Finite Group Databasebeta

← #11878861

Subgroups — #11878861

Order 1152.

1070 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#940C211yesmaximal, characteristic
2#10594808C211yesmaximal, characteristic, complemented
3#10592917C211yesmaximal, characteristic, complemented
4C3×#5218C211yesmaximal, characteristic, complemented
5#10591490C212yesmaximal, complemented
6#10591487C212yesmaximal, complemented
7#10591439C212yesmaximal, complemented
8#10591438C212yesmaximal, complemented
9#10591172C211yesmaximal, characteristic, complemented
10#10591169C211yesmaximal, characteristic, complemented
11#10591053C211yesmaximal, characteristic, complemented
12#83169—31nomaximal
13#80138—31nomaximal
14C22×C32×D4C2211yescharacteristic
15C22×C3×#67—21no—
16C22×C3×#67—21no—
17C22×C3×D12C2211yescharacteristic
18C2×#3754C2212yescomplemented
19#64133C2211yescharacteristic
20C3×#940—21no—
21C3×#940—21no—
22C3×#940C2212yes—
23C3×#940C2212yes—
24C2×C3×#214C2212yescomplemented
25C3×#924C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27#63964—21no—
28#63955—21no—
29#63918C2211yescharacteristic, complemented
30#63867—21no—
31#63866C2211yescharacteristic, complemented
32#63844C2211yescharacteristic, complemented
33Dic3×Dic6C2211yescharacteristic, complemented
34#63837—21no—
35C2×#3716C2212yescomplemented
36C2×#3715C2212yescomplemented
37#63659C2212yescomplemented
38#63657C2211yescharacteristic
39C3×#832C2212yescomplemented
40C3×#830C2211yescharacteristic
41Dic3⋊(C3⋊C8)C2212yescomplemented
42#63563C2212yescomplemented
43#63562C2212yescomplemented
44Dic3×C3⋊C8C2212yescomplemented
45C2×C3×#127—31no—
46C2×#940D311yescharacteristic
47#5622—31no—
48#5470—31no—
49C3×#450—31no—
50#5218—31no—
51#5218—31no—
52#5218—31no—
53#5218—31no—
54#5218—61no—
55#5218D311yescharacteristic, complemented
56#5175—32no—
57#5163—32no—
58#5076—32no—
59#5075—32no—
60#5075—32no—
61#5070—32no—
62#5046—31no—
63#4925—31no—
64#4762—32no—
65#4760—32no—
66#4731—31no—
67#4718—31no—
68C24×C32—21no—
69C23×C3×D3—21no—
70C2×C32×D4—21no—
71C2×C32×D4—42no—
72C2×C32×D4C2312yes—
73C22×C32×C4C2311yescharacteristic
74C2×#634C2311yescharacteristic
75C2×C3×#67—22no—
76C2×C3×#67—22no—
77C2×C3×#67—22no—
78C2×C3×#67—22no—
79C2×C3×#67—44no—
80C2×C3×#67—44no—
81C22×C3×Dic3D411yescharacteristic
82C22×C3×Dic3D411yescharacteristic
83C2×C3×D12—21no—
84C2×C3×D12—42no—
85C2×C3×D12C2312yes—
86C2×C3×Dic6C2311yescharacteristic
87C2×#627—21no—
88#3757—21no—
89#3754—42no—
90C4⋊(C3⋊Dic3)C2311yescharacteristic
91#3750—21no—
92C2×C3⋊(C3⋊C8)C2312yes—
93C3×#217—21no—
94C3×#214—42no—
95C3×C4⋊Dic3C2311yescharacteristic
96C3×Dic3⋊C4—21no—
97C3×C4×Dic3D411yescharacteristic
98C3×C4×Dic3D411yescharacteristic
99C3×C4×Dic3C2311yescharacteristic
100C3×C4×Dic3C2311yescharacteristic
101C2×C3×C3⋊C8C2312yes—
102#3724—21no—
103Dic3⋊Dic3—21no—
