Finite Group Databasebeta

← C2×#10591406 #11867931

Subgroups — C2×#10591406 #11867931

Order 1152.

1125 conjugacy classes of subgroups.

The subgroup lattice has 653 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64141C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63830C211yesmaximal, characteristic, complemented
4C2×#63817C211yesmaximal, characteristic, complemented
5C2×C3×#833C211yesmaximal, characteristic, complemented
6#10591406C218yesmaximal, direct product factor
7C2×#63577C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5160—31nomaximal
10C2×#4749—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C2×#3828C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14C2×#3754—21no—
15#64141—22no—
16#64141C2214yescomplemented
17C2×#3753—21no—
18C2×#3748C2211yescharacteristic
19C2×C3×#213—21no—
20C2×C3×#213—22no—
21C2×C3×#213—21no—
22C2×C3×#213C2214yescomplemented
23C2×C3×#208C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26#63830—22no—
27#63830C2214yescomplemented
28C2×#3716—21no—
29C2×#3714—21no—
30C2×#3712—21no—
31#63817—22no—
32#63817C2214yescomplemented
33C2×#3710—21no—
34C3×#833C2214yescomplemented
35#63577C2214yescomplemented
36#63558C2214yescomplemented
37C22×C3×D8—31no—
38C2×#932—31no—
39C2×#932—31no—
40C2×#932—31no—
41C2×#932—61no—
42C22×#213D311yescharacteristic, complemented
43C2×#908—31no—
44C2×#907—31no—
45C2×#901—31no—
46C2×C3×#100—31no—
47C2×#833—31no—
48C2×#833D311yescharacteristic, complemented
49#5160—38no—
50C2×#823—31no—
51C2×#822—31no—
52C2×#819—31no—
53#4749—38no—
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×#638—21no—
64#3828—21no—
65#3828—21no—
66#3828D412yes—
67#3828C2312yes—
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3—21no—
70C2×#634D411yescharacteristic
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77#3754—24no—
78#3753—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#213—24no—
83C3×#213—24no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208C2312yes—
87C3×#208C2312yes—
88C2×C3×C3⋊C8—21no—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8D411yescharacteristic
91C2×C3×C3⋊C8D412yes—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94#3716—24no—
95#3714—24no—
96#3712—24no—
97#3710—24no—
98C2×#472—91noSylow
99C22×C3×D4—21no—
100C22×C3×D4—31no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C2×#235—31no—
104C2×#235—31no—
105C2×#235—61no—
106C22×D12C2×D311yescharacteristic
107C2×C3×D8—34no—
108C2×C3×D8—61no—
109C2×C3×D8—61no—
110C2×C3×D8—62no—
111C2×C3×M16—31no—
112C2×C3×M16—31no—
113C22×C3×C8—31no—
114C2×#214—61no—
115C2×#214—61no—
116C2×#214—61no—
117C2×#214—62no—
118#932—34no—
119#932—34no—
120#932—34no—
121#932—64no—
122#932—62no—
123#932—62no—
124#932—62no—
125#932—64no—
126C2×#213—21no—
127C2×#213—21no—
128C2×#213—22no—
129C2×#213—61no—
130C2×#213—61no—
131C2×#213—61no—
132C2×#213—62no—
133C2×#213C2×D314yescomplemented
134C2×#208—31no—
135C2×#208—31no—
136C2×#208—61no—
137C2×#208C2×D311yescharacteristic
138C2×#208C2×D311yescharacteristic
139C22×C3⋊C8C2×D311yescharacteristic
140#908—34no—
141#908—62no—
142#907—34no—
143#907—62no—
144C2×D24—61no—
145C2×#204—61no—
146#901—34no—
147#901—62no—
148C2×ΓL(1,𝔽25)—61no—
149C2×ΓL(1,𝔽25)—61no—
150C2×D3×C8—61no—
151C2×D3×C8—61no—
152C3×#100—34no—
