Finite Group Databasebeta

← #11864443

Subgroups — #11864443

Order 1152.

1631 conjugacy classes of subgroups.

The subgroup lattice has 648 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1010C211yesmaximal, characteristic, complemented
2#10596301C211yesmaximal, characteristic, complemented
3C22×#3717C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5234C211yesmaximal, characteristic, complemented
6#10591174C214yesmaximal, complemented
7#10591163C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591084C211yesmaximal, characteristic, complemented
10#84113—31nomaximal
11#78678—31nomaximal
12C2×C32×#41C2211yescharacteristic
13C22×C4⋊(C3⋊D3)C2211yescharacteristic
14C3×#1010—24no—
15C3×#1010—24no—
16C2×C3×D3×Q8—21no—
17C2×C3×#237—21no—
18C2×C3×#237—22no—
19C2×C3×#235C2211yescharacteristic
20C2×C3×#235C2212yescomplemented
21C22×C3×Dic6C2211yescharacteristic
22C22×C3×Dic6C2212yescomplemented
23#64156—21no—
24#64149—21no—
25#64146—22no—
26#64139C2214yes—
27#64135C2211yescharacteristic
28C2×C3×#208C2211yescharacteristic
29C22×C3×C3⋊C8C2211yescharacteristic
30C2×#3717—24no—
31C2×#3717C2214yes—
32C2×#3717C2212yes—
33#63825—24no—
34C2×#3714C2212yes—
35C3×#830C2214yescomplemented
36#63566C2212yescomplemented
37#63566C2214yescomplemented
38#63563C2212yescomplemented
39C2×C3×2−1+4—31no—
40C2×#1010D311yescharacteristic, complemented
41#5830—31no—
42#5830—31no—
43#5830—61no—
44C2×#949—31no—
45C22×#215—31no—
46C2×#908—31no—
47C22×#204—31no—
48C3×#408—31no—
49#5238—34no—
50#5234D311yescharacteristic, complemented
51#5233—31no—
52#5227—34no—
53#5225—31no—
54#5120—31no—
55#5113—31no—
56#4738—34no—
57#4734—34no—
58C23×C3⋊D3—21no—
59C32×#41—22no—
60C32×#41—22no—
61C2×C32×Q8D411yescharacteristic
62C2×C32×D4D412yes—
63C2×C32×D4D411yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×#638—24no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C4⋊(C3⋊D3)—21no—
70C2×C4⋊(C3⋊D3)C2312yes—
71C2×C3×#67—21no—
72C2×C3×#67—22no—
73C22×C3×Dic3—21no—
74C22×C3×Dic3—22no—
75C3×D3×Q8—28no—
76C3×#237—216no—
77C3×#237—28no—
78C3×#235—22no—
79C3×#235—24no—
80C3×#235—24no—
81C3×#235D414yescomplemented
82C2×C3×D12C2311yescharacteristic
83C2×C3×C4×D3—21no—
84C2×C3×C4×D3—22no—
85C2×C3×Dic6—21no—
86C2×C3×Dic6—22no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6—24no—
89C2×C3×Dic6—24no—
90C2×C3×Dic6D414yescomplemented
91C2×C3×Dic6C2312yes—
92C2×C3×Dic6C2311yescharacteristic
93#3757—21no—
94#3752—24no—
95C4⋊(C3⋊Dic3)C2312yes—
96C4×C3⋊Dic3—21no—
97C3×#208—22no—
98C2×C3×C3⋊C8—22no—
99C2×C3×C3⋊C8C2312yes—
100C2×C3×C3⋊C8C2312yes—
101#3717—24no—
102#3717—28no—
103#3714—24no—
104#3010—91noSylow
105C3×2−1+4—64no—
106C3×2−1+4—64no—
107C2×C3×#41—21no—
108C2×C3×#41—31no—
109C2×C3×#41—32no—
