Finite Group Databasebeta

← #11864071

Subgroups — #11864071

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×#3830C211yesmaximal, characteristic, complemented
2C2×C3×#932C211yesmaximal, characteristic, complemented
3#10595034C211yesmaximal, characteristic, complemented
4C2×#63831C211yesmaximal, characteristic, complemented
5C3×#5215C211yesmaximal, characteristic, complemented
6#10591466C214yesmaximal, complemented
7#10591457C214yesmaximal, complemented
8#10591107C211yesmaximal, characteristic, complemented
9#10591074C211yesmaximal, characteristic, complemented
10#83945—31nomaximal
11#78927—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638—21no—
14C23×C3⋊Dic3—21no—
15C2×#3830—24no—
16C2×#3830—22no—
17C2×#3830—24no—
18C2×#3830C2214yes—
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×#634C2211yescharacteristic
21C2×C3×#235C2211yescharacteristic
22C2×C3×#214C2212yescomplemented
23C3×#932—24no—
24C2×C3×#213C2212yescomplemented
25C3×#926C2211yescharacteristic
26C2×C3×#208C2211yescharacteristic
27C2×C3×#208C2211yescharacteristic
28#63981—21no—
29#63962—21no—
30#63916C2212yescomplemented
31C4×#626—22no—
32#63871C2212yescomplemented
33C2×#3719C2212yescomplemented
34#63831—24no—
35C2×#3716C2212yescomplemented
36C3×#832C2214yescomplemented
37#63567C2214yescomplemented
38#63557C2214yescomplemented
39C22×#237—31no—
40C22×#237—31no—
41C22×#237—61no—
42C2×C3×AGL(1,ℤ/8)—31no—
43#5828—31no—
44C2×#951—31no—
45C2×#932D311yescharacteristic, complemented
46C2×#909—31no—
47#5524—31no—
48C3×#418—31no—
49#5215D311yescharacteristic, complemented
50#5173—34no—
51#5158—34no—
52#5126—31no—
53#5126—31no—
54#5120—31no—
55#5004—31no—
56#4783—34no—
57#4781—34no—
58C24×C32—21no—
59C23×C3⋊D3D411yescharacteristic
60C2×C32×D4—21no—
61C2×C32×D4—22no—
62C2×C32×D4D414yescomplemented
63C2×C32×D4C2312yes—
64C22×C32×C4C2311yescharacteristic
65C2×#638—28no—
66C2×#638—24no—
67C22×C3⋊Dic3—28no—
68C22×C3⋊Dic3—21no—
69C22×C3⋊Dic3—24no—
70C22×C3⋊Dic3D411yescharacteristic
71#3830—216no—
72#3830—28no—
73#3830—28no—
74C2×C4×C3⋊D3—22no—
75C2×C4×C3⋊D3—22no—
76C2×C4×C3⋊D3D412yes—
77C2×C4×C3⋊D3C2312yes—
78C2×#634—21no—
79C2×#634—22no—
80C2×#634D414yescomplemented
81C2×#634C2312yes—
82C2×C3×#67—21no—
83C3×#235—22no—
84C3×#235—22no—
85C2×C3×D12C2311yescharacteristic
86C2×C3×C4×D3—21no—
87C2×C3×Dic6C2311yescharacteristic
88C2×#626—22no—
89C3×#217—21no—
90C3×#214—24no—
91C3×#213—24no—
92C3×C4⋊Dic3C2312yes—
93C3×C4×Dic3—21no—
94C3×#208—22no—
95C3×#208—22no—
96C2×C3×C3⋊C8C2312yes—
97C2×C3×C3⋊C8C2312yes—
98Dic3⋊Dic3—22no—
99#3722—22no—
100(C2×D3)⋊Dic3—22no—
101#3719—24no—
102#3716—24no—
103#3005—91noSylow
104C2×C3×#41—31no—
105C22×C3×D4—21no—
106C22×C3×D4C2×D311yescharacteristic
107C22×C3×D4C2×D311yescharacteristic
