Finite Group Databasebeta

← #11864074

Subgroups — #11864074

Order 1152.

1961 conjugacy classes of subgroups.

The subgroup lattice has 665 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3828C211yesmaximal, characteristic, complemented
2C3×#5791C211yesmaximal, characteristic, complemented
3C2×#63831C211yesmaximal, characteristic, complemented
4C2×#63825C211yesmaximal, characteristic, complemented
5C3×#5207C211yesmaximal, characteristic, complemented
6#10591184C214yesmaximal, complemented
7#10591182C214yesmaximal, complemented
8#10591107C211yesmaximal, characteristic, complemented
9#10591096C211yesmaximal, characteristic, complemented
10#82928—31nomaximal
11#78638—31nomaximal
12C23×C32×C4C2211yescharacteristic
13C22×#638—21no—
14C2×#3828—22no—
15C2×#3828—24no—
16C2×#3828—24no—
17C2×#3828C2214yes—
18C22×C4⋊(C3⋊D3)C2211yescharacteristic
19C22×C4×C3⋊D3—21no—
20C22×#634C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C3×#953—21no—
23C3×#930C2212yescomplemented
24C3×#929—21no—
25C3×C4×#67—22no—
26C3×#926C2211yescharacteristic
27C3×#924C2212yescomplemented
28C2×C3×#208C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C2×#3719C2212yescomplemented
31C2×#3717C2212yescomplemented
32#63831—24no—
33C2×#3716C2212yescomplemented
34#63825—24no—
35C2×#3714C2212yescomplemented
36C3×#830C2214yescomplemented
37#63567C2214yescomplemented
38#63564C2214yescomplemented
39C22×#235—31no—
40C22×#235—31no—
41C22×#235—61no—
42C3×#525—31no—
43C2×#951—31no—
44C2×#949—31no—
45#5791D311yescharacteristic, complemented
46C2×#909—31no—
47C2×#908—31no—
48C3×#407—31no—
49#5207D311yescharacteristic, complemented
50#5131—31no—
51#5120—31no—
52#5047—34no—
53#5037—34no—
54#5004—31no—
55#5001—31no—
56#4734—34no—
57#4733—34no—
58C24×C32D411yescharacteristic
59C23×C3⋊D3—21no—
60C22×C32×C4—22no—
61C22×C32×C4—22no—
62C22×C32×C4D412yes—
63C22×C32×C4D411yescharacteristic
64C22×C32×C4C2312yes—
65C22×C32×C4C2311yescharacteristic
66C2×#638—28no—
67C2×#638—24no—
68C22×C3⋊Dic3—21no—
69#3828—216no—
70#3828—28no—
71#3828—28no—
72C2×C4⋊(C3⋊D3)—21no—
73C2×C4⋊(C3⋊D3)—22no—
74C2×C4⋊(C3⋊D3)D414yescomplemented
75C2×C4⋊(C3⋊D3)C2312yes—
76C2×C4×C3⋊D3—28no—
77C2×C4×C3⋊D3—24no—
78C2×#634—21no—
79C2×#634—22no—
80C2×#634D414yescomplemented
81C2×#634C2312yes—
82C2×C3×#67—22no—
83C2×C3×#67—21no—
84C3×#235—22no—
85C3×#235—22no—
86C2×C3×D12C2311yescharacteristic
87C2×C3×C4×D3—21no—
88C2×C3×Dic6C2311yescharacteristic
89C3×#217—22no—
90C3×#217—21no—
91C3×(C2×D3)⋊C4—22no—
92C3×C4⋊Dic3C2312yes—
93C3×Dic3⋊C4—22no—
94C3×C4×Dic3—21no—
95C3×#208—22no—
96C3×#208—22no—
97C2×C3×C3⋊C8C2312yes—
98C2×C3×C3⋊C8C2312yes—
99#3719—24no—
100#3717—24no—
101#3716—24no—
102#3714—24no—
103#3005—91noSylow
104C2×C3×#41—31no—
105C23×C3×C4—21no—
106C23×C3×C4C2×D311yescharacteristic
107C23×C3×C4C2×D311yescharacteristic
