Finite Group Databasebeta

← C2×#10594762 #11918774

Subgroups — C2×#10594762 #11918774

Order 1152.

3101 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#239C212yesmaximal, complemented
2C2×#64128C211yesmaximal, characteristic, complemented
3C2×C3×#918C212yesmaximal, complemented
4C2×#63950C212yesmaximal, complemented
5C2×#63948C212yesmaximal, complemented
6C2×#63939C212yesmaximal, complemented
7#10594762C2116yesmaximal, direct product factor
8C2×#63809C211yesmaximal, characteristic, complemented
9C2×#63794C212yesmaximal, complemented
10C2×#63791C211yesmaximal, characteristic, complemented
11C2×#5777—32nomaximal
12C2×#3832C2212yescomplemented
13C2×C3×#239C2212yes—
14C2×C3×D3×Q8C2212yescomplemented
15D3×#239—28no—
16D3×#239C22116yescomplemented
17C2×D3×D12—22no—
18C2×D3×D12C2212yescomplemented
19C2×C4×D32—22no—
20C2×C4×D32C2211yescharacteristic
21C2×#3799—22no—
22C2×#3799C2212yes—
23C2×#3796—22no—
24C2×#3796C2212yescomplemented
25C2×C32×Q16C2211yescharacteristic, complemented
26C2×#3755C2212yescomplemented
27#64128C2218yescomplemented
28C2×#3745C2211yescharacteristic, complemented
29C2×C8×C3⋊D3C2211yescharacteristic, complemented
30C2×C3×#216C2212yescomplemented
31C2×C3×#215C2212yescomplemented
32C3×#918C22116yescomplemented
33C2×C3×#204C2212yescomplemented
34C2×C3×ΓL(1,𝔽25)C2212yescomplemented
35#63950C22116yescomplemented
36#63948C22116yescomplemented
37#63939C22116yescomplemented
38C2×#3718C2211yescharacteristic, complemented
39C2×#3717C2212yescomplemented
40C2×#3714C2212yescomplemented
41C2×#3713C2211yescharacteristic, complemented
42C2×#3711C2212yescomplemented
43C2×#3710C2211yescharacteristic, complemented
44#63809C2218yescomplemented
45#63794C22116yescomplemented
46#63791C2218yescomplemented
47C2×D3×#41—32no—
48C22×#239—32no—
49C2×C3×#137—32no—
50C2×#949—32no—
51C2×#942—32no—
52#5777—332no—
53C2×#919—32no—
54C2×#919—32no—
55C2×#919—61no—
56C2×#918—32no—
57C2×#918D312yescomplemented
58C2×#916—32no—
59C2×#916—32no—
60C2×#914—32no—
61C2×#914—32no—
62C2×#908—32no—
63C2×D3×M16—32no—
64C22×D32—22no—
65C22×D32D411yescharacteristic
66C2×C32×Q8C2312yes—
67#3832—24no—
68#3832C2318yescomplemented
69C2×C4⋊(C3⋊D3)—22no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C4×C3⋊D3—22no—
72C2×C4×C3⋊D3C2311yescharacteristic
73C3×#239—24no—
74C3×#239C2318yes—
75C3×D3×Q8—24no—
76C3×D3×Q8C2318yescomplemented
77C2×C3×D12—22no—
78C2×C3×D12C2312yes—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—22no—
81C2×C3×C4×D3C2312yes—
82C2×C3×Dic6—22no—
83C2×C3×Dic6C2312yes—
84C2×#626—22no—
85C2×#626—22no—
86C2×#626—22no—
