Finite Group Databasebeta

← #25981499

Subgroups — #25981499

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19148434C211yesmaximal, characteristic, complemented
2#19146691C214yesmaximal, complemented
3#19146571C214yesmaximal, complemented
4#19146146C214yesmaximal, complemented
5#19146121C214yesmaximal, complemented
6#19145622C212yesmaximal, complemented
7#19145416C211yesmaximal, characteristic, complemented
8#19145397C211yesmaximal, characteristic, complemented
9#19145376C212yesmaximal, complemented
10#19144733C212yesmaximal, complemented
11#19143855C211yesmaximal, characteristic, complemented
12#19143847C211yesmaximal, characteristic, complemented
13#19143813C212yesmaximal, complemented
14#19143624C211yesmaximal, characteristic, complemented
15C2×C43×#547C211yesmaximal, characteristic, complemented
16C2×#13063355C2212yescomplemented
17C2×#13063350C2212yescomplemented
18C2×#13063345C2214yescomplemented
19#14583598—22no—
20#14583595C2212yescomplemented
21#14583589C2212yescomplemented
22#14583578—22no—
23#14583558C2212yescomplemented
24#14583545C2212yescomplemented
25#14583496—21no—
26#14583487—21no—
27#14583458—21no—
28#14583433C2212yes—
29#14583410C2212yes—
30C2×#13063304C2211yescharacteristic
31C2×#13063299C2211yescharacteristic
32#14583372—21no—
33#14583291C2214yescomplemented
34#14583267C2214yescomplemented
35#14583237C2214yescomplemented
36#14583232C2212yescomplemented
37#14583229C2212yescomplemented
38#14583227C2212yescomplemented
39#14583212C2212yes—
40#14583199C2214yescomplemented
41#14583155C2214yescomplemented
42#14583147C2214yescomplemented
43#14583138C2214yescomplemented
44#14583130C2214yescomplemented
45#14583114C2214yescomplemented
46#14583106C2214yescomplemented
47#14583101C2214yescomplemented
48#14583061C2214yescomplemented
49#14583061C2214yescomplemented
50#14583059C2214yescomplemented
51#14583055C2212yescomplemented
52#14583055C2212yescomplemented
53#14583054C2212yescomplemented
54#14583050C2212yescomplemented
55#14583049C2212yescomplemented
56#14583044C2214yescomplemented
57#14583044C2214yescomplemented
58#14583038C2212yes—
59#14583038C2212yes—
60#14583033C2212yes—
61#14583009C2214yescomplemented
62#14582999C2214yescomplemented
63#14582971C2214yescomplemented
64#14582971C2214yescomplemented
65#14582956C2212yescomplemented
66#14582900C2212yescomplemented
67#14582900C2212yescomplemented
68#14582895C2214yescomplemented
69#14582863C2211yescharacteristic
70#14582863C2211yescharacteristic
71C2×C22⋊(C43⋊C8)C2212yescomplemented
72C22×#41×C43C2211yescharacteristic
73C22×#41×C43C2211yescharacteristic, complemented
74C43×#547—22no—
75C43×#547—22no—
76C43×#547C2214yes—
77C43×#547C2214yescomplemented
