Finite Group Databasebeta

← #35197173

Subgroups — #35197173

Order 20224.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1052 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777913C218yesmaximal, complemented
2#23777805C211yesmaximal, characteristic, complemented
3#23777798C212yesmaximal, complemented
4#23777770C218yesmaximal, complemented
5#23777633C214yesmaximal, complemented
6#23777435C214yesmaximal, complemented
7#23777423C214yesmaximal, complemented
8#23777300C214yesmaximal, complemented
9#23777275C214yesmaximal, complemented
10#23777242C214yesmaximal, complemented
11#23777172C214yesmaximal, complemented
12#23777156C214yesmaximal, complemented
13#23777067C218yesmaximal, complemented
14#23776695C211yesmaximal, characteristic, complemented
15#532×D79C212yesmaximal, complemented
16C79×#3549C211yesmaximal, characteristic, complemented
17C2×#14579206C2218yescomplemented
18C2×#41×D79C2214yescomplemented
19#19099307C2218yescomplemented
20#19099305C2214yescomplemented
21#19099302C2218yescomplemented
22#19099300C2218yescomplemented
23#19099295C22116yescomplemented
24#19099281C2218yescomplemented
25#19099279C2212yescomplemented
26#19099278C2214yescomplemented
27#19099274C2214yescomplemented
28#19099270C2214yescomplemented
29#19099265C2218yescomplemented
30#19099260C2218yescomplemented
31#19099257C2218yescomplemented
32#19099257C2218yescomplemented
33#19099234C2214yescomplemented
34#19099233C2214yescomplemented
35#19099233C22116yescomplemented
36#19099231C2218yescomplemented
37#19099221C22116yescomplemented
38#19099218C2214yescomplemented
39#19099217C2214yescomplemented
40#19099213C2218yescomplemented
41#19099210C2218yescomplemented
42#19099207C2218yescomplemented
43#19099206C22116yescomplemented
44#19099200C22116yescomplemented
45#19099200C22116yescomplemented
46#19099200C22116yescomplemented
47D4×D316C2214yescomplemented
48#19099198C2212yescomplemented
49#19099198C2218yescomplemented
50#19099197C2218yescomplemented
51D4×C22⋊D79C2218yescomplemented
52D4×C22⋊D79C2218yescomplemented
53#19099195C2218yescomplemented
54#19099195C22116yescomplemented
55#19099177C22116yescomplemented
56#19099166C2218yescomplemented
57#19099166C2218yescomplemented
58#19099148C22116yescomplemented
59#19099147C22116yescomplemented
60#19099147C22116yescomplemented
61#19099142C2218yescomplemented
62#19099142C2218yescomplemented
63#19099141C2218yescomplemented
64#19099129C2218yescomplemented
65#19099129C2218yescomplemented
66#19099128C22116yescomplemented
67#19099127C2214yescomplemented
68#19099123C22116yescomplemented
69#19099120C2211yescharacteristic, complemented
70#19099118C2212yescomplemented
71#19099116C2214yescomplemented
72#19099114C2212yescomplemented
73#19099113C2212yescomplemented
74#19099112C2214yescomplemented
