Finite Group Databasebeta

← #25974034

Subgroups — #25974034

Order 11008.

2102 conjugacy classes of subgroups.

The subgroup lattice has 1256 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148304C211yesmaximal, characteristic, complemented
2#19148239C211yesmaximal, characteristic, complemented
3#19146907C212yesmaximal, complemented
4#19146896C212yesmaximal, complemented
5#19146812C212yesmaximal, complemented
6#19146797C212yesmaximal, complemented
7#19146692C212yesmaximal, complemented
8#19146677C212yesmaximal, complemented
9#19146572C212yesmaximal, complemented
10#19146557C212yesmaximal, complemented
11#19144958C211yesmaximal, characteristic, complemented
12#19144560C211yesmaximal, characteristic, complemented
13#19144518C211yesmaximal, characteristic, complemented
14#19144422C211yesmaximal, characteristic, complemented
15#19144284C211yesmaximal, characteristic, complemented
16#19144204C211yesmaximal, characteristic, complemented
17#19144150C211yesmaximal, characteristic, complemented
18#19143904C211yesmaximal, characteristic, complemented
19#19143837C211yesmaximal, characteristic, complemented
20#19143421C211yesmaximal, characteristic, complemented
21#19143298C211yesmaximal, characteristic, complemented
22#19143116C211yesmaximal, characteristic, complemented
23C2×C43×#417C211yesmaximal, characteristic, complemented
24C2×#13063370C2211yescharacteristic
25C2×#13063356C2211yescharacteristic, complemented
26C2×#13063351C2211yescharacteristic
27C2×#13063347C2211yescharacteristic
28C2×#13063331C2211yescharacteristic
29#14583604—21no—
30#14583604C2212yescomplemented
31#14583597—21no—
32#14583597C2212yescomplemented
33#14583584—21no—
34#14583584C2212yescomplemented
35#14583550—21no—
36#14583550C2212yescomplemented
37#14583548—21no—
38#14583548—21no—
39#14583548C2212yes—
40#14583548C2212yes—
41#14583537—21no—
42#14583537—21no—
43#14583537C2212yes—
44#14583537C2212yes—
45#14583530C2211yescharacteristic, complemented
46#14583496—22no—
47#14583480C2211yescharacteristic
48#14583473C2211yescharacteristic
49#14583473C2211yescharacteristic
50#14583458—22no—
51#14583410—22no—
52#14583410C2211yescharacteristic
53#14583410C2211yescharacteristic
54#14583410C2211yescharacteristic, complemented
55C2×#13063308—22no—
56#14583380C2211yescharacteristic
57#14583380C2211yescharacteristic, complemented
58#14583374C2211yescharacteristic
59#14583266C2212yescomplemented
60#14583260C2212yescomplemented
61#14583255C2212yescomplemented
62#14583248C2212yescomplemented
63#14583239C2212yescomplemented
64#14583238C2212yescomplemented
65#14583234C2212yescomplemented
66#14583233C2212yescomplemented
67#14583229C2212yescomplemented
68#14583228C2212yescomplemented
69#14583217C2212yescomplemented
70#14583212C2212yescomplemented
71#14583201C2212yescomplemented
72#14583197C2212yescomplemented
73#14583187C2212yescomplemented
74#14583177C2212yescomplemented
75#14583157C2211yescharacteristic, complemented
76#14583157C2211yescharacteristic, complemented
77#14583156C2212yescomplemented
78#14583152C2211yescharacteristic, complemented
79#14583152C2211yescharacteristic, complemented
80#14583148C2212yescomplemented
81#14583145C2211yescharacteristic, complemented
82#14583145C2211yescharacteristic, complemented
83#14583145C2211yescharacteristic, complemented
84#14583145C2211yescharacteristic, complemented
85#14583139C2212yescomplemented
86#14583131C2212yescomplemented
87#14583124C2212yescomplemented
88#14583117C2212yescomplemented
89#14583108C2212yescomplemented
90#14583103C2212yescomplemented
91#14583062C2212yescomplemented
92#14583061C2212yescomplemented
93#14583061C2212yescomplemented
94#14583051C2212yescomplemented
95#14583045C2212yescomplemented
96#14583044C2212yescomplemented
97#14583044C2212yescomplemented
98#14583034C2212yescomplemented
99#14583008C2212yescomplemented
100#14582996C2212yescomplemented
