Finite Group Databasebeta

← C2×#10590967 #11863725

Subgroups — C2×#10590967 #11863725

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×#3799C211yesmaximal, characteristic, complemented
2C22×#3745C211yesmaximal, characteristic, complemented
3C2×#63909C211yesmaximal, characteristic, complemented
4C22×#3717C211yesmaximal, characteristic, complemented
5C2×C3×(C2×D3)⋊C8C211yesmaximal, characteristic, complemented
6C2×C3×#816C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8#10590967C218yesmaximal, direct product factor
9C2×#4810—31nomaximal
10C2×#4734—31nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626—21no—
16C22×#626—21no—
17C22×#624—21no—
18C2×#3799—24no—
19C2×#3799—22no—
20C2×#3799—24no—
21C2×#3799C2214yescomplemented
22C22×C32×C8C2211yescharacteristic
23C2×#3745—24no—
24C2×#3745C2214yescomplemented
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C22×C3×C3⋊C8C2211yescharacteristic
27C2×#3722—21no—
28#63909—22no—
29#63909C2214yescomplemented
30C2×#3717—24no—
31C2×#3717C2214yescomplemented
32C3×(C2×D3)⋊C8C2214yescomplemented
33C3×#816C2214yescomplemented
34#63564C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×#215—31no—
38C2×#930—31no—
39C22×D24—31no—
40C22×D24—31no—
41C22×D24—61no—
42C22×#204—31no—
43C2×#895—31no—
44C2×C3×#103—31no—
45C2×C3×C22⋊C8—31no—
46C2×#821—31no—
47C2×(C2×D3)⋊C8D311yescharacteristic, complemented
48C2×#816D311yescharacteristic, complemented
49C2×#809—31no—
50#4810—38no—
51#4734—38no—
52C23×C3⋊D3—21no—
53C23×C3⋊D3—21no—
54C23×C3×D3D411yescharacteristic
55C22×C32×C4C2311yescharacteristic
56C2×C4⋊(C3⋊D3)—21no—
57C2×C4⋊(C3⋊D3)—22no—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)D414yescomplemented
62C2×C4⋊(C3⋊D3)C2312yes—
63C2×C4⋊(C3⋊D3)C2312yes—
64C22×C3×Dic3—21no—
65C22×C3×Dic3—21no—
66C22×C3×Dic3D411yescharacteristic
67C2×C3×C4×D3—22no—
68C2×C3×C4×D3—22no—
69C2×C3×C4×D3D412yes—
70C2×C3×C4×D3C2312yes—
71C2×C3×Dic6—21no—
72C2×C3×Dic6—22no—
73C2×C3×Dic6D414yescomplemented
74C2×C3×Dic6C2312yes—
75C2×#626—28no—
76C2×#626—24no—
77C2×#626—24no—
78C2×#626—44no—
79C2×#624—28no—
80C2×#624—24no—
81#3799—216no—
82#3799—28no—
83#3799—28no—
84C2×C32×C8—22no—
85C2×C32×C8C2312yes—
86#3745—28no—
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
94C22×C3×Q8—31no—
95C23×C3×C4—31no—
96C22×#67—61no—
97C22×#67—61no—
98C2×#239—34no—
99C2×#239—64no—
100C2×#239—64no—
101C2×#239—62no—
102C2×#235—34no—
103C2×#235—64no—
104C2×#235—62no—
105C2×#235—64no—
106C22×D12—31no—
107C22×D12—31no—
108C22×D12—31no—
109C22×D12—31no—
110C22×D12—61no—
111C22×D12—61no—
112C22×D12—61no—
113C22×D12—61no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C22×C4×D3C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C22×C3×C8—21no—
119C22×C3×C8—31no—
120C22×C3×C8C2×D311yescharacteristic
121C22×C3×C8C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×#215—34no—
124C2×#215—64no—
125#930—34no—
126#930—62no—
127C2×(C2×D3)⋊C4—61no—
128C2×(C2×D3)⋊C4—61no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C22×C3⋊C8C2×D311yescharacteristic
131C2×D24—34no—
132C2×D24—34no—
133C2×D24—64no—
134C2×D24—64no—
135C2×D24—64no—
136C2×D24—68no—
137C2×#204—34no—
138C2×#204—64no—
139#895—34no—
140#895—62no—
141C3×#103—34no—
142C3×C22⋊C8—34no—
143#821—34no—
144(C2×D3)⋊C8C2×D314yescomplemented
