Finite Group Databasebeta

← #11864440

Subgroups — #11864440

Order 1152.

1613 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic, complemented
3#10595045C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591588C214yesmaximal, complemented
7#10591584C214yesmaximal, complemented
8#10591083C211yesmaximal, characteristic, complemented
9#10591071C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#78960—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C3×#1007—24no—
15C3×#1007—24no—
16C2×C3×#239—21no—
17C2×C3×#239C2212yescomplemented
18C2×C3×D3×Q8—21no—
19C2×C3×D3×Q8C2212yescomplemented
20C2×C3×#235—22no—
21C2×C3×#235C2211yescharacteristic
22C2×C3×#235C2211yescharacteristic
23C2×#3755—24no—
24C2×#3755C2214yes—
25C22×C3⋊(C3⋊C8)C2211yescharacteristic
26C3×#926C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63981—22no—
29#63911—21no—
30#63909C2214yes—
31#63864—21no—
32C2×#3717C2212yes—
33#63825—24no—
34C2×#3714C2212yes—
35C3×#835C2214yescomplemented
36#63565C2212yescomplemented
37#63562C2212yescomplemented
38(C2×D3)⋊(C3⋊C8)C2214yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1007D311yescharacteristic, complemented
41#5830—31no—
42C2×#949—31no—
43C22×#215—31no—
44C22×#215—31no—
45C22×#215—61no—
46C2×#908—31no—
47#5525—31no—
48C3×#419—31no—
49#5238—34no—
50#5234—31no—
51#5233—31no—
52#5227—34no—
53#5225D311yescharacteristic, complemented
54#5129—31no—
55#5002—31no—
56#4810—34no—
57#4806—34no—
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×C4⋊(C3⋊D3)—22no—
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—21no—
68C2×C4⋊(C3⋊D3)C2312yes—
69C2×C3×#67—21no—
70C2×C3×#67D412yes—
71C3×#239—28no—
72C3×#239—24no—
73C3×#239—24no—
74C3×D3×Q8—28no—
75C3×D3×Q8—24no—
76C3×D3×Q8—24no—
77C3×#235—216no—
78C3×#235—22no—
79C3×#235—22no—
80C3×#235—22no—
81C3×#235D414yescomplemented
82C2×C3×D12—22no—
83C2×C3×D12D411yescharacteristic
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×#626—24no—
93#3755—28no—
94C2×C3⋊(C3⋊C8)—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101#3722—24no—
102#3717—24no—
103#3714—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
117#1007—24no—
118#1007—24no—
119C2×#239—21no—
120C2×#239C2×D312yescomplemented
121C2×D3×Q8—21no—
122C2×D3×Q8C2×D312yescomplemented
123C2×#235—22no—
124C2×#235C2×D311yescharacteristic
125C2×#235C2×D311yescharacteristic
126C22×D12—31no—
127C22×D12—31no—
128C22×D12—61no—
129C2×C3×M16—31no—
130C3×#117—31no—
131#949—64no—
132#947—61no—
133C2×#215—34no—
134C2×#215—34no—
135C2×#215—32no—
136C2×#215—64no—
137C2×#215—68no—
138C2×#215—64no—
139C2×#215—64no—
140#940—61no—
141#937—62no—
142C2×#213—32no—
143#930—34no—
144#926C2×D311yescharacteristic
145C2×#208C2×D311yescharacteristic
146C22×C3⋊C8—31no—
147C22×C3⋊C8—31no—
148C22×C3⋊C8—61no—
149#908—64no—
150C2×D24—32no—
151C2×#204—32no—
152#895—34no—
153#882—62no—
154#875—61no—
155#874—61no—
156C3×#103—34no—
157#835—32no—
158#835C2×D314yescomplemented
159#832—32no—
160#830—34no—
161(C2×D3)⋊C8—34no—
162#810—32no—
163#809—32no—
164C23×C32C2×D411yescharacteristic
165C22×C3⋊D3—22no—
166C22×C3⋊D3—42no—
