Finite Group Databasebeta

← #25978204

Subgroups — #25978204

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1214 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148162C211yesmaximal, characteristic, complemented
2#19148081C211yesmaximal, characteristic, complemented
3#19147620C211yesmaximal, characteristic, complemented
4#19147499C211yesmaximal, characteristic, complemented
5#19147318C211yesmaximal, characteristic, complemented
6#19147307C211yesmaximal, characteristic, complemented
7#19147189C211yesmaximal, characteristic, complemented
8#19147041C212yesmaximal, complemented
9#19146899C211yesmaximal, characteristic, complemented
10#19146836C211yesmaximal, characteristic, complemented
11#19146622C212yesmaximal, complemented
12#19146562C212yesmaximal, complemented
13#19146194C211yesmaximal, characteristic, complemented
14#19146072C212yesmaximal, complemented
15#19145186C212yesmaximal, complemented
16#19144653C212yesmaximal, complemented
17#19144646C212yesmaximal, complemented
18#19144599C211yesmaximal, characteristic, complemented
19#19144591C211yesmaximal, characteristic, complemented
20#19143561C211yesmaximal, characteristic, complemented
21C4×#13063352C212yesmaximal, complemented
22C2×C4×D344C211yesmaximal, characteristic, complemented
23C43×#3167C211yesmaximal, characteristic, complemented
24C2×#41×D43—21no—
25C2×#13063352C2212yes—
26C22×D344C2211yescharacteristic
27#14583623C2211yescharacteristic, complemented
28#14583615C2211yescharacteristic, complemented
29#14583610C2211yescharacteristic, complemented
30#14583602—21no—
31#14583591C2212yescomplemented
32#14583587—21no—
33#14583576—22no—
34#14583569C2211yescharacteristic, complemented
35#14583564C2211yescharacteristic, complemented
36#14583557—21no—
37#14583552C2211yescharacteristic, complemented
38#14583552C2211yescharacteristic, complemented
39#14583549C2212yes—
40#14583542—21no—
41#14583540C2212yescomplemented
42#14583538—22no—
43#14583534C2211yescharacteristic, complemented
44#14583533C2212yes—
45#14583446C2212yescomplemented
46#14583436—22no—
47#14583436C2212yescomplemented
48#14583411—21no—
49#14583408—22no—
50#14583406—21no—
51C4×#10621902C2212yescomplemented
52C4×#10621898C2211yescharacteristic
53C2×C4×D172C2211yescharacteristic
54C2×C4×D172C2211yescharacteristic, complemented
55C4×D4×D43C2212yescomplemented
56#117×D43—21no—
57#14583306C2212yescomplemented
58#14583285C2212yescomplemented
59#14583262C2212yescomplemented
60#14583260C2212yescomplemented
61#14583233C2212yescomplemented
62#14583227C2212yescomplemented
63#14583225C2212yescomplemented
64#14583221C2212yescomplemented
65#14583219C2212yescomplemented
66#14583210C2212yescomplemented
67#14583198C2212yescomplemented
68#14583197C2212yescomplemented
69#14583192C2212yescomplemented
70#14583188C2212yescomplemented
71#14583186C2211yescharacteristic, complemented
72#14583186C2211yescharacteristic, complemented
73#14583176C2211yescharacteristic, complemented
74#14583176C2211yescharacteristic, complemented
75#14583153C2212yescomplemented
76#14583151C2212yescomplemented
77#14583148C2212yescomplemented
78#14583142C2212yescomplemented
79#14583117C2212yes—
80#14583116C2212yescomplemented
81#14583101C2211yescharacteristic, complemented
82#14583101C2211yescharacteristic, complemented
83#14583097C2212yescomplemented
84#14583093C2212yescomplemented
85#14583091C2211yescharacteristic, complemented
86#14583091C2211yescharacteristic, complemented
87#14583049C2212yes—
88#14583048C2212yescomplemented
89#14583047C2212yescomplemented
90#14583043C2212yescomplemented
91#14583034C2212yes—
92#14583032C2212yescomplemented
93#14583029C2211yescharacteristic, complemented
94#14583029C2211yescharacteristic, complemented
95#14583010C2212yes—
96#14583008C2212yescomplemented
97#14583002C2212yescomplemented
98#14583000C2212yescomplemented