153#833—34no—
154#833C2×D314yescomplemented
155#823—34no—
156#822—34no—
157#819—34no—
158C23×C32—22no—
159C23×C32—41no—
160C23×C32—41no—
161C23×C32—82no—
162C23×C32#4111yescharacteristic
163C22×C3⋊D3—21no—
164C22×C3×D3—22no—
165C22×C3×D3—41no—
166C22×C3×D3—41no—
167C22×C3×D3—82no—
168C32×D4—22no—
169C32×D4—22no—
170C32×D4—41no—
171C32×D4—41no—
172C2×C32×C4C2×D411yescharacteristic
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D411yescharacteristic
176C2×C32×C4#4111yescharacteristic
177C2×C32×C4C2411yescharacteristic
178#638—22no—
179#638—22no—
180C2×C3⋊Dic3—21no—
181C4⋊(C3⋊D3)—21no—
182C4⋊(C3⋊D3)C2×D412yes—
183C4×C3⋊D3—22no—
184C4×C3⋊D3—22no—
185#634—21no—
186#634C2×D412yes—
187C3×D12—22no—
188C3×D12—22no—
189C3×D12—41no—
190C3×D12—41no—
191C3⋊(C3⋊C8)—22no—
192C3×C3⋊C8—22no—
193C3×C3⋊C8—22no—
194C3×C3⋊C8C2×D412yes—
195C3×C3⋊C8C2×D412yes—
196C2×AGL(1,ℤ/8)—91no—
197C2×AGL(1,ℤ/8)—91no—
198C22×D8—31no—
199C2×#131—91no—
200#472—98no—
201C2×#108—91no—
202C2×#100—31no—
203C2×#100—91no—
204C24×C3—21no—
205C24×C3—21no—
206C24×C3—41no—
207C24×C3—61no—
208C23×D3—21no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
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—22no—
222C2×C3×D4—32no—
223C2×C3×D4—41no—
224C2×C3×D4—41no—
225C2×C3×D4—41no—
226C2×C3×D4—61no—
227C2×C3×D4—61no—
228C2×C3×D4—61no—
229C2×C3×D4—61no—
230C2×C3×D4—61no—
231C2×C3×D4C22×D312yes—
232C2×C3×D4C22×D312yes—
233C22×C3×C4—21no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—61no—
237C2×#67—61no—
238C2×#67—121no—
239#235—32no—
240#235—32no—
241#235—32no—
242#235—32no—
243#235—62no—
244#235—62no—
245#235—61no—
246#235—61no—
247#235—61no—
248#235—61no—
249#235—121no—
250#235—121no—
251C2×D12—21no—
252C2×D12—21no—
253C2×D12—21no—
254C2×D12—21no—
255C2×D12—21no—
256C2×D12—31no—
257C2×D12—31no—
258C2×D12—61no—
259C2×D12C22×D312yes—
260C2×C4×D3—61no—
261C2×C4×D3—61no—
262C2×C4×D3—121no—
263C2×Dic6—31no—
264C2×Dic6—31no—
265C2×Dic6—61no—
266C3×D8—64no—
267C3×D8—64no—
268C3×M16—32no—
269C3×M16—32no—
270C3×M16—61no—
271C3×M16—61no—
272C2×C3×C8—31no—
273C2×C3×C8—31no—
274C2×C3×C8—32no—
275C2×C3×C8—32no—
276C2×C3×C8—61no—
277C2×C3×C8—61no—
278#214—64no—
279#214—64no—
280#214—64no—
281#214—68no—
282#213—24no—
283#213—24no—
284#213—64no—
285#213—64no—
286#213—64no—
287#213—68no—
288#208—21no—
289#208—21no—
290#208—32no—
291#208—32no—
292#208—62no—
293#208—62no—
294#208—61no—
295#208—61no—
296#208C22×D312yes—
297#208C22×D312yes—
298C2×C3⋊C8—21no—
299C2×C3⋊C8—21no—
300C2×C3⋊C8—62no—
301C2×C3⋊C8—61no—
302C2×C3⋊C8—61no—
303C2×C3⋊C8#6711yescharacteristic
304C2×C3⋊C8#6711yescharacteristic
305C2×C3⋊C8#6712yes—
306C2×C3⋊C8C22×D312yes—
307D24—64no—
308#204—64no—
309ΓL(1,𝔽25)—64no—
310ΓL(1,𝔽25)—64no—
311D3×C8—64no—
312D3×C8—64no—
313C22×C32—22no—
314C22×C32—42no—
315C22×C32—82no—
316C22×C32—82no—
317C22×C32—82no—
318C22×C32#12111yescharacteristic
319C22×C32#12111yescharacteristic
320C22×C32C2×#4111yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—42no—
323C2×C3×D3—42no—
324C2×C3×D3—82no—
325C2×C3×D3—82no—
326C2×C3×D3—82no—
327C32×C4#12111yescharacteristic
328C32×C4#12111yescharacteristic
329C32×C4C22×D411yescharacteristic
330C32×C4C22×D411yescharacteristic
331C3⋊Dic3—22no—
332C2×#41—91no—
333C22×D4—31no—
334C22×D4D3211yescharacteristic
