Finite Group Databasebeta

← #11856265

Subgroups — #11856265

Order 1152.

2375 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×D3×Dic3C211yesmaximal, characteristic, complemented
2C2×#64144C211yesmaximal, characteristic, complemented
3C2×C3×#937C211yesmaximal, characteristic
4C2×C3×#935C211yesmaximal, characteristic, complemented
5#10591721C214yesmaximal, complemented
6#10591706C211yesmaximal, characteristic, complemented
7#10591697C211yesmaximal, characteristic, complemented
8#10591696C211yesmaximal, characteristic, complemented
9#10591372C214yesmaximal, complemented
10#82912—31nomaximal
11#82602—31nomaximal
12C24×C3×D3C2211yescharacteristic
13C22×C32×D4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C3×#67C2212yes—
16C23×C3×Dic3C2211yescharacteristic
17C22×D3×Dic3—24no—
18C22×D3×Dic3—24no—
19C22×D3×Dic3—24no—
20C22×D3×Dic3C2214yes—
21C2×#3757C2211yescharacteristic
22C2×#3757C2212yescomplemented
23#64144—24no—
24C2×#3750C2212yescomplemented
25C2×C3×#217C2211yescharacteristic
26C2×C3×#217C2211yescharacteristic
27C2×C3×#217C2212yescomplemented
28C3×#937—24no—
29C3×#935—24no—
30C2×C3×(C2×D3)⋊C4C2212yes—
31C2×C3×Dic3⋊C4C2212yescomplemented
32C2×(C2×D3)⋊Dic3C2214yes—
33#63579C2214yescomplemented
34#63579C2214yescomplemented
35C24×Dic3—31no—
36C23×C4×D3—31no—
37C2×C3×#123—31no—
38C2×C3×#120—31no—
39C2×#937D311yescharacteristic
40C2×#935—31no—
41C2×#935—31no—
42C2×#935—61no—
43C2×#935D311yescharacteristic, complemented
44#5247—31no—
45#5220—34no—
46#5211—31no—
47#4989—34no—
48#4956—34no—
49#4955—31no—
50#4946—34no—
51#4943—31no—
52#4943—31no—
53#4943—31no—
54C24×C32C2311yescharacteristic
55C24×C32C2311yescharacteristic
56C23×C3×D3—22no—
57C23×C3×D3—22no—
58C23×C3×D3—28no—
59C23×C3×D3D414yes—
60C23×C3×D3C2312yes—
61C2×C32×D4—22no—
62C2×C32×D4—22no—
63C2×C32×D4—22no—
64C22×C32×C4C2311yescharacteristic
65C22×C3⋊Dic3—22no—
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3D414yescomplemented
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2312yes—
70C2×C3×#67—24no—
71C2×C3×#67—28no—
72C22×C3×Dic3—22no—
73C22×C3×Dic3—22no—
74C22×C3×Dic3D414yescomplemented
75C22×C3×Dic3C2312yes—
76C22×C3×Dic3C2312yes—
77C22×C3×Dic3C2312yes—
78C2×D3×Dic3—232no—
79C2×D3×Dic3—28no—
80C2×D3×Dic3—28no—
81C2×D3×Dic3—28no—
82#3757—22no—
83#3757—24no—
84#3750—24no—
85C3×#217—22no—
86C3×#217—22no—
87C3×#217—24no—
88C3×(C2×D3)⋊C4—24no—
89C3×Dic3⋊C4—24no—
90(C2×D3)⋊Dic3—28no—
91#2849—91noSylow
92C25×C3—31no—
93C24×D3C2×D311yescharacteristic
94C22×C3×D4—21no—
95C22×C3×D4—32no—
96C22×C3×D4C2×D311yescharacteristic
97C22×C3×D4C2×D311yescharacteristic
98C23×C3×C4—31no—
99C22×#67C2×D312yes—
100C23×Dic3—31no—