108C22×#67—62no—
109C22×#67—61no—
110C22×#67—61no—
111C2×#235—34no—
112C2×#235—34no—
113C2×#235—64no—
114C2×#235—64no—
115C2×#235—64no—
116C2×#235—64no—
117C2×#235—64no—
118C2×#235—68no—
119C2×#235—68no—
120C2×#235—64no—
121C2×#235—62no—
122C2×#235—62no—
123C2×#235C2×D311yescharacteristic
124C22×D12—31no—
125C22×D12—31no—
126C22×D12—61no—
127C22×C4×D3—62no—
128C22×C4×D3—61no—
129C22×C4×D3—61no—
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—61no—
133C2×C3×M16—31no—
134C2×C3×M16—31no—
135C3×#123—61no—
136C3×C22⋊Q8—32no—
137C3×#121—32no—
138C3×#120—61no—
139C3×C4×D4—62no—
140C3×#117—31no—
141#953—21no—
142#951—64no—
143#949—64no—
144C2×#216—32no—
145C2×#215—32no—
146C2×#214—32no—
147C2×#213—32no—
148#930C2×D312yescomplemented
149#929—21no—
150C4×#67—22no—
151#926C2×D311yescharacteristic
152#924C2×D312yescomplemented
153C2×#208C2×D311yescharacteristic
154C2×#208C2×D311yescharacteristic
155#909—64no—
156#908—64no—
157C2×Dic12—32no—
158C2×D24—32no—
159C2×#204—32no—
160C2×#204—32no—
161C3×C22⋊C8—34no—
162#830C2×D314yescomplemented
163#821—34no—
164#816—34no—
165#810—34no—
166#809—34no—
167C23×C32—22no—
168C23×C32—42no—
169C23×C32C2×D412yes—
170C23×C32C2×D411yescharacteristic
171C22×C3⋊D3—24no—
172C22×C3⋊D3—22no—
173C22×C3⋊D3—44no—
174C22×C3×D3—21no—
175C2×C32×C4—22no—
176C2×C32×C4—24no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4C2×D412yes—
180C2×C32×C4C2×D411yescharacteristic
181C2×C32×C4C2×D412yes—
182C2×C32×C4C2×D412yes—
183C2×C32×C4C2411yescharacteristic
184#638—216no—
185C2×C3⋊Dic3—24no—
186C2×C3⋊Dic3—22no—
187C4⋊(C3⋊D3)—24no—
188C4⋊(C3⋊D3)—22no—
189C4⋊(C3⋊D3)C2×D414yes—
190C4×C3⋊D3—216no—
191#634—24no—
192#634—22no—
193#634C2×D414yes—
194C3×#67—44no—
195C3×#67—42no—
196C2×C3×Dic3—22no—
197C2×C3×Dic3—21no—
198C3×D12—21no—
199C3×D12—21no—
200C3×C4×D3—42no—
201C3×Dic6—21no—
202C3×Dic6—21no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C2×#137—91no—
207C2×AGL(1,ℤ/8)—91no—
208#525—31no—
209#452—94no—
210#449—94no—
211#419—91no—
212#418—91no—
213#407—31no—
214C24×C3—21no—
215C24×C3D1211yescharacteristic
216C24×C3#6711yescharacteristic
217C23×D3—62no—
218C23×D3—61no—
219C23×D3—61no—
220C3×#41—62no—
221C3×#41—62no—
222C2×C3×Q8—31no—
223C2×C3×D4—31no—
224C2×C3×D4—62no—
225C2×C3×D4—61no—
226C22×C3×C4—24no—
227C22×C3×C4—24no—
228C22×C3×C4—22no—
229C22×C3×C4—22no—
230C22×C3×C4—22no—
231C22×C3×C4—22no—
232C22×C3×C4—21no—
233C22×C3×C4—22no—
234C22×C3×C4—21no—
235C22×C3×C4—22no—
236C22×C3×C4—61no—
237C22×C3×C4D1212yes—
238C22×C3×C4D1211yescharacteristic
239C22×C3×C4#6712yes—
240C22×C3×C4#6711yescharacteristic
241C22×C3×C4C22×D312yes—
242C22×C3×C4C22×D312yes—
243C22×C3×C4C22×D311yescharacteristic
244C22×C3×C4C22×D311yescharacteristic
245C2×#67—22no—
246C2×#67—21no—
247C2×#67—616no—
248C2×#67—68no—
249C2×#67—68no—
