Finite Group Databasebeta

← #11858194

Subgroups — #11858194

Order 1152.

1605 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596669C211yesmaximal, characteristic
2#10596216C211yesmaximal, characteristic, complemented
3#10594954C211yesmaximal, characteristic, complemented
4C3×#5139C211yesmaximal, characteristic, complemented
5C2×C3×#825C211yesmaximal, characteristic, complemented
6#10591111C211yesmaximal, characteristic, complemented
7C2×#63569C211yesmaximal, characteristic, complemented
8#10591009C214yesmaximal, complemented
9#10591008C214yesmaximal, complemented
10#78992—31nomaximal
11#78983—31nomaximal
12C2×#3828C2211yescharacteristic
13C2×C3×#235C2211yescharacteristic
14C2×C3×#235C2211yescharacteristic
15#64330—22no—
16#64308—21no—
17#64307C412yescomplemented
18#64307C412yescomplemented
19#64306C2214yes—
20D3×#235—22no—
21D3×#235—22no—
22#64298—21no—
23#64297C412yescomplemented
24#64297C412yescomplemented
25C2×C32×M16C2211yescharacteristic, complemented
26C2×#3748C2211yescharacteristic, complemented
27#64116—22no—
28M16×C3⋊D3C2214yescomplemented
29#64110—22no—
30C3×#926C2211yescharacteristic, complemented
31C2×C3×C4×Dic3C2211yescharacteristic, complemented
32#63952—22no—
33#63894—21no—
34C4×#624C2212yescomplemented
35#63874C2212yescomplemented
36#63844—21no—
37C3×#825C2212yescomplemented
38C3×#825C2214yescomplemented
39C3×#825C2212yescomplemented
40#63569C2212yescomplemented
41#63569C2214yescomplemented
42#63569C2212yescomplemented
43#5964—31no—
44#5964—31no—
45#5745—31no—
46#5745—31no—
47#5745—61no—
48#5522—31no—
49C4×#235—31no—
50C3×#421—31no—
51C2×C3×#104—31no—
52#5236—31no—
53C2×#837—31no—
54#5139D311yescharacteristic, complemented
55C2×#825D311yescharacteristic, complemented
56#5005—31no—
57C2×#805—31no—
58#4821—34no—
59#4821—34no—
60D3×#104—34no—
61D3×#104—34no—
62C22×C32×C4C2311yescharacteristic
63C2×#638D412yes—
64#3828C2×C412yes—
65#3828C2×C412yes—
66#3828D412yes—
67#3828D412yes—
68C2×C4⋊(C3⋊D3)D411yescharacteristic
69C2×C4×C3⋊D3C2312yes—
70C2×#634D411yescharacteristic
71C2×C3×#67—21no—
72C2×C3×#67—21no—
73C22×C3×Dic3—21no—
74C3×#235—21no—
75C3×#235—21no—
76C3×#235—21no—
77C3×#235—21no—
78C3×#235C2×C412yescomplemented
79C3×#235C2×C412yescomplemented
80C3×#235C2312yes—
81C3×#235C2312yes—
82C2×C3×D12C2×C411yescharacteristic, complemented
83C2×C3×D12C2×C411yescharacteristic, complemented
84C2×C3×C4×D3—21no—
85C2×C3×C4×D3—21no—
86C2×C3×Dic6C2×C411yescharacteristic, complemented
87C2×C3×Dic6C2×C411yescharacteristic, complemented
88#3811—24no—
89D3×#67—24no—
90D3×#67—24no—
91C2×#624—22no—
92#3805—24no—
93#3804—24no—
94#3804—24no—
95#3802C2×C414yescomplemented
96D3×D12—22no—
97D3×D12—22no—
98C4×D32—24no—
99#3799—22no—
100#3799—22no—
101#3798—24no—
102#3797C2×C414yescomplemented
103#3796C2×C414yescomplemented
104#3796C2×C414yescomplemented
105#3795—22no—
106#3795—22no—
107D3×Dic6—22no—
108D3×Dic6—22no—
