Finite Group Databasebeta

← #11784978

Subgroups — #11784978

Order 1152.

1251 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×#64307C211yesmaximal, characteristic
2#10592831C211yesmaximal, characteristic, complemented
3C3×#5139C211yesmaximal, characteristic, complemented
4C3×#5131C211yesmaximal, characteristic, complemented
5#10591232C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7#10591085C211yesmaximal, characteristic, complemented
8#70414—31nomaximal
9#70327—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C3×#235C2211yescharacteristic
12C22×C3×D12C2211yescharacteristic
13C2×D3×#67—22no—
14#64307—22no—
15#64307—22no—
16#64307—22no—
17#64307—22no—
18C2×#3802C412yescomplemented
19C2×D3×D12—21no—
20C2×#3796C412yescomplemented
21C2×#3795—21no—
22C2×C32×M16C2211yescharacteristic, complemented
23C2×#3748C2211yescharacteristic, complemented
24C3×#926C2211yescharacteristic, complemented
25C3×#926C2211yescharacteristic, complemented
26#63651—21no—
27#63650—21no—
28C3×#825—22no—
29C3×#821—22no—
30#63581—22no—
31#63569—22no—
32#63562—22no—
33C2×#1009—31no—
34C2×#1004—31no—
35C3×#421—31no—
36C3×#418—31no—
37#5236—31no—
38#5215—31no—
39#5139D311yescharacteristic, complemented
40#5132—31no—
41#5132—31no—
42#5132—61no—
43#5131D311yescharacteristic, complemented
44#5006—31no—
45#5006—31no—
46#5005—31no—
47#5001—31no—
48C23×C3×D3—21no—
49C22×D32—22no—
50C22×C32×C4C2311yescharacteristic
51C2×#638D412yes—
52#3828—21no—
53#3828—21no—
54#3828—21no—
55#3828—21no—
56C2×C4⋊(C3⋊D3)D411yescharacteristic
57C2×C4×C3⋊D3C2×C412yes—
58C2×#634D411yescharacteristic
59C2×C3×#67—21no—
60C3×#235—21no—
61C3×#235—21no—
62C3×#235D412yes—
63C3×#235D412yes—
64C2×C3×D12—21no—
65C2×C3×D12—21no—
66C2×C3×D12—21no—
67C2×C3×D12C2×C412yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×D12D412yes—
70C2×C3×D12D412yes—
71C2×C3×C4×D3—21no—
72C2×C3×Dic6C2×C411yescharacteristic
73D3×#67—28no—
74D3×#67—28no—
75C2×#626—22no—
76C2×#625—22no—
77C2×D3×Dic3—22no—
78#3802—24no—
79#3802—24no—
80D3×D12—24no—
81D3×D12—24no—
82#3796—24no—
83#3796—24no—
84#3795—24no—
85#3795—24no—
86C32×M16—21no—
87C32×M16—21no—
88C2×C32×C8—21no—
89#3748—21no—
90#3748—21no—
91C2×C3⋊(C3⋊C8)—21no—
92C3×#217—21no—
93C3×#217—21no—
94C3×C4⋊Dic3—21no—
95C3×C4⋊Dic3—21no—
96C3×C4×Dic3—21no—
97C3×C4×Dic3—21no—
98#1795—91noSylow
99C2×C3×#41—31no—
100C22×C3×D4—31no—
101C22×#67—62no—
102#1009—62no—
103#1009—62no—
104#1009—62no—
105#1009—62no—
106C2×#239—32no—
107#1004—62no—
108#1004—62no—
109#1004—62no—
110#1004—62no—
111C2×#237—32no—
112C2×#237—61no—
113C2×D3×D4—32no—
114C2×D3×D4—32no—
115C2×D3×D4—61no—
116C2×D3×D4—62no—
117C2×#235—31no—
118C2×#235—31no—
119C2×#235—61no—
120C2×#235—61no—
121C2×#235C2×D311yescharacteristic
122C22×D12—61no—