75#19099111C2212yescomplemented
76#19099111C2212yescomplemented
77#19099110C2214yescomplemented
78#19099110C2214yescomplemented
79#19099109C2214yescomplemented
80#19099108C2218yescomplemented
81#19099108C2214yescomplemented
82#19099108C2214yescomplemented
83C4⋊Q8×D79C2212yescomplemented
84C2×#14579157C2214yescomplemented
85#127×D79C2212yescomplemented
86#19099095C2214yescomplemented
87#19099094C2214yescomplemented
88#19099092C2214yescomplemented
89#124×D79C2214yescomplemented
90#19099075C2218yescomplemented
91#19099073C2214yescomplemented
92#19099073C2218yescomplemented
93#19099070C2212yescomplemented
94C2×#14579132C2218yescomplemented
95#121×D79C2214yescomplemented
96#121×D79C2218yescomplemented
97#121×D79C2214yescomplemented
98#19099043C2218yescomplemented
99#19099038C2214yescomplemented
100#19099037C2214yescomplemented
101#41×Dic79C2212yescomplemented
102C4×#11929623C2214yescomplemented
103C4×D4×D79C2214yescomplemented
104C4×D4×D79C2214yescomplemented
105C2×C42×D79C2211yescharacteristic, complemented
106H(3,𝔽4)×C79C2214yescomplemented
107#555×C79C2214yescomplemented
108#555×C79C2212yescomplemented
109D42×C79C2212yescomplemented
110D42×C79C2214yescomplemented
111#535×C79C2218yescomplemented
112#535×C79C2214yescomplemented
113#532×C79C2212yescomplemented
114#532×C79C2211yescharacteristic, complemented
115#14579206—432no—
116C2×#11929625C2314yes—
117C2×#11929624C2318yes—
118C2×#11929624C2318yes—
119C2×#11929624C2314yes—
120C2×#11929623C2314yes—
121C2×#11929623C2318yes—
122C2×#11929623C23116yes—
123C2×#11929623C2314yes—
124C2×#11929623C2318yes—
125#41×D79—416no—
126C2×Q8×D79C2314yes—
127C22×D316C2314yes—
128C22×C22⋊D79C23116yes—
129C22×C22⋊D79C23116yes—
130C2×D4×D79C2314yes—
131C2×D4×D79C23116yes—
132C2×D4×D79C2318yes—
133C2×D4×D79C2314yes—
134C2×D4×D79C2318yes—
135C2×D4×D79C2314yes—
136C22×C4×D79C2312yes—
137C22×C4×D79C2311yescharacteristic
138C22×C4×D79C2318yes—
139#14579161C2312yes—
140#14579161C2312yes—
141#14579160C2314yes—
142#14579160C2314yes—
143#14579159C2314yes—
144#14579158C2312yes—
145#14579157C2318yes—
146#14579157C23116yes—
147#14579157C2318yes—
148#14579157C2314yes—
149#14579157C2314yes—
150#14579157C2314yes—
151#14579155C23116yes—
152#14579154C2318yes—
153#14579154C23116yes—
154#14579153C2312yes—
155#14579152C2318yes—
156#14579152C2314yes—
157#14579150C2314yes—
158#14579150C2318yes—
159#14579149C2314yes—
160#14579148C2314yes—
161#14579148C2314yes—
162#14579147C23116yes—
163#14579147C2318yes—
164#14579147C2318yes—
165#14579147C23116yes—
166#14579145C23116yes—
167#14579145C23116yes—
168#14579143C23116yes—
169#14579143C23116yes—
170#14579143C23116yes—
171#14579143C2318yes—
172#14579142C23116yes—
173#14579142C2314yes—
174#14579141C2318yes—
175#14579141C2314yes—
