Finite Group Databasebeta

← #25967471

Subgroups — #25967471

Order 11008.

2118 conjugacy classes of subgroups.

The subgroup lattice has 1270 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148268C211yesmaximal, characteristic
2#536×D43C211yesmaximal, characteristic, complemented
3#19145488C212yesmaximal, complemented
4#19145488C212yesmaximal, complemented
5#19145476C212yesmaximal, complemented
6#19145474C212yesmaximal, complemented
7#19145423C212yesmaximal, complemented
8#19145417C212yesmaximal, complemented
9#19145374C212yesmaximal, complemented
10#19145368C212yesmaximal, complemented
11#19144565C211yesmaximal, characteristic, complemented
12#19144558C211yesmaximal, characteristic, complemented
13#19144541C211yesmaximal, characteristic, complemented
14#19144506C211yesmaximal, characteristic, complemented
15#19144289C211yesmaximal, characteristic, complemented
16#19144280C211yesmaximal, characteristic, complemented
17#19144249C211yesmaximal, characteristic, complemented
18#19144246C211yesmaximal, characteristic, complemented
19#19143890C211yesmaximal, characteristic, complemented
20#19143827C211yesmaximal, characteristic, complemented
21C2×#14583053C211yesmaximal, characteristic, complemented
22#19143043C211yesmaximal, characteristic, complemented
23C43×#3011C211yesmaximal, characteristic, complemented
24C2×#41×D43C2211yescharacteristic
25C22×Q8×D43C2211yescharacteristic
26C2×#13063355C2211yescharacteristic, complemented
27C22×#10621885C2211yescharacteristic, complemented
28C2×#13063333C2211yescharacteristic
29C2×#13063331C2211yescharacteristic
30Q8×C22⋊D43—21no—
31#14583560—21no—
32#14583548—21no—
33#14583548—22no—
34#14583537—22no—
35#14583537—21no—
36#14583477C2212yes—
37#14583477C2211yescharacteristic
38#14583475C2211yescharacteristic
39#14583474—21no—
40#14583473C2212yes—
41#14583473C2211yescharacteristic
42#14583473C2211yescharacteristic
43#14583472C2212yes—
44#14583472C2212yes—
45#14583471—22no—
46#14583470C2211yescharacteristic
47#14583469—21no—
48C4⋊Q8×D43—21no—
49#124×D43—21no—
50#14583406C2211yescharacteristic
51#14583406C2212yes—
52#123×D43—22no—
53C2×#13063301C2211yescharacteristic
54C2×#13063301C2212yes—
55C22⋊Q8×D43C2212yes—
56C22⋊Q8×D43C2212yes—
57#14583382C2211yescharacteristic
58#117×D43C2211yescharacteristic
59#14583241C2212yescomplemented
60#14583241C2212yescomplemented
61#14583239C2212yescomplemented
62#14583239C2211yescharacteristic, complemented
63#14583238C2212yescomplemented
64#14583238C2211yescharacteristic, complemented
65#14583237C2212yescomplemented
66#14583237C2212yescomplemented
67#14583235C2212yescomplemented
68#14583233C2211yescharacteristic
69#14583233C2212yes—
70#14583232C2212yescomplemented
71#14583230C2212yescomplemented
72#14583228C2211yescharacteristic
73#14583228C2212yes—
74#14583227C2212yescomplemented
75#14583222C2211yescharacteristic, complemented
76#14583221C2211yescharacteristic, complemented
77#14583216C2211yescharacteristic
78#14583211C2211yescharacteristic
79#14583156C2212yescomplemented
80#14583156C2212yescomplemented
81#14583156C2212yescomplemented
82#14583154C2212yescomplemented
83#14583154C2212yescomplemented
84#14583154C2212yescomplemented
85#14583144C2212yescomplemented
86#14583142C2212yescomplemented
87#14583139C2212yescomplemented
88#14583139C2212yescomplemented
89#14583139C2212yescomplemented
90#14583137C2212yescomplemented
91#14583137C2212yescomplemented
92#14583137C2212yescomplemented
93#14583127C2212yescomplemented
94#14583125C2212yescomplemented
95#14583061C2212yescomplemented
96#14583061C2212yescomplemented
