Finite Group Databasebeta

← C2×#10591521 #11863716

Subgroups — C2×#10591521 #11863716

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×#3753C211yesmaximal, characteristic, complemented
3C2×C3×#938C211yesmaximal, characteristic, complemented
4C22×C3×#214C211yesmaximal, characteristic, complemented
5#10591521C218yesmaximal, direct product factor
6C2×#63565C211yesmaximal, characteristic, complemented
7C2×#63564C211yesmaximal, characteristic, complemented
8C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×#5172—31nomaximal
10C2×#5037—31nomaximal
11C22×C32×D4C2211yescharacteristic
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×#67—21no—
14C22×C3×C4×D3C2211yescharacteristic
15C22×C3×Dic6C2211yescharacteristic
16C22×#626—21no—
17C22×#624—21no—
18C2×#3799—24no—
19C2×#3799—22no—
20C2×#3799—24no—
21C2×#3799C2214yescomplemented
22C2×#3753—24no—
23C2×#3753C2214yescomplemented
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C2×C3×#217—21no—
26C3×#938—22no—
27C3×#938C2214yescomplemented
28C2×C3×#214—24no—
29C2×C3×#214C2214yescomplemented
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C22×C3×C3⋊C8C2211yescharacteristic
32#63565C2214yescomplemented
33#63564C2214yescomplemented
34(C2×D3)⋊(C3⋊C8)C2214yescomplemented
35C22×#239—31no—
36C22×#235—31no—
37C22×C3×SD16—31no—
38C2×C3×#121—31no—
39C2×#938D311yescharacteristic, complemented
40C22×#214D311yescharacteristic, complemented
41C22×#213—31no—
42C22×#213—31no—
43C22×#213—61no—
44C2×#835—31no—
45C2×#830—31no—
46#5172—38no—
47C2×#821—31no—
48C2×(C2×D3)⋊C8—31no—
49#5037—38no—
50C2×#810—31no—
51C2×#809—31no—
52C24×C32—21no—
53C23×C3⋊D3—21no—
54C23×C3×D3D411yescharacteristic
55C2×C32×D4—22no—
56C2×C32×D4—22no—
57C2×C32×D4—21no—
58C2×C32×D4C2312yes—
59C22×C32×C4C2311yescharacteristic
60C2×C4⋊(C3⋊D3)—21no—
61C2×C4⋊(C3⋊D3)—22no—
62C2×C4⋊(C3⋊D3)D414yescomplemented
63C2×C4⋊(C3⋊D3)C2312yes—
64C2×C3×#67—24no—
65C2×C3×#67—44no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3—21no—
68C22×C3×Dic3D411yescharacteristic
69C2×C3×C4×D3—22no—
70C2×C3×C4×D3—22no—
71C2×C3×C4×D3D412yes—
72C2×C3×C4×D3C2312yes—
73C2×C3×Dic6—21no—
74C2×C3×Dic6—22no—
75C2×C3×Dic6D414yescomplemented
76C2×C3×Dic6C2312yes—
77C2×#626—28no—
78C2×#626—24no—
79C2×#624—28no—
80C2×#624—24no—
81#3799—216no—
82#3799—28no—
83#3799—28no—
84#3753—28no—
85C2×C3⋊(C3⋊C8)—22no—
86C2×C3⋊(C3⋊C8)C2312yes—
87C3×#217—24no—
88C3×#214—28no—
89C3×C4⋊Dic3—21no—
90C3×C4⋊Dic3C2312yes—
91C2×C3×C3⋊C8—22no—
92C2×C3×C3⋊C8C2312yes—
93C2×#449—91noSylow
94C22×C3×Q8—31no—
95C22×C3×D4—21no—
96C22×C3×D4—61no—
97C22×C3×D4C2×D311yescharacteristic
98C22×C3×D4C2×D311yescharacteristic
99C23×C3×C4—31no—
100C22×#67—21no—
101C22×#67—61no—
102C2×#239—34no—
103C2×#239—64no—
104C2×#239—64no—
105C2×#239—62no—
106C2×#235—34no—
107C2×#235—64no—
108C2×#235—62no—
109C2×#235—64no—
110C22×D12—31no—
111C22×D12—31no—
112C22×D12—61no—
113C22×D12—61no—
114C22×C4×D3—61no—
115C22×C4×D3—61no—
116C22×C4×D3C2×D311yescharacteristic
117C22×Dic6C2×D311yescharacteristic
118C2×C3×SD16—34no—
119C2×C3×SD16—64no—
120C22×C3×C8—31no—
121C3×#121—34no—
122C3×#121—62no—
123C2×C3×C4⋊C4—31no—
124C2×C3×C22⋊C4—61no—
125C2×#217—21no—
126#938—22no—