176#14579140C2314yes—
177#14579140C2318yes—
178#14579138C23116yes—
179#14579138C23116yes—
180#14579137C23116yes—
181#14579137C2314yes—
182#14579136C2314yes—
183#14579136C2318yes—
184#14579136C2314yes—
185#14579135C2314yes—
186#14579135C2318yes—
187#14579135C2314yes—
188#14579135C2318yes—
189#14579134C23116yes—
190#14579134C23116yes—
191#14579134C23116yes—
192#14579134C2318yes—
193#14579134C2318yes—
194#14579133C23116yes—
195#14579133C23116yes—
196#14579133C23116yes—
197#14579133C23116yes—
198#14579133C23116yes—
199#14579133C2318yes—
200#14579133C2318yes—
201#14579132C23116yes—
202#14579132C2318yes—
203#14579132C23116yes—
204#14579132C2318yes—
205#14579132C23116yes—
206#14579132C2314yes—
207#14579132C2314yes—
208#14579132C2314yes—
209#14579132C2314yes—
210#14579131C23116yes—
211#14579131C23116yes—
212#14579130C23116yes—
213#14579129C23116yes—
214#14579129C23116yes—
215#14579129C2314yes—
216#14579129C2318yes—
217#14579129C2318yes—
218Q8×Dic79C2314yes—
219C4×Dic158C23116yes—
220C4×Dic158C2314yes—
221#14579126C2314yes—
222C4×D316C23116yes—
223C4×D316C23116yes—
224C4×D316C2314yes—
225C4×D316C2314yes—
226D4×Dic79C23116yes—
227D4×Dic79C2314yes—
228D4×Dic79C2318yes—
229D4×Dic79C2314yes—
230D4×Dic79C2314yes—
231D4×Dic79C2318yes—
232D4×Dic79C2314yes—
233#14579123C2314yes—
234#14579123C2318yes—
235#14579123C2314yes—
236C4×C22⋊D79C2318yes—
237C4×C22⋊D79C2318yes—
238C4×C22⋊D79C2318yes—
239(C22⋊D79)⋊C4C2318yes—
240(C22⋊D79)⋊C4C23116yes—
241(C22⋊D79)⋊C4C23116yes—
242(C22⋊D79)⋊C4C2318yes—
243(C22⋊D79)⋊C4C2318yes—
244#14579120C2312yes—
245#14579120C2314yes—
246#14579120C2314yes—
247#14579119C2318yes—
248#14579119C2314yes—
249#14579117C2318yes—
250C2×C4⋊Dic79C2318yes—
251C4⋊C4×D79C2314yes—
252C4⋊C4×D79C2318yes—
253C4⋊C4×D79C2314yes—
254C2×C22⋊Dic79C23116yes—
255C22⋊C4×D79C2318yes—
256C22⋊C4×D79C23116yes—
257C22⋊C4×D79C2318yes—
258C2×C4×Dic79C2311yescharacteristic
259C2×C4×Dic79C2312yes—
260C2×C4×Dic79C2314yes—
261C42×D79C2312yes—
262C42×D79C2312yes—
263C42×D79C2312yes—
264C42×D79C2312yes—
265C2×#41×C79C2314yes—
266C2×#41×C79C2312yes—
267C22×D4×C79C2318yes—
268C22×D4×C79C2314yes—
269C4⋊Q8×C79C2312yes—
270C4⋊Q8×C79C2311yescharacteristic
271#127×C79C2311yescharacteristic
272#127×C79C2318yes—
273#127×C79C2312yes—
274#124×C79C2318yes—
275#124×C79C23116yes—
276#124×C79C2312yes—
277#124×C79C2314yes—
278#121×C79C2314yes—
279#121×C79C2318yes—
280#121×C79C2314yes—
281#121×C79C2318yes—
282#121×C79C2318yes—
283#121×C79C2314yes—
284#120×C79C23116yes—
285#120×C79C2318yes—
286#120×C79C2318yes—
287C4×D4×C79C2314yes—
288C4×D4×C79C2314yes—
289C4×D4×C79C2314yes—
290#117×C79C2314yes—
291#117×C79C2318yes—
292C2×C42×C79C2311yescharacteristic
293C23×D79C2411yescharacteristic
294C23×D79C2418yes—
295C23×D79C2418yes—
296#11929625—48no—
