Finite Group Databasebeta

← #11858199

Subgroups — #11858199

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×C4×#235C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4C2×#63632C211yesmaximal, characteristic, complemented
5C2×C3×#805C211yesmaximal, characteristic, complemented
6#10591113C211yesmaximal, characteristic, complemented
7#10591111C211yesmaximal, characteristic, complemented
8#10590392C214yesmaximal, complemented
9D3×#805C214yesmaximal, complemented
10#82536—31nomaximal
11#78983—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×C42C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C3×C4×#67—22no—
28C3×#926C2211yescharacteristic, complemented
29C2×C3×#208C2211yescharacteristic, complemented
30C3×C4×D12—21no—
31C3×#872C2212yescomplemented
32C3×C42×D3C2212yescomplemented
33C3×C4×Dic6—21no—
34#63815—22no—
35#63814—22no—
36D3×#208C2214yescomplemented
37#63632C2212yescomplemented
38#63632C2212yescomplemented
39C3×#805C2212yescomplemented
40C3×#805C2212yescomplemented
41#63570C2214yescomplemented
42#63569C2214yescomplemented
43#5964—31no—
44#5964—31no—
45C3×C4×#41—31no—
46#5819—31no—
47#5745—31no—
48C4×#235D311yescharacteristic, complemented
49C2×C3×#104—31no—
50#5236—31no—
51#5139—31no—
52#5005—31no—
53#5005—31no—
54#5005—34no—
55C2×#805—31no—
56C2×#805—31no—
57C2×#805—34no—
58C2×#805—61no—
59C2×#805D311yescharacteristic, complemented
60#4821—34no—
61D3×#104—34no—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C2×#638—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×D3—22no—
86C2×C3×C4×D3C2312yes—
87C2×C3×Dic6C2×C411yescharacteristic, complemented
88C2×C3×Dic6D411yescharacteristic
89#3811—24no—
90D3×#67—24no—
91D3×#67—24no—
92#3805—24no—
93#3804—24no—
94#3804—24no—
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×C42—21no—
110C32×C42C2311yescharacteristic
111C32×C42C2311yescharacteristic
112#3748—21no—
113#3748C2312yes—
114C2×C3⋊(C3⋊C8)—21no—
115C3×#217—21no—
116C3×(C2×D3)⋊C4—22no—
117C3×C4⋊Dic3—21no—
118C3×Dic3⋊C4—22no—
119C3×C4×Dic3—22no—
120C3×C4×Dic3C2312yes—
121C3×#208—21no—
122C3×#208C2312yes—
123C2×C3×C3⋊C8—21no—
124#3711—24no—
125D3×C3⋊C8—24no—
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
154C2×C3×M16—31no—
155C3×C4×Q8—61no—
156C3×C4×D4—61no—
157C3×C4×D4—62no—
158C3×#117—31no—
159C3×#117—32no—
160C2×C3×C42—21no—
161C2×C3×C42—32no—
162C2×C3×C42C2×D311yescharacteristic, complemented
163C2×C3×C42C2×D311yescharacteristic, complemented
164#948—62no—
165#948—62no—
166C4×#67—22no—
167#926C2×D311yescharacteristic, complemented
168C2×#208—31no—
169C2×#208—31no—
170C2×#208—34no—
171C2×#208—61no—
172C2×#208C2×D311yescharacteristic, complemented
173#907—62no—
174D3×M16—34no—
175#901—62no—
176C4×D12—21no—
177#872C2×D312yescomplemented
178C42×D3C2×D312yescomplemented
179C4×Dic6—21no—
180C3×#104—32no—
181C3×#104—32no—
182#837—34no—
183#825—34no—
184#805—34no—
185#805—32no—
186#805—32no—
187#805—32no—
188#805—32no—
189#805—34no—
190#805—62no—
191#805—62no—
192#805C2×D312yescomplemented
