Finite Group Databasebeta

← #25967499

Subgroups — #25967499

Order 11008.

2208 conjugacy classes of subgroups.

The subgroup lattice has 1320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148259C211yesmaximal, characteristic, complemented
2#19147927C211yesmaximal, characteristic, complemented
3#19145502C212yesmaximal, complemented
4#19145498C212yesmaximal, complemented
5#19145450C212yesmaximal, complemented
6#19145448C212yesmaximal, complemented
7#19145438C212yesmaximal, complemented
8#19145410C212yesmaximal, complemented
9#19145389C212yesmaximal, complemented
10#19145361C212yesmaximal, complemented
11#19144560C211yesmaximal, characteristic, complemented
12#19144555C211yesmaximal, characteristic, complemented
13#19144537C211yesmaximal, characteristic, complemented
14#19144506C211yesmaximal, characteristic, complemented
15#19144277C211yesmaximal, characteristic, complemented
16#19144243C211yesmaximal, characteristic, complemented
17#19144236C211yesmaximal, characteristic, complemented
18#19143871C211yesmaximal, characteristic, complemented
19#19143866C211yesmaximal, characteristic, complemented
20#19143836C211yesmaximal, characteristic, complemented
21C2×#14583047C211yesmaximal, characteristic, complemented
22#19143042C211yesmaximal, characteristic, complemented
23C43×#3063C211yesmaximal, characteristic, complemented
24C2×#13063371C2211yescharacteristic
25C22×#10621902C2211yescharacteristic, complemented
26C2×#41×D43C2211yescharacteristic
27C2×#13063350C2211yescharacteristic, complemented
28C22×#10621884C2211yescharacteristic, complemented
29C22×D344C2211yescharacteristic, complemented
30C2×#13063332C2211yescharacteristic, complemented
31#14583567—21no—
32#14583559—21no—
33#14583540—21no—
34#14583538—22no—
35#14583533—21no—
36#14583533—22no—
37#14583479C2212yescomplemented
38#14583479C2212yescomplemented
39#14583479C2212yescomplemented
40#14583474—21no—
41#14583473C2211yescharacteristic
42#14583468C2211yescharacteristic
43#14583467—21no—
44#14583465C2212yescomplemented
45#14583463C2211yescharacteristic
46#14583463C2211yescharacteristic, complemented
47#14583460—22no—
48#14583450—21no—
49#14583448—21no—
50#14583412C2212yescomplemented
51#14583412C2212yescomplemented
52#14583412C2212yescomplemented
53#14583407—22no—
54#14583406C2211yescharacteristic
55C2×#13063300C2211yescharacteristic
56#121×D43C2212yescomplemented
57#14583380C2211yescharacteristic
58#117×D43C2211yescharacteristic, complemented
59#14583239C2211yescharacteristic, complemented
60#14583239C2212yescomplemented
61#14583238C2211yescharacteristic, complemented
62#14583238C2212yescomplemented
63#14583233C2211yescharacteristic, complemented
64#14583233C2212yescomplemented
65#14583228C2211yescharacteristic, complemented
66#14583228C2212yescomplemented
67#14583226C2212yescomplemented
68#14583226C2212yescomplemented
69#14583225C2212yescomplemented
70#14583225C2212yescomplemented
71#14583222C2211yescharacteristic, complemented
72#14583221C2211yescharacteristic, complemented
73#14583219C2212yescomplemented
74#14583219C2212yescomplemented
75#14583216C2211yescharacteristic, complemented
76#14583214C2212yescomplemented
77#14583214C2212yescomplemented
78#14583211C2211yescharacteristic, complemented
79#14583152C2212yescomplemented
80#14583152C2212yescomplemented
81#14583150C2212yescomplemented
82#14583147C2212yescomplemented
83#14583147C2212yescomplemented
84#14583147C2212yescomplemented
85#14583135C2212yescomplemented
86#14583135C2212yescomplemented
87#14583133C2212yescomplemented
88#14583130C2212yescomplemented
89#14583130C2212yescomplemented
90#14583130C2212yescomplemented
91#14583060C2212yescomplemented
92#14583060C2212yescomplemented
93#14583060C2212yescomplemented
94#14583060C2212yescomplemented
95#14583048C2212yescomplemented
96#14583048C2212yescomplemented
97#14583047C2212yescomplemented
98#14583047C2212yescomplemented
99#14583047C2212yescomplemented
100#14583047C2212yescomplemented
101#14583047C2212yescomplemented
102#14583047C2212yescomplemented
103#14583043C2212yescomplemented
