Finite Group Databasebeta

← #35196099

Subgroups — #35196099

Order 20224.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777824C214yesmaximal, complemented
2#23777814C211yesmaximal, characteristic, complemented
3#23777798C212yesmaximal, complemented
4#23777792C214yesmaximal, complemented
5#23777768C214yesmaximal, complemented
6#23777755C214yesmaximal, complemented
7#23777735C212yesmaximal, complemented
8#23777731C212yesmaximal, complemented
9#23777718C218yesmaximal, complemented
10#23777540C214yesmaximal, complemented
11#23777025C212yesmaximal, complemented
12#23777001C212yesmaximal, complemented
13#23776957C214yesmaximal, complemented
14D4×#11929623C214yesmaximal, complemented
15#23776813C218yesmaximal, complemented
16#23776731C214yesmaximal, complemented
17#23776695C212yesmaximal, complemented
18#532×D79C211yesmaximal, characteristic, complemented
19C79×#3549C211yesmaximal, characteristic, complemented
20C22×#11929623C2214yescomplemented
21C2×#41×D79C2212yescomplemented
22#19099313C2214yescomplemented
23#19099313C2218yescomplemented
24#19099307C22116yescomplemented
25#19099307C2218yescomplemented
26#19099302C2218yescomplemented
27#19099302C22116yescomplemented
28#19099299C2212yescomplemented
29#19099293C2212yescomplemented
30#19099283C2214yescomplemented
31#19099276C2218yescomplemented
32#19099275C2218yescomplemented
33#19099274C2214yescomplemented
34#19099270C2214yescomplemented
35#19099265C2218yescomplemented
36#19099260C2218yescomplemented
37#19099252C2218yescomplemented
38#19099252C2218yescomplemented
39#19099244C2218yescomplemented
40#19099243C22116yescomplemented
41#19099234C2214yescomplemented
42#19099233C2214yescomplemented
43#19099231C2218yescomplemented
44D4×Dic158C2214yescomplemented
45#19099219C2218yescomplemented
46#19099218C2214yescomplemented
47#19099217C2214yescomplemented
48#19099213C2218yescomplemented
49#19099210C2218yescomplemented
50#19099207C2218yescomplemented
51#19099207C2218yescomplemented
52#19099200C22116yescomplemented
53D4×C22⋊D79C2218yescomplemented
54#19099191C2218yescomplemented
55#19099182C22116yescomplemented
56#19099180C2218yescomplemented
57#19099180C2218yescomplemented
58#19099167C22116yescomplemented
59#19099166C2218yescomplemented
60#19099166C2218yescomplemented
61#19099148C22116yescomplemented
62#19099148C22116yescomplemented
63#19099142C2218yescomplemented
64#19099142C2218yescomplemented
65#19099141C2218yescomplemented
66#19099139C2214yescomplemented
67#19099134C2214yescomplemented
68#19099133C2218yescomplemented
69#19099130C2218yescomplemented
70#19099130C2214yescomplemented
71#19099126C2218yescomplemented
72#19099123C2218yescomplemented
73#19099123C2218yescomplemented
74#19099120C2212yescomplemented
75#19099118C2212yescomplemented
76#19099118C2212yescomplemented
77#19099114C2211yescharacteristic, complemented
78#19099113C2211yescharacteristic, complemented
79#19099112C2218yescomplemented
80#19099112C2212yescomplemented
81#19099111C2212yes—
82#19099111C2211yescharacteristic
83#19099111C2218yescomplemented
84#19099111C2212yescomplemented
85#19099110C2214yescomplemented
86#19099109C2212yescomplemented
87#19099108C2218yescomplemented
88#19099108C2214yescomplemented
89C4⋊Q8×D79C2211yescharacteristic, complemented
90#127×D79C2211yescharacteristic
91#19099095C2214yescomplemented
92#19099095C2214yescomplemented
93#19099094C2214yescomplemented
94#19099094C2214yescomplemented
95#19099094C2218yescomplemented
96#19099092C2214yescomplemented
