Finite Group Databasebeta

← C2×#10590984 #11867940

Subgroups — C2×#10590984 #11867940

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×#908C211yesmaximal, characteristic, complemented
2C2×#63825C211yesmaximal, characteristic, complemented
3C22×#3714C211yesmaximal, characteristic, complemented
4C2×#63814C211yesmaximal, characteristic, complemented
5C2×#63650C211yesmaximal, characteristic, complemented
6C2×C3×#822C211yesmaximal, characteristic, complemented
7C2×#63558C211yesmaximal, characteristic, complemented
8#10590984C218yesmaximal, direct product factor
9C2×#5199—31nomaximal
10C2×#4897—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×C32×M16C2211yescharacteristic
15C2×#3748C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C22×C3×C3⋊C8C2211yescharacteristic
18C3×#908—22no—
19C3×#908C2214yescomplemented
20C2×C3×D24—21no—
21C2×C3×#204—21no—
22C2×#3717—21no—
23#63825—22no—
24#63825C2214yescomplemented
25C2×#3714—21no—
26C2×#3714—21no—
27C2×#3714—22no—
28C2×#3714—21no—
29C2×#3714C2214yescomplemented
30C2×#3711—21no—
31#63814—22no—
32#63814C2214yescomplemented
33C2×D3×C3⋊C8—21no—
34#63650C2214yescomplemented
35C3×#822C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×#949—31no—
39C2×#948—31no—
40C22×#213—31no—
41C2×#908—31no—
42C2×#908D311yescharacteristic, complemented
43C22×D24—31no—
44C2×#901—31no—
45C2×C3×#108—31no—
46C2×#833—31no—
47#5199—38no—
48C2×#823—31no—
49C2×#823—31no—
50C2×#823—31no—
51C2×#823—61no—
52C2×#822D311yescharacteristic, complemented
53#4897—38no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C22×C32×C4C2311yescharacteristic
57C2×C4⋊(C3⋊D3)—21no—
58C2×C4⋊(C3⋊D3)—21no—
59C2×C4⋊(C3⋊D3)—21no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—21no—
62C2×C4⋊(C3⋊D3)C2312yes—
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
77C32×M16—21no—
78C32×M16C2312yes—
79C2×C32×C8—21no—
80#3748—21no—
81#3748C2312yes—
82C2×C3⋊(C3⋊C8)—21no—
83C3×#208—21no—
84C3×#208C2312yes—
85C2×C3×C3⋊C8—21no—
86C2×C3×C3⋊C8D411yescharacteristic
87C2×C3×C3⋊C8D412yes—
88C2×C3×C3⋊C8D411yescharacteristic
89C2×C3×C3⋊C8C2312yes—
90C3×D24—24no—
91C3×#204—24no—
92#3717—24no—
93#3714—24no—
94#3714—24no—
95#3714—24no—
96#3711—24no—
97D3×C3⋊C8—24no—
98C2×#472—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—31no—
101C2×#235C2×D311yescharacteristic
102C22×D12—31no—
103C22×D12—31no—
104C22×D12—61no—
105C22×D12C2×D311yescharacteristic
106C3×AGL(1,ℤ/8)—34no—
107C3×AGL(1,ℤ/8)—62no—
108C2×C3×SD16—61no—
109C2×C3×D8—61no—
110C2×C3×M16—21no—
111C2×C3×M16—31no—
112C2×C3×M16C2×D311yescharacteristic
113C2×C3×M16C2×D311yescharacteristic
114C22×C3×C8—31no—
115#949—34no—
116#949—62no—
117#948—34no—
118#948—62no—
119C2×#215—61no—
120C2×#213—34no—
121C2×#213—61no—
122C2×#213—61no—
123C2×#213—61no—
124C2×#213—62no—
125C2×#208—31no—
126C2×#208—31no—
127C2×#208—61no—
128C2×#208—61no—
129C2×#208C2×D311yescharacteristic
130C22×C3⋊C8—61no—
131C22×C3⋊C8C2×D311yescharacteristic
132#908—22no—
133#908—34no—
134#908—62no—
135#908C2×D314yescomplemented
136C2×D24—21no—
137C2×D24—34no—
138C2×D24—61no—
139C2×D24—61no—
140C2×D24—62no—
141C2×D24—61no—
142C2×#204—21no—
