5160—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#214—21no—
17C3×#932—22no—
18C3×#932C2214yescomplemented
19C2×C3×#213—21no—
20C2×C3×#213—21no—
21C2×C3×#213—22no—
22C2×C3×#213—21no—
23C2×C3×#213C2214yescomplemented
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C2×#3715—21no—
27#63823—22no—
28#63823C2214yescomplemented
29C2×#3713—21no—
30C2×#3711—21no—
31#63814—22no—
32#63814C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34#63660C2214yescomplemented
35#63577C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C22×C3×D8—31no—
39C2×#949—31no—
40C2×#948—31no—
41C2×#932—31no—
42C2×#932D311yescharacteristic, complemented
43C22×#213D311yescharacteristic, complemented
44C2×#901—31no—
45C2×#833—31no—
46C2×#833—31no—
47C2×#833—31no—
48C2×#833—61no—
49#5199—38no—
50#5160—38no—
51C2×#823—31no—
52C2×#822—31no—
53C2×#819—31no—
54C24×C32—21no—
55C23×C3×D3—21no—
56C2×C32×D4—21no—
57C2×C32×D4—21no—
58C2×C32×D4—21no—
59C2×C32×D4—21no—
60C2×C32×D4—21no—
61C2×C32×D4C2312yes—
62C22×C32×C4C2311yescharacteristic
63C2×C3×#67—21no—
64C3×#235—21no—
65C3×#235—21no—
66C3×#235D412yes—
67C3×#235C2312yes—
68C2×C3×D12—21no—
69C2×C3×D12—21no—
70C2×C3×D12—21no—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12D411yescharacteristic
74C2×C3×D12C2312yes—
75C2×C3×C4×D3—21no—
76C2×C3×Dic6D411yescharacteristic
77#3748—21no—
78#3748—21no—
79#3748C2312yes—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C2×C3⋊(C3⋊C8)—21no—
83C3×#214—24no—
84C3×#213—24no—
85C3×#213—24no—
86C3×#213—24no—
87C3×#208—21no—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D412yes—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94#3715—24no—
95#3713—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#472—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—21no—
101C22×C3×D4—31no—
102C22×C3×D4C2×D311yescharacteristic
103C22×C3×D4C2×D311yescharacteristic
104C2×#235C2×D311yescharacteristic
105C22×D12C2×D311yescharacteristic
106C3×AGL(1,ℤ/8)—34no—
107C3×AGL(1,ℤ/8)—62no—
108C2×C3×SD16—61no—
109C2×C3×D8—34no—
110C2×C3×D8—61no—
111C2×C3×D8—61no—
112C2×C3×D8—62no—
113C2×C3×D8—61no—
114C2×C3×M16—31no—
115C22×C3×C8—31no—
116#949—34no—
117#949—62no—
118#948—34no—
119#948—62no—
120C2×#215—61no—
121C2×#214—21no—
122C2×#214—61no—
123#932—22no—
124#932—34no—
125#932—62no—
126#932C2×D314yescomplemented
127C2×#213—21no—
128C2×#213—21no—
129C2×#213—21no—
130C2×#213—22no—
131C2×#213—61no—
132C2×#213—61no—
133C2×#213C2×D314yescomplemented
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—31no—
137C2×#208—31no—
138C2×#208—61no—
139C2×#208—61no—
140C2×#208—61no—
141C2×#208C2×D311yescharacteristic
142C22×C3⋊C8—61no—
143C22×C3⋊C8C2×D311yescharacteristic
144#901—34no—
145#901—62no—
146C2×ΓL(1,𝔽25)—61no—
147C2×D3×C8—61no—
148#833—34no—
149#833—34no—
150#833—34no—
151#833—64no—
152#823—34no—
153#822—34no—
154#819—34no—
155C23×C32—22no—
156C23×C32—41no—
157C23×C32—41no—
158C23×C32—82no—
159C23×C32#4111yescharacteristic
160C22×C3×D3—21no—
161C22×C3×D3—22no—
162C22×C3×D3—41no—
163C22×C3×D3—41no—
164C22×C3×D3—82no—
165C32×D4—22no—
166C32×D4—22no—