109C32×M16—21no—
110C32×M16C2312yes—
111C2×C32×C8—21no—
112#3748—21no—
113#3748C2312yes—
114C2×C3⋊(C3⋊C8)—21no—
115#3743—24no—
116C8×C3⋊D3—24no—
117C3×#217—21no—
118C3×C4⋊Dic3—21no—
119C3×C4×Dic3—21no—
120C3×C4×Dic3C2311yescharacteristic
121C3×C4×Dic3C2311yescharacteristic
122C3×C4×Dic3C2312yes—
123#3724—22no—
124#3722—22no—
125Dic32—22no—
126#2901—91noSylow
127C2×C3×#41—31no—
128C2×C3×#41—31no—
129#1010—32no—
130#1010—32no—
131#1010—61no—
132#1010—61no—
133#1009—32no—
134#1009—32no—
135#1009—61no—
136#1009—61no—
137D3×#41—34no—
138D3×#41—34no—
139D3×#41—62no—
140D3×#41—62no—
141#1007—32no—
142#1007—32no—
143#1004—32no—
144#1004—32no—
145#1004—62no—
146#1004—62no—
147C2×#235—31no—
148C2×#235—31no—
149C2×#235—61no—
150C2×#235—62no—
151C2×#235—62no—
152C2×#235C2×D311yescharacteristic
153C2×#235C2×D311yescharacteristic
154C2×C3×M16—21no—
155C2×C3×M16C2×D311yescharacteristic, complemented
156C2×C3×M16C2×D311yescharacteristic, complemented
157C3×#117—31no—
158C2×C3×C42—31no—
159C4×#67—62no—
160#926C2×D311yescharacteristic, complemented
161C2×C4×Dic3C2×D311yescharacteristic, complemented
162C2×#208—31no—
163C2×#208—31no—
164C2×#208—61no—
165#907—62no—
166#907—62no—
167#907—64no—
168D3×M16—34no—
169D3×M16—34no—
170D3×M16—64no—
171#901—62no—
172#901—62no—
173#901—64no—
174#893—61no—
175#887—61no—
176#67⋊C4—62no—
177C4×D12—61no—
178#872—32no—
179#872—32no—
180C42×D3—32no—
181C42×D3—32no—
182C4×Dic6—61no—
183C3×#104—32no—
184C3×#104—32no—
185C3×#104—34no—
186#837—32no—
187#837—32no—
188#837—34no—
189#825C2×D312yescomplemented
190#825C2×D312yescomplemented
191#825C2×D314yescomplemented
192#805—32no—
193#805—32no—
194#805—34no—
195C23×C32C2×D411yescharacteristic
196C22×C3⋊D3C2×D412yes—
197C22×C3×D3—21no—
198C22×C3×D3—21no—
199C2×D32—24no—
200C2×C32×C4C22×C411yescharacteristic
201C2×C32×C4C22×C411yescharacteristic
202C2×C32×C4C2×D411yescharacteristic
203C2×C32×C4C2×D411yescharacteristic
204C2×C32×C4C2×D411yescharacteristic
205C2×C32×C4C2411yescharacteristic
206#638C22⋊C414yes—
207#638C22⋊C414yes—
208C2×C3⋊Dic3C2×D412yes—
209C4⋊(C3⋊D3)C22⋊C412yes—
210C4⋊(C3⋊D3)C22⋊C412yes—
211C4×C3⋊D3C22×C414yes—
212C4×C3⋊D3C2×D414yes—
213#634C22⋊C412yes—
214#634C22⋊C412yes—
215C3×#67—22no—
216C3×#67—22no—
217C3×#67—22no—
218C3×#67—22no—
219C2×C3×Dic3—21no—
220C2×C3×Dic3—21no—
221C2×C3×Dic3—21no—
222C2×C3×Dic3—22no—
223C2×C3×Dic3—21no—
224C2×C3×Dic3—42no—
225C3×D12—21no—
226C3×D12—21no—
227C3×D12C22×C412yes—
228C3×D12C22×C412yes—
229C3×C4×D3—22no—
230C3×C4×D3—22no—
231C3×C4×D3—22no—
232C3×C4×D3—22no—
233C3×Dic6—21no—
234C3×Dic6—21no—
235C3×Dic6C22×C412yes—
236C3×Dic6C22×C412yes—
237#627—24no—
238#626—24no—
239#626—24no—
240#625—24no—
241#624—24no—
242#624—44no—
243D3×Dic3—24no—
244D3×Dic3—24no—
245C32×C8—22no—
246C3⋊(C3⋊C8)—22no—
247#585—91no—
248#568—91no—
249C4×#41—91no—
250#421—31no—
251#421—94no—
252#421—91no—
253C2×#104—31no—
254C2×#104—94no—