167C22×C3⋊D3—82no—
168C22×C3×D3—21no—
169C22×C3×D3C2×D412yes—
170C32×Q8—24no—
171C32×Q8—22no—
172C32×Q8C2×D414yes—
173C2×C32×C4—24no—
174C2×C32×C4—22no—
175C2×C32×C4C2×D412yes—
176C2×C32×C4C2×D411yescharacteristic
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2411yescharacteristic
179C4⋊(C3⋊D3)—22no—
180C4⋊(C3⋊D3)—22no—
181C4⋊(C3⋊D3)—42no—
182C3×#67—24no—
183C3×#67—24no—
184C2×C3×Dic3—21no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C2×D412yes—
187C3×D12—28no—
188C3×D12—22no—
189C3×D12—21no—
190C3×D12C2×D412yes—
191C3×C4×D3—28no—
192C3×C4×D3—28no—
193C3×C4×D3—24no—
194C3×C4×D3—22no—
195C3×C4×D3—22no—
196C3×Dic6—28no—
197C3×Dic6—22no—
198C3×Dic6—21no—
199C3×Dic6C2×D412yes—
200#626—84no—
201C3⋊(C3⋊C8)—22no—
202C3×C3⋊C8—22no—
203C2×2−1+4—31no—
204C2×AGL(1,ℤ/8)—91no—
205C22×SD16—91no—
206#535—91no—
207#449—94no—
208#448—94no—
209#419—31no—
210#416—91no—
211#408—91no—
212C23×D3—61no—
213C23×D3—61no—
214C23×D3—121no—
215C3×#41—34no—
216C3×#41—616no—
217C3×#41—64no—
218C3×#41—68no—
219C3×#41—64no—
220C3×#41—62no—
221C3×#41—62no—
222C3×#41—62no—
223C2×C3×Q8—21no—
224C2×C3×Q8—22no—
225C2×C3×Q8—21no—
226C2×C3×Q8—22no—
227C2×C3×Q8—24no—
228C2×C3×Q8—22no—
229C2×C3×Q8—31no—
230C2×C3×Q8—31no—
231C2×C3×Q8—41no—
232C2×C3×Q8—42no—
233C2×C3×Q8—62no—
234C2×C3×Q8—64no—
235C2×C3×Q8—68no—
236C2×C3×Q8—64no—
237C2×C3×Q8D1214yescomplemented
238C2×C3×Q8#6714yescomplemented
239C2×C3×Q8C22×D312yes—
240C2×C3×Q8C22×D312yes—
241C2×C3×D4—32no—
242C2×C3×D4—31no—
243C2×C3×D4—31no—
244C2×C3×D4—62no—
245C2×C3×D4—61no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—32no—
250C22×C3×C4—41no—
251C22×C3×C4—62no—
252C22×C3×C4—62no—
253C22×C3×C4—61no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—21no—
257C2×#67—64no—
258C2×#67#6712yes—
259#239—28no—
260#239—24no—
261#239—24no—
262D3×Q8—28no—
263D3×Q8—24no—
264D3×Q8—24no—
265#235—216no—
266#235—22no—
267#235—22no—
268#235—22no—
269#235#6714yescomplemented
270C2×D12—22no—
271C2×D12—32no—
272C2×D12—32no—
273C2×D12—62no—
274C2×D12—64no—
275C2×D12—62no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—61no—
280C2×D12—61no—
281C2×D12—64no—
282C2×D12—122no—
283C2×D12—121no—
284C2×D12#6711yescharacteristic
285C2×D12C22×D311yescharacteristic
286C2×C4×D3—22no—
287C2×C4×D3—21no—
288C2×C4×D3—22no—
289C2×C4×D3C22×D312yes—
290C2×Dic6—22no—
291C2×Dic6#6711yescharacteristic
292C2×Dic6C22×D311yescharacteristic
293C3×M16—62no—
294C2×C3×C8—32no—
295C3×C4⋊C4—32no—
296C3×C22⋊C4—61no—
297C3×C42—61no—
298#217—21no—
299#215—64no—
300#215—616no—
301#215—68no—
302#215—68no—
303#213—64no—
304(C2×D3)⋊C4—64no—
305(C2×D3)⋊C4—64no—
306C4⋊Dic3C22×D312yes—
307C4×Dic3—21no—
308#208—22no—
309C2×C3⋊C8—32no—
310C2×C3⋊C8—32no—
311C2×C3⋊C8—62no—
312C2×C3⋊C8—64no—
313C2×C3⋊C8—62no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8C22×D312yes—
316D24—64no—
317#204—64no—
318C22×C32—22no—
319C22×C32#12012yes—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—42no—
322C2×C3⋊D3—44no—
323C2×C3⋊D3—84no—
324C2×C3×D3—22no—
325C2×C3×D3—22no—
326C2×C3×D3—24no—
327C2×C3×D3—42no—
328C32×C4—24no—
329C32×C4#12012yes—
