Finite Group Databasebeta

← #11856275

Subgroups — #11856275

Order 1152.

2885 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C4×C3⋊D3C211yesmaximal, characteristic, complemented
2C2×C3×#929C211yesmaximal, characteristic, complemented
3C2×#63981C211yesmaximal, characteristic
4C2×#63962C211yesmaximal, characteristic, complemented
5C3×#5211C211yesmaximal, characteristic, complemented
6#10591714C211yesmaximal, characteristic, complemented
7#10591697C211yesmaximal, characteristic, complemented
8#10591387C214yesmaximal, complemented
9#10591290C214yesmaximal, complemented
10#82912—31nomaximal
11#74146—31nomaximal
12C24×C3⋊D3C2211yescharacteristic
13C23×C32×C4C2211yescharacteristic
14C23×C3⋊Dic3C2211yescharacteristic
15C22×C4×C3⋊D3—24no—
16C22×C4×C3⋊D3—24no—
17C22×C4×C3⋊D3—24no—
18C22×C4×C3⋊D3C2214yes—
19C22×C3×#67C2211yescharacteristic
20C22×#626C2212yes—
21C2×C3×#217C2211yescharacteristic
22C2×C3×#217C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C3×#929—24no—
25C2×C3×(C2×D3)⋊C4C2212yescomplemented
26C2×C3×Dic3⋊C4C2212yescomplemented
27#63981—24no—
28C2×Dic3⋊Dic3C2212yescomplemented
29C2×#3722C2212yes—
30C2×#3722C2214yes—
31#63962—24no—
32C2×(C2×D3)⋊Dic3C2212yescomplemented
33C3×C3⋊#95C2214yescomplemented
34#63579C2214yescomplemented
35C23×C4×D3—31no—
36C23×C4×D3—31no—
37C23×C4×D3—61no—
38C2×C3×#123—31no—
39C2×#937—31no—
40C2×#935—31no—
41C2×#929D311yescharacteristic, complemented
42C2×#886—31no—
43C2×#882—31no—
44C3×#381—31no—
45#5211D311yescharacteristic, complemented
46#4989—34no—
47#4956—34no—
48#4955—31no—
49#4955—31no—
50#4943—31no—
51#4943—31no—
52#4668—34no—
53#4665—34no—
54C24×C32C2311yescharacteristic
55C23×C3⋊D3—22no—
56C23×C3⋊D3—22no—
57C23×C3⋊D3—28no—
58C23×C3⋊D3D414yes—
59C23×C3⋊D3C2312yes—
60C23×C3×D3C2311yescharacteristic
61C22×C32×C4—22no—
62C22×C32×C4—22no—
63C22×C32×C4D414yescomplemented
64C22×C32×C4C2312yes—
65C22×C3⋊Dic3—22no—
66C22×C3⋊Dic3—22no—
67C22×C3⋊Dic3D414yescomplemented
68C22×C3⋊Dic3C2312yes—
69C2×C4×C3⋊D3—232no—
70C2×C4×C3⋊D3—28no—
71C2×C4×C3⋊D3—28no—
72C2×C4×C3⋊D3—28no—
73C2×C3×#67—22no—
74C2×C3×#67—22no—
75C2×C3×#67—22no—
76C22×C3×Dic3C2311yescharacteristic
77C22×C3×Dic3C2312yes—
78C22×C3×Dic3C2312yes—
79C22×C3×Dic3C2312yes—
80C2×#626—24no—
81C2×#626—28no—
82C3×#217—22no—
83C3×#217—22no—
84C3×#217—22no—
85C3×(C2×D3)⋊C4—24no—
86C3×Dic3⋊C4—24no—
87Dic3⋊Dic3—24no—
88#3722—24no—
89#3722—28no—
90(C2×D3)⋊Dic3—24no—
91#2849—91noSylow
92C24×D3—31no—
93C24×D3—31no—
94C24×D3—61no—
95C22×C3×D4—31no—
96C23×C3×C4—21no—
97C23×C3×C4C2×D311yescharacteristic
98C23×C3×C4C2×D311yescharacteristic
99C22×#67—32no—
100C22×#67C2×D311yescharacteristic
101C23×Dic3—31no—
102C23×Dic3—31no—
103C23×Dic3—61no—
104C22×D12—32no—
105C22×C4×D3—34no—