101#14582990C2212yescomplemented
102#14582979C2212yescomplemented
103#14582975C2212yescomplemented
104#14582975C2212yescomplemented
105#14582968C2212yescomplemented
106#14582968C2212yescomplemented
107#14582939C2211yescharacteristic, complemented
108#14582939C2211yescharacteristic, complemented
109#14582937C2211yescharacteristic, complemented
110#14582925C2211yescharacteristic, complemented
111#14582908C2211yescharacteristic, complemented
112#14582904C2211yescharacteristic
113#14582902C2212yescomplemented
114#14582898C2211yescharacteristic
115#14582898C2211yescharacteristic
116#14582897C2212yescomplemented
117#14582896C2211yescharacteristic
118#14582896C2211yescharacteristic, complemented
119#14582892C2212yescomplemented
120#102×D43C2212yescomplemented
121#14582865C2211yescharacteristic
122#14582863C2211yescharacteristic, complemented
123#14582854C2211yescharacteristic, complemented
124C22×#41×C43C2211yescharacteristic
125C22×M16×C43C2211yescharacteristic, complemented
126C22×C4⋊C4×C43C2211yescharacteristic, complemented
127C43×#417C2212yescomplemented
128C43×#417C2212yescomplemented
129C43×#417C2212yescomplemented
130C43×#417C2212yescomplemented
131C2×#103×C43C2211yescharacteristic, complemented
132C2×#103×C43C2211yescharacteristic, complemented
133C2×#102×C43C2211yescharacteristic
134C2×#102×C43C2211yescharacteristic
135#13063370—24no—
136#13063370—42no—
137C2×#10621898—22no—
138C2×#10621898C2311yescharacteristic
139C2×#10621898C2311yescharacteristic
140C2×#10621898C2311yescharacteristic
141C2×#10621900—21no—
142C2×#10621900C2312yes—
143C22×C22⋊D43—22no—
144C2×D4×D43—21no—
145C2×D4×D43C2312yes—
146#13063356—42no—
147#13063351—24no—
148#13063347—42no—
149C2×Dic172C2311yescharacteristic
150C2×#10621885C2312yes—
151C2×#10621873C2311yescharacteristic
152C2×#10621873C2311yescharacteristic
153C2×#10621883C2312yes—
154C2×#10621884C2312yes—
155C2×D344C2311yescharacteristic
156C2×#10621882C2312yes—
157#13063331—42no—
158C2×#10621877C2311yescharacteristic
159C2×#10621877C2311yescharacteristic
160C2×#10621872C2312yes—
161C2×C8×D43C2312yes—
162#13063324—21no—
163#13063324C2312yes—
164#13063323—21no—
165#13063323C2312yes—
166#13063320—22no—
167#13063320—22no—
168#13063316—21no—
169#13063316C2312yes—
170#13063315—22no—
171#13063315—22no—
172#13063314—21no—
173#13063314C2312yes—
174#13063310—22no—
175#13063310—22no—
176#13063308—21no—
177#13063308—21no—
178#13063308—22no—
179#13063308—22no—
180#13063308—22no—
181#13063308—22no—
182#13063308—22no—
183#13063308—22no—
184#13063308—22no—
185#13063308—22no—
186#13063308D412yes—
187#13063306—22no—
188#13063306—22no—
189#13063305—21no—
190#13063305C2312yes—
191#13063304—22no—
192#13063304—22no—
193#13063304D411yescharacteristic
194#13063304D411yescharacteristic
195#13063304C2311yescharacteristic
196#13063304C2311yescharacteristic
197#13063304C2311yescharacteristic
198#13063304C2311yescharacteristic
199#13063303—22no—
200#13063303—22no—
201#13063301—21no—
202#13063301—21no—
203#13063301C2312yes—
204#13063301C2312yes—
205#13063300—21no—
206#13063300C2312yes—
207#13063299—22no—
208#13063299—22no—
209#13063299D411yescharacteristic
210#13063299D411yescharacteristic
211#13063299C2311yescharacteristic
212#13063299C2311yescharacteristic
213#13063299C2311yescharacteristic
214#13063299C2311yescharacteristic
215#13063297—22no—
216#13063297—22no—
217#13063297—22no—
218#13063297—22no—
219#13063294—21no—
220#13063294—21no—
221#13063294D412yes—
222#13063293—22no—
223#13063293—22no—
224#13063290—21no—
225#13063290C2312yes—
226D4×Dic43—21no—
227D4×Dic43—21no—
228D4×Dic43C2312yes—
229D4×Dic43C2312yes—
230#13063287—21no—
231#13063287C2312yes—
232C4×C22⋊D43—21no—
233C4×C22⋊D43—21no—
234C4×C22⋊D43—21no—
235C4×C22⋊D43—21no—
236C4×C22⋊D43—22no—
237C4×C22⋊D43—22no—
238C4×C22⋊D43—22no—
239C4×C22⋊D43—22no—
240C4×C22⋊D43C2312yes—
241C4×C22⋊D43C2312yes—
