Finite Group Databasebeta

← C2×#10591450 #11863721

Subgroups — C2×#10591450 #11863721

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×C3×#213C211yesmaximal, characteristic, complemented
3C2×#63908C211yesmaximal, characteristic, complemented
4C22×#3715C211yesmaximal, characteristic, complemented
5C2×#63659C211yesmaximal, characteristic, complemented
6#10591450C218yesmaximal, direct product factor
7C2×#63566C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5238—31nomaximal
10C2×#5158—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C3×#67—21no—
13C23×C3×Dic3—21no—
14C2×C3×#237—24no—
15C2×C3×#237—22no—
16C2×C3×#237—24no—
17C2×C3×#237C2214yescomplemented
18C22×C3×D12C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#625—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C2×C3×#213—24no—
25C2×C3×#213C2214yescomplemented
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×(C2×D3)⋊Dic3—21no—
28#63908—22no—
29#63908C2214yescomplemented
30C2×#3715—24no—
31C2×#3715C2214yescomplemented
32#63659C2214yescomplemented
33#63566C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#237D311yescharacteristic, complemented
37C22×C3×D8—31no—
38C22×#215—31no—
39C2×#938—31no—
40C22×#214—31no—
41C22×#213D311yescharacteristic, complemented
42C2×#930—31no—
43#5238—38no—
44C2×#835—31no—
45C2×#832—31no—
46C2×#832—31no—
47C2×#832—61no—
48C2×#830—31no—
49#5158—38no—
50C2×(C2×D3)⋊C8—31no—
51C2×#816—31no—
52C24×C32—21no—
53C23×C3×D3—21no—
54C23×C3×D3D411yescharacteristic
55C2×C32×D4—21no—
56C2×C32×D4—22no—
57C2×C32×D4D414yescomplemented
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C22×C3⋊Dic3—21no—
61C2×C3×#67—28no—
62C2×C3×#67—24no—
63C22×C3×Dic3—28no—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—24no—
66C22×C3×Dic3D411yescharacteristic
67C3×#237—216no—
68C3×#237—28no—
69C3×#237—28no—
70C2×C3×D12—22no—
71C2×C3×D12—22no—
72C2×C3×D12—21no—
73C2×C3×D12C2312yes—
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3—22no—
76C2×C3×C4×D3D412yes—
77C2×C3×C4×D3C2312yes—
78C2×C3×Dic6—21no—
79C2×C3×Dic6—22no—
80C2×C3×Dic6D414yescomplemented
81C2×C3×Dic6C2312yes—
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×#213—28no—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91(C2×D3)⋊Dic3—24no—
92#3715—28no—
93C2×#449—91noSylow
94C2×C3×#41—34no—
95C2×C3×#41—62no—
96C2×C3×#41—64no—
97C2×C3×#41—64no—
98C22×C3×Q8—31no—
99C22×C3×D4—21no—
100C22×C3×D4—31no—
101C22×C3×D4—61no—
102C22×C3×D4C2×D311yescharacteristic
103C22×C3×D4C2×D311yescharacteristic
104C23×C3×C4—31no—
105C23×C3×C4—61no—
106C22×#67—21no—
107C22×#67—61no—
108C22×#67—61no—
109C23×Dic3—21no—
110C2×#237—24no—
111C2×#237—22no—
112C2×#237—24no—
113C2×#237C2×D314yescomplemented
114C22×D12C2×D311yescharacteristic
115C22×C4×D3C2×D311yescharacteristic
116C22×Dic6C2×D311yescharacteristic
117C2×C3×D8—34no—
118C2×C3×D8—64no—
119C22×C3×C8—31no—
120C2×#217—61no—
121C2×#215—34no—
122C2×#215—64no—
123#938—34no—
124#938—62no—
125C2×#214—34no—
126C2×#214—64no—
127C2×#213—24no—
128C2×#213C2×D314yescomplemented
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#832—34no—
141#832—34no—
142#832—64no—
143#830—34no—
144(C2×D3)⋊C8—34no—
145#816—34no—
146C23×C32—24no—