297#11929624—232no—
298#11929624—416no—
299#11929624—48no—
300#11929623—216no—
301#11929623—48no—
302#11929623—416no—
303#11929623—432no—
304#11929623—416no—
305C2×Dic158C2418yes—
306C2×Dic158C2414yes—
307C2×Dic158C2414yes—
308Q8×D79—48no—
309C2×D316—48no—
310C2×D316C2414yes—
311C2×D316C2418yes—
312C2×D316C2414yes—
313C2×D316C2414yes—
314C2×D316C2418yes—
315C2×C22⋊D79—432no—
316C2×C22⋊D79—432no—
317C2×C22⋊D79C2418yes—
318C2×C22⋊D79C2418yes—
319C2×C22⋊D79C2418yes—
320C2×C22⋊D79C2418yes—
321C2×C22⋊D79C2418yes—
322C2×C22⋊D79C24116yes—
323C2×C22⋊D79C24116yes—
324C2×C22⋊D79C24116yes—
325C2×C22⋊D79C2418yes—
326D4×D79—216no—
327D4×D79—48no—
328D4×D79—416no—
329D4×D79—432no—
330D4×D79—416no—
331D4×D79—48no—
332C22×Dic79C2412yes—
333C22×Dic79C2418yes—
334C22×Dic79C2418yes—
335C22×Dic79C24116yes—
336C22×Dic79C2411yescharacteristic
337C2×C4×D79—28no—
338C2×C4×D79—416no—
339C2×C4×D79—42no—
340C2×C4×D79C2412yes—
341C2×C4×D79C2412yes—
342C2×C4×D79C2418yes—
343C2×C4×D79C2412yes—
344C2×C4×D79C2412yes—
345C2×C4×D79C2418yes—
346C2×C4×D79C24116yes—
347C2×C4×D79C2418yes—
348C2×C4×D79C2412yes—
349C2×C4×D79C2412yes—
350C4⋊Dic79C2414yes—
351C4⋊Dic79C2414yes—
352C4⋊Dic79C2414yes—
353C4⋊Dic79C24116yes—
354C4⋊Dic79C2418yes—
355C4⋊Dic79C2414yes—
356Dic79⋊C4C2418yes—
357Dic79⋊C4C2418yes—
358Dic79⋊C4C24116yes—
359Dic79⋊C4C2418yes—
360Dic79⋊C4C2418yes—
361C22⋊Dic79C2418yes—
362C22⋊Dic79C2418yes—
363C22⋊Dic79C2418yes—
364C22⋊Dic79C2418yes—
365C22⋊Dic79C24116yes—
366C22⋊Dic79C2418yes—
367C22⋊Dic79C2414yes—
368(C2×D79)⋊C4C2418yes—
369(C2×D79)⋊C4C2418yes—
370(C2×D79)⋊C4C2418yes—
371(C2×D79)⋊C4C2418yes—
372(C2×D79)⋊C4C24116yes—
373(C2×D79)⋊C4C2418yes—
374(C2×D79)⋊C4C24116yes—
375C4×Dic79C2411yescharacteristic
376C4×Dic79C2412yes—
377C4×Dic79C2411yescharacteristic
378C4×Dic79C2412yes—
379C4×Dic79C2412yes—
380C4×Dic79C2412yes—
381C4×Dic79C2412yes—
382C4×Dic79C2418yes—
383C4×Dic79C2414yes—
384C4×Dic79C2418yes—
385C24×C79C2418yes—
386#41×C79—48no—
387#41×C79—44no—
388C2×Q8×C79C2414yes—
389C2×Q8×C79C2412yes—
390C2×D4×C79—416no—
391C2×D4×C79—48no—
392C2×D4×C79C2414yes—
393C2×D4×C79C2414yes—
394C2×D4×C79C2414yes—
395C2×D4×C79C2414yes—
396C2×D4×C79C24116yes—
397C2×D4×C79C2418yes—
398C2×D4×C79C2412yes—
399C2×D4×C79C2418yes—
400C2×D4×C79C2414yes—
401C22×C4×C79C2412yes—
402C22×C4×C79C2418yes—
403C22×C4×C79C2411yescharacteristic
404C22×C4×C79C2414yes—
405C4⋊C4×C79C2414yes—
406C4⋊C4×C79C2414yes—
407C4⋊C4×C79C2414yes—
408C22⋊C4×C79C2418yes—
409C22⋊C4×C79C24116yes—
410C22⋊C4×C79C2418yes—
411C22⋊C4×C79C2418yes—
412C22⋊C4×C79C2418yes—
413C42×C79C2411yescharacteristic
414C42×C79C2412yes—
415C42×C79C2411yescharacteristic
416C42×C79C2418yes—
417C23×C79—416no—
418C23×C79—48no—
419C23×C79C2514yes—
420C23×C79C2518yes—
421C23×C79C2511yescharacteristic
