Finite Group Databasebeta

← #11864082

Subgroups — #11864082

Order 1152.

1645 conjugacy classes of subgroups.

The subgroup lattice has 641 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C2×#64151C211yesmaximal, characteristic, complemented
3#10595023C211yesmaximal, characteristic, complemented
4C2×#63830C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591599C214yesmaximal, complemented
7#10591588C214yesmaximal, complemented
8#10591085C211yesmaximal, characteristic, complemented
9#10591069C211yesmaximal, characteristic, complemented
10#84081—31nomaximal
11#78959—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×#3828C2211yescharacteristic
14C2×C3×#239—24no—
15C2×C3×#239—24no—
16C2×C3×#239—22no—
17C2×C3×#239C2214yes—
18C22×C3×D12—21no—
19C22×C3×D12C2211yescharacteristic
20C22×C3×C4×D3—21no—
21C22×C3×C4×D3C2211yescharacteristic
22C2×#3756C2212yescomplemented
23#64151—24no—
24C2×#3755C2212yescomplemented
25C2×#3748C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63977—21no—
29#63966—21no—
30#63909C2212yescomplemented
31C4×#626—22no—
32#63857C2212yescomplemented
33#63830—24no—
34C2×#3716C2212yescomplemented
35C2×#3714C2212yescomplemented
36C3×#835C2214yescomplemented
37#63562C2214yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C22×C3×#41—31no—
40C22×#239D311yescharacteristic, complemented
41C2×#942—31no—
42C2×#942—31no—
43C2×#942—61no—
44C2×#932—31no—
45#5791—31no—
46C2×#908—31no—
47#5524—31no—
48C3×#419—31no—
49#5239—34no—
50#5238—34no—
51#5225D311yescharacteristic, complemented
52#5215—31no—
53#5207—31no—
54#5126—31no—
55#5001—31no—
56#4810—34no—
57#4808—34no—
58C23×C3×D3—21no—
59C23×C3×D3D411yescharacteristic
60C2×C32×Q8—22no—
61C2×C32×Q8—21no—
62C2×C32×Q8D414yescomplemented
63C2×C32×Q8C2312yes—
64C22×C32×C4—21no—
65C22×C32×C4C2311yescharacteristic
66C2×#638—21no—
67#3828—22no—
68#3828—22no—
69C2×C4⋊(C3⋊D3)C2311yescharacteristic
70C2×C4×C3⋊D3—21no—
71C2×#634C2311yescharacteristic
72C22×C3×Dic3D411yescharacteristic
73C3×#239—216no—
74C3×#239—28no—
75C3×#239—28no—
76C2×C3×D12—28no—
77C2×C3×D12—24no—
78C2×C3×D12—21no—
79C2×C3×D12—22no—
80C2×C3×D12D414yescomplemented
81C2×C3×D12C2312yes—
82C2×C3×C4×D3—28no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3—22no—
85C2×C3×C4×D3—24no—
86C2×C3×C4×D3D412yes—
87C2×C3×C4×D3C2312yes—
88C2×#626—22no—
89#3756—24no—
90#3755—24no—
91#3748—22no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×C4⋊Dic3C2312yes—
95C3×C4×Dic3—21no—
96C3×#208—22no—
97C2×C3×C3⋊C8C2312yes—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3716—24no—
102#3714—24no—
103#3005—91noSylow
104C2×C3×#41—34no—
105C2×C3×#41—62no—
106C2×C3×#41—64no—
107C2×C3×#41—64no—