104#14583043C2212yescomplemented
105#14583034C2212yescomplemented
106#14583034C2212yescomplemented
107#14582939C2211yescharacteristic, complemented
108#14582937C2211yescharacteristic, complemented
109#14582935C2211yescharacteristic, complemented
110#14582908C2211yescharacteristic, complemented
111#14582905C2211yescharacteristic, complemented
112#14582905C2211yescharacteristic, complemented
113#14582903C2211yescharacteristic, complemented
114#14582895C2211yescharacteristic, complemented
115C2×#13063245C2211yescharacteristic, complemented
116#14582867C2211yescharacteristic
117#14582867C2212yescomplemented
118#14582865C2211yescharacteristic
119#14582865C2212yescomplemented
120#14582862C2211yescharacteristic, complemented
121#14582862C2212yescomplemented
122C2×(C2×D43)⋊C8C2211yescharacteristic, complemented
123C2×(C2×D43)⋊C8C2212yescomplemented
124C2×#137×C43C2211yescharacteristic, complemented
125C2×#131×C43C2211yescharacteristic, complemented
126C43×#537C2211yescharacteristic
127C43×#536C2211yescharacteristic, complemented
128C43×#470C2212yescomplemented
129C43×#468C2212yescomplemented
130C43×#467C2212yescomplemented
131C43×#465C2212yescomplemented
132C43×#428C2211yescharacteristic, complemented
133C43×#416C2211yescharacteristic, complemented
134C2×#103×C43C2211yescharacteristic, complemented
135#13063371—42no—
136#13063371—42no—
137C2×#10621902—21no—
138C2×#10621902—21no—
139C2×#10621902—42no—
140C2×#10621902—42no—
141C2×#10621902D411yescharacteristic
142C2×#10621902C2312yes—
143C2×#10621902C2312yes—
144C2×#10621902C2312yes—
145C2×#10621898—21no—
146C2×#10621898C2311yescharacteristic
147C2×#10621898C2312yes—
148C2×#10621900D411yescharacteristic
149C2×#10621900D412yes—
150#41×D43—42no—
151#41×D43—42no—
152C2×Q8×D43D411yescharacteristic
153C22×D172—21no—
154C22×D172—21no—
155C22×D172—21no—
156C22×D172C2311yescharacteristic
157C22×D172C2311yescharacteristic
158C2×D4×D43—22no—
159C2×D4×D43—22no—
160C2×D4×D43D412yes—
161C2×D4×D43D411yescharacteristic
162C2×D4×D43C2312yes—
163C22×C4×D43—21no—
164C22×C4×D43C2311yescharacteristic
165C22×C4×D43C2312yes—
166#13063350—42no—
167C2×#10621884—42no—
168C2×#10621884C2312yes—
169C2×#10621884C2312yes—
170C2×#10621884C2312yes—
171C2×D344—42no—
172C2×D344C2312yes—
173C2×D344C2312yes—
174C2×#10621882C2312yes—
175#13063332—42no—
176C2×#10621877C2311yescharacteristic
177C2×#10621877C2312yes—
178C22×C43⋊C8C2311yescharacteristic
179C22×C43⋊C8C2312yes—
180#13063323—21no—
181#13063322—21no—
182#13063321—21no—
183#13063321—21no—
184#13063321—22no—
185#13063314—21no—
186#13063314—21no—
187#13063314—21no—
188#13063313—21no—
189#13063311—22no—
190#13063310—22no—
191#13063310—22no—
192#13063310—22no—
193#13063308—22no—
194#13063306—21no—
195#13063303—22no—
196#13063303—22no—
197#13063303—22no—
198#13063301C2312yes—
199#13063301C2312yes—
200#13063301C2311yescharacteristic
201#13063301C2311yescharacteristic
202#13063300—22no—
203#13063300—22no—
204#13063300—22no—
205#13063300—21no—
206#13063300—21no—
207#13063300C2312yes—
208#13063300C2312yes—
209#13063300C2312yes—
210#13063300C2312yes—
211#13063299C2312yes—
212#13063299C2312yes—
213#13063299C2312yes—
214#13063299C2312yes—
215#13063298—22no—
216#13063298—22no—
217#13063298—22no—
218#13063298—22no—
219#13063298—22no—
220#13063298—22no—
221#13063298—22no—
222#13063297—22no—
223#13063296C2311yescharacteristic
224#13063296C2311yescharacteristic
225#13063295—22no—
226#13063295—22no—
227#13063295—22no—
228#13063295—22no—
229#13063295—22no—
230#13063293—21no—
231#13063293—22no—
232#13063293—22no—
233#13063293—22no—
234#13063290—21no—
235#13063287—21no—
236#13063287—22no—
237#13063287—22no—
238#13063287—22no—
239C4×C22⋊D43—22no—
240C4×C22⋊D43—21no—
241C4×C22⋊D43—21no—
242(C22⋊D43)⋊C4—22no—
243(C22⋊D43)⋊C4—22no—
244(C22⋊D43)⋊C4—22no—
245#13063284C2311yescharacteristic
246#13063284C2311yescharacteristic
247#13063283C2311yescharacteristic
248#13063283C2311yescharacteristic
249#13063283C2312yes—
250#13063282—21no—
251#13063281—21no—
252C4⋊C4×D43C2311yescharacteristic
