Finite Group Databasebeta

← #72222791

Subgroups — #72222791

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×#5193C211yesmaximal, characteristic
2C3×#79899C211yesmaximal, characteristic, complemented
3#11860692C211yesmaximal, characteristic, complemented
4#11797983C211yesmaximal, characteristic, complemented
5#11797981C211yesmaximal, characteristic, complemented
6#11797974C211yesmaximal, characteristic, complemented
7#11797972C211yesmaximal, characteristic, complemented
8#11797971C211yesmaximal, characteristic, complemented
9#11797969C211yesmaximal, characteristic, complemented
10C3×#70929C211yesmaximal, characteristic, complemented
11#11797953C211yesmaximal, characteristic, complemented
12#11797137C211yesmaximal, characteristic, complemented
13D3×#4495C211yesmaximal, characteristic, complemented
14#11796858C211yesmaximal, characteristic, complemented
15#11795944C211yesmaximal, characteristic, complemented
16#10948662—31nomaximal
17#10948658—31nomaximal
18C3×D3×#135C2211yescharacteristic
19C3×#5750—21no—
20C2×D3×D24C2211yescharacteristic
21#10593994—21no—
22C32×#444C2211yescharacteristic, complemented
23#10592892C2211yescharacteristic
24#10592410C2211yescharacteristic, complemented
25C3×#5197C2211yescharacteristic, complemented
26C3×#5193C2211yescharacteristic
27C3×#5144—21no—
28C3×#4894C2211yescharacteristic, complemented
29C3×D3×#108C2211yescharacteristic
30C3×#4824—21no—
31C3×#4821—21no—
32C3×#4717C2211yescharacteristic, complemented
33C3×#4711C2211yescharacteristic, complemented
34C3×#4708C2211yescharacteristic
35#10591038C412yescomplemented
36D3×#828C412yescomplemented
37#10591024C412yescomplemented
38D3×#826C412yescomplemented
39#10590939—21no—
40#10590771C2211yescharacteristic, complemented
41#10590768C2211yescharacteristic, complemented
42#10590745—21no—
43#10590706C2211yescharacteristic
44#10590634C2211yescharacteristic
45#10590630C2211yescharacteristic
46D3×#812C2211yescharacteristic
47D3×#812C2211yescharacteristic
48C4×#3714—21no—
49#10589432C2211yescharacteristic, complemented
50#10589361C2211yescharacteristic, complemented
51#10589360C2211yescharacteristic, complemented
52#10589332C2211yescharacteristic, complemented
53C3×#4566C2211yescharacteristic, complemented
54C3×#4495C2211yescharacteristic, complemented
55C3×#4494C2211yescharacteristic, complemented
56C3×#4466C2211yescharacteristic, complemented
57#10589138C2211yescharacteristic, complemented
58#10589137C2211yescharacteristic, complemented
59#10589128C2211yescharacteristic, complemented
60#10589126C2211yescharacteristic, complemented
61#10589124C2211yescharacteristic, complemented
62#10589123C2211yescharacteristic, complemented
63#10589105C2211yescharacteristic, complemented
64#10589105C2211yescharacteristic, complemented
65C3×#2957—31no—
66C2×#5193—31no—
67D3×#509—31no—
68#79899D311yescharacteristic, complemented
69#79867—31no—
70#78561—31no—
71C3×AGL(1,ℤ/16)—31no—
72#72076—31no—
73#71515—31no—
74#70929—31no—
75#70929—31no—
76#70929—31no—
77#70929—31no—
78#70929—31no—
79#70929—31no—
80#70929—31no—
81#70929—31no—
82#70929—61no—
83#70929D311yescharacteristic, complemented
84#70918—31no—
85C2×#4495—31no—
86#70685—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—
96C3×D3×#41—21no—
97C2×D3×D12—21no—