101C23×Dic3—31no—
102C23×Dic3—34no—
103C23×Dic3—61no—
104C23×Dic3—64no—
105C23×Dic3—64no—
106C23×Dic3—64no—
107C23×Dic3C2×D311yescharacteristic
108C22×C4×D3—34no—
109C22×C4×D3—64no—
110C22×C4×D3—64no—
111C22×C4×D3—64no—
112C3×#123—64no—
113C3×#120—64no—
114C2×C3×C4⋊C4—32no—
115C2×C3×C22⋊C4—31no—
116C2×C3×C22⋊C4—31no—
117C2×C3×C22⋊C4—32no—
118C2×C3×C22⋊C4—32no—
119C2×#217—31no—
120C2×#217—31no—
121C2×#217—32no—
122C2×#217—32no—
123C2×#217—34no—
124C2×#217—61no—
125C2×#217—62no—
126C2×#217C2×D311yescharacteristic
127C2×#217C2×D311yescharacteristic
128C2×#217C2×D312yescomplemented
129#937—24no—
130#935—24no—
131#935—64no—
132#935—64no—
133#935—68no—
134C2×(C2×D3)⋊C4—34no—
135C2×(C2×D3)⋊C4C2×D312yes—
136C2×Dic3⋊C4—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4—62no—
139C2×Dic3⋊C4C2×D312yescomplemented
140C3⋊#95—34no—
141C3⋊#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C23×C32—21no—
145C23×C32—24no—
146C23×C32—21no—
147C23×C32—21no—
148C23×C32—24no—
149C23×C32C2×D412yes—
150C23×C32C2×D412yes—
151C23×C32C2×D412yes—
152C23×C32C2411yescharacteristic
153C22×C3×D3—216no—
154C22×C3×D3—216no—
155C22×C3×D3—28no—
156C22×C3×D3—22no—
157C22×C3×D3—22no—
158C22×C3×D3—24no—
159C22×C3×D3—216no—
160C22×C3×D3C2×D414yes—
161C22×C3×D3#4118yes—
162C32×D4—44no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C3⋊Dic3—22no—
167C2×C3⋊Dic3—28no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3—24no—
171C2×C3⋊Dic3C2×D414yes—
172C3×#67—48no—
173C2×C3×Dic3—28no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—22no—
178C2×C3×Dic3—24no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3C2×D414yes—
181D3×Dic3—232no—
182C24×C4—91no—
183C2×#123—31no—
184C2×#123—91no—
185C2×#120—31no—
186#386—94no—
187#385—94no—
188#381—91no—
189#381—91no—
190#379—91no—
191C24×C3—21no—
192C24×C3—21no—
193C24×C3—32no—
194C24×C3—34no—
195C24×C3—68no—
196C24×C3—62no—
197C24×C3—62no—
198C24×C3C22×D311yescharacteristic
199C24×C3C22×D311yescharacteristic
200C24×C3C22×D311yescharacteristic
201C24×C3C22×D311yescharacteristic
202C23×D3—22no—
203C23×D3—22no—
204C23×D3—28no—
205C23×D3#6714yes—
206C23×D3C22×D312yes—
207C2×C3×D4—24no—
208C2×C3×D4—22no—
209C2×C3×D4—22no—
210C2×C3×D4—22no—
211C2×C3×D4—22no—
212C2×C3×D4—22no—
213C2×C3×D4—22no—
214C2×C3×D4—42no—
215C2×C3×D4—42no—
216C2×C3×D4—64no—
217C2×C3×D4—68no—
218C22×C3×C4—21no—
219C22×C3×C4—34no—
220C22×C3×C4—32no—
221C22×C3×C4—32no—
222C22×C3×C4—32no—
223C22×C3×C4—62no—
224C22×C3×C4—62no—
225C22×C3×C4C22×D311yescharacteristic
226C22×C3×C4C22×D311yescharacteristic
227C2×#67—28no—
228C2×#67—24no—
229C22×Dic3—22no—
230C22×Dic3—22no—
231C22×Dic3—34no—
232C22×Dic3—34no—
233C22×Dic3—32no—
