Finite Group Databasebeta

← #25968247

Subgroups — #25968247

Order 11008.

2108 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#19148330C211yesmaximal, characteristic, complemented
2#19145704C212yesmaximal, complemented
3#19145689C212yesmaximal, complemented
4#19145656C212yesmaximal, complemented
5#19145645C212yesmaximal, complemented
6#19145632C212yesmaximal, complemented
7#19145590C212yesmaximal, complemented
8#19145571C212yesmaximal, complemented
9#19145528C212yesmaximal, complemented
10#19145078C211yesmaximal, characteristic, complemented
11#19145073C211yesmaximal, characteristic, complemented
12#19144960C211yesmaximal, characteristic, complemented
13#19144949C211yesmaximal, characteristic, complemented
14#19144141C211yesmaximal, characteristic, complemented
15#19144130C211yesmaximal, characteristic, complemented
16#19144103C211yesmaximal, characteristic, complemented
17#19144094C211yesmaximal, characteristic, complemented
18#19143847C211yesmaximal, characteristic, complemented
19#19143837C211yesmaximal, characteristic, complemented
20#19143813C211yesmaximal, characteristic, complemented
21C2×#14583044C211yesmaximal, characteristic, complemented
22#19143253C211yesmaximal, characteristic, complemented
23C43×#3449C211yesmaximal, characteristic, complemented
24C2×#13063356C2211yescharacteristic, complemented
25C2×#13063351C2211yescharacteristic, complemented
26C2×#13063350C2211yescharacteristic
27C2×#13063350C2211yescharacteristic
28C2×#13063345C2211yescharacteristic
29C2×#13063345C2211yescharacteristic
30C22×#10621884C2211yescharacteristic, complemented
31C22×#10621882C2211yescharacteristic, complemented
32#14583612—21no—
33#14583597—21no—
34#14583593—21no—
35#14583573—22no—
36#14583550—21no—
37#14583539—22no—
38#14583527C2211yescharacteristic, complemented
39#14583520C2212yescomplemented
40#14583504C2212yescomplemented
41#14583468C2211yescharacteristic, complemented
42#14583449C2212yescomplemented
43#14583433C2212yescomplemented
44#14583410C2211yescharacteristic
45C2×#13063299C2211yescharacteristic
46#14583379C2211yescharacteristic, complemented
47#14583373C2211yescharacteristic, complemented
48#14583291C2212yescomplemented
49#14583289C2212yescomplemented
50#14583289C2212yescomplemented
51#14583286C2212yescomplemented
52#14583281C2212yescomplemented
53#14583281C2212yescomplemented
54#14583275C2212yescomplemented
55#14583273C2212yescomplemented
56#14583267C2212yescomplemented
57#14583263C2212yescomplemented
58#14583258C2212yescomplemented
59#14583258C2212yescomplemented
60#14583253C2212yescomplemented
61#14583253C2212yescomplemented
62#14583249C2212yescomplemented
63#14583245C2212yescomplemented
64#14583118C2212yescomplemented
65#14583118C2212yescomplemented
66#14583111C2212yescomplemented
67#14583111C2212yescomplemented
68#14583111C2212yescomplemented
69#14583111C2212yescomplemented
70#14583111C2212yescomplemented
71#14583111C2212yescomplemented
72#14583106C2212yescomplemented
73#14583101C2212yescomplemented
74#14583101C2212yescomplemented
75#14583101C2212yescomplemented
76#14583096C2212yescomplemented
77#14583091C2212yescomplemented
78#14583091C2212yescomplemented
79#14583091C2212yescomplemented
80#14583061C2211yescharacteristic, complemented
81#14583061C2212yescomplemented
82#14583061C2211yescharacteristic, complemented
83#14583061C2212yescomplemented
84#14583055C2211yescharacteristic, complemented
85#14583050C2211yescharacteristic, complemented
86#14583044C2212yes—
87#14583044C2212yes—
88#14583044C2211yescharacteristic, complemented
89#14583044C2212yescomplemented
90#14583044C2212yescomplemented
91#14583044C2212yescomplemented
92#14583044C2212yescomplemented
93#14583044C2212yescomplemented
94#14583044C2211yescharacteristic, complemented
95#14583044C2212yescomplemented
96#14583038C2211yescharacteristic, complemented
97#14583038C2212yescomplemented
98#14583033C2211yescharacteristic, complemented
99#14583033C2212yescomplemented
100#14582960C2212yescomplemented
101#14582960C2212yescomplemented