422C22×D79—24no—
423C22×D79—216no—
424C22×D79—41no—
425C22×D79—48no—
426C22×D79—48no—
427C22×D79—416no—
428C22×D79—48no—
429C22×D79C2518yes—
430C22×D79C2512yes—
431Q8×C79—44no—
432Q8×C79—42no—
433D4×C79—28no—
434D4×C79—28no—
435D4×C79—28no—
436D4×C79—416no—
437D4×C79—48no—
438D4×C79—44no—
439D4×C79—48no—
440D4×C79—44no—
441D4×C79—42no—
442C2×C4×C79—24no—
443C2×C4×C79—216no—
444C2×C4×C79—22no—
445C2×C4×C79—28no—
446C2×C4×C79C2514yes—
447C2×C4×C79C2511yescharacteristic
448C2×C4×C79C2512yes—
449C2×C4×C79C2518yes—
450C2×C4×C79C2512yes—
451C2×C4×C79C2511yescharacteristic
452C22⋊D79—216no—
453C22⋊D79—216no—
454C22⋊D79—216no—
455C22⋊D79—216no—
456C22⋊D79—416no—
457C22⋊D79—416no—
458C22⋊D79—48no—
459C22⋊D79—48no—
460C22⋊D79—416no—
461C2×Dic79—24no—
462C2×Dic79—216no—
463C2×Dic79—41no—
464C2×Dic79—48no—
465C2×Dic79—416no—
466C2×Dic79C2512yes—
467C2×Dic79C2512yes—
468C2×Dic79C2518yes—
469C2×Dic79C2518yes—
470C2×Dic79C2512yes—
471D316—216no—
472D316—28no—
473D316—28no—
474D316—44no—
475D316—48no—
476C4×D79—24no—
477C4×D79—24no—
478C4×D79—216no—
479C4×D79—24no—
480C4×D79—24no—
481C4×D79—42no—
482C4×D79—48no—
483C4×D79—48no—
484C4×D79—416no—
485C4×D79H(5,𝔽2)18yescomplemented
486Dic158—28no—
487Dic158—216no—
488Dic158—44no—
489C22×C79—28no—
490C22×C79—28no—
491C22×C79—28no—
492C22×C79—22no—
493C22×C79—28no—
494C22×C79—21no—
495C22×C79—24no—
496C22×C79—168no—
497C22×C79C2611yescharacteristic
498C2×D79—22no—
499C2×D79—22no—
500C2×D79—28no—
501C2×D79—28no—
502C2×D79—28no—
503C2×D79—44no—
504C2×D79—816no—
505C2×D79—168no—
506C2×D79C2×H(5,𝔽2)14yes—
507C4×C79—28no—
508C4×C79—22no—
509C4×C79—24no—
510C4×C79—21no—
511C4×C79C2×H(5,𝔽2)14yes—
512C4×C79#58512yes—
513Dic79—28no—
514Dic79—28no—
515Dic79—22no—
516Dic79—22no—
517Dic79C2×H(5,𝔽2)14yes—
518#62834—791nomaximal, Sylow
519C2×C79—41no—
520C2×C79—48no—
521C2×C79—44no—
522C2×C79C22×H(5,𝔽2)12yes—
523C2×C79C2×#58511yescharacteristic
524D79—24no—
525D79—48no—
526#3558—798no—
527#3549—791no—
528#3549D7911yescharacteristic, complemented
529#3548—792no—
530#3546—798no—
531#3537—794no—
532#3519—794no—
533#3519—794no—
534#3511—794no—
535#3508—794no—
536#3506—794no—
537#3498—794no—
538#3496—794no—
539#3488—798no—
540#3444—791no—
541C2×#532—792no—
542C79#6283411yescharacteristic, complemented, Sylow
543C2×H(5,𝔽2)—798no—
544C22×#41—794no—
545#562—798no—
546H(3,𝔽4)—794no—
547H(3,𝔽4)C2×D7914yescomplemented
548#560—798no—
549#560—798no—
550#559—7916no—
551#556—798no—
552#555—792no—
553#555—794no—
554#555C2×D7912yescomplemented
555#555C2×D7914yescomplemented
556#554—794no—
557#554—794no—
558#553—798no—
559#553—798no—
560#553—798no—
561#553—798no—
562#550—7916no—
563#550—794no—
564#550—798no—
565#550—794no—
566#548—7916no—
567#547—798no—
568#547—794no—
569#547—794no—
