Finite Group Databasebeta

← #11784980

Subgroups — #11784980

Order 1152.

1253 conjugacy classes of subgroups.

The subgroup lattice has 673 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1009C211yesmaximal, characteristic
2#10592935C211yesmaximal, characteristic, complemented
3C3×#5236C211yesmaximal, characteristic, complemented
4#10591231C211yesmaximal, characteristic, complemented
5#10591086C211yesmaximal, characteristic, complemented
6#10591085C211yesmaximal, characteristic, complemented
7#10591076C211yesmaximal, characteristic, complemented
8#72141—31nomaximal
9#70414—31nomaximal
10C2×C32×#41C2211yescharacteristic
11C3×#1009—22no—
12C3×#1009—22no—
13C3×#1009—22no—
14C3×#1009—22no—
15C2×C3×#239C412yescomplemented
16C2×C3×D3×D4—22no—
17C2×C3×D3×D4C412yescomplemented
18C2×C3×#235—21no—
19C2×C3×#235C2211yescharacteristic
20C22×C3×D12—21no—
21C22×C3×D12C2211yescharacteristic
22#64135C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic, complemented
25C2×C3×#208C2211yescharacteristic, complemented
26#63664—22no—
27C3×#837—22no—
28#63580—22no—
29#63563—22no—
30#63562—22no—
31#63560—21no—
32#63558—21no—
33C2×C3×H(5,𝔽2)—31no—
34C2×#1009D311yescharacteristic
35C3×#421—31no—
36#5240—31no—
37#5237—31no—
38#5236—31no—
39#5236—31no—
40#5236—61no—
41#5236D311yescharacteristic, complemented
42#5215—31no—
43#5215—31no—
44#5132—31no—
45#5131—31no—
46#5006—31no—
47#5001—31no—
48C23×C3×D3—21no—
49C23×C3×D3—22no—
50C32×#41—21no—
51C32×#41—21no—
52C32×#41D412yes—
53C32×#41D412yes—
54C2×C32×Q8C2×C411yescharacteristic
55C2×C32×D4—21no—
56C2×C32×D4C2×C411yescharacteristic
57C22×C32×C4—21no—
58C22×C32×C4C2311yescharacteristic
59C2×C3×#67—22no—
60C2×C3×#67D412yes—
61C3×#239—24no—
62C3×#239—24no—
63C3×D3×D4—28no—
64C3×D3×D4—28no—
65C3×D3×D4—24no—
66C3×D3×D4—24no—
67C3×#235—24no—
68C3×#235—24no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C3×#235—21no—
73C2×C3×D12—24no—
74C2×C3×D12—24no—
75C2×C3×D12—22no—
76C2×C3×D12—21no—
77C2×C3×D12—21no—
78C2×C3×D12—21no—
79C2×C3×D12C2×C412yes—
80C2×C3×D12D411yescharacteristic
81C2×C3×D12D412yes—
82C2×C3×D12D412yes—
83C2×C3×C4×D3—22no—
84C2×C3×C4×D3C2×C412yes—
85C2×C3×Dic6D411yescharacteristic
86#3757—21no—
87C4⋊(C3⋊Dic3)—21no—
88C4×C3⋊Dic3—21no—
89#3748—21no—
90#3748—21no—
91C2×C3⋊(C3⋊C8)—21no—
92C3×#217—21no—
93C3×C4⋊Dic3—21no—
94C3×C4×Dic3—21no—
95C3×#208—21no—
96C3×#208—21no—
97C2×C3×C3⋊C8—21no—
98#1795—91noSylow
99C3×H(5,𝔽2)—62no—
100C3×H(5,𝔽2)—62no—
101C3×H(5,𝔽2)—62no—
102C3×H(5,𝔽2)—62no—
103C2×C3×#41—21no—
104C2×C3×#41—31no—
105C2×C3×#41—32no—
106C2×C3×#41—61no—
107C2×C3×#41C2×D311yescharacteristic
108C2×C3×#41C2×D311yescharacteristic
109C22×C3×D4—32no—
110C22×C3×D4—31no—
111C22×C3×D4—61no—
112C22×C3×D4—62no—
113#1009—22no—
114#1009—22no—
115#1009—22no—
116#1009—22no—
117C2×#239Dic312yescomplemented
118C2×D3×D4—22no—