234C22×Dic3—32no—
235C22×Dic3—32no—
236C22×Dic3—32no—
237C22×Dic3—62no—
238C22×Dic3—62no—
239C22×Dic3—64no—
240C22×Dic3—68no—
241C22×Dic3—68no—
242C22×Dic3—632no—
243C22×Dic3—62no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—68no—
248C22×Dic3—122no—
249C22×Dic3—122no—
250C22×Dic3#6714yescomplemented
251C22×Dic3C22×D312yes—
252C22×Dic3C22×D312yes—
253C22×Dic3C22×D312yes—
254C2×C4×D3—68no—
255C2×C4×D3—68no—
256C2×C4×D3—632no—
257C2×C4×D3—68no—
258C3×C4⋊C4—64no—
259C3×C22⋊C4—64no—
260C3×C22⋊C4—64no—
261C3×C22⋊C4—62no—
262C3×C22⋊C4—62no—
263#217—22no—
264#217—22no—
265#217—24no—
266#217—68no—
267#217—64no—
268#217—64no—
269#217—68no—
270#217—64no—
271#217—62no—
272#217—62no—
273(C2×D3)⋊C4—24no—
274(C2×D3)⋊C4—68no—
275Dic3⋊C4—24no—
276Dic3⋊C4—64no—
277Dic3⋊C4—64no—
278Dic3⋊C4—68no—
279C22×C32—24no—
280C22×C32—24no—
281C22×C32—24no—
282C22×C32—41no—
283C22×C32—42no—
284C22×C32—42no—
285C22×C32—42no—
286C22×C32#12014yes—
287C22×C32C22×D411yescharacteristic
288C22×C32C22×D411yescharacteristic
289C22×C32C22×D411yescharacteristic
290C22×C32C2×#4114yes—
291C2×C3×D3—232no—
292C2×C3×D3—24no—
293C2×C3×D3—24no—
294C2×C3×D3—28no—
295C2×C3×D3—28no—
296C2×C3×D3#12318yescomplemented
297C32×C4—41no—
298C3⋊Dic3—24no—
299C3⋊Dic3—42no—
300C3×Dic3—24no—
301C3×Dic3—42no—
302C3×Dic3—42no—
303C25—31no—
304C22×D4—32no—
305C22×D4D3211yescharacteristic
306C23×C4—31no—
307C23×C4—94no—
308C23×C4—91no—
309C23×C4—184no—
310C23×C4—184no—
311C23×C4—184no—
312#123—64no—
313#123—184no—
314#120—64no—
315C2×C4⋊C4—32no—
316C2×C4⋊C4—92no—
317C2×C22⋊C4—31no—
318C2×C22⋊C4—31no—
319C2×C22⋊C4—32no—
320C2×C22⋊C4—32no—
321C2×C22⋊C4—94no—
322C2×C22⋊C4—91no—
323C2×C22⋊C4—92no—
324#95—94no—
325#95—94no—
326C23×C3—24no—
327C23×C3—24no—
328C23×C3—22no—
329C23×C3—21no—
330C23×C3—21no—
331C23×C3—21no—
332C23×C3—21no—
333C23×C3—24no—
334C23×C3—24no—
335C23×C3—21no—
336C23×C3—21no—
337C23×C3—21no—
338C23×C3—22no—
339C23×C3—22no—
340C23×C3—22no—
341C23×C3—34no—
342C23×C3—38no—
343C23×C3—44no—
344C23×C3—41no—
345C23×C3—41no—
346C23×C3—44no—
347C23×C3—616no—
348C23×C3—616no—
349C23×C3—616no—
350C23×C3—68no—
351C23×C3—62no—
352C23×C3—64no—
353C23×C3—62no—
354C23×C3D3×D412yes—
355C23×C3D3×D412yes—
356C23×C3D3×D412yes—
357C23×C3D3×D412yes—
358C23×C3C2×#6712yes—
359C23×C3C2×#6712yes—
360C23×C3C23×D311yescharacteristic
361C23×C3C23×D311yescharacteristic
362C22×D3—216no—
363C22×D3—216no—
364C22×D3—28no—
365C22×D3—22no—
366C22×D3—22no—
367C22×D3—24no—
368C22×D3—216no—
369C22×D3#23718yes—
370C22×D3C2×#6714yes—
371C3×D4—48no—
372C3×D4—44no—
373C3×D4—44no—
374C3×D4—128no—
375C2×C3×C4—22no—
376C2×C3×C4—21no—
377C2×C3×C4—21no—
378C2×C3×C4—21no—