78C2×C4⋊Q8×C43C2211yescharacteristic, complemented
79C2×#123×C43—21no—
80C2×#123×C43—21no—
81C2×C22⋊Q8×C43C2211yescharacteristic
82C2×C22⋊Q8×C43C2211yescharacteristic, complemented
83C2×#121×C43—21no—
84C2×C4×D4×C43C2211yescharacteristic
85C2×C4×D4×C43C2211yescharacteristic, complemented
86C22×C4⋊C4×C43—21no—
87C2×#10621898C2312yes—
88C22×Dic86C2311yescharacteristic
89C22×D172C2311yescharacteristic
90C22×C22⋊D43—21no—
91#13063355—44no—
92#13063350—44no—
93#13063345—48no—
94C2×#10621885C2314yes—
95C2×#10621885C2314yes—
96C2×#10621883C2314yes—
97C2×#10621884C2314yes—
98C2×#10621884C2314yes—
99C2×#10621882C2314yes—
100C2×#10621877C2312yes—
101C2×#10621877C2312yes—
102C22×C43⋊C8C2314yes—
103#13063320—22no—
104#13063319—22no—
105#13063318—22no—
106#13063317C2312yes—
107#13063315—22no—
108#13063313C2312yes—
109#13063311—22no—
110#13063310—22no—
111#13063308—22no—
112#13063308—22no—
113#13063307—22no—
114#13063306—22no—
115#13063304—21no—
116#13063304—21no—
117#13063304C2312yes—
118#13063304C2312yes—
119#13063304C2312yes—
120#13063303—22no—
121#13063299—21no—
122#13063299—21no—
123#13063299C2312yes—
124#13063299C2312yes—
125#13063299C2312yes—
126#13063298—22no—
127#13063297—22no—
128#13063297—22no—
129#13063294—22no—
130#13063293—22no—
131C4×Dic86C2312yes—
132C4×D172C2312yes—
133C4×C22⋊D43—22no—
134C4×C22⋊D43—22no—
135C4×C22⋊D43—22no—
136(C22⋊D43)⋊C4—22no—
137(C22⋊D43)⋊C4—22no—
138#13063284C2312yes—
139#13063282—22no—
140#13063281—22no—
141C2×C4⋊Dic43C2311yescharacteristic
142C2×C4⋊Dic43C2311yescharacteristic
143C2×Dic43⋊C4—21no—
144C2×C22⋊Dic43—21no—
145C2×(C2×D43)⋊C4—21no—
146C22⋊C4×D43—22no—
147#13063258C2314yes—
148#13063256C2314yes—
149C4⋊(C43⋊C8)C2314yes—
150#13063249C2314yes—
151#13063249C2314yes—
152#13063249C2314yes—
153#13063249C2314yes—
154#13063248C2314yes—
155#13063246C2314yes—
156#13063246C2314yes—
157#13063245C2314yes—
158C22⋊(C43⋊C8)C2312yes—
159C22⋊(C43⋊C8)C2314yes—
160C22⋊(C43⋊C8)C2312yes—
161C22⋊(C43⋊C8)C2312yes—
162C22⋊(C43⋊C8)C2312yes—
163#13063236C2314yes—
164C2×#41×C43—21no—
165C2×#41×C43—21no—
166C2×#41×C43—22no—
167C2×#41×C43—44no—
168C2×#41×C43—44no—
169C2×#41×C43C2312yes—
170C2×#41×C43C2314yes—
171C2×#41×C43C2312yes—
172C22×Q8×C43C2311yescharacteristic
173C22×Q8×C43C2311yescharacteristic
174C22×D4×C43—21no—
175C22×D4×C43—21no—
176C22×D4×C43D411yescharacteristic
177C22×D4×C43C2311yescharacteristic
178C23×C4×C43—21no—
179C23×C4×C43—21no—
180C23×C4×C43—21no—
181C23×C4×C43C2311yescharacteristic
182C23×C4×C43C2311yescharacteristic
183C4⋊Q8×C43—22no—
184C4⋊Q8×C43C2314yes—
185#123×C43—24no—
186#123×C43—24no—
187#123×C43—24no—
188#123×C43—24no—
189C22⋊Q8×C43—21no—
190C22⋊Q8×C43—21no—
191C22⋊Q8×C43—22no—
192C22⋊Q8×C43C2312yes—