108C22×C3×Q8—21no—
109C22×C3×Q8C2×D311yescharacteristic
110C22×C3×Q8C2×D311yescharacteristic
111C22×C3×D4—31no—
112C22×C3×D4—61no—
113C23×C3×C4—31no—
114C23×C3×C4—61no—
115C2×#239—24no—
116C2×#239—24no—
117C2×#239—22no—
118C2×#239C2×D314yes—
119C2×#235—31no—
120C2×#235—31no—
121C2×#235—61no—
122C22×D12—21no—
123C22×D12C2×D311yescharacteristic
124C22×C4×D3—21no—
125C22×C4×D3C2×D311yescharacteristic
126C2×C3×M16—31no—
127C3×#117—31no—
128#953—61no—
129C2×#216—32no—
130C2×#216—32no—
131C2×#216—62no—
132#942—68no—
133#942—64no—
134#942—64no—
135C2×#215—32no—
136C2×#215—32no—
137C2×#215—62no—
138C2×#214—32no—
139#932—64no—
140C2×#213—32no—
141#930—32no—
142#929—61no—
143C4×#67—62no—
144#926C2×D311yescharacteristic
145#924—32no—
146C2×#208—31no—
147C2×#208—31no—
148C2×#208—61no—
149C2×#208C2×D311yescharacteristic
150#908—64no—
151C2×D24—32no—
152C2×#204—32no—
153#897—32no—
154#895—32no—
155#886—61no—
156#882—61no—
157C4×D12—62no—
158C3×#103—34no—
159#835C2×D314yescomplemented
160#832—34no—
161#830—34no—
162(C2×D3)⋊C8—34no—
163#809—34no—
164C23×C32C2×D411yescharacteristic
165C22×C3⋊D3—21no—
166C22×C3×D3—24no—
167C22×C3×D3—22no—
168C22×C3×D3—22no—
169C22×C3×D3—42no—
170C22×C3×D3—44no—
171C22×C3×D3C2×D412yes—
172C32×Q8—24no—
173C32×Q8—22no—
174C32×Q8C2×D414yes—
175C2×C32×C4—24no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2411yescharacteristic
181#638—42no—
182C2×C3⋊Dic3—21no—
183C4⋊(C3⋊D3)—21no—
184C4⋊(C3⋊D3)—21no—
185C4×C3⋊D3—42no—
186#634—21no—
187#634—21no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C2×D412yes—
191C3×D12—216no—
192C3×D12—24no—
193C3×D12—22no—
194C3×D12C2×D414yes—
195C3×C4×D3—216no—
196C3×C4×D3—24no—
197C3×C4×D3—22no—
198C3×C4×D3—22no—
199#626—44no—
200C3⋊(C3⋊C8)—22no—
201C3×C3⋊C8—22no—
202C22×#41—31no—
203C2×#137—91no—
204C2×AGL(1,ℤ/8)—91no—
205#525—91no—
206#452—94no—
207#449—94no—
208#419—31no—
209#418—91no—
210#407—91no—
211C24×C3—31no—
212C24×C3—61no—
213C23×D3—21no—
214C23×D3#6711yescharacteristic
215C3×#41—68no—
216C3×#41—616no—
217C3×#41—68no—
218C2×C3×Q8—22no—
219C2×C3×Q8—21no—
220C2×C3×Q8—22no—
221C2×C3×Q8—21no—
222C2×C3×Q8—24no—
223C2×C3×Q8—22no—
224C2×C3×Q8—41no—
225C2×C3×Q8—42no—
226C2×C3×Q8D1214yescomplemented
227C2×C3×Q8#6714yescomplemented
228C2×C3×Q8C22×D312yes—
229C2×C3×Q8C22×D312yes—
230C2×C3×D4—34no—
231C2×C3×D4—32no—
232C2×C3×D4—64no—
233C2×C3×D4—68no—
234C2×C3×D4—62no—
235C2×C3×D4—61no—
236C22×C3×C4—21no—
237C22×C3×C4—21no—
238C22×C3×C4—21no—
239C22×C3×C4—31no—
240C22×C3×C4—32no—
241C22×C3×C4—32no—
242C22×C3×C4—41no—
243C22×C3×C4—64no—
244C22×C3×C4—68no—
245C22×C3×C4—62no—
246C22×C3×C4—62no—
247C22×C3×C4C22×D311yescharacteristic
248C22×C3×C4C22×D311yescharacteristic
