Finite Group Databasebeta

← #11857965

Subgroups — #11857965

Order 1152.

1619 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592924C211yesmaximal, characteristic, complemented
5C3×#5225C211yesmaximal, characteristic, complemented
6#10591556C214yesmaximal, complemented
7#10591550C214yesmaximal, complemented
8#10591086C211yesmaximal, characteristic, complemented
9#10591085C211yesmaximal, characteristic, complemented
10#84072—31nomaximal
11#78956—31nomaximal
12C22×C32×Q8C2211yescharacteristic
13C2×C3×#239—24no—
14C2×C3×#239—21no—
15C2×C3×#239—21no—
16C2×C3×#239C418yescomplemented
17C2×C3×#239C2212yes—
18C2×C3×#239C2212yes—
19C22×C3×D12—21no—
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3—21no—
22C22×C3×C4×D3C2211yescharacteristic
23#64135C2211yescharacteristic
24C2×#3748C2211yescharacteristic
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27D3×#217—21no—
28#63955—21no—
29D3×C4⋊Dic3C2212yescomplemented
30C4×D3×Dic3—21no—
31#63855—21no—
32#63841C2212yescomplemented
33C2×#3711C2212yescomplemented
34D3×#208—24no—
35C2×D3×C3⋊C8C2212yescomplemented
36#63662C2214yescomplemented
37C3×#835C2214yescomplemented
38#63563C2214yescomplemented
39#63562C2214yescomplemented
40C22×C3×#41—31no—
41C22×#239D311yescharacteristic
42C2×#926—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45D3×#117—31no—
46C3×#419—31no—
47#5233—34no—
48#5232—34no—
49#5225—31no—
50#5225—31no—
51#5225—61no—
52#5225D311yescharacteristic, complemented
53#5215—31no—
54#5215—31no—
55#5131—31no—
56#5001—31no—
57#4804—34no—
58#4803—34no—
59C23×C3×D3—21no—
60C23×C3×D3D411yescharacteristic
61C2×C32×Q8—22no—
62C2×C32×Q8—21no—
63C2×C32×Q8C2×C414yescomplemented
64C2×C32×Q8C2312yes—
65C22×C32×C4—21no—
66C22×C32×C4C2311yescharacteristic
67C22×C3×Dic3D411yescharacteristic
68C3×#239—28no—
69C3×#239—28no—
70C3×#239—24no—
71C3×#239—24no—
72C3×#239C2×C418yes—
73C3×#239C2×C418yescomplemented
74C2×C3×D12—28no—
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12—21no—
78C2×C3×D12—22no—
79C2×C3×D12C2×C414yescomplemented
80C2×C3×D12C2312yes—
81C2×C3×C4×D3—28no—
82C2×C3×C4×D3—22no—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2×C414yes—
85C2×C3×C4×D3D411yescharacteristic
86C2×C3×C4×D3D411yescharacteristic
87C2×C3×C4×D3D414yes—
88C2×C3×C4×D3C2311yescharacteristic
89C2×C3×C4×D3C2311yescharacteristic
90C2×D3×Dic3—22no—
91#3757—21no—
92C4⋊(C3⋊Dic3)C2312yes—
93C4×C3⋊Dic3—21no—
94#3748—22no—
95C2×C3⋊(C3⋊C8)C2312yes—
96C3×#217—21no—
97C3×C4⋊Dic3C2312yes—
98C3×C4×Dic3—21no—
99C3×#208—22no—
100C2×C3×C3⋊C8C2312yes—
101Dic3⋊Dic3—22no—
102(C2×D3)⋊Dic3—22no—
103Dic32—22no—
104#3711—24no—
105D3×C3⋊C8—24no—
106#2896—91noSylow
107C2×C3×#41—38no—
108C2×C3×#41—32no—
109C2×C3×#41—32no—
110C2×C3×#41—64no—
111C2×C3×#41—61no—
112C2×C3×#41—61no—
113C22×C3×Q8—21no—