98C32×#135C2311yescharacteristic
99C32×#131—21no—
100C2×#3745C2311yescharacteristic
101C4×C4⋊(C3⋊D3)—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
110C3×#907—21no—
111C3×#907—41no—
112C3×D3×M16—21no—
113C3×D3×M16—41no—
114C3×#904C2311yescharacteristic
115C2×C3×D24C2311yescharacteristic
116C3×#901—21no—
117C3×#901—41no—
118C2×C3×ΓL(1,𝔽25)—41no—
119C2×C3×ΓL(1,𝔽25)D411yescharacteristic
120C2×C3×D3×C8C2311yescharacteristic
121C3×C4×D12—21no—
122C3×#872D411yescharacteristic
123#63921—41no—
124D3×(C2×D3)⋊C4—41no—
125#63904—41no—
126#63894—21no—
127Dic3×D12—21no—
128#63881—41no—
129#63841—21no—
130C2×#3714—21no—
131D3×D24—21no—
132D3×D24—21no—
133D3×D24C2×C412yes—
134D3×D24C2×C412yes—
135C32×#108C2311yescharacteristic
136C32×#104—21no—
137C32×#97C2311yescharacteristic
138#63655C2×C412yescomplemented
139#63653C2×C412yescomplemented
140#63648—21no—
141#63644C2311yescharacteristic
142#63639C2311yescharacteristic
143#63639C2311yescharacteristic
144C3×#837—21no—
145C3×#828C2×C412yescomplemented
146C3×#826C2×C412yescomplemented
147C3×#825—21no—
148C3×#822—21no—
149C3×#821—21no—
150C3×#819C2311yescharacteristic
151C3×#817C2311yescharacteristic
152C3×#815C2311yescharacteristic
153C3×C8×Dic3D411yescharacteristic
154C3×#812C2311yescharacteristic
155C3×#812C2311yescharacteristic
156C3×#805—21no—
157C3×C4×C3⋊C8D411yescharacteristic
158#63575—21no—
159#63564—21no—
160#63563—21no—
161#63549C2×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
170C2×C3×#135—31no—
171C3×#568—61no—
172D3×#135C2×D311yescharacteristic
173C2×D3×D8—31no—
174#5750—21no—
175C22×D24—31no—
176#5545—61no—
177#5521—61no—
178C3×#509—31no—
179C3×#444—21no—
180C3×#444—31no—
181C3×#444—31no—
182C3×#444—31no—
183C3×#444C2×D311yescharacteristic, complemented
184C3×#444C2×D311yescharacteristic, complemented
185C3×#443—61no—
186C3×#443—61no—
187C3×#442—31no—
188C2×C3×#108—31no—
189C3×#421—61no—
190C3×#405—31no—
191#5197C2×D311yescharacteristic, complemented
192#5193—31no—
193#5193—31no—
194#5193—31no—
195#5193—32no—
196#5193—32no—
197#5193—31no—
198#5193—61no—
199#5193C2×D311yescharacteristic
200C2×#828—32no—
201#5152—31no—
202#5147—31no—
203C2×#826—32no—
204#5144—21no—
205#5131—61no—
206#5106—31no—
207C2×#812—31no—
208C2×#812—31no—
209C4×#213—61no—
210#4914—32no—
211D3×SD32—32no—
212#4911—32no—
213D3×D16—32no—
214#4908—31no—
215D3×M32—31no—
216D3×M32—31no—
217#4894C2×D311yescharacteristic, complemented
218D3×#108C2×D311yescharacteristic
219#4869—31no—
220#4860—31no—
221#4824—21no—
222#4821—21no—
223#4770—61no—
224#4756—61no—
225#4717C2×D311yescharacteristic, complemented
226#4711—31no—
227#4711—31no—
228#4711—31no—
229#4711—31no—
230#4711—61no—
231#4711C2×D311yescharacteristic, complemented
232#4708C2×D311yescharacteristic
233C4×D24—61no—
234C4×D24—61no—
235C3×#365—31no—
236C3×#361—31no—
237C3×#360—31no—
238C3×#347—31no—
239#4566—31no—
240#4566—31no—
241#4566—31no—
242#4566—31no—
243#4566—61no—
244#4566C2×D311yescharacteristic, complemented
245#4563—31no—
246#4518—31no—
247#4516—31no—
248#4513—31no—
249#4512—31no—
250#4512—31no—
251#4495—31no—
252#4495—31no—
253#4495—31no—
254#4495—31no—
255#4495—61no—
256#4495C2×D311yescharacteristic, complemented
257#4494—31no—
258#4494—31no—
259#4494—31no—
260#4494—31no—
261#4494—61no—
