Finite Group Databasebeta

← C2×#10591161 #11863724

Subgroups — C2×#10591161 #11863724

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 626 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C2×C3×#930C211yesmaximal, characteristic, complemented
3C22×#3715C211yesmaximal, characteristic, complemented
4C22×#3713C211yesmaximal, characteristic, complemented
5C2×#63657C211yesmaximal, characteristic, complemented
6#10591161C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×#63562C211yesmaximal, characteristic, complemented
9C2×#5238—31nomaximal
10C2×#5037—31nomaximal
11C23×C32×C4C2211yescharacteristic
12C22×C3×#67—21no—
13C22×C3×#67—21no—
14C2×C3×#235—22no—
15C2×C3×#235—24no—
16C2×C3×#235—24no—
17C2×C3×#235C2214yescomplemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C22×C3×Dic6C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#930—22no—
25C3×#930C2214yescomplemented
26C2×C3×(C2×D3)⋊C4—21no—
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×#3715—24no—
29C2×#3715C2214yescomplemented
30C2×#3713—24no—
31C2×#3713C2214yescomplemented
32#63657C2214yescomplemented
33#63565C2214yescomplemented
34#63562C2214yescomplemented
35C22×C3×#41—31no—
36C22×#235D311yescharacteristic, complemented
37C2×C3×#121—31no—
38C22×#215—31no—
39C22×#214—31no—
40C22×#213—31no—
41C22×#213—31no—
42C2×#930D311yescharacteristic, complemented
43#5238—38no—
44C2×#835—31no—
45C2×#832—31no—
46C2×#830—31no—
47C2×#830—31no—
48C2×#830—61no—
49#5037—38no—
50C2×#810—31no—
51C2×#809—31no—
52C24×C32D411yescharacteristic
53C23×C3×D3—21no—
54C23×C3×D3—21no—
55C22×C32×C4—22no—
56C22×C32×C4—22no—
57C22×C32×C4D411yescharacteristic
58C22×C32×C4D412yes—
59C22×C32×C4C2312yes—
60C22×C32×C4C2311yescharacteristic
61C2×C3×#67—28no—
62C2×C3×#67—24no—
63C2×C3×#67—24no—
64C2×C3×#67—44no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3—21no—
67C3×#235—216no—
68C3×#235—28no—
69C3×#235—28no—
70C2×C3×D12—21no—
71C2×C3×D12—22no—
72C2×C3×D12—22no—
73C2×C3×D12—22no—
74C2×C3×D12—21no—
75C2×C3×D12D414yescomplemented
76C2×C3×D12C2312yes—
77C2×C3×D12C2312yes—
78C2×C3×C4×D3—28no—
79C2×C3×C4×D3—24no—
80C2×C3×Dic6—21no—
81C2×C3×Dic6—22no—
82C2×C3×Dic6D414yescomplemented
83C2×C3×Dic6C2312yes—
84C2×C3⋊(C3⋊C8)—22no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C2×C3⋊(C3⋊C8)C2312yes—
88C3×(C2×D3)⋊C4—24no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91#3715—28no—
92#3713—28no—
93C2×#449—91noSylow
94C2×C3×#41—34no—
95C2×C3×#41—64no—
96C2×C3×#41—64no—
97C2×C3×#41—62no—
98C22×C3×Q8—31no—
99C22×C3×D4—31no—
100C22×C3×D4—31no—
101C22×C3×D4—61no—
102C22×C3×D4—61no—
103C23×C3×C4—21no—
104C23×C3×C4—61no—
105C23×C3×C4C2×D311yescharacteristic
106C23×C3×C4C2×D311yescharacteristic
107C22×#67—21no—
108C22×#67—21no—
109C2×#235—22no—
110C2×#235—24no—
111C2×#235—24no—
112C2×#235C2×D314yescomplemented
113C22×D12C2×D311yescharacteristic
114C22×D12C2×D311yescharacteristic
115C22×C4×D3—21no—
116C22×Dic6C2×D311yescharacteristic
117C3×#121—34no—
118C3×#121—62no—
119C2×C3×C4⋊C4—31no—
120C2×C3×C22⋊C4—61no—
121C2×#215—34no—
122C2×#215—64no—
123C2×#214—34no—
124C2×#214—64no—
125C2×#213—34no—
126C2×#213—34no—
127C2×#213—64no—
128C2×#213—64no—
129#930—22no—
130#930C2×D314yescomplemented
131C2×(C2×D3)⋊C4—21no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—31no—
136C22×C3⋊C8—31no—
137C22×C3⋊C8—61no—
138C22×C3⋊C8—61no—
139#835—34no—
