Finite Group Databasebeta

← #35196420

Subgroups — #35196420

Order 20224.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777457C218yesmaximal, complemented
2#23777369C214yesmaximal, complemented
3#23777352C214yesmaximal, complemented
4#23777262C212yesmaximal, complemented
5#23777234C214yesmaximal, complemented
6#23777203C211yesmaximal, characteristic, complemented
7#23777119C212yesmaximal, complemented
8#23777097C214yesmaximal, complemented
9#23777040C212yesmaximal, complemented
10#23777012C214yesmaximal, complemented
11#23777001C214yesmaximal, complemented
12#23776951C218yesmaximal, complemented
13#23776828C212yesmaximal, complemented
14#23776806C214yesmaximal, complemented
15#23776695C212yesmaximal, complemented
16C2×#19099094C214yesmaximal, complemented
17H(5,𝔽2)×Dic79C212yesmaximal, complemented
18C2×C4×#11929623C211yesmaximal, characteristic, complemented
19C79×#3496C211yesmaximal, characteristic, complemented
20C22×#11929623C2211yescharacteristic
21#19099299C2214yescomplemented
22#19099288C2214yescomplemented
23#19099284C2218yescomplemented
24#19099283C2214yescomplemented
25#19099282C2218yescomplemented
26#19099277C2218yescomplemented
27#19099272C2218yescomplemented
28#19099270C2214yescomplemented
29#19099270C2214yescomplemented
30#19099265C2218yescomplemented
31#19099265C2218yescomplemented
32#19099256C22116yescomplemented
33#19099255C2218yescomplemented
34#19099253C2218yescomplemented
35#19099250C22116yescomplemented
36#19099250C22116yescomplemented
37#19099248C2218yescomplemented
38#19099244C22116yescomplemented
39#19099244C22116yescomplemented
40#19099239C22116yescomplemented
41D4×Dic158C2214yescomplemented
42#19099219C2218yescomplemented
43#19099212C2218yescomplemented
44#19099212C2218yescomplemented
45#19099207C2218yescomplemented
46#19099207C2218yescomplemented
47#19099207C2218yescomplemented
48#19099194C2212yescomplemented
49#19099189C2214yescomplemented
50#19099180C2218yescomplemented
51#19099173C2218yescomplemented
52#19099158C2218yescomplemented
53#19099158C2218yescomplemented
54#19099157C22116yescomplemented
55#19099150C2218yescomplemented
56#19099148C22116yescomplemented
57#19099134C2214yescomplemented
58#19099122C2218yescomplemented
59#19099120C2212yescomplemented
60#19099118C2212yescomplemented
61#19099118C2212yescomplemented
62#19099115C2218yescomplemented
63#19099111C2212yescomplemented
64#19099111C2212yescomplemented
65#19099095C2214yescomplemented
66#19099095C2214yescomplemented
67#19099094C2218yescomplemented
68#19099094C2218yescomplemented
69#19099094C2218yescomplemented
70#19099094C2214yescomplemented
71#19099094C2218yescomplemented
72#19099094C2214yescomplemented
73#19099094C2218yescomplemented
74#19099094C2218yescomplemented
75#19099094C2218yescomplemented
76#19099094C2218yescomplemented
77#19099092C2214yescomplemented
78#19099092C2214yescomplemented
79#19099090C22116yescomplemented
80C2×#14579154C2218yescomplemented
81C2×#14579152C2214yescomplemented
82C2×#14579148C2214yescomplemented
83#19099073C2214yescomplemented
84#19099073C2214yescomplemented
85#19099070C2214yescomplemented
86#19099069C22116yescomplemented
87C2×#14579142C2218yescomplemented
88C2×#14579140C2214yescomplemented
89#19099046C2218yescomplemented
90#19099046C2214yescomplemented
91#19099038C2212yes—
92#19099038C2218yescomplemented
93#19099038C2218yescomplemented
94#41×Dic79C2214yescomplemented
95#41×Dic79C2218yescomplemented
96C4×#11929623C2214yescomplemented
97C4×#11929623C2214yescomplemented