114C22×C3×Q8C2×D311yescharacteristic
115C22×C3×Q8C2×D311yescharacteristic
116C22×C3×D4—31no—
117C22×C3×D4—61no—
118C23×C3×C4—31no—
119C23×C3×C4—61no—
120C2×#239—24no—
121C2×#239—21no—
122C2×#239—21no—
123C2×#239Dic318yescomplemented
124C2×#239C2×D312yes—
125C2×#239C2×D312yes—
126C22×D12—21no—
127C22×D12C2×D311yescharacteristic
128C22×C4×D3—21no—
129C22×C4×D3C2×D311yescharacteristic
130C2×C3×M16—31no—
131C3×#117—31no—
132C2×#217—61no—
133#926—31no—
134#926—31no—
135#926—32no—
136#926—61no—
137#926—61no—
138#926—61no—
139#926C2×D311yescharacteristic
140C2×C4⋊Dic3—32no—
141C2×C4×Dic3—61no—
142C2×#208—31no—
143C2×#208—31no—
144C2×#208—32no—
145C2×#208—61no—
146C2×#208—64no—
147C2×#208C2×D311yescharacteristic
148C22×C3⋊C8—32no—
149D3×M16—64no—
150C2×ΓL(1,𝔽25)—32no—
151C2×D3×C8—32no—
152#892—32no—
153D3×C4⋊C4—32no—
154D3×C22⋊C4—61no—
155#877—61no—
156#872—61no—
157C42×D3—61no—
158C3×#103—34no—
159#835—34no—
160#835—34no—
161#835—64no—
162#835C2×D314yescomplemented
163#832—34no—
164#832—34no—
165#821—34no—
166#809—34no—
167C23×C32C2×D411yescharacteristic
168C22×C3×D3—24no—
169C22×C3×D3—22no—
170C22×C3×D3—42no—
171C22×C3×D3—44no—
172C22×C3×D3C22⋊C414yes—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×Q8—24no—
176C32×Q8—22no—
177C32×Q8C22×C414yes—
178C2×C32×C4—24no—
179C2×C32×C4—22no—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D411yescharacteristic
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184C2×C3⋊Dic3—22no—
185C2×C3×Dic3—22no—
186C2×C3×Dic3C22⋊C414yes—
187C2×C3×Dic3C2×D411yescharacteristic
188C2×C3×Dic3C2×D411yescharacteristic
189C3×D12—28no—
190C3×D12—28no—
191C3×D12—24no—
192C3×D12—22no—
193C3×D12C22×C414yes—
194C3×C4×D3—28no—
195C3×C4×D3—28no—
196C3×C4×D3C22⋊C414yes—
197C3×C4×D3C22⋊C414yes—
198C3×C4×D3C22×C412yes—
199C3×C4×D3C22×C412yes—
200C3×C4×D3C2×D412yes—
201C3×C4×D3C2×D412yes—
202D3×Dic3—44no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C22×#41—31no—
206C22×M16—91no—
207C2×#117—91no—
208#419—31no—
209#419—91no—
210#418—91no—
211#418—91no—
212#417—94no—
213#416—94no—
214C24×C3—31no—
215C24×C3—61no—
216C23×D3—21no—
217C23×D3#6711yescharacteristic
218C3×#41—38no—
219C3×#41—38no—
220C3×#41—68no—
221C3×#41—68no—
222C3×#41—64no—
223C3×#41—64no—
224C2×C3×Q8—22no—
225C2×C3×Q8—21no—
226C2×C3×Q8—22no—
227C2×C3×Q8—21no—
228C2×C3×Q8—24no—
229C2×C3×Q8—22no—
230C2×C3×Q8—42no—
231C2×C3×Q8—41no—
232C2×C3×Q8C4×D314yescomplemented
233C2×C3×Q8C2×Dic314yescomplemented
234C2×C3×Q8C22×D312yes—
235C2×C3×Q8C22×D312yes—
236C2×C3×D4—34no—
237C2×C3×D4—32no—
238C2×C3×D4—68no—
239C2×C3×D4—62no—
240C2×C3×D4—62no—
241C2×C3×D4—61no—
242C2×C3×D4—62no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—31no—
247C22×C3×C4—34no—
248C22×C3×C4—34no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—31no—
