Finite Group Databasebeta

← #35197206

Subgroups — #35197206

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777984C218yesmaximal, complemented
2#23777867C214yesmaximal, complemented
3#23777768C214yesmaximal, complemented
4#23777721C218yesmaximal, complemented
5#23777403C214yesmaximal, complemented
6#23777352C214yesmaximal, complemented
7#23777325C218yesmaximal, complemented
8#23777301C214yesmaximal, complemented
9#23777295C212yesmaximal, complemented
10#23777286C211yesmaximal, characteristic, complemented
11#23777274C211yesmaximal, characteristic, complemented
12#23777274C214yesmaximal, complemented
13#23777188C212yesmaximal, complemented
14#23777180C211yesmaximal, characteristic, complemented
15#23777056C212yesmaximal, complemented
16#23777040C212yesmaximal, complemented
17#23776695C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×#19099111C211yesmaximal, characteristic, complemented
20C79×#3498C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yescomplemented
22C22×#11929623C2212yescomplemented
23#19099308C22116yescomplemented
24#19099302C22116yescomplemented
25#19099299C2218yescomplemented
26#19099299C2218yescomplemented
27#19099299C2214yescomplemented
28#19099291C2214yescomplemented
29#19099283C2214yescomplemented
30#19099282C2218yescomplemented
31#19099277C2218yescomplemented
32#19099272C2218yescomplemented
33#19099263C2218yescomplemented
34#19099260C2218yescomplemented
35#19099256C22116yescomplemented
36#19099253C2218yescomplemented
37#19099244C22116yescomplemented
38#19099244C22116yescomplemented
39#19099233C2218yescomplemented
40#19099233C2218yescomplemented
41#19099233C2214yescomplemented
42#19099231C2218yescomplemented
43D4×Dic158C2214yescomplemented
44#19099221C2218yescomplemented
45#19099220C2218yescomplemented
46#19099219C2218yescomplemented
47#19099218C2214yescomplemented
48#19099213C2218yescomplemented
49#19099212C2218yescomplemented
50#19099212C2218yescomplemented
51#19099207C2218yescomplemented
52#19099207C2218yescomplemented
53#19099207C22116yescomplemented
54#19099207C2218yescomplemented
55#19099207C2218yescomplemented
56#19099207C2218yescomplemented
57#19099207C2218yescomplemented
58#19099180C2218yescomplemented
59#19099180C2218yescomplemented
60#19099178C2218yescomplemented
61#19099175C2214yescomplemented
62#19099167C2218yescomplemented
63#19099167C2218yescomplemented
64#19099167C2214yescomplemented
65#19099163C22116yescomplemented
66#19099158C22116yescomplemented
67#19099148C22116yescomplemented
68#19099148C22116yescomplemented
69#19099142C2218yescomplemented
70#19099134C2212yes—
71#19099134C2212yescomplemented
72#19099134C2214yescomplemented
73#19099133C2214yescomplemented
74#19099130C2212yescomplemented
75#19099130C2214yescomplemented
76#19099130C2218yescomplemented
77#19099128C2218yescomplemented
78#19099122C2218yescomplemented
79#19099120C2214yescomplemented
80#19099120C2211yescharacteristic, complemented
81#19099118C2212yescomplemented
82#19099117C2212yescomplemented
83#19099116C2211yescharacteristic, complemented
84#19099111C2214yescomplemented
85#19099111C2214yescomplemented
86#19099111C2214yescomplemented
87#19099111C2214yescomplemented
88#19099111C2212yescomplemented
89#19099111C2214yescomplemented
90#19099111C2212yescomplemented
91#19099110C2212yescomplemented
92#19099109C2211yescharacteristic
93#19099109C2214yescomplemented
94C2×#14579161C2211yescharacteristic, complemented
95C4⋊Q8×D79C2212yescomplemented
96#19099100C2212yescomplemented
97#19099095C2212yescomplemented
98#19099095C2214yescomplemented
99#19099094C2218yescomplemented
100#19099094C2214yescomplemented
101#19099093C2214yescomplemented
102#19099092C2214yescomplemented
103#19099091C2214yescomplemented
