Finite Group Databasebeta

← #11824459

Subgroups — #11824459

Order 1152.

2145 conjugacy classes of subgroups.

The subgroup lattice has 647 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64149C211yesmaximal, characteristic, complemented
2C2×C3×#940C211yesmaximal, characteristic, complemented
3C2×#63971C214yesmaximal, complemented
4C2×#63911C211yesmaximal, characteristic, complemented
5C2×#63898C211yesmaximal, characteristic, complemented
6C3×#5221C211yesmaximal, characteristic, complemented
7#10591724C214yesmaximal, complemented
8C4×#3724C211yesmaximal, characteristic, complemented
9#10591320C211yesmaximal, characteristic, complemented
10#83177—31nomaximal
11#76348—31nomaximal
12C22×C32×D4C2211yescharacteristic
13C22×#638C2212yes—
14C22×#638C2212yes—
15C22×C4⋊(C3⋊D3)C2211yescharacteristic
16C22×C3×#67C2214yes—
17C22×C3×D12C2211yescharacteristic
18C22×#626C2214yes—
19C22×D3×Dic3C2212yes—
20#64149—24no—
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×#217C2214yes—
23C3×#940—24no—
24C2×C3×C4⋊Dic3C2211yescharacteristic
25C2×C3×C4×Dic3C2211yescharacteristic
26C2×C3×C4×Dic3C2211yescharacteristic
27#63971—216no—
28C2×#3724C2212yes—
29C2×#3722C2214yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31#63911—24no—
32#63898—24no—
33#63579C2212yes—
34C2×C3×#127—31no—
35C2×#940—31no—
36C2×#940—31no—
37C2×#940—31no—
38C2×#940—61no—
39C2×#940D311yescharacteristic, complemented
40C2×#939—34no—
41C2×D4×Dic3—31no—
42C2×#893—31no—
43C2×#884—34no—
44C2×#874—31no—
45C3×#390—31no—
46#5223—34no—
47#5221D311yescharacteristic, complemented
48#4988—31no—
49#4960—34no—
50#4939—31no—
51C4×Dic3⋊C4—31no—
52C4×Dic3⋊C4—31no—
53C24×C32C2312yes—
54C23×C3⋊D3C2312yes—
55C23×C3×D3C2312yes—
56C2×C32×D4—22no—
57C2×C32×D4—22no—
58C2×C32×D4—22no—
59C22×C32×C4C2311yescharacteristic
60C2×#638—24no—
61C2×#638—24no—
62C2×#638—28no—
63C2×#638—44no—
64C22×C3⋊Dic3C2311yescharacteristic
65C22×C3⋊Dic3C2311yescharacteristic
66C2×C4⋊(C3⋊D3)—22no—
67C2×C4⋊(C3⋊D3)—22no—
68C2×C4⋊(C3⋊D3)—22no—
69C2×C3×#67—28no—
70C2×C3×#67—28no—
71C2×C3×#67—44no—
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2312yes—
74C22×C3×Dic3C2312yes—
75C2×C3×D12—22no—
76C2×C3×D12—22no—
77C2×C3×D12D414yescomplemented
78C2×#626—28no—
79C2×#626—28no—
80C2×#626—44no—
81C2×D3×Dic3—24no—
82C2×D3×Dic3—28no—
83C4×C3⋊Dic3D414yescomplemented
84C3×#217—28no—
85C3×C4⋊Dic3—22no—
86C3×C4×Dic3—22no—
87C3×C4×Dic3—22no—
88#3724D418yescomplemented
89#3722—28no—
90(C2×D3)⋊Dic3—24no—
91#2541—91noSylow
92C22×C3×D4—21no—
93C22×C3×D4—34no—
94C22×C3×D4—31no—
95C22×C3×D4C2×D311yescharacteristic
96C22×C3×D4C2×D311yescharacteristic
97C22×#67—32no—
98C22×#67—32no—
99C22×#67—32no—
100C22×#67—32no—
101C22×#67—34no—
102C22×#67—62no—
103C22×#67—62no—
