Finite Group Databasebeta

← #72222794

Subgroups — #72222794

Order 2304.

1369 conjugacy classes of subgroups.

The subgroup lattice has 1229 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11899640C211yesmaximal, characteristic
2#11861215C211yesmaximal, characteristic, complemented
3#11860975C211yesmaximal, characteristic, complemented
4#11797977C211yesmaximal, characteristic, complemented
5#11797971C211yesmaximal, characteristic, complemented
6#11797967C211yesmaximal, characteristic, complemented
7#11797944C211yesmaximal, characteristic, complemented
8#11797930C211yesmaximal, characteristic, complemented
9#11797924C211yesmaximal, characteristic, complemented
10#11797922C211yesmaximal, characteristic, complemented
11C3×#69248C211yesmaximal, characteristic, complemented
12D3×#4487C211yesmaximal, characteristic, complemented
13#11796954C211yesmaximal, characteristic, complemented
14C3×D3×#360C211yesmaximal, characteristic, complemented
15#11795942C211yesmaximal, characteristic, complemented
16#10948642—31nomaximal
17#10948641—31nomaximal
18C3×D3×#135C2211yescharacteristic
19#10595441—21no—
20C2×#63808C2211yescharacteristic
21#10594327—21no—
22#10592896C2211yescharacteristic
23#10592892C2211yescharacteristic
24#10592568C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic
26C3×#5195C2211yescharacteristic
27C3×D3×M32C2211yescharacteristic
28C3×D3×#106C2211yescharacteristic
29C3×#4853C2211yescharacteristic, complemented
30#10591675—21no—
31#10591673—21no—
32#10591670—21no—
33#10591048C412yescomplemented
34#10591047C412yescomplemented
35#10591034C412yescomplemented
36#10591033C412yescomplemented
37#10590920C2211yescharacteristic
38#10590916C2211yescharacteristic
39D3×#819C2211yescharacteristic
40#10590819C2211yescharacteristic, complemented
41#10590768C2211yescharacteristic, complemented
42#10590693C2211yescharacteristic
43#10590636C2211yescharacteristic
44#10590634C2211yescharacteristic
45D3×#812C2211yescharacteristic
46#10590609—21no—
47#10590483—21no—
48#10590458—21no—
49C32×#360C2211yescharacteristic
50#10589382C2211yescharacteristic, complemented
51#10589378C2211yescharacteristic, complemented
52#10589353C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic
54C3×#4518C2211yescharacteristic
55C3×#4517C2211yescharacteristic, complemented
56C3×#4512C2211yescharacteristic, complemented
57C3×#4488C2211yescharacteristic
58C3×#4487C2211yescharacteristic, complemented
59#10589138C2211yescharacteristic, complemented
60#10589136C2211yescharacteristic, complemented
61#10589130C2211yescharacteristic, complemented
62#10589128C2211yescharacteristic, complemented
63#10589106C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65#83910—31no—
66#83894—31no—
67#82039—31no—
68#79899—31no—
69#79832—31no—
70#79106—31no—
71C3×#2180—31no—
72C2×C3×#360—31no—
73#71521—31no—
74#71442—31no—
75#71425—31no—
76#70929—31no—
77#70917—31no—
78C2×#4487—31no—
79D3×#365—31no—
80#69310—31no—
81#69266—31no—
82#69264—31no—
83D3×#360D311yescharacteristic, complemented
84#69249—31no—
85#69249—31no—
86#69249—31no—
87#69249—31no—
88#69249—31no—
89#69249—61no—
90#69248—31no—
91#69248—31no—
92#69248—31no—
93#69248D311yescharacteristic, complemented
94#69091—31no—
95#69087—31no—
96C3×D3×#41—21no—
97C2×#3799—21no—
98C32×#135C2311yescharacteristic
99#64157—21no—
100C2×#3745C2311yescharacteristic
101#64102—21no—
102C3×#950—21no—