98C4×#11929623C2214yescomplemented
99C4×#11929623C2214yescomplemented
100C4×#11929623C2214yescomplemented
101C4×#11929623C2214yescomplemented
102C2×C4×Dic158C2211yescharacteristic, complemented
103C2×#14579126C2211yescharacteristic, complemented
104C2×#14579126C2214yescomplemented
105C2×D4×Dic79C2211yescharacteristic
106C2×D4×Dic79C2218yescomplemented
107C2×D4×Dic79C2218yescomplemented
108C2×D4×Dic79C2214yescomplemented
109C2×C4×C22⋊D79C2212yescomplemented
110C2×(C22⋊D79)⋊C4C2212yescomplemented
111C2×#14579119C2211yescharacteristic, complemented
112C2×#14579117C2212yescomplemented
113C2×#14579117C2218yescomplemented
114C22×C4×Dic79C2212yescomplemented
115C2×C42×D79C2211yescharacteristic, complemented
116C2×H(5,𝔽2)×C79C2212yes—
117#547×C79C2214yescomplemented
118#546×C79C2218yescomplemented
119D42×C79C2214yescomplemented
120#537×C79C2212yes—
121#534×C79C2214yes—
122#532×C79C2212yes—
123C2×#121×C79C2214yes—
124C2×C4×D4×C79C2211yescharacteristic
125C2×#11929623—28no—
126C2×#11929623C2314yes—
127C2×#11929623C2314yes—
128C2×#11929623C2314yes—
129C2×#11929623C2314yes—
130C22×Dic158C2311yescharacteristic
131C22×Dic158C2314yes—
132C22×C22⋊D79C2312yes—
133C23×Dic79C2312yes—
134C23×Dic79C2312yes—
135C23×Dic79C2318yes—
136C22×C4×D79C2311yescharacteristic
137C22×C4×D79C2311yescharacteristic
138C22×C4×D79C2311yescharacteristic
139#14579161C2312yes—
140#14579161C2312yes—
141#14579160C2318yes—
142#14579159C2318yes—
143#14579156C23116yes—
144#14579154C23116yes—
145#14579154C23116yes—
146#14579154C23116yes—
147#14579154C23116yes—
148#14579154C2318yes—
149#14579154C23116yes—
150#14579154C2318yes—
151#14579153C2314yes—
152#14579152C2318yes—
153#14579152C2318yes—
154#14579152C2318yes—
155#14579152C2314yes—
156#14579152C2318yes—
157#14579152C2314yes—
158#14579151C23116yes—
159#14579151C23116yes—
160#14579148C2318yes—
161#14579148C2318yes—
162#14579148C2318yes—
163#14579148C2314yes—
164#14579148C2318yes—
165#14579148C2314yes—
166#14579147C23116yes—
167#14579145C23116yes—
168#14579144C23116yes—
169#14579143C2318yes—
170#14579143C2318yes—
171#14579142C23116yes—
172#14579142C23116yes—
173#14579142C23116yes—
174#14579142C23116yes—
175#14579142C23116yes—
176#14579142C2318yes—
177#14579141C2314yes—
178#14579141C2314yes—
179#14579140C2318yes—
180#14579140C2314yes—
181#14579140C2318yes—
182#14579140C2318yes—
183#14579140C2318yes—
184#14579140C2318yes—
185#14579140C2314yes—
186#14579138C23116yes—
187#14579138C23116yes—
188#14579138C23116yes—
189#14579138C23116yes—
190#14579137C2314yes—
191#14579137C2314yes—
192#14579133C23116yes—
193#14579133C23116yes—
194#14579133C23116yes—
195#14579132C2314yes—
196#14579132C2314yes—
197#14579132C2314yes—
198#14579132C2314yes—
199#14579130C23116yes—
200#14579129C2318yes—
201Q8×Dic79C2314yes—
202Q8×Dic79C2318yes—
203Q8×Dic79C2314yes—
204C4×Dic158C2314yes—
205C4×Dic158C2314yes—
206C4×Dic158C2314yes—
207C4×Dic158C2314yes—
208#14579126C2314yes—
209#14579126C2318yes—
210#14579126C2314yes—
211#14579126C2318yes—
212#14579126C2314yes—
213#14579126C2314yes—
214#14579126C2318yes—
215D4×Dic79C23116yes—
216D4×Dic79C23116yes—
217D4×Dic79C2318yes—
218D4×Dic79C2314yes—
219D4×Dic79C2318yes—
220D4×Dic79C2318yes—
221D4×Dic79C2318yes—
222D4×Dic79C23116yes—
223D4×Dic79C2314yes—
224D4×Dic79C2318yes—
225D4×Dic79C23116yes—
226D4×Dic79C2318yes—
227D4×Dic79C2314yes—
228D4×Dic79C2314yes—
229D4×Dic79C2314yes—
230D4×Dic79C23116yes—
231D4×Dic79C2318yes—
232D4×Dic79C2314yes—
233D4×Dic79C2318yes—