335AGL(1,ℤ/8)—94no—
336AGL(1,ℤ/8)—94no—
337AGL(1,ℤ/8)—182no—
338AGL(1,ℤ/8)—182no—
339C2×SD16—181no—
340C2×SD16—181no—
341C2×D8—34no—
342C2×D8—61no—
343C2×D8—61no—
344C2×D8—62no—
345C2×D8—181no—
346C2×D8—181no—
347#131—94no—
348#131—182no—
349C2×M16—31no—
350C2×M16—31no—
351C2×M16—91no—
352C2×M16—181no—
353C22×C8—31no—
354C22×C8—181no—
355#108—94no—
356#100—34no—
357#100—94no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—42no—
362C23×C3—42no—
363C23×C3—42no—
364C23×C3—41no—
365C23×C3—41no—
366C23×C3—41no—
367C23×C3—41no—
368C23×C3—62no—
369C23×C3—82no—
370C23×C3—82no—
371C23×C3—84no—
372C23×C3—121no—
373C23×C3—121no—
374C23×C3—242no—
375C23×C3#23511yescharacteristic
376C23×C3#23711yescharacteristic
377C22×D3—22no—
378C22×D3—41no—
379C22×D3—41no—
380C22×D3—61no—
381C22×D3—61no—
382C22×D3—82no—
383C22×D3—121no—
384C3×D4—24no—
385C3×D4—22no—
386C3×D4—22no—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—42no—
390C3×D4—42no—
391C3×D4—42no—
392C3×D4—41no—
393C3×D4—41no—
394C3×D4—41no—
395C3×D4—41no—
396C3×D4—62no—
397C3×D4—62no—
398C3×D4—121no—
399C3×D4—121no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—21no—
403C2×C3×C4—21no—
404C2×C3×C4—21no—
405C2×C3×C4—21no—
406C2×C3×C4#23511yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D411yescharacteristic
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4#23711yescharacteristic
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—62no—
419#67—62no—
420#67—62no—
421#67—62no—
422#67—122no—
423#67—122no—
424C2×Dic3—61no—
425C2×Dic3—61no—
426C2×Dic3—121no—
427D12—22no—
428D12—22no—
429D12—32no—
430D12—32no—
431D12—41no—
432D12—41no—
433D12—62no—
434D12—61no—
435D12—61no—
436D12—121no—
437C4×D3—62no—
438C4×D3—62no—
439C4×D3—62no—
440C4×D3—62no—
441C4×D3—122no—
442C4×D3—122no—
443Dic6—32no—
444Dic6—32no—
445Dic6—62no—
446Dic6—61no—
447Dic6—61no—
448Dic6—121no—
449C3×C8—32no—
450C3×C8—32no—
451C3×C8—62no—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—22no—
455C3⋊C8—64no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C3⋊C8C2×#6712yes—
459C3⋊C8C2×#6712yes—
460C2×C32—21no—
461C2×C32—21no—
462C2×C32—82no—
463C2×C32#47212yescomplemented
464C2×C32C2×#12111yescharacteristic
465C3⋊D3—42no—
466C3×D3—82no—
467C24—21no—
468C24—61no—
469#41—92no—
470#41—92no—
471#41—181no—
472#41—181no—
473C2×Q8—91no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—32no—
480C2×D4—61no—
481C2×D4—61no—
482C2×D4—61no—
483C2×D4—61no—
484C2×D4—61no—
485C2×D4—91no—
486C2×D4—181no—
487C2×D4C2×D3212yes—
488C22×C4—181no—
489C22×C4C2×D3211yescharacteristic
490SD16—184no—
491SD16—184no—
492D8—64no—
493D8—64no—
494D8—184no—
495D8—184no—
496M16—32no—
497M16—32no—
498M16—61no—
499M16—61no—
500M16—92no—
501M16—184no—
502M16—181no—
503C2×C8—32no—
504C2×C8—31no—
505C2×C8—31no—
506C2×C8—32no—
507C2×C8—61no—
508C2×C8—61no—
509C2×C8—184no—
510C2×C8—181no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—21no—
514C22×C3—21no—
515C22×C3—21no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—82no—
521C22×C3—82no—
522C22×C3—82no—
523C22×C3—82no—
524C22×C3—84no—
525C22×C3—84no—
526C22×C3—84no—
527C22×C3—82no—
528C22×C3—82no—
529C22×C3—122no—
530C22×C3—242no—
531C22×C3—242no—
532C22×C3—242no—
533C22×C3#88411yescharacteristic
534C22×C3#88411yescharacteristic