123C22×D12C2×D311yescharacteristic
124C2×C3×M16—21no—
125C2×C3×M16C2×D311yescharacteristic, complemented
126C2×C3×M16C2×D311yescharacteristic, complemented
127C3×#117—31no—
128C3×#117—31no—
129#926C2×D311yescharacteristic, complemented
130#926C2×D311yescharacteristic, complemented
131C2×#208—31no—
132C2×#208—31no—
133C2×#208—61no—
134C3×#104—62no—
135C3×#102—62no—
136#837—62no—
137#832—62no—
138#825—22no—
139#824—61no—
140#824—61no—
141#824—62no—
142#823—61no—
143#823—61no—
144#823—62no—
145#821—22no—
146#809—62no—
147#806—62no—
148#806—62no—
149#805—62no—
150C23×C32C2×D411yescharacteristic
151C22×C3⋊D3C22⋊C412yes—
152C22×C3×D3—21no—
153C22×C3×D3—22no—
154C22×C3×D3—22no—
155C22×C3×D3—22no—
156C22×C3×D3—82no—
157C2×D32—28no—
158C2×D32—84no—
159C2×C32×C4C22×C411yescharacteristic
160C2×C32×C4C2×D411yescharacteristic
161C2×C32×C4C2×D411yescharacteristic
162C2×C32×C4C2×D411yescharacteristic
163C2×C32×C4C2×D411yescharacteristic
164C2×C32×C4C2×D411yescharacteristic
165#638—22no—
166#638—22no—
167C2×C3⋊Dic3C22⋊C412yes—
168C4⋊(C3⋊D3)—21no—
169C4⋊(C3⋊D3)—21no—
170C4×C3⋊D3—22no—
171C4×C3⋊D3—22no—
172#634—21no—
173#634—21no—
174C3×#67—22no—
175C3×#67—22no—
176C2×C3×Dic3—21no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C3×D12—22no—
180C3×D12—21no—
181C3×D12—22no—
182C3×D12—22no—
183C3×D12C22⋊C414yes—
184C3×D12C22⋊C412yes—
185C3×C4×D3—22no—
186C3×C4×D3—22no—
187C3×Dic6—21no—
188C3×Dic6C22⋊C412yes—
189#626—28no—
190#625—28no—
191D3×Dic3—28no—
192C32×C8—41no—
193C3⋊(C3⋊C8)—41no—
194C2×H(5,𝔽2)—91no—
195#421—31no—
196#421—91no—
197#418—31no—
198#418—91no—
199#413—91no—
200#410—91no—
201C24×C3—61no—
202C23×D3—21no—
203C23×D3—62no—
204C23×D3—62no—
205C3×#41—32no—
206C3×#41—32no—
207C3×#41—61no—
208C3×#41—61no—
209C2×C3×Q8—31no—
210C2×C3×D4—31no—
211C2×C3×D4—32no—
212C2×C3×D4—32no—
213C2×C3×D4—32no—
214C2×C3×D4—61no—
215C2×C3×D4—61no—
216C2×C3×D4—61no—
217C2×C3×D4—61no—
218C22×C3×C4—21no—
219C22×C3×C4—61no—
220C22×C3×C4C22×D311yescharacteristic
221C22×C3×C4C22×D311yescharacteristic
222C2×#67—21no—
223C2×#67—32no—
224C2×#67—32no—
225C2×#67—62no—
226C2×#67—62no—
227C2×#67—62no—
228C2×#67—62no—
229C2×#67—68no—
230C2×#67—68no—
231C22×Dic3—62no—
232#239—64no—
233#239—64no—
234#237—64no—
235#237—64no—
236#237—64no—
237#237—64no—
238D3×D4—64no—
239D3×D4—64no—
240D3×D4—64no—
241D3×D4—64no—
242D3×D4—68no—
243D3×D4—68no—
244D3×D4—64no—
245D3×D4—64no—
246#235—21no—
247#235—21no—
248#235—64no—
249#235—64no—
250#235—61no—
251#235—61no—
252#235—61no—
253#235—61no—
254#235—61no—
255#235—61no—
256#235—61no—
257#235—61no—
258#235—121no—
259#235—121no—
260#235—121no—
261#235—121no—
262#235D1212yes—
263#235#6712yes—
264C2×D12—21no—
265C2×D12—21no—
266C2×D12—21no—
267C2×D12—31no—
268C2×D12—31no—
269C2×D12—61no—
270C2×D12—64no—
