Finite Group Databasebeta

← #35197217

Subgroups — #35197217

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#23777980C218yesmaximal, complemented
2#23777873C214yesmaximal, complemented
3#23777774C214yesmaximal, complemented
4#23777708C218yesmaximal, complemented
5#23777406C214yesmaximal, complemented
6#23777361C214yesmaximal, complemented
7#23777334C218yesmaximal, complemented
8#23777312C214yesmaximal, complemented
9#23777296C212yesmaximal, complemented
10#23777287C211yesmaximal, characteristic, complemented
11#23777277C211yesmaximal, characteristic, complemented
12#23777269C214yesmaximal, complemented
13#23777193C212yesmaximal, complemented
14#23777180C211yesmaximal, characteristic, complemented
15#23777173C211yesmaximal, characteristic, complemented
16#23777054C212yesmaximal, complemented
17#23777042C212yesmaximal, complemented
18#23776696C211yesmaximal, characteristic, complemented
19C2×#19099113C211yesmaximal, characteristic, complemented
20C79×#3444C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yescomplemented
22C2×#14579207C2212yes—
23C22×#11929624C2212yescomplemented
24#19099310C22116yescomplemented
25#19099303C22116yescomplemented
26#19099298C2214yescomplemented
27#19099296C2218yescomplemented
28#19099295C2218yescomplemented
29#19099292C2214yescomplemented
30#19099286C2214yescomplemented
31#19099285C2218yescomplemented
32#19099276C2218yescomplemented
33#19099269C2218yescomplemented
34#19099266C2218yescomplemented
35#19099257C2218yescomplemented
36#19099257C22116yescomplemented
37#19099255C2218yescomplemented
38#19099242C22116yescomplemented
39#19099237C22116yescomplemented
40#19099235C2214yescomplemented
41#19099234C2218yescomplemented
42#19099234C2214yescomplemented
43#19099232C2218yescomplemented
44#19099231C2218yescomplemented
45D4×Dic158C2214yescomplemented
46#19099225C2218yescomplemented
47#19099223C2218yescomplemented
48#19099222C2218yescomplemented
49#19099218C2218yescomplemented
50#19099218C2214yescomplemented
51#19099215C2218yescomplemented
52#19099213C2218yescomplemented
53#19099210C2218yescomplemented
54#19099209C2218yescomplemented
55#19099208C22116yescomplemented
56#19099208C2218yescomplemented
57#19099206C2218yescomplemented
58#19099204C2218yescomplemented
59#19099201C2218yescomplemented
60D4×D316C2214yescomplemented
61#19099197C2218yes—
62#19099186C2218yescomplemented
63#19099185C2218yescomplemented
64#19099184C2218yescomplemented
65#19099176C2214yescomplemented
66#19099169C2214yescomplemented
67#19099166C2218yescomplemented
68#19099164C2218yescomplemented
69#19099164C22116yescomplemented
70#19099154C22116yescomplemented
71#19099152C22116yescomplemented
72#19099146C22116yescomplemented
73#19099143C2218yescomplemented
74#19099139C2212yes—
75#19099139C2214yescomplemented
76#19099134C2212yescomplemented
77#19099133C2214yescomplemented
78#19099132C2212yescomplemented
79#19099132C2214yescomplemented
80#19099131C2214yescomplemented
81#19099129C2218yescomplemented
82#19099128C2218yescomplemented
83#19099127C2212yes—
84#19099123C2218yescomplemented
85#19099120C2211yescharacteristic, complemented
86#19099120C2212yescomplemented
87#19099118C2214yescomplemented
88#19099114C2212yescomplemented
89#19099114C2214yescomplemented
90#19099113C2211yescharacteristic
91#19099113C2214yescomplemented
92#19099113C2214yescomplemented
93#19099113C2214yescomplemented
94#19099113C2214yescomplemented
95#19099113C2214yescomplemented
96#19099113C2212yescomplemented
97#19099111C2212yescomplemented
98C2×#14579161C2211yescharacteristic, complemented
99C4⋊Q8×D79C2212yescomplemented
100C2×#14579158C2211yescharacteristic
101#127×D79C2212yescomplemented
102#19099097C2218yescomplemented
