Finite Group Databasebeta

← #11900770

Subgroups — #11900770

Order 1152.

3705 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64306C212yesmaximal, complemented
2C2×C42×C3⋊D3C211yesmaximal, characteristic, complemented
3C3×#5477C212yesmaximal, complemented
4#10595081C214yesmaximal, complemented
5#10595032C212yesmaximal, complemented
6#10594929C214yesmaximal, complemented
7#10594009C212yesmaximal, complemented
8#10594008C211yesmaximal, characteristic, complemented
9C4×#3802C214yesmaximal, complemented
10#10593972C214yesmaximal, complemented
11#10593971C212yesmaximal, complemented
12#10593909C211yesmaximal, characteristic, complemented
13#10593907C212yesmaximal, complemented
14D3×#532—32nomaximal
15C22×C4×C3⋊D3C2212yes—
16C22×C4×C3⋊D3C2211yescharacteristic
17C2×C3×#235C2214yescomplemented
18C2×#3811C2214yes—
19C2×#3805C2214yescomplemented
20#64306—216no—
21C2×#3802C2214yes—
22C2×#3802C2212yes—
23C2×C4×D32C2214yes—
24C2×#3798C2214yescomplemented
25C2×#3797C2212yes—
26C2×#3796C2214yescomplemented
27C2×C32×C42C2211yescharacteristic, complemented
28C2×C4×C3⋊Dic3C2212yescomplemented
29C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
30C42×C3⋊D3C2211yescharacteristic
31C42×C3⋊D3C2212yes—
32C42×C3⋊D3C2211yescharacteristic
33C42×C3⋊D3C2211yescharacteristic, complemented
34C42×C3⋊D3C2211yescharacteristic, complemented
35C42×C3⋊D3C2212yescomplemented
36C3×#930C2218yescomplemented
37C3×#875C2214yescomplemented
38C3×#874C2212yescomplemented
39C3×C4×D12C2218yescomplemented
40C3×#869C2212yescomplemented
41#63980C2218yescomplemented
42#63921C2218yes—
43#63919C2214yescomplemented
44#63916C2218yescomplemented
45#63915C2218yescomplemented
46#63914C2214yescomplemented
47#63914C2212yescomplemented
48#63912C2218yescomplemented
49#63902C2218yescomplemented
50C4×#625C2218yescomplemented
51#63900C2214yes—
52#63898C2218yescomplemented
53#63873C2212yescomplemented
54#63863C2214yescomplemented
55C2×D3×#41—34no—
56C3×#532—32no—
57#5832—34no—
58#5725—32no—
59D3×C4⋊Q8—32no—
60#5716—32no—
61D3×#127—32no—
62D3×#124—34no—
63#5668—34no—
64D3×#121—38no—
65#5596—38no—
66#5548—38no—
67C4×D3×D4—38no—
68#5477D312yescomplemented
69C2×C42×D3—32no—
70C2×C42×D3—61no—
71C23×C3⋊D3C2311yescharacteristic
72C22×D32C2314yes—
73C22×C32×C4C2312yes—
74C22×C32×C4C2311yescharacteristic
75C22×C3⋊Dic3C2312yes—
76C22×C3⋊Dic3C2311yescharacteristic
77C2×C4×C3⋊D3—28no—
78C2×C4×C3⋊D3D418yescomplemented
79C2×C4×C3⋊D3C2312yes—
80C2×C4×C3⋊D3C2312yes—