103C3×#948—21no—
104C3×#919C2×C411yescharacteristic, complemented
105C3×D3×Q16C2×C411yescharacteristic, complemented
106C3×#916—21no—
107C3×D3×SD16—21no—
108C3×#912C2×C411yescharacteristic, complemented
109C3×D3×D8C2×C411yescharacteristic, complemented
110C2×C3×Dic12C2311yescharacteristic
111C3×#904C2311yescharacteristic
112C2×C3×D3×C8C2311yescharacteristic
113C3×D3×C4⋊C4—21no—
114C3×#887—21no—
115#63904—41no—
116C4×#626—41no—
117#63894—21no—
118#63883—41no—
119#63855D411yescharacteristic
120#63843—21no—
121#63836—41no—
122C2×#3717—21no—
123C2×#3711—41no—
124C2×#3711D411yescharacteristic
125#63815—21no—
126#63815—41no—
127#63814—21no—
128#63814—41no—
129D3×#208—21no—
130D3×#208—41no—
131#63808—21no—
132#63808—21no—
133#63808C2×C412yes—
134#63808C2×C412yes—
135C32×M32C2311yescharacteristic
136C32×#106C2311yescharacteristic
137#63664—21no—
138#63655C2×C412yescomplemented
139#63653C2×C412yescomplemented
140#63646C2311yescharacteristic
141#63642C2311yescharacteristic
142#63639C2311yescharacteristic
143#63636—21no—
144C3×#837—21no—
145C3×#829C2×C412yescomplemented
146C3×#827C2×C412yescomplemented
147C3×#819C2311yescharacteristic
148C3×#817C2311yescharacteristic
149C3×#815C2311yescharacteristic
150C3×#812C2311yescharacteristic
151C3×#812C2311yescharacteristic
152C3×#810—21no—
153C3×#808—21no—
154C3×#798—21no—
155C3×D3×C16—21no—
156#63577—21no—
157#63569—21no—
158#63568—21no—
159#63565—21no—
160#63564—21no—
161#63553D411yescharacteristic
162Dic3×C3⋊C8D411yescharacteristic
163#63550C2×C412yescomplemented
164#63549C2×C412yescomplemented
165#63547C2×C412yescomplemented
166#63546C2×C412yescomplemented
167#63543C2×C412yescomplemented
168D3×C3⋊C16C2×C412yescomplemented
169#33469—91noSylow
170C2×C3×#135—31no—
171#5819—61no—
172D3×#135C2×D311yescharacteristic
173C2×#919—31no—
174#5750—61no—
175C2×#904—31no—
176#5574—61no—
177#5504—61no—
178C3×#510—31no—
179C2×C3×M32—31no—
180C3×#444—31no—
181C3×#441—31no—
182C2×C3×#106—31no—
183#5236—61no—
184#5197—31no—
185#5197—31no—
186#5197—31no—
187#5197—31no—
188#5197—61no—
189#5197C2×D311yescharacteristic
190#5196—61no—
191#5196—61no—
192#5195—31no—
193#5195C2×D311yescharacteristic
194#5194—32no—
195#5194—32no—
196#5193—31no—
197#5193—31no—
198#5193—31no—
199#5193—61no—
200#5184—31no—
201#5179—31no—
202#5179—32no—
203#5147—32no—
204#5144—61no—
205C2×#819—31no—
206#5101—31no—
207C2×#812—31no—
208C4×#215—61no—
209#4966—61no—
210#4919—32no—
211#4918—32no—
212#4916—32no—
213#4914—32no—
214#4908—31no—
215D3×M32—31no—
216D3×M32C2×D311yescharacteristic
217#4894—31no—
218D3×#108—31no—
219#4869—31no—
220#4869—31no—
221#4869—31no—
222#4869—61no—
223D3×#106C2×D311yescharacteristic
224#4853—31no—
225#4853C2×D311yescharacteristic, complemented
226#4852—61no—
227#4852—61no—
228#4824—61no—
229#4821—61no—
230#4803—61no—
231#4788—61no—
232#4717—31no—
233#4711—31no—
234#4708—31no—
235C3×#365—31no—
236C3×#362—31no—
237C3×#360—21no—
238C3×#360—31no—
239C3×#360—31no—
240C3×#360—31no—
241C3×#360C2×D311yescharacteristic
242C3×#360C2×D311yescharacteristic
243C3×#347—31no—
244#4566C2×D311yescharacteristic
245#4565—31no—
246#4518C2×D311yescharacteristic
247#4517—31no—
248#4517C2×D311yescharacteristic, complemented
249#4516—31no—
250#4516—31no—
251#4516—31no—
252#4516—61no—
253#4513—31no—
254#4512—31no—
255#4512—31no—
256#4512—31no—
257#4512—31no—
258#4512—31no—
259#4512—61no—
