Finite Group Databasebeta

← #11864072

Subgroups — #11864072

Order 1152.

1611 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10595022C211yesmaximal, characteristic, complemented
4C2×#63827C211yesmaximal, characteristic, complemented
5#10592914C211yesmaximal, characteristic, complemented
6#10591461C214yesmaximal, complemented
7#10591450C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#84081—31nomaximal
11#83945—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—21no—
14C23×C3×Dic3—21no—
15C2×C3×#237—24no—
16C2×C3×#237—22no—
17C2×C3×#237—24no—
18C2×C3×#237C2214yes—
19C2×C3×#235C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×Dic6C2211yescharacteristic
22#64135C2211yescharacteristic
23C2×#3748C2211yescharacteristic
24C2×C3×#214C2212yescomplemented
25C3×#932—24no—
26C2×C3×#213C2212yescomplemented
27C2×C3×#208C2211yescharacteristic
28#63976—21no—
29#63961—21no—
30#63908C2212yescomplemented
31C4×#625—22no—
32#63856C2212yescomplemented
33C2×#3718C2212yescomplemented
34#63827—24no—
35C2×#3715C2212yescomplemented
36#63659C2214yescomplemented
37#63566C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×C3×#41—31no—
40C22×#237D311yescharacteristic, complemented
41C2×C3×AGL(1,ℤ/8)—31no—
42#5828—31no—
43C2×#951—31no—
44C2×#942—31no—
45C2×#932D311yescharacteristic, complemented
46#5791—31no—
47#5239—34no—
48#5238—34no—
49#5225—31no—
50#5215—31no—
51#5215—31no—
52#5215—61no—
53#5207—31no—
54#5173—34no—
55#5158—34no—
56#5126—31no—
57#5120—31no—
58C24×C32—21no—
59C23×C3×D3D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yescomplemented
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×C3×#67—28no—
66C2×C3×#67—24no—
67C2×C3×#67—21no—
68C22×C3×Dic3—28no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—24no—
71C22×C3×Dic3D411yescharacteristic
72C3×#237—216no—
73C3×#237—28no—
74C3×#237—28no—
75C3×#235—22no—
76C3×#235—22no—
77C2×C3×D12C2311yescharacteristic
78C2×C3×C4×D3—22no—
79C2×C3×C4×D3—22no—
80C2×C3×C4×D3—21no—
81C2×C3×C4×D3D412yes—
82C2×C3×C4×D3C2312yes—
83C2×C3×Dic6—21no—
84C2×C3×Dic6—22no—
85C2×C3×Dic6D414yescomplemented
86C2×C3×Dic6C2311yescharacteristic
87C2×C3×Dic6C2312yes—
88C2×#625—22no—
89#3757—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91C4×C3⋊Dic3—21no—
92#3748—22no—
93C2×C3⋊(C3⋊C8)C2312yes—
94C3×#214—24no—
95C3×#213—24no—
96C3×#208—22no—
97C2×C3×C3⋊C8C2312yes—
98#3724—22no—
99(C2×D3)⋊Dic3—22no—
100(C2×D3)⋊Dic3—22no—
101#3718—24no—
102#3715—24no—
103#3005—91noSylow
104C2×C3×#41—34no—
105C2×C3×#41—31no—
106C2×C3×#41—62no—
107C2×C3×#41—64no—
108C2×C3×#41—64no—
109C22×C3×Q8—31no—
110C22×C3×D4—21no—