262#4494C2×D311yescharacteristic, complemented
263#4488—31no—
264#4487—31no—
265#4466—31no—
266#4466—31no—
267#4466—31no—
268#4466—31no—
269#4466—61no—
270#4466C2×D311yescharacteristic, complemented
271C22×D32—41no—
272C32×#41—21no—
273C2×C4⋊(C3⋊D3)—21no—
274C2×C4×C3⋊D3—41no—
275C3×#239—21no—
276C3×D3×Q8—21no—
277C3×#237—21no—
278C3×#237—41no—
279C3×D3×D4—21no—
280C3×D3×D4—41no—
281C3×#235—21no—
282C3×#235—41no—
283C2×C3×D12—21no—
284C2×C3×C4×D3—41no—
285C2×C3×C4×D3—41no—
286C2×C3×C4×D3C2×D411yescharacteristic
287C2×#626—41no—
288C2×#624—41no—
289C2×D3×Dic3—41no—
290D3×D12—22no—
291D3×D12—22no—
292D3×D12—41no—
293D3×D12—41no—
294C32×Q16C22×C411yescharacteristic
295C32×SD16—21no—
296C32×D8C22×C411yescharacteristic
297C32×M16—21no—
298C32×M16—41no—
299C2×C32×C8—41no—
300C2×C32×C8C2×D411yescharacteristic
301C2×C32×C8C2411yescharacteristic
302C32×C42C2×D411yescharacteristic
303#3752—41no—
304C4⋊(C3⋊Dic3)—21no—
305#3745—21no—
306#3745C22×C412yes—
307C3×#216—21no—
308C3×#215—21no—
309C3×#214—21no—
310C3×#213—21no—
311C3×(C2×D3)⋊C4—21no—
312C3×(C2×D3)⋊C4—41no—
313C3×C4⋊Dic3—21no—
314C3×Dic3⋊C4—21no—
315C3×C4×Dic3C2×D411yescharacteristic
316C3×#208—21no—
317C3×#208—41no—
318C2×C3×C3⋊C8—41no—
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×ΓL(1,𝔽25)—41no—
330C3×ΓL(1,𝔽25)—41no—
331C3×D3×C8—41no—
332C3×D3×C8—41no—
333C3×D3×C8—41no—
334C3×D3×C8C22×C411yescharacteristic
335C3×D3×C8C22×C411yescharacteristic
336C3×D3×C8#4111yescharacteristic
337C3×D3×C8#4111yescharacteristic
338#3722—41no—
339(C2×D3)⋊Dic3—41no—
340(C2×D3)⋊Dic3—41no—
341Dic32—41no—
342#3714—22no—
343#3714—22no—
344C3⋊(C3⋊C16)—21no—
345C3⋊(C3⋊C16)C22×C412yes—
346C3×C3⋊C16—21no—
347C3×C3⋊C16C22×C412yes—
348C2×#509—91no—
349#2957—31no—
350#2948—91no—
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—
363C2×C3×#41—61no—
364D3×#41—21no—
365C2×D3×D4—61no—
366C22×D12—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×SD16—61no—
377C2×C3×D8—31no—
378C2×C3×D8—31no—
379C3×#131—21no—
380C3×#131—21no—
381C3×#131—41no—
382C3×#131—61no—
383C3×#131—61no—
384C3×#131—61no—
385C3×#131—121no—
386C3×#131—121no—
387C2×C3×M16—31no—
388C2×C3×M16—61no—
389C2×C3×M16—121no—
390C2×C3×M16—121no—
391C22×C3×C8—31no—
392C3×C4×D4—61no—
393C3×#117—31no—
394#950—21no—
395#948—21no—
396D4×Dic3—61no—
397C2×#213—61no—
398C4×#67—121no—
399C2×(C2×D3)⋊C4—121no—
400#926—61no—
401#919C4×D311yescharacteristic, complemented
402D3×Q16C4×D311yescharacteristic, complemented
403#916—21no—
404D3×SD16—21no—
405#912C4×D311yescharacteristic, complemented
406D3×D8—32no—
407D3×D8—32no—
408D3×D8—61no—
409D3×D8—61no—
410D3×D8C4×D311yescharacteristic, complemented
411#907—21no—
412#907—41no—
413D3×M16—21no—
414D3×M16—41no—
415#904C22×D311yescharacteristic
416C2×D24—31no—
417C2×D24—31no—
418C2×D24—32no—
419C2×D24—32no—
420C2×D24—61no—
421C2×D24—61no—
422C2×D24—61no—
423C2×D24—61no—
424C2×D24C22×D311yescharacteristic
425#901—21no—
426#901—41no—
427C2×ΓL(1,𝔽25)—41no—
428C2×ΓL(1,𝔽25)#6711yescharacteristic
429C2×D3×C8C22×D311yescharacteristic
430#893—61no—
431#893—121no—
432#893—121no—
433#892—61no—
434#67⋊C4—121no—
435D3×C22⋊C4—121no—
436D3×C22⋊C4—121no—
437D3×C22⋊C4—121no—
438C4×D12—21no—
439C4×D12—61no—
440C4×D12—61no—
441C4×D12—61no—
442C4×D12—61no—
443C4×D12—121no—
444#872#6711yescharacteristic