102#14582956C2212yescomplemented
103#14582952C2212yescomplemented
104#14582926C2211yescharacteristic, complemented
105#14582926C2211yescharacteristic, complemented
106#14582908C2211yescharacteristic, complemented
107#14582904C2211yescharacteristic, complemented
108#14582900C2211yescharacteristic
109#14582900C2211yescharacteristic
110#14582895C2211yescharacteristic
111#14582895C2211yescharacteristic
112C2×#13063249C2211yescharacteristic, complemented
113C2×#13063246C2211yescharacteristic, complemented
114#14582863C2211yescharacteristic
115C2×C22⋊(C43⋊C8)C2211yescharacteristic
116#14582855C2211yescharacteristic, complemented
117#14582855C2211yescharacteristic, complemented
118C22×#41×C43C2211yescharacteristic
119C22×#41×C43C2211yescharacteristic
120C43×#537—21no—
121C43×#537—21no—
122C43×#536C2211yescharacteristic
123C43×#536C2211yescharacteristic
124C43×#536C2212yescomplemented
125C43×#535C2211yescharacteristic
126C43×#535C2211yescharacteristic
127C43×#535C2212yescomplemented
128C43×#534—22no—
129C43×#532C2212yescomplemented
130C43×#532C2212yescomplemented
131C43×#525—22no—
132C43×#525—21no—
133C43×#525—21no—
134C2×#117×C43C2211yescharacteristic
135C2×#10621898—22no—
136C2×#10621898C2311yescharacteristic
137C22×D172C2311yescharacteristic
138C22×C22⋊D43—21no—
139#13063356—42no—
140#13063351—42no—
141#13063350—42no—
142#13063350—42no—
143#13063345—42no—
144#13063345—42no—
145C2×#10621885C2311yescharacteristic
146C2×#10621885C2311yescharacteristic
147C2×#10621885C2312yes—
148C2×#10621883C2311yescharacteristic
149C2×#10621883C2311yescharacteristic
150C2×#10621883C2312yes—
151C2×#10621884—42no—
152C2×#10621884C2312yes—
153C2×#10621884C2312yes—
154C2×#10621884C2312yes—
155C2×#10621884C2311yescharacteristic
156C2×#10621884C2312yes—
157C2×#10621884C2311yescharacteristic
158C2×#10621884C2312yes—
159C2×#10621882—42no—
160C2×#10621882C2312yes—
161C2×#10621882C2312yes—
162C2×#10621882C2312yes—
163C2×#10621882C2311yescharacteristic
164C2×#10621882C2312yes—
165C2×#10621882C2311yescharacteristic
166C2×#10621882C2312yes—
167C2×#10621877C2311yescharacteristic
168C2×#10621877C2311yescharacteristic
169C22×C43⋊C8C2311yescharacteristic
170C22×C43⋊C8C2311yescharacteristic
171#13063325C2312yes—
172#13063324—21no—
173#13063322C2312yes—
174#13063320—22no—
175#13063319—22no—
176#13063317C2312yes—
177#13063316—21no—
178#13063313—22no—
179#13063313C2312yes—
180#13063311—22no—
181#13063310—22no—
182#13063310—22no—
183#13063308—21no—
184#13063308—22no—
185#13063307—22no—
186#13063304C2311yescharacteristic
187#13063304C2311yescharacteristic
188#13063303—22no—
189#13063302—22no—
190#13063300—21no—
191#13063300—21no—
192#13063299—21no—
193#13063299—21no—
194#13063299—22no—
195#13063299C2312yes—
196#13063299C2312yes—
197#13063299C2311yescharacteristic
198#13063299C2311yescharacteristic
199#13063298—22no—
200#13063298—22no—
201#13063295—22no—
202#13063294—21no—
203C4×Dic86C2312yes—
204C4×D172—22no—
205C4×D172C2312yes—
206C4×D172C2312yes—
207C4×D172C2312yes—
208#13063287—21no—
209#13063287—21no—
210C4×C22⋊D43—21no—
211C4×C22⋊D43—21no—
212C4×C22⋊D43—22no—
213(C22⋊D43)⋊C4—22no—
214#13063284C2311yescharacteristic
215#13063283—21no—
216#13063282—22no—
217C2×C4⋊Dic43C2311yescharacteristic
218C4⋊C4×D43—21no—
219C2×(C2×D43)⋊C4—21no—
220C22⋊C4×D43—22no—
221C4⋊(C43⋊C8)C2312yes—
222C4⋊(C43⋊C8)C2312yes—
223C4⋊(C43⋊C8)C2312yes—
224C4⋊(C43⋊C8)C2312yes—
225#13063249C2312yes—
226#13063249C2312yes—
227#13063249C2311yescharacteristic
228#13063249C2311yescharacteristic
229#13063249C2312yes—
230#13063249C2312yes—
231#13063249C2312yes—
232#13063249C2312yes—
233#13063249C2311yescharacteristic
234#13063249C2311yescharacteristic
235#13063246C2312yes—
236#13063246C2312yes—
237#13063246C2311yescharacteristic
238#13063246C2311yescharacteristic
239#13063246C2312yes—
240#13063246C2312yes—
241#13063246C2312yes—
242#13063246C2312yes—
243#13063246C2311yescharacteristic
244#13063246C2311yescharacteristic
245C22⋊(C43⋊C8)C2311yescharacteristic
