Finite Group Databasebeta

← #25967511

Subgroups — #25967511

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#19148271C211yesmaximal, characteristic, complemented
2#19147924C211yesmaximal, characteristic, complemented
3#19145503C212yesmaximal, complemented
4#19145496C212yesmaximal, complemented
5#19145476C212yesmaximal, complemented
6#19145474C212yesmaximal, complemented
7#19145436C212yesmaximal, complemented
8#19145423C212yesmaximal, complemented
9#19145387C212yesmaximal, complemented
10#19145374C212yesmaximal, complemented
11#19144560C211yesmaximal, characteristic, complemented
12#19144549C211yesmaximal, characteristic, complemented
13#19144539C211yesmaximal, characteristic, complemented
14#19144510C211yesmaximal, characteristic, complemented
15#19144284C211yesmaximal, characteristic, complemented
16#19144273C211yesmaximal, characteristic, complemented
17#19144246C211yesmaximal, characteristic, complemented
18#19144230C211yesmaximal, characteristic, complemented
19#19143886C211yesmaximal, characteristic, complemented
20#19143877C211yesmaximal, characteristic, complemented
21#19143837C211yesmaximal, characteristic, complemented
22#19143041C211yesmaximal, characteristic, complemented
23C2×C43×#452C211yesmaximal, characteristic, complemented
24C2×#13063373C2211yescharacteristic
25C22×#10621898C2211yescharacteristic
26C2×#13063356C2211yescharacteristic, complemented
27C2×#13063351C2211yescharacteristic, complemented
28C2×#13063331C2211yescharacteristic
29C2×#13063331C2211yescharacteristic
30#14583562—21no—
31#14583559—21no—
32#14583551—21no—
33#14583550—22no—
34#14583540—21no—
35#14583539—22no—
36#14583480C2211yescharacteristic
37#14583479C2212yescomplemented
38#14583477C2212yes—
39#14583477C2212yes—
40#14583473C2211yescharacteristic
41#14583473C2211yescharacteristic
42#14583473C2211yescharacteristic
43#14583472C2212yescomplemented
44#14583470—21no—
45#14583466C2211yescharacteristic
46#14583466C2211yescharacteristic
47#14583463—21no—
48#14583458—22no—
49#14583445—21no—
50#14583445—21no—
51#14583412C2212yescomplemented
52#14583410—22no—
53#14583410C2211yescharacteristic
54#14583406C2212yes—
55#14583406C2212yes—
56C22⋊Q8×D43C2212yescomplemented
57#14583380C2211yescharacteristic
58C2×#13063284C2211yescharacteristic
59#14583241C2211yescharacteristic, complemented
60#14583241C2211yescharacteristic, complemented
61#14583239C2212yescomplemented
62#14583238C2212yescomplemented
63#14583237C2212yescomplemented
64#14583237C2212yescomplemented
65#14583235C2211yescharacteristic, complemented
66#14583233C2212yescomplemented
67#14583232C2212yescomplemented
68#14583230C2211yescharacteristic, complemented
69#14583228C2212yescomplemented
70#14583227C2212yescomplemented
71#14583224C2211yescharacteristic, complemented
72#14583224C2211yescharacteristic, complemented
73#14583222C2212yescomplemented
74#14583221C2212yescomplemented
75#14583218C2211yescharacteristic, complemented
76#14583216C2212yescomplemented
77#14583213C2211yescharacteristic, complemented
78#14583211C2212yescomplemented
79#14583156C2212yescomplemented
80#14583154C2212yescomplemented
81#14583154C2212yescomplemented
82#14583151C2212yescomplemented
83#14583148C2212yescomplemented
84#14583144C2212yescomplemented
85#14583142C2212yescomplemented
86#14583142C2212yescomplemented
87#14583139C2212yescomplemented
88#14583137C2212yescomplemented
89#14583137C2212yescomplemented
90#14583134C2212yescomplemented
91#14583131C2212yescomplemented
92#14583127C2212yescomplemented
93#14583125C2212yescomplemented
94#14583125C2212yescomplemented
95#14583061C2212yes—
96#14583061C2212yescomplemented
97#14583060C2212yescomplemented
98#14583060C2212yescomplemented
99#14583053C2212yescomplemented
100#14583053C2212yescomplemented
101#14583044C2212yes—
