Finite Group Databasebeta

← #11807600

Subgroups — #11807600

Order 1152.

1707 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64146C211yesmaximal, characteristic
2C3×#5221C211yesmaximal, characteristic, complemented
3C3×#5220C211yesmaximal, characteristic, complemented
4#10591714C212yesmaximal, complemented
5#10591711C212yesmaximal, complemented
6#10591704C212yesmaximal, complemented
7#10591703C212yesmaximal, complemented
8#10591266C212yesmaximal, complemented
9#10591202C212yesmaximal, complemented
10#76434—31nomaximal
11#74882—31nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C22×#638C2212yes—
15C23×C3×Dic3C2211yescharacteristic, complemented
16C2×#3757C2211yescharacteristic
17#64146C418yescomplemented
18C2×#3752C2212yes—
19C2×C3×#217C2212yes—
20C2×C3×#217C2212yes—
21C2×C3×#217C2211yescharacteristic, complemented
22C2×C3×#217C2212yescomplemented
23C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
24C2×C3×C4×Dic3C2211yescharacteristic, complemented
25C2×#3724C2212yescomplemented
26C2×#3722C2212yes—
27C2×#3722C2212yes—
28C2×#3722C2212yes—
29C2×#3722C2212yes—
30C2×Dic32C2212yescomplemented
31C3×C3⋊#95C2212yescomplemented
32#63579C2212yescomplemented
33#63579C2212yescomplemented
34C2×#937—31no—
35C2×#937—31no—
36C2×#937—61no—
37C3×#390—31no—
38C3×#386—31no—
39#5221D311yescharacteristic, complemented
40#5220D311yescharacteristic, complemented
41#5213—32no—
42#4990—32no—
43#4958—32no—
44#4957—32no—
45#4957—32no—
46#4955—32no—
47#4955—32no—
48#4945—32no—
49#4944—32no—
50#4940—32no—
51#4670—32no—
52#4669—32no—
53C24×C32C2311yescharacteristic
54C24×C32C2311yescharacteristic
55C23×C3⋊D3—42no—
56C23×C3⋊D3—42no—
57C23×C3⋊D3—41no—
58C23×C3⋊D3—41no—
59C23×C3⋊D3C2×C414yescomplemented
60C23×C3⋊D3C2312yes—
61C2×C32×D4—41no—
62C2×C32×D4—41no—
63C2×C32×D4C2×C414yes—
64C22×C32×C4C2311yescharacteristic
65C2×#638—42no—
66C2×#638—42no—
67C2×#638C2×C418yes—
68C22×C3⋊Dic3C2312yes—
69C22×C3×Dic3—41no—
70C22×C3×Dic3—42no—
71C22×C3×Dic3C2312yes—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75#3757C2×C414yescomplemented
76#3752C2×C418yescomplemented
77C3×#217—42no—
78C3×#217—42no—
79C3×#217—41no—
80C3×#217—42no—
81C3×C4⋊Dic3—41no—
82C3×C4×Dic3—41no—
83#3724—42no—
84#3722—42no—
85#3722—42no—
86#3722—42no—
87#3722—42no—
88Dic32—42no—
89#2375—91noSylow
90C24×D3—31no—
91C24×D3—31no—
92C24×D3—61no—
93C22×C3×D4—21no—
94C22×C3×D4C2×D311yescharacteristic
95C22×C3×D4C2×D311yescharacteristic
96C23×C3×C4—31no—
97C22×#67—32no—
98C22×#67—32no—
99C22×#67—62no—
100C23×Dic3C2×D311yescharacteristic, complemented
101C2×C3×C4⋊C4—31no—
102C2×C3×C22⋊C4—32no—
103C2×C3×C22⋊C4—32no—
104C2×C3×C22⋊C4—31no—
105C2×C3×C22⋊C4—32no—
106C2×C3×C42—31no—
107C2×#217—31no—
108C2×#217—31no—
109C2×#217—61no—
110C2×#217C2×D312yes—
111C2×#217C2×D312yes—
112C2×#217C2×D311yescharacteristic, complemented
113C2×#217C2×D312yescomplemented
114#937—38no—