246C22⋊(C43⋊C8)C2311yescharacteristic
247C22⋊(C43⋊C8)C2311yescharacteristic
248C22⋊(C43⋊C8)C2311yescharacteristic
249C22⋊(C43⋊C8)C2312yes—
250C22⋊(C43⋊C8)C2312yes—
251#13063236C2312yes—
252#13063236C2312yes—
253C4×C43⋊C8C2312yes—
254C4×C43⋊C8C2312yes—
255C2×#41×C43—21no—
256C2×#41×C43—21no—
257C2×#41×C43—21no—
258C2×#41×C43—21no—
259C2×#41×C43—42no—
260C2×#41×C43—42no—
261C2×#41×C43—42no—
262C2×#41×C43—42no—
263C2×#41×C43C2311yescharacteristic
264C2×#41×C43C2311yescharacteristic
265C2×#41×C43C2312yes—
266C2×#41×C43C2311yescharacteristic
267C2×#41×C43C2312yes—
268C2×#41×C43C2311yescharacteristic
269C22×Q8×C43C2311yescharacteristic
270C22×Q8×C43C2311yescharacteristic
271C22×D4×C43—21no—
272C22×D4×C43—21no—
273C22×D4×C43C2311yescharacteristic
274C22×D4×C43C2311yescharacteristic
275C23×C4×C43—21no—
276C23×C4×C43—21no—
277C23×C4×C43C2311yescharacteristic
278C4⋊Q8×C43C2312yes—
279C4⋊Q8×C43C2312yes—
280#127×C43C2312yes—
281#127×C43C2312yes—
282#124×C43C2312yes—
283#124×C43C2312yes—
284#124×C43C2312yes—
285#124×C43C2312yes—
286#123×C43—22no—
287#123×C43—22no—
288#123×C43—22no—
289#123×C43—22no—
290C22⋊Q8×C43—21no—
291C22⋊Q8×C43—21no—
292C22⋊Q8×C43—21no—
293C22⋊Q8×C43—21no—
294C22⋊Q8×C43—22no—
295C22⋊Q8×C43—22no—
296#121×C43—22no—
297#121×C43—22no—
298#121×C43—22no—
299#121×C43—22no—
300#121×C43—21no—
301#121×C43—21no—
302#121×C43—21no—
303#121×C43—21no—
304#121×C43—22no—
305#121×C43—22no—
306#120×C43—22no—
307#120×C43—22no—
308#120×C43—22no—
309#120×C43—22no—
310C4×D4×C43—22no—
311C4×D4×C43—22no—
312C4×D4×C43—22no—
313C4×D4×C43—22no—
314#117×C43D412yes—
315#117×C43D411yescharacteristic
316#117×C43D411yescharacteristic
317#117×C43C2311yescharacteristic
318#117×C43C2311yescharacteristic
319#117×C43C2312yes—
320C2×C4⋊C4×C43D411yescharacteristic
321C2×C4⋊C4×C43D411yescharacteristic
322C2×C22⋊C4×C43D412yes—
323C2×C42×C43C2312yes—
324C24×C43—21no—
325C24×C43—21no—
326C24×C43C2×D411yescharacteristic
327C23×D43—21no—
328#41×C43—22no—
329#41×C43—22no—
330#41×C43—22no—
331#41×C43—22no—
332#41×C43—42no—
333#41×C43—42no—
334#41×C43—42no—
335#41×C43—41no—
336#41×C43—41no—
337#41×C43—42no—
338#41×C43—41no—
339#41×C43—41no—
340#41×C43—44no—
341#41×C43—44no—
342#41×C43—44no—
343#41×C43—44no—
344C2×Q8×C43—21no—
345C2×Q8×C43—21no—
346C2×Q8×C43—22no—
347C2×Q8×C43—22no—
348C2×Q8×C43—41no—
349C2×Q8×C43—41no—
350C2×Q8×C43C2412yes—
351C2×Q8×C43C2411yescharacteristic
352C2×Q8×C43C2411yescharacteristic
353C2×D4×C43—21no—
354C2×D4×C43—21no—
355C2×D4×C43—22no—
356C2×D4×C43—22no—
357C2×D4×C43—22no—
358C2×D4×C43—22no—
359C2×D4×C43—22no—
360C2×D4×C43—21no—
361C2×D4×C43—21no—
362C2×D4×C43—21no—
363C2×D4×C43—22no—
364C2×D4×C43—21no—
365C2×D4×C43—22no—
366C2×D4×C43—22no—
367C2×D4×C43—44no—
368C2×D4×C43—44no—
369C2×D4×C43—41no—
370C2×D4×C43—41no—
371C2×D4×C43C2412yes—
372C2×D4×C43C2411yescharacteristic
373C2×D4×C43C2411yescharacteristic
374C22×C4×C43—22no—
375C22×C4×C43—22no—
376C22×C4×C43—21no—
377C22×C4×C43—22no—
378C22×C4×C43—21no—
379C22×C4×C43—22no—
380C22×C4×C43—21no—
381C22×C4×C43—21no—
382C22×C4×C43—21no—
383C22×C4×C43—21no—
384C22×C4×C43—44no—
385C22×C4×C43—44no—
386C22×C4×C43C2×D411yescharacteristic
387C22×C4×C43C2×D411yescharacteristic
388C22×C4×C43C2×D411yescharacteristic
389C22×C4×C43C2×D412yes—
390C22×C4×C43C2×D412yes—
391C22×C4×C43C2411yescharacteristic
392C22×C4×C43C2411yescharacteristic
393C22×C4×C43C2411yescharacteristic
394C2×C22⋊D43—21no—
395C2×C22⋊D43—21no—
396C2×C22⋊D43—22no—
397C2×C22⋊D43—21no—
398C2×C22⋊D43—22no—
399C2×C22⋊D43—82no—
400C22×Dic43—21no—
401#10621898—22no—
402#10621898—22no—
403#10621898—84no—
404C2×D172—21no—
405C2×D172—22no—
406C2×D172—22no—
407C2×D172—22no—
408C2×D172—22no—
409C2×D172C2412yes—
410C2×D172C2411yescharacteristic
411C2×C4×D43—21no—
412C2×C4×D43—22no—
413C2×C4×D43—22no—
414C2×C4×D43—22no—
415C2×Dic86—22no—
416C2×Dic86C2411yescharacteristic
417C4⋊C4×C43—22no—
418C4⋊C4×C43—22no—
419C4⋊C4×C43—22no—
420C4⋊C4×C43—22no—
421C4⋊C4×C43C2×D411yescharacteristic
422C4⋊C4×C43C2×D411yescharacteristic