143C2×#204—61no—
144#901—34no—
145#901—62no—
146C2×ΓL(1,𝔽25)—61no—
147C2×D3×C8—61no—
148C3×#108—34no—
149#833—34no—
150#823—34no—
151#823—34no—
152#823—34no—
153#823—64no—
154#822C2×D314yescomplemented
155C23×C32#4111yescharacteristic
156C22×C3⋊D3—22no—
157C22×C3⋊D3—41no—
158C22×C3⋊D3—41no—
159C22×C3⋊D3—82no—
160C22×C3×D3—21no—
161C22×C3×D3—22no—
162C22×C3×D3—41no—
163C22×C3×D3—41no—
164C22×C3×D3—82no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4#4111yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C4⋊(C3⋊D3)—22no—
172C4⋊(C3⋊D3)—22no—
173C4⋊(C3⋊D3)—41no—
174C4⋊(C3⋊D3)—41no—
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—
188C32×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—91no—
196C2×#131—91no—
197#472—98no—
198C2×#108—31no—
199C2×#100—91no—
200C2×#100—91no—
201C24×C3—61no—
202C23×D3—21no—
203C23×D3—62no—
204C23×D3—61no—
205C23×D3—61no—
206C3×#41—32no—
207C3×#41—32no—
208C3×#41—61no—
209C3×#41—61no—
210C2×C3×Q8—31no—
211C2×C3×D4—31no—
212C2×C3×D4—32no—
213C2×C3×D4—61no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C2×C3×D4—61no—
219C22×C3×C4—21no—
220C22×C3×C4—61no—
221C22×C3×C4C22×D311yescharacteristic
222C22×C3×C4C22×D311yescharacteristic
223C2×#67—21no—
224#235—21no—
225#235—21no—
226#235#6712yes—
227#235C22×D312yes—
228C2×D12—21no—
229C2×D12—21no—
230C2×D12—21no—
231C2×D12—21no—
232C2×D12—21no—
233C2×D12—32no—
234C2×D12—32no—
235C2×D12—62no—
236C2×D12—61no—
237C2×D12—61no—
238C2×D12—61no—
239C2×D12—61no—
240C2×D12—61no—
241C2×D12—61no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—62no—
245C2×D12—61no—
246C2×D12—61no—
247C2×D12—121no—
248C2×D12—121no—
249C2×D12—121no—
250C2×D12—121no—
251C2×D12#6711yescharacteristic
252C2×D12C22×D312yes—
253C2×C4×D3—21no—
254C2×Dic6#6711yescharacteristic
255C3×SD16—64no—
256C3×D8—64no—
257C3×M16—21no—
258C3×M16—21no—
259C3×M16—22no—
260C3×M16—32no—
261C3×M16—41no—
262C3×M16—61no—
263C3×M16C22×D312yes—
264C3×M16C22×D312yes—
265C2×C3×C8—21no—
266C2×C3×C8—21no—
267C2×C3×C8—31no—
268C2×C3×C8—31no—
269C2×C3×C8—32no—
270C2×C3×C8—32no—
271C2×C3×C8—41no—
272C2×C3×C8—61no—
273#215—64no—
274#213—64no—
275#213—64no—
276#213—64no—
277#208—21no—
278#208—32no—
279#208—32no—
280#208—62no—
281#208—61no—
282#208—61no—
283#208—64no—
284#208—121no—
285#208C22×D312yes—
286C2×C3⋊C8—21no—
287C2×C3⋊C8—61no—
288C2×C3⋊C8—61no—
289C2×C3⋊C8—64no—
290C2×C3⋊C8—121no—
291C2×C3⋊C8D1211yescharacteristic
292C2×C3⋊C8D1211yescharacteristic
293C2×C3⋊C8D1212yes—
294C2×C3⋊C8C22×D312yes—
295D24—24no—
296D24—64no—
297D24—64no—
298D24—64no—
299#204—24no—
300#204—64no—
301ΓL(1,𝔽25)—64no—
302D3×C8—64no—
303C22×C32—22no—
304C22×C32#12111yescharacteristic
305C22×C32#12111yescharacteristic
306C22×C32C2×#4111yescharacteristic
307C2×C3⋊D3—42no—
308C2×C3⋊D3—82no—
309C2×C3⋊D3—82no—
310C2×C3⋊D3—82no—
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×D4—91no—
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—61no—
332C2×D8—94no—
333C2×D8—181no—
334C2×D8—181no—
335C2×D8—182no—
336C2×D8—181no—
337#131—94no—
338#131—182no—
339C2×M16—31no—
340C2×M16—91no—
341C2×M16—181no—
342C2×M16D3211yescharacteristic