81C2×C4×C3⋊D3C2312yes—
82C2×C4×C3⋊D3C2311yescharacteristic
83C2×C4×C3⋊D3C2311yescharacteristic
84C2×C4×C3⋊D3C2311yescharacteristic
85C2×C4×C3⋊D3C2311yescharacteristic
86C2×C4×C3⋊D3C2312yes—
87C2×C3×#67C2318yes—
88C3×#235—216no—
89C2×C3×D12C2314yes—
90C2×C3×D12C2318yes—
91C2×C3×C4×D3C2318yes—
92C2×C3×Dic6C2314yes—
93#3811—216no—
94C2×#627C2314yes—
95C2×#626C2318yes—
96C2×#625C2314yes—
97C2×#625C2318yes—
98C2×#624C2314yes—
99#3805—216no—
100C2×D3×Dic3C2318yes—
101#3802—28no—
102#3802—216no—
103C4×D32—216no—
104#3798—216no—
105#3797—28no—
106#3796—216no—
107C32×C42C2311yescharacteristic
108C32×C42C2312yes—
109C32×C42C2311yescharacteristic
110C4×C3⋊Dic3C2311yescharacteristic
111C4×C3⋊Dic3C2311yescharacteristic
112C4×C3⋊Dic3C2312yes—
113C4×C3⋊Dic3C2312yes—
114C4×C3⋊Dic3C2312yes—
115C4×C3⋊Dic3C2312yes—
116C4×C3⋊Dic3C2312yes—
117C3×(C2×D3)⋊C4C23116yes—
118C3×C4⋊Dic3C2318yes—
119#3724C2318yes—
120(C2×D3)⋊Dic3C23116yes—
121C2×#532—91noSylow
122C2×C3×#41—34no—
123D3×#41—632no—
124C2×#239—34no—
125C2×D3×Q8—34no—
126C2×#237—38no—
127C2×#237—34no—
128C2×D3×D4—38no—
129C2×D3×D4—34no—
130C2×D3×D4—38no—
131C2×#235—38no—
132C2×#235C2×D314yescomplemented
133C22×C4×D3—32no—
134C22×C4×D3—34no—
135C22×C4×D3—38no—
136C22×C4×D3—61no—
137C22×C4×D3—62no—
138C3×C4⋊Q8—32no—
139C3×#127—32no—
140C3×#124—34no—
141C3×#121—38no—
142C3×C4×D4—38no—
143C2×C3×C42—21no—
144C2×C3×C42C2×D312yescomplemented
145#947—34no—
146#944—34no—
147#940—34no—
148#940—38no—
149#939—316no—
150#938—38no—
151#936—34no—
152D4×Dic3—38no—
153#930C2×D318yescomplemented
154C4×#67—316no—
155C2×C4×Dic3—32no—
156C2×C4×Dic3—34no—
157C2×C4×Dic3—62no—
158C2×C4×Dic3—61no—
159#895—38no—
160#893—38no—
161D3×C4⋊C4—38no—
162#888—38no—
163#885—316no—
164#884—316no—
165#67⋊C4—316no—
166D3×C22⋊C4—316no—
167#875C2×D314yescomplemented
168#874C2×D312yescomplemented
169C4×D12C2×D318yescomplemented
170C42×D3—32no—
171C42×D3—32no—
172C42×D3—32no—
173C42×D3—34no—
174C42×D3—32no—
175C42×D3—34no—
176C42×D3—62no—
177C42×D3—61no—
178C42×D3—61no—
179C42×D3—61no—
180C42×D3—61no—
181C42×D3—62no—
182#869C2×D312yescomplemented
183C23×C32C2411yescharacteristic
184C22×C3⋊D3—24no—
185C22×C3⋊D3C2×D414yes—
186C22×C3⋊D3C2411yescharacteristic
187C22×C3⋊D3C2411yescharacteristic
188C22×C3×D3C2418yes—
189C2×D32—28no—
190C2×D32—216no—
191C2×C32×C4—24no—
192C2×C32×C4C2×D414yescomplemented
193C2×C32×C4C2412yes—
194C2×C32×C4C2411yescharacteristic
195C2×C32×C4C2411yescharacteristic
196C2×C32×C4C2412yes—