423C4⋊C4×C43C2×D411yescharacteristic
424C4⋊C4×C43C2×D411yescharacteristic
425C4⋊C4×C43C2×D412yes—
426C4⋊C4×C43C2×D412yes—
427C22⋊C4×C43—22no—
428C22⋊C4×C43—22no—
429C22⋊C4×C43—22no—
430C22⋊C4×C43—22no—
431C22⋊C4×C43—22no—
432C22⋊C4×C43—22no—
433C22⋊C4×C43—22no—
434C22⋊C4×C43—22no—
435C22⋊C4×C43C2×D412yes—
436C22⋊C4×C43C2×D412yes—
437C22⋊C4×C43C2×D412yes—
438C22⋊C4×C43C2×D412yes—
439C42×C43C2×D412yes—
440C42×C43C2×D412yes—
441C42×C43C2412yes—
442C42×C43C2412yes—
443C22⋊Dic43—21no—
444C22⋊Dic43—21no—
445C22⋊Dic43—21no—
446#10621885—41no—
447#10621885—41no—
448#10621885—42no—
449#10621884—42no—
450#10621884—42no—
451#10621884—41no—
452#10621884—41no—
453#10621884—42no—
454#10621884—42no—
455#10621884—42no—
456#10621883—41no—
457#10621883—41no—
458#10621883—42no—
459#10621882—42no—
460#10621882—42no—
461#10621882—41no—
462#10621882—41no—
463#10621882—42no—
464#10621882—42no—
465#10621882—42no—
466(C2×D43)⋊C4—22no—
467(C2×D43)⋊C4—22no—
468(C2×D43)⋊C4—22no—
469(C2×D43)⋊C4—22no—
470(C2×D43)⋊C4—22no—
471(C2×D43)⋊C4—22no—
472(C2×D43)⋊C4—21no—
473(C2×D43)⋊C4—22no—
474(C2×D43)⋊C4—21no—
475C4⋊Dic43—21no—
476C4⋊Dic43—22no—
477C4⋊Dic43C2412yes—
478C4⋊Dic43C2411yescharacteristic
479C4⋊Dic43C2411yescharacteristic
480Dic43⋊C4—22no—
481Dic43⋊C4—21no—
482Dic43⋊C4—22no—
483Dic43⋊C4—22no—
484Dic43⋊C4—21no—
485C4×Dic43—22no—
486C4×Dic43—21no—
487#10621877—22no—
488#10621877—22no—
489C2×C43⋊C8—22no—
490C2×C43⋊C8—22no—
491C2×C43⋊C8C2411yescharacteristic
492C2×C43⋊C8C2411yescharacteristic
493C2×C43⋊C8C2412yes—
494C2×C43⋊C8C2412yes—
495C2×C43⋊C8C2411yescharacteristic
496C2×C43⋊C8C2411yescharacteristic
497C23×C43—22no—
498C23×C43—21no—
499C23×C43—21no—
500C23×C43—22no—
501C23×C43—41no—
502C23×C43—41no—
503C23×C43—42no—
504C23×C43—42no—
505C23×C43—81no—
506C23×C43—81no—
507C23×C43—81no—
508C23×C43—81no—
509C23×C43C22×D411yescharacteristic
510C23×C43C22×D411yescharacteristic
511C23×C43C22×D411yescharacteristic
512C22×D43—22no—
513C22×D43—21no—
514C22×D43—42no—
515C22×D43—81no—
516C22×D43—81no—
517Q8×C43—22no—
518Q8×C43—21no—
519Q8×C43—21no—
520Q8×C43—22no—
521Q8×C43—21no—
522Q8×C43—21no—
523Q8×C43—42no—
524Q8×C43—42no—
525D4×C43—22no—
526D4×C43—21no—
527D4×C43—21no—
528D4×C43—22no—
529D4×C43—21no—
530D4×C43—21no—
531D4×C43—42no—
532D4×C43—44no—
533D4×C43—44no—
534D4×C43—42no—
535D4×C43—42no—
536D4×C43—42no—
537D4×C43—42no—
538D4×C43—42no—
539D4×C43—82no—
540D4×C43—82no—
541D4×C43—82no—
542D4×C43—82no—
543C2×C4×C43—22no—
544C2×C4×C43—22no—
545C2×C4×C43—22no—
546C2×C4×C43—21no—
547C2×C4×C43—21no—
548C2×C4×C43—21no—
549C2×C4×C43—21no—
550C2×C4×C43—22no—
551C2×C4×C43—21no—
552C2×C4×C43—21no—
553C2×C4×C43—42no—
554C2×C4×C43—42no—
555C2×C4×C43—44no—
556C2×C4×C43—42no—
557C2×C4×C43—42no—
558C2×C4×C43—44no—
559C2×C4×C43—42no—
560C2×C4×C43—42no—
561C2×C4×C43—42no—
562C2×C4×C43—42no—
563C2×C4×C43C22×D412yes—
564C2×C4×C43C22×D412yes—
565C2×C4×C43C22×D411yescharacteristic
566C2×C4×C43C22×D411yescharacteristic
567C2×C4×C43C22×D412yes—
568C2×C4×C43C22×D412yes—
569C2×C4×C43C22×D411yescharacteristic
570C2×C4×C43H(5,𝔽2)12yes—
571C2×C4×C43H(5,𝔽2)12yes—
572C2×C4×C43C2511yescharacteristic
573C22⋊D43—42no—
574C22⋊D43—44no—
575C22⋊D43—42no—
576C22⋊D43—81no—
577C22⋊D43—82no—
578C2×Dic43—21no—
579C2×Dic43—21no—
580C2×Dic43—22no—
581C2×Dic43—21no—
582C2×Dic43—81no—
583D172—22no—
584D172—21no—
585D172—22no—
586D172—21no—
587D172—42no—
588D172—82no—
589D172—82no—
590C4×D43—42no—
591C4×D43—82no—
592C4×D43—82no—
593C4×D43—82no—
594Dic86—21no—
595Dic86—21no—
596Dic86—82no—
597C43⋊C8—21no—
598C43⋊C8—21no—
599C43⋊C8—21no—
600C43⋊C8—21no—
601C43⋊C8—22no—
602C43⋊C8—22no—
603#60815—431nomaximal, Sylow
604C22×C43—21no—
605C22×C43—21no—
606C22×C43—21no—
607C22×C43—21no—
608C22×C43—21no—
609C22×C43—21no—
610C22×C43—21no—
611C22×C43—21no—
612C22×C43—42no—
613C22×C43—41no—
614C22×C43—41no—
615C22×C43—42no—
616C22×C43—41no—
617C22×C43—41no—
618C22×C43—41no—
619C22×C43—41no—
620C22×C43—42no—
621C22×C43—82no—
622C22×C43—84no—
623C22×C43—84no—
624C22×C43#53512yes—