253C4⋊C4×D43C2311yescharacteristic
254C4⋊C4×D43C2312yes—
255C2×(C2×D43)⋊C4—21no—
256C22⋊C4×D43—21no—
257C22⋊C4×D43—22no—
258C42×D43—21no—
259#13063259C2311yescharacteristic
260#13063259C2311yescharacteristic
261#13063258C2312yes—
262#13063258C2311yescharacteristic
263#13063258C2311yescharacteristic
264#13063257C2311yescharacteristic
265#13063257C2311yescharacteristic
266#13063256C2311yescharacteristic
267#13063256C2311yescharacteristic
268#13063256C2312yes—
269#13063249C2312yes—
270#13063249C2312yes—
271#13063249C2311yescharacteristic
272#13063249C2311yescharacteristic
273#13063247C2312yes—
274#13063247C2312yes—
275#13063247C2312yes—
276#13063247C2312yes—
277#13063246C2311yescharacteristic
278#13063246C2311yescharacteristic
279#13063245C2312yes—
280#13063245C2312yes—
281#13063245C2312yes—
282#13063245C2312yes—
283(C2×D43)⋊C8C2312yes—
284(C2×D43)⋊C8C2312yes—
285(C2×D43)⋊C8C2311yescharacteristic
286(C2×D43)⋊C8C2311yescharacteristic
287(C2×D43)⋊C8C2311yescharacteristic
288(C2×D43)⋊C8C2311yescharacteristic
289(C2×D43)⋊C8C2312yes—
290(C2×D43)⋊C8C2312yes—
291(C2×D43)⋊C8C2312yes—
292(C2×D43)⋊C8C2312yes—
293C2×#41×C43C2311yescharacteristic
294C2×#41×C43C2311yescharacteristic
295C22×Q8×C43C2311yescharacteristic
296#137×C43—42no—
297C2×Q16×C43C2312yes—
298C2×SD16×C43C2312yes—
299#131×C43—42no—
300C2×M16×C43C2311yescharacteristic
301C2×M16×C43C2312yes—
302C22×C8×C43C2311yescharacteristic
303C22×C8×C43C2312yes—
304C4⋊Q8×C43—21no—
305#124×C43—21no—
306#123×C43—22no—
307C22⋊Q8×C43—21no—
308C22⋊Q8×C43C2312yes—
309C22⋊Q8×C43C2312yes—
310C22⋊Q8×C43C2312yes—
311#121×C43—21no—
312#121×C43—22no—
313#121×C43C2312yes—
314#117×C43C2311yescharacteristic
315C2×C4⋊C4×C43C2311yescharacteristic
316#107×C43C2312yes—
317#106×C43C2312yes—
318#103×C43C2312yes—
319#103×C43C2312yes—
320#103×C43C2311yescharacteristic
321#103×C43C2311yescharacteristic
322#102×C43C2311yescharacteristic
323#102×C43C2311yescharacteristic
324C23×D43—21no—
325C23×D43—21no—
326C23×D43—22no—
327C23×D43C2×D411yescharacteristic
328C23×D43C2×D412yes—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—22no—
333C2×Q8×C43—21no—
334C2×Q8×C43—22no—
335C2×Q8×C43—22no—
336C2×Q8×C43C2×D411yescharacteristic
337C2×Q8×C43C2412yes—
338C2×Q8×C43C2411yescharacteristic
339C2×D4×C43—21no—
340C2×D4×C43—22no—
341C2×D4×C43C2×D412yes—
342C2×D4×C43C2×D411yescharacteristic
343C2×D4×C43C2411yescharacteristic
344C22×C4×C43—21no—
345C22×C4×C43—21no—
346C22×C4×C43—21no—
347C22×C4×C43C2412yes—
348C22×C4×C43C2411yescharacteristic
349C2×C22⋊D43—22no—
350C2×C22⋊D43—22no—
351C2×C22⋊D43—22no—
352C2×C22⋊D43—22no—
353C2×C22⋊D43—22no—
354C2×C22⋊D43—21no—
355C2×C22⋊D43—21no—
356C2×C22⋊D43C2×D412yes—
357C2×C22⋊D43C2×D412yes—
358C2×C22⋊D43C2×D412yes—
359C22×Dic43C2×D411yescharacteristic
360C22×Dic43C2×D412yes—
361#10621902—42no—
362#10621902—42no—
363#10621902—42no—
364#10621902—42no—
365#10621902—42no—
366#10621902—42no—
367#10621902—42no—
368#10621902—44no—
369#10621902—44no—
370Q8×D43—42no—
371#10621900—42no—
372#10621900—44no—
373D4×D43—44no—
374D4×D43—42no—
375D4×D43—42no—
376D4×D43—42no—
377D4×D43—48no—
378D4×D43—84no—
379#10621898—22no—
380#10621898—22no—
381#10621898—44no—
382#10621898—42no—
383#10621898—42no—
384C2×D172—21no—
385C2×D172—21no—
386C2×D172—22no—
387C2×D172—22no—
388C2×D172—22no—
389C2×D172—22no—
390C2×D172—22no—
391C2×D172—22no—
392C2×D172—22no—
393C2×D172—22no—
394C2×D172—22no—
395C2×D172—22no—
396C2×D172—22no—
397C2×D172—44no—
398C2×D172—44no—
399C2×D172—82no—
400C2×D172C2×D411yescharacteristic
401C2×D172C2×D412yes—
402C2×D172C2412yes—
403C2×D172C2412yes—
404C2×C4×D43—22no—
405C2×C4×D43—22no—
406C2×C4×D43—22no—
407C2×C4×D43—22no—
408C2×C4×D43—22no—
409C2×C4×D43—21no—
410C2×C4×D43—21no—
411C2×C4×D43—22no—
412C2×C4×D43—42no—
413C2×C4×D43—42no—
414C2×C4×D43—44no—
415C2×C4×D43C2×D411yescharacteristic
416C2×C4×D43C2×D411yescharacteristic
417C2×C4×D43C2×D412yes—
418C2×C4×D43C2×D412yes—
419C2×C4×D43C2411yescharacteristic
420C2×C4×D43C2412yes—
421C2×C4×D43C2411yescharacteristic
422C2×Dic86C2×D411yescharacteristic