570#546—798no—
571#546—7916no—
572#546—798no—
573#546—7916no—
574#546—7916no—
575#546—7916no—
576D42—798no—
577D42—798no—
578D42—798no—
579D42—792no—
580D42—798no—
581D42—798no—
582D42—7916no—
583D42—794no—
584D42C2×D7912yescomplemented
585D42C2×D7914yescomplemented
586#542—7916no—
587#540—798no—
588#540—798no—
589#538—7916no—
590#538—7916no—
591#538—7916no—
592#537—798no—
593#537—798no—
594#537—798no—
595#535—794no—
596#535—798no—
597#535—798no—
598#535—7916no—
599#535C2×D7918yescomplemented
600#535C2×D7914yescomplemented
601#534—7916no—
602#533—792no—
603#533—794no—
604#533—791no—
605#532—794no—
606#532—792no—
607#532—792no—
608#532—792no—
609#532—794no—
610#532—794no—
611#532—794no—
612#532—798no—
613#532—794no—
614#532—794no—
615#532—792no—
616#532C2×D7912yescomplemented
617#532C2×D7911yescharacteristic, complemented
618C2×C4⋊Q8—792no—
619C2×#127—794no—
620C2×#127—792no—
621#529—794no—
622#529—794no—
623#529—794no—
624C2×#124—794no—
625#525—792no—
626#525—794no—
627#525—798no—
628#525—798no—
629C2×#121—798no—
630C2×#121—794no—
631C2×#121—794no—
632C2×#121—798no—
633#520—798no—
634#518—794no—
635#518—794no—
636C4×#41—792no—
637C4×#41—794no—
638C2×C4×D4—794no—
639C2×C4×D4—794no—
640C22×C42—791no—
641H(5,𝔽2)—31632no—
642C2×#41—31616no—
643C2×#41—794no—
644C2×#41—798no—
645C2×#41—794no—
646C2×#41—798no—
647C2×#41—7916no—
648C2×#41—794no—
649C2×#41—798no—
650C2×#41—794no—
651C2×#41—798no—
652C2×#41C22×D7912yes—
653C2×#41C22×D7914yes—
654C22×Q8—794no—
655C22×D4—7916no—
656C22×D4—7916no—
657C22×D4—794no—
658C22×D4—798no—
659C22×D4—7916no—
660C22×D4—798no—
661C22×D4—794no—
662C22×D4—794no—
663C22×D4—794no—
664C22×D4C22×D7914yes—
665C22×D4C22×D7918yes—
666C23×C4—798no—
667C23×C4—791no—
668C23×C4—792no—
669C4⋊Q8—794no—
670C4⋊Q8—794no—
671C4⋊Q8—794no—
672C4⋊Q8—792no—
673C4⋊Q8—792no—
674C4⋊Q8C22×D7912yes—
675C4⋊Q8C22×D7911yescharacteristic
676#127—794no—
677#127—794no—
678#127—794no—
679#127—7916no—
680#127—798no—
681#127—798no—
682#127—792no—
683#127C22×D7912yes—
684#127C22×D7911yescharacteristic
685#127C22×D7918yes—
686#126—798no—
687#126—7916no—
688#126—7916no—
689#125—794no—
690#125—798no—
691#125—792no—
692#124—794no—
693#124—798no—
694#124—794no—
695#124—794no—
696#124—798no—
697#124—798no—
698#124—7916no—
699#124—7916no—
700#124—794no—
701#124C22×D7914yes—
702#124C22×D7912yes—
703#124C22×D7918yes—
704#124C22×D79116yes—
705#123—794no—
706#123—7916no—
707#123—798no—
708#123—7916no—
709#123—7916no—
710#123—7916no—
711#123—7916no—
712#123—7916no—
713C22⋊Q8—794no—
714C22⋊Q8—7916no—
715C22⋊Q8—794no—
716C22⋊Q8—798no—
717C22⋊Q8—794no—
718C22⋊Q8—798no—
719C22⋊Q8—7916no—
720C22⋊Q8—7916no—
721#121—794no—
722#121—794no—
723#121—794no—
724#121—798no—
725#121—798no—
726#121—7916no—
727#121—798no—