625C22×C43C23×D411yescharacteristic
626C2×D43—42no—
627C2×D43—41no—
628C2×D43—42no—
629C2×D43—41no—
630C2×D43—42no—
631C2×D43—41no—
632C2×D43—162no—
633C4×C43—22no—
634C4×C43—22no—
635C4×C43—22no—
636C4×C43—22no—
637C4×C43—21no—
638C4×C43—21no—
639C4×C43—42no—
640C4×C43—41no—
641C4×C43—41no—
642C4×C43#53512yes—
643C4×C43C2×H(5,𝔽2)11yescharacteristic
644C4×C43C2×H(5,𝔽2)11yescharacteristic
645Dic43—41no—
646Dic43—41no—
647Dic43—42no—
648Dic43—41no—
649#3494—431no—
650#3449D4311yescharacteristic, complemented
651#3225—432no—
652#3224—432no—
653#3221—432no—
654#3220—432no—
655#3219—432no—
656#3214—432no—
657#3212—432no—
658#3207—432no—
659#3155—431no—
660#3154—431no—
661#3137—431no—
662#3136—431no—
663#3046—431no—
664#3045—431no—
665#3042—431no—
666#3041—431no—
667#3006—431no—
668#3005—431no—
669#3002—431no—
670C2×#449—431no—
671#2924—431no—
672C2×C43—22no—
673C2×C43—41no—
674C2×C43—41no—
675C2×C43—82no—
676C2×C43—81no—
677C2×C43—81no—
678C2×C43C2×#53511yescharacteristic
679C2×C43#358411yescharacteristic
680C2×C43#358511yescharacteristic
681D43—81no—
682D43—82no—
683C22×#41C2×D4311yescharacteristic
684C22×#41C2×D4311yescharacteristic
685C2×#137—431no—
686C2×AGL(1,ℤ/8)—431no—
687C2×AGL(1,ℤ/8)—431no—
688C2×AGL(1,ℤ/8)—431no—
689C2×#135—431no—
690C2×#135—431no—
691C22×SD16—431no—
692C22×D8—431no—
693#555—861no—
694#553—861no—
695#553—861no—
696#551—862no—
697#547—861no—
698#546—862no—
699#544—431no—
700#542—432no—
701#540—432no—
702#537—21no—
703#537—21no—
704#536C2×D4311yescharacteristic
705#536C2×D4311yescharacteristic
706#536C2×D4312yescomplemented
707#535—431no—
708#535C2×D4311yescharacteristic
709#535C2×D4311yescharacteristic
710#535C2×D4312yescomplemented
711#534—22no—
712#532—432no—
713#532C2×D4312yescomplemented
714#532C2×D4312yescomplemented
715#529—432no—
716#525—22no—
717#525—21no—
718#525—21no—
719#525—431no—
720C2×#121—431no—
721#520—431no—
722#518—431no—
723C2×#117C2×D4311yescharacteristic
724#497—432no—
725#496—432no—
726#496—432no—
727#496—432no—
728#495—432no—
729#495—432no—
730#493—432no—
731#492—432no—
732#491—432no—
733#490—432no—
734#489—432no—
735#489—432no—
736#488—432no—
737#488—432no—
738#487—432no—
739#486—432no—
740#464—432no—
741#464—432no—
742#463—432no—
743#463—432no—
744#463—432no—
745#463—432no—
746#463—432no—
747#463—432no—
748#462—432no—
749#461—432no—
750#461—432no—
751#461—432no—
752#460—432no—
753#459—432no—
754#459—432no—
755#459—432no—
756#452—431no—
757#452—432no—
758#452—431no—
759#452—432no—
760#451—431no—
761#450—431no—
762#449—432no—
763#449—432no—
764#449—431no—
765#449—432no—
766#449—432no—
767#449—432no—
768#449—432no—
769#449—431no—
770#449—432no—
771#449—432no—
772#448—431no—
773#448—432no—
774#447—431no—
775#447—432no—
776#433—432no—
777#433—432no—
778#432—432no—
779#431—432no—
780#424—431no—
781#424—431no—
782#419—431no—
783#418—431no—
784#417—431no—
785#417—431no—
786#416—431no—
787#416—431no—
788C2×#103—431no—
789C2×#102—431no—
790#407—431no—
791C2×C22⋊C8—431no—
792#405—431no—
793#405—431no—
794C43#6081511yescharacteristic, complemented, Sylow
795C2×#41—21no—
796C2×#41—21no—
797C2×#41—21no—
798C2×#41—21no—
799C2×#41—42no—
800C2×#41—42no—
801C2×#41—42no—
802C2×#41—42no—
803C2×#41—431no—
804C2×#41—862no—
805C2×#41C22×D4311yescharacteristic
806C2×#41C22×D4311yescharacteristic
807C2×#41C22×D4311yescharacteristic
808C2×#41C22×D4312yes—
809C2×#41C22×D4311yescharacteristic
810C2×#41C22×D4312yes—
811C22×Q8C22×D4311yescharacteristic
812C22×Q8C22×D4311yescharacteristic
813C22×D4—21no—
814C22×D4—21no—
815C22×D4—431no—
816C22×D4—861no—
817C22×D4C22×D4311yescharacteristic
818C22×D4C22×D4311yescharacteristic
819C23×C4—21no—
820C23×C4—21no—
821C23×C4C22×D4311yescharacteristic
822#137—1722no—
823AGL(1,ℤ/8)—1722no—
824AGL(1,ℤ/8)—1722no—
825AGL(1,ℤ/8)—1722no—
826#135—1722no—
827#135—1722no—
828C2×Q16—431no—
829C2×Q16—431no—
830C2×Q16—432no—
831C2×SD16—432no—
832C2×SD16—432no—
833C2×SD16—431no—
834C2×SD16—431no—
835C2×SD16—432no—
836C2×SD16—432no—
837C2×SD16—432no—