102#14583044C2212yescomplemented
103#14583043C2212yescomplemented
104#14583043C2212yescomplemented
105#14583036C2212yescomplemented
106#14583036C2212yescomplemented
107#14582939C2211yescharacteristic, complemented
108#14582939C2211yescharacteristic, complemented
109#14582937C2211yescharacteristic, complemented
110#14582937C2211yescharacteristic, complemented
111#14582908C2211yescharacteristic, complemented
112#14582908C2211yescharacteristic, complemented
113#14582908C2211yescharacteristic, complemented
114#14582904C2211yescharacteristic, complemented
115#14582896C2211yescharacteristic, complemented
116#14582896C2211yescharacteristic, complemented
117#14582865C2211yescharacteristic
118#14582865C2211yescharacteristic
119#14582864C2212yescomplemented
120#14582864C2212yescomplemented
121#14582863C2211yescharacteristic
122#14582861C2212yescomplemented
123C22⋊C8×D43C2212yescomplemented
124C22×#41×C43C2211yescharacteristic
125C22×Q16×C43C2211yescharacteristic, complemented
126C22×SD16×C43C2211yescharacteristic, complemented
127C2×C22⋊Q8×C43C2211yescharacteristic
128C43×#452C2212yes—
129C43×#452C2212yes—
130C43×#452C2212yescomplemented
131C43×#452C2212yescomplemented
132C2×#103×C43C2211yescharacteristic, complemented
133C2×#102×C43C2211yescharacteristic, complemented
134C2×C22⋊C8×C43C2211yescharacteristic
135#13063373—42no—
136#13063373—42no—
137C2×#10621902—21no—
138C2×#10621902C2312yes—
139C2×#10621898—22no—
140C2×#10621898—42no—
141C2×#10621898—42no—
142C2×#10621898D411yescharacteristic
143C2×#10621898D412yes—
144C2×#10621898D411yescharacteristic
145C2×#10621898C2311yescharacteristic
146C2×#10621898C2311yescharacteristic
147C2×#10621898C2312yes—
148C2×#10621898C2311yescharacteristic
149C22×Dic86D411yescharacteristic
150C2×Q8×D43—21no—
151C2×Q8×D43C2312yes—
152C22×D172D411yescharacteristic
153C22×C22⋊D43D412yes—
154C22×C4×D43C2312yes—
155#13063356—42no—
156#13063351—42no—
157C2×#10621885C2312yes—
158C2×#10621883C2312yes—
159C2×#10621884C2312yes—
160C2×#10621882C2312yes—
161#13063331—42no—
162#13063331—42no—
163C2×#10621877C2311yescharacteristic
164C2×#10621877C2311yescharacteristic
165C2×#10621872C2312yes—
166C2×#10621872C2312yes—
167C2×C8×D43C2312yes—
168C2×C8×D43C2312yes—
169#13063324—22no—
170#13063323—21no—
171#13063323—21no—
172#13063323—21no—
173#13063321—21no—
174#13063321—21no—
175#13063314—21no—
176#13063314—21no—
177#13063314—21no—
178#13063312—21no—
179#13063312—21no—
180#13063311—22no—
181#13063310—22no—
182#13063310—22no—
183#13063308—21no—
184#13063308—22no—
185#13063308—22no—
186#13063308—22no—
187#13063307—22no—
188#13063306—22no—
189#13063306—22no—
190#13063305—21no—
191#13063305C2312yes—
192#13063304—22no—
193#13063304—22no—
194#13063304C2311yescharacteristic
195#13063304C2311yescharacteristic
196#13063303—22no—
197#13063303—22no—
198#13063302—22no—
199#13063301C2312yes—
200#13063301C2312yes—
201#13063301C2312yes—
202#13063301C2312yes—
203#13063301C2312yes—
204#13063301C2312yes—
205#13063300—21no—
206#13063300—22no—
207#13063300C2312yes—
208#13063299—22no—
209#13063299—22no—
210#13063299—22no—
211#13063299C2311yescharacteristic
212#13063299C2311yescharacteristic
213#13063298—22no—
214#13063298—22no—
215#13063297—22no—
216#13063297—22no—
217#13063297—22no—
218#13063297—22no—
219#13063296C2312yes—
220#13063296C2312yes—
221#13063296C2312yes—
222#13063296C2312yes—
223#13063295—22no—
224#13063294—21no—
225#13063294—22no—
226#13063294—22no—
227#13063293—22no—
228#13063293—22no—
229#13063290—21no—
230#13063287—21no—
231#13063287—22no—
232C4×C22⋊D43—21no—
233C4×C22⋊D43—21no—
234C4×C22⋊D43—22no—
235C4×C22⋊D43—22no—
236C4×C22⋊D43—22no—
237C4×C22⋊D43—22no—
238C4×C22⋊D43—22no—
239(C22⋊D43)⋊C4—22no—
240#13063284—21no—
241#13063284—21no—
242#13063284C2311yescharacteristic
