Finite Group Databasebeta

← #11905977

Subgroups — #11905977

Order 1152.

3651 conjugacy classes of subgroups.

The subgroup lattice has 661 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64307C212yesmaximal, complemented
2C4×#3828C211yesmaximal, characteristic, complemented
3C3×#5477C211yesmaximal, characteristic, complemented
4C2×C3×#874C211yesmaximal, characteristic, complemented
5#10595069C218yesmaximal, complemented
6#10595040C212yesmaximal, complemented
7#10594010C214yesmaximal, complemented
8#10594008C212yesmaximal, complemented
9#10594004C214yesmaximal, complemented
10#10593907C212yesmaximal, complemented
11#10593906C214yesmaximal, complemented
12#86242—31nomaximal
13#86195—31nomaximal
14C2×#3828C2211yescharacteristic
15C2×C3×#235C2212yescomplemented
16C22×C3×D12C2212yescomplemented
17C22×C3×D12C2214yescomplemented
18C2×D3×#67C2218yescomplemented
19#64307—216no—
20C2×#3802C2214yescomplemented
21C2×#3802C2218yescomplemented
22C2×D3×D12C2214yescomplemented
23C2×#3796C2214yescomplemented
24C2×#3795C2214yescomplemented
25C2×C32×C42C2211yescharacteristic, complemented
26C4×#638C2214yescomplemented
27#64135C2211yescharacteristic, complemented
28C4×C4⋊(C3⋊D3)C2212yescomplemented
29#64081C2212yescomplemented
30C42×C3⋊D3C2212yescomplemented
31C4×#634C2212yescomplemented
32C3×#930C2214yescomplemented
33C3×#875C2212yescomplemented
34C3×#874C2214yescomplemented
35C3×#874C2212yescomplemented
36C3×#874C2211yescharacteristic, complemented
37C3×#874C2212yescomplemented
38C3×C4×D12C2214yescomplemented
39C3×#869C2211yescharacteristic, complemented
40#63976C2218yescomplemented
41#63922C22116yescomplemented
42#63916C2218yescomplemented
43#63914C2218yescomplemented
44#63914C2214yescomplemented
45#63908C2218yescomplemented
46#63898C2218yescomplemented
47#63885C22116yescomplemented
48#63863C2214yescomplemented
49C2×#1009—32no—
50C2×#1004—32no—
51C3×#532—31no—
52C2×C3×#127—31no—
53#5830—32no—
54#5805—32no—
55D4×#67—38no—
56#5725—32no—
57#5718—34no—
58#5717—34no—
59#5716—32no—
60#5715—34no—
61D3×#127—32no—
62D3×#127—32no—
63#5674—34no—
64#5609—38no—
65#5553—34no—
66D4×D12—34no—
67#5477D311yescharacteristic, complemented
68C2×#874D311yescharacteristic, complemented
69C4×#235—31no—
70C4×#235—31no—
71C4×#235—61no—
72C23×C3×D3C2314yes—
73C22×D32C2318yes—
74C22×C32×C4C2312yes—
75C22×C32×C4C2311yescharacteristic
76C2×#638C2312yes—
77#3828D418yescomplemented
78C2×C4⋊(C3⋊D3)C2311yescharacteristic
79C2×C4×C3⋊D3C2314yes—
80C2×C4×C3⋊D3C2312yes—
81C2×#634C2311yescharacteristic
82C2×C3×#67C2314yes—
83C3×#235—28no—
84C2×C3×D12—28no—
85C2×C3×D12—48no—
86C2×C3×D12C2314yes—