193#805C2×D312yescomplemented
194C23×C32C2×D411yescharacteristic
195C22×C3⋊D3—21no—
196C22×C3×D3—21no—
197C22×C3×D3C2×D412yes—
198C2×D32—24no—
199C2×C32×C4—21no—
200C2×C32×C4—21no—
201C2×C32×C4—42no—
202C2×C32×C4C22×C411yescharacteristic
203C2×C32×C4C22×C411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2×D411yescharacteristic
206C2×C32×C4C2×D411yescharacteristic
207C2×C32×C4C2411yescharacteristic
208#638—22no—
209#638—22no—
210C2×C3⋊Dic3—21no—
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×D3—44no—
231C3×C4×D3C22×C414yes—
232C3×C4×D3C2×D414yes—
233C3×Dic6—21no—
234C3×Dic6C22⋊C412yes—
235C3×Dic6C22⋊C412yes—
236C3×Dic6C22×C412yes—
237#627—24no—
238#626—24no—
239#626—24no—
240#625—24no—
241#624—24no—
242D3×Dic3—24no—
243D3×Dic3—24no—
244C3⋊(C3⋊C8)—22no—
245C3×C3⋊C8—22no—
246#585—91no—
247#568—91no—
248C4×#41—31no—
249#421—94no—
250#421—91no—
251#421—91no—
252C2×#104—31no—
253C2×#104—94no—
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—21no—
271C22×C3×C4—21no—
272C22×C3×C4—32no—
273C22×C3×C4—41no—
274C22×C3×C4—62no—
275C22×C3×C4—61no—
276C22×C3×C4C22×D311yescharacteristic
277C22×C3×C4C22×D311yescharacteristic
278C2×#67—21no—
279C2×#67—64no—
280C2×#67—61no—
281C2×#67—61no—
282C2×#67—64no—
283C2×#67—121no—
284C2×#67#6712yes—
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#235D1212yes—
335#235D1212yes—
336#235C22×D312yes—
337C2×D12—31no—
338C2×D12—31no—
339C2×D12—34no—
340C2×D12—61no—
341C2×D12—62no—
342C2×D12C4×D311yescharacteristic, complemented
343C2×D12#6711yescharacteristic
344C2×C4×D3—21no—
345C2×C4×D3—22no—
346C2×C4×D3—64no—
347C2×C4×D3—61no—
348C2×C4×D3—61no—
349C2×C4×D3—64no—
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×Dic6#6711yescharacteristic
359C3×M16—32no—
360C3×M16—61no—
361C2×C3×C8—61no—
362C3×C4⋊C4—62no—
363C3×C4⋊C4—61no—
364C3×C22⋊C4—62no—
365C3×C22⋊C4—61no—
366C3×C42—21no—
367C3×C42—21no—
368C3×C42—21no—
369C3×C42—21no—
370C3×C42—32no—
371C3×C42—41no—
372C3×C42—62no—
373C3×C42C22×D311yescharacteristic
374C3×C42C22×D311yescharacteristic
375C3×C42C22×D311yescharacteristic
376C3×C42C22×D311yescharacteristic
377#217—21no—
378(C2×D3)⋊C4—22no—
379C4⋊Dic3—21no—
380Dic3⋊C4—22no—
381C4×Dic3—22no—
382C4×Dic3C22×D312yes—
383#208—21no—
384#208—32no—
385#208—32no—
386#208—62no—
387#208—64no—
388#208—61no—
389#208—61no—
390#208—121no—
391#208C22×D312yes—
392C2×C3⋊C8—21no—
393C2×C3⋊C8—64no—
394C2×C3⋊C8—61no—
395C2×C3⋊C8—61no—
396C2×C3⋊C8—121no—
397ΓL(1,𝔽25)—64no—
398D3×C8—64no—
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×C4—22no—
411C32×C4—41no—
412C32×C4C2×C22⋊C411yescharacteristic
413C32×C4C2×C22⋊C411yescharacteristic
414C32×C4C23×C411yescharacteristic
415C32×C4C22×D411yescharacteristic
416C3⋊Dic3—22no—
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—182no—
434#131—182no—
435C2×M16—31no—
436C2×M16—94no—
437C2×M16—91no—
438C4×Q8—61no—
439C4×D4—61no—
440C4×D4—62no—
441#117—31no—
442#117—32no—
443C2×C42—32no—
444C2×C42D3211yescharacteristic, complemented
445#104—32no—