167C32×D4—41no—
168C32×D4—41no—
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4#4111yescharacteristic
174C2×C32×C4C2411yescharacteristic
175C3×#67—22no—
176C3×#67—22no—
177C2×C3×Dic3—21no—
178C3×D12—21no—
179C3×D12—22no—
180C3×D12—22no—
181C3×D12—41no—
182C3×D12—41no—
183C3×D12C2×D412yes—
184C3×C4×D3—22no—
185C3×C4×D3—22no—
186C3×Dic6—21no—
187C3×Dic6C2×D412yes—
188C3⋊(C3⋊C8)—22no—
189C3⋊(C3⋊C8)—22no—
190C3×C3⋊C8—22no—
191C3×C3⋊C8C2×D412yes—
192C3×C3⋊C8C2×D412yes—
193C2×AGL(1,ℤ/8)—31no—
194C2×AGL(1,ℤ/8)—91no—
195C22×D8—31no—
196C2×#131—91no—
197#472—98no—
198C2×#108—91no—
199C2×#100—91no—
200C2×#100—91no—
201C24×C3—22no—
202C24×C3—21no—
203C24×C3—21no—
204C24×C3—61no—
205C23×D3—21no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C2×C3×Q8—31no—
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—21no—
214C2×C3×D4—21no—
215C2×C3×D4—21no—
216C2×C3×D4—21no—
217C2×C3×D4—21no—
218C2×C3×D4—21no—
219C2×C3×D4—21no—
220C2×C3×D4—21no—
221C2×C3×D4—21no—
222C2×C3×D4—22no—
223C2×C3×D4—31no—
224C2×C3×D4—32no—
225C2×C3×D4—41no—
226C2×C3×D4—41no—
227C2×C3×D4—41no—
228C2×C3×D4—41no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4—61no—
232C2×C3×D4—61no—
233C2×C3×D4—61no—
234C2×C3×D4—61no—
235C2×C3×D4C22×D312yes—
236C2×C3×D4C22×D312yes—
237C22×C3×C4—21no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242#235—21no—
243#235—21no—
244#235#6712yes—
245#235C22×D312yes—
246C2×D12—21no—
247C2×D12—21no—
248C2×D12—21no—
249C2×D12—21no—
250C2×D12—21no—
251C2×D12#6711yescharacteristic
252C2×D12C22×D312yes—
253C2×C4×D3—21no—
254C2×Dic6#6711yescharacteristic
255C3×SD16—64no—
256C3×D8—64no—
257C3×D8—64no—
258C3×D8—64no—
259C3×M16—32no—
260C3×M16—61no—
261C2×C3×C8—31no—
262C2×C3×C8—31no—
263C2×C3×C8—32no—
264C2×C3×C8—32no—
265C2×C3×C8—61no—
266#215—64no—
267#214—24no—
268#214—64no—
269#213—24no—
270#213—24no—
271#213—24no—
272#213—64no—
273#213—64no—
274#208—21no—
275#208—32no—
276#208—32no—
277#208—32no—
278#208—32no—
279#208—62no—
280#208—62no—
281#208—61no—
282#208—61no—
283#208—61no—
284#208—61no—
285#208—64no—
286#208—121no—
287#208—121no—
288#208C22×D312yes—
289C2×C3⋊C8—21no—
290C2×C3⋊C8—61no—
291C2×C3⋊C8—61no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8—61no—
294C2×C3⋊C8—64no—
295C2×C3⋊C8—121no—
296C2×C3⋊C8—121no—
297C2×C3⋊C8#6711yescharacteristic
298C2×C3⋊C8#6711yescharacteristic
299C2×C3⋊C8#6712yes—
300C2×C3⋊C8C22×D312yes—
301ΓL(1,𝔽25)—64no—
302D3×C8—64no—
303C22×C32—22no—
304C22×C32—42no—
305C22×C32—82no—
306C22×C32—82no—
307C22×C32—82no—
308C22×C32#12111yescharacteristic
309C22×C32#12111yescharacteristic
310C22×C32C2×#4111yescharacteristic
311C2×C3×D3—22no—
312C2×C3×D3—42no—
313C2×C3×D3—42no—
314C2×C3×D3—82no—
315C2×C3×D3—82no—
316C2×C3×D3—82no—
317C32×C4#12111yescharacteristic
318C32×C4#12111yescharacteristic
319C32×C4C22×D411yescharacteristic
320C32×C4C22×D411yescharacteristic
321C3×Dic3—22no—
322C2×#41—31no—
323C22×D4—31no—
324C22×D4D3211yescharacteristic
325AGL(1,ℤ/8)—34no—
326AGL(1,ℤ/8)—62no—
327AGL(1,ℤ/8)—94no—
328AGL(1,ℤ/8)—182no—
329C2×SD16—61no—
330C2×SD16—181no—
