Finite Group Databasebeta

← #25977191

Subgroups — #25977191

Order 11008.

1826 conjugacy classes of subgroups.

The subgroup lattice has 1238 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#41×Dic86C211yesmaximal, characteristic, complemented
2C2×#14583605C211yesmaximal, characteristic, complemented
3#19147553C212yesmaximal, complemented
4#19147552C212yesmaximal, complemented
5#19147543C212yesmaximal, complemented
6#19147538C212yesmaximal, complemented
7#19147508C212yesmaximal, complemented
8#19147497C212yesmaximal, complemented
9#19147473C212yesmaximal, complemented
10#19147457C212yesmaximal, complemented
11#19145145C211yesmaximal, characteristic, complemented
12#19145144C211yesmaximal, characteristic, complemented
13#19145139C211yesmaximal, characteristic, complemented
14#19144415C211yesmaximal, characteristic, complemented
15#19144406C211yesmaximal, characteristic, complemented
16#19144394C211yesmaximal, characteristic, complemented
17#19144391C211yesmaximal, characteristic, complemented
18#19144391C211yesmaximal, characteristic, complemented
19#19143546C211yesmaximal, characteristic, complemented
20#19143408C211yesmaximal, characteristic
21#19143408C211yesmaximal, characteristic
22C4×#13063350C211yesmaximal, characteristic
23C43×#3080C211yesmaximal, characteristic, complemented
24C2×#13063350C2211yescharacteristic
25Q8×Dic86C2211yescharacteristic, complemented
26#14583628C2211yescharacteristic, complemented
27#14583625C2211yescharacteristic, complemented
28#14583625C2211yescharacteristic, complemented
29#14583608—21no—
30#14583608—21no—
31#14583608C2211yescharacteristic, complemented
32#14583608C2211yescharacteristic, complemented
33#14583606—21no—
34#14583606C2211yescharacteristic, complemented
35#14583605—21no—
36#14583605—21no—
37#14583605—21no—
38#14583605—21no—
39#14583605C2212yes—
40#14583605C2212yes—
41#14583605C2212yes—
42#14583605C2212yes—
43D4×Dic86—21no—
44D4×Dic86C2211yescharacteristic, complemented
45#14583456—21no—
46#14583456C2211yescharacteristic
47#14583452—21no—
48#14583452—21no—
49#14583452C2211yescharacteristic
50#14583452C2211yescharacteristic
51C2×#13063324C2211yescharacteristic
52C2×#13063316C2211yescharacteristic
53C2×#13063305—21no—
54C2×#13063303—21no—
55C2×#13063303—21no—
56#41×Dic43C2211yescharacteristic
57#41×Dic43C2211yescharacteristic
58C2×C4×Dic86—21no—
59C2×C4×Dic86C2211yescharacteristic
60C2×C4×D172C2211yescharacteristic
61C2×#13063287C2211yescharacteristic
62C2×#13063287C2211yescharacteristic
63C2×C4⋊C4×D43—21no—
64#14583309C2212yescomplemented
65#14583309C2212yescomplemented
66#14583307C2212yescomplemented
67#14583307C2212yescomplemented
68#14583306C2212yescomplemented
69#14583306C2212yescomplemented
70#14583303C2212yescomplemented
71#14583300C2212yescomplemented
72#14583299C2212yescomplemented
73#14583298C2212yescomplemented
74#14583298C2212yescomplemented
75#14583296C2212yescomplemented
76#14583208C2212yescomplemented
77#14583204C2212yescomplemented
78#14583202C2212yes—
79#14583202C2212yes—
80#14583201C2212yescomplemented
81#14583200C2212yes—
82#14583200C2212yes—
83#14583198C2212yes—
84#14583198C2212yes—
85#14583197C2212yescomplemented
86#14583192C2212yescomplemented
87#14583190C2212yes—
88#14583188C2212yes—
89#14583188C2212yes—
90#14583187C2212yescomplemented
91#14583182C2212yescomplemented
92#14583180C2212yes—
93#14583178C2212yes—
94#14583178C2212yes—
95#14583177C2212yescomplemented
96#14583028C2212yescomplemented
97#14583028C2212yescomplemented
98#14583026C2212yescomplemented
99#14583023C2212yescomplemented
100#14583009C2212yes—
101#14583008C2212yes—
102#14583008C2212yes—
103#14583002C2212yes—
104#14583002C2212yes—
105#14582997C2212yes—