103#19099097C2214yescomplemented
104#19099097C2212yescomplemented
105#19099097C2212yescomplemented
106#19099097C2214yescomplemented
107C2×#14579149C2212yescomplemented
108C2×#14579149C2214yescomplemented
109#19099074C2211yescharacteristic
110#19099074C2211yescharacteristic, complemented
111#19099074C2214yescomplemented
112#19099071C2218yescomplemented
113#123×D79C2218yescomplemented
114C2×#14579135C2214yescomplemented
115#19099045C2218yescomplemented
116#19099040C2212yescomplemented
117#19099037C2212yescomplemented
118#19099035C2218yescomplemented
119C4×#11929624C2211yescharacteristic
120C4×#11929624C2214yescomplemented
121C4×#11929624C2211yescharacteristic, complemented
122C2×C4×D316C2214yescomplemented
123#533×C79C2211yescharacteristic, complemented
124#533×C79C2212yescomplemented
125#532×C79C2211yescharacteristic
126#532×C79C2212yescomplemented
127#529×C79C2214yescomplemented
128#529×C79C2214yescomplemented
129#529×C79C2214yescomplemented
130#525×C79C2212yescomplemented
131#525×C79C2214yescomplemented
132C4×#41×C79C2212yescomplemented
133C4×#41×C79C2214yescomplemented
134C22×C42×C79C2211yescharacteristic, complemented
135#14579208—48no—
136#14579207—48no—
137C2×#11929625C2314yes—
138C2×#11929625C2318yes—
139C2×#11929624—48no—
140C2×#11929624C2311yescharacteristic
141C2×#11929624C2311yescharacteristic
142C2×#11929624C2314yes—
143C2×#11929624C2314yes—
144C2×#11929624C2314yes—
145C2×#11929624C2318yes—
146C2×#11929624C2318yes—
147C2×#11929623C2318yes—
148C2×#11929623C2314yes—
149C22×Dic158C2312yes—
150C22×Dic158C2314yes—
151C2×Q8×D79C2314yes—
152C22×D316C2312yes—
153C22×D316C2314yes—
154C22×D316C2314yes—
155C22×C22⋊D79C2314yes—
156C2×D4×D79C2318yes—
157C2×D4×D79C2314yes—
158C2×D4×D79C2318yes—
159C22×C4×D79C2314yes—
160#14579161C2314yes—
161#14579161C2311yescharacteristic
162#14579161C2312yes—
163#14579161C2312yes—
164#14579161C2314yes—
165#14579161C2312yes—
166#14579160C2318yes—
167#14579159C2314yes—
168#14579158C2312yes—
169#14579158C2314yes—
170#14579158C2314yes—
171#14579158C2312yes—
172#14579158C2311yescharacteristic
173#14579157C2318yes—
174#14579157C23116yes—
175#14579157C2314yes—
176#14579156C23116yes—
177#14579156C23116yes—
178#14579155C23116yes—
179#14579155C2314yes—
180#14579155C2314yes—
181#14579153C2314yes—
182#14579153C2312yes—
183#14579152C23116yes—
184#14579152C2318yes—
185#14579150C2318yes—
186#14579150C2314yes—
187#14579149C2314yes—
188#14579149C2314yes—
189#14579149C2314yes—
190#14579149C23116yes—
191#14579149C2314yes—
192#14579149C2318yes—
193#14579149C2311yescharacteristic
194#14579149C2314yes—
195#14579149C2311yescharacteristic
196#14579148C2314yes—
197#14579147C23116yes—
198#14579147C23116yes—
199#14579146C23116yes—
200#14579146C23116yes—
201#14579145C2318yes—
202#14579145C23116yes—
203#14579144C2314yes—
204#14579144C2314yes—
205#14579144C23116yes—
206#14579144C2312yes—
207#14579144C2312yes—
208#14579143C23116yes—
209#14579143C23116yes—
210#14579143C23116yes—
211#14579143C23116yes—
212#14579142C2318yes—
213#14579141C2318yes—
214#14579141C23116yes—
215#14579140C2318yes—
216#14579140C2312yes—
217#14579140C2312yes—
218#14579140C2314yes—
219#14579140C2314yes—
220#14579139C23116yes—
221#14579139C23116yes—
222#14579138C23116yes—
223#14579137C2318yes—
224#14579136C23116yes—
225#14579136C2318yes—
226#14579136C23116yes—
227#14579136C2318yes—
228#14579136C2318yes—
229#14579135C2318yes—
230#14579135C2318yes—
231#14579135C23116yes—
232#14579135C2318yes—
233#14579135C2318yes—
234#14579135C2314yes—
235#14579135C2312yes—
236#14579135C2312yes—
237#14579135C2314yes—
238#14579135C2318yes—
239#14579134C23116yes—
240#14579134C23116yes—
241#14579134C23116yes—
242#14579134C23116yes—