242#13063284—22no—
243#13063284C2311yescharacteristic
244#13063284C2311yescharacteristic
245#13063284C2311yescharacteristic
246#13063283—21no—
247#13063283C2312yes—
248C2×Dic43⋊C4—22no—
249C2×Dic43⋊C4—22no—
250C4⋊C4×D43—21no—
251C4⋊C4×D43C2312yes—
252C2×C22⋊Dic43—22no—
253C2×(C2×D43)⋊C4—22no—
254C2×(C2×D43)⋊C4—22no—
255#13063259C2311yescharacteristic
256#13063259C2311yescharacteristic
257#13063258C2312yes—
258#13063258C2312yes—
259#13063257C2311yescharacteristic
260#13063257C2311yescharacteristic
261#13063256C2312yes—
262#13063256C2312yes—
263Dic43⋊C8C2312yes—
264Dic43⋊C8C2312yes—
265#13063250C2311yescharacteristic
266#13063250C2311yescharacteristic
267#13063250C2311yescharacteristic
268#13063250C2311yescharacteristic
269#13063249C2312yes—
270#13063249C2312yes—
271#13063248C2312yes—
272#13063248C2312yes—
273#13063247C2311yescharacteristic
274#13063247C2311yescharacteristic
275#13063247C2311yescharacteristic
276#13063247C2311yescharacteristic
277#13063246C2312yes—
278#13063246C2312yes—
279#13063245C2312yes—
280#13063245C2312yes—
281C22⋊(C43⋊C8)C2312yes—
282C22⋊(C43⋊C8)C2312yes—
283(C2×D43)⋊C8C2312yes—
284(C2×D43)⋊C8C2312yes—
285#13063235C2312yes—
286C8×Dic43C2312yes—
287C2×#41×C43—21no—
288C2×#41×C43—21no—
289C2×#41×C43—24no—
290C2×#41×C43—42no—
291C2×#41×C43C2312yes—
292C2×#41×C43C2312yes—
293C22×Q8×C43C2311yescharacteristic
294C22×D4×C43—21no—
295C22×D4×C43C2311yescharacteristic
296C23×C4×C43—21no—
297C23×C4×C43—21no—
298C23×C4×C43C2311yescharacteristic
299C2×M16×C43—42no—
300C2×M16×C43C2311yescharacteristic
301C2×M16×C43C2311yescharacteristic
302C2×M16×C43C2311yescharacteristic
303C2×M16×C43C2311yescharacteristic
304C22×C8×C43C2311yescharacteristic
305C22×C8×C43C2311yescharacteristic
306C2×C4⋊C4×C43—21no—
307C2×C4⋊C4×C43—21no—
308C2×C4⋊C4×C43—21no—
309C2×C4⋊C4×C43C2312yes—
310C2×C4⋊C4×C43C2312yes—
311C2×C4⋊C4×C43C2311yescharacteristic
312C2×C4⋊C4×C43C2311yescharacteristic
313#103×C43C2312yes—
314#103×C43C2312yes—
315#103×C43C2312yes—
316#103×C43C2312yes—
317#102×C43C2312yes—
318#102×C43C2312yes—
319#102×C43C2312yes—
320#102×C43C2312yes—
321C24×C43—21no—
322C24×C43C2×D411yescharacteristic
323C23×D43—22no—
324#41×C43—24no—
325#41×C43—24no—
326#41×C43—42no—
327#41×C43—42no—
328#41×C43—44no—
329#41×C43—44no—
330C2×Q8×C43—21no—
331C2×Q8×C43—22no—
332C2×Q8×C43—22no—
333C2×Q8×C43C2412yes—
334C2×D4×C43—21no—
335C2×D4×C43—22no—
336C2×D4×C43—22no—
337C2×D4×C43—22no—
338C2×D4×C43—44no—
339C2×D4×C43#4114yescomplemented
340C2×D4×C43C2412yes—
341C22×C4×C43—22no—
342C22×C4×C43—22no—
343C22×C4×C43—22no—
344C22×C4×C43—22no—
345C22×C4×C43—22no—
346C22×C4×C43—21no—
347C22×C4×C43—21no—
348C22×C4×C43—22no—
349C22×C4×C43—21no—
350C22×C4×C43—44no—
351C22×C4×C43—82no—
352C22×C4×C43C2×D411yescharacteristic
353C22×C4×C43C2×D411yescharacteristic
354C22×C4×C43C2×D411yescharacteristic
355C22×C4×C43C2411yescharacteristic
356C22×C4×C43C2411yescharacteristic
357C22×C4×C43C2411yescharacteristic
358C2×C22⋊D43—22no—
359C2×C22⋊D43—21no—
360C2×C22⋊D43—21no—
361C2×C22⋊D43—21no—
362C2×C22⋊D43—21no—
363C2×C22⋊D43—21no—
364C2×C22⋊D43—21no—
365C2×C22⋊D43—22no—
366C2×C22⋊D43—48no—
367C2×C22⋊D43C2×D412yes—
368C2×C22⋊D43C2×D412yes—
369C2×C22⋊D43C2×D412yes—
370C22×Dic43—22no—
371C22×Dic43—22no—
372C22×Dic43—22no—
373#10621900—24no—
374#10621900—42no—
375#10621900—44no—
376D4×D43—24no—
377D4×D43—42no—
378D4×D43—44no—
379#10621898—22no—
380#10621898—22no—
381#10621898—22no—
382#10621898—22no—
383#10621898—22no—
384#10621898—22no—
385#10621898—84no—
386C2×D172—22no—
387C2×D172C2×D411yescharacteristic
388C2×D172C2411yescharacteristic
389C2×D172C2411yescharacteristic
390C2×C4×D43—21no—
391C2×C4×D43—21no—
392C2×C4×D43—22no—
393C2×C4×D43—22no—
394C2×C4×D43C2412yes—
395C2×Dic86—22no—
396C2×Dic86C2×D411yescharacteristic
397C2×Dic86C2411yescharacteristic
398C2×Dic86C2411yescharacteristic
399M16×C43—41no—
400M16×C43—41no—