330C32×C4C22×D411yescharacteristic
331C32×C4C22×D411yescharacteristic
332C3×Dic3—22no—
333C3×Dic3—22no—
334C3×Dic3—42no—
3352−1+4—64no—
3362−1+4—64no—
337C2×#41—31no—
338C2×#41—32no—
339C2×#41—31no—
340C2×#41—62no—
341C2×#41—61no—
342C22×Q8—32no—
343C22×Q8—61no—
344C22×Q8D3211yescharacteristic
345C22×D4—91no—
346AGL(1,ℤ/8)—184no—
347C2×SD16—92no—
348C2×SD16—94no—
349C2×SD16—184no—
350C2×D8—92no—
351C2×M16—31no—
352C22×C8—91no—
353#127—181no—
354#124—181no—
355#121—94no—
356#120—182no—
357#117—31no—
358#103—34no—
359#103—92no—
360#102—92no—
361C22⋊C8—94no—
362C23×C3—21no—
363C23×C3—32no—
364C23×C3—61no—
365C23×C3D3×D411yescharacteristic
366C23×C3C2×#6711yescharacteristic
367C22×D3—21no—
368C22×D3—62no—
369C22×D3—62no—
370C22×D3—122no—
371C22×D3—124no—
372C22×D3—122no—
373C22×D3—122no—
374C22×D3—242no—
375C22×D3—242no—
376C22×D3—244no—
377C22×D3C2×#6712yes—
378C3×Q8—24no—
379C3×Q8—24no—
380C3×Q8—22no—
381C3×Q8—22no—
382C3×Q8—24no—
383C3×Q8—32no—
384C3×Q8—42no—
385C3×Q8—44no—
386C3×Q8—68no—
387C3×Q8—62no—
388C3×Q8—61no—
389C3×Q8C2×D1214yes—
390C3×Q8C2×#6714yes—
391C3×D4—32no—
392C3×D4—68no—
393C3×D4—64no—
394C3×D4—64no—
395C3×D4—62no—
396C3×D4—61no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—32no—
406C2×C3×C4—42no—
407C2×C3×C4—44no—
408C2×C3×C4—68no—
409C2×C3×C4—68no—
410C2×C3×C4—61no—
411C2×C3×C4—64no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4C2×D1212yes—
416C2×C3×C4D3×D411yescharacteristic
417C2×C3×C4D3×D412yes—
418C2×C3×C4C2×#6712yes—
419C2×C3×C4C2×#6711yescharacteristic
420C2×C3×C4C2×#6712yes—
421C2×C3×C4C23×D311yescharacteristic
422C2×C3×C4C23×D311yescharacteristic
423#67—24no—
424#67—24no—
425#67—244no—
426C2×Dic3—21no—
427C2×Dic3—22no—
428C2×Dic3C2×#6712yes—
429D12—28no—
430D12—22no—
431D12—21no—
432D12—64no—
433D12—62no—
434D12—62no—
435D12—62no—
436D12—62no—
437D12—122no—
438D12—124no—
439D12—122no—
440D12—122no—
441D12—244no—
442D12C2×#6712yes—
443C4×D3—28no—
444C4×D3—28no—
445C4×D3—24no—
446C4×D3—22no—
447C4×D3—22no—
448Dic6—28no—
449Dic6—22no—
450Dic6—21no—
451Dic6C2×#6712yes—
452C3×C8—62no—
453C3⋊C8—22no—
454C3⋊C8—64no—
455C3⋊C8—62no—
456C3⋊C8—62no—
457C2×C32—22no—
458C2×C32C2×#12011yescharacteristic
459C2×C32#57712yes—
460C3⋊D3—82no—
461C3×D3—42no—
462C3×D3—42no—
463C24—181no—
464#41—34no—
465#41—616no—
466#41—64no—
467#41—68no—
468#41—64no—
469#41—62no—
470#41—62no—
471#41—62no—
472C2×Q8—21no—
473C2×Q8—22no—
474C2×Q8—31no—
475C2×Q8—31no—
476C2×Q8—62no—
477C2×Q8—64no—
478C2×Q8—68no—
479C2×Q8—64no—
480C2×Q8#62614yescomplemented
481C2×Q8C2×D3212yes—
482C2×D4—32no—
483C2×D4—31no—
484C2×D4—31no—
485C2×D4—62no—
486C2×D4—61no—
487C2×D4—92no—
488C2×D4—184no—
489C2×D4—182no—
490C2×D4—182no—
491C2×D4—181no—
492C22×C4—21no—
493C22×C4—32no—
494C22×C4—62no—
495C22×C4—62no—
496C22×C4—61no—
497C22×C4C2×D3211yescharacteristic
498SD16—184no—
499SD16—188no—
500D8—184no—
501M16—62no—
502C2×C8—32no—
503C2×C8—92no—
504C2×C8—182no—
505C4⋊C4—32no—
506C22⋊C4—61no—
507C22⋊C4—184no—
508C42—61no—
509C22×C3—24no—
510C22×C3—22no—
511C22×C3—22no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—64no—