243#13063284C2311yescharacteristic
244#13063284C2311yescharacteristic
245#13063284C2311yescharacteristic
246#13063284C2311yescharacteristic
247#13063283C2312yes—
248C2×C4⋊Dic43C2311yescharacteristic
249C2×C4⋊Dic43C2311yescharacteristic
250C4⋊C4×D43—22no—
251C4⋊C4×D43C2312yes—
252C2×C22⋊Dic43—21no—
253C22⋊C4×D43—22no—
254C2×C4×Dic43—21no—
255#13063259C2311yescharacteristic
256#13063259C2311yescharacteristic
257#13063259C2311yescharacteristic
258#13063259C2311yescharacteristic
259#13063258C2312yes—
260#13063258C2312yes—
261#13063257C2311yescharacteristic
262#13063257C2311yescharacteristic
263#13063257C2311yescharacteristic
264#13063257C2311yescharacteristic
265#13063256C2312yes—
266#13063256C2312yes—
267#13063250C2311yescharacteristic
268#13063250C2311yescharacteristic
269#13063250C2311yescharacteristic
270#13063250C2311yescharacteristic
271#13063249C2312yes—
272#13063249C2312yes—
273#13063249C2312yes—
274#13063249C2312yes—
275#13063249C2312yes—
276#13063249C2312yes—
277#13063247C2311yescharacteristic
278#13063247C2311yescharacteristic
279#13063247C2311yescharacteristic
280#13063247C2311yescharacteristic
281#13063246C2312yes—
282#13063246C2312yes—
283C22⋊(C43⋊C8)C2312yes—
284C22⋊(C43⋊C8)C2312yes—
285(C2×D43)⋊C8C2312yes—
286(C2×D43)⋊C8C2312yes—
287(C2×D43)⋊C8C2312yes—
288(C2×D43)⋊C8C2312yes—
289C2×#41×C43—21no—
290C2×#41×C43—21no—
291C2×#41×C43—42no—
292C2×#41×C43—42no—
293C2×#41×C43C2312yes—
294C2×#41×C43C2312yes—
295C22×Q8×C43C2311yescharacteristic
296C22×Q8×C43C2311yescharacteristic
297C22×D4×C43—21no—
298C22×D4×C43C2311yescharacteristic
299C23×C4×C43—21no—
300C23×C4×C43C2311yescharacteristic
301C2×Q16×C43—42no—
302C2×Q16×C43C2312yes—
303C2×Q16×C43C2312yes—
304C2×SD16×C43—42no—
305C2×SD16×C43C2312yes—
306C2×SD16×C43C2312yes—
307C22×C8×C43C2311yescharacteristic
308C22×C8×C43C2311yescharacteristic
309C22⋊Q8×C43—21no—
310C22⋊Q8×C43—21no—
311C22⋊Q8×C43C2312yes—
312C22⋊Q8×C43C2312yes—
313C2×C4⋊C4×C43—21no—
314C2×C4⋊C4×C43C2311yescharacteristic
315C2×C22⋊C4×C43—21no—
316#103×C43C2312yes—
317#103×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320C22⋊C8×C43C2311yescharacteristic
321C22⋊C8×C43C2311yescharacteristic
322C22⋊C8×C43C2311yescharacteristic
323C22⋊C8×C43C2311yescharacteristic
324C24×C43—21no—
325C24×C43C2×D411yescharacteristic
326C23×D43C2×D412yes—
327#41×C43—42no—
328#41×C43—42no—
329#41×C43—42no—
330#41×C43—42no—
331#41×C43—44no—
332#41×C43—44no—
333C2×Q8×C43—21no—
334C2×Q8×C43—21no—
335C2×Q8×C43—22no—
336C2×Q8×C43—22no—
337C2×Q8×C43—22no—
338C2×Q8×C43—22no—
339C2×Q8×C43C2412yes—
340C2×Q8×C43C2412yes—
341C2×D4×C43—21no—
342C2×D4×C43—22no—
343C2×D4×C43—22no—
344C2×D4×C43—22no—
345C2×D4×C43—22no—
346C2×D4×C43—44no—
347C2×D4×C43C2412yes—
348C22×C4×C43—22no—
349C22×C4×C43—22no—
350C22×C4×C43—22no—
351C22×C4×C43—22no—
352C22×C4×C43—21no—
353C22×C4×C43—21no—
354C22×C4×C43—21no—
355C22×C4×C43—44no—
356C22×C4×C43C2×D411yescharacteristic
357C22×C4×C43C2×D411yescharacteristic
358C22×C4×C43C2×D411yescharacteristic
359C22×C4×C43C2411yescharacteristic
360C22×C4×C43C2411yescharacteristic
361C22×C4×C43C2411yescharacteristic
362C2×C22⋊D43—21no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—22no—
367C2×C22⋊D43—22no—
368C2×C22⋊D43—22no—
369C2×C22⋊D43—44no—
370C2×C22⋊D43C2×D412yes—
371C2×C22⋊D43C2×D412yes—
372C2×C22⋊D43C2×D412yes—
373C2×C22⋊D43C2×D412yes—
374C22×Dic43—21no—
375C22×Dic43—21no—
376C22×Dic43C2×D412yes—
377#10621902—42no—
378#10621902—42no—
379#10621902—44no—
380Q8×D43—42no—
381Q8×D43—42no—
382Q8×D43—44no—
383#10621898—22no—
384#10621898—22no—
385#10621898—22no—
386#10621898—22no—
387#10621898—22no—
388#10621898—22no—
389#10621898—42no—
390#10621898—42no—
391#10621898—42no—
392#10621898—42no—
393#10621898—44no—
394#10621898—48no—
395C2×D172—22no—
396C2×D172—22no—
