Finite Group Databasebeta

← #11864124

Subgroups — #11864124

Order 1152.

1711 conjugacy classes of subgroups.

The subgroup lattice has 1063 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64312C211yesmaximal, characteristic, complemented
2C2×C3×#911C211yesmaximal, characteristic, complemented
3D3×#938C211yesmaximal, characteristic, complemented
4C2×#63934C211yesmaximal, characteristic, complemented
5#10592855C211yesmaximal, characteristic, complemented
6C3×#5158C211yesmaximal, characteristic, complemented
7#10591521C211yesmaximal, characteristic, complemented
8#10591518C211yesmaximal, characteristic, complemented
9#10591456C211yesmaximal, characteristic, complemented
10#10591450C211yesmaximal, characteristic, complemented
11#10591414C211yesmaximal, characteristic, complemented
12#10590936C211yesmaximal, characteristic, complemented
13#10590824C211yesmaximal, characteristic, complemented
14#10590823C211yesmaximal, characteristic, complemented
15#10590671C211yesmaximal, characteristic, complemented
16#83946—31nomaximal
17#80084—31nomaximal
18C2×D4×C3⋊D3C2211yescharacteristic, complemented
19C2×C3×#237C2211yescharacteristic
20C2×C3×#237C2211yescharacteristic, complemented
21C2×C3×D3×D4C2211yescharacteristic, complemented
22C2×#3811—21no—
23C2×D3×#67—21no—
24C22×#624—21no—
25C2×#3804—21no—
26C2×#3804—21no—
27#64312—24no—
28#64312—24no—
29C2×C4×D32C2211yescharacteristic
30C2×#3799C2211yescharacteristic
31C2×#3799C2211yescharacteristic, complemented
32C2×#3797C2211yescharacteristic, complemented
33C2×C32×D8C2211yescharacteristic, complemented
34#64147C2211yescharacteristic
35C2×#3753C2211yescharacteristic, complemented
36C3×#938C2211yescharacteristic, complemented
37C2×C3×#214C2211yescharacteristic, complemented
38C2×C3×#214C2211yescharacteristic, complemented
39C2×C3×#213C2211yescharacteristic, complemented
40C3×#911—24no—
41C2×C3×#204C2211yescharacteristic, complemented
42C2×C3×ΓL(1,𝔽25)C2211yescharacteristic, complemented
43#63970—21no—
44D3×#217—21no—
45#63958—21no—
46#63934—24no—
47#63916C2211yescharacteristic
48#63908C2211yescharacteristic, complemented
49D3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×#3715C2211yescharacteristic, complemented
51C2×#3714C2211yescharacteristic, complemented
52C2×#3711C2211yescharacteristic, complemented
53#63659C2211yescharacteristic, complemented
54#63648C2211yescharacteristic, complemented
55#63647C2211yescharacteristic, complemented
56C3×#832C2211yescharacteristic, complemented
57C3×(C2×D3)⋊C8C2211yescharacteristic, complemented
58C3×#816C2211yescharacteristic, complemented
59#63566C2211yescharacteristic, complemented
60#63566C2211yescharacteristic, complemented
61#63565C2211yescharacteristic, complemented
62#63564C2211yescharacteristic, complemented
63#63557C2211yescharacteristic, complemented
64(C2×D3)⋊(C3⋊C8)C2211yescharacteristic, complemented
65C2×D3×#41—31no—
66C2×D3×#41—31no—
67C2×C3×AGL(1,ℤ/8)—31no—
68C2×#938—31no—
69C2×#932—31no—
70C2×#914—31no—
