Finite Group Databasebeta

← #11857906

Subgroups — #11857906

Order 1152.

1733 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic
2C2×#63791C211yesmaximal, characteristic, complemented
3D32×C4⋊C4C211yesmaximal, characteristic, complemented
4C3⋊D3×#102C211yesmaximal, characteristic, complemented
5C3×#4771C212yesmaximal, complemented
6#10591416C211yesmaximal, characteristic, complemented
7#10591414C212yesmaximal, complemented
8#10590672C211yesmaximal, characteristic, complemented
9#10590671C212yesmaximal, complemented
10#10590609C212yesmaximal, complemented
11#10590601C211yesmaximal, characteristic, complemented
12D3×#417—32nomaximal
13C2×D4×C3⋊D3C2211yescharacteristic
14C2×C3×#237C2212yes—
15C2×#3811—21no—
16C22×#624—21no—
17C2×#3804—22no—
18#64312—24no—
19#64312C418yescomplemented
20C2×C4×D32—21no—
21C2×C4×D32C2211yescharacteristic
22C2×#3799C2212yes—
23C2×#3797C2211yescharacteristic
24C2×C8×C3⋊D3C2211yescharacteristic
25C4⋊C4×C3⋊D3C2211yescharacteristic
26C2×C3×ΓL(1,𝔽25)C2212yescomplemented
27C3×D3×C4⋊C4C2212yescomplemented
28#63900C2211yescharacteristic
29D3×C4⋊Dic3C2212yescomplemented
30#63883—21no—
31D3×Dic3⋊C4—22no—
32C2×#3711C2212yescomplemented
33C2×#3710C2211yescharacteristic
34#63791—24no—
35C32×#102C2211yescharacteristic, complemented
36#63659C2211yescharacteristic, complemented
37#63648C2211yescharacteristic, complemented
38#63636C2211yescharacteristic, complemented
39C3×#832C2212yescomplemented
40C3×#816C2212yescomplemented
41C3×#810C2212yescomplemented
42#63566C2212yescomplemented
43#63565C2212yescomplemented
44#63564C2212yescomplemented
45C2×D3×#41—32no—
46C2×D3×M16—32no—
47C2×D3×C4⋊C4—32no—
48C3×#417—32no—
49#5232—32no—
50#5133—32no—
51#4966—32no—
52#4803—32no—
53#4803—32no—
54D3×#103—32no—
55D3×#103—32no—
56#4771—32no—
57#4771D312yescomplemented
58D3×#102—32no—
59D3×#102—32no—
60D3×#102—61no—
61C23×C3⋊D3—21no—
62C22×D32D411yescharacteristic
63C2×C32×D4C2311yescharacteristic
64C2×#638—21no—
65D4×C3⋊D3—22no—
66D4×C3⋊D3C2×C414yescomplemented
67C2×C4⋊(C3⋊D3)C2311yescharacteristic
68C2×C4×C3⋊D3—21no—
69C2×C4×C3⋊D3C2311yescharacteristic
70C2×C3×#67—22no—
71C22×C3×Dic3—22no—
72C3×#237—24no—
73C3×#237C2×C418yescomplemented
74C2×C3×C4×D3—22no—
75C2×C3×C4×D3C2312yes—
76C2×C3×Dic6C2312yes—
77#3811—28no—
78C2×#627—21no—
79C2×#626—22no—
80C2×#624—21no—
81C2×#624—22no—
82C2×#624—28no—
83C2×#624—21no—
84C2×#624D411yescharacteristic
85#3804—216no—
86C2×D3×Dic3—22no—
87C2×D3×Dic3D412yes—
88C4×D32—44no—
89C4×D32C2×C414yes—
90C4×D32D414yes—
91#3799—24no—
92#3799C2×C418yescomplemented
93#3797—22no—
94#3797C2×C414yescomplemented
95C2×C32×C8C2311yescharacteristic
96C32×C4⋊C4C2311yescharacteristic
97C4⋊(C3⋊Dic3)C2311yescharacteristic
98#3750—21no—
99C2×C3⋊(C3⋊C8)C2311yescharacteristic