104Dic3⋊Dic3—21no—
105Dic3⋊Dic3—21no—
106Dic3⋊Dic3—21no—
107Dic32—21no—
108Dic32—21no—
109#3716—42no—
110#3715—42no—
111#3208—91noSylow
112C22×C3×D4—21no—
113C22×C3×D4—31no—
114C22×C3×D4—61no—
115C22×C3×D4—61no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C2×D311yescharacteristic
118C22×#67—21no—
119C22×#67—21no—
120C22×D12C2×D311yescharacteristic
121C2×C3×SD16—32no—
122C3×#127—32no—
123C3×#127—32no—
124C3×#127—61no—
125C3×#127—61no—
126C3×C22⋊Q8—31no—
127C2×C3×C42—31no—
128Q8×Dic3—31no—
129#944—31no—
130C2×#215—32no—
131#940—21no—
132#940—21no—
133#940C2×D312yes—
134#940C2×D312yes—
135C2×#214—32no—
136C2×#214—32no—
137C2×#214—32no—
138C2×#214—32no—
139C2×#214—62no—
140C2×#214C2×D312yescomplemented
141#926—61no—
142#924—31no—
143#924—31no—
144#924—61no—
145#924—61no—
146#924C2×D311yescharacteristic
147C2×C4×Dic3C2×D311yescharacteristic
148C2×#204—32no—
149#889—61no—
150#888—31no—
151#887—31no—
152#887—61no—
153#878—61no—
154#877—61no—
155#870—61no—
156#869—31no—
157#869—31no—
158C4×Dic6—31no—
159C4×Dic6—31no—
160C4×Dic6—61no—
161C3×#102—32no—
162C3×C22⋊C8—31no—
163#832—32no—
164#832—32no—
165#832—32no—
166#832—32no—
167#832—62no—
168#832C2×D312yescomplemented
169#830—31no—
170#830—31no—
171#830—61no—
172#830C2×D311yescharacteristic
173#821—32no—
174Dic3⋊C8—32no—
175C8×Dic3—32no—
176#809—32no—
177C4⋊(C3⋊C8)—32no—
178C4×C3⋊C8—32no—
179C23×C32—22no—
180C23×C32—42no—
181C23×C32—42no—
182C23×C32—42no—
183C23×C32C2×D411yescharacteristic
184C22×C3×D3—22no—
185C22×C3×D3—42no—
186C22×C3×D3—42no—
187C22×C3×D3—42no—
188C32×D4—22no—
189C32×D4—22no—
190C32×D4—42no—
191C2×C32×C4—22no—
192C2×C32×C4C2×D411yescharacteristic
193C2×C32×C4C2411yescharacteristic
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196#634—22no—
197C3×#67—44no—
198C3×#67—44no—
199C3×#67—44no—
200C3×#67—44no—
201C2×C3×Dic3—22no—
202C2×C3×Dic3—21no—
203C2×C3×Dic3—21no—
204C2×C3×Dic3SD1614yescomplemented
205C2×C3×Dic3C2×D411yescharacteristic
206C2×C3×Dic3C2×D411yescharacteristic
207C2×C3×Dic3C2×D411yescharacteristic
208C2×C3×Dic3C2×D411yescharacteristic
209C3×D12—22no—
210C3×D12—22no—
211C3×D12—42no—
212C3×Dic6—22no—
213#627—42no—
214C3⋊(C3⋊C8)—22no—
215C3×C3⋊C8—22no—
216#533—91no—
217C2×#127—31no—
218#492—92no—
219#486—92no—
220#460—92no—
221#460—92no—
222#450—31no—
223#450—91no—
224#450—91no—
225#450—91no—
226#431—91no—
227C24×C3—21no—
228C24×C3—21no—
229C24×C3—41no—
230C24×C3—61no—
231C23×D3—21no—
232C2×C3×Q8—31no—
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—22no—
236C2×C3×D4—32no—
237C2×C3×D4—41no—
238C2×C3×D4—42no—
239C2×C3×D4—42no—
240C2×C3×D4—44no—
241C2×C3×D4—62no—
242C2×C3×D4—62no—
243C2×C3×D4—62no—
244C2×C3×D4—62no—
245C2×C3×D4—61no—
246C2×C3×D4—122no—
247C2×C3×D4—124no—
248C2×C3×D4—124no—
249C2×C3×D4C22×D312yes—
250C2×C3×D4C22×D312yes—
251C22×C3×C4—21no—
252C22×C3×C4—31no—