379C2×C3×C4—21no—
380C2×C3×C4—21no—
381C2×C3×C4—21no—
382C2×C3×C4—34no—
383C2×C3×C4—41no—
384C2×C3×C4—41no—
385C2×C3×C4—68no—
386C2×C3×C4—62no—
387C2×C3×C4—62no—
388C2×C3×C4—62no—
389C2×C3×C4—62no—
390C2×C3×C4—64no—
391C2×C3×C4—64no—
392#67—48no—
393C2×Dic3—28no—
394C2×Dic3—22no—
395C2×Dic3—22no—
396C2×Dic3—24no—
397C2×Dic3—24no—
398C2×Dic3—22no—
399C2×Dic3—22no—
400C2×Dic3—34no—
401C2×Dic3—34no—
402C2×Dic3—64no—
403C2×Dic3—632no—
404C2×Dic3—68no—
405C2×Dic3—68no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—62no—
409C2×Dic3—62no—
410C2×Dic3—64no—
411C2×Dic3—62no—
412C2×Dic3—62no—
413C2×Dic3—64no—
414C2×Dic3—64no—
415C2×Dic3—124no—
416C2×Dic3—122no—
417C2×Dic3—122no—
418C2×Dic3—128no—
419C2×Dic3C2×#6714yes—
420C4×D3—632no—
421C2×C32—24no—
422C2×C32—81no—
423C2×C32C2×#12011yescharacteristic
424C2×C32C2×#12312yes—
425C2×C32#52512yes—
426C2×C32#52512yes—
427C3×D3—28no—
428C24—32no—
429C24—34no—
430C24—68no—
431C24—62no—
432C24—62no—
433C24C2×D3211yescharacteristic
434C24C2×D3211yescharacteristic
435C2×D4—22no—
436C2×D4—22no—
437C2×D4—22no—
438C2×D4—64no—
439C2×D4—68no—
440C22×C4—32no—
441C22×C4—34no—
442C22×C4—32no—
443C22×C4—32no—
444C22×C4—62no—
445C22×C4—62no—
446C22×C4—92no—
447C22×C4—94no—
448C22×C4—92no—
449C22×C4—188no—
450C22×C4—188no—
451C22×C4—188no—
452C22×C4—1832no—
453C22×C4—182no—
454C22×C4—182no—
455C22×C4C2×D3211yescharacteristic
456C4⋊C4—64no—
457C4⋊C4—184no—
458C22⋊C4—64no—
459C22⋊C4—64no—
460C22⋊C4—62no—
461C22⋊C4—62no—
462C22⋊C4—188no—
463C22⋊C4—184no—
464C22⋊C4—182no—
465C22×C3—24no—
466C22×C3—24no—
467C22×C3—24no—
468C22×C3—24no—
469C22×C3—24no—
470C22×C3—24no—
471C22×C3—24no—
472C22×C3—21no—
473C22×C3—21no—
474C22×C3—21no—
475C22×C3—24no—
476C22×C3—38no—
477C22×C3—44no—
478C22×C3—44no—
479C22×C3—44no—
480C22×C3—42no—
481C22×C3—44no—
482C22×C3—42no—
483C22×C3—42no—
484C22×C3—42no—
485C22×C3—41no—
486C22×C3—41no—
487C22×C3—42no—
488C22×C3—42no—
489C22×C3—42no—
490C22×C3—632no—
491C22×C3—64no—
492C22×C3—68no—
493C22×C3—64no—
494C22×C3—68no—
495C22×C3—82no—
496C22×C3—82no—
497C22×C3#93714yes—
498C22×C3#93714yes—
499C22×C3C2×D3×D411yescharacteristic
500C22×C3C2×D3×D411yescharacteristic
501C22×C3C2×D3×D411yescharacteristic
502C22×C3C2×D3×D411yescharacteristic
503C22×C3C2×#23714yes—
504C22×C3D3×#4114yes—
505C22×C3C22×#6711yescharacteristic
506C22×C3C22×#6711yescharacteristic
507C2×D3—232no—
508C2×D3—24no—
509C2×D3—24no—
510C2×D3—28no—
511C2×D3—28no—
512C2×D3#93518yescomplemented
513C3×C4—42no—
514C3×C4—41no—
515C3×C4—41no—
516C3×C4—64no—
517C3×C4—122no—
518C3×C4—122no—
519Dic3—24no—
520Dic3—42no—
521Dic3—42no—
522Dic3—64no—
523Dic3—64no—
524Dic3—124no—
525Dic3—124no—
526Dic3—122no—