97#19099092C22116yescomplemented
98#19099092C2214yescomplemented
99#124×D79C2212yescomplemented
100#19099073C2218yescomplemented
101#19099073C2214yescomplemented
102#19099073C2214yescomplemented
103#19099070C2214yescomplemented
104#19099069C22116yescomplemented
105#19099069C2218yescomplemented
106#19099069C2218yescomplemented
107#121×D79C2214yescomplemented
108#41×Dic79C2214yescomplemented
109#19099031C2218yescomplemented
110C4×#11929623C2214yescomplemented
111C4×#11929623C2214yescomplemented
112C2×D4×Dic79C2218yescomplemented
113C4×D4×D79C2214yescomplemented
114#117×D79C2214yescomplemented
115C2×C42×D79C2211yescharacteristic, complemented
116H(3,𝔽4)×C79C2214yescomplemented
117#555×C79C2214yescomplemented
118#555×C79C2212yescomplemented
119D42×C79C2214yescomplemented
120D42×C79C2212yescomplemented
121#535×C79C2214yescomplemented
122#535×C79C2218yescomplemented
123#532×C79C2211yescharacteristic
124#532×C79C2212yescomplemented
125C2×#11929625C2312yes—
126C2×#11929624C2314yes—
127C2×#11929624C2318yes—
128C2×#11929624C2312yes—
129C2×#11929623—416no—
130C2×#11929623C2314yes—
131C2×#11929623C2318yes—
132C2×#11929623C2318yes—
133C2×#11929623C2314yes—
134C2×#11929623C2312yes—
135C2×#11929623C2314yes—
136C2×#11929623C2318yes—
137#41×D79—48no—
138C22×Dic158C2314yes—
139C2×Q8×D79C2312yes—
140C22×C22⋊D79C2318yes—
141C2×D4×D79C2314yes—
142C2×D4×D79C2314yes—
143C2×D4×D79C2312yes—
144C23×Dic79C2318yes—
145C22×C4×D79C2311yescharacteristic
146C22×C4×D79C2314yes—
147C22×C4×D79C2312yes—
148#14579161C2318yes—
149#14579161C2312yes—
150#14579161C2312yes—
151#14579161C2311yescharacteristic
152#14579160C2314yes—
153#14579160C2318yes—
154#14579159C2318yes—
155#14579159C2312yes—
156#14579158C2311yescharacteristic
157#14579157C2314yes—
158#14579157C2318yes—
159#14579157C2318yes—
160#14579157C2312yes—
161#14579154C2318yes—
162#14579154C23116yes—
163#14579154C23116yes—
164#14579154C23116yes—
165#14579154C2318yes—
166#14579153C23116yes—
167#14579153C2314yes—
168#14579152C2314yes—
169#14579152C2318yes—
170#14579152C2314yes—
171#14579150C2312yes—
172#14579149C2318yes—
173#14579149C2312yes—
174#14579148C2318yes—
175#14579148C2318yes—
176#14579148C2314yes—
177#14579148C2318yes—
178#14579148C2314yes—
179#14579148C2312yes—
180#14579147C2318yes—
181#14579147C23116yes—
182#14579145C2318yes—
183#14579145C2318yes—
184#14579145C23116yes—
185#14579143C23116yes—
186#14579143C23116yes—
187#14579143C23116yes—
188#14579143C2318yes—
189#14579143C2318yes—
190#14579142C2318yes—
191#14579142C23116yes—
192#14579142C2318yes—
193#14579142C23116yes—
194#14579142C2318yes—
195#14579141C2314yes—
196#14579141C2318yes—
197#14579141C2314yes—
198#14579140C2314yes—
199#14579140C2318yes—
200#14579140C2314yes—
201#14579140C2318yes—
202#14579138C23116yes—
203#14579138C23116yes—
204#14579138C23116yes—
205#14579138C23116yes—
206#14579137C23116yes—
207#14579137C2314yes—
208#14579137C2314yes—
209#14579136C2314yes—
210#14579135C2314yes—
211#14579135C2318yes—
212#14579134C23116yes—
213#14579134C23116yes—
214#14579134C2318yes—
215#14579133C23116yes—
216#14579133C23116yes—
217#14579133C23116yes—
218#14579133C2318yes—
219#14579133C23116yes—
220#14579133C23116yes—
221#14579132C23116yes—
222#14579132C2314yes—
223#14579132C23116yes—
224#14579132C2318yes—
225#14579132C23116yes—
226#14579132C2314yes—
227#14579132C2314yes—
228#14579132C2314yes—
229#14579132C2314yes—
230#14579130C2318yes—
231#14579130C23116yes—
232#14579130C2318yes—
233#14579129C23116yes—
