Finite Group Databasebeta

← #11866183

Subgroups — #11866183

Order 1152.

1122 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63794C211yesmaximal, characteristic, complemented
2C2×D3×D24C211yesmaximal, characteristic, complemented
3#10594001C211yesmaximal, characteristic, complemented
4#10593994C211yesmaximal, characteristic, complemented
5#10592542C211yesmaximal, characteristic, complemented
6C3×#4844C211yesmaximal, characteristic, complemented
7C3×#4839C211yesmaximal, characteristic, complemented
8#10590939C211yesmaximal, characteristic, complemented
9#10590770C211yesmaximal, characteristic, complemented
10#10590765C211yesmaximal, characteristic, complemented
11#10590754C211yesmaximal, characteristic, complemented
12#10590753C211yesmaximal, characteristic, complemented
13#10590690C211yesmaximal, characteristic, complemented
14#10590356C211yesmaximal, characteristic, complemented
15#10590349C211yesmaximal, characteristic, complemented
16#80536—31nomaximal
17#79086—31nomaximal
18C2×D3×D12C2211yescharacteristic
19C2×D3×D12C2211yescharacteristic
20C2×#3799C2211yescharacteristic
21C2×#3745C2211yescharacteristic
22C2×#3745C2211yescharacteristic, complemented
23#64083C2211yescharacteristic, complemented
24C4×C4⋊(C3⋊D3)C2211yescharacteristic, complemented
25C2×C3×D24C2211yescharacteristic
26C2×C3×#204C2211yescharacteristic, complemented
27C2×C3×ΓL(1,𝔽25)C2211yescharacteristic
28C2×C3×D3×C8C2211yescharacteristic
29C3×#875C2211yescharacteristic, complemented
30C3×C4×D12C2211yescharacteristic, complemented
31C3×#872C2211yescharacteristic
32#63923—21no—
33#63923—21no—
34#63921—21no—
35D3×(C2×D3)⋊C4—21no—
36#63911C2211yescharacteristic, complemented
37#63910—21no—
38#63910—21no—
39#63904—21no—
40#63894C2211yescharacteristic, complemented
41Dic3×D12C2211yescharacteristic, complemented
42#63881—21no—
43#63864C2211yescharacteristic, complemented
44#63841C2211yescharacteristic
45C2×#3717C2211yescharacteristic, complemented
46C2×#3714C2211yescharacteristic
47C2×#3714C2211yescharacteristic
48C2×#3714C2211yescharacteristic, complemented
49#63794—24no—
50D3×D24—24no—
51C32×C4⋊C8C2211yescharacteristic, complemented
52#63648C2211yescharacteristic, complemented
53#63648C2211yescharacteristic, complemented
54C3×#821C2211yescharacteristic, complemented
55C3×#816C2211yescharacteristic, complemented
56C3×Dic3⋊C8C2211yescharacteristic, complemented
57C3×Dic3⋊C8C2211yescharacteristic, complemented
58C3×C4⋊(C3⋊C8)C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63564C2211yescharacteristic, complemented