234C4×C22⋊D79C2318yes—
235C4×C22⋊D79C2318yes—
236C4×C22⋊D79C2318yes—
237C4×C22⋊D79C2318yes—
238(C22⋊D79)⋊C4C2318yes—
239(C22⋊D79)⋊C4C2318yes—
240(C22⋊D79)⋊C4C2318yes—
241(C22⋊D79)⋊C4C2318yes—
242#14579120C2318yes—
243#14579120C2314yes—
244#14579120C23116yes—
245#14579120C2318yes—
246#14579119C2314yes—
247#14579119C2314yes—
248#14579119C2314yes—
249#14579119C2314yes—
250#14579117C23116yes—
251#14579117C2318yes—
252#14579117C2318yes—
253#14579117C2318yes—
254#14579117C23116yes—
255#14579117C2318yes—
256#14579117C23116yes—
257C2×C4⋊Dic79C2318yes—
258C2×C4⋊Dic79C2318yes—
259C2×C4⋊Dic79C2314yes—
260C2×C4⋊Dic79C2311yescharacteristic
261C2×Dic79⋊C4C2312yes—
262C2×Dic79⋊C4C2312yes—
263C2×Dic79⋊C4C2318yes—
264C2×Dic79⋊C4C2318yes—
265C2×Dic79⋊C4C2318yes—
266C2×C22⋊Dic79C2318yes—
267C2×C22⋊Dic79C2318yes—
268C2×C22⋊Dic79C2318yes—
269C2×C22⋊Dic79C2318yes—
270C2×C22⋊Dic79C23116yes—
271C2×C22⋊Dic79C2312yes—
272C2×(C2×D79)⋊C4C2312yes—
273C2×C4×Dic79C2311yescharacteristic
274C2×C4×Dic79C2311yescharacteristic
275C2×C4×Dic79C2311yescharacteristic
276C2×C4×Dic79C2314yes—
277C2×C4×Dic79C2312yes—
278C2×C4×Dic79C2312yes—
279C2×C4×Dic79C2312yes—
280C2×C4×Dic79C2314yes—
281C2×C4×Dic79C2314yes—
282C2×C4×Dic79C2314yes—
283C2×C4×Dic79C2318yes—
284C2×C4×Dic79C2318yes—
285C42×D79C2312yes—
286C42×D79C2312yes—
287C42×D79C2312yes—
288C42×D79C2312yes—
289H(5,𝔽2)×C79—216no—
290C2×#41×C79C2318yes—
291C2×#41×C79C2314yes—
292C22×D4×C79C2318yes—
293C22×D4×C79C2318yes—
294C22×D4×C79C2314yes—
295C22×D4×C79C2311yescharacteristic
296C23×C4×C79C2312yes—
297C4⋊Q8×C79C2312yes—
298#127×C79C2312yes—
299#124×C79C2314yes—
300#123×C79C23116yes—
301C22⋊Q8×C79C2318yes—
302#121×C79C2318yes—
303#121×C79C2314yes—
304#121×C79C2318yes—
305#121×C79C2318yes—
306#121×C79C2314yes—
307#121×C79C2318yes—
308#120×C79C23116yes—
309C4×D4×C79C2314yes—
310C4×D4×C79C2314yes—
311C4×D4×C79C2314yes—
312C4×D4×C79C2314yes—
313C2×C4⋊C4×C79C2311yescharacteristic
314C2×C4⋊C4×C79C2314yes—
315C2×C22⋊C4×C79C2312yes—
316C2×C22⋊C4×C79C2318yes—
317C2×C42×C79C2311yescharacteristic
318C23×D79C2411yescharacteristic
319#11929623—216no—
320#11929623—216no—
321#11929623—48no—
322#11929623—48no—
323C2×Dic158—24no—
324C2×Dic158—48no—
325C2×Dic158C2414yes—
326C2×Dic158C2414yes—
327C2×Dic158C2418yes—
328C2×Dic158C2414yes—
329C2×C22⋊D79—28no—
330C2×C22⋊D79C2418yes—
331C2×C22⋊D79C2418yes—
332C2×C22⋊D79C2418yes—
333C22×Dic79—28no—
334C22×Dic79—44no—
335C22×Dic79—416no—
336C22×Dic79C2412yes—
337C22×Dic79C2414yes—
338C22×Dic79C2414yes—
339C22×Dic79C2418yes—
340C22×Dic79C2414yes—
341C22×Dic79C2411yescharacteristic
342C22×Dic79C2411yescharacteristic
343C22×Dic79C2418yes—
344C22×Dic79C2418yes—
345C22×Dic79C2412yes—
346C22×Dic79C2411yescharacteristic
347C22×Dic79C2414yes—
348C22×Dic79C2418yes—
349C22×Dic79C24116yes—
350C2×C4×D79—24no—
351C2×C4×D79—42no—
352C2×C4×D79—42no—
353C2×C4×D79C2412yes—
354C2×C4×D79C2412yes—
355C2×C4×D79C2412yes—
356C2×C4×D79C2412yes—
357C2×C4×D79C2412yes—
358C2×C4×D79C2412yes—
359C4⋊Dic79C2414yes—
360C4⋊Dic79C2414yes—
361C4⋊Dic79C2414yes—
362C4⋊Dic79C24116yes—
363C4⋊Dic79C2418yes—
364C4⋊Dic79C2418yes—
365C4⋊Dic79C2414yes—
366C4⋊Dic79C2414yes—
367C4⋊Dic79C2418yes—
368Dic79⋊C4C2418yes—
369Dic79⋊C4C2418yes—
370Dic79⋊C4C2418yes—
371Dic79⋊C4C2418yes—
372Dic79⋊C4C2418yes—
373Dic79⋊C4C24116yes—
374Dic79⋊C4C24116yes—
375Dic79⋊C4C24116yes—
376Dic79⋊C4C2418yes—
377C22⋊Dic79C2418yes—
378C22⋊Dic79C2418yes—
379C22⋊Dic79C2418yes—
380C22⋊Dic79C2418yes—
381C22⋊Dic79C24116yes—
