Finite Group Databasebeta

← #11860961

Subgroups — #11860961

Order 1152.

1115 conjugacy classes of subgroups.

The subgroup lattice has 625 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10595994C211yesmaximal, characteristic, complemented
2C3×#5523C211yesmaximal, characteristic, complemented
3C2×#63829C211yesmaximal, characteristic
4C3×#4997C211yesmaximal, characteristic, complemented
5C2×#63573C211yesmaximal, characteristic, complemented
6#10591106C211yesmaximal, characteristic, complemented
7#10591088C211yesmaximal, characteristic, complemented
8#10590383C212yesmaximal, complemented
9C4×#3717C212yesmaximal, complemented
10C4×#3716C212yesmaximal, complemented
11#10590346C212yesmaximal, complemented
12#82558—31nomaximal
13#78574—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2211yescharacteristic
16C32×#117C2211yescharacteristic
17C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
18#64101—21no—
19C4⋊C4×C3⋊D3—21no—
20#64090—22no—
21C4×C4⋊(C3⋊D3)C2212yes—
22C4×#634C2212yes—
23C2×C3×C4⋊Dic3C2211yescharacteristic
24C2×C3×#208C2211yescharacteristic
25C22×C3×C3⋊C8C2211yescharacteristic
26C3×#892—21no—
27C3×D3×C4⋊C4—21no—
28C3×#67⋊C4—22no—
29C3×C4×D12C2212yes—
30C3×C4×Dic6C2212yes—
31C2×#3719C2211yescharacteristic
32C2×#3717C2211yescharacteristic
33#63829C418yescomplemented
34C2×#3716C2211yescharacteristic
35C2×#3714C2211yescharacteristic
36C3×#803C2212yes—
37C3×C4×C3⋊C8C2212yes—
38#63573C2212yes—
39#63573C2212yes—
40#63567C2212yes—
41#63566C2212yes—
42#63564C2212yes—
43#63563C2212yes—
44C3×#520—31no—
45C2×#950—31no—
46C2×#904—31no—
47#5523—31no—
48#5523—31no—
49#5523—61no—
50#5523D311yescharacteristic, complemented
51C3×#405—31no—
52#5232—31no—
53#5133—31no—
54#5133—31no—
55C2×#817—31no—
56#5030—32no—
57C4×#215—32no—
58C4×#214—32no—
59#5014—32no—
60#4997D311yescharacteristic, complemented
61#4966—31no—
62C2×#808—31no—
63#4716—32no—
64#4711—32no—
65C4×#204—32no—
66C4×#204—32no—
67C22×C32×C4C2311yescharacteristic
68C2×#638—21no—
69C22×C3⋊Dic3—21no—
70#3828—22no—
71#3828C2×C414yescomplemented
72C2×C4⋊(C3⋊D3)C2311yescharacteristic
73C2×C4×C3⋊D3—21no—
74C2×C4×C3⋊D3—22no—
75C2×#634C2311yescharacteristic
76C2×C3×#67—21no—
77C22×C3×Dic3—21no—
78C3×#235—22no—
79C3×#235C2×C414yescomplemented
80C2×C3×D12C2311yescharacteristic
81C2×C3×C4×D3—21no—
82C2×C3×C4×D3—22no—
83C2×C3×Dic6C2311yescharacteristic
84C32×C4⋊C4D411yescharacteristic
85C32×C4⋊C4D411yescharacteristic
86C32×C22⋊C4D412yes—
87C32×C42C2312yes—
88#3752—22no—
89C4⋊(C3⋊Dic3)—21no—
90C4⋊(C3⋊Dic3)C2312yes—
91#3750—22no—
92C4×C3⋊Dic3—22no—
93C3×(C2×D3)⋊C4—22no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3C2312yes—
96C3×Dic3⋊C4—22no—
97C3×C4×Dic3—22no—
98C3×#208—22no—
99C2×C3×C3⋊C8C2×C414yescomplemented
100C2×C3×C3⋊C8C2312yes—