111C22×C3×D4—61no—
112C22×C3×D4C2×D311yescharacteristic
113C22×C3×D4C2×D311yescharacteristic
114C23×C3×C4—31no—
115C23×C3×C4—61no—
116C22×#67—21no—
117C23×Dic3—21no—
118C2×#237—24no—
119C2×#237—22no—
120C2×#237—24no—
121C2×#237C2×D314yes—
122C2×#235C2×D311yescharacteristic
123C22×C4×D3C2×D311yescharacteristic
124C22×Dic6C2×D311yescharacteristic
125C3×AGL(1,ℤ/8)—64no—
126C2×C3×SD16—32no—
127C2×C3×D8—32no—
128C2×C3×M16—31no—
129#953—61no—
130#951—64no—
131#946—32no—
132C2×#216—32no—
133C2×#216—32no—
134#942—64no—
135C2×#215—32no—
136#938—32no—
137#937—61no—
138#935—61no—
139C2×#214—32no—
140C2×#214C2×D312yescomplemented
141#932—24no—
142C2×#213C2×D312yescomplemented
143#930—32no—
144#929—61no—
145C4×#67—62no—
146C4×#67—62no—
147#926—31no—
148#926—31no—
149#926—61no—
150#924—32no—
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—61no—
154C2×#208C2×D311yescharacteristic
155#835—34no—
156#832—34no—
157#832—34no—
158#832—64no—
159#830—34no—
160(C2×D3)⋊C8—34no—
161#816—34no—
162C23×C32—24no—
163C23×C32—22no—
164C23×C32—44no—
165C23×C32C2×D411yescharacteristic
166C22×C3×D3—22no—
167C22×C3×D3—21no—
168C22×C3×D3—42no—
169C22×C3×D3C2×D412yes—
170C32×D4—24no—
171C32×D4—22no—
172C32×D4C2×D414yes—
173C2×C32×C4C2×D411yescharacteristic
174C2×C32×C4C2×D412yes—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2411yescharacteristic
177C2×C3⋊Dic3—22no—
178C3×#67—216no—
179C3×#67—42no—
180C2×C3×Dic3—216no—
181C2×C3×Dic3—24no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—22no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3C2×D412yes—
186C3×D12—21no—
187C3×D12—21no—
188C3×C4×D3—24no—
189C3×C4×D3—22no—
190C3×C4×D3—22no—
191C3×C4×D3—42no—
192C3×Dic6—24no—
193C3×Dic6—22no—
194C3×Dic6—21no—
195C3×Dic6—21no—
196C3×Dic6C2×D414yes—
197#625—44no—
198C3⋊(C3⋊C8)—22no—
199C3×C3⋊C8—22no—
200C22×#41—31no—
201C2×#137—91no—
202C2×AGL(1,ℤ/8)—31no—
203#525—91no—
204#452—94no—
205#449—94no—
206#419—91no—
207#418—91no—
208#407—91no—
209C24×C3—21no—
210C24×C3—21no—
211C24×C3—31no—
212C24×C3—41no—
213C23×D3#6711yescharacteristic
214C3×#41—68no—
215C3×#41—616no—
216C3×#41—68no—
217C3×#41—62no—
218C3×#41—62no—
219C2×C3×Q8—34no—
220C2×C3×Q8—32no—
221C2×C3×Q8—31no—
222C2×C3×Q8—61no—
223C2×C3×Q8—62no—
224C2×C3×D4—21no—
225C2×C3×D4—22no—
226C2×C3×D4—21no—
227C2×C3×D4—22no—
228C2×C3×D4—24no—
229C2×C3×D4—22no—
230C2×C3×D4—31no—
231C2×C3×D4—42no—
232C2×C3×D4—41no—
233C2×C3×D4—64no—
234C2×C3×D4—68no—
235C2×C3×D4—61no—
236C2×C3×D4#6714yescomplemented
237C2×C3×D4#6714yescomplemented
238C2×C3×D4C22×D312yes—
239C2×C3×D4C22×D312yes—
240C22×C3×C4—21no—
241C22×C3×C4—31no—
242C22×C3×C4—32no—