71C2×#911D311yescharacteristic, complemented
72D3×#121—31no—
73C3×#449—31no—
74#5238—31no—
75#5232—31no—
76#5172—31no—
77#5172—31no—
78#5170—31no—
79#5170—31no—
80#5170—31no—
81#5158—31no—
82#5158D311yescharacteristic, complemented
83#5156—31no—
84#5156—31no—
85#5156—31no—
86#5156—61no—
87#5133—31no—
88#5126—31no—
89#5037—31no—
90#4806—31no—
91#4803—31no—
92#4773—31no—
93#4771—31no—
94#4734—31no—
95#4726—31no—
96C23×C3⋊D3—21no—
97C23×C3×D3—21no—
98C22×D32D411yescharacteristic
99C2×C32×D4C2311yescharacteristic
100C2×C32×D4C2311yescharacteristic
101C2×#638—21no—
102C2×#638—21no—
103D4×C3⋊D3—22no—
104D4×C3⋊D3—22no—
105C2×C4⋊(C3⋊D3)C2311yescharacteristic
106C2×C4×C3⋊D3C2311yescharacteristic
107C2×C3×#67—21no—
108C2×C3×#67—21no—
109C2×C3×#67—21no—
110C2×C3×#67—21no—
111C22×C3×Dic3—21no—
112C22×C3×Dic3—21no—
113C3×#237—22no—
114C3×#237—22no—
115C3×#237—22no—
116C3×#237D414yescomplemented
117C3×D3×D4—22no—
118C3×D3×D4—22no—
119C2×C3×D12C2311yescharacteristic
120C2×C3×C4×D3C2311yescharacteristic
121C2×C3×C4×D3C2311yescharacteristic
122C2×C3×Dic6C2311yescharacteristic
123C2×C3×Dic6C2311yescharacteristic
124#3811—28no—
125D3×#67—44no—
126C2×#627—21no—
127C2×#626—21no—
128C2×#626—21no—
129C2×#626—21no—
130C2×#625—21no—
131C2×#624—28no—
132C2×#624—21no—
133C2×#624—21no—
134C2×#624—21no—
135C2×#624D411yescharacteristic
136#3804—28no—
137#3804—28no—
138C2×D3×Dic3—21no—
139C2×D3×Dic3D411yescharacteristic
140C2×D3×Dic3D411yescharacteristic
141C4×D32—22no—
142C4×D32—22no—
143#3799—22no—
144#3799—22no—
145#3799—22no—
146#3799D414yescomplemented
147#3797—22no—
148#3797—22no—
149C32×D8—22no—
150C2×C32×C8C2311yescharacteristic
151#3757—21no—
152#3753—22no—
153C4⋊(C3⋊Dic3)C2311yescharacteristic
154C2×C3⋊(C3⋊C8)C2311yescharacteristic
155C3×#217—21no—
156C3×#214—22no—
157C3×#214—22no—
158C3×#213—22no—
159C3×C4⋊Dic3C2311yescharacteristic
160C2×C3×C3⋊C8C2311yescharacteristic
161C2×C3×C3⋊C8C2311yescharacteristic
162C3×#204—22no—
163C3×ΓL(1,𝔽25)—22no—
164Dic3⋊Dic3—21no—
165(C2×D3)⋊Dic3—21no—
166(C2×D3)⋊Dic3—21no—
167#3715—22no—
168#3714—22no—
169#3711—22no—
170#3006—91noSylow
171C2×C3×#41—31no—
172C2×C3×#41—31no—
173C22×C3×D4—31no—
174C22×#67—61no—
175D3×#41—64no—
176D3×#41—64no—
177D3×#41—64no—
178D3×#41—64no—
179C2×#239—31no—
180C2×#239—31no—
181C2×D3×Q8—31no—
182C2×D3×Q8—31no—
183C2×#237—61no—
184C2×#237—61no—
185C2×#237C2×D311yescharacteristic
186C2×#237C2×D311yescharacteristic, complemented
187C2×D3×D4—31no—
188C2×D3×D4—31no—
189C2×D3×D4—61no—
190C2×D3×D4—61no—
191C2×D3×D4—61no—
192C2×D3×D4—61no—
193C2×D3×D4C2×D311yescharacteristic, complemented
194C2×#235—31no—
195C2×#235—31no—
196C2×#235—61no—
197C2×#235—61no—
198C22×C4×D3—31no—
199C22×C4×D3—31no—
200C22×C4×D3—61no—
201C22×C4×D3—61no—
202C3×AGL(1,ℤ/8)—64no—
203C2×C3×SD16—31no—
204C2×C3×SD16—31no—
205C2×C3×SD16—31no—
206C2×C3×D8—21no—
207C2×C3×D8—31no—
208C2×C3×D8C2×D311yescharacteristic, complemented
209C2×C3×D8C2×D311yescharacteristic, complemented
210C2×C3×M16—31no—