193C22⋊Q8×C43C2312yes—
194C22⋊Q8×C43C2314yes—
195#121×C43—24no—
196#121×C43—24no—
197C4×D4×C43—22no—
198C4×D4×C43D412yes—
199C4×D4×C43D412yes—
200C4×D4×C43C2314yes—
201C4×D4×C43C2312yes—
202C4×D4×C43C2312yes—
203C2×C4⋊C4×C43—21no—
204C2×C4⋊C4×C43—21no—
205C2×C4⋊C4×C43—21no—
206C2×C4⋊C4×C43—21no—
207C2×C4⋊C4×C43—24no—
208C2×C4⋊C4×C43—24no—
209C2×C4⋊C4×C43D411yescharacteristic
210C2×C4⋊C4×C43C2311yescharacteristic
211C2×C22⋊C4×C43—21no—
212C2×C22⋊C4×C43—21no—
213C2×C22⋊C4×C43—21no—
214C2×C22⋊C4×C43D411yescharacteristic
215C2×C22⋊C4×C43D411yescharacteristic
216C2×C42×C43C2311yescharacteristic
217C24×C43—21no—
218C24×C43C2×D411yescharacteristic
219C24×C43C2×D411yescharacteristic
220C23×D43—21no—
221#41×C43—28no—
222#41×C43—24no—
223#41×C43—24no—
224#41×C43—44no—
225#41×C43—42no—
226#41×C43—42no—
227#41×C43—44no—
228#41×C43—44no—
229#41×C43—48no—
230C2×Q8×C43—21no—
231C2×Q8×C43—21no—
232C2×Q8×C43—42no—
233C2×Q8×C43—42no—
234C2×Q8×C43C2412yes—
235C2×Q8×C43C2412yes—
236C2×D4×C43—24no—
237C2×D4×C43—21no—
238C2×D4×C43—22no—
239C2×D4×C43—24no—
240C2×D4×C43—22no—
241C2×D4×C43—42no—
242C2×D4×C43—44no—
243C2×D4×C43—44no—
244C2×D4×C43C2×D412yes—
245C2×D4×C43C2×D412yes—
246C2×D4×C43C2412yes—
247C22×C4×C43—24no—
248C22×C4×C43—24no—
249C22×C4×C43—22no—
250C22×C4×C43—22no—
251C22×C4×C43—21no—
252C22×C4×C43—21no—
253C22×C4×C43—21no—
254C22×C4×C43—44no—
255C22×C4×C43—44no—
256C22×C4×C43—42no—
257C22×C4×C43—42no—
258C22×C4×C43—44no—
259C22×C4×C43C2×D411yescharacteristic
260C22×C4×C43C2×D411yescharacteristic
261C22×C4×C43C2×D411yescharacteristic
262C22×C4×C43C2×D411yescharacteristic
263C22×C4×C43C2×D411yescharacteristic
264C22×C4×C43C2×D411yescharacteristic
265C22×C4×C43C2×D412yes—
266C22×C4×C43C2411yescharacteristic
267C22×C4×C43C2411yescharacteristic
268C22×C4×C43C2411yescharacteristic
269C22×C4×C43C2412yes—
270C2×C22⋊D43—22no—
271C2×C22⋊D43—22no—
272C2×C22⋊D43—22no—
273C2×C22⋊D43—22no—
274C2×C22⋊D43—44no—
275C22×Dic43—21no—
276C22×Dic43—21no—
277C22×Dic43—21no—
278#10621898—44no—
279C2×D172—21no—
280C2×D172—42no—
281C2×D172C2412yes—
282C2×C4×D43—22no—
283C2×C4×D43—22no—
284C2×Dic86—21no—
285C2×Dic86—42no—
286C2×Dic86C2412yes—
287C4⋊C4×C43—24no—
288C4⋊C4×C43—24no—
289C4⋊C4×C43—22no—
290C4⋊C4×C43—22no—
291C4⋊C4×C43—24no—
292C4⋊C4×C43—21no—
293C4⋊C4×C43C2×D412yes—
294C4⋊C4×C43C2×D412yes—
295C4⋊C4×C43C2412yes—
296C22⋊C4×C43—24no—
297C22⋊C4×C43—22no—
298C22⋊C4×C43—24no—
299C22⋊C4×C43—22no—
300C22⋊C4×C43C2×D412yes—
301C22⋊C4×C43C2×D412yes—
302C22⋊C4×C43C2×D412yes—
303C22⋊C4×C43C2×D412yes—
304C42×C43C2×D412yes—
305C42×C43C2412yes—
306C22⋊Dic43—22no—
307C22⋊Dic43—22no—
308C22⋊Dic43—22no—
309C22⋊Dic43—22no—
310#10621885—44no—
311#10621885—44no—
312#10621884—44no—