243C22×C3×C4—32no—
244C22×C3×C4—64no—
245C22×C3×C4—68no—
246C22×C3×C4—61no—
247C22×C3×C4—62no—
248C22×C3×C4—62no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—28no—
253C2×#67—24no—
254C2×#67—21no—
255C2×#67—62no—
256C2×#67—62no—
257C22×Dic3—28no—
258C22×Dic3—21no—
259C22×Dic3—24no—
260C22×Dic3#6711yescharacteristic
261#237—216no—
262#237—28no—
263#237—28no—
264#235—22no—
265#235—22no—
266C2×D12C22×D311yescharacteristic
267C2×C4×D3—22no—
268C2×C4×D3—22no—
269C2×C4×D3—21no—
270C2×C4×D3#6712yes—
271C2×C4×D3C22×D312yes—
272C2×Dic6—22no—
273C2×Dic6—21no—
274C2×Dic6#6714yescomplemented
275C2×Dic6C22×D311yescharacteristic
276C2×Dic6C22×D312yes—
277C3×SD16—64no—
278C3×D8—64no—
279C3×M16—62no—
280C2×C3×C8—32no—
281#217—62no—
282#217—61no—
283#217—61no—
284#217—62no—
285#217—121no—
286#216—64no—
287#216—64no—
288#215—64no—
289#214—24no—
290#214—64no—
291#213—24no—
292(C2×D3)⋊C4—62no—
293(C2×D3)⋊C4—62no—
294C4⋊Dic3—32no—
295C4⋊Dic3—32no—
296C4⋊Dic3—62no—
297Dic3⋊C4—62no—
298Dic3⋊C4—62no—
299C4×Dic3—61no—
300C4×Dic3—61no—
301C4×Dic3—121no—
302#208—22no—
303#208—62no—
304#208—62no—
305#208—122no—
306C2×C3⋊C8—32no—
307C2×C3⋊C8—32no—
308C2×C3⋊C8—62no—
309C2×C3⋊C8C22×D312yes—
310C22×C32—22no—
311C22×C32—24no—
312C22×C32—48no—
313C22×C32—44no—
314C22×C32#12012yes—
315C22×C32C22×D411yescharacteristic
316C2×C3×D3—22no—
317C2×C3×D3—22no—
318C2×C3×D3—22no—
319C2×C3×D3—44no—
320C2×C3×D3—41no—
321C2×C3×D3—42no—
322C32×C4#12012yes—
323C32×C4C22×D411yescharacteristic
324C32×C4C22×D411yescharacteristic
325C3⋊Dic3—42no—
326C3×Dic3—24no—
327C3×Dic3—22no—
328C3×Dic3—41no—
329C2×#41—34no—
330C2×#41—31no—
331C2×#41—62no—
332C2×#41—64no—
333C2×#41—64no—
334C22×Q8—31no—
335C22×D4—61no—
336C22×D4D3211yescharacteristic
337C23×C4—31no—
338C23×C4—61no—
339#137—184no—
340AGL(1,ℤ/8)—64no—
341C2×Q16—92no—
342C2×SD16—32no—
343C2×SD16—92no—
344C2×D8—32no—
345C2×M16—31no—
346C2×M16—91no—
347#123—181no—
348C22⋊Q8—92no—
349#121—92no—
350#120—181no—
351C4×D4—182no—
352#117—91no—
353#103—94no—
354#102—94no—
355C22⋊C8—94no—
356C23×C3—24no—
357C23×C3—24no—
358C23×C3—22no—
359C23×C3—22no—
360C23×C3—21no—
361C23×C3—32no—
362C23×C3—42no—
363C23×C3—44no—
364C23×C3—44no—
365C23×C3—44no—
366C23×C3—62no—
367C23×C3—61no—
368C23×C3—84no—
369C23×C3—122no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×#6711yescharacteristic
372C22×D3—22no—
373C22×D3—21no—
374C22×D3—42no—
375C22×D3C2×#6712yes—
376C3×Q8—34no—
377C3×Q8—64no—
378C3×Q8—62no—
379C3×Q8—61no—
380C3×Q8—61no—
381C3×D4—24no—
382C3×D4—24no—
383C3×D4—22no—
384C3×D4—22no—
385C3×D4—24no—
386C3×D4—42no—
387C3×D4—44no—
388C3×D4—616no—