106C22×C4×D3—34no—
107C22×C4×D3—64no—
108C22×C4×D3—64no—
109C22×C4×D3—64no—
110C22×C4×D3—64no—
111C22×C4×D3—64no—
112C22×C4×D3—68no—
113C22×C4×D3—68no—
114C22×C4×D3—68no—
115C22×C4×D3—64no—
116C22×C4×D3—64no—
117C3×#123—64no—
118C2×C3×C4⋊C4—32no—
119C2×C3×C22⋊C4—31no—
120C2×C3×C22⋊C4—31no—
121C2×C3×C22⋊C4—31no—
122C2×C3×C22⋊C4—32no—
123C2×#217—32no—
124C2×#217C2×D311yescharacteristic
125C2×#217C2×D311yescharacteristic
126C2×#217C2×D311yescharacteristic
127#937—64no—
128#935—64no—
129#929—24no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—34no—
132C2×(C2×D3)⋊C4—32no—
133C2×(C2×D3)⋊C4—34no—
134C2×(C2×D3)⋊C4—32no—
135C2×(C2×D3)⋊C4C2×D312yescomplemented
136C2×C4⋊Dic3—32no—
137C2×Dic3⋊C4—32no—
138C2×Dic3⋊C4C2×D312yescomplemented
139#886—64no—
140#882—64no—
141C3×#95—34no—
142C3⋊#95—34no—
143C3⋊#95—34no—
144C3⋊#95C2×D314yescomplemented
145C23×C32—24no—
146C23×C32C2×D412yes—
147C23×C32C2×D412yes—
148C23×C32C2×D412yes—
149C23×C32C2411yescharacteristic
150C22×C3⋊D3—216no—
151C22×C3⋊D3—216no—
152C22×C3⋊D3—28no—
153C22×C3⋊D3—22no—
154C22×C3⋊D3—22no—
155C22×C3⋊D3—24no—
156C22×C3⋊D3—216no—
157C22×C3⋊D3C2×D414yes—
158C22×C3⋊D3#4118yes—
159C22×C3×D3—21no—
160C22×C3×D3—21no—
161C22×C3×D3—21no—
162C22×C3×D3—24no—
163C2×C32×C4—28no—
164C2×C32×C4—22no—
165C2×C32×C4—22no—
166C2×C32×C4C2×D414yes—
167C2×C3⋊Dic3—28no—
168C2×C3⋊Dic3—22no—
169C2×C3⋊Dic3—22no—
170C2×C3⋊Dic3C2×D414yes—
171C4×C3⋊D3—232no—
172C3×#67—44no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—21no—
175C2×C3×Dic3—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—21no—
178C2×C3×Dic3—22no—
179C2×C3×Dic3—24no—
180C2×C3×Dic3—24no—
181C2×C3×Dic3—24no—
182#626—48no—
183C24×C4—91no—
184C2×#123—31no—
185C2×#123—91no—
186C2×#120—91no—
187#386—94no—
188#385—94no—
189#381—31no—
190#381—91no—
191#379—91no—
192C24×C3—21no—
193C24×C3—31no—
194C24×C3C22×D311yescharacteristic
195C24×C3C22×D311yescharacteristic
196C23×D3—32no—
197C23×D3—32no—
198C23×D3—34no—
199C23×D3—34no—
200C23×D3—64no—
201C23×D3—62no—
202C23×D3—68no—
203C23×D3—68no—
204C23×D3—64no—
205C23×D3—64no—
206C23×D3—616no—
207C23×D3—62no—
208C23×D3—62no—
209C23×D3—62no—
210C23×D3—62no—
211C23×D3C22×D311yescharacteristic
212C2×C3×D4—62no—
213C2×C3×D4—62no—
214C2×C3×D4—62no—
215C22×C3×C4—24no—
216C22×C3×C4—24no—
217C22×C3×C4—22no—
218C22×C3×C4—22no—
219C22×C3×C4—22no—
220C22×C3×C4—22no—
221C22×C3×C4—24no—
222C22×C3×C4—22no—
223C22×C3×C4—32no—
224C22×C3×C4—32no—
225C22×C3×C4—32no—
226C22×C3×C4—31no—
227C22×C3×C4D1214yescomplemented
228C22×C3×C4#6714yescomplemented
229C22×C3×C4C22×D312yes—
230C22×C3×C4C22×D312yes—
231C2×#67—22no—
232C2×#67—22no—
233C2×#67—22no—
234C2×#67—64no—
235C2×#67—68no—
236C22×Dic3—34no—
237C22×Dic3—34no—
238C22×Dic3—32no—
