Finite Group Databasebeta

← #11858201

Subgroups — #11858201

Order 1152.

1553 conjugacy classes of subgroups.

The subgroup lattice has 801 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596669C211yesmaximal, characteristic
2C3×#5522C211yesmaximal, characteristic, complemented
3#10594776C211yesmaximal, characteristic, complemented
4#10592704C211yesmaximal, characteristic, complemented
5C3×#5005C211yesmaximal, characteristic, complemented
6C2×#63570C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8#10590392C214yesmaximal, complemented
9D3×#805C214yesmaximal, complemented
10#82536—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
25C32×#117C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27C2×C3×C4×Dic3C2211yescharacteristic, complemented
28C2×C3×#208C2211yescharacteristic, complemented
29C3×#893—21no—
30C3×#887—21no—
31C3×#67⋊C4—22no—
32C3×#872C2212yescomplemented
33C3×C42×D3C2212yescomplemented
34#63815—22no—
35#63814—22no—
36D3×#208C2214yescomplemented
37#63632C2214yescomplemented
38C3×#805C2214yescomplemented
39#63570C2212yescomplemented
40#63570C2212yescomplemented
41#63569C2212yescomplemented
42#63569C2212yescomplemented
43#5964—31no—
44#5964—31no—
45C3×C4×#41—31no—
46#5819—31no—
47#5745—31no—
48#5522D311yescharacteristic, complemented
49C3×#421—31no—
50C2×#837—31no—
51C2×#825—31no—
52#5005—31no—
53#5005—31no—
54#5005—34no—
55#5005—61no—
56#5005D311yescharacteristic, complemented
57C2×#805—31no—
58C2×#805—31no—
59C2×#805—34no—
60#4821—34no—
61D3×#104—34no—
62C22×C32×C4C2311yescharacteristic
63C2×#638—21no—
64#3828—21no—
65#3828—21no—
66#3828C2×C412yescomplemented
67#3828C2312yes—
68C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
69C2×C4×C3⋊D3—21no—
70C2×#634C2×C411yescharacteristic, complemented
71C2×C3×#67—21no—
72C2×C3×#67D412yes—
73C22×C3×Dic3—21no—
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×C4⋊C4—21no—
110C32×C22⋊C4—21no—
111C32×C42C2312yes—
112#3748—21no—
113#3748C2312yes—
114C2×C3⋊(C3⋊C8)—21no—
115C3×(C2×D3)⋊C4—22no—
116C3×Dic3⋊C4—22no—
117C3×C4×Dic3—21no—
118C3×C4×Dic3—22no—
119C3×C4×Dic3C2311yescharacteristic
120C3×C4×Dic3C2311yescharacteristic
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—62no—
157C3×C4×D4—61no—
158C3×#117—21no—
159C3×#117—32no—
160C3×#117C2×D311yescharacteristic, complemented
161C3×#117C2×D311yescharacteristic, complemented
162C2×C3×C42—31no—
163C2×C3×C42—32no—
164#948—62no—
165#948—62no—
166C2×C4×Dic3C2×D311yescharacteristic, complemented
167C2×#208—31no—
168C2×#208—31no—
169C2×#208—34no—
170C2×#208—61no—
171C2×#208C2×D311yescharacteristic, complemented
172#907—62no—
173D3×M16—34no—
174#901—62no—
175#893—21no—
176#887—21no—
177#67⋊C4—22no—
178#872C2×D312yescomplemented
179C42×D3C2×D312yescomplemented
180C3×#104—34no—
181#837—32no—
182#837—32no—
183#825—32no—
184#825—32no—
185#805—32no—
186#805—32no—
187#805—34no—
188#805—34no—
189#805—32no—
190#805—32no—
191#805—64no—
192#805C2×D314yescomplemented
193C23×C32C2×D411yescharacteristic
194C22×C3⋊D3—21no—