446#104—32no—
447#104—94no—
448#104—94no—
449#104—92no—
450#104—92no—
451C23×C3—21no—
452C23×C3—32no—
453C23×C3—61no—
454C23×C3D3×D411yescharacteristic
455C23×C3C2×#6711yescharacteristic
456C22×D3—21no—
457C22×D3—64no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—64no—
461C22×D3—121no—
462C22×D3C2×#6712yes—
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—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—32no—
486C2×C3×C4—34no—
487C2×C3×C4—34no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—42no—
491C2×C3×C4—42no—
492C2×C3×C4—44no—
493C2×C3×C4—61no—
494C2×C3×C4—62no—
495C2×C3×C4—62no—
496C2×C3×C4—62no—
497C2×C3×C4—124no—
498C2×C3×C4C2×C4×D311yescharacteristic
499C2×C3×C4C2×C4×D311yescharacteristic
500C2×C3×C4C2×C4×D311yescharacteristic
501C2×C3×C4C2×C4×D311yescharacteristic
502C2×C3×C4C2×D1211yescharacteristic
503C2×C3×C4C2×D1211yescharacteristic
504C2×C3×C4D3×D411yescharacteristic
505C2×C3×C4D3×D411yescharacteristic
506C2×C3×C4D3×D411yescharacteristic
507C2×C3×C4C2×#6711yescharacteristic
508C2×C3×C4C23×D311yescharacteristic
509C2×C3×C4C23×D311yescharacteristic
510#67—22no—
511#67—22no—
512#67—64no—
513#67—64no—
514#67—62no—
515#67—62no—
516#67—62no—
517#67—62no—
518#67—64no—
519#67—64no—
520#67—122no—
521#67—122no—
522#67(C2×D3)⋊C414yes—
523#67(C2×D3)⋊C414yes—
524C2×Dic3—21no—
525C2×Dic3—22no—
526C2×Dic3—64no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—64no—
530C2×Dic3—121no—
531C2×Dic3C2×#6712yes—
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—44no—
547C4×D3—64no—
548C4×D3—64no—
549C4×D3—64no—
550C4×D3—62no—
551C4×D3—62no—
552C4×D3—62no—
553C4×D3—62no—
554C4×D3—64no—
555C4×D3—122no—
556C4×D3—122no—
557C4×D3C2×C4×D314yes—
558C4×D3C2×D1214yes—
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—62no—
572C3⋊C8—22no—
573C3⋊C8—62no—
574C3⋊C8—62no—
575C3⋊C8—122no—
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—21no—
624C22×C4—32no—
625C22×C4—62no—
626C22×C4—61no—
627C22×C4—184no—
628C22×C4—181no—
629C22×C4C2×D3211yescharacteristic
630M16—32no—
631M16—61no—
632M16—92no—
633M16—184no—
634M16—181no—
635C2×C8—61no—
636C2×C8—184no—
637C2×C8—181no—
638C4⋊C4—62no—
639C4⋊C4—61no—
640C22⋊C4—62no—
641C22⋊C4—61no—
642C42—21no—
643C42—32no—
644C42—62no—
645C42C2×D3211yescharacteristic
646C42C2×D3211yescharacteristic
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×C3C2×D3×D411yescharacteristic
662C22×C3C22×#6711yescharacteristic
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—22no—
676C3×C4—22no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—21no—
680C3×C4—21no—
681C3×C4—34no—
682C3×C4—42no—
683C3×C4—41no—
684C3×C4—41no—
685C3×C4—42no—
686C3×C4—62no—
687C3×C4—122no—
688C3×C4D3×C22⋊C411yescharacteristic
689C3×C4D3×C22⋊C411yescharacteristic
690C3×C4C2×(C2×D3)⋊C411yescharacteristic
691C3×C4C2×(C2×D3)⋊C411yescharacteristic
692C3×C4C22×C4×D311yescharacteristic
693C3×C4C22×C4×D311yescharacteristic
694C3×C4C22×D1211yescharacteristic
695C3×C4C2×D3×D411yescharacteristic
696Dic3—22no—
