Finite Group Databasebeta

← #11864442

Subgroups — #11864442

Order 1152.

1539 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C3×#215C211yesmaximal, characteristic, complemented
3#10595040C211yesmaximal, characteristic, complemented
4C2×#63823C211yesmaximal, characteristic, complemented
5#10592924C211yesmaximal, characteristic, complemented
6#10591586C214yesmaximal, complemented
7#10591583C214yesmaximal, complemented
8#10591084C211yesmaximal, characteristic, complemented
9#10591070C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#83860—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C3×#1007—24no—
14C3×#1007—24no—
15C2×C3×#239—21no—
16C2×C3×#239C2212yescomplemented
17C2×C3×D3×Q8—21no—
18C2×C3×D3×Q8C2212yescomplemented
19C2×C3×#235—22no—
20C2×C3×#235C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C22×C3×D12C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C2×C3×#215—24no—
26C2×C3×#215C2214yes—
27C22×C3×C3⋊C8C2211yescharacteristic
28#63976—22no—
29#63914—21no—
30#63908C2214yes—
31#63863—21no—
32C2×#3715C2212yes—
33#63823—24no—
34C2×#3713C2212yes—
35#63662C2214yescomplemented
36#63566C2212yescomplemented
37#63563C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1007D311yescharacteristic, complemented
41C22×C3×SD16—31no—
42#5830—31no—
43C2×#949—31no—
44C22×#215D311yescharacteristic, complemented
45#5805—31no—
46C2×#932—31no—
47#5238—34no—
48#5234—31no—
49#5233—31no—
50#5227—34no—
51#5225—31no—
52#5225—31no—
53#5225—61no—
54#5172—34no—
55#5170—34no—
56#5113—31no—
57#5110—31no—
58C23×C3×D3—21no—
59C2×C32×Q8—21no—
60C2×C32×Q8—22no—
61C2×C32×Q8D414yescomplemented
62C2×C32×Q8C2312yes—
63C22×C32×C4—21no—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—21no—
66C2×C3×#67D412yes—
67C3×#239—28no—
68C3×#239—24no—
69C3×#239—24no—
70C3×D3×Q8—28no—
71C3×D3×Q8—24no—
72C3×D3×Q8—24no—
73C3×#235—216no—
74C3×#235—22no—
75C3×#235—22no—
76C3×#235—22no—
77C3×#235D414yescomplemented
78C2×C3×D12—22no—
79C2×C3×D12—22no—
80C2×C3×D12—22no—
81C2×C3×D12—21no—
82C2×C3×D12D411yescharacteristic
83C2×C3×D12C2312yes—
84C2×C3×D12C2311yescharacteristic
85C2×C3×C4×D3—22no—
86C2×C3×C4×D3—21no—
87C2×C3×C4×D3—22no—
88C2×C3×C4×D3C2312yes—
89C2×C3×Dic6—22no—
90C2×C3×Dic6D411yescharacteristic
91C2×C3×Dic6C2311yescharacteristic
92C2×#625—24no—
93#3757—21no—
94C4⋊(C3⋊Dic3)C2312yes—
95C4×C3⋊Dic3—21no—
96#3748—22no—
97C2×C3⋊(C3⋊C8)C2312yes—
98C3×#215—28no—
99C2×C3×C3⋊C8—22no—
100C2×C3×C3⋊C8C2312yes—
101(C2×D3)⋊Dic3—24no—
102#3715—24no—
103#3713—24no—
104#3010—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—31no—
108C2×C3×#41—32no—
109C2×C3×#41—31no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C22×C3×Q8—21no—
113C22×C3×Q8—32no—
114C22×C3×Q8—61no—
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×Q8C2×D311yescharacteristic
117C22×C3×D4—31no—
118#1007—24no—
119#1007—24no—
120C2×#239—21no—
121C2×#239C2×D312yescomplemented
122C2×D3×Q8—21no—
123C2×D3×Q8C2×D312yescomplemented
124C2×#235—22no—
125C2×#235C2×D311yescharacteristic
126C2×#235C2×D311yescharacteristic
127C22×D12C2×D311yescharacteristic
128C2×C3×SD16—34no—
129C2×C3×SD16—64no—
130C22×C3×C8—31no—
131#953—62no—
132#949—64no—
133#947—61no—
134C2×#215—24no—
135C2×#215—32no—