211C3×#121—31no—
212C2×#217—61no—
213C2×#215—31no—
214#939—61no—
215#938—31no—
216#938—31no—
217#938—31no—
218#938—31no—
219#938—61no—
220#938—61no—
221#938—61no—
222#938C2×D311yescharacteristic, complemented
223C2×#214—31no—
224C2×#214C2×D311yescharacteristic, complemented
225C2×#214C2×D311yescharacteristic, complemented
226#932—64no—
227C2×#213—31no—
228C2×#213—31no—
229C2×#213—31no—
230C2×#213—61no—
231C2×#213C2×D311yescharacteristic, complemented
232#930—31no—
233C2×C4⋊Dic3—31no—
234C2×#208—31no—
235#914—64no—
236#911—24no—
237C2×D24—31no—
238C2×#204C2×D311yescharacteristic, complemented
239C2×ΓL(1,𝔽25)—31no—
240C2×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
241#895—31no—
242D3×C4⋊C4—31no—
243#884—61no—
244D3×C22⋊C4—61no—
245C3×#103—31no—
246C3×#102—31no—
247C3×C22⋊C8—31no—
248#835—31no—
249#835—31no—
250#835—31no—
251#832—31no—
252#832—31no—
253#832—61no—
254#832C2×D311yescharacteristic, complemented
255#830—31no—
256#821—31no—
257#821—31no—
258#821—31no—
259#821—61no—
260(C2×D3)⋊C8—31no—
261(C2×D3)⋊C8—31no—
262(C2×D3)⋊C8—31no—
263(C2×D3)⋊C8—31no—
264(C2×D3)⋊C8—31no—
265(C2×D3)⋊C8—61no—
266(C2×D3)⋊C8C2×D311yescharacteristic, complemented
267#816—31no—
268#816—31no—
269#816C2×D311yescharacteristic, complemented
270#810—31no—
271#809—31no—
272C23×C32—21no—
273C23×C32—21no—
274C22×C3⋊D3—24no—
275C22×C3⋊D3—21no—
276C22×C3⋊D3—42no—
277C22×C3⋊D3—42no—
278C22×C3⋊D3C2×D411yescharacteristic
279C22×C3×D3—21no—
280C22×C3×D3—42no—
281C22×C3×D3—42no—
282C22×C3×D3—42no—
283C22×C3×D3C2×D411yescharacteristic
284C22×C3×D3C2×D411yescharacteristic
285C2×D32—22no—
286C2×D32—22no—
287C2×D32—41no—
288C32×D4—21no—
289C32×D4—21no—
290C32×D4—21no—
291C32×D4C2×D412yescomplemented
292C2×C32×C4C2411yescharacteristic
293#638—24no—
294#638—42no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3C2×D411yescharacteristic
297C4⋊(C3⋊D3)—21no—
298C4⋊(C3⋊D3)C2×D412yescomplemented
299C4×C3⋊D3—21no—
300C4×C3⋊D3—21no—
301C3×#67—24no—
302C3×#67—24no—
303C3×#67—42no—
304C3×#67—42no—
305C2×C3×Dic3—24no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—24no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3C2×D411yescharacteristic
311C2×C3×Dic3C2×D411yescharacteristic
312C3×D12—21no—
313C3×D12—21no—
314C3×C4×D3—21no—
315C3×C4×D3—21no—
316C3×C4×D3C2×D412yes—
317C3×C4×D3C2×D412yes—
318C3×Dic6—21no—
319C3×Dic6—21no—
320C3×Dic6C2×D412yescomplemented
321C3×Dic6C2×D412yescomplemented
322#627—24no—
323#626—24no—
324#626—24no—
325#626—42no—
326#625—42no—
327#624—24no—
328#624—24no—
329#624—24no—
330#624—22no—
331D3×Dic3—22no—
332D3×Dic3—22no—
333D3×Dic3—42no—
334C32×C8—21no—
335C3⋊(C3⋊C8)—21no—
336C3×C3⋊C8—21no—
337C3×C3⋊C8—21no—
338C22×#41—91no—
339C2×AGL(1,ℤ/8)—31no—
340C2×AGL(1,ℤ/8)—91no—
341C2×#121—91no—
342#449—31no—
343#449—91no—
344#449—91no—
345#449—91no—
346#448—91no—
347#448—91no—
348#447—91no—
349#447—91no—
350#417—91no—
351#417—91no—
352#407—91no—
353C24×C3—61no—
354C23×D3—21no—
355C23×D3—31no—
356C23×D3—31no—
357C23×D3—61no—