108C22×#67—61no—
109C22×#67—61no—
110C22×#67—62no—
111C23×Dic3—61no—
112C23×Dic3—61no—
113C23×Dic3—62no—
114C2×#237—34no—
115C2×#237—34no—
116C2×#237—64no—
117C2×#237—64no—
118C2×#237—64no—
119C2×#237—62no—
120C2×#237—62no—
121C2×#237—64no—
122C2×#237—68no—
123C2×#237—68no—
124C2×#237—64no—
125C2×#237—64no—
126C2×#235C2×D311yescharacteristic
127C22×C4×D3—31no—
128C22×C4×D3—31no—
129C22×C4×D3—61no—
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—61no—
133C3×AGL(1,ℤ/8)—64no—
134C2×C3×SD16—32no—
135C2×C3×D8—32no—
136C2×C3×M16—31no—
137C2×C3×M16—31no—
138C3×#117—31no—
139#951—64no—
140#946—32no—
141C2×#216—32no—
142#938—32no—
143#937—61no—
144#935—61no—
145C2×#214—32no—
146C2×#214C2×D312yescomplemented
147#932—24no—
148C2×#213C2×D312yescomplemented
149C4×#67—62no—
150#926C2×D311yescharacteristic
151C2×#208C2×D311yescharacteristic
152C2×#208C2×D311yescharacteristic
153#909—64no—
154C2×Dic12—32no—
155C2×#204—32no—
156#897—32no—
157#895—32no—
158#886—61no—
159#882—61no—
160C4×D12—62no—
161C3×#102—34no—
162#832C2×D314yescomplemented
163(C2×D3)⋊C8—34no—
164(C2×D3)⋊C8—34no—
165#816—34no—
166#810—34no—
167C23×C32—24no—
168C23×C32—22no—
169C23×C32—44no—
170C23×C32C2×D411yescharacteristic
171C22×C3⋊D3—22no—
172C22×C3⋊D3—42no—
173C22×C3⋊D3C2×D412yes—
174C22×C3×D3—21no—
175C32×D4—24no—
176C32×D4—22no—
177C32×D4C2×D414yes—
178C2×C32×C4C2×D412yes—
179C2×C32×C4C2×D411yescharacteristic
180C2×C32×C4C2×D412yes—
181C2×C32×C4C2411yescharacteristic
182#638—216no—
183C2×C3⋊Dic3—216no—
184C2×C3⋊Dic3—24no—
185C2×C3⋊Dic3—22no—
186C2×C3⋊Dic3—22no—
187C2×C3⋊Dic3C2×D412yes—
188C4×C3⋊D3—24no—
189C4×C3⋊D3—22no—
190C4×C3⋊D3—22no—
191#634—24no—
192#634—22no—
193#634C2×D414yes—
194C3×#67—42no—
195C2×C3×Dic3—22no—
196C2×C3×Dic3—21no—
197C3×D12—21no—
198C3×D12—21no—
199C3×C4×D3—42no—
200C3×Dic6—21no—
201C3×Dic6—21no—
202#626—44no—
203C3×C3⋊C8—22no—
204C3×C3⋊C8—22no—
205C22×#41—91no—
206C2×#137—91no—
207C2×AGL(1,ℤ/8)—31no—
208#525—91no—
209#452—94no—
210#449—94no—
211#419—91no—
212#418—31no—
213#407—91no—
214C24×C3—22no—
215C24×C3—21no—
216C24×C3—21no—
217C23×D3—31no—
218C23×D3—31no—
219C23×D3—61no—
220C3×#41—62no—
221C3×#41—62no—
222C2×C3×Q8—31no—
223C2×C3×D4—24no—
224C2×C3×D4—22no—
225C2×C3×D4—21no—
226C2×C3×D4—22no—
227C2×C3×D4—21no—
228C2×C3×D4—22no—
229C2×C3×D4—24no—
230C2×C3×D4—22no—
231C2×C3×D4—31no—
232C2×C3×D4—61no—
233C2×C3×D4D1214yescomplemented
234C2×C3×D4#6714yescomplemented
235C2×C3×D4C22×D312yes—
236C2×C3×D4C22×D312yes—
237C22×C3×C4—21no—
238C22×C3×C4—61no—
239C22×C3×C4C22×D311yescharacteristic
240C22×C3×C4C22×D311yescharacteristic
241C2×#67—21no—
242C2×#67—62no—
243C2×#67—64no—
244C2×#67—64no—
245C2×#67—68no—
246C2×#67—616no—
247C2×#67—68no—
248C2×#67—68no—
249C22×Dic3—31no—
250C22×Dic3—31no—
251C22×Dic3—61no—