255C2×#104—91no—
256C3×#41—32no—
257C3×#41—32no—
258C3×#41—32no—
259C3×#41—32no—
260C3×#41—61no—
261C3×#41—61no—
262C3×#41—61no—
263C3×#41—61no—
264C2×C3×Q8—31no—
265C2×C3×Q8—31no—
266C2×C3×D4—31no—
267C2×C3×D4—31no—
268C2×C3×D4—61no—
269C2×C3×D4—61no—
270C22×C3×C4—21no—
271C22×C3×C4—61no—
272C22×C3×C4—61no—
273C22×C3×C4—61no—
274C22×C3×C4C22×D311yescharacteristic
275C22×C3×C4C22×D311yescharacteristic
276C2×#67—21no—
277C2×#67—21no—
278C2×#67—32no—
279C2×#67—32no—
280C2×#67—62no—
281C2×#67—64no—
282C2×#67—64no—
283C22×Dic3—21no—
284#239—34no—
285#239—34no—
286#239—62no—
287#239—62no—
288D3×Q8—34no—
289D3×Q8—34no—
290D3×Q8—62no—
291D3×Q8—62no—
292#237—34no—
293#237—34no—
294#237—62no—
295#237—62no—
296#237—64no—
297#237—64no—
298#237—64no—
299#237—64no—
300D3×D4—34no—
301D3×D4—34no—
302D3×D4—62no—
303D3×D4—62no—
304D3×D4—64no—
305D3×D4—64no—
306D3×D4—64no—
307D3×D4—64no—
308#235—21no—
309#235—21no—
310#235—21no—
311#235—21no—
312#235—32no—
313#235—32no—
314#235—32no—
315#235—32no—
316#235—32no—
317#235—32no—
318#235—32no—
319#235—32no—
320#235—62no—
321#235—62no—
322#235—62no—
323#235—62no—
324#235—62no—
325#235—62no—
326#235—62no—
327#235—62no—
328#235—64no—
329#235—64no—
330#235—64no—
331#235—64no—
332#235C4×D312yescomplemented
333#235C4×D312yescomplemented
334#235C22×D312yes—
335#235C22×D312yes—
336C2×D12—31no—
337C2×D12—31no—
338C2×D12—61no—
339C2×D12—62no—
340C2×D12—62no—
341C2×D12C4×D311yescharacteristic, complemented
342C2×D12C4×D311yescharacteristic, complemented
343C2×C4×D3—21no—
344C2×C4×D3—21no—
345C2×C4×D3—32no—
346C2×C4×D3—32no—
347C2×C4×D3—62no—
348C2×C4×D3—64no—
349C2×C4×D3—64no—
350C2×C4×D3—62no—
351C2×C4×D3—62no—
352C2×Dic6—31no—
353C2×Dic6—31no—
354C2×Dic6—61no—
355C2×Dic6—62no—
356C2×Dic6—62no—
357C2×Dic6C4×D311yescharacteristic, complemented
358C2×Dic6C4×D311yescharacteristic, complemented
359C3×M16—22no—
360C3×M16—21no—
361C3×M16—21no—
362C3×M16—22no—
363C3×M16C22×D312yes—
364C3×M16C22×D312yes—
365C2×C3×C8—22no—
366C2×C3×C8—21no—
367C2×C3×C8—21no—
368C3×C4⋊C4—61no—
369C3×C22⋊C4—61no—
370C3×C42—31no—
371C3×C42—32no—
372C3×C42—31no—
373C3×C42—61no—
374#217—21no—
375(C2×D3)⋊C4—62no—
376(C2×D3)⋊C4—62no—
377C4⋊Dic3—21no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380C4×Dic3—21no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3C22×D311yescharacteristic
384C4×Dic3C22×D312yes—
385C4×Dic3C22×D311yescharacteristic
386#208—32no—
387#208—32no—
388#208—62no—
389#208—62no—
390#208—61no—
391#208—61no—
392C2×C3⋊C8—62no—
393C2×C3⋊C8—61no—
394C2×C3⋊C8—61no—
395ΓL(1,𝔽25)—64no—
396ΓL(1,𝔽25)—64no—
397ΓL(1,𝔽25)—68no—
398D3×C8—64no—
399D3×C8—64no—
400D3×C8—68no—
401C22×C32—41no—
402C22×C32C2×C22⋊C411yescharacteristic
403C22×C32C2×C22⋊C411yescharacteristic
404C22×C32C22×D411yescharacteristic
405C2×C3⋊D3—42no—
406C2×C3⋊D3C2×C22⋊C414yes—
407C2×C3×D3—22no—
408C2×C3×D3—22no—
409C2×C3×D3—81no—