331C2×D8—34no—
332C2×D8—61no—
333C2×D8—61no—
334C2×D8—62no—
335C2×D8—61no—
336C2×D8—181no—
337#131—94no—
338#131—182no—
339C2×M16—31no—
340C2×M16—91no—
341C2×M16—91no—
342C2×M16—181no—
343C22×C8—31no—
344C22×C8—181no—
345#108—94no—
346#100—94no—
347#100—94no—
348C23×C3—24no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—21no—
352C23×C3—42no—
353C23×C3—42no—
354C23×C3—41no—
355C23×C3—41no—
356C23×C3—41no—
357C23×C3—41no—
358C23×C3—61no—
359C23×C3—62no—
360C23×C3—82no—
361C23×C3—82no—
362C23×C3—84no—
363C23×C3—121no—
364C23×C3—121no—
365C23×C3—242no—
366C23×C3#23711yescharacteristic
367C23×C3#23711yescharacteristic
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—41no—
371C22×D3—41no—
372C22×D3—82no—
373C3×Q8—32no—
374C3×Q8—61no—
375C3×D4—22no—
376C3×D4—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—32no—
380C3×D4—42no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—41no—
388C3×D4—62no—
389C3×D4—62no—
390C3×D4—61no—
391C3×D4—62no—
392C3×D4—62no—
393C3×D4—121no—
394C3×D4—121no—
395C2×C3×C4—21no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—61no—
402C2×C3×C4—62no—
403C2×C3×C4—62no—
404C2×C3×C4D3×D411yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4#23711yescharacteristic
409C2×C3×C4#23711yescharacteristic
410C2×C3×C4C2×#6711yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6711yescharacteristic
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—22no—
417#67—22no—
418C2×Dic3—21no—
419D12—21no—
420D12—22no—
421D12—22no—
422D12—41no—
423D12—41no—
424D12C2×#6712yes—
425C4×D3—22no—
426C4×D3—22no—
427Dic6—21no—
428Dic6C2×#6712yes—
429C3×C8—32no—
430C3×C8—32no—
431C3×C8—62no—
432C3⋊C8—22no—
433C3⋊C8—62no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C3⋊C8—122no—
438C3⋊C8—122no—
439C3⋊C8C2×#6712yes—
440C3⋊C8C2×#6712yes—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32—82no—
444C2×C32#47212yescomplemented
445C2×C32C2×#12111yescharacteristic
446C3×D3—42no—
447C3×D3—82no—
448C24—21no—
449C24—61no—
450#41—32no—
451#41—32no—
452#41—61no—
453#41—61no—
454C2×Q8—31no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—32no—
461C2×D4—31no—
462C2×D4—61no—
463C2×D4—61no—
464C2×D4—61no—
465C2×D4—61no—
466C2×D4—61no—
467C2×D4—61no—
468C2×D4C2×D3212yes—
469C22×C4—61no—
470C22×C4C2×D3211yescharacteristic
471SD16—64no—
472SD16—184no—
473D8—64no—
474D8—64no—
475D8—64no—
476D8—184no—
477M16—32no—
478M16—61no—
479M16—92no—
480M16—92no—
481M16—184no—
482M16—181no—
483M16—181no—
484C2×C8—32no—
485C2×C8—31no—
486C2×C8—31no—
487C2×C8—32no—
488C2×C8—61no—
489C2×C8—184no—
490C2×C8—181no—
491C2×C8—181no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—42no—
498C22×C3—44no—
499C22×C3—42no—
500C22×C3—42no—
501C22×C3—62no—
502C22×C3—82no—
503C22×C3—82no—
504C22×C3—82no—
505C22×C3—82no—
506C22×C3—84no—
507C22×C3—84no—
508C22×C3—84no—
509C22×C3—82no—
510C22×C3—82no—
511C22×C3—122no—
512C22×C3—122no—
513C22×C3—242no—
514C22×C3—242no—
515C22×C3—242no—
516C22×C3#93811yescharacteristic
517C22×C3#93811yescharacteristic
518C22×C3#93911yescharacteristic
519C22×C3#93911yescharacteristic