104C2×#14579148C2212yescomplemented
105C2×#14579148C2214yescomplemented
106#19099075C2211yescharacteristic, complemented
107#19099073C2214yescomplemented
108#19099072C2214yescomplemented
109#19099070C2211yescharacteristic
110#19099070C2212yescomplemented
111#19099069C2218yescomplemented
112C2×#14579142C2218yescomplemented
113C2×#14579132C2214yescomplemented
114#19099042C2218yescomplemented
115#19099040C2212yescomplemented
116#19099038C2212yescomplemented
117#19099038C2218yescomplemented
118#41×Dic79C2212yescomplemented
119C4×#11929624C2214yescomplemented
120C4×#11929624C2211yescharacteristic, complemented
121C4×#11929623C2214yescomplemented
122C2×D4×Dic79C2214yescomplemented
123C2×C42×D79C2211yescharacteristic, complemented
124C2×H(5,𝔽2)×C79C2212yes—
125#550×C79C2214yescomplemented
126D42×C79C2218yes—
127D42×C79C2214yescomplemented
128#535×C79C2212yes—
129#535×C79C2214yescomplemented
130#532×C79C2211yescharacteristic
131#532×C79C2212yescomplemented
132C2×#127×C79C2211yescharacteristic
133C2×#127×C79C2212yescomplemented
134C4×#41×C79C2211yescharacteristic
135#14579208—48no—
136C2×#11929624C2311yescharacteristic
137C2×#11929624C2314yes—
138C2×#11929624C2314yes—
139C2×#11929623—48no—
140C2×#11929623C2318yes—
141C2×#11929623C2314yes—
142C2×#11929623C2318yes—
143C2×#11929623C2314yes—
144C2×#11929623C2318yes—
145C2×#11929623C2318yes—
146C22×Dic158C2312yes—
147C22×Dic158C2314yes—
148C2×Q8×D79C2314yes—
149C22×C22⋊D79C2314yes—
150C23×Dic79C2314yes—
151C22×C4×D79C2311yescharacteristic
152C22×C4×D79C2312yes—
153#14579161C2312yes—
154#14579161C2314yes—
155#14579161C2312yes—
156#14579161C2312yes—
157#14579160C2318yes—
158#14579160C2312yes—
159#14579159C2314yes—
160#14579159C2314yes—
161#14579159C2311yescharacteristic
162#14579157C23116yes—
163#14579157C2314yes—
164#14579157C2311yescharacteristic
165#14579156C2314yes—
166#14579154C2318yes—
167#14579154C23116yes—
168#14579154C23116yes—
169#14579154C23116yes—
170#14579154C2314yes—
171#14579153C2312yes—
172#14579153C2318yes—
173#14579152C2314yes—
174#14579152C2312yes—
175#14579151C2314yes—
176#14579151C23116yes—
177#14579150C2311yescharacteristic
178#14579148C23116yes—
179#14579148C23116yes—
180#14579148C2318yes—
181#14579148C2314yes—
182#14579148C2314yes—
183#14579148C2314yes—
184#14579148C2314yes—
185#14579148C2318yes—
186#14579148C2314yes—
187#14579148C2311yescharacteristic
188#14579148C2314yes—
189#14579147C2314yes—
190#14579147C23116yes—
191#14579146C2314yes—
192#14579145C2312yes—
193#14579144C23116yes—
194#14579143C2314yes—
195#14579143C23116yes—
196#14579143C2318yes—
197#14579142C23116yes—
198#14579142C23116yes—
199#14579142C23116yes—
200#14579142C23116yes—
201#14579142C23116yes—
202#14579142C23116yes—
203#14579142C2318yes—
204#14579142C2318yes—
205#14579142C2312yes—
206#14579142C2314yes—
207#14579141C2314yes—
208#14579141C2312yes—
209#14579140C2318yes—
210#14579140C23116yes—
211#14579140C2318yes—
212#14579140C2318yes—
213#14579140C2314yes—
214#14579139C2314yes—
215#14579138C23116yes—
216#14579138C23116yes—
217#14579138C23116yes—
218#14579138C2314yes—
219#14579137C2312yes—
220#14579137C2314yes—
221#14579136C2312yes—
222#14579134C23116yes—
223#14579134C2314yes—
224#14579133C23116yes—
225#14579133C23116yes—
226#14579133C23116yes—
227#14579133C23116yes—
228#14579133C23116yes—
229#14579133C23116yes—
230#14579133C2314yes—
231#14579132C23116yes—
232#14579132C2318yes—
233#14579132C2318yes—
234#14579132C2314yes—
235#14579132C2318yes—
236#14579132C2318yes—
237#14579132C2318yes—
238#14579132C2312yes—
239#14579132C2314yes—
240#14579132C2318yes—
241#14579132C2318yes—
242#14579131C2312yes—
243#14579130C23116yes—
244#14579130C23116yes—
245#14579130C2318yes—