61#63564C2211yescharacteristic, complemented
62#63563C2211yescharacteristic, complemented
63C2×#914—31no—
64C2×D3×D8—31no—
65C2×#908—31no—
66C22×D24—31no—
67#5674—31no—
68#5545—31no—
69#5525—31no—
70#5521—31no—
71C3×#463—31no—
72C3×#424—31no—
73#5165—31no—
74#5150—31no—
75#5131—31no—
76#5113—31no—
77#5057—31no—
78#5015—31no—
79#4844—31no—
80#4844—31no—
81#4844—31no—
82#4844D311yescharacteristic, complemented
83#4843—31no—
84#4843—31no—
85#4843—31no—
86#4843—31no—
87#4843—31no—
88#4843—61no—
89#4839D311yescharacteristic, complemented
90#4819—31no—
91#4804—31no—
92#4786—31no—
93#4770—31no—
94C22×D32—21no—
95C22×D32—21no—
96C2×C4⋊(C3⋊D3)—21no—
97C2×C4⋊(C3⋊D3)—21no—
98C2×C4⋊(C3⋊D3)C2311yescharacteristic
99C2×C4⋊(C3⋊D3)C2311yescharacteristic
100C2×C4⋊(C3⋊D3)C2311yescharacteristic
101C2×C4×C3⋊D3—21no—
102C2×C3×D12C2311yescharacteristic
103C2×C3×D12C2311yescharacteristic
104C2×C3×C4×D3—21no—
105C2×C3×C4×D3C2311yescharacteristic
106C2×C3×Dic6C2311yescharacteristic
107C2×#626—21no—
108C2×#626—21no—
109C2×#626—21no—
110C2×#626—21no—
111C2×#626—21no—
112C2×#624—21no—
113C2×#624—21no—
114C2×D3×Dic3—21no—
115D3×D12—22no—
116D3×D12—22no—
117D3×D12—22no—
118D3×D12D414yescomplemented
119#3799—22no—
120#3799—22no—
121C2×C32×C8C2311yescharacteristic
122C2×C32×C8C2311yescharacteristic
123C32×C42C2311yescharacteristic
124#3752—21no—
125C4⋊(C3⋊Dic3)C2311yescharacteristic
126#3745—22no—
127#3745—22no—
128C3×(C2×D3)⋊C4—21no—
129C3×(C2×D3)⋊C4—21no—
130C3×(C2×D3)⋊C4—21no—
131C3×(C2×D3)⋊C4D411yescharacteristic
132C3×(C2×D3)⋊C4D411yescharacteristic
133C3×C4⋊Dic3C2311yescharacteristic
134C3×Dic3⋊C4D411yescharacteristic
135C3×Dic3⋊C4D411yescharacteristic
136C3×C4×Dic3C2311yescharacteristic
137C2×C3×C3⋊C8C2311yescharacteristic
138C2×C3×C3⋊C8C2311yescharacteristic
139C3×D24—22no—
140C3×#204—22no—
141C3×ΓL(1,𝔽25)—22no—
142C3×D3×C8—22no—
143#3722—21no—
144#3722—21no—
145#3722—21no—
146(C2×D3)⋊Dic3—21no—
147(C2×D3)⋊Dic3—21no—
148Dic32—21no—
149#3717—22no—
150#3714—22no—
151#3714—22no—
152#3714—22no—
153#3041—91noSylow
154C2×#239—31no—
155C2×D3×D4—31no—
156C2×D3×D4—31no—
157C2×#235—31no—
158C22×D12—31no—
159C22×D12—31no—
160C2×C3×SD16—31no—
161C2×C3×D8—31no—
162C2×C3×M16—31no—
163C22×C3×C8—31no—
164C3×#124—31no—
165C3×C4×D4—31no—
166C3×#117—31no—
167#947—31no—
168C2×#215—31no—
169#940—31no—
170D4×Dic3—31no—
171C2×#213—31no—
172C2×#213—31no—
173C2×#213—31no—
174C4×#67—61no—
175C2×(C2×D3)⋊C4—61no—
176#926—31no—
177#914—64no—
178D3×D8—64no—
179#908—64no—
180C2×D24—31no—
181C2×D24—31no—
