Finite Group Databasebeta

← #72222789

Subgroups — #72222789

Order 2304.

1413 conjugacy classes of subgroups.

The subgroup lattice has 1261 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D3×#5147C211yesmaximal, characteristic
2#11861222C211yesmaximal, characteristic, complemented
3C3×#79867C211yesmaximal, characteristic, complemented
4#11797980C211yesmaximal, characteristic, complemented
5#11797978C211yesmaximal, characteristic, complemented
6#11797974C211yesmaximal, characteristic, complemented
7#11797973C211yesmaximal, characteristic, complemented
8#11797968C211yesmaximal, characteristic, complemented
9#11797966C211yesmaximal, characteristic, complemented
10C3×#70918C211yesmaximal, characteristic, complemented
11#11797947C211yesmaximal, characteristic, complemented
12#11797130C211yesmaximal, characteristic, complemented
13D3×#4563C211yesmaximal, characteristic, complemented
14#11796856C211yesmaximal, characteristic, complemented
15#11795944C211yesmaximal, characteristic, complemented
16#10948660—31nomaximal
17#10948658—31nomaximal
18C2×C3×D3×D8C2211yescharacteristic
19C3×#5545—21no—
20D3×#904C2211yescharacteristic
21#10594668—21no—
22C32×#442C2211yescharacteristic, complemented
23#10592846C2211yescharacteristic
24#10592416C2211yescharacteristic, complemented
25C3×#5152C2211yescharacteristic, complemented
26C3×#5147C2211yescharacteristic
27C3×C4×#213—21no—
28C3×#4869C2211yescharacteristic, complemented
29C3×#4860C2211yescharacteristic
30C3×#4770—21no—
31C3×#4756—21no—
32C3×#4717C2211yescharacteristic, complemented
33C3×#4711C2211yescharacteristic, complemented
34C3×#4708C2211yescharacteristic
35#10591033C412yescomplemented
36#10591031C412yescomplemented
37D3×#827C412yescomplemented
38D3×#826C412yescomplemented
39#10590923—21no—
40#10590918C2211yescharacteristic, complemented
41#10590916C2211yescharacteristic, complemented
42D3×#819C2211yescharacteristic
43#10590633C2211yescharacteristic
44#10590630C2211yescharacteristic
45D3×#812C2211yescharacteristic
46D3×#812C2211yescharacteristic
47#10590392—21no—
48#10590341—21no—
49#10589429C2211yescharacteristic, complemented
50#10589354C2211yescharacteristic, complemented
51#10589353C2211yescharacteristic, complemented
52#10589332C2211yescharacteristic, complemented
53C3×#4563C2211yescharacteristic, complemented
54C3×#4488C2211yescharacteristic, complemented
55C3×#4487C2211yescharacteristic, complemented
56C3×#4466C2211yescharacteristic, complemented
57#10589138C2211yescharacteristic, complemented
58#10589136C2211yescharacteristic, complemented
59#10589127C2211yescharacteristic, complemented
60#10589126C2211yescharacteristic, complemented
61#10589125C2211yescharacteristic, complemented
62#10589123C2211yescharacteristic, complemented
63#10589105C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C3×#2948—31no—
66C2×#5147—31no—
67D3×#509—31no—
68#79899—31no—
69#79867D311yescharacteristic, complemented
70#78580—31no—
71C3×AGL(1,ℤ/16)—31no—
72C2×#4563—31no—
73#71515—31no—
74#70929—31no—
75#70918—31no—
76#70918—31no—
77#70918—31no—
78#70918—31no—
79#70918—31no—
80#70918—31no—
81#70918—31no—
82#70918—31no—
83#70918—61no—
84#70918D311yescharacteristic, complemented
85#70656—31no—
86#70650—31no—
87#69884—31no—
88#69312—31no—
89#69310—31no—
90D3×#361—31no—
91#69254—31no—
92#69251—31no—
93#69249—31no—
94#69091—31no—
95#69087—31no—
96C2×C3×D3×D4—21no—
97D3×#235—21no—
98C2×C32×D8C2311yescharacteristic
99C32×C4×D4—21no—
100#64113C2311yescharacteristic
101#64110—21no—
102C3×D4×Dic3—21no—
103C2×C3×#213—21no—