87C2×#624—22no—
88C2×#624D411yescharacteristic
89C2×D3×Dic3—22no—
90C2×D3×Dic3D412yes—
91D3×D12—216no—
92D3×D12—24no—
93D3×D12C2318yescomplemented
94C4×D32—216no—
95C4×D32D414yes—
96C4×D32C2314yes—
97#3799—24no—
98#3799—216no—
99#3799C2318yes—
100#3796—24no—
101#3796—216no—
102#3796C2318yescomplemented
103C32×Q16C2314yescomplemented
104C2×C32×C8C2311yescharacteristic
105#3755C2318yescomplemented
106C2×C3⋊(C3⋊C8)C2311yescharacteristic
107#3745C2314yescomplemented
108C8×C3⋊D3C2314yescomplemented
109C3×#216C2318yescomplemented
110C3×#215C2318yescomplemented
111C2×C3×C3⋊C8C2312yes—
112C3×#204C2318yescomplemented
113C3×ΓL(1,𝔽25)C2318yescomplemented
114#3718C2314yescomplemented
115#3717C2318yescomplemented
116#3714C2318yescomplemented
117#3713C2314yescomplemented
118#3711C2318yescomplemented
119#3710C2314yescomplemented
120C2×#575—91noSylow
121C2×C3×#41—32no—
122C22×C3×Q8—32no—
123D3×#41—316no—
124D3×#41—68no—
125C2×#239—32no—
126C2×#239—32no—
127C2×#239—316no—
128C2×#239—32no—
129C2×#239—32no—
130C2×#239—62no—
131C2×#239—62no—
132C2×#239—62no—
133C2×#239—68no—
134C2×#239C2×D312yes—
135C2×D3×Q8C2×D312yescomplemented
136C2×#237—32no—
137C2×#237—62no—
138C2×D3×D4—32no—
139C2×D3×D4—62no—
140C2×#235—32no—
141C2×#235—62no—
142C22×D12—32no—
143C22×D12—62no—
144C22×C4×D3—32no—
145C22×C4×D3—62no—
146C22×C4×D3—62no—
147C3×#137—316no—
148C2×C3×Q16—21no—
149C2×C3×Q16—32no—
150C2×C3×Q16C2×D312yescomplemented
151C2×C3×SD16—32no—
152C2×C3×SD16—32no—
153C2×C3×M16—32no—
154#949—316no—
155C2×#216—32no—
156C2×#216C2×D312yescomplemented
157#942—316no—
158C2×#215—32no—
159C2×#215—32no—
160C2×#215—32no—
161C2×#215—62no—
162C2×#215C2×D312yescomplemented
163C2×#213—32no—
164C2×#213—32no—
165C2×#208—32no—
166#919—316no—
167#919—316no—
168#919—68no—
169#918—316no—
170#918C2×D3116yescomplemented
171#916—316no—
172#916—316no—
173#914—316no—
174#914—316no—
175#908—316no—
176D3×M16—316no—
177C2×D24—32no—
178C2×D24—32no—
179C2×D24—61no—
180C2×#204—32no—
181C2×#204C2×D312yescomplemented
182C2×ΓL(1,𝔽25)—32no—
183C2×ΓL(1,𝔽25)C2×D312yescomplemented
184C2×D3×C8—32no—
185C2×D3×C8—32no—
186C2×D3×C8—61no—
187C22×C3⋊D3—22no—
188C22×C3⋊D3C2×D411yescharacteristic
189C22×C3×D3—22no—
190C22×C3×D3C2×D412yes—
191C2×D32—28no—
192C2×D32—42no—
193C2×D32—48no—
194C2×D32C2×D414yes—
195C32×Q8—22no—
196C32×Q8C2414yes—
197C2×C32×C4—22no—
198C2×C32×C4C2411yescharacteristic
199C2×C3⋊Dic3C2×D411yescharacteristic
200C4⋊(C3⋊D3)—28no—
201C4⋊(C3⋊D3)—22no—
202C4⋊(C3⋊D3)C2414yes—
203C4×C3⋊D3—28no—
204C4×C3⋊D3C2×D412yes—
205C4×C3⋊D3C2412yes—
206C2×C3×Dic3—22no—
