Finite Group Databasebeta

← #25967517

Subgroups — #25967517

Order 11008.

2140 conjugacy classes of subgroups.

The subgroup lattice has 1290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148268C211yesmaximal, characteristic, complemented
2#19147927C211yesmaximal, characteristic, complemented
3#19145503C212yesmaximal, complemented
4#19145496C212yesmaximal, complemented
5#19145481C212yesmaximal, complemented
6#19145481C212yesmaximal, complemented
7#19145436C212yesmaximal, complemented
8#19145428C212yesmaximal, complemented
9#19145387C212yesmaximal, complemented
10#19145379C212yesmaximal, complemented
11#19144558C211yesmaximal, characteristic, complemented
12#19144554C211yesmaximal, characteristic, complemented
13#19144541C211yesmaximal, characteristic, complemented
14#19144506C211yesmaximal, characteristic, complemented
15#19144280C211yesmaximal, characteristic, complemented
16#19144278C211yesmaximal, characteristic, complemented
17#19144246C211yesmaximal, characteristic, complemented
18#19144237C211yesmaximal, characteristic, complemented
19#19143881C211yesmaximal, characteristic, complemented
20#19143836C211yesmaximal, characteristic, complemented
21C2×#14583060C211yesmaximal, characteristic, complemented
22#19143043C211yesmaximal, characteristic, complemented
23C43×#3011C211yesmaximal, characteristic, complemented
24C22×#10621902C2211yescharacteristic
25C2×#41×D43C2211yescharacteristic
26C2×#13063350C2211yescharacteristic, complemented
27C22×#10621884C2211yescharacteristic, complemented
28C2×#13063333C2211yescharacteristic
29C2×#13063331C2211yescharacteristic
30Q8×C22⋊D43—21no—
31#14583560—21no—
32#14583548—22no—
33#14583548—21no—
34#14583537—22no—
35#14583537—21no—
36#14583479C2212yes—
37#14583479C2212yes—
38#14583477C2211yescharacteristic
39#14583477C2212yescomplemented
40#14583474—21no—
41#14583473C2211yescharacteristic
42#14583473C2211yescharacteristic
43#14583473C2212yescomplemented
44#14583468C2211yescharacteristic
45#14583467—21no—
46#14583463C2211yescharacteristic
47#14583460—22no—
48#14583450—21no—
49#14583448—21no—
50#14583412C2212yes—
51#14583412C2212yes—
52#14583407—22no—
53#14583406C2211yescharacteristic
54#14583406C2212yescomplemented
55C2×#13063301C2211yescharacteristic
56C2×#13063301C2212yescomplemented
57#14583382C2211yescharacteristic
58#117×D43C2211yescharacteristic
59#14583239C2211yescharacteristic, complemented
60#14583239C2212yescomplemented
61#14583238C2211yescharacteristic, complemented
62#14583238C2212yescomplemented
63#14583237C2212yescomplemented
64#14583237C2212yescomplemented
65#14583233C2211yescharacteristic, complemented
66#14583233C2212yescomplemented
67#14583232C2212yescomplemented
68#14583228C2211yescharacteristic, complemented
69#14583228C2212yescomplemented
70#14583227C2212yescomplemented
71#14583224C2212yescomplemented
72#14583224C2212yescomplemented
73#14583222C2211yescharacteristic, complemented
74#14583221C2211yescharacteristic, complemented
75#14583218C2212yescomplemented
76#14583216C2211yescharacteristic, complemented
77#14583213C2212yescomplemented
78#14583211C2211yescharacteristic, complemented
79#14583154C2212yescomplemented
80#14583154C2212yescomplemented
81#14583154C2212yescomplemented
82#14583151C2212yescomplemented
83#14583148C2212yescomplemented
84#14583148C2212yescomplemented
85#14583148C2212yescomplemented
86#14583142C2212yescomplemented
87#14583137C2212yescomplemented
88#14583137C2212yescomplemented
89#14583137C2212yescomplemented
90#14583134C2212yescomplemented
91#14583131C2212yescomplemented
92#14583131C2212yescomplemented
93#14583131C2212yescomplemented
94#14583125C2212yescomplemented
95#14583060C2212yes—
96#14583060C2212yes—
97#14583060C2212yes—
98#14583060C2212yescomplemented
99#14583060C2212yescomplemented
100#14583060C2212yescomplemented
101#14583044C2212yescomplemented