313#10621884—44no—
314#10621883—28no—
315#10621882—28no—
316(C2×D43)⋊C4—22no—
317(C2×D43)⋊C4—22no—
318(C2×D43)⋊C4—22no—
319(C2×D43)⋊C4—22no—
320(C2×D43)⋊C4—22no—
321(C2×D43)⋊C4—22no—
322C4⋊Dic43—21no—
323C4⋊Dic43—21no—
324C4⋊Dic43C2412yes—
325C4⋊Dic43C2412yes—
326Dic43⋊C4—22no—
327Dic43⋊C4—22no—
328Dic43⋊C4—22no—
329Dic43⋊C4—22no—
330Dic43⋊C4—22no—
331Dic43⋊C4—22no—
332C4×Dic43—22no—
333C4×Dic43—22no—
334#10621877—42no—
335#10621877—42no—
336C2×C43⋊C8—44no—
337C2×C43⋊C8C2414yes—
338C2×C43⋊C8C2414yes—
339C23×C43—24no—
340C23×C43—22no—
341C23×C43—22no—
342C23×C43—22no—
343C23×C43—41no—
344C23×C43—41no—
345C23×C43—41no—
346C23×C43—41no—
347C23×C43—42no—
348C23×C43—42no—
349C23×C43C22×D411yescharacteristic
350C23×C43C22×D412yes—
351C23×C43C22×D411yescharacteristic
352C23×C43C22×D411yescharacteristic
353C22×D43—22no—
354C22×D43—42no—
355C22×D43—81no—
356C22×D43—81no—
357Q8×C43—22no—
358Q8×C43—24no—
359Q8×C43—22no—
360Q8×C43—42no—
361Q8×C43—42no—
362D4×C43—24no—
363D4×C43—22no—
364D4×C43—42no—
365D4×C43—42no—
366D4×C43—44no—
367D4×C43—44no—
368D4×C43—48no—
369D4×C43H(5,𝔽2)14yes—
370C2×C4×C43—22no—
371C2×C4×C43—24no—
372C2×C4×C43—22no—
373C2×C4×C43—22no—
374C2×C4×C43—22no—
375C2×C4×C43—22no—
376C2×C4×C43—22no—
377C2×C4×C43—22no—
378C2×C4×C43—41no—
379C2×C4×C43—41no—
380C2×C4×C43—41no—
381C2×C4×C43—42no—
382C2×C4×C43—41no—
383C2×C4×C43—41no—
384C2×C4×C43—44no—
385C2×C4×C43—48no—
386C2×C4×C43—44no—
387C2×C4×C43—48no—
388C2×C4×C43—42no—
389C2×C4×C43—42no—
390C2×C4×C43—42no—
391C2×C4×C43C22×D412yes—
392C2×C4×C43C22×D412yes—
393C2×C4×C43C22×D411yescharacteristic
394C2×C4×C43C22×D411yescharacteristic
395C2×C4×C43C22×D412yes—
396C2×C4×C43C22×D411yescharacteristic
397C2×C4×C43C2511yescharacteristic
398C22⋊D43—44no—
399C22⋊D43—44no—
400C22⋊D43—82no—
401C22⋊D43—82no—
402C2×Dic43—22no—
403C2×Dic43—22no—
404C2×Dic43—22no—
405C2×Dic43—42no—
406C2×Dic43—81no—
407C2×Dic43—81no—
408D172—24no—
409D172—81no—
410C4×D43—82no—
411C4×D43—82no—
412Dic86—24no—
413Dic86—81no—
414C43⋊C8—24no—
415C43⋊C8—24no—
416#61575—431nomaximal, Sylow
417C22×C43—21no—
418C22×C43—21no—
419C22×C43—21no—
420C22×C43—21no—
421C22×C43—22no—
422C22×C43—21no—
423C22×C43—24no—
424C22×C43—21no—
425C22×C43—22no—
426C22×C43—21no—
427C22×C43—21no—
428C22×C43—22no—
429C22×C43—48no—
430C22×C43—42no—
431C22×C43—42no—
432C22×C43—82no—
433C22×C43—82no—
434C22×C43#57512yes—
435C22×C43C23×D411yescharacteristic
436C2×D43—42no—
437C2×D43—42no—
438C2×D43—42no—
439C2×D43—162no—
440C4×C43—22no—
441C4×C43—21no—
442C4×C43—22no—
443C4×C43—21no—
444C4×C43—21no—
445C4×C43—22no—
446C4×C43—42no—
447C4×C43—42no—
448C4×C43—42no—
449C4×C43C2×H(5,𝔽2)12yes—
450Dic43—42no—
451Dic43—42no—
452Dic43—42no—