252C22×Dic3—64no—
253C22×Dic3—64no—
254C22×Dic3—62no—
255C22×Dic3—68no—
256C22×Dic3—616no—
257C22×Dic3—68no—
258C22×Dic3—68no—
259C22×Dic3—61no—
260C22×Dic3—61no—
261#237—68no—
262#237—68no—
263#237—616no—
264#237—632no—
265#237—616no—
266#237—616no—
267#237—616no—
268#237—68no—
269#237—68no—
270#235—22no—
271#235—22no—
272C2×D12—62no—
273C2×D12C22×D311yescharacteristic
274C2×C4×D3—21no—
275C2×C4×D3—32no—
276C2×C4×D3—32no—
277C2×C4×D3—32no—
278C2×C4×D3—32no—
279C2×C4×D3—62no—
280C2×C4×D3—62no—
281C2×C4×D3—64no—
282C2×C4×D3—64no—
283C2×C4×D3—62no—
284C2×C4×D3—62no—
285C2×C4×D3—62no—
286C2×C4×D3—62no—
287C2×Dic6—34no—
288C2×Dic6—34no—
289C2×Dic6—32no—
290C2×Dic6—32no—
291C2×Dic6—64no—
292C2×Dic6—62no—
293C2×Dic6—64no—
294C2×Dic6—62no—
295C2×Dic6—62no—
296C2×Dic6—61no—
297C2×Dic6—61no—
298C2×Dic6—62no—
299C2×Dic6C22×D311yescharacteristic
300C3×SD16—64no—
301C3×D8—64no—
302C3×M16—62no—
303C3×M16—62no—
304C2×C3×C8—32no—
305C2×C3×C8—32no—
306C3×C4⋊C4—32no—
307C3×C22⋊C4—61no—
308C3×C42—61no—
309#217—21no—
310#217—62no—
311#216—64no—
312#214—24no—
313#214—64no—
314#213—24no—
315(C2×D3)⋊C4—62no—
316(C2×D3)⋊C4—62no—
317(C2×D3)⋊C4—62no—
318C4⋊Dic3—62no—
319C4⋊Dic3C22×D312yes—
320Dic3⋊C4—62no—
321C4×Dic3—21no—
322#208—22no—
323#208—22no—
324C2×C3⋊C8C22×D312yes—
325C2×C3⋊C8C22×D312yes—
326Dic12—64no—
327#204—64no—
328C22×C32—22no—
329C22×C32—24no—
330C22×C32—48no—
331C22×C32—44no—
332C22×C32#12012yes—
333C22×C32C22×D411yescharacteristic
334C2×C3⋊D3—22no—
335C2×C3⋊D3—22no—
336C2×C3⋊D3—22no—
337C2×C3⋊D3—44no—
338C2×C3×D3—41no—
339C2×C3×D3—42no—
340C32×C4#12012yes—
341C32×C4C22×D411yescharacteristic
342C32×C4C22×D411yescharacteristic
343C3⋊Dic3—24no—
344C3⋊Dic3—22no—
345C3×Dic3—41no—
346C3×Dic3—42no—
347C2×#41—31no—
348C2×#41—94no—
349C2×#41—182no—
350C2×#41—184no—
351C2×#41—184no—
352C22×Q8—91no—
353C22×D4—181no—
354C22×D4D3211yescharacteristic
355C23×C4—91no—
356C23×C4—181no—
357#137—184no—
358AGL(1,ℤ/8)—64no—
359C2×Q16—92no—
360C2×SD16—32no—
361C2×SD16—92no—
362C2×D8—32no—
363C2×M16—31no—
364C2×M16—31no—
365#123—181no—
366C22⋊Q8—92no—
367#121—92no—
368#120—181no—
369C4×D4—182no—
370#117—31no—
371#103—94no—
372#102—34no—
373C22⋊C8—94no—
374C23×C3—24no—
375C23×C3—28no—
376C23×C3—24no—
377C23×C3—24no—
378C23×C3—22no—
379C23×C3—22no—
380C23×C3—21no—
381C23×C3—48no—
382C23×C3—44no—
383C23×C3—44no—
384C23×C3—61no—
385C23×C3D3×D411yescharacteristic
386C23×C3D3×D411yescharacteristic
387C22×D3—21no—
388C22×D3—32no—
389C22×D3—32no—
390C22×D3—62no—
391C22×D3—64no—
392C22×D3—62no—
393C22×D3—62no—
394C22×D3—122no—
395C22×D3—122no—
396C22×D3—124no—
397C3×Q8—61no—
398C3×Q8—61no—
399C3×D4—24no—
400C3×D4—28no—
401C3×D4—24no—
402C3×D4—24no—
403C3×D4—22no—
404C3×D4—22no—
405C3×D4—24no—
406C3×D4—61no—