358C23×D3—61no—
359C23×D3—121no—
360C3×#41—34no—
361C3×#41—62no—
362C3×#41—62no—
363C3×#41—62no—
364C2×C3×Q8—31no—
365C2×C3×Q8—31no—
366C2×C3×D4—21no—
367C2×C3×D4—21no—
368C2×C3×D4—31no—
369C2×C3×D4—62no—
370C2×C3×D4—62no—
371C2×C3×D4—61no—
372C2×C3×D4—61no—
373C2×C3×D4—61no—
374C2×C3×D4—61no—
375C2×C3×D4C22×D311yescharacteristic
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D311yescharacteristic
378C2×C3×D4C22×D311yescharacteristic
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—61no—
382C22×C3×C4—61no—
383C2×#67—21no—
384C2×#67—21no—
385C2×#67—21no—
386C2×#67—21no—
387C2×#67—61no—
388C2×#67—61no—
389C2×#67—61no—
390C2×#67—61no—
391C2×#67—61no—
392C2×#67—61no—
393C2×#67—61no—
394C2×#67—61no—
395C2×#67—61no—
396C2×#67—121no—
397C2×#67—121no—
398C2×#67—124no—
399C22×Dic3—21no—
400C22×Dic3—21no—
401C22×Dic3—31no—
402C22×Dic3—31no—
403C22×Dic3—61no—
404#239—34no—
405#239—62no—
406#239—62no—
407#239—62no—
408D3×Q8—62no—
409D3×Q8—62no—
410D3×Q8—62no—
411D3×Q8—62no—
412#237—22no—
413#237—22no—
414#237—22no—
415#237—68no—
416#237—68no—
417#237#6714yescomplemented
418D3×D4—22no—
419D3×D4—22no—
420D3×D4—62no—
421D3×D4—62no—
422D3×D4—68no—
423D3×D4—68no—
424D3×D4—62no—
425D3×D4—62no—
426D3×D4—122no—
427D3×D4—122no—
428D3×D4—124no—
429#235—34no—
430#235—62no—
431#235—62no—
432#235—68no—
433#235—68no—
434#235—62no—
435C2×D12—31no—
436C2×D12—31no—
437C2×D12—61no—
438C2×D12—61no—
439C2×D12—61no—
440C2×D12—61no—
441C2×D12C22×D311yescharacteristic
442C2×C4×D3—31no—
443C2×C4×D3—31no—
444C2×C4×D3—31no—
445C2×C4×D3—31no—
446C2×C4×D3—31no—
447C2×C4×D3—31no—
448C2×C4×D3—61no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—61no—
452C2×C4×D3—61no—
453C2×C4×D3—61no—
454C2×C4×D3—61no—
455C2×C4×D3—68no—
456C2×C4×D3—68no—
457C2×C4×D3—61no—
458C2×C4×D3—61no—
459C2×C4×D3—62no—
460C2×C4×D3—62no—
461C2×C4×D3—61no—
462C2×C4×D3C22×D311yescharacteristic
463C2×C4×D3C22×D311yescharacteristic
464C2×Dic6—61no—
465C2×Dic6—61no—
466C2×Dic6C22×D311yescharacteristic
467C2×Dic6C22×D311yescharacteristic
468C3×SD16—62no—
469C3×SD16—62no—
470C3×SD16—62no—
471C3×D8—22no—
472C3×D8—22no—
473C3×D8—42no—
474C3×D8—62no—
475C3×M16—62no—
476C2×C3×C8—21no—
477C2×C3×C8—31no—
478C2×C3×C8—31no—
479C2×C3×C8C22×D311yescharacteristic
480C2×C3×C8C22×D311yescharacteristic
481C3×C4⋊C4—31no—
482C3×C22⋊C4—61no—
483#217—21no—
484#217—61no—
485#217—61no—
486#217—61no—
487#217—61no—
488#217—121no—
489#215—62no—
490#214—22no—
491#214—22no—
492#214—62no—
493#213—22no—
494#213—62no—
495#213—62no—
496#213—62no—
497#213—122no—
498(C2×D3)⋊C4—61no—
499(C2×D3)⋊C4—61no—
500C4⋊Dic3—31no—
501C4⋊Dic3—31no—
502C4⋊Dic3—61no—
503C4⋊Dic3—61no—
504C4⋊Dic3C22×D311yescharacteristic
505Dic3⋊C4—61no—
506#208—62no—
507C2×C3⋊C8—31no—
508C2×C3⋊C8—31no—
509C2×C3⋊C8—61no—
510C2×C3⋊C8C22×D311yescharacteristic
511C2×C3⋊C8C22×D311yescharacteristic
512D24—62no—
513#204—22no—
514ΓL(1,𝔽25)—22no—
515ΓL(1,𝔽25)—62no—
516C22×C32—22no—
517C22×C32—41no—
518C22×C32—41no—
519C22×C32—41no—