382C22⋊Dic79C2418yes—
383C22⋊Dic79C2418yes—
384C22⋊Dic79C24116yes—
385C22⋊Dic79C24116yes—
386C22⋊Dic79C24116yes—
387(C2×D79)⋊C4C2418yes—
388(C2×D79)⋊C4C2418yes—
389(C2×D79)⋊C4C2418yes—
390C4×Dic79C2411yescharacteristic
391C4×Dic79C2411yescharacteristic
392C4×Dic79C2412yes—
393C4×Dic79C2411yescharacteristic
394C4×Dic79C2411yescharacteristic
395C4×Dic79C2412yes—
396C4×Dic79C2412yes—
397C4×Dic79C2412yes—
398C4×Dic79C2414yes—
399C4×Dic79C2414yes—
400C4×Dic79C2414yes—
401C4×Dic79C2418yes—
402C4×Dic79C2414yes—
403C4×Dic79C2414yes—
404C4×Dic79C2414yes—
405C4×Dic79C24116yes—
406C4×Dic79C2418yes—
407C4×Dic79C2418yes—
408C24×C79C2418yes—
409C24×C79C2412yes—
410#41×C79—232no—
411#41×C79—216no—
412C2×Q8×C79C2414yes—
413C2×D4×C79—232no—
414C2×D4×C79—232no—
415C2×D4×C79—48no—
416C2×D4×C79#4118yescomplemented
417C2×D4×C79C2414yes—
418C2×D4×C79C24116yes—
419C2×D4×C79C2418yes—
420C2×D4×C79C2414yes—
421C2×D4×C79C2414yes—
422C2×D4×C79C2418yes—
423C2×D4×C79C2414yes—
424C22×C4×C79—44no—
425C22×C4×C79C2414yes—
426C22×C4×C79C2411yescharacteristic
427C22×C4×C79C2418yes—
428C22×C4×C79C2418yes—
429C22×C4×C79C2411yescharacteristic
430C22×C4×C79C2414yes—
431C22×C4×C79C2412yes—
432C22×C4×C79C2411yescharacteristic
433C4⋊C4×C79C2414yes—
434C4⋊C4×C79C2414yes—
435C4⋊C4×C79C2418yes—
436C4⋊C4×C79C2414yes—
437C22⋊C4×C79C2418yes—
438C22⋊C4×C79C2418yes—
439C22⋊C4×C79C24116yes—
440C22⋊C4×C79C2418yes—
441C42×C79C2412yes—
442C42×C79C2412yes—
443C23×C79—216no—
444C23×C79—42no—
445C23×C79—42no—
446C23×C79—48no—
447C23×C79—48no—
448C23×C79C2×#4118yes—
449C23×C79C2518yes—
450C23×C79C2511yescharacteristic
451C23×C79C2514yes—
452C22×D79—22no—
453C22×D79—41no—
454C22×D79—41no—
455C22×D79C2512yes—
456Q8×C79—28no—
457D4×C79—232no—
458D4×C79—216no—
459D4×C79—28no—
460D4×C79—28no—
461D4×C79—44no—
462D4×C79—48no—
463D4×C79C2×#41116yes—
464C2×C4×C79—216no—
465C2×C4×C79—216no—
466C2×C4×C79—22no—
467C2×C4×C79—28no—
468C2×C4×C79—41no—
469C2×C4×C79—44no—
470C2×C4×C79—42no—
471C2×C4×C79C2×#4114yes—
472C2×C4×C79C2511yescharacteristic
473C2×C4×C79C2518yes—
474C2×C4×C79C2514yes—
475C2×C4×C79C2512yes—
476C2×C4×C79C2512yes—
477C2×C4×C79C2511yescharacteristic
478C22⋊D79—216no—
479C22⋊D79—48no—
480C22⋊D79—48no—
481C2×Dic79—22no—
482C2×Dic79—24no—
483C2×Dic79—28no—
484C2×Dic79—28no—
485C2×Dic79—22no—
486C2×Dic79—28no—
487C2×Dic79—216no—
488C2×Dic79—41no—
489C2×Dic79—48no—
490C2×Dic79—416no—
491C2×Dic79—44no—
492C2×Dic79—42no—
493C2×Dic79—48no—
494C2×Dic79—48no—
495C2×Dic79C2514yes—
496C2×Dic79C2511yescharacteristic
497C2×Dic79C2511yescharacteristic
498C2×Dic79C2512yes—
499C2×Dic79C2511yescharacteristic
500C2×Dic79C2518yes—
501C2×Dic79C2514yes—
502C2×Dic79C2518yes—
503C2×Dic79C2511yescharacteristic
504C4×D79—24no—
505C4×D79—24no—
506C4×D79—24no—
507C4×D79—24no—
508C4×D79—42no—
509C4×D79—42no—
510Dic158—28no—
511Dic158—28no—
512Dic158—48no—
513Dic158—44no—
514C22×C79—21no—
515C22×C79—24no—
516C22×C79—21no—
517C22×C79—24no—
518C22×C79—28no—
519C22×C79—28no—
520C22×C79—28no—
521C22×C79—48no—
522C22×C79—816no—
523C22×C79C22×#4118yes—
524C22×C79C22×#4112yes—
525C22×C79C2611yescharacteristic
526C2×D79—22no—
527C2×D79—22no—
528C2×D79—22no—
529C2×D79—44no—
530C4×C79—28no—
531C4×C79—21no—
532C4×C79—24no—
533C4×C79—22no—
534C4×C79C22×#4114yes—
535C4×C79#58512yes—
536Dic79—24no—
537Dic79—21no—
538Dic79—21no—
539Dic79—28no—
540Dic79—28no—
541Dic79—22no—
542Dic79—21no—
543Dic79—24no—
544Dic79#58512yes—
545#62781—791nomaximal, Sylow
546C2×C79—22no—