145#816C2×D314yescomplemented
146#809—34no—
147C23×C32C2×D411yescharacteristic
148C22×C3⋊D3—24no—
149C22×C3⋊D3—22no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—42no—
152C22×C3⋊D3—42no—
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—
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D412yes—
162C2×C32×C4C2×D412yes—
163C2×C32×C4C2411yescharacteristic
164C4⋊(C3⋊D3)—22no—
165C4⋊(C3⋊D3)—24no—
166C4⋊(C3⋊D3)—22no—
167C4⋊(C3⋊D3)—22no—
168C4⋊(C3⋊D3)—42no—
169C4⋊(C3⋊D3)C2×D414yescomplemented
170C2×C3×Dic3—22no—
171C2×C3×Dic3—24no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—42no—
175C2×C3×Dic3C2×D412yes—
176C3×C4×D3—24no—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179C3×Dic6—24no—
180C3×Dic6—22no—
181C3×Dic6C2×D414yescomplemented
182#626—216no—
183#626—48no—
184#624—216no—
185C32×C8—22no—
186C3×C3⋊C8—22no—
187C22×#41—91no—
188C22×SD16—91no—
189C22×D8—91no—
190C2×#121—91no—
191#449—98no—
192C2×#103—31no—
193C2×#102—91no—
194C2×C22⋊C8—31no—
195C24×C3—31no—
196C23×D3—61no—
197C23×D3—61no—
198C23×D3—61no—
199C23×D3—61no—
200C23×D3—121no—
201C23×D3—121no—
202C23×D3D1211yescharacteristic
203C2×C3×Q8—34no—
204C2×C3×Q8—32no—
205C2×C3×Q8—61no—
206C2×C3×Q8—62no—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—32no—
210C22×C3×C4—32no—
211C22×C3×C4—61no—
212C22×C3×C4—62no—
213C22×C3×C4—62no—
214C22×C3×C4—61no—
215C22×C3×C4C22×D311yescharacteristic
216C22×C3×C4C22×D311yescharacteristic
217C2×#67—64no—
218C2×#67—68no—
219C2×#67—64no—
220C2×#67—124no—
221C22×Dic3—21no—
222C22×Dic3—21no—
223C22×Dic3D1211yescharacteristic
224#239—68no—
225#239—68no—
226#239—616no—
227#235—68no—
228#235—616no—
229#235—68no—
230C2×D12—34no—
231C2×D12—34no—
232C2×D12—32no—
233C2×D12—32no—
234C2×D12—32no—
235C2×D12—32no—
236C2×D12—64no—
237C2×D12—62no—
238C2×D12—62no—
239C2×D12—68no—
240C2×D12—64no—
241C2×D12—62no—
242C2×D12—61no—
243C2×D12—61no—
244C2×D12—62no—
245C2×D12—64no—
246C2×D12—62no—
247C2×D12—62no—
248C2×D12—62no—
249C2×D12—62no—
250C2×D12—64no—
251C2×D12—61no—
252C2×D12—61no—
253C2×D12—122no—
254C2×D12—121no—
255C2×D12—122no—
256C2×D12—121no—
257C2×D12—124no—
258C2×C4×D3—22no—
259C2×C4×D3—22no—
260C2×C4×D3—64no—
261C2×C4×D3—68no—
262C2×C4×D3—68no—
263C2×C4×D3—64no—
264C2×C4×D3D1212yes—
265C2×C4×D3C22×D312yes—
266C2×Dic6—21no—
267C2×Dic6—22no—
268C2×Dic6D1214yescomplemented
269C2×Dic6C22×D312yes—
270C2×C3×C8—24no—
271C2×C3×C8—22no—
272C2×C3×C8—22no—
273C2×C3×C8—22no—
274C2×C3×C8—32no—
275C2×C3×C8—62no—
276C2×C3×C8C22×D312yes—
277C2×C3×C8C22×D312yes—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—61no—
280#215—68no—
281(C2×D3)⋊C4—64no—
282(C2×D3)⋊C4—64no—
283C4⋊Dic3—21no—
284C4⋊Dic3C22×D312yes—
285C2×C3⋊C8—22no—
286C2×C3⋊C8C22×D312yes—
287D24—68no—
288D24—68no—
289D24—616no—
290#204—68no—
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—42no—
299C2×C3⋊D3—48no—
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—22no—
311C3×Dic3—24no—
312C3×Dic3—42no—
313C2×#41—94no—
314C2×#41—182no—
315C2×#41—184no—
316C2×#41—184no—
317C22×Q8—31no—
318C22×D4—91no—
319C22×D4—91no—
320C22×D4—181no—
321C22×D4—181no—
322C23×C4—31no—
323C23×C4—181no—
324C2×SD16—94no—
325C2×SD16—184no—
326C2×D8—94no—
327C2×D8—184no—
328C22×C8—31no—
329C22×C8D3211yescharacteristic
330#121—94no—
331#121—182no—
332C2×C4⋊C4—31no—