234#14579129C2318yes—
235Q8×Dic79C2314yes—
236Q8×Dic79C2314yes—
237C4×Dic158C2314yes—
238C4×Dic158C2314yes—
239#14579126C2318yes—
240#14579126C2314yes—
241#14579126C2314yes—
242C4×D316C2314yes—
243D4×Dic79C2314yes—
244D4×Dic79C2318yes—
245D4×Dic79C2318yes—
246D4×Dic79C2318yes—
247D4×Dic79C23116yes—
248D4×Dic79C2314yes—
249D4×Dic79C2314yes—
250D4×Dic79C2314yes—
251D4×Dic79C23116yes—
252D4×Dic79C2314yes—
253D4×Dic79C2318yes—
254#14579123C2318yes—
255#14579123C2314yes—
256C4×C22⋊D79C2318yes—
257C4×C22⋊D79C2318yes—
258C4×C22⋊D79C2318yes—
259(C22⋊D79)⋊C4C23116yes—
260(C22⋊D79)⋊C4C2318yes—
261(C22⋊D79)⋊C4C2318yes—
262(C22⋊D79)⋊C4C2318yes—
263(C22⋊D79)⋊C4C23116yes—
264#14579120C2314yes—
265#14579120C2318yes—
266#14579120C2314yes—
267#14579119C2314yes—
268#14579119C2314yes—
269#14579118C23116yes—
270#14579118C2318yes—
271#14579117C2318yes—
272#14579117C2318yes—
273#14579117C2318yes—
274C2×C4⋊Dic79C2318yes—
275C4⋊C4×D79C2318yes—
276C4⋊C4×D79C2314yes—
277C2×C22⋊Dic79C23116yes—
278C22⋊C4×D79C2318yes—
279C22⋊C4×D79C2318yes—
280C2×C4×Dic79C2312yes—
281C2×C4×Dic79C2311yescharacteristic
282C2×C4×Dic79C2318yes—
283C42×D79C2312yes—
284C42×D79C2311yescharacteristic
285C42×D79C2311yescharacteristic
286C42×D79C2311yescharacteristic
287C42×D79C2311yescharacteristic
288C42×D79C2312yes—
289C42×D79C2318yes—
290C2×#41×C79C2314yes—
291C2×#41×C79C2312yes—
292C22×D4×C79C2318yes—
293C22×D4×C79C2314yes—
294C4⋊Q8×C79C2311yescharacteristic
295C4⋊Q8×C79C2312yes—
296#127×C79C2318yes—
297#127×C79C2312yes—
298#127×C79C2311yescharacteristic
299#124×C79C23116yes—
300#124×C79C2312yes—
301#124×C79C2314yes—
302#124×C79C2318yes—
303#121×C79C2314yes—
304#121×C79C2318yes—
305#121×C79C2314yes—
306#121×C79C2318yes—
307#121×C79C2314yes—
308#121×C79C2318yes—
309#120×C79C2318yes—
310#120×C79C23116yes—
311#120×C79C2318yes—
312C4×D4×C79C2314yes—
313C4×D4×C79C2314yes—
314C4×D4×C79C2314yes—
315#117×C79C2314yes—
316#117×C79C2318yes—
317C2×C42×C79C2311yescharacteristic
318C23×D79C2414yes—
319C23×D79C2411yescharacteristic
320#11929625—44no—
321#11929624—416no—
322#11929624—48no—
323#11929624—44no—
324#11929623—216no—
325#11929623—416no—
326#11929623—416no—
327#11929623—48no—
328#11929623—48no—
329#11929623—44no—
330#11929623—416no—
331C2×Dic158—48no—
332C2×Dic158C2414yes—
333C2×Dic158C2414yes—
334C2×Dic158C2412yes—
335C2×Dic158C2414yes—
336C2×Dic158C2418yes—
337Q8×D79—44no—
338C2×D316C2414yes—
339C2×D316C2412yes—
340C2×D316C2414yes—
341C2×C22⋊D79—416no—
342C2×C22⋊D79C2418yes—
343C2×C22⋊D79C24116yes—
344C2×C22⋊D79C2414yes—
345C2×C22⋊D79C2414yes—
346C2×C22⋊D79C2414yes—
347C2×C22⋊D79C2418yes—
348C2×C22⋊D79C24116yes—
349C2×C22⋊D79C2418yes—
350D4×D79—48no—
351D4×D79—48no—
352D4×D79—44no—
353C22×Dic79—416no—
354C22×Dic79C2411yescharacteristic
355C22×Dic79C2418yes—
356C22×Dic79C2414yes—
357C22×Dic79C2418yes—
358C22×Dic79C24116yes—
359C22×Dic79C2418yes—
360C22×Dic79C2412yes—
361C2×C4×D79—24no—
362C2×C4×D79—216no—
363C2×C4×D79—44no—
364C2×C4×D79C2411yescharacteristic
365C2×C4×D79C2414yes—
366C2×C4×D79C2414yes—
367C2×C4×D79C2414yes—
368C2×C4×D79C2411yescharacteristic
369C2×C4×D79C2412yes—
370C2×C4×D79C2411yescharacteristic
371C2×C4×D79C2412yes—
372C2×C4×D79C24116yes—
373C2×C4×D79C2412yes—
374C2×C4×D79C2412yes—
375C2×C4×D79C2411yescharacteristic
376C4⋊Dic79C2414yes—
377C4⋊Dic79C2414yes—
378C4⋊Dic79C2414yes—
379C4⋊Dic79C24116yes—
380C4⋊Dic79C2418yes—
381C4⋊Dic79C2418yes—
382C4⋊Dic79C2414yes—
383C4⋊Dic79C2414yes—
384Dic79⋊C4C24116yes—