517C22×C3—122no—
518C22×C3#88212yes—
519C22×C3#95312yes—
520C22×C3C2×D3×D411yescharacteristic
521C22×C3C22×#6711yescharacteristic
522C2×D3—24no—
523C2×D3—22no—
524C2×D3—22no—
525C2×D3—42no—
526C2×D3—124no—
527C2×D3—122no—
528C2×D3—124no—
529C2×D3—124no—
530C2×D3—122no—
531C2×D3—244no—
532C2×D3—248no—
533C2×D3—244no—
534C2×D3—244no—
535C3×C4—24no—
536C3×C4—24no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—22no—
540C3×C4—44no—
541C3×C4—62no—
542C3×C4—62no—
543C3×C4—122no—
544C3×C4#88212yes—
545C3×C4#95312yes—
546C3×C4C22×D1211yescharacteristic
547C3×C4C2×D3×D411yescharacteristic
548C3×C4C22×#6711yescharacteristic
549C3×C4C22×#6711yescharacteristic
550Dic3—22no—
551Dic3—22no—
552Dic3—42no—
553C32#301011yescharacteristic, complemented, Sylow
554C23—32no—
555C23—61no—
556C23—182no—
557C23—362no—
558C23—722no—
559C23D3×#6711yescharacteristic
560Q8—22no—
561Q8—24no—
562Q8—32no—
563Q8—68no—
564Q8—61no—
565Q8—62no—
566Q8C2×#62614yes—
567D4—32no—
568D4—68no—
569D4—64no—
570D4—64no—
571D4—61no—
572D4—62no—
573D4—182no—
574D4—182no—
575D4—362no—
576D4—724no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—32no—
580C2×C4—68no—
581C2×C4—68no—
582C2×C4—61no—
583C2×C4—62no—
584C2×C4—62no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4C2×#62612yes—
588C2×C4D3×#6712yes—
589C2×C4D3×#6711yescharacteristic
590C2×C4C22×D3211yescharacteristic
591C8—62no—
592C8—182no—
593C2×C3—24no—
594C2×C3—22no—
595C2×C3—22no—
596C2×C3—21no—
597C2×C3—22no—
598C2×C3—122no—
599C2×C3—122no—
600C2×C3C2×#88211yescharacteristic
601C2×C3#577812yes—
602C2×C3#583712yes—
603C2×C3C2×#95311yescharacteristic
604D3—42no—
605D3—42no—
606D3—244no—
607D3—242no—
608D3—242no—
609C22—22no—
610C22—62no—
611C22—62no—
612C22—64no—
613C22—122no—
614C22—362no—
615C22—364no—
616C22—724no—
617C22#6397712yes—
618C22C2×D3×#6711yescharacteristic
619C4—24no—
620C4—62no—
621C4—62no—
622C4—122no—
623C4#6397712yes—
624C4C22×#62611yescharacteristic
625C4C2×D3×#6711yescharacteristic
626C3—21no—
627C3#7896011yescharacteristic, complemented
628C3#8411311yescharacteristic, complemented
629C2—22no—
630C2—122no—
631C2—122no—
632C2—722no—
633C2#1059531912yes—
634C2C2×#6397711yescharacteristic
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×#3755C2semidirect
3. #10595045C2semidirect
4. C2×#63825C2semidirect
5. C3×#5225C2semidirect
6. #10591588C2semidirect
7. #10591584C2semidirect
8. #10591083C2semidirect
9. #10591071C2semidirect
17. C2×C3×#239C22semidirect
19. C2×C3×D3×Q8C22semidirect
35. C3×#835C22semidirect
36. #63565C22semidirect
37. #63562C22semidirect
38. (C2×D3)⋊(C3⋊C8)C22semidirect
40. C2×#1007D3semidirect
53. #5225D3semidirect
61. C2×C32×Q8D4semidirect
81. C3×#235D4semidirect
120. C2×#239C2×D3semidirect
122. C2×D3×Q8C2×D3semidirect
158. #835C2×D3semidirect
237. C2×C3×Q8D12semidirect
238. C2×C3×Q8#67semidirect
269. #235#67semidirect
480. C2×Q8#626semidirect
553. C32#3010semidirect
627. C3#78960semidirect
628. 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×#37552
#105950452
C2×#638252
C3×#52252
#105915882
#105915842
#105910832
#105910712
#841133
#789603