Finite Group Databasebeta

← #11857960

Subgroups — #11857960

Order 1152.

1639 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#237C211yesmaximal, characteristic
2D3×#926C211yesmaximal, characteristic, complemented
3C2×D3×#208C211yesmaximal, characteristic, complemented
4#10592914C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591420C214yesmaximal, complemented
7#10591414C214yesmaximal, complemented
8#10591100C211yesmaximal, characteristic, complemented
9#10591099C211yesmaximal, characteristic, complemented
10#84072—31nomaximal
11#78924—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×C3×#67—21no—
14C23×C3×Dic3—21no—
15C2×C3×#237—21no—
16C2×C3×#237—21no—
17C2×C3×#237—24no—
18C2×C3×#237C418yescomplemented
19C2×C3×#237C2212yes—
20C2×C3×#237C2212yes—
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
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#63659C2214yescomplemented
37C3×#832C2214yescomplemented
38#63566C2214yescomplemented
39#63565C2214yescomplemented
40C22×C3×#41—31no—
41C22×#237D311yescharacteristic
42C2×#926—31no—
43C22×#208—31no—
44C2×D3×M16—31no—
45D3×#117—31no—
46C3×#418—31no—
47#5233—34no—
48#5232—34no—
49#5225—31no—
50#5225—31no—
51#5215—31no—
52#5215—31no—
53#5215—61no—
54#5215D311yescharacteristic, complemented
55#5120—31no—
56#5004—31no—
57#4772—34no—
58#4771—34no—
59C24×C32—21no—
60C23×C3×D3D411yescharacteristic
61C2×C32×D4—21no—
62C2×C32×D4—22no—
63C2×C32×D4C2×C414yescomplemented
64C2×C32×D4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×C3×#67—28no—
67C2×C3×#67—22no—
68C2×C3×#67—22no—
69C22×C3×Dic3—21no—
70C22×C3×Dic3—28no—
71C22×C3×Dic3—22no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3D411yescharacteristic
74C3×#237—28no—
75C3×#237—28no—
76C3×#237—24no—
77C3×#237—24no—
78C3×#237C2×C418yes—
79C3×#237C2×C418yescomplemented
80C2×C3×C4×D3C2×C414yes—
81C2×C3×C4×D3D411yescharacteristic
82C2×C3×C4×D3D411yescharacteristic
83C2×C3×C4×D3D414yes—
84C2×C3×C4×D3C2311yescharacteristic
85C2×C3×C4×D3C2311yescharacteristic
86C2×C3×Dic6—21no—
87C2×C3×Dic6—22no—
88C2×C3×Dic6C2×C414yescomplemented
89C2×C3×Dic6C2312yes—
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—31no—
114C22×C3×D4—21no—
115C22×C3×D4—61no—
116C22×C3×D4C2×D311yescharacteristic
117C22×C3×D4C2×D311yescharacteristic
118C23×C3×C4—31no—
119C23×C3×C4—61no—
120C22×#67—21no—
121C23×Dic3—21no—
122C2×#237—21no—
123C2×#237—21no—
124C2×#237—24no—
125C2×#237Dic318yescomplemented
126C2×#237C2×D312yes—
127C2×#237C2×D312yes—
128C22×C4×D3C2×D311yescharacteristic
129C22×Dic6C2×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×#102—34no—
159#835—34no—
160#835—34no—
161#832—34no—
162#832—34no—
163#832—64no—
164#832C2×D314yescomplemented
165#816—34no—
166#810—34no—
167C23×C32—24no—
168C23×C32—22no—
169C23×C32—44no—
170C23×C32C2×D411yescharacteristic
171C22×C3×D3—42no—
172C22×C3×D3C22⋊C414yes—
173C22×C3×D3C2×D411yescharacteristic
174C22×C3×D3C2×D411yescharacteristic
175C32×D4—24no—
176C32×D4—22no—