87C2×C3×D12C2314yes—
88C2×C3×D12C2314yes—
89C2×C3×D12C2312yes—
90C2×C3×D12C2318yes—
91C2×C3×D12C2318yes—
92C2×C3×C4×D3C2314yes—
93C2×C3×Dic6C2312yes—
94D3×#67—232no—
95C2×#626C2318yes—
96C2×#625C2318yes—
97C2×#625C23116yes—
98C2×D3×Dic3C2318yes—
99#3802—216no—
100#3802—416no—
101D3×D12—216no—
102#3796—216no—
103#3795—216no—
104C32×C42C2312yes—
105C32×C42C2311yescharacteristic
106C32×C42C2311yescharacteristic
107#3757C2312yes—
108#3752C2314yes—
109C4⋊(C3⋊Dic3)C2312yes—
110#3750C2314yes—
111C4×C3⋊Dic3C2314yes—
112C4×C3⋊Dic3C2312yes—
113C3×(C2×D3)⋊C4C2318yes—
114C3×C4⋊Dic3C2314yes—
115(C2×D3)⋊Dic3C23116yes—
116#3498—91noSylow
117C2×C3×#41—32no—
118C22×C3×D4—32no—
119C22×C3×D4—34no—
120C22×#67—38no—
121#1009—616no—
122C2×#239—34no—
123#1004—616no—
124C2×#237—34no—
125C2×#237—34no—
126C2×D3×D4—38no—
127C2×D3×D4—34no—
128C2×D3×D4—34no—
129C2×D3×D4—38no—
130C2×D3×D4—38no—
131C2×D3×D4—34no—
132C2×#235—31no—
133C2×#235—31no—
134C2×#235—34no—
135C2×#235—61no—
136C2×#235C2×D312yescomplemented
137C22×D12—34no—
138C22×D12C2×D312yescomplemented
139C22×D12C2×D314yescomplemented
140C3×C4⋊Q8—31no—
141C3×#127—31no—
142C3×#127—32no—
143C3×#127—32no—
144C3×#127—34no—
145C3×#124—32no—
146C3×#121—34no—
147C3×C4×D4—34no—
148C2×C3×C42—21no—
149C2×C3×C42C2×D311yescharacteristic, complemented
150C2×C3×C42C2×D311yescharacteristic, complemented
151#953—38no—
152#947—34no—
153#940—34no—
154#940—34no—
155#940—38no—
156#940—38no—
157#939—316no—
158#938—38no—
159#938—38no—
160#937—38no—
161#937—316no—
162#936—34no—
163D4×Dic3—38no—
164#930—38no—
165#930C2×D314yescomplemented
166C4×#67—34no—
167C4×#67—34no—
168C4×#67—64no—
169#926—31no—
170#926—31no—
171#926—61no—
172#895—38no—
173#893—38no—
174#884—316no—
175#882—316no—
176#875C2×D312yescomplemented
177#874C2×D312yescomplemented
178#874C2×D311yescharacteristic, complemented
179#874C2×D312yescomplemented
180#874C2×D314yescomplemented
181C4×D12—32no—
182C4×D12—32no—
183C4×D12—62no—
184C4×D12C2×D314yescomplemented
185#872—32no—
186#872—32no—
187#872—62no—
188C42×D3—32no—
189C42×D3—32no—
190C42×D3—62no—
191#869C2×D311yescharacteristic, complemented
192C4×Dic6—32no—
193C4×Dic6—32no—
194C4×Dic6—62no—
195C23×C32C2411yescharacteristic
196C22×C3⋊D3C2412yes—
197C22×C3×D3—28no—
198C22×C3×D3—48no—
199C22×C3×D3C2414yes—
200C22×C3×D3C2418yes—
201C2×D32—216no—
202C2×D32—416no—
203C2×C32×C4—24no—
204C2×C32×C4C2×D414yescomplemented
205C2×C32×C4C2412yes—
206C2×C32×C4C2411yescharacteristic
207C2×C32×C4C2411yescharacteristic
208C2×C32×C4C2412yes—
209#638C2×D418yescomplemented
210C2×C3⋊Dic3C2414yes—
211C2×C3⋊Dic3C2412yes—
212C4⋊(C3⋊D3)C2×D414yescomplemented
