Finite Group Databasebeta

← #11858193

Subgroups — #11858193

Order 1152.

1561 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596669C211yesmaximal, characteristic
2C3×#5745C211yesmaximal, characteristic, complemented
3#10594958C211yesmaximal, characteristic, complemented
4C2×#63652C211yesmaximal, characteristic, complemented
5C3×#5139C211yesmaximal, characteristic, complemented
6#10591113C211yesmaximal, characteristic, complemented
7C2×#63568C211yesmaximal, characteristic, complemented
8#10591005C214yesmaximal, complemented
9D3×#825C214yesmaximal, complemented
10#83817—31nomaximal
11#78992—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15#64330—22no—
16#64308C412yescomplemented
17#64307—21no—
18#64307C412yescomplemented
19#64306—22no—
20D3×#235—22no—
21D3×#235C2214yes—
22#64298C412yescomplemented
23#64297—21no—
24#64297C412yescomplemented
25C2×C32×M16C2211yescharacteristic, complemented
26C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
27C3×#926C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×#907—22no—
30C3×D3×M16C2214yescomplemented
31C3×#901—22no—
32#67⋊Dic3—22no—
33#63898—21no—
34C4×D3×Dic3C2212yescomplemented
35#63855C2212yescomplemented
36#63843—21no—
37#63652C2212yescomplemented
38#63652C2212yescomplemented
39C3×#825C2214yescomplemented
40#63570C2214yescomplemented
41#63568C2212yescomplemented
42#63568C2212yescomplemented
43#5964—31no—
44#5964—31no—
45C3×#568—31no—
46Dic3×#41—31no—
47#5745D311yescharacteristic, complemented
48#5522—31no—
49C3×#421—31no—
50C2×#837—31no—
51#5139—31no—
52#5139—34no—
53#5139D311yescharacteristic, complemented
54C2×#825—31no—
55C2×#825—31no—
56C2×#825—31no—
57C2×#825—34no—
58C2×#825—61no—
59#5005—31no—
60#4821—34no—
61D3×#104—34no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64C22×C3⋊Dic3—21no—
65#3828—21no—
66#3828—21no—
67#3828C2×C412yescomplemented
68#3828C2312yes—
69C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
70C2×C4×C3⋊D3—21no—
71C2×#634C2×C411yescharacteristic, complemented
72C2×C3×#67—21no—
73C2×C3×#67D412yes—
74C3×#235—21no—
75C3×#235—21no—
76C3×#235C2×C412yes—
77C3×#235C2×C412yes—
78C3×#235C2×C412yescomplemented
79C3×#235D412yes—
80C3×#235D412yes—
81C3×#235C2312yes—
82C2×C3×D12C2×C411yescharacteristic, complemented
83C2×C3×D12D411yescharacteristic
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3C2312yes—
86C2×C3×Dic6C2×C411yescharacteristic, complemented
87C2×C3×Dic6D411yescharacteristic
88#3811—24no—
89D3×#67—24no—
90D3×#67—24no—
91#3805—24no—
92#3804—24no—
93#3804—24no—
94C2×D3×Dic3—22no—
95#3802—22no—
96D3×D12—22no—
97D3×D12C2×C414yescomplemented
98C4×D32—24no—
99#3799—22no—
100#3799C2×C414yescomplemented
101#3798—24no—
102#3797—22no—
103#3796—22no—
104#3796—22no—
105#3795—22no—
106#3795C2×C414yescomplemented
107D3×Dic6—22no—
108D3×Dic6C2×C414yescomplemented
109C32×M16—21no—
110C32×M16C2312yes—
111C2×C32×C8—21no—