197C2×C3⋊Dic3—24no—
198C2×C3⋊Dic3C2×D414yescomplemented
199C2×C3⋊Dic3C2412yes—
200C2×C3⋊Dic3C2411yescharacteristic
201C2×C3⋊Dic3C2411yescharacteristic
202C2×C3⋊Dic3C2412yes—
203C4×C3⋊D3—24no—
204C4×C3⋊D3—24no—
205C4×C3⋊D3—24no—
206C4×C3⋊D3C2×D414yes—
207C4×C3⋊D3C2×D414yes—
208C4×C3⋊D3C2×D414yescomplemented
209C4×C3⋊D3C2×D414yescomplemented
210C4×C3⋊D3#4118yescomplemented
211C3×#67—216no—
212C2×C3×Dic3C2418yes—
213C3×D12—28no—
214C3×D12—216no—
215C3×C4×D3—216no—
216C3×Dic6—28no—
217#627—28no—
218#626—216no—
219#625—28no—
220#625—216no—
221#624—28no—
222D3×Dic3—216no—
223C22×#41—92no—
224#532—32no—
225#532—94no—
226#532—94no—
227#532—92no—
228#532—92no—
229#532—92no—
230C2×C4⋊Q8—91no—
231C2×#127—91no—
232C2×#124—92no—
233C2×#121—94no—
234C2×C4×D4—94no—
235C22×C42—91no—
236C23×D3—32no—
237C23×D3—38no—
238C23×D3—61no—
239C3×#41—616no—
240C2×C3×Q8—34no—
241C2×C3×D4—38no—
242C2×C3×D4—38no—
243C2×C3×D4—34no—
244C22×C3×C4—22no—
245C22×C3×C4—21no—
246C22×C3×C4—38no—
247C22×C3×C4C22×D314yes—
248C22×C3×C4C22×D312yes—
249C2×#67—316no—
250C2×#67—38no—
251C2×#67—38no—
252C2×#67C22×D318yes—
253C22×Dic3—32no—
254C22×Dic3—34no—
255C22×Dic3—38no—
256C22×Dic3—61no—
257C22×Dic3—62no—
258#239—616no—
259D3×Q8—616no—
260#237—616no—
261#237—632no—
262D3×D4—632no—
263D3×D4—616no—
264D3×D4—632no—
265#235—216no—
266#235—632no—
267C2×D12—38no—
268C2×D12C22×D318yes—
269C2×D12C22×D314yes—
270C2×C4×D3—316no—
271C2×C4×D3—34no—
272C2×C4×D3—32no—
273C2×C4×D3—32no—
274C2×C4×D3—32no—
275C2×C4×D3—32no—
276C2×C4×D3—38no—
277C2×C4×D3—34no—
278C2×C4×D3—34no—
279C2×C4×D3—34no—
280C2×C4×D3—38no—
281C2×C4×D3—62no—
282C2×C4×D3—61no—
283C2×C4×D3—61no—
284C2×C4×D3—61no—
285C2×C4×D3—61no—
286C2×C4×D3—62no—
287C2×C4×D3—62no—
288C2×C4×D3—62no—
289C2×C4×D3—68no—
290C2×C4×D3—632no—
291C2×C4×D3—616no—
292C2×C4×D3—616no—
293C2×C4×D3C22×D318yes—
294C2×Dic6—38no—
295C2×Dic6C22×D314yes—
296C3×C4⋊C4—38no—
297C3×C22⋊C4—316no—
298C3×C42—21no—
299C3×C42—21no—
300C3×C42—22no—
301C3×C42C22×D312yes—
302C3×C42C22×D314yes—
303C3×C42C22×D312yes—
304#217—316no—
305(C2×D3)⋊C4—316no—
306(C2×D3)⋊C4C22×D3116yes—
307C4⋊Dic3C22×D318yes—
308Dic3⋊C4—316no—
309C4×Dic3—34no—
310C4×Dic3—34no—
311C4×Dic3—34no—
312C4×Dic3—34no—
313C4×Dic3—34no—
314C4×Dic3—32no—
315C4×Dic3—32no—
316C4×Dic3—62no—
317C4×Dic3—62no—
318C4×Dic3—61no—
319C4×Dic3—62no—
320C4×Dic3—61no—
321C4×Dic3—62no—
322C4×Dic3—62no—
323C22×C32—22no—
324C22×C32C22×D412yes—
325C22×C32C2511yescharacteristic