520C22×C32—41no—
521C22×C32—41no—
522C22×C32C22×D411yescharacteristic
523C2×C3⋊D3—21no—
524C2×C3⋊D3—21no—
525C2×C3⋊D3—22no—
526C2×C3⋊D3—48no—
527C2×C3⋊D3—41no—
528C2×C3⋊D3—41no—
529C2×C3⋊D3AGL(1,ℤ/8)12yescomplemented
530C2×C3×D3—21no—
531C2×C3×D3—21no—
532C2×C3×D3—21no—
533C2×C3×D3—21no—
534C2×C3×D3—21no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3—41no—
538C2×C3×D3—84no—
539C2×C3×D3#12012yes—
540D32—44no—
541C32×C4C22×D411yescharacteristic
542C32×C4C22×D411yescharacteristic
543C3⋊Dic3—21no—
544C3⋊Dic3—41no—
545C3×Dic3—21no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3#12012yes—
550C2×#41—31no—
551C2×#41—31no—
552C2×#41—91no—
553C2×#41—91no—
554C2×#41—181no—
555C2×#41—181no—
556C2×#41—184no—
557C2×#41—184no—
558C22×Q8—91no—
559C22×D4—31no—
560C22×D4—91no—
561C22×D4—181no—
562C22×D4—181no—
563C23×C4—91no—
564C23×C4—181no—
565AGL(1,ℤ/8)—64no—
566AGL(1,ℤ/8)—184no—
567C2×SD16—31no—
568C2×SD16—31no—
569C2×SD16—31no—
570C2×SD16—91no—
571C2×D8—31no—
572C2×D8—91no—
573C2×D8—91no—
574C2×D8D3211yescharacteristic, complemented
575C2×M16—31no—
576C2×M16—91no—
577#121—31no—
578#121—91no—
579#121—91no—
580#121—91no—
581#121—181no—
582#121—181no—
583C2×C4⋊C4—91no—
584C2×C22⋊C4—181no—
585#103—31no—
586#103—91no—
587#103—91no—
588#103—91no—
589#102—31no—
590#102—91no—
591#102—91no—
592#102—91no—
593C22⋊C8—31no—
594C22⋊C8—91no—
595C22⋊C8—91no—
596C22⋊C8—91no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—31no—
602C23×C3—31no—
603C23×C3—41no—
604C23×C3—41no—
605C23×C3—61no—
606C23×C3—122no—
607C23×C3—122no—
608C23×C3—122no—
609C22×D3—21no—
610C22×D3—31no—
611C22×D3—31no—
612C22×D3—42no—
613C22×D3—42no—
614C22×D3—42no—
615C22×D3—61no—
616C22×D3—62no—
617C22×D3—62no—
618C22×D3—62no—
619C22×D3—64no—
620C22×D3—64no—
621C22×D3—61no—
622C22×D3—61no—
623C22×D3—62no—
624C22×D3—121no—
625C22×D3—124no—
626C22×D3—121no—
627C22×D3—121no—
628C22×D3—122no—
629C22×D3—122no—
630C22×D3—122no—
631C22×D3—122no—
632C22×D3—242no—
633C22×D3—242no—
634C22×D3D3×D411yescharacteristic
635C22×D3D3×D411yescharacteristic
636C3×Q8—32no—
637C3×Q8—32no—
638C3×Q8—61no—
639C3×Q8—61no—
640C3×D4—21no—
641C3×D4—21no—
642C3×D4—21no—
643C3×D4—21no—
644C3×D4—21no—
645C3×D4—21no—
646C3×D4—22no—
647C3×D4—41no—
648C3×D4—41no—
649C3×D4—41no—
650C3×D4—64no—
651C3×D4—64no—
652C3×D4—61no—
653C3×D4—61no—
654C3×D4—122no—
655C3×D4—122no—
656C3×D4D3×D412yescomplemented
657C3×D4C2×#6712yescomplemented
658C2×C3×C4—21no—
659C2×C3×C4—31no—
660C2×C3×C4—32no—
661C2×C3×C4—32no—
662C2×C3×C4—31no—
663C2×C3×C4—64no—
664C2×C3×C4—64no—
665C2×C3×C4—61no—
666C2×C3×C4—61no—
667C2×C3×C4—61no—
668C2×C3×C4—61no—
669C2×C3×C4—61no—
670C2×C3×C4C23×D311yescharacteristic
671C2×C3×C4C23×D311yescharacteristic
672#67—24no—
673#67—24no—
674#67—42no—
675#67—42no—
676#67—64no—
677#67—64no—
678#67—64no—
679#67—64no—
680#67—124no—
681#67—122no—
682#67—122no—
683#67—122no—
684#67—122no—
685#67—122no—
686#67—242no—
687C2×Dic3—24no—
688C2×Dic3—21no—
689C2×Dic3—21no—
690C2×Dic3—24no—