104C3×C4×#67—41no—
105C2×C3×(C2×D3)⋊C4—41no—
106C3×D3×D8—21no—
107C3×D3×D8—21no—
108C3×D3×D8C2×C412yes—
109C3×D3×D8C2×C412yes—
110C3×#904C2311yescharacteristic
111C2×C3×D24C2311yescharacteristic
112C3×#901—21no—
113C2×C3×ΓL(1,𝔽25)D411yescharacteristic
114C2×C3×D3×C8C2311yescharacteristic
115C3×#893—21no—
116C3×#892—21no—
117C3×#67⋊C4—41no—
118C3×D3×C22⋊C4—41no—
119C3×C4×D12—21no—
120C3×#872D411yescharacteristic
121#63829—21no—
122#63817—21no—
123#63814—21no—
124D3×#208—21no—
125#63808C2×C411yescharacteristic, complemented
126#63807C2×C411yescharacteristic, complemented
127#63806—21no—
128#63805—41no—
129#63804—41no—
130D3×Dic12C2×C411yescharacteristic, complemented
131D3×D24C2×C411yescharacteristic, complemented
132D3×#204—21no—
133#63791—41no—
134D3×ΓL(1,𝔽25)—41no—
135C32×#106C2311yescharacteristic
136C32×#102—21no—
137C32×#97C2311yescharacteristic
138#63654C2×C412yescomplemented
139#63653C2×C412yescomplemented
140#63646C2311yescharacteristic
141#63639C2311yescharacteristic
142#63639C2311yescharacteristic
143#63632—21no—
144C3×#832—21no—
145C3×#827C2×C412yescomplemented
146C3×#826C2×C412yescomplemented
147C3×#821—21no—
148C3×#819C2311yescharacteristic
149C3×#817C2311yescharacteristic
150C3×#815C2311yescharacteristic
151C3×C8×Dic3D411yescharacteristic
152C3×#812C2311yescharacteristic
153C3×#812C2311yescharacteristic
154C3×#809—21no—
155C3×#807—21no—
156C3×#805—21no—
157C3×C4×C3⋊C8D411yescharacteristic
158#63577—21no—
159#63570—21no—
160#63569—21no—
161#63548C2×C412yescomplemented
162#63547C2×C412yescomplemented
163#63546C2×C412yescomplemented
164#63545C2×C412yescomplemented
165#63543—21no—
166#63543C2×C412yescomplemented
167D3×C3⋊C16—21no—
168D3×C3⋊C16C2×C412yescomplemented
169#33471—91noSylow
170C22×C3×D8—31no—
171C3×#518—61no—
172D3×#135—31no—
173C2×D3×D8C2×D311yescharacteristic
174#5750—61no—
175#5745—61no—
176C2×#904—31no—
177#5545—21no—
178C3×#509—31no—
179C3×#444—31no—
180C3×#442—21no—
181C3×#442—31no—
182C3×#442—31no—
183C3×#442—31no—
184C3×#442C2×D311yescharacteristic, complemented
185C3×#442C2×D311yescharacteristic, complemented
186C3×C4×D8—61no—
187C3×C4×D8—61no—
188C3×#427—31no—
189C3×#418—61no—
190C3×#405—31no—
191#5197—31no—
192#5193—31no—
193#5152C2×D311yescharacteristic, complemented
194C2×#827—32no—
195#5147—31no—
196#5147—31no—
197#5147—31no—
198#5147—32no—
199#5147—32no—
200#5147—31no—
201#5147—61no—
202#5147C2×D311yescharacteristic
203C2×#826—32no—
204#5144—61no—
205C2×#819—31no—
206C2×#812—31no—
207C2×#812—31no—
208C4×#213—21no—
209#5005—61no—
210#4914—32no—
211D3×SD32—32no—
212#4911—32no—
213D3×D16—32no—
214#4908—31no—
215D3×M32—31no—
216D3×M32—31no—
217#4894—31no—
218D3×#108—31no—
219#4869C2×D311yescharacteristic, complemented
220#4860C2×D311yescharacteristic
221#4824—61no—
222#4821—61no—
223#4770—21no—
224#4756—21no—
225#4717—31no—
226#4717—31no—
227#4717—31no—
228#4717—31no—
229#4717—61no—
230#4717C2×D311yescharacteristic, complemented
231#4711C2×D311yescharacteristic, complemented
232#4708C2×D311yescharacteristic
233#4700—61no—
234#4700—61no—
235C3×#365—31no—
236C3×#361—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4563—31no—
241#4563—31no—
242#4563—31no—
243#4563—31no—
244#4563—61no—
245#4563C2×D311yescharacteristic, complemented
246#4518—31no—
247#4516—31no—
248#4513—31no—
249#4512—31no—
250#4512—31no—
251#4495—31no—
252#4494—31no—
253#4488—31no—
254#4488—31no—
255#4488—31no—
256#4488—31no—
257#4488—61no—
258#4488C2×D311yescharacteristic, complemented
259#4487—31no—
260#4487—31no—
261#4487—31no—
262#4487—31no—