106C4×#10621884C2212yes—
107#14582984C2212yes—
108#14582984C2212yes—
109C4×#10621882C2212yes—
110#14582979C2212yes—
111#14582979C2212yes—
112#14582942C2211yescharacteristic
113#14582941C2211yescharacteristic
114#14582941C2211yescharacteristic
115#14582939C2211yescharacteristic
116#14582939C2211yescharacteristic
117#14582939C2211yescharacteristic
118#14582939C2211yescharacteristic
119#14582922C2211yescharacteristic
120#14582922C2211yescharacteristic
121#14582905C2211yescharacteristic
122#14582905C2211yescharacteristic
123#14582903C2211yescharacteristic
124#14582900C2211yescharacteristic
125C4×#10621877C2211yescharacteristic
126M16×Dic43C2211yescharacteristic
127M16×Dic43C2211yescharacteristic
128C2×#125×C43C2211yescharacteristic
129C4×#41×C43C2211yescharacteristic
130C43×#479C2212yescomplemented
131C43×#479C2212yescomplemented
132C43×#478C2212yescomplemented
133C43×#478C2212yescomplemented
134C43×#428C2211yescharacteristic
135C43×#428C2211yescharacteristic
136C43×#423C2211yescharacteristic
137C43×#417C2211yescharacteristic
138C43×#417C2211yescharacteristic
139C22×Dic86—21no—
140C22×Dic86—21no—
141C22×Dic86D411yescharacteristic
142C22×D172C2311yescharacteristic
143C22×C4×D43—21no—
144C22×C4×D43—21no—
145C22×C4×D43—21no—
146#13063350Q818yescomplemented
147C2×#10621884C2312yes—
148C2×#10621882C2312yes—
149C2×#10621877C2311yescharacteristic
150C2×#10621877C2311yescharacteristic
151#13063325—21no—
152#13063325—21no—
153#13063325C2311yescharacteristic
154#13063325C2311yescharacteristic
155#13063324—21no—
156#13063324—21no—
157#13063324—21no—
158#13063324—21no—
159#13063324—21no—
160#13063324—21no—
161#13063324C2311yescharacteristic
162#13063324C2312yes—
163#13063324C2311yescharacteristic
164#13063324C2311yescharacteristic
165#13063324C2312yes—
166#13063324C2311yescharacteristic
167#13063317—21no—
168#13063317—21no—
169#13063317C2311yescharacteristic
170#13063317C2311yescharacteristic
171#13063316—21no—
172#13063316—21no—
173#13063316—21no—
174#13063316—21no—
175#13063316—21no—
176#13063316—21no—
177#13063316C2311yescharacteristic
178#13063316C2312yes—
179#13063316C2311yescharacteristic
180#13063316C2311yescharacteristic
181#13063316C2312yes—
182#13063316C2311yescharacteristic
183#13063305—22no—
184#13063305—22no—
185#13063305—22no—
186#13063305—22no—
187#13063304—21no—
188#13063304—21no—
189#13063304—21no—
190#13063304—21no—
191#13063304—21no—
192#13063304—21no—
193#13063303—22no—
194#13063303—22no—
195#13063303—22no—
196#13063303—22no—
197#13063303—22no—
198#13063303—22no—
199#13063303—22no—
200#13063303—22no—
201#13063302—21no—
202#13063302—21no—
203#13063302—21no—
204#13063302—21no—
205#13063302—21no—
206#13063302—21no—
207#13063302—21no—
208#13063302—21no—
209#13063302—21no—
210#13063302—21no—
211#13063302—21no—
212#13063302—21no—
213Q8×Dic43C2311yescharacteristic
214Q8×Dic43C2311yescharacteristic
215Q8×Dic43C2311yescharacteristic
216Q8×Dic43C2311yescharacteristic
217C4×Dic86—21no—
218C4×Dic86—21no—
219C4×Dic86—21no—
220C4×Dic86—21no—
221C4×Dic86—21no—
222C4×Dic86—21no—
223C4×Dic86—21no—
224C4×Dic86—21no—
225C4×Dic86—21no—
226C4×Dic86—21no—
227C4×Dic86D411yescharacteristic
228C4×Dic86D411yescharacteristic
229C4×Dic86D411yescharacteristic
230C4×Dic86D411yescharacteristic
231C4×Dic86C2311yescharacteristic
232C4×Dic86C2311yescharacteristic
233C4×Dic86C2311yescharacteristic
234C4×Dic86C2311yescharacteristic
235C4×D172—21no—
236C4×D172—21no—
237C4×D172C2312yes—
238C4×D172C2312yes—
239D4×Dic43—21no—
240D4×Dic43—21no—
241D4×Dic43—21no—
242D4×Dic43—21no—
243D4×Dic43C2311yescharacteristic
244D4×Dic43C2311yescharacteristic
245D4×Dic43C2311yescharacteristic
246D4×Dic43C2311yescharacteristic
247#13063287—21no—