182C2×D24—31no—
183C2×D24—31no—
184C2×D24—31no—
185C2×D24—31no—
186C2×D24—31no—
187C2×D24—61no—
188C2×D24—61no—
189C2×D24—64no—
190C2×D24C2×D311yescharacteristic
191C2×#204—31no—
192C2×#204C2×D311yescharacteristic, complemented
193C2×ΓL(1,𝔽25)C2×D311yescharacteristic
194C2×D3×C8C2×D311yescharacteristic
195#895—61no—
196#895—61no—
197#893—31no—
198#893—61no—
199#893—61no—
200#892—31no—
201#884—61no—
202#884—61no—
203#882—61no—
204#882—61no—
205#882—61no—
206#882—61no—
207#67⋊C4—61no—
208D3×C22⋊C4—61no—
209D3×C22⋊C4—61no—
210D3×C22⋊C4—61no—
211#875—31no—
212#875C2×D311yescharacteristic, complemented
213#874—31no—
214#874—31no—
215#874—31no—
216#874—61no—
217C4×D12—31no—
218C4×D12—31no—
219C4×D12—31no—
220C4×D12—31no—
221C4×D12—61no—
222C4×D12C2×D311yescharacteristic, complemented
223#872C2×D311yescharacteristic
224C3×C4⋊C8—21no—
225C3×C4⋊C8—31no—
226C3×C4⋊C8—31no—
227C3×C4⋊C8—31no—
228C3×C4⋊C8C2×D311yescharacteristic, complemented
229C3×C4⋊C8C2×D311yescharacteristic, complemented
230C3×#103—31no—
231C3×#102—31no—
232#835—31no—
233#832—31no—
234#821—31no—
235#821—31no—
236#821—31no—
237#821—31no—
238#821—31no—
239#821—31no—
240#821—31no—
241#821—61no—
242#821—61no—
243#821C2×D311yescharacteristic, complemented
244#816—31no—
245#816C2×D311yescharacteristic, complemented
246Dic3⋊C8C2×D311yescharacteristic, complemented
247Dic3⋊C8C2×D311yescharacteristic, complemented
248#809—31no—
249#809—31no—
250C4⋊(C3⋊C8)C2×D311yescharacteristic, complemented
251C22×C3⋊D3—21no—
252C22×C3⋊D3—21no—
253C22×C3⋊D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3C2×D411yescharacteristic
257C2×D32—24no—
258C2×D32—42no—
259C2×D32—81no—
260C2×D32—81no—
261C2×D32—81no—
262C2×D32—81no—
263C2×C32×C4C2×D411yescharacteristic
264C2×C32×C4C2×D411yescharacteristic
265C2×C32×C4C2411yescharacteristic
266C2×C3⋊Dic3—21no—
267C4⋊(C3⋊D3)—21no—
268C4⋊(C3⋊D3)—21no—
269C4⋊(C3⋊D3)—21no—
270C4⋊(C3⋊D3)—21no—
271C4⋊(C3⋊D3)—21no—
272C4⋊(C3⋊D3)—81no—
273C4⋊(C3⋊D3)—81no—
274C4⋊(C3⋊D3)C2×D412yes—
275C4×C3⋊D3—81no—
276C2×C3×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C2×D411yescharacteristic
279C2×C3×Dic3C2×D411yescharacteristic
280C2×C3×Dic3C2×D411yescharacteristic
281C3×D12—21no—
282C3×D12—21no—
283C3×D12—21no—
284C3×D12C2×D412yes—
285C3×C4×D3—81no—
286C3×C4×D3C2×D412yes—
287C3×C4×D3#4112yes—
288C3×Dic6—21no—
289C3×Dic6—21no—
290#626—24no—
291#626—42no—
292#626—42no—
293#626—81no—
294#626—81no—
295#624—42no—
296#624—81no—
297D3×Dic3—81no—
298C32×C8—21no—
299C32×C8—21no—
300C3×C3⋊C8—21no—
301C3×C3⋊C8—21no—