271C2×D12—64no—
272C2×D12—62no—
273C2×D12C4×D312yes—
274C2×D12C4×D311yescharacteristic
275C2×D12D1212yes—
276C2×D12#6712yes—
277C2×C4×D3—21no—
278C2×C4×D3—32no—
279C2×C4×D3—32no—
280C2×C4×D3—62no—
281C2×C4×D3—62no—
282C2×Dic6—31no—
283C2×Dic6—31no—
284C2×Dic6—61no—
285C2×Dic6C4×D311yescharacteristic
286C3×M16—22no—
287C3×M16—21no—
288C3×M16—21no—
289C3×M16—21no—
290C3×M16—21no—
291C3×M16—41no—
292C2×C3×C8—21no—
293C2×C3×C8—21no—
294C2×C3×C8—41no—
295C3×C4⋊C4—61no—
296C3×C4⋊C4—61no—
297C3×C22⋊C4—61no—
298C3×C22⋊C4—61no—
299C3×C42—61no—
300C3×C42—61no—
301#217—21no—
302#217—21no—
303C4⋊Dic3—21no—
304C4⋊Dic3—21no—
305C4×Dic3—21no—
306C4×Dic3—21no—
307#208—62no—
308#208—61no—
309#208—61no—
310#208—61no—
311#208—61no—
312#208—121no—
313C2×C3⋊C8—61no—
314C2×C3⋊C8—61no—
315C2×C3⋊C8—121no—
316C22×C32—41no—
317C22×C32C2×C22⋊C411yescharacteristic
318C22×C32#12011yescharacteristic
319C22×C32#12011yescharacteristic
320C2×C3⋊D3—22no—
321C2×C3⋊D3—42no—
322C2×C3×D3—24no—
323C2×C3×D3—22no—
324C2×C3×D3—42no—
325C2×C3×D3—44no—
326C2×C3×D3—82no—
327C2×C3×D3—82no—
328D32—88no—
329C32×C4C2×C22⋊C411yescharacteristic
330C32×C4C2×C22⋊C411yescharacteristic
331C32×C4#12011yescharacteristic
332C32×C4#12011yescharacteristic
333C3⋊Dic3—22no—
334C3×Dic3—22no—
335C3×Dic3—81no—
336C3×Dic3—81no—
337H(5,𝔽2)—182no—
338H(5,𝔽2)—182no—
339H(5,𝔽2)—182no—
340H(5,𝔽2)—182no—
341C2×#41—31no—
342C2×#41—91no—
343C2×#41—92no—
344C2×#41—181no—
345C22×D4—31no—
346C22×D4—92no—
347C22×D4—181no—
348C22×D4—182no—
349C2×M16—91no—
350C2×M16D3211yescharacteristic, complemented
351#117—31no—
352#117—31no—
353#104—62no—
354#104—182no—
355#102—62no—
356#102—182no—
357#101—181no—
358#100—181no—
359#99—182no—
360C23×C3—21no—
361C23×C3—62no—
362C23×C3—61no—
363C23×C3—62no—
364C23×C3—62no—
365C23×C3—242no—
366C23×C3D3×D411yescharacteristic
367C23×C3D3×D411yescharacteristic
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—22no—
372C22×D3—32no—
373C22×D3—32no—
374C22×D3—62no—
375C22×D3—68no—
376C22×D3—68no—
377C22×D3—82no—
378C22×D3—244no—
379C22×D3—244no—
380C3×Q8—32no—
381C3×Q8—61no—
382C3×D4—32no—
383C3×D4—34no—
384C3×D4—62no—
385C3×D4—62no—
386C3×D4—62no—
387C3×D4—61no—
388C3×D4—62no—
389C3×D4—62no—
390C2×C3×C4—21no—
391C2×C3×C4—21no—
392C2×C3×C4—21no—
393C2×C3×C4—21no—
394C2×C3×C4—21no—
395C2×C3×C4—21no—
396C2×C3×C4—61no—
397C2×C3×C4—62no—
398C2×C3×C4—62no—
399C2×C3×C4—121no—
400C2×C3×C4—121no—
401C2×C3×C4C2×C4×D311yescharacteristic
402C2×C3×C4C2×C4×D311yescharacteristic
403C2×C3×C4C2×D1211yescharacteristic
404C2×C3×C4C2×D1211yescharacteristic
405C2×C3×C4D3×D411yescharacteristic
406C2×C3×C4D3×D411yescharacteristic
407C2×C3×C4D3×D411yescharacteristic
408C2×C3×C4D3×D411yescharacteristic
409C2×C3×C4D3×D411yescharacteristic