385Dic79⋊C4C2418yes—
386Dic79⋊C4C2418yes—
387Dic79⋊C4C2418yes—
388Dic79⋊C4C2418yes—
389Dic79⋊C4C2418yes—
390Dic79⋊C4C24116yes—
391C22⋊Dic79C2418yes—
392C22⋊Dic79C2418yes—
393C22⋊Dic79C2418yes—
394C22⋊Dic79C24116yes—
395C22⋊Dic79C24116yes—
396C22⋊Dic79C2418yes—
397C22⋊Dic79C2418yes—
398C22⋊Dic79C2418yes—
399C22⋊Dic79C2418yes—
400(C2×D79)⋊C4C2418yes—
401(C2×D79)⋊C4C2418yes—
402(C2×D79)⋊C4C2418yes—
403(C2×D79)⋊C4C24116yes—
404(C2×D79)⋊C4C2418yes—
405C4×Dic79C2412yes—
406C4×Dic79C2411yescharacteristic
407C4×Dic79C2412yes—
408C4×Dic79C2418yes—
409C4×Dic79C2412yes—
410C4×Dic79C2412yes—
411C4×Dic79C2412yes—
412C4×Dic79C2411yescharacteristic
413C4×Dic79C2418yes—
414C4×Dic79C2418yes—
415C4×Dic79C2418yes—
416C24×C79C2418yes—
417#41×C79—44no—
418#41×C79—48no—
419C2×Q8×C79C2412yes—
420C2×Q8×C79C2414yes—
421C2×D4×C79—48no—
422C2×D4×C79—416no—
423C2×D4×C79C2414yes—
424C2×D4×C79C2414yes—
425C2×D4×C79C2414yes—
426C2×D4×C79C2418yes—
427C2×D4×C79C2412yes—
428C2×D4×C79C2414yes—
429C2×D4×C79C2414yes—
430C2×D4×C79C24116yes—
431C2×D4×C79C2418yes—
432C22×C4×C79C2414yes—
433C22×C4×C79C2411yescharacteristic
434C22×C4×C79C2418yes—
435C22×C4×C79C2412yes—
436C4⋊C4×C79C2414yes—
437C4⋊C4×C79C2414yes—
438C4⋊C4×C79C2414yes—
439C22⋊C4×C79C2418yes—
440C22⋊C4×C79C24116yes—
441C22⋊C4×C79C2418yes—
442C22⋊C4×C79C2418yes—
443C22⋊C4×C79C2418yes—
444C42×C79C2412yes—
445C42×C79C2411yescharacteristic
446C42×C79C2411yescharacteristic
447C42×C79C2418yes—
448C23×C79—48no—
449C23×C79—416no—
450C23×C79C2514yes—
451C23×C79C2511yescharacteristic
452C23×C79C2518yes—
453C22×D79—22no—
454C22×D79—28no—
455C22×D79—42no—
456C22×D79—48no—
457C22×D79C2514yes—
458C22×D79C2511yescharacteristic
459C22×D79C2511yescharacteristic
460Q8×C79—42no—
461Q8×C79—44no—
462D4×C79—28no—
463D4×C79—28no—
464D4×C79—28no—
465D4×C79—44no—
466D4×C79—42no—
467D4×C79—48no—
468D4×C79—416no—
469D4×C79—48no—
470D4×C79—44no—
471C2×C4×C79—28no—
472C2×C4×C79—22no—
473C2×C4×C79—24no—
474C2×C4×C79—216no—
475C2×C4×C79C2512yes—
476C2×C4×C79C2518yes—
477C2×C4×C79C2514yes—
478C2×C4×C79C2511yescharacteristic
479C2×C4×C79C2511yescharacteristic
480C2×C4×C79C2512yes—
481C22⋊D79—216no—
482C22⋊D79—48no—
483C22⋊D79—44no—
484C22⋊D79—44no—
485C22⋊D79—44no—
486C22⋊D79—416no—
487C22⋊D79—48no—
488C22⋊D79—416no—
489C2×Dic79—28no—
490C2×Dic79—22no—
491C2×Dic79—216no—
492C2×Dic79—42no—
493C2×Dic79—48no—
494C2×Dic79—416no—
495C2×Dic79—48no—
496C2×Dic79C2512yes—
497C2×Dic79C2518yes—
498C2×Dic79C2512yes—
499C2×Dic79C2511yescharacteristic
500C2×Dic79C2518yes—
501C2×Dic79C2514yes—
502C2×Dic79C2511yescharacteristic
503D316—28no—
504D316—44no—
505D316—42no—
506C4×D79—22no—
507C4×D79—28no—
508C4×D79—28no—
509C4×D79—22no—
510C4×D79—24no—
511C4×D79—24no—
512C4×D79—28no—
513C4×D79—22no—
514C4×D79—42no—
515C4×D79—42no—
516C4×D79—416no—
517C4×D79H(5,𝔽2)14yes—
518Dic158—28no—
519Dic158—28no—
520Dic158—44no—
521Dic158—42no—
522Dic158—48no—
523C22×C79—28no—
524C22×C79—21no—
525C22×C79—24no—
526C22×C79—28no—
527C22×C79—28no—
528C22×C79—28no—
529C22×C79—22no—
530C22×C79—816no—
531C22×C79C2611yescharacteristic
532C2×D79—22no—
533C2×D79—24no—
534C2×D79—21no—
535C2×D79—22no—
536C2×D79—28no—
537C2×D79—44no—
538C2×D79—88no—
539C2×D79C2×H(5,𝔽2)12yes—
540C4×C79—24no—
541C4×C79—21no—
542C4×C79—28no—
543C4×C79—22no—
544C4×C79C2×H(5,𝔽2)12yes—
545C4×C79#58514yes—
546Dic79—28no—
547Dic79—21no—
548Dic79—24no—
549Dic79—22no—
550Dic79—28no—
551Dic79—22no—
552Dic79C2×H(5,𝔽2)12yes—
553#62759—791nomaximal, Sylow