207C2×C3×Dic3C2×D412yes—
208C3×D12—28no—
209C3×D12—22no—
210C3×D12C2414yes—
211C3×C4×D3—28no—
212C3×C4×D3—28no—
213C3×C4×D3C2×D414yes—
214C3×C4×D3C2414yes—
215C3×Dic6—22no—
216C3×Dic6—28no—
217C3×Dic6C2414yes—
218#626—28no—
219#626—28no—
220#626—28no—
221#624—28no—
222#624C2×D414yes—
223D3×Dic3—28no—
224D3×Dic3C2×D418yes—
225C32×C8C2412yes—
226C3⋊(C3⋊C8)C2412yes—
227C3×C3⋊C8C2414yes—
228C22×#41—92no—
229#575—916no—
230C2×#137—32no—
231C2×#137—92no—
232C2×AGL(1,ℤ/8)—92no—
233C2×AGL(1,ℤ/8)—92no—
234C2×#135—91no—
235C2×#135—92no—
236C2×#135—91no—
237C22×M16—91no—
238C23×D3—32no—
239C23×D3—62no—
240C23×D3—62no—
241C3×#41—38no—
242C3×#41—64no—
243C2×C3×Q8—22no—
244C2×C3×Q8—38no—
245C2×C3×Q8—32no—
246C2×C3×Q8—62no—
247C2×C3×Q8—64no—
248C2×C3×Q8C22×D312yes—
249C2×C3×Q8C22×D312yes—
250C2×C3×D4—32no—
251C2×C3×D4—62no—
252C22×C3×C4—32no—
253C22×C3×C4—62no—
254C22×C3×C4—62no—
255C2×#67—62no—
256C2×#67—62no—
257C2×#67—62no—
258C22×Dic3—32no—
259C22×Dic3—62no—
260#239—24no—
261#239—38no—
262#239—38no—
263#239—38no—
264#239—38no—
265#239—68no—
266#239—616no—
267#239—616no—
268#239—64no—
269#239—64no—
270#239—64no—
271#239—64no—
272#239—124no—
273#239C22×D318yes—
274D3×Q8—24no—
275D3×Q8C22×D318yescomplemented
276#237—38no—
277#237—64no—
278#237—616no—
279D3×D4—38no—
280D3×D4—616no—
281D3×D4—64no—
282#235—38no—
283#235—616no—
284#235—64no—
285C2×D12—22no—
286C2×D12—32no—
287C2×D12—32no—
288C2×D12—38no—
289C2×D12—62no—
290C2×D12—64no—
291C2×D12—616no—
292C2×D12—62no—
293C2×D12—62no—
294C2×D12—62no—
295C2×D12—62no—
296C2×D12—62no—
297C2×D12—122no—
298C2×D12C22×D312yes—
299C2×C4×D3—22no—
300C2×C4×D3—22no—
301C2×C4×D3—32no—
302C2×C4×D3—32no—
303C2×C4×D3—32no—
304C2×C4×D3—38no—
305C2×C4×D3—38no—
306C2×C4×D3—61no—
307C2×C4×D3—616no—
308C2×C4×D3—616no—
309C2×C4×D3—62no—
310C2×C4×D3—62no—
311C2×C4×D3—62no—
312C2×C4×D3—62no—
313C2×C4×D3—62no—
314C2×C4×D3—122no—
315C2×C4×D3C22×D312yes—
316C2×Dic6—22no—
317C2×Dic6C22×D312yes—
318C3×Q16—24no—
319C3×Q16—38no—
320C3×Q16C22×D318yescomplemented
321C3×SD16—38no—
322C3×SD16—38no—
323C3×M16—38no—
324C2×C3×C8—21no—
325C2×C3×C8—32no—
326C2×C3×C8C22×D312yes—
327#216—38no—
328#216C22×D318yescomplemented
329#215—38no—
330#215—38no—
331#215—38no—
332#215—68no—
333#215C22×D318yescomplemented
334#213—38no—
335#213—38no—
336#208—38no—
337C2×C3⋊C8—32no—
338C2×C3⋊C8—61no—
339C2×C3⋊C8C22×D312yes—
340D24—38no—
341D24—38no—
342D24—64no—
343#204—38no—
344#204C22×D318yescomplemented
345ΓL(1,𝔽25)—38no—
346ΓL(1,𝔽25)C22×D318yescomplemented
347D3×C8—38no—
348D3×C8—38no—
349D3×C8—64no—
350C22×C32C22×D411yescharacteristic