119C2×D3×D4Dic312yescomplemented
120C2×#235—21no—
121C2×#235C2×D311yescharacteristic
122C22×D12—21no—
123C22×D12C2×D311yescharacteristic
124C2×C3×M16—31no—
125C3×#117—31no—
126#926—31no—
127#926—31no—
128#926—61no—
129#926C2×D311yescharacteristic, complemented
130C2×#208—31no—
131C2×#208—31no—
132C2×#208—61no—
133C2×#208C2×D311yescharacteristic, complemented
134C3×#104—62no—
135#837—22no—
136#837—64no—
137#837—62no—
138#837—62no—
139#836—61no—
140#834—62no—
141#833—61no—
142#832—62no—
143#832—62no—
144#824—61no—
145#823—61no—
146#821—62no—
147#809—62no—
148#806—62no—
149C23×C32—21no—
150C23×C32C2×D411yescharacteristic
151C22×C3×D3—22no—
152C22×C3×D3—28no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—82no—
156C22×C3×D3—84no—
157C22×C3×D3C22⋊C412yes—
158C32×Q8—21no—
159C32×Q8C22⋊C412yes—
160C32×D4—22no—
161C32×D4—22no—
162C32×D4—21no—
163C32×D4C22⋊C412yes—
164C2×C32×C4—21no—
165C2×C32×C4—22no—
166C2×C32×C4—22no—
167C2×C32×C4C22×C411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4C2×D411yescharacteristic
171C2×C32×C4C2×D411yescharacteristic
172C2×C32×C4C2×D411yescharacteristic
173C2×C3⋊Dic3—41no—
174C3×#67—28no—
175C3×#67—22no—
176C3×#67—22no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3C22⋊C412yes—
179C3×D12—28no—
180C3×D12—22no—
181C3×D12—21no—
182C3×D12—22no—
183C3×D12—21no—
184C3×D12—22no—
185C3×D12C22⋊C414yes—
186C3×C4×D3—28no—
187C3×C4×D3—22no—
188C3×C4×D3—22no—
189C3×Dic6—21no—
190C3×Dic6—21no—
191C3⋊(C3⋊C8)—41no—
192C3×C3⋊C8—41no—
193C2×H(5,𝔽2)—31no—
194#421—31no—
195#421—91no—
196#418—91no—
197#418—91no—
198#413—91no—
199#410—91no—
200C24×C3—62no—
201C24×C3—61no—
202C23×D3—21no—
203C23×D3—22no—
204C3×#41—21no—
205C3×#41—21no—
206C3×#41—21no—
207C3×#41—21no—
208C3×#41—22no—
209C3×#41—22no—
210C3×#41—41no—
211C3×#41—41no—
212C3×#41—64no—
213C3×#41—64no—
214C3×#41—64no—
215C3×#41—64no—
216C3×#41—61no—
217C3×#41—61no—
218C3×#41—61no—
219C3×#41—61no—
220C3×#41D1212yes—
221C3×#41#6712yes—
222C3×#41#6712yes—
223C3×#41#6712yes—
224C2×C3×Q8—21no—
225C2×C3×Q8—31no—
226C2×C3×Q8C4×D311yescharacteristic
227C2×C3×Q8C2×Dic311yescharacteristic
228C2×C3×D4—21no—
229C2×C3×D4—21no—
230C2×C3×D4—21no—
231C2×C3×D4—32no—
232C2×C3×D4—32no—
233C2×C3×D4—32no—
234C2×C3×D4—32no—
235C2×C3×D4—31no—
236C2×C3×D4—41no—
237C2×C3×D4—62no—
238C2×C3×D4—64no—
239C2×C3×D4—64no—
240C2×C3×D4—62no—
241C2×C3×D4—64no—
242C2×C3×D4—68no—
243C2×C3×D4—68no—
244C2×C3×D4—64no—
245C2×C3×D4—61no—
246C2×C3×D4—61no—
247C2×C3×D4—61no—
248C2×C3×D4C4×D311yescharacteristic
249C2×C3×D4C2×Dic311yescharacteristic
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4—21no—
253C22×C3×C4—32no—
254C22×C3×C4—41no—
255C22×C3×C4—62no—
256C22×C3×C4C22×D311yescharacteristic
257C22×C3×C4C22×D311yescharacteristic
258C2×#67—22no—
259C2×#67#6712yes—
260#239—24no—
261#239—24no—
262D3×D4—28no—