239C22×Dic3—32no—
240C22×Dic3—64no—
241C22×Dic3—62no—
242C22×Dic3—64no—
243C22×Dic3—64no—
244C22×Dic3—62no—
245C22×Dic3—62no—
246C22×Dic3—62no—
247C22×Dic3—62no—
248C22×Dic3C22×D312yes—
249C22×Dic3C22×D312yes—
250C22×Dic3C22×D312yes—
251C22×Dic3C22×D311yescharacteristic
252C2×D12—64no—
253C2×D12—68no—
254C2×C4×D3—68no—
255C2×C4×D3—68no—
256C2×C4×D3—68no—
257C2×C4×D3—68no—
258C2×C4×D3—616no—
259C2×C4×D3—616no—
260C2×C4×D3—664no—
261C2×C4×D3—632no—
262C2×C4×D3—632no—
263C2×C4×D3—616no—
264C2×C4×D3—68no—
265C2×C4×D3—68no—
266C3×C4⋊C4—64no—
267C3×C22⋊C4—62no—
268C3×C22⋊C4—62no—
269C3×C22⋊C4—62no—
270C3×C22⋊C4—64no—
271#217—22no—
272#217—22no—
273#217—22no—
274#217—64no—
275(C2×D3)⋊C4—24no—
276(C2×D3)⋊C4—64no—
277(C2×D3)⋊C4—68no—
278(C2×D3)⋊C4—68no—
279(C2×D3)⋊C4—64no—
280(C2×D3)⋊C4—64no—
281C4⋊Dic3—64no—
282Dic3⋊C4—24no—
283Dic3⋊C4—64no—
284C22×C32—24no—
285C22×C32—24no—
286C22×C32—24no—
287C22×C32#12014yes—
288C22×C32C22×D411yescharacteristic
289C22×C32C22×D411yescharacteristic
290C22×C32C22×D411yescharacteristic
291C22×C32C2×#4114yes—
292C2×C3⋊D3—232no—
293C2×C3⋊D3—24no—
294C2×C3⋊D3—24no—
295C2×C3⋊D3—28no—
296C2×C3⋊D3—28no—
297C2×C3⋊D3#12318yescomplemented
298C2×C3×D3—41no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—42no—
302C32×C4—24no—
303C3⋊Dic3—24no—
304C3×Dic3—41no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C3×Dic3—42no—
308C25—91no—
309C22×D4—31no—
310C22×D4—92no—
311C23×C4—91no—
312C23×C4—94no—
313C23×C4—184no—
314C23×C4—184no—
315C23×C4—184no—
316C23×C4D3211yescharacteristic
317#123—64no—
318#123—184no—
319#120—184no—
320C2×C4⋊C4—32no—
321C2×C4⋊C4—92no—
322C2×C22⋊C4—31no—
323C2×C22⋊C4—31no—
324C2×C22⋊C4—31no—
325C2×C22⋊C4—32no—
326C2×C22⋊C4—92no—
327C2×C22⋊C4—94no—
328C2×C22⋊C4—92no—
329#95—34no—
330#95—94no—
331C23×C3—28no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—21no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—61no—
339C23×C3—61no—
340C23×C3—61no—
341C23×C3—64no—
342C23×C3C2×D1212yes—
343C23×C3D3×D412yes—
344C23×C3D3×D412yes—
345C23×C3D3×D412yes—
346C23×C3D3×D412yes—
347C23×C3C2×#6712yes—
348C23×C3C23×D311yescharacteristic
349C23×C3C23×D311yescharacteristic
350C22×D3—21no—
351C22×D3—21no—
352C22×D3—24no—
353C22×D3—21no—
354C22×D3—34no—
355C22×D3—34no—
356C22×D3—38no—
357C22×D3—38no—
358C22×D3—64no—
359C22×D3—68no—
360C22×D3—616no—
361C22×D3—616no—
362C22×D3—64no—
363C22×D3—64no—
364C22×D3—616no—
365C22×D3—632no—
366C22×D3—632no—
367C22×D3—632no—
368C22×D3—616no—
369C22×D3—616no—
370C22×D3—616no—
371C22×D3—616no—
372C22×D3—68no—
373C22×D3—68no—
374C22×D3—68no—
375C22×D3—62no—
376C22×D3—62no—
377C22×D3—62no—
378C22×D3—64no—
379C22×D3—64no—
380C22×D3—62no—
381C3×D4—124no—
382C2×C3×C4—24no—
383C2×C3×C4—24no—
384C2×C3×C4—216no—