97#14583055C2212yescomplemented
98#14583055C2212yescomplemented
99#14583053C2212yes—
100#14583053C2212yes—
101#14583053C2212yes—
102#14583053C2212yescomplemented
103#14583053C2212yescomplemented
104#14583053C2212yescomplemented
105#14583036C2212yes—
106#14583036C2212yescomplemented
107#14582942C2211yescharacteristic, complemented
108#14582941C2211yescharacteristic, complemented
109#14582937C2211yescharacteristic, complemented
110#14582935C2211yescharacteristic, complemented
111#14582909C2211yescharacteristic, complemented
112#14582908C2211yescharacteristic, complemented
113#14582908C2211yescharacteristic, complemented
114#14582895C2211yescharacteristic, complemented
115C2×#13063250C2211yescharacteristic, complemented
116C2×#13063249C2211yescharacteristic, complemented
117#14582866C2211yescharacteristic
118#14582864C2212yes—
119#14582864C2212yes—
120#14582862C2211yescharacteristic
121#14582861C2212yes—
122C2×(C2×D43)⋊C8C2211yescharacteristic
123C22⋊C8×D43C2212yes—
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×#10621902D411yescharacteristic
136C2×#10621898C2311yescharacteristic
137C2×#10621898C2312yes—
138C2×#10621900D411yescharacteristic
139C2×#10621900D412yes—
140#41×D43—42no—
141#41×D43—42no—
142C22×Dic86—21no—
143C22×Dic86C2311yescharacteristic
144C2×Q8×D43—21no—
145C2×Q8×D43—21no—
146C2×Q8×D43—42no—
147C2×Q8×D43—42no—
148C2×Q8×D43D411yescharacteristic
149C2×Q8×D43C2312yes—
150C2×Q8×D43C2312yes—
151C2×D4×D43D412yes—
152C2×D4×D43D411yescharacteristic
153C22×C4×D43—21no—
154C22×C4×D43C2311yescharacteristic
155C22×C4×D43C2312yes—
156#13063355—42no—
157C2×#10621885—42no—
158C2×#10621885C2312yes—
159C2×#10621885C2312yes—
160C2×#10621885C2312yes—
161C2×#10621883C2312yes—
162#13063333—42no—
163#13063331—42no—
164C2×#10621877C2311yescharacteristic
165C2×#10621872C2312yes—
166C2×#10621872C2312yes—
167C22×C43⋊C8C2311yescharacteristic
168C2×C8×D43C2312yes—
169C2×C8×D43C2312yes—
170#13063325—21no—
171#13063324—22no—
172#13063324—22no—
173#13063323—21no—
174#13063323—21no—
175#13063323—22no—
176#13063323—21no—
177#13063314—21no—
178#13063314—22no—
179#13063314—21no—
180#13063313—21no—
181#13063312—21no—
182#13063311—22no—
183#13063311—22no—
184#13063310—22no—
185#13063310—22no—
186#13063309—22no—
187#13063308—22no—
188#13063308—22no—
189#13063308—22no—
190#13063308—22no—
191#13063307—22no—
192#13063307—22no—
193#13063306—22no—
194#13063306—21no—
195#13063306—22no—
196#13063305C2312yes—
197#13063305C2312yes—
198#13063304—21no—
199#13063304—22no—
200#13063304C2312yes—
201#13063304C2312yes—
202#13063303—22no—
203#13063303—22no—
204#13063302—22no—
205#13063302—22no—
206#13063301—21no—
207#13063301—22no—
208#13063301—21no—
209#13063301—22no—
210#13063301C2312yes—
211#13063301C2311yescharacteristic
212#13063301C2312yes—
213#13063301C2311yescharacteristic
214#13063301C2312yes—
215#13063301C2312yes—
216#13063301C2312yes—
217#13063301C2312yes—
218#13063301C2312yes—
219#13063299—21no—
220#13063299—22no—
221#13063297—22no—
222#13063297—22no—
223#13063297—22no—
224#13063296C2312yes—
225#13063296C2311yescharacteristic
226#13063296C2311yescharacteristic
227#13063293—21no—
228#13063293—22no—
229Q8×Dic43—21no—
230D4×Dic43—22no—
231D4×Dic43—21no—
232C4×C22⋊D43—21no—
233C4×C22⋊D43—22no—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—22no—
236#13063284C2311yescharacteristic
237#13063284C2311yescharacteristic
238#13063284C2312yes—
239#13063283C2311yescharacteristic
240#13063283C2311yescharacteristic
241#13063282—21no—
242#13063281—21no—
243C2×C4⋊Dic43C2311yescharacteristic