302C2×AGL(1,ℤ/8)—91no—
303C22×D8—91no—
304#535—91no—
305#518—91no—
306#463—31no—
307#463—91no—
308#463—91no—
309#463—91no—
310#459—91no—
311#459—91no—
312#459—91no—
313#459—91no—
314#424—31no—
315#418—91no—
316#416—91no—
317C23×D3—61no—
318C23×D3—61no—
319C23×D3—61no—
320C23×D3—61no—
321C2×C3×Q8—31no—
322C2×C3×D4—31no—
323C2×C3×D4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—61no—
326C2×#67—61no—
327C2×#67—61no—
328C2×#67—61no—
329C2×#67—61no—
330C2×#67—61no—
331C22×Dic3—61no—
332#239—62no—
333#239—62no—
334D3×D4—34no—
335D3×D4—62no—
336D3×D4—62no—
337D3×D4—62no—
338#235—62no—
339#235—62no—
340C2×D12—31no—
341C2×D12—31no—
342C2×D12—34no—
343C2×D12—31no—
344C2×D12—31no—
345C2×D12—31no—
346C2×D12—31no—
347C2×D12—61no—
348C2×D12—61no—
349C2×D12—61no—
350C2×D12—62no—
351C2×D12—62no—
352C2×D12—62no—
353C2×D12—61no—
354C2×D12—61no—
355C2×D12—61no—
356C2×D12—61no—
357C2×D12—61no—
358C2×D12—61no—
359C2×D12—61no—
360C2×D12—61no—
361C2×D12—61no—
362C2×D12—121no—
363C2×D12—121no—
364C2×D12C22×D311yescharacteristic
365C2×D12C22×D311yescharacteristic
366C2×C4×D3—21no—
367C2×C4×D3—61no—
368C2×C4×D3—61no—
369C2×C4×D3—61no—
370C2×C4×D3—61no—
371C2×C4×D3—61no—
372C2×C4×D3—61no—
373C2×C4×D3—61no—
374C2×C4×D3—121no—
375C2×C4×D3C22×D311yescharacteristic
376C2×Dic6C22×D311yescharacteristic
377C3×SD16—62no—
378C3×D8—62no—
379C3×M16—62no—
380C2×C3×C8—21no—
381C2×C3×C8—21no—
382C2×C3×C8—31no—
383C2×C3×C8—31no—
384C2×C3×C8—62no—
385C2×C3×C8C22×D311yescharacteristic
386C2×C3×C8C22×D311yescharacteristic
387C2×C3×C8C22×D311yescharacteristic
388C2×C3×C8C22×D311yescharacteristic
389C3×C4⋊C4—31no—
390C3×C4⋊C4—31no—
391C3×C4⋊C4—31no—
392C3×C22⋊C4—31no—
393C3×C22⋊C4—31no—
394C3×C22⋊C4—61no—
395C3×C22⋊C4—61no—
396C3×C22⋊C4—61no—
397C3×C42—21no—
398C3×C42—31no—
399C3×C42C22×D311yescharacteristic
400C3×C42C22×D311yescharacteristic
401#217—61no—
402#217—61no—
403#215—62no—
404#213—62no—
405#213—62no—
406#213—62no—
407(C2×D3)⋊C4—21no—
408(C2×D3)⋊C4—21no—
409(C2×D3)⋊C4—21no—
410(C2×D3)⋊C4—61no—
411(C2×D3)⋊C4—61no—
412(C2×D3)⋊C4—61no—
413(C2×D3)⋊C4—61no—
414(C2×D3)⋊C4—61no—
415(C2×D3)⋊C4—61no—
416(C2×D3)⋊C4—61no—
417(C2×D3)⋊C4—61no—
418(C2×D3)⋊C4—61no—
419(C2×D3)⋊C4—61no—
420(C2×D3)⋊C4—121no—
421(C2×D3)⋊C4D1211yescharacteristic
422(C2×D3)⋊C4D1211yescharacteristic
423C4⋊Dic3—31no—
424C4⋊Dic3—31no—
425C4⋊Dic3—61no—
426C4⋊Dic3C22×D311yescharacteristic
427Dic3⋊C4D1211yescharacteristic
428Dic3⋊C4D1211yescharacteristic
429C4×Dic3—61no—
430C4×Dic3—61no—
431C4×Dic3C22×D311yescharacteristic