248#13063287—21no—
249#13063287—21no—
250#13063287—21no—
251#13063287C2312yes—
252#13063287C2312yes—
253#13063287C2312yes—
254#13063287C2312yes—
255#13063284—21no—
256#13063284—21no—
257#13063284C2311yescharacteristic
258#13063284C2311yescharacteristic
259C2×C4⋊Dic43—21no—
260C2×C4⋊Dic43—21no—
261C2×C4⋊Dic43D411yescharacteristic
262C2×C4⋊Dic43C2311yescharacteristic
263C2×Dic43⋊C4—21no—
264C2×Dic43⋊C4—21no—
265C2×Dic43⋊C4—21no—
266C2×Dic43⋊C4—21no—
267C2×Dic43⋊C4D411yescharacteristic
268C2×Dic43⋊C4D411yescharacteristic
269C4⋊C4×D43—22no—
270C4⋊C4×D43—22no—
271C4⋊C4×D43—22no—
272C4⋊C4×D43—22no—
273C2×(C2×D43)⋊C4—21no—
274C2×(C2×D43)⋊C4—21no—
275C2×(C2×D43)⋊C4—21no—
276C2×C4×Dic43—21no—
277C2×C4×Dic43—21no—
278C2×C4×Dic43C2311yescharacteristic
279C2×C4×Dic43C2311yescharacteristic
280#13063259C2312yes—
281#13063259C2312yes—
282#13063258C2312yes—
283#13063258C2312yes—
284#13063258C2312yes—
285#13063258C2312yes—
286#13063258C2312yes—
287#13063257C2312yes—
288#13063257C2312yes—
289#13063256C2312yes—
290#13063256C2312yes—
291#13063256C2312yes—
292#13063256C2312yes—
293#13063256C2312yes—
294Dic43⋊C8C2312yes—
295Dic43⋊C8C2312yes—
296Dic43⋊C8C2312yes—
297Dic43⋊C8C2312yes—
298#13063249C2312yes—
299#13063247C2312yes—
300#13063247C2312yes—
301#13063247C2312yes—
302#13063247C2312yes—
303#13063246C2312yes—
304#13063245C2312yes—
305#13063245C2312yes—
306#13063236C2312yes—
307#13063235C2312yes—
308#13063235C2312yes—
309C4×C43⋊C8C2312yes—
310C8×Dic43C2312yes—
311C8×Dic43C2312yes—
312C2×#41×C43C2311yescharacteristic
313C2×M16×C43C2311yescharacteristic
314C2×M16×C43C2311yescharacteristic
315#125×C43—21no—
316#125×C43—21no—
317#125×C43C2312yes—
318#125×C43C2312yes—
319C4×Q8×C43C2311yescharacteristic
320C4×Q8×C43C2311yescharacteristic
321C4×D4×C43—21no—
322C4×D4×C43—21no—
323C4×D4×C43C2311yescharacteristic
324C4×D4×C43C2311yescharacteristic
325#117×C43—21no—
326#117×C43C2311yescharacteristic
327C2×C4⋊C4×C43—21no—
328C2×C4⋊C4×C43—21no—
329C2×C4⋊C4×C43C2311yescharacteristic
330C2×C4⋊C4×C43C2311yescharacteristic
331C2×C42×C43—21no—
332C2×C42×C43C2311yescharacteristic
333#107×C43C2312yes—
334#107×C43C2312yes—
335#106×C43C2312yes—
336#106×C43C2312yes—
337C4⋊C8×C43C2312yes—
338C4⋊C8×C43C2312yes—
339#103×C43C2312yes—
340#103×C43C2312yes—
341#102×C43C2312yes—
342#102×C43C2312yes—
343C23×D43—21no—
344#41×C43—22no—
345#41×C43C2×Q814yes—
346C2×Q8×C43C2411yescharacteristic
347C2×D4×C43—21no—
348C2×D4×C43C2411yescharacteristic
349C22×C4×C43—21no—
350C22×C4×C43—21no—
351C22×C4×C43—21no—
352C22×C4×C43—21no—
353C22×C4×C43—21no—
354C22×C4×C43C2×D411yescharacteristic
355C22×C4×C43C2×D411yescharacteristic
356C22×C4×C43C2411yescharacteristic
357C22×Dic43—21no—
358C22×Dic43—21no—
359C22×Dic43—21no—
360C22×Dic43—21no—
361C22×Dic43—21no—
362C22×Dic43C2×D411yescharacteristic
363C22×Dic43C2×D411yescharacteristic
364C22×Dic43C2×D411yescharacteristic
365C22×Dic43C2×D411yescharacteristic
366C2×D172—21no—
367C2×D172—22no—
368C2×D172C2×Q814yescomplemented
369C2×D172C2412yes—
370C2×C4×D43—22no—
371C2×C4×D43—22no—
372C2×C4×D43—22no—
373C2×C4×D43—22no—
374C2×C4×D43—22no—
375C2×C4×D43—22no—
376C2×C4×D43—44no—
377C2×C4×D43—82no—
378C2×C4×D43—82no—
379C2×Dic86—21no—
380C2×Dic86—21no—
381C2×Dic86—21no—
382C2×Dic86—21no—
383C2×Dic86—21no—
384C2×Dic86—21no—
385C2×Dic86—22no—
386C2×Dic86—22no—
387C2×Dic86—42no—
388C2×Dic86—44no—
389C2×Dic86—82no—
390C2×Dic86C2×D411yescharacteristic
391C2×Dic86C2×D411yescharacteristic
392C2×Dic86C2×D411yescharacteristic
393C2×Dic86C2×D411yescharacteristic
394M16×C43—22no—
395M16×C43—22no—
396C2×C8×C43C2412yes—
397C2×C8×C43C2412yes—
398C4⋊C4×C43—22no—
399C4⋊C4×C43—22no—
400C4⋊C4×C43—22no—
401C4⋊C4×C43—22no—