250C2×#67—68no—
251C2×#67—64no—
252C2×#67—64no—
253C22×Dic3—62no—
254C22×Dic3—61no—
255C22×Dic3—61no—
256#235—22no—
257#235—22no—
258#235—68no—
259#235—68no—
260#235—68no—
261#235—68no—
262#235—616no—
263#235—616no—
264#235—632no—
265#235—616no—
266#235—616no—
267C2×D12—34no—
268C2×D12—34no—
269C2×D12—32no—
270C2×D12—32no—
271C2×D12—64no—
272C2×D12—62no—
273C2×D12—62no—
274C2×D12—64no—
275C2×D12—61no—
276C2×D12—62no—
277C2×D12—62no—
278C2×D12—61no—
279C2×D12C22×D311yescharacteristic
280C2×C4×D3—21no—
281C2×C4×D3—616no—
282C2×C4×D3—68no—
283C2×C4×D3—68no—
284C2×C4×D3—68no—
285C2×C4×D3—64no—
286C2×C4×D3—64no—
287C2×Dic6—34no—
288C2×Dic6—34no—
289C2×Dic6—32no—
290C2×Dic6—32no—
291C2×Dic6—64no—
292C2×Dic6—62no—
293C2×Dic6—62no—
294C2×Dic6—64no—
295C2×Dic6—61no—
296C2×Dic6—62no—
297C2×Dic6—62no—
298C2×Dic6—61no—
299C2×Dic6C22×D311yescharacteristic
300C3×M16—62no—
301C3×M16—62no—
302C2×C3×C8—32no—
303C2×C3×C8—32no—
304C3×C4⋊C4—32no—
305C3×C4⋊C4—62no—
306C3×C22⋊C4—61no—
307C3×C22⋊C4—62no—
308C3×C22⋊C4—62no—
309C3×C42—61no—
310#217—22no—
311#217—21no—
312#216—64no—
313#215—64no—
314#214—64no—
315#213—64no—
316(C2×D3)⋊C4—22no—
317C4⋊Dic3C22×D312yes—
318Dic3⋊C4—22no—
319C4×Dic3—21no—
320#208—22no—
321#208—22no—
322C2×C3⋊C8C22×D312yes—
323C2×C3⋊C8C22×D312yes—
324Dic12—64no—
325D24—64no—
326#204—64no—
327#204—64no—
328C22×C32—22no—
329C22×C32—22no—
330C22×C32—22no—
331C22×C32—22no—
332C22×C32—44no—
333C22×C32#12012yes—
334C22×C32C22×D411yescharacteristic
335C2×C3⋊D3—24no—
336C2×C3⋊D3—48no—
337C2×C3⋊D3—44no—
338C2×C3×D3—41no—
339C2×C3×D3—42no—
340C32×C4—22no—
341C32×C4#12012yes—
342C32×C4C22×D411yescharacteristic
343C32×C4C22×D411yescharacteristic
344C3⋊Dic3—24no—
345C3×Dic3—41no—
346C3×Dic3—42no—
347C2×#41—31no—
348C2×#41—94no—
349C2×#41—184no—
350C2×#41—184no—
351C2×#41—182no—
352C22×Q8—91no—
353C22×D4—91no—
354C22×D4—181no—
355C23×C4—181no—
356C23×C4D3211yescharacteristic
357#137—184no—
358AGL(1,ℤ/8)—184no—
359C2×Q16—92no—
360C2×SD16—92no—
361C2×SD16—92no—
362C2×D8—92no—
363C2×M16—31no—
364C2×M16—31no—
365#123—61no—
366C22⋊Q8—32no—
367#121—32no—
368#120—61no—
369C4×D4—62no—
370#117—31no—
371#103—94no—
372#102—94no—
373C22⋊C8—34no—
374C23×C3—24no—
375C23×C3—22no—
376C23×C3—22no—
377C23×C3—21no—
378C23×C3—22no—
379C23×C3—42no—
380C23×C3—42no—
381C23×C3—44no—
382C23×C3—61no—
383C23×C3C2×D1212yes—
384C23×C3C2×D1211yescharacteristic
385C23×C3C2×#6712yes—
386C23×C3C2×#6711yescharacteristic
387C22×D3—21no—
388C22×D3—64no—
389C22×D3—68no—
390C22×D3—64no—
391C22×D3—64no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—128no—
395C22×D3—124no—
396C22×D3—124no—
397C3×Q8—61no—
398C3×Q8—61no—
399C3×D4—61no—
400C3×D4—61no—
401C3×D4—124no—
402C3×D4—122no—
403C2×C3×C4—24no—
404C2×C3×C4—24no—
405C2×C3×C4—24no—
406C2×C3×C4—28no—
407C2×C3×C4—22no—
408C2×C3×C4—22no—