410C2×C3×C4D3×D411yescharacteristic
411C2×C3×C4C2×#6711yescharacteristic
412C2×C3×C4C2×#6711yescharacteristic
413#67—22no—
414#67—22no—
415#67—68no—
416#67—68no—
417#67—68no—
418#67—62no—
419#67—62no—
420#67—62no—
421#67—62no—
422#67—122no—
423#67—122no—
424C2×Dic3—21no—
425C2×Dic3—32no—
426C2×Dic3—32no—
427C2×Dic3—41no—
428C2×Dic3—41no—
429C2×Dic3—62no—
430C2×Dic3—68no—
431D12—22no—
432D12—21no—
433D12—22no—
434D12—22no—
435D12—68no—
436D12—61no—
437D12—61no—
438D12—61no—
439D12—61no—
440D12—121no—
441D12—121no—
442D12(C2×D3)⋊C414yes—
443D12(C2×D3)⋊C412yes—
444C4×D3—22no—
445C4×D3—22no—
446C4×D3—68no—
447C4×D3—62no—
448C4×D3—62no—
449C4×D3—62no—
450C4×D3—62no—
451C4×D3—122no—
452C4×D3—122no—
453Dic6—21no—
454Dic6—61no—
455Dic6—61no—
456Dic6—61no—
457Dic6—61no—
458Dic6—121no—
459Dic6—121no—
460Dic6(C2×D3)⋊C412yes—
461C3×C8—42no—
462C3×C8—41no—
463C3×C8—41no—
464C3⋊C8—122no—
465C3⋊C8—121no—
466C3⋊C8—121no—
467C2×C32—21no—
468C2×C32—21no—
469C2×C32—21no—
470C2×C32#37911yescharacteristic
471C3⋊D3—42no—
472C3×D3—42no—
473C3×D3—44no—
474C24—61no—
475C24—182no—
476#41—32no—
477#41—32no—
478#41—61no—
479#41—61no—
480#41—184no—
481#41—184no—
482#41—184no—
483#41—184no—
484#41—181no—
485#41—181no—
486#41—181no—
487#41—181no—
488C2×Q8—31no—
489C2×Q8—91no—
490C2×D4—32no—
491C2×D4—31no—
492C2×D4—32no—
493C2×D4—32no—
494C2×D4—61no—
495C2×D4—61no—
496C2×D4—61no—
497C2×D4—61no—
498C2×D4—92no—
499C2×D4—91no—
500C2×D4—184no—
501C2×D4—184no—
502C2×D4—182no—
503C2×D4—182no—
504C2×D4—184no—
505C2×D4—184no—
506C2×D4—188no—
507C2×D4—188no—
508C22×C4—61no—
509C22×C4—92no—
510C22×C4—182no—
511C22×C4C2×D3211yescharacteristic
512M16—21no—
513M16—21no—
514M16—181no—
515M16—181no—
516C2×C8—21no—
517C2×C8—181no—
518C4⋊C4—61no—
519C4⋊C4—61no—
520C22⋊C4—61no—
521C22⋊C4—61no—
522C42—61no—
523C42—61no—
524C22×C3—21no—
525C22×C3—21no—
526C22×C3—21no—
527C22×C3—41no—
528C22×C3—41no—
529C22×C3—64no—
530C22×C3—62no—
531C22×C3—81no—
532C22×C3—122no—
533C22×C3—124no—
534C22×C3—242no—
535C22×C3—242no—
536C22×C3D3×C22⋊C411yescharacteristic
537C22×C3D3×C22⋊C411yescharacteristic
538C22×C3#88211yescharacteristic
539C22×C3#88211yescharacteristic
540C22×C3#93711yescharacteristic
541C22×C3#93711yescharacteristic
542C2×D3—22no—
543C2×D3—24no—
544C2×D3—44no—
545C2×D3—42no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—82no—
549C2×D3—82no—
550C2×D3—122no—
551C2×D3—122no—
552C2×D3—122no—
553C2×D3—242no—
554C2×D3—248no—
555C2×D3—248no—
556C3×C4—21no—
557C3×C4—21no—
558C3×C4—21no—
559C3×C4—21no—
560C3×C4—62no—
561C3×C4—241no—
562C3×C4—241no—
563C3×C4D3×C22⋊C411yescharacteristic
564C3×C4D3×C22⋊C411yescharacteristic
565C3×C4#88211yescharacteristic
566C3×C4#88211yescharacteristic
567C3×C4C2×(C2×D3)⋊C411yescharacteristic
568C3×C4C2×(C2×D3)⋊C411yescharacteristic