244C2×C4⋊Dic43C2312yes—
245C2×Dic43⋊C4—21no—
246C2×Dic43⋊C4—22no—
247C4⋊C4×D43—22no—
248C4⋊C4×D43—22no—
249C4⋊C4×D43C2311yescharacteristic
250C4⋊C4×D43C2311yescharacteristic
251C2×(C2×D43)⋊C4—21no—
252C2×(C2×D43)⋊C4—22no—
253C22⋊C4×D43—21no—
254C22⋊C4×D43—22no—
255C22⋊C4×D43—22no—
256C42×D43—21no—
257#13063259C2311yescharacteristic
258#13063259C2311yescharacteristic
259#13063259C2312yes—
260#13063258C2311yescharacteristic
261#13063258C2311yescharacteristic
262#13063258C2312yes—
263#13063257C2312yes—
264#13063257C2311yescharacteristic
265#13063257C2311yescharacteristic
266#13063256C2312yes—
267#13063256C2311yescharacteristic
268#13063256C2311yescharacteristic
269#13063250C2312yes—
270#13063250C2312yes—
271#13063250C2312yes—
272#13063250C2312yes—
273#13063249C2312yes—
274#13063249C2312yes—
275#13063249C2312yes—
276#13063249C2312yes—
277#13063249C2311yescharacteristic
278#13063249C2311yescharacteristic
279#13063249C2312yes—
280#13063249C2312yes—
281#13063246C2311yescharacteristic
282#13063246C2311yescharacteristic
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285(C2×D43)⋊C8C2311yescharacteristic
286(C2×D43)⋊C8C2311yescharacteristic
287(C2×D43)⋊C8C2312yes—
288(C2×D43)⋊C8C2311yescharacteristic
289(C2×D43)⋊C8C2311yescharacteristic
290(C2×D43)⋊C8C2312yes—
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×D43C2×D411yescharacteristic
325C23×D43C2×D412yes—
326#41×C43—22no—
327#41×C43—22no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—42no—
331#41×C43—42no—
332#41×C43—48no—
333#41×C43—44no—
334C2×Q8×C43—21no—
335C2×Q8×C43—22no—
336C2×Q8×C43—21no—
337C2×Q8×C43—22no—
338C2×Q8×C43—22no—
339C2×Q8×C43—22no—
340C2×Q8×C43—22no—
341C2×Q8×C43—42no—
342C2×Q8×C43—42no—
343C2×Q8×C43—44no—
344C2×Q8×C43C2×D411yescharacteristic
345C2×Q8×C43C2412yes—
346C2×Q8×C43C2411yescharacteristic
347C2×Q8×C43C2412yes—
348C2×D4×C43—22no—
349C2×D4×C43—21no—
350C2×D4×C43C2×D412yes—
351C2×D4×C43C2×D411yescharacteristic
352C2×D4×C43C2411yescharacteristic
353C22×C4×C43—22no—
354C22×C4×C43—21no—
355C22×C4×C43—21no—
356C22×C4×C43—22no—
357C22×C4×C43—21no—
358C22×C4×C43C2412yes—
359C22×C4×C43C2411yescharacteristic
360C2×C22⋊D43—21no—
361C2×C22⋊D43—22no—
362C2×C22⋊D43—21no—
363C2×C22⋊D43C2×D412yes—
364C2×C22⋊D43C2×D412yes—
365C2×C22⋊D43C2×D412yes—
366C22×Dic43—21no—
367C22×Dic43—22no—
368C22×Dic43—21no—
369C22×Dic43C2×D411yescharacteristic
370C22×Dic43C2×D412yes—
371#10621902—42no—
372Q8×D43—42no—
373Q8×D43—42no—
374Q8×D43—42no—
375Q8×D43—42no—
376Q8×D43—42no—
377Q8×D43—44no—
378Q8×D43—44no—
379#10621900—42no—
380#10621900—44no—
381D4×D43—44no—
382D4×D43—42no—
383#10621898—22no—
384#10621898—22no—
385#10621898—42no—
386#10621898—42no—
387C2×D172C2×D411yescharacteristic
388C2×D172C2×D412yes—
389C2×C4×D43—22no—
390C2×C4×D43—22no—
391C2×C4×D43—21no—
392C2×C4×D43—21no—
393C2×C4×D43—22no—
394C2×C4×D43—22no—
395C2×C4×D43—44no—
396C2×C4×D43—42no—
397C2×C4×D43—42no—
398C2×C4×D43C2×D411yescharacteristic
399C2×C4×D43C2×D411yescharacteristic
400C2×C4×D43C2×D412yes—
401C2×C4×D43C2×D412yes—
402C2×C4×D43C2411yescharacteristic
403C2×C4×D43C2411yescharacteristic
404C2×C4×D43C2412yes—
405C2×Dic86—22no—
406C2×Dic86—22no—
407C2×Dic86—21no—
408C2×Dic86—22no—
409C2×Dic86—22no—
410C2×Dic86—44no—
411C2×Dic86C2×D411yescharacteristic
412C2×Dic86C2×D412yes—
413C2×Dic86C2412yes—
414Q16×C43—42no—
415Q16×C43—42no—
416Q16×C43—42no—
417SD16×C43—42no—
418M16×C43—22no—
419C2×C8×C43—22no—
420C2×C8×C43C2411yescharacteristic
421C2×C8×C43C2411yescharacteristic
422C2×C8×C43C2412yes—
423C4⋊C4×C43—22no—
424C4⋊C4×C43—22no—
425C4⋊C4×C43C2411yescharacteristic