453#3505—431no—
454C2×#547D4311yescharacteristic, complemented
455#3315—434no—
456#3307—434no—
457#3269—434no—
458#3267—434no—
459#3218—432no—
460#3195—431no—
461#3193—431no—
462#3190—432no—
463#3114—432no—
464#3007—431no—
465#3006—431no—
466#3002—432no—
467#2973—431no—
468C2×C43—22no—
469C2×C43—41no—
470C2×C43—41no—
471C2×C43—42no—
472C2×C43—44no—
473C2×C43#348411yescharacteristic
474C2×C43C2×#57511yescharacteristic
475C2×C43#358611yescharacteristic
476D43—82no—
477C22×#41C2×D4311yescharacteristic
478C22×#41C2×D4311yescharacteristic, complemented
479C2×#137—432no—
480C2×AGL(1,ℤ/8)—432no—
481C2×#135—434no—
482#553—432no—
483#553—862no—
484#552—432no—
485#551—862no—
486#548—432no—
487#547—22no—
488#547—22no—
489#547C2×D4314yes—
490#547C2×D4314yescomplemented
491#546—432no—
492#539—861no—
493#538—861no—
494#534—861no—
495C2×C4⋊Q8C2×D4311yescharacteristic, complemented
496#529—432no—
497#525—432no—
498C2×#123—21no—
499C2×#123—21no—
500C2×C22⋊Q8—431no—
501C2×C22⋊Q8C2×D4311yescharacteristic
502C2×C22⋊Q8C2×D4311yescharacteristic, complemented
503C2×#121—21no—
504C2×#121—431no—
505#518—861no—
506C2×C4×D4C2×D4311yescharacteristic
507C2×C4×D4C2×D4311yescharacteristic, complemented
508C22×C4⋊C4—21no—
509#497—434no—
510#491—434no—
511#485—434no—
512#484—432no—
513#483—432no—
514#483—432no—
515#480—432no—
516#478—434no—
517#470—434no—
518#468—434no—
519#467—434no—
520#465—434no—
521#463—434no—
522#462—434no—
523#461—434no—
524#452—434no—
525#452—434no—
526#452—434no—
527#451—432no—
528#451—432no—
529#451—432no—
530#450—432no—
531#450—432no—
532#449—434no—
533#449—434no—
534#448—432no—
535#448—432no—
536#447—432no—
537#442—434no—
538#440—434no—
539#435—434no—
540#435—434no—
541#432—432no—
542#417—432no—
543#417—432no—
544#416—434no—
545#407—431no—
546#407—431no—
547C2×C22⋊C8—432no—
548C43#6157511yescharacteristic, complemented, Sylow
549C2×#41—21no—
550C2×#41—21no—
551C2×#41—22no—
552C2×#41—44no—
553C2×#41—44no—
554C2×#41—432no—
555C2×#41C22×D4312yes—
556C2×#41C22×D4314yes—
557C2×#41C22×D4312yes—
558C22×Q8—431no—
559C22×Q8C22×D4311yescharacteristic
560C22×Q8C22×D4311yescharacteristic
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—431no—
564C22×D4—861no—
565C22×D4C22⋊D4311yescharacteristic
566C22×D4C22×D4311yescharacteristic
567C23×C4—21no—
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C22×D4311yescharacteristic
571C23×C4C22×D4311yescharacteristic
572#137—1724no—
573AGL(1,ℤ/8)—1724no—
574#135—1728no—
575C2×Q16—434no—
576C2×Q16—434no—
577C2×SD16—434no—
578C2×SD16—434no—
579C2×SD16—434no—
580C2×D8—434no—
581C2×M16—432no—
582C2×M16—432no—
583C22×C8—434no—
584C4⋊Q8—22no—
585C4⋊Q8C22×D4314yes—
586#126—862no—
587#126—862no—