527Dic3—122no—
528C32#284911yescharacteristic, complemented, Sylow
529C23—24no—
530C23—24no—
531C23—21no—
532C23—21no—
533C23—21no—
534C23—38no—
535C23—34no—
536C23—616no—
537C23—616no—
538C23—616no—
539C23—64no—
540C23—62no—
541C23—62no—
542C23—68no—
543C23D3×#6712yes—
544C23D3×#6712yes—
545C23#381112yes—
546C23C22×D3211yescharacteristic
547D4—44no—
548D4—128no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—34no—
553C2×C4—62no—
554C2×C4—62no—
555C2×C4—68no—
556C2×C4—64no—
557C2×C4—64no—
558C2×C4—62no—
559C2×C4—62no—
560C2×C4—94no—
561C2×C4—1832no—
562C2×C4—182no—
563C2×C4—182no—
564C2×C4—188no—
565C2×C4—184no—
566C2×C4—182no—
567C2×C3—24no—
568C2×C3—24no—
569C2×C3—22no—
570C2×C3—22no—
571C2×C3—22no—
572C2×C3—21no—
573C2×C3—44no—
574C2×C3—68no—
575C2×C3—82no—
576C2×C3—81no—
577C2×C3—81no—
578C2×C3#558612yes—
579C2×C3#558612yes—
580C2×C3D3×#12312yes—
581C2×C3#565612yes—
582C2×C3C2×#93512yes—
583C2×C3C2×#93711yescharacteristic
584C2×C3C2×#93711yescharacteristic
585C2×C3#582812yes—
586D3—28no—
587C22—24no—
588C22—24no—
589C22—24no—
590C22—38no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—41no—
595C22—632no—
596C22—64no—
597C22—68no—
598C22—68no—
599C22—64no—
600C22#6398314yes—
601C22D3×#23714yes—
602C22C2×D3×#6711yescharacteristic
603C22C2×D3×#6711yescharacteristic
604C22C2×#381111yescharacteristic
605C4—41no—
606C4—64no—
607C4—122no—
608C4—122no—
609C4—184no—
610C4—362no—
611C3—21no—
612C3#8260211yescharacteristic, complemented
613C3#8291211yescharacteristic, complemented
614C2—24no—
615C2—68no—
616C2—81no—
617C2D3×#93512yes—
618C2#1059515412yes—
619C2#1059516012yes—
620C2C2×#6398311yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
prime radicalC2×C3×#937C2
hypercenterC22×D4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C23×D3×Dic3C2semidirect
2. C2×#64144C2semidirect
4. C2×C3×#935C2semidirect
5. #10591721C2semidirect
6. #10591706C2semidirect
7. #10591697C2semidirect
8. #10591696C2semidirect
9. #10591372C2semidirect
22. C2×#3757C22semidirect
24. C2×#3750C22semidirect
27. C2×C3×#217C22semidirect
31. C2×C3×Dic3⋊C4C22semidirect
33. #63579C22semidirect
34. #63579C22semidirect
43. C2×#935D3semidirect
67. C22×C3⋊Dic3D4semidirect
74. C22×C3×Dic3D4semidirect
128. C2×#217C2×D3semidirect
139. C2×Dic3⋊C4C2×D3semidirect
250. C22×Dic3#67semidirect
296. C2×C3×D3#123semidirect
512. C2×D3#935semidirect
528. C32#2849semidirect
612. C3#82602semidirect
613. C3#82912semidirect

Maximal subgroups

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

subgroupindex
C23×D3×Dic32
C2×#641442
C2×C3×#9372
C2×C3×#9352
#105917212
#105917062
#105916972
#105916962
#105913722
#829123
#826023