397C2×D172—42no—
398C2×D172C2×D411yescharacteristic
399C2×D172C2×D411yescharacteristic
400C2×D172C2×D412yes—
401C2×D172C2411yescharacteristic
402C2×C4×D43—21no—
403C2×C4×D43—22no—
404C2×C4×D43—22no—
405C2×C4×D43—22no—
406C2×C4×D43—42no—
407C2×C4×D43—42no—
408C2×C4×D43C2×D412yes—
409C2×C4×D43C2×D412yes—
410C2×C4×D43C2412yes—
411C2×C4×D43C2412yes—
412C2×Dic86—22no—
413C2×Dic86—42no—
414C2×Dic86C2×D411yescharacteristic
415C2×Dic86C2×D411yescharacteristic
416C2×Dic86C2×D412yes—
417C2×Dic86C2411yescharacteristic
418Q16×C43—42no—
419Q16×C43—42no—
420SD16×C43—42no—
421SD16×C43—42no—
422C2×C8×C43—22no—
423C2×C8×C43—22no—
424C2×C8×C43C2411yescharacteristic
425C2×C8×C43C2411yescharacteristic
426C2×C8×C43C2411yescharacteristic
427C2×C8×C43C2411yescharacteristic
428C4⋊C4×C43—22no—
429C4⋊C4×C43—22no—
430C4⋊C4×C43—21no—
431C4⋊C4×C43C2412yes—
432C22⋊C4×C43—22no—
433C22⋊C4×C43—22no—
434C22⋊Dic43—22no—
435C22⋊Dic43—22no—
436C22⋊Dic43—22no—
437C22⋊Dic43—22no—
438C22⋊Dic43—21no—
439C22⋊Dic43—21no—
440C22⋊Dic43—21no—
441C22⋊Dic43—21no—
442C22⋊Dic43—21no—
443C22⋊Dic43—21no—
444C22⋊Dic43—21no—
445#10621885—42no—
446#10621884—42no—
447#10621883—42no—
448#10621882—42no—
449(C2×D43)⋊C4—21no—
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—22no—
456(C2×D43)⋊C4—22no—
457(C2×D43)⋊C4—22no—
458(C2×D43)⋊C4—22no—
459(C2×D43)⋊C4—22no—
460C4⋊Dic43—21no—
461C4⋊Dic43—21no—
462C4⋊Dic43—22no—
463C4⋊Dic43C2411yescharacteristic
464C4⋊Dic43C2411yescharacteristic
465C4⋊Dic43C2411yescharacteristic
466C4⋊Dic43C2411yescharacteristic
467C4⋊Dic43C2411yescharacteristic
468C4⋊Dic43C2411yescharacteristic
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—22no—
472Dic43⋊C4—22no—
473Dic43⋊C4—22no—
474Dic43⋊C4—22no—
475Dic43⋊C4—22no—
476Dic43⋊C4—22no—
477Dic43⋊C4—22no—
478C4×Dic43—21no—
479C4×Dic43—21no—
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—22no—
484#10621877—22no—
485#10621877—22no—
486C2×C43⋊C8C2412yes—
487C2×C43⋊C8C2412yes—
488#10621872—42no—
489#10621872—42no—
490C8×D43—42no—
491C8×D43—42no—
492C23×C43—22no—
493C23×C43—22no—
494C23×C43—41no—
495C23×C43—41no—
496C23×C43—42no—
497C23×C43—81no—
498C23×C43—81no—
499C23×C43C22×D411yescharacteristic
500C23×C43C22×D411yescharacteristic
501C23×C43C22×D411yescharacteristic
502C22×D43—21no—
503C22×D43—42no—
504C22×D43—42no—
505C22×D43—42no—
506C22×D43C22×D412yes—
507C22×D43C22×D412yes—
508Q8×C43—22no—
509Q8×C43—22no—
510Q8×C43—22no—
511Q8×C43—22no—
512Q8×C43—42no—
513Q8×C43—42no—
514D4×C43—22no—
515D4×C43—22no—
516D4×C43—44no—
517D4×C43—44no—
518D4×C43—42no—
519C2×C4×C43—22no—
520C2×C4×C43—22no—
521C2×C4×C43—22no—
522C2×C4×C43—21no—
523C2×C4×C43—21no—
524C2×C4×C43—21no—
525C2×C4×C43—21no—
526C2×C4×C43—22no—
527C2×C4×C43—22no—
528C2×C4×C43—22no—
529C2×C4×C43—44no—
530C2×C4×C43—44no—
531C2×C4×C43—42no—
532C2×C4×C43—42no—
533C2×C4×C43—81no—
534C2×C4×C43C22×D411yescharacteristic
535C2×C4×C43C22×D411yescharacteristic
536C2×C4×C43C22×D411yescharacteristic
537C2×C4×C43H(5,𝔽2)12yes—
538C2×C4×C43H(5,𝔽2)12yes—
539C2×C4×C43C2511yescharacteristic
540C22⋊D43—24no—
541C22⋊D43—24no—
542C22⋊D43—42no—
543C22⋊D43—42no—
544C22⋊D43—42no—
545C22⋊D43—42no—
546C22⋊D43—82no—
547C22⋊D43—82no—
548C22⋊D43—82no—
549C22⋊D43—82no—
550C22⋊D43—81no—
551C2×Dic43—21no—
552C2×Dic43—21no—
553C2×Dic43—21no—
554C2×Dic43—21no—
555C2×Dic43—21no—
556C2×Dic43—21no—
557C2×Dic43—21no—
558C2×Dic43—42no—
559C2×Dic43—81no—
560C2×Dic43—81no—
561C2×Dic43C22×D412yes—
562C2×Dic43C22×D412yes—
563D172—22no—
564D172—22no—
565D172—21no—
566D172—21no—
567D172—42no—
568D172—44no—
569D172—82no—
570C4×D43—22no—
571C4×D43—22no—
572C4×D43—22no—
573C4×D43—22no—
574C4×D43—42no—
575C4×D43—42no—
576C4×D43—44no—
577C4×D43—44no—
578C4×D43—42no—
579C4×D43—82no—
580Dic86—22no—
581Dic86—22no—
582Dic86—21no—
583Dic86—21no—