195C22×C3×D3—21no—
196C22×C3×D3C2×D412yes—
197C2×D32—24no—
198C2×C32×C4—22no—
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—
208C4⋊(C3⋊D3)—21no—
209C4⋊(C3⋊D3)C22×C412yes—
210C4×C3⋊D3—22no—
211C4×C3⋊D3—22no—
212#634—21no—
213#634C22×C412yes—
214C3×#67—22no—
215C3×#67—22no—
216C3×#67C22⋊C414yes—
217C3×#67C22⋊C414yes—
218C2×C3×Dic3—21no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—42no—
222C2×C3×Dic3C2×D412yes—
223C3×D12—21no—
224C3×D12C22⋊C412yes—
225C3×D12C22⋊C412yes—
226C3×D12C22×C412yes—
227C3×C4×D3—22no—
228C3×C4×D3—22no—
229C3×C4×D3—44no—
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—
243C3⋊(C3⋊C8)—22no—
244C3×C3⋊C8—22no—
245#585—91no—
246#568—91no—
247C4×#41—31no—
248#421—31no—
249#421—94no—
250#421—91no—
251C2×#104—94no—
252C2×#104—91no—
253C2×#104—91no—
254C3×#41—32no—
255C3×#41—32no—
256C3×#41—32no—
257C3×#41—32no—
258C3×#41—32no—
259C3×#41—32no—
260C3×#41—61no—
261C3×#41—61no—
262C2×C3×Q8—31no—
263C2×C3×Q8—31no—
264C2×C3×D4—32no—
265C2×C3×D4—31no—
266C2×C3×D4—31no—
267C2×C3×D4—61no—
268C22×C3×C4—21no—
269C22×C3×C4—32no—
270C22×C3×C4—62no—
271C22×C3×C4—61no—
272C22×C3×C4—61no—
273C22×C3×C4C22×D311yescharacteristic
274C22×C3×C4C22×D311yescharacteristic
275C2×#67—21no—
276C2×#67—64no—
277C2×#67—61no—
278C2×#67—61no—
279C2×#67—64no—
280C2×#67—121no—
281C2×#67#6712yes—
282C22×Dic3—21no—
283#239—34no—
284#239—62no—
285#239—62no—
286#239—62no—
287D3×Q8—34no—
288D3×Q8—62no—
289D3×Q8—62no—
290D3×Q8—62no—
291#237—34no—
292#237—62no—
293#237—62no—
294#237—64no—
295#237—64no—
296#237—64no—
297#237—64no—
298#237—62no—
299D3×D4—34no—
300D3×D4—62no—
301D3×D4—62no—
302D3×D4—64no—
303D3×D4—64no—
304D3×D4—64no—
305D3×D4—64no—
306D3×D4—62no—
307#235—21no—
308#235—21no—
309#235—32no—
310#235—32no—
311#235—32no—
312#235—32no—
313#235—34no—
314#235—34no—
315#235—62no—
316#235—62no—
317#235—64no—
318#235—64no—
319#235—61no—
320#235—61no—
321#235—61no—
322#235—61no—
323#235—64no—
324#235—62no—
325#235—64no—
326#235—62no—
327#235—121no—
328#235—121no—
329#235C4×D312yes—
330#235C4×D312yes—
331#235C4×D312yescomplemented
332#235D1212yes—
333#235D1212yes—
334#235C22×D312yes—
335C2×D12—31no—
336C2×D12—31no—
337C2×D12—34no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12C4×D311yescharacteristic, complemented
341C2×D12#6711yescharacteristic
342C2×C4×D3—21no—
343C2×C4×D3—22no—
344C2×C4×D3—64no—
345C2×C4×D3—61no—
346C2×C4×D3—61no—
347C2×C4×D3—64no—
348C2×C4×D3—121no—
349C2×C4×D3C22×D312yes—
350C2×Dic6—31no—
351C2×Dic6—31no—
352C2×Dic6—34no—
353C2×Dic6—61no—
354C2×Dic6—62no—
355C2×Dic6C4×D311yescharacteristic, complemented
356C2×Dic6#6711yescharacteristic
357C3×M16—32no—
358C3×M16—61no—
359C2×C3×C8—61no—
360C3×C4⋊C4—21no—
361C3×C4⋊C4—21no—
362C3×C4⋊C4—41no—
363C3×C4⋊C4—62no—
364C3×C22⋊C4—21no—
365C3×C22⋊C4—21no—
366C3×C22⋊C4—41no—
367C3×C22⋊C4—62no—
368C3×C42—22no—
369C3×C42—31no—
370C3×C42—31no—
371C3×C42—62no—
372C3×C42—61no—
373C3×C42C22×D312yes—
374C3×C42C22×D312yes—
375(C2×D3)⋊C4—22no—
376Dic3⋊C4—22no—
377C4×Dic3—21no—
378C4×Dic3—22no—