140#832—34no—
141#830—34no—
142#830—34no—
143#830—64no—
144#810—34no—
145#809—34no—
146C23×C32—22no—
147C23×C32—22no—
148C23×C32—22no—
149C23×C32C2×D412yes—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—24no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—42no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3—42no—
159C2×C32×C4—22no—
160C2×C32×C4—24no—
161C2×C32×C4—22no—
162C2×C32×C4—22no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2411yescharacteristic
168C3×#67—216no—
169C3×#67—48no—
170C2×C3×Dic3—24no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—42no—
174C3×D12—24no—
175C3×D12—22no—
176C3×D12—22no—
177C3×D12—22no—
178C3×D12—42no—
179C3×D12C2×D414yescomplemented
180C3×C4×D3—216no—
181C3×Dic6—24no—
182C3×Dic6—22no—
183C3×Dic6C2×D414yescomplemented
184C3⋊(C3⋊C8)—22no—
185C3⋊(C3⋊C8)—22no—
186C22×#41—31no—
187C22×SD16—91no—
188C22×D8—91no—
189C2×#121—31no—
190#449—98no—
191C2×#103—91no—
192C2×#102—91no—
193C2×C22⋊C8—91no—
194C24×C3—21no—
195C24×C3—61no—
196C24×C3—61no—
197C24×C3#6711yescharacteristic
198C24×C3#6711yescharacteristic
199C23×D3—21no—
200C23×D3—21no—
201C3×#41—68no—
202C3×#41—68no—
203C3×#41—616no—
204C2×C3×Q8—34no—
205C2×C3×Q8—32no—
206C2×C3×Q8—62no—
207C2×C3×Q8—61no—
208C2×C3×D4—34no—
209C2×C3×D4—32no—
210C2×C3×D4—32no—
211C2×C3×D4—68no—
212C2×C3×D4—64no—
213C2×C3×D4—64no—
214C2×C3×D4—62no—
215C2×C3×D4—61no—
216C2×C3×D4—62no—
217C2×C3×D4—62no—
218C2×C3×D4—61no—
219C2×C3×D4—124no—
220C22×C3×C4—22no—
221C22×C3×C4—22no—
222C22×C3×C4—22no—
223C22×C3×C4—22no—
224C22×C3×C4—22no—
225C22×C3×C4—21no—
226C22×C3×C4—21no—
227C22×C3×C4—22no—
228C22×C3×C4—42no—
229C22×C3×C4—42no—
230C22×C3×C4—68no—
231C22×C3×C4—61no—
232C22×C3×C4—64no—
233C22×C3×C4—61no—
234C22×C3×C4#6711yescharacteristic
235C22×C3×C4#6712yes—
236C22×C3×C4#6711yescharacteristic
237C22×C3×C4#6712yes—
238C22×C3×C4C22×D312yes—
239C22×C3×C4C22×D312yes—
240C22×C3×C4C22×D311yescharacteristic
241C22×C3×C4C22×D311yescharacteristic
242C2×#67—28no—
243C2×#67—24no—
244C2×#67—24no—
245C2×#67—44no—
246C22×Dic3—21no—
247C22×Dic3—21no—
248#235—216no—
249#235—28no—
250#235—28no—
251C2×D12—21no—
252C2×D12—22no—
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—24no—
261C2×Dic6—21no—
262C2×Dic6—22no—
263C2×Dic6#6714yescomplemented
264C2×Dic6C22×D312yes—
265C3×C4⋊C4—32no—
266C3×C4⋊C4—61no—
267C3×C22⋊C4—64no—
268#215—68no—
269#214—68no—
270#213—68no—
271#213—68no—
272(C2×D3)⋊C4—24no—
273C4⋊Dic3—21no—
274C4⋊Dic3C22×D312yes—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—32no—
278C2×C3⋊C8—32no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—62no—
281C2×C3⋊C8—62no—
282C2×C3⋊C8—62no—
283C2×C3⋊C8—62no—
284C2×C3⋊C8—62no—
285C2×C3⋊C8—122no—
286C2×C3⋊C8—122no—
287C22×C32—22no—
288C22×C32—22no—
289C22×C32—22no—
290C22×C32—44no—
291C22×C32#12012yes—
292C22×C32#13512yes—
293C22×C32AGL(1,ℤ/8)12yes—
294C22×C32C22×D411yescharacteristic
295C2×C3×D3—24no—
296C2×C3×D3—42no—
297C2×C3×D3—42no—
298C2×C3×D3—48no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C32×C4—22no—
304C32×C4#12012yes—
305C32×C4C22×D411yescharacteristic
306C32×C4C22×D411yescharacteristic
307C3×Dic3—24no—
308C3×Dic3—42no—
309C2×#41—34no—
310C2×#41—64no—
311C2×#41—64no—
312C2×#41—62no—
313C22×Q8—31no—
314C22×D4—31no—
315C22×D4—31no—
316C22×D4—61no—
317C22×D4—61no—
318C23×C4—61no—
319C23×C4D3211yescharacteristic