177C32×D4C22×C414yes—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182C2×C3⋊Dic3—22no—
183C3×#67—28no—
184C3×#67—28no—
185C2×C3×Dic3—24no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—28no—
188C2×C3×Dic3—28no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3C22⋊C414yes—
191C2×C3×Dic3C2×D411yescharacteristic
192C2×C3×Dic3C2×D411yescharacteristic
193C3×C4×D3C22⋊C414yes—
194C3×C4×D3C22⋊C414yes—
195C3×C4×D3C22×C412yes—
196C3×C4×D3C22×C412yes—
197C3×C4×D3C2×D412yes—
198C3×C4×D3C2×D412yes—
199C3×Dic6—24no—
200C3×Dic6—22no—
201C3×Dic6C22×C414yes—
202D3×Dic3—44no—
203C3⋊(C3⋊C8)—22no—
204C3×C3⋊C8—22no—
205C22×#41—31no—
206C22×M16—91no—
207C2×#117—91no—
208#419—91no—
209#419—91no—
210#418—31no—
211#418—91no—
212#417—94no—
213#416—94no—
214C24×C3—21no—
215C24×C3—21no—
216C24×C3—31no—
217C24×C3—41no—
218C23×D3#6711yescharacteristic
219C3×#41—38no—
220C3×#41—38no—
221C3×#41—68no—
222C3×#41—68no—
223C3×#41—64no—
224C3×#41—64no—
225C2×C3×Q8—34no—
226C2×C3×Q8—32no—
227C2×C3×Q8—62no—
228C2×C3×Q8—61no—
229C2×C3×D4—21no—
230C2×C3×D4—22no—
231C2×C3×D4—21no—
232C2×C3×D4—22no—
233C2×C3×D4—24no—
234C2×C3×D4—22no—
235C2×C3×D4—42no—
236C2×C3×D4—41no—
237C2×C3×D4—68no—
238C2×C3×D4—62no—
239C2×C3×D4—62no—
240C2×C3×D4C4×D314yescomplemented
241C2×C3×D4C2×Dic314yescomplemented
242C2×C3×D4C22×D312yes—
243C2×C3×D4C22×D312yes—
244C22×C3×C4—21no—
245C22×C3×C4—31no—
246C22×C3×C4—34no—
247C22×C3×C4—34no—
248C22×C3×C4—31no—
249C22×C3×C4—31no—
250C22×C3×C4—31no—
251C22×C3×C4—31no—
252C22×C3×C4—68no—
253C22×C3×C4—62no—
254C22×C3×C4—62no—
255C22×C3×C4—61no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—28no—
259C2×#67—22no—
260C2×#67—22no—
261C22×Dic3—21no—
262C22×Dic3—28no—
263C22×Dic3—22no—
264C22×Dic3—22no—
265C22×Dic3—62no—
266C22×Dic3#6711yescharacteristic
267#237—28no—
268#237—28no—
269#237—24no—
270#237—24no—
271#237C2×Dic318yes—
272#237C2×Dic318yescomplemented
273C2×C4×D3—62no—
274C2×C4×D3C2×Dic314yes—
275C2×C4×D3#6711yescharacteristic
276C2×C4×D3#6711yescharacteristic
277C2×C4×D3#6714yes—
278C2×C4×D3C22×D311yescharacteristic
279C2×C4×D3C22×D311yescharacteristic
280C2×Dic6—21no—
281C2×Dic6—22no—
282C2×Dic6C2×Dic314yescomplemented
283C2×Dic6C22×D312yes—
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×C32—24no—
321C22×C32—48no—
322C22×C32—44no—
323C22×C32C2×C22⋊C412yes—
324C22×C32C22×D411yescharacteristic
325C2×C3×D3—22no—
326C2×C3×D3—22no—
327C2×C3×D3—44no—
328C2×C3×D3C2×C22⋊C412yes—
329C2×C3×D3C2×C22⋊C412yes—
330C32×C4C2×C22⋊C412yes—
331C32×C4C23×C411yescharacteristic
332C32×C4C22×D411yescharacteristic
333C3⋊Dic3—42no—
334C3×Dic3—24no—
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×Q8—31no—
345C22×D4—61no—
346C22×D4D3211yescharacteristic
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—94no—
363#103—94no—
364#102—34no—
365#102—94no—
366C23×C3—24no—
367C23×C3—24no—
368C23×C3—22no—
369C23×C3—22no—
370C23×C3—21no—
371C23×C3—31no—
372C23×C3—31no—
373C23×C3—34no—
374C23×C3—42no—
375C23×C3—44no—
376C23×C3—44no—