432C2×C3⋊C8C22×D311yescharacteristic
433C2×C3⋊C8C22×D311yescharacteristic
434D24—22no—
435D24—62no—
436D24—62no—
437D24—62no—
438D24—62no—
439D24—62no—
440D24—62no—
441D24—62no—
442D24—122no—
443D24—122no—
444#204—22no—
445#204—62no—
446ΓL(1,𝔽25)—22no—
447D3×C8—22no—
448C22×C32C22×D411yescharacteristic
449C2×C3⋊D3—22no—
450C2×C3⋊D3—41no—
451C2×C3⋊D3—41no—
452C2×C3⋊D3—41no—
453C2×C3⋊D3—41no—
454C2×C3⋊D3—41no—
455C2×C3⋊D3—41no—
456C2×C3⋊D3—41no—
457C2×C3⋊D3—41no—
458C2×C3×D3—21no—
459C2×C3×D3—21no—
460C2×C3×D3—22no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C2×C3×D3—41no—
465C2×C3×D3—41no—
466C2×C3×D3#12112yes—
467D32—84no—
468D32—84no—
469C32×C4—21no—
470C32×C4—21no—
471C32×C4C22×D411yescharacteristic
472C32×C4C2×#4111yescharacteristic
473C3⋊Dic3—41no—
474C3×Dic3—21no—
475C3×Dic3—21no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3#12112yes—
479C2×#41—91no—
480C22×D4—91no—
481C22×D4—91no—
482AGL(1,ℤ/8)—184no—
483C2×SD16—31no—
484C2×SD16—91no—
485C2×D8—31no—
486C2×D8—91no—
487C2×D8—91no—
488C2×D8—91no—
489C2×D8—91no—
490C2×D8—91no—
491C2×D8—184no—
492C2×M16—31no—
493C22×C8—31no—
494#127—91no—
495#127—91no—
496#124—31no—
497#124—91no—
498#121—181no—
499#121—181no—
500#120—181no—
501#120—181no—
502C4×D4—31no—
503C4×D4—91no—
504C4×D4—91no—
505C4×D4—91no—
506C4×D4—181no—
507C4×D4—181no—
508#117—31no—
509#117—91no—
510C2×C22⋊C4—181no—
511C2×C22⋊C4—181no—
512C4⋊C8—31no—
513C4⋊C8—31no—
514C4⋊C8—31no—
515C4⋊C8D3211yescharacteristic, complemented
516#103—31no—
517#103—91no—
518#102—31no—
519#102—91no—
520#102—91no—
521#102—91no—
522#102—91no—
523#102—91no—
524C23×C3—31no—
525C23×C3—61no—
526C23×C3—61no—
527C22×D3—21no—
528C22×D3—21no—
529C22×D3—64no—
530C22×D3—61no—
531C22×D3—61no—
532C22×D3—64no—
533C22×D3—61no—
534C22×D3—61no—
535C22×D3—61no—
536C22×D3—61no—
537C22×D3—121no—
538C22×D3—121no—
539C22×D3—121no—
540C22×D3—122no—
541C22×D3—122no—
542C22×D3—241no—
543C22×D3—241no—
544C22×D3—241no—
545C22×D3—241no—
546C22×D3—241no—
547C22×D3—241no—
548C22×D3—241no—
549C22×D3—241no—
550C22×D3C2×D1211yescharacteristic
551C3×Q8—61no—
552C3×Q8—61no—
553C3×D4—32no—
554C3×D4—61no—
555C3×D4—61no—
556C3×D4—61no—
557C2×C3×C4—21no—
558C2×C3×C4—21no—
559C2×C3×C4—21no—
560C2×C3×C4—31no—
561C2×C3×C4—32no—
562C2×C3×C4—32no—
563C2×C3×C4—31no—
564C2×C3×C4—31no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—241no—
568C2×C3×C4C2×D1211yescharacteristic
569C2×C3×C4C2×D1211yescharacteristic
570C2×C3×C4D3×D411yescharacteristic
571C2×C3×C4D3×D411yescharacteristic
572C2×C3×C4C23×D311yescharacteristic