243#14579133C23116yes—
244#14579132C23116yes—
245#14579132C2318yes—
246#14579131C23116yes—
247#14579131C23116yes—
248#14579131C2318yes—
249#14579130C2312yes—
250#14579130C2312yes—
251#14579129C23116yes—
252#14579129C2318yes—
253Q8×Dic79C2318yes—
254C4×Dic158C2318yes—
255C4×Dic158C2312yes—
256C4×Dic158C2312yes—
257C4×Dic158C2314yes—
258C4×Dic158C2314yes—
259#14579126C2318yes—
260C4×D316C2318yes—
261C4×D316C2318yes—
262C4×D316C23116yes—
263C4×D316C2318yes—
264C4×D316C2312yes—
265C4×D316C2314yes—
266C4×D316C2318yes—
267C4×D316C2314yes—
268C4×D316C2312yes—
269C4×D316C2318yes—
270D4×Dic79C2318yes—
271#14579123C23116yes—
272#14579123C2318yes—
273#14579123C2318yes—
274#14579123C2318yes—
275C4×C22⋊D79C23116yes—
276C4×C22⋊D79C2314yes—
277C4×C22⋊D79C2314yes—
278C4×C22⋊D79C2314yes—
279C4×C22⋊D79C2314yes—
280C4×C22⋊D79C2314yes—
281C4×C22⋊D79C2314yes—
282(C22⋊D79)⋊C4C23116yes—
283#14579120C2314yes—
284#14579120C2311yescharacteristic
285#14579120C2311yescharacteristic
286#14579119C2318yes—
287#14579118C2314yes—
288#14579118C23116yes—
289#14579118C2312yes—
290#14579118C2312yes—
291#14579118C2314yes—
292#14579117C2318yes—
293C2×C4⋊Dic79C2314yes—
294C4⋊C4×D79C2318yes—
295C4⋊C4×D79C23116yes—
296C2×(C2×D79)⋊C4C23116yes—
297C2×(C2×D79)⋊C4C2318yes—
298C22⋊C4×D79C23116yes—
299C22⋊C4×D79C2318yes—
300C42×D79C2312yes—
301C42×D79C2312yes—
302C2×#41×C79C2312yes—
303C2×#41×C79C2314yes—
304C23×C4×C79C2311yescharacteristic
305C23×C4×C79C2312yes—
306C4⋊Q8×C79C2311yescharacteristic
307C4⋊Q8×C79C2312yes—
308#127×C79C2311yescharacteristic
309#126×C79C2318yes—
310#125×C79C2312yes—
311#125×C79C2314yes—
312#124×C79C2314yes—
313#124×C79C2312yes—
314#123×C79C2318yes—
315#123×C79C2314yes—
316C22⋊Q8×C79C2314yes—
317C22⋊Q8×C79C2314yes—
318C22⋊Q8×C79C2314yes—
319#121×C79C2314yes—
320#121×C79C2314yes—
321#121×C79C2314yes—
322#120×C79C2314yes—
323C4×Q8×C79C2314yes—
324C4×Q8×C79C2314yes—
325C4×Q8×C79C2314yes—
326C4×D4×C79C2318yes—
327C4×D4×C79C2314yes—
328C4×D4×C79C2314yes—
329C4×D4×C79C2318yes—
330C4×D4×C79C2314yes—
331C4×D4×C79C2318yes—
332#117×C79C2312yes—
333#117×C79C2314yes—
334#117×C79C2318yes—
335#117×C79C2314yes—
336C2×C42×C79C2311yescharacteristic
337C2×C42×C79C2312yes—
338C2×C42×C79C2312yes—
339C2×C42×C79C2312yes—
340C2×C42×C79C2312yes—
341C2×C42×C79C2311yescharacteristic
342C2×C42×C79C2312yes—
343C2×C42×C79C2314yes—
344C23×D79C2414yes—
345C23×D79C2418yes—
346#11929625—416no—
347#11929625—48no—
348#11929624—24no—
349#11929624—24no—
350#11929624—416no—
351#11929624—416no—
352#11929624—48no—
353#11929624—48no—
354#11929624—48no—
355#11929623—416no—
356#11929623—48no—
357C2×Dic158—28no—
358C2×Dic158—48no—
359C2×Dic158C2414yes—
360C2×Dic158C2411yescharacteristic
361C2×Dic158C2414yes—
362C2×Dic158C2411yescharacteristic
363C2×Dic158C2418yes—
364C2×Dic158C2414yes—
365Q8×D79—48no—
366C2×D316—28no—
367C2×D316—48no—
368C2×D316—48no—
369C2×D316C2411yescharacteristic
370C2×D316C2414yes—
371C2×D316C2414yes—
372C2×D316C2411yescharacteristic
373C2×D316C2418yes—
374C2×D316C2414yes—
375C2×D316C24116yes—
376C2×D316C2418yes—
377C2×D316C2418yes—
378C2×C22⋊D79—48no—
379C2×C22⋊D79C2412yes—
380C2×C22⋊D79C2412yes—
381C2×C22⋊D79C2418yes—
382C2×C22⋊D79C24116yes—
383C2×C22⋊D79C2414yes—
384C2×C22⋊D79C2414yes—
385C2×C22⋊D79C2418yes—
386C2×C22⋊D79C24116yes—
387D4×D79—416no—
388D4×D79—48no—
389D4×D79—416no—
390C22×Dic79C2414yes—
391C22×Dic79C2418yes—
392C2×C4×D79—48no—
393C2×C4×D79C2412yes—
394C2×C4×D79C2414yes—
395C2×C4×D79C2412yes—
396C2×C4×D79C2414yes—
397C2×C4×D79C2418yes—
398C2×C4×D79C24116yes—
399C2×C4×D79C2418yes—
400C2×C4×D79C24116yes—
401C4⋊Dic79C2418yes—
402C4⋊Dic79C24116yes—
403C4⋊Dic79C2418yes—
404C4⋊Dic79C2412yes—
405C4⋊Dic79C2412yes—