691C2×Dic3—21no—
692C2×Dic3—31no—
693C2×Dic3—31no—
694C2×Dic3—61no—
695C2×Dic3—62no—
696C2×Dic3—62no—
697C2×Dic3—61no—
698C2×Dic3—61no—
699C2×Dic3—121no—
700C2×Dic3—122no—
701C2×Dic3D3×D411yescharacteristic
702C2×Dic3D3×D411yescharacteristic
703D12—21no—
704D12—21no—
705D12—32no—
706D12—32no—
707D12—62no—
708D12—64no—
709D12—64no—
710D12—61no—
711D12—61no—
712D12—121no—
713D12—122no—
714C4×D3—21no—
715C4×D3—21no—
716C4×D3—62no—
717C4×D3—64no—
718C4×D3—64no—
719C4×D3—64no—
720C4×D3—64no—
721C4×D3—64no—
722C4×D3—62no—
723C4×D3—62no—
724C4×D3—61no—
725C4×D3—61no—
726C4×D3—61no—
727C4×D3—61no—
728C4×D3—62no—
729C4×D3—64no—
730C4×D3—121no—
731C4×D3—121no—
732C4×D3—122no—
733C4×D3D3×D412yes—
734C4×D3C2×#6712yes—
735Dic6—21no—
736Dic6—21no—
737Dic6—64no—
738Dic6—64no—
739Dic6D3×D412yescomplemented
740Dic6C2×#6712yescomplemented
741C3×C8—21no—
742C3×C8—21no—
743C3×C8—41no—
744C3×C8—61no—
745C3×C8—61no—
746C3⋊C8—21no—
747C3⋊C8—21no—
748C3⋊C8—61no—
749C3⋊C8—61no—
750C3⋊C8—121no—
751C2×C32—42no—
752C2×C32—81no—
753C2×C32C2×#12011yescharacteristic
754C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
755C2×C32#57511yescharacteristic
756C3⋊D3—22no—
757C3⋊D3—42no—
758C3×D3—22no—
759C3×D3—41no—
760C3×D3—81no—
761C24—61no—
762C24—91no—
763C24—181no—
764#41—34no—
765#41—62no—
766#41—62no—
767#41—62no—
768#41—94no—
769#41—182no—
770#41—188no—
771#41—188no—
772#41—182no—
773#41—182no—
774C2×Q8—31no—
775C2×Q8—31no—
776C2×Q8—181no—
777C2×Q8—182no—
778C2×Q8—182no—
779C2×D4—31no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—61no—
783C2×D4—61no—
784C2×D4—61no—
785C2×D4—61no—
786C2×D4—91no—
787C2×D4—181no—
788C2×D4—181no—
789C2×D4—181no—
790C2×D4—181no—
791C2×D4—182no—
792C2×D4—188no—
793C2×D4—182no—
794C2×D4—181no—
795C2×D4—181no—
796C2×D4—364no—
797C2×D4C2×D3211yescharacteristic
798C2×D4C2×D3211yescharacteristic
799C22×C4—31no—
800C22×C4—31no—
801C22×C4—61no—
802C22×C4—61no—
803C22×C4—91no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—182no—
808C22×C4—182no—
809C22×C4—181no—
810C22×C4—181no—
811C22×C4—181no—
812C22×C4—188no—
813C22×C4—181no—
814SD16—62no—
815SD16—62no—
816SD16—62no—
817SD16—182no—
818D8—22no—
819D8—62no—
820D8—182no—
821D8—182no—
822M16—62no—
823M16—182no—
824C2×C8—31no—
825C2×C8—31no—
826C2×C8—91no—
827C2×C8C2×D3211yescharacteristic
828C4⋊C4—31no—
829C4⋊C4—91no—
830C4⋊C4—181no—
831C22⋊C4—61no—
832C22⋊C4—181no—
833C22⋊C4—181no—
834C22⋊C4—181no—
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—21no—
838C22×C3—32no—
839C22×C3—42no—
840C22×C3—41no—
841C22×C3—41no—
842C22×C3—41no—
843C22×C3—41no—
844C22×C3—41no—
845C22×C3—41no—
846C22×C3—41no—
847C22×C3—41no—
848C22×C3—41no—
849C22×C3—41no—
850C22×C3—61no—
851C22×C3—61no—
852C22×C3—61no—
853C22×C3—61no—
854C22×C3—61no—
855C22×C3—81no—
856C22×C3—81no—
857C22×C3—81no—
858C22×C3—81no—
859C22×C3—81no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3—244no—
864C22×C3C2×D3×D411yescharacteristic
865C22×C3C2×D3×D411yescharacteristic
866C2×D3—21no—