101C2×C3×C3⋊C8C2311yescharacteristic
102C2×C3×C3⋊C8C2311yescharacteristic
103#3719C2×C414yescomplemented
104#3717C2×C414yescomplemented
105#3716C2×C414yescomplemented
106#3714C2×C414yescomplemented
107#2952—91noSylow
108C2×C3×#41—31no—
109C2×#235—31no—
110C2×#235—31no—
111C2×#235—61no—
112C2×#235C2×D311yescharacteristic
113C2×C3×M16—31no—
114C22×C3×C8—31no—
115C3×C4×Q8—32no—
116C3×C4×D4—32no—
117C3×C4×D4—62no—
118C3×#117—21no—
119C3×#117—61no—
120C3×#117C2×D311yescharacteristic
121C3×#117C2×D311yescharacteristic
122C2×C3×C4⋊C4—31no—
123C2×C3×C4⋊C4—61no—
124#950—38no—
125C2×#216—31no—
126C2×#215—31no—
127C2×#214—31no—
128C2×#213—31no—
129C2×C4⋊Dic3—31no—
130C2×C4⋊Dic3—31no—
131C2×C4⋊Dic3—61no—
132C2×C4⋊Dic3C2×D311yescharacteristic
133C2×#208C2×D311yescharacteristic
134C22×C3⋊C8C2×D311yescharacteristic
135C2×Dic12—31no—
136#904—38no—
137C2×D24—31no—
138C2×#204—31no—
139C2×#204—31no—
140#892—21no—
141#892—62no—
142#892—61no—
143#892—61no—
144D3×C4⋊C4—21no—
145D3×C4⋊C4—62no—
146D3×C4⋊C4—61no—
147D3×C4⋊C4—61no—
148#67⋊C4—22no—
149#67⋊C4—64no—
150#67⋊C4—62no—
151#67⋊C4—62no—
152C4×D12—32no—
153C4×D12—32no—
154C4×D12—62no—
155C4×D12C2×D312yes—
156C4×Dic6—32no—
157C4×Dic6—32no—
158C4×Dic6—62no—
159C4×Dic6C2×D312yes—
160C3×#97—32no—
161C3×C4×C8—32no—
162#835—32no—
163#832—32no—
164#821—32no—
165#821—32no—
166#817—32no—
167#817—32no—
168#816—32no—
169#816—32no—
170#810—32no—
171#809—32no—
172#808—32no—
173#808—32no—
174#803C2×D312yes—
175C4×C3⋊C8C2×D312yes—
176C23×C32C2×D411yescharacteristic
177C22×C3⋊D3—21no—
178C22×C3×D3—21no—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D411yescharacteristic
183C2×C32×C4#4112yes—
184C2×C32×C4C2411yescharacteristic
185#638—24no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—22no—
188C2×C3⋊Dic3—81no—
189C4⋊(C3⋊D3)—21no—
190C4⋊(C3⋊D3)C22×C412yes—
191C4×C3⋊D3—24no—
192C4×C3⋊D3—82no—
193#634—21no—
194#634C22×C412yes—
195C3×#67—24no—
196C2×C3×Dic3—21no—
197C2×C3×Dic3—22no—
198C2×C3×Dic3—81no—
199C3×D12—21no—
200C3×D12C22×C412yes—
201C3×C4×D3—24no—
202C3×C4×D3—82no—
203C3×Dic6—21no—
204C3×Dic6C22×C412yes—
205C3×C3⋊C8—22no—
206C3×C3⋊C8C22×C412yes—
207C3×C3⋊C8C22×C412yes—
208C2×#135—91no—
209#520—31no—
210#520—91no—
211#442—92no—
212#441—92no—
213C4×SD16—92no—
214C4×SD16—92no—
215C2×#106—91no—
216#417—91no—
217#417—91no—
218#405—31no—
219C3×#41—34no—
220C3×#41—62no—
221C2×C3×Q8—31no—
222C2×C3×D4—31no—
223C2×C3×D4—61no—
224C22×C3×C4—21no—
225C22×C3×C4—61no—
226C22×C3×C4—61no—
227C22×C3×C4—62no—
228C22×C3×C4C22×D311yescharacteristic
229C22×C3×C4C22×D311yescharacteristic
230C2×#67—21no—
231C2×#67—62no—
232C2×#67—61no—
233C2×#67—61no—
234C22×Dic3—21no—
235C22×Dic3—62no—
236C22×Dic3—61no—
237C22×Dic3—61no—
238#235—22no—
239#235—34no—
240#235—34no—
241#235—64no—
242#235—64no—
243#235—62no—