99C4×#10621884C2212yescomplemented
100C4×#10621884C2212yescomplemented
101C4×D344C2211yescharacteristic
102C4×D344C2211yescharacteristic
103C4×D344C2211yescharacteristic
104C4×D344C2211yescharacteristic
105C4×D344C2211yescharacteristic, complemented
106C4×D344C2211yescharacteristic, complemented
107C4×D344C2211yescharacteristic, complemented
108C4×D344C2211yescharacteristic, complemented
109C4×#10621882C2212yescomplemented
110C4×#10621882C2212yescomplemented
111#14582978C2211yescharacteristic, complemented
112#14582978C2211yescharacteristic, complemented
113#14582970C2212yescomplemented
114#14582970C2212yescomplemented
115#14582952C2211yescharacteristic, complemented
116#14582950C2212yescomplemented
117#14582938C2212yescomplemented
118C2×#13063259C2211yescharacteristic, complemented
119#14582902C2212yescomplemented
120#14582899C2212yescomplemented
121C2×#13063247C2211yescharacteristic
122C2×#13063247C2211yescharacteristic, complemented
123C4×#10621872C2212yescomplemented
124C43×#533C2211yescharacteristic, complemented
125C43×#532C2211yescharacteristic
126C43×#498C2211yescharacteristic, complemented
127C43×#492C2211yescharacteristic, complemented
128C43×#487C2211yescharacteristic, complemented
129C43×#486C2211yescharacteristic, complemented
130C43×#465C2212yescomplemented
131C43×#465C2212yescomplemented
132C4×SD16×C43C2212yescomplemented
133C4×SD16×C43C2212yescomplemented
134C2×C4×C8×C43C2211yescharacteristic, complemented
135C2×#10621902—21no—
136C2×#10621902C2312yes—
137C2×#10621898—22no—
138C2×#10621898D411yescharacteristic
139C2×#10621900—22no—
140C2×#10621900—21no—
141#41×D43—48no—
142C2×Q8×D43—21no—
143C22×D172C2311yescharacteristic
144C22×D172C2311yescharacteristic
145C2×D4×D43—22no—
146C2×D4×D43—21no—
147C2×D4×D43C2312yes—
148C22×C4×D43—21no—
149C22×C4×D43—21no—
150C22×C4×D43—22no—
151#13063352—28no—
152C2×#10621884C2312yes—
153C2×#10621884C2312yes—
154C2×D344—24no—
155C2×D344C2311yescharacteristic
156C2×D344C2311yescharacteristic
157C2×D344C2311yescharacteristic
158C2×D344C2311yescharacteristic
159C2×#10621882C2312yes—
160C2×#10621882C2312yes—
161C2×#10621872C2312yes—
162C2×#10621872C2312yes—
163#13063324C2312yes—
164#13063321C2312yes—
165#13063320—22no—
166#13063320—22no—
167#13063320—22no—
168#13063316—22no—
169#13063316C2312yes—
170#13063314—22no—
171#13063314C2312yes—
172#13063311—22no—
173#13063310—22no—
174#13063310—22no—
175#13063310—22no—
176#13063310—22no—
177#13063309—22no—
178#13063307—22no—
179#13063306—22no—
180#13063305—21no—
181#13063305—21no—
182#13063303—22no—
183#13063302—22no—
184#13063301—21no—
185#13063301—21no—
186#13063301—22no—
187#13063301C2312yes—
188#13063300—21no—
189#13063300—21no—
190#13063300—22no—
191#13063300C2312yes—
192#13063300C2312yes—
193#13063298—22no—
194#13063298—22no—
195#13063297—22no—
196#13063296—21no—
197#13063296—21no—
198#13063296C2312yes—
199#13063295—22no—
200#13063295—22no—
201#13063293—22no—
202#13063293—22no—
203Q8×Dic43C2312yes—
204C4×Dic86D411yescharacteristic
205C4×Dic86C2311yescharacteristic
206C4×D172—22no—
207C4×D172—22no—
208C4×D172—21no—
209C4×D172—21no—
210C4×D172—21no—
211C4×D172—21no—
212C4×D172D411yescharacteristic
213C4×D172C2311yescharacteristic
214C4×D172C2311yescharacteristic
215C4×D172C2311yescharacteristic
216C4×D172C2311yescharacteristic
217C4×D172C2311yescharacteristic
218C4×D172C2311yescharacteristic
219C4×D172C2311yescharacteristic
220C4×D172C2311yescharacteristic
221C4×D172C2311yescharacteristic
222D4×Dic43C2312yes—
223#13063287—22no—
224#13063287C2312yes—
225#13063287C2312yes—
226C4×C22⋊D43—22no—
227C4×C22⋊D43—22no—
228C4×C22⋊D43D412yes—
229C4×C22⋊D43C2312yes—
230(C22⋊D43)⋊C4—22no—
231#13063284D411yescharacteristic
232#13063283—21no—
233#13063283—21no—
234#13063283—22no—
235#13063283C2312yes—
236#13063282—22no—
237#13063282D412yes—