326C2×C3⋊D3—22no—
327C2×C3⋊D3—28no—
328C2×C3⋊D3C22×D412yes—
329C2×C3⋊D3C22×D412yes—
330C2×C3⋊D3C2×#4114yes—
331C2×C3×D3—28no—
332C2×C3×D3—216no—
333D32—416no—
334C32×C4—22no—
335C32×C4C22×D412yes—
336C32×C4C22×D412yes—
337C32×C4C2×#4114yescomplemented
338C3⋊Dic3—22no—
339C3⋊Dic3C22×D412yes—
340C3⋊Dic3C22×D412yes—
341C3⋊Dic3C2×#4114yescomplemented
342C3×Dic3—28no—
343C2×#41—34no—
344C2×#41—94no—
345C2×#41—94no—
346C2×#41—94no—
347C2×#41—1816no—
348C22×Q8—92no—
349C22×D4—94no—
350C22×D4—94no—
351C22×D4—92no—
352C23×C4—94no—
353C23×C4—91no—
354C23×C4—92no—
355C4⋊Q8—32no—
356C4⋊Q8—94no—
357C4⋊Q8—92no—
358#127—32no—
359#127—94no—
360#127—92no—
361#124—34no—
362#124—98no—
363#124—94no—
364#121—38no—
365#121—98no—
366#121—98no—
367#121—98no—
368C4×D4—38no—
369C4×D4—98no—
370C4×D4—98no—
371C4×D4—98no—
372C2×C4⋊C4—94no—
373C2×C22⋊C4—98no—
374C2×C42—92no—
375C2×C42—91no—
376C2×C42—92no—
377C2×C42—91no—
378C2×C42—91no—
379C2×C42—91no—
380C2×C42—91no—
381C2×C42—92no—
382C2×C42D3211yescharacteristic, complemented
383C23×C3—21no—
384C23×C3—38no—
385C23×C3C23×D312yes—
386C22×D3—32no—
387C22×D3—38no—
388C22×D3—32no—
389C22×D3—64no—
390C22×D3—61no—
391C22×D3—61no—
392C22×D3—616no—
393C22×D3—632no—
394C22×D3—68no—
395C22×D3—68no—
396C22×D3C23×D318yes—
397C3×Q8—68no—
398C3×D4—616no—
399C3×D4—68no—
400C3×D4—616no—
401C2×C3×C4—28no—
402C2×C3×C4—28no—
403C2×C3×C4—22no—
404C2×C3×C4—21no—
405C2×C3×C4—22no—
406C2×C3×C4—21no—
407C2×C3×C4—24no—
408C2×C3×C4—38no—
409C2×C3×C4—616no—
410C2×C3×C4D3×D418yescomplemented
411C2×C3×C4C23×D314yes—
412C2×C3×C4C23×D312yes—
413C2×C3×C4C23×D314yes—
414C2×C3×C4C23×D312yes—
415#67—216no—
416#67—616no—
417#67—616no—
418#67—632no—
419C2×Dic3—38no—
420C2×Dic3—34no—
421C2×Dic3—32no—
422C2×Dic3—32no—
423C2×Dic3—34no—
424C2×Dic3—64no—
425C2×Dic3—62no—
426C2×Dic3—61no—
427C2×Dic3—61no—
428C2×Dic3—62no—
429C2×Dic3—616no—
430C2×Dic3—68no—
431C2×Dic3—68no—
432C2×Dic3C23×D318yes—
433D12—28no—
434D12—216no—
435D12—616no—
436C4×D3—216no—
437C4×D3—38no—
438C4×D3—38no—
439C4×D3—38no—
440C4×D3—38no—
441C4×D3—316no—
442C4×D3—64no—
443C4×D3—64no—
444C4×D3—64no—
445C4×D3—64no—
446C4×D3—68no—
447C4×D3—616no—
448C4×D3—68no—
449C4×D3—616no—
450C4×D3—68no—
451C4×D3—68no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—68no—
455Dic6—28no—
456Dic6—616no—
457C2×C32—22no—
458C2×C32C23×D411yescharacteristic
459C2×C32C22×#4112yes—
460C3⋊D3—22no—
461C3⋊D3#53214yescomplemented
462C3×D3—48no—
463C24—94no—
464C24—91no—