406C4⋊Dic79C2414yes—
407C4⋊Dic79C2414yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C24116yes—
410Dic79⋊C4C24116yes—
411Dic79⋊C4C2414yes—
412Dic79⋊C4C2414yes—
413Dic79⋊C4C2414yes—
414Dic79⋊C4C2414yes—
415Dic79⋊C4C2414yes—
416C22⋊Dic79C2412yes—
417C22⋊Dic79C24116yes—
418C22⋊Dic79C2412yes—
419C22⋊Dic79C2414yes—
420C22⋊Dic79C2414yes—
421(C2×D79)⋊C4C2414yes—
422(C2×D79)⋊C4C24116yes—
423(C2×D79)⋊C4C24116yes—
424(C2×D79)⋊C4C2414yes—
425(C2×D79)⋊C4C24116yes—
426(C2×D79)⋊C4C24116yes—
427(C2×D79)⋊C4C24116yes—
428(C2×D79)⋊C4C2414yes—
429(C2×D79)⋊C4C2414yes—
430(C2×D79)⋊C4C2414yes—
431(C2×D79)⋊C4C2414yes—
432(C2×D79)⋊C4C24116yes—
433C4×Dic79C2412yes—
434C4×Dic79C2414yes—
435C4×Dic79C2414yes—
436C4×Dic79C2412yes—
437C4×Dic79C24116yes—
438C24×C79C2411yescharacteristic
439#41×C79—28no—
440#41×C79—48no—
441C2×Q8×C79C2412yes—
442C2×Q8×C79C2414yes—
443C2×D4×C79C2414yes—
444C2×D4×C79C2412yes—
445C2×D4×C79C2414yes—
446C2×D4×C79C2418yes—
447C22×C4×C79—24no—
448C22×C4×C79—44no—
449C22×C4×C79C2414yes—
450C22×C4×C79C2412yes—
451C22×C4×C79C2412yes—
452C22×C4×C79C2412yes—
453C22×C4×C79C2412yes—
454C22×C4×C79C2412yes—
455C22×C4×C79C2411yescharacteristic
456C22×C4×C79C2412yes—
457C22×C4×C79C2412yes—
458C22×C4×C79C2412yes—
459C22×C4×C79C2418yes—
460C22×C4×C79C2411yescharacteristic
461C4⋊C4×C79C2414yes—
462C4⋊C4×C79C2414yes—
463C4⋊C4×C79C2414yes—
464C4⋊C4×C79C2418yes—
465C4⋊C4×C79C2418yes—
466C4⋊C4×C79C2418yes—
467C22⋊C4×C79C2414yes—
468C22⋊C4×C79C2418yes—
469C22⋊C4×C79C2418yes—
470C22⋊C4×C79C2418yes—
471C22⋊C4×C79C2418yes—
472C42×C79C2411yescharacteristic
473C42×C79C2412yes—
474C42×C79C2411yescharacteristic
475C42×C79C2412yes—
476C42×C79C2412yes—
477C42×C79C2412yes—
478C42×C79C2411yescharacteristic
479C42×C79C2412yes—
480C42×C79C2412yes—
481C42×C79C2411yescharacteristic
482C42×C79C2418yes—
483C42×C79C2414yes—
484C23×C79—22no—
485C23×C79—42no—
486C23×C79C2514yes—
487C23×C79C2512yes—
488C23×C79C2511yescharacteristic
489C22×D79—28no—
490C22×D79—48no—
491C22×D79—48no—
492C22×D79—416no—
493C22×D79C2512yes—
494C22×D79C2518yes—
495C22×D79C2512yes—
496Q8×C79—24no—
497Q8×C79—28no—
498D4×C79—28no—
499D4×C79—24no—
500D4×C79—28no—
501D4×C79—48no—
502C2×C4×C79—22no—
503C2×C4×C79—28no—
504C2×C4×C79—24no—
505C2×C4×C79—24no—
506C2×C4×C79—24no—
507C2×C4×C79—24no—
508C2×C4×C79—24no—
509C2×C4×C79—42no—
510C2×C4×C79—42no—
511C2×C4×C79—42no—
512C2×C4×C79—48no—
513C2×C4×C79H(5,𝔽2)14yes—
514C2×C4×C79C2518yes—
515C2×C4×C79C2512yes—
516C2×C4×C79C2512yes—
517C2×C4×C79C2512yes—
518C2×C4×C79C2512yes—
519C2×C4×C79C2514yes—
520C2×C4×C79C2511yescharacteristic
521C2×C4×C79C2511yescharacteristic
522C2×C4×C79C2512yes—
523C22⋊D79—24no—
524C22⋊D79—24no—
525C22⋊D79—48no—
526C22⋊D79—416no—
527C22⋊D79—416no—
528C22⋊D79—48no—
529C22⋊D79—44no—
530C22⋊D79—44no—
531C2×Dic79—28no—
532C2×Dic79—48no—
533C2×Dic79C2514yes—
534C2×Dic79C2512yes—
535C2×Dic79C2514yes—
536C2×Dic79C2518yes—
537C2×Dic79C2512yes—
538D316—28no—
539D316—28no—
540D316—22no—
541D316—22no—
542D316—216no—
543D316—48no—
544D316—48no—
545D316—44no—
546D316—416no—
547C4×D79—24no—
548C4×D79—24no—
549C4×D79—28no—
550C4×D79—28no—
551C4×D79—416no—
552C4×D79—48no—
553C4×D79—48no—
554C4×D79—416no—
555Dic158—28no—
556Dic158—28no—
557Dic158—22no—
558Dic158—22no—
559Dic158—48no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—22no—
563C22×C79—24no—
564C22×C79—22no—
565C22×C79—28no—
566C22×C79—22no—
567C22×C79—44no—
568C22×C79C2×H(5,𝔽2)12yes—
569C22×C79C2611yescharacteristic
570C2×D79—22no—
571C2×D79—22no—
572C2×D79—28no—
573C2×D79—24no—
574C2×D79—216no—
575C2×D79—24no—
576C2×D79—88no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—24no—
580C4×C79—22no—
581C4×C79—22no—
582C4×C79—22no—
583C4×C79—28no—