238#13063281—22no—
239C2×C4⋊Dic43C2311yescharacteristic
240C2×C4⋊Dic43C2311yescharacteristic
241C4⋊C4×D43—21no—
242C4⋊C4×D43—21no—
243C4⋊C4×D43C2312yes—
244C2×(C2×D43)⋊C4—21no—
245C2×(C2×D43)⋊C4—21no—
246C22⋊C4×D43—22no—
247C22⋊C4×D43—22no—
248C42×D43—22no—
249C42×D43C2312yes—
250#13063259C2311yescharacteristic
251#13063259C2311yescharacteristic
252#13063259C2311yescharacteristic
253#13063259C2311yescharacteristic
254#13063258C2312yes—
255#13063258C2312yes—
256#13063256C2312yes—
257#13063256C2312yes—
258C4⋊(C43⋊C8)C2311yescharacteristic
259C4⋊(C43⋊C8)C2311yescharacteristic
260Dic43⋊C8C2312yes—
261Dic43⋊C8C2312yes—
262#13063249C2312yes—
263#13063249C2312yes—
264#13063247C2311yescharacteristic
265#13063247C2311yescharacteristic
266#13063247C2311yescharacteristic
267#13063247C2311yescharacteristic
268#13063247C2311yescharacteristic
269#13063247C2311yescharacteristic
270#13063247C2311yescharacteristic
271#13063247C2311yescharacteristic
272#13063246C2312yes—
273#13063246C2312yes—
274#13063245C2312yes—
275#13063245C2312yes—
276#13063245C2312yes—
277#13063245C2312yes—
278C22⋊(C43⋊C8)C2312yes—
279(C2×D43)⋊C8C2312yes—
280(C2×D43)⋊C8C2312yes—
281#13063235C2312yes—
282#13063235C2312yes—
283C4×C43⋊C8C2312yes—
284C2×#41×C43—21no—
285C2×SD16×C43C2312yes—
286C2×SD16×C43C2312yes—
287C22×C8×C43C2311yescharacteristic
288C22×C8×C43C2311yescharacteristic
289C4⋊Q8×C43C2311yescharacteristic
290C4⋊Q8×C43C2311yescharacteristic
291C4⋊Q8×C43C2311yescharacteristic
292#127×C43C2311yescharacteristic
293#125×C43—21no—
294#124×C43—21no—
295C22⋊Q8×C43—21no—
296C22⋊Q8×C43C2312yes—
297#121×C43—21no—
298#121×C43C2312yes—
299C4×Q8×C43—21no—
300C4×Q8×C43C2312yes—
301C4×D4×C43—21no—
302C4×D4×C43C2312yes—
303#117×C43—21no—
304C2×C42×C43C2311yescharacteristic
305#106×C43C2312yes—
306#106×C43C2312yes—
307#103×C43C2312yes—
308#103×C43C2312yes—
309#102×C43C2312yes—
310#102×C43C2312yes—
311C4×C8×C43C2311yescharacteristic
312C4×C8×C43C2311yescharacteristic
313C4×C8×C43C2311yescharacteristic
314C4×C8×C43C2311yescharacteristic
315C23×D43—21no—
316C23×D43—21no—
317C23×D43—22no—
318#41×C43—44no—
319C2×Q8×C43—21no—
320C2×Q8×C43—21no—
321C2×Q8×C43C2412yes—
322C2×D4×C43—21no—
323C2×D4×C43—21no—
324C2×D4×C43—22no—
325C2×D4×C43C2412yes—
326C22×C4×C43—22no—
327C22×C4×C43C2×D411yescharacteristic
328C22×C4×C43C2×D411yescharacteristic
329C22×C4×C43C2411yescharacteristic
330C2×C22⋊D43—22no—
331C2×C22⋊D43—22no—
332C2×C22⋊D43—22no—
333C2×C22⋊D43—22no—
334C2×C22⋊D43C2×D412yes—
335C22×Dic43—22no—
336C22×Dic43—21no—
337C22×Dic43—21no—
338#10621902—24no—
339#10621902—42no—
340#10621902—44no—
341Q8×D43—44no—
342#10621900—44no—
343#10621900—48no—
344D4×D43—24no—
345D4×D43—42no—
346D4×D43—44no—
347D4×D43—48no—
348#10621898—24no—
349#10621898—48no—
350C2×D172—21no—
351C2×D172—21no—
352C2×D172—22no—
353C2×D172—22no—
354C2×D172—22no—
355C2×D172—22no—
356C2×D172—22no—
357C2×D172—41no—
358C2×D172—41no—
359C2×D172C2×D411yescharacteristic
360C2×D172C2411yescharacteristic
361C2×D172C2411yescharacteristic
362C2×D172C2411yescharacteristic
363C2×D172C2411yescharacteristic
364C2×C4×D43—21no—
365C2×C4×D43—21no—
366C2×C4×D43—21no—
367C2×C4×D43—21no—
368C2×C4×D43—21no—
369C2×C4×D43—21no—
370C2×C4×D43—21no—
371C2×C4×D43—21no—
372C2×C4×D43—22no—
373C2×C4×D43—22no—
374C2×C4×D43—22no—
375C2×C4×D43—22no—
376C2×C4×D43—48no—
377C2×C4×D43—44no—
378C2×C4×D43—44no—
379C2×C4×D43C2×D412yes—
380C2×C4×D43C2×D412yes—
381C2×C4×D43C2412yes—
382C2×Dic86—22no—
383C2×Dic86C2×D411yescharacteristic
384SD16×C43—24no—
385SD16×C43—42no—
386C2×C8×C43—22no—
387C2×C8×C43—41no—
388C2×C8×C43C2411yescharacteristic
389C2×C8×C43C2411yescharacteristic
390C2×C8×C43C2411yescharacteristic
391C2×C8×C43C2411yescharacteristic
392C4⋊C4×C43—21no—
393C4⋊C4×C43—21no—
394C4⋊C4×C43—21no—
395C4⋊C4×C43—21no—
396C4⋊C4×C43—22no—
397C4⋊C4×C43—22no—