409C2×C3×C4—24no—
410C2×C3×C4—24no—
411C2×C3×C4—22no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—22no—
415C2×C3×C4—21no—
416C2×C3×C4—21no—
417C2×C3×C4—22no—
418C2×C3×C4—22no—
419C2×C3×C4—22no—
420C2×C3×C4—62no—
421C2×C3×C4—61no—
422C2×C3×C4—122no—
423C2×C3×C4C2×D1212yes—
424C2×C3×C4C2×D1211yescharacteristic
425C2×C3×C4D3×D412yes—
426C2×C3×C4D3×D412yes—
427C2×C3×C4D3×D412yes—
428C2×C3×C4D3×D412yes—
429C2×C3×C4C2×#6712yes—
430C2×C3×C4C2×#6711yescharacteristic
431C2×C3×C4C23×D311yescharacteristic
432C2×C3×C4C23×D311yescharacteristic
433#67—44no—
434#67—42no—
435#67—632no—
436#67—616no—
437#67—616no—
438C2×Dic3—22no—
439C2×Dic3—21no—
440C2×Dic3—64no—
441C2×Dic3—68no—
442C2×Dic3—64no—
443C2×Dic3—64no—
444C2×Dic3—62no—
445C2×Dic3—62no—
446D12—21no—
447D12—21no—
448D12—34no—
449D12—34no—
450D12—64no—
451D12—64no—
452D12—68no—
453D12—64no—
454D12—64no—
455D12—62no—
456D12—62no—
457C4×D3—42no—
458C4×D3—632no—
459C4×D3—616no—
460C4×D3—616no—
461Dic6—21no—
462Dic6—21no—
463Dic6—34no—
464Dic6—34no—
465Dic6—64no—
466Dic6—64no—
467Dic6—68no—
468Dic6—64no—
469Dic6—64no—
470Dic6—62no—
471Dic6—62no—
472C3×C8—62no—
473C3×C8—62no—
474C3⋊C8—22no—
475C3⋊C8—22no—
476C2×C32—22no—
477C2×C32—42no—
478C2×C32C2×#12011yescharacteristic
479C2×C32#57512yes—
480C3⋊D3—44no—
481C3×D3—81no—
482C24—181no—
483C24#62611yescharacteristic
484#41—62no—
485#41—62no—
486#41—188no—
487#41—188no—
488#41—1816no—
489C2×Q8—31no—
490C2×Q8—92no—
491C2×Q8—94no—
492C2×Q8—181no—
493C2×Q8—182no—
494C2×D4—31no—
495C2×D4—62no—
496C2×D4—61no—
497C2×D4—92no—
498C2×D4—94no—
499C2×D4—188no—
500C2×D4—184no—
501C2×D4—181no—
502C2×D4—182no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—61no—
506C22×C4—188no—
507C22×C4—181no—
508C22×C4—184no—
509C22×C4#62612yes—
510C22×C4#62611yescharacteristic
511C22×C4C2×D3212yes—
512C22×C4C2×D3211yescharacteristic
513Q16—184no—
514SD16—184no—
515SD16—184no—
516D8—184no—
517M16—62no—
518M16—62no—
519C2×C8—32no—
520C2×C8—32no—
521C4⋊C4—32no—
522C4⋊C4—62no—
523C22⋊C4—61no—
524C22⋊C4—62no—
525C22⋊C4—62no—
526C42—61no—
527C22×C3—24no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—24no—
531C22×C3—22no—
532C22×C3—22no—
533C22×C3—22no—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—22no—
539C22×C3—42no—
540C22×C3—42no—
541C22×C3—48no—
542C22×C3—44no—
543C22×C3—44no—
544C22×C3—121no—
545C22×C3—122no—
546C22×C3#88212yes—
547C22×C3#93712yes—
548C22×C3C22×D1211yescharacteristic
549C22×C3C22×#6711yescharacteristic
550C2×D3—41no—
551C2×D3—42no—
552C2×D3—68no—
553C2×D3—64no—
554C2×D3—64no—
555C2×D3—1216no—
556C2×D3—128no—
557C2×D3—128no—
558C2×D3—128no—
559C2×D3—124no—
560C2×D3—124no—
561C3×C4—24no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—21no—
565C3×C4—21no—
566C3×C4—22no—
567C3×C4—121no—
568C3×C4—122no—
569C3×C4#88212yes—