584C4×C79C2×H(5,𝔽2)12yes—
585C4×C79C2×H(5,𝔽2)12yes—
586C4×C79#58514yes—
587Dic79—22no—
588Dic79—22no—
589Dic79—28no—
590Dic79—24no—
591Dic79—24no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—44no—
595C2×C79—42no—
596C2×C79C22×H(5,𝔽2)11yescharacteristic
597C2×C79C2×#58512yes—
598D79—42no—
599D79—48no—
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#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444D7911yescharacteristic, complemented
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)—792no—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—794no—
629#559—798no—
630#557—794no—
631#556—798no—
632#556—794no—
633#555—798no—
634#554—798no—
635#553—798no—
636#553—798no—
637#553—7916no—
638#552—798no—
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—794no—
644#550—798no—
645#550—794no—
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—798no—
658#546—798no—
659#546—7916no—
660#546—798no—
661D42—798no—
662D42—794no—
663#542—798no—
664#542—798no—
665#542—798no—
666#541—794no—
667#540—794no—
668#540—798no—
669#540—798no—
670#540—7916no—
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—792no—
676#536—794no—
677#536—792no—
678#536—794no—
679#535—792no—
680#535—794no—
681#535—798no—
682#535—798no—
683#535—792no—
684#535—794no—
685#534—798no—
686#533—794no—
687#533—791no—
688#533—792no—
689#533C2×D7911yescharacteristic, complemented
690#533C2×D7912yescomplemented
691#532—792no—
692#532—794no—
693#532—792no—
694#532—794no—
695#532—794no—
696#532—794no—
697#532—794no—
698#532—791no—
699#532—792no—
700#532—794no—
701#532C2×D7911yescharacteristic
702#532C2×D7912yescomplemented
703C2×C4⋊Q8—792no—
704C2×C4⋊Q8—791no—
705C2×#127—792no—
706C2×#127—791no—
707#529—794no—
708#529—792no—
709#529—792no—
710#529—794no—
711#529—798no—
712#529C2×D7914yescomplemented
713#529C2×D7914yescomplemented
714#529C2×D7914yescomplemented
715C2×#124—792no—
716C2×#124—794no—
717#525—791no—
718#525—791no—
719#525—794no—
720#525—798no—
721#525C2×D7912yescomplemented
722#525C2×D7914yescomplemented
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519—792no—
727#518—798no—
728#518—792no—
729C4×#41—791no—
730C4×#41—791no—
731C4×#41—794no—
732C4×#41C2×D7912yescomplemented
733C4×#41C2×D7914yescomplemented
734C2×C4×D4—794no—
735C22×C42C2×D7911yescharacteristic, complemented
7362−1+4—3168no—
737H(5,𝔽2)—3168no—
738C2×#41—3168no—
739C2×#41—798no—
740C2×#41—794no—
741C2×#41—798no—
742C2×#41—794no—
743C2×#41—794no—
744C2×#41—798no—
745C2×#41—798no—
746C2×#41—794no—
747C2×#41—794no—
748C2×#41—791no—
749C2×#41—791no—
750C2×#41C22×D7912yes—
751C2×#41C22×D7914yes—
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8—792no—
755C22×D4—794no—
756C22×D4—798no—
757C22×D4—798no—
758C22×D4—794no—
759C22×D4—794no—
760C22×D4—794no—
761C22×D4—792no—
762C23×C4—794no—
763C23×C4C22×D7911yescharacteristic
764C23×C4C22×D7912yes—
765C4⋊Q8—794no—
766C4⋊Q8—798no—
767C4⋊Q8—792no—
768C4⋊Q8—792no—
769C4⋊Q8—794no—
770C4⋊Q8—791no—
771C4⋊Q8—792no—
772C4⋊Q8—794no—
773C4⋊Q8C22×D7911yescharacteristic
774C4⋊Q8C22×D7912yes—
775#127—794no—
776#127—798no—
777#127—7916no—
778#127—792no—
779#127—792no—
780#127—794no—
781#127—791no—
782#127—794no—
783#127C22×D7911yescharacteristic
784#126—7916no—
785#126—7916no—
786#126—794no—
787#126—794no—
788#126—7916no—
789#126C22×D7918yes—
790#125—798no—
791#125—7916no—
792#125—792no—
793#125—794no—
794#125C22×D7912yes—
795#125C22×D7914yes—
796#124—794no—
797#124—798no—
798#124—794no—
799#124—7916no—
800#124—7916no—
801#124—791no—
802#124—794no—
803#124—794no—
804#124—798no—
805#124—794no—
806#124—794no—
807#124—7916no—
808#124—791no—
809#124—794no—
810#124C22×D7912yes—
811#124C22×D7914yes—