343C22×C8—31no—
344C22×C8—181no—
345#108—34no—
346#100—94no—
347#100—94no—
348C23×C3—21no—
349C23×C3—61no—
350C23×C3—62no—
351C23×C3—121no—
352C23×C3—121no—
353C23×C3—242no—
354C23×C3#23711yescharacteristic
355C23×C3#23911yescharacteristic
356C22×D3—21no—
357C22×D3—22no—
358C22×D3—41no—
359C22×D3—41no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—82no—
364C22×D3—122no—
365C22×D3—122no—
366C22×D3—121no—
367C22×D3—121no—
368C22×D3—121no—
369C22×D3—121no—
370C22×D3—242no—
371C22×D3—242no—
372C22×D3—244no—
373C3×Q8—32no—
374C3×Q8—61no—
375C3×D4—32no—
376C3×D4—62no—
377C3×D4—62no—
378C3×D4—61no—
379C3×D4—62no—
380C3×D4—62no—
381C3×D4—121no—
382C3×D4—121no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—21no—
386C2×C3×C4—21no—
387C2×C3×C4—21no—
388C2×C3×C4—21no—
389C2×C3×C4—61no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4C2×D1211yescharacteristic
393C2×C3×C4C2×D1211yescharacteristic
394C2×C3×C4D3×D411yescharacteristic
395C2×C3×C4D3×D411yescharacteristic
396C2×C3×C4D3×D411yescharacteristic
397C2×C3×C4D3×D411yescharacteristic
398C2×C3×C4#23711yescharacteristic
399C2×C3×C4#23911yescharacteristic
400C2×C3×C4C2×#6711yescharacteristic
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C23×D311yescharacteristic
403C2×C3×C4C23×D311yescharacteristic
404#67—22no—
405#67—22no—
406C2×Dic3—21no—
407D12—21no—
408D12—22no—
409D12—22no—
410D12—41no—
411D12—41no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—62no—
416D12—122no—
417D12—122no—
418D12—122no—
419D12—122no—
420D12—121no—
421D12—121no—
422D12—121no—
423D12—121no—
424D12C2×#6712yes—
425C4×D3—22no—
426C4×D3—22no—
427Dic6—21no—
428Dic6C2×#6712yes—
429C3×C8—22no—
430C3×C8—22no—
431C3×C8—32no—
432C3×C8—32no—
433C3×C8—42no—
434C3×C8—62no—
435C3⋊C8—22no—
436C3⋊C8—62no—
437C3⋊C8—62no—
438C3⋊C8—122no—
439C3⋊C8C2×D1212yes—
440C3⋊C8C2×D1212yes—
441C2×C32—21no—
442C2×C32—21no—
443C2×C32#47212yescomplemented
444C2×C32C2×#12111yescharacteristic
445C3⋊D3—82no—
446C3×D3—42no—
447C3×D3—82no—
448C24—61no—
449C24—181no—
450#41—32no—
451#41—32no—
452#41—61no—
453#41—61no—
454C2×Q8—31no—
455C2×D4—32no—
456C2×D4—31no—
457C2×D4—61no—
458C2×D4—61no—
459C2×D4—61no—
460C2×D4—61no—
461C2×D4—61no—
462C2×D4—61no—
463C2×D4—92no—
464C2×D4—181no—
465C2×D4—181no—
466C2×D4—181no—
467C2×D4—181no—
468C2×D4—181no—
469C22×C4—61no—
470C22×C4C2×D3211yescharacteristic
471SD16—64no—
472SD16—184no—
473D8—64no—
474D8—184no—
475D8—184no—
476D8—184no—
477M16—21no—
478M16—32no—
479M16—61no—
480M16—92no—
481M16—184no—
482M16—181no—
483M16C2×D3212yes—
484C2×C8—21no—
485C2×C8—32no—
486C2×C8—31no—
487C2×C8—31no—
488C2×C8—32no—
489C2×C8—61no—
490C2×C8—184no—
491C2×C8—181no—
492C22×C3—22no—
493C22×C3—22no—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—42no—
498C22×C3—62no—
499C22×C3—122no—
500C22×C3—122no—
501C22×C3—242no—
502C22×C3—242no—
503C22×C3—242no—
504C22×C3#89511yescharacteristic
505C22×C3#89511yescharacteristic
506C22×C3#93911yescharacteristic
507C22×C3#93911yescharacteristic
508C22×C3C2×#23711yescharacteristic
509C22×C3C2×#23911yescharacteristic
510C2×D3—22no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—82no—