213C4×C3⋊D3—28no—
214C4×C3⋊D3C2×D418yescomplemented
215#634C2×D414yescomplemented
216C3×#67—28no—
217C2×C3×Dic3C2414yes—
218C3×D12—28no—
219C3×D12—28no—
220C3×D12—24no—
221C3×D12—28no—
222C3×D12—216no—
223C3×D12—48no—
224C3×C4×D3—28no—
225C3×Dic6—24no—
226#626—216no—
227#625—216no—
228#625—416no—
229D3×Dic3—216no—
230C2×H(5,𝔽2)—92no—
231#550—94no—
232D42—94no—
233D42—98no—
234#535—94no—
235#535—92no—
236#532—31no—
237#532—92no—
238C2×#127—31no—
239C2×#127—92no—
240C4×#41—91no—
241C24×C3—34no—
242C23×D3—38no—
243C23×D3—38no—
244C23×D3C22×D314yes—
245C3×#41—68no—
246C2×C3×Q8—32no—
247C2×C3×D4—34no—
248C2×C3×D4—38no—
249C2×C3×D4—34no—
250C2×C3×D4—34no—
251C2×C3×D4—34no—
252C2×C3×D4—32no—
253C2×C3×D4—38no—
254C2×C3×D4—68no—
255C2×C3×D4—128no—
256C22×C3×C4—21no—
257C22×C3×C4—22no—
258C22×C3×C4—34no—
259C22×C3×C4C22×D312yes—
260C22×C3×C4C22×D312yes—
261C22×C3×C4C22×D311yescharacteristic
262C22×C3×C4C22×D311yescharacteristic
263C2×#67—32no—
264C2×#67—32no—
265C2×#67—38no—
266C2×#67—38no—
267C2×#67—316no—
268C2×#67—316no—
269C2×#67—38no—
270C2×#67—62no—
271C2×#67—632no—
272C2×#67C22×D314yes—
273C22×Dic3—38no—
274#239—616no—
275#237—616no—
276#237—616no—
277D3×D4—616no—
278D3×D4—616no—
279D3×D4—616no—
280D3×D4—632no—
281D3×D4—1216no—
282D3×D4—1216no—
283#235—28no—
284#235—38no—
285#235—38no—
286#235—68no—
287#235—616no—
288C2×D12—28no—
289C2×D12—31no—
290C2×D12—31no—
291C2×D12—38no—
292C2×D12—48no—
293C2×D12—61no—
294C2×D12—616no—
295C2×D12C22×D314yes—
296C2×D12C22×D318yes—
297C2×D12C22×D314yes—
298C2×D12C22×D314yes—
299C2×D12C22×D312yes—
300C2×D12C22×D318yes—
301C2×C4×D3—32no—
302C2×C4×D3—32no—
303C2×C4×D3—38no—
304C2×C4×D3—34no—
305C2×C4×D3—34no—
306C2×C4×D3—62no—
307C2×C4×D3—64no—
308C2×C4×D3C22×D314yes—
309C2×Dic6—31no—
310C2×Dic6—31no—
311C2×Dic6—61no—
312C2×Dic6C22×D312yes—
313C3×C4⋊C4—34no—
314C3×C22⋊C4—38no—
315C3×C42—22no—
316C3×C42—21no—
317C3×C42—21no—
318C3×C42C22×D312yes—
319C3×C42C22×D312yes—
320C3×C42C22×D311yescharacteristic
321C3×C42C22×D311yescharacteristic
322C3×C42C22×D311yescharacteristic
323C3×C42C22×D311yescharacteristic
324#217—32no—
325#217—32no—
326#217—316no—
327#217—62no—
328(C2×D3)⋊C4—316no—
329(C2×D3)⋊C4—34no—
330(C2×D3)⋊C4—34no—
331(C2×D3)⋊C4—64no—
332(C2×D3)⋊C4C22×D318yes—
333C4⋊Dic3—32no—
334C4⋊Dic3—32no—
335C4⋊Dic3—62no—
336C4⋊Dic3C22×D314yes—
337Dic3⋊C4—34no—
338Dic3⋊C4—34no—
339Dic3⋊C4—64no—
340C4×Dic3—34no—
341C4×Dic3—34no—
342C4×Dic3—32no—
343C4×Dic3—32no—
344C4×Dic3—64no—
345C4×Dic3—62no—
346C22×C32—22no—
347C22×C32C22×D412yes—
348C22×C32C2511yescharacteristic
349C2×C3⋊D3—24no—
350C2×C3⋊D3C22×D414yes—