588#126—862no—
589#125—432no—
590#125—862no—
591#124—432no—
592#124—862no—
593#123—24no—
594#123—24no—
595#123—24no—
596#123—24no—
597#123—862no—
598#123—862no—
599#123—862no—
600#123—862no—
601#123—862no—
602C22⋊Q8—21no—
603C22⋊Q8—21no—
604C22⋊Q8—22no—
605C22⋊Q8—432no—
606C22⋊Q8—432no—
607C22⋊Q8—432no—
608C22⋊Q8—861no—
609C22⋊Q8—861no—
610C22⋊Q8—862no—
611C22⋊Q8C22×D4312yes—
612C22⋊Q8C22×D4312yes—
613C22⋊Q8C22×D4314yes—
614#121—24no—
615#121—24no—
616#121—432no—
617#121—432no—
618#121—432no—
619#121—862no—
620#121—862no—
621#121—861no—
622#121—861no—
623#121—862no—
624#120—862no—
625#120—862no—
626C4×Q8—432no—
627C4×D4—22no—
628C4×D4—432no—
629C4×D4—862no—
630C4×D4—862no—
631C4×D4—862no—
632C4×D4—862no—
633C4×D4—862no—
634C4×D4C22⋊D4312yes—
635C4×D4C22⋊D4312yes—
636C4×D4C22×D4314yes—
637C4×D4C22×D4312yes—
638C4×D4C22×D4312yes—
639#117—432no—
640#117—862no—
641#117—862no—
642C2×C4⋊C4—21no—
643C2×C4⋊C4—21no—
644C2×C4⋊C4—21no—
645C2×C4⋊C4—21no—
646C2×C4⋊C4—24no—
647C2×C4⋊C4—24no—
648C2×C4⋊C4—431no—
649C2×C4⋊C4—431no—
650C2×C4⋊C4—861no—
651C2×C4⋊C4C22⋊D4311yescharacteristic
652C2×C4⋊C4C22×D4311yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—861no—
657C2×C22⋊C4—861no—
658C2×C22⋊C4—862no—
659C2×C22⋊C4C22⋊D4311yescharacteristic
660C2×C22⋊C4C22⋊D4311yescharacteristic
661C2×C42C22×D4311yescharacteristic
662#107—434no—
663#106—434no—
664C4⋊C8—434no—
665#103—434no—
666#103—434no—
667#103—434no—
668#103—434no—
669#103—434no—
670#102—434no—
671#102—434no—
672#102—434no—
673C22⋊C8—432no—
674C22⋊C8—432no—
675C22⋊C8—434no—
676C22⋊C8—432no—
677C22⋊C8—432no—
678#97—434no—
679C24—21no—
680C24—861no—
681C24C2×C22⋊D4311yescharacteristic
682C24C2×C22⋊D4311yescharacteristic
683#41—28no—
684#41—24no—
685#41—24no—
686#41—44no—
687#41—42no—
688#41—42no—
689#41—44no—
690#41—44no—
691#41—48no—
692#41—1724no—
693C2×Q8—21no—
694C2×Q8—21no—
695C2×Q8—42no—
696C2×Q8—42no—
697C2×Q8—432no—
698C2×Q8—861no—
699C2×Q8—1722no—
700C2×Q8C23×D4312yes—
701C2×Q8C23×D4312yes—
702C2×D4—24no—
703C2×D4—22no—
704C2×D4—24no—
705C2×D4—22no—
706C2×D4—21no—
707C2×D4—42no—
708C2×D4—44no—
709C2×D4—44no—
710C2×D4—432no—
711C2×D4—862no—
712C2×D4—862no—
713C2×D4—862no—
714C2×D4—862no—
715C2×D4—861no—
716C2×D4—1722no—
717C2×D4—1724no—
718C2×D4C2×C22⋊D4312yes—
719C2×D4C2×C22⋊D4312yes—
720C2×D4C23×D4312yes—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—24no—
725C22×C4—24no—
726C22×C4—22no—
727C22×C4—22no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—44no—
731C22×C4—44no—
732C22×C4—44no—
733C22×C4—861no—
734C22×C4—861no—
735C22×C4—861no—
736C22×C4—862no—
737C22×C4—862no—
738C22×C4C2×C22⋊D4311yescharacteristic
739C22×C4C2×C22⋊D4311yescharacteristic
740C22×C4C2×C22⋊D4311yescharacteristic