263#4487—61no—
264#4487C2×D311yescharacteristic, complemented
265#4466—31no—
266#4466—31no—
267#4466—31no—
268#4466—31no—
269#4466—61no—
270#4466C2×D311yescharacteristic, complemented
271C23×C3×D3—41no—
272C2×C32×D4—21no—
273C22×C32×C4—41no—
274#3828—21no—
275C2×C3×#67—41no—
276C22×C3×Dic3—41no—
277C3×D3×D4—22no—
278C3×D3×D4—22no—
279C3×D3×D4—41no—
280C3×D3×D4—41no—
281C3×#235—21no—
282C2×C3×D12—21no—
283C2×C3×C4×D3—41no—
284C2×C3×C4×D3—41no—
285C2×C3×C4×D3C2×D411yescharacteristic
286D3×#67—41no—
287#3804—41no—
288D3×D12—21no—
289C4×D32—41no—
290#3799—21no—
291#3798—41no—
292#3795—21no—
293D3×Dic6—21no—
294C32×D8—21no—
295C32×D8C22×C412yes—
296C2×C32×C8C2×D411yescharacteristic
297C2×C32×C8C2411yescharacteristic
298C32×C4⋊C4—21no—
299C32×C22⋊C4—41no—
300C32×C42C2×D411yescharacteristic
301#3748—21no—
302#3746C22×C411yescharacteristic
303#3745C22×C411yescharacteristic
304#3744—21no—
305#3743—41no—
306C8×C3⋊D3—41no—
307C3×#217—41no—
308C3×#213—22no—
309C3×#213—22no—
310C3×(C2×D3)⋊C4—21no—
311C3×(C2×D3)⋊C4—41no—
312C3×(C2×D3)⋊C4—41no—
313C3×(C2×D3)⋊C4—41no—
314C3×C4⋊Dic3—21no—
315C3×Dic3⋊C4—21no—
316C3×C4×Dic3—41no—
317C3×C4×Dic3C2×D411yescharacteristic
318C3×#208—21no—
319C2×C3×C3⋊C8C2×D411yescharacteristic
320C2×C3×C3⋊C8C2×D411yescharacteristic
321C3×Dic12C22×C411yescharacteristic
322C3×D24—21no—
323C3×D24C22×C412yes—
324C3×D24C22×C411yescharacteristic
325C3×#204—21no—
326C3×ΓL(1,𝔽25)—21no—
327C3×ΓL(1,𝔽25)—21no—
328C3×ΓL(1,𝔽25)—41no—
329C3×D3×C8—41no—
330C3×D3×C8C22×C411yescharacteristic
331C3×D3×C8C22×C411yescharacteristic
332C3×D3×C8#4111yescharacteristic
333C3×D3×C8#4111yescharacteristic
334#3719—21no—
335#3717—21no—
336#3716—21no—
337#3714—21no—
338#3712—41no—
339#3711—41no—
340#3711—41no—
341#3710—41no—
342D3×C3⋊C8—41no—
343D3×C3⋊C8—41no—
344C3⋊(C3⋊C16)—21no—
345C3⋊(C3⋊C16)C22×C412yes—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348C2×#509—91no—
349#2957—91no—
350#2948—31no—
351AGL(1,ℤ/16)—31no—
352AGL(1,ℤ/16)—91no—
353AGL(1,ℤ/16)—91no—
354AGL(1,ℤ/16)—91no—
355AGL(1,ℤ/16)—91no—
356AGL(1,ℤ/16)—91no—
357AGL(1,ℤ/16)—91no—
358AGL(1,ℤ/16)—91no—
359#2155—91no—
360C2×#361—91no—
361#2145—91no—
362#2110—91no—
363C22×C3×D4—61no—
364D3×#41—61no—
365C2×D3×D4—21no—
366C2×#235—61no—
367C3×#135—31no—
368C2×C3×D8—21no—
369C2×C3×D8—32no—
370C2×C3×D8—32no—
371C2×C3×D8—31no—
372C2×C3×D8—61no—
373C2×C3×D8—61no—
374C2×C3×D8—61no—
375C2×C3×D8C22×D311yescharacteristic
376C2×C3×D8C22×D311yescharacteristic
377C3×#131—61no—
378C2×C3×M16—31no—
379C22×C3×C8—31no—
380C3×C4×D4—21no—
381C3×C4×D4—21no—
382C3×C4×D4—41no—
383C3×C4×D4—61no—
384C3×C4×D4—61no—
385C3×C4×D4—61no—
386C3×C4×D4—121no—
387C3×C4×D4—121no—
388C3×#117—31no—
389C3×#117—61no—
390C2×C3×C22⋊C4—121no—
391C2×C3×C22⋊C4—121no—
392#950—61no—
393#948—61no—
394D4×Dic3—21no—
395C2×#213—21no—
396C4×#67—41no—
397C2×(C2×D3)⋊C4—41no—
398C2×#208—61no—
399#919—31no—
400D3×Q16—31no—
401#916—61no—
402D3×SD16—61no—
403#912—31no—
404D3×D8—21no—
405D3×D8—21no—
406D3×D8—31no—
407D3×D8C4×D312yes—
408D3×D8C4×D312yes—
409#907—61no—
410#907—121no—
411#907—121no—
412#907—121no—
413D3×M16—61no—
414D3×M16—121no—
415D3×M16—121no—
416D3×M16—121no—
417C2×Dic12—31no—
418#904—31no—
419#904—31no—
420#904—31no—
421#904—31no—
422#904—61no—
423#904—61no—
424#904—61no—
425#904C22×D311yescharacteristic
426C2×D24—31no—
427C2×D24C22×D311yescharacteristic
428C2×#204—61no—
429#901—21no—
430#901—61no—
431#901—61no—
432#901—61no—
433#901—61no—
434#901—121no—
435#901—121no—
436C2×ΓL(1,𝔽25)—121no—
437C2×ΓL(1,𝔽25)#6711yescharacteristic
438C2×D3×C8C22×D311yescharacteristic