249C2×#67—62no—
250C2×#67—61no—
251C2×#67—61no—
252C2×#67—121no—
253C22×Dic3#6711yescharacteristic
254#239—216no—
255#239—28no—
256#239—28no—
257#235—64no—
258#235—62no—
259#235—62no—
260#235—62no—
261#235—62no—
262#235—122no—
263C2×D12—28no—
264C2×D12—24no—
265C2×D12—22no—
266C2×D12—21no—
267C2×D12—31no—
268C2×D12—31no—
269C2×D12—61no—
270C2×D12—62no—
271C2×D12#6714yescomplemented
272C2×D12C22×D312yes—
273C2×C4×D3—28no—
274C2×C4×D3—22no—
275C2×C4×D3—22no—
276C2×C4×D3—24no—
277C2×C4×D3—61no—
278C2×C4×D3—61no—
279C2×C4×D3—121no—
280C2×C4×D3#6712yes—
281C2×C4×D3C22×D312yes—
282C2×Dic6—31no—
283C2×Dic6—31no—
284C2×Dic6—61no—
285C3×M16—62no—
286C2×C3×C8—32no—
287C3×C4⋊C4—32no—
288C3×C22⋊C4—61no—
289C3×C42—61no—
290#217—21no—
291#217—62no—
292#216—68no—
293#216—64no—
294#216—64no—
295#215—68no—
296#215—64no—
297#215—64no—
298#214—64no—
299#213—64no—
300(C2×D3)⋊C4—62no—
301(C2×D3)⋊C4—62no—
302(C2×D3)⋊C4—62no—
303C4⋊Dic3—62no—
304C4⋊Dic3C22×D312yes—
305Dic3⋊C4—62no—
306C4×Dic3—21no—
307#208—22no—
308#208—64no—
309#208—62no—
310#208—62no—
311C2×C3⋊C8—32no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8C22×D312yes—
315D24—64no—
316#204—64no—
317C22×C32—22no—
318C22×C32#12012yes—
319C22×C32C22×D411yescharacteristic
320C2×C3⋊D3—41no—
321C2×C3⋊D3—42no—
322C2×C3×D3—22no—
323C2×C3×D3—24no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—44no—
327C2×C3×D3—48no—
328C2×C3×D3—44no—
329C32×C4—24no—
330C32×C4#12012yes—
331C32×C4C22×D411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—41no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—34no—
337C2×#41—62no—
338C2×#41—64no—
339C2×#41—64no—
340C2×#41—91no—
341C22×Q8D3211yescharacteristic
342C22×D4—31no—
343C22×D4—61no—
344C23×C4—31no—
345C23×C4—61no—
346#137—184no—
347AGL(1,ℤ/8)—184no—
348C2×Q16—92no—
349C2×SD16—92no—
350C2×SD16—92no—
351C2×D8—92no—
352C2×M16—31no—
353C2×M16—91no—
354#123—181no—
355C22⋊Q8—92no—
356#121—92no—
357#120—181no—
358C4×D4—182no—
359#117—31no—
360#103—34no—
361#102—94no—
362C22⋊C8—94no—
363C23×C3—21no—
364C23×C3—32no—
365C23×C3—64no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—122no—
369C23×C3—124no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×#6711yescharacteristic
372C22×D3—22no—
373C22×D3—24no—
374C22×D3—22no—
375C22×D3—42no—
376C22×D3—44no—
377C22×D3—61no—
378C22×D3—61no—
379C22×D3—121no—
380C22×D3C2×#6712yes—
381C3×Q8—24no—
382C3×Q8—24no—
383C3×Q8—22no—
384C3×Q8—22no—
385C3×Q8—24no—
386C3×Q8—42no—
387C3×Q8—44no—
388C3×Q8C2×D1214yes—
389C3×Q8C2×#6714yes—
390C3×D4—34no—
391C3×D4—616no—
392C3×D4—64no—
393C3×D4—62no—
394C2×C3×C4—24no—
395C2×C3×C4—24no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—21no—
