Finite Group Databasebeta

← #11858077

Subgroups — #11858077

Order 1152.

1533 conjugacy classes of subgroups.

The subgroup lattice has 668 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64297C211yesmaximal, characteristic
2C3×#5504C211yesmaximal, characteristic, complemented
3C2×#63814C211yesmaximal, characteristic, complemented
4#10592665C211yesmaximal, characteristic, complemented
5C2×C3×#810C211yesmaximal, characteristic, complemented
6#10591105C211yesmaximal, characteristic, complemented
7#10591099C211yesmaximal, characteristic, complemented
8#10590610C212yesmaximal, complemented
9#10590609C212yesmaximal, complemented
10#10590600C212yesmaximal, complemented
11D3×#810C212yesmaximal, complemented
12#82570—31nomaximal
13#78790—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C22×C3×Dic6C2211yescharacteristic
17C2×#3804—22no—
18C2×#3799C2212yes—
19C2×#3797—21no—
20#64297—24no—
21#64297C418yescomplemented
22C2×#3796—21no—
23C2×D3×Dic6C2212yes—
24C2×C32×C4⋊C4C2211yescharacteristic
25C2×#3748C2211yescharacteristic
26C3×C4×#67—22no—
27C3×#926C2211yescharacteristic
28C22×C3×C3⋊C8C2211yescharacteristic
29C3×#893—21no—
30C3×#892C2212yes—
31C3×D3×C4⋊C4C2212yes—
32C3×#887—21no—
33C2×#3711C2212yes—
34#63814—24no—
35C2×D3×C3⋊C8C2212yes—
36#63637C2212yes—
37#63636C2212yes—
38C3×#810C2212yes—
39C3×#810C2212yes—
40#63567C2211yescharacteristic
41#63567C2211yescharacteristic
42#63565C2212yes—
43#63565C2212yes—
44#63564C2211yescharacteristic
45#63564C2211yescharacteristic
46C2×#1010—31no—
47C2×#1007—31no—
48C3×#520—31no—
49C2×#948—31no—
50C2×#901—31no—
51#5504D311yescharacteristic, complemented
52C2×C3×#103—31no—
53#5225—31no—
54#5113—31no—
55#5004—31no—
56#5004—32no—
57#5002—31no—
58#5002—32no—
59C2×#810—32no—
60C2×#810D311yescharacteristic, complemented
61#4966—31no—
62#4966—31no—
63#4966—32no—
64#4966—61no—
65#4804—32no—
66#4803—32no—
67#4802—32no—
68D3×#103—32no—
69C22×C32×C4—21no—
70C22×C32×C4C2311yescharacteristic
71C2×#638—21no—
72#3828—22no—
73#3828C2×C414yescomplemented
74C2×C4⋊(C3⋊D3)C2311yescharacteristic
75C2×C4×C3⋊D3—21no—
76C2×#634C2311yescharacteristic
77C2×C3×#67D412yes—
78C22×C3×Dic3—21no—
79C3×#235C2×C414yes—
80C3×#235D414yes—
81C2×C3×D12D411yescharacteristic
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3C2312yes—
84C2×C3×Dic6—21no—
85C2×C3×Dic6—22no—
86C2×C3×Dic6C2×C414yescomplemented
87C2×C3×Dic6D411yescharacteristic
88C2×C3×Dic6C2312yes—
89C2×#627—22no—
90C2×#626—22no—
91C2×#624—22no—
92#3804—216no—
93C2×D3×Dic3—22no—
94#3799—24no—
95#3799C2×C418yescomplemented
96#3797—28no—
97#3796—28no—
98D3×Dic6—24no—
99D3×Dic6C2×C418yescomplemented
100C32×C4⋊C4—21no—
101C32×C4⋊C4C2312yes—
102#3748—22no—
103C2×C3⋊(C3⋊C8)C2312yes—
104C3×#217—21no—
105C3×(C2×D3)⋊C4—22no—
106C3×C4⋊Dic3C2311yescharacteristic
107C3×C4⋊Dic3C2311yescharacteristic
108C3×Dic3⋊C4—22no—