465#41—616no—
466#41—1816no—
467#41—1816no—
468#41—1816no—
469C2×Q8—34no—
470C2×Q8—94no—
471C2×Q8—188no—
472C2×D4—38no—
473C2×D4—38no—
474C2×D4—34no—
475C2×D4—98no—
476C2×D4—98no—
477C2×D4—94no—
478C2×D4—188no—
479C2×D4—1816no—
480C2×D4—1816no—
481C22×C4—38no—
482C22×C4—94no—
483C22×C4—98no—
484C22×C4—91no—
485C22×C4—92no—
486C22×C4—91no—
487C22×C4—91no—
488C22×C4—91no—
489C22×C4—91no—
490C22×C4—98no—
491C22×C4—92no—
492C22×C4—92no—
493C22×C4—92no—
494C22×C4—92no—
495C22×C4—188no—
496C22×C4—1816no—
497C22×C4C2×D3212yes—
498C22×C4C2×D3211yescharacteristic
499C4⋊C4—38no—
500C4⋊C4—98no—
501C22⋊C4—316no—
502C22⋊C4—916no—
503C42—92no—
504C42—92no—
505C42—92no—
506C42—91no—
507C42—91no—
508C42—92no—
509C42—92no—
510C42C2×D3211yescharacteristic
511C42C2×D3211yescharacteristic
512C42C2×D3212yes—
513C22×C3—24no—
514C22×C3—24no—
515C22×C3—22no—
516C22×C3—21no—
517C22×C3—68no—
518C22×C3—616no—
519C22×C3C2×D3×D414yes—
520C22×C3C24×D312yes—
521C2×D3—28no—
522C2×D3—216no—
523C2×D3—34no—
524C2×D3—38no—
525C2×D3—34no—
526C2×D3—62no—
527C2×D3—62no—
528C2×D3—64no—
529C2×D3—616no—
530C2×D3—64no—
531C2×D3—616no—
532C2×D3—64no—
533C2×D3—1232no—
534C3×C4—24no—
535C3×C4—24no—
536C3×C4—22no—
537C3×C4—22no—
538C3×C4—24no—
539C3×C4—68no—
540C3×C4C2×D3×D414yes—
541C3×C4C2×D3×D414yes—
542C3×C4D3×#4118yescomplemented
543Dic3—28no—
544Dic3—34no—
545Dic3—34no—
546Dic3—38no—
547Dic3—62no—
548Dic3—62no—
549Dic3—64no—
550Dic3—64no—
551Dic3—64no—
552C32C2×#53211yescharacteristic, complemented, Sylow
553C23—38no—
554C23—91no—
555C23—94no—
556C23—91no—
557C23—184no—
558C23—188no—
559C23—1816no—
560C23C22×D3211yescharacteristic
561Q8—68no—
562Q8—188no—
563D4—616no—
564D4—68no—
565D4—616no—
566D4—1816no—
567D4—188no—
568D4—1816no—
569C2×C4—24no—
570C2×C4—38no—
571C2×C4—616no—
572C2×C4—94no—
573C2×C4—92no—
574C2×C4—91no—
575C2×C4—91no—
576C2×C4—94no—
577C2×C4—94no—
578C2×C4—94no—
579C2×C4—94no—
580C2×C4—98no—
581C2×C4—92no—
582C2×C4—184no—
583C2×C4—184no—
584C2×C4—188no—
585C2×C4—1816no—
586C2×C4—184no—
587C2×C4—184no—
588C2×C4#380214yescomplemented
589C2×C4C22×D3212yes—
590C2×C4C22×D3211yescharacteristic
591C2×C4C22×D3212yes—
592C2×C4C22×D3211yescharacteristic
593C2×C3—24no—
594C2×C3—24no—
595C2×C3—21no—
596C2×C3—22no—
597C2×C3—128no—
598C2×C3C22×D3×D412yes—
599C2×C3C2×D3×#4114yes—
600D3—38no—
601D3—48no—
602D3—64no—
603D3—64no—
604D3—64no—
605C22—22no—
606C22—68no—
607C22—616no—
608C22—92no—
609C22—94no—
610C22—92no—
611C22—188no—