253C22×C3×C4—31no—
254C22×C3×C4C22×D311yescharacteristic
255C22×C3×C4C22×D311yescharacteristic
256C2×#67—22no—
257C2×#67—22no—
258C2×#67—22no—
259C2×#67—22no—
260C2×#67—44no—
261C2×#67—44no—
262C22×Dic3#6711yescharacteristic
263C22×Dic3#6711yescharacteristic
264C2×D12—21no—
265C2×D12—42no—
266C2×D12C22×D312yes—
267C2×Dic6—31no—
268C2×Dic6—31no—
269C2×Dic6—61no—
270C2×Dic6—61no—
271C2×Dic6—61no—
272C2×Dic6C22×D311yescharacteristic
273C3×SD16—122no—
274C2×C3×C8—32no—
275C3×C4⋊C4—31no—
276C3×C4⋊C4—61no—
277C3×C22⋊C4—61no—
278C3×C42—31no—
279C3×C42—31no—
280C3×C42—31no—
281C3×C42—31no—
282#217—21no—
283#217—61no—
284#217—61no—
285#217—121no—
286#215—122no—
287#214—42no—
288#214—122no—
289#214—122no—
290#214—122no—
291#214—122no—
292#214—124no—
293C4⋊Dic3—31no—
294C4⋊Dic3—31no—
295C4⋊Dic3—61no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3—61no—
300C4⋊Dic3C22×D311yescharacteristic
301Dic3⋊C4—21no—
302Dic3⋊C4—61no—
303Dic3⋊C4—61no—
304Dic3⋊C4—61no—
305Dic3⋊C4—61no—
306Dic3⋊C4—61no—
307Dic3⋊C4—61no—
308Dic3⋊C4—61no—
309Dic3⋊C4—61no—
310Dic3⋊C4—121no—
311C4×Dic3—61no—
312C4×Dic3—61no—
313C4×Dic3—61no—
314C4×Dic3—61no—
315C4×Dic3#6711yescharacteristic
316C4×Dic3#6711yescharacteristic
317C4×Dic3C22×D311yescharacteristic
318C4×Dic3C22×D311yescharacteristic
319C2×C3⋊C8—32no—
320C2×C3⋊C8—32no—
321C2×C3⋊C8—62no—
322C2×C3⋊C8C22×D312yes—
323#204—122no—
324C22×C32—21no—
325C22×C32—21no—
326C22×C32—42no—
327C22×C32—42no—
328C22×C32—42no—
329C22×C32—84no—
330C22×C32C2×SD1612yes—
331C22×C32C22×D411yescharacteristic
332C2×C3×D3—42no—
333C2×C3×D3—42no—
334C2×C3×D3—42no—
335C2×C3×D3—84no—
336C32×C4—21no—
337C32×C4H(5,𝔽2)12yes—
338C3⋊Dic3—41no—
339C3⋊Dic3—41no—
340C3×Dic3—21no—
341C3×Dic3—41no—
342C3×Dic3—41no—
343C3×Dic3C2×SD1612yes—
344C3×Dic3C2×SD1612yes—
345C3×Dic3AGL(1,ℤ/8)12yes—
346C22×D4—31no—
347C22×D4—61no—
348C22×D4—61no—
349C22×D4D3211yescharacteristic
350C2×SD16—32no—
351C2×SD16—92no—
352C2×SD16—92no—
353C2×SD16—92no—
354C4⋊Q8—91no—
355C4⋊Q8—91no—
356#127—32no—
357#127—32no—
358#127—61no—
359#127—61no—
360#125—181no—
361C22⋊Q8—31no—
362C22⋊Q8—91no—
363C22⋊Q8—181no—
364C4×Q8—91no—
365C4×Q8—91no—
366C4×Q8—181no—
367#117—181no—
368C2×C42—31no—
369C4⋊C8—92no—
370#102—32no—
371#102—92no—
372#102—92no—
373#102—92no—
374C22⋊C8—31no—
375C22⋊C8—91no—
376C4×C8—92no—
377C23×C3—22no—
378C23×C3—22no—
379C23×C3—21no—
380C23×C3—42no—
381C23×C3—42no—
382C23×C3—42no—
383C23×C3—42no—
384C23×C3—42no—
385C23×C3—44no—
386C23×C3—42no—
387C23×C3—42no—
388C23×C3—62no—
389C23×C3—82no—
390C23×C3—82no—
391C23×C3—122no—
392C23×C3—122no—
393C23×C3—122no—
394C23×C3D3×D411yescharacteristic
395C23×C3C2×#6711yescharacteristic
396C22×D3—22no—
397C22×D3—42no—
398C22×D3—42no—
399C22×D3—42no—
400C3×Q8—62no—
401C3×D4—24no—
402C3×D4—22no—
403C3×D4—22no—
404C3×D4—22no—
405C3×D4—22no—
