Finite Group Databasebeta

← C2×#10591452 #11863719

Subgroups — C2×#10591452 #11863719

Order 1152.

1793 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C22×#3753C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×#832C211yesmaximal, characteristic, complemented
6#10591452C218yesmaximal, direct product factor
7C2×#63565C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5238—31nomaximal
10C2×#4781—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×#67—21no—
14C23×C3×Dic3—21no—
15C2×C3×#237—24no—
16C2×C3×#237—22no—
17C2×C3×#237—24no—
18C2×C3×#237C2214yescomplemented
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#626—21no—
22C2×#3753—24no—
23C2×#3753C2214yescomplemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×#3722—21no—
28#63909—22no—
29#63909C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×#832C2214yescomplemented
33#63565C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×C3×#41—31no—
36C22×#237D311yescharacteristic, complemented
37C22×#215—31no—
38C22×#213—31no—
39C22×#213—31no—
40C22×#213—61no—
41C2×#930—31no—
42C22×#204—31no—
43C2×#895—31no—
44C2×C3×#102—31no—
45#5238—38no—
46C2×#835—31no—
47C2×#832D311yescharacteristic, complemented
48C2×#830—31no—
49C2×(C2×D3)⋊C8—31no—
50C2×#810—31no—
51#4781—38no—
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
60C2×C4⋊(C3⋊D3)—22no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)—21no—
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C3×#67—28no—
65C2×C3×#67—24no—
66C22×C3×Dic3—28no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3—24no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3D411yescharacteristic
71C3×#237—216no—
72C3×#237—28no—
73C3×#237—28no—
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×#626—24no—
83C2×#626—44no—
84#3753—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×C4⋊Dic3—21no—
88C3×C4⋊Dic3C2312yes—
89C2×C3×C3⋊C8—22no—
90C2×C3×C3⋊C8C2312yes—
91#3722—24no—
92#3717—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—61no—
101C22×C3×D4C2×D311yescharacteristic
102C22×C3×D4C2×D311yescharacteristic
103C23×C3×C4—31no—
104C23×C3×C4—61no—
105C22×#67—21no—
106C22×#67—61no—
107C23×Dic3—21no—
108C2×#237—24no—
109C2×#237—22no—
110C2×#237—24no—
111C2×#237C2×D314yescomplemented
112C22×D12—31no—
113C22×D12—31no—
114C22×D12—61no—
115C22×D12—61no—
116C22×C4×D3C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C22×C3×C8—31no—
119C2×C3×C4⋊C4—31no—
120C2×#215—34no—
121C2×#215—64no—
122C2×#213—34no—
123C2×#213—34no—
124C2×#213—64no—
125C2×#213—68no—
126C2×#213—64no—
127C2×#213—64no—
128#930—34no—
129#930—62no—
130C2×(C2×D3)⋊C4—61no—
131C2×(C2×D3)⋊C4—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C22×C3⋊C8—31no—
134C22×C3⋊C8—31no—
135C22×C3⋊C8—61no—
136C22×C3⋊C8C2×D311yescharacteristic
137C2×#204—34no—
138C2×#204—64no—
139#895—34no—
140#895—62no—
141C3×#102—34no—
142#835—34no—
143#832C2×D314yescomplemented
144#830—34no—
145(C2×D3)⋊C8—34no—
146#810—34no—
147C23×C32—24no—
148C23×C32—22no—
149C23×C32—42no—
150C23×C32—42no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—22no—
153C22×C3⋊D3—42no—
154C22×C3⋊D3—42no—
155C22×C3⋊D3—42no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—22no—
159C22×C3×D3C2×D412yes—
160C32×D4—24no—
161C32×D4—22no—
162C32×D4C2×D414yescomplemented
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2411yescharacteristic
