Finite Group Databasebeta

← C2×#10591677 #11867936

Subgroups — C2×#10591677 #11867936

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×#64158C211yesmaximal, characteristic, complemented
2C2×C3×#949C211yesmaximal, characteristic, complemented
3C2×C3×#948C211yesmaximal, characteristic, complemented
4C22×#3714C211yesmaximal, characteristic, complemented
5#10591677C218yesmaximal, direct product factor
6C2×#63577C211yesmaximal, characteristic, complemented
7C2×#63559C211yesmaximal, characteristic, complemented
8C2×#63558C211yesmaximal, characteristic, complemented
9C2×#5199—31nomaximal
10C2×#5142—31nomaximal
11C2×C32×#41C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×D12C2211yescharacteristic
14#64158—22no—
15#64158C2214yescomplemented
16C2×#3755—21no—
17C2×#3753—21no—
18C2×#3748C2211yescharacteristic
19C3×#949—22no—
20C3×#949C2214yescomplemented
21C3×#948—22no—
22C3×#948C2214yescomplemented
23C2×C3×#215—21no—
24C2×C3×#213—21no—
25C2×C3×#208—21no—
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28C22×C3×C3⋊C8—21no—
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3714—21no—
31C2×#3714—21no—
32C2×#3714—22no—
33C2×#3714C2214yescomplemented
34#63577C2214yescomplemented
35#63559C2214yescomplemented
36#63558C2214yescomplemented
37C2×C3×AGL(1,ℤ/8)—31no—
38C2×C3×#131—31no—
39C2×#949—31no—
40C2×#949—31no—
41C2×#949—61no—
42C2×#949D311yescharacteristic, complemented
43C2×#948D311yescharacteristic, complemented
44C22×#213—31no—
45C22×D24—31no—
46C2×#833—31no—
47#5199—38no—
48#5142—38no—
49C2×#823—31no—
50C2×#823—31no—
51C2×#823—31no—
52C2×#822—31no—
53C2×#819—31no—
54C23×C3⋊D3—21no—
55C23×C3×D3—21no—
56C32×#41—21no—
57C32×#41—21no—
58C32×#41D412yes—
59C32×#41C2312yes—
60C2×C32×Q8D411yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4D411yescharacteristic
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C4⋊(C3⋊D3)—21no—
66C2×C4⋊(C3⋊D3)—21no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)—21no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×D12—21no—
72C2×C3×D12—21no—
73C2×C3×D12—21no—
74C2×C3×D12—21no—
75C2×C3×D12—21no—
76C2×C3×D12C2312yes—
77#3755—24no—
78#3753—24no—
79#3748—21no—
80#3748C2312yes—
81C2×C3⋊(C3⋊C8)—21no—
82C3×#215—24no—
83C3×#213—24no—
84C3×#208—21no—
85C3×#208—21no—
86C3×#208—24no—
87C3×#208C2312yes—
88C3×#208C2312yes—
89C2×C3×C3⋊C8—21no—
90C2×C3×C3⋊C8—21no—
91C2×C3×C3⋊C8—24no—
92C2×C3×C3⋊C8D411yescharacteristic
93C2×C3×C3⋊C8D411yescharacteristic
94C2×C3×C3⋊C8D412yes—
95C2×C3×C3⋊C8C2312yes—
96#3714—24no—
97#3714—24no—
98C2×#472—91noSylow
99C2×C3×#41—21no—
100C2×C3×#41C2×D311yescharacteristic
101C2×C3×#41C2×D311yescharacteristic
102C22×C3×D4—31no—
103C22×D12—31no—
104C22×D12—31no—
105C22×D12—61no—
106C22×D12C2×D311yescharacteristic
107C3×AGL(1,ℤ/8)—34no—
108C3×AGL(1,ℤ/8)—62no—
109C2×C3×SD16—61no—
110C2×C3×D8—61no—
111C3×#131—34no—
112C3×#131—62no—
113C2×C3×M16—31no—
114C2×C3×M16—31no—
115C2×C3×M16—61no—
116C22×C3×C8—31no—
117C22×C3×C8—61no—
118#949—22no—
119#949—34no—
120#949—34no—
121#949—64no—
122#949—64no—
123#949—62no—
124#949—62no—
125#949C2×D314yescomplemented
126#948—22no—
127#948C2×D314yescomplemented
128C2×#215—21no—
129C2×#215—62no—
130C2×#215—61no—
131C2×#215—61no—
132C2×#213—21no—
133C2×#213—34no—
134C2×#213—62no—
135C2×#213—61no—
136C2×#213—61no—
137C2×#213—61no—
