Finite Group Databasebeta

← C2×#10591586 #11863733

Subgroups — C2×#10591586 #11863733

Order 1152.

1705 conjugacy classes of subgroups.

The subgroup lattice has 619 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5C2×#63662C211yesmaximal, characteristic, complemented
6#10591586C218yesmaximal, direct product factor
7C2×#63563C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5238—31nomaximal
10C2×#5172—31nomaximal
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#239—24no—
13C2×C3×#239—24no—
14C2×C3×#239—22no—
15C2×C3×#239C2214yescomplemented
16C22×C3×D12—21no—
17C22×C3×D12C2211yescharacteristic
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3—21no—
20C22×C3×C4×D3C2211yescharacteristic
21C22×#625—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×#215—24no—
25C2×C3×#215C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yescomplemented
30C2×#3713—24no—
31C2×#3713C2214yescomplemented
32#63662C2214yescomplemented
33#63563C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#239D311yescharacteristic, complemented
37C22×C3×SD16—31no—
38C22×#215D311yescharacteristic, complemented
39C2×#938—31no—
40C22×#213—31no—
41C22×#213—31no—
42C2×#930—31no—
43#5238—38no—
44C2×#835—31no—
45C2×#835—31no—
46C2×#835—61no—
47C2×#832—31no—
48C2×#830—31no—
49#5172—38no—
50C2×#821—31no—
51C2×(C2×D3)⋊C8—31no—
52C23×C3×D3—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C2×C32×Q8—22no—
56C2×C32×Q8—21no—
57C2×C32×Q8D414yescomplemented
58C2×C32×Q8C2312yes—
59C22×C32×C4—21no—
60C22×C32×C4C2311yescharacteristic
61C22×C3⋊Dic3—21no—
62C22×C3×Dic3D411yescharacteristic
63C3×#239—216no—
64C3×#239—28no—
65C3×#239—28no—
66C2×C3×D12—28no—
67C2×C3×D12—24no—
68C2×C3×D12—21no—
69C2×C3×D12—22no—
70C2×C3×D12—22no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12D414yescomplemented
74C2×C3×D12C2312yes—
75C2×C3×D12C2312yes—
76C2×C3×C4×D3—28no—
77C2×C3×C4×D3—22no—
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—24no—
80C2×C3×C4×D3D412yes—
81C2×C3×C4×D3C2312yes—
82C2×#625—24no—
83C2×#625—44no—
84C4⋊(C3⋊Dic3)—21no—
85C4⋊(C3⋊Dic3)C2312yes—
86C2×C3⋊(C3⋊C8)—22no—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×#215—28no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91(C2×D3)⋊Dic3—24no—
92#3713—28no—
93C2×#449—91noSylow
94C2×C3×#41—34no—
95C2×C3×#41—62no—
96C2×C3×#41—64no—
97C2×C3×#41—64no—
98C22×C3×Q8—21no—
99C22×C3×Q8C2×D311yescharacteristic
100C22×C3×Q8C2×D311yescharacteristic
101C22×C3×D4—31no—
102C22×C3×D4—31no—
103C22×C3×D4—61no—
104C23×C3×C4—31no—
105C23×C3×C4—61no—
106C22×#67—61no—
107C22×#67—61no—
108C2×#239—24no—
109C2×#239—24no—
110C2×#239—22no—
111C2×#239C2×D314yescomplemented
112C22×D12—21no—
113C22×D12C2×D311yescharacteristic
114C22×D12C2×D311yescharacteristic
115C22×C4×D3—21no—
116C22×C4×D3C2×D311yescharacteristic
117C2×C3×SD16—34no—
118C2×C3×SD16—64no—
119C22×C3×C8—31no—
120C2×#217—61no—
121C2×#215—24no—
122C2×#215C2×D314yescomplemented
123#938—34no—
124#938—62no—
125C2×#213—34no—
126C2×#213—34no—
127C2×#213—64no—
128C2×#213—64no—
129#930—34no—
130#930—62no—
131C2×(C2×D3)⋊C4—61no—
132C2×C4⋊Dic3—31no—
133C2×C4⋊Dic3—31no—
134C2×C4⋊Dic3—61no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8C2×D311yescharacteristic
139#835—34no—
140#835—34no—
141#835—64no—
142#832—34no—
143#830—34no—
144#821—34no—
145(C2×D3)⋊C8—34no—
146C23×C32C2×D411yescharacteristic
147C22×C3×D3—24no—
148C22×C3×D3—22no—