351C2×C3⋊D3—22no—
352C2×C3⋊D3—24no—
353C2×C3⋊D3—44no—
354C2×C3⋊D3C22×D412yes—
355C2×C3×D3—24no—
356C2×C3×D3—24no—
357C2×C3×D3—44no—
358C2×C3×D3C22×D414yes—
359D32—44no—
360D32—416no—
361C32×C4—24no—
362C32×C4C22×D411yescharacteristic
363C32×C4C2511yescharacteristic
364C3⋊Dic3C22×D412yes—
365C3×Dic3—24no—
366C3×Dic3C22×D414yes—
367C2×#41—32no—
368C2×#41—92no—
369C2×#41—92no—
370C2×#41—916no—
371C2×#41—92no—
372C2×#41—182no—
373C2×#41—182no—
374C2×#41—188no—
375C22×Q8—32no—
376C22×D4—92no—
377C22×D4—182no—
378C23×C4—91no—
379C23×C4—182no—
380#137—316no—
381#137—916no—
382AGL(1,ℤ/8)—916no—
383AGL(1,ℤ/8)—916no—
384#135—98no—
385#135—916no—
386#135—98no—
387C2×Q16—32no—
388C2×Q16—91no—
389C2×Q16D3211yescharacteristic, complemented
390C2×SD16—32no—
391C2×SD16—32no—
392C2×SD16—92no—
393C2×SD16—92no—
394C2×D8—92no—
395C2×D8—91no—
396C2×D8—91no—
397C2×M16—32no—
398C2×M16—92no—
399C2×M16—98no—
400C22×C8—91no—
401C22×C8—91no—
402C23×C3—32no—
403C23×C3—62no—
404C22×D3—22no—
405C22×D3—32no—
406C22×D3—38no—
407C22×D3—61no—
408C22×D3—68no—
409C22×D3—62no—
410C22×D3—62no—
411C22×D3—68no—
412C22×D3—122no—
413C22×D3—124no—
414C22×D3—128no—
415C22×D3—128no—
416C22×D3D3×D412yes—
417C3×Q8—22no—
418C3×Q8—22no—
419C3×Q8—24no—
420C3×Q8—34no—
421C3×Q8—42no—
422C3×Q8—68no—
423C3×Q8—62no—
424C3×Q8C23×D314yes—
425C3×Q8C23×D314yes—
426C3×D4—34no—
427C3×D4—68no—
428C3×D4—62no—
429C2×C3×C4—22no—
430C2×C3×C4—22no—
431C2×C3×C4—21no—
432C2×C3×C4—32no—
433C2×C3×C4—34no—
434C2×C3×C4—34no—
435C2×C3×C4—42no—
436C2×C3×C4—68no—
437C2×C3×C4—68no—
438C2×C3×C4—62no—
439C2×C3×C4C23×D312yes—
440#67—68no—
441#67—68no—
442#67—68no—
443C2×Dic3—22no—
444C2×Dic3—32no—
445C2×Dic3—38no—
446C2×Dic3—61no—
447C2×Dic3—68no—
448C2×Dic3D3×D412yes—
449D12—28no—
450D12—22no—
451D12—34no—
452D12—34no—
453D12—64no—
454D12—68no—
455D12—68no—
456D12—68no—
457D12—68no—
458D12—68no—
459D12—62no—
460D12—62no—
461D12—122no—
462D12—128no—
463D12C23×D314yes—
464C4×D3—28no—
465C4×D3—28no—
466C4×D3—38no—
467C4×D3—34no—
468C4×D3—34no—
469C4×D3—38no—
470C4×D3—62no—
471C4×D3—62no—
472C4×D3—68no—
473C4×D3—68no—
474C4×D3—68no—
475C4×D3—68no—
476C4×D3—68no—
477C4×D3—128no—
478C4×D3D3×D414yes—
479C4×D3C23×D314yes—
480Dic6—22no—
481Dic6—28no—
482Dic6C23×D314yes—
483C3×C8—22no—
484C3×C8—34no—
485C3×C8C23×D314yes—
486C3⋊C8—34no—
487C3⋊C8—62no—
488C3⋊C8C23×D314yes—
489C2×C32#57512yescomplemented
490C2×C32C23×D411yescharacteristic
491C3⋊D3—22no—
492C3⋊D3—44no—
493C3×D3—24no—
494C3×D3—44no—
495C24—91no—
496C24—182no—
497#41—38no—
498#41—64no—
499#41—98no—
500#41—98no—
501#41—98no—