439#893—21no—
440#892—21no—
441#67⋊C4—41no—
442D3×C22⋊C4—41no—
443C4×D12—21no—
444#872#6711yescharacteristic
445C3×SD32—32no—
446C3×D16—32no—
447C3×M32—31no—
448C3×M32—31no—
449C3×#108—31no—
450C3×#107—61no—
451C3×#106—21no—
452C3×#106—31no—
453C3×#106C22×D311yescharacteristic
454C3×#106C22×D311yescharacteristic
455C3×#104—61no—
456C3×#102—21no—
457C3×#102—21no—
458C3×#102—41no—
459C3×#102—61no—
460C3×#102—61no—
461C3×#102—61no—
462C3×#97—21no—
463C3×#97—31no—
464C3×#97C22×D311yescharacteristic
465C3×#97C22×D311yescharacteristic
466C3×C4×C8—31no—
467C3×C4×C8—31no—
468#837—61no—
469#832—21no—
470#828—32no—
471#827—32no—
472#827—32no—
473#827—32no—
474#827—32no—
475#827—62no—
476#827C4×D312yescomplemented
477#826—32no—
478#826—32no—
479#826—32no—
480#826—32no—
481#826—32no—
482#826—62no—
483#826C4×D312yescomplemented
484#825—61no—
485#822—61no—
486#821—21no—
487#819—31no—
488#819—31no—
489#819—61no—
490#819—61no—
491#819C22×D311yescharacteristic
492#817C22×D311yescharacteristic
493#815C22×D311yescharacteristic
494C8×Dic3#6711yescharacteristic
495#812—31no—
496#812—31no—
497#812—32no—
498#812—31no—
499#812—31no—
500#812—61no—
501#812—61no—
502#812—61no—
503#812C22×D311yescharacteristic
504#812C22×D311yescharacteristic
505C2×C3⋊C16—32no—
506C2×C3⋊C16—61no—
507#809—21no—
508#807—21no—
509#805—21no—
510#805—61no—
511#805—61no—
512#805—61no—
513#805—61no—
514#805—121no—
515C4×C3⋊C8#6711yescharacteristic
516#800—32no—
517D48—32no—
518#798—32no—
519#798—61no—
520D3×C16—32no—
521D3×C16—61no—
522C23×C32—41no—
523C22×C3×D3—41no—
524C22×C3×D3—42no—
525C22×C3×D3—42no—
526C22×C3×D3—161no—
527C22×C3×D3—161no—
528C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
529C2×D32—41no—
530C32×D4—22no—
531C32×D4—41no—
532C2×C32×C4—21no—
533C2×C32×C4—41no—
534C2×C32×C4—161no—
535C2×C32×C4C22×D411yescharacteristic
536#638—41no—
537C4⋊(C3⋊D3)—21no—
538C4×C3⋊D3—41no—
539#634—21no—
540C3×#67—41no—
541C3×#67—42no—
542C3×#67—42no—
543C2×C3×Dic3—21no—
544C2×C3×Dic3—41no—
545C2×C3×Dic3—161no—
546C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
547C3×D12—21no—
548C3×D12—22no—
549C3×D12—41no—
550C3×C4×D3—41no—
551C3×C4×D3—161no—
552C3×C4×D3—161no—
553C3×C4×D3C4×D411yescharacteristic
554C3×C4×D3C4×D411yescharacteristic
555C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
556C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
557C3×Dic6—21no—
558#627—41no—
559#626—41no—
560#626—41no—
561#625—41no—
562#624—41no—
563D3×Dic3—41no—
564D3×Dic3—41no—
565C32×C8—21no—
566C32×C8C23×C411yescharacteristic
567C32×C8C2×#4111yescharacteristic
568C3⋊(C3⋊C8)—41no—
569C3×C3⋊C8—21no—
570C3×C3⋊C8—41no—
571C3×C3⋊C8C4×D411yescharacteristic
572C3×C3⋊C8C4×D411yescharacteristic
573C2×#135—91no—
574C22×D8—31no—
575#568—181no—
576#518—61no—
577#509—31no—
578#509—91no—
579#509—92no—
580#509—92no—
581#509—91no—
582#509—91no—
583C2×SD32—92no—
584C2×D16—92no—
585C2×M32—91no—
586C2×M32—91no—
587#444—31no—
588#444—91no—
589#444—91no—
590#444—91no—
591#443—181no—
592#443—181no—
593#442—31no—
594#442—31no—
595#442—31no—
596#442D3211yescharacteristic, complemented
597C4×D8—61no—
598C4×D8—61no—
599C2×#108—91no—
600#427—31no—
601#421—181no—
602#418—61no—
603#405—31no—
604#365—31no—
605#365—91no—
606#365—91no—
607#365—91no—
608#361—31no—
609#361—91no—
610#361—91no—
611#361—91no—
612#360—31no—
613#360—91no—
614#360—91no—
615#360—91no—
616#347—31no—
617#347—91no—
618#347—91no—
619#347—91no—
620C24×C3—121no—
621C23×D3—41no—
622C3×#41—61no—
623C2×C3×D4—21no—
624C2×C3×D4—21no—
625C2×C3×D4—41no—