138C2×#213—61no—
139C2×#213—62no—
140C2×#208—21no—
141C2×#208—31no—
142C2×#208—31no—
143C2×#208—61no—
144C2×#208C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—21no—
147C22×C3⋊C8C2×D311yescharacteristic
148C2×D24—34no—
149C2×D24—61no—
150C2×D24—61no—
151C2×D24—62no—
152#833—34no—
153#823—34no—
154#823—34no—
155#823—34no—
156#822—34no—
157#819—34no—
158C23×C32—21no—
159C23×C32#4111yescharacteristic
160C22×C3⋊D3—22no—
161C22×C3⋊D3—41no—
162C22×C3⋊D3—41no—
163C22×C3⋊D3—82no—
164C22×C3×D3—22no—
165C22×C3×D3—41no—
166C22×C3×D3—41no—
167C22×C3×D3—82no—
168C32×Q8—21no—
169C32×Q8C2×D412yes—
170C32×D4—22no—
171C32×D4—22no—
172C32×D4—21no—
173C32×D4C2×D412yes—
174C2×C32×C4—21no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D411yescharacteristic
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4#4111yescharacteristic
182C2×C32×C4C2411yescharacteristic
183C4⋊(C3⋊D3)—22no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—41no—
186C4⋊(C3⋊D3)—41no—
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)—31no—
197C2×AGL(1,ℤ/8)—91no—
198C22×D8—91no—
199C2×#131—31no—
200#472—98no—
201C2×#108—91no—
202C2×#100—91no—
203C2×#100—91no—
204C24×C3—61no—
205C23×D3—21no—
206C23×D3—61no—
207C23×D3—61no—
208C23×D3—121no—
209C3×#41—21no—
210C3×#41—21no—
211C3×#41—21no—
212C3×#41—21no—
213C3×#41—22no—
214C3×#41—22no—
215C3×#41—41no—
216C3×#41—41no—
217C3×#41D1212yes—
218C3×#41#6712yes—
219C3×#41C22×D312yes—
220C3×#41C22×D312yes—
221C2×C3×Q8—21no—
222C2×C3×Q8D1211yescharacteristic
223C2×C3×Q8#6711yescharacteristic
224C2×C3×D4—21no—
225C2×C3×D4—21no—
226C2×C3×D4—21no—
227C2×C3×D4—32no—
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×D4D1211yescharacteristic
235C2×C3×D4#6711yescharacteristic
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—41no—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×D12—21no—
243C2×D12—21no—
244C2×D12—21no—
245C2×D12—21no—
246C2×D12—21no—
247C2×D12—32no—
248C2×D12—32no—
249C2×D12—62no—
250C2×D12—62no—
251C2×D12—62no—
252C2×D12—61no—
253C2×D12—61no—
254C2×D12—61no—
255C2×D12—61no—
256C2×D12—61no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—61no—
260C2×D12—61no—
261C2×D12—61no—
262C2×D12—121no—
263C2×D12—121no—
264C2×D12—121no—
265C2×D12C22×D312yes—
266C3×SD16—64no—
267C3×D8—64no—
268C3×M16—32no—
269C3×M16—32no—
270C3×M16—64no—
271C3×M16—61no—
272C3×M16—61no—
273C2×C3×C8—31no—
274C2×C3×C8—31no—
275C2×C3×C8—32no—
276C2×C3×C8—32no—
277C2×C3×C8—64no—
278C2×C3×C8—61no—
279C2×C3×C8—61no—
280#215—24no—
281#215—68no—
282#215—64no—
283#215—64no—
284#213—24no—
285#213—68no—
286#213—64no—
287#213—64no—
288#213—64no—
289#213—64no—
290#208—21no—
291#208—21no—
292#208—24no—
293#208—32no—
294#208—32no—
295#208—62no—
296#208—62no—
297#208—61no—
298#208—61no—
299#208C22×D312yes—
300#208C22×D312yes—
301C2×C3⋊C8—21no—
302C2×C3⋊C8—21no—
303C2×C3⋊C8—24no—
304C2×C3⋊C8—62no—
305C2×C3⋊C8—61no—
306C2×C3⋊C8—61no—
307C2×C3⋊C8#6711yescharacteristic
308C2×C3⋊C8#6711yescharacteristic
309C2×C3⋊C8#6712yes—
310C2×C3⋊C8C22×D312yes—
311D24—64no—
312D24—64no—
313C22×C32—22no—
314C22×C32—22no—
315C22×C32—42no—
316C22×C32#12111yescharacteristic
317C22×C32#12111yescharacteristic
318C22×C32C2×#4111yescharacteristic
319C2×C3⋊D3—42no—
320C2×C3⋊D3—82no—
321C2×C3⋊D3—82no—
322C2×C3⋊D3—82no—
323C2×C3×D3—42no—
324C2×C3×D3—82no—
325C2×C3×D3—82no—