554C2×C79—41no—
555C2×C79—44no—
556C2×C79—48no—
557C2×C79C22×H(5,𝔽2)11yescharacteristic
558C2×C79C2×#58512yes—
559D79—22no—
560D79—41no—
561D79—44no—
562#3551—794no—
563#3550—791no—
564#3549D7911yescharacteristic, complemented
565#3548—792no—
566#3547—794no—
567#3546—794no—
568#3545—794no—
569#3544—792no—
570#3543—792no—
571#3542—798no—
572#3529—794no—
573#3483—792no—
574#3481—792no—
575#3475—794no—
576D4×#41—794no—
577#3460—798no—
578#3449—794no—
579#3444—792no—
580C2×#532—791no—
581C79#6275911yescharacteristic, complemented, Sylow
582C22×#41—792no—
583C22×#41—794no—
584#563—798no—
585#563—794no—
586#562—7916no—
587#562—798no—
588H(3,𝔽4)C2×D7914yescomplemented
589#560—7916no—
590#560—798no—
591#559—792no—
592Q82—792no—
593#556—794no—
594#555—798no—
595#555—798no—
596#555C2×D7914yescomplemented
597#555C2×D7912yescomplemented
598#554—794no—
599#554—794no—
600#553—798no—
601#553—798no—
602#552—798no—
603#552—798no—
604#551—7916no—
605#551—798no—
606#550—794no—
607#550—798no—
608#550—794no—
609D4×Q8—794no—
610#548—798no—
611#547—798no—
612#547—794no—
613#547—794no—
614#546—798no—
615#546—798no—
616#546—798no—
617#546—7916no—
618D42—798no—
619D42C2×D7914yescomplemented
620D42C2×D7912yescomplemented
621#544—798no—
622#542—7916no—
623#542—798no—
624#542—798no—
625#540—7916no—
626#540—798no—
627#540—798no—
628#538—7916no—
629#538—7916no—
630#537—798no—
631#537—798no—
632#537—798no—
633#536—794no—
634#536—798no—
635#536—794no—
636#535—794no—
637#535—798no—
638#535—798no—
639#535C2×D7914yescomplemented
640#535C2×D7918yescomplemented
641#534—798no—
642#534—798no—
643#533—792no—
644#533—792no—
645#533—792no—
646#532—792no—
647#532—791no—
648#532—791no—
649#532—792no—
650#532—792no—
651#532—798no—
652#532—792no—
653#532—798no—
654#532—794no—
655#532—798no—
656#532—794no—
657#532—791no—
658#532C2×D7911yescharacteristic
659#532C2×D7912yescomplemented
660C2×C4⋊Q8—791no—
661C2×#127—791no—
662#529—794no—
663#529—794no—
664#529—7916no—
665#529—794no—
666#529—794no—
667#529—798no—
668#529—794no—
669#529—794no—
670C2×#124—792no—
671#525—794no—
672#525—794no—
673#525—794no—
674#525—798no—
675#525—798no—
676#525—798no—
677#525—7916no—
678C2×#121—794no—
679C4×#41—794no—
680C4×#41—794no—
681C4×#41—794no—
682C4×#41—798no—
683C2×C4×D4—798no—
684C2×C4×D4—794no—
685C2×#117—794no—
686C22×C42—791no—
687C2×#41—31616no—
688C2×#41—3168no—
689C2×#41—792no—
690C2×#41—794no—
691C2×#41—792no—
692C2×#41—794no—
693C2×#41—798no—
694C2×#41—798no—
695C2×#41—798no—
696C2×#41—794no—
697C2×#41—798no—
698C2×#41—794no—
699C2×#41—792no—
700C2×#41C22×D7914yes—
701C2×#41C22×D7912yes—
702C22×Q8—792no—
703C22×Q8—794no—
704C22×D4—798no—
705C22×D4—794no—
706C22×D4—794no—
707C22×D4—792no—
708C22×D4C22×D7918yes—
709C22×D4C22×D7914yes—
710C23×C4—798no—
711C23×C4—792no—
712C23×C4—794no—
713C23×C4—791no—
714C4⋊Q8—792no—
715C4⋊Q8—798no—
716C4⋊Q8—794no—
717C4⋊Q8—798no—
718C4⋊Q8—791no—
719C4⋊Q8—792no—
720C4⋊Q8—792no—
721C4⋊Q8—798no—
722C4⋊Q8C22×D7911yescharacteristic
723C4⋊Q8C22×D7912yes—
724#127—794no—
725#127—792no—
726#127—798no—
727#127—798no—
728#127—791no—
729#127C22×D7911yescharacteristic
730#127C22×D7912yes—
731#127C22×D7918yes—
732#126—798no—
733#126—798no—
734#126—7916no—
735#126—7916no—
736#126—7916no—
737#125—794no—
738#125—794no—
739#125—798no—
740#125—794no—
741#125—7916no—
742#124—792no—
743#124—792no—
744#124—794no—
745#124—794no—
746#124—798no—
747#124—798no—
748#124—798no—
749#124—798no—
750#124—7916no—
751#124—792no—
