Finite Group Databasebeta

← #11811933

Subgroups — #11811933

Order 1152.

4044 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×#64149C212yesmaximal, complemented
3C2×#64146C212yesmaximal, complemented
4C2×#64093C211yesmaximal, characteristic, complemented
5C2×#64091C212yesmaximal, complemented
6C32×#392C211yesmaximal, characteristic, complemented
7#10592922C211yesmaximal, characteristic, complemented
8#10592659C211yesmaximal, characteristic, complemented
9#10592656C212yesmaximal, complemented
10#10592370C211yesmaximal, characteristic, complemented
11#10592365C211yesmaximal, characteristic, complemented
12#76673—34nomaximal
13C24×C3⋊D3C2212yes—
14C22×C32×D4C2211yescharacteristic
15C22×C32×D4C2212yescomplemented
16C22×#638C2211yescharacteristic
17C22×#638C2212yes—
18C22×#638C2211yescharacteristic, complemented
19C22×#638C2212yescomplemented
20C22×#638C2212yescomplemented
21C2×D4×C3⋊D3—28no—
22C2×D4×C3⋊D3—24no—
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C4⋊(C3⋊D3)C2211yescharacteristic
25C22×C4⋊(C3⋊D3)C2212yescomplemented
26C22×C4×C3⋊D3C2211yescharacteristic
27C2×C32×C22⋊C4C2212yescomplemented
28C2×C32×C22⋊C4C2211yescharacteristic, complemented
29C2×#3757C2212yescomplemented
30#64149—28no—
31#64146—28no—
32C2×#3752C2212yes—
33C2×#3752C2211yescharacteristic, complemented
34C2×#3752C2212yescomplemented
35C2×#3752C2212yescomplemented
36C2×#3750C2211yescharacteristic, complemented
37C2×C4×C3⋊Dic3C2212yescomplemented
38#64093—24no—
39#64091—28no—
40C32×#95C2211yescharacteristic, complemented
41#63658C2211yescharacteristic, complemented
42C22×D3×D4—34no—
43C2×#940—38no—
44C2×#937—38no—
45C2×#884—34no—
46C2×#882—38no—
47C3×#392D314yescomplemented
48#5223—34no—
49#4960—34no—
50#4957—38no—
51#4671—34no—
52#4666—34no—
53C24×C32C2311yescharacteristic
54C24×C32C2312yes—
55C23×C3⋊D3—24no—
56C23×C3⋊D3—24no—
57C23×C3⋊D3—24no—
58C23×C3⋊D3—24no—
59C23×C3⋊D3—24no—
60C23×C3⋊D3—42no—
61C23×C3⋊D3—42no—
62C23×C3⋊D3C2311yescharacteristic
63C23×C3⋊D3C2312yes—
64C23×C3⋊D3C2311yescharacteristic
65C2×C32×D4—24no—
66C2×C32×D4—24no—
67C2×C32×D4—22no—
68C2×C32×D4—24no—
69C2×C32×D4—42no—
70C22×C32×C4C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2312yes—
73C2×#638—24no—
74C2×#638—22no—
75C2×#638—24no—
76C2×#638—24no—
77C2×#638—24no—
78C2×#638—24no—
79C2×#638—22no—
80C2×#638—24no—
81C2×#638—24no—
82C2×#638—24no—
83C2×#638—42no—
84C2×#638—42no—
85C2×#638D418yescomplemented
86C22×C3⋊Dic3C2311yescharacteristic
87C22×C3⋊Dic3C2312yes—
88C22×C3⋊Dic3C2311yescharacteristic
89D4×C3⋊D3—232no—
90C2×C4⋊(C3⋊D3)—24no—
91C2×C4⋊(C3⋊D3)—22no—
92C2×C4⋊(C3⋊D3)—24no—
93C2×C4⋊(C3⋊D3)—22no—
94C2×C4⋊(C3⋊D3)—24no—
95C2×C4⋊(C3⋊D3)—24no—
96C2×C4⋊(C3⋊D3)—42no—
97C2×C4×C3⋊D3—24no—
98C2×C4×C3⋊D3D414yescomplemented
99C32×C22⋊C4—22no—
100C32×C22⋊C4—24no—
101#3757—24no—
102#3752—22no—