399C2×C3×C4—22no—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—32no—
403C2×C3×C4—42no—
404C2×C3×C4—44no—
405C2×C3×C4—616no—
406C2×C3×C4—62no—
407C2×C3×C4—64no—
408C2×C3×C4—62no—
409C2×C3×C4—62no—
410C2×C3×C4—62no—
411C2×C3×C4C2×D1212yes—
412C2×C3×C4D3×D411yescharacteristic
413C2×C3×C4D3×D412yes—
414C2×C3×C4C2×#6712yes—
415C2×C3×C4C2×#6711yescharacteristic
416C2×C3×C4C2×#6712yes—
417C2×C3×C4C23×D311yescharacteristic
418C2×C3×C4C23×D311yescharacteristic
419#67—124no—
420#67—124no—
421#67—122no—
422#67—122no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—61no—
426C2×Dic3—61no—
427C2×Dic3—121no—
428C2×Dic3C2×#6712yes—
429D12—216no—
430D12—24no—
431D12—22no—
432D12—62no—
433D12—61no—
434D12—61no—
435D12—61no—
436D12—61no—
437D12—121no—
438D12—124no—
439D12C2×#6714yes—
440C4×D3—216no—
441C4×D3—24no—
442C4×D3—22no—
443C4×D3—22no—
444C4×D3—124no—
445C4×D3—122no—
446C4×D3—122no—
447Dic6—62no—
448Dic6—61no—
449Dic6—61no—
450Dic6—61no—
451Dic6—61no—
452Dic6—121no—
453C3×C8—62no—
454C3⋊C8—22no—
455C3⋊C8—64no—
456C3⋊C8—62no—
457C3⋊C8—62no—
458C2×C32—22no—
459C2×C32C2×#12011yescharacteristic
460C2×C32#57512yes—
461C3⋊D3—81no—
462C3×D3—42no—
463C3×D3—44no—
464C24—31no—
465C24—61no—
466#41—68no—
467#41—616no—
468#41—68no—
469#41—182no—
470#41—182no—
471C2×Q8—21no—
472C2×Q8—22no—
473C2×Q8—91no—
474C2×Q8#62614yescomplemented
475C2×Q8C2×D3212yes—
476C2×D4—32no—
477C2×D4—34no—
478C2×D4—64no—
479C2×D4—68no—
480C2×D4—62no—
481C2×D4—61no—
482C2×D4—91no—
483C2×D4—182no—
484C2×D4—181no—
485C22×C4—21no—
486C22×C4—31no—
487C22×C4—32no—
488C22×C4—32no—
489C22×C4—64no—
490C22×C4—68no—
491C22×C4—62no—
492C22×C4—62no—
493C22×C4—181no—
494C22×C4C2×D3211yescharacteristic
495Q16—184no—
496SD16—184no—
497SD16—184no—
498D8—184no—
499M16—62no—
500M16—182no—
501C2×C8—32no—
502C2×C8—92no—
503C4⋊C4—32no—
504C4⋊C4—182no—
505C22⋊C4—61no—
506C22⋊C4—182no—
507C22⋊C4—182no—
508C42—61no—
509C22×C3—22no—
510C22×C3—22no—
511C22×C3—21no—
512C22×C3—22no—
513C22×C3—42no—
514C22×C3—64no—
515C22×C3—62no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—124no—
519C22×C3—128no—
520C22×C3—124no—
521C22×C3#88212yes—
522C22×C3#95312yes—
523C22×C3C2×D3×D411yescharacteristic
524C22×C3C22×#6711yescharacteristic
525C2×D3—22no—
526C2×D3—22no—
527C2×D3—22no—
528C2×D3—24no—
529C2×D3—44no—
530C2×D3—48no—
531C2×D3—44no—
532C2×D3—122no—
533C2×D3—121no—
534C2×D3—122no—
535C2×D3—122no—
536C2×D3—121no—
537C2×D3—242no—
538C3×C4—24no—
539C3×C4—24no—
540C3×C4—21no—
541C3×C4—21no—
542C3×C4—22no—
543C3×C4—44no—
544C3×C4—62no—
545C3×C4—122no—
546C3×C4#88212yes—
547C3×C4#95312yes—
548C3×C4C22×D1211yescharacteristic
549C3×C4C2×D3×D411yescharacteristic