104C22×#67C2×D314yes—
105C23×Dic3—32no—
106C22×D12—31no—
107C22×D12—31no—
108C22×D12—34no—
109C22×D12—61no—
110C22×D12C2×D311yescharacteristic
111C22×C4×D3—32no—
112C3×#127—64no—
113C2×C3×C4⋊C4—31no—
114C2×C3×C22⋊C4—34no—
115C2×C3×C42—31no—
116C2×C3×C42—31no—
117C2×#217—32no—
118C2×#217C2×D314yes—
119#940—24no—
120#940—64no—
121#940—64no—
122#940—64no—
123#940—68no—
124#939—616no—
125D4×Dic3—64no—
126C2×(C2×D3)⋊C4—32no—
127C2×(C2×D3)⋊C4—34no—
128C2×(C2×D3)⋊C4—34no—
129C2×C4⋊Dic3C2×D311yescharacteristic
130C2×Dic3⋊C4—32no—
131C2×Dic3⋊C4—32no—
132C2×C4×Dic3—31no—
133C2×C4×Dic3—31no—
134C2×C4×Dic3—61no—
135C2×C4×Dic3C2×D311yescharacteristic
136C2×C4×Dic3C2×D311yescharacteristic
137#893—64no—
138#884—616no—
139#874—64no—
140C3⋊#95—32no—
141C3⋊#95—32no—
142C23×C32—22no—
143C23×C32—24no—
144C23×C32—22no—
145C23×C32—22no—
146C23×C32—24no—
147C23×C32C2411yescharacteristic
148C22×C3⋊D3—22no—
149C22×C3⋊D3—24no—
150C22×C3⋊D3—22no—
151C22×C3⋊D3—22no—
152C22×C3⋊D3—24no—
153C22×C3×D3—22no—
154C22×C3×D3—24no—
155C22×C3×D3—22no—
156C22×C3×D3—24no—
157C22×C3×D3C2×D414yes—
158C32×D4—44no—
159C2×C32×C4C2×D412yes—
160C2×C32×C4C2×D412yes—
161C2×C32×C4#4112yes—
162#638—48no—
163#638—48no—
164C2×C3⋊Dic3—22no—
165C2×C3⋊Dic3C2×D412yes—
166C2×C3⋊Dic3C2×D414yes—
167C2×C3⋊Dic3C2×D412yes—
168C4⋊(C3⋊D3)—44no—
169C3×#67—416no—
170C2×C3×Dic3—22no—
171C2×C3×Dic3—22no—
172C2×C3×Dic3—22no—
173C2×C3×Dic3—22no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—24no—
176C2×C3×Dic3C2×D414yes—
177C2×C3×Dic3C2×D414yes—
178C3×D12—28no—
179#626—416no—
180D3×Dic3—48no—
181C2×#127—31no—
182C2×#127—91no—
183C2×#127—91no—
184C2×#121—94no—
185C2×C4×D4—91no—
186#392—94no—
187#390—31no—
188#390—91no—
189C4×C4⋊C4—91no—
190C24×C3—22no—
191C24×C3—32no—
192C24×C3C22×D312yes—
193C24×C3C22×D312yes—
194C23×D3—32no—
195C23×D3—32no—
196C23×D3—62no—
197C23×D3C22×D312yes—
198C2×C3×D4—24no—
199C2×C3×D4—22no—
200C2×C3×D4—22no—
201C2×C3×D4—22no—
202C2×C3×D4—22no—
203C2×C3×D4—22no—
204C2×C3×D4—22no—
205C2×C3×D4—34no—
206C2×C3×D4—42no—
207C2×C3×D4—42no—
208C2×C3×D4—68no—
209C2×C3×D4—68no—
210C2×C3×D4—62no—
211C2×C3×D4—62no—
212C2×C3×D4—124no—
213C22×C3×C4—21no—
214C22×C3×C4—32no—
215C22×C3×C4—32no—
216C22×C3×C4—32no—
217C22×C3×C4C22×D311yescharacteristic
218C22×C3×C4C22×D311yescharacteristic
219C2×#67—28no—
220C2×#67—28no—
221C2×#67—44no—
222C2×#67—68no—
223C2×#67—68no—
224C2×#67—68no—
225C2×#67—64no—
226C2×#67—64no—
227C2×#67—64no—
228C2×#67—64no—
229C2×#67—68no—
230C2×#67—68no—
231C2×#67—68no—
232C2×#67—128no—
233C2×#67—124no—
234C2×#67—124no—
235C2×#67—124no—
236C2×#67—128no—
237C22×Dic3—31no—
238C22×Dic3—31no—
239C22×Dic3—31no—
240C22×Dic3—31no—
241C22×Dic3—61no—
242C22×Dic3—61no—
243C22×Dic3—64no—
244C22×Dic3—68no—