112C4×C3⋊Dic3—21no—
113C4×C3⋊Dic3C2311yescharacteristic
114C4×C3⋊Dic3C2311yescharacteristic
115C3×#217—21no—
116C3×C4⋊Dic3—21no—
117C3×C4×Dic3C2312yes—
118C3×#208—21no—
119C3×#208C2312yes—
120C2×C3×C3⋊C8—21no—
121C3×ΓL(1,𝔽25)—24no—
122C3×D3×C8—24no—
123Dic3⋊Dic3—22no—
124(C2×D3)⋊Dic3—22no—
125Dic32—22no—
126#2901—91noSylow
127C2×C3×#41—31no—
128C2×C3×#41—31no—
129#1010—32no—
130#1010—32no—
131#1010—32no—
132#1010—61no—
133#1009—32no—
134#1009—32no—
135#1009—32no—
136#1009—61no—
137D3×#41—34no—
138D3×#41—62no—
139D3×#41—62no—
140D3×#41—62no—
141#1007—32no—
142#1007—61no—
143#1004—32no—
144#1004—61no—
145#1004—62no—
146#1004—62no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—34no—
150C2×#235—61no—
151C2×#235—62no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C3×#131—62no—
155C3×#131—62no—
156C2×C3×M16—21no—
157C2×C3×M16—31no—
158C2×C3×M16—34no—
159C2×C3×M16C2×D311yescharacteristic, complemented
160C2×C3×M16C2×D311yescharacteristic, complemented
161C3×#117—31no—
162Q8×Dic3—61no—
163D4×Dic3—61no—
164D4×Dic3—62no—
165#926—32no—
166#926C2×D311yescharacteristic, complemented
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—32no—
170C2×C4×Dic3—61no—
171C2×#208C2×D311yescharacteristic, complemented
172#907—22no—
173D3×M16C2×D314yescomplemented
174#901—22no—
175#893—61no—
176#887—61no—
177#67⋊C4—62no—
178#872—32no—
179C42×D3—32no—
180C3×#104—34no—
181#837—32no—
182#837—32no—
183#825—32no—
184#825—32no—
185#825—32no—
186#825—32no—
187#825—32no—
188#825—32no—
189#825—34no—
190#825—62no—
191#825—62no—
192#825C2×D314yescomplemented
193#805—34no—
194C23×C32C2×D411yescharacteristic
195C22×C3⋊D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3C2×D412yes—
198C2×D32—24no—
199C2×C32×C4C22×C411yescharacteristic
200C2×C32×C4C22×C411yescharacteristic
201C2×C32×C4C2×D411yescharacteristic
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2411yescharacteristic
205#638—22no—
206#638—22no—
207C2×C3⋊Dic3—21no—
208C2×C3⋊Dic3—21no—
209C2×C3⋊Dic3—21no—
210C2×C3⋊Dic3—42no—
211C4⋊(C3⋊D3)—21no—
212C4⋊(C3⋊D3)C22×C412yes—
213C4×C3⋊D3—22no—
214C4×C3⋊D3—22no—
215#634—21no—
216#634C22×C412yes—
217C3×#67—22no—
218C3×#67—22no—
219C3×#67C22⋊C414yes—
220C3×#67C22⋊C414yes—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3C2×D412yes—
224C3×D12—21no—
225C3×D12C22⋊C412yes—
226C3×D12C22⋊C412yes—
227C3×D12C22×C412yes—
228C3×C4×D3—22no—
229C3×C4×D3—22no—
230C3×C4×D3C22×C414yes—
231C3×C4×D3C2×D414yes—
232C3×Dic6—21no—
233C3×Dic6C22⋊C412yes—
234C3×Dic6C22⋊C412yes—
235C3×Dic6C22×C412yes—
236#627—24no—
237#626—24no—
238#626—24no—
239#625—24no—
240#624—24no—
241D3×Dic3—24no—
242D3×Dic3—24no—
243D3×Dic3—44no—
244C32×C8—22no—
245C3×C3⋊C8—22no—
246#585—91no—
247#568—31no—
248C4×#41—91no—
249#421—31no—
250#421—94no—
251#421—91no—
252C2×#104—94no—
253C2×#104—91no—
254C2×#104—91no—
255C3×#41—32no—
256C3×#41—32no—
257C3×#41—32no—
258C3×#41—32no—
259C3×#41—32no—