550C3×C4C22×#6711yescharacteristic
551C3×C4C22×#6711yescharacteristic
552Dic3—22no—
553Dic3—42no—
554Dic3—122no—
555Dic3—121no—
556Dic3—121no—
557C32#300511yescharacteristic, complemented, Sylow
558C23—32no—
559C23—62no—
560C23—64no—
561C23—62no—
562C23—122no—
563C23—124no—
564C23—181no—
565C23D3×#6711yescharacteristic
566Q8—22no—
567Q8—24no—
568Q8—181no—
569Q8—181no—
570Q8C2×#62614yes—
571D4—34no—
572D4—616no—
573D4—62no—
574D4—64no—
575D4—181no—
576D4—181no—
577D4—364no—
578D4—362no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—32no—
582C2×C4—616no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—62no—
586C2×C4—64no—
587C2×C4—62no—
588C2×C4—181no—
589C2×C4—362no—
590C2×C4C2×#62612yes—
591C2×C4D3×#6712yes—
592C2×C4D3×#6711yescharacteristic
593C2×C4C22×D3211yescharacteristic
594C8—62no—
595C8—182no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—21no—
599C2×C3—22no—
600C2×C3—42no—
601C2×C3—122no—
602C2×C3—124no—
603C2×C3C2×#88211yescharacteristic
604C2×C3#577712yes—
605C2×C3#582212yes—
606C2×C3C2×#95311yescharacteristic
607D3—42no—
608D3—44no—
609D3—242no—
610D3—241no—
611D3—241no—
612C22—22no—
613C22—64no—
614C22—62no—
615C22—62no—
616C22—62no—
617C22—124no—
618C22—128no—
619C22—124no—
620C22—361no—
621C22—362no—
622C22#6397712yes—
623C22C2×D3×#6711yescharacteristic
624C4—24no—
625C4—62no—
626C4—122no—
627C4—361no—
628C4#6397712yes—
629C4C22×#62611yescharacteristic
630C4C2×D3×#6711yescharacteristic
631C3—21no—
632C3#7895911yescharacteristic, complemented
633C3#8408111yescharacteristic, complemented
634C2—22no—
635C2—122no—
636C2—124no—
637C2—721no—
638C2#1059531712yes—
639C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
hypercenterC22×Q8D32
hypocenterC32#3005
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. C22×C3×#239C2semidirect
2. C2×#64151C2semidirect
3. #10595023C2semidirect
4. C2×#63830C2semidirect
5. C3×#5225C2semidirect
6. #10591599C2semidirect
7. #10591588C2semidirect
8. #10591085C2semidirect
9. #10591069C2semidirect
22. C2×#3756C22semidirect
24. C2×#3755C22semidirect
30. #63909C22semidirect
32. #63857C22semidirect
34. C2×#3716C22semidirect
35. C2×#3714C22semidirect
36. C3×#835C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C22×#239D3semidirect
51. #5225D3semidirect
62. C2×C32×Q8D4semidirect
80. C2×C3×D12D4semidirect
159. #835C2×D3semidirect
226. C2×C3×Q8D12semidirect
227. C2×C3×Q8#67semidirect
271. C2×D12#67semidirect
474. C2×Q8#626semidirect
557. C32#3005semidirect
632. C3#78959semidirect
633. C3#84081semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C2×#641512
#105950232
C2×#638302
C3×#52252
#105915992
#105915882
#105910852
#105910692
#840813
#789593