812#123—798no—
813#123—792no—
814#123—792no—
815#123—794no—
816#123—794no—
817#123—7916no—
818#123—7916no—
819#123—7916no—
820#123—798no—
821#123—7916no—
822#123—7916no—
823#123—7916no—
824#123—7916no—
825#123—7916no—
826#123C22×D7914yes—
827#123C22×D7918yes—
828C22⋊Q8—798no—
829C22⋊Q8—792no—
830C22⋊Q8—792no—
831C22⋊Q8—794no—
832C22⋊Q8—794no—
833C22⋊Q8—798no—
834C22⋊Q8—7916no—
835C22⋊Q8—798no—
836C22⋊Q8—7916no—
837C22⋊Q8—7916no—
838C22⋊Q8—7916no—
839C22⋊Q8C22×D7914yes—
840C22⋊Q8C22×D7914yes—
841C22⋊Q8C22×D7914yes—
842#121—798no—
843#121—7916no—
844#121—7916no—
845#121—798no—
846#121—798no—
847#121—798no—
848#121—798no—
849#121—792no—
850#121—794no—
851#121—792no—
852#121—794no—
853#121—798no—
854#121—7916no—
855#121—798no—
856#121—798no—
857#121—798no—
858#121—7916no—
859#121—7916no—
860#121—7916no—
861#121—7916no—
862#121—7916no—
863#121—7916no—
864#121C22×D7914yes—
865#121C22×D7914yes—
866#121C22×D7914yes—
867#120—792no—
868#120—792no—
869#120—798no—
870#120—7916no—
871#120—798no—
872#120—7916no—
873#120—7916no—
874#120C22×D7914yes—
875C4×Q8—798no—
876C4×Q8—798no—
877C4×Q8—792no—
878C4×Q8—792no—
879C4×Q8—794no—
880C4×Q8—794no—
881C4×Q8—798no—
882C4×Q8C22×D7914yes—
883C4×Q8C22×D7914yes—
884C4×Q8C22×D7914yes—
885C4×D4—798no—
886C4×D4—794no—
887C4×D4—794no—
888C4×D4—794no—
889C4×D4—794no—
890C4×D4—794no—
891C4×D4—794no—
892C4×D4—7916no—
893C4×D4—798no—
894C4×D4—798no—
895C4×D4—7916no—
896C4×D4—798no—
897C4×D4—7916no—
898C4×D4—798no—
899C4×D4—798no—
900C4×D4—798no—
901C4×D4—798no—
902C4×D4—792no—
903C4×D4—794no—
904C4×D4—794no—
905C4×D4—792no—
906C4×D4—798no—
907C4×D4—7916no—
908C4×D4C22×D7914yes—
909C4×D4C22×D7918yes—
910C4×D4C22×D7918yes—
911C4×D4C22×D7918yes—
912C4×D4C22×D7914yes—
913C4×D4C22×D7914yes—
914#117—791no—
915#117—791no—
916#117—794no—
917#117—798no—
918#117—798no—
919#117—794no—
920#117—794no—
921#117—792no—
922#117—792no—
923#117—7916no—
924#117C22×D7912yes—
925#117C22×D7914yes—
926#117C22×D7914yes—
927#117C22×D7918yes—
928C2×C4⋊C4—794no—
929C2×C4⋊C4—7916no—
930C2×C4⋊C4—798no—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—7916no—
933C2×C22⋊C4—798no—
934C2×C22⋊C4—7916no—
935C2×C42—792no—
936C2×C42—792no—
937C2×C42C22×D7912yes—
938C2×C42C22×D7911yescharacteristic
939C2×C42C22×D7912yes—
940C2×C42C22×D7914yes—
941C2×C42C22×D7911yescharacteristic
942C2×C42C22×D7912yes—
943C2×C42C22×D7912yes—
944C2×C42C22×D7912yes—
945C24—798no—
946C24—794no—
947C24C23×D7911yescharacteristic
948#41—28no—
949#41—48no—
950#41—31616no—
951#41—31616no—
952#41—3168no—
953#41—3168no—
954#41—3168no—
955#41—3168no—
956#41—31616no—
957#41—31616no—
958#41—3168no—
959#41—1584no—
960#41—1584no—
961C2×Q8—3168no—
962C2×Q8—3168no—
963C2×Q8—794no—
964C2×Q8—798no—
965C2×Q8—791no—
966C2×Q8—794no—
967C2×Q8—794no—
968C2×Q8—791no—
969C2×Q8—1588no—
970C2×Q8C23×D7914yes—
971C2×Q8C23×D7912yes—
972C2×D4—3168no—
973C2×D4—3168no—
974C2×D4—31616no—
975C2×D4—31616no—
976C2×D4—3168no—
977C2×D4—3168no—
978C2×D4—794no—
979C2×D4—7916no—
980C2×D4—794no—
981C2×D4—798no—
982C2×D4—7916no—
983C2×D4—798no—
984C2×D4—792no—
985C2×D4—792no—
986C2×D4—794no—
987C2×D4—7916no—
988C2×D4—798no—
989C2×D4—798no—
990C2×D4—798no—
991C2×D4—791no—
992C2×D4—794no—
993C2×D4—794no—
994C2×D4—791no—
995C2×D4—1588no—
996C2×D4C23×D7914yes—
997C2×D4C23×D7914yes—
998C2×D4C23×D7912yes—
999C2×D4C23×D7918yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—3168no—
1003C22×C4—798no—
1004C22×C4—7916no—
1005C22×C4—7916no—
1006C22×C4—798no—
1007C22×C4—798no—
1008C22×C4—794no—
1009C22×C4—794no—
1010C22×C4—794no—
1011C22×C4—792no—
1012C22×C4—792no—
1013C22×C4C23×D7912yes—
1014C22×C4C23×D7912yes—
1015C22×C4C23×D7912yes—
1016C22×C4C23×D7912yes—
1017C22×C4C23×D7912yes—