102#14583044C2212yescomplemented
103#14583043C2212yes—
104#14583043C2212yescomplemented
105#14583038C2212yescomplemented
106#14583038C2212yescomplemented
107#14582942C2211yescharacteristic, complemented
108#14582941C2211yescharacteristic, complemented
109#14582937C2211yescharacteristic, complemented
110#14582935C2211yescharacteristic, complemented
111#14582908C2211yescharacteristic, complemented
112#14582908C2211yescharacteristic, complemented
113#14582905C2211yescharacteristic, complemented
114#14582895C2211yescharacteristic, complemented
115C2×#13063249C2211yescharacteristic, complemented
116C2×#13063247C2211yescharacteristic, complemented
117#14582866C2211yescharacteristic
118#14582864C2212yescomplemented
119#14582864C2212yescomplemented
120#14582862C2211yescharacteristic
121#14582861C2212yescomplemented
122C2×(C2×D43)⋊C8C2211yescharacteristic
123C22⋊C8×D43C2212yescomplemented
124C2×2−1+4×C43C2211yescharacteristic
125C2×#137×C43C2211yescharacteristic, complemented
126C22×Q16×C43C2211yescharacteristic, complemented
127C43×#536C2211yescharacteristic
128C43×#452C2212yescomplemented
129C43×#452C2212yescomplemented
130C43×#451C2212yescomplemented
131C43×#451C2212yescomplemented
132C43×#419C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C43×#408C2211yescharacteristic
135C2×#10621902—21no—
136C2×#10621902—21no—
137C2×#10621902—42no—
138C2×#10621902—42no—
139C2×#10621902D411yescharacteristic
140C2×#10621902C2312yes—
141C2×#10621902C2312yes—
142C2×#10621898C2311yescharacteristic
143C2×#10621898C2312yes—
144C2×#10621900D412yes—
145C2×#10621900D411yescharacteristic
146#41×D43—42no—
147#41×D43—42no—
148C2×Q8×D43D411yescharacteristic
149C22×D172—21no—
150C22×D172C2311yescharacteristic
151C2×D4×D43D412yes—
152C2×D4×D43D411yescharacteristic
153C22×C4×D43—21no—
154C22×C4×D43C2311yescharacteristic
155C22×C4×D43C2312yes—
156#13063350—42no—
157C2×#10621884—42no—
158C2×#10621884C2312yes—
159C2×#10621884C2312yes—
160C2×#10621884C2312yes—
161C2×#10621882C2312yes—
162#13063333—42no—
163#13063331—42no—
164C2×#10621877C2311yescharacteristic
165C2×#10621872C2312yes—
166C2×#10621872C2312yes—
167C22×C43⋊C8C2311yescharacteristic
168C2×C8×D43C2312yes—
169C2×C8×D43C2312yes—
170#13063323—21no—
171#13063323—22no—
172#13063323—21no—
173#13063322—21no—
174#13063321—21no—
175#13063314—21no—
176#13063314—21no—
177#13063314—22no—
178#13063314—21no—
179#13063313—21no—
180#13063310—22no—
181#13063310—22no—
182#13063308—22no—
183#13063308—22no—
184#13063308—22no—
185#13063308—22no—
186#13063306—21no—
187#13063306—22no—
188#13063304—21no—
189#13063304—22no—
190#13063303—22no—
191#13063303—22no—
192#13063301—21no—
193#13063301—22no—
194#13063301—21no—
195#13063301—22no—
196#13063301C2312yes—
197#13063301C2311yescharacteristic
198#13063301C2312yes—
199#13063301C2311yescharacteristic
200#13063301C2312yes—
201#13063301C2312yes—
202#13063301C2312yes—
203#13063301C2312yes—
204#13063301C2312yes—
205#13063300—22no—
206#13063300—22no—
207#13063300C2312yes—
208#13063300C2312yes—
209#13063299—21no—
210#13063299—22no—
211#13063299C2312yes—
212#13063299C2312yes—
213#13063298—22no—
214#13063298—22no—
215#13063298—22no—
216#13063298—22no—
217#13063297—22no—
218#13063297—22no—
219#13063297—22no—
220#13063296C2311yescharacteristic
221#13063296C2311yescharacteristic
222#13063296C2312yes—
223#13063295—22no—
224#13063295—22no—
225#13063295—22no—
226#13063293—21no—
227#13063293—22no—
228#13063293—22no—
229Q8×Dic43—21no—
230D4×Dic43—22no—
231D4×Dic43—21no—
232#13063287—22no—
233#13063287—22no—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—22no—
236C4×C22⋊D43—21no—
237C4×C22⋊D43—22no—
238(C22⋊D43)⋊C4—22no—
239(C22⋊D43)⋊C4—22no—
240#13063284C2311yescharacteristic
241#13063284C2311yescharacteristic
242#13063284C2312yes—
243#13063283C2311yescharacteristic
244#13063283C2311yescharacteristic
245#13063282—21no—