741C22×C4C2×C22⋊D4311yescharacteristic
742C22×C4C2×C22⋊D4311yescharacteristic
743C22×C4C2×C22⋊D4311yescharacteristic
744C22×C4C2×C22⋊D4312yes—
745C22×C4C23×D4311yescharacteristic
746C22×C4C23×D4311yescharacteristic
747C22×C4C23×D4311yescharacteristic
748C22×C4C23×D4312yes—
749Q16—1724no—
750Q16—1724no—
751SD16—868no—
752SD16—1724no—
753SD16—1724no—
754D8—868no—
755M16—1722no—
756M16—1722no—
757C2×C8—434no—
758C2×C8—434no—
759C2×C8—1724no—
760C4⋊C4—24no—
761C4⋊C4—24no—
762C4⋊C4—22no—
763C4⋊C4—22no—
764C4⋊C4—24no—
765C4⋊C4—21no—
766C4⋊C4—432no—
767C4⋊C4—432no—
768C4⋊C4—861no—
769C4⋊C4—861no—
770C4⋊C4—862no—
771C4⋊C4—862no—
772C4⋊C4—862no—
773C4⋊C4—862no—
774C4⋊C4—862no—
775C4⋊C4—862no—
776C4⋊C4C2×C22⋊D4312yes—
777C4⋊C4C2×C22⋊D4312yes—
778C4⋊C4C23×D4312yes—
779C22⋊C4—22no—
780C22⋊C4—24no—
781C22⋊C4—22no—
782C22⋊C4—24no—
783C22⋊C4—862no—
784C22⋊C4—862no—
785C22⋊C4—862no—
786C22⋊C4—862no—
787C22⋊C4—862no—
788C22⋊C4—862no—
789C22⋊C4—862no—
790C22⋊C4—862no—
791C22⋊C4—862no—
792C22⋊C4—862no—
793C22⋊C4C2×C22⋊D4312yes—
794C22⋊C4C2×C22⋊D4312yes—
795C22⋊C4C2×C22⋊D4312yes—
796C22⋊C4C2×C22⋊D4312yes—
797C42—862no—
798C42—862no—
799C42C2×C22⋊D4312yes—
800C42C23×D4312yes—
801C23—24no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—42no—
810C23—42no—
811C23—862no—
812C23—3441no—
813C23—3441no—
814C23—1722no—
815C23C22×C22⋊D4311yescharacteristic
816C23C22×C22⋊D4312yes—
817C23C22×C22⋊D4311yescharacteristic
818C23C22×C22⋊D4311yescharacteristic
819Q8—22no—
820Q8—24no—
821Q8—22no—
822Q8—42no—
823Q8—42no—
824Q8—864no—
825Q8—3441no—
826D4—24no—
827D4—22no—
828D4—42no—
829D4—42no—
830D4—44no—
831D4—48no—
832D4—44no—
833D4—864no—
834D4—3441no—
835D4—3442no—
836D4—3442no—
837D4—1724no—
838D4—1724no—
839D4#1306337014yes—
840C2×C4—22no—
841C2×C4—24no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—42no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—48no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—48no—
858C2×C4—42no—
859C2×C4—42no—
860C2×C4—42no—
861C2×C4—862no—
862C2×C4—862no—
863C2×C4—862no—
864C2×C4—3442no—
865C2×C4—3442no—
866C2×C4—3441no—
867C2×C4—3441no—
868C2×C4—1722no—
869C2×C4C22×C22⋊D4312yes—
870C2×C4C22×C22⋊D4312yes—
871C2×C4C22×C22⋊D4311yescharacteristic
872C2×C4C22×C22⋊D4312yes—
873C2×C4C22×C22⋊D4311yescharacteristic
874C2×C4C22×C22⋊D4311yescharacteristic
875C2×C4C24×D4311yescharacteristic
876C8—864no—
877C8—864no—
878C22—21no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—22no—
885C22—21no—
886C22—21no—
887C22—22no—
888C22—21no—
889C22—24no—
890C22—48no—
891C22—42no—
892C22—42no—
893C22—82no—
894C22—82no—
895C22—1722no—
896C22—1722no—
897C22—1722no—
898C22—6882no—
899C22#1458369712yes—