385C2×C3×C4—28no—
386C2×C3×C4—28no—
387C2×C3×C4—22no—
388C2×C3×C4—22no—
389C2×C3×C4—22no—
390C2×C3×C4—22no—
391C2×C3×C4—24no—
392C2×C3×C4—62no—
393C2×C3×C4—61no—
394C2×C3×C4—61no—
395C2×C3×C4—62no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—64no—
399C2×C3×C4—64no—
400C2×C3×C4—64no—
401C2×C3×C4C2×D1214yes—
402C2×C3×C4C2×#6714yes—
403#67—44no—
404#67—128no—
405C2×Dic3—22no—
406C2×Dic3—21no—
407C2×Dic3—21no—
408C2×Dic3—22no—
409C2×Dic3—24no—
410C2×Dic3—24no—
411C2×Dic3—24no—
412C2×Dic3—21no—
413C2×Dic3—22no—
414C2×Dic3—34no—
415C2×Dic3—34no—
416C2×Dic3—64no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—616no—
420C2×Dic3—68no—
421C2×Dic3—68no—
422C2×Dic3—62no—
423C2×Dic3—62no—
424C2×Dic3—62no—
425C2×Dic3—62no—
426D12—128no—
427C4×D3—664no—
428C4×D3—632no—
429C4×D3—632no—
430C2×C32—24no—
431C2×C32C2×#12011yescharacteristic
432C2×C32C2×#12312yes—
433C2×C32#52512yes—
434C2×C32#52512yes—
435C3⋊D3—28no—
436C3×D3—81no—
437C24—31no—
438C24—92no—
439C24—94no—
440C24—188no—
441C24—182no—
442C24—182no—
443C24C2×D3211yescharacteristic
444C2×D4—62no—
445C2×D4—62no—
446C2×D4—62no—
447C2×D4—184no—
448C2×D4—188no—
449C22×C4—22no—
450C22×C4—22no—
451C22×C4—32no—
452C22×C4—32no—
453C22×C4—32no—
454C22×C4—31no—
455C22×C4—92no—
456C22×C4—94no—
457C22×C4—188no—
458C22×C4—188no—
459C22×C4—1832no—
460C22×C4—182no—
461C22×C4—182no—
462C22×C4—188no—
463C22×C4#62614yescomplemented
464C22×C4C2×D3212yes—
465C4⋊C4—64no—
466C4⋊C4—184no—
467C22⋊C4—62no—
468C22⋊C4—62no—
469C22⋊C4—62no—
470C22⋊C4—64no—
471C22⋊C4—184no—
472C22⋊C4—188no—
473C22⋊C4—184no—
474C22×C3—28no—
475C22×C3—28no—
476C22×C3—28no—
477C22×C3—24no—
478C22×C3—24no—
479C22×C3—24no—
480C22×C3—24no—
481C22×C3—24no—
482C22×C3—24no—
483C22×C3—24no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—24no—
488C22×C3—122no—
489C22×C3—122no—
490C22×C3—121no—
491C22×C3—122no—
492C22×C3#88214yes—
493C22×C3#93714yes—
494C22×C3C22×D1211yescharacteristic
495C22×C3C2×D3×D411yescharacteristic
496C22×C3C2×D3×D411yescharacteristic
497C22×C3C2×D3×D411yescharacteristic
498C22×C3C2×D3×D411yescharacteristic
499C22×C3D3×#4114yes—
500C22×C3D3×#4114yes—
501C22×C3C22×#6711yescharacteristic
502C2×D3—38no—
503C2×D3—38no—
504C2×D3—42no—
505C2×D3—42no—
506C2×D3—41no—
507C2×D3—42no—
508C2×D3—68no—
509C2×D3—68no—
510C2×D3—664no—
511C2×D3—632no—
512C2×D3—632no—
513C2×D3—68no—
514C2×D3—616no—
515C2×D3—616no—
516C2×D3—64no—
517C2×D3—64no—
518C2×D3—68no—
519C2×D3—68no—
520C2×D3—64no—
521C2×D3—68no—
522C2×D3—64no—
523C2×D3—68no—
524C3×C4—28no—
525C3×C4—24no—
526C3×C4—24no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4—121no—
530C3×C4—122no—
531Dic3—42no—
532Dic3—42no—
533Dic3—41no—
534Dic3—42no—
535Dic3—68no—
536Dic3—64no—