697Dic3—42no—
698Dic3—62no—
699Dic3—62no—
700Dic3—122no—
701Dic3C2×(C2×D3)⋊C414yes—
702C32#290111yescharacteristic, complemented, Sylow
703C23—32no—
704C23—61no—
705C23—184no—
706C23—181no—
707C23D3×#6711yescharacteristic
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—21no—
731C2×C4—21no—
732C2×C4—32no—
733C2×C4—34no—
734C2×C4—34no—
735C2×C4—42no—
736C2×C4—61no—
737C2×C4—62no—
738C2×C4—62no—
739C2×C4—62no—
740C2×C4—124no—
741C2×C4—184no—
742C2×C4—184no—
743C2×C4—184no—
744C2×C4—181no—
745C2×C4—182no—
746C2×C4—182no—
747C2×C4C4×D3211yescharacteristic
748C2×C4C4×D3211yescharacteristic
749C2×C4D3×D1211yescharacteristic
750C2×C4D3×D1211yescharacteristic
751C2×C4D3×#6711yescharacteristic
752C2×C4C22×D3211yescharacteristic
753C8—62no—
754C8—182no—
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×#6711yescharacteristic
785C4—22no—
786C4—34no—
787C4—41no—
788C4—62no—
789C4—122no—
790C4—182no—
791C4D3×(C2×D3)⋊C411yescharacteristic
792C4D3×(C2×D3)⋊C411yescharacteristic
793C4C2×C4×D3211yescharacteristic
794C4C2×D3×D1211yescharacteristic
795C3—21no—
796C3#7898311yescharacteristic, complemented
797C3#8253611yescharacteristic, complemented
798C2—21no—
799C2—21no—
800C2—21no—
801C2—64no—
802C2—122no—
803C2—362no—
804C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×C42C22
socleC2×C32C22×C22⋊C4
prime radical#10596669C2
cosocleC2×C32×C4C24
hypercenterC2×C42D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C3×C4×#235C2semidirect
3. #10594776C2semidirect
4. C2×#63632C2semidirect
5. C2×C3×#805C2semidirect
6. #10591113C2semidirect
7. #10591111C2semidirect
8. #10590392C2semidirect
9. D3×#805C2semidirect
16. #64308C4semidirect
18. #64307C4semidirect
22. #64298C4semidirect
24. #64297C4semidirect
25. C2×C32×C42C22semidirect
26. C2×#3748C22semidirect
28. C3×#926C22semidirect
29. C2×C3×#208C22semidirect
31. C3×#872C22semidirect
32. C3×C42×D3C22semidirect
36. D3×#208C22semidirect
37. #63632C22semidirect
38. #63632C22semidirect
39. C3×#805C22semidirect
40. C3×#805C22semidirect
41. #63570C22semidirect
42. #63569C22semidirect
48. C4×#235D3semidirect
59. C2×#805D3semidirect
67. #3828C2×C4semidirect
69. C2×C4⋊(C3⋊D3)C2×C4semidirect
71. C2×#634C2×C4semidirect
78. C3×#235C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
87. C2×C3×Dic6C2×C4semidirect
97. D3×D12C2×C4semidirect
100. #3799C2×C4semidirect
106. #3795C2×C4semidirect
108. D3×Dic6C2×C4semidirect
162. C2×C3×C42C2×D3semidirect
163. C2×C3×C42C2×D3semidirect
167. #926C2×D3semidirect
172. C2×#208C2×D3semidirect
177. #872C2×D3semidirect
178. C42×D3C2×D3semidirect
192. #805C2×D3semidirect
193. #805C2×D3semidirect
333. #235C4×D3semidirect
342. C2×D12C4×D3semidirect
357. C2×Dic6C4×D3semidirect
444. C2×C42D32semidirect
702. C32#2901semidirect
796. C3#78983semidirect
797. C3#82536semidirect

Maximal subgroups

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

subgroupindex
#105966692
C3×C4×#2352
#105947762
C2×#636322
C2×C3×#8052
#105911132
#105911112
#105903922
D3×#8052
#825363
#789833