426C4⋊C4×C43C2411yescharacteristic
427C22⋊C4×C43—21no—
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C42×C43—21no—
431C22⋊Dic43—21no—
432C22⋊Dic43—21no—
433C22⋊Dic43—22no—
434C22⋊Dic43—21no—
435C22⋊Dic43—22no—
436C22⋊Dic43—22no—
437C22⋊Dic43—22no—
438C22⋊Dic43—21no—
439#10621885—42no—
440#10621885—42no—
441#10621885—42no—
442#10621883—42no—
443(C2×D43)⋊C4—21no—
444(C2×D43)⋊C4—21no—
445(C2×D43)⋊C4—22no—
446(C2×D43)⋊C4—22no—
447(C2×D43)⋊C4—22no—
448(C2×D43)⋊C4—22no—
449(C2×D43)⋊C4—22no—
450(C2×D43)⋊C4—21no—
451(C2×D43)⋊C4—22no—
452(C2×D43)⋊C4—22no—
453(C2×D43)⋊C4—22no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—21no—
456C4⋊Dic43—22no—
457C4⋊Dic43—21no—
458C4⋊Dic43—22no—
459C4⋊Dic43—22no—
460C4⋊Dic43C2411yescharacteristic
461C4⋊Dic43C2411yescharacteristic
462C4⋊Dic43C2412yes—
463C4⋊Dic43C2411yescharacteristic
464C4⋊Dic43C2411yescharacteristic
465Dic43⋊C4—22no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—22no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472Dic43⋊C4—21no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—21no—
477Dic43⋊C4—22no—
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—24no—
498C22×D43—41no—
499C22×D43—42no—
500C22×D43—42no—
501C22×D43C22×D412yes—
502C22×D43C22×D411yescharacteristic
503C22×D43C22×D411yescharacteristic
504Q8×C43—22no—
505Q8×C43—22no—
506Q8×C43—21no—
507Q8×C43—22no—
508Q8×C43—22no—
509Q8×C43—22no—
510Q8×C43—21no—
511Q8×C43—44no—
512Q8×C43—42no—
513Q8×C43—42no—
514D4×C43—24no—
515D4×C43—22no—
516D4×C43—21no—
517D4×C43—21no—
518D4×C43—44no—
519D4×C43—42no—
520C2×C4×C43—22no—
521C2×C4×C43—22no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—22no—
525C2×C4×C43—21no—
526C2×C4×C43—22no—
527C2×C4×C43—44no—
528C2×C4×C43—44no—
529C2×C4×C43—42no—
530C2×C4×C43—42no—
531C2×C4×C43—42no—
532C2×C4×C43C22×D412yes—
533C2×C4×C43C22×D411yescharacteristic
534C2×C4×C43H(5,𝔽2)12yes—
535C2×C4×C43H(5,𝔽2)12yes—
536C2×C4×C43C2511yescharacteristic
537C22⋊D43—24no—
538C22⋊D43—42no—
539C22⋊D43—42no—
540C22⋊D43—42no—
541C22⋊D43—81no—
542C22⋊D43—82no—
543C2×Dic43—22no—
544C2×Dic43—21no—
545C2×Dic43—21no—
546C2×Dic43—21no—
547C2×Dic43—22no—
548C2×Dic43—21no—
549C2×Dic43—22no—
550C2×Dic43—42no—
551C2×Dic43—42no—
552C2×Dic43—81no—
553C2×Dic43—82no—
554C2×Dic43C22×D411yescharacteristic
555C2×Dic43C22×D412yes—
556C2×Dic43C22×D411yescharacteristic
557D172—22no—
558D172—42no—
559C4×D43—22no—
560C4×D43—22no—
561C4×D43—22no—
562C4×D43—22no—
563C4×D43—21no—
564C4×D43—21no—
565C4×D43—21no—
566C4×D43—21no—
567C4×D43—42no—
568C4×D43—42no—
569C4×D43—42no—
570C4×D43—44no—
571C4×D43—44no—
572C4×D43—42no—
573Dic86—22no—
574Dic86—22no—
575Dic86—22no—
576Dic86—42no—
577Dic86—44no—
578Dic86—44no—
579Dic86—42no—
580C8×C43—21no—
581C8×C43—22no—
582C8×C43—21no—
583C43⋊C8—21no—
584C43⋊C8—22no—
585C43⋊C8—21no—
586#60759—431nomaximal, Sylow
587C22×C43—21no—
588C22×C43—21no—
589C22×C43—22no—
590C22×C43—22no—
591C22×C43—22no—
592C22×C43—41no—
593C22×C43—41no—
594C22×C43—41no—
595C22×C43#53412yes—
596C22×C43C23×D411yescharacteristic
597C2×D43—21no—
598C2×D43—21no—
599C2×D43—21no—
600C2×D43—22no—
601C2×D43—21no—
602C2×D43—22no—
603C2×D43—21no—
604C2×D43—22no—
605C2×D43—44no—
606C2×D43—84no—
607C2×D43#57812yes—
608C4×C43—22no—
609C4×C43—41no—
610C4×C43—42no—
611C4×C43—42no—
612C4×C43—41no—
613C4×C43—41no—
614C4×C43#53412yes—
615C4×C43C2×H(5,𝔽2)11yescharacteristic
616C4×C43C2×H(5,𝔽2)11yescharacteristic
617Dic43—22no—
618Dic43—21no—
619Dic43—21no—
620Dic43—41no—
621Dic43—42no—
622Dic43—41no—
623Dic43—42no—
624Dic43—41no—
625Dic43—41no—