547C2×C79—28no—
548C2×C79—48no—
549C2×C79C23×#4111yescharacteristic
550C2×C79C2×#58511yescharacteristic
551C2×C79C2×#58511yescharacteristic
552D79—42no—
553#3521—798no—
554#3515—794no—
555#3514—794no—
556#3507—792no—
557#3505—794no—
558#3501—791no—
559#3496D7911yescharacteristic, complemented
560#3493—792no—
561#3491—794no—
562#3485—792no—
563#3482—794no—
564#3481—794no—
565#3475—798no—
566#3461—792no—
567#3459—794no—
568#3444—792no—
569C2×#529—794no—
570C4×H(5,𝔽2)—792no—
571C2×C4×#41—791no—
572C79#6278111yescharacteristic, complemented, Sylow
573C2×H(5,𝔽2)C2×D7912yes—
574C22×#41—791no—
575#559—794no—
576#557—794no—
577#556—798no—
578#556—798no—
579#556—794no—
580#555—798no—
581#554—794no—
582#554—794no—
583#554—798no—
584#553—7916no—
585#553—798no—
586#553—798no—
587#552—7916no—
588#552—7916no—
589#552—798no—
590#552—798no—
591#552—798no—
592#551—7916no—
593#551—7916no—
594#551—7916no—
595D4×Q8—794no—
596#548—798no—
597#547—798no—
598#547—798no—
599#547C2×D7914yescomplemented
600#546—798no—
601#546—798no—
602#546—798no—
603#546C2×D7918yescomplemented
604D42C2×D7914yescomplemented
605#544—792no—
606#543—794no—
607#542—798no—
608#541—798no—
609#539—7916no—
610#539—798no—
611#539—798no—
612#538—798no—
613#538—7916no—
614#537C2×D7912yes—
615#536—794no—
616#534—798no—
617#534C2×D7914yes—
618#533—792no—
619#533—792no—
620#533—798no—
621#533—792no—
622#532—792no—
623#532—792no—
624#532C2×D7912yes—
625#529—794no—
626#529—794no—
627#529—7916no—
628#529—794no—
629#529—798no—
630#529—798no—
631#529—798no—
632#529—798no—
633#529—798no—
634#529—798no—
635#529—798no—
636#529—794no—
637#529—798no—
638#529—794no—
639#529—794no—
640C2×#126—798no—
641C2×#125—794no—
642C2×#124—794no—
643#525—794no—
644#525—794no—
645#525—794no—
646#525—7916no—
647C2×#123—798no—
648C2×C22⋊Q8—794no—
649C2×#121C2×D7914yes—
650#520—794no—
651#520—798no—
652#518—792no—
653#518—798no—
654#518—798no—
655C4×#41—794no—
656C4×#41—798no—
657C4×#41—794no—
658C4×#41—794no—
659C4×#41—794no—
660C4×#41—794no—
661C4×#41—794no—
662C4×#41—794no—
663C2×C4×Q8—791no—
664C2×C4×Q8—794no—
665C2×C4×Q8—791no—
666C2×C4×D4—791no—
667C2×C4×D4—798no—
668C2×C4×D4—798no—
669C2×C4×D4—794no—
670C2×C4×D4—792no—
671C2×C4×D4—792no—
672C2×C4×D4C2×D7911yescharacteristic
673C2×#117—791no—
674C2×#117—792no—
675C2×#117—798no—
676C22×C42—792no—
677C22×C42—791no—
678H(5,𝔽2)—216no—
679C2×#41—794no—
680C2×#41—794no—
681C2×#41—794no—
682C2×#41—794no—
683C2×#41—1588no—
684C2×#41C22×D7914yes—
685C2×#41C22×D7918yes—
686C22×Q8—794no—
687C22×Q8—791no—
688C22×D4—792no—
689C22×D4C22×D7918yes—
690C22×D4C22×D7918yes—
691C22×D4C22×D7914yes—
692C22×D4C22×D7911yescharacteristic
693C23×C4—798no—
694C23×C4—792no—
695C23×C4—791no—
696C23×C4—791no—
697C23×C4—792no—
698C23×C4—791no—
699C23×C4C22×D7912yes—
700C4⋊Q8—798no—
701C4⋊Q8—798no—
702C4⋊Q8—792no—
703C4⋊Q8—792no—
704C4⋊Q8C22×D7912yes—
705#127C22×D7912yes—
706#126—7916no—
707#126—798no—
708#126—7916no—
709#126—7916no—
710#126—7916no—
711#126—798no—
712#126—7916no—
713#126—7916no—
714#125—794no—
715#125—798no—
716#125—798no—
717#125—798no—
718#125—794no—
719#125—7916no—
720#125—798no—
721#125—7916no—
722#125—794no—
723#124—794no—
724#124—798no—
725#124—798no—
726#124—798no—
727#124—794no—
728#124—798no—
729#124—7916no—
730#124C22×D7914yes—
731#123—798no—
732#123—7916no—
733#123—7916no—
734#123—7916no—
735#123—7916no—
736#123—7916no—
737#123—7916no—
738#123—798no—
739#123—798no—
740#123—7916no—
741#123C22×D79116yes—
742C22⋊Q8—794no—