136C2×#215C2×D314yes—
137#940—61no—
138#940—61no—
139#938—34no—
140#937—62no—
141#936—61no—
142C2×#214—32no—
143#932—64no—
144C2×#213—32no—
145C2×#213—32no—
146#930—34no—
147#926—31no—
148#926—31no—
149#926—61no—
150C2×#208—31no—
151C2×#208—31no—
152C2×#208—61no—
153C22×C3⋊C8C2×D311yescharacteristic
154#835—34no—
155#835—34no—
156#835—32no—
157#835—64no—
158#832—32no—
159#830—34no—
160#821—32no—
161(C2×D3)⋊C8—34no—
162#816—32no—
163C23×C32C2×D411yescharacteristic
164C22×C3×D3—21no—
165C22×C3×D3—22no—
166C22×C3×D3—42no—
167C22×C3×D3—82no—
168C22×C3×D3C2×D412yes—
169C32×Q8—24no—
170C32×Q8—22no—
171C32×Q8C2×D414yes—
172C2×C32×C4—24no—
173C2×C32×C4—22no—
174C2×C32×C4C2×D411yescharacteristic
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D412yes—
177C2×C32×C4C2411yescharacteristic
178C2×C3⋊Dic3—22no—
179C3×#67—24no—
180C3×#67—24no—
181C2×C3×Dic3—21no—
182C2×C3×Dic3C2×D412yes—
183C3×D12—28no—
184C3×D12—22no—
185C3×D12—21no—
186C3×D12—22no—
187C3×D12—22no—
188C3×D12—42no—
189C3×D12C2×D412yes—
190C3×C4×D3—28no—
191C3×C4×D3—28no—
192C3×C4×D3—24no—
193C3×C4×D3—22no—
194C3×C4×D3—22no—
195C3×Dic6—28no—
196C3×Dic6—22no—
197C3×Dic6—21no—
198C3×Dic6C2×D412yes—
199#625—84no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C2×2−1+4—31no—
203C2×AGL(1,ℤ/8)—91no—
204C22×SD16—31no—
205#535—91no—
206#449—94no—
207#448—94no—
208#419—91no—
209#416—91no—
210#408—91no—
211C24×C3—61no—
212C23×D3—21no—
213C3×#41—34no—
214C3×#41—616no—
215C3×#41—64no—
216C3×#41—68no—
217C3×#41—64no—
218C3×#41—62no—
219C3×#41—62no—
220C3×#41—62no—
221C2×C3×Q8—21no—
222C2×C3×Q8—22no—
223C2×C3×Q8—21no—
224C2×C3×Q8—22no—
225C2×C3×Q8—24no—
226C2×C3×Q8—22no—
227C2×C3×Q8—31no—
228C2×C3×Q8—31no—
229C2×C3×Q8—41no—
230C2×C3×Q8—42no—
231C2×C3×Q8—62no—
232C2×C3×Q8—64no—
233C2×C3×Q8—68no—
234C2×C3×Q8—64no—
235C2×C3×Q8#6714yescomplemented
236C2×C3×Q8#6714yescomplemented
237C2×C3×Q8C22×D312yes—
238C2×C3×Q8C22×D312yes—
239C2×C3×D4—32no—
240C2×C3×D4—31no—
241C2×C3×D4—31no—
242C2×C3×D4—32no—
243C2×C3×D4—62no—
244C2×C3×D4—61no—
245C2×C3×D4—62no—
246C2×C3×D4—62no—
247C2×C3×D4—61no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—32no—
252C22×C3×C4—41no—
253C22×C3×C4—62no—
254C22×C3×C4—62no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—21no—
259C2×#67—64no—
260C2×#67—64no—
261C2×#67#6712yes—
262#239—28no—
263#239—24no—
264#239—24no—
265D3×Q8—28no—
266D3×Q8—24no—
267D3×Q8—24no—
268#235—216no—
269#235—22no—
270#235—22no—
271#235—22no—
272#235#6714yescomplemented
273C2×D12—22no—
274C2×D12—22no—
275C2×D12—22no—
276C2×D12—21no—
277C2×D12#6711yescharacteristic
278C2×D12C22×D312yes—
279C2×D12C22×D311yescharacteristic
280C2×C4×D3—22no—
281C2×C4×D3—21no—
282C2×C4×D3—22no—
283C2×C4×D3C22×D312yes—
284C2×Dic6—22no—
285C2×Dic6#6711yescharacteristic
286C2×Dic6C22×D311yescharacteristic
287C3×SD16—68no—
288C2×C3×C8—32no—
289C2×C3×C8—62no—
290#217—61no—
291#217—61no—
292#217—64no—
293#217—121no—
294#215—28no—
295#215—64no—
296#214—64no—
297#213—64no—
298#213—64no—
299(C2×D3)⋊C4—64no—
300C4⋊Dic3—32no—
301C4⋊Dic3—32no—
302C4⋊Dic3—62no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—121no—
306#208—62no—
307#208—62no—
308#208—122no—
309C2×C3⋊C8—22no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—62no—