423C2×Dic86C2×D412yes—
424Q16×C43—42no—
425SD16×C43—42no—
426M16×C43—22no—
427M16×C43—42no—
428C2×C8×C43—22no—
429C2×C8×C43—42no—
430C2×C8×C43C2411yescharacteristic
431C2×C8×C43C2411yescharacteristic
432C2×C8×C43C2412yes—
433C4⋊C4×C43—21no—
434C4⋊C4×C43—22no—
435C4⋊C4×C43—22no—
436C4⋊C4×C43—22no—
437C4⋊C4×C43C2411yescharacteristic
438C4⋊C4×C43C2411yescharacteristic
439C4⋊C4×C43C2412yes—
440C22⋊C4×C43—22no—
441C22⋊C4×C43—21no—
442C22⋊C4×C43—22no—
443C22⋊C4×C43—22no—
444C22⋊C4×C43—22no—
445C42×C43—21no—
446C22⋊Dic43—21no—
447C22⋊Dic43—21no—
448C22⋊Dic43—21no—
449C22⋊Dic43—21no—
450#10621884—42no—
451#10621884—42no—
452#10621884—42no—
453#10621882—42no—
454(C2×D43)⋊C4—22no—
455(C2×D43)⋊C4—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460(C2×D43)⋊C4—22no—
461(C2×D43)⋊C4—22no—
462(C2×D43)⋊C4—21no—
463(C2×D43)⋊C4—21no—
464(C2×D43)⋊C4—22no—
465(C2×D43)⋊C4—21no—
466(C2×D43)⋊C4—21no—
467(C2×D43)⋊C4—22no—
468(C2×D43)⋊C4—22no—
469C4⋊Dic43C2411yescharacteristic
470C4⋊Dic43C2411yescharacteristic
471C4⋊Dic43C2411yescharacteristic
472C4⋊Dic43C2411yescharacteristic
473Dic43⋊C4—21no—
474Dic43⋊C4—21no—
475Dic43⋊C4—22no—
476Dic43⋊C4—21no—
477Dic43⋊C4—22no—
478Dic43⋊C4—22no—
479Dic43⋊C4—21no—
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—21no—
484C4×Dic43—22no—
485#10621877—22no—
486#10621877—42no—
487C2×C43⋊C8—22no—
488C2×C43⋊C8—42no—
489C2×C43⋊C8C2411yescharacteristic
490C2×C43⋊C8C2411yescharacteristic
491C2×C43⋊C8C2412yes—
492D344—42no—
493D344—42no—
494C23×C43—21no—
495C23×C43C22×D412yes—
496C23×C43C22×D411yescharacteristic
497C22×D43—22no—
498C22×D43—22no—
499C22×D43—22no—
500C22×D43—42no—
501C22×D43—41no—
502C22×D43—42no—
503C22×D43—42no—
504C22×D43—41no—
505C22×D43—44no—
506C22×D43—42no—
507C22×D43—42no—
508C22×D43—82no—
509C22×D43—82no—
510C22×D43—81no—
511C22×D43—81no—
512C22×D43—81no—
513C22×D43—81no—
514C22×D43C22×D412yes—
515C22×D43C22×D411yescharacteristic
516C22×D43C22×D411yescharacteristic
517Q8×C43—22no—
518Q8×C43—22no—
519Q8×C43—21no—
520Q8×C43—22no—
521Q8×C43—21no—
522Q8×C43—42no—
523D4×C43—24no—
524D4×C43—22no—
525D4×C43—21no—
526D4×C43—21no—
527D4×C43—42no—
528D4×C43—82no—
529C2×C4×C43—22no—
530C2×C4×C43—22no—
531C2×C4×C43—21no—
532C2×C4×C43—21no—
533C2×C4×C43—22no—
534C2×C4×C43—21no—
535C2×C4×C43—22no—
536C2×C4×C43—42no—
537C2×C4×C43—42no—
538C2×C4×C43—81no—
539C2×C4×C43C22×D412yes—
540C2×C4×C43C22×D411yescharacteristic
541C2×C4×C43H(5,𝔽2)12yes—
542C2×C4×C43H(5,𝔽2)12yes—
543C2×C4×C43C2511yescharacteristic
544C22⋊D43—24no—
545C22⋊D43—42no—
546C22⋊D43—42no—
547C22⋊D43—44no—
548C22⋊D43—42no—
549C22⋊D43—81no—
550C22⋊D43—82no—
551C22⋊D43—82no—
552C22⋊D43—82no—
553C22⋊D43—82no—
554C2×Dic43—22no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—21no—
559C2×Dic43—42no—
560C2×Dic43C22×D411yescharacteristic
561C2×Dic43C22×D412yes—
562C2×Dic43C22×D411yescharacteristic
563D172—22no—
564D172—22no—
565D172—22no—
566D172—22no—
567D172—22no—
568D172—42no—
569D172—44no—
570D172—44no—
571D172—44no—
572D172—44no—
573D172—42no—
574D172—42no—
575D172—82no—
576D172—82no—
577D172—82no—
578C4×D43—22no—
579C4×D43—22no—
580C4×D43—21no—
581C4×D43—21no—
582C4×D43—21no—
583C4×D43—21no—
584C4×D43—22no—
585C4×D43—22no—
586C4×D43—42no—
587C4×D43—42no—
588C4×D43—44no—
589C4×D43—44no—
590C4×D43—44no—
591C4×D43—81no—
592C4×D43—81no—
593C4×D43—82no—
594Dic86—22no—
595Dic86—42no—
596C8×C43—21no—
597C8×C43—21no—
598C8×C43—22no—
599C43⋊C8—21no—
600C43⋊C8—21no—
601C43⋊C8—22no—
602#60760—431nomaximal, Sylow
603C22×C43—21no—
604C22×C43—21no—
605C22×C43—22no—
606C22×C43—22no—
607C22×C43—22no—
608C22×C43—41no—
609C22×C43—41no—
610C22×C43—41no—
611C22×C43#53412yes—
612C22×C43C23×D411yescharacteristic
613C2×D43—21no—
614C2×D43—22no—
615C2×D43—21no—
616C2×D43—21no—
617C2×D43—22no—
618C2×D43—21no—
619C2×D43—21no—
620C2×D43—21no—
621C2×D43—22no—
622C2×D43—42no—
623C2×D43—42no—
624C2×D43—42no—
625C2×D43—42no—
626C2×D43—42no—
627C2×D43—42no—
628C2×D43—82no—
629C2×D43—84no—
630C2×D43—84no—
631C2×D43—164no—
632C2×D43—162no—
633C4×C43—22no—
634C4×C43—41no—