398C4⋊C4×C43C2412yes—
399C4⋊C4×C43C2412yes—
400C22⋊C4×C43—22no—
401C22⋊C4×C43—22no—
402C22⋊C4×C43—22no—
403C42×C43—22no—
404C42×C43C2×D411yescharacteristic
405C42×C43C2×D411yescharacteristic
406C42×C43C2411yescharacteristic
407C42×C43C2411yescharacteristic
408C22⋊Dic43—22no—
409C22⋊Dic43—22no—
410C22⋊Dic43C2×D412yes—
411#10621884—24no—
412#10621884—42no—
413#10621882—24no—
414#10621882—42no—
415(C2×D43)⋊C4—21no—
416(C2×D43)⋊C4—21no—
417(C2×D43)⋊C4—21no—
418(C2×D43)⋊C4—21no—
419(C2×D43)⋊C4—21no—
420(C2×D43)⋊C4—21no—
421(C2×D43)⋊C4—21no—
422(C2×D43)⋊C4—21no—
423(C2×D43)⋊C4—22no—
424(C2×D43)⋊C4—22no—
425(C2×D43)⋊C4—22no—
426(C2×D43)⋊C4—22no—
427(C2×D43)⋊C4—22no—
428(C2×D43)⋊C4—22no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4C2×D412yes—
432(C2×D43)⋊C4C2×D412yes—
433C4⋊Dic43—21no—
434C4⋊Dic43—21no—
435C4⋊Dic43—22no—
436C4⋊Dic43—22no—
437C4⋊Dic43C2×D411yescharacteristic
438C4⋊Dic43C2×D411yescharacteristic
439C4⋊Dic43C2411yescharacteristic
440C4⋊Dic43C2411yescharacteristic
441C4⋊Dic43C2411yescharacteristic
442C4⋊Dic43C2411yescharacteristic
443Dic43⋊C4—22no—
444Dic43⋊C4—22no—
445Dic43⋊C4—22no—
446Dic43⋊C4—22no—
447Dic43⋊C4C2×D412yes—
448Dic43⋊C4C2×D412yes—
449C4×Dic43—22no—
450C4×Dic43—22no—
451C4×Dic43C2×D412yes—
452C4×Dic43C2×D412yes—
453C4×Dic43C2412yes—
454C2×C43⋊C8C2412yes—
455C2×C43⋊C8C2412yes—
456D344—22no—
457D344—22no—
458D344—22no—
459D344#4114yescomplemented
460#10621872—24no—
461#10621872—42no—
462C23×C43—22no—
463C23×C43C22×D411yescharacteristic
464C22×D43—21no—
465C22×D43—21no—
466C22×D43—21no—
467C22×D43—21no—
468C22×D43—44no—
469C22×D43—42no—
470C22×D43—42no—
471C22×D43—44no—
472C22×D43—42no—
473C22×D43—42no—
474C22×D43—82no—
475C22×D43—81no—
476C22×D43—81no—
477C22×D43C22×D412yes—
478Q8×C43—22no—
479Q8×C43—22no—
480Q8×C43—42no—
481Q8×C43—81no—
482D4×C43—22no—
483D4×C43—22no—
484D4×C43—44no—
485D4×C43—42no—
486D4×C43—81no—
487C2×C4×C43—21no—
488C2×C4×C43—21no—
489C2×C4×C43—22no—
490C2×C4×C43—22no—
491C2×C4×C43—22no—
492C2×C4×C43—41no—
493C2×C4×C43—44no—
494C2×C4×C43AGL(1,ℤ/8)14yescomplemented
495C2×C4×C43C22×D411yescharacteristic
496C2×C4×C43C22×D411yescharacteristic
497C2×C4×C43C22×D411yescharacteristic
498C2×C4×C43C22×D411yescharacteristic
499C2×C4×C43C22×D411yescharacteristic
500C2×C4×C43C2511yescharacteristic
501C22⋊D43—24no—
502C22⋊D43—44no—
503C22⋊D43—44no—
504C22⋊D43—44no—
505C22⋊D43—82no—
506C2×Dic43—21no—
507C2×Dic43—21no—
508C2×Dic43—21no—
509C2×Dic43—21no—
510C2×Dic43—44no—
511C2×Dic43—42no—
512C2×Dic43—42no—
513C2×Dic43C22×D412yes—
514C2×Dic43C22×D412yes—
515C2×Dic43C22×D412yes—
516D172—22no—
517D172—21no—
518D172—21no—
519D172—21no—
520D172—21no—
521D172—21no—
522D172—21no—
523D172—42no—
524D172—42no—
525D172—44no—
526D172—44no—
527D172—82no—
528D172C2×#4112yes—
529D172C2×#4112yescomplemented
530C4×D43—24no—
531C4×D43—22no—
532C4×D43—22no—
533C4×D43—42no—
534C4×D43—44no—
535C4×D43—44no—
536C4×D43—44no—
537C4×D43—42no—
538C4×D43—42no—
539C4×D43—42no—
540C4×D43—42no—
541C4×D43—42no—
542C4×D43—42no—
543C4×D43—42no—
544C4×D43—42no—
545C4×D43—82no—
546Dic86—22no—
547Dic86—44no—
548C8×C43—21no—
549C8×C43—21no—
550C8×C43—21no—
551C8×C43C2×#4112yescomplemented
552C43⋊C8—22no—
553C43⋊C8—22no—
554#61437—431nomaximal, Sylow
555C22×C43—21no—
556C22×C43—21no—
557C22×C43—42no—
558C22×C43—42no—
559C22×C43—42no—
560C22×C43C2×AGL(1,ℤ/8)12yes—
561C22×C43C23×D411yescharacteristic
562C2×D43—22no—
563C2×D43—22no—
564C2×D43—22no—
565C2×D43—22no—
566C2×D43—22no—
567C2×D43—41no—
568C2×D43—41no—
569C2×D43—41no—
570C2×D43—41no—
571C2×D43—41no—
572C2×D43—41no—
573C2×D43—41no—
574C2×D43—41no—
575C2×D43—41no—
576C2×D43—41no—
577C2×D43—88no—
578C2×D43—84no—
579C2×D43—84no—
580C4×C43—21no—
581C4×C43—21no—
582C4×C43—21no—
583C4×C43—42no—
584C4×C43—42no—
585C4×C43—42no—
586C4×C43C2×AGL(1,ℤ/8)12yes—
587C4×C43C2×AGL(1,ℤ/8)12yes—