351C2×C3×D3—28no—
352C2×C3×D3—24no—
353C2×C3×D3—28no—
354C2×C3×D3—216no—
355C2×C3×D3—88no—
356D32—816no—
357C32×C4—22no—
358C32×C4C22×D412yes—
359C32×C4C22×D412yes—
360C32×C4H(5,𝔽2)14yescomplemented
361C3⋊Dic3—24no—
362C3⋊Dic3C22×D414yes—
363C3×Dic3—24no—
364H(5,𝔽2)—1816no—
365C2×#41—32no—
366C2×#41—94no—
367C2×#41—94no—
368C2×#41—91no—
369C22×D4—32no—
370C22×D4—34no—
371C22×D4—94no—
372C22×D4—94no—
373C22×D4—98no—
374C22×D4—98no—
375C4⋊Q8—31no—
376#127—32no—
377#127—32no—
378#127—34no—
379#127—31no—
380#127—94no—
381#127—98no—
382#124—32no—
383#124—94no—
384#121—34no—
385#121—916no—
386#121—98no—
387#121—98no—
388#120—916no—
389#120—98no—
390C4×Q8—92no—
391C4×D4—34no—
392C4×D4—98no—
393C4×D4—94no—
394C4×D4—92no—
395#117—91no—
396#117—92no—
397C2×C42—92no—
398C2×C42D3211yescharacteristic, complemented
399C23×C3—21no—
400C23×C3—38no—
401C23×C3—34no—
402C23×C3—68no—
403C23×C3—128no—
404C23×C3C23×D311yescharacteristic
405C23×C3C23×D311yescharacteristic
406C22×D3—28no—
407C22×D3—32no—
408C22×D3—32no—
409C22×D3—48no—
410C22×D3—62no—
411C22×D3—616no—
412C22×D3—616no—
413C22×D3—1216no—
414C22×D3—1216no—
415C22×D3C23×D318yes—
416C22×D3C23×D314yes—
417C3×Q8—64no—
418C3×D4—68no—
419C3×D4—64no—
420C3×D4—68no—
421C3×D4—68no—
422C3×D4—68no—
423C3×D4—616no—
424C3×D4—128no—
425C2×C3×C4—24no—
426C2×C3×C4—24no—
427C2×C3×C4—21no—
428C2×C3×C4—22no—
429C2×C3×C4—21no—
430C2×C3×C4—22no—
431C2×C3×C4—24no—
432C2×C3×C4—34no—
433C2×C3×C4—44no—
434C2×C3×C4—68no—
435C2×C3×C4D3×D414yescomplemented
436C2×C3×C4D3×D414yescomplemented
437C2×C3×C4C23×D312yes—
438C2×C3×C4C23×D312yes—
439C2×C3×C4C23×D311yescharacteristic
440C2×C3×C4C23×D311yescharacteristic
441C2×C3×C4C23×D311yescharacteristic
442C2×C3×C4C23×D311yescharacteristic
443C2×C3×C4C23×D312yes—
444C2×C3×C4C23×D312yes—
445#67—28no—
446#67—38no—
447#67—38no—
448#67—68no—
449#67—616no—
450#67—616no—
451#67—616no—
452#67—1216no—
453#67—1216no—
454C2×Dic3—32no—
455C2×Dic3—32no—
456C2×Dic3—34no—
457C2×Dic3—34no—
458C2×Dic3—62no—
459C2×Dic3—64no—
460C2×Dic3—616no—
461C2×Dic3C23×D314yes—
462D12—28no—
463D12—28no—
464D12—24no—
465D12—216no—
466D12—28no—
467D12—34no—
468D12—34no—
469D12—48no—
470D12—64no—
471D12—616no—
472C4×D3—28no—
473C4×D3—38no—
474C4×D3—38no—
475C4×D3—68no—
476C4×D3—616no—
477C4×D3—68no—
478C4×D3—68no—
479C4×D3—128no—
480Dic6—24no—
481Dic6—34no—
482Dic6—34no—
483Dic6—64no—
484C2×C32—22no—
485C2×C32C23×D411yescharacteristic
486C2×C32C2×H(5,𝔽2)12yes—
487C3⋊D3—24no—
488C3×D3—44no—
489C3×D3—48no—
490C24—34no—
491C24—98no—
492#41—68no—
493#41—98no—
494#41—1816no—
495#41—1816no—
496C2×Q8—32no—
497C2×Q8—91no—