743C22⋊Q8—794no—
744C22⋊Q8—794no—
745C22⋊Q8—798no—
746C22⋊Q8—798no—
747C22⋊Q8—798no—
748C22⋊Q8—794no—
749C22⋊Q8—798no—
750C22⋊Q8—798no—
751C22⋊Q8—794no—
752C22⋊Q8—794no—
753C22⋊Q8—7916no—
754C22⋊Q8—7916no—
755C22⋊Q8—7916no—
756C22⋊Q8—7916no—
757C22⋊Q8C22×D7918yes—
758#121—794no—
759#121—794no—
760#121—794no—
761#121—794no—
762#121—7916no—
763#121—7916no—
764#121—7916no—
765#121C22×D7914yes—
766#121C22×D7918yes—
767#121C22×D7918yes—
768#121C22×D7918yes—
769#121C22×D7914yes—
770#121C22×D7918yes—
771#120—7916no—
772#120—798no—
773#120C22×D79116yes—
774C4×Q8—794no—
775C4×Q8—794no—
776C4×Q8—798no—
777C4×Q8—794no—
778C4×Q8—794no—
779C4×Q8—794no—
780C4×Q8—798no—
781C4×Q8—798no—
782C4×Q8—798no—
783C4×Q8—794no—
784C4×Q8—794no—
785C4×Q8—794no—
786C4×Q8—794no—
787C4×Q8—794no—
788C4×D4—794no—
789C4×D4—798no—
790C4×D4—7916no—
791C4×D4—794no—
792C4×D4—794no—
793C4×D4—794no—
794C4×D4—7916no—
795C4×D4—7916no—
796C4×D4—798no—
797C4×D4—7916no—
798C4×D4—798no—
799C4×D4—798no—
800C4×D4—798no—
801C4×D4—798no—
802C4×D4—798no—
803C4×D4—794no—
804C4×D4—798no—
805C4×D4—7916no—
806C4×D4—794no—
807C4×D4—798no—
808C4×D4—798no—
809C4×D4—798no—
810C4×D4—798no—
811C4×D4—798no—
812C4×D4—798no—
813C4×D4—798no—
814C4×D4—798no—
815C4×D4C22×D7914yes—
816C4×D4C22×D7914yes—
817C4×D4C22×D7914yes—
818C4×D4C22×D7914yes—
819#117—794no—
820#117—798no—
821#117—7916no—
822#117—798no—
823#117—794no—
824#117—794no—
825#117—794no—
826#117—794no—
827#117—798no—
828#117—798no—
829#117—798no—
830#117—7916no—
831#117—7916no—
832#117—7916no—
833#117—798no—
834C2×C4⋊C4—791no—
835C2×C4⋊C4—792no—
836C2×C4⋊C4—792no—
837C2×C4⋊C4—798no—
838C2×C4⋊C4—798no—
839C2×C4⋊C4—798no—
840C2×C4⋊C4—798no—
841C2×C4⋊C4—794no—
842C2×C4⋊C4—798no—
843C2×C4⋊C4C22×D7911yescharacteristic
844C2×C4⋊C4C22×D7914yes—
845C2×C22⋊C4—792no—
846C2×C22⋊C4—798no—
847C2×C22⋊C4—798no—
848C2×C22⋊C4—798no—
849C2×C22⋊C4—7916no—
850C2×C22⋊C4—798no—
851C2×C22⋊C4—792no—
852C2×C22⋊C4C22×D7912yes—
853C2×C22⋊C4C22×D7918yes—
854C2×C42—794no—
855C2×C42—792no—
856C2×C42—791no—
857C2×C42—798no—
858C2×C42—791no—
859C2×C42—794no—
860C2×C42—792no—
861C2×C42—792no—
862C2×C42—798no—
863C2×C42—794no—
864C2×C42—794no—
865C2×C42—791no—
866C2×C42—792no—
867C2×C42—792no—
868C2×C42—792no—
869C2×C42—792no—
870C2×C42C22×D7911yescharacteristic
871C24—791no—
872C24C23×D7918yes—
873C24C23×D7912yes—
874#41—232no—
875#41—216no—
876#41—3168no—
877#41—3168no—
878#41—15816no—
879#41—15816no—
880C2×Q8—3168no—
881C2×Q8—794no—
882C2×Q8—798no—
883C2×Q8—794no—
884C2×Q8—794no—
885C2×Q8—1584no—
886C2×Q8C23×D7914yes—
887C2×D4—232no—
888C2×D4—232no—
889C2×D4—48no—
890C2×D4—798no—
891C2×D4—798no—
892C2×D4—798no—
893C2×D4—1588no—
894C2×D4#1192962318yescomplemented
895C2×D4C23×D7918yes—
896C2×D4C23×D79116yes—
897C2×D4C23×D7914yes—
898C2×D4C23×D7914yes—
899C2×D4C23×D7918yes—
900C2×D4C23×D7914yes—
901C2×D4C23×D7914yes—
902C22×C4—44no—
903C22×C4—3162no—
904C22×C4—3162no—
905C22×C4—3164no—
906C22×C4—31616no—
907C22×C4—792no—
908C22×C4—791no—
909C22×C4—794no—
910C22×C4—798no—
911C22×C4—798no—
912C22×C4—798no—
913C22×C4—7916no—
914C22×C4—792no—
915C22×C4—792no—
916C22×C4—791no—
917C22×C4—794no—
918C22×C4—791no—
919C22×C4—794no—
920C22×C4—794no—
921C22×C4—792no—
922C22×C4—798no—
923C22×C4—792no—
924C22×C4—792no—
925C22×C4—792no—
926C22×C4—792no—
927C22×C4—1588no—
928C22×C4—1584no—
929C22×C4C23×D7911yescharacteristic
930C22×C4C23×D7914yes—
931C22×C4C23×D7918yes—
932C22×C4C23×D7918yes—
933C22×C4C23×D7912yes—
934C22×C4C23×D7914yes—