100C8×C3⋊D3—22no—
101C3×C4⋊Dic3C2312yes—
102C3×Dic3⋊C4—22no—
103C2×C3×C3⋊C8C2312yes—
104C3×ΓL(1,𝔽25)—24no—
105#3724—21no—
106Dic3⋊Dic3—22no—
107#3711—24no—
108#3710—22no—
109C2×#417—91noSylow
110C2×C3×#41—32no—
111D3×#41—316no—
112D3×#41—68no—
113C2×#239—32no—
114C2×D3×Q8—32no—
115C2×#237—62no—
116C2×#237C2×D312yes—
117C2×D3×D4—32no—
118C2×D3×D4—61no—
119C2×D3×D4—62no—
120C2×#235—32no—
121C2×#235—62no—
122C22×C4×D3—32no—
123C22×C4×D3—62no—
124C22×C4×D3—62no—
125C2×C3×M16—32no—
126C2×C3×C4⋊C4—32no—
127C2×C4⋊Dic3—32no—
128C2×Dic3⋊C4—62no—
129C2×#208—32no—
130D3×M16—68no—
131C2×ΓL(1,𝔽25)—32no—
132C2×ΓL(1,𝔽25)C2×D312yescomplemented
133C2×D3×C8—32no—
134C2×D3×C8—32no—
135C2×D3×C8—61no—
136D3×C4⋊C4—32no—
137D3×C4⋊C4—32no—
138D3×C4⋊C4—32no—
139D3×C4⋊C4—61no—
140D3×C4⋊C4—62no—
141D3×C4⋊C4—62no—
142D3×C4⋊C4C2×D312yescomplemented
143C3×#103—32no—
144C3×#103—32no—
145C3×#102—21no—
146C3×#102—32no—
147C3×#102C2×D312yescomplemented
148#835—32no—
149#835—32no—
150#832—32no—
151#832—61no—
152#832C2×D312yescomplemented
153#821—32no—
154#821—32no—
155#821—61no—
156#816—32no—
157#816C2×D312yescomplemented
158#810—32no—
159#810C2×D312yescomplemented
160#809—32no—
161#809—32no—
162#809—61no—
163C23×C32—21no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—24no—
166C22×C3⋊D3—42no—
167C22×C3⋊D3—42no—
168C22×C3⋊D3C2×D411yescharacteristic
169C22×C3×D3C2×D412yes—
170C2×D32—22no—
171C2×D32—22no—
172C2×D32C22⋊C414yes—
173C32×D4—21no—
174C32×D4C22×C412yescomplemented
175C2×C32×C4—21no—
176C2×C32×C4C2411yescharacteristic
177#638—24no—
178C2×C3⋊Dic3—21no—
179C2×C3⋊Dic3C2×D411yescharacteristic
180C4⋊(C3⋊D3)—21no—
181C4⋊(C3⋊D3)C22×C412yescomplemented
182C4×C3⋊D3—42no—
183C4×C3⋊D3C22×C412yes—
184C4×C3⋊D3C2×D412yes—
185C3×#67—28no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3C2×D412yes—
190C3×C4×D3—44no—
191C3×C4×D3C22×C414yes—
192C3×C4×D3C2×D414yes—
193C3×Dic6—22no—
194C3×Dic6C22×C414yescomplemented
195#627—24no—
196#626—28no—
197#624—24no—
198#624—28no—
199#624—42no—
200#624C22⋊C414yes—
201D3×Dic3—44no—
202D3×Dic3C22⋊C418yes—
203C32×C8—21no—
204C3⋊(C3⋊C8)—21no—
205C3×C3⋊C8—22no—
206C22×#41—91no—
207C22×M16—91no—
208C22×C4⋊C4—91no—
209#417—32no—
210#417—92no—
211#417—92no—
212#417—92no—
213C2×#103—91no—
214C2×#103—91no—
215C2×#102—91no—
216C2×#102—91no—
217C23×D3—32no—
218C23×D3—62no—
219C23×D3—121no—
220C3×#41—38no—
221C3×#41—64no—
222C2×C3×Q8—32no—
223C2×C3×D4—21no—
224C2×C3×D4—62no—
225C2×C3×D4C22×D312yes—
226C22×C3×C4—32no—
227C22×C3×C4—62no—
228C22×C3×C4—62no—
229C2×#67—22no—
230C2×#67—62no—
231C2×#67—62no—
232C2×#67—121no—
233C22×Dic3—22no—
234C22×Dic3—32no—
235C22×Dic3—62no—
236#239—38no—
237#239—64no—
238D3×Q8—38no—
239D3×Q8—64no—
240#237—24no—
241#237—616no—
242#237C4×D318yescomplemented