115#937—38no—
116#937—68no—
117C2×(C2×D3)⋊C4—32no—
118C2×(C2×D3)⋊C4—32no—
119C2×(C2×D3)⋊C4—32no—
120C2×(C2×D3)⋊C4—32no—
121C2×(C2×D3)⋊C4—32no—
122C2×(C2×D3)⋊C4—32no—
123C2×(C2×D3)⋊C4—32no—
124C2×(C2×D3)⋊C4—32no—
125C2×(C2×D3)⋊C4—32no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—62no—
128C2×C4⋊Dic3C2×D311yescharacteristic, complemented
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4—32no—
131C2×C4×Dic3—32no—
132C2×C4×Dic3—32no—
133C2×C4×Dic3C2×D311yescharacteristic, complemented
134C3×#95—32no—
135C3⋊#95—32no—
136C3⋊#95—32no—
137C3⋊#95—32no—
138C3⋊#95—32no—
139C3⋊#95C2×D312yescomplemented
140C23×C32—21no—
141C23×C32—21no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32—22no—
145C23×C32—21no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32C22×C412yes—
149C23×C32C22×C412yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—22no—
152C22×C3⋊D3—22no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—48no—
158C22×C3⋊D3—44no—
159C22×C3⋊D3—44no—
160C22×C3⋊D3—48no—
161C22×C3⋊D3—44no—
162C22×C3⋊D3C22×C414yes—
163C32×D4—44no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4C22×C412yes—
167#638—48no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C22×C414yes—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—22no—
180C2×C3×Dic3—22no—
181C2×C3×Dic3—22no—
182C2×C3×Dic3—22no—
183C2×C3×Dic3—44no—
184C2×#120—91no—
185#390—31no—
186#390—92no—
187#388—92no—
188#388—92no—
189#388—92no—
190#386—31no—
191#386—92no—
192#379—92no—
193C24×C3—21no—
194C24×C3—21no—
195C24×C3C22×D311yescharacteristic
196C24×C3C22×D311yescharacteristic
197C24×C3C22×D311yescharacteristic
198C24×C3C22×D311yescharacteristic
199C23×D3—32no—
200C23×D3—32no—
201C23×D3—34no—
202C23×D3—34no—
203C23×D3—62no—
204C23×D3—64no—
205C23×D3—121no—
206C23×D3—121no—
207C23×D3—121no—
208C23×D3—121no—
209C23×D3—122no—
210C23×D3—122no—
211C23×D3—122no—
212C23×D3—122no—
213C23×D3—124no—
214C23×D3—124no—
215C23×D3—122no—
216C23×D3—122no—
217C2×C3×D4—24no—
218C2×C3×D4—41no—
219C2×C3×D4—41no—
220C2×C3×D4—41no—
221C2×C3×D4—41no—
222C2×C3×D4—42no—
223C2×C3×D4—42no—
224C2×C3×D4C4×D314yes—
225C2×C3×D4C4×D314yes—
226C22×C3×C4—21no—
227C22×C3×C4—32no—
228C22×C3×C4—32no—
229C22×C3×C4—32no—
230C22×C3×C4—32no—
231C22×C3×C4—121no—
232C22×C3×C4—122no—
233C22×C3×C4C22×D311yescharacteristic
234C22×C3×C4C22×D311yescharacteristic
235C2×#67—38no—
236C2×#67—38no—
237C2×#67—68no—
238C2×#67—122no—
239C2×#67—122no—
240C2×#67—122no—
241C2×#67—122no—
242C2×#67—124no—
243C2×#67—124no—
244C22×Dic3—32no—
245C22×Dic3—32no—
246C22×Dic3—41no—
247C22×Dic3—42no—
248C22×Dic3—62no—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C3×C4⋊C4—121no—
254C3×C22⋊C4—121no—
255C3×C22⋊C4—122no—
256C3×C22⋊C4—122no—
257C3×C22⋊C4—122no—
258C3×C42—121no—
259#217—34no—
260#217—34no—
261#217—42no—
262#217—42no—
263#217—41no—
264#217—42no—
265#217—64no—
266(C2×D3)⋊C4—38no—
267(C2×D3)⋊C4—38no—