445C3×SD32—32no—
446C3×D16—32no—
447C3×M32—31no—
448C3×M32—31no—
449C3×#108—21no—
450C3×#108—31no—
451C3×#108—61no—
452C3×#108C22×D311yescharacteristic
453C3×#108C22×D311yescharacteristic
454C3×#106—31no—
455C3×#104—21no—
456C3×#104—21no—
457C3×#104—41no—
458C3×#104—61no—
459C3×#104—61no—
460C3×#104—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—21no—
469#832—61no—
470#828—32no—
471#828—32no—
472#828—32no—
473#828—32no—
474#828—62no—
475#828C4×D312yescomplemented
476#827—32no—
477#826—32no—
478#826—32no—
479#826—32no—
480#826—32no—
481#826—32no—
482#826—62no—
483#826C4×D312yescomplemented
484#825—21no—
485#822—21no—
486#821—21no—
487#821—61no—
488#821—61no—
489#821—61no—
490#821—61no—
491#821—121no—
492#819C22×D311yescharacteristic
493#818—61no—
494#817—31no—
495#817—31no—
496#817—61no—
497#817C22×D311yescharacteristic
498#815C22×D311yescharacteristic
499C8×Dic3#6711yescharacteristic
500#812—31no—
501#812—31no—
502#812—32no—
503#812—31no—
504#812—31no—
505#812—61no—
506#812—61no—
507#812—61no—
508#812C22×D311yescharacteristic
509#812C22×D311yescharacteristic
510C2×C3⋊C16—32no—
511C2×C3⋊C16—61no—
512#809—61no—
513#807—61no—
514#805—21no—
515C4×C3⋊C8#6711yescharacteristic
516#800—32no—
517D48—32no—
518#798—32no—
519#798—61no—
520D3×C16—32no—
521D3×C16—61no—
522C22×C3⋊D3—41no—
523C22×C3×D3—41no—
524C22×C3×D3—41no—
525C22×C3×D3AGL(1,ℤ/8)11yescharacteristic
526C2×D32—42no—
527C2×D32—42no—
528C2×D32—161no—
529C2×D32—161no—
530C32×Q8—21no—
531C32×D4—21no—
532C32×D4—41no—
533C2×C32×C4—21no—
534C2×C32×C4—41no—
535C2×C32×C4C22×D411yescharacteristic
536C2×C3⋊Dic3—41no—
537C4⋊(C3⋊D3)—22no—
538C4⋊(C3⋊D3)—41no—
539C4×C3⋊D3—161no—
540C3×#67—41no—
541C3×#67—41no—
542C3×#67—41no—
543C2×C3×Dic3—21no—
544C2×C3×Dic3—41no—
545C2×C3×Dic3—41no—
546C2×C3×Dic3AGL(1,ℤ/8)11yescharacteristic
547C3×D12—22no—
548C3×D12—21no—
549C3×D12—41no—
550C3×D12—41no—
551C3×C4×D3—41no—
552C3×C4×D3—41no—
553C3×C4×D3—41no—
554C3×C4×D3—161no—
555C3×C4×D3C4×D411yescharacteristic
556C3×C4×D3C4×D411yescharacteristic
557C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
558C3×C4×D3AGL(1,ℤ/8)11yescharacteristic
559C3×Dic6—21no—
560C3×Dic6—41no—
561#626—42no—
562#626—42no—
563#624—161no—
564D3×Dic3—161no—
565C32×C8—21no—
566C32×C8—41no—
567C32×C8C23×C411yescharacteristic
568C32×C8C2×#4111yescharacteristic
569C3×C3⋊C8—21no—
570C3×C3⋊C8—41no—
571C3×C3⋊C8C4×D411yescharacteristic
572C3×C3⋊C8C4×D411yescharacteristic
573C2×#135—31no—
574C22×D8—91no—
575#568—61no—
576#518—181no—
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—31no—
589#444—31no—
590#444D3211yescharacteristic, complemented
591#443—61no—
592#443—61no—
593#442—31no—
594#442—91no—
595#442—91no—
596#442—91no—
597C4×D8—181no—
598C4×D8—181no—
599C2×#108—31no—
600#427—91no—
601#421—61no—
602#418—181no—
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—
620C23×D3—121no—
621C23×D3—121no—
622C3×#41—21no—
623C3×#41—21no—
624C3×#41—41no—
625C3×#41—61no—
626C3×#41—61no—
627C3×#41—61no—
628C3×#41—121no—
629C3×#41—121no—
630C2×C3×Q8—61no—
631C2×C3×D4—61no—
632C2×C3×D4—61no—
633C2×C3×D4—121no—
634C22×C3×C4—31no—
635C22×C3×C4—121no—
636C22×C3×C4—121no—
637C2×#67—121no—
638C22×Dic3—121no—
639#239—21no—
640D3×Q8—21no—
641#237—21no—
642#237—41no—
643D3×D4—21no—