900C22C23×C22⋊D4311yescharacteristic
901C4—22no—
902C4—22no—
903C4—22no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—42no—
908C4—42no—
909C4—42no—
910C4—1722no—
911C4—1722no—
912C4—1722no—
913C4C2×#1306337012yes—
914C2—22no—
915C2—41no—
916C2—41no—
917C2—42no—
918C2—44no—
919C2—3442no—
920C2#1914823011yescharacteristic
921C2C2×#1458369711yescharacteristic
922C2#1914938211yescharacteristic
subgroupG/H
centerC22C23×C22⋊D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#547C2
socleC22×C43C23×D4
hypercenterC2×#547D43
hypocenterC43#61575
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. #19148434C2semidirect
2. #19146691C2semidirect
3. #19146571C2semidirect
4. #19146146C2semidirect
5. #19146121C2semidirect
6. #19145622C2semidirect
7. #19145416C2semidirect
8. #19145397C2semidirect
9. #19145376C2semidirect
10. #19144733C2semidirect
11. #19143855C2semidirect
12. #19143847C2semidirect
13. #19143813C2semidirect
14. #19143624C2semidirect
15. C2×C43×#547C2semidirect
16. C2×#13063355C22semidirect
17. C2×#13063350C22semidirect
18. C2×#13063345C22semidirect
20. #14583595C22semidirect
21. #14583589C22semidirect
23. #14583558C22semidirect
24. #14583545C22semidirect
33. #14583291C22semidirect
34. #14583267C22semidirect
35. #14583237C22semidirect
36. #14583232C22semidirect
37. #14583229C22semidirect
38. #14583227C22semidirect
40. #14583199C22semidirect
41. #14583155C22semidirect
42. #14583147C22semidirect
43. #14583138C22semidirect
44. #14583130C22semidirect
45. #14583114C22semidirect
46. #14583106C22semidirect
47. #14583101C22semidirect
48. #14583061C22semidirect
49. #14583061C22semidirect
50. #14583059C22semidirect
51. #14583055C22semidirect
52. #14583055C22semidirect
53. #14583054C22semidirect
54. #14583050C22semidirect
55. #14583049C22semidirect
56. #14583044C22semidirect
57. #14583044C22semidirect
61. #14583009C22semidirect
62. #14582999C22semidirect
63. #14582971C22semidirect
64. #14582971C22semidirect
65. #14582956C22semidirect
66. #14582900C22semidirect
67. #14582900C22semidirect
68. #14582895C22semidirect
71. C2×C22⋊(C43⋊C8)C22semidirect
73. C22×#41×C43C22semidirect
77. C43×#547C22semidirect
78. C2×C4⋊Q8×C43C22semidirect
82. C2×C22⋊Q8×C43C22semidirect
85. C2×C4×D4×C43C22semidirect
454. C2×#547D43semidirect
478. C22×#41C2×D43semidirect
490. #547C2×D43semidirect
495. C2×C4⋊Q8C2×D43semidirect
502. C2×C22⋊Q8C2×D43semidirect
507. C2×C4×D4C2×D43semidirect
548. C43#61575semidirect

Maximal subgroups

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

subgroupindex
#191484342
#191466912
#191465712
#191461462
#191461212
#191456222
#191454162
#191453972
#191453762
#191447332
#191438552
#191438472
#191438132
#191436242
C2×C43×#5472
#6157543