260C3×#41—32no—
261C3×#41—61no—
262C3×#41—61no—
263C2×C3×Q8—31no—
264C2×C3×Q8—31no—
265C2×C3×D4—32no—
266C2×C3×D4—31no—
267C2×C3×D4—31no—
268C2×C3×D4—61no—
269C22×C3×C4—21no—
270C22×C3×C4—32no—
271C22×C3×C4—61no—
272C22×C3×C4C22×D311yescharacteristic
273C22×C3×C4C22×D311yescharacteristic
274C2×#67—21no—
275C2×#67—64no—
276C2×#67—61no—
277C2×#67—61no—
278C2×#67—64no—
279C2×#67—121no—
280C2×#67D1212yes—
281C22×Dic3—62no—
282C22×Dic3—61no—
283C22×Dic3—61no—
284C22×Dic3—121no—
285#239—34no—
286#239—62no—
287#239—62no—
288#239—62no—
289D3×Q8—34no—
290D3×Q8—62no—
291D3×Q8—62no—
292D3×Q8—62no—
293#237—34no—
294#237—62no—
295#237—62no—
296#237—64no—
297#237—64no—
298#237—64no—
299#237—64no—
300#237—62no—
301D3×D4—34no—
302D3×D4—62no—
303D3×D4—62no—
304D3×D4—64no—
305D3×D4—64no—
306D3×D4—64no—
307D3×D4—64no—
308D3×D4—62no—
309#235—21no—
310#235—21no—
311#235—32no—
312#235—32no—
313#235—32no—
314#235—32no—
315#235—34no—
316#235—34no—
317#235—62no—
318#235—62no—
319#235—64no—
320#235—64no—
321#235—61no—
322#235—61no—
323#235—61no—
324#235—61no—
325#235—64no—
326#235—62no—
327#235—64no—
328#235—62no—
329#235—121no—
330#235—121no—
331#235C4×D312yes—
332#235C4×D312yes—
333#235C4×D312yescomplemented
334#235#6712yes—
335#235#6712yes—
336#235C22×D312yes—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—34no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12C4×D311yescharacteristic, complemented
343C2×D12D1211yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—64no—
346C2×C4×D3—61no—
347C2×C4×D3—61no—
348C2×C4×D3—64no—
349C2×C4×D3—62no—
350C2×C4×D3—121no—
351C2×C4×D3C22×D312yes—
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—34no—
355C2×Dic6—61no—
356C2×Dic6—62no—
357C2×Dic6C4×D311yescharacteristic, complemented
358C2×Dic6D1211yescharacteristic
359C3×M16—21no—
360C3×M16—21no—
361C3×M16—22no—
362C3×M16—32no—
363C3×M16—41no—
364C3×M16—64no—
365C3×M16—61no—
366C3×M16C22×D312yes—
367C3×M16C22×D312yes—
368C2×C3×C8—21no—
369C2×C3×C8—21no—
370C2×C3×C8—41no—
371C2×C3×C8—64no—
372C2×C3×C8—61no—
373C3×C4⋊C4—61no—
374C3×C22⋊C4—61no—
375C3×C42—32no—
376#217—21no—
377#217—62no—
378(C2×D3)⋊C4—62no—
379C4⋊Dic3—21no—
380C4⋊Dic3—62no—
381Dic3⋊C4—62no—
382C4×Dic3—31no—
383C4×Dic3—31no—
384C4×Dic3—31no—
385C4×Dic3—31no—
386C4×Dic3—61no—
387C4×Dic3—61no—
388C4×Dic3—62no—
389C4×Dic3—61no—
390C4×Dic3—61no—
391C4×Dic3—62no—
392C4×Dic3—121no—
393C4×Dic3C22×D312yes—
394#208—21no—
395#208C22×D312yes—
396C2×C3⋊C8—21no—
397ΓL(1,𝔽25)—24no—
398D3×C8—24no—
399C22×C32—41no—
400C22×C32C2×C22⋊C411yescharacteristic
401C22×C32C2×C22⋊C411yescharacteristic
402C22×C32C22×D411yescharacteristic
403C2×C3⋊D3—22no—
404C2×C3⋊D3—81no—
405C2×C3×D3—22no—
406C2×C3×D3—42no—
407C2×C3×D3—81no—
408C2×C3×D3C2×C22⋊C414yes—
409D32—84no—
410C32×C4C2×C22⋊C411yescharacteristic
411C32×C4C2×C22⋊C411yescharacteristic
412C32×C4C23×C411yescharacteristic
413C32×C4C22×D411yescharacteristic