109C3×C4×Dic3—21no—
110C3×C4×Dic3—22no—
111C2×C3×C3⋊C8—22no—
112C2×C3×C3⋊C8C2311yescharacteristic
113C2×C3×C3⋊C8C2311yescharacteristic
114#3711—24no—
115D3×C3⋊C8—24no—
116#2898—91noSylow
117C2×C3×#41—31no—
118C22×C3×Q8—31no—
119#1010—38no—
120#1010—64no—
121#1007—38no—
122#1007—64no—
123C2×#239—32no—
124C2×#239—61no—
125C2×D3×Q8—32no—
126C2×D3×Q8—61no—
127C2×D3×Q8—61no—
128C2×#237—61no—
129C2×#237—62no—
130C2×#235—31no—
131C2×#235—31no—
132C2×#235—32no—
133C2×#235—61no—
134C2×#235—62no—
135C2×#235C2×D311yescharacteristic
136C22×Dic6—32no—
137C22×Dic6C2×D311yescharacteristic
138C22×C3×C8—31no—
139C3×C4×Q8—61no—
140C3×C4×D4—61no—
141C3×C4×D4—62no—
142C3×#117—31no—
143C3×#117—32no—
144C2×C3×C4⋊C4—21no—
145C2×C3×C4⋊C4—32no—
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C4⋊C4C2×D311yescharacteristic
148#948—64no—
149C4×#67—22no—
150#926C2×D311yescharacteristic
151C2×#208—31no—
152C2×#208—31no—
153C2×#208—32no—
154C2×#208—61no—
155C22×C3⋊C8—32no—
156C22×C3⋊C8C2×D311yescharacteristic
157#901—64no—
158C2×ΓL(1,𝔽25)—32no—
159C2×D3×C8—32no—
160#893—21no—
161#892C2×D312yes—
162D3×C4⋊C4C2×D312yes—
163#887—21no—
164C3×#103—32no—
165C3×#103—32no—
166#835—32no—
167#835—32no—
168#821—31no—
169#821—31no—
170#816—31no—
171#816—31no—
172#810—32no—
173#810—32no—
174#810—32no—
175#810—32no—
176#810—31no—
177#810—31no—
178#810—62no—
179#810C2×D312yes—
180#810C2×D312yes—
181#809—32no—
182#809—32no—
183#809—31no—
184#809—31no—
185#809—62no—
186C23×C32C2×D411yescharacteristic
187C22×C3⋊D3—21no—
188C22×C3×D3C2×D412yes—
189C2×C32×C4—22no—
190C2×C32×C4—81no—
191C2×C32×C4C22×C412yes—
192C2×C32×C4C2×D412yes—
193C2×C32×C4C2×D411yescharacteristic
194C2×C32×C4C2411yescharacteristic
195#638—24no—
196C2×C3⋊Dic3—21no—
197C4⋊(C3⋊D3)—21no—
198C4⋊(C3⋊D3)C22×C412yes—
199C4×C3⋊D3—24no—
200#634—21no—
201#634C22×C412yes—
202C3×#67C22⋊C418yes—
203C2×C3×Dic3—24no—
204C2×C3×Dic3—22no—
205C2×C3×Dic3—21no—
206C2×C3×Dic3—21no—
207C2×C3×Dic3C2×D412yes—
208C3×D12C22⋊C414yes—
209C3×C4×D3—82no—
210C3×C4×D3C22×C414yes—
211C3×C4×D3C2×D414yes—
212C3×Dic6—24no—
213C3×Dic6—22no—
214C3×Dic6C22⋊C414yes—
215C3×Dic6C22×C414yes—
216#627—28no—
217#626—28no—
218#624—28no—
219D3×Dic3—28no—
220C3⋊(C3⋊C8)—22no—
221C3×C3⋊C8—21no—
222C3×C3⋊C8—21no—
223C2×2−1+4—91no—
224C2×#131—91no—
225#520—31no—
226#419—92no—
227#419—91no—
228#417—92no—
229#417—91no—
230#416—92no—
231#416—91no—
232C2×#103—31no—
233C2×#103—92no—
234C3×#41—34no—
235C3×#41—34no—
236C2×C3×Q8—31no—
237C2×C3×Q8—34no—
238C2×C3×Q8—32no—
239C2×C3×Q8—62no—
240C2×C3×Q8—61no—
241C2×C3×D4—32no—
242C2×C3×D4—31no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—32no—
247C22×C3×C4—41no—
248C22×C3×C4—62no—
249C22×C3×C4—61no—
250C22×C3×C4C22×D311yescharacteristic
251C22×C3×C4C22×D311yescharacteristic
252C2×#67—62no—
253C2×#67—61no—
254C2×#67—61no—
255C2×#67—121no—
256C2×#67#6712yes—