588C4×C43C22×#4111yescharacteristic
589C4×C43#58511yescharacteristic
590Dic43—22no—
591Dic43—22no—
592Dic43—22no—
593Dic43—41no—
594Dic43—41no—
595Dic43—41no—
596Dic43—41no—
597#3475—431no—
598D4×#41—431no—
599#3397—431no—
600#3384—431no—
601#3367—431no—
602#3366—431no—
603#3354—431no—
604#3343—432no—
605#3330—431no—
606#3325—431no—
607#3310—432no—
608#3306—432no—
609#3272—431no—
610#3264—432no—
611#3171—432no—
612#3167D4311yescharacteristic, complemented
613#3106—432no—
614#3105—432no—
615#3101—431no—
616#3100—431no—
617#2965—431no—
618C4×AGL(1,ℤ/8)—432no—
619C2×C4×D8—431no—
620C2×C43—22no—
621C2×C43—82no—
622C2×C43D4×#4111yescharacteristic
623C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
624C2×C43#358411yescharacteristic
625D43—42no—
626D43—42no—
627D43—42no—
628D43—81no—
629D43—81no—
630C22×#41—861no—
631C2×AGL(1,ℤ/8)—432no—
632C22×D8—431no—
633#556—431no—
634#555—431no—
635#554—431no—
636#553—861no—
637#552—432no—
638#552—861no—
639#551—862no—
640#550—431no—
641D4×Q8—431no—
642#548—861no—
643#547—431no—
644#547—432no—
645#547—431no—
646#546—432no—
647#546—862no—
648#546—861no—
649D42—431no—
650D42—432no—
651#533C2×D4311yescharacteristic, complemented
652#532—432no—
653#532C2×D4311yescharacteristic
654#529—432no—
655#529—862no—
656#525—861no—
657#525—862no—
658#525—861no—
659C4×#41—431no—
660C4×#41—432no—
661C2×C4×D4—432no—
662C2×C4×D4—431no—
663C2×C4×D4—431no—
664C2×#117—861no—
665#501—432no—
666#498C2×D4311yescharacteristic, complemented
667#496—432no—
668#492C2×D4311yescharacteristic, complemented
669#490—432no—
670#489—432no—
671#487C2×D4311yescharacteristic, complemented
672#486C2×D4311yescharacteristic, complemented
673#484—432no—
674#483—432no—
675#482—432no—
676#482—432no—
677#481—432no—
678#480—432no—
679#478—432no—
680#478—432no—
681#477—432no—
682#476—431no—
683#476—431no—
684#476—432no—
685#474—431no—
686#474—431no—
687#469—432no—
688#469—432no—
689#468—432no—
690#468—432no—
691#465C2×D4312yescomplemented
692#465C2×D4312yescomplemented
693#463—432no—
694#463—432no—
695#461—431no—
696#461—431no—
697#460—432no—
698#459—431no—
699#459—431no—
700#459—432no—
701#450—432no—
702#450—432no—
703#449—432no—
704#449—432no—
705#447—432no—
706#447—432no—
707#446—431no—
708#446—431no—
709#442—432no—
710#442—432no—
711#440—432no—
712#440—432no—
713C4×SD16—432no—
714C4×SD16—432no—
715C4×SD16C2×D4312yescomplemented
716C4×SD16C2×D4312yescomplemented
717C4×D8—432no—
718C4×D8—432no—
719C4×D8—431no—
720C4×D8—431no—
721C4×D8—431no—
722C4×D8—431no—
723C4×D8—431no—
724C4×D8—431no—
725C4×D8—431no—
726C4×D8—431no—
727#436—431no—
728#436—431no—
729#435—432no—
730#435—432no—
731#431—431no—
732#431—432no—
733#428—432no—
734C2×#107—431no—
735#418—432no—
736#417—432no—
737C2×#102—431no—
738C2×#102—431no—
739C4×M16—432no—
740C2×C4×C8C2×D4311yescharacteristic, complemented
741C43#6143711yescharacteristic, complemented, Sylow
742C2×#41—21no—
743C2×#41—431no—
744C2×#41—432no—
745C2×#41—862no—
746C2×#41—862no—
747C2×#41—861no—
748C2×#41—861no—
749C2×#41—1728no—
750C22×Q8—861no—
751C22×D4—432no—
752C22×D4—431no—
753C22×D4—431no—
754C22×D4—862no—
755C22×D4—861no—
756C23×C4—862no—
757C23×C4—861no—
758C23×C4—861no—
759AGL(1,ℤ/8)—868no—
760C2×SD16—432no—
761C2×SD16—432no—
762C2×SD16C22×D4312yes—
763C2×SD16C22×D4312yes—
764C2×D8—432no—
765C2×D8—432no—
766C2×D8—431no—
767C2×D8—431no—
768C2×D8—431no—
769C2×D8—431no—
770C2×D8—864no—
771C2×M16—432no—
772C2×M16—432no—
773C22×C8C22×D4311yescharacteristic
774C22×C8C22×D4311yescharacteristic
775C4⋊Q8—432no—
776C4⋊Q8C22×D4311yescharacteristic
777C4⋊Q8C22×D4311yescharacteristic
778C4⋊Q8C22×D4311yescharacteristic
779#127—432no—
780#127C22×D4311yescharacteristic
781#126—862no—
782#126—862no—
783#126—862no—
784#125—21no—
785#125—432no—
786#125—862no—
787#124—21no—
788#124—432no—
789#124—862no—