313C2×C3⋊C8C22×D312yes—
314C22×C32—22no—
315C22×C32#12012yes—
316C22×C32C22×D411yescharacteristic
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—24no—
320C2×C3×D3—42no—
321C2×C3×D3—42no—
322C2×C3×D3—44no—
323C2×C3×D3—84no—
324C32×C4—24no—
325C32×C4#12012yes—
326C32×C4C22×D411yescharacteristic
327C32×C4C22×D411yescharacteristic
328C3⋊Dic3—42no—
329C3×Dic3—22no—
330C3×Dic3—22no—
3312−1+4—64no—
3322−1+4—64no—
333C2×#41—31no—
334C2×#41—32no—
335C2×#41—31no—
336C2×#41—62no—
337C2×#41—61no—
338C22×Q8—32no—
339C22×Q8—61no—
340C22×Q8D3211yescharacteristic
341C22×D4—31no—
342AGL(1,ℤ/8)—184no—
343C2×SD16—34no—
344C2×SD16—64no—
345C2×SD16—92no—
346C2×D8—92no—
347C2×M16—91no—
348C22×C8—31no—
349#127—181no—
350#124—181no—
351#121—94no—
352#120—182no—
353#117—91no—
354#103—92no—
355#103—94no—
356#102—92no—
357C22⋊C8—94no—
358C23×C3—21no—
359C23×C3—32no—
360C23×C3—61no—
361C23×C3—62no—
362C23×C3—122no—
363C23×C3—242no—
364C23×C3D3×D411yescharacteristic
365C23×C3C2×#6711yescharacteristic
366C22×D3—21no—
367C22×D3—22no—
368C22×D3—42no—
369C22×D3—82no—
370C22×D3C2×#6712yes—
371C3×Q8—24no—
372C3×Q8—24no—
373C3×Q8—22no—
374C3×Q8—22no—
375C3×Q8—24no—
376C3×Q8—32no—
377C3×Q8—42no—
378C3×Q8—44no—
379C3×Q8—68no—
380C3×Q8—62no—
381C3×Q8—61no—
382C3×Q8C2×#6714yes—
383C3×Q8C2×#6714yes—
384C3×D4—32no—
385C3×D4—68no—
386C3×D4—64no—
387C3×D4—64no—
388C3×D4—62no—
389C3×D4—61no—
390C3×D4—62no—
391C3×D4—62no—
392C3×D4—122no—
393C2×C3×C4—24no—
394C2×C3×C4—24no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—32no—
402C2×C3×C4—42no—
403C2×C3×C4—44no—
404C2×C3×C4—68no—
405C2×C3×C4—68no—
406C2×C3×C4—61no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4D3×D412yes—
412C2×C3×C4C2×#6712yes—
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C2×#6711yescharacteristic
415C2×C3×C4C2×#6712yes—
416C2×C3×C4C23×D311yescharacteristic
417C2×C3×C4C23×D311yescharacteristic
418#67—24no—
419#67—24no—
420#67—244no—
421#67—244no—
422C2×Dic3—21no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—122no—
426C2×Dic3C2×#6712yes—
427D12—28no—
428D12—22no—
429D12—22no—
430D12—21no—
431D12—22no—
432D12—42no—
433D12C2×#6712yes—
434C4×D3—28no—
435C4×D3—28no—
436C4×D3—24no—
437C4×D3—22no—
438C4×D3—22no—
439Dic6—28no—
440Dic6—22no—
441Dic6—21no—
442Dic6C2×#6712yes—
443C3×C8—62no—
444C3⋊C8—22no—
445C3⋊C8—62no—
446C3⋊C8—62no—
447C3⋊C8—122no—
448C2×C32—22no—
449C2×C32C2×#12011yescharacteristic
450C2×C32#57712yes—
451C3×D3—42no—
452C3×D3—42no—
453C3×D3—82no—
454C24—61no—
455#41—34no—
456#41—616no—
457#41—64no—
458#41—68no—
459#41—64no—
460#41—62no—
461#41—62no—
462#41—62no—
463C2×Q8—21no—
464C2×Q8—22no—
465C2×Q8—31no—
466C2×Q8—31no—
467C2×Q8—62no—
468C2×Q8—64no—
469C2×Q8—68no—
470C2×Q8—64no—
471C2×Q8#62514yescomplemented
472C2×Q8C2×D3212yes—
473C2×D4—32no—
474C2×D4—31no—
475C2×D4—32no—
476C2×D4—31no—
477C2×D4—62no—
478C2×D4—61no—
479C2×D4—62no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4—184no—
483C22×C4—21no—
484C22×C4—32no—
485C22×C4—62no—
486C22×C4—62no—
487C22×C4—61no—
488C22×C4C2×D3211yescharacteristic
489SD16—68no—
490SD16—184no—
491D8—184no—
492M16—182no—
493C2×C8—32no—
494C2×C8—62no—
495C2×C8—92no—
496C4⋊C4—92no—
497C22⋊C4—184no—
498C22⋊C4—181no—