260#4512C2×D311yescharacteristic, complemented
261#4495—31no—
262#4494—31no—
263#4488C2×D311yescharacteristic
264#4487—31no—
265#4487—31no—
266#4487—31no—
267#4487—31no—
268#4487—61no—
269#4487C2×D311yescharacteristic, complemented
270#4466—31no—
271C32×#41—21no—
272C2×C4⋊(C3⋊D3)—21no—
273C2×C4×C3⋊D3—41no—
274C3×#239—21no—
275C3×D3×Q8—21no—
276C3×#237—21no—
277C3×#237—41no—
278C3×D3×D4—21no—
279C3×D3×D4—41no—
280C3×#235—21no—
281C3×#235—41no—
282C2×C3×C4×D3—41no—
283C2×C3×C4×D3—41no—
284C2×C3×C4×D3C2×D411yescharacteristic
285C2×C3×Dic6—21no—
286C2×#626—41no—
287C2×#624—41no—
288C2×#624—41no—
289#3799—22no—
290#3799—22no—
291#3799—41no—
292#3799—41no—
293C32×Q16C22×C411yescharacteristic
294C32×SD16—21no—
295C32×D8C22×C411yescharacteristic
296C2×C32×C8C2411yescharacteristic
297C32×C4⋊C4—21no—
298#3752—41no—
299C4×C3⋊Dic3C2×D411yescharacteristic
300#3748—21no—
301#3748—41no—
302C2×C3⋊(C3⋊C8)—41no—
303C2×C3⋊(C3⋊C8)C2×D411yescharacteristic
304#3745—21no—
305#3745C22×C412yes—
306C3×#216—21no—
307C3×#215—21no—
308C3×#214—21no—
309C3×#213—21no—
310C3×C4⋊Dic3—21no—
311C3×Dic3⋊C4—41no—
312C3×Dic3⋊C4—41no—
313C3×C4×Dic3—41no—
314C3×C4×Dic3C2×D411yescharacteristic
315C3×#208—21no—
316C3×#208—41no—
317C2×C3×C3⋊C8—41no—
318C2×C3×C3⋊C8C2×D411yescharacteristic
319C2×C3×C3⋊C8C2×D411yescharacteristic
320C3×Dic12—21no—
321C3×Dic12C22×C411yescharacteristic
322C3×Dic12C22×C412yes—
323C3×D24C22×C411yescharacteristic
324C3×#204—21no—
325C3×D3×C8C22×C411yescharacteristic
326C3×D3×C8C22×C411yescharacteristic
327C3×D3×C8#4111yescharacteristic
328C3×D3×C8#4111yescharacteristic
329Dic3⋊Dic3—21no—
330Dic3⋊Dic3—41no—
331#3722—41no—
332(C2×D3)⋊Dic3—21no—
333Dic32—41no—
334#3717—22no—
335#3717—22no—
336#3711—21no—
337#3711—21no—
338#3711—41no—
339#3711—41no—
340#3711—41no—
341D3×C3⋊C8—41no—
342D3×C3⋊C8—41no—
343D3×C3⋊C8—41no—
344C32×C16—21no—
345C3⋊(C3⋊C16)C22×C412yes—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348#3414—91no—
349#2957—91no—
350#2952—91no—
351AGL(1,ℤ/16)—91no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355#2180—31no—
356#2180—91no—
357#2180—91no—
358#2180—91no—
359C2×#365—91no—
360#2148—91no—
361C2×#360—31no—
362#2110—91no—
363C2×C3×#41—61no—
364D3×#41—21no—
365C2×#239—61no—
366C2×#235—61no—
367C3×#135—21no—
368C3×#135—31no—
369C3×#135—31no—
370C3×#135—31no—
371C3×#135—61no—
372C3×#135—61no—
373C3×#135C22×D311yescharacteristic
374C3×#135C22×D311yescharacteristic
375C2×C3×Q16—31no—
376C2×C3×Q16—31no—
377C2×C3×SD16—61no—
378C2×C3×D8—31no—
379C3×#131—61no—
380C22×C3×C8—31no—
381C3×C4×Q8—61no—
382C2×C3×C4⋊C4—61no—
383#950—21no—
384#948—21no—
385#948—61no—
386#948—61no—
387#948—61no—
388#948—61no—
389#948—121no—
390#948—121no—
391#948—121no—
392Q8×Dic3—61no—
393C2×#215—61no—
394C4×#67—121no—
395C4×#67—121no—
396#926—31no—
397C2×#208—31no—
398C2×#208—61no—
399C2×#208—121no—
400C2×#208—121no—
401#919—32no—
402#919—32no—
403#919—61no—
404#919—61no—
405#919C4×D311yescharacteristic, complemented
406D3×Q16C4×D311yescharacteristic, complemented
407#916—21no—
408D3×SD16—21no—
409#912C4×D311yescharacteristic, complemented
410D3×D8C4×D311yescharacteristic, complemented
411#907—61no—
412#907—121no—
413D3×M16—61no—
414D3×M16—121no—
415C2×Dic12C22×D311yescharacteristic
416#904—32no—
417#904—32no—
418#904—61no—
419#904—61no—
420#904C22×D311yescharacteristic
421C2×D24—31no—
422C2×D24—31no—
423C2×D24—61no—
424C2×#204—61no—
425#901—61no—