268(C2×D3)⋊C4—68no—
269(C2×D3)⋊C4—122no—
270(C2×D3)⋊C4—122no—
271(C2×D3)⋊C4—122no—
272(C2×D3)⋊C4—122no—
273(C2×D3)⋊C4—122no—
274(C2×D3)⋊C4—122no—
275(C2×D3)⋊C4—122no—
276(C2×D3)⋊C4—122no—
277C4⋊Dic3—41no—
278Dic3⋊C4—122no—
279Dic3⋊C4—122no—
280C4×Dic3—41no—
281C4×Dic3—122no—
282C4×Dic3—122no—
283C22×C32—22no—
284C22×C32—24no—
285C22×C32—22no—
286C22×C32—24no—
287C22×C32—41no—
288C22×C32—42no—
289C22×C32—41no—
290C22×C32—41no—
291C22×C32—42no—
292C22×C32—41no—
293C22×C32C23×C411yescharacteristic
294C22×C32H(5,𝔽2)11yescharacteristic
295C22×C32H(5,𝔽2)11yescharacteristic
296C22×C32H(5,𝔽2)12yes—
297C22×C32H(5,𝔽2)12yes—
298C2×C3⋊D3—24no—
299C2×C3⋊D3—24no—
300C2×C3⋊D3—24no—
301C2×C3⋊D3—416no—
302C2×C3⋊D3—42no—
303C2×C3⋊D3—42no—
304C2×C3⋊D3—42no—
305C2×C3⋊D3—42no—
306C32×C4—22no—
307C3⋊Dic3—24no—
308C3×Dic3—42no—
309C3×Dic3—42no—
310C3×Dic3—42no—
311C3×Dic3—42no—
312C25—91no—
313C22×D4—92no—
314C22×D4D3211yescharacteristic
315C23×C4—31no—
316#120—98no—
317C2×C4⋊C4—31no—
318C2×C4⋊C4—92no—
319C2×C22⋊C4—32no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—31no—
322C2×C22⋊C4—32no—
323C2×C22⋊C4—91no—
324C2×C22⋊C4—92no—
325C2×C22⋊C4—92no—
326C2×C22⋊C4—92no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4—92no—
329C2×C42—31no—
330C2×C42—92no—
331#95—32no—
332#95—92no—
333#95—92no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—21no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—21no—
341C23×C3—22no—
342C23×C3—21no—
343C23×C3—21no—
344C23×C3—21no—
345C23×C3—21no—
346C23×C3—21no—
347C23×C3—21no—
348C23×C3—22no—
349C23×C3—22no—
350C23×C3—22no—
351C23×C3—22no—
352C23×C3—21no—
353C23×C3—22no—
354C23×C3—22no—
355C23×C3—42no—
356C23×C3—42no—
357C23×C3—42no—
358C23×C3—42no—
359C23×C3—41no—
360C23×C3—41no—
361C23×C3C2×C4×D312yes—
362C23×C3C2×C4×D312yes—
363C23×C3C2×C4×D312yes—
364C23×C3C2×C4×D312yes—
365C23×C3C23×D311yescharacteristic
366C23×C3C23×D311yescharacteristic
367C22×D3—34no—
368C22×D3—34no—
369C22×D3—64no—
370C22×D3—64no—
371C22×D3—64no—
372C22×D3—62no—
373C22×D3—62no—
374C22×D3—62no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—62no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—62no—
382C22×D3—62no—
383C22×D3—62no—
384C22×D3—122no—
385C22×D3—122no—
386C22×D3—122no—
387C22×D3—122no—
388C22×D3—124no—
389C22×D3—124no—
390C22×D3—128no—
391C22×D3—128no—
392C22×D3—1216no—
393C22×D3—128no—
394C22×D3—128no—
395C22×D3—1216no—
396C22×D3—128no—
397C22×D3—124no—
398C22×D3—124no—
399C22×D3—124no—
400C22×D3—124no—
401C22×D3—128no—
402C22×D3—128no—
403C3×D4—44no—
404C3×D4—44no—
405C3×D4—48no—
406C2×C3×C4—21no—
407C2×C3×C4—21no—
408C2×C3×C4—21no—
409C2×C3×C4—21no—
410C2×C3×C4—22no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—62no—
419C2×C3×C4—62no—
420C2×C3×C4—62no—
421C2×C3×C4—62no—
422C2×C3×C4—62no—
423C2×C3×C4—62no—
424C2×C3×C4—62no—
425C2×C3×C4—124no—
426C2×C3×C4C2×C4×D312yes—