635C4×C43—42no—
636C4×C43—41no—
637C4×C43—41no—
638C4×C43—42no—
639C4×C43#53412yes—
640C4×C43C2×H(5,𝔽2)11yescharacteristic
641C4×C43C2×H(5,𝔽2)11yescharacteristic
642Dic43—22no—
643Dic43—21no—
644Dic43—21no—
645Dic43—41no—
646Dic43—41no—
647Dic43—41no—
648Dic43—41no—
649#3488—431no—
650#3449—431no—
651#3204—432no—
652#3203—432no—
653#3198—432no—
654#3198—432no—
655#3197—432no—
656#3194—432no—
657#3191—432no—
658#3188—432no—
659#3097—431no—
660#3096—431no—
661#3094—431no—
662#3091—431no—
663#3063D4311yescharacteristic, complemented
664#3062—431no—
665#3058—431no—
666#3057—431no—
667#3009—431no—
668#3008—431no—
669#3005—431no—
670C2×#449—431no—
671#2880—431no—
672C2×C43—22no—
673C2×C43—42no—
674C2×C43—81no—
675C2×C43C2×#53411yescharacteristic
676C2×C43#358411yescharacteristic
677C2×C43#358511yescharacteristic
678D43—41no—
679D43—41no—
680D43—42no—
681D43—82no—
682D43—82no—
683C2×H(5,𝔽2)—431no—
684C22×#41—431no—
685C22×#41—431no—
686C2×#137C2×D4311yescharacteristic, complemented
687C2×AGL(1,ℤ/8)—431no—
688C22×SD16—431no—
689C22×D8—431no—
690C2×#131—431no—
691C2×#131C2×D4311yescharacteristic, complemented
692#550—861no—
693#548—861no—
694#546—862no—
695#546—861no—
696D42—862no—
697D42—861no—
698#537—432no—
699#537—432no—
700#537—432no—
701#537C2×D4311yescharacteristic
702#536—431no—
703#536—861no—
704#536C2×D4311yescharacteristic, complemented
705#535—431no—
706#535—431no—
707#535—432no—
708#535—431no—
709#535—861no—
710#534—862no—
711#532—861no—
712#532—861no—
713#525—431no—
714#525—432no—
715#525—432no—
716#525—432no—
717#525—862no—
718C2×#121—432no—
719C2×#121—431no—
720#520—431no—
721C2×#117—431no—
722#485—431no—
723#485—431no—
724#485—432no—
725#485—432no—
726#484—431no—
727#484—432no—
728#483—431no—
729#483—432no—
730#482—432no—
731#482—432no—
732#482—432no—
733#482—432no—
734#482—431no—
735#482—431no—
736#481—432no—
737#481—432no—
738#481—431no—
739#480—432no—
740#480—432no—
741#480—431no—
742#470C2×D4312yescomplemented
743#469—432no—
744#469—432no—
745#469—432no—
746#468—432no—
747#468—432no—
748#468—432no—
749#468C2×D4312yescomplemented
750#467C2×D4312yescomplemented
751#466—432no—
752#466—432no—
753#466—432no—
754#465—432no—
755#465—432no—
756#465—432no—
757#465C2×D4312yescomplemented
758#452—432no—
759#452—432no—
760#452—432no—
761#452—432no—
762#450—432no—
763#450—432no—
764#449—432no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—432no—
770#449—432no—
771#449—432no—
772#447—432no—
773#447—432no—
774#428—431no—
775#428C2×D4311yescharacteristic, complemented
776#427—431no—
777#427—431no—
778#419—431no—
779#418—431no—
780#418—431no—
781#418—431no—
782#416—431no—
783#416C2×D4311yescharacteristic, complemented
784C2×#103C2×D4311yescharacteristic, complemented
785C2×#102—431no—
786#408—431no—
787#408—432no—
788#408—431no—
789#408—432no—
790#407—431no—
791#407—432no—
792C2×C22⋊C8—431no—
793C2×C22⋊C8—432no—
794C43#6076011yescharacteristic, complemented, Sylow
795H(5,𝔽2)—1722no—
796H(5,𝔽2)—1722no—
797C2×#41—431no—
798C2×#41—432no—
799C2×#41—431no—
800C2×#41—431no—
801C2×#41—432no—
802C2×#41—432no—
803C2×#41—432no—
804C2×#41—432no—
805C2×#41—861no—
806C2×#41—861no—
807C2×#41—861no—
808C2×#41—1722no—
809C2×#41—1722no—
810C2×#41—1722no—
811C2×#41—1722no—
812C2×#41C22×D4311yescharacteristic
813C2×#41C22×D4311yescharacteristic
814C22×Q8—431no—
815C22×Q8C22×D4311yescharacteristic
816C22×D4—432no—
817C22×D4—431no—
818C22×D4—432no—
819C22×D4—431no—
820C22×D4—431no—
821C22×D4—861no—
822C22×D4—861no—
823C22×D4—861no—
824C22×D4—862no—
825C22×D4—862no—
826C23×C4—431no—
827C23×C4—432no—
828C23×C4—861no—
829#137—42no—
830AGL(1,ℤ/8)—1722no—
831C2×Q16C22×D4312yes—
832C2×SD16—432no—
833C2×SD16—432no—
834C2×SD16—432no—
835C2×SD16—1722no—
836C2×SD16C22×D4312yes—
837C2×D8—432no—
838C2×D8—432no—
839C2×D8—432no—
840C2×D8—1722no—
841#131—42no—
842#131—1722no—
843C2×M16—431no—
844C2×M16—432no—
845C2×M16C22×D4311yescharacteristic
846C2×M16C22×D4312yes—
847C22×C8—431no—
848C22×C8—432no—
849C22×C8C22×D4311yescharacteristic
850C22×C8C22×D4312yes—
851C4⋊Q8—21no—