257C22×Dic3—21no—
258C22×Dic3—62no—
259#239—38no—
260#239—68no—
261#239—64no—
262D3×Q8—38no—
263D3×Q8—68no—
264D3×Q8—64no—
265D3×Q8—68no—
266#237—68no—
267#237—616no—
268#235—34no—
269#235—34no—
270#235—38no—
271#235—64no—
272#235—64no—
273#235—62no—
274#235—62no—
275#235—616no—
276#235—122no—
277#235C4×D314yes—
278#235D1214yes—
279C2×D12—31no—
280C2×D12—31no—
281C2×D12—61no—
282C2×D12—62no—
283C2×D12#6711yescharacteristic
284C2×C4×D3—22no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×C4×D3—61no—
288C2×C4×D3—61no—
289C2×C4×D3—62no—
290C2×C4×D3—121no—
291C2×C4×D3C22×D312yes—
292C2×Dic6—21no—
293C2×Dic6—22no—
294C2×Dic6—31no—
295C2×Dic6—31no—
296C2×Dic6—38no—
297C2×Dic6—61no—
298C2×Dic6—64no—
299C2×Dic6—62no—
300C2×Dic6—62no—
301C2×Dic6C4×D314yescomplemented
302C2×Dic6#6711yescharacteristic
303C2×Dic6C22×D312yes—
304C2×C3×C8—31no—
305C2×C3×C8—31no—
306C2×C3×C8—62no—
307C3×C4⋊C4—21no—
308C3×C4⋊C4—21no—
309C3×C4⋊C4—22no—
310C3×C4⋊C4—31no—
311C3×C4⋊C4—31no—
312C3×C4⋊C4—41no—
313C3×C4⋊C4—62no—
314C3×C4⋊C4C22×D312yes—
315C3×C4⋊C4C22×D312yes—
316C3×C22⋊C4—62no—
317C3×C22⋊C4—61no—
318C3×C42—62no—
319C3×C42—61no—
320#217—21no—
321(C2×D3)⋊C4—22no—
322C4⋊Dic3C22×D311yescharacteristic
323C4⋊Dic3C22×D311yescharacteristic
324Dic3⋊C4—22no—
325C4×Dic3—21no—
326C4×Dic3—22no—
327#208—64no—
328#208—62no—
329#208—62no—
330#208—122no—
331C2×C3⋊C8—22no—
332C2×C3⋊C8—32no—
333C2×C3⋊C8—32no—
334C2×C3⋊C8—62no—
335C2×C3⋊C8—64no—
336C2×C3⋊C8C22×D311yescharacteristic
337C2×C3⋊C8C22×D311yescharacteristic
338ΓL(1,𝔽25)—64no—
339D3×C8—64no—
340C22×C32—21no—
341C22×C32—21no—
342C22×C32C2×C22⋊C412yes—
343C22×C32C22×D411yescharacteristic
344C2×C3⋊D3—22no—
345C2×C3⋊D3—41no—
346C2×C3⋊D3—41no—
347C2×C3×D3—22no—
348C2×C3×D3—22no—
349C2×C3×D3C2×C22⋊C414yes—
350C32×C4—42no—
351C32×C4C2×C22⋊C412yes—
352C32×C4C23×C411yescharacteristic
353C32×C4C22×D411yescharacteristic
354C3⋊Dic3—22no—
355C3×Dic3—24no—
356C3×Dic3—41no—
357C3×Dic3—41no—
358C3×Dic3C2×C22⋊C414yes—
3592−1+4—98no—
3602−1+4—184no—
361C2×#41—31no—
362C2×#41—92no—
363C2×#41—91no—
364C2×#41—182no—
365C2×#41—181no—
366C22×Q8—31no—
367C22×Q8—92no—
368C22×Q8—181no—
369#131—184no—
370C2×M16—92no—
371C2×M16—91no—
372C22×C8—31no—
373C22×C8—92no—
374C4×Q8—61no—
375C4×D4—61no—
376C4×D4—62no—
377#117—31no—
378#117—32no—
379C2×C4⋊C4—32no—
380C2×C4⋊C4D3211yescharacteristic
381#103—32no—
382#103—32no—
383#103—91no—
384#103—91no—
385#103—92no—
386#103—92no—
387#103—92no—
388#102—91no—
389#102—91no—
390#102—92no—
391C23×C3—21no—
392C23×C3—32no—
393C23×C3D3×D411yescharacteristic
394C23×C3C2×#6711yescharacteristic
395C22×D3—61no—
396C22×D3—61no—
397C22×D3—121no—
398C22×D3C2×#6712yes—
399C3×Q8—34no—
400C3×Q8—34no—
401C3×Q8—64no—
402C3×Q8—62no—
403C3×D4—38no—
404C3×D4—34no—
405C2×C3×C4—22no—
406C2×C3×C4—22no—
407C2×C3×C4—21no—
408C2×C3×C4—22no—
409C2×C3×C4—22no—
410C2×C3×C4—21no—