573C2×C3×C4C23×D311yescharacteristic
574#67—64no—
575#67—122no—
576#67—122no—
577#67—241no—
578#67—241no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—121no—
584C2×Dic3—241no—
585C2×Dic3C2×D1211yescharacteristic
586C2×Dic3C2×D1211yescharacteristic
587C2×Dic3C2×D1211yescharacteristic
588D12—21no—
589D12—21no—
590D12—21no—
591D12—32no—
592D12—32no—
593D12—62no—
594D12—64no—
595D12—61no—
596D12—61no—
597D12—61no—
598D12—61no—
599D12—61no—
600D12—61no—
601D12—61no—
602D12—61no—
603D12—61no—
604D12—61no—
605D12—121no—
606D12—121no—
607D12—121no—
608D12—121no—
609D12—121no—
610D12—122no—
611D12—122no—
612D12—241no—
613D12—241no—
614D12—241no—
615D12—241no—
616D12—242no—
617D12—242no—
618D12—241no—
619D12—241no—
620D12D3×D412yes—
621C4×D3—81no—
622C4×D3—122no—
623C4×D3—122no—
624C4×D3—241no—
625C4×D3—241no—
626C4×D3—241no—
627C4×D3—241no—
628C4×D3—241no—
629C4×D3—242no—
630C4×D3D3×D412yes—
631C4×D3#23912yes—
632Dic6—21no—
633Dic6—21no—
634C3×C8—21no—
635C3×C8—21no—
636C3×C8—21no—
637C3×C8—21no—
638C3×C8—41no—
639C3×C8—41no—
640C3×C8—61no—
641C3×C8—61no—
642C3⋊C8—21no—
643C3⋊C8—21no—
644C2×C32C2×#12111yescharacteristic
645C2×C32#57611yescharacteristic
646C2×C32#57611yescharacteristic
647C3⋊D3—42no—
648C3⋊D3—81no—
649C3⋊D3—81no—
650C3×D3—22no—
651C3×D3—42no—
652C3×D3—81no—
653C24—181no—
654C24—181no—
655#41—182no—
656#41—182no—
657C2×Q8—31no—
658C2×D4—31no—
659C2×D4—31no—
660C2×D4—94no—
661C2×D4—91no—
662C2×D4—91no—
663C2×D4—91no—
664C2×D4—182no—
665C2×D4—182no—
666C2×D4—182no—
667C2×D4—181no—
668C2×D4—181no—
669C2×D4—181no—
670C2×D4—181no—
671C2×D4—181no—
672C2×D4—181no—
673C2×D4—181no—
674C22×C4—31no—
675C22×C4—61no—
676C22×C4—181no—
677C22×C4—181no—
678C22×C4—181no—
679C22×C4—181no—
680SD16—62no—
681SD16—182no—
682D8—62no—
683D8—182no—
684D8—182no—
685D8—182no—
686D8—182no—
687D8—182no—
688M16—62no—
689C2×C8—31no—
690C2×C8—31no—
691C2×C8—62no—
692C2×C8C2×D3211yescharacteristic
693C2×C8C2×D3211yescharacteristic
694C4⋊C4—31no—
695C4⋊C4—31no—
696C4⋊C4—31no—
697C4⋊C4—91no—
698C22⋊C4—31no—
699C22⋊C4—31no—
700C22⋊C4—61no—
701C22⋊C4—61no—
702C22⋊C4—61no—
703C22⋊C4—181no—
704C22⋊C4—181no—
705C22⋊C4—181no—
706C22⋊C4—181no—
707C22⋊C4—181no—
708C22⋊C4—181no—
709C42—31no—
710C42—181no—
711C42C2×D3211yescharacteristic
712C22×C3—21no—
713C22×C3—32no—
714C22×C3—61no—
715C22×C3—61no—
716C22×C3—62no—
717C22×C3—121no—
718C22×C3—121no—
719C22×C3—121no—
720C22×C3—121no—
721C22×C3—121no—
722C22×C3C22×D1211yescharacteristic
723C22×C3C2×D3×D411yescharacteristic
724C2×D3—21no—