246#14579129C2312yes—
247#14579129C2314yes—
248Q8×Dic79C2314yes—
249C4×Dic158C2318yes—
250C4×Dic158C2318yes—
251C4×Dic158C2312yes—
252C4×Dic158C2314yes—
253C4×Dic158C2314yes—
254C4×Dic158C2314yes—
255#14579126C2314yes—
256#14579126C2318yes—
257C4×D316C2312yes—
258C4×D316C2314yes—
259C4×D316C2314yes—
260D4×Dic79C2318yes—
261D4×Dic79C23116yes—
262D4×Dic79C23116yes—
263D4×Dic79C2314yes—
264D4×Dic79C2318yes—
265D4×Dic79C2318yes—
266D4×Dic79C2318yes—
267D4×Dic79C2318yes—
268D4×Dic79C2318yes—
269D4×Dic79C2318yes—
270D4×Dic79C2314yes—
271D4×Dic79C2318yes—
272D4×Dic79C2318yes—
273C4×C22⋊D79C23116yes—
274C4×C22⋊D79C2314yes—
275C4×C22⋊D79C2314yes—
276C4×C22⋊D79C2314yes—
277C4×C22⋊D79C2314yes—
278C4×C22⋊D79C2314yes—
279C4×C22⋊D79C2318yes—
280(C22⋊D79)⋊C4C2318yes—
281(C22⋊D79)⋊C4C23116yes—
282#14579120C2314yes—
283#14579120C2314yes—
284#14579120C2318yes—
285#14579120C2311yescharacteristic
286#14579120C2312yes—
287#14579119C2314yes—
288#14579118C2314yes—
289#14579118C2314yes—
290#14579118C2312yes—
291#14579117C23116yes—
292#14579117C2318yes—
293#14579117C2318yes—
294C2×C4⋊Dic79C2314yes—
295C2×Dic79⋊C4C23116yes—
296C4⋊C4×D79C2318yes—
297C2×C22⋊Dic79C23116yes—
298C2×C22⋊Dic79C23116yes—
299C2×C22⋊Dic79C2318yes—
300C2×C22⋊Dic79C2318yes—
301C2×C4×Dic79C2312yes—
302C2×C4×Dic79C2311yescharacteristic
303C2×C4×Dic79C2314yes—
304C42×D79C2312yes—
305C42×D79C2312yes—
306C42×D79C2312yes—
307C42×D79C2312yes—
308C42×D79C2312yes—
309H(5,𝔽2)×C79—48no—
310C2×#41×C79C2312yes—
311C2×#41×C79C2311yescharacteristic
312C2×#41×C79C2314yes—
313C2×#41×C79C2314yes—
314C22×D4×C79C2312yes—
315C22×D4×C79C2314yes—
316C22×D4×C79C2314yes—
317C22×D4×C79C2318yes—
318C22×D4×C79C2318yes—
319C22×D4×C79C2314yes—
320C4⋊Q8×C79C2311yescharacteristic
321#127×C79C2318yes—
322#127×C79C2312yes—
323#127×C79C2314yes—
324#127×C79C2314yes—
325#127×C79C2312yes—
326#127×C79C2311yescharacteristic
327#124×C79C2314yes—
328#124×C79C2312yes—
329#121×C79C2318yes—
330#121×C79C23116yes—
331#121×C79C2318yes—
332#121×C79C2314yes—
333#120×C79C23116yes—
334#120×C79C2318yes—
335C4×Q8×C79C2312yes—
336C4×D4×C79C2318yes—
337C4×D4×C79C2314yes—
338C4×D4×C79C2314yes—
339C4×D4×C79C2312yes—
340#117×C79C2312yes—
341#117×C79C2311yescharacteristic
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2411yescharacteristic
345#11929624—24no—
346#11929624—48no—
347#11929624—48no—
348#11929623—416no—
349#11929623—416no—
350#11929623—416no—
351#11929623—48no—
352#11929623—416no—
353#11929623—48no—
354C2×Dic158—28no—
355C2×Dic158—48no—
356C2×Dic158C2414yes—
357C2×Dic158C2411yescharacteristic
358C2×Dic158C2414yes—
359C2×Dic158C2414yes—
360C2×Dic158C2418yes—
361C2×Dic158C2414yes—
362Q8×D79—48no—
363C2×D316C2411yescharacteristic
364C2×D316C2414yes—
365C2×C22⋊D79—48no—
366C2×C22⋊D79C2412yes—
367C2×C22⋊D79C2418yes—
368C2×C22⋊D79C24116yes—
369C2×C22⋊D79C2418yes—
370C2×C22⋊D79C24116yes—
371C2×C22⋊D79C2414yes—
372C2×C22⋊D79C2414yes—
373C22×Dic79—48no—
374C22×Dic79C2414yes—
375C22×Dic79C2411yescharacteristic
376C22×Dic79C2418yes—
377C22×Dic79C24116yes—
378C22×Dic79C2418yes—
379C22×Dic79C24116yes—
380C22×Dic79C2412yes—
381C2×C4×D79—24no—
382C2×C4×D79—44no—
383C2×C4×D79C2412yes—
384C2×C4×D79C2412yes—
385C2×C4×D79C2412yes—
386C2×C4×D79C2414yes—
387C2×C4×D79C2412yes—
388C2×C4×D79C2412yes—
389C2×C4×D79C2418yes—
390C2×C4×D79C2412yes—
391C2×C4×D79C2412yes—
392C4⋊Dic79C2418yes—
393C4⋊Dic79C2418yes—
394C4⋊Dic79C2414yes—
395C4⋊Dic79C2412yes—
396C4⋊Dic79C2414yes—
397C4⋊Dic79C2414yes—
398C4⋊Dic79C2414yes—
399C4⋊Dic79C2418yes—
400Dic79⋊C4C24116yes—
401Dic79⋊C4C2414yes—
402Dic79⋊C4C2418yes—
403Dic79⋊C4C24116yes—
404Dic79⋊C4C2414yes—
405Dic79⋊C4C2418yes—
406Dic79⋊C4C24116yes—
407Dic79⋊C4C2414yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C2414yes—