245C22×Dic3C22×D312yes—
246C22×Dic3C22×D312yes—
247C22×Dic3C22×D312yes—
248C2×D12—22no—
249C2×D12—22no—
250C2×D12—64no—
251C2×D12—68no—
252C2×D12—68no—
253C2×D12—62no—
254C2×D12—62no—
255C2×D12—62no—
256C2×D12—62no—
257C2×D12—62no—
258C2×D12—62no—
259C2×D12—122no—
260C2×D12—122no—
261C2×D12—124no—
262C2×D12#6714yescomplemented
263C2×C4×D3—68no—
264C2×C4×D3—64no—
265C3×C4⋊C4—62no—
266C3×C22⋊C4—68no—
267C3×C42—62no—
268C3×C42—62no—
269#217—28no—
270#217—64no—
271(C2×D3)⋊C4—68no—
272(C2×D3)⋊C4—64no—
273(C2×D3)⋊C4—68no—
274C4⋊Dic3—22no—
275Dic3⋊C4—38no—
276Dic3⋊C4—38no—
277C4×Dic3—22no—
278C4×Dic3—22no—
279C4×Dic3—34no—
280C4×Dic3—34no—
281C4×Dic3—64no—
282C22×C32—42no—
283C22×C32—42no—
284C22×C32—42no—
285C22×C32—44no—
286C22×C32—44no—
287C22×C32C22×D411yescharacteristic
288C22×C32C22×D412yes—
289C22×C32C22×D411yescharacteristic
290C22×C32C2×#4111yescharacteristic
291C22×C32H(5,𝔽2)12yes—
292C2×C3⋊D3—42no—
293C2×C3⋊D3—42no—
294C2×C3⋊D3—42no—
295C2×C3⋊D3—44no—
296C2×C3⋊D3—44no—
297C2×C3×D3—24no—
298C2×C3×D3—28no—
299C2×C3×D3—42no—
300C2×C3×D3—42no—
301C2×C3×D3—44no—
302C32×C4#12114yescomplemented
303C3⋊Dic3—22no—
304C3⋊Dic3#12714yescomplemented
305C3×Dic3—24no—
306C3×Dic3—24no—
307C3×Dic3—42no—
308C22×D4—34no—
309C22×D4—31no—
310C22×D4—94no—
311C22×D4—92no—
312C22×D4—92no—
313C22×D4—91no—
314C22×D4D3211yescharacteristic
315C23×C4—92no—
316#127—64no—
317#127—184no—
318#127—184no—
319#121—1816no—
320C4×D4—184no—
321C2×C4⋊C4—31no—
322C2×C4⋊C4—92no—
323C2×C22⋊C4—34no—
324C2×C22⋊C4—94no—
325C2×C22⋊C4—92no—
326C2×C42—31no—
327C2×C42—31no—
328C2×C42—91no—
329#95—92no—
330C23×C3—24no—
331C23×C3—22no—
332C23×C3—24no—
333C23×C3—24no—
334C23×C3—22no—
335C23×C3—22no—
336C23×C3—22no—
337C23×C3—22no—
338C23×C3—24no—
339C23×C3—24no—
340C23×C3—22no—
341C23×C3—21no—
342C23×C3—34no—
343C23×C3—44no—
344C23×C3—44no—
345C23×C3—42no—
346C23×C3—42no—
347C23×C3—62no—
348C23×C3—62no—
349C23×C3—64no—
350C23×C3—64no—
351C23×C3C23×D311yescharacteristic
352C23×C3C23×D311yescharacteristic
353C22×D3—22no—
354C22×D3—24no—
355C22×D3—22no—
356C22×D3—24no—
357C22×D3—64no—
358C22×D3—62no—
359C22×D3—64no—
360C22×D3—64no—
361C22×D3—62no—
362C22×D3—62no—
363C22×D3—62no—
364C22×D3—62no—
365C22×D3—64no—
366C22×D3—64no—
367C22×D3—62no—
368C22×D3—122no—
369C22×D3—122no—
370C22×D3—124no—
371C22×D3—124no—
372C22×D3C2×#6714yes—
373C3×D4—48no—
374C3×D4—44no—
375C3×D4—44no—
376C3×D4—68no—
377C3×D4—1216no—
378C2×C3×C4—22no—
379C2×C3×C4—22no—
380C2×C3×C4—22no—
381C2×C3×C4—34no—
382C2×C3×C4—34no—
383C2×C3×C4—62no—
384C2×C3×C4—62no—
385C2×C3×C4—62no—
386C2×C3×C4—62no—
387C2×C3×C4—64no—
388C2×C3×C4—62no—
389C2×C3×C4#23512yes—
390C2×C3×C4D3×D412yes—
391C2×C3×C4D3×D412yes—
392C2×C3×C4D3×D412yes—
393C2×C3×C4#23712yes—