427C2×C3×C4C2×C4×D312yes—
428#67—128no—
429#67—128no—
430#67—1216no—
431C2×Dic3—22no—
432C2×Dic3—22no—
433C2×Dic3—22no—
434C2×Dic3—22no—
435C2×Dic3—22no—
436C2×Dic3—22no—
437C2×Dic3—22no—
438C2×Dic3—22no—
439C2×Dic3—22no—
440C2×Dic3—22no—
441C2×Dic3—22no—
442C2×Dic3—22no—
443C2×Dic3—34no—
444C2×Dic3—34no—
445C2×Dic3—44no—
446C2×Dic3—64no—
447C2×Dic3—62no—
448C2×Dic3—62no—
449C2×Dic3—62no—
450C2×Dic3—62no—
451C2×Dic3—122no—
452C2×Dic3—122no—
453C2×C32—42no—
454C2×C32—42no—
455C2×C32#51811yescharacteristic
456C2×C32#51812yes—
457C2×C32#56011yescharacteristic
458C2×C32#56012yes—
459C2×C32H(3,𝔽4)11yescharacteristic
460C3⋊D3—44no—
461C24—92no—
462C24—94no—
463C24—362no—
464C24—362no—
465C24—361no—
466C24—361no—
467C24C2×D3211yescharacteristic
468C24C2×D3211yescharacteristic
469C2×D4—41no—
470C2×D4—41no—
471C2×D4—98no—
472C2×D4—362no—
473C2×D4—362no—
474C2×D4#62414yes—
475C22×C4—32no—
476C22×C4—32no—
477C22×C4—32no—
478C22×C4—32no—
479C22×C4—92no—
480C22×C4—122no—
481C22×C4—121no—
482C22×C4C2×D3211yescharacteristic
483C4⋊C4—121no—
484C4⋊C4—362no—
485C22⋊C4—94no—
486C22⋊C4—98no—
487C22⋊C4—122no—
488C22⋊C4—122no—
489C22⋊C4—122no—
490C22⋊C4—121no—
491C22⋊C4—362no—
492C22⋊C4—362no—
493C22⋊C4—362no—
494C22⋊C4—362no—
495C42—121no—
496C42—362no—
497C22×C3—24no—
498C22×C3—22no—
499C22×C3—22no—
500C22×C3—22no—
501C22×C3—22no—
502C22×C3—24no—
503C22×C3—24no—
504C22×C3—24no—
505C22×C3—24no—
506C22×C3—22no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—44no—
512C22×C3—44no—
513C22×C3—42no—
514C22×C3—42no—
515C22×C3—44no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—41no—
524C22×C3—41no—
525C22×C3—42no—
526C22×C3—42no—
527C22×C3—42no—
528C22×C3—42no—
529C22×C3—81no—
530C22×C3—82no—
531C22×C3—81no—
532C22×C3C22×C4×D311yescharacteristic
533C22×C3C22×C4×D311yescharacteristic
534C22×C3#100412yes—
535C22×C3#100412yes—
536C22×C3#100411yescharacteristic
537C22×C3#100411yescharacteristic
538C22×C3#100411yescharacteristic
539C22×C3#100411yescharacteristic
540C22×C3#100912yes—
541C22×C3#100912yes—
542C2×D3—68no—
543C2×D3—64no—
544C2×D3—64no—
545C2×D3—64no—
546C2×D3—64no—
547C2×D3—64no—
548C2×D3—64no—
549C2×D3—124no—
550C2×D3—124no—
551C2×D3—124no—
552C2×D3—124no—
553C2×D3—124no—
554C2×D3—124no—
555C2×D3—1232no—
556C2×D3—1216no—
557C2×D3—1216no—
558C2×D3—122no—
559C2×D3—122no—
560C2×D3—122no—
561C2×D3—122no—
562C2×D3—122no—
563C2×D3—122no—
564C2×D3—122no—
565C2×D3—122no—
566C3×C4—22no—
567C3×C4—22no—
568C3×C4—42no—
569C3×C4—122no—
570C3×C4—122no—
571C3×C4—122no—
572C3×C4—122no—
573Dic3—42no—
574Dic3—42no—
575Dic3—42no—
576Dic3—42no—
577Dic3—64no—
578Dic3—64no—
579Dic3—124no—
580C32#237511yescharacteristic, complemented, Sylow
581C23—22no—
582C23—22no—
583C23—22no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—94no—
590C23—182no—
591C23—182no—
592C23—182no—
593C23—182no—
594C23—182no—
595C23—182no—
596C23—368no—
597C23—364no—