498C2×D4—34no—
499C2×D4—34no—
500C2×D4—38no—
501C2×D4—34no—
502C2×D4—32no—
503C2×D4—34no—
504C2×D4—38no—
505C2×D4—68no—
506C2×D4—98no—
507C2×D4—92no—
508C2×D4—98no—
509C2×D4—916no—
510C2×D4—91no—
511C2×D4—128no—
512C2×D4—1816no—
513C2×D4—1816no—
514C2×D4—1832no—
515C2×D4—3616no—
516C22×C4—34no—
517C22×C4—98no—
518C22×C4—92no—
519C22×C4—94no—
520C22×C4C2×D3212yes—
521C22×C4C2×D3211yescharacteristic
522C4⋊C4—34no—
523C4⋊C4—94no—
524C4⋊C4—92no—
525C22⋊C4—38no—
526C22⋊C4—916no—
527C22⋊C4—92no—
528C22⋊C4—94no—
529C42—92no—
530C42—94no—
531C42C2×D3211yescharacteristic
532C42C2×D3211yescharacteristic
533C42C2×D3212yes—
534C22×C3—22no—
535C22×C3—22no—
536C22×C3—22no—
537C22×C3—21no—
538C22×C3—42no—
539C22×C3—68no—
540C22×C3—64no—
541C22×C3—68no—
542C22×C3—616no—
543C22×C3—248no—
544C22×C3C2×D3×D412yes—
545C22×C3C2×D3×D412yes—
546C22×C3C24×D311yescharacteristic
547C22×C3C24×D311yescharacteristic
548C2×D3—24no—
549C2×D3—28no—
550C2×D3—216no—
551C2×D3—28no—
552C2×D3—34no—
553C2×D3—34no—
554C2×D3—64no—
555C2×D3—64no—
556C2×D3—64no—
557C2×D3—88no—
558C2×D3—124no—
559C2×D3—2416no—
560C2×D3—2416no—
561C3×C4—22no—
562C3×C4—22no—
563C3×C4—22no—
564C3×C4—22no—
565C3×C4—24no—
566C3×C4—42no—
567C3×C4—64no—
568C3×C4C2×D3×D412yes—
569C3×C4C2×D3×D412yes—
570C3×C4C2×D3×D412yes—
571C3×C4C2×D3×D412yes—
572C3×C4#100414yescomplemented
573C3×C4#100914yescomplemented
574Dic3—24no—
575Dic3—34no—
576Dic3—34no—
577Dic3—64no—
578Dic3—64no—
579Dic3—64no—
580Dic3—124no—
581C32#349811yescharacteristic, complemented, Sylow
582C23—34no—
583C23—38no—
584C23—68no—
585C23—92no—
586C23—128no—
587C23—1816no—
588C23—3616no—
589C23C22×D3211yescharacteristic
590Q8—64no—
591Q8—94no—
592D4—68no—
593D4—68no—
594D4—68no—
595D4—64no—
596D4—616no—
597D4—68no—
598D4—98no—
599D4—94no—
600D4—128no—
601D4—1816no—
602D4—1816no—
603D4—3616no—
604C2×C4—24no—
605C2×C4—34no—
606C2×C4—68no—
607C2×C4—92no—
608C2×C4—98no—
609C2×C4—94no—
610C2×C4—1816no—
611C2×C4—188no—
612C2×C4#380214yescomplemented
613C2×C4C22×D3212yes—
614C2×C4C22×D3211yescharacteristic
615C2×C4C22×D3211yescharacteristic
616C2×C4C22×D3212yes—
617C2×C3—22no—
618C2×C3—22no—
619C2×C3—21no—
620C2×C3—22no—
621C2×C3—42no—
622C2×C3—124no—
623C2×C3—128no—
624C2×C3C22×D3×D411yescharacteristic
625C2×C3C22×D3×D411yescharacteristic
626C2×C3C2×#100412yes—
627C2×C3C2×#100912yes—
628D3—48no—
629D3—44no—
630D3—64no—
631D3—64no—
632D3—124no—
633C22—22no—
634C22—64no—
635C22—68no—
636C22—616no—
637C22—68no—
638C22—94no—
639C22—184no—
640C22—248no—
641C22—7216no—
642C22C2×#380212yes—
643C22C23×D3211yescharacteristic
644C4—22no—
645C4—64no—
646C4—94no—
647C4—184no—