394C2×C3×C4C2×#6712yes—
395#67—416no—
396#67—1216no—
397#67—128no—
398#67—128no—
399#67—1216no—
400#67—1216no—
401#67—128no—
402#67—128no—
403C2×Dic3—22no—
404C2×Dic3—22no—
405C2×Dic3—22no—
406C2×Dic3—22no—
407C2×Dic3—22no—
408C2×Dic3—24no—
409C2×Dic3—32no—
410C2×Dic3—32no—
411C2×Dic3—34no—
412C2×Dic3—34no—
413C2×Dic3—32no—
414C2×Dic3—32no—
415C2×Dic3—62no—
416C2×Dic3—62no—
417C2×Dic3—64no—
418C2×Dic3—64no—
419C2×Dic3—62no—
420C2×Dic3—62no—
421C2×Dic3—128no—
422C2×Dic3D3×D414yes—
423C2×Dic3D3×D414yes—
424D12—28no—
425D12—128no—
426D12—1216no—
427D12—124no—
428D12—124no—
429C4×D3—128no—
430C2×C32—82no—
431C2×C32C2×#12111yescharacteristic
432C2×C32C2×#12711yescharacteristic
433C2×C32#53511yescharacteristic
434C2×C32D4212yes—
435C2×C32#55012yes—
436C3⋊D3—82no—
437C3×D3—44no—
438C24—32no—
439C24—92no—
440C24C2×D3212yes—
441C2×D4—22no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—34no—
445C2×D4—68no—
446C2×D4—68no—
447C2×D4—62no—
448C2×D4—62no—
449C2×D4—124no—
450C2×D4—188no—
451C2×D4—188no—
452C2×D4—188no—
453C2×D4—184no—
454C2×D4—184no—
455C2×D4—182no—
456C2×D4—182no—
457C2×D4—182no—
458C2×D4—364no—
459C2×D4—364no—
460C22×C4—32no—
461C22×C4—32no—
462C22×C4—32no—
463C22×C4—91no—
464C22×C4—91no—
465C22×C4—184no—
466C22×C4—188no—
467C22×C4C2×D3211yescharacteristic
468C4⋊C4—62no—
469C4⋊C4—98no—
470C22⋊C4—68no—
471C22⋊C4—188no—
472C22⋊C4—184no—
473C42—62no—
474C42—62no—
475C42—94no—
476C22×C3—22no—
477C22×C3—22no—
478C22×C3—21no—
479C22×C3—21no—
480C22×C3—21no—
481C22×C3—44no—
482C22×C3—44no—
483C22×C3—44no—
484C22×C3—42no—
485C22×C3—42no—
486C22×C3—42no—
487C22×C3—42no—
488C22×C3—44no—
489C22×C3—42no—
490C22×C3—44no—
491C22×C3—42no—
492C22×C3—44no—
493C22×C3—44no—
494C22×C3—64no—
495C22×C3—68no—
496C22×C3—84no—
497C22×C3—84no—
498C22×C3—122no—
499C22×C3—122no—
500C22×C3—124no—
501C22×C3C2×#23511yescharacteristic
502C22×C3C2×D3×D412yes—
503C22×C3C2×D3×D412yes—
504C22×C3C2×D3×D411yescharacteristic
505C22×C3C2×D3×D411yescharacteristic
506C22×C3C2×D3×D411yescharacteristic
507C22×C3C2×#23711yescharacteristic
508C22×C3#100412yes—
509C22×C3#100912yes—
510C22×C3C22×#6711yescharacteristic
511C2×D3—28no—
512C2×D3—24no—
513C2×D3—42no—
514C2×D3—42no—
515C2×D3—44no—
516C2×D3—124no—
517C2×D3—124no—
518C2×D3—124no—
519C2×D3—122no—
520C2×D3—122no—
521C2×D3—122no—
522C2×D3—122no—
523C2×D3—124no—
524C2×D3—122no—
525C2×D3—124no—
526C2×D3—122no—
527C2×D3—124no—
528C2×D3—124no—
529C2×D3—244no—
530C2×D3—244no—
531C3×C4—24no—
532C3×C4—64no—
533C3×C4—64no—
534C3×C4—122no—
535C3×C4#88414yescomplemented
536C3×C4#93914yescomplemented
537Dic3—24no—
538Dic3—24no—
539Dic3—34no—
540Dic3—34no—
541Dic3—42no—
542Dic3—64no—
543Dic3—64no—
544Dic3—62no—
545Dic3—62no—
546C32#254111yescharacteristic, complemented, Sylow