411C2×C3×C4—32no—
412C2×C3×C4—34no—
413C2×C3×C4—34no—
414C2×C3×C4—42no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—61no—
418C2×C3×C4—61no—
419C2×C3×C4—81no—
420C2×C3×C4—81no—
421C2×C3×C4—82no—
422C2×C3×C4—242no—
423C2×C3×C4C2×C4×D312yes—
424C2×C3×C4C2×C4×D312yes—
425C2×C3×C4C2×D1212yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D411yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C23×D311yescharacteristic
430C2×C3×C4C23×D311yescharacteristic
431#67—68no—
432#67—64no—
433#67—64no—
434#67—124no—
435#67(C2×D3)⋊C418yes—
436C2×Dic3—24no—
437C2×Dic3—22no—
438C2×Dic3—21no—
439C2×Dic3—21no—
440C2×Dic3—68no—
441C2×Dic3—61no—
442C2×Dic3—61no—
443C2×Dic3—121no—
444C2×Dic3C2×#6712yes—
445D12—32no—
446D12—32no—
447D12—62no—
448D12—68no—
449D12—61no—
450D12—61no—
451D12—121no—
452D12(C2×D3)⋊C414yes—
453C4×D3—68no—
454C4×D3—68no—
455C4×D3—64no—
456C4×D3—64no—
457C4×D3—68no—
458C4×D3—82no—
459C4×D3—124no—
460C4×D3C2×C4×D314yes—
461C4×D3C2×D1214yes—
462Dic6—24no—
463Dic6—22no—
464Dic6—32no—
465Dic6—32no—
466Dic6—62no—
467Dic6—68no—
468Dic6—61no—
469Dic6—61no—
470Dic6—68no—
471Dic6—121no—
472Dic6(C2×D3)⋊C414yes—
473Dic6C2×C4×D314yes—
474C3×C8—61no—
475C3×C8—61no—
476C3⋊C8—21no—
477C3⋊C8—21no—
478C3⋊C8—62no—
479C3⋊C8—62no—
480C3⋊C8—122no—
481C2×C32—22no—
482C2×C32C22×C22⋊C411yescharacteristic
483C2×C32#57711yescharacteristic
484C2×C32#57811yescharacteristic
485C3⋊D3—42no—
486C3×D3—24no—
487#41—34no—
488#41—34no—
489#41—98no—
490#41—94no—
491#41—184no—
492#41—1816no—
493#41—188no—
494#41—182no—
495C2×Q8—31no—
496C2×Q8—32no—
497C2×Q8—34no—
498C2×Q8—62no—
499C2×Q8—61no—
500C2×Q8—98no—
501C2×Q8—91no—
502C2×Q8—182no—
503C2×Q8—184no—
504C2×Q8—188no—
505C2×D4—32no—
506C2×D4—31no—
507C2×D4—91no—
508C2×D4—182no—
509C2×D4—181no—
510C22×C4—21no—
511C22×C4—32no—
512C22×C4—62no—
513C22×C4—61no—
514C22×C4—182no—
515C22×C4—182no—
516C22×C4—181no—
517C22×C4C2×D3211yescharacteristic
518M16—184no—
519M16—182no—
520C2×C8—31no—
521C2×C8—31no—
522C2×C8—62no—
523C2×C8—92no—
524C2×C8—184no—
525C4⋊C4—21no—
526C4⋊C4—31no—
527C4⋊C4—31no—
528C4⋊C4—62no—
529C4⋊C4C2×D3212yes—
530C22⋊C4—62no—
531C22⋊C4—61no—
532C42—62no—
533C42—61no—
534C22×C3—21no—
535C22×C3—21no—
536C22×C3—21no—
537C22×C3—21no—
538C22×C3—21no—
539C22×C3—22no—
540C22×C3—34no—
541C22×C3—41no—
542C22×C3—41no—
543C22×C3—62no—
544C22×C3—62no—
545C22×C3D3×C22⋊C412yes—
546C22×C3C2×(C2×D3)⋊C412yes—
547C22×C3C2×D3×D411yescharacteristic
548C22×C3C22×#6711yescharacteristic
549C2×D3—22no—
550C2×D3—22no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—122no—
554C2×D3—121no—
555C2×D3—121no—
556C2×D3—121no—
557C2×D3—121no—
558C2×D3—241no—
559C2×D3—241no—
560C2×D3C2×(C2×D3)⋊C414yes—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—22no—
564C3×C4—34no—
565C3×C4—42no—
566C3×C4—42no—
567C3×C4—64no—
568C3×C4—82no—
569C3×C4—121no—
570C3×C4—121no—