263D3×D4—28no—
264D3×D4—24no—
265D3×D4—24no—
266#235—24no—
267#235—24no—
268#235—21no—
269#235—21no—
270#235—21no—
271#235—21no—
272C2×D12—24no—
273C2×D12—24no—
274C2×D12—22no—
275C2×D12—21no—
276C2×D12—21no—
277C2×D12—21no—
278C2×D12C2×Dic312yes—
279C2×D12#6711yescharacteristic
280C2×D12#6712yes—
281C2×D12#6712yes—
282C2×C4×D3—22no—
283C2×C4×D3C2×Dic312yes—
284C2×Dic6#6711yescharacteristic
285C3×M16—61no—
286C3×M16—61no—
287C2×C3×C8—61no—
288C3×C4⋊C4—61no—
289C3×C22⋊C4—61no—
290C3×C42—61no—
291#217—21no—
292#217—61no—
293#217—61no—
294#217—121no—
295C4⋊Dic3—21no—
296C4⋊Dic3—61no—
297C4⋊Dic3—61no—
298C4⋊Dic3—121no—
299C4×Dic3—21no—
300C4×Dic3—62no—
301C4×Dic3—61no—
302C4×Dic3—61no—
303#208—21no—
304#208—21no—
305#208—62no—
306#208—61no—
307#208—61no—
308#208—61no—
309#208—61no—
310#208—121no—
311C2×C3⋊C8—21no—
312C2×C3⋊C8—61no—
313C2×C3⋊C8—61no—
314C2×C3⋊C8—121no—
315C22×C32—22no—
316C22×C32—41no—
317C22×C32—42no—
318C22×C32C2×C22⋊C411yescharacteristic
319C22×C32#12011yescharacteristic
320C22×C32#12011yescharacteristic
321C2×C3×D3—22no—
322C2×C3×D3—24no—
323C2×C3×D3—44no—
324C2×C3×D3—42no—
325C2×C3×D3—82no—
326C2×C3×D3—82no—
327C2×C3×D3—88no—
328C32×C4—22no—
329C32×C4C2×C22⋊C411yescharacteristic
330C32×C4C2×C22⋊C411yescharacteristic
331C32×C4#12011yescharacteristic
332C32×C4#12011yescharacteristic
333C3⋊Dic3—81no—
334C3×Dic3—22no—
335C3×Dic3—81no—
336H(5,𝔽2)—62no—
337H(5,𝔽2)—62no—
338H(5,𝔽2)—62no—
339H(5,𝔽2)—62no—
340C2×#41—31no—
341C2×#41—32no—
342C2×#41—61no—
343C2×#41D3211yescharacteristic
344C22×D4—32no—
345C22×D4—31no—
346C22×D4—61no—
347C22×D4—62no—
348C2×M16—31no—
349C2×M16—91no—
350#117—31no—
351#117—91no—
352#104—62no—
353#104—182no—
354#102—182no—
355#102—182no—
356#101—181no—
357#100—181no—
358#99—182no—
359C23×C3—21no—
360C23×C3—21no—
361C23×C3—21no—
362C23×C3—32no—
363C23×C3—41no—
364C23×C3—68no—
365C23×C3—62no—
366C23×C3—62no—
367C23×C3—62no—
368C23×C3—242no—
369C23×C3—244no—
370C23×C3D3×D411yescharacteristic
371C23×C3C2×#6711yescharacteristic
372C22×D3—22no—
373C22×D3—28no—
374C22×D3—22no—
375C22×D3—22no—
376C22×D3—82no—
377C22×D3—84no—
378C22×D3#21712yes—
379C3×Q8—21no—
380C3×Q8—21no—
381C3×Q8—22no—
382C3×Q8—41no—
383C3×Q8—61no—
384C3×Q8—61no—
385C3×Q8(C2×D3)⋊C412yes—
386C3×Q8#21712yes—
387C3×D4—22no—
388C3×D4—22no—
389C3×D4—22no—
390C3×D4—22no—
391C3×D4—21no—
392C3×D4—21no—
393C3×D4—22no—
394C3×D4—34no—
395C3×D4—41no—
396C3×D4—42no—
397C3×D4—42no—
398C3×D4—68no—
399C3×D4—68no—
400C3×D4—62no—
401C3×D4—62no—
402C3×D4—62no—
403C3×D4—61no—
404C3×D4—62no—
405C3×D4—62no—
406C3×D4—61no—
407C3×D4(C2×D3)⋊C412yes—
408C3×D4#21712yes—
409C2×C3×C4—21no—
410C2×C3×C4—21no—
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—21no—
418C2×C3×C4—21no—
419C2×C3×C4—21no—
420C2×C3×C4—21no—
421C2×C3×C4—32no—
422C2×C3×C4—42no—
423C2×C3×C4—42no—