852C4⋊Q8—861no—
853#127—861no—
854#127—862no—
855#127—861no—
856#127—861no—
857#124—21no—
858#124—861no—
859#124—862no—
860#124—861no—
861#124—861no—
862#124—861no—
863#123—22no—
864#123—862no—
865#123—862no—
866#123—862no—
867#123—862no—
868#123—861no—
869C22⋊Q8—21no—
870C22⋊Q8—431no—
871C22⋊Q8—432no—
872C22⋊Q8—432no—
873C22⋊Q8—431no—
874C22⋊Q8—862no—
875C22⋊Q8—862no—
876C22⋊Q8—862no—
877C22⋊Q8C22×D4312yes—
878C22⋊Q8C22×D4312yes—
879C22⋊Q8C22×D4312yes—
880#121—22no—
881#121—21no—
882#121—431no—
883#121—431no—
884#121—432no—
885#121—432no—
886#121—432no—
887#121—432no—
888#121—432no—
889#121—432no—
890#121—432no—
891#121—432no—
892#121—862no—
893#121—862no—
894#121—862no—
895#121—862no—
896#121—862no—
897#121—862no—
898#121—862no—
899#121—861no—
900#121—861no—
901#121—862no—
902#121—862no—
903#121—862no—
904#121—862no—
905#121C22×D4312yes—
906#120—862no—
907#120—862no—
908#120—862no—
909#120—862no—
910#120—862no—
911#120—862no—
912#120—861no—
913#120—862no—
914#120—862no—
915C4×Q8—861no—
916C4×D4—862no—
917C4×D4—862no—
918C4×D4—862no—
919C4×D4—862no—
920C4×D4—862no—
921C4×D4—862no—
922C4×D4—861no—
923C4×D4—861no—
924C4×D4—861no—
925C4×D4—862no—
926#117—431no—
927#117—431no—
928#117—431no—
929#117—431no—
930#117—432no—
931#117—861no—
932#117—861no—
933#117C22×D4311yescharacteristic
934C2×C4⋊C4—431no—
935C2×C4⋊C4—431no—
936C2×C4⋊C4—432no—
937C2×C4⋊C4C22×D4311yescharacteristic
938C2×C22⋊C4—862no—
939C2×C22⋊C4—861no—
940C2×C22⋊C4—861no—
941C2×C42—861no—
942#107—431no—
943#107—431no—
944#107—431no—
945#107—431no—
946#107—432no—
947#107C22×D4312yes—
948#106—431no—
949#106—431no—
950#106—431no—
951#106—431no—
952#106—432no—
953#106C22×D4312yes—
954#103—431no—
955#103—431no—
956#103—432no—
957#103—432no—
958#103C22×D4312yes—
959#103C22×D4312yes—
960#103C22×D4311yescharacteristic
961#103C22×D4311yescharacteristic
962#102—431no—
963#102—431no—
964#102—432no—
965#102—432no—
966#102—432no—
967#102—432no—
968#102—432no—
969#102—432no—
970#102—432no—
971#102—432no—
972#102C22×D4311yescharacteristic
973#102C22×D4311yescharacteristic
974C22⋊C8—431no—
975C22⋊C8—431no—
976C22⋊C8—432no—
977C22⋊C8—432no—
978C22⋊C8—431no—
979C22⋊C8—431no—
980C22⋊C8—432no—
981C22⋊C8—432no—
982C22⋊C8—432no—
983C22⋊C8—432no—
984C24—431no—
985C24—432no—
986C24—862no—
987C24—861no—
988C24—861no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—22no—
993#41—862no—
994#41—862no—
995#41—1722no—
996#41—1722no—
997#41—1724no—
998#41—1724no—
999#41—1722no—
1000#41—1722no—
1001#41—1722no—
1002#41—1722no—
1003#41—1722no—
1004#41—1722no—
1005#41—1722no—
1006#41—1722no—
1007#41—1724no—
1008#41—1724no—
1009C2×Q8—21no—
1010C2×Q8—22no—
1011C2×Q8—22no—
1012C2×Q8—431no—
1013C2×Q8—432no—
1014C2×Q8—1722no—
1015C2×Q8D4×D4311yescharacteristic
1016C2×Q8C23×D4312yes—
1017C2×Q8C23×D4311yescharacteristic
1018C2×D4—21no—
1019C2×D4—22no—
1020C2×D4—432no—
1021C2×D4—432no—
1022C2×D4—432no—
1023C2×D4—431no—
1024C2×D4—432no—
1025C2×D4—432no—
1026C2×D4—432no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—862no—
1030C2×D4—862no—
1031C2×D4—862no—
1032C2×D4—862no—
1033C2×D4—862no—
1034C2×D4—862no—
1035C2×D4—861no—
1036C2×D4—862no—
1037C2×D4—862no—
1038C2×D4—862no—
1039C2×D4—862no—
1040C2×D4—861no—
1041C2×D4—861no—
1042C2×D4—861no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—862no—
1046C2×D4—862no—
1047C2×D4—3442no—
1048C2×D4—3444no—
1049C2×D4—1724no—
1050C2×D4—1724no—
1051C2×D4—1722no—
1052C2×D4—1722no—
1053C2×D4—1722no—
1054C2×D4—1724no—
1055C2×D4—1728no—
1056C2×D4D4×D4312yes—
1057C2×D4D4×D4311yescharacteristic
1058C2×D4C23×D4311yescharacteristic
1059C22×C4—21no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—431no—
1063C22×C4—432no—
1064C22×C4—431no—
1065C22×C4—431no—
1066C22×C4—431no—
1067C22×C4—432no—
1068C22×C4—431no—
1069C22×C4—432no—
1070C22×C4—432no—
1071C22×C4—862no—
1072C22×C4—862no—
1073C22×C4—862no—
1074C22×C4—861no—
1075C22×C4—861no—
1076C22×C4—862no—
1077C22×C4—862no—
1078C22×C4—862no—
1079C22×C4—1722no—
1080C22×C4—1722no—
1081C22×C4—1724no—
1082C22×C4C23×D4312yes—