149C22×C3×D3—22no—
150C22×C3×D3—22no—
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—42no—
154C22×C3×D3—42no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3C2×D412yes—
159C32×Q8—24no—
160C32×Q8—22no—
161C32×Q8C2×D414yescomplemented
162C2×C32×C4—24no—
163C2×C32×C4—22no—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D412yes—
167C2×C32×C4C2411yescharacteristic
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—42no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3C2×D412yes—
172C3×D12—216no—
173C3×D12—24no—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—22no—
177C3×D12—42no—
178C3×D12C2×D414yescomplemented
179C3×C4×D3—216no—
180C3×C4×D3—24no—
181C3×C4×D3—22no—
182C3×C4×D3—22no—
183#625—48no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—22no—
186C22×#41—31no—
187C22×SD16—31no—
188C22×D8—91no—
189C2×#121—91no—
190#449—98no—
191C2×#103—91no—
192C2×#102—91no—
193C2×C22⋊C8—91no—
194C24×C3—31no—
195C24×C3—61no—
196C24×C3—61no—
197C23×D3—21no—
198C23×D3—21no—
199C23×D3#6711yescharacteristic
200C3×#41—68no—
201C3×#41—616no—
202C3×#41—68no—
203C2×C3×Q8—22no—
204C2×C3×Q8—21no—
205C2×C3×Q8—22no—
206C2×C3×Q8—21no—
207C2×C3×Q8—24no—
208C2×C3×Q8—22no—
209C2×C3×Q8—42no—
210C2×C3×Q8—41no—
211C2×C3×Q8#6714yescomplemented
212C2×C3×Q8#6714yescomplemented
213C2×C3×Q8C22×D312yes—
214C2×C3×Q8C22×D312yes—
215C2×C3×D4—34no—
216C2×C3×D4—32no—
217C2×C3×D4—32no—
218C2×C3×D4—64no—
219C2×C3×D4—68no—
220C2×C3×D4—61no—
221C2×C3×D4—62no—
222C2×C3×D4—62no—
223C2×C3×D4—62no—
224C2×C3×D4—61no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—21no—
228C22×C3×C4—31no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—41no—
232C22×C3×C4—64no—
233C22×C3×C4—68no—
234C22×C3×C4—62no—
235C22×C3×C4—62no—
236C22×C3×C4C22×D311yescharacteristic
237C22×C3×C4C22×D311yescharacteristic
238C2×#67—64no—
239C2×#67—64no—
240C2×#67—124no—
241C2×#67—124no—
242C22×Dic3—61no—
243C22×Dic3—61no—
244C22×Dic3—121no—
245C22×Dic3#6711yescharacteristic
246#239—216no—
247#239—28no—
248#239—28no—
249C2×D12—28no—
250C2×D12—24no—
251C2×D12—22no—
252C2×D12—21no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12#6714yescomplemented
257C2×D12C22×D312yes—
258C2×D12C22×D312yes—
259C2×C4×D3—28no—
260C2×C4×D3—22no—
261C2×C4×D3—22no—
262C2×C4×D3—24no—
263C2×C4×D3#6712yes—
264C2×C4×D3C22×D312yes—
265C3×SD16—68no—
266C2×C3×C8—32no—
267C2×C3×C8—62no—
268#217—64no—
269#215—28no—
270#213—68no—
271#213—68no—
272(C2×D3)⋊C4—64no—
273C4⋊Dic3—32no—
274C4⋊Dic3—32no—
275C4⋊Dic3—62no—
276C4⋊Dic3—61no—
277C4⋊Dic3—61no—
278C4⋊Dic3—121no—
279C2×C3⋊C8—22no—
280C2×C3⋊C8—32no—
281C2×C3⋊C8—32no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—122no—
286C2×C3⋊C8C22×D312yes—
287C22×C32#12012yes—
288C22×C32#13512yes—
289C22×C32AGL(1,ℤ/8)12yes—
290C22×C32C22×D411yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—24no—
293C2×C3×D3—22no—
294C2×C3×D3—22no—
295C2×C3×D3—42no—
296C2×C3×D3—42no—
297C2×C3×D3—44no—
298C2×C3×D3—48no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C32×C4—24no—
304C32×C4#12012yes—
305C32×C4C22×D411yescharacteristic
306C32×C4C22×D411yescharacteristic
307C3⋊Dic3—42no—
308C3×Dic3—22no—
309C2×#41—34no—
310C2×#41—62no—
311C2×#41—64no—
312C2×#41—64no—
313C22×Q8D3211yescharacteristic
314C22×D4—31no—
315C22×D4—31no—
316C22×D4—61no—
317C22×D4—181no—
318C23×C4—31no—
319C23×C4—61no—
320C2×SD16—34no—
321C2×SD16—64no—
322C2×D8—94no—
323C2×D8—184no—