626C2×C3×D4—62no—
627C2×C3×D4—62no—
628C2×C3×D4—61no—
629C2×C3×D4—121no—
630C2×C3×D4—121no—
631C2×C3×D4—121no—
632C22×C3×C4—31no—
633C22×C3×C4—41no—
634C22×C3×C4—41no—
635C22×C3×C4—81no—
636C22×C3×C4—121no—
637C22×C3×C4—121no—
638C22×C3×C4—121no—
639C2×#67—41no—
640C2×#67—121no—
641C22×Dic3—41no—
642#239—61no—
643D3×Q8—61no—
644#237—61no—
645#237—121no—
646D3×D4—22no—
647D3×D4—22no—
648D3×D4—41no—
649D3×D4—41no—
650D3×D4—61no—
651D3×D4—121no—
652#235—21no—
653#235—61no—
654#235—61no—
655#235—61no—
656#235—61no—
657#235—121no—
658#235—121no—
659#235—121no—
660#235—121no—
661C2×D12—21no—
662C2×D12—61no—
663C2×C4×D3—41no—
664C2×C4×D3—41no—
665C2×C4×D3—121no—
666C2×C4×D3—121no—
667C2×C4×D3C2×#6711yescharacteristic
668C2×Dic6—61no—
669C3×Q16—31no—
670C3×SD16—61no—
671C3×D8—21no—
672C3×D8—21no—
673C3×D8—22no—
674C3×D8—32no—
675C3×D8—31no—
676C3×D8—41no—
677C3×D8—62no—
678C3×D8—62no—
679C3×D8—61no—
680C3×D8C2×C4×D312yes—
681C3×D8C2×C4×D312yes—
682C3×M16—61no—
683C3×M16—61no—
684C3×M16—61no—
685C3×M16—121no—
686C2×C3×C8—21no—
687C2×C3×C8—21no—
688C2×C3×C8—31no—
689C2×C3×C8—31no—
690C2×C3×C8—31no—
691C2×C3×C8—31no—
692C2×C3×C8—31no—
693C2×C3×C8—31no—
694C2×C3×C8—121no—
695C2×C3×C8D3×D411yescharacteristic
696C2×C3×C8C2×#6711yescharacteristic
697C2×C3×C8C23×D311yescharacteristic
698C2×C3×C8C23×D311yescharacteristic
699C3×C4⋊C4—21no—
700C3×C4⋊C4—21no—
701C3×C4⋊C4—41no—
702C3×C4⋊C4—61no—
703C3×C4⋊C4—61no—
704C3×C22⋊C4—41no—
705C3×C22⋊C4—41no—
706C3×C22⋊C4—61no—
707C3×C22⋊C4—81no—
708C3×C22⋊C4—121no—
709C3×C22⋊C4—121no—
710C3×C22⋊C4—121no—
711C3×C22⋊C4—121no—
712C3×C42—21no—
713C3×C42—31no—
714C3×C42—121no—
715C3×C42D3×D411yescharacteristic
716C3×C42C2×#6711yescharacteristic
717#217—41no—
718#216—61no—
719#215—61no—
720#214—61no—
721#213—22no—
722#213—22no—
723#213—61no—
724(C2×D3)⋊C4—21no—
725(C2×D3)⋊C4—41no—
726(C2×D3)⋊C4—41no—
727(C2×D3)⋊C4—41no—
728C4⋊Dic3—21no—
729Dic3⋊C4—21no—
730C4×Dic3—41no—
731C4×Dic3C2×#6711yescharacteristic
732#208—21no—
733#208—61no—
734#208—61no—
735#208—121no—
736#208—121no—
737#208—121no—
738C2×C3⋊C8—121no—
739C2×C3⋊C8—121no—
740C2×C3⋊C8C2×#6711yescharacteristic
741C2×C3⋊C8C2×#6711yescharacteristic
742Dic12—31no—
743Dic12—31no—
744Dic12—61no—
745Dic12—61no—
746Dic12C2×C4×D311yescharacteristic
747D24—21no—
748D24—31no—
749D24—31no—
750D24—61no—
751D24—61no—
752D24C2×C4×D312yes—
753D24C2×C4×D311yescharacteristic
754#204—21no—
755#204—61no—
756#204—61no—
757#204—61no—
758#204—61no—
759#204—121no—
760ΓL(1,𝔽25)—21no—
761ΓL(1,𝔽25)—21no—
762ΓL(1,𝔽25)—41no—
763ΓL(1,𝔽25)—121no—
764ΓL(1,𝔽25)—121no—
765ΓL(1,𝔽25)—121no—
766ΓL(1,𝔽25)—121no—
767ΓL(1,𝔽25)—121no—
768ΓL(1,𝔽25)—121no—
769ΓL(1,𝔽25)—241no—
770D3×C8—41no—
771D3×C8—121no—
772D3×C8—121no—
773D3×C8—121no—
774D3×C8—121no—
775D3×C8—121no—
776D3×C8—121no—
777D3×C8—241no—
778D3×C8C2×C4×D311yescharacteristic
779D3×C8C2×C4×D311yescharacteristic
780D3×C8#23511yescharacteristic
781D3×C8#23511yescharacteristic
782C3×C16—32no—
783C3×C16—61no—
784C3⋊C16—21no—
785C3⋊C16—32no—
786C3⋊C16—32no—
787C3⋊C16—62no—
788C3⋊C16—61no—
789C3⋊C16—61no—
790C3⋊C16—121no—
791C3⋊C16C2×C4×D312yes—
792C22×C32—42no—
793C22×C32—81no—
794C22×C32—81no—
795C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
796C2×C3⋊D3—41no—
797C2×C3×D3—41no—
798C2×C3×D3—41no—
799C2×C3×D3—42no—
800C2×C3×D3—81no—
801C2×C3×D3—81no—
802C2×C3×D3—162no—
803C2×C3×D3—162no—
804C2×C3×D3#44211yescharacteristic
805C2×C3×D3#44211yescharacteristic
806D32—161no—
807C32×C4—41no—
808C32×C4—81no—
809C32×C4C2×C4×D411yescharacteristic