502#41—184no—
503#41—1816no—
504#41—1816no—
505#41—184no—
506#41—184no—
507C2×Q8—38no—
508C2×Q8—32no—
509C2×Q8—62no—
510C2×Q8—64no—
511C2×Q8C2×D3212yes—
512C2×D4—32no—
513C2×D4—62no—
514C2×D4—98no—
515C2×D4—92no—
516C2×D4—182no—
517C2×D4—184no—
518C2×D4—182no—
519C2×D4—1816no—
520C2×D4—182no—
521C2×D4—182no—
522C22×C4—32no—
523C22×C4—62no—
524C22×C4—62no—
525C22×C4—94no—
526C22×C4—91no—
527C22×C4—94no—
528C22×C4—92no—
529C22×C4—91no—
530C22×C4—182no—
531C22×C4—182no—
532C22×C4—1816no—
533C22×C4—182no—
534Q16—38no—
535Q16—94no—
536Q16C2×D3214yescomplemented
537SD16—38no—
538SD16—38no—
539SD16—98no—
540SD16—98no—
541D8—98no—
542D8—94no—
543D8—94no—
544M16—38no—
545M16—98no—
546C2×C8—32no—
547C2×C8—94no—
548C2×C8—91no—
549C2×C8—94no—
550C2×C8C2×D3211yescharacteristic
551C22×C3—21no—
552C22×C3—34no—
553C22×C3—64no—
554C22×C3—64no—
555C22×C3—124no—
556C22×C3C2×D3×D412yes—
557C2×D3—24no—
558C2×D3—24no—
559C2×D3—34no—
560C2×D3—44no—
561C2×D3—62no—
562C2×D3—64no—
563C2×D3—64no—
564C2×D3—64no—
565C2×D3—122no—
566C2×D3—124no—
567C2×D3—128no—
568C2×D3—1216no—
569C2×D3—1216no—
570C2×D3—124no—
571C2×D3—124no—
572C2×D3—244no—
573C2×D3C2×D3×D414yes—
574C3×C4—24no—
575C3×C4—24no—
576C3×C4—21no—
577C3×C4—21no—
578C3×C4—34no—
579C3×C4—44no—
580C3×C4—64no—
581C3×C4C2×D3×D412yes—
582C3×C4C24×D312yes—
583Dic3—24no—
584Dic3—34no—
585Dic3—62no—
586Dic3C2×D3×D414yes—
587C32C2×#57511yescharacteristic, complemented, Sylow
588C23—32no—
589C23—62no—
590C23—94no—
591C23—91no—
592C23—188no—
593C23—182no—
594C23—362no—
595C23—368no—
596Q8—22no—
597Q8—34no—
598Q8—68no—
599Q8—62no—
600Q8C22×D3214yes—
601D4—34no—
602D4—68no—
603D4—62no—
604D4—94no—
605D4—188no—
606D4—188no—
607D4—188no—
608D4—188no—
609D4—182no—
610C2×C4—22no—
611C2×C4—32no—
612C2×C4—34no—
613C2×C4—34no—
614C2×C4—68no—
615C2×C4—68no—
616C2×C4—62no—
617C2×C4—94no—
618C2×C4—98no—
619C2×C4—91no—
620C2×C4—92no—
621C2×C4—92no—
622C2×C4—188no—
623C2×C4—188no—
624C2×C4—188no—
625C2×C4C22×D3211yescharacteristic
626C8—34no—
627C8—92no—
628C8C22×D3212yes—
629C2×C3—21no—
630C2×C3—22no—
631C2×C3—64no—
632C2×C3—124no—
633C2×C3#577714yescomplemented
634C2×C3C22×D3×D412yes—
635D3—24no—
636D3—44no—
637D3—64no—
638D3—122no—
639D3—124no—
640D3—124no—
641D3—244no—
642C22—34no—
643C22—64no—
644C22—64no—
645C22—92no—
646C22—124no—
647C22—182no—
648C22—184no—
649C22—364no—
650C22—3616no—
651C22—364no—
652C22D32×D411yescharacteristic
653C4—24no—
654C4—34no—
655C4—64no—
656C4—92no—
657C4D32×D411yescharacteristic
658C4C23×D3211yescharacteristic
659C3—21no—
660C3C2×#577712yescomplemented
661C2—64no—