514C2×D3—82no—
515C2×D3—82no—
516C2×D3—124no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—242no—
520C2×D3—242no—
521C2×D3—244no—
522C2×D3—244no—
523C2×D3—242no—
524C2×D3—242no—
525C2×D3—242no—
526C2×D3—242no—
527C2×D3—244no—
528C3×C4—21no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—21no—
532C3×C4—62no—
533C3×C4#89511yescharacteristic
534C3×C4#89511yescharacteristic
535C3×C4#93911yescharacteristic
536C3×C4#93911yescharacteristic
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—22no—
542C32C2×#47211yescharacteristic, complemented, Sylow
543C23—61no—
544C23—62no—
545C23—121no—
546C23—121no—
547C23—182no—
548C23—242no—
549C23—361no—
550C23—361no—
551C23—722no—
552C23#379611yescharacteristic
553Q8—32no—
554Q8—61no—
555D4—32no—
556D4—62no—
557D4—62no—
558D4—62no—
559D4—62no—
560D4—61no—
561D4—121no—
562D4—121no—
563D4—182no—
564D4—182no—
565D4—361no—
566D4—361no—
567C2×C4—61no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4#379611yescharacteristic
571C2×C4D3×D1211yescharacteristic
572C2×C4D3×D1211yescharacteristic
573C2×C4D3×#6711yescharacteristic
574C2×C4D3×#6711yescharacteristic
575C2×C4C22×D3211yescharacteristic
576C8—22no—
577C8—32no—
578C8—32no—
579C8—62no—
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—122no—
590C2×C3—242no—
591C2×C3#489712yescomplemented
592C2×C3#519912yescomplemented
593C2×C3C2×#89511yescharacteristic
594C2×C3C2×#93911yescharacteristic
595D3—42no—
596D3—82no—
597D3—244no—
598D3—242no—
599D3—242no—
600C22—22no—
601C22—62no—
602C22—122no—
603C22—122no—
604C22—242no—
605C22—242no—
606C22—242no—
607C22—362no—
608C22—722no—
609C22—722no—
610C22—722no—
611C22#6388611yescharacteristic
612C22#6388611yescharacteristic
613C22C2×#379611yescharacteristic
614C4—62no—
615C4#6388611yescharacteristic
616C4#6388611yescharacteristic
617C4C2×D3×D1211yescharacteristic
618C4C2×D3×#6711yescharacteristic
619C3—21no—
620C3C2×#489711yescharacteristic, complemented
621C3C2×#519911yescharacteristic, complemented
622C2—21no—
623C2—21no—
624C2—122no—
625C2—242no—
626C2—722no—
627C2#1059098412yesdirect product factor
628C2C2×#6388611yescharacteristic
subgroupG/H
centerC22#63886
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32#121
hypercenterC2×M16D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
1. C2×C3×#908C2semidirect
2. C2×#63825C2semidirect
3. C22×#3714C2semidirect
4. C2×#63814C2semidirect
5. C2×#63650C2semidirect
6. C2×C3×#822C2semidirect
7. C2×#63558C2semidirect
8. #10590984C2direct (N × H)
19. C3×#908C22semidirect
24. #63825C22semidirect
29. C2×#3714C22semidirect
32. #63814C22semidirect
34. #63650C22semidirect
35. C3×#822C22semidirect
36. #63558C22semidirect
42. C2×#908D3semidirect
52. C2×#822D3semidirect
135. #908C2×D3semidirect
154. #822C2×D3semidirect
443. C2×C32#472semidirect
542. C32C2×#472semidirect
591. C2×C3#4897semidirect
592. C2×C3#5199semidirect
620. C3C2×#4897semidirect
621. C3C2×#5199semidirect
627. C2#10590984direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C3×#9082
C2×#638252
C22×#37142
C2×#638142
C2×#636502
C2×C3×#8222
C2×#635582
#105909842
C2×#51993
C2×#48973