535C22×C3#93811yescharacteristic
536C22×C3#93811yescharacteristic
537C22×C3C2×#23511yescharacteristic
538C22×C3C2×#23711yescharacteristic
539C2×D3—42no—
540C2×D3—62no—
541C2×D3—62no—
542C2×D3—82no—
543C2×D3—82no—
544C2×D3—82no—
545C2×D3—122no—
546C2×D3—122no—
547C2×D3—122no—
548C2×D3—242no—
549C3×C4—21no—
550C3×C4—21no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4#88411yescharacteristic
554C3×C4#88411yescharacteristic
555C3×C4#93811yescharacteristic
556C3×C4#93811yescharacteristic
557C3×C4C2×D3×D411yescharacteristic
558C3×C4C2×D3×D411yescharacteristic
559C3×C4C2×D3×D411yescharacteristic
560C3×C4C22×#6711yescharacteristic
561Dic3—62no—
562Dic3—62no—
563Dic3—122no—
564C32C2×#47211yescharacteristic, complemented, Sylow
565C23—22no—
566C23—41no—
567C23—41no—
568C23—62no—
569C23—82no—
570C23—121no—
571C23—121no—
572C23—181no—
573C23—242no—
574C23#380411yescharacteristic
575Q8—92no—
576Q8—181no—
577D4—22no—
578D4—22no—
579D4—41no—
580D4—41no—
581D4—62no—
582D4—62no—
583D4—92no—
584D4—121no—
585D4—121no—
586D4—182no—
587D4—182no—
588D4—181no—
589C2×C4—181no—
590C2×C4—182no—
591C2×C4—182no—
592C2×C4#380411yescharacteristic
593C2×C4D3×#6711yescharacteristic
594C2×C4D3×#6711yescharacteristic
595C2×C4#381111yescharacteristic
596C2×C4#381111yescharacteristic
597C2×C4C22×D3211yescharacteristic
598C8—32no—
599C8—32no—
600C8—62no—
601C8—62no—
602C8—182no—
603C2×C3—21no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—22no—
609C2×C3—41no—
610C2×C3—41no—
611C2×C3—84no—
612C2×C3—82no—
613C2×C3—82no—
614C2×C3—242no—
615C2×C3#474912yescomplemented
616C2×C3#516012yescomplemented
617C2×C3C2×#88411yescharacteristic
618C2×C3C2×#93811yescharacteristic
619D3—82no—
620D3—122no—
621D3—122no—
622D3—242no—
623C22—22no—
624C22—42no—
625C22—82no—
626C22—82no—
627C22—82no—
628C22—122no—
629C22—182no—
630C22—242no—
631C22—242no—
632C22—242no—
633C22—362no—
634C22#6395811yescharacteristic
635C22#6395811yescharacteristic
636C22C2×#380411yescharacteristic
637C4—182no—
638C4#6395811yescharacteristic
639C4#6395811yescharacteristic
640C4C2×D3×#6711yescharacteristic
641C4C2×#381111yescharacteristic
642C3—21no—
643C3C2×#474911yescharacteristic, complemented
644C3C2×#516011yescharacteristic, complemented
645C2—21no—
646C2—21no—
647C2—82no—
648C2—242no—
649C2—362no—
650C2#1059140612yesdirect product factor
651C2C2×#6395811yescharacteristic
subgroupG/H
centerC22#63958
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×#64141C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63830C2semidirect
4. C2×#63817C2semidirect
5. C2×C3×#833C2semidirect
6. #10591406C2direct (N × H)
7. C2×#63577C2semidirect
8. C2×#63558C2semidirect
16. #64141C22semidirect
22. C2×C3×#213C22semidirect
27. #63830C22semidirect
32. #63817C22semidirect
34. C3×#833C22semidirect
35. #63577C22semidirect
36. #63558C22semidirect
42. C22×#213D3semidirect
48. C2×#833D3semidirect
133. C2×#213C2×D3semidirect
154. #833C2×D3semidirect
463. C2×C32#472semidirect
564. C32C2×#472semidirect
615. C2×C3#4749semidirect
616. C2×C3#5160semidirect
643. C3C2×#4749semidirect
644. C3C2×#5160semidirect
650. C2#10591406direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641412
C22×C3×#2132
C2×#638302
C2×#638172
C2×C3×#8332
#105914062
C2×#635772
C2×#635582
C2×#51603
C2×#47493