410C22⋊Dic79C2412yes—
411C22⋊Dic79C2414yes—
412C22⋊Dic79C2414yes—
413C22⋊Dic79C2414yes—
414C22⋊Dic79C24116yes—
415C22⋊Dic79C2418yes—
416C22⋊Dic79C24116yes—
417C22⋊Dic79C24116yes—
418C22⋊Dic79C24116yes—
419C22⋊Dic79C24116yes—
420C22⋊Dic79C24116yes—
421C22⋊Dic79C2418yes—
422(C2×D79)⋊C4C2414yes—
423(C2×D79)⋊C4C2414yes—
424(C2×D79)⋊C4C2414yes—
425(C2×D79)⋊C4C2414yes—
426(C2×D79)⋊C4C2414yes—
427(C2×D79)⋊C4C2418yes—
428C4×Dic79C2411yescharacteristic
429C4×Dic79C2412yes—
430C4×Dic79C2412yes—
431C4×Dic79C2411yescharacteristic
432C4×Dic79C2412yes—
433C4×Dic79C2412yes—
434C4×Dic79C2412yes—
435C4×Dic79C2412yes—
436C4×Dic79C2414yes—
437C4×Dic79C2418yes—
438C4×Dic79C2414yes—
439C4×Dic79C24116yes—
440C24×C79C2414yes—
441C24×C79C2418yes—
442#41×C79—28no—
443#41×C79—24no—
444#41×C79—48no—
445#41×C79—48no—
446C2×Q8×C79C2412yes—
447C2×Q8×C79C2411yescharacteristic
448C2×D4×C79—28no—
449C2×D4×C79—48no—
450C2×D4×C79—416no—
451C2×D4×C79—48no—
452C2×D4×C79—48no—
453C2×D4×C79—416no—
454C2×D4×C79C2414yes—
455C2×D4×C79C2414yes—
456C2×D4×C79C2414yes—
457C2×D4×C79C2412yes—
458C2×D4×C79C2418yes—
459C2×D4×C79C2414yes—
460C2×D4×C79C2412yes—
461C2×D4×C79C2411yescharacteristic
462C2×D4×C79C2418yes—
463C2×D4×C79C24116yes—
464C2×D4×C79C2418yes—
465C2×D4×C79C2418yes—
466C22×C4×C79C2414yes—
467C22×C4×C79C2414yes—
468C22×C4×C79C2412yes—
469C22×C4×C79C2412yes—
470C22×C4×C79C2418yes—
471C22×C4×C79C2411yescharacteristic
472C4⋊C4×C79C2412yes—
473C4⋊C4×C79C2414yes—
474C4⋊C4×C79C2414yes—
475C22⋊C4×C79C2412yes—
476C22⋊C4×C79C2414yes—
477C22⋊C4×C79C24116yes—
478C22⋊C4×C79C2418yes—
479C42×C79C2411yescharacteristic
480C42×C79C2411yescharacteristic
481C42×C79C2412yes—
482C42×C79C2412yes—
483C42×C79C2414yes—
484C23×C79—28no—
485C23×C79—48no—
486C23×C79—48no—
487C23×C79—416no—
488C23×C79C2512yes—
489C23×C79C2514yes—
490C23×C79C2518yes—
491C23×C79C2511yescharacteristic
492C22×D79—22no—
493C22×D79—42no—
494C22×D79C2512yes—
495C22×D79C2512yes—
496Q8×C79—24no—
497Q8×C79—22no—
498D4×C79—28no—
499D4×C79—24no—
500D4×C79—28no—
501D4×C79—28no—
502D4×C79—24no—
503D4×C79—22no—
504D4×C79—216no—
505D4×C79—28no—
506D4×C79—48no—
507D4×C79—48no—
508D4×C79—416no—
509D4×C79—48no—
510C2×C4×C79—28no—
511C2×C4×C79—24no—
512C2×C4×C79—24no—
513C2×C4×C79—28no—
514C2×C4×C79—48no—
515C2×C4×C79H(5,𝔽2)14yes—
516C2×C4×C79C2514yes—
517C2×C4×C79C2512yes—
518C2×C4×C79C2514yes—
519C2×C4×C79C2512yes—
520C2×C4×C79C2511yescharacteristic
521C2×C4×C79C2511yescharacteristic
522C2×C4×C79C2512yes—
523C22⋊D79—24no—
524C22⋊D79—416no—
525C22⋊D79—416no—
526C22⋊D79—48no—
527C22⋊D79—48no—
528C22⋊D79—44no—
529C22⋊D79—44no—
530C2×Dic79—22no—
531C2×Dic79—28no—
532C2×Dic79—42no—
533C2×Dic79—416no—
534C2×Dic79—48no—
535C2×Dic79—416no—
536C2×Dic79—48no—
537C2×Dic79C2512yes—
538C2×Dic79C2512yes—
539C2×Dic79C2518yes—
540C2×Dic79C2512yes—
541C2×Dic79C2514yes—
542C2×Dic79C2512yes—
543C2×Dic79C2518yes—
544D316—22no—
545D316—44no—
546C4×D79—24no—
547C4×D79—24no—
548C4×D79—24no—
549C4×D79—24no—
550C4×D79—24no—
551C4×D79—28no—
552C4×D79—42no—
553C4×D79—42no—
554C4×D79—48no—
555Dic158—28no—
556Dic158—28no—
557Dic158—22no—
558Dic158—28no—
559Dic158—48no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—24no—
563C22×C79—28no—
564C22×C79—22no—
565C22×C79—24no—
566C22×C79—216no—
567C22×C79—28no—
568C22×C79—88no—
569C22×C79—168no—
570C22×C79C2×H(5,𝔽2)12yes—
571C22×C79C2611yescharacteristic
572C2×D79—22no—
573C2×D79—22no—
574C2×D79—24no—
575C2×D79—22no—
576C2×D79—22no—
577C2×D79—44no—
578C4×C79—22no—
579C4×C79—24no—
580C4×C79—24no—
581C4×C79—22no—
582C4×C79C2×H(5,𝔽2)12yes—
583C4×C79C2×H(5,𝔽2)12yes—
584C4×C79#58514yes—
585Dic79—22no—
586Dic79—28no—
587Dic79—22no—
588Dic79—28no—