520C22×C3C2×#23711yescharacteristic
521C22×C3C2×#23711yescharacteristic
522C2×D3—22no—
523C2×D3—42no—
524C2×D3—42no—
525C2×D3—82no—
526C2×D3—82no—
527C2×D3—82no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—62no—
533C3×C4#93811yescharacteristic
534C3×C4#93811yescharacteristic
535C3×C4#93911yescharacteristic
536C3×C4#93911yescharacteristic
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—22no—
542C32C2×#47211yescharacteristic, complemented, Sylow
543C23—22no—
544C23—41no—
545C23—41no—
546C23—61no—
547C23—62no—
548C23—82no—
549C23—121no—
550C23—121no—
551C23—242no—
552C23#380511yescharacteristic
553Q8—32no—
554Q8—61no—
555D4—22no—
556D4—22no—
557D4—32no—
558D4—41no—
559D4—41no—
560D4—62no—
561D4—62no—
562D4—62no—
563D4—62no—
564D4—61no—
565D4—121no—
566D4—121no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4#380511yescharacteristic
571C2×C4D3×#6711yescharacteristic
572C2×C4D3×#6711yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4D3×#6711yescharacteristic
575C2×C4C22×D3211yescharacteristic
576C8—32no—
577C8—32no—
578C8—62no—
579C8—182no—
580C8—182no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—21no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—41no—
588C2×C3—41no—
589C2×C3—84no—
590C2×C3—82no—
591C2×C3—82no—
592C2×C3—122no—
593C2×C3—242no—
594C2×C3#516012yescomplemented
595C2×C3#519912yescomplemented
596C2×C3C2×#93811yescharacteristic
597C2×C3C2×#93911yescharacteristic
598D3—42no—
599D3—82no—
600C22—22no—
601C22—42no—
602C22—62no—
603C22—82no—
604C22—82no—
605C22—82no—
606C22—122no—
607C22—122no—
608C22—242no—
609C22—242no—
610C22—242no—
611C22#6397011yescharacteristic
612C22#6397011yescharacteristic
613C22C2×#380511yescharacteristic
614C4—62no—
615C4#6397011yescharacteristic
616C4#6397011yescharacteristic
617C4C2×D3×#6711yescharacteristic
618C4C2×D3×#6711yescharacteristic
619C3—21no—
620C3C2×#516011yescharacteristic, complemented
621C3C2×#519911yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—82no—
625C2—122no—
626C2—242no—
627C2#1059150512yesdirect product factor
628C2C2×#6397011yescharacteristic
subgroupG/H
centerC22#63970
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32#121
hypercenterC22×D4D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#932C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63823C2semidirect
4. C2×#63814C2semidirect
5. C2×#63660C2semidirect
6. #10591505C2direct (N × H)
7. C2×#63577C2semidirect
8. C2×#63558C2semidirect
18. C3×#932C22semidirect
23. C2×C3×#213C22semidirect
28. #63823C22semidirect
32. #63814C22semidirect
34. #63660C22semidirect
35. #63577C22semidirect
36. #63558C22semidirect
42. C2×#932D3semidirect
43. C22×#213D3semidirect
126. #932C2×D3semidirect
133. C2×#213C2×D3semidirect
444. C2×C32#472semidirect
542. C32C2×#472semidirect
594. C2×C3#5160semidirect
595. C2×C3#5199semidirect
620. C3C2×#5160semidirect
621. C3C2×#5199semidirect
627. C2#10591505direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9322
C22×C3×#2132
C2×#638232
C2×#638142
C2×#636602
#105915052
C2×#635772
C2×#635582
C2×#51993
C2×#51603