410C2×C3×D3—81no—
411D32—84no—
412C32×C4C2×C22⋊C411yescharacteristic
413C32×C4C2×C22⋊C411yescharacteristic
414C32×C4C23×C411yescharacteristic
415C32×C4C22×D411yescharacteristic
416C3⋊Dic3C2×C22⋊C414yes—
417C3×Dic3—22no—
418C3×Dic3—22no—
419C3×Dic3—22no—
420C3×Dic3—42no—
421C3×Dic3—41no—
4222−1+4—92no—
4232−1+4—92no—
4242−1+4—181no—
425H(5,𝔽2)—92no—
426H(5,𝔽2)—92no—
427H(5,𝔽2)—182no—
428H(5,𝔽2)—181no—
429C2×#41—31no—
430C2×#41—31no—
431C2×#41—91no—
432C2×#41—94no—
433C2×#41—182no—
434C2×#41—182no—
435#131—182no—
436#131—182no—
437C2×M16—91no—
438C2×M16—94no—
439C2×M16D3211yescharacteristic, complemented
440C4×Q8—181no—
441C4×D4—181no—
442C4×D4—182no—
443#117—31no—
444#117—92no—
445C2×C42—31no—
446C2×C42—92no—
447#104—32no—
448#104—32no—
449#104—34no—
450#104—92no—
451#104—92no—
452#104—94no—
453C23×C3—21no—
454C23×C3—61no—
455C23×C3—61no—
456C23×C3D3×D411yescharacteristic
457C23×C3D3×D411yescharacteristic
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—32no—
461C22×D3—32no—
462C22×D3—62no—
463C22×D3—64no—
464C22×D3—64no—
465C3×Q8—32no—
466C3×Q8—32no—
467C3×Q8—61no—
468C3×Q8—61no—
469C3×D4—32no—
470C3×D4—32no—
471C3×D4—62no—
472C3×D4—62no—
473C3×D4—62no—
474C3×D4—62no—
475C3×D4—61no—
476C3×D4—61no—
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—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—62no—
487C2×C3×C4—62no—
488C2×C3×C4—62no—
489C2×C3×C4—62no—
490C2×C3×C4—62no—
491C2×C3×C4—61no—
492C2×C3×C4—122no—
493C2×C3×C4C2×C4×D311yescharacteristic
494C2×C3×C4C2×C4×D311yescharacteristic
495C2×C3×C4C2×C4×D311yescharacteristic
496C2×C3×C4C2×C4×D311yescharacteristic
497C2×C3×C4D3×D411yescharacteristic
498C2×C3×C4D3×D411yescharacteristic
499C2×C3×C4D3×D411yescharacteristic
500C2×C3×C4D3×D411yescharacteristic
501C2×C3×C4D3×D411yescharacteristic
502C2×C3×C4D3×D411yescharacteristic
503C2×C3×C4C23×D311yescharacteristic
504C2×C3×C4C23×D311yescharacteristic
505#67—22no—
506#67—22no—
507#67—22no—
508#67—22no—
509#67—34no—
510#67—34no—
511#67—34no—
512#67—34no—
513#67—64no—
514#67—64no—
515#67—64no—
516#67—64no—
517#67—64no—
518#67—64no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—22no—
524C2×Dic3—32no—
525C2×Dic3—32no—
526C2×Dic3—42no—
527C2×Dic3—62no—
528C2×Dic3—64no—
529C2×Dic3—64no—
530D12—21no—
531D12—21no—
532D12—32no—
533D12—32no—
534D12—32no—
535D12—32no—
536D12—62no—
537D12—62no—
538D12—64no—
539D12—64no—
540D12C2×C4×D312yes—
541D12C2×C4×D312yes—
542C4×D3—22no—
543C4×D3—22no—
544C4×D3—22no—
545C4×D3—22no—
546C4×D3—34no—
547C4×D3—34no—
548C4×D3—34no—
549C4×D3—34no—
550C4×D3—64no—
551C4×D3—64no—
552C4×D3—64no—
553C4×D3—64no—
554C4×D3—64no—
555C4×D3—64no—
556C4×D3—124no—
557C4×D3—124no—
558Dic6—21no—
559Dic6—21no—
560Dic6—32no—
561Dic6—32no—
562Dic6—32no—
563Dic6—32no—
564Dic6—62no—
565Dic6—62no—
566Dic6—64no—
567Dic6—64no—
568Dic6C2×C4×D312yes—
569Dic6C2×C4×D312yes—
570C3×C8—24no—
571C3×C8—22no—
572C3×C8—22no—