589Dic79—22no—
590Dic79—24no—
591Dic79—22no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—48no—
595C2×C79—44no—
596C2×C79—42no—
597C2×C79C22×H(5,𝔽2)11yescharacteristic
598C2×C79C2×#58512yes—
599D79—42no—
600D79—42no—
601#3562—798no—
602#3554—794no—
603#3546—794no—
604#3542—798no—
605#3517—794no—
606#3514—794no—
607#3513—798no—
608#3511—794no—
609#3510—792no—
610#3509—791no—
611#3508—791no—
612#3508—794no—
613#3500—792no—
614#3499—791no—
615#3498D7911yescharacteristic, complemented
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444—791no—
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)C2×D7912yes—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—798no—
629#559—794no—
630#557—794no—
631#556—798no—
632#556—794no—
633#555—798no—
634#554—798no—
635#553—7916no—
636#553—798no—
637#553—798no—
638#552—798no—
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—794no—
644#550—798no—
645#550C2×D7914yescomplemented
646D4×Q8—794no—
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—798no—
652#547—798no—
653#547—794no—
654#546—798no—
655#546—798no—
656#546—798no—
657#546—7916no—
658#546—798no—
659#546—798no—
660#546—798no—
661D42C2×D7918yes—
662D42C2×D7914yescomplemented
663#542—798no—
664#542—798no—
665#542—798no—
666#541—794no—
667#540—798no—
668#540—798no—
669#540—794no—
670#540—7916no—
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—792no—
676#536—792no—
677#536—794no—
678#536—794no—
679#535—792no—
680#535—794no—
681#535—798no—
682#535—798no—
683#535C2×D7912yes—
684#535C2×D7914yescomplemented
685#534—798no—
686#533—792no—
687#533—792no—
688#533—791no—
689#533—791no—
690#533—794no—
691#532—791no—
692#532—794no—
693#532—794no—
694#532—794no—
695#532—794no—
696#532—794no—
697#532—792no—
698#532—792no—
699#532—794no—
700#532—792no—
701#532C2×D7911yescharacteristic
702#532C2×D7912yescomplemented
703C2×C4⋊Q8—792no—
704C2×C4⋊Q8—791no—
705C2×#127C2×D7911yescharacteristic
706C2×#127C2×D7912yescomplemented
707#529—794no—
708#529—794no—
709#529—798no—
710#529—792no—
711#529—794no—
712#529—792no—
713#529—794no—
714#529—794no—
715C2×#124—792no—
716C2×#124—794no—
717#525—791no—
718#525—792no—
719#525—794no—
720#525—798no—
721#525—794no—
722#525—791no—
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519—792no—
727#518—792no—
728#518—798no—
729C4×#41—792no—
730C4×#41—794no—
731C4×#41—791no—
732C4×#41—794no—
733C4×#41C2×D7911yescharacteristic
734C2×C4×D4—794no—
735C22×C42—791no—
7362−1+4—3168no—
737H(5,𝔽2)—48no—
738C2×#41—3168no—
739C2×#41—794no—
740C2×#41—798no—
741C2×#41—798no—
742C2×#41—798no—
743C2×#41—798no—
744C2×#41—794no—
745C2×#41—794no—
746C2×#41—794no—
747C2×#41—791no—
748C2×#41C22×D7912yes—
749C2×#41C22×D7911yescharacteristic
750C2×#41C22×D7914yes—
751C2×#41C22×D7914yes—
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8—792no—
755C22×D4—794no—
756C22×D4C22×D7912yes—
757C22×D4C22×D7914yes—
758C22×D4C22×D7918yes—
759C22×D4C22×D7918yes—
760C22×D4C22×D7914yes—
761C22×D4C22×D7914yes—
762C23×C4—794no—
763C23×C4—792no—
764C23×C4—791no—
765C4⋊Q8—794no—
766C4⋊Q8—791no—
767C4⋊Q8—794no—
768C4⋊Q8—798no—
769C4⋊Q8—792no—
770C4⋊Q8—792no—
771C4⋊Q8—792no—
772C4⋊Q8—794no—
773C4⋊Q8—792no—
774C4⋊Q8C22×D7911yescharacteristic
775#127—791no—
776#127—794no—
777#127—7916no—
778#127C22×D7912yes—
779#127C22×D7912yes—
780#127C22×D7914yes—
781#127C22×D7911yescharacteristic
782#127C22×D7914yes—
783#127C22×D7918yes—
784#126—794no—
785#126—798no—
786#126—794no—
787#126—7916no—
788#126—7916no—
789#126—7916no—
790#125—792no—
791#125—794no—
792#125—794no—
793#125—7916no—
794#125—792no—
795#125—798no—
796#124—791no—
797#124—791no—
798#124—794no—
799#124—794no—
800#124—798no—
801#124—794no—
802#124—794no—