547C23—24no—
548C23—24no—
549C23—22no—
550C23—22no—
551C23—22no—
552C23—34no—
553C23—64no—
554C23—64no—
555C23—62no—
556C23—62no—
557C23—184no—
558C23—184no—
559C23—182no—
560C23—182no—
561C23—182no—
562C23C22×D3211yescharacteristic
563D4—44no—
564D4—68no—
565D4—1216no—
566D4—3616no—
567D4—368no—
568D4—368no—
569D4—364no—
570C2×C4—34no—
571C2×C4—34no—
572C2×C4—62no—
573C2×C4—62no—
574C2×C4—62no—
575C2×C4—62no—
576C2×C4—64no—
577C2×C4—62no—
578C2×C4—94no—
579C2×C4—92no—
580C2×C4—92no—
581C2×C4—182no—
582C2×C4—368no—
583C2×C4#380412yes—
584C2×C4D3×#6712yes—
585C2×C4#381112yes—
586C2×C3—22no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—22no—
590C2×C3—21no—
591C2×C3—84no—
592C2×C3—82no—
593C2×C3—82no—
594C2×C3—124no—
595C2×C3C2×#88411yescharacteristic
596C2×C3#555312yes—
597C2×C3#560912yes—
598C2×C3#567411yescharacteristic
599C2×C3D3×#12711yescharacteristic
600C2×C3D3×#12711yescharacteristic
601C2×C3#571511yescharacteristic
602C2×C3#571812yes—
603C2×C3D4×#6712yes—
604C2×C3C2×#93911yescharacteristic
605D3—44no—
606D3—244no—
607D3—242no—
608D3—242no—
609C22—44no—
610C22—42no—
611C22—42no—
612C22—44no—
613C22—42no—
614C22—64no—
615C22—68no—
616C22—124no—
617C22—122no—
618C22—122no—
619C22—364no—
620C22—362no—
621C22—362no—
622C22—364no—
623C22—362no—
624C22D32×D412yes—
625C22#6431412yes—
626C22C2×#380411yescharacteristic
627C22C2×D3×#6711yescharacteristic
628C22C2×#381111yescharacteristic
629C4—64no—
630C4—64no—
631C4—94no—
632C4—122no—
633C4—182no—
634C4#6397114yescomplemented
635C3—21no—
636C3#7634811yescharacteristic, complemented
637C3#8317711yescharacteristic, complemented
638C2—82no—
639C2—124no—
640C2—722no—
641C2#1059514312yes—
642C2#1059516811yescharacteristic
643C2#1059528812yes—
644C2#1059530011yescharacteristic
645C2C2×#6397111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC22×C32×D4C22
hypercenterC22×D4D32
hypocenterC32#2541
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C2×#64149C2semidirect
2. C2×C3×#940C2semidirect
3. C2×#63971C2semidirect
4. C2×#63911C2semidirect
5. C2×#63898C2semidirect
6. C3×#5221C2semidirect
7. #10591724C2semidirect
8. C4×#3724C2semidirect
9. #10591320C2semidirect
39. C2×#940D3semidirect
47. #5221D3semidirect
77. C2×C3×D12D4semidirect
83. C4×C3⋊Dic3D4semidirect
88. #3724D4semidirect
262. C2×D12#67semidirect
302. C32×C4#121semidirect
304. C3⋊Dic3#127semidirect
535. C3×C4#884semidirect
536. C3×C4#939semidirect
546. C32#2541semidirect
634. C4#63971semidirect
636. C3#76348semidirect
637. C3#83177semidirect

Maximal subgroups

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

subgroupindex
C2×#641492
C2×C3×#9402
C2×#639712
C2×#639112
C2×#638982
C3×#52212
#105917242
C4×#37242
#105913202
#831773
#763483