103#3752—24no—
104#3752—24no—
105#3752D418yescomplemented
106#3750—22no—
107C4×C3⋊Dic3—24no—
108#2433—91noSylow
109C24×D3—38no—
110C22×C3×D4C2×D314yes—
111C22×C3×D4C2×D318yescomplemented
112C22×#67—38no—
113C22×#67—34no—
114C22×#67—34no—
115C22×#67—38no—
116C22×#67—38no—
117C2×D3×D4—616no—
118C2×D3×D4—632no—
119C22×D12—34no—
120C22×D12—34no—
121C22×D12—38no—
122C22×C4×D3—34no—
123C2×C3×C22⋊C4C2×D318yescomplemented
124C2×C3×C22⋊C4C2×D314yescomplemented
125C2×#217—38no—
126#940—632no—
127#937—632no—
128C2×(C2×D3)⋊C4—38no—
129C2×(C2×D3)⋊C4—38no—
130C2×(C2×D3)⋊C4—34no—
131C2×(C2×D3)⋊C4—38no—
132C2×Dic3⋊C4—34no—
133C2×C4×Dic3—38no—
134#884—616no—
135#882—632no—
136C3×#95C2×D314yescomplemented
137C3⋊#95—34no—
138C23×C32—22no—
139C23×C32—22no—
140C23×C32—22no—
141C23×C32—22no—
142C23×C32—22no—
143C23×C32—22no—
144C23×C32—21no—
145C23×C32—22no—
146C23×C32—22no—
147C23×C32—21no—
148C23×C32—21no—
149C23×C32C2×D414yes—
150C23×C32C2411yescharacteristic
151C22×C3⋊D3—22no—
152C22×C3⋊D3—21no—
153C22×C3⋊D3—21no—
154C22×C3⋊D3—216no—
155C22×C3⋊D3—22no—
156C22×C3⋊D3—22no—
157C22×C3⋊D3—22no—
158C22×C3⋊D3—22no—
159C22×C3⋊D3—22no—
160C22×C3⋊D3—22no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—22no—
163C22×C3⋊D3—22no—
164C22×C3⋊D3—21no—
165C22×C3⋊D3—21no—
166C22×C3⋊D3—48no—
167C22×C3⋊D3—48no—
168C22×C3⋊D3—48no—
169C22×C3⋊D3—48no—
170C22×C3⋊D3—48no—
171C22×C3⋊D3—48no—
172C22×C3⋊D3C2×D414yes—
173C22×C3⋊D3C2×D414yes—
174C22×C3⋊D3C2×D412yes—
175C32×D4—28no—
176C32×D4—48no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4—22no—
180C2×C32×C4—21no—
181C2×C32×C4—22no—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2×D414yescomplemented
184#638—216no—
185#638—48no—
186#638—48no—
187#638—44no—
188#638—44no—
189C2×C3⋊Dic3—22no—
190C2×C3⋊Dic3—22no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—22no—
193C2×C3⋊Dic3C2×D414yes—
194C2×C3⋊Dic3C2×D412yes—
195C2×C3⋊Dic3C2×D414yescomplemented
196C4⋊(C3⋊D3)—28no—
197C4⋊(C3⋊D3)—48no—
198C4⋊(C3⋊D3)—44no—
199C4×C3⋊D3—28no—
200C23×D4—91no—
201C2×#127—92no—
202C2×#121—91no—
203C2×#120—92no—
204C2×#120—92no—
205#392—91no—
206#392—91no—
207#392—91no—
208#392C3⋊D311yescharacteristic, complemented
209#390—92no—
210C4×C22⋊C4—91no—
211C24×C3C22×D314yes—
212C24×C3C22×D318yes—
213C23×D3—34no—
214C23×D3—38no—
215C23×D3—34no—
216C23×D3—616no—
217C23×D3—616no—
218C23×D3—616no—
219C23×D3—616no—
220C23×D3—616no—
221C23×D3—128no—
222C23×D3—128no—
223C2×C3×D4—216no—
224C2×C3×D4—216no—
225C2×C3×D4—28no—
226C2×C3×D4—216no—
227C2×C3×D4—48no—
228C22×C3×C4C22×D314yes—
229C22×C3×C4C22×D314yes—
230C22×C3×C4C22×D318yes—
231C2×#67—332no—
232C2×#67—616no—
233C2×#67—616no—
234C2×#67—616no—
235C2×#67—68no—
236C2×#67—616no—
237C2×#67—616no—
238C2×#67—68no—
239C2×#67—616no—
240C2×#67—616no—
241C2×#67—616no—
242C2×#67—128no—
243C2×#67—128no—