414C3⋊Dic3—22no—
415C3⋊Dic3—22no—
416C3⋊Dic3—41no—
417C3×Dic3—22no—
418C3×Dic3—42no—
419C3×Dic3C2×C22⋊C414yes—
4202−1+4—92no—
4212−1+4—92no—
4222−1+4—181no—
423H(5,𝔽2)—92no—
424H(5,𝔽2)—92no—
425H(5,𝔽2)—182no—
426H(5,𝔽2)—181no—
427C2×#41—31no—
428C2×#41—31no—
429C2×#41—94no—
430C2×#41—91no—
431C2×#41—182no—
432C2×#41—182no—
433#131—62no—
434#131—62no—
435C2×M16—31no—
436C2×M16—34no—
437C2×M16D3211yescharacteristic, complemented
438C4×Q8—181no—
439C4×D4—182no—
440C4×D4—181no—
441#117—31no—
442#117—92no—
443C2×C42—92no—
444C2×C42—91no—
445#104—34no—
446#104—94no—
447#104—92no—
448#104—92no—
449#104—92no—
450#104—92no—
451C23×C3—21no—
452C23×C3—32no—
453C23×C3—61no—
454C23×C3C2×D1211yescharacteristic
455C23×C3D3×D411yescharacteristic
456C22×D3—21no—
457C22×D3—64no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—64no—
461C22×D3—121no—
462C22×D3C2×D1212yes—
463C3×Q8—32no—
464C3×Q8—32no—
465C3×Q8—32no—
466C3×Q8—61no—
467C3×D4—34no—
468C3×D4—34no—
469C3×D4—32no—
470C3×D4—32no—
471C3×D4—32no—
472C3×D4—62no—
473C3×D4—62no—
474C3×D4—61no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—32no—
482C2×C3×C4—34no—
483C2×C3×C4—34no—
484C2×C3×C4—61no—
485C2×C3×C4—62no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4C2×C4×D311yescharacteristic
489C2×C3×C4C2×C4×D311yescharacteristic
490C2×C3×C4C2×C4×D311yescharacteristic
491C2×C3×C4C2×C4×D311yescharacteristic
492C2×C3×C4C2×D1211yescharacteristic
493C2×C3×C4D3×D411yescharacteristic
494C2×C3×C4D3×D411yescharacteristic
495C2×C3×C4D3×D411yescharacteristic
496C2×C3×C4C2×#6711yescharacteristic
497C2×C3×C4C2×#6711yescharacteristic
498C2×C3×C4C23×D311yescharacteristic
499C2×C3×C4C23×D311yescharacteristic
500#67—22no—
501#67—22no—
502#67—64no—
503#67—64no—
504#67—62no—
505#67—62no—
506#67—62no—
507#67—62no—
508#67—64no—
509#67—64no—
510#67—122no—
511#67—122no—
512#67(C2×D3)⋊C414yes—
513#67(C2×D3)⋊C414yes—
514C2×Dic3—21no—
515C2×Dic3—22no—
516C2×Dic3—64no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—64no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—124no—
528C2×Dic3—122no—
529C2×Dic3—122no—
530C2×Dic3—124no—
531C2×Dic3C2×D1212yes—
532D12—21no—
533D12—32no—
534D12—32no—
535D12—62no—
536D12—64no—
537D12—64no—
538D12—61no—
539D12—61no—
540D12—121no—
541D12(C2×D3)⋊C412yes—
542D12(C2×D3)⋊C412yes—
543D12C2×C4×D312yes—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—64no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—62no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—64no—
554C4×D3—122no—
555C4×D3—122no—
556C4×D3—124no—
557C4×D3C2×C4×D314yes—
558C4×D3C2×#6714yes—
559Dic6—21no—
560Dic6—32no—
561Dic6—32no—
562Dic6—62no—
563Dic6—64no—
564Dic6—61no—
565Dic6—61no—
566Dic6—64no—
567Dic6—121no—
568Dic6(C2×D3)⋊C412yes—
569Dic6(C2×D3)⋊C412yes—
570Dic6C2×C4×D312yes—
571C3×C8—22no—
572C3×C8—22no—
573C3×C8—42no—
574C3×C8—62no—