147C23×C32—22no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—22no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—42no—
156C22×C3×D3—42no—
157C22×C3×D3—42no—
158C22×C3×D3C2×D412yes—
159C32×D4—24no—
160C32×D4—22no—
161C32×D4C2×D414yescomplemented
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D412yes—
165C2×C32×C4C2411yescharacteristic
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—42no—
168C3×#67—216no—
169C2×C3×Dic3—216no—
170C2×C3×Dic3—24no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3C2×D412yes—
174C3×D12—22no—
175C3×D12—22no—
176C3×D12—42no—
177C3×C4×D3—24no—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—24no—
181C3×Dic6—22no—
182C3×Dic6C2×D414yescomplemented
183#625—48no—
184C3⋊(C3⋊C8)—22no—
185C3×C3⋊C8—22no—
186C22×#41—31no—
187C22×SD16—91no—
188C22×D8—31no—
189C2×#121—91no—
190#449—98no—
191C2×#103—91no—
192C2×#102—91no—
193C2×C22⋊C8—91no—
194C24×C3—21no—
195C24×C3—21no—
196C24×C3—31no—
197C24×C3—41no—
198C24×C3—61no—
199C23×D3—21no—
200C23×D3#6711yescharacteristic
201C3×#41—68no—
202C3×#41—616no—
203C3×#41—68no—
204C2×C3×Q8—34no—
205C2×C3×Q8—32no—
206C2×C3×Q8—61no—
207C2×C3×Q8—62no—
208C2×C3×D4—21no—
209C2×C3×D4—22no—
210C2×C3×D4—21no—
211C2×C3×D4—22no—
212C2×C3×D4—24no—
213C2×C3×D4—22no—
214C2×C3×D4—32no—
215C2×C3×D4—42no—
216C2×C3×D4—41no—
217C2×C3×D4—64no—
218C2×C3×D4—68no—
219C2×C3×D4—62no—
220C2×C3×D4—62no—
221C2×C3×D4—61no—
222C2×C3×D4#6714yescomplemented
223C2×C3×D4#6714yescomplemented
224C2×C3×D4C22×D312yes—
225C2×C3×D4C22×D312yes—
226C22×C3×C4—21no—
227C22×C3×C4—31no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—64no—
231C22×C3×C4—68no—
232C22×C3×C4—61no—
233C22×C3×C4—62no—
234C22×C3×C4—62no—
235C22×C3×C4C22×D311yescharacteristic
236C22×C3×C4C22×D311yescharacteristic
237C2×#67—28no—
238C2×#67—24no—
239C2×#67—64no—
240C2×#67—64no—
241C2×#67—124no—
242C2×#67—124no—
243C22×Dic3—28no—
244C22×Dic3—21no—
245C22×Dic3—24no—
246C22×Dic3—61no—
247C22×Dic3—61no—
248C22×Dic3—121no—
249C22×Dic3#6711yescharacteristic
250#237—216no—
251#237—28no—
252#237—28no—
253C2×D12—22no—
254C2×D12—22no—
255C2×D12—21no—
256C2×D12C22×D312yes—
257C2×C4×D3—22no—
258C2×C4×D3—22no—
259C2×C4×D3#6712yes—
260C2×C4×D3C22×D312yes—
261C2×Dic6—22no—
262C2×Dic6—21no—
263C2×Dic6#6714yescomplemented
264C2×Dic6C22×D312yes—
265C3×D8—68no—
266C2×C3×C8—32no—
267C2×C3×C8—62no—
268#217—64no—
269#215—68no—
270#214—68no—
271#213—28no—
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—24no—
288C22×C32—42no—
289C22×C32—42no—
290C22×C32—48no—
291C22×C32#12012yes—
292C22×C32#13512yes—
293C22×C32AGL(1,ℤ/8)12yes—
294C22×C32C22×D411yescharacteristic
295C2×C3×D3—22no—
296C2×C3×D3—22no—
297C2×C3×D3—22no—
298C2×C3×D3—44no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C2×C3×D3—84no—
303C32×C4#12012yes—
304C32×C4C22×D411yescharacteristic
305C32×C4C22×D411yescharacteristic
306C3⋊Dic3—42no—
307C3×Dic3—24no—
308C3×Dic3—22no—
309C2×#41—34no—
310C2×#41—62no—
311C2×#41—64no—
312C2×#41—64no—
313C22×Q8—31no—
314C22×D4—31no—
315C22×D4—61no—
316C22×D4—181no—
317C22×D4D3211yescharacteristic
318C23×C4—31no—
319C23×C4—61no—
320C2×SD16—94no—
321C2×SD16—184no—
322C2×D8—34no—
323C2×D8—64no—