406C3×D4—42no—
407C3×D4—42no—
408C3×D4—42no—
409C3×D4—44no—
410C3×D4—62no—
411C3×D4—62no—
412C3×D4—122no—
413C3×D4—124no—
414C3×D4—124no—
415C3×D4—124no—
416C3×D4—124no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—34no—
422C2×C3×C4—31no—
423C2×C3×C4—31no—
424C2×C3×C4—31no—
425C2×C3×C4—31no—
426C2×C3×C4—42no—
427C2×C3×C4—62no—
428C2×C3×C4—61no—
429C2×C3×C4—61no—
430C2×C3×C4D3×D411yescharacteristic
431C2×C3×C4C2×#6711yescharacteristic
432C2×C3×C4C23×D311yescharacteristic
433C2×C3×C4C23×D311yescharacteristic
434#67—44no—
435#67—44no—
436#67—44no—
437#67—44no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—21no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—61no—
444C2×Dic3—61no—
445C2×Dic3—121no—
446C2×Dic3—121no—
447C2×Dic3#21414yescomplemented
448C2×Dic3C2×#6711yescharacteristic
449C2×Dic3C2×#6711yescharacteristic
450C2×Dic3C2×#6711yescharacteristic
451C2×Dic3C2×#6711yescharacteristic
452D12—22no—
453D12—22no—
454D12—42no—
455Dic6—22no—
456Dic6—62no—
457Dic6—62no—
458Dic6—122no—
459Dic6—122no—
460Dic6—122no—
461C3×C8—62no—
462C3⋊C8—22no—
463C3⋊C8—62no—
464C3⋊C8—62no—
465C3⋊C8—122no—
466C2×C32—22no—
467C2×C32—82no—
468C2×C32#53511yescharacteristic
469C2×C32C22×SD1611yescharacteristic
470C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
471C3×D3—82no—
472C24—21no—
473C24—61no—
474C2×Q8—31no—
475C2×Q8—91no—
476C2×Q8—181no—
477C2×D4—21no—
478C2×D4—32no—
479C2×D4—42no—
480C2×D4—62no—
481C2×D4—62no—
482C2×D4—62no—
483C2×D4—62no—
484C2×D4—61no—
485C2×D4—122no—
486C2×D4—124no—
487C2×D4—124no—
488C2×D4C2×D3212yes—
489C22×C4—31no—
490C22×C4—31no—
491C22×C4C2×D3211yescharacteristic
492SD16—122no—
493SD16—362no—
494SD16—362no—
495SD16—362no—
496C2×C8—32no—
497C2×C8—92no—
498C4⋊C4—31no—
499C4⋊C4—61no—
500C4⋊C4—91no—
501C4⋊C4—181no—
502C4⋊C4—181no—
503C4⋊C4—181no—
504C4⋊C4—181no—
505C4⋊C4—181no—
506C4⋊C4—181no—
507C22⋊C4—61no—
508C22⋊C4—181no—
509C42—31no—
510C42—31no—
511C42—31no—
512C42—31no—
513C42—181no—
514C42—181no—
515C22×C3—21no—
516C22×C3—21no—
517C22×C3—21no—
518C22×C3—21no—
519C22×C3—21no—
520C22×C3—22no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—44no—
524C22×C3—42no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—42no—
530C22×C3—82no—
531C22×C3—82no—
532C22×C3—84no—
533C22×C3—84no—
534C22×C3—88no—
535C22×C3—122no—
536C22×C3—122no—
537C22×C3—122no—
538C22×C3—244no—
539C22×C3D3×SD1612yes—
540C22×C3C2×#21412yes—
541C22×C3C2×D3×D411yescharacteristic
542C22×C3C22×#6711yescharacteristic
543C2×D3—42no—
544C2×D3—42no—
545C2×D3—42no—
546C2×D3—84no—
547C3×C4—21no—
548C3×C4—21no—
549C3×C4—22no—
550C3×C4—32no—
551C3×C4—32no—
552C3×C4—32no—
553C3×C4—41no—
554C3×C4—61no—
555C3×C4—121no—
556C3×C4—121no—
557C3×C4#100412yes—
558C3×C4#100412yes—
559Dic3—21no—
560Dic3—41no—
561Dic3—41no—
562Dic3—121no—
563Dic3—121no—
564Dic3—121no—