127#938C2×D314yescomplemented
128C2×#214—24no—
129C2×#214C2×D314yescomplemented
130C2×#213—34no—
131C2×#213—34no—
132C2×#213—64no—
133C2×#213—64no—
134C2×#213—64no—
135C2×#213—68no—
136C2×C4⋊Dic3C2×D311yescharacteristic
137C22×C3⋊C8—31no—
138C22×C3⋊C8—31no—
139C22×C3⋊C8—61no—
140C22×C3⋊C8C2×D311yescharacteristic
141#835—34no—
142#830—34no—
143#821—34no—
144(C2×D3)⋊C8—34no—
145#810—34no—
146#809—34no—
147C23×C32—22no—
148C23×C32—42no—
149C23×C32—42no—
150C23×C32—42no—
151C23×C32C2×D411yescharacteristic
152C22×C3⋊D3—24no—
153C22×C3⋊D3—22no—
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—22no—
161C32×D4—22no—
162C32×D4—42no—
163C2×C32×C4C2×D412yes—
164C2×C32×C4C2×D411yescharacteristic
165C2×C32×C4C2×D412yes—
166C2×C32×C4C2411yescharacteristic
167C4⋊(C3⋊D3)—24no—
168C4⋊(C3⋊D3)—22no—
169C4⋊(C3⋊D3)C2×D414yescomplemented
170C3×#67—48no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—24no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—42no—
176C2×C3×Dic3C2×D412yes—
177C3×C4×D3—24no—
178C3×C4×D3—22no—
179C3×C4×D3—22no—
180C3×Dic6—24no—
181C3×Dic6—22no—
182C3×Dic6C2×D414yescomplemented
183#626—216no—
184#624—216no—
185C3⋊(C3⋊C8)—22no—
186C3×C3⋊C8—22no—
187C22×#41—91no—
188C22×SD16—31no—
189C22×D8—91no—
190C2×#121—31no—
191#449—98no—
192C2×#103—91no—
193C2×#102—91no—
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
203C2×C3×Q8—34no—
204C2×C3×Q8—32no—
205C2×C3×Q8—62no—
206C2×C3×Q8—61no—
207C2×C3×D4—24no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—21no—
212C2×C3×D4—22no—
213C2×C3×D4—21no—
214C2×C3×D4—22no—
215C2×C3×D4—42no—
216C2×C3×D4—41no—
217C2×C3×D4—64no—
218C2×C3×D4—124no—
219C2×C3×D4C22×D312yes—
220C2×C3×D4C22×D312yes—
221C22×C3×C4—21no—
222C22×C3×C4—31no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—61no—
226C22×C3×C4—62no—
227C22×C3×C4—62no—
228C22×C3×C4—61no—
229C22×C3×C4C22×D311yescharacteristic
230C22×C3×C4C22×D311yescharacteristic
231C2×#67—24no—
232C2×#67—44no—
233C2×#67—64no—
234C2×#67—68no—
235C22×Dic3—21no—
236C22×Dic3—21no—
237C22×Dic3#6711yescharacteristic
238#239—68no—
239#239—68no—
240#239—616no—
241#235—68no—
242#235—616no—
243#235—68no—
244C2×D12—34no—
245C2×D12—34no—
246C2×D12—32no—
247C2×D12—32no—
248C2×D12—64no—
249C2×D12—62no—
250C2×D12—68no—
251C2×D12—64no—
252C2×D12—61no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—61no—
256C2×D12—122no—
257C2×D12—121no—
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×D3#6712yes—
265C2×C4×D3C22×D312yes—
266C2×Dic6—21no—
267C2×Dic6—22no—
268C2×Dic6#6714yescomplemented
269C2×Dic6C22×D312yes—
270C3×SD16—68no—
271C2×C3×C8—32no—
272C2×C3×C8—62no—
273C3×C4⋊C4—32no—
274C3×C4⋊C4—61no—
275C3×C22⋊C4—64no—
276#217—24no—
277#214—28no—
278#213—68no—
279#213—68no—
280#213—616no—
281C4⋊Dic3—21no—
282C4⋊Dic3C22×D312yes—
283C2×C3⋊C8—22no—
284C2×C3⋊C8—32no—
285C2×C3⋊C8—32no—
286C2×C3⋊C8—62no—
287C2×C3⋊C8—64no—
288C2×C3⋊C8—62no—
289C2×C3⋊C8—62no—
290C2×C3⋊C8C22×D312yes—
291C22×C32—42no—
292C22×C32—42no—
293C22×C32—42no—
294C22×C32—84no—
295C22×C32#12012yes—
296C22×C32#13512yes—
297C22×C32AGL(1,ℤ/8)12yes—
298C22×C32C22×D411yescharacteristic
299C2×C3⋊D3—24no—
300C2×C3⋊D3—42no—
301C2×C3⋊D3—42no—