246#13063281—21no—
247C2×C4⋊Dic43C2311yescharacteristic
248C2×C4⋊Dic43C2312yes—
249C2×Dic43⋊C4—21no—
250C2×Dic43⋊C4—22no—
251C4⋊C4×D43C2311yescharacteristic
252C4⋊C4×D43C2311yescharacteristic
253C2×(C2×D43)⋊C4—21no—
254C2×(C2×D43)⋊C4—22no—
255C22⋊C4×D43—21no—
256C42×D43—21no—
257#13063259C2311yescharacteristic
258#13063259C2311yescharacteristic
259#13063259C2312yes—
260#13063258C2312yes—
261#13063258C2311yescharacteristic
262#13063258C2311yescharacteristic
263#13063257C2312yes—
264#13063257C2311yescharacteristic
265#13063257C2311yescharacteristic
266#13063256C2311yescharacteristic
267#13063256C2311yescharacteristic
268#13063256C2312yes—
269#13063249C2312yes—
270#13063249C2312yes—
271#13063249C2312yes—
272#13063249C2312yes—
273#13063249C2312yes—
274#13063249C2312yes—
275#13063249C2311yescharacteristic
276#13063249C2311yescharacteristic
277#13063247C2312yes—
278#13063247C2312yes—
279#13063247C2312yes—
280#13063247C2312yes—
281#13063246C2311yescharacteristic
282#13063246C2311yescharacteristic
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285(C2×D43)⋊C8C2312yes—
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2311yescharacteristic
288(C2×D43)⋊C8C2311yescharacteristic
289(C2×D43)⋊C8C2311yescharacteristic
290(C2×D43)⋊C8C2311yescharacteristic
2912−1+4×C43—42no—
2922−1+4×C43—42no—
293C2×#41×C43—22no—
294C2×#41×C43—21no—
295C2×#41×C43C2311yescharacteristic
296C2×#41×C43C2312yes—
297C2×#41×C43C2311yescharacteristic
298C22×Q8×C43—21no—
299C22×Q8×C43C2311yescharacteristic
300C22×Q8×C43C2311yescharacteristic
301C22×Q8×C43C2312yes—
302#137×C43—42no—
303C2×Q16×C43—42no—
304C2×Q16×C43C2312yes—
305C2×Q16×C43C2312yes—
306C2×Q16×C43C2312yes—
307C2×SD16×C43C2312yes—
308C2×M16×C43C2311yescharacteristic
309C22×C8×C43C2311yescharacteristic
310C4⋊Q8×C43—21no—
311#124×C43—21no—
312#123×C43—22no—
313C22⋊Q8×C43C2312yes—
314C22⋊Q8×C43C2312yes—
315#117×C43C2311yescharacteristic
316#103×C43C2311yescharacteristic
317#103×C43C2312yes—
318#103×C43C2312yes—
319#103×C43C2311yescharacteristic
320#102×C43C2311yescharacteristic
321#102×C43C2311yescharacteristic
322C22⋊C8×C43C2312yes—
323C22⋊C8×C43C2312yes—
324C23×D43—21no—
325C23×D43C2×D411yescharacteristic
326C23×D43C2×D412yes—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—42no—
332#41×C43—42no—
333#41×C43—48no—
334#41×C43—44no—
335C2×Q8×C43—21no—
336C2×Q8×C43—22no—
337C2×Q8×C43—21no—
338C2×Q8×C43—22no—
339C2×Q8×C43—22no—
340C2×Q8×C43—22no—
341C2×Q8×C43—22no—
342C2×Q8×C43—42no—
343C2×Q8×C43—42no—
344C2×Q8×C43—44no—
345C2×Q8×C43C2×D411yescharacteristic
346C2×Q8×C43C2412yes—
347C2×Q8×C43C2411yescharacteristic
348C2×Q8×C43C2412yes—
349C2×D4×C43—22no—
350C2×D4×C43—21no—
351C2×D4×C43C2×D412yes—
352C2×D4×C43C2×D411yescharacteristic
353C2×D4×C43C2411yescharacteristic
354C22×C4×C43—22no—
355C22×C4×C43—21no—
356C22×C4×C43—21no—
357C22×C4×C43—22no—
358C22×C4×C43—21no—
359C22×C4×C43C2412yes—
360C22×C4×C43C2411yescharacteristic
361C2×C22⋊D43—22no—
362C2×C22⋊D43—22no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—22no—
365C2×C22⋊D43—21no—
366C2×C22⋊D43C2×D412yes—
367C2×C22⋊D43C2×D412yes—
368C2×C22⋊D43C2×D412yes—
369C22×Dic43—22no—
370C22×Dic43—21no—
371C22×Dic43C2×D411yescharacteristic
372C22×Dic43C2×D412yes—
373#10621902—42no—
374#10621902—42no—
375#10621902—42no—
376#10621902—42no—
377#10621902—42no—
378#10621902—44no—
379#10621902—44no—
380Q8×D43—42no—
381#10621900—42no—
382#10621900—44no—
383D4×D43—44no—
384D4×D43—42no—
385#10621898—22no—
386#10621898—22no—
387#10621898—42no—
388#10621898—42no—
389C2×D172—21no—
390C2×D172—22no—
391C2×D172—22no—
392C2×D172—22no—
393C2×D172—22no—
394C2×D172—22no—
395C2×D172—22no—
396C2×D172—44no—
397C2×D172C2×D411yescharacteristic
398C2×D172C2×D412yes—
399C2×D172C2412yes—
400C2×C4×D43—22no—
401C2×C4×D43—22no—
402C2×C4×D43—22no—
403C2×C4×D43—22no—
404C2×C4×D43—21no—
405C2×C4×D43—21no—