810C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
811C3⋊Dic3—41no—
812C3×Dic3—41no—
813C3×Dic3—41no—
814C3×Dic3—81no—
815C3×Dic3#44211yescharacteristic
816C3×Dic3#44211yescharacteristic
817C2×#41—181no—
818C22×D4—61no—
819#135—31no—
820#135—91no—
821#135—91no—
822#135—91no—
823#135—181no—
824#135—181no—
825C2×Q16—91no—
826C2×SD16—181no—
827C2×D8—32no—
828C2×D8—32no—
829C2×D8—31no—
830C2×D8—61no—
831C2×D8—61no—
832C2×D8—61no—
833C2×D8—91no—
834C2×D8C2×D3211yescharacteristic
835#131—61no—
836#131—181no—
837#131—181no—
838#131—181no—
839#131—361no—
840#131—361no—
841C2×M16—31no—
842C2×M16—181no—
843C2×M16—361no—
844C2×M16—361no—
845C22×C8—31no—
846C4×D4—21no—
847C4×D4—61no—
848C4×D4—61no—
849C4×D4—61no—
850C4×D4—121no—
851C4×D4—121no—
852#117—31no—
853#117—61no—
854C2×C22⋊C4—121no—
855C2×C22⋊C4—121no—
856SD32—32no—
857SD32—92no—
858SD32—92no—
859SD32—92no—
860D16—32no—
861D16—92no—
862D16—92no—
863D16—92no—
864M32—31no—
865M32—31no—
866M32—92no—
867M32—91no—
868M32—91no—
869M32—181no—
870C2×C16—92no—
871C2×C16—181no—
872#108—31no—
873#108—91no—
874#108—181no—
875#107—61no—
876#106—31no—
877#106C2×D3211yescharacteristic
878#104—61no—
879#104—181no—
880#104—181no—
881#104—181no—
882#102—21no—
883#102—61no—
884#102—61no—
885#102—61no—
886#97—31no—
887#97C2×D3211yescharacteristic
888C4×C8—31no—
889C4×C8—31no—
890C23×C3—31no—
891C23×C3—41no—
892C23×C3—41no—
893C23×C3—81no—
894C23×C3—122no—
895C23×C3—122no—
896C23×C3—121no—
897C23×C3—481no—
898C23×C3—481no—
899C22×D3—41no—
900C22×D3—42no—
901C22×D3—42no—
902C22×D3—121no—
903C22×D3—121no—
904C22×D3—161no—
905C22×D3—161no—
906C22×D3#93211yescharacteristic
907C3×Q8—61no—
908C3×D4—22no—
909C3×D4—22no—
910C3×D4—42no—
911C3×D4—41no—
912C3×D4—41no—
913C3×D4—61no—
914C3×D4—62no—
915C3×D4—81no—
916C3×D4—122no—
917C3×D4—122no—
918C3×D4—121no—
919C3×D4—121no—
920C2×C3×C4—21no—
921C2×C3×C4—21no—
922C2×C3×C4—21no—
923C2×C3×C4—31no—
924C2×C3×C4—31no—
925C2×C3×C4—31no—
926C2×C3×C4—31no—
927C2×C3×C4—31no—
928C2×C3×C4—41no—
929C2×C3×C4—41no—
930C2×C3×C4—41no—
931C2×C3×C4—61no—
932C2×C3×C4—81no—
933C2×C3×C4—121no—
934C2×C3×C4—121no—
935C2×C3×C4—161no—
936C2×C3×C4—161no—
937C2×C3×C4—162no—
938C2×C3×C4—481no—
939C2×C3×C4—481no—
940C2×C3×C4—481no—
941C2×C3×C4C2×D3×D411yescharacteristic
942C2×C3×C4C22×#6711yescharacteristic
943#67—41no—
944#67—42no—
945#67—42no—
946#67—121no—
947#67—121no—
948#67—121no—
949#67—121no—
950#67—121no—
951#67—121no—
952#67—241no—
953C2×Dic3—21no—
954C2×Dic3—41no—
955C2×Dic3—121no—
956C2×Dic3—121no—
957C2×Dic3—161no—
958C2×Dic3#93211yescharacteristic
959D12—22no—
960D12—21no—
961D12—41no—
962D12—61no—
963D12—61no—
964D12—121no—
965D12—121no—
966D12—121no—
967C4×D3—41no—
968C4×D3—121no—
969C4×D3—121no—
970C4×D3—121no—
971C4×D3—121no—
972C4×D3—121no—
973C4×D3—121no—
974C4×D3—161no—
975C4×D3—161no—
976C4×D3—241no—
977C4×D3C4×#6711yescharacteristic
978C4×D3C4×#6711yescharacteristic
979C4×D3#94911yescharacteristic
980C4×D3#94911yescharacteristic
981Dic6—21no—
982Dic6—61no—
983Dic6—61no—
984Dic6—121no—
985Dic6—121no—
986Dic6—121no—
987C3×C8—21no—
988C3×C8—21no—
989C3×C8—21no—
990C3×C8—21no—
991C3×C8—31no—
992C3×C8—31no—
993C3×C8—41no—
994C3×C8—61no—
995C3×C8—121no—
996C3×C8C22×C4×D311yescharacteristic
997C3×C8C22×C4×D311yescharacteristic
998C3×C8C2×#23511yescharacteristic
999C3×C8D3×#4111yescharacteristic
1000C3⋊C8—21no—
1001C3⋊C8—41no—
1002C3⋊C8—121no—
1003C3⋊C8—121no—
1004C3⋊C8—241no—
1005C3⋊C8C4×#6711yescharacteristic
1006C3⋊C8C4×#6711yescharacteristic
1007C2×C32—21no—
1008C2×C32—82no—
1009C2×C32C2×#44211yescharacteristic