626#3489—431no—
627C2×#536—431no—
628#3202—432no—
629#3202—432no—
630#3201—432no—
631#3201—432no—
632#3196—432no—
633#3195—432no—
634#3190—432no—
635#3189—432no—
636#3097—431no—
637#3097—431no—
638#3095—431no—
639#3091—431no—
640#3063—431no—
641#3063—431no—
642#3059—431no—
643#3059—431no—
644#3011—431no—
645#3011D4311yescharacteristic, complemented
646#3004—431no—
647C2×#451—431no—
648#2880—431no—
649C2×C43—22no—
650C2×C43—42no—
651C2×C43—81no—
652C2×C43C2×#53411yescharacteristic
653C2×C43C2×#57811yescharacteristic
654C2×C43#358611yescharacteristic
655D43—22no—
656D43—41no—
657D43—42no—
658C2×2−1+4C2×D4311yescharacteristic
659C22×#41—431no—
660C23×Q8—431no—
661C2×#137—431no—
662C2×#137C2×D4311yescharacteristic, complemented
663C22×Q16—431no—
664C22×Q16C2×D4311yescharacteristic, complemented
665C2×#131—431no—
666C2×#131—431no—
667D4×Q8—861no—
668#548—861no—
669#547—862no—
670#547—861no—
671#546—862no—
672#546—861no—
673#537—432no—
674#537—431no—
675#536—431no—
676#536—431no—
677#536—432no—
678#536—431no—
679#536—432no—
680#536—432no—
681#536—431no—
682#536—862no—
683#536—861no—
684#536—861no—
685#536C2×D4311yescharacteristic
686C2×C4⋊Q8—861no—
687C2×#124—861no—
688#525—431no—
689#525—432no—
690C2×#123—862no—
691C2×C22⋊Q8—431no—
692C2×C22⋊Q8—432no—
693C2×C22⋊Q8—432no—
694C2×C22⋊Q8—432no—
695#520—431no—
696C2×#117—431no—
697#485—432no—
698#485—432no—
699#485—431no—
700#485—431no—
701#485—432no—
702#485—432no—
703#485—432no—
704#485—432no—
705#484—432no—
706#484—431no—
707#484—432no—
708#484—432no—
709#483—432no—
710#483—431no—
711#483—432no—
712#483—432no—
713#482—431no—
714#482—431no—
715#481—431no—
716#480—431no—
717#470—432no—
718#470—432no—
719#470—432no—
720#470—432no—
721#470—432no—
722#470—432no—
723#468—432no—
724#468—432no—
725#467—432no—
726#467—432no—
727#467—432no—
728#467—432no—
729#467—432no—
730#467—432no—
731#465—432no—
732#465—432no—
733#452—432no—
734#452—432no—
735#452C2×D4312yescomplemented
736#452C2×D4312yescomplemented
737#451—432no—
738#451—432no—
739#451—432no—
740#451—432no—
741#451—432no—
742#451—432no—
743#451—432no—
744#451—432no—
745#451C2×D4312yescomplemented
746#451C2×D4312yescomplemented
747#448—432no—
748#448—432no—
749#428—431no—
750#428—431no—
751#427—431no—
752#427—431no—
753#419—431no—
754#419—431no—
755#419—431no—
756#419C2×D4311yescharacteristic, complemented
757#416—431no—
758#416C2×D4311yescharacteristic, complemented
759C2×#103—431no—
760C2×#103—431no—
761#408—431no—
762#408—432no—
763#408—432no—
764#408C2×D4311yescharacteristic
765#407—431no—
766#407—432no—
767C2×C22⋊C8—431no—
768C2×C22⋊C8—432no—
769C43#6075911yescharacteristic, complemented, Sylow
7702−1+4—42no—
7712−1+4—42no—
772C2×#41—22no—
773C2×#41—21no—
774C2×#41—431no—
775C2×#41—432no—
776C2×#41—431no—
777C2×#41—431no—
778C2×#41—432no—
779C2×#41—1722no—
780C2×#41—1722no—
781C2×#41C22×D4311yescharacteristic
782C2×#41C22×D4312yes—
783C2×#41C22×D4311yescharacteristic
784C22×Q8—21no—
785C22×Q8—431no—
786C22×Q8—432no—
787C22×Q8—432no—
788C22×Q8—431no—
789C22×Q8—861no—
790C22×Q8—861no—
791C22×Q8—861no—
792C22×Q8—1722no—
793C22×Q8—1722no—
794C22×Q8C22×D4311yescharacteristic
795C22×Q8C22×D4311yescharacteristic
796C22×Q8C22×D4312yes—
797C22×D4—432no—
798C22×D4—431no—
799C23×C4—431no—
800C23×C4—432no—
801C23×C4—861no—
802#137—42no—
803#137—1722no—
804C2×Q16—42no—
805C2×Q16—432no—
806C2×Q16—432no—
807C2×Q16—432no—
808C2×Q16—1722no—
809C2×Q16C22×D4312yes—
810C2×Q16C22×D4312yes—
811C2×Q16C22×D4312yes—
812C2×SD16—432no—
813C2×SD16C22×D4312yes—
814#131—1722no—
815#131—1722no—
816C2×M16—431no—