426#901—121no—
427C2×ΓL(1,𝔽25)—31no—
428C2×ΓL(1,𝔽25)—121no—
429C2×D3×C8C22×D311yescharacteristic
430#893—61no—
431#893—61no—
432#893—61no—
433#893—121no—
434#893—121no—
435#892—121no—
436D3×C4⋊C4—21no—
437D3×C4⋊C4—121no—
438D3×C4⋊C4—121no—
439#887—21no—
440#887—61no—
441C4×D12—61no—
442C4×D12—121no—
443#872—31no—
444#872—121no—
445C3×Q32—32no—
446C3×SD32—32no—
447C3×M32—21no—
448C3×M32—31no—
449C3×M32—31no—
450C3×M32—61no—
451C3×M32C22×D311yescharacteristic
452C3×M32C22×D311yescharacteristic
453C2×C3×C16—61no—
454C3×#108—31no—
455C3×#106—21no—
456C3×#106—31no—
457C3×#106—61no—
458C3×#106C22×D311yescharacteristic
459C3×#106C22×D311yescharacteristic
460C3×#104—61no—
461C3×#103—61no—
462C3×#97—31no—
463#837—21no—
464#837—61no—
465#837—61no—
466#837—61no—
467#837—61no—
468#837—121no—
469#835—61no—
470#829—32no—
471#829—32no—
472#829C4×D312yescomplemented
473#828—32no—
474#828—32no—
475#828—32no—
476#828—32no—
477#828—62no—
478#827—32no—
479#827C4×D312yescomplemented
480#826—32no—
481#826—32no—
482#826—32no—
483#826—62no—
484#825—61no—
485#822—61no—
486#821—61no—
487#819—31no—
488#819—31no—
489#819—61no—
490#819—61no—
491#819C22×D311yescharacteristic
492#817C22×D311yescharacteristic
493#815—31no—
494#815—31no—
495#815—61no—
496#815C22×D311yescharacteristic
497C8×Dic3—31no—
498C8×Dic3—31no—
499C8×Dic3—31no—
500#812—31no—
501#812—31no—
502#812—32no—
503#812—61no—
504#812C22×D311yescharacteristic
505#812C22×D311yescharacteristic
506C2×C3⋊C16—32no—
507#810—21no—
508#810—61no—
509#809—61no—
510#809—61no—
511#809—61no—
512#809—121no—
513#808—21no—
514#805—61no—
515C4×C3⋊C8—31no—
516#800—32no—
517D48—32no—
518#798—21no—
519#798—32no—
520D3×C16—21no—
521D3×C16—32no—
522C22×C3⋊D3—41no—
523C22×C3×D3—41no—
524C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
525C32×Q8—21no—
526C32×D4—21no—
527C32×D4—41no—
528C2×C32×C4—41no—
529C2×C32×C4—41no—
530C2×C32×C4C22×D411yescharacteristic
531C2×C3⋊Dic3—21no—
532C4⋊(C3⋊D3)—22no—
533C4⋊(C3⋊D3)—41no—
534C4×C3⋊D3—161no—
535C3×#67—41no—
536C3×#67—41no—
537C3×#67—41no—
538C2×C3×Dic3—21no—
539C2×C3×Dic3—41no—
540C2×C3×Dic3—41no—
541C2×C3×Dic3—41no—
542C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
543C3×D12—21no—
544C3×D12—41no—
545C3×C4×D3—41no—
546C3×C4×D3—41no—
547C3×C4×D3—41no—
548C3×C4×D3—161no—
549C3×C4×D3C4×D411yescharacteristic
550C3×C4×D3C4×D411yescharacteristic
551C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
552C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
553C3×Dic6—22no—
554C3×Dic6—21no—
555C3×Dic6—41no—
556C3×Dic6—41no—
557#626—42no—
558#626—42no—
559#624—42no—
560#624—42no—
561#624—161no—
562C32×C8C23×C411yescharacteristic
563C32×C8C2×#4111yescharacteristic
564C3⋊(C3⋊C8)—21no—
565C3⋊(C3⋊C8)—41no—
566C3×C3⋊C8—21no—
567C3×C3⋊C8—41no—
568C3×C3⋊C8C4×D411yescharacteristic
569C3×C3⋊C8C4×D411yescharacteristic
570C2×#135—31no—
571C2×#135—91no—
572#568—181no—
573#520—181no—
574#510—31no—
575#510—92no—
576#510—91no—
577#509—91no—
578#509—92no—
579#509—91no—
580#508—92no—
581#508—92no—
582C2×M32—31no—
583C2×M32—91no—
584#444—31no—
585#444—91no—
586#444—91no—
587#444—91no—
588#443—181no—
589#443—181no—
590#442—91no—
591#442—91no—
592#441—31no—
593#441—91no—
594C4×SD16—181no—
595C4×SD16—181no—
596C2×#108—91no—
597C2×#106—31no—
598#421—181no—
599#417—181no—
600#405—91no—
601#365—31no—
602#365—91no—
603#365—91no—
604#365—91no—
605#362—31no—