499C42—181no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—21no—
503C22×C3—22no—
504C22×C3—42no—
505C22×C3—64no—
506C22×C3—62no—
507C22×C3—62no—
508C22×C3—122no—
509C22×C3—124no—
510C22×C3—122no—
511C22×C3—244no—
512C22×C3#93712yes—
513C22×C3#95312yes—
514C22×C3C2×D3×D411yescharacteristic
515C22×C3C22×#6711yescharacteristic
516C2×D3—24no—
517C2×D3—22no—
518C2×D3—22no—
519C2×D3—42no—
520C2×D3—44no—
521C2×D3—42no—
522C2×D3—84no—
523C3×C4—24no—
524C3×C4—24no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—22no—
528C3×C4—44no—
529C3×C4—62no—
530C3×C4—62no—
531C3×C4#93712yes—
532C3×C4#95312yes—
533C3×C4C2×D3×D411yescharacteristic
534C3×C4C22×#6711yescharacteristic
535C3×C4C22×#6711yescharacteristic
536C3×C4C22×#6711yescharacteristic
537Dic3—22no—
538Dic3—22no—
539Dic3—122no—
540Dic3—122no—
541Dic3—242no—
542C32#301011yescharacteristic, complemented, Sylow
543C23—32no—
544C23—61no—
545C23—62no—
546C23—122no—
547C23—242no—
548C23D3×#6711yescharacteristic
549Q8—22no—
550Q8—24no—
551Q8—32no—
552Q8—68no—
553Q8—61no—
554Q8—62no—
555Q8C2×#62514yes—
556D4—32no—
557D4—68no—
558D4—64no—
559D4—64no—
560D4—61no—
561D4—62no—
562D4—62no—
563D4—62no—
564D4—122no—
565D4—724no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—32no—
569C2×C4—68no—
570C2×C4—68no—
571C2×C4—61no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—64no—
575C2×C4—182no—
576C2×C4C2×#62512yes—
577C2×C4D3×#6712yes—
578C2×C4D3×#6711yescharacteristic
579C2×C4C22×D3211yescharacteristic
580C8—62no—
581C8—182no—
582C2×C3—22no—
583C2×C3—22no—
584C2×C3—21no—
585C2×C3—22no—
586C2×C3—42no—
587C2×C3—122no—
588C2×C3—122no—
589C2×C3—242no—
590C2×C3#576212yes—
591C2×C3C2×#93711yescharacteristic
592C2×C3#583712yes—
593C2×C3C2×#95311yescharacteristic
594D3—42no—
595D3—42no—
596D3—82no—
597C22—22no—
598C22—62no—
599C22—62no—
600C22—64no—
601C22—122no—
602C22—122no—
603C22—124no—
604C22—244no—
605C22#6397612yes—
606C22C2×D3×#6711yescharacteristic
607C4—24no—
608C4—62no—
609C4—62no—
610C4—362no—
611C4#6397612yes—
612C4C22×#62511yescharacteristic
613C4C2×D3×#6711yescharacteristic
614C3—21no—
615C3#8386011yescharacteristic, complemented
616C3#8411311yescharacteristic, complemented
617C2—22no—
618C2—122no—
619C2—122no—
620C2—242no—
621C2#1059531812yes—
622C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3010
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C22×C3×#215C2semidirect
3. #10595040C2semidirect
4. C2×#63823C2semidirect
5. #10592924C2semidirect
6. #10591586C2semidirect
7. #10591583C2semidirect
8. #10591084C2semidirect
9. #10591070C2semidirect
16. C2×C3×#239C22semidirect
18. C2×C3×D3×Q8C22semidirect
35. #63662C22semidirect
36. #63566C22semidirect
37. #63563C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C2×#1007D3semidirect
44. C22×#215D3semidirect
61. C2×C32×Q8D4semidirect
77. C3×#235D4semidirect
121. C2×#239C2×D3semidirect
123. C2×D3×Q8C2×D3semidirect
235. C2×C3×Q8#67semidirect
236. C2×C3×Q8#67semidirect
272. #235#67semidirect
471. C2×Q8#625semidirect
542. C32#3010semidirect
615. C3#83860semidirect
616. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×#2152
#105950402
C2×#638232
#105929242
#105915862
#105915832
#105910842
#105910702
#841133
#838603