644D3×D4—41no—
645D3×D4—62no—
646D3×D4—62no—
647D3×D4—121no—
648D3×D4—121no—
649#235—21no—
650#235—41no—
651C2×D12—21no—
652C2×D12—62no—
653C2×D12—62no—
654C2×D12—61no—
655C2×D12—61no—
656C2×D12—121no—
657C2×D12—121no—
658C2×D12—121no—
659C2×D12—121no—
660C2×C4×D3—41no—
661C2×C4×D3—41no—
662C2×C4×D3—121no—
663C2×C4×D3—121no—
664C2×C4×D3—121no—
665C2×C4×D3—121no—
666C2×C4×D3—121no—
667C2×C4×D3—241no—
668C2×C4×D3C2×#6711yescharacteristic
669C3×Q16—21no—
670C3×Q16—31no—
671C3×Q16—61no—
672C3×Q16C2×C4×D311yescharacteristic
673C3×Q16C2×C4×D311yescharacteristic
674C3×SD16—21no—
675C3×SD16—21no—
676C3×SD16—41no—
677C3×SD16—61no—
678C3×SD16—61no—
679C3×SD16—61no—
680C3×D8—21no—
681C3×D8—31no—
682C3×D8—32no—
683C3×D8—61no—
684C3×D8—61no—
685C3×D8C2×C4×D311yescharacteristic
686C3×D8C2×C4×D311yescharacteristic
687C3×M16—21no—
688C3×M16—21no—
689C3×M16—41no—
690C3×M16—41no—
691C3×M16—41no—
692C3×M16—61no—
693C3×M16—61no—
694C3×M16—61no—
695C3×M16—81no—
696C3×M16—121no—
697C3×M16—121no—
698C3×M16—121no—
699C3×M16—121no—
700C2×C3×C8—21no—
701C2×C3×C8—21no—
702C2×C3×C8—31no—
703C2×C3×C8—31no—
704C2×C3×C8—31no—
705C2×C3×C8—31no—
706C2×C3×C8—31no—
707C2×C3×C8—31no—
708C2×C3×C8—41no—
709C2×C3×C8—41no—
710C2×C3×C8—81no—
711C2×C3×C8—121no—
712C2×C3×C8—121no—
713C2×C3×C8—121no—
714C2×C3×C8—121no—
715C2×C3×C8D3×D411yescharacteristic
716C2×C3×C8C2×#6711yescharacteristic
717C2×C3×C8C23×D311yescharacteristic
718C2×C3×C8C23×D311yescharacteristic
719C3×C4⋊C4—61no—
720C3×C4⋊C4—61no—
721C3×C22⋊C4—61no—
722C3×C22⋊C4—121no—
723C3×C42—21no—
724C3×C42—31no—
725C3×C42D3×D411yescharacteristic
726C3×C42C2×#6711yescharacteristic
727#217—121no—
728#217—121no—
729#216—21no—
730#215—21no—
731#214—21no—
732#213—21no—
733#213—62no—
734#213—62no—
735(C2×D3)⋊C4—21no—
736(C2×D3)⋊C4—41no—
737(C2×D3)⋊C4—121no—
738(C2×D3)⋊C4—121no—
739(C2×D3)⋊C4—121no—
740(C2×D3)⋊C4—121no—
741(C2×D3)⋊C4—121no—
742(C2×D3)⋊C4—121no—
743(C2×D3)⋊C4—241no—
744C4⋊Dic3—21no—
745C4⋊Dic3—61no—
746C4⋊Dic3—61no—
747C4⋊Dic3—121no—
748Dic3⋊C4—21no—
749C4×Dic3—121no—
750C4×Dic3—121no—
751C4×Dic3C2×#6711yescharacteristic
752#208—21no—
753#208—41no—
754C2×C3⋊C8—41no—
755C2×C3⋊C8C2×#6711yescharacteristic
756C2×C3⋊C8C2×#6711yescharacteristic
757Dic12C2×C4×D311yescharacteristic
758D24—21no—
759D24—32no—
760D24—32no—
761D24—62no—
762D24—62no—
763D24—62no—
764D24—61no—
765D24—61no—
766D24—121no—
767D24C2×C4×D311yescharacteristic
768D24C2×C4×D312yes—
769#204—21no—
770ΓL(1,𝔽25)—21no—
771ΓL(1,𝔽25)—21no—
772ΓL(1,𝔽25)—41no—
773ΓL(1,𝔽25)—41no—
774ΓL(1,𝔽25)—41no—
775D3×C8—41no—
776D3×C8—41no—
777D3×C8—41no—
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—41no—
793C22×C32C2×AGL(1,ℤ/8)11yescharacteristic
794C2×C3⋊D3—42no—
795C2×C3⋊D3—81no—
796C2×C3⋊D3—81no—
797C2×C3×D3—41no—
798C2×C3×D3—42no—
799C2×C3×D3—41no—
800C2×C3×D3—81no—
801C2×C3×D3—81no—
802C2×C3×D3—161no—
803C2×C3×D3#44211yescharacteristic
804C2×C3×D3#44211yescharacteristic
805D32—162no—
806D32—162no—
807C32×C4—41no—
808C32×C4—41no—
809C32×C4C2×C4×D411yescharacteristic
810C32×C4C2×AGL(1,ℤ/8)11yescharacteristic
811C3⋊Dic3—81no—
812C3×Dic3—41no—
813C3×Dic3—41no—
814C3×Dic3—81no—
815C3×Dic3#44211yescharacteristic
816C3×Dic3#44211yescharacteristic
817C2×#41—61no—
818C22×D4—181no—
819#135—31no—
820#135—31no—