401M16×C43—41no—
402M16×C43—41no—
403C2×C8×C43—22no—
404C2×C8×C43—22no—
405C2×C8×C43C2411yescharacteristic
406C2×C8×C43C2411yescharacteristic
407C2×C8×C43C2411yescharacteristic
408C2×C8×C43C2411yescharacteristic
409C4⋊C4×C43—21no—
410C4⋊C4×C43—21no—
411C4⋊C4×C43—22no—
412C4⋊C4×C43—22no—
413C4⋊C4×C43C2412yes—
414C4⋊C4×C43C2412yes—
415C22⋊Dic43—22no—
416C22⋊Dic43—22no—
417C22⋊Dic43—21no—
418C22⋊Dic43—21no—
419C22⋊Dic43—21no—
420C22⋊Dic43—21no—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43C2×D412yes—
424C22⋊Dic43C2×D412yes—
425C22⋊Dic43C2×D412yes—
426#10621885—42no—
427#10621884—42no—
428#10621883—24no—
429#10621882—24no—
430(C2×D43)⋊C4—21no—
431(C2×D43)⋊C4—21no—
432(C2×D43)⋊C4—21no—
433(C2×D43)⋊C4—21no—
434(C2×D43)⋊C4—22no—
435(C2×D43)⋊C4—22no—
436(C2×D43)⋊C4—22no—
437(C2×D43)⋊C4—22no—
438(C2×D43)⋊C4—22no—
439(C2×D43)⋊C4—22no—
440(C2×D43)⋊C4—22no—
441(C2×D43)⋊C4—22no—
442(C2×D43)⋊C4C2×D412yes—
443(C2×D43)⋊C4C2×D412yes—
444C4⋊Dic43—22no—
445C4⋊Dic43—22no—
446C4⋊Dic43C2×D411yescharacteristic
447C4⋊Dic43C2×D411yescharacteristic
448C4⋊Dic43C2411yescharacteristic
449C4⋊Dic43C2411yescharacteristic
450C4⋊Dic43C2411yescharacteristic
451C4⋊Dic43C2411yescharacteristic
452Dic43⋊C4—21no—
453Dic43⋊C4—21no—
454Dic43⋊C4—21no—
455Dic43⋊C4—21no—
456Dic43⋊C4—22no—
457Dic43⋊C4—22no—
458Dic43⋊C4—22no—
459Dic43⋊C4—22no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—22no—
463Dic43⋊C4—22no—
464Dic43⋊C4C2×D412yes—
465Dic43⋊C4C2×D412yes—
466C4×Dic43—21no—
467C4×Dic43—21no—
468C4×Dic43—22no—
469C4×Dic43—22no—
470C4×Dic43C2412yes—
471#10621877—22no—
472#10621877—22no—
473C2×C43⋊C8C2412yes—
474C2×C43⋊C8C2412yes—
475Dic172—41no—
476D344—41no—
477#10621873—41no—
478#10621873—41no—
479#10621872—42no—
480C8×D43—42no—
481C23×C43—22no—
482C23×C43—22no—
483C23×C43—24no—
484C23×C43—41no—
485C23×C43—41no—
486C23×C43—81no—
487C23×C43—81no—
488C23×C43C22×D411yescharacteristic
489C23×C43C22×D411yescharacteristic
490C23×C43C22×D411yescharacteristic
491C22×D43—21no—
492C22×D43—21no—
493C22×D43—44no—
494C22×D43—82no—
495C22×D43—82no—
496C22×D43C22×D412yes—
497Q8×C43—22no—
498Q8×C43—22no—
499Q8×C43—42no—
500D4×C43—24no—
501D4×C43—22no—
502D4×C43—44no—
503D4×C43—44no—
504D4×C43C2×#4114yes—
505C2×C4×C43—22no—
506C2×C4×C43—22no—
507C2×C4×C43—22no—
508C2×C4×C43—21no—
509C2×C4×C43—21no—
510C2×C4×C43—21no—
511C2×C4×C43—21no—
512C2×C4×C43—22no—
513C2×C4×C43—22no—
514C2×C4×C43—22no—
515C2×C4×C43—44no—
516C2×C4×C43—44no—
517C2×C4×C43—44no—
518C2×C4×C43—42no—
519C2×C4×C43—81no—
520C2×C4×C43—82no—
521C2×C4×C43—81no—
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C22×D411yescharacteristic
525C2×C4×C43C2×#4112yes—
526C2×C4×C43H(5,𝔽2)12yes—
527C2×C4×C43C2511yescharacteristic
528C22⋊D43—24no—
529C22⋊D43—42no—
530C22⋊D43—42no—
531C22⋊D43—44no—
532C22⋊D43—44no—
533C22⋊D43—42no—
534C22⋊D43—42no—
535C22⋊D43—42no—
536C22⋊D43—42no—
537C22⋊D43—81no—
538C22⋊D43—81no—
539C2×Dic43—21no—
540C2×Dic43—21no—
541C2×Dic43—21no—
542C2×Dic43—21no—
543C2×Dic43—21no—
544C2×Dic43—21no—
545C2×Dic43—44no—
546C2×Dic43—82no—
547C2×Dic43—82no—
548C2×Dic43C22×D412yes—
549C2×Dic43C22×D412yes—
550C2×Dic43C22×D412yes—
551D172—22no—
552D172—21no—
553D172—21no—
554D172—21no—
555D172—21no—
556D172—82no—
557C4×D43—22no—
558C4×D43—22no—
559C4×D43—42no—
560C4×D43—42no—
561C4×D43—82no—
562C4×D43—82no—
563Dic86—22no—
564Dic86—21no—
565Dic86—21no—
566Dic86—21no—
567Dic86—21no—
568Dic86—82no—
569C8×C43—21no—
570C8×C43—21no—
571C8×C43—21no—
572C8×C43—21no—
573C43⋊C8—22no—
574C43⋊C8—22no—
575#61177—431nomaximal, Sylow
576C22×C43—21no—
577C22×C43—21no—
578C22×C43—21no—
579C22×C43—21no—
580C22×C43—21no—
581C22×C43—21no—
582C22×C43—24no—
583C22×C43—21no—
584C22×C43—21no—
585C22×C43—44no—
586C22×C43—42no—
587C22×C43—42no—
588C22×C43—84no—
589C22×C43#54612yes—
590C22×C43C23×D411yescharacteristic
591C2×D43—22no—
592C2×D43—22no—
593C2×D43—22no—