575C3⋊C8—22no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32C22×C22⋊C411yescharacteristic
580C3⋊D3—42no—
581C3×D3—24no—
582C3×D3—42no—
583#41—32no—
584#41—32no—
585#41—32no—
586#41—32no—
587#41—32no—
588#41—32no—
589#41—61no—
590#41—61no—
591#41—94no—
592#41—94no—
593#41—92no—
594#41—92no—
595#41—184no—
596#41—184no—
597#41—184no—
598#41—182no—
599#41—182no—
600#41—184no—
601#41—182no—
602#41—182no—
603#41—181no—
604#41—181no—
605C2×Q8—31no—
606C2×Q8—31no—
607C2×Q8—94no—
608C2×Q8—91no—
609C2×Q8—182no—
610C2×Q8—182no—
611C2×D4—32no—
612C2×D4—31no—
613C2×D4—31no—
614C2×D4—61no—
615C2×D4—94no—
616C2×D4—91no—
617C2×D4—182no—
618C2×D4—184no—
619C2×D4—182no—
620C2×D4—184no—
621C2×D4—184no—
622C2×D4—181no—
623C22×C4—32no—
624C22×C4—61no—
625C22×C4—184no—
626C22×C4—182no—
627C22×C4—181no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630M16—21no—
631M16—32no—
632M16—64no—
633M16—61no—
634M16C2×D3212yes—
635C2×C8—21no—
636C2×C8—64no—
637C2×C8—61no—
638C4⋊C4—61no—
639C4⋊C4—182no—
640C22⋊C4—61no—
641C22⋊C4—182no—
642C42—32no—
643C42—91no—
644C42—91no—
645C42—182no—
646C42—181no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—34no—
651C22×C3—41no—
652C22×C3—41no—
653C22×C3—42no—
654C22×C3—62no—
655C22×C3—122no—
656C22×C3—241no—
657C22×C3D3×C22⋊C411yescharacteristic
658C22×C3D3×C22⋊C411yescharacteristic
659C22×C3C2×(C2×D3)⋊C411yescharacteristic
660C22×C3C2×(C2×D3)⋊C411yescharacteristic
661C22×C3C22×D1211yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—42no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—81no—
668C2×D3—122no—
669C2×D3—244no—
670C2×D3—244no—
671C2×D3—241no—
672C2×D3—241no—
673C2×D3—242no—
674C2×D3C2×(C2×D3)⋊C414yes—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—34no—
680C3×C4—62no—
681C3×C4—122no—
682C3×C4D3×C22⋊C411yescharacteristic
683C3×C4D3×C22⋊C411yescharacteristic
684C3×C4C2×(C2×D3)⋊C411yescharacteristic
685C3×C4C2×(C2×D3)⋊C411yescharacteristic
686C3×C4C22×C4×D311yescharacteristic
687C3×C4C22×C4×D311yescharacteristic
688C3×C4C2×D3×D411yescharacteristic
689C3×C4C22×#6711yescharacteristic
690Dic3—22no—
691Dic3—42no—
692Dic3—62no—
693Dic3—62no—
694Dic3—62no—
695Dic3—62no—
696Dic3—122no—
697Dic3—122no—
698Dic3—121no—
699Dic3—121no—
700Dic3—122no—
701Dic3C2×(C2×D3)⋊C414yes—
702C32#290111yescharacteristic, complemented, Sylow
703C23—32no—
704C23—61no—
705C23—184no—
706C23—181no—
707C23D3×D1211yescharacteristic
708Q8—32no—
709Q8—32no—
710Q8—32no—
711Q8—61no—
712Q8—92no—
713Q8—184no—
714Q8—181no—
715D4—34no—
716D4—34no—
717D4—32no—
718D4—32no—
719D4—32no—
720D4—62no—
721D4—62no—
722D4—61no—
723D4—92no—
724D4—184no—
725D4—184no—
726D4—184no—
727D4—182no—
728D4—182no—
729D4—181no—
730C2×C4—32no—
731C2×C4—34no—
732C2×C4—34no—
733C2×C4—61no—
734C2×C4—62no—
735C2×C4—62no—
736C2×C4—62no—
737C2×C4—184no—
738C2×C4—184no—
739C2×C4—184no—
740C2×C4—181no—
741C2×C4—181no—
742C2×C4—182no—
743C2×C4—182no—
744C2×C4—181no—
745C2×C4—364no—