110C2×C3×#41—62no—
111C2×C3×#41—61no—
112C2×C3×#41C2×D311yescharacteristic
113C2×C3×#41C2×D311yescharacteristic
114C22×C3×Q8—31no—
115C22×C3×Q8—32no—
116C22×C3×Q8—61no—
117#1010—24no—
118#1010—24no—
119C2×D3×Q8—21no—
120C2×#237—21no—
121C2×#237—22no—
122C2×#235C2×D311yescharacteristic
123C2×#235C2×D312yescomplemented
124C22×D12—31no—
125C22×D12—31no—
126C22×D12—61no—
127C22×Dic6C2×D311yescharacteristic
128C22×Dic6C2×D312yescomplemented
129C2×C3×M16—31no—
130C22×C3×C8—31no—
131#949—64no—
132#947—62no—
133#947—61no—
134#947—61no—
135C2×#215—32no—
136C2×#215—34no—
137C2×#215—64no—
138#940—62no—
139#940—61no—
140#940—61no—
141#937—64no—
142#937—62no—
143#937—62no—
144C2×#213—32no—
145#930—34no—
146#930—34no—
147#930—64no—
148#926—31no—
149#926—31no—
150#926—61no—
151C2×#208C2×D311yescharacteristic
152C22×C3⋊C8C2×D311yescharacteristic
153#908—64no—
154C2×D24—32no—
155C2×#204—34no—
156C2×#204—32no—
157C2×#204—64no—
158C3×C22⋊C8—34no—
159#835—34no—
160#835—32no—
161#832—32no—
162#830C2×D314yescomplemented
163#821—32no—
164#816—34no—
165#816—32no—
166C23×C32C2×D412yes—
167C23×C32C2×D411yescharacteristic
168C22×C3⋊D3—22no—
169C22×C3⋊D3—42no—
170C22×C3⋊D3—82no—
171C22×C3×D3—21no—
172C32×Q8—22no—
173C32×D4—24no—
174C32×D4—22no—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4C2×D412yes—
178C2×C32×C4C2×D411yescharacteristic
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182#638—84no—
183C2×C3⋊Dic3—22no—
184C4⋊(C3⋊D3)—22no—
185C4⋊(C3⋊D3)—22no—
186C4⋊(C3⋊D3)—42no—
187C3×#67—28no—
188C3×#67—24no—
189C2×C3×Dic3—28no—
190C2×C3×Dic3—24no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3—21no—
193C3×D12—21no—
194C3×D12C2×D412yes—
195C3×C4×D3—28no—
196C3×C4×D3—24no—
197C3×Dic6—28no—
198C3×Dic6—24no—
199C3×Dic6—22no—
200C3×Dic6—21no—
201C3×Dic6C2×D412yes—
202C3×Dic6C2×D414yes—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C2×2−1+4—31no—
206C2×AGL(1,ℤ/8)—91no—
207C22×SD16—91no—
208#535—91no—
209#449—94no—
210#448—94no—
211#419—91no—
212#416—91no—
213#408—31no—
214C23×D3—62no—
215C23×D3—61no—
216C23×D3—61no—
217C3×#41—22no—
218C3×#41—22no—
219C3×#41—22no—
220C3×#41—22no—
221C3×#41—34no—
222C3×#41—42no—
223C3×#41—42no—
224C3×#41—64no—
225C3×#41—64no—
226C3×#41—616no—
227C3×#41—68no—
228C3×#41—62no—
229C2×C3×Q8—21no—
230C2×C3×Q8—34no—
231C2×C3×Q8—32no—
232C2×C3×Q8—31no—
233C2×C3×Q8—64no—
234C2×C3×Q8—64no—
235C2×C3×Q8—68no—
236C2×C3×Q8—62no—
237C2×C3×Q8—61no—
238C2×C3×Q8—62no—
239C2×C3×Q8D1211yescharacteristic
240C2×C3×Q8#6711yescharacteristic
241C2×C3×D4—22no—
242C2×C3×D4—21no—
243C2×C3×D4—31no—
244C2×C3×D4—62no—
245C2×C3×D4—61no—
246C2×C3×D4D1212yes—
247C2×C3×D4D1211yescharacteristic
248C2×C3×D4#6712yes—
249C2×C3×D4#6711yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4—22no—