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—24no—
334C23×C3—24no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—21no—
338C23×C3—32no—
339C23×C3—42no—
340C23×C3—44no—
341C23×C3—42no—
342C23×C3—42no—
343C23×C3—42no—
344C23×C3—42no—
345C23×C3—62no—
346C23×C3—62no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—82no—
350C23×C3—82no—
351C23×C3—122no—
352C23×C3—122no—
353C23×C3—122no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—22no—
360C22×D3—42no—
361C22×D3—42no—
362C22×D3—42no—
363C22×D3C2×#6712yes—
364C3×Q8—34no—
365C3×Q8—64no—
366C3×Q8—62no—
367C3×D4—24no—
368C3×D4—24no—
369C3×D4—22no—
370C3×D4—22no—
371C3×D4—24no—
372C3×D4—42no—
373C3×D4—44no—
374C3×D4—616no—
375C3×D4—62no—
376C3×D4—62no—
377C3×D4—122no—
378C3×D4C2×#6714yescomplemented
379C3×D4C2×#6714yescomplemented
380C2×C3×C4—21no—
381C2×C3×C4—22no—
382C2×C3×C4—22no—
383C2×C3×C4—21no—
384C2×C3×C4—32no—
385C2×C3×C4—616no—
386C2×C3×C4—62no—
387C2×C3×C4—64no—
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—216no—
401#67—128no—
402#67—128no—
403C2×Dic3—216no—
404C2×Dic3—24no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—122no—
412C2×Dic3—242no—
413C2×Dic3C2×#6712yes—
414D12—22no—
415D12—22no—
416D12—42no—
417C4×D3—24no—
418C4×D3—22no—
419C4×D3—22no—
420Dic6—24no—
421Dic6—22no—
422Dic6C2×#6714yescomplemented
423C3×C8—62no—
424C3⋊C8—22no—
425C3⋊C8—62no—
426C3⋊C8—62no—
427C3⋊C8—122no—
428C2×C32—44no—
429C2×C32#44914yescomplemented
430C2×C32C2×#12011yescharacteristic
431C2×C32C2×#13511yescharacteristic
432C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
433C3×D3—42no—
434C3×D3—82no—
435C24—21no—
436C24—31no—
437C24—61no—
438#41—68no—
439#41—616no—
440#41—68no—
441C2×Q8—32no—
442C2×Q8—34no—
443C2×Q8—62no—
444C2×Q8—61no—
445C2×D4—22no—
446C2×D4—21no—
447C2×D4—32no—
448C2×D4—64no—
449C2×D4—68no—
450C2×D4—62no—
451C2×D4—62no—
452C2×D4—61no—
453C2×D4—184no—
454C2×D4—364no—
455C2×D4#62514yescomplemented
456C2×D4C2×D3212yes—
457C22×C4—31no—
458C22×C4—32no—
459C22×C4—32no—
460C22×C4—64no—
461C22×C4—68no—
462C22×C4—61no—
463C22×C4—62no—
464C22×C4—62no—
465C22×C4—181no—
466C22×C4C2×D3211yescharacteristic
467SD16—188no—
468D8—68no—
469C2×C8—32no—
470C2×C8—62no—
471C2×C8—92no—
472C2×C8—182no—
473C4⋊C4—92no—
474C4⋊C4—181no—
475C22⋊C4—184no—
476C22×C3—24no—
477C22×C3—24no—
478C22×C3—21no—
479C22×C3—22no—
480C22×C3—22no—
481C22×C3—22no—
482C22×C3—44no—
483C22×C3—48no—
484C22×C3—48no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—82no—
493C22×C3—82no—
494C22×C3—88no—
495C22×C3—124no—
496C22×C3—122no—
497C22×C3—122no—
498C22×C3—122no—
499C22×C3—244no—
500C22×C3#91112yes—
501C22×C3#91212yes—
502C22×C3#93712yes—
503C22×C3#94912yes—
504C22×C3#95012yes—
505C22×C3#95312yes—
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C22×#6711yescharacteristic
508C2×D3—22no—
509C2×D3—22no—
510C2×D3—22no—
511C2×D3—44no—
512C2×D3—42no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—84no—
516C3×C4—21no—
517C3×C4—21no—
518C3×C4—22no—
519C3×C4—62no—
520C3×C4—64no—
521C3×C4#93712yes—
522C3×C4#95312yes—
523C3×C4C2×D3×D411yescharacteristic
524C3×C4C22×#6711yescharacteristic
525C3×C4C22×#6711yescharacteristic
526C3×C4C22×#6711yescharacteristic