406C2×C4×D43—42no—
407C2×C4×D43—42no—
408C2×C4×D43—44no—
409C2×C4×D43C2×D411yescharacteristic
410C2×C4×D43C2×D411yescharacteristic
411C2×C4×D43C2×D412yes—
412C2×C4×D43C2×D412yes—
413C2×C4×D43C2411yescharacteristic
414C2×C4×D43C2411yescharacteristic
415C2×C4×D43C2412yes—
416C2×Dic86C2×D411yescharacteristic
417C2×Dic86C2×D412yes—
418Q16×C43—42no—
419Q16×C43—42no—
420Q16×C43—42no—
421SD16×C43—42no—
422M16×C43—22no—
423C2×C8×C43—22no—
424C2×C8×C43C2411yescharacteristic
425C2×C8×C43C2411yescharacteristic
426C2×C8×C43C2412yes—
427C4⋊C4×C43—22no—
428C4⋊C4×C43—22no—
429C4⋊C4×C43C2411yescharacteristic
430C4⋊C4×C43C2411yescharacteristic
431C22⋊C4×C43—21no—
432C22⋊C4×C43—22no—
433C22⋊C4×C43—22no—
434C42×C43—21no—
435C22⋊Dic43—21no—
436C22⋊Dic43—22no—
437C22⋊Dic43—21no—
438C22⋊Dic43—21no—
439C22⋊Dic43—22no—
440C22⋊Dic43—21no—
441#10621884—42no—
442#10621884—42no—
443#10621884—42no—
444#10621882—42no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—21no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—21no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—21no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460C4⋊Dic43—22no—
461C4⋊Dic43—21no—
462C4⋊Dic43C2411yescharacteristic
463C4⋊Dic43C2411yescharacteristic
464C4⋊Dic43C2411yescharacteristic
465C4⋊Dic43C2412yes—
466C4⋊Dic43C2411yescharacteristic
467Dic43⋊C4—21no—
468Dic43⋊C4—21no—
469Dic43⋊C4—22no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—21no—
478C4×Dic43—21no—
479C4×Dic43—22no—
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483#10621877—22no—
484C2×C43⋊C8—22no—
485C2×C43⋊C8C2411yescharacteristic
486C2×C43⋊C8C2411yescharacteristic
487C2×C43⋊C8C2412yes—
488#10621872—42no—
489#10621872—42no—
490C8×D43—42no—
491C8×D43—42no—
492C23×C43—21no—
493C23×C43C22×D412yes—
494C23×C43C22×D411yescharacteristic
495C22×D43—22no—
496C22×D43—22no—
497C22×D43—42no—
498C22×D43—41no—
499C22×D43—42no—
500C22×D43—41no—
501C22×D43—42no—
502C22×D43—42no—
503C22×D43—81no—
504C22×D43—81no—
505C22×D43C22×D411yescharacteristic
506C22×D43C22×D412yes—
507C22×D43C22×D411yescharacteristic
508Q8×C43—22no—
509Q8×C43—22no—
510Q8×C43—21no—
511Q8×C43—22no—
512Q8×C43—22no—
513Q8×C43—22no—
514Q8×C43—21no—
515Q8×C43—44no—
516Q8×C43—42no—
517Q8×C43—42no—
518D4×C43—24no—
519D4×C43—22no—
520D4×C43—21no—
521D4×C43—21no—
522D4×C43—44no—
523D4×C43—42no—
524C2×C4×C43—22no—
525C2×C4×C43—22no—
526C2×C4×C43—21no—
527C2×C4×C43—21no—
528C2×C4×C43—22no—
529C2×C4×C43—21no—
530C2×C4×C43—22no—
531C2×C4×C43—44no—
532C2×C4×C43—44no—
533C2×C4×C43—42no—
534C2×C4×C43—42no—
535C2×C4×C43—42no—
536C2×C4×C43C22×D412yes—
537C2×C4×C43C22×D411yescharacteristic
538C2×C4×C43H(5,𝔽2)12yes—
539C2×C4×C43H(5,𝔽2)12yes—
540C2×C4×C43C2511yescharacteristic
541C22⋊D43—24no—
542C22⋊D43—42no—
543C22⋊D43—42no—
544C22⋊D43—42no—
545C22⋊D43—81no—
546C22⋊D43—82no—
547C22⋊D43—82no—
548C22⋊D43—82no—
549C2×Dic43—22no—
550C2×Dic43—21no—
551C2×Dic43—21no—
552C2×Dic43—21no—
553C2×Dic43—22no—
554C2×Dic43—21no—
555C2×Dic43—42no—
556C2×Dic43—81no—
557C2×Dic43—82no—
558C2×Dic43C22×D411yescharacteristic
559C2×Dic43C22×D412yes—
560C2×Dic43C22×D411yescharacteristic
561D172—22no—
562D172—22no—
563D172—22no—
564D172—42no—
565D172—44no—
566D172—44no—
567D172—42no—
568D172—82no—
569D172—82no—
570C4×D43—22no—
571C4×D43—22no—
572C4×D43—22no—
573C4×D43—22no—
574C4×D43—21no—
575C4×D43—21no—
576C4×D43—21no—
577C4×D43—21no—
578C4×D43—42no—
579C4×D43—42no—
580C4×D43—44no—
581C4×D43—44no—
582C4×D43—81no—
583C4×D43—81no—
584Dic86—22no—
585Dic86—42no—
586C8×C43—21no—
587C8×C43—22no—
588C8×C43—21no—
589C43⋊C8—21no—
590C43⋊C8—22no—
591C43⋊C8—21no—
592#60761—431nomaximal, Sylow
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—22no—
596C22×C43—22no—
597C22×C43—22no—
598C22×C43—41no—
599C22×C43—41no—
600C22×C43—41no—
601C22×C43#53412yes—
602C22×C43C23×D411yescharacteristic
603C2×D43—21no—
604C2×D43—21no—