244C22×Dic3—34no—
245C22×Dic3—38no—
246C22×Dic3—34no—
247D3×D4—6128no—
248C2×D12—616no—
249C2×D12—68no—
250C2×D12—616no—
251C2×D12—68no—
252C2×D12—616no—
253C2×D12—616no—
254C2×D12—128no—
255C2×C4×D3—316no—
256C2×C4×D3—616no—
257C3×C22⋊C4—28no—
258C3×C22⋊C4—216no—
259#217—616no—
260(C2×D3)⋊C4—332no—
261(C2×D3)⋊C4—616no—
262(C2×D3)⋊C4—68no—
263(C2×D3)⋊C4—616no—
264Dic3⋊C4—68no—
265C4×Dic3—616no—
266C22×C32—24no—
267C22×C32—24no—
268C22×C32—24no—
269C22×C32—42no—
270C22×C32—42no—
271C22×C32—42no—
272C22×C32—42no—
273C22×C32—41no—
274C22×C32—41no—
275C22×C32—41no—
276C22×C32—42no—
277C22×C32—42no—
278C22×C32C22×D411yescharacteristic
279C22×C32C22×D412yes—
280C22×C32C22×D412yes—
281C22×C32H(5,𝔽2)11yescharacteristic
282C22×C32H(5,𝔽2)11yescharacteristic
283C2×C3⋊D3—22no—
284C2×C3⋊D3—22no—
285C2×C3⋊D3—24no—
286C2×C3⋊D3—24no—
287C2×C3⋊D3—24no—
288C2×C3⋊D3—24no—
289C2×C3⋊D3—24no—
290C2×C3⋊D3—432no—
291C2×C3⋊D3—42no—
292C2×C3⋊D3—42no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—41no—
296C2×C3⋊D3—41no—
297C2×C3⋊D3—41no—
298C2×C3⋊D3—42no—
299C2×C3⋊D3—42no—
300C2×C3⋊D3#12714yescomplemented
301C32×C4—22no—
302C32×C4—24no—
303C32×C4—41no—
304C3⋊Dic3—24no—
305C3⋊Dic3—41no—
306C3⋊Dic3#12014yescomplemented
307C25—92no—
308C22×D4—92no—
309C22×D4—91no—
310C22×D4—91no—
311C22×D4—92no—
312C22×D4—92no—
313C22×D4—91no—
314C22×D4—91no—
315C22×D4—92no—
316C22×D4—184no—
317C22×D4—188no—
318C22×D4C2×C3⋊D311yescharacteristic
319C22×D4C2×C3⋊D312yescomplemented
320C23×C4—91no—
321#127—188no—
322#121—184no—
323#120—188no—
324#120—188no—
325C2×C4⋊C4—91no—
326C2×C22⋊C4—92no—
327C2×C22⋊C4—92no—
328C2×C22⋊C4—92no—
329C2×C22⋊C4—92no—
330C2×C22⋊C4—91no—
331C2×C22⋊C4C2×C3⋊D312yescomplemented
332C2×C22⋊C4C2×C3⋊D311yescharacteristic, complemented
333C2×C42—92no—
334#95—91no—
335#95C2×C3⋊D311yescharacteristic, complemented
336C23×C3—28no—
337C23×C3—28no—
338C23×C3—28no—
339C23×C3—28no—
340C23×C3—28no—
341C23×C3—28no—
342C23×C3—24no—
343C23×C3—28no—
344C23×C3—28no—
345C23×C3—24no—
346C23×C3—24no—
347C23×C3D3×D4116yes—
348C23×C3C23×D314yes—
349C22×D3—316no—
350C22×D3—38no—
351C22×D3—316no—
352C22×D3—68no—
353C22×D3—64no—
354C22×D3—64no—
355C22×D3—664no—
356C22×D3—68no—
357C22×D3—68no—
358C22×D3—68no—
359C22×D3—68no—
360C22×D3—68no—
361C22×D3—68no—
362C22×D3—64no—
363C22×D3—68no—
364C22×D3—68no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—1232no—
368C22×D3—1232no—
369C22×D3—1232no—
370C22×D3—1232no—
371C22×D3—1232no—
372C22×D3—1232no—
373C3×D4—232no—
374C3×D4—432no—
375C2×C3×C4—28no—
376C2×C3×C4—28no—
377C2×C3×C4—28no—
378C2×C3×C4—24no—
379C2×C3×C4—28no—
380C2×C3×C4D3×D418yes—
381C2×C3×C4D3×D4116yescomplemented
382#67—664no—
383#67—1216no—
384#67—1232no—
385#67—1232no—
386#67—1216no—
387C2×Dic3—316no—
388C2×Dic3—38no—
389C2×Dic3—316no—
390C2×Dic3—68no—
391C2×Dic3—68no—
392C2×Dic3—64no—