817C2×M16—432no—
818C2×M16—432no—
819C2×M16C22×D4311yescharacteristic
820C22×C8—431no—
821C22×C8—432no—
822C22×C8—432no—
823C22×C8C22×D4311yescharacteristic
824C4⋊Q8—21no—
825C4⋊Q8—861no—
826C4⋊Q8—862no—
827C4⋊Q8—862no—
828C4⋊Q8—861no—
829C4⋊Q8—861no—
830C4⋊Q8—862no—
831C4⋊Q8—861no—
832#124—21no—
833#124—861no—
834#124—862no—
835#124—862no—
836#124—861no—
837#124—861no—
838#124—862no—
839#124—861no—
840#123—22no—
841#123—862no—
842#123—862no—
843#123—862no—
844#123—862no—
845#123—862no—
846#123—862no—
847#123—862no—
848#123—862no—
849#123—862no—
850#123—861no—
851#123—862no—
852#123—862no—
853C22⋊Q8—432no—
854C22⋊Q8—431no—
855C22⋊Q8—432no—
856C22⋊Q8—432no—
857C22⋊Q8—432no—
858C22⋊Q8—432no—
859C22⋊Q8—432no—
860C22⋊Q8—431no—
861C22⋊Q8—432no—
862C22⋊Q8—432no—
863C22⋊Q8—432no—
864C22⋊Q8—432no—
865C22⋊Q8—432no—
866C22⋊Q8—862no—
867C22⋊Q8—862no—
868C22⋊Q8—862no—
869C22⋊Q8—862no—
870C22⋊Q8—861no—
871C22⋊Q8—862no—
872C22⋊Q8—861no—
873C22⋊Q8—862no—
874C22⋊Q8—861no—
875C22⋊Q8—862no—
876C22⋊Q8C22×D4312yes—
877C22⋊Q8C22×D4312yes—
878#121—431no—
879#121—431no—
880#121—432no—
881#121—861no—
882#121—862no—
883#121—862no—
884#121—862no—
885#121—862no—
886#120—861no—
887#120—862no—
888C4×Q8—861no—
889C4×D4—861no—
890C4×D4—862no—
891C4×D4—861no—
892C4×D4—862no—
893C4×D4—862no—
894C4×D4—861no—
895#117—431no—
896#117—431no—
897#117—432no—
898#117—431no—
899#117—431no—
900#117—861no—
901#117—861no—
902#117C22×D4311yescharacteristic
903C2×C4⋊C4—431no—
904C2×C4⋊C4—432no—
905C2×C4⋊C4—431no—
906C2×C4⋊C4—431no—
907C2×C4⋊C4—862no—
908C2×C4⋊C4—862no—
909C2×C4⋊C4—861no—
910C2×C4⋊C4—862no—
911C2×C22⋊C4—861no—
912C2×C22⋊C4—862no—
913C2×C22⋊C4—862no—
914C2×C22⋊C4—861no—
915C2×C22⋊C4—862no—
916C2×C42—861no—
917#107—431no—
918#107—431no—
919#107—432no—
920#107—431no—
921#107—431no—
922#107—432no—
923#106—431no—
924#106—431no—
925#106—432no—
926#106—431no—
927#106—431no—
928#106—432no—
929#103—432no—
930#103—432no—
931#103—431no—
932#103—431no—
933#103—432no—
934#103—432no—
935#103—432no—
936#103—432no—
937#103—432no—
938#103—432no—
939#103—432no—
940#103—432no—
941#103C22×D4311yescharacteristic
942#103C22×D4311yescharacteristic
943#103C22×D4312yes—
944#103C22×D4312yes—
945#102—431no—
946#102—431no—
947#102C22×D4311yescharacteristic
948#102C22×D4311yescharacteristic
949C22⋊C8—432no—
950C22⋊C8—432no—
951C22⋊C8—431no—
952C22⋊C8—432no—
953C22⋊C8—431no—
954C22⋊C8—431no—
955C22⋊C8—431no—
956C22⋊C8—432no—
957C22⋊C8C22×D4312yes—
958C22⋊C8C22×D4312yes—
959C24—431no—
960C24—432no—
961#41—22no—
962#41—22no—
963#41—22no—
964#41—22no—
965#41—42no—
966#41—42no—
967#41—48no—
968#41—44no—
969#41—862no—
970#41—862no—
971#41—1722no—
972#41—1722no—
973#41—1724no—
974#41—1722no—
975#41—1722no—
976C2×Q8—22no—
977C2×Q8—21no—
978C2×Q8—21no—
979C2×Q8—22no—
980C2×Q8—22no—
981C2×Q8—22no—
982C2×Q8—22no—
983C2×Q8—42no—
984C2×Q8—42no—
985C2×Q8—44no—
986C2×Q8—431no—
987C2×Q8—432no—
988C2×Q8—432no—
989C2×Q8—862no—
990C2×Q8—862no—
991C2×Q8—861no—
992C2×Q8—862no—
993C2×Q8—862no—
994C2×Q8—1724no—
995C2×Q8—1722no—
996C2×Q8—1722no—
997C2×Q8—1722no—
998C2×Q8—1722no—
999C2×Q8—1722no—
1000C2×Q8—1724no—
1001C2×Q8—1724no—
1002C2×Q8D4×D4311yescharacteristic
1003C2×Q8C23×D4312yes—
1004C2×Q8C23×D4312yes—
1005C2×Q8C23×D4311yescharacteristic
1006C2×D4—22no—
1007C2×D4—21no—
1008C2×D4—432no—
1009C2×D4—432no—
1010C2×D4—432no—
1011C2×D4—431no—
1012C2×D4—432no—
1013C2×D4—862no—
1014C2×D4—861no—
1015C2×D4—861no—
1016C2×D4—1722no—
1017C2×D4—1724no—
1018C2×D4D4×D4312yes—
1019C2×D4D4×D4311yescharacteristic
1020C2×D4C23×D4311yescharacteristic
1021C22×C4—22no—