584Dic86—42no—
585Dic86—44no—
586C8×C43—21no—
587C8×C43—21no—
588C8×C43—21no—
589C8×C43—21no—
590C43⋊C8—22no—
591C43⋊C8—22no—
592#60761—431nomaximal, Sylow
593C22×C43—21no—
594C22×C43—21no—
595C22×C43—21no—
596C22×C43—21no—
597C22×C43—21no—
598C22×C43—21no—
599C22×C43—21no—
600C22×C43—21no—
601C22×C43—42no—
602C22×C43—42no—
603C22×C43—42no—
604C22×C43—82no—
605C22×C43—84no—
606C22×C43#53412yes—
607C22×C43C23×D411yescharacteristic
608C2×D43—22no—
609C2×D43—22no—
610C2×D43—22no—
611C2×D43—22no—
612C2×D43—22no—
613C2×D43—22no—
614C2×D43—41no—
615C2×D43—41no—
616C2×D43—41no—
617C2×D43—84no—
618C4×C43—21no—
619C4×C43—21no—
620C4×C43—42no—
621C4×C43—42no—
622C4×C43—42no—
623C4×C43#53412yes—
624C4×C43C2×H(5,𝔽2)11yescharacteristic
625C4×C43C2×H(5,𝔽2)11yescharacteristic
626Dic43—22no—
627Dic43—22no—
628Dic43—41no—
629Dic43—41no—
630Dic43—41no—
631Dic43—41no—
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#3011—431no—
654#3010—431no—
655#3005—431no—
656C2×#452D4311yescharacteristic, complemented
657#2880—431no—
658C2×C43—22no—
659C2×C43—41no—
660C2×C43—41no—
661C2×C43—82no—
662C2×C43C2×#53411yescharacteristic
663C2×C43#358411yescharacteristic
664C2×C43#358611yescharacteristic
665D43—42no—
666D43—42no—
667D43—81no—
668C2×2−1+4—431no—
669C22×#41—431no—
670C22×#41C2×D4311yescharacteristic
671C2×#137—431no—
672C2×AGL(1,ℤ/8)—431no—
673C22×Q16C2×D4311yescharacteristic, complemented
674C22×SD16C2×D4311yescharacteristic, complemented
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—432no—
685#537—432no—
686#537—431no—
687#536—431no—
688#536—431no—
689#536—431no—
690#536—432no—
691#536—861no—
692#535—431no—
693#535—431no—
694#535—861no—
695#534—862no—
696#532—861no—
697#532—861no—
698#525—432no—
699#525—432no—
700#525—431no—
701#525—432no—
702#525—862no—
703C2×C22⋊Q8—432no—
704C2×C22⋊Q8C2×D4311yescharacteristic
705#520—431no—
706C2×#117—431no—
707#485—432no—
708#485—432no—
709#485—432no—
710#485—432no—
711#485—431no—
712#485—431no—
713#484—432no—
714#484—432no—
715#484—431no—
716#483—432no—
717#483—432no—
718#483—431no—
719#482—432no—
720#482—432no—
721#482—431no—
722#482—431no—
723#481—432no—
724#481—431no—
725#480—432no—
726#480—431no—
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#452C2×D4312yes—
748#452C2×D4312yes—
749#452C2×D4312yescomplemented
750#452C2×D4312yescomplemented
751#451—432no—
752#451—432no—
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#419—431no—
766#418—431no—
767#416—431no—
768#416—431no—
769C2×#103C2×D4311yescharacteristic, complemented
770C2×#102C2×D4311yescharacteristic, complemented
771#408—431no—
772#408—431no—
773#408—432no—
774#408—432no—
775#407—431no—
776#407—432no—
777C2×C22⋊C8—432no—
778C2×C22⋊C8C2×D4311yescharacteristic
779C43#6076111yescharacteristic, complemented, Sylow
7802−1+4—1722no—
7812−1+4—1722no—
782C2×#41—21no—
783C2×#41—21no—
784C2×#41—42no—
785C2×#41—42no—
786C2×#41—432no—
787C2×#41—431no—
788C2×#41—431no—
789C2×#41—431no—
790C2×#41—431no—
791C2×#41—432no—
792C2×#41—432no—
793C2×#41—431no—
794C2×#41—862no—
795C2×#41—861no—
796C2×#41—1722no—
797C2×#41—1722no—
798C2×#41C22×D4312yes—
799C2×#41C22×D4312yes—
800C22×Q8—431no—
801C22×Q8—432no—
802C22×Q8—861no—
803C22×Q8C22×D4311yescharacteristic
804C22×Q8C22×D4311yescharacteristic
805C22×D4—21no—
806C22×D4—432no—
807C22×D4—431no—
808C22×D4C22×D4311yescharacteristic
809C23×C4—21no—
810C23×C4—432no—
811C23×C4C22×D4311yescharacteristic
812#137—1722no—
813AGL(1,ℤ/8)—1722no—
814C2×Q16—42no—
815C2×Q16—432no—
816C2×Q16C22×D4312yes—
817C2×Q16C22×D4312yes—
818C2×SD16—42no—
819C2×SD16—432no—
820C2×SD16—432no—
821C2×SD16C22×D4312yes—
822C2×SD16C22×D4312yes—
823C2×D8—432no—
824#131—1722no—
825#131—1722no—
826C2×M16—431no—
827C2×M16—431no—
828C2×M16—432no—
829C2×M16—432no—
830C22×C8—432no—
831C22×C8—432no—