393C2×Dic3—68no—
394D12—632no—
395D12—1232no—
396D12—1216no—
397C4×D3—632no—
398C2×C32—44no—
399C2×C32—81no—
400C2×C32C2×#12011yescharacteristic
401C2×C32C2×#12711yescharacteristic
402C2×C32#53511yescharacteristic
403C2×C32D4212yes—
404C2×C32D4212yes—
405C3⋊D3—24no—
406C3⋊D3—44no—
407C3⋊D3—81no—
408C24—91no—
409C24—92no—
410C24—91no—
411C24—184no—
412C24—184no—
413C24—184no—
414C24—184no—
415C24—184no—
416C24—362no—
417C24—362no—
418C24C22×C3⋊D311yescharacteristic
419C24C22×C3⋊D312yes—
420C2×D4—24no—
421C2×D4—24no—
422C2×D4—22no—
423C2×D4—24no—
424C2×D4—42no—
425C2×D4—98no—
426C2×D4—184no—
427C2×D4—184no—
428C2×D4—182no—
429C2×D4—184no—
430C2×D4—184no—
431C2×D4—184no—
432C2×D4—184no—
433C2×D4—184no—
434C2×D4—182no—
435C2×D4—184no—
436C2×D4—1832no—
437C2×D4—184no—
438C2×D4—182no—
439C2×D4—184no—
440C2×D4—184no—
441C2×D4—182no—
442C2×D4—184no—
443C2×D4—362no—
444C2×D4—362no—
445C2×D4—362no—
446C22×C4—91no—
447C22×C4—92no—
448C22×C4—94no—
449C22×C4—91no—
450C22×C4—184no—
451C22×C4C22×C3⋊D311yescharacteristic
452C22×C4C22×C3⋊D311yescharacteristic
453C22×C4C22×C3⋊D312yes—
454C4⋊C4—182no—
455C22⋊C4—22no—
456C22⋊C4—24no—
457C22⋊C4—98no—
458C22⋊C4—184no—
459C22⋊C4—184no—
460C22⋊C4—182no—
461C22⋊C4—184no—
462C42—184no—
463C22×C3—216no—
464C22×C3—216no—
465C22×C3—216no—
466C22×C3—48no—
467C22×C3—48no—
468C22×C3—48no—
469C22×C3—48no—
470C22×C3—44no—
471C22×C3—44no—
472C22×C3—48no—
473C22×C3—44no—
474C22×C3—48no—
475C22×C3C2×D3×D414yes—
476C22×C3C2×D3×D418yes—
477C22×C3C2×D3×D418yes—
478C22×C3#100414yes—
479C22×C3#100914yes—
480C2×D3—316no—
481C2×D3—68no—
482C2×D3—616no—
483C2×D3—68no—
484C2×D3—616no—
485C2×D3—616no—
486C2×D3—616no—
487C2×D3—616no—
488C2×D3—12128no—
489C2×D3—128no—
490C2×D3—128no—
491C2×D3—128no—
492C2×D3—128no—
493C2×D3—124no—
494C2×D3—124no—
495C2×D3—128no—
496C2×D3—124no—
497C2×D3—128no—
498C3×C4—28no—
499C3×C4—216no—
500C3×C4—44no—
501Dic3—316no—
502Dic3—616no—
503Dic3—124no—
504C32#243311yescharacteristic, complemented, Sylow
505C23—22no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—22no—
510C23—22no—
511C23—21no—
512C23—22no—
513C23—22no—
514C23—21no—
515C23—21no—
516C23—94no—
517C23—92no—
518C23—94no—
519C23—1816no—
520C23—182no—
521C23—181no—
522C23—181no—
523C23—182no—
524C23—182no—
525C23—182no—
526C23—182no—
527C23—182no—
528C23—182no—
529C23—181no—
530C23—182no—
531C23—182no—
532C23—181no—
533C23—181no—
534C23—368no—
535C23—368no—
536C23—368no—
537C23—368no—
538C23—368no—
539C23—368no—
540C23D4×C3⋊D314yes—
541C23C23×C3⋊D311yescharacteristic
542D4—28no—
543D4—48no—
544D4—188no—
545D4—1816no—
546D4—368no—
547D4—364no—
548D4—364no—
549D4—368no—
550D4—368no—
551D4—364no—
552C2×C4—22no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—21no—
557C2×C4—94no—
558C2×C4—92no—
559C2×C4—94no—
560C2×C4—188no—