752#124—798no—
753#124C22×D7912yes—
754#124C22×D7914yes—
755#124C22×D79116yes—
756#124C22×D7918yes—
757#123—798no—
758#123—798no—
759#123—798no—
760#123—7916no—
761#123—7916no—
762#123—798no—
763#123—798no—
764#123—798no—
765#123—7916no—
766#123—798no—
767#123—7916no—
768#123—7916no—
769#123—7916no—
770C22⋊Q8—794no—
771C22⋊Q8—794no—
772C22⋊Q8—7916no—
773C22⋊Q8—794no—
774C22⋊Q8—794no—
775C22⋊Q8—798no—
776C22⋊Q8—798no—
777C22⋊Q8—794no—
778C22⋊Q8—794no—
779C22⋊Q8—798no—
780C22⋊Q8—7916no—
781C22⋊Q8—7916no—
782C22⋊Q8—7916no—
783C22⋊Q8—7916no—
784#121—798no—
785#121—794no—
786#121—794no—
787#121—794no—
788#121—794no—
789#121—794no—
790#121—7916no—
791#121—798no—
792#121—7916no—
793#121—7916no—
794#121—7916no—
795#121—7916no—
796#121—7916no—
797#121—7916no—
798#121—7916no—
799#121—794no—
800#121—798no—
801#121—794no—
802#121—798no—
803#121—7916no—
804#121—7916no—
805#121C22×D7914yes—
806#121C22×D7914yes—
807#121C22×D7914yes—
808#121C22×D7918yes—
809#121C22×D7918yes—
810#121C22×D7918yes—
811#120—798no—
812#120—798no—
813#120—7916no—
814#120—798no—
815#120—7916no—
816#120C22×D7918yes—
817#120C22×D7918yes—
818#120C22×D79116yes—
819C4×Q8—794no—
820C4×Q8—794no—
821C4×Q8—794no—
822C4×Q8—794no—
823C4×Q8—798no—
824C4×Q8—794no—
825C4×Q8—794no—
826C4×D4—794no—
827C4×D4—794no—
828C4×D4—7916no—
829C4×D4—798no—
830C4×D4—798no—
831C4×D4—7916no—
832C4×D4—794no—
833C4×D4—798no—
834C4×D4—798no—
835C4×D4—794no—
836C4×D4—794no—
837C4×D4—798no—
838C4×D4—798no—
839C4×D4—798no—
840C4×D4—794no—
841C4×D4—798no—
842C4×D4—798no—
843C4×D4—798no—
844C4×D4—7916no—
845C4×D4—798no—
846C4×D4—7916no—
847C4×D4—794no—
848C4×D4C22×D7914yes—
849C4×D4C22×D7914yes—
850C4×D4C22×D7914yes—
851#117—794no—
852#117—794no—
853#117—798no—
854#117—794no—
855#117—794no—
856#117—798no—
857#117—798no—
858#117—798no—
859#117—798no—
860#117—7916no—
861#117C22×D7914yes—
862#117C22×D7918yes—
863C2×C4⋊C4—798no—
864C2×C4⋊C4—798no—
865C2×C4⋊C4—794no—
866C2×C22⋊C4—7916no—
867C2×C22⋊C4—798no—
868C2×C22⋊C4—798no—
869C2×C42—798no—
870C2×C42—792no—
871C2×C42—791no—
872C2×C42—798no—
873C2×C42—792no—
874C2×C42—791no—
875C2×C42—791no—
876C2×C42—791no—
877C2×C42—791no—
878C2×C42—792no—
879C2×C42C22×D7911yescharacteristic
880C24—794no—
881C24—791no—
882C24C23×D7918yes—
883#41—44no—
884#41—48no—
885#41—31616no—
886#41—3168no—
887#41—3164no—
888#41—31616no—
889#41—3168no—
890#41—31616no—
891#41—3164no—
892#41—3168no—
893#41—31616no—
894#41—3164no—
895#41—15816no—
896C2×Q8—3168no—
897C2×Q8—3164no—
898C2×Q8—792no—
899C2×Q8—794no—
900C2×Q8—798no—
901C2×Q8—794no—
902C2×Q8—794no—
903C2×Q8C23×D7914yes—
904C2×Q8C23×D7912yes—
905C2×D4—48no—
906C2×D4—416no—
907C2×D4—31616no—
908C2×D4—3168no—
909C2×D4—3164no—
910C2×D4—3168no—
911C2×D4—798no—
912C2×D4—7916no—
913C2×D4—798no—
914C2×D4—794no—
915C2×D4—794no—
916C2×D4—7916no—
917C2×D4—794no—
918C2×D4—798no—
919C2×D4—794no—
920C2×D4—792no—
921C2×D4—794no—
922C2×D4C23×D7914yes—
923C2×D4C23×D7914yes—
924C2×D4C23×D7914yes—
925C2×D4C23×D79116yes—
926C2×D4C23×D7918yes—
927C2×D4C23×D7914yes—
928C2×D4C23×D7912yes—
929C2×D4C23×D7914yes—
930C2×D4C23×D7918yes—
931C22×C4—3164no—
932C22×C4—31616no—
933C22×C4—792no—
934C22×C4—798no—
935C22×C4—7916no—
936C22×C4—798no—
937C22×C4—792no—
938C22×C4—792no—
939C22×C4—7916no—
940C22×C4—791no—
941C22×C4—791no—
942C22×C4—798no—
943C22×C4—794no—
944C22×C4—792no—
945C22×C4—792no—
946C22×C4—794no—
947C22×C4—791no—
948C22×C4—791no—
949C22×C4—791no—
950C22×C4—794no—
951C22×C4—794no—
952C22×C4—15816no—