605C2×D43—22no—
606C2×D43—21no—
607C2×D43—21no—
608C2×D43—22no—
609C2×D43—21no—
610C2×D43—21no—
611C2×D43—22no—
612C2×D43—42no—
613C2×D43—42no—
614C2×D43—42no—
615C2×D43—82no—
616C2×D43—84no—
617C2×D43—84no—
618C4×C43—22no—
619C4×C43—41no—
620C4×C43—41no—
621C4×C43—42no—
622C4×C43—42no—
623C4×C43—41no—
624C4×C43#53412yes—
625C4×C43C2×H(5,𝔽2)11yescharacteristic
626C4×C43C2×H(5,𝔽2)11yescharacteristic
627Dic43—22no—
628Dic43—21no—
629Dic43—21no—
630Dic43—41no—
631Dic43—42no—
632Dic43—41no—
633Dic43—41no—
634Dic43—41no—
635#3489—431no—
636#3449—431no—
637#3204—432no—
638#3203—432no—
639#3201—432no—
640#3201—432no—
641#3197—432no—
642#3196—432no—
643#3191—432no—
644#3190—432no—
645#3097—431no—
646#3096—431no—
647#3095—431no—
648#3091—431no—
649#3063—431no—
650#3062—431no—
651#3059—431no—
652#3057—431no—
653#3011D4311yescharacteristic, complemented
654#3010—431no—
655#3005—431no—
656C2×#452—431no—
657#2880—431no—
658C2×C43—22no—
659C2×C43—42no—
660C2×C43—81no—
661C2×C43C2×#53411yescharacteristic
662C2×C43#358411yescharacteristic
663C2×C43#358611yescharacteristic
664D43—41no—
665D43—42no—
666D43—41no—
667D43—82no—
668C2×2−1+4C2×D4311yescharacteristic
669C22×#41—431no—
670C22×#41—431no—
671C2×#137C2×D4311yescharacteristic, complemented
672C2×AGL(1,ℤ/8)—431no—
673C22×Q16C2×D4311yescharacteristic, complemented
674C22×SD16—431no—
675C2×#131—431no—
676C2×#131—431no—
677D4×Q8—861no—
678#548—861no—
679#547—862no—
680#547—861no—
681#546—862no—
682#546—861no—
683#537—432no—
684#537—431no—
685#537—432no—
686#537—432no—
687#536—431no—
688#536—432no—
689#536—431no—
690#536—861no—
691#536C2×D4311yescharacteristic
692#535—431no—
693#535—431no—
694#535—861no—
695#534—862no—
696#532—861no—
697#532—861no—
698#525—431no—
699#525—432no—
700#525—432no—
701#525—432no—
702#525—862no—
703C2×C22⋊Q8—431no—
704C2×C22⋊Q8—432no—
705#520—431no—
706C2×#117—431no—
707#485—432no—
708#485—432no—
709#485—431no—
710#485—431no—
711#485—432no—
712#485—432no—
713#484—432no—
714#484—431no—
715#484—432no—
716#483—432no—
717#483—431no—
718#483—432no—
719#482—431no—
720#482—431no—
721#482—432no—
722#482—432no—
723#481—431no—
724#481—432no—
725#480—431no—
726#480—432no—
727#470—432no—
728#470—432no—
729#470—432no—
730#469—432no—
731#468—432no—
732#468—432no—
733#468—432no—
734#468—432no—
735#467—432no—
736#467—432no—
737#467—432no—
738#466—432no—
739#465—432no—
740#465—432no—
741#465—432no—
742#465—432no—
743#452—432no—
744#452—432no—
745#452—432no—
746#452—432no—
747#452—432no—
748#452—432no—
749#452C2×D4312yescomplemented
750#452C2×D4312yescomplemented
751#451C2×D4312yescomplemented
752#451C2×D4312yescomplemented
753#449—432no—
754#449—432no—
755#449—432no—
756#449—432no—
757#448—432no—
758#448—432no—
759#428—431no—
760#428—431no—
761#427—431no—
762#427—431no—
763#419—431no—
764#419—431no—
765#419C2×D4311yescharacteristic, complemented
766#418—431no—
767#416—431no—
768#416C2×D4311yescharacteristic, complemented
769C2×#103—431no—
770C2×#102—431no—
771#408—431no—
772#408—432no—
773#408—432no—
774#408C2×D4311yescharacteristic
775#407—431no—
776#407—432no—
777C2×C22⋊C8—431no—
778C2×C22⋊C8—432no—
779C43#6076111yescharacteristic, complemented, Sylow
7802−1+4—42no—
7812−1+4—42no—
782C2×#41—22no—
783C2×#41—21no—
784C2×#41—431no—
785C2×#41—432no—
786C2×#41—431no—
787C2×#41—431no—
788C2×#41—432no—
789C2×#41—432no—
790C2×#41—432no—
791C2×#41—861no—
792C2×#41—861no—
793C2×#41—1722no—
794C2×#41—1722no—
795C2×#41—1722no—
796C2×#41—1722no—
797C2×#41C22×D4311yescharacteristic
798C2×#41C22×D4312yes—
799C2×#41C22×D4311yescharacteristic
800C22×Q8—21no—
801C22×Q8—431no—
802C22×Q8C22×D4311yescharacteristic
803C22×Q8C22×D4311yescharacteristic
804C22×Q8C22×D4312yes—
805C22×D4—432no—
806C22×D4—431no—
807C22×D4—431no—
808C22×D4—861no—
809C23×C4—431no—
810C23×C4—432no—
811C23×C4—861no—
812#137—42no—
813AGL(1,ℤ/8)—1722no—