867C2×D3—21no—
868C2×D3—21no—
869C2×D3—21no—
870C2×D3—21no—
871C2×D3—32no—
872C2×D3—32no—
873C2×D3—41no—
874C2×D3—41no—
875C2×D3—41no—
876C2×D3—62no—
877C2×D3—61no—
878C2×D3—61no—
879C2×D3—61no—
880C2×D3—61no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—84no—
884C2×D3—121no—
885C2×D3—121no—
886C2×D3—122no—
887C2×D3—124no—
888C2×D3—124no—
889C2×D3—128no—
890C2×D3—128no—
891C2×D3—121no—
892C2×D3—121no—
893C2×D3—121no—
894C2×D3—121no—
895C2×D3—248no—
896C2×D3—241no—
897C2×D3—241no—
898C2×D3#93712yes—
899C3×C4—21no—
900C3×C4—21no—
901C3×C4—32no—
902C3×C4—62no—
903C3×C4—61no—
904C3×C4—62no—
905C3×C4—121no—
906C3×C4C2×D3×D411yescharacteristic
907C3×C4C2×D3×D411yescharacteristic
908C3×C4C2×D3×D411yescharacteristic
909C3×C4C22×#6711yescharacteristic
910Dic3—22no—
911Dic3—22no—
912Dic3—21no—
913Dic3—41no—
914Dic3—61no—
915Dic3—61no—
916Dic3—121no—
917Dic3—121no—
918Dic3—121no—
919Dic3—241no—
920Dic3#93712yes—
921C32#300611yescharacteristic, complemented, Sylow
922C23—21no—
923C23—21no—
924C23—31no—
925C23—31no—
926C23—61no—
927C23—91no—
928C23—122no—
929C23—122no—
930C23—122no—
931C23—184no—
932C23—182no—
933C23—182no—
934C23—181no—
935C23—362no—
936C23—362no—
937C23—361no—
938Q8—32no—
939Q8—32no—
940Q8—61no—
941Q8—61no—
942Q8—184no—
943D4—21no—
944D4—21no—
945D4—21no—
946D4—64no—
947D4—64no—
948D4—61no—
949D4—61no—
950D4—92no—
951D4—122no—
952D4—122no—
953D4—184no—
954D4—184no—
955D4—184no—
956D4—181no—
957D4—362no—
958D4—362no—
959D4—362no—
960D4D3×#6712yescomplemented
961C2×C4—31no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—31no—
965C2×C4—64no—
966C2×C4—64no—
967C2×C4—61no—
968C2×C4—61no—
969C2×C4—61no—
970C2×C4—61no—
971C2×C4—61no—
972C2×C4—91no—
973C2×C4—182no—
974C2×C4—184no—
975C2×C4—182no—
976C2×C4—184no—
977C2×C4—184no—
978C2×C4—182no—
979C2×C4—181no—
980C2×C4—181no—
981C2×C4—181no—
982C2×C4—362no—
983C2×C4C22×D3211yescharacteristic
984C8—21no—
985C8—61no—
986C8—61no—
987C8—181no—
988C2×C3—21no—
989C2×C3—21no—
990C2×C3—21no—
991C2×C3—42no—
992C2×C3—42no—
993C2×C3—62no—
994C2×C3—82no—
995C2×C3—81no—
996C2×C3—81no—
997C2×C3—121no—
998C2×C3—161no—
999C2×C3—241no—
1000C2×C3D3×#12011yescharacteristic
1001C2×C3#576811yescharacteristic
1002C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1003C2×C3D3×AGL(1,ℤ/8)11yescharacteristic
1004C2×C3#577311yescharacteristic
1005C2×C3C2×#93711yescharacteristic
1006D3—22no—
1007D3—41no—
1008D3—62no—
1009D3—62no—
1010D3—81no—
1011D3—122no—
1012D3—122no—
1013D3—122no—
1014D3—242no—
1015C22—22no—
1016C22—32no—
1017C22—41no—
1018C22—41no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—61no—
1023C22—61no—
1024C22—61no—
1025C22—61no—
1026C22—61no—
1027C22—92no—
1028C22—121no—
1029C22—121no—
1030C22—121no—
1031C22—181no—
1032C22—181no—
1033C22—182no—
1034C22—244no—
1035C22—368no—
1036C22—364no—
1037C22—361no—
1038C22—361no—
1039C22D32×D411yescharacteristic
1040C4—32no—
1041C4—61no—
1042C4—62no—
1043C4—62no—
1044C4—121no—
1045C4—181no—
1046C4—361no—