377C23×C3—44no—
378C23×C3—84no—
379C23×C3—122no—
380C23×C3D3×D411yescharacteristic
381C23×C3C2×#6711yescharacteristic
382C22×D3—42no—
383C22×D3#21714yes—
384C22×D3C2×#6711yescharacteristic
385C22×D3C2×#6711yescharacteristic
386C3×Q8—34no—
387C3×Q8—64no—
388C3×Q8—62no—
389C3×D4—24no—
390C3×D4—24no—
391C3×D4—22no—
392C3×D4—22no—
393C3×D4—24no—
394C3×D4—42no—
395C3×D4—44no—
396C3×D4—68no—
397C3×D4—68no—
398C3×D4C2×C4×D314yes—
399C3×D4C22×Dic314yes—
400C2×C3×C4—21no—
401C2×C3×C4—22no—
402C2×C3×C4—22no—
403C2×C3×C4—21no—
404C2×C3×C4—34no—
405C2×C3×C4—31no—
406C2×C3×C4—31no—
407C2×C3×C4—34no—
408C2×C3×C4—34no—
409C2×C3×C4—32no—
410C2×C3×C4—32no—
411C2×C3×C4—32no—
412C2×C3×C4—32no—
413C2×C3×C4—68no—
414C2×C3×C4—68no—
415C2×C3×C4—64no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4C2×C4×D312yes—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D412yes—
421C2×C3×C4C22×Dic312yes—
422C2×C3×C4C2×#6711yescharacteristic
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—28no—
427#67—28no—
428C2×Dic3—24no—
429C2×Dic3—22no—
430C2×Dic3—28no—
431C2×Dic3—28no—
432C2×Dic3—22no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—122no—
436C2×Dic3—124no—
437C2×Dic3#21714yes—
438C2×Dic3C2×#6711yescharacteristic
439C2×Dic3C2×#6711yescharacteristic
440C4×D3—124no—
441C4×D3#21714yes—
442C4×D3#21714yes—
443C4×D3C22×Dic312yes—
444C4×D3C22×Dic312yes—
445C4×D3C2×#6712yes—
446C4×D3C2×#6712yes—
447Dic6—24no—
448Dic6—22no—
449Dic6C22×Dic314yes—
450C3×C8—62no—
451C3⋊C8—22no—
452C3⋊C8—62no—
453C3⋊C8—62no—
454C3⋊C8—122no—
455C2×C32—22no—
456C2×C32—44no—
457C2×C32C22×C22⋊C411yescharacteristic
458C2×C32#57512yes—
459C3×D3—22no—
460C3×D3—22no—
461C24—21no—
462C24—31no—
463#41—38no—
464#41—38no—
465#41—64no—
466#41—64no—
467#41—68no—
468#41—68no—
469C2×Q8—32no—
470C2×Q8—34no—
471C2×Q8—61no—
472C2×Q8—62no—
473C2×D4—22no—
474C2×D4—21no—
475C2×D4—62no—
476C2×D4—62no—
477C2×D4—68no—
478C2×D4D3×Dic314yescomplemented
479C2×D4C2×D3212yes—
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—61no—
491C22×C4—182no—
492C22×C4C2×D3211yescharacteristic
493M16—62no—
494M16—184no—
495M16—182no—
496C2×C8—32no—
497C2×C8—92no—
498C2×C8—184no—
499C4⋊C4—32no—
500C4⋊C4—92no—
501C4⋊C4—182no—
502C22⋊C4—61no—
503C22⋊C4—182no—
504C22⋊C4—181no—
505C42—61no—
506C42—182no—
507C42—181no—
508C22×C3—22no—
509C22×C3—22no—
510C22×C3—24no—
511C22×C3—24no—
512C22×C3—21no—
513C22×C3—22no—
514C22×C3—32no—
515C22×C3—32no—
516C22×C3—42no—
517C22×C3—44no—
518C22×C3—48no—
519C22×C3—48no—
520C22×C3—44no—
521C22×C3—44no—
522C22×C3—62no—
523C22×C3—62no—
524C22×C3—84no—
525C22×C3—88no—
526C22×C3—124no—
527C22×C3D3×C22⋊C412yes—
528C22×C3C2×#21712yes—
529C22×C3C2×D3×D411yescharacteristic
530C22×C3C22×#6711yescharacteristic
531C2×D3—22no—
532C2×D3—22no—
533C2×D3—44no—
534C2×D3C2×#21712yes—
535C2×D3C2×#21712yes—
536C3×C4—21no—
537C3×C4—21no—
538C3×C4—22no—
539C3×C4—32no—
540C3×C4—32no—
541C3×C4—64no—
542C3×C4—122no—
543C3×C4D3×C22⋊C412yes—
544C3×C4C2×#21712yes—