935C22×C4C23×D7911yescharacteristic
936C22×C4C23×D7911yescharacteristic
937C4⋊C4—798no—
938C4⋊C4—798no—
939C4⋊C4—798no—
940C4⋊C4—798no—
941C4⋊C4—798no—
942C4⋊C4—7916no—
943C4⋊C4—7916no—
944C4⋊C4—7916no—
945C4⋊C4—798no—
946C4⋊C4—794no—
947C4⋊C4—794no—
948C4⋊C4—794no—
949C4⋊C4—7916no—
950C4⋊C4—798no—
951C4⋊C4—798no—
952C4⋊C4—794no—
953C4⋊C4—798no—
954C4⋊C4—794no—
955C4⋊C4C23×D7914yes—
956C4⋊C4C23×D7914yes—
957C4⋊C4C23×D7918yes—
958C4⋊C4C23×D7914yes—
959C22⋊C4—798no—
960C22⋊C4—798no—
961C22⋊C4—798no—
962C22⋊C4—7916no—
963C22⋊C4—798no—
964C22⋊C4—798no—
965C22⋊C4—798no—
966C22⋊C4—7916no—
967C22⋊C4—7916no—
968C22⋊C4—7916no—
969C22⋊C4—798no—
970C22⋊C4—798no—
971C22⋊C4—798no—
972C22⋊C4C23×D7918yes—
973C22⋊C4C23×D7918yes—
974C22⋊C4C23×D79116yes—
975C22⋊C4C23×D7918yes—
976C42—791no—
977C42—791no—
978C42—792no—
979C42—791no—
980C42—791no—
981C42—794no—
982C42—792no—
983C42—798no—
984C42—794no—
985C42—792no—
986C42—794no—
987C42—792no—
988C42—794no—
989C42—794no—
990C42—794no—
991C42—798no—
992C42—7916no—
993C42—798no—
994C42C23×D7912yes—
995C42C23×D7912yes—
996C23—216no—
997C23—42no—
998C23—42no—
999C23—48no—
1000C23—48no—
1001C23—3161no—
1002C23—3161no—
1003C23—792no—
1004C23—1582no—
1005C23C2×#1192962318yes—
1006C23C24×D7918yes—
1007C23C24×D7911yescharacteristic
1008C23C24×D7914yes—
1009Q8—28no—
1010Q8—3168no—
1011Q8—3164no—
1012Q8—1588no—
1013Q8—1588no—
1014D4—232no—
1015D4—216no—
1016D4—28no—
1017D4—28no—
1018D4—48no—
1019D4—44no—
1020D4—3168no—
1021D4—3168no—
1022D4—15816no—
1023D4C2×#11929623116yes—
1024C2×C4—216no—
1025C2×C4—22no—
1026C2×C4—28no—
1027C2×C4—216no—
1028C2×C4—44no—
1029C2×C4—42no—
1030C2×C4—41no—
1031C2×C4—3162no—
1032C2×C4—3162no—
1033C2×C4—3162no—
1034C2×C4—3164no—
1035C2×C4—31616no—
1036C2×C4—3168no—
1037C2×C4—3161no—
1038C2×C4—3168no—
1039C2×C4—3168no—
1040C2×C4—791no—
1041C2×C4—791no—
1042C2×C4—791no—
1043C2×C4—791no—
1044C2×C4—794no—
1045C2×C4—792no—
1046C2×C4—798no—
1047C2×C4—794no—
1048C2×C4—798no—
1049C2×C4—1584no—
1050C2×C4—1582no—
1051C2×C4—1588no—
1052C2×C4—15816no—
1053C2×C4—1582no—
1054C2×C4—1584no—
1055C2×C4—1588no—
1056C2×C4—1588no—
1057C2×C4—1584no—
1058C2×C4—1584no—
1059C2×C4—1584no—
1060C2×C4C2×#1192962314yes—
1061C2×C4C24×D7911yescharacteristic
1062C2×C4C24×D7914yes—
1063C2×C4C24×D7918yes—
1064C2×C4C24×D7912yes—
1065C2×C4C24×D7911yescharacteristic
1066C2×C4C24×D7912yes—
1067C22—21no—
1068C22—24no—
1069C22—21no—
1070C22—24no—
1071C22—28no—
1072C22—28no—
1073C22—28no—
1074C22—48no—
1075C22—816no—
1076C22—3164no—
1077C22—1582no—
1078C22—1582no—
1079C22—1582no—
1080C22C22×#1192962318yes—
1081C22C22×#1192962312yes—
1082C22C25×D7911yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—792no—
1088C4—1581no—
1089C4—1581no—
1090C4—1584no—
1091C4—1581no—
1092C4—1584no—
1093C4—1588no—
1094C4—1582no—
1095C4—1588no—
1096C4C22×#1192962314yes—
1097C4#1909939812yes—
1098C2—22no—
1099C2—28no—
1100C2—48no—
1101C2—3162no—
1102C2C23×#1192962311yescharacteristic
1103C2#585×D7911yescharacteristic
1104C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3496C2
hypercenter#3496D79
hypocenterC79#62781
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3496

Complements

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

NH ≅ G/Ntype
1. #23777457C2semidirect
2. #23777369C2semidirect
3. #23777352C2semidirect
4. #23777262C2semidirect
5. #23777234C2semidirect
6. #23777203C2semidirect
7. #23777119C2semidirect
8. #23777097C2semidirect
9. #23777040C2semidirect