565Dic3—121no—
566Dic3—241no—
567Dic3—241no—
568Dic3#93212yes—
569Dic3C2×#21412yes—
570Dic3C2×#21412yes—
571C32#320811yescharacteristic, complemented, Sylow
572C23—22no—
573C23—42no—
574C23—42no—
575C23—42no—
576C23—62no—
577C23—122no—
578C23—122no—
579C23—122no—
580C23D3×#6711yescharacteristic
581Q8—62no—
582Q8—182no—
583Q8—362no—
584D4—22no—
585D4—22no—
586D4—42no—
587D4—62no—
588D4—62no—
589D4—122no—
590D4—124no—
591D4—124no—
592D4—124no—
593D4—124no—
594C2×C4—22no—
595C2×C4—31no—
596C2×C4—31no—
597C2×C4—31no—
598C2×C4—34no—
599C2×C4—31no—
600C2×C4—62no—
601C2×C4—61no—
602C2×C4—61no—
603C2×C4—181no—
604C2×C4—181no—
605C2×C4D3×#6711yescharacteristic
606C2×C4C22×D3211yescharacteristic
607C8—62no—
608C8—182no—
609C2×C3—22no—
610C2×C3—22no—
611C2×C3—21no—
612C2×C3—21no—
613C2×C3—21no—
614C2×C3—42no—
615C2×C3—84no—
616C2×C3—82no—
617C2×C3—82no—
618C2×C3—242no—
619C2×C3#559211yescharacteristic
620C2×C3C2×D3×SD1611yescharacteristic
621C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
622C2×C3C2×#93211yescharacteristic
623C2×C3C22×#21411yescharacteristic
624C2×C3#580511yescharacteristic
625D3—82no—
626C22—21no—
627C22—21no—
628C22—42no—
629C22—42no—
630C22—42no—
631C22—84no—
632C22—122no—
633C22—122no—
634C22—122no—
635C22—244no—
636C22D3×#21412yes—
637C22C2×D3×#6711yescharacteristic
638C4—21no—
639C4—32no—
640C4—32no—
641C4—32no—
642C4—61no—
643C4—121no—
644C4—121no—
645C4—361no—
646C4—361no—
647C4#6433012yes—
648C3—21no—
649C3#8013811yescharacteristic, complemented
650C3#8316911yescharacteristic, complemented
651C2—22no—
652C2—82no—
653C2—242no—
654C2D3×#93211yescharacteristic
655C2C2×D3×#21411yescharacteristic
656C2#1059551311yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC2×C3×#940C2
hypercenterC22×D4D32
hypocenterC32#3208
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
2. #10594808C2semidirect
3. #10592917C2semidirect
4. C3×#5218C2semidirect
5. #10591490C2semidirect
6. #10591487C2semidirect
7. #10591439C2semidirect
8. #10591438C2semidirect
9. #10591172C2semidirect
10. #10591169C2semidirect
11. #10591053C2semidirect
18. C2×#3754C22semidirect
24. C2×C3×#214C22semidirect
29. #63918C22semidirect
31. #63866C22semidirect
32. #63844C22semidirect
33. Dic3×Dic6C22semidirect
35. C2×#3716C22semidirect
36. C2×#3715C22semidirect
37. #63659C22semidirect
39. C3×#832C22semidirect
41. Dic3⋊(C3⋊C8)C22semidirect
42. #63563C22semidirect
43. #63562C22semidirect
44. Dic3×C3⋊C8C22semidirect
55. #5218D3semidirect
140. C2×#214C2×D3semidirect
168. #832C2×D3semidirect
204. C2×C3×Dic3SD16semidirect
447. C2×Dic3#214semidirect
571. C32#3208semidirect
649. C3#80138semidirect
650. C3#83169semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9402
#105948082
#105929172
C3×#52182
#105914902
#105914872
#105914392
#105914382
#105911722
#105911692
#105910532
#831693
#801383