953C22×C4—1584no—
954C22×C4C23×D7912yes—
955C22×C4C23×D7911yescharacteristic
956C22×C4C23×D7918yes—
957C22×C4C23×D7914yes—
958C4⋊C4—7916no—
959C4⋊C4—798no—
960C4⋊C4—798no—
961C4⋊C4—798no—
962C4⋊C4—798no—
963C4⋊C4—7916no—
964C4⋊C4—798no—
965C4⋊C4—794no—
966C4⋊C4—794no—
967C4⋊C4—794no—
968C4⋊C4—7916no—
969C4⋊C4—798no—
970C4⋊C4—798no—
971C4⋊C4—794no—
972C4⋊C4—794no—
973C4⋊C4C23×D7914yes—
974C4⋊C4C23×D7914yes—
975C4⋊C4C23×D7914yes—
976C22⋊C4—798no—
977C22⋊C4—798no—
978C22⋊C4—798no—
979C22⋊C4—7916no—
980C22⋊C4—7916no—
981C22⋊C4—798no—
982C22⋊C4—798no—
983C22⋊C4—798no—
984C22⋊C4—798no—
985C22⋊C4—798no—
986C22⋊C4—798no—
987C22⋊C4—798no—
988C22⋊C4—7916no—
989C22⋊C4—798no—
990C22⋊C4C23×D7918yes—
991C22⋊C4C23×D7918yes—
992C22⋊C4C23×D7918yes—
993C22⋊C4C23×D7918yes—
994C22⋊C4C23×D79116yes—
995C42—792no—
996C42—791no—
997C42—798no—
998C42—792no—
999C42—792no—
1000C42—792no—
1001C42—792no—
1002C42—791no—
1003C42—798no—
1004C42—798no—
1005C42—798no—
1006C42C23×D7912yes—
1007C42C23×D7911yescharacteristic
1008C42C23×D7911yescharacteristic
1009C42C23×D7918yes—
1010C23—48no—
1011C23—416no—
1012C23—3162no—
1013C23—3168no—
1014C23—791no—
1015C23—794no—
1016C23—791no—
1017C23—1582no—
1018C23—1588no—
1019C23C24×D7914yes—
1020C23C24×D7911yescharacteristic
1021C23C24×D7918yes—
1022Q8—42no—
1023Q8—44no—
1024Q8—3164no—
1025Q8—3168no—
1026Q8—3162no—
1027Q8—1588no—
1028Q8—1588no—
1029D4—28no—
1030D4—28no—
1031D4—28no—
1032D4—416no—
1033D4—48no—
1034D4—44no—
1035D4—42no—
1036D4—48no—
1037D4—44no—
1038D4—3164no—
1039D4—3162no—
1040D4—3168no—
1041D4—3164no—
1042D4—3164no—
1043D4—31616no—
1044D4—3164no—
1045D4—31616no—
1046D4—3168no—
1047D4—15816no—
1048D4—1588no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—216no—
1053C2×C4—3162no—
1054C2×C4—3162no—
1055C2×C4—31616no—
1056C2×C4—3168no—
1057C2×C4—31616no—
1058C2×C4—3162no—
1059C2×C4—3168no—
1060C2×C4—791no—
1061C2×C4—794no—
1062C2×C4—792no—
1063C2×C4—798no—
1064C2×C4—792no—
1065C2×C4—791no—
1066C2×C4—798no—
1067C2×C4—794no—
1068C2×C4—1588no—
1069C2×C4—1582no—
1070C2×C4—1582no—
1071C2×C4—1588no—
1072C2×C4—1588no—
1073C2×C4—15816no—
1074C2×C4—1582no—
1075C2×C4—1588no—
1076C2×C4—1582no—
1077C2×C4—1584no—
1078C2×C4—1584no—
1079C2×C4C24×D7912yes—
1080C2×C4C24×D7918yes—
1081C2×C4C24×D7914yes—
1082C2×C4C24×D7911yescharacteristic
1083C2×C4C24×D7911yescharacteristic
1084C2×C4C24×D7912yes—
1085C22—24no—
1086C22—21no—
1087C22—28no—
1088C22—22no—
1089C22—28no—
1090C22—28no—
1091C22—28no—
1092C22—816no—
1093C22—3164no—
1094C22—792no—
1095C22—6328no—
1096C22—1581no—
1097C22—1584no—
1098C22—1588no—
1099C22—1582no—
1100C22—1582no—
1101C22C25×D7911yescharacteristic
1102C4—24no—
1103C4—21no—
1104C4—28no—
1105C4—22no—
1106C4—792no—
1107C4—1584no—
1108C4—1588no—
1109C4—1581no—
1110C4—1582no—
1111C4—1588no—
1112C4—1582no—
1113C4H(5,𝔽2)×D7912yes—
1114C4#1909939814yes—
1115C2—44no—
1116C2—48no—
1117C2—41no—
1118C2—3161no—
1119C2—3164no—
1120C2—1582no—
1121C2C2×H(5,𝔽2)×D7911yescharacteristic
1122C2C2×#1909939812yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3549C2
hypercenter#3549D79
hypocenterC79#62759
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #23777824C2semidirect
2. #23777814C2semidirect
3. #23777798C2semidirect
4. #23777792C2semidirect
5. #23777768C2semidirect
6. #23777755C2semidirect
7. #23777735C2semidirect
8. #23777731C2semidirect
9. #23777718C2semidirect
10. #23777540C2semidirect
11. #23777025C2semidirect
12. #23777001C2semidirect