832C22×C8C22×D4311yescharacteristic
833C22×C8C22×D4311yescharacteristic
834C4⋊Q8—862no—
835C4⋊Q8—861no—
836C4⋊Q8—861no—
837C4⋊Q8—861no—
838#127—861no—
839#127—861no—
840#124—862no—
841#124—861no—
842#124—861no—
843#124—861no—
844#124—861no—
845#124—861no—
846#123—862no—
847#123—862no—
848#123—862no—
849#123—862no—
850#123—862no—
851#123—862no—
852#123—862no—
853#123—862no—
854#123—861no—
855C22⋊Q8—21no—
856C22⋊Q8—21no—
857C22⋊Q8—432no—
858C22⋊Q8—432no—
859C22⋊Q8—432no—
860C22⋊Q8—432no—
861C22⋊Q8—432no—
862C22⋊Q8—432no—
863C22⋊Q8—431no—
864C22⋊Q8—431no—
865C22⋊Q8—432no—
866C22⋊Q8—862no—
867C22⋊Q8—862no—
868C22⋊Q8—862no—
869C22⋊Q8—861no—
870C22⋊Q8—862no—
871C22⋊Q8—862no—
872C22⋊Q8C22×D4312yes—
873C22⋊Q8C22×D4312yes—
874#121—432no—
875#121—432no—
876#121—432no—
877#121—432no—
878#121—431no—
879#121—431no—
880#121—432no—
881#121—862no—
882#121—862no—
883#121—862no—
884#121—861no—
885#121—862no—
886#121—862no—
887#121—862no—
888#121—862no—
889#121—862no—
890#121—862no—
891#121—862no—
892#120—862no—
893#120—862no—
894#120—862no—
895#120—862no—
896#120—862no—
897#120—861no—
898C4×Q8—861no—
899C4×D4—862no—
900C4×D4—862no—
901C4×D4—861no—
902C4×D4—862no—
903C4×D4—862no—
904C4×D4—862no—
905C4×D4—862no—
906C4×D4—862no—
907C4×D4—861no—
908C4×D4—861no—
909#117—431no—
910#117—431no—
911#117—431no—
912#117—431no—
913#117—431no—
914#117—432no—
915#117—861no—
916#117—861no—
917C2×C4⋊C4—21no—
918C2×C4⋊C4—431no—
919C2×C4⋊C4—431no—
920C2×C4⋊C4—432no—
921C2×C4⋊C4—862no—
922C2×C4⋊C4C22×D4311yescharacteristic
923C2×C22⋊C4—21no—
924C2×C22⋊C4—862no—
925C2×C22⋊C4—861no—
926C2×C42—861no—
927#107—431no—
928#107—431no—
929#107—431no—
930#107—431no—
931#107—432no—
932#107—432no—
933#106—431no—
934#106—431no—
935#106—431no—
936#106—431no—
937#106—432no—
938#106—432no—
939#103—432no—
940#103—432no—
941#103—432no—
942#103—432no—
943#103—432no—
944#103—432no—
945#103—431no—
946#103—431no—
947#103—431no—
948#103—431no—
949#103C22×D4312yes—
950#103C22×D4312yes—
951#102—432no—
952#102—432no—
953#102—431no—
954#102—431no—
955#102—431no—
956#102—431no—
957#102C22×D4312yes—
958#102C22×D4312yes—
959C22⋊C8—432no—
960C22⋊C8—432no—
961C22⋊C8—432no—
962C22⋊C8—432no—
963C22⋊C8—432no—
964C22⋊C8—432no—
965C22⋊C8C22×D4311yescharacteristic
966C22⋊C8C22×D4311yescharacteristic
967C22⋊C8C22×D4311yescharacteristic
968C22⋊C8C22×D4311yescharacteristic
969C24—21no—
970C24—432no—
971C24D4×D4311yescharacteristic
972#41—42no—
973#41—42no—
974#41—42no—
975#41—42no—
976#41—44no—
977#41—44no—
978#41—862no—
979#41—862no—
980#41—862no—
981#41—862no—
982#41—862no—
983#41—862no—
984#41—1722no—
985#41—1722no—
986#41—1724no—
987#41—1722no—
988#41—1722no—
989#41—1728no—
990#41—1722no—
991#41—1722no—
992#41—1724no—
993C2×Q8—21no—
994C2×Q8—21no—
995C2×Q8—22no—
996C2×Q8—22no—
997C2×Q8—22no—
998C2×Q8—22no—
999C2×Q8—431no—
1000C2×Q8—431no—
1001C2×Q8—432no—
1002C2×Q8—431no—
1003C2×Q8—862no—
1004C2×Q8—1722no—
1005C2×Q8—1722no—
1006C2×Q8—1722no—
1007C2×Q8—1724no—
1008C2×Q8C23×D4312yes—
1009C2×Q8C23×D4312yes—
1010C2×D4—22no—
1011C2×D4—22no—
1012C2×D4—21no—
1013C2×D4—22no—
1014C2×D4—22no—
1015C2×D4—44no—
1016C2×D4—432no—
1017C2×D4—432no—
1018C2×D4—432no—
1019C2×D4—432no—
1020C2×D4—431no—
1021C2×D4—431no—
1022C2×D4—432no—
1023C2×D4—431no—
1024C2×D4—862no—
1025C2×D4—862no—
1026C2×D4—862no—
1027C2×D4—862no—
1028C2×D4—862no—
1029C2×D4—862no—
1030C2×D4—861no—
1031C2×D4—861no—
1032C2×D4—861no—
1033C2×D4—1722no—
1034C2×D4—1724no—
1035C2×D4C23×D4312yes—
1036C22×C4—22no—
1037C22×C4—22no—
1038C22×C4—21no—
1039C22×C4—21no—
1040C22×C4—21no—
1041C22×C4—22no—
1042C22×C4—22no—
1043C22×C4—44no—
1044C22×C4—432no—
1045C22×C4—432no—
1046C22×C4—432no—
1047C22×C4—432no—
1048C22×C4—432no—
1049C22×C4—862no—
1050C22×C4—862no—
1051C22×C4—862no—
1052C22×C4—861no—