253C22×C3×C4—41no—
254C22×C3×C4—68no—
255C22×C3×C4—62no—
256C22×C3×C4—62no—
257C22×C3×C4C22×D311yescharacteristic
258C22×C3×C4C22×D311yescharacteristic
259C22×Dic3—62no—
260C22×Dic3#6711yescharacteristic
261#239—28no—
262#239—28no—
263#239—24no—
264#239—24no—
265#239C2×Dic318yes—
266#239C2×Dic318yescomplemented
267C2×D12—28no—
268C2×D12—22no—
269C2×D12—22no—
270C2×D12—21no—
271C2×D12—22no—
272C2×D12C2×Dic314yescomplemented
273C2×D12C22×D312yes—
274C2×C4×D3—28no—
275C2×C4×D3—22no—
276C2×C4×D3—22no—
277C2×C4×D3—62no—
278C2×C4×D3C2×Dic314yes—
279C2×C4×D3#6711yescharacteristic
280C2×C4×D3#6711yescharacteristic
281C2×C4×D3#6714yes—
282C2×C4×D3C22×D311yescharacteristic
283C2×C4×D3C22×D311yescharacteristic
284C3×M16—62no—
285C2×C3×C8—32no—
286C3×C4⋊C4—32no—
287C3×C22⋊C4—61no—
288C3×C42—61no—
289#217—21no—
290#217—62no—
291#217—61no—
292#217—61no—
293#217—121no—
294(C2×D3)⋊C4—62no—
295C4⋊Dic3—32no—
296C4⋊Dic3—32no—
297C4⋊Dic3—62no—
298C4⋊Dic3—62no—
299C4⋊Dic3C22×D312yes—
300Dic3⋊C4—62no—
301C4×Dic3—21no—
302C4×Dic3—62no—
303C4×Dic3—61no—
304C4×Dic3—61no—
305C4×Dic3—62no—
306C4×Dic3—121no—
307#208—22no—
308#208—64no—
309#208—62no—
310#208—62no—
311#208—122no—
312C2×C3⋊C8—32no—
313C2×C3⋊C8—32no—
314C2×C3⋊C8—62no—
315C2×C3⋊C8—64no—
316C2×C3⋊C8C22×D312yes—
317ΓL(1,𝔽25)—64no—
318D3×C8—64no—
319C22×C32—22no—
320C22×C32C2×C22⋊C412yes—
321C22×C32C22×D411yescharacteristic
322C2×C3×D3—22no—
323C2×C3×D3—22no—
324C2×C3×D3—24no—
325C2×C3×D3—44no—
326C2×C3×D3—48no—
327C2×C3×D3—44no—
328C2×C3×D3C2×C22⋊C412yes—
329C2×C3×D3C2×C22⋊C412yes—
330C32×C4—24no—
331C32×C4C2×C22⋊C412yes—
332C32×C4C23×C411yescharacteristic
333C32×C4C22×D411yescharacteristic
334C3⋊Dic3—42no—
335C3×Dic3—42no—
336C3×Dic3C2×C22⋊C412yes—
337C3×Dic3C2×C22⋊C412yes—
338C2×#41—38no—
339C2×#41—32no—
340C2×#41—32no—
341C2×#41—61no—
342C2×#41—61no—
343C2×#41—64no—
344C22×Q8D3211yescharacteristic
345C22×D4—31no—
346C22×D4—61no—
347C23×C4—31no—
348C23×C4—61no—
349C2×M16—31no—
350C2×M16—92no—
351C2×M16—91no—
352C2×M16—184no—
353C22×C8—92no—
354#117—31no—
355#117—92no—
356#117—91no—
357#117—181no—
358#117—181no—
359C2×C4⋊C4—92no—
360C2×C22⋊C4—181no—
361C2×C42—181no—
362#103—34no—
363#103—94no—
364#102—94no—
365#102—94no—
366C23×C3—21no—
367C23×C3—31no—
368C23×C3—31no—
369C23×C3—34no—
370C23×C3—64no—
371C23×C3—62no—
372C23×C3—122no—
373C23×C3—124no—
374C23×C3D3×D411yescharacteristic
375C23×C3C2×#6711yescharacteristic
376C22×D3—24no—
377C22×D3—22no—
378C22×D3—42no—
379C22×D3—44no—
380C22×D3#21714yes—
381C22×D3C2×#6711yescharacteristic
382C22×D3C2×#6711yescharacteristic
383C3×Q8—24no—
384C3×Q8—24no—
385C3×Q8—22no—
386C3×Q8—22no—
387C3×Q8—24no—
388C3×Q8—42no—
389C3×Q8—44no—
390C3×Q8C2×C4×D314yes—
391C3×Q8C22×Dic314yes—
392C3×D4—34no—
393C3×D4—68no—
394C3×D4—68no—
395C3×D4—64no—
396C3×D4—62no—