814C2×Q16—42no—
815C2×Q16C22×D4312yes—
816C2×Q16C22×D4312yes—
817C2×Q16C22×D4312yes—
818C2×SD16—432no—
819C2×SD16—432no—
820C2×SD16—432no—
821C2×SD16—1722no—
822C2×SD16C22×D4312yes—
823C2×D8—432no—
824#131—1722no—
825#131—1722no—
826C2×M16—431no—
827C2×M16—432no—
828C2×M16—432no—
829C2×M16C22×D4311yescharacteristic
830C22×C8—431no—
831C22×C8—432no—
832C22×C8—432no—
833C22×C8C22×D4311yescharacteristic
834C4⋊Q8—21no—
835C4⋊Q8—861no—
836C4⋊Q8—861no—
837C4⋊Q8—862no—
838#127—861no—
839#127—861no—
840#124—21no—
841#124—861no—
842#124—861no—
843#124—861no—
844#124—862no—
845#124—861no—
846#123—22no—
847#123—862no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—861no—
854#123—862no—
855C22⋊Q8—432no—
856C22⋊Q8—431no—
857C22⋊Q8—432no—
858C22⋊Q8—432no—
859C22⋊Q8—432no—
860C22⋊Q8—431no—
861C22⋊Q8—432no—
862C22⋊Q8—432no—
863C22⋊Q8—432no—
864C22⋊Q8—862no—
865C22⋊Q8—862no—
866C22⋊Q8—861no—
867C22⋊Q8—862no—
868C22⋊Q8—861no—
869C22⋊Q8—862no—
870C22⋊Q8—861no—
871C22⋊Q8—862no—
872C22⋊Q8C22×D4312yes—
873C22⋊Q8C22×D4312yes—
874#121—431no—
875#121—431no—
876#121—432no—
877#121—432no—
878#121—432no—
879#121—432no—
880#121—432no—
881#121—862no—
882#121—862no—
883#121—862no—
884#121—862no—
885#121—862no—
886#121—862no—
887#121—861no—
888#121—862no—
889#121—862no—
890#121—862no—
891#121—862no—
892#120—862no—
893#120—862no—
894#120—862no—
895#120—861no—
896#120—862no—
897#120—862no—
898C4×Q8—861no—
899C4×D4—862no—
900C4×D4—862no—
901C4×D4—862no—
902C4×D4—862no—
903C4×D4—861no—
904C4×D4—862no—
905C4×D4—861no—
906C4×D4—862no—
907C4×D4—862no—
908C4×D4—861no—
909#117—431no—
910#117—431no—
911#117—432no—
912#117—431no—
913#117—431no—
914#117—861no—
915#117—861no—
916#117C22×D4311yescharacteristic
917C2×C4⋊C4—431no—
918C2×C4⋊C4—432no—
919C2×C4⋊C4—431no—
920C2×C4⋊C4—431no—
921C2×C4⋊C4—861no—
922C2×C4⋊C4—862no—
923C2×C22⋊C4—861no—
924C2×C22⋊C4—861no—
925C2×C22⋊C4—862no—
926C2×C42—861no—
927#107—431no—
928#107—431no—
929#107—432no—
930#107—431no—
931#107—431no—
932#107—432no—
933#106—431no—
934#106—431no—
935#106—432no—
936#106—431no—
937#106—431no—
938#106—432no—
939#103—432no—
940#103—432no—
941#103—431no—
942#103—431no—
943#103—432no—
944#103—432no—
945#103—432no—
946#103—432no—
947#103C22×D4311yescharacteristic
948#103C22×D4311yescharacteristic
949#103C22×D4312yes—
950#103C22×D4312yes—
951#102—431no—
952#102—431no—
953#102—432no—
954#102—432no—
955#102—432no—
956#102—432no—
957#102C22×D4311yescharacteristic
958#102C22×D4311yescharacteristic
959C22⋊C8—432no—
960C22⋊C8—432no—
961C22⋊C8—431no—
962C22⋊C8—432no—
963C22⋊C8—431no—
964C22⋊C8—431no—
965C22⋊C8—431no—
966C22⋊C8—432no—
967C22⋊C8C22×D4312yes—
968C22⋊C8C22×D4312yes—
969C24—431no—
970C24—432no—
971C24—861no—
972#41—22no—
973#41—22no—
974#41—22no—
975#41—22no—
976#41—42no—
977#41—42no—
978#41—48no—
979#41—44no—
980#41—862no—
981#41—862no—
982#41—1722no—
983#41—1722no—
984#41—1724no—
985#41—1722no—
986#41—1722no—
987#41—1722no—
988#41—1722no—
989#41—1722no—
990#41—1722no—
991#41—1724no—
992#41—1724no—
993C2×Q8—22no—
994C2×Q8—21no—
995C2×Q8—21no—
996C2×Q8—22no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—22no—
1000C2×Q8—42no—
1001C2×Q8—42no—
1002C2×Q8—44no—
1003C2×Q8—431no—
1004C2×Q8—432no—
1005C2×Q8—1722no—
1006C2×Q8D4×D4311yescharacteristic
1007C2×Q8C23×D4312yes—
1008C2×Q8C23×D4312yes—
1009C2×Q8C23×D4311yescharacteristic
1010C2×D4—22no—
1011C2×D4—21no—
1012C2×D4—432no—
1013C2×D4—432no—
1014C2×D4—432no—
1015C2×D4—431no—
1016C2×D4—432no—
1017C2×D4—432no—
1018C2×D4—862no—
1019C2×D4—862no—
1020C2×D4—862no—
1021C2×D4—862no—
1022C2×D4—862no—
1023C2×D4—861no—
1024C2×D4—862no—
1025C2×D4—862no—
1026C2×D4—861no—
1027C2×D4—861no—
1028C2×D4—862no—
1029C2×D4—862no—
1030C2×D4—1724no—
1031C2×D4—1722no—
1032C2×D4—1724no—
1033C2×D4D4×D4312yes—
1034C2×D4D4×D4311yescharacteristic
1035C2×D4C23×D4311yescharacteristic
1036C22×C4—22no—