1053C22×C4—861no—
1054C22×C4—861no—
1055C22×C4—1722no—
1056C22×C4—1722no—
1057C22×C4D4×D4311yescharacteristic
1058C22×C4D4×D4311yescharacteristic
1059C22×C4D4×D4311yescharacteristic
1060C22×C4C23×D4311yescharacteristic
1061C22×C4C23×D4311yescharacteristic
1062C22×C4C23×D4311yescharacteristic
1063Q16—42no—
1064Q16—42no—
1065Q16—1722no—
1066SD16—42no—
1067SD16—42no—
1068SD16—1722no—
1069SD16—1722no—
1070D8—1722no—
1071M16—862no—
1072M16—862no—
1073M16—1722no—
1074M16—1722no—
1075C2×C8—22no—
1076C2×C8—22no—
1077C2×C8—432no—
1078C2×C8—432no—
1079C2×C8—1722no—
1080C2×C8—1722no—
1081C2×C8C23×D4311yescharacteristic
1082C2×C8C23×D4311yescharacteristic
1083C2×C8C23×D4311yescharacteristic
1084C2×C8C23×D4311yescharacteristic
1085C4⋊C4—22no—
1086C4⋊C4—22no—
1087C4⋊C4—21no—
1088C4⋊C4—431no—
1089C4⋊C4—431no—
1090C4⋊C4—431no—
1091C4⋊C4—431no—
1092C4⋊C4—431no—
1093C4⋊C4—431no—
1094C4⋊C4—862no—
1095C4⋊C4—862no—
1096C4⋊C4—862no—
1097C4⋊C4—862no—
1098C4⋊C4—862no—
1099C4⋊C4—862no—
1100C4⋊C4—862no—
1101C4⋊C4—862no—
1102C4⋊C4—861no—
1103C4⋊C4—861no—
1104C4⋊C4—861no—
1105C4⋊C4—861no—
1106C4⋊C4C23×D4312yes—
1107C22⋊C4—22no—
1108C22⋊C4—22no—
1109C22⋊C4—862no—
1110C22⋊C4—862no—
1111C22⋊C4—862no—
1112C22⋊C4—862no—
1113C22⋊C4—862no—
1114C22⋊C4—862no—
1115C22⋊C4—862no—
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—861no—
1125C22⋊C4—861no—
1126C22⋊C4—861no—
1127C22⋊C4—861no—
1128C22⋊C4—861no—
1129C22⋊C4—861no—
1130C22⋊C4—861no—
1131C42—862no—
1132C42—861no—
1133C42—861no—
1134C42—861no—
1135C42—861no—
1136C42—861no—
1137C23—22no—
1138C23—22no—
1139C23—41no—
1140C23—41no—
1141C23—42no—
1142C23—81no—
1143C23—81no—
1144C23—432no—
1145C23—432no—
1146C23—861no—
1147C23—1722no—
1148C23—1722no—
1149C23—1722no—
1150C23C2×D4×D4311yescharacteristic
1151C23C2×D4×D4311yescharacteristic
1152C23C2×D4×D4311yescharacteristic
1153Q8—22no—
1154Q8—22no—
1155Q8—22no—
1156Q8—22no—
1157Q8—42no—
1158Q8—42no—
1159Q8—862no—
1160Q8—862no—
1161Q8—861no—
1162Q8—861no—
1163Q8—1722no—
1164Q8—1724no—
1165D4—22no—
1166D4—22no—
1167D4—44no—
1168D4—44no—
1169D4—42no—
1170D4—864no—
1171D4—864no—
1172D4—862no—
1173D4—862no—
1174D4—861no—
1175D4—861no—
1176D4—3442no—
1177D4—3441no—
1178D4—3442no—
1179D4—3442no—
1180D4—3442no—
1181D4—3442no—
1182D4—1722no—
1183D4—1724no—
1184D4—1722no—
1185D4—1722no—
1186D4—1722no—
1187D4—1722no—
1188C2×C4—22no—
1189C2×C4—22no—
1190C2×C4—22no—
1191C2×C4—21no—
1192C2×C4—21no—
1193C2×C4—21no—
1194C2×C4—21no—
1195C2×C4—22no—
1196C2×C4—22no—
1197C2×C4—22no—
1198C2×C4—44no—
1199C2×C4—44no—
1200C2×C4—42no—
1201C2×C4—42no—
1202C2×C4—81no—
1203C2×C4—432no—
1204C2×C4—432no—
1205C2×C4—862no—
1206C2×C4—862no—
1207C2×C4—862no—
1208C2×C4—862no—
1209C2×C4—861no—
1210C2×C4—861no—
1211C2×C4—861no—
1212C2×C4—861no—
1213C2×C4—861no—
1214C2×C4—861no—
1215C2×C4—861no—
1216C2×C4—3442no—
1217C2×C4—3441no—
1218C2×C4—3441no—
1219C2×C4—1722no—
1220C2×C4—1722no—
1221C2×C4—1724no—
1222C2×C4—1724no—
1223C2×C4—1722no—
1224C2×C4—1722no—
1225C2×C4C2×D4×D4311yescharacteristic
1226C2×C4C2×D4×D4311yescharacteristic
1227C2×C4C2×D4×D4311yescharacteristic
1228C2×C4#1306337012yes—
1229C2×C4#1306337012yes—
1230C2×C4C24×D4311yescharacteristic
1231C8—21no—
1232C8—21no—
1233C8—21no—
1234C8—21no—
1235C8—862no—
1236C8—862no—
1237C22—21no—
1238C22—21no—
1239C22—21no—
1240C22—21no—
1241C22—21no—
1242C22—21no—
1243C22—21no—
1244C22—21no—
1245C22—42no—
1246C22—42no—
1247C22—42no—
1248C22—82no—
1249C22—84no—
1250C22—862no—
1251C22—862no—
1252C22—862no—
1253C22—862no—
1254C22—862no—
1255C22—862no—
1256C22—3444no—
1257C22—1721no—
1258C22—1721no—
1259C22—1721no—
1260C22#1458345912yes—
1261C22C22×D4×D4311yescharacteristic
1262C4—21no—
1263C4—21no—
1264C4—42no—
1265C4—42no—
1266C4—42no—
1267C4—862no—
1268C4—862no—
1269C4—1721no—
1270C4—1721no—
1271C4—1721no—