573C3⋊C8—64no—
574C3⋊C8—62no—
575C3⋊C8—62no—
576C2×C32—21no—
577C2×C32—21no—
578C2×C32—21no—
579C2×C32C22×C22⋊C411yescharacteristic
580C3⋊D3—24no—
581C3×D3—42no—
582C3×D3—42no—
583#41—32no—
584#41—32no—
585#41—32no—
586#41—32no—
587#41—61no—
588#41—61no—
589#41—61no—
590#41—61no—
591#41—92no—
592#41—92no—
593#41—92no—
594#41—92no—
595#41—94no—
596#41—94no—
597#41—184no—
598#41—184no—
599#41—184no—
600#41—182no—
601#41—182no—
602#41—182no—
603#41—182no—
604#41—184no—
605C2×Q8—31no—
606C2×Q8—31no—
607C2×Q8—91no—
608C2×Q8—94no—
609C2×Q8—182no—
610C2×Q8—182no—
611C2×D4—31no—
612C2×D4—31no—
613C2×D4—61no—
614C2×D4—61no—
615C2×D4—94no—
616C2×D4—92no—
617C2×D4—91no—
618C2×D4—182no—
619C2×D4—182no—
620C2×D4—184no—
621C2×D4—184no—
622C2×D4—184no—
623C22×C4—61no—
624C22×C4—61no—
625C22×C4—61no—
626C22×C4—92no—
627C22×C4—184no—
628C22×C4—182no—
629C22×C4C2×D3211yescharacteristic
630M16—21no—
631M16—92no—
632M16—184no—
633M16—181no—
634M16C2×D3212yes—
635C2×C8—21no—
636C2×C8—184no—
637C2×C8—181no—
638C4⋊C4—61no—
639C4⋊C4—182no—
640C22⋊C4—61no—
641C22⋊C4—182no—
642C42—31no—
643C42—31no—
644C42—32no—
645C42—61no—
646C42—182no—
647C22×C3—21no—
648C22×C3—21no—
649C22×C3—21no—
650C22×C3—41no—
651C22×C3—41no—
652C22×C3—62no—
653C22×C3—62no—
654C22×C3—81no—
655C22×C3—241no—
656C22×C3—241no—
657C22×C3D3×C22⋊C411yescharacteristic
658C22×C3D3×C22⋊C411yescharacteristic
659C22×C3D3×C22⋊C411yescharacteristic
660C22×C3D3×C22⋊C411yescharacteristic
661C22×C3C2×D3×D411yescharacteristic
662C22×C3C2×D3×D411yescharacteristic
663C2×D3—22no—
664C2×D3—22no—
665C2×D3—34no—
666C2×D3—34no—
667C2×D3—64no—
668C2×D3—81no—
669C2×D3—81no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—242no—
673C2×D3—244no—
674C2×D3—244no—
675C3×C4—21no—
676C3×C4—21no—
677C3×C4—21no—
678C3×C4—21no—
679C3×C4—62no—
680C3×C4—62no—
681C3×C4—62no—
682C3×C4—122no—
683C3×C4—121no—
684C3×C4D3×C22⋊C411yescharacteristic
685C3×C4D3×C22⋊C411yescharacteristic
686C3×C4D3×C22⋊C411yescharacteristic
687C3×C4D3×C22⋊C411yescharacteristic
688C3×C4C22×C4×D311yescharacteristic
689C3×C4C22×C4×D311yescharacteristic
690C3×C4C2×D3×D411yescharacteristic
691C3×C4C2×D3×D411yescharacteristic
692Dic3—22no—
693Dic3—22no—
694Dic3—22no—
695Dic3—34no—
696Dic3—34no—
697Dic3—42no—
698Dic3—41no—
699Dic3—64no—
700C32#290111yescharacteristic, complemented, Sylow
701C23—61no—
702C23—61no—
703C23—92no—
704C23—184no—
705C23#380211yescharacteristic
706Q8—32no—
707Q8—32no—
708Q8—61no—
709Q8—61no—
710Q8—92no—
711Q8—92no—
712Q8—184no—
713D4—32no—
714D4—32no—
715D4—62no—
716D4—62no—
717D4—62no—
718D4—62no—
719D4—61no—
720D4—61no—
721D4—94no—
722D4—94no—
723D4—92no—
724D4—92no—
725D4—184no—
726D4—184no—
727D4—184no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—62no—
732C2×C4—62no—
733C2×C4—62no—
734C2×C4—62no—
735C2×C4—61no—
736C2×C4—62no—
737C2×C4—92no—
738C2×C4—94no—
739C2×C4—94no—
740C2×C4—122no—