243D3×D4—38no—
244D3×D4—64no—
245D3×D4—64no—
246D3×D4—616no—
247D3×D4—122no—
248#235—38no—
249#235—64no—
250#235—616no—
251C2×D12—32no—
252C2×D12—61no—
253C2×D12—62no—
254C2×C4×D3—22no—
255C2×C4×D3—32no—
256C2×C4×D3—32no—
257C2×C4×D3—32no—
258C2×C4×D3—38no—
259C2×C4×D3—38no—
260C2×C4×D3—61no—
261C2×C4×D3—616no—
262C2×C4×D3—62no—
263C2×C4×D3—62no—
264C2×C4×D3—62no—
265C2×C4×D3—62no—
266C2×C4×D3—62no—
267C2×C4×D3—62no—
268C2×C4×D3—121no—
269C2×C4×D3—128no—
270C2×C4×D3C22×D312yes—
271C2×Dic6—62no—
272C2×Dic6C22×D312yes—
273C3×M16—64no—
274C2×C3×C8—21no—
275C2×C3×C8—32no—
276C2×C3×C8C22×D312yes—
277C3×C4⋊C4—21no—
278C3×C4⋊C4—32no—
279C3×C4⋊C4—62no—
280C3×C4⋊C4C22×D312yes—
281C4⋊Dic3—32no—
282C4⋊Dic3—61no—
283C4⋊Dic3—62no—
284C4⋊Dic3C22×D312yes—
285Dic3⋊C4—22no—
286Dic3⋊C4—62no—
287Dic3⋊C4—62no—
288Dic3⋊C4—62no—
289Dic3⋊C4—121no—
290#208—64no—
291C2×C3⋊C8—32no—
292C2×C3⋊C8—61no—
293C2×C3⋊C8C22×D312yes—
294ΓL(1,𝔽25)—24no—
295ΓL(1,𝔽25)—64no—
296D3×C8—64no—
297D3×C8—64no—
298D3×C8—122no—
299C22×C32—22no—
300C22×C32—41no—
301C22×C32—41no—
302C22×C32C22×D411yescharacteristic
303C2×C3⋊D3—22no—
304C2×C3⋊D3—41no—
305C2×C3⋊D3—41no—
306C2×C3⋊D3—48no—
307C2×C3⋊D3C2×C22⋊C412yes—
308C2×C3⋊D3AGL(1,ℤ/8)12yes—
309C2×C3⋊D3#13712yes—
310C2×C3×D3—22no—
311C2×C3×D3—22no—
312C2×C3×D3C2×C22⋊C414yes—
313D32—28no—
314C32×C4—41no—
315C32×C4C23×C411yescharacteristic
316C32×C4C22×D411yescharacteristic
317C3⋊Dic3—41no—
318C3⋊Dic3C2×C22⋊C412yes—
319C3×Dic3—24no—
320C3×Dic3—42no—
321C3×Dic3C2×C22⋊C414yes—
322C2×#41—32no—
323C2×#41—92no—
324C2×#41—98no—
325C2×#41—182no—
326C2×#41—184no—
327C22×Q8—91no—
328C22×D4—91no—
329C22×D4—181no—
330C23×C4—91no—
331C23×C4—181no—
332C23×C4—181no—
333C2×M16—32no—
334C2×M16—92no—
335C2×M16—184no—
336C22×C8—91no—
337C22×C8—91no—
338C2×C4⋊C4—32no—
339C2×C4⋊C4—91no—
340C2×C4⋊C4—92no—
341C2×C4⋊C4—91no—
342C2×C4⋊C4—181no—
343C2×C4⋊C4—182no—
344#103—32no—
345#103—32no—
346#103—92no—
347#103—92no—
348#102—32no—
349#102—92no—
350#102—91no—
351#102—91no—
352#102—91no—
353#102D3211yescharacteristic, complemented
354C23×C3—22no—
355C23×C3—32no—
356C23×C3—41no—
357C22×D3—32no—
358C22×D3—38no—
359C22×D3—61no—
360C22×D3—64no—
361C22×D3—64no—
362C22×D3—68no—
363C22×D3—62no—
364C22×D3—124no—
365C22×D3—121no—
366C22×D3—124no—
367C22×D3—124no—
368C22×D3—242no—
369C22×D3—242no—
370C22×D3D3×D412yes—
371C3×Q8—34no—
372C3×Q8—62no—
373C3×D4—22no—
374C3×D4—22no—
375C3×D4—41no—
376C3×D4—68no—
377C3×D4C2×C4×D314yescomplemented
378C2×C3×C4—22no—
379C2×C3×C4—21no—
380C2×C3×C4—32no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—41no—
384C2×C3×C4—68no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—124no—
388C2×C3×C4C23×D312yes—
389#67—28no—
390#67—68no—
391#67—68no—
392#67—124no—
393C2×Dic3—22no—
394C2×Dic3—28no—