1083C22×C4C23×D4311yescharacteristic
1084Q16—42no—
1085SD16—42no—
1086SD16—1722no—
1087SD16—1722no—
1088SD16—1722no—
1089D8—1722no—
1090D8—1722no—
1091D8—1722no—
1092M16—22no—
1093M16—42no—
1094M16—862no—
1095M16—1722no—
1096C2×C8—22no—
1097C2×C8—42no—
1098C2×C8—431no—
1099C2×C8—431no—
1100C2×C8—432no—
1101C2×C8—862no—
1102C2×C8—1722no—
1103C2×C8C23×D4312yes—
1104C2×C8C23×D4311yescharacteristic
1105C2×C8C23×D4311yescharacteristic
1106C4⋊C4—21no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—431no—
1111C4⋊C4—431no—
1112C4⋊C4—431no—
1113C4⋊C4—431no—
1114C4⋊C4—861no—
1115C4⋊C4—861no—
1116C4⋊C4—862no—
1117C4⋊C4—861no—
1118C4⋊C4—861no—
1119C4⋊C4—862no—
1120C4⋊C4—862no—
1121C4⋊C4C23×D4311yescharacteristic
1122C4⋊C4C23×D4311yescharacteristic
1123C4⋊C4C23×D4312yes—
1124C22⋊C4—21no—
1125C22⋊C4—22no—
1126C22⋊C4—22no—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—862no—
1130C22⋊C4—862no—
1131C22⋊C4—862no—
1132C22⋊C4—862no—
1133C22⋊C4—861no—
1134C22⋊C4—861no—
1135C22⋊C4—862no—
1136C22⋊C4—861no—
1137C22⋊C4—861no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—861no—
1141C22⋊C4—861no—
1142C22⋊C4—861no—
1143C22⋊C4—861no—
1144C22⋊C4—862no—
1145C22⋊C4—862no—
1146C22⋊C4—862no—
1147C22⋊C4—862no—
1148C42—21no—
1149C42—861no—
1150C42—861no—
1151C42—862no—
1152C42—861no—
1153C42—861no—
1154C23—21no—
1155C23—431no—
1156C23—432no—
1157C23—431no—
1158C23—862no—
1159C23—862no—
1160C23—862no—
1161C23—3441no—
1162C23—3441no—
1163C23—3441no—
1164C23—3441no—
1165C23—3442no—
1166C23—3442no—
1167C23—1722no—
1168C23—1721no—
1169C23—1722no—
1170C23—1721no—
1171C23—1722no—
1172C23—1724no—
1173C23—1722no—
1174C23—1722no—
1175C23C2×D4×D4312yes—
1176C23C2×D4×D4311yescharacteristic
1177Q8—22no—
1178Q8—22no—
1179Q8—21no—
1180Q8—22no—
1181Q8—21no—
1182Q8—42no—
1183Q8—862no—
1184Q8—1722no—
1185D4—24no—
1186D4—22no—
1187D4—21no—
1188D4—21no—
1189D4—42no—
1190D4—82no—
1191D4—864no—
1192D4—862no—
1193D4—862no—
1194D4—862no—
1195D4—862no—
1196D4—862no—
1197D4—3442no—
1198D4—3442no—
1199D4—3442no—
1200D4—3442no—
1201D4—3442no—
1202D4—3442no—
1203D4—3442no—
1204D4—3441no—
1205D4—1722no—
1206D4—1724no—
1207D4—1724no—
1208D4—1724no—
1209D4—1724no—
1210D4—1722no—
1211D4—1722no—
1212D4—1724no—
1213D4—1722no—
1214D4—1722no—
1215D4—1722no—
1216C2×C4—22no—
1217C2×C4—22no—
1218C2×C4—21no—
1219C2×C4—21no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—22no—
1223C2×C4—42no—
1224C2×C4—42no—
1225C2×C4—81no—
1226C2×C4—431no—
1227C2×C4—432no—
1228C2×C4—431no—
1229C2×C4—862no—
1230C2×C4—862no—
1231C2×C4—862no—
1232C2×C4—861no—
1233C2×C4—861no—
1234C2×C4—862no—
1235C2×C4—861no—
1236C2×C4—861no—
1237C2×C4—862no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—861no—
1241C2×C4—861no—
1242C2×C4—3442no—
1243C2×C4—3441no—
1244C2×C4—3441no—
1245C2×C4—1722no—
1246C2×C4—1722no—
1247C2×C4—1724no—
1248C2×C4—1724no—
1249C2×C4—1724no—
1250C2×C4—1722no—
1251C2×C4C2×D4×D4312yes—
1252C2×C4C2×D4×D4311yescharacteristic
1253C2×C4#1306337012yes—
1254C2×C4#1306337112yes—
1255C2×C4C24×D4311yescharacteristic
1256C8—21no—
1257C8—21no—
1258C8—22no—
1259C8—861no—
1260C8—861no—
1261C8—862no—
1262C22—21no—
1263C22—21no—
1264C22—22no—
1265C22—22no—
1266C22—22no—
1267C22—41no—
1268C22—41no—
1269C22—41no—
1270C22—861no—
1271C22—862no—
1272C22—861no—
1273C22—861no—
1274C22—862no—
1275C22—861no—
1276C22—861no—
1277C22—861no—
1278C22—862no—
1279C22—3444no—
1280C22—3442no—
1281C22—3444no—
1282C22—1722no—
1283C22—1722no—
1284C22—1722no—
1285C22—1722no—
1286C22—1722no—
1287C22—1722no—
1288C22—6882no—
1289C22—6884no—
1290C22#1458345712yes—
1291C22C22×D4×D4311yescharacteristic
1292C4—22no—
1293C4—41no—
1294C4—42no—
1295C4—41no—
1296C4—41no—
1297C4—42no—
1298C4—861no—
1299C4—861no—
1300C4—862no—
1301C4—1721no—
1302C4—1721no—
1303C4—1721no—
1304C4—1721no—
1305C4#1458345712yes—
1306C4C2×#1306337011yescharacteristic
1307C4C2×#1306337111yescharacteristic
1308C2—22no—
1309C2—42no—
1310C2—81no—
1311C2—3442no—
1312C2—3442no—
1313C2—1721no—
1314C2—1722no—
1315C2—1721no—
1316C2C2×#1458345711yescharacteristic