320C2×SD16—94no—
321C2×SD16—184no—
322C2×D8—94no—
323C2×D8—184no—
324C22×C8—91no—
325C22×C8—91no—
326#121—34no—
327#121—62no—
328C2×C4⋊C4—31no—
329C2×C22⋊C4—61no—
330#103—94no—
331#102—94no—
332C22⋊C8—94no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—64no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—122no—
348C23×C3—122no—
349C23×C3—122no—
350C23×C3—122no—
351C23×C3—122no—
352C23×C3C2×#6712yes—
353C23×C3C2×#6712yes—
354C23×C3C2×#6711yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C22×D3—24no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—42no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3—42no—
364C3×Q8—34no—
365C3×Q8—64no—
366C3×Q8—62no—
367C3×D4—34no—
368C3×D4—616no—
369C3×D4—64no—
370C3×D4—62no—
371C3×D4—62no—
372C3×D4—62no—
373C3×D4—128no—
374C3×D4—122no—
375C2×C3×C4—22no—
376C2×C3×C4—22no—
377C2×C3×C4—24no—
378C2×C3×C4—24no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—21no—
385C2×C3×C4—22no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—42no—
389C2×C3×C4—42no—
390C2×C3×C4—44no—
391C2×C3×C4—42no—
392C2×C3×C4—616no—
393C2×C3×C4—64no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—122no—
397C2×C3×C4D3×D412yes—
398C2×C3×C4D3×D412yes—
399C2×C3×C4C2×#6712yes—
400C2×C3×C4C2×#6712yes—
401C2×C3×C4C2×#6711yescharacteristic
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6712yes—
404C2×C3×C4C2×#6712yes—
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—216no—
408#67—48no—
409C2×Dic3—24no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—42no—
413D12—24no—
414D12—22no—
415D12—22no—
416D12—22no—
417D12—42no—
418D12C2×#6714yescomplemented
419C4×D3—216no—
420Dic6—24no—
421Dic6—22no—
422Dic6C2×#6714yescomplemented
423C3⋊C8—62no—
424C3⋊C8—62no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C3⋊C8—122no—
429C2×C32—42no—
430C2×C32#44914yescomplemented
431C2×C32C2×#12011yescharacteristic
432C2×C32C2×#13511yescharacteristic
433C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
434C3×D3—44no—
435C3×D3—82no—
436C24—61no—
437C24—61no—
438C24#62511yescharacteristic
439#41—68no—
440#41—68no—
441#41—616no—
442C2×Q8—32no—
443C2×Q8—34no—
444C2×Q8—61no—
445C2×Q8—62no—
446C2×D4—32no—
447C2×D4—32no—
448C2×D4—34no—
449C2×D4—68no—
450C2×D4—64no—
451C2×D4—64no—
452C2×D4—61no—
453C2×D4—61no—
454C2×D4—62no—
455C2×D4—62no—
456C2×D4—62no—
457C2×D4—124no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—68no—
461C22×C4—61no—
462C22×C4—64no—
463C22×C4—61no—
464C22×C4#62512yes—
465C22×C4#62511yescharacteristic
466C22×C4C2×D3212yes—
467C22×C4C2×D3211yescharacteristic
468SD16—188no—
469D8—188no—
470C2×C8—92no—
471C2×C8—92no—
472C2×C8—182no—
473C2×C8—182no—
474C4⋊C4—32no—
475C4⋊C4—61no—
476C22⋊C4—64no—
477C22×C3—24no—
478C22×C3—22no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—22no—
483C22×C3—22no—
484C22×C3—21no—
485C22×C3—22no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—48no—
491C22×C3—44no—
492C22×C3—44no—
493C22×C3—64no—
494C22×C3—122no—
495C22×C3—128no—
496C22×C3—122no—
497C22×C3—122no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—244no—
501C22×C3#93212yes—
502C22×C3#93712yes—
503C22×C3#94912yes—
504C22×C3#95012yes—
505C22×C3#95012yes—
506C22×C3#95312yes—
507C22×C3C22×#6711yescharacteristic
508C22×C3C22×#6711yescharacteristic
509C2×D3—24no—
510C2×D3—48no—
511C2×D3—42no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—42no—