1022C22×C4—21no—
1023C22×C4—21no—
1024C22×C4—22no—
1025C22×C4—21no—
1026C22×C4—431no—
1027C22×C4—432no—
1028C22×C4—431no—
1029C22×C4—431no—
1030C22×C4—431no—
1031C22×C4—431no—
1032C22×C4—432no—
1033C22×C4—432no—
1034C22×C4—432no—
1035C22×C4—861no—
1036C22×C4—861no—
1037C22×C4—862no—
1038C22×C4—862no—
1039C22×C4—862no—
1040C22×C4—862no—
1041C22×C4—862no—
1042C22×C4—861no—
1043C22×C4—861no—
1044C22×C4—1722no—
1045C22×C4—1722no—
1046C22×C4—1724no—
1047C22×C4C23×D4312yes—
1048C22×C4C23×D4311yescharacteristic
1049Q16—42no—
1050Q16—42no—
1051Q16—42no—
1052Q16—1722no—
1053Q16—1722no—
1054Q16—1722no—
1055SD16—42no—
1056SD16—1722no—
1057M16—22no—
1058M16—862no—
1059M16—1722no—
1060M16—1722no—
1061C2×C8—22no—
1062C2×C8—431no—
1063C2×C8—431no—
1064C2×C8—432no—
1065C2×C8—862no—
1066C2×C8—1722no—
1067C2×C8—1722no—
1068C2×C8C23×D4311yescharacteristic
1069C2×C8C23×D4311yescharacteristic
1070C2×C8C23×D4312yes—
1071C4⋊C4—22no—
1072C4⋊C4—22no—
1073C4⋊C4—431no—
1074C4⋊C4—431no—
1075C4⋊C4—432no—
1076C4⋊C4—431no—
1077C4⋊C4—431no—
1078C4⋊C4—861no—
1079C4⋊C4—861no—
1080C4⋊C4—862no—
1081C4⋊C4—861no—
1082C4⋊C4—862no—
1083C4⋊C4—862no—
1084C4⋊C4—862no—
1085C4⋊C4—862no—
1086C4⋊C4—862no—
1087C4⋊C4—862no—
1088C4⋊C4—862no—
1089C4⋊C4—861no—
1090C4⋊C4—862no—
1091C4⋊C4—862no—
1092C4⋊C4—861no—
1093C4⋊C4—862no—
1094C4⋊C4—862no—
1095C4⋊C4C23×D4311yescharacteristic
1096C4⋊C4C23×D4311yescharacteristic
1097C22⋊C4—21no—
1098C22⋊C4—22no—
1099C22⋊C4—22no—
1100C22⋊C4—862no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C22⋊C4—862no—
1105C22⋊C4—862no—
1106C22⋊C4—862no—
1107C22⋊C4—862no—
1108C22⋊C4—862no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—861no—
1113C22⋊C4—861no—
1114C22⋊C4—861no—
1115C22⋊C4—862no—
1116C22⋊C4—861no—
1117C22⋊C4—862no—
1118C22⋊C4—862no—
1119C22⋊C4—862no—
1120C22⋊C4—861no—
1121C42—21no—
1122C42—861no—
1123C42—861no—
1124C42—861no—
1125C42—862no—
1126C42—861no—
1127C23—21no—
1128C23—431no—
1129C23—432no—
1130C23—431no—
1131C23—864no—
1132C23—862no—
1133C23—862no—
1134C23—1722no—
1135C23—1722no—
1136C23—1721no—
1137C23C2×D4×D4312yes—
1138C23C2×D4×D4311yescharacteristic
1139Q8—22no—
1140Q8—22no—
1141Q8—22no—
1142Q8—22no—
1143Q8—21no—
1144Q8—22no—
1145Q8—21no—
1146Q8—44no—
1147Q8—42no—
1148Q8—42no—
1149Q8—862no—
1150Q8—862no—
1151Q8—862no—
1152Q8—1722no—
1153Q8—1724no—
1154Q8—1724no—
1155Q8—1722no—
1156D4—24no—
1157D4—22no—
1158D4—21no—
1159D4—21no—
1160D4—44no—
1161D4—42no—
1162D4—864no—
1163D4—862no—
1164D4—3442no—
1165D4—3441no—
1166D4—1722no—
1167D4—1722no—
1168D4—1722no—
1169D4—1722no—
1170C2×C4—22no—
1171C2×C4—22no—
1172C2×C4—21no—
1173C2×C4—21no—
1174C2×C4—22no—
1175C2×C4—22no—
1176C2×C4—21no—
1177C2×C4—44no—
1178C2×C4—44no—
1179C2×C4—42no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—431no—
1183C2×C4—432no—
1184C2×C4—431no—
1185C2×C4—862no—
1186C2×C4—862no—
1187C2×C4—862no—
1188C2×C4—862no—
1189C2×C4—862no—
1190C2×C4—861no—
1191C2×C4—861no—
1192C2×C4—861no—
1193C2×C4—861no—
1194C2×C4—861no—
1195C2×C4—861no—
1196C2×C4—861no—
1197C2×C4—862no—
1198C2×C4—861no—
1199C2×C4—862no—
1200C2×C4—3441no—
1201C2×C4—3442no—
1202C2×C4—1722no—
1203C2×C4—1722no—
1204C2×C4—1722no—
1205C2×C4—1724no—
1206C2×C4—1724no—
1207C2×C4—1722no—
1208C2×C4—1722no—
1209C2×C4—1722no—
1210C2×C4C2×D4×D4312yes—
1211C2×C4C2×D4×D4311yescharacteristic
1212C2×C4#1306337012yes—
1213C2×C4#1306337012yes—
1214C2×C4C24×D4311yescharacteristic
1215C8—21no—
1216C8—21no—
1217C8—22no—
1218C8—861no—
1219C8—861no—
1220C8—862no—
1221C22—21no—
1222C22—21no—
1223C22—22no—
1224C22—22no—
1225C22—22no—
1226C22—41no—