424C2×C3×C4—41no—
425C2×C3×C4—68no—
426C2×C3×C4—62no—
427C2×C3×C4—62no—
428C2×C3×C4—121no—
429C2×C3×C4C2×C4×D311yescharacteristic
430C2×C3×C4C2×D1211yescharacteristic
431C2×C3×C4D3×D411yescharacteristic
432C2×C3×C4D3×D411yescharacteristic
433C2×C3×C4D3×D411yescharacteristic
434C2×C3×C4C22×Dic311yescharacteristic
435C2×C3×C4C2×#6711yescharacteristic
436C2×C3×C4C2×#6711yescharacteristic
437C2×C3×C4C2×#6711yescharacteristic
438C2×C3×C4C2×#6711yescharacteristic
439C2×C3×C4C2×#6711yescharacteristic
440C2×C3×C4C2×#6711yescharacteristic
441#67—28no—
442#67—22no—
443#67—22no—
444C2×Dic3—41no—
445C2×Dic3—122no—
446C2×Dic3—121no—
447C2×Dic3—121no—
448C2×Dic3#21712yes—
449D12—28no—
450D12—22no—
451D12—21no—
452D12—22no—
453D12—21no—
454D12—22no—
455D12#21714yes—
456C4×D3—28no—
457C4×D3—22no—
458C4×D3—22no—
459Dic6—21no—
460Dic6—21no—
461C3×C8—121no—
462C3⋊C8—41no—
463C3⋊C8—122no—
464C3⋊C8—121no—
465C3⋊C8—121no—
466C2×C32—21no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—42no—
470C2×C32#37911yescharacteristic
471C3×D3—44no—
472C3×D3—42no—
473C24—62no—
474C24—61no—
475#41—21no—
476#41—21no—
477#41—64no—
478#41—64no—
479#41—64no—
480#41—64no—
481#41—61no—
482#41—61no—
483#41—61no—
484#41—61no—
485#41#62512yes—
486#41#62612yes—
487C2×Q8—31no—
488C2×Q8D3×Dic311yescharacteristic
489C2×D4—21no—
490C2×D4—32no—
491C2×D4—32no—
492C2×D4—32no—
493C2×D4—32no—
494C2×D4—31no—
495C2×D4—62no—
496C2×D4—64no—
497C2×D4—64no—
498C2×D4—62no—
499C2×D4—64no—
500C2×D4—68no—
501C2×D4—68no—
502C2×D4—64no—
503C2×D4—61no—
504C2×D4—61no—
505C2×D4—61no—
506C2×D4D3×Dic311yescharacteristic
507C22×C4—21no—
508C22×C4—32no—
509C22×C4—62no—
510C22×C4C2×D3211yescharacteristic
511M16—61no—
512M16—61no—
513M16—181no—
514M16—181no—
515C2×C8—61no—
516C2×C8—181no—
517C4⋊C4—61no—
518C4⋊C4—181no—
519C22⋊C4—61no—
520C22⋊C4—181no—
521C42—61no—
522C42—181no—
523C22×C3—22no—
524C22×C3—22no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—21no—
528C22×C3—42no—
529C22×C3—41no—
530C22×C3—41no—
531C22×C3—42no—
532C22×C3—42no—
533C22×C3—64no—
534C22×C3—62no—
535C22×C3—81no—
536C22×C3—82no—
537C22×C3—122no—
538C22×C3—124no—
539C22×C3—242no—
540C22×C3—242no—
541C22×C3—248no—
542C22×C3D3×C22⋊C411yescharacteristic
543C22×C3#88211yescharacteristic
544C22×C3#93711yescharacteristic
545C22×C3C2×#21711yescharacteristic
546C22×C3#95311yescharacteristic
547C22×C3#95311yescharacteristic
548C2×D3—22no—
549C2×D3—24no—
550C2×D3—44no—
551C2×D3—42no—
552C2×D3—82no—
553C2×D3—82no—
554C2×D3—88no—
555C3×C4—22no—
556C3×C4—22no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—21no—
561C3×C4—42no—
562C3×C4—62no—
563C3×C4—241no—
564C3×C4D3×C22⋊C411yescharacteristic
565C3×C4#88211yescharacteristic
566C3×C4C2×(C2×D3)⋊C411yescharacteristic
567C3×C4#93711yescharacteristic
568C3×C4C2×#21711yescharacteristic
569C3×C4C2×#21711yescharacteristic