302C2×C3⋊D3—48no—
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—61no—
319C22×D4—91no—
320C22×D4—181no—
321C22×D4D3211yescharacteristic
322C23×C4—31no—
323C23×C4—181no—
324C2×SD16—34no—
325C2×SD16—64no—
326C2×D8—94no—
327C2×D8—184no—
328C22×C8—31no—
329C22×C8—91no—
330#121—34no—
331#121—62no—
332C2×C4⋊C4—31no—
333C2×C22⋊C4—61no—
334#103—94no—
335#102—94no—
336C22⋊C8—94no—
337C23×C3—22no—
338C23×C3—22no—
339C23×C3—21no—
340C23×C3—32no—
341C23×C3—42no—
342C23×C3—44no—
343C23×C3—42no—
344C23×C3—42no—
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—64no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—122no—
364C22×D3—124no—
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—22no—
377C3×D4—22no—
378C3×D4—22no—
379C3×D4—22no—
380C3×D4—42no—
381C3×D4—44no—
382C3×D4—42no—
383C3×D4—42no—
384C3×D4—128no—
385C2×C3×C4—21no—
386C2×C3×C4—22no—
387C2×C3×C4—21no—
388C2×C3×C4—22no—
389C2×C3×C4—32no—
390C2×C3×C4—62no—
391C2×C3×C4—64no—
392C2×C3×C4—62no—
393C2×C3×C4—64no—
394C2×C3×C4—62no—
395C2×C3×C4—62no—
396C2×C3×C4—62no—
397C2×C3×C4—122no—
398C2×C3×C4D3×D411yescharacteristic
399C2×C3×C4D3×D412yes—
400C2×C3×C4D3×D412yes—
401C2×C3×C4D3×D412yes—
402C2×C3×C4C2×#6711yescharacteristic
403C2×C3×C4C2×#6712yes—
404C2×C3×C4C23×D311yescharacteristic
405C2×C3×C4C23×D311yescharacteristic
406#67—48no—
407#67—616no—
408C2×Dic3—24no—
409C2×Dic3—22no—
410C2×Dic3—22no—
411C2×Dic3—22no—
412C2×Dic3—42no—
413C2×Dic3C2×#6712yes—
414D12—34no—
415D12—34no—
416D12—64no—
417D12—616no—
418D12—64no—
419D12—64no—
420D12—62no—
421D12—62no—
422D12—122no—
423D12—124no—
424C4×D3—24no—
425C4×D3—22no—
426C4×D3—22no—
427C4×D3—616no—
428C4×D3—616no—
429Dic6—24no—
430Dic6—22no—
431Dic6C2×#6714yescomplemented
432C3×C8—62no—
433C3⋊C8—22no—
434C3⋊C8—64no—
435C3⋊C8—62no—
436C3⋊C8—62no—
437C2×C32—82no—
438C2×C32#44914yescomplemented
439C2×C32C2×#12011yescharacteristic
440C2×C32C2×#13511yescharacteristic
441C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
442C3⋊D3—44no—
443C3×D3—42no—
444C24—21no—
445C24—31no—
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—22no—
455C2×D4—21no—
456C2×D4—22no—
457C2×D4—64no—
458C2×D4—92no—
459C2×D4—94no—
460C2×D4—124no—
461C2×D4—184no—
462C2×D4—188no—
463C2×D4—182no—
464C2×D4—181no—
465C2×D4C2×D3212yes—
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—68no—
477D8—188no—
478C2×C8—32no—
479C2×C8—62no—
480C2×C8—92no—
481C2×C8—182no—
482C4⋊C4—32no—
483C4⋊C4—61no—
484C22⋊C4—64no—
485C22×C3—21no—
486C22×C3—22no—
487C22×C3—22no—
488C22×C3—22no—
489C22×C3—44no—
490C22×C3—42no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—42no—
495C22×C3—42no—
496C22×C3—62no—
497C22×C3—62no—
498C22×C3—62no—
499C22×C3—82no—
500C22×C3—82no—
501C22×C3—88no—
502C22×C3—84no—
503C22×C3—84no—
504C22×C3—124no—
505C22×C3#91412yes—
506C22×C3#91612yes—
507C22×C3#93212yes—
508C22×C3#93712yes—
509C22×C3#93712yes—
510C22×C3#95012yes—
511C22×C3C2×D3×D411yescharacteristic
512C22×C3C22×#6711yescharacteristic
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—22no—
516C2×D3—44no—
517C2×D3—64no—
518C2×D3—64no—
519C2×D3—124no—
520C2×D3—128no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—122no—
524C2×D3—128no—