803#124—7916no—
804#124—794no—
805#124—794no—
806#124—798no—
807#124—7916no—
808#124—794no—
809#124—7916no—
810#124C22×D7912yes—
811#124C22×D7914yes—
812#123—792no—
813#123—794no—
814#123—798no—
815#123—798no—
816#123—7916no—
817#123—7916no—
818#123—7916no—
819#123—7916no—
820#123—7916no—
821#123—7916no—
822#123—7916no—
823#123—794no—
824#123—792no—
825#123—794no—
826#123—798no—
827#123—7916no—
828C22⋊Q8—792no—
829C22⋊Q8—794no—
830C22⋊Q8—794no—
831C22⋊Q8—798no—
832C22⋊Q8—798no—
833C22⋊Q8—798no—
834C22⋊Q8—7916no—
835C22⋊Q8—794no—
836C22⋊Q8—792no—
837C22⋊Q8—794no—
838C22⋊Q8—794no—
839C22⋊Q8—7916no—
840C22⋊Q8—7916no—
841C22⋊Q8—7916no—
842#121—798no—
843#121—798no—
844#121—798no—
845#121—798no—
846#121—794no—
847#121—792no—
848#121—794no—
849#121—794no—
850#121—7916no—
851#121—798no—
852#121—798no—
853#121—798no—
854#121—7916no—
855#121—7916no—
856#121—7916no—
857#121—7916no—
858#121—7916no—
859#121—7916no—
860#121—792no—
861#121—794no—
862#121—7916no—
863#121C22×D7914yes—
864#121C22×D7918yes—
865#121C22×D7918yes—
866#121C22×D79116yes—
867#120—798no—
868#120—7916no—
869#120—7916no—
870#120—792no—
871#120—794no—
872#120—792no—
873#120C22×D7918yes—
874#120C22×D79116yes—
875C4×Q8—794no—
876C4×Q8—794no—
877C4×Q8—798no—
878C4×Q8—792no—
879C4×Q8—794no—
880C4×Q8—794no—
881C4×Q8—794no—
882C4×Q8—798no—
883C4×Q8—798no—
884C4×Q8C22×D7912yes—
885C4×D4—798no—
886C4×D4—798no—
887C4×D4—798no—
888C4×D4—798no—
889C4×D4—794no—
890C4×D4—798no—
891C4×D4—794no—
892C4×D4—7916no—
893C4×D4—7916no—
894C4×D4—798no—
895C4×D4—798no—
896C4×D4—798no—
897C4×D4—798no—
898C4×D4—794no—
899C4×D4—794no—
900C4×D4—794no—
901C4×D4—798no—
902C4×D4—794no—
903C4×D4—794no—
904C4×D4—7916no—
905C4×D4—798no—
906C4×D4—7916no—
907C4×D4—794no—
908C4×D4—794no—
909C4×D4—792no—
910C4×D4C22×D7914yes—
911C4×D4C22×D7914yes—
912C4×D4C22×D7912yes—
913C4×D4C22×D7918yes—
914#117—791no—
915#117—794no—
916#117—792no—
917#117—794no—
918#117—798no—
919#117—794no—
920#117—798no—
921#117—798no—
922#117—7916no—
923#117—794no—
924#117—794no—
925#117—792no—
926#117C22×D7911yescharacteristic
927#117C22×D7912yes—
928C2×C4⋊C4—794no—
929C2×C4⋊C4—7916no—
930C2×C4⋊C4—798no—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—798no—
933C2×C22⋊C4—7916no—
934C2×C22⋊C4—7916no—
935C2×C42—792no—
936C2×C42—794no—
937C2×C42—791no—
938C2×C42—792no—
939C2×C42—792no—
940C2×C42—792no—
941C2×C42—792no—
942C2×C42—792no—
943C2×C42C22×D7912yes—
944C2×C42C22×D7911yescharacteristic
945C24—791no—
946C24C23×D7914yes—
947C24C23×D7918yes—
948#41—24no—
949#41—28no—
950#41—48no—
951#41—48no—
952#41—3168no—
953#41—3168no—
954#41—31616no—
955#41—31616no—
956#41—3168no—
957#41—31616no—
958#41—3168no—
959#41—31616no—
960#41—1584no—
961C2×Q8—3168no—
962C2×Q8—3168no—
963C2×Q8—794no—
964C2×Q8—798no—
965C2×Q8—794no—
966C2×Q8—791no—
967C2×Q8—794no—
968C2×Q8—794no—
969C2×Q8—1588no—
970C2×Q8C23×D7912yes—
971C2×Q8C23×D7911yescharacteristic
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—48no—
976C2×D4—416no—
977C2×D4—416no—
978C2×D4—3168no—
979C2×D4—794no—
980C2×D4—794no—
981C2×D4—798no—
982C2×D4—7916no—
983C2×D4—798no—
984C2×D4—7916no—
985C2×D4—792no—
986C2×D4—794no—
987C2×D4—791no—
988C2×D4C23×D7918yes—
989C2×D4C23×D7914yes—
990C2×D4C23×D7914yes—
991C2×D4C23×D7914yes—
992C2×D4C23×D7912yes—
993C2×D4C23×D7914yes—
994C2×D4C23×D7912yes—
995C2×D4C23×D7911yescharacteristic
996C2×D4C23×D7918yes—
997C2×D4C23×D79116yes—
998C2×D4C23×D7918yes—
999C2×D4C23×D7918yes—
1000C22×C4—3164no—
1001C22×C4—3168no—
1002C22×C4—792no—
1003C22×C4—798no—
1004C22×C4—7916no—
1005C22×C4—798no—
1006C22×C4—7916no—
1007C22×C4—792no—
1008C22×C4—792no—
1009C22×C4—798no—
1010C22×C4—791no—
1011C22×C4—794no—
1012C22×C4—792no—