571C3×C4D3×C22⋊C412yes—
572C3×C4C2×(C2×D3)⋊C412yes—
573C3×C4C22×C4×D311yescharacteristic
574C3×C4C22×C4×D311yescharacteristic
575C3×C4C22×D1211yescharacteristic
576C3×C4C2×D3×D411yescharacteristic
577Dic3—24no—
578Dic3—41no—
579Dic3—41no—
580Dic3—62no—
581Dic3—62no—
582Dic3—122no—
583Dic3C2×(C2×D3)⋊C414yes—
584C32#289811yescharacteristic, complemented, Sylow
585C23—32no—
586C23—181no—
587C23D3×#6711yescharacteristic
588Q8—34no—
589Q8—34no—
590Q8—62no—
591Q8—64no—
592Q8—92no—
593Q8—188no—
594Q8—181no—
595D4—38no—
596D4—34no—
597D4—92no—
598D4—188no—
599D4—184no—
600D4—181no—
601C2×C4—22no—
602C2×C4—32no—
603C2×C4—34no—
604C2×C4—34no—
605C2×C4—62no—
606C2×C4—64no—
607C2×C4—61no—
608C2×C4—61no—
609C2×C4—81no—
610C2×C4—188no—
611C2×C4—188no—
612C2×C4—181no—
613C2×C4—184no—
614C2×C4—242no—
615C2×C4C4×D3212yes—
616C2×C4D3×D1212yes—
617C2×C4D3×#6711yescharacteristic
618C2×C4C22×D3211yescharacteristic
619C8—61no—
620C8—61no—
621C8—182no—
622C2×C3—22no—
623C2×C3—22no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—42no—
628C2×C3—64no—
629C2×C3C2×D3×C22⋊C411yescharacteristic
630C2×C3#576211yescharacteristic
631C2×C3#576611yescharacteristic
632C2×C3C22×(C2×D3)⋊C411yescharacteristic
633C2×C3#583611yescharacteristic
634C2×C3#583811yescharacteristic
635D3—24no—
636D3—122no—
637D3—122no—
638D3—242no—
639C22—21no—
640C22—21no—
641C22—34no—
642C22—62no—
643C22—62no—
644C22—182no—
645C22—361no—
646C22—361no—
647C22D3×(C2×D3)⋊C412yes—
648C22C2×D3×#6711yescharacteristic
649C4—34no—
650C4—42no—
651C4—64no—
652C4—121no—
653C4—121no—
654C4—182no—
655C4D3×(C2×D3)⋊C412yes—
656C4C2×C4×D3211yescharacteristic
657C4C2×D3×D1211yescharacteristic
658C3—21no—
659C3#7879011yescharacteristic, complemented
660C3#8257011yescharacteristic, complemented
661C2—22no—
662C2—64no—
663C2—362no—
664C2C2×D3×(C2×D3)⋊C411yescharacteristic
665C2#1059510511yescharacteristic
666C2#1059532711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32C22×D4
prime radicalC2×#64297C2
cosocleC2×C32×C4C24
hypercenterC2×C4⋊C4D32
hypocenterC32#2898
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#5504C2semidirect
3. C2×#63814C2semidirect
4. #10592665C2semidirect
5. C2×C3×#810C2semidirect
6. #10591105C2semidirect
7. #10591099C2semidirect
8. #10590610C2semidirect
9. #10590609C2semidirect
10. #10590600C2semidirect
11. D3×#810C2semidirect
21. #64297C4semidirect
51. #5504D3semidirect
60. C2×#810D3semidirect
73. #3828C2×C4semidirect
86. C2×C3×Dic6C2×C4semidirect
95. #3799C2×C4semidirect
99. D3×Dic6C2×C4semidirect
301. C2×Dic6C4×D3semidirect
584. C32#2898semidirect
659. C3#78790semidirect
660. C3#82570semidirect

Maximal subgroups

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

subgroupindex
C2×#642972
C3×#55042
C2×#638142
#105926652
C2×C3×#8102
#105911052
#105910992
#105906102
#105906092
#105906002
D3×#8102
#825703
#787903