741C2×C4—184no—
742C2×C4—184no—
743C2×C4—184no—
744C2×C4—364no—
745C2×C4C4×D3211yescharacteristic
746C2×C4C4×D3211yescharacteristic
747C2×C4#380211yescharacteristic
748C2×C4#381111yescharacteristic
749C2×C4#381111yescharacteristic
750C2×C4C22×D3211yescharacteristic
751C8—22no—
752C8—182no—
753C2×C3—21no—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—41no—
761C2×C3—41no—
762C2×C3—41no—
763C2×C3—122no—
764C2×C3—122no—
765C2×C3C2×D3×C22⋊C411yescharacteristic
766C2×C3C2×D3×C22⋊C411yescharacteristic
767D3—42no—
768D3—42no—
769D3—64no—
770D3—64no—
771D3—124no—
772C22—41no—
773C22—62no—
774C22—62no—
775C22—94no—
776C22—241no—
777C22—241no—
778C22—362no—
779C22—724no—
780C22#6392111yescharacteristic
781C22#6392111yescharacteristic
782C22C2×#380211yescharacteristic
783C4—62no—
784C4—62no—
785C4—62no—
786C4—94no—
787C4—121no—
788C4—122no—
789C4#6392111yescharacteristic
790C4#6392111yescharacteristic
791C4C2×C4×D3211yescharacteristic
792C4C2×#381111yescharacteristic
793C3—21no—
794C3#7898311yescharacteristic, complemented
795C3#7899211yescharacteristic, complemented
796C2—21no—
797C2—21no—
798C2—21no—
799C2—122no—
800C2—122no—
801C2—184no—
802C2C2×#6392111yescharacteristic
subgroupG/H
centerC4C2×#3811
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. #10596216C2semidirect
3. #10594954C2semidirect
4. C3×#5139C2semidirect
5. C2×C3×#825C2semidirect
6. #10591111C2semidirect
7. C2×#63569C2semidirect
8. #10591009C2semidirect
9. #10591008C2semidirect
17. #64307C4semidirect
18. #64307C4semidirect
23. #64297C4semidirect
24. #64297C4semidirect
25. C2×C32×M16C22semidirect
26. C2×#3748C22semidirect
28. M16×C3⋊D3C22semidirect
30. C3×#926C22semidirect
31. C2×C3×C4×Dic3C22semidirect
34. C4×#624C22semidirect
35. #63874C22semidirect
37. C3×#825C22semidirect
38. C3×#825C22semidirect
39. C3×#825C22semidirect
40. #63569C22semidirect
41. #63569C22semidirect
42. #63569C22semidirect
54. #5139D3semidirect
55. C2×#825D3semidirect
78. C3×#235C2×C4semidirect
79. C3×#235C2×C4semidirect
82. C2×C3×D12C2×C4semidirect
83. C2×C3×D12C2×C4semidirect
86. C2×C3×Dic6C2×C4semidirect
87. C2×C3×Dic6C2×C4semidirect
95. #3802C2×C4semidirect
102. #3797C2×C4semidirect
103. #3796C2×C4semidirect
104. #3796C2×C4semidirect
155. C2×C3×M16C2×D3semidirect
156. C2×C3×M16C2×D3semidirect
160. #926C2×D3semidirect
161. C2×C4×Dic3C2×D3semidirect
189. #825C2×D3semidirect
190. #825C2×D3semidirect
191. #825C2×D3semidirect
332. #235C4×D3semidirect
333. #235C4×D3semidirect
341. C2×D12C4×D3semidirect
342. C2×D12C4×D3semidirect
357. C2×Dic6C4×D3semidirect
358. C2×Dic6C4×D3semidirect
439. C2×M16D32semidirect
700. C32#2901semidirect
794. C3#78983semidirect
795. C3#78992semidirect

Maximal subgroups

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

subgroupindex
#105966692
#105962162
#105949542
C3×#51392
C2×C3×#8252
#105911112
C2×#635692
#105910092
#105910082
#789923
#789833