1037C22×C4—21no—
1038C22×C4—21no—
1039C22×C4—22no—
1040C22×C4—21no—
1041C22×C4—431no—
1042C22×C4—432no—
1043C22×C4—431no—
1044C22×C4—431no—
1045C22×C4—431no—
1046C22×C4—431no—
1047C22×C4—432no—
1048C22×C4—432no—
1049C22×C4—432no—
1050C22×C4—862no—
1051C22×C4—862no—
1052C22×C4—861no—
1053C22×C4—861no—
1054C22×C4—862no—
1055C22×C4—862no—
1056C22×C4—862no—
1057C22×C4—861no—
1058C22×C4—1722no—
1059C22×C4—1722no—
1060C22×C4—1724no—
1061C22×C4C23×D4312yes—
1062C22×C4C23×D4311yescharacteristic
1063Q16—42no—
1064Q16—42no—
1065Q16—42no—
1066SD16—42no—
1067SD16—1722no—
1068SD16—1722no—
1069SD16—1722no—
1070D8—1722no—
1071M16—22no—
1072M16—862no—
1073M16—1722no—
1074M16—1722no—
1075C2×C8—22no—
1076C2×C8—431no—
1077C2×C8—431no—
1078C2×C8—432no—
1079C2×C8—862no—
1080C2×C8—1722no—
1081C2×C8—1722no—
1082C2×C8C23×D4311yescharacteristic
1083C2×C8C23×D4311yescharacteristic
1084C2×C8C23×D4312yes—
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—432no—
1088C4⋊C4—431no—
1089C4⋊C4—431no—
1090C4⋊C4—431no—
1091C4⋊C4—431no—
1092C4⋊C4—861no—
1093C4⋊C4—861no—
1094C4⋊C4—862no—
1095C4⋊C4—861no—
1096C4⋊C4—862no—
1097C4⋊C4—862no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—861no—
1103C4⋊C4—862no—
1104C4⋊C4—861no—
1105C4⋊C4C23×D4311yescharacteristic
1106C4⋊C4C23×D4311yescharacteristic
1107C22⋊C4—21no—
1108C22⋊C4—22no—
1109C22⋊C4—22no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—861no—
1116C22⋊C4—862no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—862no—
1121C22⋊C4—862no—
1122C22⋊C4—861no—
1123C22⋊C4—861no—
1124C22⋊C4—862no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—862no—
1128C22⋊C4—861no—
1129C22⋊C4—862no—
1130C22⋊C4—862no—
1131C42—21no—
1132C42—861no—
1133C42—861no—
1134C42—861no—
1135C42—862no—
1136C42—861no—
1137C23—21no—
1138C23—431no—
1139C23—432no—
1140C23—431no—
1141C23—862no—
1142C23—862no—
1143C23—3441no—
1144C23—3441no—
1145C23—1722no—
1146C23—1721no—
1147C23—1721no—
1148C23—1722no—
1149C23—1722no—
1150C23—1722no—
1151C23C2×D4×D4312yes—
1152C23C2×D4×D4311yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—21no—
1157Q8—22no—
1158Q8—22no—
1159Q8—21no—
1160Q8—44no—
1161Q8—42no—
1162Q8—42no—
1163Q8—862no—
1164Q8—1722no—
1165D4—24no—
1166D4—22no—
1167D4—21no—
1168D4—21no—
1169D4—44no—
1170D4—42no—
1171D4—864no—
1172D4—862no—
1173D4—862no—
1174D4—862no—
1175D4—3442no—
1176D4—3442no—
1177D4—3442no—
1178D4—3442no—
1179D4—3441no—
1180D4—3442no—
1181D4—1722no—
1182D4—1724no—
1183D4—1724no—
1184D4—1722no—
1185D4—1722no—
1186D4—1722no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—21no—
1191C2×C4—21no—
1192C2×C4—22no—
1193C2×C4—22no—
1194C2×C4—21no—
1195C2×C4—44no—
1196C2×C4—44no—
1197C2×C4—42no—
1198C2×C4—42no—
1199C2×C4—42no—
1200C2×C4—431no—
1201C2×C4—432no—
1202C2×C4—431no—
1203C2×C4—862no—
1204C2×C4—862no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—861no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—862no—
1216C2×C4—861no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—3441no—
1220C2×C4—3442no—
1221C2×C4—1722no—
1222C2×C4—1722no—
1223C2×C4—1724no—
1224C2×C4—1724no—
1225C2×C4—1722no—
1226C2×C4C2×D4×D4312yes—
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4#1306337012yes—
1229C2×C4#1306337012yes—
1230C2×C4C24×D4311yescharacteristic
1231C8—21no—
1232C8—21no—
1233C8—22no—
1234C8—861no—
1235C8—861no—
1236C8—862no—
1237C22—21no—
1238C22—21no—
1239C22—22no—
1240C22—22no—
1241C22—22no—
1242C22—41no—
1243C22—41no—
1244C22—41no—
1245C22—861no—
1246C22—862no—
1247C22—861no—
1248C22—861no—
1249C22—862no—
1250C22—861no—
1251C22—861no—
1252C22—861no—
1253C22—862no—
1254C22—3444no—
1255C22—3442no—
1256C22—3444no—
1257C22—1722no—
1258C22—1722no—
1259C22—1722no—
1260C22#1458345912yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—22no—
1263C4—41no—
1264C4—41no—
1265C4—42no—
1266C4—41no—
1267C4—42no—
1268C4—861no—