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)—42no—
170C3×#67—216no—
171C2×C3×Dic3—216no—
172C2×C3×Dic3—24no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—42no—
177C2×C3×Dic3C2×D412yes—
178C3×C4×D3—24no—
179C3×C4×D3—22no—
180C3×C4×D3—22no—
181C3×Dic6—24no—
182C3×Dic6—22no—
183C3×Dic6C2×D414yescomplemented
184#626—48no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—22no—
187C22×#41—31no—
188C22×SD16—91no—
189C22×D8—91no—
190C2×#121—91no—
191#449—98no—
192C2×#103—91no—
193C2×#102—31no—
194C2×C22⋊C8—91no—
195C24×C3—21no—
196C24×C3—21no—
197C24×C3—31no—
198C24×C3—41no—
199C23×D3—61no—
200C23×D3—61no—
201C23×D3—121no—
202C23×D3#6711yescharacteristic
203C3×#41—68no—
204C3×#41—616no—
205C3×#41—68no—
206C2×C3×Q8—34no—
207C2×C3×Q8—32no—
208C2×C3×Q8—62no—
209C2×C3×Q8—61no—
210C2×C3×D4—21no—
211C2×C3×D4—22no—
212C2×C3×D4—21no—
213C2×C3×D4—22no—
214C2×C3×D4—24no—
215C2×C3×D4—22no—
216C2×C3×D4—42no—
217C2×C3×D4—41no—
218C2×C3×D4—64no—
219C2×C3×D4—68no—
220C2×C3×D4D1214yescomplemented
221C2×C3×D4#6714yescomplemented
222C2×C3×D4C22×D312yes—
223C2×C3×D4C22×D312yes—
224C22×C3×C4—21no—
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—32no—
228C22×C3×C4—64no—
229C22×C3×C4—68no—
230C22×C3×C4—61no—
231C22×C3×C4—62no—
232C22×C3×C4—62no—
233C22×C3×C4—61no—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—28no—
237C2×#67—24no—
238C2×#67—64no—
239C2×#67—124no—
240C22×Dic3—28no—
241C22×Dic3—21no—
242C22×Dic3—24no—
243C22×Dic3—21no—
244C22×Dic3#6711yescharacteristic
245#237—216no—
246#237—28no—
247#237—28no—
248C2×D12—32no—
249C2×D12—32no—
250C2×D12—62no—
251C2×D12—64no—
252C2×D12—62no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—64no—
257C2×D12—61no—
258C2×D12—61no—
259C2×D12—122no—
260C2×D12—121no—
261C2×D12—124no—
262C2×C4×D3—22no—
263C2×C4×D3—22no—
264C2×C4×D3#6712yes—
265C2×C4×D3C22×D312yes—
266C2×Dic6—22no—
267C2×Dic6—21no—
268C2×Dic6#6714yescomplemented
269C2×Dic6C22×D312yes—
270C2×C3×C8—32no—
271C2×C3×C8—62no—
272C3×C4⋊C4—32no—
273C3×C4⋊C4—61no—
274#215—68no—
275#213—616no—
276#213—68no—
277#213—68no—
278(C2×D3)⋊C4—64no—
279(C2×D3)⋊C4—64no—
280C4⋊Dic3—21no—
281C4⋊Dic3C22×D312yes—
282C2×C3⋊C8—22no—
283C2×C3⋊C8—32no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—62no—
286C2×C3⋊C8—64no—
287C2×C3⋊C8—62no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8C22×D312yes—
290#204—68no—
291C22×C32—24no—
292C22×C32—42no—
293C22×C32—42no—
294C22×C32—48no—
295C22×C32#12012yes—
296C22×C32#13512yes—
297C22×C32AGL(1,ℤ/8)12yes—
298C22×C32C22×D411yescharacteristic
299C2×C3⋊D3—42no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—84no—
303C2×C3×D3—22no—
304C2×C3×D3—22no—
305C2×C3×D3—22no—
306C2×C3×D3—44no—
307C32×C4#12012yes—
308C32×C4C22×D411yescharacteristic
309C32×C4C22×D411yescharacteristic
310C3×Dic3—24no—
311C3×Dic3—22no—
312C3×Dic3—42no—
313C2×#41—34no—
314C2×#41—62no—
315C2×#41—64no—
316C2×#41—64no—
317C22×Q8—31no—
318C22×D4—61no—
319C22×D4—91no—
320C22×D4—181no—
321C22×D4D3211yescharacteristic
322C23×C4—31no—
323C23×C4—61no—
324C2×SD16—94no—
325C2×SD16—184no—
326C2×D8—94no—
327C2×D8—184no—
328C22×C8—31no—
329C22×C8—91no—
330#121—94no—
331#121—182no—
332C2×C4⋊C4—31no—
333C2×C22⋊C4—181no—
334#103—94no—
335#102—34no—
336C22⋊C8—94no—
337C23×C3—24no—
338C23×C3—24no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—32no—