402C4⋊C4×C43—21no—
403C4⋊C4×C43—21no—
404C4⋊C4×C43—21no—
405C4⋊C4×C43—21no—
406C4⋊C4×C43C2412yes—
407C4⋊C4×C43C2412yes—
408C4⋊C4×C43C2411yescharacteristic
409C4⋊C4×C43C2411yescharacteristic
410C22⋊C4×C43—21no—
411C22⋊C4×C43—21no—
412C22⋊C4×C43—21no—
413C42×C43—21no—
414C42×C43—21no—
415C42×C43—21no—
416C42×C43C2×D411yescharacteristic
417C42×C43C2×D411yescharacteristic
418C42×C43C2411yescharacteristic
419C42×C43C2411yescharacteristic
420C22⋊Dic43—21no—
421C22⋊Dic43—21no—
422C22⋊Dic43—21no—
423C22⋊Dic43—21no—
424C22⋊Dic43—21no—
425C22⋊Dic43—21no—
426#10621884C2×Q818yescomplemented
427#10621882C2×Q818yescomplemented
428(C2×D43)⋊C4—22no—
429(C2×D43)⋊C4—22no—
430(C2×D43)⋊C4—22no—
431(C2×D43)⋊C4—22no—
432(C2×D43)⋊C4—22no—
433(C2×D43)⋊C4—22no—
434C4⋊Dic43—21no—
435C4⋊Dic43—21no—
436C4⋊Dic43—21no—
437C4⋊Dic43—22no—
438C4⋊Dic43—22no—
439C4⋊Dic43—21no—
440C4⋊Dic43—21no—
441C4⋊Dic43—21no—
442C4⋊Dic43—21no—
443C4⋊Dic43—21no—
444C4⋊Dic43—21no—
445C4⋊Dic43—21no—
446C4⋊Dic43—21no—
447C4⋊Dic43C2×D411yescharacteristic
448C4⋊Dic43C2×D411yescharacteristic
449C4⋊Dic43C2×D411yescharacteristic
450C4⋊Dic43C2×D411yescharacteristic
451C4⋊Dic43C2412yes—
452C4⋊Dic43C2411yescharacteristic
453C4⋊Dic43C2411yescharacteristic
454C4⋊Dic43C2411yescharacteristic
455C4⋊Dic43C2411yescharacteristic
456Dic43⋊C4—21no—
457Dic43⋊C4—21no—
458Dic43⋊C4—21no—
459Dic43⋊C4—21no—
460Dic43⋊C4—22no—
461Dic43⋊C4—22no—
462Dic43⋊C4—21no—
463Dic43⋊C4—21no—
464Dic43⋊C4—21no—
465Dic43⋊C4—21no—
466Dic43⋊C4—22no—
467Dic43⋊C4—22no—
468Dic43⋊C4—21no—
469Dic43⋊C4—21no—
470Dic43⋊C4—21no—
471Dic43⋊C4—21no—
472Dic43⋊C4C2×D411yescharacteristic
473Dic43⋊C4C2×D411yescharacteristic
474Dic43⋊C4C2×D411yescharacteristic
475Dic43⋊C4C2×D411yescharacteristic
476Dic43⋊C4C2×D411yescharacteristic
477Dic43⋊C4C2×D411yescharacteristic
478Dic43⋊C4C2×D411yescharacteristic
479Dic43⋊C4C2×D411yescharacteristic
480C4×Dic43—21no—
481C4×Dic43—21no—
482C4×Dic43—21no—
483C4×Dic43—21no—
484C4×Dic43—21no—
485C4×Dic43—21no—
486C4×Dic43C2×D411yescharacteristic
487C4×Dic43C2×D411yescharacteristic
488C4×Dic43C2×D411yescharacteristic
489C4×Dic43C2×D411yescharacteristic
490C4×Dic43C2411yescharacteristic
491C4×Dic43C2411yescharacteristic
492C4×Dic43C2411yescharacteristic
493C4×Dic43C2411yescharacteristic
494#10621877—22no—
495#10621877C2×Q814yescomplemented
496C2×C43⋊C8C2412yes—
497C2×C43⋊C8C2412yes—
498C23×C43—21no—
499C23×C43C22×D411yescharacteristic
500C22×D43—24no—
501C22×D43—22no—
502C22×D43—42no—
503C22×D43—42no—
504Q8×C43—21no—
505Q8×C43C22×Q812yes—
506D4×C43—24no—
507D4×C43—21no—
508D4×C43C22×Q812yes—
509C2×C4×C43—21no—
510C2×C4×C43—24no—
511C2×C4×C43—21no—
512C2×C4×C43—21no—
513C2×C4×C43—22no—
514C2×C4×C43—22no—
515C2×C4×C43—41no—
516C2×C4×C43—41no—
517C2×C4×C43—42no—
518C2×C4×C43—42no—
519C2×C4×C43—42no—
520C2×C4×C43—81no—
521C2×C4×C43C22×D411yescharacteristic
522C2×C4×C43C22×D411yescharacteristic
523C2×C4×C43C22×D411yescharacteristic
524C2×C4×C43C22×D411yescharacteristic
525C2×C4×C43C22×D411yescharacteristic
526C2×C4×C43C22×Q812yes—
527C2×C4×C432−1+412yes—
528C2×C4×C43C2511yescharacteristic
529C2×Dic43—22no—
530C2×Dic43—21no—
531C2×Dic43—21no—
532C2×Dic43—21no—
533C2×Dic43—21no—
534C2×Dic43—22no—
535C2×Dic43—41no—
536C2×Dic43—41no—
537C2×Dic43—41no—
538C2×Dic43—42no—
539C2×Dic43—42no—
540C2×Dic43—42no—
541C2×Dic43—81no—
542C2×Dic43—81no—
543C2×Dic43C22×D411yescharacteristic
544C2×Dic43C22×D411yescharacteristic
545C2×Dic43C22×D411yescharacteristic
546C2×Dic43C22×D411yescharacteristic
547C2×Dic43C22×D411yescharacteristic
548C2×Dic43C22×D411yescharacteristic
549C2×Dic43C22×D411yescharacteristic
550C2×Dic43C22×D411yescharacteristic
551D172—24no—
552D172—22no—
553D172C22×Q814yes—
554C4×D43—44no—