379C4×Dic3C22×D311yescharacteristic
380C4×Dic3C22×D311yescharacteristic
381#208—21no—
382#208—32no—
383#208—32no—
384#208—62no—
385#208—64no—
386#208—61no—
387#208—61no—
388#208—121no—
389#208C22×D312yes—
390C2×C3⋊C8—21no—
391C2×C3⋊C8—64no—
392C2×C3⋊C8—61no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—121no—
395ΓL(1,𝔽25)—64no—
396D3×C8—64no—
397C22×C32—41no—
398C22×C32C2×C22⋊C411yescharacteristic
399C22×C32C2×C22⋊C411yescharacteristic
400C22×C32C22×D411yescharacteristic
401C2×C3⋊D3—22no—
402C2×C3⋊D3—81no—
403C2×C3×D3—22no—
404C2×C3×D3—42no—
405C2×C3×D3—81no—
406C2×C3×D3C2×C22⋊C414yes—
407D32—84no—
408C32×C4—42no—
409C32×C4C2×C22⋊C411yescharacteristic
410C32×C4C2×C22⋊C411yescharacteristic
411C32×C4C23×C411yescharacteristic
412C32×C4C22×D411yescharacteristic
413C3⋊Dic3—22no—
414C3×Dic3—22no—
415C3×Dic3—22no—
416C3×Dic3—41no—
417C3×Dic3C2×C22⋊C414yes—
4182−1+4—92no—
4192−1+4—92no—
4202−1+4—181no—
421H(5,𝔽2)—92no—
422H(5,𝔽2)—92no—
423H(5,𝔽2)—182no—
424H(5,𝔽2)—181no—
425C2×#41—31no—
426C2×#41—31no—
427C2×#41—94no—
428C2×#41—91no—
429C2×#41—182no—
430C2×#41—182no—
431#131—182no—
432#131—182no—
433C2×M16—31no—
434C2×M16—94no—
435C2×M16—91no—
436C4×Q8—61no—
437C4×D4—62no—
438C4×D4—61no—
439#117—32no—
440#117D3211yescharacteristic, complemented
441C2×C42—31no—
442C2×C42—32no—
443#104—34no—
444#104—92no—
445#104—92no—
446#104—92no—
447#104—92no—
448#104—94no—
449C23×C3—21no—
450C23×C3—32no—
451C23×C3—61no—
452C23×C3D3×D411yescharacteristic
453C23×C3C2×#6711yescharacteristic
454C22×D3—21no—
455C22×D3—64no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—64no—
459C22×D3—121no—
460C22×D3C2×#6712yes—
461C3×Q8—32no—
462C3×Q8—32no—
463C3×Q8—32no—
464C3×Q8—61no—
465C3×D4—34no—
466C3×D4—34no—
467C3×D4—32no—
468C3×D4—32no—
469C3×D4—32no—
470C3×D4—62no—
471C3×D4—62no—
472C3×D4—61no—
473C2×C3×C4—22no—
474C2×C3×C4—22no—
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—42no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—61no—
490C2×C3×C4—124no—
491C2×C3×C4—122no—
492C2×C3×C4C2×C4×D311yescharacteristic
493C2×C3×C4C2×C4×D311yescharacteristic
494C2×C3×C4C2×C4×D311yescharacteristic
495C2×C3×C4C2×C4×D311yescharacteristic
496C2×C3×C4C2×D1211yescharacteristic
497C2×C3×C4C2×D1211yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4C2×#6711yescharacteristic
502C2×C3×C4C23×D311yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504#67—22no—
505#67—22no—
506#67—64no—
507#67—64no—
508#67—62no—
509#67—62no—
510#67—62no—
511#67—62no—
512#67—64no—
513#67—64no—
514#67—122no—
515#67—122no—
516#67(C2×D3)⋊C414yes—
517#67(C2×D3)⋊C414yes—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—42no—
522C2×Dic3—64no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—64no—
526C2×Dic3—121no—
527C2×Dic3C2×#6712yes—
528D12—21no—
529D12—32no—
530D12—32no—
531D12—62no—
532D12—64no—
533D12—64no—
534D12—61no—
535D12—61no—
536D12—121no—
537D12(C2×D3)⋊C412yes—
538D12(C2×D3)⋊C412yes—
539D12C2×C4×D312yes—
540C4×D3—22no—
541C4×D3—22no—
542C4×D3—44no—
543C4×D3—64no—