10. #23777012C2semidirect
11. #23777001C2semidirect
12. #23776951C2semidirect
13. #23776828C2semidirect
14. #23776806C2semidirect
15. #23776695C2semidirect
16. C2×#19099094C2semidirect
17. H(5,𝔽2)×Dic79C2semidirect
18. C2×C4×#11929623C2semidirect
19. C79×#3496C2semidirect
21. #19099299C22semidirect
22. #19099288C22semidirect
23. #19099284C22semidirect
24. #19099283C22semidirect
25. #19099282C22semidirect
26. #19099277C22semidirect
27. #19099272C22semidirect
28. #19099270C22semidirect
29. #19099270C22semidirect
30. #19099265C22semidirect
31. #19099265C22semidirect
32. #19099256C22semidirect
33. #19099255C22semidirect
34. #19099253C22semidirect
35. #19099250C22semidirect
36. #19099250C22semidirect
37. #19099248C22semidirect
38. #19099244C22semidirect
39. #19099244C22semidirect
40. #19099239C22semidirect
41. D4×Dic158C22semidirect
42. #19099219C22semidirect
43. #19099212C22semidirect
44. #19099212C22semidirect
45. #19099207C22semidirect
46. #19099207C22semidirect
47. #19099207C22semidirect
48. #19099194C22semidirect
49. #19099189C22semidirect
50. #19099180C22semidirect
51. #19099173C22semidirect
52. #19099158C22semidirect
53. #19099158C22semidirect
54. #19099157C22semidirect
55. #19099150C22semidirect
56. #19099148C22semidirect
57. #19099134C22semidirect
58. #19099122C22semidirect
59. #19099120C22semidirect
60. #19099118C22semidirect
61. #19099118C22semidirect
62. #19099115C22semidirect
63. #19099111C22semidirect
64. #19099111C22semidirect
65. #19099095C22semidirect
66. #19099095C22semidirect
67. #19099094C22semidirect
68. #19099094C22semidirect
69. #19099094C22semidirect
70. #19099094C22semidirect
71. #19099094C22semidirect
72. #19099094C22semidirect
73. #19099094C22semidirect
74. #19099094C22semidirect
75. #19099094C22semidirect
76. #19099094C22semidirect
77. #19099092C22semidirect
78. #19099092C22semidirect
79. #19099090C22semidirect
80. C2×#14579154C22semidirect
81. C2×#14579152C22semidirect
82. C2×#14579148C22semidirect
83. #19099073C22semidirect
84. #19099073C22semidirect
85. #19099070C22semidirect
86. #19099069C22semidirect
87. C2×#14579142C22semidirect
88. C2×#14579140C22semidirect
89. #19099046C22semidirect
90. #19099046C22semidirect
92. #19099038C22semidirect
93. #19099038C22semidirect
94. #41×Dic79C22semidirect
95. #41×Dic79C22semidirect
96. C4×#11929623C22semidirect
97. C4×#11929623C22semidirect
98. C4×#11929623C22semidirect
99. C4×#11929623C22semidirect
100. C4×#11929623C22semidirect
101. C4×#11929623C22semidirect
102. C2×C4×Dic158C22semidirect
103. C2×#14579126C22semidirect
104. C2×#14579126C22semidirect
106. C2×D4×Dic79C22semidirect
107. C2×D4×Dic79C22semidirect
108. C2×D4×Dic79C22semidirect
109. C2×C4×C22⋊D79C22semidirect
110. C2×(C22⋊D79)⋊C4C22semidirect
111. C2×#14579119C22semidirect
112. C2×#14579117C22semidirect
113. C2×#14579117C22semidirect
114. C22×C4×Dic79C22semidirect
115. C2×C42×D79C22semidirect
117. #547×C79C22semidirect
118. #546×C79C22semidirect
119. D42×C79C22semidirect
416. C2×D4×C79#41semidirect
559. #3496D79semidirect
572. C79#62781semidirect
599. #547C2×D79semidirect
603. #546C2×D79semidirect
604. D42C2×D79semidirect
894. C2×D4#11929623semidirect

Maximal subgroups

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

subgroupindex
#237774572
#237773692
#237773522
#237772622
#237772342
#237772032
#237771192
#237770972
#237770402
#237770122
#237770012
#237769512
#237768282
#237768062
#237766952
C2×#190990942
H(5,𝔽2)×Dic792
C2×C4×#119296232
C79×#34962
#6278179