555C4×D43—44no—
556C4×D43—82no—
557C4×D43—82no—
558C4×D43—82no—
559C4×D43—82no—
560Dic86—22no—
561Dic86—22no—
562Dic86—41no—
563Dic86—41no—
564Dic86—42no—
565Dic86—42no—
566Dic86—42no—
567Dic86—81no—
568Dic86—81no—
569Dic86—82no—
570Dic86—82no—
571Dic86—81no—
572C8×C43—22no—
573C8×C43—22no—
574C43⋊C8—22no—
575C43⋊C8C22×Q814yes—
576#61367—431nomaximal, Sylow
577C22×C43—21no—
578C22×C43—21no—
579C22×C43—22no—
580C22×C43—41no—
581C22×C43—41no—
582C22×C43D4×Q812yes—
583C22×C43C23×D411yescharacteristic
584C2×D43—24no—
585C2×D43—48no—
586C2×D43—42no—
587C2×D43—42no—
588C4×C43—21no—
589C4×C43—21no—
590C4×C43—22no—
591C4×C43—21no—
592C4×C43—21no—
593C4×C43—42no—
594C4×C43—41no—
595C4×C43—41no—
596C4×C43—42no—
597C4×C43D4×Q812yes—
598C4×C43C23×Q811yescharacteristic
599C4×C43C2×2−1+411yescharacteristic
600Dic43—21no—
601Dic43—21no—
602Dic43—21no—
603Dic43—21no—
604Dic43—21no—
605Dic43—21no—
606Dic43—21no—
607Dic43—42no—
608Dic43—41no—
609Dic43—41no—
610Dic43—41no—
611Dic43—41no—
612Dic43#57512yes—
613Q8×#41—431no—
614C2×#554—431no—
615#3389—432no—
616#3389—432no—
617#3388—432no—
618#3388—432no—
619#3385—432no—
620#3384—432no—
621#3381—432no—
622#3380—432no—
623#3166—431no—
624#3166—431no—
625#3165—431no—
626#3080—431no—
627#3080D4311yescharacteristic, complemented
628#3079—431no—
629#3077—431no—
630#3077—431no—
631#3077—431no—
632Q8×M16—431no—
633C4×AGL(1,ℤ/8)—431no—
634C4×AGL(1,ℤ/8)—431no—
635C4×AGL(1,ℤ/8)—431no—
636C2×C43—22no—
637C2×C43—42no—
638C2×C43C2×D4×Q811yescharacteristic
639C2×C43C2×#57511yescharacteristic
640C2×C43#358511yescharacteristic
641D43—44no—
642C2×AGL(1,ℤ/8)—431no—
643Q82—431no—
644#557—431no—
645#557—431no—
646#557—431no—
647#554—432no—
648#554—432no—
649#554—432no—
650#554—432no—
651#554—431no—
652#554—431no—
653#554—431no—
654#554—861no—
655#554—861no—
656#554—861no—
657#554—861no—
658#554—861no—
659#554—861no—
660#554—861no—
661D4×Q8—431no—
662D4×Q8—861no—
663#533—431no—
664#533—431no—
665#533—431no—
666#533—861no—
667#533—861no—
668#533—861no—
669C2×C4⋊Q8—431no—
670C2×#125—431no—
671C2×#125C2×D4311yescharacteristic
672C2×C22⋊Q8—861no—
673C2×C22⋊Q8—861no—
674C2×C22⋊Q8—861no—
675C4×#41—431no—
676C4×#41—431no—
677C4×#41C2×D4311yescharacteristic
678C2×C4×Q8—431no—
679C2×C4×Q8—861no—
680C2×C4×D4—431no—
681C2×C4×D4—431no—
682C2×C4×D4—431no—
683C22×C4⋊C4—861no—
684#501—432no—
685#501—432no—
686#501—432no—
687#501—432no—
688#501—432no—
689#501—432no—
690#500—432no—
691#499—432no—
692#499—432no—
693#499—432no—
694#499—432no—
695#498—432no—
696#479—432no—
697#479—432no—
698#479C2×D4312yescomplemented
699#479C2×D4312yescomplemented
700#478—432no—
701#478—432no—
702#478—432no—
703#478—432no—
704#478—432no—
705#478—432no—
706#478—432no—
707#478—432no—
708#478C2×D4312yescomplemented
709#478C2×D4312yescomplemented
710#477—432no—
711#476—432no—
712#476—432no—
713#476—432no—
714#476—432no—
715#475—432no—
716#474—432no—
717#474—432no—
718#474—432no—
719#474—432no—
720#446—432no—
721#446—432no—
722#446—432no—
723C8×Q8—432no—
724#442—432no—
725#442—432no—
726#442—432no—
727#440—432no—
728#440—432no—
729#440—432no—
730C4×SD16—432no—
731C4×SD16—432no—
732C4×SD16—432no—
733C4×D8—432no—
734C4×D8—432no—
735C4×D8—432no—
736#428—431no—
737#428—431no—
738#428—431no—
739#428—431no—
740#428—431no—
741#428—431no—
742#428—431no—
743#428C2×D4311yescharacteristic
744#428C2×D4311yescharacteristic
745#423—431no—
746#423—431no—
747#423C2×D4311yescharacteristic
748#418—431no—
749#418—431no—
750#418—431no—
751#417—431no—
752#417C2×D4311yescharacteristic
753#417C2×D4311yescharacteristic
754C4×M16—431no—
755C4×M16—431no—
756C4×M16—431no—
757C43#6136711yescharacteristic, complemented, Sylow
758C2×#41C22×D4311yescharacteristic