252C22×C3×C4—62no—
253C22×C3×C4—61no—
254C22×C3×C4—62no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D312yes—
257C22×C3×C4C22×D312yes—
258C22×C3×C4C22×D311yescharacteristic
259C22×C3×C4C22×D311yescharacteristic
260C2×#67—21no—
261C2×#67—22no—
262C2×#67—68no—
263C2×#67—64no—
264C2×#67—64no—
265C22×Dic3—21no—
266C22×Dic3—22no—
267D3×Q8—28no—
268#237—216no—
269#237—28no—
270#235—22no—
271#235—24no—
272#235—24no—
273#235#6714yescomplemented
274C2×D12—32no—
275C2×D12—32no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—62no—
279C2×D12—62no—
280C2×D12—62no—
281C2×D12—62no—
282C2×D12—61no—
283C2×D12—61no—
284C2×D12—122no—
285C2×D12—122no—
286C2×D12C22×D311yescharacteristic
287C2×C4×D3—21no—
288C2×C4×D3—22no—
289C2×Dic6—21no—
290C2×Dic6—22no—
291C2×Dic6—22no—
292C2×Dic6—24no—
293C2×Dic6—24no—
294C2×Dic6#6714yescomplemented
295C2×Dic6C22×D312yes—
296C2×Dic6C22×D311yescharacteristic
297C3×M16—62no—
298C2×C3×C8—32no—
299C2×C3×C8—32no—
300C2×C3×C8—62no—
301#217—62no—
302#217—61no—
303#217—61no—
304#215—68no—
305#215—64no—
306#213—64no—
307(C2×D3)⋊C4—68no—
308(C2×D3)⋊C4—64no—
309(C2×D3)⋊C4—64no—
310C4⋊Dic3—32no—
311C4⋊Dic3—32no—
312C4⋊Dic3—62no—
313C4×Dic3—62no—
314C4×Dic3—61no—
315C4×Dic3—61no—
316#208—22no—
317C2×C3⋊C8—22no—
318C2×C3⋊C8C22×D312yes—
319C2×C3⋊C8C22×D312yes—
320D24—64no—
321#204—68no—
322#204—64no—
323C22×C32—22no—
324C22×C32—22no—
325C22×C32—24no—
326C22×C32#12012yes—
327C22×C32C22×D411yescharacteristic
328C2×C3⋊D3—42no—
329C2×C3⋊D3—44no—
330C2×C3⋊D3—84no—
331C2×C3×D3—22no—
332C2×C3×D3—42no—
333C32×C4—22no—
334C32×C4#12012yes—
335C32×C4C22×D411yescharacteristic
336C32×C4C22×D411yescharacteristic
337C3⋊Dic3—42no—
338C3×Dic3—22no—
339C3×Dic3—24no—
3402−1+4—64no—
3412−1+4—64no—
342C2×#41—31no—
343C2×#41—32no—
344C2×#41—62no—
345C2×#41—61no—
346C2×#41D3211yescharacteristic
347C22×Q8—31no—
348C22×Q8—32no—
349C22×Q8—61no—
350C22×D4—91no—
351AGL(1,ℤ/8)—184no—
352C2×SD16—94no—
353C2×SD16—92no—
354C2×SD16—184no—
355C2×D8—92no—
356C2×M16—31no—
357C22×C8—31no—
358#127—181no—
359#124—181no—
360#121—94no—
361#120—182no—
362#117—91no—
363#103—92no—
364#103—94no—
365#102—92no—
366C22⋊C8—34no—
367C23×C3—21no—
368C23×C3—22no—
369C23×C3—61no—
370C23×C3C2×D1212yes—
371C23×C3C2×D1211yescharacteristic
372C23×C3C2×#6712yes—
373C23×C3C2×#6711yescharacteristic
374C22×D3—21no—
375C22×D3—64no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—124no—
379C22×D3—122no—
380C22×D3—122no—
381C22×D3—242no—
382C22×D3—242no—
383C22×D3—244no—
384C3×Q8—22no—
385C3×Q8—22no—
386C3×Q8—34no—
387C3×Q8—32no—
388C3×Q8—42no—
389C3×Q8—68no—
390C3×Q8—64no—
391C3×Q8—62no—
392C3×Q8—61no—
393C3×D4—24no—
394C3×D4—24no—
395C3×D4—22no—
396C3×D4—22no—