606#362—91no—
607#361—91no—
608#361—91no—
609#360—31no—
610#360—31no—
611#360—31no—
612#360D3211yescharacteristic
613#347—31no—
614#347—91no—
615#347—91no—
616#347—91no—
617C3×#41—21no—
618C3×#41—21no—
619C3×#41—41no—
620C3×#41—61no—
621C3×#41—61no—
622C3×#41—61no—
623C3×#41—121no—
624C3×#41—121no—
625C2×C3×Q8—61no—
626C2×C3×Q8—61no—
627C2×C3×D4—61no—
628C2×C3×D4—121no—
629C22×C3×C4—31no—
630C22×C3×C4—121no—
631C22×C3×C4—121no—
632C2×#67—121no—
633#239—21no—
634#239—62no—
635#239—62no—
636#239—121no—
637#239—121no—
638D3×Q8—21no—
639#237—21no—
640#237—41no—
641D3×D4—21no—
642D3×D4—41no—
643#235—21no—
644#235—41no—
645#235—62no—
646#235—62no—
647#235—121no—
648#235—121no—
649C2×D12—61no—
650C2×D12—61no—
651C2×D12—121no—
652C2×D12—121no—
653C2×C4×D3—41no—
654C2×C4×D3—41no—
655C2×C4×D3—121no—
656C2×C4×D3—121no—
657C2×C4×D3—121no—
658C2×C4×D3—121no—
659C2×C4×D3—121no—
660C2×C4×D3—121no—
661C2×C4×D3—241no—
662C2×C4×D3D3×D411yescharacteristic
663C2×Dic6—21no—
664C3×Q16—21no—
665C3×Q16—31no—
666C3×Q16—32no—
667C3×Q16—61no—
668C3×Q16—61no—
669C3×Q16C2×C4×D311yescharacteristic
670C3×Q16C2×C4×D311yescharacteristic
671C3×SD16—21no—
672C3×SD16—21no—
673C3×SD16—41no—
674C3×SD16—61no—
675C3×SD16—61no—
676C3×SD16—61no—
677C3×D8—21no—
678C3×D8—31no—
679C3×D8—61no—
680C3×D8C2×C4×D311yescharacteristic
681C3×D8C2×C4×D311yescharacteristic
682C3×M16—61no—
683C3×M16—121no—
684C2×C3×C8—21no—
685C2×C3×C8—31no—
686C2×C3×C8—31no—
687C2×C3×C8—31no—
688C2×C3×C8—31no—
689C2×C3×C8—31no—
690C2×C3×C8—31no—
691C2×C3×C8—121no—
692C2×C3×C8C23×D311yescharacteristic
693C2×C3×C8C23×D311yescharacteristic
694C3×C4⋊C4—21no—
695C3×C4⋊C4—21no—
696C3×C4⋊C4—41no—
697C3×C4⋊C4—61no—
698C3×C4⋊C4—121no—
699C3×C4⋊C4—121no—
700C3×C42—31no—
701C3×C42—121no—
702#217—61no—
703#216—21no—
704#215—21no—
705#215—62no—
706#215—62no—
707#214—21no—
708#213—21no—
709(C2×D3)⋊C4—61no—
710(C2×D3)⋊C4—121no—
711(C2×D3)⋊C4—121no—
712(C2×D3)⋊C4—121no—
713(C2×D3)⋊C4—121no—
714(C2×D3)⋊C4—241no—
715C4⋊Dic3—21no—
716C4⋊Dic3—61no—
717C4⋊Dic3—121no—
718Dic3⋊C4—41no—
719Dic3⋊C4—41no—
720Dic3⋊C4—61no—
721Dic3⋊C4—121no—
722C4×Dic3—31no—
723C4×Dic3—31no—
724C4×Dic3—41no—
725C4×Dic3—61no—
726C4×Dic3—121no—
727C4×Dic3—121no—
728C4×Dic3D3×D411yescharacteristic
729#208—21no—
730#208—41no—
731#208—61no—
732#208—61no—
733#208—61no—
734#208—61no—
735#208—121no—
736#208—121no—
737#208—121no—
738#208—121no—
739#208—121no—
740#208—121no—
741#208—241no—
742C2×C3⋊C8—31no—
743C2×C3⋊C8—31no—
744C2×C3⋊C8—41no—
745C2×C3⋊C8—61no—
746C2×C3⋊C8—121no—
747C2×C3⋊C8—121no—
748C2×C3⋊C8—121no—
749C2×C3⋊C8—121no—
750C2×C3⋊C8—121no—
751C2×C3⋊C8—241no—
752C2×C3⋊C8D3×D411yescharacteristic
753C2×C3⋊C8D3×D411yescharacteristic
754Dic12—21no—
755Dic12C2×C4×D311yescharacteristic
756Dic12C2×C4×D312yes—
757D24—32no—
758D24—32no—
759D24—62no—
760D24—61no—
761D24—61no—
762D24—121no—
763D24C2×C4×D311yescharacteristic
764#204—21no—
765#204—62no—
766#204—62no—
767ΓL(1,𝔽25)—61no—
768ΓL(1,𝔽25)—61no—
769ΓL(1,𝔽25)—121no—
770ΓL(1,𝔽25)—121no—
771ΓL(1,𝔽25)—121no—
772D3×C8—121no—
773D3×C8—121no—
774D3×C8—121no—
775D3×C8C2×C4×D311yescharacteristic
776D3×C8C2×C4×D311yescharacteristic
777D3×C8#23711yescharacteristic
778D3×C8#23711yescharacteristic
779C3×C16—21no—
780C3×C16—21no—
781C3×C16—32no—
782C3×C16—41no—
783C3×C16—61no—
784C3⋊C16—21no—
785C3⋊C16—32no—
786C3⋊C16—32no—
787C3⋊C16—62no—
788C3⋊C16C2×C4×D312yes—
789C22×C32—41no—