759C22×Q8—431no—
760C22×Q8—861no—
761C22×Q8—861no—
762C22×D4—431no—
763C23×C4—861no—
764C23×C4—861no—
765C23×C4—861no—
766AGL(1,ℤ/8)—438no—
767C2×SD16—432no—
768C2×D8—432no—
769C2×M16—431no—
770C2×M16—431no—
771C2×M16C22×D4311yescharacteristic
772C2×M16C22×D4311yescharacteristic
773C4⋊Q8—432no—
774C4⋊Q8—432no—
775C4⋊Q8—431no—
776C4⋊Q8—431no—
777C4⋊Q8—431no—
778C4⋊Q8—431no—
779C4⋊Q8—431no—
780C4⋊Q8—431no—
781C4⋊Q8—861no—
782C4⋊Q8—861no—
783C4⋊Q8—861no—
784C4⋊Q8—861no—
785C4⋊Q8—861no—
786C4⋊Q8—861no—
787C4⋊Q8—861no—
788C4⋊Q8—861no—
789#125—21no—
790#125—21no—
791#125—432no—
792#125—432no—
793#125—431no—
794#125—431no—
795#125—431no—
796#125—431no—
797#125—431no—
798#125—431no—
799#125—861no—
800#125—861no—
801#125—861no—
802#125—861no—
803#125—861no—
804#125—861no—
805#125—861no—
806#125—861no—
807#125C22×D4312yes—
808#125C22×D4312yes—
809C22⋊Q8—861no—
810C22⋊Q8—861no—
811C22⋊Q8—861no—
812C22⋊Q8—861no—
813C22⋊Q8—861no—
814C22⋊Q8—861no—
815C22⋊Q8—861no—
816C22⋊Q8—861no—
817C22⋊Q8—861no—
818C22⋊Q8—861no—
819C22⋊Q8—861no—
820C22⋊Q8—861no—
821C22⋊Q8—862no—
822C22⋊Q8—862no—
823C22⋊Q8—862no—
824C22⋊Q8—862no—
825C22⋊Q8—862no—
826C22⋊Q8—862no—
827C22⋊Q8—862no—
828C22⋊Q8—862no—
829C22⋊Q8—862no—
830C22⋊Q8—862no—
831C22⋊Q8—862no—
832C22⋊Q8—862no—
833C22⋊Q8—861no—
834C22⋊Q8—861no—
835C22⋊Q8—861no—
836C22⋊Q8—861no—
837C22⋊Q8—861no—
838C22⋊Q8—861no—
839C4×Q8—431no—
840C4×Q8—431no—
841C4×Q8—431no—
842C4×Q8—431no—
843C4×Q8—431no—
844C4×Q8—431no—
845C4×Q8—431no—
846C4×Q8—431no—
847C4×Q8—431no—
848C4×Q8—431no—
849C4×Q8—431no—
850C4×Q8—431no—
851C4×Q8—861no—
852C4×Q8—861no—
853C4×Q8—861no—
854C4×Q8—861no—
855C4×Q8—861no—
856C4×Q8—861no—
857C4×Q8—861no—
858C4×Q8—861no—
859C4×Q8—861no—
860C4×Q8—861no—
861C4×Q8C22×D4311yescharacteristic
862C4×Q8C22×D4311yescharacteristic
863C4×D4—21no—
864C4×D4—21no—
865C4×D4—431no—
866C4×D4—431no—
867C4×D4—431no—
868C4×D4—431no—
869C4×D4—432no—
870C4×D4—432no—
871C4×D4—432no—
872C4×D4—432no—
873C4×D4—432no—
874C4×D4—432no—
875C4×D4—861no—
876C4×D4—861no—
877C4×D4—861no—
878C4×D4—861no—
879C4×D4—861no—
880C4×D4—861no—
881C4×D4—861no—
882C4×D4—861no—
883C4×D4—861no—
884C4×D4—861no—
885C4×D4C22×D4311yescharacteristic
886C4×D4C22×D4311yescharacteristic
887#117—21no—
888#117—431no—
889#117—431no—
890#117—861no—
891#117—861no—
892#117C22×D4311yescharacteristic
893C2×C4⋊C4—21no—
894C2×C4⋊C4—21no—
895C2×C4⋊C4—431no—
896C2×C4⋊C4—431no—
897C2×C4⋊C4—431no—
898C2×C4⋊C4—431no—
899C2×C4⋊C4—862no—
900C2×C4⋊C4—862no—
901C2×C4⋊C4—862no—
902C2×C4⋊C4—862no—
903C2×C4⋊C4—861no—
904C2×C4⋊C4—861no—
905C2×C4⋊C4—861no—
906C2×C4⋊C4—861no—
907C2×C4⋊C4—861no—
908C2×C4⋊C4—861no—
909C2×C4⋊C4C22×D4311yescharacteristic
910C2×C4⋊C4C22×D4311yescharacteristic
911C2×C22⋊C4—861no—
912C2×C22⋊C4—861no—
913C2×C22⋊C4—861no—
914C2×C42—21no—
915C2×C42—431no—
916C2×C42—431no—
917C2×C42—861no—
918C2×C42—861no—
919C2×C42C22×D4311yescharacteristic
920#107—432no—
921#107—432no—
922#107—432no—
923#107—432no—
924#107—432no—
925#107—432no—
926#107—432no—
927#107C22×D4312yes—
928#107C22×D4312yes—
929#106—432no—
930#106—432no—
931#106—432no—
932#106—432no—
933#106—432no—
934#106—432no—
935#106—432no—
936#106C22×D4312yes—
937#106C22×D4312yes—
938C4⋊C8—432no—
939C4⋊C8—432no—
940C4⋊C8—432no—
941C4⋊C8—432no—
942C4⋊C8C22×D4312yes—
943C4⋊C8C22×D4312yes—
944#103—432no—
945#103C22×D4312yes—
946#103C22×D4312yes—
947#102—432no—
948#102—432no—
949#102—432no—
950#102—432no—
951#102—432no—
952#102—432no—
953#102—432no—
954#102C22×D4312yes—
955#102C22×D4312yes—
956#97—432no—
957#97—432no—
958#97—432no—
959C4×C8—432no—
960C4×C8—432no—
961C4×C8—432no—
962C24—861no—
963#41—22no—
964#41Q8×D4314yes—
965C2×Q8—431no—
966C2×Q8—431no—