1269C4—861no—
1270C4—862no—
1271C4—1722no—
1272C4—1721no—
1273C4—1721no—
1274C4—1721no—
1275C4—1721no—
1276C4#1458345912yes—
1277C4C2×#1306337011yescharacteristic
1278C4C2×#1306337011yescharacteristic
1279C2—22no—
1280C2—42no—
1281C2—81no—
1282C2—3442no—
1283C2—1721no—
1284C2—1721no—
1285C2—1722no—
1286C2C2×#1458345911yescharacteristic
1287C2#1914936511yescharacteristic
1288C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3011C2
socleC22×C43C23×D4
hypercenter#3011D43
hypocenterC43#60761
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3011

Complements

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

NH ≅ G/Ntype
1. #19148268C2semidirect
2. #19147927C2semidirect
3. #19145503C2semidirect
4. #19145496C2semidirect
5. #19145481C2semidirect
6. #19145481C2semidirect
7. #19145436C2semidirect
8. #19145428C2semidirect
9. #19145387C2semidirect
10. #19145379C2semidirect
11. #19144558C2semidirect
12. #19144554C2semidirect
13. #19144541C2semidirect
14. #19144506C2semidirect
15. #19144280C2semidirect
16. #19144278C2semidirect
17. #19144246C2semidirect
18. #19144237C2semidirect
19. #19143881C2semidirect
20. #19143836C2semidirect
21. C2×#14583060C2semidirect
22. #19143043C2semidirect
23. C43×#3011C2semidirect
26. C2×#13063350C22semidirect
27. C22×#10621884C22semidirect
39. #14583477C22semidirect
43. #14583473C22semidirect
54. #14583406C22semidirect
56. C2×#13063301C22semidirect
59. #14583239C22semidirect
60. #14583239C22semidirect
61. #14583238C22semidirect
62. #14583238C22semidirect
63. #14583237C22semidirect
64. #14583237C22semidirect
65. #14583233C22semidirect
66. #14583233C22semidirect
67. #14583232C22semidirect
68. #14583228C22semidirect
69. #14583228C22semidirect
70. #14583227C22semidirect
71. #14583224C22semidirect
72. #14583224C22semidirect
73. #14583222C22semidirect
74. #14583221C22semidirect
75. #14583218C22semidirect
76. #14583216C22semidirect
77. #14583213C22semidirect
78. #14583211C22semidirect
79. #14583154C22semidirect
80. #14583154C22semidirect
81. #14583154C22semidirect
82. #14583151C22semidirect
83. #14583148C22semidirect
84. #14583148C22semidirect
85. #14583148C22semidirect
86. #14583142C22semidirect
87. #14583137C22semidirect
88. #14583137C22semidirect
89. #14583137C22semidirect
90. #14583134C22semidirect
91. #14583131C22semidirect
92. #14583131C22semidirect
93. #14583131C22semidirect
94. #14583125C22semidirect
98. #14583060C22semidirect
99. #14583060C22semidirect
100. #14583060C22semidirect
101. #14583044C22semidirect
102. #14583044C22semidirect
104. #14583043C22semidirect
105. #14583038C22semidirect
106. #14583038C22semidirect
107. #14582942C22semidirect
108. #14582941C22semidirect
109. #14582937C22semidirect
110. #14582935C22semidirect
111. #14582908C22semidirect
112. #14582908C22semidirect
113. #14582905C22semidirect
114. #14582895C22semidirect
115. C2×#13063249C22semidirect
116. C2×#13063247C22semidirect
118. #14582864C22semidirect
119. #14582864C22semidirect
121. #14582861C22semidirect
123. C22⋊C8×D43C22semidirect
125. C2×#137×C43C22semidirect
126. C22×Q16×C43C22semidirect
128. C43×#452C22semidirect
129. C43×#452C22semidirect
130. C43×#451C22semidirect
131. C43×#451C22semidirect
132. C43×#419C22semidirect
133. C43×#416C22semidirect
653. #3011D43semidirect
671. C2×#137C2×D43semidirect
673. C22×Q16C2×D43semidirect
749. #452C2×D43semidirect
750. #452C2×D43semidirect
751. #451C2×D43semidirect
752. #451C2×D43semidirect
765. #419C2×D43semidirect
768. #416C2×D43semidirect
779. C43#60761semidirect

Maximal subgroups

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

subgroupindex
#191482682
#191479272
#191455032
#191454962
#191454812
#191454362
#191454282
#191453872
#191453792
#191445582
#191445542
#191445412
#191445062
#191442802
#191442782
#191442462
#191442372
#191438812
#191438362
C2×#145830602
#191430432
C43×#30112
#6076143