790C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
791C2×C3⋊D3—42no—
792C2×C3⋊D3—81no—
793C2×C3⋊D3—81no—
794C2×C3×D3—41no—
795C2×C3×D3—41no—
796C2×C3×D3—161no—
797C2×C3×D3#44211yescharacteristic
798C2×C3×D3#44211yescharacteristic
799C32×C4—41no—
800C32×C4—81no—
801C32×C4C2×C4×D411yescharacteristic
802C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
803C3⋊Dic3—41no—
804C3×Dic3—41no—
805C3×Dic3—42no—
806C3×Dic3—41no—
807C3×Dic3—81no—
808C3×Dic3#44211yescharacteristic
809C3×Dic3#44211yescharacteristic
810C2×#41—61no—
811C2×#41—181no—
812#135—31no—
813#135—31no—
814#135—31no—
815#135—61no—
816#135—61no—
817#135—92no—
818#135—92no—
819#135—181no—
820#135—181no—
821#135C2×D3211yescharacteristic
822C2×Q16—31no—
823C2×Q16—31no—
824C2×SD16—61no—
825C2×SD16—181no—
826C2×D8—31no—
827C2×D8—91no—
828#131—61no—
829#131—181no—
830#131—181no—
831#131—181no—
832#131—361no—
833#131—361no—
834C2×M16—91no—
835C2×M16—181no—
836C2×M16—361no—
837C2×M16—361no—
838C22×C8—31no—
839C4×Q8—61no—
840C4×Q8—181no—
841C4×D4—181no—
842C4×D4—181no—
843C4×D4—361no—
844C4×D4—361no—
845#117—91no—
846#117—361no—
847C2×C4⋊C4—61no—
848C2×C4⋊C4—361no—
849Q32—32no—
850Q32—92no—
851SD32—32no—
852SD32—92no—
853SD32—92no—
854SD32—92no—
855D16—92no—
856D16—92no—
857M32—31no—
858M32—31no—
859M32—61no—
860M32—92no—
861M32—91no—
862M32C2×D3211yescharacteristic
863C2×C16—61no—
864C2×C16—92no—
865#108—31no—
866#108—91no—
867#108—181no—
868#106—31no—
869#106—61no—
870#106C2×D3211yescharacteristic
871#104—61no—
872#104—181no—
873#104—181no—
874#104—181no—
875#103—61no—
876#103—181no—
877#102—181no—
878#102—181no—
879#97—31no—
880#97—91no—
881C4×C8—91no—
882C4×C8—91no—
883C23×C3—31no—
884C23×C3—121no—
885C22×D3—41no—
886C22×D3—121no—
887C22×D3—121no—
888C22×D3—241no—
889C22×D3#91111yescharacteristic
890C3×Q8—21no—
891C3×Q8—21no—
892C3×Q8—41no—
893C3×Q8—62no—
894C3×Q8—61no—
895C3×Q8—121no—
896C3×Q8—121no—
897C3×D4—21no—
898C3×D4—21no—
899C3×D4—41no—
900C3×D4—41no—
901C3×D4—41no—
902C3×D4—61no—
903C3×D4—81no—
904C3×D4—121no—
905C3×D4—121no—
906C3×D4—121no—
907C3×D4—121no—
908C2×C3×C4—21no—
909C2×C3×C4—31no—
910C2×C3×C4—31no—
911C2×C3×C4—31no—
912C2×C3×C4—31no—
913C2×C3×C4—31no—
914C2×C3×C4—41no—
915C2×C3×C4—41no—
916C2×C3×C4—41no—
917C2×C3×C4—41no—
918C2×C3×C4—61no—
919C2×C3×C4—81no—
920C2×C3×C4—81no—
921C2×C3×C4—121no—
922C2×C3×C4—121no—
923C2×C3×C4—121no—
924C2×C3×C4—121no—
925C2×C3×C4—121no—
926C2×C3×C4—121no—
927C2×C3×C4—481no—
928C2×C3×C4C2×D3×D411yescharacteristic
929C2×C3×C4C2×D3×D411yescharacteristic
930#67—41no—
931#67—41no—
932#67—41no—
933#67—122no—
934#67—122no—
935C2×Dic3—21no—
936C2×Dic3—41no—
937C2×Dic3—41no—
938C2×Dic3—41no—
939C2×Dic3—61no—
940C2×Dic3—61no—
941C2×Dic3—121no—
942C2×Dic3#91111yescharacteristic
943D12—21no—
944D12—41no—
945D12—62no—
946D12—62no—
947D12—122no—
948D12—122no—
949D12—122no—
950D12—121no—
951D12—121no—
952D12—241no—
953C4×D3—41no—
954C4×D3—41no—
955C4×D3—41no—
956C4×D3—122no—
957C4×D3—122no—
958C4×D3—122no—
959C4×D3—122no—
960C4×D3—161no—
961C4×D3—481no—
962C4×D3—481no—
963C4×D3—481no—
964C4×D3—481no—
965C4×D3—482no—
966C4×D3#67⋊C411yescharacteristic
967C4×D3#67⋊C411yescharacteristic
968C4×D3#91411yescharacteristic
969C4×D3#91411yescharacteristic
970Dic6—21no—
971Dic6—22no—
972Dic6—41no—
973Dic6—41no—
974C3×C8—21no—
975C3×C8—21no—
976C3×C8—31no—
977C3×C8—31no—
978C3×C8—61no—
979C3×C8—121no—