612C22—182no—
613C22—3616no—
614C22C2×#380212yes—
615C22C23×D3211yescharacteristic
616C4—22no—
617C4—68no—
618C4—92no—
619C4—92no—
620C4—94no—
621C4—182no—
622C4C2×#380212yes—
623C4C2×#380212yes—
624C4#6430614yescomplemented
625C3—21no—
626C3D3×#53212yescomplemented
627C2—22no—
628C2—94no—
629C2—128no—
630C2—182no—
631C2C22×#380211yescharacteristic
632C2C2×#6430612yes—
subgroupG/H
centerC2×C4C22×D32
commutator, socle, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32C2×#532
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64306C2semidirect
2. C2×C42×C3⋊D3C2semidirect
3. C3×#5477C2semidirect
4. #10595081C2semidirect
5. #10595032C2semidirect
6. #10594929C2semidirect
7. #10594009C2semidirect
8. #10594008C2semidirect
9. C4×#3802C2semidirect
10. #10593972C2semidirect
11. #10593971C2semidirect
12. #10593909C2semidirect
13. #10593907C2semidirect
17. C2×C3×#235C22semidirect
19. C2×#3805C22semidirect
24. C2×#3798C22semidirect
26. C2×#3796C22semidirect
27. C2×C32×C42C22semidirect
28. C2×C4×C3⋊Dic3C22semidirect
29. C2×C4×C3⋊Dic3C22semidirect
33. C42×C3⋊D3C22semidirect
34. C42×C3⋊D3C22semidirect
35. C42×C3⋊D3C22semidirect
36. C3×#930C22semidirect
37. C3×#875C22semidirect
38. C3×#874C22semidirect
39. C3×C4×D12C22semidirect
40. C3×#869C22semidirect
41. #63980C22semidirect
43. #63919C22semidirect
44. #63916C22semidirect
45. #63915C22semidirect
46. #63914C22semidirect
47. #63914C22semidirect
48. #63912C22semidirect
49. #63902C22semidirect
50. C4×#625C22semidirect
52. #63898C22semidirect
53. #63873C22semidirect
54. #63863C22semidirect
68. #5477D3semidirect
78. C2×C4×C3⋊D3D4semidirect
132. C2×#235C2×D3semidirect
144. C2×C3×C42C2×D3semidirect
153. #930C2×D3semidirect
167. #875C2×D3semidirect
168. #874C2×D3semidirect
169. C4×D12C2×D3semidirect
182. #869C2×D3semidirect
192. C2×C32×C4C2×D4semidirect
198. C2×C3⋊Dic3C2×D4semidirect
208. C4×C3⋊D3C2×D4semidirect
209. C4×C3⋊D3C2×D4semidirect
210. C4×C3⋊D3#41semidirect
337. C32×C4C2×#41semidirect
341. C3⋊Dic3C2×#41semidirect
382. C2×C42D32semidirect
410. C2×C3×C4D3×D4semidirect
461. C3⋊D3#532semidirect
542. C3×C4D3×#41semidirect
552. C32C2×#532semidirect
588. C2×C4#3802semidirect
624. C4#64306semidirect
626. C3D3×#532semidirect

Maximal subgroups

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

subgroupindex
C2×#643062
C2×C42×C3⋊D32
C3×#54772
#105950812
#105950322
#105949292
#105940092
#105940082
C4×#38022
#105939722
#105939712
#105939092
#105939072
D3×#5323