1317C2#1914936511yescharacteristic
1318C2#1914937311yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3063C2
socleC22×C43C23×D4
hypercenter#3063D43
hypocenterC43#60760
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#41 ◁ #3063

Complements

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

NH ≅ G/Ntype
1. #19148259C2semidirect
2. #19147927C2semidirect
3. #19145502C2semidirect
4. #19145498C2semidirect
5. #19145450C2semidirect
6. #19145448C2semidirect
7. #19145438C2semidirect
8. #19145410C2semidirect
9. #19145389C2semidirect
10. #19145361C2semidirect
11. #19144560C2semidirect
12. #19144555C2semidirect
13. #19144537C2semidirect
14. #19144506C2semidirect
15. #19144277C2semidirect
16. #19144243C2semidirect
17. #19144236C2semidirect
18. #19143871C2semidirect
19. #19143866C2semidirect
20. #19143836C2semidirect
21. C2×#14583047C2semidirect
22. #19143042C2semidirect
23. C43×#3063C2semidirect
25. C22×#10621902C22semidirect
27. C2×#13063350C22semidirect
28. C22×#10621884C22semidirect
29. C22×D344C22semidirect
30. C2×#13063332C22semidirect
37. #14583479C22semidirect
38. #14583479C22semidirect
39. #14583479C22semidirect
44. #14583465C22semidirect
46. #14583463C22semidirect
50. #14583412C22semidirect
51. #14583412C22semidirect
52. #14583412C22semidirect
56. #121×D43C22semidirect
58. #117×D43C22semidirect
59. #14583239C22semidirect
60. #14583239C22semidirect
61. #14583238C22semidirect
62. #14583238C22semidirect
63. #14583233C22semidirect
64. #14583233C22semidirect
65. #14583228C22semidirect
66. #14583228C22semidirect
67. #14583226C22semidirect
68. #14583226C22semidirect
69. #14583225C22semidirect
70. #14583225C22semidirect
71. #14583222C22semidirect
72. #14583221C22semidirect
73. #14583219C22semidirect
74. #14583219C22semidirect
75. #14583216C22semidirect
76. #14583214C22semidirect
77. #14583214C22semidirect
78. #14583211C22semidirect
79. #14583152C22semidirect
80. #14583152C22semidirect
81. #14583150C22semidirect
82. #14583147C22semidirect
83. #14583147C22semidirect
84. #14583147C22semidirect
85. #14583135C22semidirect
86. #14583135C22semidirect
87. #14583133C22semidirect
88. #14583130C22semidirect
89. #14583130C22semidirect
90. #14583130C22semidirect
91. #14583060C22semidirect
92. #14583060C22semidirect
93. #14583060C22semidirect
94. #14583060C22semidirect
95. #14583048C22semidirect
96. #14583048C22semidirect
97. #14583047C22semidirect
98. #14583047C22semidirect
99. #14583047C22semidirect
100. #14583047C22semidirect
101. #14583047C22semidirect
102. #14583047C22semidirect
103. #14583043C22semidirect
104. #14583043C22semidirect
105. #14583034C22semidirect
106. #14583034C22semidirect
107. #14582939C22semidirect
108. #14582937C22semidirect
109. #14582935C22semidirect
110. #14582908C22semidirect
111. #14582905C22semidirect
112. #14582905C22semidirect
113. #14582903C22semidirect
114. #14582895C22semidirect
115. C2×#13063245C22semidirect
117. #14582867C22semidirect
119. #14582865C22semidirect
120. #14582862C22semidirect
121. #14582862C22semidirect
122. C2×(C2×D43)⋊C8C22semidirect
123. C2×(C2×D43)⋊C8C22semidirect
124. C2×#137×C43C22semidirect
125. C2×#131×C43C22semidirect
127. C43×#536C22semidirect
128. C43×#470C22semidirect
129. C43×#468C22semidirect
130. C43×#467C22semidirect
131. C43×#465C22semidirect
132. C43×#428C22semidirect
133. C43×#416C22semidirect
134. C2×#103×C43C22semidirect
663. #3063D43semidirect
686. C2×#137C2×D43semidirect
691. C2×#131C2×D43semidirect
704. #536C2×D43semidirect
742. #470C2×D43semidirect
749. #468C2×D43semidirect
750. #467C2×D43semidirect
757. #465C2×D43semidirect
775. #428C2×D43semidirect
783. #416C2×D43semidirect
784. C2×#103C2×D43semidirect
794. C43#60760semidirect

Maximal subgroups

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

subgroupindex
#191482592
#191479272
#191455022
#191454982
#191454502
#191454482
#191454382
#191454102
#191453892
#191453612
#191445602
#191445552
#191445372
#191445062
#191442772
#191442432
#191442362
#191438712
#191438662
#191438362
C2×#145830472
#191430422
C43×#30632
#6076043