1010C3⋊D3—81no—
1011C3×D3—21no—
1012C3×D3—21no—
1013C3×D3—81no—
1014C3×D3—82no—
1015C24—121no—
1016#41—61no—
1017#41—181no—
1018#41—181no—
1019#41—181no—
1020#41—361no—
1021#41—361no—
1022C2×Q8—181no—
1023C2×D4—21no—
1024C2×D4—62no—
1025C2×D4—62no—
1026C2×D4—61no—
1027C2×D4—121no—
1028C2×D4—121no—
1029C2×D4—121no—
1030C2×D4—181no—
1031C2×D4—361no—
1032C22×C4—31no—
1033C22×C4—41no—
1034C22×C4—121no—
1035C22×C4—121no—
1036C22×C4—121no—
1037C22×C4—361no—
1038Q16—31no—
1039Q16—91no—
1040Q16—181no—
1041SD16—61no—
1042SD16—181no—
1043SD16—181no—
1044SD16—181no—
1045D8—21no—
1046D8—31no—
1047D8—32no—
1048D8—62no—
1049D8—62no—
1050D8—61no—
1051D8—91no—
1052D8—181no—
1053D8C4×D3212yes—
1054M16—61no—
1055M16—61no—
1056M16—61no—
1057M16—121no—
1058M16—181no—
1059M16—361no—
1060M16—361no—
1061M16—361no—
1062M16—361no—
1063C2×C8—31no—
1064C2×C8—31no—
1065C2×C8—31no—
1066C2×C8—31no—
1067C2×C8—31no—
1068C2×C8—31no—
1069C2×C8—121no—
1070C2×C8—361no—
1071C2×C8—361no—
1072C2×C8—361no—
1073C2×C8—361no—
1074C2×C8D3×#6711yescharacteristic
1075C2×C8C22×D3211yescharacteristic
1076C4⋊C4—21no—
1077C4⋊C4—61no—
1078C4⋊C4—61no—
1079C22⋊C4—41no—
1080C22⋊C4—61no—
1081C22⋊C4—121no—
1082C22⋊C4—121no—
1083C22⋊C4—121no—
1084C22⋊C4—121no—
1085C42—31no—
1086C42—121no—
1087C42D3×#6711yescharacteristic
1088C16—32no—
1089C16—61no—
1090C16—92no—
1091C16—181no—
1092C22×C3—21no—
1093C22×C3—31no—
1094C22×C3—31no—
1095C22×C3—42no—
1096C22×C3—42no—
1097C22×C3—82no—
1098C22×C3—81no—
1099C22×C3—81no—
1100C22×C3—81no—
1101C22×C3—81no—
1102C22×C3—121no—
1103C22×C3—121no—
1104C22×C3—122no—
1105C22×C3—161no—
1106C22×C3—161no—
1107C22×C3—241no—
1108C22×C3—241no—
1109C22×C3—482no—
1110C22×C3—482no—
1111C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1112C22×C3C2×#93211yescharacteristic
1113C2×D3—41no—
1114C2×D3—42no—
1115C2×D3—41no—
1116C2×D3—81no—
1117C2×D3—81no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—162no—
1121C2×D3—162no—
1122C2×D3—241no—
1123C2×D3—481no—
1124C2×D3—481no—
1125C2×D3#501411yescharacteristic
1126C2×D3#501411yescharacteristic
1127C3×C4—21no—
1128C3×C4—21no—
1129C3×C4—31no—
1130C3×C4—31no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—81no—
1134C3×C4—81no—
1135C3×C4—81no—
1136C3×C4—121no—
1137C3×C4—121no—
1138C3×C4—161no—
1139C3×C4—241no—
1140C3×C4C4×D3×D411yescharacteristic
1141C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1142C3×C4C2×C4×#6711yescharacteristic
1143C3×C4C2×#94911yescharacteristic
1144Dic3—41no—
1145Dic3—41no—
1146Dic3—81no—
1147Dic3—121no—
1148Dic3—121no—
1149Dic3—241no—
1150Dic3#501411yescharacteristic
1151Dic3#501411yescharacteristic
1152C32#3347111yescharacteristic, complemented, Sylow
1153C23—31no—
1154C23—41no—
1155C23—122no—
1156C23—122no—
1157C23—121no—
1158C23—361no—
1159C23—481no—
1160C23—481no—
1161Q8—61no—
1162Q8—181no—
1163Q8—361no—
1164D4—22no—
1165D4—41no—
1166D4—62no—
1167D4—61no—
1168D4—122no—
1169D4—122no—
1170D4—121no—
1171D4—121no—
1172D4—181no—
1173D4—361no—
1174D4—361no—
1175D4—361no—
1176D4—361no—
1177C2×C4—21no—
1178C2×C4—31no—
1179C2×C4—31no—
1180C2×C4—31no—
1181C2×C4—31no—
1182C2×C4—31no—
1183C2×C4—41no—
1184C2×C4—61no—
1185C2×C4—121no—
1186C2×C4—121no—
1187C2×C4—161no—
1188C2×C4—361no—
1189C2×C4—361no—
1190C2×C4—361no—
1191C2×C4—361no—
1192C2×C4—481no—
1193C2×C4—481no—
1194C2×C4—481no—
1195C2×C4C2×D3×#6711yescharacteristic
1196C8—21no—
1197C8—31no—
1198C8—31no—
1199C8—61no—
1200C8—121no—
1201C8—361no—
1202C8C2×C4×D3211yescharacteristic
1203C8D3×#23511yescharacteristic
1204C2×C3—21no—
1205C2×C3—21no—