570C3×C4#95311yescharacteristic
571C3×C4#95311yescharacteristic
572Dic3—22no—
573Dic3—81no—
574Dic3—241no—
575Dic3—241no—
576Dic3—242no—
577C32#179511yescharacteristic, complemented, Sylow
578C23—21no—
579C23—32no—
580C23—68no—
581C23—62no—
582C23—62no—
583C23—62no—
584C23—242no—
585C23—244no—
586C23D3×#6711yescharacteristic
587Q8—21no—
588Q8—61no—
589Q8—61no—
590Q8(C2×D3)⋊Dic312yes—
591D4—22no—
592D4—22no—
593D4—21no—
594D4—34no—
595D4—68no—
596D4—68no—
597D4—62no—
598D4—62no—
599D4—62no—
600D4—62no—
601D4—61no—
602D4—62no—
603D4—61no—
604D4(C2×D3)⋊Dic312yes—
605C2×C4—21no—
606C2×C4—22no—
607C2×C4—22no—
608C2×C4—32no—
609C2×C4—68no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—121no—
613C2×C4—361no—
614C2×C4C2×D3×Dic311yescharacteristic
615C2×C4C2×#62511yescharacteristic
616C2×C4C2×#62611yescharacteristic
617C2×C4D3×#6711yescharacteristic
618C2×C4D3×#6711yescharacteristic
619C2×C4D3×#6711yescharacteristic
620C8—121no—
621C8—361no—
622C2×C3—21no—
623C2×C3—21no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—21no—
628C2×C3—21no—
629C2×C3—41no—
630C2×C3—41no—
631C2×C3—41no—
632C2×C3—42no—
633C2×C3—42no—
634C2×C3—82no—
635C2×C3—124no—
636C2×C3—122no—
637C2×C3#495511yescharacteristic
638C2×C3#524711yescharacteristic
639D3—44no—
640D3—42no—
641C22—22no—
642C22—41no—
643C22—42no—
644C22—64no—
645C22—62no—
646C22—122no—
647C22—124no—
648C22—242no—
649C22—242no—
650C22—248no—
651C22D3×#21711yescharacteristic
652C22#6397611yescharacteristic
653C22#6397711yescharacteristic
654C4—22no—
655C4—62no—
656C4—241no—
657C4—721no—
658C4C2×(C2×D3)⋊Dic311yescharacteristic
659C4D3×#21711yescharacteristic
660C4#6397611yescharacteristic
661C4#6397711yescharacteristic
662C3—21no—
663C3#7041411yescharacteristic, complemented
664C3#7214111yescharacteristic, complemented
665C2—21no—
666C2—21no—
667C2—21no—
668C2—42no—
669C2—124no—
670C2—122no—
671C2#1059170611yescharacteristic
subgroupG/H
centerC2#10591706
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×#41C22
socleC2×C32#379
prime radicalC2×C3×#1009C2
cosocleC22×C32×C4C23
hypercenterC2×#41D32
hypocenterC32#1795
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. #10592935C2semidirect
3. C3×#5236C2semidirect
4. #10591231C2semidirect
5. #10591086C2semidirect
6. #10591085C2semidirect
7. #10591076C2semidirect
15. C2×C3×#239C4semidirect
17. C2×C3×D3×D4C4semidirect
22. #64135C22semidirect
23. C2×#3748C22semidirect
24. C3×#926C22semidirect
25. C2×C3×#208C22semidirect
41. #5236D3semidirect
117. C2×#239Dic3semidirect
119. C2×D3×D4Dic3semidirect
129. #926C2×D3semidirect
133. C2×#208C2×D3semidirect
577. C32#1795semidirect
663. C3#70414semidirect
664. C3#72141semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10092
#105929352
C3×#52362
#105912312
#105910862
#105910852
#105910762
#721413
#704143