1272C4—1721no—
1273C4—1721no—
1274C4—1721no—
1275C4—1721no—
1276C4#1458345912yes—
1277C4C2×#1306337011yescharacteristic
1278C4C2×#1306337011yescharacteristic
1279C2—22no—
1280C2—41no—
1281C2—41no—
1282C2—82no—
1283C2—3441no—
1284C2—1722no—
1285C2—1722no—
1286C2C2×#1458345911yescharacteristic
1287C2#1914936411yescharacteristic
1288C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#452C2
socleC22×C43C23×D4
hypercenterC2×#452D43
hypocenterC43#60761
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#452

Complements

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

NH ≅ G/Ntype
1. #19148271C2semidirect
2. #19147924C2semidirect
3. #19145503C2semidirect
4. #19145496C2semidirect
5. #19145476C2semidirect
6. #19145474C2semidirect
7. #19145436C2semidirect
8. #19145423C2semidirect
9. #19145387C2semidirect
10. #19145374C2semidirect
11. #19144560C2semidirect
12. #19144549C2semidirect
13. #19144539C2semidirect
14. #19144510C2semidirect
15. #19144284C2semidirect
16. #19144273C2semidirect
17. #19144246C2semidirect
18. #19144230C2semidirect
19. #19143886C2semidirect
20. #19143877C2semidirect
21. #19143837C2semidirect
22. #19143041C2semidirect
23. C2×C43×#452C2semidirect
26. C2×#13063356C22semidirect
27. C2×#13063351C22semidirect
37. #14583479C22semidirect
43. #14583472C22semidirect
51. #14583412C22semidirect
56. C22⋊Q8×D43C22semidirect
59. #14583241C22semidirect
60. #14583241C22semidirect
61. #14583239C22semidirect
62. #14583238C22semidirect
63. #14583237C22semidirect
64. #14583237C22semidirect
65. #14583235C22semidirect
66. #14583233C22semidirect
67. #14583232C22semidirect
68. #14583230C22semidirect
69. #14583228C22semidirect
70. #14583227C22semidirect
71. #14583224C22semidirect
72. #14583224C22semidirect
73. #14583222C22semidirect
74. #14583221C22semidirect
75. #14583218C22semidirect
76. #14583216C22semidirect
77. #14583213C22semidirect
78. #14583211C22semidirect
79. #14583156C22semidirect
80. #14583154C22semidirect
81. #14583154C22semidirect
82. #14583151C22semidirect
83. #14583148C22semidirect
84. #14583144C22semidirect
85. #14583142C22semidirect
86. #14583142C22semidirect
87. #14583139C22semidirect
88. #14583137C22semidirect
89. #14583137C22semidirect
90. #14583134C22semidirect
91. #14583131C22semidirect
92. #14583127C22semidirect
93. #14583125C22semidirect
94. #14583125C22semidirect
96. #14583061C22semidirect
97. #14583060C22semidirect
98. #14583060C22semidirect
99. #14583053C22semidirect
100. #14583053C22semidirect
102. #14583044C22semidirect
103. #14583043C22semidirect
104. #14583043C22semidirect
105. #14583036C22semidirect
106. #14583036C22semidirect
107. #14582939C22semidirect
108. #14582939C22semidirect
109. #14582937C22semidirect
110. #14582937C22semidirect
111. #14582908C22semidirect
112. #14582908C22semidirect
113. #14582908C22semidirect
114. #14582904C22semidirect
115. #14582896C22semidirect
116. #14582896C22semidirect
119. #14582864C22semidirect
120. #14582864C22semidirect
122. #14582861C22semidirect
123. C22⋊C8×D43C22semidirect
125. C22×Q16×C43C22semidirect
126. C22×SD16×C43C22semidirect
130. C43×#452C22semidirect
131. C43×#452C22semidirect
132. C2×#103×C43C22semidirect
133. C2×#102×C43C22semidirect
656. C2×#452D43semidirect
673. C22×Q16C2×D43semidirect
674. C22×SD16C2×D43semidirect
749. #452C2×D43semidirect
750. #452C2×D43semidirect
769. C2×#103C2×D43semidirect
770. C2×#102C2×D43semidirect
779. C43#60761semidirect

Maximal subgroups

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

subgroupindex
#191482712
#191479242
#191455032
#191454962
#191454762
#191454742
#191454362
#191454232
#191453872
#191453742
#191445602
#191445492
#191445392
#191445102
#191442842
#191442732
#191442462
#191442302
#191438862
#191438772
#191438372
#191430412
C2×C43×#4522
#6076143