544C4×D3—64no—
545C4×D3—64no—
546C4×D3—62no—
547C4×D3—62no—
548C4×D3—62no—
549C4×D3—62no—
550C4×D3—64no—
551C4×D3—122no—
552C4×D3—122no—
553C4×D3C2×C4×D314yes—
554C4×D3C2×D1214yes—
555Dic6—21no—
556Dic6—32no—
557Dic6—32no—
558Dic6—62no—
559Dic6—64no—
560Dic6—61no—
561Dic6—61no—
562Dic6—64no—
563Dic6—121no—
564Dic6(C2×D3)⋊C412yes—
565Dic6(C2×D3)⋊C412yes—
566Dic6C2×C4×D312yes—
567C3×C8—62no—
568C3⋊C8—22no—
569C3⋊C8—62no—
570C3⋊C8—62no—
571C3⋊C8—122no—
572C2×C32—21no—
573C2×C32—21no—
574C2×C32—21no—
575C2×C32C22×C22⋊C411yescharacteristic
576C3⋊D3—42no—
577C3×D3—24no—
578C3×D3—42no—
579#41—32no—
580#41—32no—
581#41—32no—
582#41—32no—
583#41—32no—
584#41—32no—
585#41—61no—
586#41—61no—
587#41—94no—
588#41—94no—
589#41—92no—
590#41—92no—
591#41—184no—
592#41—184no—
593#41—184no—
594#41—182no—
595#41—182no—
596#41—184no—
597#41—182no—
598#41—182no—
599#41—181no—
600#41—181no—
601C2×Q8—31no—
602C2×Q8—31no—
603C2×Q8—94no—
604C2×Q8—91no—
605C2×Q8—182no—
606C2×Q8—182no—
607C2×D4—32no—
608C2×D4—31no—
609C2×D4—31no—
610C2×D4—61no—
611C2×D4—94no—
612C2×D4—91no—
613C2×D4—182no—
614C2×D4—184no—
615C2×D4—182no—
616C2×D4—184no—
617C2×D4—184no—
618C2×D4—181no—
619C22×C4—32no—
620C22×C4—62no—
621C22×C4—61no—
622C22×C4—61no—
623C22×C4—184no—
624C22×C4—181no—
625C22×C4C2×D3211yescharacteristic
626M16—32no—
627M16—61no—
628M16—92no—
629M16—184no—
630M16—181no—
631C2×C8—61no—
632C2×C8—184no—
633C2×C8—181no—
634C4⋊C4—21no—
635C4⋊C4—62no—
636C22⋊C4—21no—
637C22⋊C4—62no—
638C42—31no—
639C42—31no—
640C42—62no—
641C42—61no—
642C42C2×D3212yes—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—34no—
647C22×C3—41no—
648C22×C3—41no—
649C22×C3—62no—
650C22×C3—81no—
651C22×C3—122no—
652C22×C3—241no—
653C22×C3D3×C22⋊C411yescharacteristic
654C22×C3D3×C22⋊C411yescharacteristic
655C22×C3C2×(C2×D3)⋊C411yescharacteristic
656C22×C3C2×(C2×D3)⋊C411yescharacteristic
657C22×C3C2×D3×D411yescharacteristic
658C22×C3C22×#6711yescharacteristic
659C2×D3—22no—
660C2×D3—42no—
661C2×D3—62no—
662C2×D3—62no—
663C2×D3—81no—
664C2×D3—122no—
665C2×D3—244no—
666C2×D3—244no—
667C2×D3—241no—
668C2×D3—241no—
669C2×D3—242no—
670C2×D3C2×(C2×D3)⋊C414yes—
671C3×C4—21no—
672C3×C4—21no—
673C3×C4—21no—
674C3×C4—21no—
675C3×C4—34no—
676C3×C4—42no—
677C3×C4—42no—
678C3×C4—62no—
679C3×C4—62no—
680C3×C4—82no—
681C3×C4—121no—
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×C4C22×D1211yescharacteristic
689C3×C4C2×D3×D411yescharacteristic
690Dic3—22no—
691Dic3—22no—
692Dic3—41no—
693Dic3—62no—
694Dic3—62no—
695Dic3—122no—
696Dic3C2×(C2×D3)⋊C414yes—
697C32#290111yescharacteristic, complemented, Sylow
698C23—32no—
699C23—61no—
700C23—184no—
701C23—181no—
702C23D3×#6711yescharacteristic
703Q8—32no—
704Q8—32no—
705Q8—32no—
706Q8—61no—
707Q8—92no—
708Q8—184no—
709Q8—181no—
710D4—34no—
711D4—34no—
712D4—32no—
713D4—32no—
714D4—32no—
715D4—62no—
716D4—62no—
717D4—61no—
718D4—92no—
719D4—184no—
720D4—184no—
721D4—184no—
722D4—182no—
723D4—182no—
724D4—181no—
725C2×C4—22no—
726C2×C4—32no—
727C2×C4—34no—