790#124—862no—
791#123—862no—
792#123—862no—
793#123—862no—
794#123—862no—
795#123—862no—
796#123—862no—
797#123—862no—
798C22⋊Q8—21no—
799C22⋊Q8—432no—
800C22⋊Q8—862no—
801C22⋊Q8—862no—
802C22⋊Q8—861no—
803C22⋊Q8—861no—
804C22⋊Q8—861no—
805C22⋊Q8—861no—
806C22⋊Q8—862no—
807C22⋊Q8C22×D4312yes—
808#121—21no—
809#121—432no—
810#121—432no—
811#121—432no—
812#121—862no—
813#121—862no—
814#121—862no—
815#121—861no—
816#121—861no—
817#121—861no—
818#121—861no—
819#121—862no—
820#121C22×D4312yes—
821#120—862no—
822#120—862no—
823#120—862no—
824#120—862no—
825C4×Q8—21no—
826C4×Q8—431no—
827C4×Q8—431no—
828C4×Q8—432no—
829C4×Q8C22×D4312yes—
830C4×D4—21no—
831C4×D4—432no—
832C4×D4—432no—
833C4×D4—432no—
834C4×D4—432no—
835C4×D4—432no—
836C4×D4—431no—
837C4×D4—431no—
838C4×D4—431no—
839C4×D4—431no—
840C4×D4—431no—
841C4×D4—431no—
842C4×D4—431no—
843C4×D4—431no—
844C4×D4—431no—
845C4×D4—431no—
846C4×D4—862no—
847C4×D4—862no—
848C4×D4—862no—
849C4×D4—862no—
850C4×D4—862no—
851C4×D4—862no—
852C4×D4—861no—
853C4×D4—861no—
854C4×D4—861no—
855C4×D4—861no—
856C4×D4C22×D4312yes—
857#117—21no—
858#117—431no—
859#117—432no—
860#117—432no—
861#117—862no—
862#117—862no—
863#117—862no—
864#117—861no—
865#117—861no—
866C2×C4⋊C4—431no—
867C2×C4⋊C4—431no—
868C2×C4⋊C4—432no—
869C2×C4⋊C4—861no—
870C2×C4⋊C4—861no—
871C2×C22⋊C4—862no—
872C2×C22⋊C4—862no—
873C2×C22⋊C4—861no—
874C2×C22⋊C4—861no—
875C2×C42—432no—
876C2×C42—862no—
877C2×C42C22×D4311yescharacteristic
878#107—431no—
879#107—431no—
880#107—431no—
881#107—431no—
882#107—432no—
883#107—432no—
884#106—432no—
885#106—432no—
886#106C22×D4312yes—
887#106C22×D4312yes—
888C4⋊C8—432no—
889C4⋊C8—432no—
890C4⋊C8—431no—
891C4⋊C8—431no—
892#103—432no—
893#103—432no—
894#103C22×D4312yes—
895#103C22×D4312yes—
896#102—432no—
897#102—432no—
898#102—431no—
899#102—431no—
900#102—431no—
901#102—431no—
902#102—431no—
903#102—431no—
904#102—431no—
905#102—431no—
906#102—432no—
907#102—432no—
908#102—432no—
909#102—432no—
910#102C22×D4312yes—
911#102C22×D4312yes—
912C22⋊C8—432no—
913C22⋊C8—432no—
914C22⋊C8—432no—
915#97—432no—
916#97—432no—
917C4×C8—432no—
918C4×C8C22×D4311yescharacteristic
919C4×C8C22×D4311yescharacteristic
920C4×C8C22×D4311yescharacteristic
921C4×C8C22×D4311yescharacteristic
922C24—862no—
923C24—861no—
924C24—861no—
925#41—44no—
926#41—864no—
927#41—864no—
928#41—1728no—
929#41—1722no—
930#41—1728no—
931#41—1724no—
932#41—1724no—
933C2×Q8—21no—
934C2×Q8—21no—
935C2×Q8—431no—
936C2×Q8—862no—
937C2×Q8—1724no—
938C2×Q8C23×D4312yes—
939C2×D4—22no—
940C2×D4—21no—
941C2×D4—21no—
942C2×D4—432no—
943C2×D4—431no—
944C2×D4—431no—
945C2×D4—431no—
946C2×D4—431no—
947C2×D4—431no—
948C2×D4—862no—
949C2×D4—862no—
950C2×D4—862no—
951C2×D4—862no—
952C2×D4—862no—
953C2×D4—862no—
954C2×D4—862no—
955C2×D4—862no—
956C2×D4—864no—
957C2×D4—862no—
958C2×D4—861no—
959C2×D4—861no—
960C2×D4—1721no—
961C2×D4—1721no—
962C2×D4—1722no—
963C2×D4—1728no—
964C2×D4—1724no—
965C2×D4C23×D4312yes—
966C22×C4—22no—
967C22×C4—432no—
968C22×C4—432no—
969C22×C4—432no—
970C22×C4—862no—
971C22×C4—862no—
972C22×C4—862no—
973C22×C4—862no—
974C22×C4—862no—
975C22×C4—861no—
976C22×C4—861no—
977C22×C4—861no—
978C22×C4—861no—
979C22×C4—861no—
980C22×C4—861no—
981C22×C4—861no—
982C22×C4—861no—
983C22×C4—861no—
984C22×C4—861no—
985C22×C4—1728no—
986C22×C4—1724no—
987C22×C4—1724no—
988C22×C4D4×D4311yescharacteristic
989C22×C4D4×D4311yescharacteristic
990C22×C4C23×D4311yescharacteristic
991SD16—24no—
992SD16—42no—
993SD16—864no—
994SD16—1722no—
995D8—434no—
996D8—862no—
997D8—862no—
998D8—864no—
999D8—862no—
1000D8—1722no—
1001M16—864no—
1002M16—1722no—
1003C2×C8—22no—
1004C2×C8—41no—
1005C2×C8—432no—
1006C2×C8—432no—
1007C2×C8C23×D4311yescharacteristic
1008C2×C8C23×D4311yescharacteristic
1009C2×C8C23×D4311yescharacteristic
1010C2×C8C23×D4311yescharacteristic