407C3×D4—61no—
408C3×D4—122no—
409C3×D4C2×D1214yes—
410C3×D4C2×#6714yes—
411C2×C3×C4—21no—
412C2×C3×C4—22no—
413C2×C3×C4—22no—
414C2×C3×C4—21no—
415C2×C3×C4—61no—
416C2×C3×C4—62no—
417C2×C3×C4—122no—
418C2×C3×C4C2×D1212yes—
419C2×C3×C4D3×D411yescharacteristic
420C2×C3×C4D3×D412yes—
421C2×C3×C4D3×D411yescharacteristic
422C2×C3×C4D3×D412yes—
423C2×C3×C4C2×#6712yes—
424C2×C3×C4C23×D311yescharacteristic
425C2×C3×C4C23×D311yescharacteristic
426#67—42no—
427#67—632no—
428#67—616no—
429#67—616no—
430#67—124no—
431C2×Dic3—22no—
432C2×Dic3—21no—
433C2×Dic3—32no—
434C2×Dic3—32no—
435C2×Dic3—62no—
436C2×Dic3—64no—
437C2×Dic3—68no—
438C2×Dic3—64no—
439C2×Dic3—632no—
440C2×Dic3—616no—
441C2×Dic3—616no—
442C2×Dic3—64no—
443C2×Dic3—62no—
444C2×Dic3—64no—
445C2×Dic3—62no—
446C2×Dic3—62no—
447C2×Dic3—62no—
448D12—21no—
449D12—21no—
450D12—124no—
451C4×D3—42no—
452C4×D3—64no—
453C4×D3—64no—
454C4×D3—68no—
455C4×D3—64no—
456C4×D3—64no—
457C4×D3—62no—
458C4×D3—62no—
459C4×D3—62no—
460C4×D3—62no—
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—44no—
478C2×C32C2×#12011yescharacteristic
479C2×C32#57512yes—
480C3⋊D3—42no—
481C3×D3—81no—
482C24—21no—
483C24—91no—
484#41—62no—
485#41—62no—
486#41—188no—
487#41—1816no—
488#41—188no—
489C2×Q8—31no—
490C2×Q8—92no—
491C2×Q8—94no—
492C2×Q8—182no—
493C2×Q8—181no—
494C2×D4—22no—
495C2×D4—21no—
496C2×D4—31no—
497C2×D4—61no—
498C2×D4—182no—
499C2×D4—184no—
500C2×D4—188no—
501C2×D4#62614yescomplemented
502C2×D4C2×D3212yes—
503C22×C4—61no—
504C22×C4—91no—
505C22×C4—92no—
506C22×C4—92no—
507C22×C4—184no—
508C22×C4—188no—
509C22×C4—181no—
510C22×C4—182no—
511C22×C4—182no—
512C22×C4C2×D3211yescharacteristic
513Q16—184no—
514SD16—64no—
515SD16—184no—
516D8—64no—
517M16—62no—
518M16—62no—
519C2×C8—32no—
520C2×C8—32no—
521C4⋊C4—32no—
522C4⋊C4—182no—
523C22⋊C4—61no—
524C22⋊C4—182no—
525C22⋊C4—182no—
526C42—61no—
527C22×C3—24no—
528C22×C3—22no—
529C22×C3—22no—
530C22×C3—28no—
531C22×C3—24no—
532C22×C3—24no—
533C22×C3—21no—
534C22×C3—22no—
535C22×C3—416no—
536C22×C3—48no—
537C22×C3—48no—
538C22×C3—48no—
539C22×C3—44no—
540C22×C3—44no—
541C22×C3—121no—
542C22×C3—122no—
543C22×C3#88212yes—
544C22×C3#93712yes—
545C22×C3C2×D3×D411yescharacteristic
546C22×C3C2×D3×D411yescharacteristic
547C2×D3—42no—
548C2×D3—41no—
549C2×D3—64no—
550C2×D3—62no—
551C2×D3—62no—
552C2×D3—62no—
553C2×D3—62no—
554C2×D3—62no—
555C2×D3—62no—
556C2×D3—122no—
557C2×D3—122no—
558C2×D3—128no—
559C2×D3—124no—
560C2×D3—124no—
561C3×C4—21no—
562C3×C4—21no—
563C3×C4—22no—
564C3×C4—121no—
565C3×C4—122no—
566C3×C4#88212yes—
567C3×C4#93712yes—
568C3×C4C22×D1211yescharacteristic
569C3×C4C2×D3×D411yescharacteristic
570C3×C4C2×D3×D411yescharacteristic
571C3×C4C22×#6711yescharacteristic
572Dic3—42no—
573Dic3—41no—