561C2×C4—182no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—181no—
565C2×C4D4×C3⋊D312yes—
566C2×C4D4×C3⋊D314yescomplemented
567C2×C3—416no—
568C2×C3—84no—
569C2×C3D3×#12014yes—
570C2×C3#559018yes—
571C2×C3#560714yes—
572C2×C3#560918yes—
573C2×C3D3×#12714yes—
574D3—616no—
575D3—1216no—
576D3—244no—
577C22—24no—
578C22—24no—
579C22—24no—
580C22—42no—
581C22—42no—
582C22—42no—
583C22—42no—
584C22—41no—
585C22—41no—
586C22—42no—
587C22—41no—
588C22—42no—
589C22—94no—
590C22—182no—
591C22—184no—
592C22—182no—
593C22—184no—
594C22—184no—
595C22—184no—
596C22—184no—
597C22—3632no—
598C22—362no—
599C22—362no—
600C22—362no—
601C22—362no—
602C22—361no—
603C22—361no—
604C22—362no—
605C22—361no—
606C22—362no—
607C22C2×D4×C3⋊D311yescharacteristic
608C22C2×D4×C3⋊D312yes—
609C22C2×D4×C3⋊D312yes—
610C22#6436111yescharacteristic
611C22#6436611yescharacteristic
612C4—22no—
613C4—24no—
614C4—41no—
615C4—94no—
616C4—184no—
617C4—361no—
618C3#7667314yescomplemented
619C2—44no—
620C2—81no—
621C2—184no—
622C2—364no—
623C2—721no—
624C2C3⋊D3×#12011yescharacteristic
625C2#1059606112yes—
626C2#1059607811yescharacteristic
627C2#1059608012yes—
628C2C3⋊D3×#12711yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#392C2
hypercenter#392C3⋊D3
hypocenterC32#2433
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C22×D4×C3⋊D3C2semidirect
2. C2×#64149C2semidirect
3. C2×#64146C2semidirect
4. C2×#64093C2semidirect
5. C2×#64091C2semidirect
6. C32×#392C2semidirect
7. #10592922C2semidirect
8. #10592659C2semidirect
9. #10592656C2semidirect
10. #10592370C2semidirect
11. #10592365C2semidirect
15. C22×C32×D4C22semidirect
18. C22×#638C22semidirect
19. C22×#638C22semidirect
20. C22×#638C22semidirect
25. C22×C4⋊(C3⋊D3)C22semidirect
27. C2×C32×C22⋊C4C22semidirect
28. C2×C32×C22⋊C4C22semidirect
29. C2×#3757C22semidirect
33. C2×#3752C22semidirect
34. C2×#3752C22semidirect
35. C2×#3752C22semidirect
36. C2×#3750C22semidirect
37. C2×C4×C3⋊Dic3C22semidirect
40. C32×#95C22semidirect
41. #63658C22semidirect
47. C3×#392D3semidirect
85. C2×#638D4semidirect
98. C2×C4×C3⋊D3D4semidirect
105. #3752D4semidirect
111. C22×C3×D4C2×D3semidirect
123. C2×C3×C22⋊C4C2×D3semidirect
124. C2×C3×C22⋊C4C2×D3semidirect
136. C3×#95C2×D3semidirect
183. C2×C32×C4C2×D4semidirect
195. C2×C3⋊Dic3C2×D4semidirect
208. #392C3⋊D3semidirect
300. C2×C3⋊D3#127semidirect
306. C3⋊Dic3#120semidirect
319. C22×D4C2×C3⋊D3semidirect
331. C2×C22⋊C4C2×C3⋊D3semidirect
332. C2×C22⋊C4C2×C3⋊D3semidirect
335. #95C2×C3⋊D3semidirect
381. C2×C3×C4D3×D4semidirect
504. C32#2433semidirect
566. C2×C4D4×C3⋊D3semidirect
618. C3#76673semidirect

Maximal subgroups

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

subgroupindex
C22×D4×C3⋊D32
C2×#641492
C2×#641462
C2×#640932
C2×#640912
C32×#3922
#105929222
#105926592
#105926562
#105923702
#105923652
#766733