821#135—31no—
822#135—61no—
823#135—61no—
824#135C2×D3211yescharacteristic
825C2×Q16—31no—
826C2×SD16—61no—
827C2×D8—31no—
828C2×D8—31no—
829C2×D8—92no—
830C2×D8—92no—
831C2×D8—91no—
832C2×D8—181no—
833C2×D8—181no—
834C2×D8—181no—
835#131—21no—
836#131—61no—
837#131—61no—
838#131—61no—
839#131—121no—
840#131—121no—
841C2×M16—31no—
842C2×M16—61no—
843C2×M16—121no—
844C2×M16—121no—
845C22×C8—31no—
846C4×D4—61no—
847C4×D4—181no—
848C4×D4—181no—
849C4×D4—181no—
850C4×D4—361no—
851C4×D4—361no—
852#117—31no—
853#117—181no—
854C2×C22⋊C4—361no—
855C2×C22⋊C4—361no—
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—61no—
874#108C2×D3211yescharacteristic
875#107—181no—
876#106—31no—
877#106—91no—
878#104—21no—
879#104—61no—
880#104—61no—
881#104—61no—
882#102—61no—
883#102—181no—
884#102—181no—
885#102—181no—
886#97—31no—
887#97C2×D3211yescharacteristic
888C4×C8—31no—
889C4×C8—31no—
890C23×C3—31no—
891C23×C3—121no—
892C23×C3—121no—
893C22×D3—41no—
894C22×D3—41no—
895C22×D3—122no—
896C22×D3—122no—
897C22×D3—121no—
898C22×D3—121no—
899C22×D3—122no—
900C22×D3—122no—
901C22×D3—241no—
902C22×D3—481no—
903C22×D3—481no—
904C22×D3—481no—
905C22×D3—481no—
906C22×D3#94911yescharacteristic
907C3×Q8—21no—
908C3×Q8—21no—
909C3×Q8—41no—
910C3×Q8—61no—
911C3×Q8—121no—
912C3×D4—21no—
913C3×D4—21no—
914C3×D4—41no—
915C3×D4—41no—
916C3×D4—41no—
917C3×D4—62no—
918C3×D4—61no—
919C3×D4—81no—
920C3×D4—121no—
921C3×D4—121no—
922C3×D4—121no—
923C3×D4—121no—
924C3×D4—121no—
925C2×C3×C4—21no—
926C2×C3×C4—21no—
927C2×C3×C4—21no—
928C2×C3×C4—31no—
929C2×C3×C4—31no—
930C2×C3×C4—31no—
931C2×C3×C4—31no—
932C2×C3×C4—31no—
933C2×C3×C4—41no—
934C2×C3×C4—41no—
935C2×C3×C4—41no—
936C2×C3×C4—61no—
937C2×C3×C4—81no—
938C2×C3×C4—121no—
939C2×C3×C4—121no—
940C2×C3×C4—121no—
941C2×C3×C4—121no—
942C2×C3×C4—121no—
943C2×C3×C4—481no—
944C2×C3×C4C2×D3×D411yescharacteristic
945C2×C3×C4C22×#6711yescharacteristic
946#67—41no—
947#67—41no—
948#67—41no—
949#67—122no—
950#67—122no—
951C2×Dic3—21no—
952C2×Dic3—41no—
953C2×Dic3—41no—
954C2×Dic3—121no—
955C2×Dic3—121no—
956C2×Dic3—241no—
957C2×Dic3—481no—
958C2×Dic3#94911yescharacteristic
959D12—21no—
960D12—22no—
961D12—41no—
962D12—41no—
963D12—62no—
964D12—62no—
965D12—122no—
966D12—122no—
967D12—122no—
968D12—121no—
969D12—121no—
970D12—241no—
971C4×D3—41no—
972C4×D3—41no—
973C4×D3—41no—
974C4×D3—161no—
975C4×D3—481no—
976C4×D3—481no—
977C4×D3—481no—
978C4×D3—481no—
979C4×D3—481no—
980C4×D3—482no—
981C4×D3C4×#6711yescharacteristic
982C4×D3C4×#6711yescharacteristic
983C4×D3#93211yescharacteristic
984C4×D3#93211yescharacteristic
985Dic6—21no—
986Dic6—41no—
987C3×C8—21no—
988C3×C8—21no—
989C3×C8—21no—
990C3×C8—21no—
991C3×C8—31no—
992C3×C8—31no—
993C3×C8—41no—
994C3×C8—41no—
995C3×C8—41no—
996C3×C8—61no—
997C3×C8—81no—
998C3×C8—121no—
999C3×C8C22×C4×D311yescharacteristic
1000C3×C8C22×C4×D311yescharacteristic
1001C3×C8C2×#23511yescharacteristic
1002C3×C8D3×#4111yescharacteristic
1003C3⋊C8—21no—
1004C3⋊C8—41no—
1005C3⋊C8C4×#6711yescharacteristic
1006C3⋊C8C4×#6711yescharacteristic
1007C2×C32—21no—
1008C2×C32—81no—
1009C2×C32C2×#44211yescharacteristic
1010C3⋊D3—82no—
1011C3×D3—21no—
1012C3×D3—21no—
1013C3×D3—82no—
1014C3×D3—81no—
1015C24—361no—
1016#41—21no—
1017#41—61no—
1018#41—61no—
1019#41—61no—