244#235—62no—
245#235C4×D314yescomplemented
246C2×D12—31no—
247C2×D12—31no—
248C2×D12—61no—
249C2×D12C22×D311yescharacteristic
250C2×C4×D3—21no—
251C2×C4×D3—22no—
252C2×C4×D3—62no—
253C2×C4×D3—61no—
254C2×C4×D3—61no—
255C2×C4×D3—64no—
256C2×C4×D3—62no—
257C2×C4×D3—62no—
258C2×Dic6—31no—
259C2×Dic6—31no—
260C2×Dic6—61no—
261C2×Dic6C22×D311yescharacteristic
262C3×M16—62no—
263C2×C3×C8—34no—
264C2×C3×C8—31no—
265C2×C3×C8—31no—
266C2×C3×C8—32no—
267C3×C4⋊C4—21no—
268C3×C4⋊C4—21no—
269C3×C4⋊C4—32no—
270C3×C4⋊C4—62no—
271C3×C4⋊C4—61no—
272C3×C4⋊C4D1211yescharacteristic
273C3×C4⋊C4D1211yescharacteristic
274C3×C4⋊C4#6711yescharacteristic
275C3×C4⋊C4#6711yescharacteristic
276C3×C22⋊C4—22no—
277C3×C22⋊C4—62no—
278C3×C22⋊C4D1212yes—
279C3×C22⋊C4#6712yes—
280C3×C42—22no—
281C3×C42—62no—
282C3×C42C22×D312yes—
283C3×C42C22×D312yes—
284#216—34no—
285#215—34no—
286#214—34no—
287#213—34no—
288(C2×D3)⋊C4—22no—
289(C2×D3)⋊C4—64no—
290(C2×D3)⋊C4—62no—
291(C2×D3)⋊C4—62no—
292C4⋊Dic3—21no—
293C4⋊Dic3—32no—
294C4⋊Dic3—32no—
295C4⋊Dic3—62no—
296C4⋊Dic3—62no—
297C4⋊Dic3—61no—
298C4⋊Dic3—61no—
299C4⋊Dic3C22×D312yes—
300Dic3⋊C4—22no—
301Dic3⋊C4—64no—
302Dic3⋊C4—62no—
303Dic3⋊C4—62no—
304C4×Dic3—22no—
305C4×Dic3—64no—
306C4×Dic3—62no—
307C4×Dic3—62no—
308#208—22no—
309C2×C3⋊C8C4×D314yescomplemented
310C2×C3⋊C8C22×D312yes—
311C2×C3⋊C8C22×D311yescharacteristic
312C2×C3⋊C8C22×D311yescharacteristic
313Dic12—34no—
314D24—34no—
315#204—34no—
316#204—34no—
317C22×C32—21no—
318C22×C32—21no—
319C22×C32C4×D412yes—
320C22×C32C22×D411yescharacteristic
321C2×C3⋊D3—22no—
322C2×C3⋊D3—41no—
323C2×C3⋊D3—41no—
324C2×C3×D3—22no—
325C2×C3×D3—41no—
326C2×C3×D3—41no—
327C32×C4—22no—
328C32×C4—22no—
329C32×C4C4×D412yes—
330C32×C4C23×C411yescharacteristic
331C32×C4C2×#4111yescharacteristic
332C3⋊Dic3—22no—
333C3⋊Dic3—42no—
334C3×Dic3—22no—
335C3×Dic3—42no—
336C2×#41—31no—
337C2×#41—91no—
338#135—98no—
339C2×Q16—91no—
340C2×SD16—91no—
341C2×SD16—91no—
342C2×D8—91no—
343C2×M16—31no—
344C22×C8—31no—
345C4×Q8—32no—
346C4×Q8—92no—
347C4×D4—32no—
348C4×D4—62no—
349C4×D4—92no—
350C4×D4—182no—
351#117—61no—
352#117—181no—
353#117D3211yescharacteristic
354C2×C4⋊C4—31no—
355C2×C4⋊C4—61no—
356C2×C4⋊C4—91no—
357C2×C4⋊C4—181no—
358#106—92no—
359#106—92no—
360#103—92no—
361#103—92no—
362#102—92no—
363#102—92no—
364#97—32no—
365C4×C8—32no—
366C23×C3—21no—
367C23×C3—61no—
368C23×C3C2×D1211yescharacteristic
369C23×C3C2×#6711yescharacteristic
370C22×D3—21no—
371C22×D3—62no—
372C22×D3—61no—
373C22×D3—61no—
374C3×Q8—32no—
375C3×Q8—61no—
376C3×D4—32no—
377C3×D4—64no—
378C3×D4—61no—
379C2×C3×C4—21no—
380C2×C3×C4—22no—
381C2×C3×C4—22no—
382C2×C3×C4—21no—
383C2×C3×C4—22no—
384C2×C3×C4—22no—
385C2×C3×C4—61no—
386C2×C3×C4—64no—
387C2×C3×C4—62no—
388C2×C3×C4—242no—
389C2×C3×C4—241no—