598C23—364no—
599C23—368no—
600C23—364no—
601C23C2×#62412yes—
602C23C2×#62412yes—
603C23C22×D3211yescharacteristic
604D4—44no—
605D4—368no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—62no—
614C2×C4—62no—
615C2×C4—62no—
616C2×C4—62no—
617C2×C4—62no—
618C2×C4—62no—
619C2×C4—62no—
620C2×C4—94no—
621C2×C4—124no—
622C2×C4—182no—
623C2×C4—182no—
624C2×C4C2×#62412yes—
625C2×C3—22no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—22no—
629C2×C3—21no—
630C2×C3—44no—
631C2×C3—42no—
632C2×C3—42no—
633C2×C3—42no—
634C2×C3—42no—
635C2×C3—82no—
636C2×C3#548611yescharacteristic
637C2×C3#548611yescharacteristic
638C2×C3#554512yes—
639C2×C3#554512yes—
640C2×C3#559411yescharacteristic
641C2×C3#562012yes—
642C2×C3#562012yes—
643C2×C3#566611yescharacteristic
644C2×C3#568311yescharacteristic
645C2×C3#572011yescharacteristic
646D3—128no—
647D3—124no—
648D3—124no—
649C22—24no—
650C22—24no—
651C22—22no—
652C22—22no—
653C22—41no—
654C22—41no—
655C22—42no—
656C22—42no—
657C22—41no—
658C22—41no—
659C22—184no—
660C22—184no—
661C22—184no—
662C22—3616no—
663C22—362no—
664C22—362no—
665C22—362no—
666C22—362no—
667C22#6431412yes—
668C22#6431412yes—
669C22C22×#62411yescharacteristic
670C22#6433011yescharacteristic
671C22#6433011yescharacteristic
672C4—22no—
673C4—122no—
674C4—122no—
675C4—122no—
676C4—122no—
677C4—184no—
678C3—21no—
679C3#7488211yescharacteristic, complemented
680C3#7643411yescharacteristic, complemented
681C2—42no—
682C2—42no—
683C2—364no—
684C2#1059522312yes—
685C2#1059526211yescharacteristic
686C2#1059526412yes—
687C2#1059526611yescharacteristic
688C2#1059551011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC22×C32×D4C22
socle, cosocleC23×C32C24
prime radicalC2×#64146C2
hypercenterC22×D4D32
hypocenterC32#2375
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
2. C3×#5221C2semidirect
3. C3×#5220C2semidirect
4. #10591714C2semidirect
5. #10591711C2semidirect
6. #10591704C2semidirect
7. #10591703C2semidirect
8. #10591266C2semidirect
9. #10591202C2semidirect
15. C23×C3×Dic3C22semidirect
17. #64146C4semidirect
21. C2×C3×#217C22semidirect
22. C2×C3×#217C22semidirect
23. C2×C3×C4⋊Dic3C22semidirect
24. C2×C3×C4×Dic3C22semidirect
25. C2×#3724C22semidirect
30. C2×Dic32C22semidirect
31. C3×C3⋊#95C22semidirect
32. #63579C22semidirect
33. #63579C22semidirect
39. #5221D3semidirect
40. #5220D3semidirect
59. C23×C3⋊D3C2×C4semidirect
75. #3757C2×C4semidirect
76. #3752C2×C4semidirect
100. C23×Dic3C2×D3semidirect
112. C2×#217C2×D3semidirect
113. C2×#217C2×D3semidirect
128. C2×C4⋊Dic3C2×D3semidirect
133. C2×C4×Dic3C2×D3semidirect
139. C3⋊#95C2×D3semidirect
580. C32#2375semidirect
679. C3#74882semidirect
680. C3#76434semidirect

Maximal subgroups

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

subgroupindex
C2×#641462
C3×#52212
C3×#52202
#105917142
#105917112
#105917042
#105917032
#105912662
#105912022
#764343
#748823