324C22×C8—31no—
325C22×C8—91no—
326#121—94no—
327#121—182no—
328C2×C4⋊C4—91no—
329C2×C22⋊C4—181no—
330#103—94no—
331#102—94no—
332C22⋊C8—94no—
333C23×C3—21no—
334C23×C3—32no—
335C23×C3—62no—
336C23×C3—62no—
337C23×C3—64no—
338C23×C3—62no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—122no—
342C23×C3—122no—
343C23×C3—122no—
344C23×C3—122no—
345C23×C3—122no—
346C23×C3D3×D411yescharacteristic
347C23×C3C2×#6711yescharacteristic
348C22×D3—22no—
349C22×D3—22no—
350C22×D3—22no—
351C22×D3—24no—
352C22×D3—22no—
353C22×D3—22no—
354C22×D3—42no—
355C22×D3—42no—
356C22×D3—42no—
357C22×D3—42no—
358C22×D3—42no—
359C22×D3C2×#6712yes—
360C3×Q8—24no—
361C3×Q8—24no—
362C3×Q8—22no—
363C3×Q8—22no—
364C3×Q8—24no—
365C3×Q8—42no—
366C3×Q8—44no—
367C3×Q8C2×#6714yescomplemented
368C3×Q8C2×#6714yescomplemented
369C3×D4—34no—
370C3×D4—616no—
371C3×D4—64no—
372C3×D4—62no—
373C3×D4—62no—
374C3×D4—62no—
375C3×D4—122no—
376C2×C3×C4—24no—
377C2×C3×C4—24no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—32no—
385C2×C3×C4—42no—
386C2×C3×C4—44no—
387C2×C3×C4—616no—
388C2×C3×C4—62no—
389C2×C3×C4—64no—
390C2×C3×C4—62no—
391C2×C3×C4—62no—
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4D3×D412yes—
394C2×C3×C4C2×#6712yes—
395C2×C3×C4C2×#6712yes—
396C2×C3×C4C2×#6711yescharacteristic
397C2×C3×C4C2×#6712yes—
398C2×C3×C4C23×D311yescharacteristic
399C2×C3×C4C23×D311yescharacteristic
400#67—128no—
401#67—128no—
402C2×Dic3—22no—
403C2×Dic3—62no—
404C2×Dic3—62no—
405C2×Dic3—122no—
406C2×Dic3—122no—
407C2×Dic3—122no—
408C2×Dic3—242no—
409C2×Dic3C2×#6712yes—
410D12—216no—
411D12—24no—
412D12—22no—
413D12—22no—
414D12—22no—
415D12—42no—
416D12C2×#6714yescomplemented
417C4×D3—216no—
418C4×D3—24no—
419C4×D3—22no—
420C4×D3—22no—
421C3×C8—62no—
422C3⋊C8—22no—
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—122no—
426C2×C32#44914yescomplemented
427C2×C32C2×#12011yescharacteristic
428C2×C32C2×#13511yescharacteristic
429C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
430C3×D3—42no—
431C3×D3—44no—
432C3×D3—82no—
433C24—31no—
434C24—61no—
435C24—61no—
436#41—68no—
437#41—616no—
438#41—68no—
439C2×Q8—21no—
440C2×Q8—22no—
441C2×Q8#62514yescomplemented
442C2×Q8C2×D3212yes—
443C2×D4—32no—
444C2×D4—32no—
445C2×D4—34no—
446C2×D4—64no—
447C2×D4—68no—
448C2×D4—62no—
449C2×D4—62no—
450C2×D4—61no—
451C2×D4—62no—
452C2×D4—61no—
453C2×D4—184no—
454C2×D4—364no—
455C22×C4—21no—
456C22×C4—31no—
457C22×C4—32no—
458C22×C4—32no—
459C22×C4—64no—
460C22×C4—68no—
461C22×C4—62no—
462C22×C4—62no—
463C22×C4—181no—
464C22×C4C2×D3211yescharacteristic
465SD16—68no—
466D8—188no—
467C2×C8—32no—
468C2×C8—62no—
469C2×C8—92no—
470C2×C8—182no—
471C4⋊C4—92no—
472C4⋊C4—181no—
473C22⋊C4—184no—
474C22×C3—21no—
475C22×C3—22no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—62no—
479C22×C3—62no—
480C22×C3—64no—
481C22×C3—62no—
482C22×C3—124no—
483C22×C3—128no—
484C22×C3—122no—
485C22×C3—122no—
486C22×C3—122no—
487C22×C3—122no—
488C22×C3—122no—
489C22×C3—244no—
490C22×C3#91412yes—
491C22×C3#91612yes—
492C22×C3#93712yes—
493C22×C3#94912yes—
494C22×C3#95012yes—
495C22×C3#95312yes—
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C22×#6711yescharacteristic
498C2×D3—22no—
499C2×D3—22no—
500C2×D3—22no—
501C2×D3—24no—
502C2×D3—44no—
503C2×D3—48no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—42no—
507C2×D3—42no—
508C2×D3—42no—
509C2×D3—84no—
510C3×C4—24no—