1011C4⋊C4—21no—
1012C4⋊C4—21no—
1013C4⋊C4—22no—
1014C4⋊C4—21no—
1015C4⋊C4—22no—
1016C4⋊C4—21no—
1017C4⋊C4—431no—
1018C4⋊C4—431no—
1019C4⋊C4—432no—
1020C4⋊C4—432no—
1021C4⋊C4—431no—
1022C4⋊C4—431no—
1023C4⋊C4—431no—
1024C4⋊C4—431no—
1025C4⋊C4—862no—
1026C4⋊C4—862no—
1027C4⋊C4—862no—
1028C4⋊C4—862no—
1029C4⋊C4—862no—
1030C4⋊C4—862no—
1031C4⋊C4—861no—
1032C4⋊C4—861no—
1033C4⋊C4C23×D4312yes—
1034C4⋊C4C23×D4312yes—
1035C22⋊C4—22no—
1036C22⋊C4—22no—
1037C22⋊C4—22no—
1038C22⋊C4—432no—
1039C22⋊C4—432no—
1040C22⋊C4—432no—
1041C22⋊C4—862no—
1042C22⋊C4—862no—
1043C22⋊C4—862no—
1044C22⋊C4—862no—
1045C22⋊C4—862no—
1046C22⋊C4—862no—
1047C22⋊C4—862no—
1048C22⋊C4—862no—
1049C22⋊C4—862no—
1050C22⋊C4—862no—
1051C22⋊C4—861no—
1052C22⋊C4—861no—
1053C22⋊C4—861no—
1054C22⋊C4—861no—
1055C22⋊C4—861no—
1056C22⋊C4—861no—
1057C22⋊C4—861no—
1058C22⋊C4—861no—
1059C42—22no—
1060C42—432no—
1061C42—432no—
1062C42—432no—
1063C42—862no—
1064C42—862no—
1065C42D4×D4311yescharacteristic
1066C42D4×D4311yescharacteristic
1067C42C23×D4311yescharacteristic
1068C42C23×D4311yescharacteristic
1069C23—22no—
1070C23—432no—
1071C23—861no—
1072C23—861no—
1073C23—861no—
1074C23—861no—
1075C23—3441no—
1076C23—3441no—
1077C23—3442no—
1078C23—1722no—
1079C23—1722no—
1080C23—1724no—
1081C23—1724no—
1082C23—1722no—
1083C23—1722no—
1084C23C2×D4×D4311yescharacteristic
1085Q8—22no—
1086Q8—22no—
1087Q8—42no—
1088Q8—81no—
1089Q8—862no—
1090Q8—1724no—
1091D4—22no—
1092D4—22no—
1093D4—44no—
1094D4—42no—
1095D4—81no—
1096D4—432no—
1097D4—432no—
1098D4—864no—
1099D4—862no—
1100D4—861no—
1101D4—861no—
1102D4—861no—
1103D4—861no—
1104D4—861no—
1105D4—861no—
1106D4—3442no—
1107D4—3442no—
1108D4—1722no—
1109D4—1722no—
1110D4—1724no—
1111D4—1724no—
1112D4—1724no—
1113D4—1724no—
1114D4—1724no—
1115C2×C4—21no—
1116C2×C4—21no—
1117C2×C4—22no—
1118C2×C4—22no—
1119C2×C4—22no—
1120C2×C4—41no—
1121C2×C4—44no—
1122C2×C4—432no—
1123C2×C4—432no—
1124C2×C4—432no—
1125C2×C4—864no—
1126C2×C4—862no—
1127C2×C4—862no—
1128C2×C4—861no—
1129C2×C4—861no—
1130C2×C4—861no—
1131C2×C4—861no—
1132C2×C4—3442no—
1133C2×C4—1722no—
1134C2×C4—1724no—
1135C2×C4—1724no—
1136C2×C4—1724no—
1137C2×C4—1724no—
1138C2×C4—1722no—
1139C2×C4—1722no—
1140C2×C4—1722no—
1141C2×C4—1722no—
1142C2×C4—1722no—
1143C2×C4—1722no—
1144C2×C4—1722no—
1145C2×C4—1722no—
1146C2×C4—1722no—
1147C2×C4—1722no—
1148C2×C4#1306335214yescomplemented
1149C2×C4C2×D4×D4311yescharacteristic
1150C2×C4C2×D4×D4311yescharacteristic
1151C2×C4C2×D4×D4311yescharacteristic
1152C2×C4C2×D4×D4311yescharacteristic
1153C2×C4C2×D4×D4311yescharacteristic
1154C2×C4C24×D4311yescharacteristic
1155C8—21no—
1156C8—21no—
1157C8—21no—
1158C8—862no—
1159C8—862no—
1160C8#41×D4312yescomplemented
1161C22—21no—
1162C22—21no—
1163C22—42no—
1164C22—42no—
1165C22—42no—
1166C22—862no—
1167C22—862no—
1168C22—862no—
1169C22—862no—
1170C22—862no—
1171C22—3444no—
1172C22—3444no—
1173C22—3448no—
1174C22—1721no—
1175C22—1721no—
1176C22—1721no—
1177C22—1721no—
1178C22—1721no—
1179C22—1721no—
1180C22—1721no—
1181C22—1721no—
1182C22—1721no—
1183C22—1721no—
1184C22C2×#1306335212yes—
1185C22C22×D4×D4311yescharacteristic
1186C4—21no—
1187C4—21no—
1188C4—21no—
1189C4—42no—
1190C4—42no—
1191C4—42no—
1192C4—862no—
1193C4—862no—
1194C4—862no—
1195C4—1721no—
1196C4—1721no—
1197C4—1721no—
1198C4—1721no—
1199C4C2×#1306335212yes—
1200C4C2×#1306335212yes—
1201C4C2×#41×D4311yescharacteristic
1202C4#1458373511yescharacteristic
1203C2—22no—
1204C2—82no—
1205C2—3441no—
1206C2—3441no—
1207C2—1722no—
1208C2—1722no—
1209C2—1722no—
1210C2#1914808111yescharacteristic
1211C2C22×#1306335211yescharacteristic
1212C2#1914936411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3167C2
socleC22×C43C23×D4
hypercenter#3167D43
hypocenterC43#61437
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3167

Complements