333C2×C22⋊C4—181no—
334#103—34no—
335#102—94no—
336C22⋊C8—34no—
337C23×C3—21no—
338C23×C3—32no—
339C23×C3—62no—
340C23×C3—62no—
341C23×C3—62no—
342C23×C3C2×D1211yescharacteristic
343C23×C3D3×D411yescharacteristic
344C22×D3—22no—
345C22×D3—22no—
346C22×D3—22no—
347C22×D3—64no—
348C22×D3—64no—
349C22×D3—62no—
350C22×D3—62no—
351C22×D3—62no—
352C22×D3—62no—
353C22×D3—122no—
354C22×D3—124no—
355C22×D3—122no—
356C22×D3—122no—
357C22×D3—122no—
358C22×D3—122no—
359C22×D3—122no—
360C22×D3—124no—
361C22×D3—122no—
362C22×D3—122no—
363C22×D3—122no—
364C22×D3—122no—
365C22×D3—122no—
366C22×D3—122no—
367C22×D3—242no—
368C22×D3—242no—
369C22×D3—242no—
370C22×D3—242no—
371C22×D3C2×D1212yes—
372C3×Q8—34no—
373C3×Q8—64no—
374C3×Q8—62no—
375C2×C3×C4—21no—
376C2×C3×C4—22no—
377C2×C3×C4—21no—
378C2×C3×C4—22no—
379C2×C3×C4—32no—
380C2×C3×C4—62no—
381C2×C3×C4—64no—
382C2×C3×C4—62no—
383C2×C3×C4—64no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—122no—
388C2×C3×C4C2×D1211yescharacteristic
389C2×C3×C4C2×D1212yes—
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D412yes—
392C2×C3×C4D3×D412yes—
393C2×C3×C4D3×D412yes—
394C2×C3×C4C23×D311yescharacteristic
395C2×C3×C4C23×D311yescharacteristic
396#67—616no—
397#67—128no—
398C2×Dic3—24no—
399C2×Dic3—22no—
400C2×Dic3—22no—
401C2×Dic3—22no—
402C2×Dic3—42no—
403C2×Dic3C2×D1212yes—
404D12—34no—
405D12—34no—
406D12—64no—
407D12—64no—
408D12—616no—
409D12—64no—
410D12—64no—
411D12—62no—
412D12—62no—
413D12—62no—
414D12—62no—
415D12—62no—
416D12—62no—
417D12—122no—
418D12—122no—
419D12—124no—
420D12—124no—
421D12—128no—
422D12—122no—
423D12—122no—
424C4×D3—24no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—616no—
428C4×D3—616no—
429Dic6—24no—
430Dic6—22no—
431Dic6C2×D1214yescomplemented
432C3×C8—24no—
433C3×C8—22no—
434C3×C8—22no—
435C3×C8—62no—
436C3⋊C8—22no—
437C2×C32#44914yescomplemented
438C2×C32C2×#12011yescharacteristic
439C2×C32C2×#13511yescharacteristic
440C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
441C3⋊D3—44no—
442C3⋊D3—82no—
443C3×D3—42no—
444C24—31no—
445C24—181no—
446C24—181no—
447#41—188no—
448#41—188no—
449#41—1816no—
450C2×Q8—32no—
451C2×Q8—34no—
452C2×Q8—61no—
453C2×Q8—62no—
454C2×D4—92no—
455C2×D4—92no—
456C2×D4—94no—
457C2×D4—184no—
458C2×D4—188no—
459C2×D4—184no—
460C2×D4—182no—
461C2×D4—181no—
462C2×D4—182no—
463C2×D4—181no—
464C2×D4—182no—
465C2×D4—364no—
466C22×C4—31no—
467C22×C4—32no—
468C22×C4—32no—
469C22×C4—61no—
470C22×C4—62no—
471C22×C4—62no—
472C22×C4—61no—
473C22×C4—184no—
474C22×C4—188no—
475C22×C4C2×D3211yescharacteristic
476SD16—188no—
477D8—188no—
478C2×C8—22no—
479C2×C8—32no—
480C2×C8—62no—
481C2×C8C2×D3212yes—
482C4⋊C4—32no—
483C4⋊C4—61no—
484C22⋊C4—184no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—62no—
490C22×C3—62no—
491C22×C3—62no—
492C22×C3—124no—
493C22×C3#88212yes—
494C22×C3#88212yes—
495C22×C3#90412yes—
496C22×C3#90812yes—
497C22×C3#91412yes—
498C22×C3#91912yes—
499C22×C3C22×D1211yescharacteristic
500C22×C3C2×D3×D411yescharacteristic
501C2×D3—22no—
502C2×D3—22no—
503C2×D3—22no—
504C2×D3—44no—
505C2×D3—64no—
506C2×D3—64no—
507C2×D3—124no—
508C2×D3—122no—
509C2×D3—122no—
510C2×D3—128no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—128no—
514C2×D3—124no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—122no—