326C2×C3×D3—82no—
327C32×C4—22no—
328C32×C4#12111yescharacteristic
329C32×C4#12111yescharacteristic
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C2×#41D3211yescharacteristic
333C22×D4—31no—
334C22×D4—91no—
335AGL(1,ℤ/8)—34no—
336AGL(1,ℤ/8)—62no—
337AGL(1,ℤ/8)—94no—
338AGL(1,ℤ/8)—182no—
339C2×SD16—61no—
340C2×SD16—181no—
341C2×D8—61no—
342C2×D8—94no—
343C2×D8—181no—
344C2×D8—181no—
345C2×D8—182no—
346C2×D8—181no—
347#131—34no—
348#131—62no—
349C2×M16—31no—
350C2×M16—31no—
351C2×M16—61no—
352C2×M16—91no—
353C22×C8—31no—
354C22×C8—61no—
355#108—94no—
356#100—94no—
357#100—94no—
358C23×C3—21no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—41no—
362C23×C3—62no—
363C23×C3—121no—
364C23×C3—121no—
365C23×C3—242no—
366C23×C3#23511yescharacteristic
367C23×C3#23711yescharacteristic
368C22×D3—22no—
369C22×D3—41no—
370C22×D3—41no—
371C22×D3—62no—
372C22×D3—62no—
373C22×D3—82no—
374C22×D3—122no—
375C22×D3—122no—
376C22×D3—122no—
377C22×D3—121no—
378C22×D3—121no—
379C22×D3—121no—
380C22×D3—121no—
381C22×D3—244no—
382C22×D3—242no—
383C22×D3—242no—
384C3×Q8—21no—
385C3×Q8—21no—
386C3×Q8—22no—
387C3×Q8—41no—
388C3×Q8C2×D1212yes—
389C3×Q8C2×#6712yes—
390C3×D4—22no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—22no—
394C3×D4—21no—
395C3×D4—21no—
396C3×D4—22no—
397C3×D4—41no—
398C3×D4—42no—
399C3×D4—42no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—121no—
403C3×D4—121no—
404C3×D4C2×D1212yes—
405C3×D4C2×#6712yes—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—21no—
413C2×C3×C4—21no—
414C2×C3×C4—21no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—21no—
418C2×C3×C4—42no—
419C2×C3×C4—42no—
420C2×C3×C4—41no—
421C2×C3×C4C2×D1211yescharacteristic
422C2×C3×C4C2×D1211yescharacteristic
423C2×C3×C4#23511yescharacteristic
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4#23711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C23×D311yescharacteristic
433D12—22no—
434D12—22no—
435D12—41no—
436D12—41no—
437D12—64no—
438D12—62no—
439D12—62no—
440D12—62no—
441D12—62no—
442D12—122no—
443D12—122no—
444D12—122no—
445D12—121no—
446D12—121no—
447D12—121no—
448D12—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—42no—
463C2×C32#47212yescomplemented
464C2×C32C2×#12111yescharacteristic
465C3⋊D3—82no—
466C3×D3—82no—
467C24—61no—
468C24—181no—
469#41—21no—
470#41—21no—
471#41#62612yes—
472#41C2×D3212yes—
473C2×Q8#62611yescharacteristic
474C2×D4—21no—
475C2×D4—32no—
476C2×D4—61no—
477C2×D4—61no—
478C2×D4—61no—
479C2×D4—61no—
480C2×D4—61no—
481C2×D4—92no—
482C2×D4—181no—
483C2×D4—181no—
484C2×D4—181no—
485C2×D4—181no—
486C2×D4—181no—
487C2×D4#62611yescharacteristic
488C22×C4—21no—
489C22×C4C2×D3211yescharacteristic
490SD16—64no—
491SD16—184no—
492D8—64no—
493D8—184no—
494D8—184no—
495D8—184no—
496M16—32no—
497M16—32no—
498M16—64no—
499M16—61no—
500M16—61no—
501M16—92no—
502M16—181no—
503C2×C8—32no—
504C2×C8—31no—
505C2×C8—31no—
506C2×C8—32no—
507C2×C8—64no—
508C2×C8—61no—
509C2×C8—61no—
510C2×C8—181no—
511C22×C3—22no—
512C22×C3—22no—
513C22×C3—22no—
514C22×C3—22no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—42no—
519C22×C3—42no—
520C22×C3—42no—
521C22×C3—42no—
522C22×C3—82no—
523C22×C3—122no—
524C22×C3—242no—
525C22×C3—242no—
526C22×C3—242no—
527C22×C3#93011yescharacteristic
528C22×C3#93011yescharacteristic