343C23×C3—42no—
344C23×C3—44no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—42no—
348C23×C3—42no—
349C23×C3—62no—
350C23×C3—62no—
351C23×C3—62no—
352C23×C3—82no—
353C23×C3—82no—
354C23×C3D3×D411yescharacteristic
355C23×C3C2×#6711yescharacteristic
356C22×D3—22no—
357C22×D3—22no—
358C22×D3—22no—
359C22×D3—62no—
360C22×D3—62no—
361C22×D3—122no—
362C22×D3—124no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—122no—
368C22×D3—122no—
369C22×D3—242no—
370C22×D3—242no—
371C22×D3C2×#6712yes—
372C3×Q8—34no—
373C3×Q8—64no—
374C3×Q8—62no—
375C3×D4—24no—
376C3×D4—24no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—24no—
380C3×D4—42no—
381C3×D4—44no—
382C3×D4—616no—
383C3×D4C2×D1214yescomplemented
384C3×D4C2×#6714yescomplemented
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—22no—
388C2×C3×C4—21no—
389C2×C3×C4—32no—
390C2×C3×C4—616no—
391C2×C3×C4—62no—
392C2×C3×C4—64no—
393C2×C3×C4—62no—
394C2×C3×C4—64no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—62no—
398C2×C3×C4—122no—
399C2×C3×C4C2×D1212yes—
400C2×C3×C4D3×D411yescharacteristic
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6712yes—
403C2×C3×C4C2×#6711yescharacteristic
404C2×C3×C4C2×#6712yes—
405C2×C3×C4C23×D311yescharacteristic
406C2×C3×C4C23×D311yescharacteristic
407#67—216no—
408#67—128no—
409C2×Dic3—216no—
410C2×Dic3—24no—
411C2×Dic3—22no—
412C2×Dic3—22no—
413C2×Dic3—22no—
414C2×Dic3—42no—
415C2×Dic3C2×#6712yes—
416D12—64no—
417D12—62no—
418D12—62no—
419D12—62no—
420D12—62no—
421D12—122no—
422D12—124no—
423D12—128no—
424D12—122no—
425D12—122no—
426C4×D3—24no—
427C4×D3—22no—
428C4×D3—22no—
429Dic6—24no—
430Dic6—22no—
431Dic6C2×#6714yescomplemented
432C3×C8—62no—
433C3⋊C8—22no—
434C3⋊C8—64no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C2×C32—44no—
438C2×C32#44914yescomplemented
439C2×C32C2×#12011yescharacteristic
440C2×C32C2×#13511yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C3⋊D3—82no—
443C3×D3—42no—
444C24—21no—
445C24—31no—
446C24—181no—
447#41—68no—
448#41—616no—
449#41—68no—
450C2×Q8—32no—
451C2×Q8—34no—
452C2×Q8—62no—
453C2×Q8—61no—
454C2×D4—22no—
455C2×D4—21no—
456C2×D4—64no—
457C2×D4—68no—
458C2×D4—92no—
459C2×D4—184no—
460C2×D4—182no—
461C2×D4—182no—
462C2×D4—181no—
463C2×D4—364no—
464C2×D4#62614yescomplemented
465C2×D4C2×D3212yes—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—64no—
470C22×C4—68no—
471C22×C4—61no—
472C22×C4—62no—
473C22×C4—62no—
474C22×C4—61no—
475C22×C4C2×D3211yescharacteristic
476SD16—188no—
477D8—188no—
478C2×C8—32no—
479C2×C8—62no—
480C2×C8—92no—
481C2×C8—182no—
482C4⋊C4—32no—
483C4⋊C4—61no—
484C22⋊C4—184no—
485C22×C3—24no—
486C22×C3—24no—
487C22×C3—21no—
488C22×C3—22no—
489C22×C3—22no—
490C22×C3—22no—
491C22×C3—44no—
492C22×C3—48no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—48no—
496C22×C3—42no—
497C22×C3—42no—
498C22×C3—62no—
499C22×C3—62no—
500C22×C3—62no—
501C22×C3—82no—
502C22×C3—82no—
503C22×C3—88no—
504C22×C3—124no—
505C22×C3#88212yes—
506C22×C3#91112yes—
507C22×C3#91612yes—
508C22×C3#94912yes—
509C22×C3#95012yes—
510C22×C3#95312yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C22×#6711yescharacteristic
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—44no—
517C2×D3—124no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—242no—
525C2×D3—242no—
526C2×D3—248no—
527C2×D3—244no—