516C2×D3—84no—
517C3×C4—22no—
518C3×C4—22no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—22no—
522C3×C4—42no—
523C3×C4—64no—
524C3×C4—122no—
525C3×C4#93712yes—
526C3×C4#95312yes—
527C3×C4C2×D3×D411yescharacteristic
528C3×C4C2×D3×D411yescharacteristic
529C3×C4C22×#6711yescharacteristic
530C3×C4C22×#6711yescharacteristic
531Dic3—24no—
532Dic3—42no—
533C32C2×#44911yescharacteristic, complemented, Sylow
534C23—22no—
535C23—22no—
536C23—22no—
537C23—62no—
538C23—64no—
539C23—62no—
540C23—122no—
541C23—122no—
542C23—122no—
543C23—122no—
544C23—122no—
545C23C2×#62512yes—
546C23C2×#62511yescharacteristic
547Q8—34no—
548Q8—62no—
549Q8—64no—
550D4—34no—
551D4—616no—
552D4—62no—
553D4—62no—
554D4—62no—
555D4—64no—
556D4—128no—
557D4—122no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—24no—
562C2×C4—616no—
563C2×C4—62no—
564C2×C4—64no—
565C2×C4—62no—
566C2×C4—122no—
567C2×C4C2×#62512yes—
568C2×C4C2×#62511yescharacteristic
569C2×C4D3×#6712yes—
570C2×C4D3×#6712yes—
571C2×C4C22×D3211yescharacteristic
572C8—182no—
573C8—182no—
574C2×C3—21no—
575C2×C3—24no—
576C2×C3—21no—
577C2×C3—21no—
578C2×C3—44no—
579C2×C3—42no—
580C2×C3—42no—
581C2×C3—124no—
582C2×C3—242no—
583C2×C3#503714yescomplemented
584C2×C3#523814yescomplemented
585C2×C3C2×#93211yescharacteristic
586C2×C3C2×#93711yescharacteristic
587C2×C3C2×#94911yescharacteristic
588C2×C3C2×#95011yescharacteristic
589C2×C3C2×#95011yescharacteristic
590C2×C3C2×#95311yescharacteristic
591D3—44no—
592D3—82no—
593C22—22no—
594C22—22no—
595C22—22no—
596C22—44no—
597C22—64no—
598C22—128no—
599C22—122no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—122no—
604C22—244no—
605C22#6382212yes—
606C22#6382312yes—
607C22#6397612yes—
608C22C22×#62511yescharacteristic
609C4—22no—
610C4—64no—
611C4—122no—
612C4#6397612yes—
613C4C2×D3×#6711yescharacteristic
614C4C2×D3×#6711yescharacteristic
615C3—21no—
616C3C2×#503711yescharacteristic, complemented
617C3C2×#523811yescharacteristic, complemented
618C2—42no—
619C2—124no—
620C2—242no—
621C2#1059116114yesdirect product factor
622C2C2×#6382211yescharacteristic
623C2C2×#6382311yescharacteristic
624C2C2×#6397611yescharacteristic
subgroupG/H
centerC23C2×#625
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC23×C32C2×D4
hypercenterC23×C4D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C2×C3×#930C2semidirect
3. C22×#3715C2semidirect
4. C22×#3713C2semidirect
5. C2×#63657C2semidirect
6. #10591161C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×#63562C2semidirect
17. C2×C3×#235C22semidirect
25. C3×#930C22semidirect
29. C2×#3715C22semidirect
31. C2×#3713C22semidirect
32. #63657C22semidirect
33. #63565C22semidirect
34. #63562C22semidirect
36. C22×#235D3semidirect
42. C2×#930D3semidirect
75. C2×C3×D12D4semidirect
82. C2×C3×Dic6D4semidirect
112. C2×#235C2×D3semidirect
130. #930C2×D3semidirect
179. C3×D12C2×D4semidirect
183. C3×Dic6C2×D4semidirect
256. C2×D12#67semidirect
263. C2×Dic6#67semidirect
418. D12C2×#67semidirect
422. Dic6C2×#67semidirect
430. C2×C32#449semidirect
533. C32C2×#449semidirect
583. C2×C3#5037semidirect
584. C2×C3#5238semidirect
616. C3C2×#5037semidirect
617. C3C2×#5238semidirect
621. C2#10591161direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C2×C3×#9302
C22×#37152
C22×#37132
C2×#636572
#105911612
C2×#635652
C2×#635622
C2×#52383
C2×#50373