397C2×C3×C4—24no—
398C2×C3×C4—24no—
399C2×C3×C4—22no—
400C2×C3×C4—22no—
401C2×C3×C4—21no—
402C2×C3×C4—22no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—34no—
406C2×C3×C4—31no—
407C2×C3×C4—31no—
408C2×C3×C4—34no—
409C2×C3×C4—34no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—32no—
414C2×C3×C4—42no—
415C2×C3×C4—44no—
416C2×C3×C4—68no—
417C2×C3×C4—68no—
418C2×C3×C4—62no—
419C2×C3×C4C2×C4×D312yes—
420C2×C3×C4D3×D411yescharacteristic
421C2×C3×C4D3×D412yes—
422C2×C3×C4C22×Dic312yes—
423C2×C3×C4C2×#6711yescharacteristic
424C2×C3×C4C2×#6712yes—
425C2×C3×C4C23×D311yescharacteristic
426C2×C3×C4C23×D311yescharacteristic
427C2×Dic3—22no—
428C2×Dic3—62no—
429C2×Dic3—62no—
430C2×Dic3—122no—
431C2×Dic3—124no—
432C2×Dic3#21714yes—
433C2×Dic3C2×#6711yescharacteristic
434C2×Dic3C2×#6711yescharacteristic
435D12—28no—
436D12—28no—
437D12—24no—
438D12—22no—
439D12C22×Dic314yes—
440C4×D3—28no—
441C4×D3—28no—
442C4×D3—124no—
443C4×D3#21714yes—
444C4×D3#21714yes—
445C4×D3C22×Dic312yes—
446C4×D3C22×Dic312yes—
447C4×D3C2×#6712yes—
448C4×D3C2×#6712yes—
449C3×C8—62no—
450C3⋊C8—22no—
451C3⋊C8—62no—
452C3⋊C8—62no—
453C3⋊C8—122no—
454C2×C32—22no—
455C2×C32C22×C22⋊C411yescharacteristic
456C2×C32#57512yes—
457C3×D3—22no—
458C3×D3—22no—
459C3×D3—44no—
460C24—31no—
461C24—61no—
462#41—38no—
463#41—38no—
464#41—64no—
465#41—64no—
466#41—68no—
467#41—68no—
468C2×Q8—21no—
469C2×Q8—22no—
470C2×Q8D3×Dic314yescomplemented
471C2×Q8C2×D3212yes—
472C2×D4—32no—
473C2×D4—34no—
474C2×D4—62no—
475C2×D4—62no—
476C2×D4—68no—
477C2×D4—62no—
478C2×D4—61no—
479C22×C4—21no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—31no—
483C22×C4—34no—
484C22×C4—31no—
485C22×C4—31no—
486C22×C4—34no—
487C22×C4—62no—
488C22×C4—62no—
489C22×C4—68no—
490C22×C4—182no—
491C22×C4C2×D3211yescharacteristic
492M16—62no—
493M16—184no—
494M16—182no—
495C2×C8—32no—
496C2×C8—92no—
497C2×C8—184no—
498C4⋊C4—32no—
499C4⋊C4—92no—
500C4⋊C4—182no—
501C22⋊C4—61no—
502C22⋊C4—182no—
503C22⋊C4—181no—
504C42—61no—
505C42—182no—
506C42—181no—
507C22×C3—22no—
508C22×C3—22no—
509C22×C3—21no—
510C22×C3—22no—
511C22×C3—32no—
512C22×C3—32no—
513C22×C3—42no—
514C22×C3—62no—
515C22×C3—62no—
516C22×C3—64no—
517C22×C3—124no—
518C22×C3—128no—
519C22×C3—124no—
520C22×C3D3×C22⋊C412yes—
521C22×C3C2×#21712yes—
522C22×C3C2×D3×D411yescharacteristic
523C22×C3C22×#6711yescharacteristic
524C2×D3—22no—
525C2×D3—22no—
526C2×D3—24no—
527C2×D3—44no—
528C2×D3—48no—
529C2×D3—44no—
530C2×D3C2×#21712yes—
531C2×D3C2×#21712yes—
532C3×C4—24no—
533C3×C4—24no—
534C3×C4—21no—
535C3×C4—21no—
536C3×C4—22no—
537C3×C4—32no—
538C3×C4—32no—
539C3×C4—44no—
540C3×C4—122no—
541C3×C4D3×C22⋊C412yes—
542C3×C4C2×#21712yes—
543C3×C4C22×C4×D311yescharacteristic
544C3×C4C2×D3×D411yescharacteristic
545C3×C4C23×Dic311yescharacteristic