397C3×D4—32no—
398C3×D4—42no—
399C3×D4—44no—
400C3×D4—68no—
401C3×D4—64no—
402C3×D4—61no—
403C2×C3×C4—22no—
404C2×C3×C4—22no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—22no—
410C2×C3×C4—22no—
411C2×C3×C4—22no—
412C2×C3×C4—42no—
413C2×C3×C4—42no—
414C2×C3×C4—68no—
415C2×C3×C4—68no—
416C2×C3×C4—64no—
417C2×C3×C4—62no—
418C2×C3×C4—61no—
419C2×C3×C4—64no—
420C2×C3×C4C2×D1212yes—
421C2×C3×C4C2×D1211yescharacteristic
422C2×C3×C4D3×D412yes—
423C2×C3×C4D3×D412yes—
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C2×#6711yescharacteristic
426C2×C3×C4C2×#6712yes—
427C2×C3×C4C2×#6712yes—
428C2×C3×C4C23×D311yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430#67—28no—
431#67—24no—
432#67—244no—
433#67—244no—
434#67—248no—
435C2×Dic3—28no—
436C2×Dic3—24no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—64no—
440C2×Dic3—62no—
441C2×Dic3—62no—
442D12—21no—
443D12—62no—
444D12—62no—
445D12—62no—
446D12—62no—
447D12—122no—
448D12—122no—
449D12—124no—
450D12—122no—
451D12—122no—
452D12C2×#6712yes—
453C4×D3—28no—
454C4×D3—24no—
455Dic6—28no—
456Dic6—24no—
457Dic6—22no—
458Dic6—21no—
459Dic6C2×#6712yes—
460Dic6C2×#6714yes—
461C3×C8—62no—
462C3×C8—62no—
463C3⋊C8—22no—
464C3⋊C8—22no—
465C2×C32—22no—
466C2×C32—42no—
467C2×C32C2×#12011yescharacteristic
468C2×C32#57712yes—
469C3⋊D3—82no—
470C3×D3—42no—
471C24—181no—
472#41—22no—
473#41—22no—
474#41—34no—
475#41—64no—
476#41—64no—
477#41—616no—
478#41—68no—
479#41—62no—
480C2×Q8—32no—
481C2×Q8—31no—
482C2×Q8—34no—
483C2×Q8—64no—
484C2×Q8—64no—
485C2×Q8—68no—
486C2×Q8—62no—
487C2×Q8—61no—
488C2×Q8—62no—
489C2×Q8#62611yescharacteristic
490C2×D4—31no—
491C2×D4—62no—
492C2×D4—61no—
493C2×D4—92no—
494C2×D4—184no—
495C2×D4—181no—
496C2×D4—182no—
497C2×D4—182no—
498C2×D4#62612yes—
499C2×D4#62611yescharacteristic
500C22×C4—62no—
501C22×C4—61no—
502C22×C4—62no—
503C22×C4—61no—
504C22×C4C2×D3212yes—
505C22×C4C2×D3211yescharacteristic
506SD16—188no—
507SD16—184no—
508D8—184no—
509M16—62no—
510C2×C8—32no—
511C2×C8—32no—
512C2×C8—62no—
513C4⋊C4—92no—
514C22⋊C4—181no—
515C22⋊C4—184no—
516C42—181no—
517C22×C3—22no—
518C22×C3—22no—
519C22×C3—22no—
520C22×C3—24no—
521C22×C3—24no—
522C22×C3—22no—
523C22×C3—21no—
524C22×C3—22no—
525C22×C3—42no—
526C22×C3—44no—
527C22×C3—42no—
528C22×C3—62no—
529C22×C3—122no—
530C22×C3#88212yes—
531C22×C3#95312yes—
532C22×C3C22×D1211yescharacteristic
533C22×C3C22×#6711yescharacteristic
534C2×D3—22no—
535C2×D3—42no—
536C2×D3—124no—
537C2×D3—128no—
538C2×D3—122no—
539C2×D3—124no—
540C2×D3—124no—
541C2×D3—122no—
542C2×D3—244no—
543C2×D3—244no—
544C2×D3—248no—
545C3×C4—22no—
546C3×C4—22no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—22no—
550C3×C4—42no—
551C3×C4—64no—
552C3×C4—62no—