838C2×SD16—431no—
839C2×SD16—431no—
840C2×SD16—432no—
841C2×SD16—1722no—
842C2×D8—432no—
843C2×D8—432no—
844C2×D8—431no—
845C2×D8—431no—
846C2×D8—432no—
847C2×D8—432no—
848C2×D8—432no—
849C2×D8—1722no—
850C2×M16—431no—
851C2×M16—431no—
852C22×C8—431no—
853C22×C8—431no—
854C4⋊Q8—432no—
855C4⋊Q8—861no—
856C4⋊Q8C22×D4312yes—
857C4⋊Q8C22×D4312yes—
858#127—432no—
859#127C22×D4312yes—
860#127C22×D4312yes—
861#126—862no—
862#126—862no—
863#125—432no—
864#125—861no—
865#124—432no—
866#124—862no—
867#124—862no—
868#124C22×D4312yes—
869#124C22×D4312yes—
870#124C22×D4312yes—
871#124C22×D4312yes—
872#123—22no—
873#123—22no—
874#123—22no—
875#123—22no—
876#123—861no—
877#123—862no—
878#123—862no—
879#123—862no—
880#123—862no—
881C22⋊Q8—21no—
882C22⋊Q8—21no—
883C22⋊Q8—21no—
884C22⋊Q8—21no—
885C22⋊Q8—22no—
886C22⋊Q8—22no—
887C22⋊Q8—431no—
888C22⋊Q8—431no—
889C22⋊Q8—862no—
890C22⋊Q8—862no—
891#121—22no—
892#121—22no—
893#121—22no—
894#121—22no—
895#121—21no—
896#121—21no—
897#121—21no—
898#121—21no—
899#121—22no—
900#121—22no—
901#121—432no—
902#121—432no—
903#121—431no—
904#121—431no—
905#121—861no—
906#121—861no—
907#121—862no—
908#121—861no—
909#121—861no—
910#121—862no—
911#121—862no—
912#120—22no—
913#120—22no—
914#120—22no—
915#120—22no—
916#120—861no—
917#120—862no—
918C4×Q8—432no—
919C4×D4—22no—
920C4×D4—22no—
921C4×D4—22no—
922C4×D4—22no—
923C4×D4—432no—
924C4×D4—432no—
925C4×D4—432no—
926C4×D4—861no—
927C4×D4—861no—
928C4×D4—862no—
929C4×D4—861no—
930C4×D4—861no—
931C4×D4—862no—
932C4×D4—862no—
933#117—431no—
934#117—861no—
935#117—862no—
936#117C22⋊D4312yes—
937#117C22⋊D4311yescharacteristic
938#117C22⋊D4311yescharacteristic
939#117C22×D4311yescharacteristic
940#117C22×D4311yescharacteristic
941#117C22×D4312yes—
942C2×C4⋊C4—431no—
943C2×C4⋊C4—861no—
944C2×C4⋊C4C22⋊D4311yescharacteristic
945C2×C4⋊C4C22⋊D4311yescharacteristic
946C2×C22⋊C4—861no—
947C2×C22⋊C4—862no—
948C2×C22⋊C4C22⋊D4312yes—
949C2×C42C22×D4312yes—
950C4⋊C8—432no—
951C4⋊C8—432no—
952C4⋊C8—432no—
953C4⋊C8—432no—
954#103—432no—
955#103—432no—
956#103—431no—
957#103—431no—
958#103—431no—
959#103—431no—
960#103—432no—
961#103—432no—
962#103—432no—
963#103—432no—
964#102—432no—
965#102—432no—
966#102—431no—
967#102—431no—
968#102—431no—
969#102—431no—
970#102—432no—
971#102—432no—
972#102—432no—
973#102—432no—
974C22⋊C8—431no—
975C22⋊C8—431no—
976C22⋊C8—431no—
977C22⋊C8—431no—
978C22⋊C8—432no—
979C22⋊C8—432no—
980#97—432no—
981#97—432no—
982C4×C8—432no—
983C4×C8—432no—
984C24—21no—
985C24—21no—
986C24—861no—
987C24C2×C22⋊D4311yescharacteristic
988#41—22no—
989#41—22no—
990#41—22no—
991#41—22no—
992#41—42no—
993#41—42no—
994#41—42no—
995#41—41no—
996#41—41no—
997#41—42no—
998#41—41no—
999#41—41no—
1000#41—44no—
1001#41—44no—
1002#41—44no—
1003#41—44no—
1004#41—862no—
1005#41—862no—
1006#41—3444no—
1007C2×Q8—21no—
1008C2×Q8—21no—
1009C2×Q8—22no—
1010C2×Q8—22no—
1011C2×Q8—41no—
1012C2×Q8—41no—
1013C2×Q8—431no—
1014C2×Q8—862no—
1015C2×Q8C23×D4312yes—
1016C2×Q8C23×D4311yescharacteristic
1017C2×Q8C23×D4311yescharacteristic
1018C2×D4—22no—
1019C2×D4—21no—
1020C2×D4—21no—
1021C2×D4—21no—
1022C2×D4—22no—
1023C2×D4—21no—
1024C2×D4—21no—
1025C2×D4—21no—
1026C2×D4—22no—
1027C2×D4—22no—
1028C2×D4—22no—
1029C2×D4—22no—
1030C2×D4—22no—
1031C2×D4—22no—
1032C2×D4—41no—
1033C2×D4—41no—
1034C2×D4—44no—
1035C2×D4—44no—
1036C2×D4—432no—
1037C2×D4—431no—
1038C2×D4—861no—
1039C2×D4—862no—
1040C2×D4—861no—
1041C2×D4—861no—
1042C2×D4—862no—
1043C2×D4—862no—
1044C2×D4—862no—
1045C2×D4—861no—
1046C2×D4—862no—
1047C2×D4—862no—
1048C2×D4—3442no—
1049C2×D4C23×D4312yes—
1050C2×D4C23×D4311yescharacteristic
1051C2×D4C23×D4311yescharacteristic
1052C22×C4—22no—
1053C22×C4—22no—
1054C22×C4—21no—
1055C22×C4—21no—
1056C22×C4—21no—
1057C22×C4—22no—
1058C22×C4—21no—
1059C22×C4—22no—
1060C22×C4—21no—
1061C22×C4—21no—
1062C22×C4—44no—
1063C22×C4—44no—
1064C22×C4—861no—
1065C22×C4—862no—
1066C22×C4—862no—
1067C22×C4—862no—
1068C22×C4—861no—
1069C22×C4C2×C22⋊D4311yescharacteristic