746C2×C4—362no—
747C2×C4C4×D3211yescharacteristic
748C2×C4C4×D3211yescharacteristic
749C2×C4D3×D1211yescharacteristic
750C2×C4D3×#6711yescharacteristic
751C2×C4D3×#6711yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—22no—
754C8—62no—
755C2×C3—22no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—21no—
762C2×C3—21no—
763C2×C3—41no—
764C2×C3—41no—
765C2×C3—64no—
766C2×C3—122no—
767C2×C3C2×D3×C22⋊C411yescharacteristic
768C2×C3C22×(C2×D3)⋊C411yescharacteristic
769D3—24no—
770D3—42no—
771D3—122no—
772D3—122no—
773D3—242no—
774C22—34no—
775C22—41no—
776C22—62no—
777C22—122no—
778C22—182no—
779C22—241no—
780C22—721no—
781C22—724no—
782C22D3×(C2×D3)⋊C411yescharacteristic
783C22D3×(C2×D3)⋊C411yescharacteristic
784C22C2×D3×D1211yescharacteristic
785C4—34no—
786C4—62no—
787C4—122no—
788C4—182no—
789C4—182no—
790C4—361no—
791C4D3×(C2×D3)⋊C411yescharacteristic
792C4D3×(C2×D3)⋊C411yescharacteristic
793C4C2×C4×D3211yescharacteristic
794C4C2×D3×#6711yescharacteristic
795C3—21no—
796C3#7899211yescharacteristic, complemented
797C3#8381711yescharacteristic, complemented
798C2—21no—
799C2—21no—
800C2—21no—
801C2—64no—
802C2—122no—
803C2—362no—
804C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4C2×D3×#67
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC2×C32C22×C22⋊C4
prime radical#10596669C2
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C3×#5745C2semidirect
3. #10594958C2semidirect
4. C2×#63652C2semidirect
5. C3×#5139C2semidirect
6. #10591113C2semidirect
7. C2×#63568C2semidirect
8. #10591005C2semidirect
9. D3×#825C2semidirect
16. #64308C4semidirect
18. #64307C4semidirect
22. #64298C4semidirect
24. #64297C4semidirect
25. C2×C32×M16C22semidirect
26. C2×C4×C3⋊Dic3C22semidirect
27. C3×#926C22semidirect
28. C2×C3×#208C22semidirect
30. C3×D3×M16C22semidirect
34. C4×D3×Dic3C22semidirect
35. #63855C22semidirect
37. #63652C22semidirect
38. #63652C22semidirect
39. C3×#825C22semidirect
40. #63570C22semidirect
41. #63568C22semidirect
42. #63568C22semidirect
47. #5745D3semidirect
53. #5139D3semidirect
67. #3828C2×C4semidirect
69. C2×C4⋊(C3⋊D3)C2×C4semidirect
71. C2×#634C2×C4semidirect
78. C3×#235C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
86. C2×C3×Dic6C2×C4semidirect
97. D3×D12C2×C4semidirect
100. #3799C2×C4semidirect
106. #3795C2×C4semidirect
108. D3×Dic6C2×C4semidirect
159. C2×C3×M16C2×D3semidirect
160. C2×C3×M16C2×D3semidirect
166. #926C2×D3semidirect
171. C2×#208C2×D3semidirect
173. D3×M16C2×D3semidirect
192. #825C2×D3semidirect
333. #235C4×D3semidirect
342. C2×D12C4×D3semidirect
357. C2×Dic6C4×D3semidirect
437. C2×M16D32semidirect
702. C32#2901semidirect
796. C3#78992semidirect
797. C3#83817semidirect

Maximal subgroups

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

subgroupindex
#105966692
C3×#57452
#105949582
C2×#636522
C3×#51392
#105911132
C2×#635682
#105910052
D3×#8252
#838173
#789923