980C3×C8C22×C4×D311yescharacteristic
981C3×C8C22×C4×D311yescharacteristic
982C3×C8C2×#23711yescharacteristic
983C3×C8D3×#4111yescharacteristic
984C3⋊C8—21no—
985C3⋊C8—41no—
986C3⋊C8—61no—
987C3⋊C8—61no—
988C3⋊C8—121no—
989C3⋊C8—121no—
990C3⋊C8—121no—
991C3⋊C8—241no—
992C3⋊C8#67⋊C411yescharacteristic
993C3⋊C8#67⋊C411yescharacteristic
994C2×C32—21no—
995C2×C32—81no—
996C2×C32C2×#44211yescharacteristic
997C3⋊D3—82no—
998C3×D3—21no—
999C3×D3—21no—
1000C3×D3—81no—
1001#41—21no—
1002#41—61no—
1003#41—61no—
1004#41—61no—
1005#41—121no—
1006#41—121no—
1007#41—182no—
1008#41—182no—
1009#41—361no—
1010#41—361no—
1011C2×Q8—61no—
1012C2×Q8—61no—
1013C2×D4—61no—
1014C2×D4—121no—
1015C2×D4—181no—
1016C2×D4—361no—
1017C22×C4—31no—
1018C22×C4—121no—
1019C22×C4—121no—
1020C22×C4—361no—
1021C22×C4—361no—
1022C22×C4—361no—
1023Q16—32no—
1024Q16—31no—
1025Q16—61no—
1026Q16—61no—
1027Q16C4×D3211yescharacteristic
1028SD16—21no—
1029SD16—61no—
1030SD16—61no—
1031SD16—61no—
1032SD16—182no—
1033SD16—182no—
1034D8—31no—
1035D8—61no—
1036D8—92no—
1037D8—181no—
1038D8C4×D3211yescharacteristic
1039M16—61no—
1040M16—121no—
1041M16—181no—
1042M16—181no—
1043M16—181no—
1044M16—361no—
1045M16—361no—
1046M16—361no—
1047M16—361no—
1048C2×C8—31no—
1049C2×C8—31no—
1050C2×C8—31no—
1051C2×C8—31no—
1052C2×C8—31no—
1053C2×C8—31no—
1054C2×C8—91no—
1055C2×C8—121no—
1056C2×C8—361no—
1057C2×C8—361no—
1058C2×C8—361no—
1059C2×C8—361no—
1060C2×C8C22×D3211yescharacteristic
1061C4⋊C4—21no—
1062C4⋊C4—61no—
1063C4⋊C4—121no—
1064C4⋊C4—121no—
1065C4⋊C4—181no—
1066C4⋊C4—361no—
1067C22⋊C4—181no—
1068C22⋊C4—361no—
1069C22⋊C4—361no—
1070C42—31no—
1071C42—91no—
1072C42—121no—
1073C42—361no—
1074C16—21no—
1075C16—32no—
1076C16—61no—
1077C16—92no—
1078C22×C3—21no—
1079C22×C3—31no—
1080C22×C3—31no—
1081C22×C3—41no—
1082C22×C3—41no—
1083C22×C3—81no—
1084C22×C3—121no—
1085C22×C3—121no—
1086C22×C3—481no—
1087C22×C3C2×#91111yescharacteristic
1088C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1089C2×D3—41no—
1090C2×D3—41no—
1091C2×D3—122no—
1092C2×D3—122no—
1093C2×D3—161no—
1094C2×D3—242no—
1095C2×D3—241no—
1096C2×D3—241no—
1097C2×D3—241no—
1098C2×D3—241no—
1099C2×D3—481no—
1100C2×D3—481no—
1101C2×D3#478511yescharacteristic
1102C2×D3#478511yescharacteristic
1103C3×C4—21no—
1104C3×C4—21no—
1105C3×C4—31no—
1106C3×C4—31no—
1107C3×C4—41no—
1108C3×C4—41no—
1109C3×C4—81no—
1110C3×C4—81no—
1111C3×C4—81no—
1112C3×C4—121no—
1113C3×C4—122no—
1114C3×C4—121no—
1115C3×C4—161no—
1116C3×C4—241no—
1117C3×C4C2×#67⋊C411yescharacteristic
1118C3×C4C4×D3×D411yescharacteristic
1119C3×C4C2×#91411yescharacteristic
1120C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1121Dic3—41no—
1122Dic3—41no—
1123Dic3—42no—
1124Dic3—81no—
1125Dic3—121no—
1126Dic3—121no—
1127Dic3—241no—
1128Dic3#478511yescharacteristic
1129Dic3#478511yescharacteristic
1130C32#3346911yescharacteristic, complemented, Sylow
1131C23—31no—
1132C23—121no—
1133C23—361no—
1134Q8—21no—
1135Q8—61no—
1136Q8—62no—
1137Q8—121no—
1138Q8—121no—
1139D4—21no—
1140D4—41no—
1141D4—61no—
1142D4—121no—
1143D4—121no—
1144D4—121no—
1145D4—121no—
1146D4—182no—
1147D4—362no—
1148D4—362no—
1149D4—361no—
1150C2×C4—31no—
1151C2×C4—31no—
1152C2×C4—31no—
1153C2×C4—31no—
1154C2×C4—31no—
1155C2×C4—41no—
1156C2×C4—41no—
1157C2×C4—61no—
1158C2×C4—121no—
1159C2×C4—121no—
1160C2×C4—121no—
1161C2×C4—121no—
1162C2×C4—121no—
1163C2×C4—121no—
1164C2×C4—181no—