1047C4D32×D411yescharacteristic
1048C4C2×D3×#6711yescharacteristic
1049C3—21no—
1050C3#8008411yescharacteristic, complemented
1051C3#8394611yescharacteristic, complemented
1052C2—42no—
1053C2—62no—
1054C2—81no—
1055C2—121no—
1056C2—182no—
1057C2—241no—
1058C2—362no—
1059C2#1059472611yescharacteristic
1060C2#1059472911yescharacteristic
1061C2D3×#93711yescharacteristic
subgroupG/H
centerC22D32×D4
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC2×C32×D8C22
socleC22×C32C22×D4
hypercenterC2×D8D32
hypocenterC32#3006
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×D8

Complements

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

NH ≅ G/Ntype
1. C2×#64312C2semidirect
2. C2×C3×#911C2semidirect
3. D3×#938C2semidirect
4. C2×#63934C2semidirect
5. #10592855C2semidirect
6. C3×#5158C2semidirect
7. #10591521C2semidirect
8. #10591518C2semidirect
9. #10591456C2semidirect
10. #10591450C2semidirect
11. #10591414C2semidirect
12. #10590936C2semidirect
13. #10590824C2semidirect
14. #10590823C2semidirect
15. #10590671C2semidirect
18. C2×D4×C3⋊D3C22semidirect
20. C2×C3×#237C22semidirect
21. C2×C3×D3×D4C22semidirect
31. C2×#3799C22semidirect
32. C2×#3797C22semidirect
33. C2×C32×D8C22semidirect
35. C2×#3753C22semidirect
36. C3×#938C22semidirect
37. C2×C3×#214C22semidirect
38. C2×C3×#214C22semidirect
39. C2×C3×#213C22semidirect
41. C2×C3×#204C22semidirect
42. C2×C3×ΓL(1,𝔽25)C22semidirect
48. #63908C22semidirect
49. D3×C4⋊Dic3C22semidirect
50. C2×#3715C22semidirect
51. C2×#3714C22semidirect
52. C2×#3711C22semidirect
53. #63659C22semidirect
54. #63648C22semidirect
55. #63647C22semidirect
56. C3×#832C22semidirect
57. C3×(C2×D3)⋊C8C22semidirect
58. C3×#816C22semidirect
59. #63566C22semidirect
60. #63566C22semidirect
61. #63565C22semidirect
62. #63564C22semidirect
63. #63557C22semidirect
64. (C2×D3)⋊(C3⋊C8)C22semidirect
71. C2×#911D3semidirect
82. #5158D3semidirect
116. C3×#237D4semidirect
146. #3799D4semidirect
186. C2×#237C2×D3semidirect
193. C2×D3×D4C2×D3semidirect
208. C2×C3×D8C2×D3semidirect
209. C2×C3×D8C2×D3semidirect
222. #938C2×D3semidirect
224. C2×#214C2×D3semidirect
225. C2×#214C2×D3semidirect
231. C2×#213C2×D3semidirect
238. C2×#204C2×D3semidirect
240. C2×ΓL(1,𝔽25)C2×D3semidirect
254. #832C2×D3semidirect
266. (C2×D3)⋊C8C2×D3semidirect
269. #816C2×D3semidirect
291. C32×D4C2×D4semidirect
298. C4⋊(C3⋊D3)C2×D4semidirect
320. C3×Dic6C2×D4semidirect
321. C3×Dic6C2×D4semidirect
417. #237#67semidirect
529. C2×C3⋊D3AGL(1,ℤ/8)semidirect
574. C2×D8D32semidirect
656. C3×D4D3×D4semidirect
657. C3×D4C2×#67semidirect
739. Dic6D3×D4semidirect
740. Dic6C2×#67semidirect
921. C32#3006semidirect
960. D4D3×#67semidirect
1050. C3#80084semidirect
1051. C3#83946semidirect

Maximal subgroups

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

subgroupindex
C2×#643122
C2×C3×#9112
D3×#9382
C2×#639342
#105928552
C3×#51582
#105915212
#105915182
#105914562
#105914502
#105914142
#105909362
#105908242
#105908232
#105906712
#839463
#800843