1020#41—121no—
1021#41—121no—
1022C2×Q8—61no—
1023C2×D4—61no—
1024C2×D4—61no—
1025C2×D4—121no—
1026C2×D4—182no—
1027C2×D4—182no—
1028C2×D4—181no—
1029C2×D4—361no—
1030C2×D4—361no—
1031C2×D4—361no—
1032C22×C4—31no—
1033C22×C4—121no—
1034C22×C4—121no—
1035C22×C4—361no—
1036C22×C4—361no—
1037C22×C4—361no—
1038Q16—31no—
1039Q16—61no—
1040Q16C4×D3211yescharacteristic
1041SD16—21no—
1042SD16—61no—
1043SD16—61no—
1044SD16—61no—
1045D8—32no—
1046D8—31no—
1047D8—61no—
1048D8—61no—
1049D8—92no—
1050D8—182no—
1051D8—182no—
1052D8—181no—
1053D8C4×D3211yescharacteristic
1054M16—21no—
1055M16—41no—
1056M16—61no—
1057M16—61no—
1058M16—61no—
1059M16—121no—
1060M16—121no—
1061M16—121no—
1062M16—121no—
1063C2×C8—31no—
1064C2×C8—31no—
1065C2×C8—31no—
1066C2×C8—31no—
1067C2×C8—31no—
1068C2×C8—31no—
1069C2×C8—41no—
1070C2×C8—121no—
1071C2×C8—121no—
1072C2×C8—121no—
1073C2×C8—121no—
1074C2×C8D3×#6711yescharacteristic
1075C2×C8C22×D3211yescharacteristic
1076C4⋊C4—61no—
1077C4⋊C4—61no—
1078C4⋊C4—181no—
1079C22⋊C4—61no—
1080C22⋊C4—121no—
1081C22⋊C4—361no—
1082C22⋊C4—361no—
1083C22⋊C4—361no—
1084C22⋊C4—361no—
1085C42—31no—
1086C42—361no—
1087C42D3×#6711yescharacteristic
1088C16—32no—
1089C16—61no—
1090C16—92no—
1091C16—181no—
1092C22×C3—21no—
1093C22×C3—31no—
1094C22×C3—31no—
1095C22×C3—41no—
1096C22×C3—41no—
1097C22×C3—81no—
1098C22×C3—121no—
1099C22×C3—122no—
1100C22×C3—121no—
1101C22×C3—241no—
1102C22×C3—241no—
1103C22×C3—481no—
1104C22×C3D3×AGL(1,ℤ/8)11yescharacteristic
1105C22×C3C2×#94911yescharacteristic
1106C2×D3—41no—
1107C2×D3—41no—
1108C2×D3—42no—
1109C2×D3—81no—
1110C2×D3—81no—
1111C2×D3—122no—
1112C2×D3—122no—
1113C2×D3—161no—
1114C2×D3—242no—
1115C2×D3—241no—
1116C2×D3—241no—
1117C2×D3—241no—
1118C2×D3—241no—
1119C2×D3—481no—
1120C2×D3—481no—
1121C2×D3—482no—
1122C2×D3—482no—
1123C2×D3—482no—
1124C2×D3—482no—
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—41no—
1134C3×C4—41no—
1135C3×C4—81no—
1136C3×C4—81no—
1137C3×C4—121no—
1138C3×C4—121no—
1139C3×C4—241no—
1140C3×C4C4×D3×D411yescharacteristic
1141C3×C4D3×AGL(1,ℤ/8)11yescharacteristic
1142C3×C4C2×C4×#6711yescharacteristic
1143C3×C4C2×#93211yescharacteristic
1144Dic3—41no—
1145Dic3—41no—
1146Dic3—81no—
1147Dic3—241no—
1148Dic3—241no—
1149Dic3—481no—
1150Dic3#501411yescharacteristic
1151Dic3#501411yescharacteristic
1152C32#3347111yescharacteristic, complemented, Sylow
1153C23—31no—
1154C23—121no—
1155C23—121no—
1156C23—362no—
1157C23—362no—
1158C23—361no—
1159C23—1441no—
1160C23—1441no—
1161Q8—21no—
1162Q8—61no—
1163Q8—121no—
1164D4—21no—
1165D4—41no—
1166D4—62no—
1167D4—61no—
1168D4—121no—
1169D4—121no—
1170D4—121no—
1171D4—121no—
1172D4—121no—
1173D4—182no—
1174D4—362no—
1175D4—362no—
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—121no—
1188C2×C4—121no—
1189C2×C4—121no—
1190C2×C4—361no—
1191C2×C4—481no—
1192C2×C4—1441no—
1193C2×C4—1441no—
1194C2×C4—1441no—
1195C2×C4C2×D3×#6711yescharacteristic
1196C8—21no—
1197C8—31no—
1198C8—31no—
1199C8—41no—
1200C8—61no—
1201C8—121no—
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—81no—
1211C2×C3—81no—
1212C2×C3—161no—
1213C2×C3—241no—
1214C2×C3—242no—
1215C2×C3D3×#44211yescharacteristic
1216C2×C3C2×#501411yescharacteristic
1217D3—21no—
1218D3—21no—
1219D3—82no—
1220D3—81no—