1206C2×C3—21no—
1207C2×C3—41no—
1208C2×C3—61no—
1209C2×C3—61no—
1210C2×C3—82no—
1211C2×C3—82no—
1212C2×C3—162no—
1213C2×C3—242no—
1214C2×C3—241no—
1215C2×C3D3×#44211yescharacteristic
1216C2×C3C2×#501411yescharacteristic
1217D3—21no—
1218D3—21no—
1219D3—81no—
1220D3—82no—
1221D3—241no—
1222D3—241no—
1223D3—481no—
1224C22—31no—
1225C22—31no—
1226C22—42no—
1227C22—81no—
1228C22—81no—
1229C22—121no—
1230C22—121no—
1231C22—122no—
1232C22—241no—
1233C22—241no—
1234C22—361no—
1235C22—482no—
1236C22—482no—
1237C22—1441no—
1238C22D3×#93211yescharacteristic
1239C4—31no—
1240C4—31no—
1241C4—41no—
1242C4—81no—
1243C4—121no—
1244C4—121no—
1245C4—241no—
1246C4—361no—
1247C4C4×D3×#6711yescharacteristic
1248C4D3×#94911yescharacteristic
1249C3—21no—
1250C3#1094865811yescharacteristic, complemented
1251C3#1094866011yescharacteristic, complemented
1252C2—21no—
1253C2—61no—
1254C2—61no—
1255C2—82no—
1256C2—242no—
1257C2—241no—
1258C2—721no—
1259C2D3×#501411yescharacteristic
subgroupG/H
centerC2D3×#5014
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#442C22
socleC2×C32C2×#442
prime radicalD3×#5147C2
cosocleC2×C32×C8C24
hypercenter#442D32
hypocenterC32#33471
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #442

Complements

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

NH ≅ G/Ntype
2. #11861222C2semidirect
3. C3×#79867C2semidirect
4. #11797980C2semidirect
5. #11797978C2semidirect
6. #11797974C2semidirect
7. #11797973C2semidirect
8. #11797968C2semidirect
9. #11797966C2semidirect
10. C3×#70918C2semidirect
11. #11797947C2semidirect
12. #11797130C2semidirect
13. D3×#4563C2semidirect
14. #11796856C2semidirect
15. #11795944C2semidirect
22. C32×#442C22semidirect
24. #10592416C22semidirect
25. C3×#5152C22semidirect
28. C3×#4869C22semidirect
32. C3×#4717C22semidirect
33. C3×#4711C22semidirect
35. #10591033C4semidirect
36. #10591031C4semidirect
37. D3×#827C4semidirect
38. D3×#826C4semidirect
40. #10590918C22semidirect
41. #10590916C22semidirect
49. #10589429C22semidirect
50. #10589354C22semidirect
51. #10589353C22semidirect
52. #10589332C22semidirect
53. C3×#4563C22semidirect
54. C3×#4488C22semidirect
55. C3×#4487C22semidirect
56. C3×#4466C22semidirect
57. #10589138C22semidirect
58. #10589136C22semidirect
59. #10589127C22semidirect
60. #10589126C22semidirect
61. #10589125C22semidirect
62. #10589123C22semidirect
63. #10589105C22semidirect
64. #10589105C22semidirect
69. #79867D3semidirect
84. #70918D3semidirect
125. #63808C2×C4semidirect
126. #63807C2×C4semidirect
130. D3×Dic12C2×C4semidirect
131. D3×D24C2×C4semidirect
138. #63654C2×C4semidirect
139. #63653C2×C4semidirect
145. C3×#827C2×C4semidirect
146. C3×#826C2×C4semidirect
161. #63548C2×C4semidirect
162. #63547C2×C4semidirect
163. #63546C2×C4semidirect
164. #63545C2×C4semidirect
166. #63543C2×C4semidirect
168. D3×C3⋊C16C2×C4semidirect
184. C3×#442C2×D3semidirect
185. C3×#442C2×D3semidirect
193. #5152C2×D3semidirect
219. #4869C2×D3semidirect
230. #4717C2×D3semidirect
231. #4711C2×D3semidirect
245. #4563C2×D3semidirect
258. #4488C2×D3semidirect
264. #4487C2×D3semidirect
270. #4466C2×D3semidirect
476. #827C4×D3semidirect
483. #826C4×D3semidirect
596. #442D32semidirect
1152. C32#33471semidirect
1250. C3#10948658semidirect
1251. C3#10948660semidirect

Maximal subgroups

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

subgroupindex
D3×#51472
#118612222
C3×#798672
#117979802
#117979782
#117979742
#117979732
#117979682
#117979662
C3×#709182
#117979472
#117971302
D3×#45632
#117968562
#117959442
#109486603
#109486583