511C3×C4—24no—
512C3×C4—21no—
513C3×C4—21no—
514C3×C4—22no—
515C3×C4—44no—
516C3×C4—62no—
517C3×C4#93712yes—
518C3×C4#95312yes—
519C3×C4C2×D3×D411yescharacteristic
520C3×C4C22×#6711yescharacteristic
521C3×C4C22×#6711yescharacteristic
522C3×C4C22×#6711yescharacteristic
523Dic3—22no—
524Dic3—122no—
525Dic3—122no—
526Dic3—242no—
527C32C2×#44911yescharacteristic, complemented, Sylow
528C23—32no—
529C23—62no—
530C23—62no—
531C23—62no—
532C23—64no—
533C23—62no—
534C23—62no—
535C23—122no—
536C23—122no—
537C23—122no—
538C23—122no—
539C23—122no—
540C23D3×#6711yescharacteristic
541Q8—22no—
542Q8—24no—
543Q8C2×#62514yescomplemented
544D4—34no—
545D4—616no—
546D4—62no—
547D4—62no—
548D4—62no—
549D4—64no—
550D4—122no—
551D4—368no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—32no—
555C2×C4—616no—
556C2×C4—62no—
557C2×C4—62no—
558C2×C4—62no—
559C2×C4—64no—
560C2×C4—182no—
561C2×C4—362no—
562C2×C4C2×#62512yes—
563C2×C4D3×#6712yes—
564C2×C4D3×#6711yescharacteristic
565C2×C4C22×D3211yescharacteristic
566C8—62no—
567C8—182no—
568C2×C3—21no—
569C2×C3—24no—
570C2×C3—21no—
571C2×C3—21no—
572C2×C3—122no—
573C2×C3—124no—
574C2×C3—242no—
575C2×C3#517214yescomplemented
576C2×C3#523814yescomplemented
577C2×C3C2×#91411yescharacteristic
578C2×C3C2×#91611yescharacteristic
579C2×C3C2×#93711yescharacteristic
580C2×C3C2×#94911yescharacteristic
581C2×C3C2×#95011yescharacteristic
582C2×C3C2×#95311yescharacteristic
583D3—42no—
584D3—44no—
585D3—82no—
586C22—62no—
587C22—64no—
588C22—62no—
589C22—62no—
590C22—122no—
591C22—124no—
592C22—128no—
593C22—122no—
594C22—122no—
595C22—122no—
596C22—122no—
597C22—244no—
598C22#6393912yes—
599C22#6394712yes—
600C22#6397612yes—
601C22C2×D3×#6711yescharacteristic
602C4—24no—
603C4—62no—
604C4—362no—
605C4#6397612yes—
606C4C22×#62511yescharacteristic
607C4C2×D3×#6711yescharacteristic
608C3—21no—
609C3C2×#517211yescharacteristic, complemented
610C3C2×#523811yescharacteristic, complemented
611C2—122no—
612C2—124no—
613C2—242no—
614C2#1059158614yesdirect product factor
615C2C2×#6393911yescharacteristic
616C2C2×#6394711yescharacteristic
617C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
hypercenterC22×Q8D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×C3×#215C2semidirect
3. C2×#63908C2semidirect
4. C22×#3713C2semidirect
5. C2×#63662C2semidirect
6. #10591586C2direct (N × H)
7. C2×#63563C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
15. C2×C3×#239C22semidirect
25. C2×C3×#215C22semidirect
29. #63908C22semidirect
31. C2×#3713C22semidirect
32. #63662C22semidirect
33. #63563C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C22×#239D3semidirect
38. C22×#215D3semidirect
57. C2×C32×Q8D4semidirect
73. C2×C3×D12D4semidirect
111. C2×#239C2×D3semidirect
122. C2×#215C2×D3semidirect
161. C32×Q8C2×D4semidirect
178. C3×D12C2×D4semidirect
211. C2×C3×Q8#67semidirect
212. C2×C3×Q8#67semidirect
256. C2×D12#67semidirect
367. C3×Q8C2×#67semidirect
368. C3×Q8C2×#67semidirect
416. D12C2×#67semidirect
426. C2×C32#449semidirect
441. C2×Q8#625semidirect
527. C32C2×#449semidirect
543. Q8C2×#625semidirect
575. C2×C3#5172semidirect
576. C2×C3#5238semidirect
609. C3C2×#5172semidirect
610. C3C2×#5238semidirect
614. C2#10591586direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×C3×#2152
C2×#639082
C22×#37132
C2×#636622
#105915862
C2×#635632
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52383
C2×#51723