518C2×D3—122no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—242no—
522C2×D3—242no—
523C2×D3—248no—
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#88212yes—
537C3×C4C22×D1211yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C2×D3×D411yescharacteristic
541Dic3—24no—
542Dic3—22no—
543Dic3—42no—
544C32C2×#44911yescharacteristic, complemented, Sylow
545C23—32no—
546C23—62no—
547C23—62no—
548C23—62no—
549C23—182no—
550C23—184no—
551C23—182no—
552C23—362no—
553C23—362no—
554C23—362no—
555C23—362no—
556C23—362no—
557C23D3×D1211yescharacteristic
558Q8—34no—
559Q8—62no—
560Q8—64no—
561D4—94no—
562D4—1816no—
563D4—182no—
564D4—182no—
565D4—182no—
566D4—184no—
567D4—368no—
568D4—362no—
569C2×C4—32no—
570C2×C4—62no—
571C2×C4—62no—
572C2×C4—64no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—64no—
576C2×C4—62no—
577C2×C4—122no—
578C2×C4—1816no—
579C2×C4D3×D1212yes—
580C2×C4D3×D1211yescharacteristic
581C2×C4#381112yes—
582C2×C4C22×D3211yescharacteristic
583C8—22no—
584C8—62no—
585C2×C3—21no—
586C2×C3—21no—
587C2×C3—24no—
588C2×C3—21no—
589C2×C3—122no—
590C2×C3#473414yescomplemented
591C2×C3#481014yescomplemented
592C2×C3C2×#88211yescharacteristic
593C2×C3C2×#88211yescharacteristic
594C2×C3C2×#90411yescharacteristic
595C2×C3C2×#90811yescharacteristic
596C2×C3C2×#91411yescharacteristic
597C2×C3C2×#91911yescharacteristic
598D3—42no—
599D3—124no—
600D3—124no—
601D3—244no—
602D3—244no—
603D3—242no—
604D3—242no—
605C22—62no—
606C22—62no—
607C22—62no—
608C22—124no—
609C22—184no—
610C22—362no—
611C22—362no—
612C22—368no—
613C22—362no—
614C22—362no—
615C22—362no—
616C22—724no—
617C22#6379412yes—
618C22#6380812yes—
619C22#6392312yes—
620C22C2×D3×D1211yescharacteristic
621C4—62no—
622C4—64no—
623C4—122no—
624C4#6392312yes—
625C4C2×D3×D1211yescharacteristic
626C4C2×#381111yescharacteristic
627C3—21no—
628C3C2×#473411yescharacteristic, complemented
629C3C2×#481011yescharacteristic, complemented
630C2—122no—
631C2—364no—
632C2—722no—
633C2#1059096714yesdirect product factor
634C2C2×#6379411yescharacteristic
635C2C2×#6380811yescharacteristic
636C2C2×#6392311yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
hypercenterC22×C8D32
hypocenterC32C2×#449
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×#3799C2semidirect
2. C22×#3745C2semidirect
3. C2×#63909C2semidirect
4. C22×#3717C2semidirect
5. C2×C3×(C2×D3)⋊C8C2semidirect
6. C2×C3×#816C2semidirect
7. C2×#63564C2semidirect
8. #10590967C2direct (N × H)
21. C2×#3799C22semidirect
24. C2×#3745C22semidirect
29. #63909C22semidirect
31. C2×#3717C22semidirect
32. C3×(C2×D3)⋊C8C22semidirect
33. C3×#816C22semidirect
34. #63564C22semidirect
47. C2×(C2×D3)⋊C8D3semidirect
48. C2×#816D3semidirect
61. C2×C4⋊(C3⋊D3)D4semidirect
73. C2×C3×Dic6D4semidirect
144. (C2×D3)⋊C8C2×D3semidirect
145. #816C2×D3semidirect
169. C4⋊(C3⋊D3)C2×D4semidirect
181. C3×Dic6C2×D4semidirect
268. C2×Dic6D12semidirect
431. Dic6C2×D12semidirect
437. C2×C32#449semidirect
544. C32C2×#449semidirect
590. C2×C3#4734semidirect
591. C2×C3#4810semidirect
628. C3C2×#4734semidirect
629. C3C2×#4810semidirect
633. C2#10590967direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37992
C22×#37452
C2×#639092
C22×#37172
C2×C3×(C2×D3)⋊C82
C2×C3×#8162
C2×#635642
#105909672
C2×#48103
C2×#47343