967C2×Q8—431no—
968C2×Q8—431no—
969C2×Q8—861no—
970C2×Q8—861no—
971C2×Q8—862no—
972C2×Q8—862no—
973C2×Q8—861no—
974C2×Q8—861no—
975C2×Q8—861no—
976C2×Q8—861no—
977C2×Q8—3442no—
978C2×Q8—1722no—
979C2×Q8—1724no—
980C2×Q8C23×D4311yescharacteristic
981C2×D4—21no—
982C2×D4—434no—
983C2×D4—432no—
984C2×D4—861no—
985C2×D4—862no—
986C2×D4C23×D4311yescharacteristic
987C22×C4—21no—
988C22×C4—21no—
989C22×C4—21no—
990C22×C4—21no—
991C22×C4—21no—
992C22×C4—431no—
993C22×C4—431no—
994C22×C4—431no—
995C22×C4—431no—
996C22×C4—862no—
997C22×C4—862no—
998C22×C4—862no—
999C22×C4—862no—
1000C22×C4—861no—
1001C22×C4—861no—
1002C22×C4—861no—
1003C22×C4—861no—
1004C22×C4—861no—
1005C22×C4—862no—
1006C22×C4—862no—
1007C22×C4—3442no—
1008C22×C4—3442no—
1009C22×C4—1724no—
1010C22×C4D4×D4311yescharacteristic
1011C22×C4D4×D4311yescharacteristic
1012C22×C4C23×D4311yescharacteristic
1013SD16—438no—
1014D8—438no—
1015M16—22no—
1016M16—22no—
1017M16—434no—
1018M16—862no—
1019C2×C8—432no—
1020C2×C8—432no—
1021C2×C8C23×D4312yes—
1022C2×C8C23×D4312yes—
1023C4⋊C4—22no—
1024C4⋊C4—22no—
1025C4⋊C4—22no—
1026C4⋊C4—22no—
1027C4⋊C4—21no—
1028C4⋊C4—21no—
1029C4⋊C4—21no—
1030C4⋊C4—21no—
1031C4⋊C4—431no—
1032C4⋊C4—431no—
1033C4⋊C4—431no—
1034C4⋊C4—431no—
1035C4⋊C4—431no—
1036C4⋊C4—431no—
1037C4⋊C4—431no—
1038C4⋊C4—431no—
1039C4⋊C4—431no—
1040C4⋊C4—431no—
1041C4⋊C4—431no—
1042C4⋊C4—431no—
1043C4⋊C4—431no—
1044C4⋊C4—431no—
1045C4⋊C4—431no—
1046C4⋊C4—431no—
1047C4⋊C4—432no—
1048C4⋊C4—862no—
1049C4⋊C4—862no—
1050C4⋊C4—862no—
1051C4⋊C4—862no—
1052C4⋊C4—861no—
1053C4⋊C4—861no—
1054C4⋊C4—861no—
1055C4⋊C4—861no—
1056C4⋊C4—861no—
1057C4⋊C4—861no—
1058C4⋊C4—862no—
1059C4⋊C4—862no—
1060C4⋊C4—861no—
1061C4⋊C4—861no—
1062C4⋊C4—861no—
1063C4⋊C4—861no—
1064C4⋊C4—861no—
1065C4⋊C4—861no—
1066C4⋊C4—861no—
1067C4⋊C4—861no—
1068C4⋊C4—861no—
1069C4⋊C4—861no—
1070C4⋊C4—861no—
1071C4⋊C4—861no—
1072C4⋊C4—861no—
1073C4⋊C4—861no—
1074C4⋊C4—861no—
1075C4⋊C4—861no—
1076C4⋊C4—861no—
1077C4⋊C4C23×D4311yescharacteristic
1078C4⋊C4C23×D4311yescharacteristic
1079C4⋊C4C23×D4312yes—
1080C4⋊C4C23×D4312yes—
1081C22⋊C4—21no—
1082C22⋊C4—21no—
1083C22⋊C4—21no—
1084C22⋊C4—862no—
1085C22⋊C4—862no—
1086C22⋊C4—862no—
1087C22⋊C4—862no—
1088C22⋊C4—861no—
1089C22⋊C4—861no—
1090C22⋊C4—861no—
1091C22⋊C4—861no—
1092C22⋊C4—861no—
1093C22⋊C4—861no—
1094C22⋊C4—862no—
1095C22⋊C4—862no—
1096C42—21no—
1097C42—21no—
1098C42—21no—
1099C42—431no—
1100C42—431no—
1101C42—431no—
1102C42—431no—
1103C42—431no—
1104C42—431no—
1105C42—431no—
1106C42—431no—
1107C42—861no—
1108C42—861no—
1109C42—861no—
1110C42—861no—
1111C42—861no—
1112C42—861no—
1113C42D4×D4311yescharacteristic
1114C42D4×D4311yescharacteristic
1115C42C23×D4311yescharacteristic
1116C42C23×D4311yescharacteristic
1117C23—21no—
1118C23—864no—
1119C23—862no—
1120C23—1722no—
1121C23—1722no—
1122C23C2×D4×D4311yescharacteristic
1123Q8—21no—
1124Q8—862no—
1125Q8—862no—
1126Q8—3441no—
1127Q8—3442no—
1128Q8—3442no—
1129Q8—3441no—
1130Q8—3441no—
1131Q8—1721no—
1132Q8—1721no—
1133Q8—1722no—
1134Q8—1722no—
1135Q8—1722no—
1136Q8C2×Q8×D4312yes—
1137D4—24no—
1138D4—21no—
1139D4—434no—
1140D4—864no—
1141D4—862no—
1142D4C2×Q8×D4312yes—
1143C2×C4—21no—
1144C2×C4—24no—
1145C2×C4—21no—
1146C2×C4—21no—
1147C2×C4—22no—
1148C2×C4—22no—
1149C2×C4—41no—
1150C2×C4—41no—
1151C2×C4—42no—
1152C2×C4—42no—
1153C2×C4—42no—
1154C2×C4—81no—
1155C2×C4—431no—
1156C2×C4—431no—
1157C2×C4—431no—
1158C2×C4—431no—
1159C2×C4—431no—
1160C2×C4—431no—
1161C2×C4—431no—
1162C2×C4—431no—
1163C2×C4—862no—
1164C2×C4—861no—
1165C2×C4—861no—
1166C2×C4—861no—
1167C2×C4—861no—
1168C2×C4—862no—
1169C2×C4—3442no—
1170C2×C4—3442no—
1171C2×C4—3442no—
1172C2×C4—3442no—
1173C2×C4—3441no—
1174C2×C4—3441no—