594C2×D43—41no—
595C2×D43—41no—
596C2×D43—41no—
597C2×D43—41no—
598C2×D43—41no—
599C2×D43—41no—
600C2×D43—164no—
601C4×C43—21no—
602C4×C43—21no—
603C4×C43—42no—
604C4×C43—42no—
605C4×C43—42no—
606C4×C43#54612yes—
607C4×C43C22×#4111yescharacteristic
608C4×C43C2×H(5,𝔽2)11yescharacteristic
609Dic43—22no—
610Dic43—22no—
611Dic43—22no—
612Dic43—41no—
613Dic43—41no—
614Dic43—41no—
615Dic43—41no—
616Dic43—41no—
617Dic43—41no—
618#3492—431no—
619#3485—431no—
620#3331—432no—
621#3330—432no—
622#3323—432no—
623#3322—432no—
624#3315—432no—
625#3314—432no—
626#3307—432no—
627#3306—432no—
628#3137—431no—
629#3097—431no—
630#3092—431no—
631#3081—431no—
632#3063—431no—
633#3054—431no—
634#3046—431no—
635#3012—431no—
636#3005—431no—
637#2946—431no—
638#2930—431no—
639#2897—431no—
640C2×#417D4311yescharacteristic, complemented
641C2×C43—22no—
642C2×C43—44no—
643C2×C43—41no—
644C2×C43—41no—
645C2×C43C2×#54611yescharacteristic
646C2×C43#358511yescharacteristic
647C2×C43#358611yescharacteristic
648D43—42no—
649D43—81no—
650D43—81no—
651C2×H(5,𝔽2)—431no—
652C22×#41C2×D4311yescharacteristic
653C2×#137—431no—
654C2×AGL(1,ℤ/8)—431no—
655C2×#135—431no—
656C2×#131—431no—
657C22×M16C2×D4311yescharacteristic, complemented
658#554—432no—
659#554—861no—
660#553—432no—
661#553—861no—
662#552—432no—
663#552—861no—
664#547—432no—
665#547—432no—
666#547—432no—
667#547—861no—
668#547—861no—
669#547—861no—
670#546—432no—
671#546—432no—
672#546—861no—
673#546—861no—
674#544—431no—
675#539—862no—
676#537—431no—
677#536—431no—
678#536—431no—
679#534—862no—
680#525—431no—
681#525—431no—
682#525—431no—
683#525—862no—
684C2×#123—862no—
685#520—431no—
686#520—431no—
687#518—431no—
688C22×C4⋊C4C2×D4311yescharacteristic, complemented
689#491—432no—
690#489—432no—
691#488—432no—
692#487—432no—
693#485—432no—
694#485—432no—
695#484—432no—
696#484—432no—
697#483—432no—
698#483—432no—
699#481—432no—
700#480—432no—
701#478—432no—
702#478—432no—
703#476—432no—
704#474—432no—
705#470—431no—
706#470—431no—
707#470—432no—
708#469—431no—
709#469—431no—
710#468—431no—
711#468—431no—
712#468—431no—
713#468—431no—
714#468—432no—
715#467—432no—
716#465—432no—
717#464—432no—
718#463—432no—
719#462—432no—
720#461—432no—
721#452—432no—
722#452—432no—
723#452—432no—
724#450—432no—
725#449—432no—
726#449—432no—
727#449—432no—
728#447—432no—
729#442—432no—
730#440—432no—
731C4×SD16—432no—
732C4×D8—432no—
733#436—432no—
734#436—432no—
735#435—432no—
736#435—432no—
737#428—431no—
738#428—431no—
739#427—431no—
740#424—431no—
741#419—431no—
742#418—431no—
743#418—432no—
744#417—431no—
745#417—431no—
746#417—432no—
747#417C2×D4312yescomplemented
748#417C2×D4312yescomplemented
749#417C2×D4312yescomplemented
750#417C2×D4312yescomplemented
751#416—431no—
752#416—431no—
753#416—432no—
754C2×#103C2×D4311yescharacteristic, complemented
755C2×#103C2×D4311yescharacteristic, complemented
756C2×#102—432no—
757C2×#102C2×D4311yescharacteristic
758C2×#102C2×D4311yescharacteristic
759#408—431no—
760#407—431no—
761#405—431no—
762C43#6117711yescharacteristic, complemented, Sylow
763H(5,𝔽2)—864no—
764H(5,𝔽2)—1722no—
765C2×#41—21no—
766C2×#41—21no—
767C2×#41—24no—
768C2×#41—42no—
769C2×#41—431no—
770C2×#41—432no—
771C2×#41—431no—
772C2×#41—431no—
773C2×#41—862no—
774C2×#41—861no—
775C2×#41C22×D4312yes—
776C2×#41C22×D4312yes—
777C22×Q8C22×D4311yescharacteristic
778C22×D4—21no—
779C22×D4—432no—
780C22×D4—861no—
781C22×D4—862no—
782C22×D4C22×D4311yescharacteristic
783C23×C4—21no—
784C23×C4—21no—
785C23×C4C22×D4311yescharacteristic
786#137—1722no—
787AGL(1,ℤ/8)—864no—
788#135—1722no—
789C2×Q16—432no—
790C2×Q16—431no—
791C2×SD16—432no—
792C2×SD16—432no—
793C2×SD16—431no—
794C2×SD16—431no—
795C2×D8—432no—
796C2×D8—431no—
797#131—1722no—
798C2×M16—42no—
799C2×M16—431no—
800C2×M16—431no—
801C2×M16—432no—
802C2×M16C22×D4311yescharacteristic