1013C22×C4—792no—
1014C22×C4—792no—
1015C22×C4—792no—
1016C22×C4—794no—
1017C22×C4—792no—
1018C22×C4—1584no—
1019C22×C4C23×D7912yes—
1020C22×C4C23×D7914yes—
1021C22×C4C23×D7914yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D7918yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—794no—
1026C4⋊C4—798no—
1027C4⋊C4—7916no—
1028C4⋊C4—7916no—
1029C4⋊C4—794no—
1030C4⋊C4—798no—
1031C4⋊C4—794no—
1032C4⋊C4—794no—
1033C4⋊C4—794no—
1034C4⋊C4—7916no—
1035C4⋊C4—798no—
1036C4⋊C4—798no—
1037C4⋊C4—794no—
1038C4⋊C4—792no—
1039C4⋊C4—794no—
1040C4⋊C4—794no—
1041C4⋊C4—794no—
1042C4⋊C4—798no—
1043C4⋊C4C23×D7914yes—
1044C4⋊C4C23×D7912yes—
1045C4⋊C4C23×D7914yes—
1046C22⋊C4—792no—
1047C22⋊C4—794no—
1048C22⋊C4—794no—
1049C22⋊C4—794no—
1050C22⋊C4—798no—
1051C22⋊C4—7916no—
1052C22⋊C4—7916no—
1053C22⋊C4—7916no—
1054C22⋊C4—7916no—
1055C22⋊C4—7916no—
1056C22⋊C4—7916no—
1057C22⋊C4—798no—
1058C22⋊C4—794no—
1059C22⋊C4—794no—
1060C22⋊C4—794no—
1061C22⋊C4—798no—
1062C22⋊C4—794no—
1063C22⋊C4—794no—
1064C22⋊C4C23×D7912yes—
1065C22⋊C4C23×D79116yes—
1066C22⋊C4C23×D7918yes—
1067C22⋊C4C23×D7914yes—
1068C42—791no—
1069C42—792no—
1070C42—792no—
1071C42—791no—
1072C42—792no—
1073C42—792no—
1074C42—792no—
1075C42—798no—
1076C42—792no—
1077C42—794no—
1078C42—794no—
1079C42—7916no—
1080C42C23×D7911yescharacteristic
1081C42C23×D7911yescharacteristic
1082C42C23×D7912yes—
1083C42C23×D7914yes—
1084C42C23×D7912yes—
1085C23—28no—
1086C23—48no—
1087C23—48no—
1088C23—416no—
1089C23—3162no—
1090C23—792no—
1091C23—792no—
1092C23—1582no—
1093C23C24×D7912yes—
1094C23C24×D7914yes—
1095C23C24×D7918yes—
1096C23C24×D7911yescharacteristic
1097Q8—24no—
1098Q8—22no—
1099Q8—3168no—
1100Q8—3164no—
1101Q8—1582no—
1102Q8—1588no—
1103Q8—1588no—
1104Q8—1588no—
1105D4—24no—
1106D4—28no—
1107D4—28no—
1108D4—28no—
1109D4—22no—
1110D4—24no—
1111D4—216no—
1112D4—28no—
1113D4—48no—
1114D4—48no—
1115D4—48no—
1116D4—416no—
1117D4—3164no—
1118D4—31616no—
1119D4—3164no—
1120D4—3168no—
1121D4—31616no—
1122D4—3164no—
1123D4—3168no—
1124D4—1584no—
1125D4—1582no—
1126C2×C4—24no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—48no—
1131C2×C4—3162no—
1132C2×C4—3162no—
1133C2×C4—3168no—
1134C2×C4—31616no—
1135C2×C4—3162no—
1136C2×C4—3168no—
1137C2×C4—3168no—
1138C2×C4—31616no—
1139C2×C4—792no—
1140C2×C4—792no—
1141C2×C4—798no—
1142C2×C4—792no—
1143C2×C4—794no—
1144C2×C4—792no—
1145C2×C4—798no—
1146C2×C4—1582no—
1147C2×C4—1588no—
1148C2×C4—1584no—
1149C2×C4—1584no—
1150C2×C4—1584no—
1151C2×C4—1584no—
1152C2×C4—1584no—
1153C2×C4—1588no—
1154C2×C4#1457920614yes—
1155C2×C4C24×D7914yes—
1156C2×C4C24×D7912yes—
1157C2×C4C24×D7914yes—
1158C2×C4C24×D7912yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—24no—
1164C22—22no—
1165C22—28no—
1166C22—24no—
1167C22—216no—
1168C22—28no—
1169C22—88no—
1170C22—168no—
1171C22—3164no—
1172C22—1582no—
1173C22—1582no—
1174C22—1582no—
1175C22—1582no—
1176C22—1584no—
1177C22C2×#1457920612yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—24no—
1183C4—1582no—
1184C4—1588no—
1185C4—1582no—
1186C4—1582no—
1187C4—1584no—
1188C4—1588no—
1189C4—1582no—
1190C4C2×#1457920612yes—
1191C4C2×#1457920612yes—
1192C4#1909939814yes—
1193C2—22no—
1194C2—48no—
1195C2—42no—
1196C2—44no—
1197C2—3162no—
1198C2—3162no—
1199C2C22×#1457920611yescharacteristic
1200C2C2×#1909939812yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3498C2
hypercenter#3498D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3498

Complements

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

NH ≅ G/Ntype
1. #23777984C2semidirect
2. #23777867C2semidirect
3. #23777768C2semidirect
4. #23777721C2semidirect
5. #23777403C2semidirect
6. #23777352C2semidirect
7. #23777325C2semidirect