725C2×D3—21no—
726C2×D3—22no—
727C2×D3—41no—
728C2×D3—41no—
729C2×D3—41no—
730C2×D3—41no—
731C2×D3—41no—
732C2×D3—62no—
733C2×D3—62no—
734C2×D3—122no—
735C2×D3—121no—
736C2×D3—121no—
737C2×D3—121no—
738C2×D3—121no—
739C2×D3—121no—
740C2×D3—121no—
741C2×D3—121no—
742C2×D3—121no—
743C2×D3—121no—
744C2×D3—121no—
745C2×D3—121no—
746C2×D3—121no—
747C2×D3—121no—
748C2×D3—121no—
749C2×D3—121no—
750C2×D3—121no—
751C2×D3—241no—
752C2×D3—241no—
753C2×D3—241no—
754C2×D3—241no—
755C2×D3—241no—
756C2×D3—241no—
757C2×D3—241no—
758C2×D3—241no—
759C2×D3—244no—
760C2×D3—244no—
761C2×D3—244no—
762C2×D3—244no—
763C2×D3#89512yes—
764C3×C4—22no—
765C3×C4—21no—
766C3×C4—21no—
767C3×C4—21no—
768C3×C4—21no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—32no—
772C3×C4—41no—
773C3×C4—61no—
774C3×C4—61no—
775C3×C4—121no—
776C3×C4—121no—
777C3×C4C2×D3×D411yescharacteristic
778C3×C4C2×D3×D411yescharacteristic
779C3×C4C2×#23911yescharacteristic
780C3×C4D3×#4111yescharacteristic
781Dic3—21no—
782Dic3—21no—
783Dic3—41no—
784Dic3—41no—
785Dic3—121no—
786Dic3—121no—
787Dic3—241no—
788Dic3#89512yes—
789C32#304111yescharacteristic, complemented, Sylow
790C23—31no—
791C23—61no—
792C23—61no—
793C23—184no—
794C23—181no—
795C23—181no—
796C23—181no—
797C23—362no—
798C23—721no—
799C23—721no—
800C23—721no—
801C23—721no—
802Q8—61no—
803Q8—61no—
804D4—32no—
805D4—61no—
806D4—61no—
807D4—61no—
808D4—92no—
809D4—184no—
810D4—181no—
811D4—181no—
812D4—181no—
813D4—181no—
814D4—181no—
815D4—362no—
816D4—362no—
817D4—721no—
818D4—721no—
819D4—721no—
820D4—721no—
821C2×C4—31no—
822C2×C4—32no—
823C2×C4—32no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—61no—
827C2×C4—61no—
828C2×C4—181no—
829C2×C4—241no—
830C2×C4—362no—
831C2×C4—721no—
832C2×C4—721no—
833C2×C4—721no—
834C2×C4D3×D1211yescharacteristic
835C2×C4D3×D1211yescharacteristic
836C2×C4C22×D3211yescharacteristic
837C8—21no—
838C8—21no—
839C8—61no—
840C8—61no—
841C2×C3—21no—
842C2×C3—21no—
843C2×C3—21no—
844C2×C3—62no—
845C2×C3—122no—
846C2×C3—241no—
847C2×C3C2×#89511yescharacteristic
848C2×C3D3×#12111yescharacteristic
849C2×C3#575211yescharacteristic
850C2×C3#575211yescharacteristic
851C2×C3#576911yescharacteristic
852C2×C3#577411yescharacteristic
853D3—22no—
854D3—42no—
855D3—81no—
856D3—122no—
857D3—122no—
858D3—242no—
859D3—241no—
860D3—241no—
861D3—241no—
862D3—241no—
863D3—481no—
864D3—481no—
865C22—32no—
866C22—61no—
867C22—61no—
868C22—62no—
869C22—121no—
870C22—121no—
871C22—121no—
872C22—121no—
873C22—121no—
874C22—182no—
875C22—361no—
876C22—361no—