662C2—124no—
663C2—182no—
664C2—364no—
665C2#1059476212yesdirect product factor
666C2C2×D32×D411yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC32×C4C25
FrattiniC4C23×D32
FittingC2×C32×Q16C22
socleC22×C32C22×D4
hypercenterC2×Q16D32
hypocenterC32C2×#575
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×Q16

Complements

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

NH ≅ G/Ntype
1. C2×D3×#239C2semidirect
2. C2×#64128C2semidirect
3. C2×C3×#918C2semidirect
4. C2×#63950C2semidirect
5. C2×#63948C2semidirect
6. C2×#63939C2semidirect
7. #10594762C2direct (N × H)
8. C2×#63809C2semidirect
9. C2×#63794C2semidirect
10. C2×#63791C2semidirect
12. C2×#3832C22semidirect
14. C2×C3×D3×Q8C22semidirect
16. D3×#239C22semidirect
18. C2×D3×D12C22semidirect
24. C2×#3796C22semidirect
25. C2×C32×Q16C22semidirect
26. C2×#3755C22semidirect
27. #64128C22semidirect
28. C2×#3745C22semidirect
29. C2×C8×C3⋊D3C22semidirect
30. C2×C3×#216C22semidirect
31. C2×C3×#215C22semidirect
32. C3×#918C22semidirect
33. C2×C3×#204C22semidirect
34. C2×C3×ΓL(1,𝔽25)C22semidirect
35. #63950C22semidirect
36. #63948C22semidirect
37. #63939C22semidirect
38. C2×#3718C22semidirect
39. C2×#3717C22semidirect
40. C2×#3714C22semidirect
41. C2×#3713C22semidirect
42. C2×#3711C22semidirect
43. C2×#3710C22semidirect
44. #63809C22semidirect
45. #63794C22semidirect
46. #63791C22semidirect
57. C2×#918D3semidirect
68. #3832C23semidirect
76. C3×D3×Q8C23semidirect
93. D3×D12C23semidirect
102. #3796C23semidirect
103. C32×Q16C23semidirect
105. #3755C23semidirect
107. #3745C23semidirect
108. C8×C3⋊D3C23semidirect
109. C3×#216C23semidirect
110. C3×#215C23semidirect
112. C3×#204C23semidirect
113. C3×ΓL(1,𝔽25)C23semidirect
114. #3718C23semidirect
115. #3717C23semidirect
116. #3714C23semidirect
117. #3713C23semidirect
118. #3711C23semidirect
119. #3710C23semidirect
135. C2×D3×Q8C2×D3semidirect
150. C2×C3×Q16C2×D3semidirect
156. C2×#216C2×D3semidirect
162. C2×#215C2×D3semidirect
170. #918C2×D3semidirect
181. C2×#204C2×D3semidirect
183. C2×ΓL(1,𝔽25)C2×D3semidirect
275. D3×Q8C22×D3semidirect
320. C3×Q16C22×D3semidirect
328. #216C22×D3semidirect
333. #215C22×D3semidirect
344. #204C22×D3semidirect
346. ΓL(1,𝔽25)C22×D3semidirect
389. C2×Q16D32semidirect
489. C2×C32#575semidirect
536. Q16C2×D32semidirect
587. C32C2×#575semidirect
633. C2×C3#5777semidirect
660. C3C2×#5777semidirect
665. C2#10594762direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D3×#2392
C2×#641282
C2×C3×#9182
C2×#639502
C2×#639482
C2×#639392
#105947622
C2×#638092
C2×#637942
C2×#637912
C2×#57773