728C2×C4—34no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—61no—
734C2×C4—124no—
735C2×C4—122no—
736C2×C4—184no—
737C2×C4—184no—
738C2×C4—184no—
739C2×C4—181no—
740C2×C4—182no—
741C2×C4—182no—
742C2×C4C4×D3211yescharacteristic
743C2×C4C4×D3211yescharacteristic
744C2×C4D3×D1211yescharacteristic
745C2×C4D3×D1211yescharacteristic
746C2×C4D3×#6711yescharacteristic
747C2×C4C22×D3211yescharacteristic
748C8—62no—
749C8—182no—
750C2×C3—21no—
751C2×C3—21no—
752C2×C3—21no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—41no—
758C2×C3—41no—
759C2×C3—41no—
760C2×C3—64no—
761C2×C3—122no—
762C2×C3C2×D3×C22⋊C411yescharacteristic
763C2×C3C22×(C2×D3)⋊C411yescharacteristic
764D3—24no—
765D3—42no—
766D3—122no—
767D3—122no—
768D3—242no—
769C22—34no—
770C22—41no—
771C22—62no—
772C22—122no—
773C22—182no—
774C22—241no—
775C22—721no—
776C22—724no—
777C22D3×(C2×D3)⋊C411yescharacteristic
778C22D3×(C2×D3)⋊C411yescharacteristic
779C22C2×D3×#6711yescharacteristic
780C4—34no—
781C4—42no—
782C4—62no—
783C4—62no—
784C4—121no—
785C4—182no—
786C4D3×(C2×D3)⋊C411yescharacteristic
787C4D3×(C2×D3)⋊C411yescharacteristic
788C4C2×C4×D3211yescharacteristic
789C4C2×D3×D1211yescharacteristic
790C3—21no—
791C3#7899211yescharacteristic, complemented
792C3#8253611yescharacteristic, complemented
793C2—21no—
794C2—21no—
795C2—21no—
796C2—64no—
797C2—122no—
798C2—362no—
799C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
centerC4C2×D3×D12
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC32×#117C22
socleC2×C32C22×C22⋊C4
prime radical#10596669C2
cosocleC2×C32×C4C24
hypercenter#117D32
hypocenterC32#2901
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. C3×#5522C2semidirect
3. #10594776C2semidirect
4. #10592704C2semidirect
5. C3×#5005C2semidirect
6. C2×#63570C2semidirect
7. C2×#63569C2semidirect
8. #10590392C2semidirect
9. D3×#805C2semidirect
16. #64308C4semidirect
18. #64307C4semidirect
22. #64298C4semidirect
24. #64297C4semidirect
25. C32×#117C22semidirect
26. C2×#3748C22semidirect
27. C2×C3×C4×Dic3C22semidirect
28. C2×C3×#208C22semidirect
32. C3×#872C22semidirect
33. C3×C42×D3C22semidirect
36. D3×#208C22semidirect
37. #63632C22semidirect
38. C3×#805C22semidirect
39. #63570C22semidirect
40. #63570C22semidirect
41. #63569C22semidirect
42. #63569C22semidirect
48. #5522D3semidirect
56. #5005D3semidirect
66. #3828C2×C4semidirect
68. C2×C4⋊(C3⋊D3)C2×C4semidirect
70. 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
160. C3×#117C2×D3semidirect
161. C3×#117C2×D3semidirect
166. C2×C4×Dic3C2×D3semidirect
171. C2×#208C2×D3semidirect
178. #872C2×D3semidirect
179. C42×D3C2×D3semidirect
192. #805C2×D3semidirect
331. #235C4×D3semidirect
340. C2×D12C4×D3semidirect
355. C2×Dic6C4×D3semidirect
440. #117D32semidirect
697. C32#2901semidirect
791. C3#78992semidirect
792. C3#82536semidirect

Maximal subgroups

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

subgroupindex
#105966692
C3×#55222
#105947762
#105927042
C3×#50052
C2×#635702
C2×#635692
#105903922
D3×#8052
#825363
#789923