569C3×C4#93711yescharacteristic
570C3×C4#93711yescharacteristic
571Dic3—22no—
572Dic3—62no—
573Dic3—62no—
574Dic3—81no—
575Dic3—81no—
576Dic3—122no—
577C32#179511yescharacteristic, complemented, Sylow
578C23—61no—
579C23—62no—
580C23—62no—
581C23—62no—
582C23—92no—
583C23—188no—
584C23—242no—
585C23—724no—
586C23#380211yescharacteristic
587Q8—32no—
588Q8—61no—
589Q8—181no—
590Q8—181no—
591D4—34no—
592D4—32no—
593D4—62no—
594D4—62no—
595D4—62no—
596D4—61no—
597D4—62no—
598D4—62no—
599D4—188no—
600D4—188no—
601D4—182no—
602D4—182no—
603D4—181no—
604D4—181no—
605C2×C4—61no—
606C2×C4—62no—
607C2×C4—62no—
608C2×C4—92no—
609C2×C4—121no—
610C2×C4—121no—
611C2×C4—188no—
612C2×C4—182no—
613C2×C4—182no—
614C2×C4C4×D3211yescharacteristic
615C2×C4D3×D1211yescharacteristic
616C2×C4D3×D1211yescharacteristic
617C2×C4D3×#6711yescharacteristic
618C2×C4D3×#6711yescharacteristic
619C2×C4#381111yescharacteristic
620C8—41no—
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—124no—
633C2×C3—122no—
634C2×C3#495511yescharacteristic
635C2×C3#495511yescharacteristic
636D3—42no—
637D3—44no—
638D3—122no—
639D3—122no—
640D3—242no—
641C22—41no—
642C22—62no—
643C22—64no—
644C22—124no—
645C22—122no—
646C22—182no—
647C22—242no—
648C22—242no—
649C22—362no—
650C22—728no—
651C22#6392111yescharacteristic
652C22#6392211yescharacteristic
653C22#6392211yescharacteristic
654C4—62no—
655C4—182no—
656C4—241no—
657C4—241no—
658C4D3×(C2×D3)⋊C411yescharacteristic
659C4D3×(C2×D3)⋊C411yescharacteristic
660C4#6392311yescharacteristic
661C4#6398311yescharacteristic
662C3—21no—
663C3#7032711yescharacteristic, complemented
664C3#7041411yescharacteristic, complemented
665C2—21no—
666C2—21no—
667C2—21no—
668C2—124no—
669C2—122no—
670C2—362no—
671C2#1059139911yescharacteristic
subgroupG/H
centerC2#10591399
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#379
prime radicalC2×#64307C2
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1795
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. #10592831C2semidirect
3. C3×#5139C2semidirect
4. C3×#5131C2semidirect
5. #10591232C2semidirect
6. #10591111C2semidirect
7. #10591085C2semidirect
18. C2×#3802C4semidirect
20. C2×#3796C4semidirect
22. C2×C32×M16C22semidirect
23. C2×#3748C22semidirect
24. C3×#926C22semidirect
25. C3×#926C22semidirect
39. #5139D3semidirect
43. #5131D3semidirect
125. C2×C3×M16C2×D3semidirect
126. C2×C3×M16C2×D3semidirect
129. #926C2×D3semidirect
130. #926C2×D3semidirect
350. C2×M16D32semidirect
577. C32#1795semidirect
663. C3#70327semidirect
664. C3#70414semidirect

Maximal subgroups

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

subgroupindex
C2×#643072
#105928312
C3×#51392
C3×#51312
#105912322
#105911112
#105910852
#704143
#703273