648C4C2×#380212yes—
649C4C2×#380212yes—
650C4#6430714yescomplemented
651C3—21no—
652C3#8619511yescharacteristic, complemented
653C3#8624211yescharacteristic, complemented
654C2—22no—
655C2—128no—
656C2—124no—
657C2—184no—
658C2C22×#380211yescharacteristic
659C2C2×#6430712yes—
subgroupG/H
center, FrattiniC22C23×D32
commutator, socle, cosocleC22×C32C25
FittingC2×C32×C42C22
hypercenterC2×C42D32
hypocenterC32#3498
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64307C2semidirect
2. C4×#3828C2semidirect
3. C3×#5477C2semidirect
4. C2×C3×#874C2semidirect
5. #10595069C2semidirect
6. #10595040C2semidirect
7. #10594010C2semidirect
8. #10594008C2semidirect
9. #10594004C2semidirect
10. #10593907C2semidirect
11. #10593906C2semidirect
15. C2×C3×#235C22semidirect
16. C22×C3×D12C22semidirect
17. C22×C3×D12C22semidirect
18. C2×D3×#67C22semidirect
20. C2×#3802C22semidirect
21. C2×#3802C22semidirect
22. C2×D3×D12C22semidirect
23. C2×#3796C22semidirect
24. C2×#3795C22semidirect
25. C2×C32×C42C22semidirect
26. C4×#638C22semidirect
27. #64135C22semidirect
28. C4×C4⋊(C3⋊D3)C22semidirect
29. #64081C22semidirect
30. C42×C3⋊D3C22semidirect
31. C4×#634C22semidirect
32. C3×#930C22semidirect
33. C3×#875C22semidirect
34. C3×#874C22semidirect
35. C3×#874C22semidirect
36. C3×#874C22semidirect
37. C3×#874C22semidirect
38. C3×C4×D12C22semidirect
39. C3×#869C22semidirect
40. #63976C22semidirect
41. #63922C22semidirect
42. #63916C22semidirect
43. #63914C22semidirect
44. #63914C22semidirect
45. #63908C22semidirect
46. #63898C22semidirect
47. #63885C22semidirect
48. #63863C22semidirect
67. #5477D3semidirect
68. C2×#874D3semidirect
77. #3828D4semidirect
136. C2×#235C2×D3semidirect
138. C22×D12C2×D3semidirect
139. C22×D12C2×D3semidirect
149. C2×C3×C42C2×D3semidirect
150. C2×C3×C42C2×D3semidirect
165. #930C2×D3semidirect
176. #875C2×D3semidirect
177. #874C2×D3semidirect
178. #874C2×D3semidirect
179. #874C2×D3semidirect
180. #874C2×D3semidirect
184. C4×D12C2×D3semidirect
191. #869C2×D3semidirect
204. C2×C32×C4C2×D4semidirect
209. #638C2×D4semidirect
212. C4⋊(C3⋊D3)C2×D4semidirect
214. C4×C3⋊D3C2×D4semidirect
215. #634C2×D4semidirect
360. C32×C4H(5,𝔽2)semidirect
398. C2×C42D32semidirect
435. C2×C3×C4D3×D4semidirect
436. C2×C3×C4D3×D4semidirect
572. C3×C4#1004semidirect
573. C3×C4#1009semidirect
581. C32#3498semidirect
612. C2×C4#3802semidirect
650. C4#64307semidirect
652. C3#86195semidirect
653. C3#86242semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
C4×#38282
C3×#54772
C2×C3×#8742
#105950692
#105950402
#105940102
#105940082
#105940042
#105939072
#105939062
#862423
#861953