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

NH ≅ G/Ntype
1. #19148162C2semidirect
2. #19148081C2semidirect
3. #19147620C2semidirect
4. #19147499C2semidirect
5. #19147318C2semidirect
6. #19147307C2semidirect
7. #19147189C2semidirect
8. #19147041C2semidirect
9. #19146899C2semidirect
10. #19146836C2semidirect
11. #19146622C2semidirect
12. #19146562C2semidirect
13. #19146194C2semidirect
14. #19146072C2semidirect
15. #19145186C2semidirect
16. #19144653C2semidirect
17. #19144646C2semidirect
18. #19144599C2semidirect
19. #19144591C2semidirect
20. #19143561C2semidirect
21. C4×#13063352C2semidirect
22. C2×C4×D344C2semidirect
23. C43×#3167C2semidirect
27. #14583623C22semidirect
28. #14583615C22semidirect
29. #14583610C22semidirect
31. #14583591C22semidirect
34. #14583569C22semidirect
35. #14583564C22semidirect
37. #14583552C22semidirect
38. #14583552C22semidirect
41. #14583540C22semidirect
43. #14583534C22semidirect
45. #14583446C22semidirect
47. #14583436C22semidirect
51. C4×#10621902C22semidirect
54. C2×C4×D172C22semidirect
55. C4×D4×D43C22semidirect
57. #14583306C22semidirect
58. #14583285C22semidirect
59. #14583262C22semidirect
60. #14583260C22semidirect
61. #14583233C22semidirect
62. #14583227C22semidirect
63. #14583225C22semidirect
64. #14583221C22semidirect
65. #14583219C22semidirect
66. #14583210C22semidirect
67. #14583198C22semidirect
68. #14583197C22semidirect
69. #14583192C22semidirect
70. #14583188C22semidirect
71. #14583186C22semidirect
72. #14583186C22semidirect
73. #14583176C22semidirect
74. #14583176C22semidirect
75. #14583153C22semidirect
76. #14583151C22semidirect
77. #14583148C22semidirect
78. #14583142C22semidirect
80. #14583116C22semidirect
81. #14583101C22semidirect
82. #14583101C22semidirect
83. #14583097C22semidirect
84. #14583093C22semidirect
85. #14583091C22semidirect
86. #14583091C22semidirect
88. #14583048C22semidirect
89. #14583047C22semidirect
90. #14583043C22semidirect
92. #14583032C22semidirect
93. #14583029C22semidirect
94. #14583029C22semidirect
96. #14583008C22semidirect
97. #14583002C22semidirect
98. #14583000C22semidirect
99. C4×#10621884C22semidirect
100. C4×#10621884C22semidirect
105. C4×D344C22semidirect
106. C4×D344C22semidirect
107. C4×D344C22semidirect
108. C4×D344C22semidirect
109. C4×#10621882C22semidirect
110. C4×#10621882C22semidirect
111. #14582978C22semidirect
112. #14582978C22semidirect
113. #14582970C22semidirect
114. #14582970C22semidirect
115. #14582952C22semidirect
116. #14582950C22semidirect
117. #14582938C22semidirect
118. C2×#13063259C22semidirect
119. #14582902C22semidirect
120. #14582899C22semidirect
122. C2×#13063247C22semidirect
123. C4×#10621872C22semidirect
124. C43×#533C22semidirect
126. C43×#498C22semidirect
127. C43×#492C22semidirect
128. C43×#487C22semidirect
129. C43×#486C22semidirect
130. C43×#465C22semidirect
131. C43×#465C22semidirect
132. C4×SD16×C43C22semidirect
133. C4×SD16×C43C22semidirect
134. C2×C4×C8×C43C22semidirect
459. D344#41semidirect
494. C2×C4×C43AGL(1,ℤ/8)semidirect
529. D172C2×#41semidirect
551. C8×C43C2×#41semidirect
612. #3167D43semidirect
651. #533C2×D43semidirect
666. #498C2×D43semidirect
668. #492C2×D43semidirect
671. #487C2×D43semidirect
672. #486C2×D43semidirect
691. #465C2×D43semidirect
692. #465C2×D43semidirect
715. C4×SD16C2×D43semidirect
716. C4×SD16C2×D43semidirect
740. C2×C4×C8C2×D43semidirect
741. C43#61437semidirect
1148. C2×C4#13063352semidirect
1160. C8#41×D43semidirect

Maximal subgroups

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

subgroupindex
#191481622
#191480812
#191476202
#191474992
#191473182
#191473072
#191471892
#191470412
#191468992
#191468362
#191466222
#191465622
#191461942
#191460722
#191451862
#191446532
#191446462
#191445992
#191445912
#191435612
C4×#130633522
C2×C4×D3442
C43×#31672
#6143743