1070C22×C4C2×C22⋊D4311yescharacteristic
1071C22×C4C2×C22⋊D4311yescharacteristic
1072C22×C4C2×C22⋊D4312yes—
1073C22×C4C2×C22⋊D4312yes—
1074C22×C4C23×D4311yescharacteristic
1075C22×C4C23×D4311yescharacteristic
1076C22×C4C23×D4311yescharacteristic
1077Q16—1721no—
1078Q16—1721no—
1079Q16—1722no—
1080SD16—1721no—
1081SD16—1721no—
1082SD16—1722no—
1083SD16—1722no—
1084SD16—1722no—
1085SD16—1721no—
1086SD16—1721no—
1087SD16—1722no—
1088SD16—1722no—
1089SD16—1722no—
1090D8—1722no—
1091D8—1722no—
1092D8—1721no—
1093D8—1721no—
1094D8—1722no—
1095D8—1722no—
1096D8—1722no—
1097M16—862no—
1098M16—862no—
1099C2×C8—431no—
1100C2×C8—431no—
1101C2×C8—432no—
1102C2×C8—432no—
1103C2×C8—431no—
1104C2×C8—431no—
1105C2×C8—862no—
1106C2×C8—862no—
1107C4⋊C4—22no—
1108C4⋊C4—22no—
1109C4⋊C4—22no—
1110C4⋊C4—22no—
1111C4⋊C4—432no—
1112C4⋊C4—431no—
1113C4⋊C4—431no—
1114C4⋊C4—861no—
1115C4⋊C4—862no—
1116C4⋊C4—861no—
1117C4⋊C4—862no—
1118C4⋊C4—862no—
1119C4⋊C4—862no—
1120C4⋊C4—861no—
1121C4⋊C4C2×C22⋊D4311yescharacteristic
1122C4⋊C4C2×C22⋊D4311yescharacteristic
1123C4⋊C4C2×C22⋊D4311yescharacteristic
1124C4⋊C4C2×C22⋊D4311yescharacteristic
1125C4⋊C4C2×C22⋊D4312yes—
1126C4⋊C4C2×C22⋊D4312yes—
1127C22⋊C4—22no—
1128C22⋊C4—22no—
1129C22⋊C4—22no—
1130C22⋊C4—22no—
1131C22⋊C4—22no—
1132C22⋊C4—22no—
1133C22⋊C4—22no—
1134C22⋊C4—22no—
1135C22⋊C4—861no—
1136C22⋊C4—861no—
1137C22⋊C4—861no—
1138C22⋊C4—862no—
1139C22⋊C4—862no—
1140C22⋊C4—862no—
1141C22⋊C4—862no—
1142C22⋊C4—862no—
1143C22⋊C4—862no—
1144C22⋊C4—861no—
1145C22⋊C4—862no—
1146C22⋊C4—861no—
1147C22⋊C4C2×C22⋊D4312yes—
1148C22⋊C4C2×C22⋊D4312yes—
1149C22⋊C4C2×C22⋊D4312yes—
1150C22⋊C4C2×C22⋊D4312yes—
1151C42—861no—
1152C42—862no—
1153C42C2×C22⋊D4312yes—
1154C42C2×C22⋊D4312yes—
1155C42C23×D4312yes—
1156C42C23×D4312yes—
1157C23—22no—
1158C23—22no—
1159C23—21no—
1160C23—21no—
1161C23—41no—
1162C23—41no—
1163C23—42no—
1164C23—42no—
1165C23—81no—
1166C23—81no—
1167C23—81no—
1168C23—81no—
1169C23—862no—
1170C23—861no—
1171C23—3441no—
1172C23—3441no—
1173C23—1722no—
1174C23C22×C22⋊D4311yescharacteristic
1175C23C22×C22⋊D4311yescharacteristic
1176C23C22×C22⋊D4311yescharacteristic
1177Q8—22no—
1178Q8—21no—
1179Q8—21no—
1180Q8—22no—
1181Q8—21no—
1182Q8—21no—
1183Q8—42no—
1184Q8—42no—
1185Q8—861no—
1186Q8—861no—
1187Q8—3442no—
1188D4—22no—
1189D4—21no—
1190D4—21no—
1191D4—22no—
1192D4—21no—
1193D4—21no—
1194D4—42no—
1195D4—44no—
1196D4—44no—
1197D4—42no—
1198D4—42no—
1199D4—42no—
1200D4—42no—
1201D4—42no—
1202D4—82no—
1203D4—82no—
1204D4—82no—
1205D4—82no—
1206D4—862no—
1207D4—861no—
1208D4—862no—
1209D4—861no—
1210D4—3442no—
1211D4—3442no—
1212D4—3442no—
1213D4—3441no—
1214D4—1724no—
1215D4—1722no—
1216D4—1722no—
1217D4—1722no—
1218C2×C4—22no—
1219C2×C4—22no—
1220C2×C4—22no—
1221C2×C4—21no—
1222C2×C4—21no—
1223C2×C4—21no—
1224C2×C4—21no—
1225C2×C4—22no—
1226C2×C4—21no—
1227C2×C4—21no—
1228C2×C4—42no—
1229C2×C4—42no—
1230C2×C4—44no—
1231C2×C4—42no—
1232C2×C4—42no—
1233C2×C4—44no—
1234C2×C4—42no—
1235C2×C4—42no—
1236C2×C4—42no—
1237C2×C4—42no—
1238C2×C4—861no—
1239C2×C4—861no—
1240C2×C4—861no—
1241C2×C4—862no—
1242C2×C4—3442no—
1243C2×C4—3442no—
1244C2×C4—3442no—
1245C2×C4—3441no—
1246C2×C4—1722no—
1247C2×C4C22×C22⋊D4312yes—
1248C2×C4C22×C22⋊D4311yescharacteristic
1249C2×C4C22×C22⋊D4312yes—
1250C2×C4C22×C22⋊D4312yes—
1251C2×C4C22×C22⋊D4312yes—
1252C2×C4C22×C22⋊D4311yescharacteristic
1253C2×C4C22×C22⋊D4311yescharacteristic
1254C2×C4#1306337012yes—
1255C2×C4#1306337012yes—
1256C2×C4C24×D4311yescharacteristic
1257C8—861no—
1258C8—861no—
1259C8—861no—
1260C8—861no—
1261C8—862no—
1262C8—862no—
1263C22—21no—
1264C22—21no—
1265C22—21no—
1266C22—21no—
1267C22—21no—
1268C22—21no—
1269C22—21no—
1270C22—21no—
1271C22—42no—
1272C22—41no—
1273C22—41no—
1274C22—42no—
1275C22—41no—
1276C22—41no—
1277C22—42no—
1278C22—41no—
1279C22—41no—
1280C22—82no—
1281C22—84no—
1282C22—84no—
1283C22—1722no—
1284C22—1721no—
1285C22—1721no—
1286C22—1722no—
1287C22—1721no—
1288C22—1722no—
1289C22—6882no—
1290C22#1458346612yes—