395C2×Dic3—22no—
396C2×Dic3—32no—
397C2×Dic3—38no—
398C2×Dic3—61no—
399C2×Dic3—62no—
400C2×Dic3—121no—
401C2×Dic3—124no—
402C2×Dic3D3×D412yes—
403D12—34no—
404D12—62no—
405D12—68no—
406D12—62no—
407D12—121no—
408C4×D3—38no—
409C4×D3—34no—
410C4×D3—34no—
411C4×D3—38no—
412C4×D3—44no—
413C4×D3—62no—
414C4×D3—62no—
415C4×D3—68no—
416C4×D3—68no—
417C4×D3—68no—
418C4×D3—124no—
419C4×D3—124no—
420C4×D3—124no—
421C4×D3—242no—
422C4×D3C2×C4×D314yes—
423C4×D3D3×D414yes—
424Dic6—22no—
425Dic6—68no—
426Dic6C2×C4×D314yescomplemented
427C3×C8—22no—
428C3×C8—41no—
429C3×C8—62no—
430C3⋊C8—22no—
431C3⋊C8—62no—
432C3⋊C8—121no—
433C2×C32—42no—
434C2×C32C22×C22⋊C411yescharacteristic
435C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
436C2×C32C2×#13711yescharacteristic
437C3⋊D3—42no—
438C3⋊D3#41714yescomplemented
439C3×D3—24no—
440C24—91no—
441C24—181no—
442#41—38no—
443#41—64no—
444#41—98no—
445#41—184no—
446#41—1816no—
447C2×Q8—32no—
448C2×Q8—94no—
449C2×Q8—181no—
450C2×Q8—182no—
451C2×D4—62no—
452C2×D4—94no—
453C2×D4—91no—
454C2×D4—182no—
455C2×D4—182no—
456C2×D4—181no—
457C2×D4—188no—
458C2×D4C2×D3211yescharacteristic
459C22×C4—32no—
460C22×C4—62no—
461C22×C4—62no—
462C22×C4—91no—
463C22×C4—94no—
464C22×C4—94no—
465C22×C4—92no—
466C22×C4—91no—
467C22×C4—181no—
468C22×C4—182no—
469C22×C4—188no—
470C22×C4—181no—
471C22×C4—181no—
472C22×C4—182no—
473C22×C4—364no—
474M16—64no—
475M16—184no—
476C2×C8—32no—
477C2×C8—91no—
478C2×C8—182no—
479C2×C8—182no—
480C2×C8C2×D3211yescharacteristic
481C4⋊C4—32no—
482C4⋊C4—62no—
483C4⋊C4—91no—
484C4⋊C4—181no—
485C4⋊C4—182no—
486C4⋊C4—181no—
487C4⋊C4C2×D3211yescharacteristic
488C22×C3—24no—
489C22×C3—21no—
490C22×C3—34no—
491C22×C3—42no—
492C22×C3—42no—
493C22×C3—42no—
494C22×C3—62no—
495C22×C3—62no—
496C22×C3—81no—
497C22×C3—81no—
498C22×C3C2×D3×D412yes—
499C2×D3—22no—
500C2×D3—22no—
501C2×D3—34no—
502C2×D3—34no—
503C2×D3—34no—
504C2×D3—62no—
505C2×D3—62no—
506C2×D3—62no—
507C2×D3—616no—
508C2×D3—64no—
509C2×D3—122no—
510C2×D3—1216no—
511C2×D3—122no—
512C2×D3—122no—
513C2×D3—248no—
514C2×D3—241no—
515C2×D3—241no—
516C2×D3D3×C22⋊C414yes—
517C3×C4—21no—
518C3×C4—21no—
519C3×C4—34no—
520C3×C4—42no—
521C3×C4—64no—
522C3×C4—81no—
523C3×C4—122no—
524C3×C4C22×C4×D312yes—
525C3×C4C2×D3×D412yes—
526Dic3—24no—
527Dic3—34no—
528Dic3—42no—
529Dic3—62no—
530Dic3—122no—
531Dic3—241no—
532Dic3D3×C22⋊C414yes—
533C32C2×#41711yescharacteristic, complemented, Sylow
534C23—21no—
535C23—32no—
536C23—94no—
537C23—91no—
538C23—184no—
539C23—182no—
540C23—182no—
541C23—181no—
542C23—362no—
543C23—362no—
544Q8—34no—
545Q8—62no—
546Q8—184no—
547D4—21no—
548D4—68no—
549D4—92no—
550D4—188no—
551D4—184no—
552D4—181no—
553D4C4×D3212yescomplemented
554C2×C4—21no—
555C2×C4—32no—
556C2×C4—34no—