570C3×C4#93712yes—
571C3×C4C2×D3×D411yescharacteristic
572C3×C4C2×D3×D411yescharacteristic
573C3×C4C2×D3×D411yescharacteristic
574C3×C4C2×D3×D411yescharacteristic
575Dic3—41no—
576Dic3—42no—
577Dic3—68no—
578Dic3—64no—
579Dic3—64no—
580C32#300511yescharacteristic, complemented, Sylow
581C23—22no—
582C23—42no—
583C23—61no—
584C23—182no—
585C23—184no—
586C23—364no—
587C23C2×#62612yes—
588C23C2×#62611yescharacteristic
589Q8—61no—
590Q8—61no—
591Q8—94no—
592Q8—182no—
593Q8—184no—
594D4—61no—
595D4—61no—
596D4—94no—
597D4—124no—
598D4—122no—
599D4—1816no—
600D4—182no—
601D4—184no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—62no—
607C2×C4—61no—
608C2×C4—122no—
609C2×C4—1816no—
610C2×C4—182no—
611C2×C4—184no—
612C2×C4C2×#62612yes—
613C2×C4C2×#62611yescharacteristic
614C2×C4#381112yes—
615C2×C4#381112yes—
616C2×C4C22×D3211yescharacteristic
617C8—62no—
618C8—62no—
619C2×C3—24no—
620C2×C3—22no—
621C2×C3—22no—
622C2×C3—21no—
623C2×C3—22no—
624C2×C3—44no—
625C2×C3—42no—
626C2×C3—42no—
627C2×C3—241no—
628C2×C3C2×#88211yescharacteristic
629C2×C3#574812yes—
630C2×C3C2×#93711yescharacteristic
631C2×C3#582212yes—
632D3—81no—
633D3—128no—
634D3—124no—
635D3—124no—
636C22—22no—
637C22—22no—
638C22—22no—
639C22—22no—
640C22—44no—
641C22—121no—
642C22—122no—
643C22—184no—
644C22—368no—
645C22—364no—
646C22#6398112yes—
647C22C22×#62611yescharacteristic
648C4—22no—
649C4—121no—
650C4—122no—
651C4—184no—
652C4#6398112yes—
653C4C2×#381111yescharacteristic
654C4C2×#381111yescharacteristic
655C3—21no—
656C3#7863811yescharacteristic, complemented
657C3#8292811yescharacteristic, complemented
658C2—22no—
659C2—42no—
660C2—241no—
661C2—364no—
662C2#1059479512yes—
663C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C22×#626
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC23×C32×C4C22
socleC22×C32C22×D4
hypercenterC23×C4D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3828C2semidirect
2. C3×#5791C2semidirect
3. C2×#63831C2semidirect
4. C2×#63825C2semidirect
5. C3×#5207C2semidirect
6. #10591184C2semidirect
7. #10591182C2semidirect
8. #10591107C2semidirect
9. #10591096C2semidirect
23. C3×#930C22semidirect
27. C3×#924C22semidirect
30. C2×#3719C22semidirect
31. C2×#3717C22semidirect
33. C2×#3716C22semidirect
35. C2×#3714C22semidirect
36. C3×#830C22semidirect
37. #63567C22semidirect
38. #63564C22semidirect
45. #5791D3semidirect
49. #5207D3semidirect
74. C2×C4⋊(C3⋊D3)D4semidirect
80. C2×#634D4semidirect
148. #930C2×D3semidirect
152. #924C2×D3semidirect
162. #830C2×D3semidirect
580. C32#3005semidirect
656. C3#78638semidirect
657. C3#82928semidirect

Maximal subgroups

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

subgroupindex
C22×#38282
C3×#57912
C2×#638312
C2×#638252
C3×#52072
#105911842
#105911822
#105911072
#105910962
#829283
#786383