389C3×D4—61no—
390C3×D4—61no—
391C3×D4—122no—
392C3×D4C2×#6714yes—
393C3×D4C2×#6714yes—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—21no—
398C2×C3×C4—32no—
399C2×C3×C4—616no—
400C2×C3×C4—62no—
401C2×C3×C4—64no—
402C2×C3×C4—62no—
403C2×C3×C4—64no—
404C2×C3×C4—62no—
405C2×C3×C4—62no—
406C2×C3×C4—61no—
407C2×C3×C4—122no—
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D412yes—
410C2×C3×C4C2×#6712yes—
411C2×C3×C4C2×#6712yes—
412C2×C3×C4C2×#6711yescharacteristic
413C2×C3×C4C2×#6712yes—
414C2×C3×C4C23×D311yescharacteristic
415C2×C3×C4C23×D311yescharacteristic
416#67—216no—
417#67—42no—
418#67—124no—
419#67—124no—
420C2×Dic3—216no—
421C2×Dic3—24no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—21no—
425C2×Dic3—62no—
426C2×Dic3—62no—
427C2×Dic3—122no—
428C2×Dic3C2×#6712yes—
429D12—21no—
430D12—21no—
431C4×D3—24no—
432C4×D3—22no—
433C4×D3—22no—
434C4×D3—42no—
435Dic6—24no—
436Dic6—22no—
437Dic6—21no—
438Dic6—21no—
439Dic6C2×#6714yes—
440C3×C8—62no—
441C3⋊C8—22no—
442C3⋊C8—62no—
443C3⋊C8—62no—
444C3⋊C8—122no—
445C2×C32—22no—
446C2×C32—44no—
447C2×C32C2×#12011yescharacteristic
448C2×C32#57512yes—
449C3×D3—42no—
450C3×D3—81no—
451C24—21no—
452C24—31no—
453#41—68no—
454#41—616no—
455#41—68no—
456#41—62no—
457#41—62no—
458C2×Q8—32no—
459C2×Q8—31no—
460C2×Q8—34no—
461C2×Q8—62no—
462C2×Q8—61no—
463C2×D4—22no—
464C2×D4—21no—
465C2×D4—31no—
466C2×D4—64no—
467C2×D4—68no—
468C2×D4—61no—
469C2×D4—182no—
470C2×D4#62514yescomplemented
471C2×D4C2×D3212yes—
472C22×C4—31no—
473C22×C4—32no—
474C22×C4—32no—
475C22×C4—64no—
476C22×C4—68no—
477C22×C4—61no—
478C22×C4—62no—
479C22×C4—62no—
480C22×C4—61no—
481C22×C4C2×D3211yescharacteristic
482Q16—184no—
483SD16—64no—
484SD16—184no—
485D8—64no—
486M16—62no—
487M16—182no—
488C2×C8—32no—
489C2×C8—92no—
490C4⋊C4—92no—
491C4⋊C4—182no—
492C22⋊C4—182no—
493C22⋊C4—182no—
494C22⋊C4—181no—
495C42—181no—
496C22×C3—22no—
497C22×C3—22no—
498C22×C3—24no—
499C22×C3—24no—
500C22×C3—21no—
501C22×C3—22no—
502C22×C3—42no—
503C22×C3—44no—
504C22×C3—48no—
505C22×C3—48no—
506C22×C3—44no—
507C22×C3—44no—
508C22×C3—62no—
509C22×C3—62no—
510C22×C3—62no—
511C22×C3—84no—
512C22×C3—88no—
513C22×C3—124no—
514C22×C3—122no—
515C22×C3—121no—
516C22×C3#93712yes—
517C22×C3#95312yes—
518C22×C3C2×D3×D411yescharacteristic
519C22×C3C22×#6711yescharacteristic
520C2×D3—22no—
521C2×D3—22no—
522C2×D3—22no—
523C2×D3—44no—
524C2×D3—42no—
525C2×D3—41no—
526C3×C4—21no—
527C3×C4—21no—
528C3×C4—22no—
529C3×C4—62no—
530C3×C4—64no—
531C3×C4—121no—
532C3×C4#93712yes—
533C3×C4#95312yes—
534C3×C4C2×D3×D411yescharacteristic
535C3×C4C22×#6711yescharacteristic