1018C22×C4C23×D7911yescharacteristic
1019C22×C4C23×D7914yes—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7912yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D7918yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—794no—
1026C4⋊C4—7916no—
1027C4⋊C4—794no—
1028C4⋊C4—794no—
1029C4⋊C4—794no—
1030C4⋊C4—794no—
1031C4⋊C4—794no—
1032C4⋊C4—7916no—
1033C4⋊C4—798no—
1034C4⋊C4—798no—
1035C4⋊C4—7916no—
1036C4⋊C4—792no—
1037C4⋊C4—792no—
1038C4⋊C4—794no—
1039C4⋊C4—794no—
1040C4⋊C4C23×D7914yes—
1041C4⋊C4C23×D7918yes—
1042C4⋊C4C23×D7914yes—
1043C4⋊C4C23×D7914yes—
1044C4⋊C4C23×D7918yes—
1045C4⋊C4C23×D7918yes—
1046C22⋊C4—792no—
1047C22⋊C4—7916no—
1048C22⋊C4—792no—
1049C22⋊C4—794no—
1050C22⋊C4—794no—
1051C22⋊C4—794no—
1052C22⋊C4—794no—
1053C22⋊C4—7916no—
1054C22⋊C4—7916no—
1055C22⋊C4—7916no—
1056C22⋊C4—7916no—
1057C22⋊C4—7916no—
1058C22⋊C4—794no—
1059C22⋊C4—794no—
1060C22⋊C4—794no—
1061C22⋊C4—7916no—
1062C22⋊C4—794no—
1063C22⋊C4C23×D7914yes—
1064C22⋊C4C23×D7918yes—
1065C22⋊C4C23×D7918yes—
1066C22⋊C4C23×D7918yes—
1067C22⋊C4C23×D7918yes—
1068C42—792no—
1069C42—794no—
1070C42—794no—
1071C42—792no—
1072C42—7916no—
1073C42C23×D7911yescharacteristic
1074C42C23×D7911yescharacteristic
1075C42C23×D7912yes—
1076C42C23×D7911yescharacteristic
1077C42C23×D7912yes—
1078C42C23×D7911yescharacteristic
1079C42C23×D7912yes—
1080C42C23×D7912yes—
1081C42C23×D7912yes—
1082C42C23×D7912yes—
1083C42C23×D7918yes—
1084C42C23×D7914yes—
1085C23—22no—
1086C23—42no—
1087C23—3168no—
1088C23—3168no—
1089C23—31616no—
1090C23—792no—
1091C23—798no—
1092C23—792no—
1093C23—1588no—
1094C23C24×D7914yes—
1095C23C24×D7912yes—
1096C23C24×D7911yescharacteristic
1097Q8—24no—
1098Q8—28no—
1099Q8—3168no—
1100Q8—3164no—
1101Q8—1582no—
1102Q8—1588no—
1103Q8—1588no—
1104Q8—1582no—
1105D4—28no—
1106D4—24no—
1107D4—28no—
1108D4—48no—
1109D4—3168no—
1110D4—3168no—
1111D4—3164no—
1112D4—31616no—
1113D4—3168no—
1114D4—31616no—
1115D4—31616no—
1116D4—3164no—
1117D4—3164no—
1118D4—3168no—
1119D4—1584no—
1120D4—1584no—
1121D4—1582no—
1122D4—1588no—
1123D4—1588no—
1124D4—1582no—
1125D4—15816no—
1126C2×C4—22no—
1127C2×C4—24no—
1128C2×C4—24no—
1129C2×C4—28no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—48no—
1137C2×C4—31616no—
1138C2×C4—3168no—
1139C2×C4—3168no—
1140C2×C4—31616no—
1141C2×C4—3168no—
1142C2×C4—794no—
1143C2×C4—794no—
1144C2×C4—792no—
1145C2×C4—798no—
1146C2×C4—792no—
1147C2×C4—1588no—
1148C2×C4—1584no—
1149C2×C4—1584no—
1150C2×C4—1588no—
1151C2×C4—1588no—
1152C2×C4#1457920714yes—
1153C2×C4C24×D7918yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7912yes—
1156C2×C4C24×D7912yes—
1157C2×C4C24×D7912yes—
1158C2×C4C24×D7914yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—24no—
1165C22—22no—
1166C22—22no—
1167C22—28no—
1168C22—44no—
1169C22—6328no—
1170C22—1582no—
1171C22—1588no—
1172C22—1582no—
1173C22—15816no—
1174C22—1584no—
1175C22—1584no—
1176C22—12648no—
1177C22C2×#1457920712yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—28no—
1185C4—1582no—
1186C4—1588no—
1187C4—1582no—
1188C4—1584no—
1189C4—1584no—
1190C4C2×#1457920712yes—
1191C4C2×#1457920712yes—
1192C4#1909939914yes—
1193C2—22no—
1194C2—42no—
1195C2—44no—
1196C2—3168no—
1197C2—3162no—
1198C2—3162no—
1199C2C22×#1457920711yescharacteristic
1200C2C2×#1909939912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23777980C2semidirect
2. #23777873C2semidirect
3. #23777774C2semidirect
4. #23777708C2semidirect
5. #23777406C2semidirect
6. #23777361C2semidirect
7. #23777334C2semidirect
8. #23777312C2semidirect
9. #23777296C2semidirect
10. #23777287C2semidirect
11. #23777277C2semidirect
12. #23777269C2semidirect
13. #23777193C2semidirect
14. #23777180C2semidirect