1165C2×C4—362no—
1166C2×C4—362no—
1167C2×C4—481no—
1168C2×C4—1441no—
1169C2×C4—1441no—
1170C2×C4D32×D411yescharacteristic
1171C8—31no—
1172C8—31no—
1173C8—61no—
1174C8—121no—
1175C8—181no—
1176C8—361no—
1177C8C2×C4×D3211yescharacteristic
1178C8D3×#23711yescharacteristic
1179C2×C3—21no—
1180C2×C3—21no—
1181C2×C3—21no—
1182C2×C3—41no—
1183C2×C3—61no—
1184C2×C3—61no—
1185C2×C3—81no—
1186C2×C3—81no—
1187C2×C3—161no—
1188C2×C3—241no—
1189C2×C3C2×#478511yescharacteristic
1190C2×C3D3×#44211yescharacteristic
1191D3—21no—
1192D3—21no—
1193D3—81no—
1194D3—242no—
1195D3—242no—
1196D3—482no—
1197C22—31no—
1198C22—31no—
1199C22—41no—
1200C22—121no—
1201C22—121no—
1202C22—362no—
1203C22—481no—
1204C22—721no—
1205C22—721no—
1206C22D3×#91111yescharacteristic
1207C4—31no—
1208C4—31no—
1209C4—41no—
1210C4—81no—
1211C4—121no—
1212C4—121no—
1213C4—122no—
1214C4—241no—
1215C4—361no—
1216C4D3×#67⋊C411yescharacteristic
1217C4D3×#91411yescharacteristic
1218C3—21no—
1219C3#1094864111yescharacteristic, complemented
1220C3#1094864211yescharacteristic, complemented
1221C2—21no—
1222C2—61no—
1223C2—61no—
1224C2—81no—
1225C2—241no—
1226C2—722no—
1227C2D3×#478511yescharacteristic
subgroupG/H
centerC2D3×#4785
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#360C22
socleC2×C32C2×#442
prime radical#11899640C2
cosocleC2×C32×C8C24
hypercenter#360D32
hypocenterC32#33469
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #11861215C2semidirect
3. #11860975C2semidirect
4. #11797977C2semidirect
5. #11797971C2semidirect
6. #11797967C2semidirect
7. #11797944C2semidirect
8. #11797930C2semidirect
9. #11797924C2semidirect
10. #11797922C2semidirect
11. C3×#69248C2semidirect
12. D3×#4487C2semidirect
13. #11796954C2semidirect
14. C3×D3×#360C2semidirect
15. #11795942C2semidirect
24. #10592568C22semidirect
29. C3×#4853C22semidirect
33. #10591048C4semidirect
34. #10591047C4semidirect
35. #10591034C4semidirect
36. #10591033C4semidirect
40. #10590819C22semidirect
41. #10590768C22semidirect
50. #10589382C22semidirect
51. #10589378C22semidirect
52. #10589353C22semidirect
55. C3×#4517C22semidirect
56. C3×#4512C22semidirect
58. C3×#4487C22semidirect
59. #10589138C22semidirect
60. #10589136C22semidirect
61. #10589130C22semidirect
62. #10589128C22semidirect
63. #10589106C22semidirect
64. #10589105C22semidirect
83. D3×#360D3semidirect
93. #69248D3semidirect
104. C3×#919C2×C4semidirect
105. C3×D3×Q16C2×C4semidirect
108. C3×#912C2×C4semidirect
109. C3×D3×D8C2×C4semidirect
138. #63655C2×C4semidirect
139. #63653C2×C4semidirect
145. C3×#829C2×C4semidirect
146. C3×#827C2×C4semidirect
163. #63550C2×C4semidirect
164. #63549C2×C4semidirect
165. #63547C2×C4semidirect
166. #63546C2×C4semidirect
167. #63543C2×C4semidirect
168. D3×C3⋊C16C2×C4semidirect
225. #4853C2×D3semidirect
248. #4517C2×D3semidirect
260. #4512C2×D3semidirect
269. #4487C2×D3semidirect
405. #919C4×D3semidirect
406. D3×Q16C4×D3semidirect
409. #912C4×D3semidirect
410. D3×D8C4×D3semidirect
472. #829C4×D3semidirect
479. #827C4×D3semidirect
1130. C32#33469semidirect
1219. C3#10948641semidirect
1220. C3#10948642semidirect

Maximal subgroups

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

subgroupindex
#118996402
#118612152
#118609752
#117979772
#117979712
#117979672
#117979442
#117979302
#117979242
#117979222
C3×#692482
D3×#44872
#117969542
C3×D3×#3602
#117959422
#109486423
#109486413