803C2×M16C22×D4311yescharacteristic
804C2×M16C22×D4311yescharacteristic
805C2×M16C22×D4311yescharacteristic
806C22×C8—432no—
807C22×C8C22×D4311yescharacteristic
808C22×C8C22×D4311yescharacteristic
809C4⋊Q8—432no—
810C4⋊Q8—432no—
811C4⋊Q8—861no—
812C4⋊Q8—861no—
813#126—862no—
814#126—862no—
815#125—432no—
816#125—862no—
817#125—862no—
818#125—861no—
819#124—432no—
820#124—861no—
821#123—432no—
822#123—862no—
823#123—862no—
824#123—862no—
825#123—862no—
826#123—862no—
827#123—862no—
828#123—862no—
829#123—862no—
830#123—862no—
831#123—862no—
832#123—862no—
833#123—862no—
834#123—861no—
835#123—861no—
836C22⋊Q8—431no—
837C22⋊Q8—431no—
838C22⋊Q8—432no—
839C22⋊Q8—432no—
840C22⋊Q8—431no—
841C22⋊Q8—431no—
842C22⋊Q8—431no—
843C22⋊Q8—431no—
844C22⋊Q8—432no—
845C22⋊Q8—862no—
846C22⋊Q8—862no—
847C22⋊Q8—862no—
848C22⋊Q8—862no—
849C22⋊Q8—861no—
850C22⋊Q8—861no—
851C22⋊Q8—861no—
852#121—431no—
853#121—431no—
854#121—431no—
855#121—431no—
856#121—431no—
857#121—431no—
858#121—432no—
859#121—862no—
860#121—862no—
861#121—861no—
862#121—862no—
863#121—862no—
864#121—862no—
865#121—862no—
866#120—432no—
867#120—862no—
868#120—862no—
869#120—861no—
870#120—861no—
871C4×Q8—432no—
872C4×Q8—861no—
873C4×D4—432no—
874C4×D4—432no—
875C4×D4—432no—
876C4×D4—432no—
877C4×D4—432no—
878C4×D4—862no—
879C4×D4—862no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4—862no—
884C4×D4—862no—
885C4×D4—861no—
886C4×D4—861no—
887C4×D4—861no—
888C4×D4—861no—
889#117—431no—
890#117—431no—
891#117—431no—
892#117—432no—
893#117—862no—
894#117—861no—
895C2×C4⋊C4—21no—
896C2×C4⋊C4—21no—
897C2×C4⋊C4—21no—
898C2×C4⋊C4—432no—
899C2×C4⋊C4—861no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—862no—
902C2×C4⋊C4C22×D4311yescharacteristic
903C2×C4⋊C4C22×D4311yescharacteristic
904C2×C4⋊C4C22×D4312yes—
905C2×C4⋊C4C22×D4312yes—
906C2×C22⋊C4—862no—
907C2×C22⋊C4—862no—
908C2×C22⋊C4—862no—
909#107—431no—
910#107—431no—
911#107—432no—
912#107—432no—
913#106—431no—
914#106—431no—
915#106—432no—
916#106—432no—
917C4⋊C8—432no—
918C4⋊C8—432no—
919#103—432no—
920#103—432no—
921#103—431no—
922#103—431no—
923#103—431no—
924#103—431no—
925#103—432no—
926#103—432no—
927#103C22×D4312yes—
928#103C22×D4312yes—
929#103C22×D4312yes—
930#103C22×D4312yes—
931#102—432no—
932#102—432no—
933#102—431no—
934#102—431no—
935#102—431no—
936#102—431no—
937#102—432no—
938#102—432no—
939#102C22×D4312yes—
940#102C22×D4312yes—
941#102C22×D4312yes—
942#102C22×D4312yes—
943C22⋊C8—432no—
944C22⋊C8—432no—
945C22⋊C8—432no—
946C22⋊C8—432no—
947#97—432no—
948C4×C8—432no—
949C24—21no—
950C24—862no—
951C24D4×D4311yescharacteristic
952#41—24no—
953#41—24no—
954#41—42no—
955#41—42no—
956#41—44no—
957#41—44no—
958#41—862no—
959#41—862no—
960#41—864no—
961#41—862no—
962#41—862no—
963#41—862no—
964#41—862no—
965#41—3444no—
966#41—1722no—
967#41—1724no—
968C2×Q8—21no—
969C2×Q8—22no—
970C2×Q8—22no—
971C2×Q8—431no—
972C2×Q8—431no—
973C2×Q8—431no—
974C2×Q8—862no—
975C2×Q8C23×D4312yes—
976C2×D4—22no—
977C2×D4—22no—
978C2×D4—21no—
979C2×D4—22no—
980C2×D4—44no—
981C2×D4—432no—
982C2×D4—432no—
983C2×D4—432no—
984C2×D4—431no—
985C2×D4—431no—
986C2×D4—431no—
987C2×D4—862no—
988C2×D4—862no—
989C2×D4—864no—
990C2×D4—861no—
991C2×D4—861no—
992C2×D4—862no—
993C2×D4—861no—
994C2×D4—861no—
995C2×D4—861no—
996C2×D4—861no—
997C2×D4—1722no—
998C2×D4—1724no—
999C2×D4—1728no—
1000C2×D4#1062189814yescomplemented
1001C2×D4C23×D4312yes—
1002C22×C4—22no—
1003C22×C4—22no—
1004C22×C4—22no—
1005C22×C4—21no—
1006C22×C4—21no—
1007C22×C4—22no—
1008C22×C4—21no—
1009C22×C4—22no—
1010C22×C4—22no—
1011C22×C4—44no—
1012C22×C4—82no—
1013C22×C4—432no—
1014C22×C4—862no—
1015C22×C4—862no—
1016C22×C4—862no—
1017C22×C4—862no—
1018C22×C4—862no—
1019C22×C4—861no—
1020C22×C4—861no—
1021C22×C4D4×D4311yescharacteristic
1022C22×C4D4×D4311yescharacteristic
1023C22×C4D4×D4311yescharacteristic