574Dic3—68no—
575Dic3—64no—
576Dic3—64no—
577Dic3—62no—
578Dic3—64no—
579Dic3—62no—
580C32#300511yescharacteristic, complemented, Sylow
581C23—22no—
582C23—24no—
583C23—44no—
584C23—61no—
585C23—92no—
586C23—182no—
587C23—362no—
588C23#381111yescharacteristic
589Q8—61no—
590Q8—61no—
591Q8—94no—
592Q8—182no—
593Q8—184no—
594D4—22no—
595D4—24no—
596D4—61no—
597D4—61no—
598D4—122no—
599D4—1816no—
600D4—364no—
601D4C2×#62614yes—
602C2×C4—62no—
603C2×C4—61no—
604C2×C4—92no—
605C2×C4—122no—
606C2×C4—1816no—
607C2×C4—182no—
608C2×C4—182no—
609C2×C4—184no—
610C2×C4—182no—
611C2×C4—182no—
612C2×C4—184no—
613C2×C4C2×#62612yes—
614C2×C4#381112yes—
615C2×C4#381111yescharacteristic
616C2×C4C22×D3211yescharacteristic
617C8—62no—
618C8—62no—
619C2×C3—24no—
620C2×C3—22no—
621C2×C3—22no—
622C2×C3—22no—
623C2×C3—21no—
624C2×C3—48no—
625C2×C3—44no—
626C2×C3—44no—
627C2×C3—241no—
628C2×C3C2×#88211yescharacteristic
629C2×C3#577312yes—
630C2×C3#577312yes—
631C2×C3C2×#93711yescharacteristic
632D3—81no—
633D3—124no—
634D3—122no—
635D3—122no—
636C22—22no—
637C22—24no—
638C22—48no—
639C22—44no—
640C22—122no—
641C22—121no—
642C22—182no—
643C22—182no—
644C22—182no—
645C22—364no—
646C22#6398112yes—
647C22C2×#381111yescharacteristic
648C4—122no—
649C4—121no—
650C4—182no—
651C4—184no—
652C4#6398112yes—
653C4C22×#62611yescharacteristic
654C4C2×#381111yescharacteristic
655C3—21no—
656C3#7892711yescharacteristic, complemented
657C3#8394511yescharacteristic, complemented
658C2—22no—
659C2—44no—
660C2—241no—
661C2—362no—
662C2#1059510112yes—
663C2C2×#6398111yescharacteristic
subgroupG/H
centerC22C2×#3811
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC22×C32×D4C22
socleC22×C32C22×D4
hypercenterC22×D4D32
hypocenterC32#3005
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C2×C3×#932C2semidirect
3. #10595034C2semidirect
4. C2×#63831C2semidirect
5. C3×#5215C2semidirect
6. #10591466C2semidirect
7. #10591457C2semidirect
8. #10591107C2semidirect
9. #10591074C2semidirect
22. C2×C3×#214C22semidirect
24. C2×C3×#213C22semidirect
30. #63916C22semidirect
32. #63871C22semidirect
33. C2×#3719C22semidirect
35. C2×#3716C22semidirect
36. C3×#832C22semidirect
37. #63567C22semidirect
38. #63557C22semidirect
45. C2×#932D3semidirect
49. #5215D3semidirect
62. C2×C32×D4D4semidirect
80. C2×#634D4semidirect
146. C2×#214C2×D3semidirect
148. C2×#213C2×D3semidirect
162. #832C2×D3semidirect
233. C2×C3×D4D12semidirect
234. C2×C3×D4#67semidirect
501. C2×D4#626semidirect
580. C32#3005semidirect
656. C3#78927semidirect
657. C3#83945semidirect

Maximal subgroups

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

subgroupindex
C22×#38302
C2×C3×#9322
#105950342
C2×#638312
C3×#52152
#105914662
#105914572
#105911072
#105910742
#839453
#789273