553C3×C4#88212yes—
554C3×C4#95312yes—
555C3×C4C2×D3×D411yescharacteristic
556C3×C4C2×D3×D411yescharacteristic
557C3×C4C22×#6711yescharacteristic
558C3×C4C22×#6711yescharacteristic
559Dic3—22no—
560Dic3—24no—
561Dic3—124no—
562Dic3—122no—
563Dic3—122no—
564C32#301011yescharacteristic, complemented, Sylow
565C23—61no—
566C23—182no—
567C23—362no—
568C23—722no—
569C23C2×#62612yes—
570C23C2×#62611yescharacteristic
571Q8—22no—
572Q8—34no—
573Q8—32no—
574Q8—68no—
575Q8—62no—
576Q8—61no—
577Q8—64no—
578D4—24no—
579D4—22no—
580D4—32no—
581D4—68no—
582D4—64no—
583D4—61no—
584D4—182no—
585D4—182no—
586D4—362no—
587D4—724no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—68no—
591C2×C4—68no—
592C2×C4—62no—
593C2×C4—61no—
594C2×C4—64no—
595C2×C4—64no—
596C2×C4—182no—
597C2×C4C2×#62612yes—
598C2×C4C2×#62611yescharacteristic
599C2×C4D3×#6712yes—
600C2×C4D3×#6712yes—
601C2×C4C22×D3211yescharacteristic
602C8—62no—
603C8—62no—
604C2×C3—22no—
605C2×C3—22no—
606C2×C3—22no—
607C2×C3—21no—
608C2×C3—42no—
609C2×C3—42no—
610C2×C3—42no—
611C2×C3—82no—
612C2×C3—122no—
613C2×C3C2×#88211yescharacteristic
614C2×C3#575112yes—
615C2×C3#583712yes—
616C2×C3C2×#95311yescharacteristic
617D3—42no—
618D3—244no—
619D3—242no—
620D3—242no—
621C22—22no—
622C22—24no—
623C22—22no—
624C22—62no—
625C22—122no—
626C22—364no—
627C22—362no—
628C22—724no—
629C22#6397712yes—
630C22C22×#62611yescharacteristic
631C4—22no—
632C4—64no—
633C4—62no—
634C4—362no—
635C4#6397712yes—
636C4C2×D3×#6711yescharacteristic
637C4C2×D3×#6711yescharacteristic
638C3—21no—
639C3#7867811yescharacteristic, complemented
640C3#8411311yescharacteristic, complemented
641C2—22no—
642C2—42no—
643C2—122no—
644C2—722no—
645C2#1059544812yes—
646C2C2×#6397711yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×#41C22
socleC22×C32C22×D4
hypercenterC2×#41D32
hypocenterC32#3010
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. #10596301C2semidirect
3. C22×#3717C2semidirect
4. C2×#63825C2semidirect
5. C3×#5234C2semidirect
6. #10591174C2semidirect
7. #10591163C2semidirect
8. #10591100C2semidirect
9. #10591084C2semidirect
20. C2×C3×#235C22semidirect
22. C22×C3×Dic6C22semidirect
35. C3×#830C22semidirect
36. #63566C22semidirect
37. #63566C22semidirect
38. #63563C22semidirect
40. C2×#1010D3semidirect
50. #5234D3semidirect
81. C3×#235D4semidirect
90. C2×C3×Dic6D4semidirect
123. C2×#235C2×D3semidirect
128. C22×Dic6C2×D3semidirect
162. #830C2×D3semidirect
273. #235#67semidirect
294. C2×Dic6#67semidirect
564. C32#3010semidirect
639. C3#78678semidirect
640. C3#84113semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10102
#105963012
C22×#37172
C2×#638252
C3×#52342
#105911742
#105911632
#105911002
#105910842
#841133
#786783