1227C22—41no—
1228C22—41no—
1229C22—432no—
1230C22—861no—
1231C22—861no—
1232C22—862no—
1233C22—861no—
1234C22—862no—
1235C22—861no—
1236C22—861no—
1237C22—862no—
1238C22—3444no—
1239C22—1724no—
1240C22#1458345912yes—
1241C22C22×D4×D4311yescharacteristic
1242C4—22no—
1243C4—41no—
1244C4—41no—
1245C4—42no—
1246C4—41no—
1247C4—42no—
1248C4—861no—
1249C4—861no—
1250C4—862no—
1251C4—1721no—
1252C4—1721no—
1253C4—1722no—
1254C4—1721no—
1255C4—1721no—
1256C4—1722no—
1257C4#1458345912yes—
1258C4C2×#1306337011yescharacteristic
1259C4C2×#1306337011yescharacteristic
1260C2—22no—
1261C2—42no—
1262C2—81no—
1263C2—862no—
1264C2—1722no—
1265C2—1721no—
1266C2C2×#1458345911yescharacteristic
1267C2#578×D4311yescharacteristic
1268C2#1914938011yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3011C2
socleC22×C43C23×D4
prime radical#19148268C2
hypercenter#3011D43
hypocenterC43#60759
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
2. #536×D43C2semidirect
3. #19145488C2semidirect
4. #19145488C2semidirect
5. #19145476C2semidirect
6. #19145474C2semidirect
7. #19145423C2semidirect
8. #19145417C2semidirect
9. #19145374C2semidirect
10. #19145368C2semidirect
11. #19144565C2semidirect
12. #19144558C2semidirect
13. #19144541C2semidirect
14. #19144506C2semidirect
15. #19144289C2semidirect
16. #19144280C2semidirect
17. #19144249C2semidirect
18. #19144246C2semidirect
19. #19143890C2semidirect
20. #19143827C2semidirect
21. C2×#14583053C2semidirect
22. #19143043C2semidirect
23. C43×#3011C2semidirect
26. C2×#13063355C22semidirect
27. C22×#10621885C22semidirect
59. #14583241C22semidirect
60. #14583241C22semidirect
61. #14583239C22semidirect
62. #14583239C22semidirect
63. #14583238C22semidirect
64. #14583238C22semidirect
65. #14583237C22semidirect
66. #14583237C22semidirect
67. #14583235C22semidirect
70. #14583232C22semidirect
71. #14583230C22semidirect
74. #14583227C22semidirect
75. #14583222C22semidirect
76. #14583221C22semidirect
79. #14583156C22semidirect
80. #14583156C22semidirect
81. #14583156C22semidirect
82. #14583154C22semidirect
83. #14583154C22semidirect
84. #14583154C22semidirect
85. #14583144C22semidirect
86. #14583142C22semidirect
87. #14583139C22semidirect
88. #14583139C22semidirect
89. #14583139C22semidirect
90. #14583137C22semidirect
91. #14583137C22semidirect
92. #14583137C22semidirect
93. #14583127C22semidirect
94. #14583125C22semidirect
95. #14583061C22semidirect
96. #14583061C22semidirect
97. #14583055C22semidirect
98. #14583055C22semidirect
102. #14583053C22semidirect
103. #14583053C22semidirect
104. #14583053C22semidirect
106. #14583036C22semidirect
107. #14582942C22semidirect
108. #14582941C22semidirect
109. #14582937C22semidirect
110. #14582935C22semidirect
111. #14582909C22semidirect
112. #14582908C22semidirect
113. #14582908C22semidirect
114. #14582895C22semidirect
115. C2×#13063250C22semidirect
116. C2×#13063249C22semidirect
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
645. #3011D43semidirect
662. C2×#137C2×D43semidirect
664. C22×Q16C2×D43semidirect
735. #452C2×D43semidirect
736. #452C2×D43semidirect
745. #451C2×D43semidirect
746. #451C2×D43semidirect
756. #419C2×D43semidirect
758. #416C2×D43semidirect
769. C43#60759semidirect

Maximal subgroups

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

subgroupindex
#191482682
#536×D432
#191454882
#191454762
#191454742
#191454232
#191454172
#191453742
#191453682
#191445652
#191445582
#191445412
#191445062
#191442892
#191442802
#191442492
#191442462
#191438902
#191438272
C2×#145830532
#191430432
C43×#30112
#6075943