15. #23777173C2semidirect
16. #23777054C2semidirect
17. #23777042C2semidirect
18. #23776696C2semidirect
19. C2×#19099113C2semidirect
20. C79×#3444C2semidirect
21. C2×#14579208C22semidirect
23. C22×#11929624C22semidirect
24. #19099310C22semidirect
25. #19099303C22semidirect
26. #19099298C22semidirect
27. #19099296C22semidirect
28. #19099295C22semidirect
29. #19099292C22semidirect
30. #19099286C22semidirect
31. #19099285C22semidirect
32. #19099276C22semidirect
33. #19099269C22semidirect
34. #19099266C22semidirect
35. #19099257C22semidirect
36. #19099257C22semidirect
37. #19099255C22semidirect
38. #19099242C22semidirect
39. #19099237C22semidirect
40. #19099235C22semidirect
41. #19099234C22semidirect
42. #19099234C22semidirect
43. #19099232C22semidirect
44. #19099231C22semidirect
45. D4×Dic158C22semidirect
46. #19099225C22semidirect
47. #19099223C22semidirect
48. #19099222C22semidirect
49. #19099218C22semidirect
50. #19099218C22semidirect
51. #19099215C22semidirect
52. #19099213C22semidirect
53. #19099210C22semidirect
54. #19099209C22semidirect
55. #19099208C22semidirect
56. #19099208C22semidirect
57. #19099206C22semidirect
58. #19099204C22semidirect
59. #19099201C22semidirect
60. D4×D316C22semidirect
62. #19099186C22semidirect
63. #19099185C22semidirect
64. #19099184C22semidirect
65. #19099176C22semidirect
66. #19099169C22semidirect
67. #19099166C22semidirect
68. #19099164C22semidirect
69. #19099164C22semidirect
70. #19099154C22semidirect
71. #19099152C22semidirect
72. #19099146C22semidirect
73. #19099143C22semidirect
75. #19099139C22semidirect
76. #19099134C22semidirect
77. #19099133C22semidirect
78. #19099132C22semidirect
79. #19099132C22semidirect
80. #19099131C22semidirect
81. #19099129C22semidirect
82. #19099128C22semidirect
84. #19099123C22semidirect
85. #19099120C22semidirect
86. #19099120C22semidirect
87. #19099118C22semidirect
88. #19099114C22semidirect
89. #19099114C22semidirect
91. #19099113C22semidirect
92. #19099113C22semidirect
93. #19099113C22semidirect
94. #19099113C22semidirect
95. #19099113C22semidirect
96. #19099113C22semidirect
97. #19099111C22semidirect
98. C2×#14579161C22semidirect
99. C4⋊Q8×D79C22semidirect
101. #127×D79C22semidirect
102. #19099097C22semidirect
103. #19099097C22semidirect
104. #19099097C22semidirect
105. #19099097C22semidirect
106. #19099097C22semidirect
107. C2×#14579149C22semidirect
108. C2×#14579149C22semidirect
110. #19099074C22semidirect
111. #19099074C22semidirect
112. #19099071C22semidirect
113. #123×D79C22semidirect
114. C2×#14579135C22semidirect
115. #19099045C22semidirect
116. #19099040C22semidirect
117. #19099037C22semidirect
118. #19099035C22semidirect
120. C4×#11929624C22semidirect
121. C4×#11929624C22semidirect
122. C2×C4×D316C22semidirect
123. #533×C79C22semidirect
124. #533×C79C22semidirect
126. #532×C79C22semidirect
127. #529×C79C22semidirect
128. #529×C79C22semidirect
129. #529×C79C22semidirect
130. #525×C79C22semidirect
131. #525×C79C22semidirect
132. C4×#41×C79C22semidirect
133. C4×#41×C79C22semidirect
134. C22×C42×C79C22semidirect
619. #3444D79semidirect
621. C79#62836semidirect
689. #533C2×D79semidirect
690. #533C2×D79semidirect
702. #532C2×D79semidirect
712. #529C2×D79semidirect
713. #529C2×D79semidirect
714. #529C2×D79semidirect
721. #525C2×D79semidirect
722. #525C2×D79semidirect
732. C4×#41C2×D79semidirect
733. C4×#41C2×D79semidirect
735. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779802
#237778732
#237777742
#237777082
#237774062
#237773612
#237773342
#237773122
#237772962
#237772872
#237772772
#237772692
#237771932
#237771802
#237771732
#237770542
#237770422
#237766962
C2×#190991132
C79×#34442
#6283679