527Dic3—24no—
528Dic3—22no—
529Dic3—122no—
530Dic3—122no—
531Dic3—242no—
532C32C2×#44911yescharacteristic, complemented, Sylow
533C23—22no—
534C23—24no—
535C23—32no—
536C23—42no—
537C23—42no—
538C23—62no—
539C23—62no—
540C23—62no—
541C23—62no—
542C23—122no—
543C23—122no—
544C23—122no—
545C23D3×#6711yescharacteristic
546Q8—34no—
547Q8—62no—
548Q8—64no—
549D4—22no—
550D4—24no—
551D4—616no—
552D4—62no—
553D4—62no—
554D4—122no—
555D4—368no—
556D4C2×#62514yescomplemented
557C2×C4—32no—
558C2×C4—616no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—64no—
562C2×C4—62no—
563C2×C4—62no—
564C2×C4—64no—
565C2×C4—182no—
566C2×C4—362no—
567C2×C4C2×#62512yes—
568C2×C4D3×#6712yes—
569C2×C4D3×#6711yescharacteristic
570C2×C4C22×D3211yescharacteristic
571C8—62no—
572C8—182no—
573C2×C3—21no—
574C2×C3—21no—
575C2×C3—21no—
576C2×C3—24no—
577C2×C3—44no—
578C2×C3—44no—
579C2×C3—84no—
580C2×C3—122no—
581C2×C3—242no—
582C2×C3#515814yescomplemented
583C2×C3#523814yescomplemented
584C2×C3C2×#91111yescharacteristic
585C2×C3C2×#91211yescharacteristic
586C2×C3C2×#93711yescharacteristic
587C2×C3C2×#94911yescharacteristic
588C2×C3C2×#95011yescharacteristic
589C2×C3C2×#95311yescharacteristic
590D3—42no—
591D3—82no—
592C22—24no—
593C22—42no—
594C22—42no—
595C22—48no—
596C22—62no—
597C22—62no—
598C22—62no—
599C22—124no—
600C22—122no—
601C22—122no—
602C22—122no—
603C22—244no—
604C22#6392512yes—
605C22#6393312yes—
606C22#6397612yes—
607C22C2×D3×#6711yescharacteristic
608C4—62no—
609C4—64no—
610C4—362no—
611C4#6397612yes—
612C4C22×#62511yescharacteristic
613C4C2×D3×#6711yescharacteristic
614C3—21no—
615C3C2×#515811yescharacteristic, complemented
616C3C2×#523811yescharacteristic, complemented
617C2—44no—
618C2—122no—
619C2—242no—
620C2#1059145014yesdirect product factor
621C2C2×#6392511yescharacteristic
622C2C2×#6393311yescharacteristic
623C2C2×#6397611yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC23×C32C2×D4
hypercenterC22×D4D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C22×C3×#213C2semidirect
3. C2×#63908C2semidirect
4. C22×#3715C2semidirect
5. C2×#63659C2semidirect
6. #10591450C2direct (N × H)
7. C2×#63566C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
17. C2×C3×#237C22semidirect
25. C2×C3×#213C22semidirect
29. #63908C22semidirect
31. C2×#3715C22semidirect
32. #63659C22semidirect
33. #63566C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C22×#237D3semidirect
41. C22×#213D3semidirect
57. C2×C32×D4D4semidirect
80. C2×C3×Dic6D4semidirect
113. C2×#237C2×D3semidirect
128. C2×#213C2×D3semidirect
161. C32×D4C2×D4semidirect
182. C3×Dic6C2×D4semidirect
222. C2×C3×D4#67semidirect
223. C2×C3×D4#67semidirect
263. C2×Dic6#67semidirect
378. C3×D4C2×#67semidirect
379. C3×D4C2×#67semidirect
422. Dic6C2×#67semidirect
429. C2×C32#449semidirect
455. C2×D4#625semidirect
532. C32C2×#449semidirect
556. D4C2×#625semidirect
582. C2×C3#5158semidirect
583. C2×C3#5238semidirect
615. C3C2×#5158semidirect
616. C3C2×#5238semidirect
620. C2#10591450direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C22×C3×#2132
C2×#639082
C22×#37152
C2×#636592
#105914502
C2×#635662
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52383
C2×#51583