390C2×C3×C4C2×C4×D312yes—
391C2×C3×C4C2×C4×D312yes—
392C2×C3×C4C2×D1212yes—
393C2×C3×C4C2×D1212yes—
394C2×C3×C4C2×D1211yescharacteristic
395C2×C3×C4#23512yes—
396C2×C3×C4#23512yes—
397C2×C3×C4C2×#6712yes—
398C2×C3×C4C2×#6712yes—
399C2×C3×C4C2×#6711yescharacteristic
400C2×C3×C4C23×D311yescharacteristic
401C2×C3×C4C23×D311yescharacteristic
402#67—24no—
403#67—68no—
404#67—64no—
405#67—64no—
406C2×Dic3—21no—
407C2×Dic3—22no—
408C2×Dic3—62no—
409C2×Dic3—61no—
410C2×Dic3—61no—
411C2×Dic3—64no—
412C2×Dic3—62no—
413C2×Dic3—62no—
414C2×Dic3—81no—
415C2×Dic3—241no—
416C2×Dic3—241no—
417C2×Dic3—242no—
418D12—21no—
419D12—32no—
420D12—32no—
421D12—62no—
422D12—62no—
423D12—61no—
424D12—61no—
425D12C2×C4×D312yes—
426C4×D3—24no—
427C4×D3—68no—
428C4×D3—64no—
429C4×D3—64no—
430C4×D3—82no—
431C4×D3—242no—
432C4×D3—242no—
433C4×D3—244no—
434Dic6—21no—
435Dic6—32no—
436Dic6—32no—
437Dic6—62no—
438Dic6—62no—
439Dic6—61no—
440Dic6—61no—
441Dic6C2×C4×D312yes—
442C3×C8—32no—
443C3×C8—32no—
444C3×C8—62no—
445C3⋊C8—22no—
446C3⋊C8C2×C4×D312yes—
447C3⋊C8C2×C4×D312yes—
448C2×C32—22no—
449C2×C32C2×C4×D411yescharacteristic
450C2×C32#57711yescharacteristic
451C2×C32#57711yescharacteristic
452C3⋊D3—42no—
453C3×D3—42no—
454#41—34no—
455#41—62no—
456#41—94no—
457#41—182no—
458C2×Q8—31no—
459C2×Q8—91no—
460C2×D4—31no—
461C2×D4—61no—
462C2×D4—91no—
463C2×D4—181no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—62no—
467C22×C4—181no—
468C22×C4—181no—
469C22×C4—182no—
470C22×C4C2×D3211yescharacteristic
471Q16—94no—
472SD16—94no—
473SD16—94no—
474D8—94no—
475M16—62no—
476C2×C8—31no—
477C2×C8—31no—
478C2×C8—34no—
479C2×C8—32no—
480C4⋊C4—32no—
481C4⋊C4—61no—
482C4⋊C4—62no—
483C4⋊C4—92no—
484C4⋊C4—181no—
485C4⋊C4—182no—
486C4⋊C4#62611yescharacteristic
487C4⋊C4#62611yescharacteristic
488C22⋊C4—62no—
489C22⋊C4—182no—
490C22⋊C4#62612yes—
491C42—62no—
492C42—182no—
493C42C2×D3212yes—
494C22×C3—21no—
495C22×C3—21no—
496C22×C3—21no—
497C22×C3—21no—
498C22×C3—21no—
499C22×C3—22no—
500C22×C3—41no—
501C22×C3—41no—
502C22×C3—62no—
503C22×C3—121no—
504C22×C3—121no—
505C22×C3C4×D1212yes—
506C22×C3C4×#6712yes—
507C22×C3C22×D1211yescharacteristic
508C22×C3C22×#6711yescharacteristic
509C2×D3—22no—
510C2×D3—41no—
511C2×D3—41no—
512C2×D3—64no—
513C2×D3—62no—
514C2×D3—62no—
515C2×D3—122no—
516C2×D3—122no—
517C2×D3—121no—
518C2×D3—121no—
519C2×D3—121no—
520C2×D3—121no—
521C3×C4—22no—
522C3×C4—22no—
523C3×C4—22no—
524C3×C4—22no—
525C3×C4—21no—
526C3×C4—21no—
527C3×C4—22no—
528C3×C4—42no—
529C3×C4—42no—
530C3×C4—62no—
531C3×C4—122no—
532C3×C4C4×D1212yes—
533C3×C4C4×#6712yes—
534C3×C4C22×C4×D311yescharacteristic
535C3×C4C22×C4×D311yescharacteristic
536C3×C4C2×#23511yescharacteristic
537C3×C4C2×#23511yescharacteristic
538Dic3—22no—
539Dic3—42no—
540Dic3—64no—