546C3×C4C22×#6711yescharacteristic
547Dic3—42no—
548Dic3—122no—
549Dic3—122no—
550Dic3—242no—
551Dic3C2×#21712yes—
552Dic3C2×#21712yes—
553C32#289611yescharacteristic, complemented, Sylow
554C23—31no—
555C23—31no—
556C23—34no—
557C23—62no—
558C23—64no—
559C23—122no—
560C23—124no—
561C23D3×#6711yescharacteristic
562Q8—22no—
563Q8—24no—
564Q8C2×D3×Dic314yes—
565D4—34no—
566D4—68no—
567D4—68no—
568D4—62no—
569D4—64no—
570C2×C4—22no—
571C2×C4—24no—
572C2×C4—31no—
573C2×C4—31no—
574C2×C4—34no—
575C2×C4—32no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—34no—
580C2×C4—34no—
581C2×C4—68no—
582C2×C4—68no—
583C2×C4—62no—
584C2×C4—182no—
585C2×C4—364no—
586C2×C4C2×D3×Dic312yes—
587C2×C4D3×#6712yes—
588C2×C4D3×#6711yescharacteristic
589C2×C4C22×D3211yescharacteristic
590C8—62no—
591C8—182no—
592C2×C3—22no—
593C2×C3—22no—
594C2×C3—21no—
595C2×C3—22no—
596C2×C3—42no—
597C2×C3—62no—
598C2×C3—62no—
599C2×C3—124no—
600C2×C3C2×D3×C22⋊C411yescharacteristic
601C2×C3#577712yes—
602C2×C3#582212yes—
603C2×C3C22×#21711yescharacteristic
604D3—22no—
605D3—22no—
606D3—44no—
607C22—22no—
608C22—32no—
609C22—32no—
610C22—62no—
611C22—62no—
612C22—64no—
613C22—124no—
614C22—128no—
615C22—124no—
616C22D3×#21712yes—
617C22C2×D3×#6711yescharacteristic
618C4—24no—
619C4—32no—
620C4—32no—
621C4—122no—
622C4—362no—
623C4D3×#21712yes—
624C4C22×D3×Dic311yescharacteristic
625C4C2×D3×#6711yescharacteristic
626C3—21no—
627C3#7895611yescharacteristic, complemented
628C3#8407211yescharacteristic, complemented
629C2—22no—
630C2—62no—
631C2—62no—
632C2—124no—
633C2#1059531712yes—
634C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×Q8C22
socleC22×C32C22×D4
prime radicalC22×C3×#239C2
cosocleC2×C32×C4C24
hypercenterC22×Q8D32
hypocenterC32#2896
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. D3×#926C2semidirect
3. C2×D3×#208C2semidirect
4. #10592924C2semidirect
5. C3×#5225C2semidirect
6. #10591556C2semidirect
7. #10591550C2semidirect
8. #10591086C2semidirect
9. #10591085C2semidirect
16. C2×C3×#239C4semidirect
29. D3×C4⋊Dic3C22semidirect
32. #63841C22semidirect
33. C2×#3711C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63662C22semidirect
37. C3×#835C22semidirect
38. #63563C22semidirect
39. #63562C22semidirect
52. #5225D3semidirect
63. C2×C32×Q8C2×C4semidirect
73. C3×#239C2×C4semidirect
79. C2×C3×D12C2×C4semidirect
123. C2×#239Dic3semidirect
162. #835C2×D3semidirect
232. C2×C3×Q8C4×D3semidirect
233. C2×C3×Q8C2×Dic3semidirect
266. #239C2×Dic3semidirect
272. C2×D12C2×Dic3semidirect
470. C2×Q8D3×Dic3semidirect
553. C32#2896semidirect
627. C3#78956semidirect
628. C3#84072semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2392
D3×#9262
C2×D3×#2082
#105929242
C3×#52252
#105915562
#105915502
#105910862
#105910852
#840723
#789563