545C3×C4C22×C4×D311yescharacteristic
546C3×C4C2×D3×D411yescharacteristic
547C3×C4C23×Dic311yescharacteristic
548C3×C4C22×#6711yescharacteristic
549Dic3—24no—
550Dic3—42no—
551Dic3—122no—
552Dic3—122no—
553Dic3—242no—
554Dic3C2×#21712yes—
555Dic3C2×#21712yes—
556C32#289611yescharacteristic, complemented, Sylow
557C23—22no—
558C23—24no—
559C23—31no—
560C23—31no—
561C23—34no—
562C23—44no—
563C23—122no—
564C23D3×#6711yescharacteristic
565Q8—34no—
566Q8—62no—
567Q8—64no—
568D4—22no—
569D4—24no—
570D4—68no—
571D4—68no—
572D4C2×D3×Dic314yes—
573C2×C4—31no—
574C2×C4—31no—
575C2×C4—34no—
576C2×C4—32no—
577C2×C4—32no—
578C2×C4—32no—
579C2×C4—32no—
580C2×C4—34no—
581C2×C4—34no—
582C2×C4—68no—
583C2×C4—68no—
584C2×C4—62no—
585C2×C4—64no—
586C2×C4—62no—
587C2×C4—182no—
588C2×C4—364no—
589C2×C4C2×D3×Dic312yes—
590C2×C4D3×#6712yes—
591C2×C4D3×#6711yescharacteristic
592C2×C4C22×D3211yescharacteristic
593C8—62no—
594C8—182no—
595C2×C3—22no—
596C2×C3—22no—
597C2×C3—22no—
598C2×C3—21no—
599C2×C3—42no—
600C2×C3—44no—
601C2×C3—44no—
602C2×C3—62no—
603C2×C3—62no—
604C2×C3—84no—
605C2×C3C2×D3×C22⋊C411yescharacteristic
606C2×C3#577312yes—
607C2×C3#582212yes—
608C2×C3C22×#21711yescharacteristic
609D3—22no—
610D3—22no—
611C22—22no—
612C22—24no—
613C22—32no—
614C22—32no—
615C22—48no—
616C22—44no—
617C22—62no—
618C22—62no—
619C22—124no—
620C22D3×#21712yes—
621C22C2×D3×#6711yescharacteristic
622C4—32no—
623C4—32no—
624C4—64no—
625C4—122no—
626C4—362no—
627C4D3×#21712yes—
628C4C22×D3×Dic311yescharacteristic
629C4C2×D3×#6711yescharacteristic
630C3—21no—
631C3#7892411yescharacteristic, complemented
632C3#8407211yescharacteristic, complemented
633C2—22no—
634C2—44no—
635C2—62no—
636C2—62no—
637C2#1059509512yes—
638C2C2×D3×#21711yescharacteristic
subgroupG/H
centerC22C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
prime radicalC22×C3×#237C2
cosocleC2×C32×C4C24
hypercenterC22×D4D32
hypocenterC32#2896
LCSG ▷ 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. D3×#926C2semidirect
3. C2×D3×#208C2semidirect
4. #10592914C2semidirect
5. C3×#5215C2semidirect
6. #10591420C2semidirect
7. #10591414C2semidirect
8. #10591100C2semidirect
9. #10591099C2semidirect
18. C2×C3×#237C4semidirect
29. D3×C4⋊Dic3C22semidirect
32. #63841C22semidirect
33. C2×#3711C22semidirect
35. C2×D3×C3⋊C8C22semidirect
36. #63659C22semidirect
37. C3×#832C22semidirect
38. #63566C22semidirect
39. #63565C22semidirect
54. #5215D3semidirect
63. C2×C32×D4C2×C4semidirect
79. C3×#237C2×C4semidirect
88. C2×C3×Dic6C2×C4semidirect
125. C2×#237Dic3semidirect
164. #832C2×D3semidirect
240. C2×C3×D4C4×D3semidirect
241. C2×C3×D4C2×Dic3semidirect
272. #237C2×Dic3semidirect
282. C2×Dic6C2×Dic3semidirect
478. C2×D4D3×Dic3semidirect
556. C32#2896semidirect
631. C3#78924semidirect
632. C3#84072semidirect

Maximal subgroups

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

subgroupindex
C22×C3×#2372
D3×#9262
C2×D3×#2082
#105929142
C3×#52152
#105914202
#105914142
#105911002
#105910992
#840723
#789243