1175C2×C4—1724no—
1176C2×C4—1724no—
1177C2×C4—1722no—
1178C2×C4—1721no—
1179C2×C4—1721no—
1180C2×C4—1721no—
1181C2×C4—1722no—
1182C2×C4—1722no—
1183C2×C4C2×D4×D4311yescharacteristic
1184C2×C4C2×D4×D4311yescharacteristic
1185C2×C4C2×D4×D4311yescharacteristic
1186C2×C4C2×D4×D4311yescharacteristic
1187C2×C4C2×D4×D4311yescharacteristic
1188C2×C4C2×Q8×D4312yes—
1189C2×C4#1306337212yes—
1190C2×C4C24×D4311yescharacteristic
1191C8—22no—
1192C8—22no—
1193C8—434no—
1194C8—862no—
1195C22—21no—
1196C22—21no—
1197C22—22no—
1198C22—41no—
1199C22—41no—
1200C22—864no—
1201C22—1728no—
1202C22—1722no—
1203C22—1722no—
1204C22#1458356212yes—
1205C22C22×D4×D4311yescharacteristic
1206C4—21no—
1207C4—21no—
1208C4—22no—
1209C4—21no—
1210C4—21no—
1211C4—42no—
1212C4—41no—
1213C4—42no—
1214C4—41no—
1215C4—432no—
1216C4—861no—
1217C4—861no—
1218C4—861no—
1219C4—861no—
1220C4—861no—
1221C4—861no—
1222C4—861no—
1223C4—1721no—
1224C4—1721no—
1225C4—1722no—
1226C4—1721no—
1227C4—1721no—
1228C4#1458356212yes—
1229C4C22×Q8×D4311yescharacteristic
1230C4C2×#1306337211yescharacteristic
1231C2—22no—
1232C2—42no—
1233C2—1724no—
1234C2C2×#1458356211yescharacteristic
1235C2#575×D4311yescharacteristic
1236C2#1914937211yescharacteristic
subgroupG/H
centerC22C22×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC43×#3080C2
socleC22×C43C23×D4
prime radicalC2×#13063350C22
hypercenter#3080D43
hypocenterC43#61367
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3080

Complements

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

NH ≅ G/Ntype
1. #41×Dic86C2semidirect
2. C2×#14583605C2semidirect
3. #19147553C2semidirect
4. #19147552C2semidirect
5. #19147543C2semidirect
6. #19147538C2semidirect
7. #19147508C2semidirect
8. #19147497C2semidirect
9. #19147473C2semidirect
10. #19147457C2semidirect
11. #19145145C2semidirect
12. #19145144C2semidirect
13. #19145139C2semidirect
14. #19144415C2semidirect
15. #19144406C2semidirect
16. #19144394C2semidirect
17. #19144391C2semidirect
18. #19144391C2semidirect
19. #19143546C2semidirect
23. C43×#3080C2semidirect
25. Q8×Dic86C22semidirect
26. #14583628C22semidirect
27. #14583625C22semidirect
28. #14583625C22semidirect
31. #14583608C22semidirect
32. #14583608C22semidirect
34. #14583606C22semidirect
44. D4×Dic86C22semidirect
64. #14583309C22semidirect
65. #14583309C22semidirect
66. #14583307C22semidirect
67. #14583307C22semidirect
68. #14583306C22semidirect
69. #14583306C22semidirect
70. #14583303C22semidirect
71. #14583300C22semidirect
72. #14583299C22semidirect
73. #14583298C22semidirect
74. #14583298C22semidirect
75. #14583296C22semidirect
76. #14583208C22semidirect
77. #14583204C22semidirect
80. #14583201C22semidirect
85. #14583197C22semidirect
86. #14583192C22semidirect
90. #14583187C22semidirect
91. #14583182C22semidirect
95. #14583177C22semidirect
96. #14583028C22semidirect
97. #14583028C22semidirect
98. #14583026C22semidirect
99. #14583023C22semidirect
130. C43×#479C22semidirect
131. C43×#479C22semidirect
132. C43×#478C22semidirect
133. C43×#478C22semidirect
146. #13063350Q8semidirect
368. C2×D172C2×Q8semidirect
426. #10621884C2×Q8semidirect
427. #10621882C2×Q8semidirect
495. #10621877C2×Q8semidirect
627. #3080D43semidirect
698. #479C2×D43semidirect
699. #479C2×D43semidirect
708. #478C2×D43semidirect
709. #478C2×D43semidirect
757. C43#61367semidirect

Maximal subgroups

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

subgroupindex
#41×Dic862
C2×#145836052
#191475532
#191475522
#191475432
#191475382
#191475082
#191474972
#191474732
#191474572
#191451452
#191451442
#191451392
#191444152
#191444062
#191443942
#191443912
#191435462
#191434082
C4×#130633502
C43×#30802
#6136743