1024C22×C4C23×D4311yescharacteristic
1025C22×C4C23×D4311yescharacteristic
1026C22×C4C23×D4311yescharacteristic
1027Q16—1721no—
1028Q16—1722no—
1029SD16—864no—
1030SD16—1721no—
1031SD16—1721no—
1032SD16—1722no—
1033D8—864no—
1034D8—1721no—
1035M16—41no—
1036M16—41no—
1037M16—41no—
1038M16—41no—
1039M16—862no—
1040M16—862no—
1041M16—1722no—
1042C2×C8—22no—
1043C2×C8—22no—
1044C2×C8—432no—
1045C2×C8—432no—
1046C2×C8—1722no—
1047C2×C8C23×D4311yescharacteristic
1048C2×C8C23×D4311yescharacteristic
1049C2×C8C23×D4311yescharacteristic
1050C2×C8C23×D4311yescharacteristic
1051C4⋊C4—21no—
1052C4⋊C4—21no—
1053C4⋊C4—22no—
1054C4⋊C4—22no—
1055C4⋊C4—431no—
1056C4⋊C4—432no—
1057C4⋊C4—432no—
1058C4⋊C4—431no—
1059C4⋊C4—431no—
1060C4⋊C4—431no—
1061C4⋊C4—431no—
1062C4⋊C4—431no—
1063C4⋊C4—862no—
1064C4⋊C4—862no—
1065C4⋊C4—862no—
1066C4⋊C4—862no—
1067C4⋊C4—862no—
1068C4⋊C4—862no—
1069C4⋊C4—862no—
1070C4⋊C4—862no—
1071C4⋊C4—862no—
1072C4⋊C4—862no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4C23×D4312yes—
1078C4⋊C4C23×D4312yes—
1079C22⋊C4—432no—
1080C22⋊C4—432no—
1081C22⋊C4—432no—
1082C22⋊C4—432no—
1083C22⋊C4—432no—
1084C22⋊C4—862no—
1085C22⋊C4—862no—
1086C22⋊C4—862no—
1087C22⋊C4—862no—
1088C22⋊C4—862no—
1089C22⋊C4—862no—
1090C22⋊C4—862no—
1091C22⋊C4—862no—
1092C22⋊C4—862no—
1093C22⋊C4—862no—
1094C22⋊C4—861no—
1095C22⋊C4—861no—
1096C22⋊C4—861no—
1097C22⋊C4—861no—
1098C22⋊C4—861no—
1099C22⋊C4—861no—
1100C22⋊C4—861no—
1101C22⋊C4—861no—
1102C22⋊C4—861no—
1103C22⋊C4—861no—
1104C42—432no—
1105C42—862no—
1106C42—862no—
1107C42—861no—
1108C42—861no—
1109C23—22no—
1110C23—22no—
1111C23—24no—
1112C23—41no—
1113C23—41no—
1114C23—81no—
1115C23—81no—
1116C23—432no—
1117C23—861no—
1118C23—861no—
1119C23—3442no—
1120C23—3442no—
1121C23—1724no—
1122C23C2×D4×D4311yescharacteristic
1123C23C2×D4×D4311yescharacteristic
1124C23C2×D4×D4311yescharacteristic
1125Q8—22no—
1126Q8—22no—
1127Q8—42no—
1128Q8—862no—
1129Q8—861no—
1130Q8—861no—
1131Q8—861no—
1132Q8—861no—
1133Q8—3442no—
1134D4—22no—
1135D4—24no—
1136D4—44no—
1137D4—44no—
1138D4—864no—
1139D4—861no—
1140D4—861no—
1141D4—861no—
1142D4—861no—
1143D4—862no—
1144D4—3442no—
1145D4—3441no—
1146D4—3441no—
1147D4—1722no—
1148D4—1722no—
1149D4—1724no—
1150D4—1724no—
1151D4—1722no—
1152D4—1722no—
1153D4—1722no—
1154D4—1722no—
1155D4C2×#1062189814yes—
1156C2×C4—22no—
1157C2×C4—21no—
1158C2×C4—21no—
1159C2×C4—21no—
1160C2×C4—21no—
1161C2×C4—22no—
1162C2×C4—22no—
1163C2×C4—22no—
1164C2×C4—22no—
1165C2×C4—22no—
1166C2×C4—44no—
1167C2×C4—44no—
1168C2×C4—44no—
1169C2×C4—42no—
1170C2×C4—81no—
1171C2×C4—82no—
1172C2×C4—81no—
1173C2×C4—432no—
1174C2×C4—432no—
1175C2×C4—432no—
1176C2×C4—862no—
1177C2×C4—862no—
1178C2×C4—861no—
1179C2×C4—861no—
1180C2×C4—861no—
1181C2×C4—861no—
1182C2×C4—861no—
1183C2×C4—861no—
1184C2×C4—3442no—
1185C2×C4—3442no—
1186C2×C4—3442no—
1187C2×C4—3442no—
1188C2×C4—1724no—
1189C2×C4—1722no—
1190C2×C4—1722no—
1191C2×C4C2×D4×D4311yescharacteristic
1192C2×C4C2×D4×D4311yescharacteristic
1193C2×C4C2×D4×D4311yescharacteristic
1194C2×C4C2×#1062189812yes—
1195C2×C4#1306337012yes—
1196C2×C4C24×D4311yescharacteristic
1197C8—21no—
1198C8—21no—
1199C8—21no—
1200C8—21no—
1201C8—862no—
1202C8—862no—
1203C22—21no—
1204C22—21no—
1205C22—21no—
1206C22—21no—
1207C22—24no—
1208C22—21no—
1209C22—21no—
1210C22—21no—
1211C22—21no—
1212C22—44no—
1213C22—42no—
1214C22—42no—
1215C22—84no—
1216C22—862no—
1217C22—862no—
1218C22—862no—
1219C22—1721no—
1220C22—1721no—
1221C22—1721no—
1222C22—1721no—
1223C22—1721no—
1224C22—1721no—
1225C22—6884no—
1226C22#1458353912yes—
1227C22C22×D4×D4311yescharacteristic
1228C4—21no—
1229C4—21no—
1230C4—42no—
1231C4—42no—
1232C4—42no—
1233C4—862no—
1234C4—862no—
1235C4—862no—
1236C4—1721no—
1237C4—1721no—
1238C4—1721no—
1239C4—1721no—
1240C4—1721no—
1241C4—1721no—
1242C4#1458353912yes—
1243C4C22×#1062189811yescharacteristic