1221D3—242no—
1222D3—242no—
1223D3—482no—
1224C22—31no—
1225C22—31no—
1226C22—41no—
1227C22—121no—
1228C22—121no—
1229C22—122no—
1230C22—241no—
1231C22—241no—
1232C22—362no—
1233C22—481no—
1234C22—721no—
1235C22—721no—
1236C22—1442no—
1237C22—1442no—
1238C22D3×#94911yescharacteristic
1239C4—31no—
1240C4—31no—
1241C4—41no—
1242C4—41no—
1243C4—121no—
1244C4—121no—
1245C4—241no—
1246C4—721no—
1247C4C4×D3×#6711yescharacteristic
1248C4D3×#93211yescharacteristic
1249C3—21no—
1250C3#1094865811yescharacteristic, complemented
1251C3#1094866211yescharacteristic, complemented
1252C2—21no—
1253C2—61no—
1254C2—61no—
1255C2—81no—
1256C2—242no—
1257C2—241no—
1258C2—722no—
1259C2D3×#501411yescharacteristic
subgroupG/H
centerC2D3×#5014
commutatorC32×C8C23×C4
FrattiniC2×C8C22×D32
FittingC32×#444C22
socleC2×C32C2×#442
prime radicalD3×#5193C2
cosocleC2×C32×C8C24
hypercenter#444D32
hypocenterC32#33471
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ #97 ◁ #444

Complements

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

NH ≅ G/Ntype
2. C3×#79899C2semidirect
3. #11860692C2semidirect
4. #11797983C2semidirect
5. #11797981C2semidirect
6. #11797974C2semidirect
7. #11797972C2semidirect
8. #11797971C2semidirect
9. #11797969C2semidirect
10. C3×#70929C2semidirect
11. #11797953C2semidirect
12. #11797137C2semidirect
13. D3×#4495C2semidirect
14. #11796858C2semidirect
15. #11795944C2semidirect
22. C32×#444C22semidirect
24. #10592410C22semidirect
25. C3×#5197C22semidirect
28. C3×#4894C22semidirect
32. C3×#4717C22semidirect
33. C3×#4711C22semidirect
35. #10591038C4semidirect
36. D3×#828C4semidirect
37. #10591024C4semidirect
38. D3×#826C4semidirect
40. #10590771C22semidirect
41. #10590768C22semidirect
49. #10589432C22semidirect
50. #10589361C22semidirect
51. #10589360C22semidirect
52. #10589332C22semidirect
53. C3×#4566C22semidirect
54. C3×#4495C22semidirect
55. C3×#4494C22semidirect
56. C3×#4466C22semidirect
57. #10589138C22semidirect
58. #10589137C22semidirect
59. #10589128C22semidirect
60. #10589126C22semidirect
61. #10589124C22semidirect
62. #10589123C22semidirect
63. #10589105C22semidirect
64. #10589105C22semidirect
68. #79899D3semidirect
83. #70929D3semidirect
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×#828C2×C4semidirect
146. C3×#826C2×C4semidirect
161. #63549C2×C4semidirect
162. #63547C2×C4semidirect
163. #63546C2×C4semidirect
164. #63545C2×C4semidirect
166. #63543C2×C4semidirect
168. D3×C3⋊C16C2×C4semidirect
183. C3×#444C2×D3semidirect
184. C3×#444C2×D3semidirect
191. #5197C2×D3semidirect
217. #4894C2×D3semidirect
225. #4717C2×D3semidirect
231. #4711C2×D3semidirect
244. #4566C2×D3semidirect
256. #4495C2×D3semidirect
262. #4494C2×D3semidirect
270. #4466C2×D3semidirect
401. #919C4×D3semidirect
402. D3×Q16C4×D3semidirect
405. #912C4×D3semidirect
410. D3×D8C4×D3semidirect
475. #828C4×D3semidirect
483. #826C4×D3semidirect
590. #444D32semidirect
1152. C32#33471semidirect
1250. C3#10948658semidirect
1251. C3#10948662semidirect

Maximal subgroups

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

subgroupindex
D3×#51932
C3×#798992
#118606922
#117979832
#117979812
#117979742
#117979722
#117979712
#117979692
C3×#709292
#117979532
#117971372
D3×#44952
#117968582
#117959442
#109486623
#109486583