525C2×D3—122no—
526C2×D3—248no—
527C2×D3—242no—
528C2×D3—242no—
529C3×C4—21no—
530C3×C4—21no—
531C3×C4—22no—
532C3×C4—62no—
533C3×C4—64no—
534C3×C4—122no—
535C3×C4#93712yes—
536C3×C4#93712yes—
537C3×C4C2×D3×D411yescharacteristic
538C3×C4C2×D3×D411yescharacteristic
539C3×C4C2×D3×D411yescharacteristic
540C3×C4C22×#6711yescharacteristic
541Dic3—24no—
542Dic3—22no—
543Dic3—42no—
544C32C2×#44911yescharacteristic, complemented, Sylow
545C23—22no—
546C23—32no—
547C23—42no—
548C23—42no—
549C23—42no—
550C23—62no—
551C23—62no—
552C23—62no—
553C23—182no—
554C23—184no—
555C23—362no—
556C23—362no—
557C23D3×#6711yescharacteristic
558Q8—34no—
559Q8—62no—
560Q8—64no—
561D4—22no—
562D4—22no—
563D4—42no—
564D4—94no—
565D4—128no—
566D4—1816no—
567D4—182no—
568D4—184no—
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×#6712yes—
580C2×C4D3×#6711yescharacteristic
581C2×C4#381112yes—
582C2×C4C22×D3211yescharacteristic
583C8—62no—
584C8—182no—
585C2×C3—24no—
586C2×C3—21no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—84no—
590C2×C3—82no—
591C2×C3—82no—
592C2×C3—122no—
593C2×C3#503714yescomplemented
594C2×C3#517214yescomplemented
595C2×C3C2×#91411yescharacteristic
596C2×C3C2×#91611yescharacteristic
597C2×C3C2×#93211yescharacteristic
598C2×C3C2×#93711yescharacteristic
599C2×C3C2×#93711yescharacteristic
600C2×C3C2×#95011yescharacteristic
601D3—42no—
602D3—124no—
603D3—124no—
604D3—244no—
605C22—42no—
606C22—42no—
607C22—42no—
608C22—62no—
609C22—62no—
610C22—62no—
611C22—84no—
612C22—124no—
613C22—184no—
614C22—368no—
615C22—362no—
616C22—362no—
617C22#6393412yes—
618C22#6393512yes—
619C22#6398312yes—
620C22C2×D3×#6711yescharacteristic
621C4—62no—
622C4—64no—
623C4—122no—
624C4#6398312yes—
625C4C2×D3×#6711yescharacteristic
626C4C2×#381111yescharacteristic
627C3—21no—
628C3C2×#503711yescharacteristic, complemented
629C3C2×#517211yescharacteristic, complemented
630C2—82no—
631C2—122no—
632C2—364no—
633C2#1059152114yesdirect product factor
634C2C2×#6393411yescharacteristic
635C2C2×#6393511yescharacteristic
636C2C2×#6398311yescharacteristic
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×#3799C2semidirect
2. C22×#3753C2semidirect
3. C2×C3×#938C2semidirect
4. C22×C3×#214C2semidirect
5. #10591521C2direct (N × H)
6. C2×#63565C2semidirect
7. C2×#63564C2semidirect
8. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
21. C2×#3799C22semidirect
23. C2×#3753C22semidirect
27. C3×#938C22semidirect
29. C2×C3×#214C22semidirect
32. #63565C22semidirect
33. #63564C22semidirect
34. (C2×D3)⋊(C3⋊C8)C22semidirect
39. C2×#938D3semidirect
40. C22×#214D3semidirect
62. C2×C4⋊(C3⋊D3)D4semidirect
75. C2×C3×Dic6D4semidirect
127. #938C2×D3semidirect
129. C2×#214C2×D3semidirect
169. C4⋊(C3⋊D3)C2×D4semidirect
182. C3×Dic6C2×D4semidirect
268. C2×Dic6#67semidirect
431. Dic6C2×#67semidirect
438. C2×C32#449semidirect
544. C32C2×#449semidirect
593. C2×C3#5037semidirect
594. C2×C3#5172semidirect
628. C3C2×#5037semidirect
629. C3C2×#5172semidirect
633. C2#10591521direct (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×#37532
C2×C3×#9382
C22×C3×#2142
#105915212
C2×#635652
C2×#635642
C2×(C2×D3)⋊(C3⋊C8)2
C2×#51723
C2×#50373