1244C4C2×#1306337011yescharacteristic
1245C2—22no—
1246C2—41no—
1247C2—41no—
1248C2—44no—
1249C2—3441no—
1250C2—3441no—
1251C2—1722no—
1252C2C2×#1458353911yescharacteristic
1253C2#1914937111yescharacteristic
1254C2#1914937811yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#417C2
socleC22×C43C23×D4
hypercenterC2×#417D43
hypocenterC43#61177
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#417

Complements

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

NH ≅ G/Ntype
1. #19148304C2semidirect
2. #19148239C2semidirect
3. #19146907C2semidirect
4. #19146896C2semidirect
5. #19146812C2semidirect
6. #19146797C2semidirect
7. #19146692C2semidirect
8. #19146677C2semidirect
9. #19146572C2semidirect
10. #19146557C2semidirect
11. #19144958C2semidirect
12. #19144560C2semidirect
13. #19144518C2semidirect
14. #19144422C2semidirect
15. #19144284C2semidirect
16. #19144204C2semidirect
17. #19144150C2semidirect
18. #19143904C2semidirect
19. #19143837C2semidirect
20. #19143421C2semidirect
21. #19143298C2semidirect
22. #19143116C2semidirect
23. C2×C43×#417C2semidirect
25. C2×#13063356C22semidirect
30. #14583604C22semidirect
32. #14583597C22semidirect
34. #14583584C22semidirect
36. #14583550C22semidirect
45. #14583530C22semidirect
54. #14583410C22semidirect
57. #14583380C22semidirect
59. #14583266C22semidirect
60. #14583260C22semidirect
61. #14583255C22semidirect
62. #14583248C22semidirect
63. #14583239C22semidirect
64. #14583238C22semidirect
65. #14583234C22semidirect
66. #14583233C22semidirect
67. #14583229C22semidirect
68. #14583228C22semidirect
69. #14583217C22semidirect
70. #14583212C22semidirect
71. #14583201C22semidirect
72. #14583197C22semidirect
73. #14583187C22semidirect
74. #14583177C22semidirect
75. #14583157C22semidirect
76. #14583157C22semidirect
77. #14583156C22semidirect
78. #14583152C22semidirect
79. #14583152C22semidirect
80. #14583148C22semidirect
81. #14583145C22semidirect
82. #14583145C22semidirect
83. #14583145C22semidirect
84. #14583145C22semidirect
85. #14583139C22semidirect
86. #14583131C22semidirect
87. #14583124C22semidirect
88. #14583117C22semidirect
89. #14583108C22semidirect
90. #14583103C22semidirect
91. #14583062C22semidirect
92. #14583061C22semidirect
93. #14583061C22semidirect
94. #14583051C22semidirect
95. #14583045C22semidirect
96. #14583044C22semidirect
97. #14583044C22semidirect
98. #14583034C22semidirect
99. #14583008C22semidirect
100. #14582996C22semidirect
101. #14582990C22semidirect
102. #14582979C22semidirect
103. #14582975C22semidirect
104. #14582975C22semidirect
105. #14582968C22semidirect
106. #14582968C22semidirect
107. #14582939C22semidirect
108. #14582939C22semidirect
109. #14582937C22semidirect
110. #14582925C22semidirect
111. #14582908C22semidirect
113. #14582902C22semidirect
116. #14582897C22semidirect
118. #14582896C22semidirect
119. #14582892C22semidirect
120. #102×D43C22semidirect
122. #14582863C22semidirect
123. #14582854C22semidirect
125. C22×M16×C43C22semidirect
126. C22×C4⋊C4×C43C22semidirect
127. C43×#417C22semidirect
128. C43×#417C22semidirect
129. C43×#417C22semidirect
130. C43×#417C22semidirect
131. C2×#103×C43C22semidirect
132. C2×#103×C43C22semidirect
339. C2×D4×C43#41semidirect
640. C2×#417D43semidirect
657. C22×M16C2×D43semidirect
688. C22×C4⋊C4C2×D43semidirect
747. #417C2×D43semidirect
748. #417C2×D43semidirect
749. #417C2×D43semidirect
750. #417C2×D43semidirect
754. C2×#103C2×D43semidirect
755. C2×#103C2×D43semidirect
762. C43#61177semidirect
1000. C2×D4#10621898semidirect

Maximal subgroups

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

subgroupindex
#191483042
#191482392
#191469072
#191468962
#191468122
#191467972
#191466922
#191466772
#191465722
#191465572
#191449582
#191445602
#191445182
#191444222
#191442842
#191442042
#191441502
#191439042
#191438372
#191434212
#191432982
#191431162
C2×C43×#4172
#6117743