541Dic3—62no—
542Dic3—62no—
543Dic3—124no—
544Dic3—122no—
545Dic3—122no—
546C32#295211yescharacteristic, complemented, Sylow
547C23—61no—
548C23—181no—
549C23C2×#62611yescharacteristic
550Q8—32no—
551Q8—61no—
552Q8—92no—
553Q8—181no—
554D4—32no—
555D4—64no—
556D4—61no—
557D4—92no—
558D4—184no—
559D4—181no—
560C2×C4—61no—
561C2×C4—64no—
562C2×C4—62no—
563C2×C4—181no—
564C2×C4—184no—
565C2×C4—182no—
566C2×C4—242no—
567C2×C4—241no—
568C2×C4—722no—
569C2×C4—721no—
570C2×C4#379812yes—
571C2×C4C4×D3212yes—
572C2×C4C2×#62612yes—
573C2×C4C2×#62612yes—
574C2×C4C2×#62611yescharacteristic
575C2×C4C22×D3211yescharacteristic
576C8—32no—
577C8—32no—
578C8—62no—
579C2×C3—22no—
580C2×C3—22no—
581C2×C3—21no—
582C2×C3—21no—
583C2×C3—21no—
584C2×C3—42no—
585C2×C3—122no—
586C2×C3C2×C4×D1211yescharacteristic
587C2×C3#575111yescharacteristic
588C2×C3#575111yescharacteristic
589C2×C3C2×C4×#6711yescharacteristic
590C2×C3#583611yescharacteristic
591C2×C3#583711yescharacteristic
592D3—42no—
593D3—124no—
594D3—122no—
595D3—122no—
596C22—21no—
597C22—21no—
598C22—62no—
599C22—121no—
600C22—121no—
601C22—182no—
602C22—361no—
603C22—361no—
604C22C4×#62612yes—
605C22C22×#62611yescharacteristic
606C4—22no—
607C4—22no—
608C4—62no—
609C4—122no—
610C4—182no—
611C4—362no—
612C4C4×#62612yes—
613C4C2×#379811yescharacteristic
614C4C2×C4×D3211yescharacteristic
615C3—21no—
616C3#7857411yescharacteristic, complemented
617C3#8255811yescharacteristic, complemented
618C2—22no—
619C2—122no—
620C2—362no—
621C2C2×C4×#62611yescharacteristic
622C2#1059544711yescharacteristic
623C2#1059544811yescharacteristic
subgroupG/H
centerC22C22×#626
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC22×C32C22×D4
prime radicalC2×#63829C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2952
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117

Complements

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

NH ≅ G/Ntype
1. #10595994C2semidirect
2. C3×#5523C2semidirect
4. C3×#4997C2semidirect
5. C2×#63573C2semidirect
6. #10591106C2semidirect
7. #10591088C2semidirect
8. #10590383C2semidirect
9. C4×#3717C2semidirect
10. C4×#3716C2semidirect
11. #10590346C2semidirect
33. #63829C4semidirect
50. #5523D3semidirect
60. #4997D3semidirect
71. #3828C2×C4semidirect
79. C3×#235C2×C4semidirect
99. C2×C3×C3⋊C8C2×C4semidirect
103. #3719C2×C4semidirect
104. #3717C2×C4semidirect
105. #3716C2×C4semidirect
106. #3714C2×C4semidirect
245. #235C4×D3semidirect
309. C2×C3⋊C8C4×D3semidirect
546. C32#2952semidirect
616. C3#78574semidirect
617. C3#82558semidirect

Maximal subgroups

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

subgroupindex
#105959942
C3×#55232
C2×#638292
C3×#49972
C2×#635732
#105911062
#105910882
#105903832
C4×#37172
C4×#37162
#105903462
#825583
#785743