8. #23777301C2semidirect
9. #23777295C2semidirect
10. #23777286C2semidirect
11. #23777274C2semidirect
12. #23777274C2semidirect
13. #23777188C2semidirect
14. #23777180C2semidirect
15. #23777056C2semidirect
16. #23777040C2semidirect
17. #23776695C2semidirect
18. #23776693C2semidirect
19. C2×#19099111C2semidirect
20. C79×#3498C2semidirect
21. C2×#14579208C22semidirect
22. C22×#11929623C22semidirect
23. #19099308C22semidirect
24. #19099302C22semidirect
25. #19099299C22semidirect
26. #19099299C22semidirect
27. #19099299C22semidirect
28. #19099291C22semidirect
29. #19099283C22semidirect
30. #19099282C22semidirect
31. #19099277C22semidirect
32. #19099272C22semidirect
33. #19099263C22semidirect
34. #19099260C22semidirect
35. #19099256C22semidirect
36. #19099253C22semidirect
37. #19099244C22semidirect
38. #19099244C22semidirect
39. #19099233C22semidirect
40. #19099233C22semidirect
41. #19099233C22semidirect
42. #19099231C22semidirect
43. D4×Dic158C22semidirect
44. #19099221C22semidirect
45. #19099220C22semidirect
46. #19099219C22semidirect
47. #19099218C22semidirect
48. #19099213C22semidirect
49. #19099212C22semidirect
50. #19099212C22semidirect
51. #19099207C22semidirect
52. #19099207C22semidirect
53. #19099207C22semidirect
54. #19099207C22semidirect
55. #19099207C22semidirect
56. #19099207C22semidirect
57. #19099207C22semidirect
58. #19099180C22semidirect
59. #19099180C22semidirect
60. #19099178C22semidirect
61. #19099175C22semidirect
62. #19099167C22semidirect
63. #19099167C22semidirect
64. #19099167C22semidirect
65. #19099163C22semidirect
66. #19099158C22semidirect
67. #19099148C22semidirect
68. #19099148C22semidirect
69. #19099142C22semidirect
71. #19099134C22semidirect
72. #19099134C22semidirect
73. #19099133C22semidirect
74. #19099130C22semidirect
75. #19099130C22semidirect
76. #19099130C22semidirect
77. #19099128C22semidirect
78. #19099122C22semidirect
79. #19099120C22semidirect
80. #19099120C22semidirect
81. #19099118C22semidirect
82. #19099117C22semidirect
83. #19099116C22semidirect
84. #19099111C22semidirect
85. #19099111C22semidirect
86. #19099111C22semidirect
87. #19099111C22semidirect
88. #19099111C22semidirect
89. #19099111C22semidirect
90. #19099111C22semidirect
91. #19099110C22semidirect
93. #19099109C22semidirect
94. C2×#14579161C22semidirect
95. C4⋊Q8×D79C22semidirect
96. #19099100C22semidirect
97. #19099095C22semidirect
98. #19099095C22semidirect
99. #19099094C22semidirect
100. #19099094C22semidirect
101. #19099093C22semidirect
102. #19099092C22semidirect
103. #19099091C22semidirect
104. C2×#14579148C22semidirect
105. C2×#14579148C22semidirect
106. #19099075C22semidirect
107. #19099073C22semidirect
108. #19099072C22semidirect
110. #19099070C22semidirect
111. #19099069C22semidirect
112. C2×#14579142C22semidirect
113. C2×#14579132C22semidirect
114. #19099042C22semidirect
115. #19099040C22semidirect
116. #19099038C22semidirect
117. #19099038C22semidirect
118. #41×Dic79C22semidirect
119. C4×#11929624C22semidirect
120. C4×#11929624C22semidirect
121. C4×#11929623C22semidirect
122. C2×D4×Dic79C22semidirect
123. C2×C42×D79C22semidirect
125. #550×C79C22semidirect
127. D42×C79C22semidirect
129. #535×C79C22semidirect
131. #532×C79C22semidirect
133. C2×#127×C79C22semidirect
615. #3498D79semidirect
621. C79#62836semidirect
645. #550C2×D79semidirect
662. D42C2×D79semidirect
684. #535C2×D79semidirect
702. #532C2×D79semidirect
706. C2×#127C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779842
#237778672
#237777682
#237777212
#237774032
#237773522
#237773252
#237773012
#237772952
#237772862
#237772742
#237771882
#237771802
#237770562
#237770402
#237766952
#237766932
C2×#190991112
C79×#34982
#6283679