528C2×D3—244no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—62no—
533C3×C4—64no—
534C3×C4—122no—
535C3×C4#88212yes—
536C3×C4#95312yes—
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C22×#6711yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—24no—
542Dic3—22no—
543Dic3—42no—
544C32C2×#44911yescharacteristic, complemented, Sylow
545C23—22no—
546C23—24no—
547C23—32no—
548C23—42no—
549C23—42no—
550C23—62no—
551C23—62no—
552C23—62no—
553C23—182no—
554C23—362no—
555C23—362no—
556C23—362no—
557C23D3×#6711yescharacteristic
558Q8—34no—
559Q8—62no—
560Q8—64no—
561D4—22no—
562D4—24no—
563D4—616no—
564D4—182no—
565D4—182no—
566D4—368no—
567D4—362no—
568D4C2×#62614yescomplemented
569C2×C4—32no—
570C2×C4—616no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—64no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—64no—
577C2×C4—62no—
578C2×C4—122no—
579C2×C4C2×#62612yes—
580C2×C4D3×#6712yes—
581C2×C4D3×#6711yescharacteristic
582C2×C4C22×D3211yescharacteristic
583C8—62no—
584C8—182no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—24no—
589C2×C3—44no—
590C2×C3—44no—
591C2×C3—84no—
592C2×C3—122no—
593C2×C3#478114yescomplemented
594C2×C3#523814yescomplemented
595C2×C3C2×#88211yescharacteristic
596C2×C3C2×#91111yescharacteristic
597C2×C3C2×#91611yescharacteristic
598C2×C3C2×#94911yescharacteristic
599C2×C3C2×#95011yescharacteristic
600C2×C3C2×#95311yescharacteristic
601D3—42no—
602D3—244no—
603D3—242no—
604D3—242no—
605C22—24no—
606C22—42no—
607C22—42no—
608C22—48no—
609C22—62no—
610C22—62no—
611C22—62no—
612C22—124no—
613C22—362no—
614C22—362no—
615C22—362no—
616C22—724no—
617C22#6392512yes—
618C22#6393512yes—
619C22#6397712yes—
620C22C2×D3×#6711yescharacteristic
621C4—62no—
622C4—64no—
623C4—122no—
624C4#6397712yes—
625C4C22×#62611yescharacteristic
626C4C2×D3×#6711yescharacteristic
627C3—21no—
628C3C2×#478111yescharacteristic, complemented
629C3C2×#523811yescharacteristic, complemented
630C2—44no—
631C2—122no—
632C2—722no—
633C2#1059145214yesdirect product factor
634C2C2×#6392511yescharacteristic
635C2C2×#6393511yescharacteristic
636C2C2×#6397711yescharacteristic
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×#3753C2semidirect
3. C2×#63909C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×#832C2semidirect
6. #10591452C2direct (N × H)
7. C2×#63565C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
18. C2×C3×#237C22semidirect
23. C2×#3753C22semidirect
29. #63909C22semidirect
31. C2×#3717C22semidirect
32. C3×#832C22semidirect
33. #63565C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
36. C22×#237D3semidirect
47. C2×#832D3semidirect
57. C2×C32×D4D4semidirect
80. C2×C3×Dic6D4semidirect
111. C2×#237C2×D3semidirect
143. #832C2×D3semidirect
162. C32×D4C2×D4semidirect
183. C3×Dic6C2×D4semidirect
220. C2×C3×D4D12semidirect
221. C2×C3×D4#67semidirect
268. C2×Dic6#67semidirect
383. C3×D4C2×D12semidirect
384. C3×D4C2×#67semidirect
431. Dic6C2×#67semidirect
438. C2×C32#449semidirect
464. C2×D4#626semidirect
544. C32C2×#449semidirect
568. D4C2×#626semidirect
593. C2×C3#4781semidirect
594. C2×C3#5238semidirect
628. C3C2×#4781semidirect
629. C3C2×#5238semidirect
633. C2#10591452direct (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×#37532
C2×#639092
C22×#37172
C2×C3×#8322
#105914522
C2×#635652
C2×(C2×D3)⋊(C3⋊C8)2
C2×#52383
C2×#47813