1291C22C23×C22⋊D4311yescharacteristic
1292C4—22no—
1293C4—22no—
1294C4—22no—
1295C4—22no—
1296C4—21no—
1297C4—21no—
1298C4—42no—
1299C4—41no—
1300C4—41no—
1301C4—1721no—
1302C4—1722no—
1303C4—1721no—
1304C4—1721no—
1305C4#1458346612yes—
1306C4C2×#1306337011yescharacteristic
1307C4C2×#1306337011yescharacteristic
1308C2—22no—
1309C2—41no—
1310C2—41no—
1311C2—82no—
1312C2—81no—
1313C2—81no—
1314C2—3442no—
1315C2—3441no—
1316C2C2×#1458346611yescharacteristic
1317C2#1914936611yescharacteristic
1318C2#1914937411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3449C2
socleC22×C43C23×D4
hypercenter#3449D43
hypocenterC43#60815
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×#117 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #19148330C2semidirect
2. #19145704C2semidirect
3. #19145689C2semidirect
4. #19145656C2semidirect
5. #19145645C2semidirect
6. #19145632C2semidirect
7. #19145590C2semidirect
8. #19145571C2semidirect
9. #19145528C2semidirect
10. #19145078C2semidirect
11. #19145073C2semidirect
12. #19144960C2semidirect
13. #19144949C2semidirect
14. #19144141C2semidirect
15. #19144130C2semidirect
16. #19144103C2semidirect
17. #19144094C2semidirect
18. #19143847C2semidirect
19. #19143837C2semidirect
20. #19143813C2semidirect
21. C2×#14583044C2semidirect
22. #19143253C2semidirect
23. C43×#3449C2semidirect
24. C2×#13063356C22semidirect
25. C2×#13063351C22semidirect
30. C22×#10621884C22semidirect
31. C22×#10621882C22semidirect
38. #14583527C22semidirect
39. #14583520C22semidirect
40. #14583504C22semidirect
41. #14583468C22semidirect
42. #14583449C22semidirect
43. #14583433C22semidirect
46. #14583379C22semidirect
47. #14583373C22semidirect
48. #14583291C22semidirect
49. #14583289C22semidirect
50. #14583289C22semidirect
51. #14583286C22semidirect
52. #14583281C22semidirect
53. #14583281C22semidirect
54. #14583275C22semidirect
55. #14583273C22semidirect
56. #14583267C22semidirect
57. #14583263C22semidirect
58. #14583258C22semidirect
59. #14583258C22semidirect
60. #14583253C22semidirect
61. #14583253C22semidirect
62. #14583249C22semidirect
63. #14583245C22semidirect
64. #14583118C22semidirect
65. #14583118C22semidirect
66. #14583111C22semidirect
67. #14583111C22semidirect
68. #14583111C22semidirect
69. #14583111C22semidirect
70. #14583111C22semidirect
71. #14583111C22semidirect
72. #14583106C22semidirect
73. #14583101C22semidirect
74. #14583101C22semidirect
75. #14583101C22semidirect
76. #14583096C22semidirect
77. #14583091C22semidirect
78. #14583091C22semidirect
79. #14583091C22semidirect
80. #14583061C22semidirect
81. #14583061C22semidirect
82. #14583061C22semidirect
83. #14583061C22semidirect
84. #14583055C22semidirect
85. #14583050C22semidirect
88. #14583044C22semidirect
89. #14583044C22semidirect
90. #14583044C22semidirect
91. #14583044C22semidirect
92. #14583044C22semidirect
93. #14583044C22semidirect
94. #14583044C22semidirect
95. #14583044C22semidirect
96. #14583038C22semidirect
97. #14583038C22semidirect
98. #14583033C22semidirect
99. #14583033C22semidirect
100. #14582960C22semidirect
101. #14582960C22semidirect
102. #14582956C22semidirect
103. #14582952C22semidirect
104. #14582926C22semidirect
105. #14582926C22semidirect
106. #14582908C22semidirect
107. #14582904C22semidirect
112. C2×#13063249C22semidirect
113. C2×#13063246C22semidirect
116. #14582855C22semidirect
117. #14582855C22semidirect
124. C43×#536C22semidirect
127. C43×#535C22semidirect
129. C43×#532C22semidirect
130. C43×#532C22semidirect
650. #3449D43semidirect
706. #536C2×D43semidirect
710. #535C2×D43semidirect
713. #532C2×D43semidirect
714. #532C2×D43semidirect
794. C43#60815semidirect

Maximal subgroups

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

subgroupindex
#191483302
#191457042
#191456892
#191456562
#191456452
#191456322
#191455902
#191455712
#191455282
#191450782
#191450732
#191449602
#191449492
#191441412
#191441302
#191441032
#191440942
#191438472
#191438372
#191438132
C2×#145830442
#191432532
C43×#34492
#6081543