877C22—361no—
878C22—361no—
879C22—361no—
880C22—361no—
881C22—361no—
882C22—361no—
883C22—724no—
884C22—724no—
885C22C2×D3×D1211yescharacteristic
886C4—21no—
887C4—21no—
888C4—32no—
889C4—61no—
890C4—61no—
891C4—121no—
892C4—121no—
893C4—361no—
894C4D32×D411yescharacteristic
895C4D3×#23911yescharacteristic
896C3—21no—
897C3#7908611yescharacteristic, complemented
898C3#8053611yescharacteristic, complemented
899C2—62no—
900C2—122no—
901C2—241no—
902C2—362no—
903C2—721no—
904C2—721no—
905C2D3×#89511yescharacteristic
906C2#1059468011yescharacteristic
907C2#1059471411yescharacteristic
subgroupG/H
centerC22C2×D3×D12
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4⋊C8C22
socleC22×C32C22×D4
hypercenterC4⋊C8D32
hypocenterC32#3041
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
1. C2×#63794C2semidirect
2. C2×D3×D24C2semidirect
3. #10594001C2semidirect
4. #10593994C2semidirect
5. #10592542C2semidirect
6. C3×#4844C2semidirect
7. C3×#4839C2semidirect
8. #10590939C2semidirect
9. #10590770C2semidirect
10. #10590765C2semidirect
11. #10590754C2semidirect
12. #10590753C2semidirect
13. #10590690C2semidirect
14. #10590356C2semidirect
15. #10590349C2semidirect
22. C2×#3745C22semidirect
23. #64083C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
26. C2×C3×#204C22semidirect
29. C3×#875C22semidirect
30. C3×C4×D12C22semidirect
36. #63911C22semidirect
40. #63894C22semidirect
41. Dic3×D12C22semidirect
43. #63864C22semidirect
45. C2×#3717C22semidirect
48. C2×#3714C22semidirect
51. C32×C4⋊C8C22semidirect
52. #63648C22semidirect
53. #63648C22semidirect
54. C3×#821C22semidirect
55. C3×#816C22semidirect
56. C3×Dic3⋊C8C22semidirect
57. C3×Dic3⋊C8C22semidirect
58. C3×C4⋊(C3⋊C8)C22semidirect
59. #63566C22semidirect
60. #63564C22semidirect
61. #63564C22semidirect
62. #63563C22semidirect
82. #4844D3semidirect
89. #4839D3semidirect
118. D3×D12D4semidirect
192. C2×#204C2×D3semidirect
212. #875C2×D3semidirect
222. C4×D12C2×D3semidirect
228. C3×C4⋊C8C2×D3semidirect
229. C3×C4⋊C8C2×D3semidirect
243. #821C2×D3semidirect
245. #816C2×D3semidirect
246. Dic3⋊C8C2×D3semidirect
247. Dic3⋊C8C2×D3semidirect
250. C4⋊(C3⋊C8)C2×D3semidirect
515. C4⋊C8D32semidirect
789. C32#3041semidirect
897. C3#79086semidirect
898. C3#80536semidirect

Maximal subgroups

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

subgroupindex
C2×#637942
C2×D3×D242
#105940012
#105939942
#105925422
C3×#48442
C3×#48392
#105909392
#105907702
#105907652
#105907542
#105907532
#105906902
#105903562
#105903492
#805363
#790863