537Dic3—64no—
538C32#284911yescharacteristic, complemented, Sylow
539C23—24no—
540C23—64no—
541C23—61no—
542C23—61no—
543C23—61no—
544C23—98no—
545C23—94no—
546C23—1816no—
547C23—1816no—
548C23—1816no—
549C23—184no—
550C23—182no—
551C23—182no—
552C23—188no—
553C23C2×#62612yes—
554C23#381112yes—
555C23#381112yes—
556C23C22×D3211yescharacteristic
557D4—124no—
558D4—368no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—28no—
562C2×C4—64no—
563C2×C4—64no—
564C2×C4—64no—
565C2×C4—62no—
566C2×C4—61no—
567C2×C4—62no—
568C2×C4—62no—
569C2×C4—61no—
570C2×C4—61no—
571C2×C4—94no—
572C2×C4—1832no—
573C2×C4—182no—
574C2×C4—182no—
575C2×C4—188no—
576C2×C4C2×#62614yes—
577C2×C3—28no—
578C2×C3—24no—
579C2×C3—24no—
580C2×C3—22no—
581C2×C3—22no—
582C2×C3—21no—
583C2×C3—22no—
584C2×C3—241no—
585C2×C3C2×#88211yescharacteristic
586C2×C3#552412yes—
587C2×C3D3×#12312yes—
588C2×C3D3×#12312yes—
589C2×C3#565612yes—
590C2×C3#565612yes—
591C2×C3C2×#93711yescharacteristic
592C2×C3#582812yes—
593D3—616no—
594D3—68no—
595D3—68no—
596D3—81no—
597C22—24no—
598C22—24no—
599C22—24no—
600C22—98no—
601C22—122no—
602C22—122no—
603C22—121no—
604C22—122no—
605C22—1832no—
606C22—184no—
607C22—188no—
608C22—184no—
609C22—188no—
610C22#6398114yes—
611C22#6430614yes—
612C22C22×#62611yescharacteristic
613C22C2×#381111yescharacteristic
614C22C2×#381111yescharacteristic
615C4—24no—
616C4—122no—
617C4—122no—
618C4—121no—
619C4—122no—
620C4—184no—
621C3—21no—
622C3#7414611yescharacteristic, complemented
623C3#8291211yescharacteristic, complemented
624C2—24no—
625C2—188no—
626C2—241no—
627C2#1059492012yes—
628C2#1059503412yes—
629C2#1059507912yes—
630C2C2×#6398111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC23×C32×C4C22
prime radicalC2×#63981C2
hypercenterC23×C4D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C23×C4×C3⋊D3C2semidirect
2. C2×C3×#929C2semidirect
4. C2×#63962C2semidirect
5. C3×#5211C2semidirect
6. #10591714C2semidirect
7. #10591697C2semidirect
8. #10591387C2semidirect
9. #10591290C2semidirect
25. C2×C3×(C2×D3)⋊C4C22semidirect
26. C2×C3×Dic3⋊C4C22semidirect
28. C2×Dic3⋊Dic3C22semidirect
32. C2×(C2×D3)⋊Dic3C22semidirect
33. C3×C3⋊#95C22semidirect
34. #63579C22semidirect
41. C2×#929D3semidirect
45. #5211D3semidirect
63. C22×C32×C4D4semidirect
67. C22×C3⋊Dic3D4semidirect
135. C2×(C2×D3)⋊C4C2×D3semidirect
138. C2×Dic3⋊C4C2×D3semidirect
144. C3⋊#95C2×D3semidirect
227. C22×C3×C4D12semidirect
228. C22×C3×C4#67semidirect
297. C2×C3⋊D3#123semidirect
463. C22×C4#626semidirect
538. C32#2849semidirect
622. C3#74146semidirect
623. C3#82912semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×C3×#9292
C2×#639812
C2×#639622
C3×#52112
#105917142
#105916972
#105913872
#105912902
#829123
#741463