557C2×C4—34no—
558C2×C4—68no—
559C2×C4—62no—
560C2×C4—62no—
561C2×C4—94no—
562C2×C4—98no—
563C2×C4—91no—
564C2×C4—92no—
565C2×C4—92no—
566C2×C4—124no—
567C2×C4—188no—
568C2×C4—184no—
569C2×C4—181no—
570C2×C4—362no—
571C2×C4—362no—
572C2×C4—364no—
573C2×C4C22×D3211yescharacteristic
574C8—21no—
575C8—62no—
576C8—181no—
577C2×C3—21no—
578C2×C3—21no—
579C2×C3—21no—
580C2×C3—44no—
581C2×C3—64no—
582C2×C3—82no—
583C2×C3C2×D3×C22⋊C412yes—
584C2×C3D3×AGL(1,ℤ/8)12yes—
585C2×C3D3×#13712yes—
586D3—24no—
587D3—38no—
588D3—64no—
589D3—124no—
590D3—242no—
591C22—22no—
592C22—34no—
593C22—41no—
594C22—41no—
595C22—62no—
596C22—62no—
597C22—92no—
598C22—92no—
599C22—92no—
600C22—188no—
601C22—182no—
602C22—368no—
603C22—361no—
604C22—361no—
605C22D32×D411yescharacteristic
606C4—34no—
607C4—41no—
608C4—64no—
609C4—92no—
610C4—122no—
611C4—361no—
612C4C2×C4×D3211yescharacteristic
613C4D32×D411yescharacteristic
614C3—21no—
615C3D3×#41712yescomplemented
616C2—42no—
617C2—64no—
618C2—94no—
619C2—362no—
620C2D32×C22⋊C411yescharacteristic
621C2#1059472611yescharacteristic
622C2#1059474211yescharacteristic
subgroupG/H
centerC22D32×D4
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#102C22
socleC22×C32C22×D4
prime radicalC2×#64312C2
cosocleC2×C32×C4C24
hypercenter#102D32
hypocenterC32C2×#417
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. C2×#63791C2semidirect
3. D32×C4⋊C4C2semidirect
4. C3⋊D3×#102C2semidirect
5. C3×#4771C2semidirect
6. #10591416C2semidirect
7. #10591414C2semidirect
8. #10590672C2semidirect
9. #10590671C2semidirect
10. #10590609C2semidirect
11. #10590601C2semidirect
19. #64312C4semidirect
26. C2×C3×ΓL(1,𝔽25)C22semidirect
27. C3×D3×C4⋊C4C22semidirect
29. D3×C4⋊Dic3C22semidirect
32. C2×#3711C22semidirect
35. C32×#102C22semidirect
36. #63659C22semidirect
37. #63648C22semidirect
38. #63636C22semidirect
39. C3×#832C22semidirect
40. C3×#816C22semidirect
41. C3×#810C22semidirect
42. #63566C22semidirect
43. #63565C22semidirect
44. #63564C22semidirect
57. #4771D3semidirect
66. D4×C3⋊D3C2×C4semidirect
73. C3×#237C2×C4semidirect
92. #3799C2×C4semidirect
94. #3797C2×C4semidirect
132. C2×ΓL(1,𝔽25)C2×D3semidirect
142. D3×C4⋊C4C2×D3semidirect
147. C3×#102C2×D3semidirect
152. #832C2×D3semidirect
157. #816C2×D3semidirect
159. #810C2×D3semidirect
174. C32×D4C22×C4semidirect
181. C4⋊(C3⋊D3)C22×C4semidirect
194. C3×Dic6C22×C4semidirect
242. #237C4×D3semidirect
353. #102D32semidirect
377. C3×D4C2×C4×D3semidirect
426. Dic6C2×C4×D3semidirect
438. C3⋊D3#417semidirect
533. C32C2×#417semidirect
553. D4C4×D32semidirect
615. C3D3×#417semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×#637912
D32×C4⋊C42
C3⋊D3×#1022
C3×#47712
#105914162
#105914142
#105906722
#105906712
#105906092
#105906012
D3×#4173