13. #23776957C2semidirect
14. D4×#11929623C2semidirect
15. #23776813C2semidirect
16. #23776731C2semidirect
17. #23776695C2semidirect
18. #532×D79C2semidirect
19. C79×#3549C2semidirect
20. C22×#11929623C22semidirect
21. C2×#41×D79C22semidirect
22. #19099313C22semidirect
23. #19099313C22semidirect
24. #19099307C22semidirect
25. #19099307C22semidirect
26. #19099302C22semidirect
27. #19099302C22semidirect
28. #19099299C22semidirect
29. #19099293C22semidirect
30. #19099283C22semidirect
31. #19099276C22semidirect
32. #19099275C22semidirect
33. #19099274C22semidirect
34. #19099270C22semidirect
35. #19099265C22semidirect
36. #19099260C22semidirect
37. #19099252C22semidirect
38. #19099252C22semidirect
39. #19099244C22semidirect
40. #19099243C22semidirect
41. #19099234C22semidirect
42. #19099233C22semidirect
43. #19099231C22semidirect
44. D4×Dic158C22semidirect
45. #19099219C22semidirect
46. #19099218C22semidirect
47. #19099217C22semidirect
48. #19099213C22semidirect
49. #19099210C22semidirect
50. #19099207C22semidirect
51. #19099207C22semidirect
52. #19099200C22semidirect
53. D4×C22⋊D79C22semidirect
54. #19099191C22semidirect
55. #19099182C22semidirect
56. #19099180C22semidirect
57. #19099180C22semidirect
58. #19099167C22semidirect
59. #19099166C22semidirect
60. #19099166C22semidirect
61. #19099148C22semidirect
62. #19099148C22semidirect
63. #19099142C22semidirect
64. #19099142C22semidirect
65. #19099141C22semidirect
66. #19099139C22semidirect
67. #19099134C22semidirect
68. #19099133C22semidirect
69. #19099130C22semidirect
70. #19099130C22semidirect
71. #19099126C22semidirect
72. #19099123C22semidirect
73. #19099123C22semidirect
74. #19099120C22semidirect
75. #19099118C22semidirect
76. #19099118C22semidirect
77. #19099114C22semidirect
78. #19099113C22semidirect
79. #19099112C22semidirect
80. #19099112C22semidirect
83. #19099111C22semidirect
84. #19099111C22semidirect
85. #19099110C22semidirect
86. #19099109C22semidirect
87. #19099108C22semidirect
88. #19099108C22semidirect
89. C4⋊Q8×D79C22semidirect
91. #19099095C22semidirect
92. #19099095C22semidirect
93. #19099094C22semidirect
94. #19099094C22semidirect
95. #19099094C22semidirect
96. #19099092C22semidirect
97. #19099092C22semidirect
98. #19099092C22semidirect
99. #124×D79C22semidirect
100. #19099073C22semidirect
101. #19099073C22semidirect
102. #19099073C22semidirect
103. #19099070C22semidirect
104. #19099069C22semidirect
105. #19099069C22semidirect
106. #19099069C22semidirect
107. #121×D79C22semidirect
108. #41×Dic79C22semidirect
109. #19099031C22semidirect
110. C4×#11929623C22semidirect
111. C4×#11929623C22semidirect
112. C2×D4×Dic79C22semidirect
113. C4×D4×D79C22semidirect
114. #117×D79C22semidirect
115. C2×C42×D79C22semidirect
116. H(3,𝔽4)×C79C22semidirect
117. #555×C79C22semidirect
118. #555×C79C22semidirect
119. D42×C79C22semidirect
120. D42×C79C22semidirect
121. #535×C79C22semidirect
122. #535×C79C22semidirect
124. #532×C79C22semidirect
564. #3549D79semidirect
581. C79#62759semidirect
588. H(3,𝔽4)C2×D79semidirect
596. #555C2×D79semidirect
597. #555C2×D79semidirect
619. D42C2×D79semidirect
620. D42C2×D79semidirect
639. #535C2×D79semidirect
640. #535C2×D79semidirect
659. #532C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778242
#237778142
#237777982
#237777922
#237777682
#237777552
#237777352
#237777312
#237777182
#237775402
#237770252
#237770012
#237769572
D4×#119296232
#237768132
#237767312
#237766952
#532×D792
C79×#35492
#6275979