529C22×C3#93911yescharacteristic
530C22×C3#93911yescharacteristic
531C22×C3C2×#23511yescharacteristic
532C22×C3C2×#23711yescharacteristic
533C2×D3—42no—
534C2×D3—82no—
535C2×D3—82no—
536C2×D3—82no—
537C2×D3—124no—
538C2×D3—122no—
539C2×D3—122no—
540C2×D3—242no—
541C2×D3—242no—
542C2×D3—244no—
543C2×D3—244no—
544C2×D3—244no—
545C2×D3—242no—
546C2×D3—242no—
547C2×D3—242no—
548C2×D3—242no—
549C3×C4—22no—
550C3×C4—22no—
551C3×C4—21no—
552C3×C4—21no—
553C3×C4—21no—
554C3×C4—21no—
555C3×C4—42no—
556C3×C4#93011yescharacteristic
557C3×C4#93011yescharacteristic
558C3×C4#93911yescharacteristic
559C3×C4#93911yescharacteristic
560C3×C4C22×D1211yescharacteristic
561C3×C4C2×D3×D411yescharacteristic
562C3×C4C22×#6711yescharacteristic
563C3×C4C22×#6711yescharacteristic
564C32C2×#47211yescharacteristic, complemented, Sylow
565C23—21no—
566C23—62no—
567C23—121no—
568C23—121no—
569C23—182no—
570C23—242no—
571C23—361no—
572C23—361no—
573C23—722no—
574C23#380411yescharacteristic
575Q8—21no—
576Q8C2×#62612yes—
577D4—22no—
578D4—22no—
579D4—21no—
580D4—62no—
581D4—62no—
582D4—121no—
583D4—121no—
584D4—182no—
585D4—182no—
586D4—361no—
587D4—361no—
588D4C2×#62612yes—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4#380411yescharacteristic
593C2×C4C2×#62611yescharacteristic
594C2×C4C2×#62611yescharacteristic
595C2×C4D3×#6711yescharacteristic
596C2×C4D3×#6711yescharacteristic
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—42no—
612C2×C3—42no—
613C2×C3—82no—
614C2×C3—242no—
615C2×C3#514212yescomplemented
616C2×C3#519912yescomplemented
617C2×C3C2×#93011yescharacteristic
618C2×C3C2×#93911yescharacteristic
619D3—82no—
620D3—244no—
621D3—242no—
622D3—242no—
623C22—22no—
624C22—22no—
625C22—42no—
626C22—122no—
627C22—242no—
628C22—242no—
629C22—242no—
630C22—362no—
631C22—722no—
632C22—722no—
633C22—722no—
634C22#6397811yescharacteristic
635C22#6397811yescharacteristic
636C22C2×#380411yescharacteristic
637C4—22no—
638C4#6397811yescharacteristic
639C4#6397811yescharacteristic
640C4C22×#62611yescharacteristic
641C4C2×D3×#6711yescharacteristic
642C3—21no—
643C3C2×#514211yescharacteristic, complemented
644C3C2×#519911yescharacteristic, complemented
645C2—21no—
646C2—21no—
647C2—42no—
648C2—242no—
649C2—722no—
650C2#1059167712yesdirect product factor
651C2C2×#6397811yescharacteristic
subgroupG/H
centerC22#63978
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32#121
hypercenterC2×#41D32
hypocenterC32C2×#472
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#64158C2semidirect
2. C2×C3×#949C2semidirect
3. C2×C3×#948C2semidirect
4. C22×#3714C2semidirect
5. #10591677C2direct (N × H)
6. C2×#63577C2semidirect
7. C2×#63559C2semidirect
8. C2×#63558C2semidirect
15. #64158C22semidirect
20. C3×#949C22semidirect
22. C3×#948C22semidirect
33. C2×#3714C22semidirect
34. #63577C22semidirect
35. #63559C22semidirect
36. #63558C22semidirect
42. C2×#949D3semidirect
43. C2×#948D3semidirect
125. #949C2×D3semidirect
127. #948C2×D3semidirect
463. C2×C32#472semidirect
564. C32C2×#472semidirect
615. C2×C3#5142semidirect
616. C2×C3#5199semidirect
643. C3C2×#5142semidirect
644. C3C2×#5199semidirect
650. C2#10591677direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641582
C2×C3×#9492
C2×C3×#9482
C22×#37142
#105916772
C2×#635772
C2×#635592
C2×#635582
C2×#51993
C2×#51423