536C3×C4C22×#6711yescharacteristic
537C3×C4C22×#6711yescharacteristic
538Dic3—24no—
539Dic3—22no—
540Dic3—41no—
541Dic3—122no—
542Dic3—122no—
543Dic3—242no—
544C32#300511yescharacteristic, complemented, Sylow
545C23—22no—
546C23—24no—
547C23—32no—
548C23—44no—
549C23—62no—
550C23—61no—
551C23—122no—
552C23D3×#6711yescharacteristic
553Q8—34no—
554Q8—62no—
555Q8—64no—
556Q8—61no—
557Q8—61no—
558D4—22no—
559D4—24no—
560D4—616no—
561D4—61no—
562D4—61no—
563D4—122no—
564D4—364no—
565D4C2×#62514yes—
566C2×C4—32no—
567C2×C4—616no—
568C2×C4—62no—
569C2×C4—62no—
570C2×C4—64no—
571C2×C4—62no—
572C2×C4—62no—
573C2×C4—64no—
574C2×C4—61no—
575C2×C4—122no—
576C2×C4—182no—
577C2×C4C2×#62512yes—
578C2×C4D3×#6712yes—
579C2×C4D3×#6711yescharacteristic
580C2×C4C22×D3211yescharacteristic
581C8—62no—
582C8—182no—
583C2×C3—22no—
584C2×C3—22no—
585C2×C3—22no—
586C2×C3—21no—
587C2×C3—42no—
588C2×C3—44no—
589C2×C3—44no—
590C2×C3—84no—
591C2×C3—122no—
592C2×C3—241no—
593C2×C3#577312yes—
594C2×C3C2×#93711yescharacteristic
595C2×C3#582212yes—
596C2×C3C2×#95311yescharacteristic
597D3—42no—
598D3—81no—
599C22—22no—
600C22—24no—
601C22—48no—
602C22—44no—
603C22—62no—
604C22—62no—
605C22—62no—
606C22—124no—
607C22—122no—
608C22—121no—
609C22#6397612yes—
610C22C2×D3×#6711yescharacteristic
611C4—62no—
612C4—64no—
613C4—121no—
614C4—362no—
615C4#6397612yes—
616C4C22×#62511yescharacteristic
617C4C2×D3×#6711yescharacteristic
618C3—21no—
619C3#8394511yescharacteristic, complemented
620C3#8408111yescharacteristic, complemented
621C2—22no—
622C2—44no—
623C2—122no—
624C2—241no—
625C2#1059509512yes—
626C2C2×#6397611yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#237C2semidirect
2. C2×C3×#932C2semidirect
3. #10595022C2semidirect
4. C2×#63827C2semidirect
5. #10592914C2semidirect
6. #10591461C2semidirect
7. #10591450C2semidirect
8. #10591100C2semidirect
9. #10591069C2semidirect
24. C2×C3×#214C22semidirect
26. C2×C3×#213C22semidirect
30. #63908C22semidirect
32. #63856C22semidirect
33. C2×#3718C22semidirect
35. C2×#3715C22semidirect
36. #63659C22semidirect
37. #63566C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C22×#237D3semidirect
45. C2×#932D3semidirect
62. C2×C32×D4D4semidirect
85. C2×C3×Dic6D4semidirect
140. C2×#214C2×D3semidirect
142. C2×#213C2×D3semidirect
236. C2×C3×D4#67semidirect
237. C2×C3×D4#67semidirect
274. C2×Dic6#67semidirect
470. C2×D4#625semidirect
544. C32#3005semidirect
619. C3#83945semidirect
620. C3#84081semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
C2×C3×#9322
#105950222
C2×#638272
#105929142
#105914612
#105914502
#105911002
#105910692
#840813
#839453