728#121—798no—
729#121—7916no—
730#121—7916no—
731#121—794no—
732#121—7916no—
733#121—7916no—
734#121—7916no—
735#121—7916no—
736#121—7916no—
737#121—794no—
738#121—794no—
739#121—798no—
740#121—798no—
741#121—794no—
742#121—794no—
743#121—798no—
744#121—798no—
745#121—798no—
746#121—7916no—
747#121—7916no—
748#121—7916no—
749#121C22×D7914yes—
750#121C22×D7914yes—
751#121C22×D7918yes—
752#121C22×D7914yes—
753#121C22×D7918yes—
754#121C22×D7918yes—
755#120—7916no—
756#120—794no—
757#120—7916no—
758#120—798no—
759#120—7916no—
760#120—798no—
761#120—7916no—
762#120—7916no—
763#120C22×D7918yes—
764#120C22×D79116yes—
765#120C22×D7918yes—
766C4×Q8—794no—
767C4×Q8—794no—
768C4×Q8—794no—
769C4×Q8—7916no—
770C4×D4—794no—
771C4×D4—794no—
772C4×D4—798no—
773C4×D4—794no—
774C4×D4—794no—
775C4×D4—7916no—
776C4×D4—798no—
777C4×D4—798no—
778C4×D4—798no—
779C4×D4—798no—
780C4×D4—794no—
781C4×D4—794no—
782C4×D4—798no—
783C4×D4—798no—
784C4×D4—798no—
785C4×D4—798no—
786C4×D4—7916no—
787C4×D4—7916no—
788C4×D4—794no—
789C4×D4—794no—
790C4×D4—7916no—
791C4×D4—7916no—
792C4×D4C22×D7914yes—
793C4×D4C22×D7914yes—
794C4×D4C22×D7914yes—
795#117—794no—
796#117—792no—
797#117—794no—
798#117—794no—
799#117—798no—
800#117—798no—
801#117C22×D7914yes—
802#117C22×D7918yes—
803C2×C4⋊C4—798no—
804C2×C4⋊C4—794no—
805C2×C4⋊C4—794no—
806C2×C4⋊C4—798no—
807C2×C22⋊C4—7916no—
808C2×C22⋊C4—798no—
809C2×C22⋊C4—798no—
810C2×C22⋊C4—7916no—
811C2×C42—794no—
812C2×C42—791no—
813C2×C42—792no—
814C2×C42—792no—
815C2×C42—792no—
816C2×C42—792no—
817C2×C42—792no—
818C2×C42C22×D7911yescharacteristic
819C24—798no—
820C24—798no—
821C24—791no—
822C24C23×D7918yes—
823#41—48no—
824#41—44no—
825#41—31616no—
826#41—3168no—
827#41—31616no—
828#41—31616no—
829#41—31632no—
830#41—3168no—
831#41—3168no—
832#41—15832no—
833#41—15816no—
834C2×Q8—3168no—
835C2×Q8—794no—
836C2×Q8—794no—
837C2×Q8—798no—
838C2×Q8C23×D7912yes—
839C2×Q8C23×D7914yes—
840C2×D4—416no—
841C2×D4—48no—
842C2×D4—3168no—
843C2×D4—31616no—
844C2×D4—31632no—
845C2×D4—31632no—
846C2×D4—3168no—
847C2×D4—31616no—
848C2×D4—3168no—
849C2×D4—31632no—
850C2×D4—798no—
851C2×D4—7916no—
852C2×D4—798no—
853C2×D4—7916no—
854C2×D4—7916no—
855C2×D4—798no—
856C2×D4—798no—
857C2×D4—798no—
858C2×D4—798no—
859C2×D4—798no—
860C2×D4—794no—
861C2×D4—794no—
862C2×D4—798no—
863C2×D4—794no—
864C2×D4—15816no—
865C2×D4C23×D7914yes—
866C2×D4C23×D7914yes—
867C2×D4C23×D7914yes—
868C2×D4C23×D7912yes—
869C2×D4C23×D7914yes—
870C2×D4C23×D7918yes—
871C2×D4C23×D79116yes—
872C2×D4C23×D7914yes—
873C2×D4C23×D7918yes—
874C22×C4—3162no—
875C22×C4—31616no—
876C22×C4—791no—
877C22×C4—798no—
878C22×C4—7916no—
879C22×C4—792no—
880C22×C4—798no—
881C22×C4—798no—
882C22×C4—7916no—
883C22×C4—792no—
884C22×C4—792no—
885C22×C4—798no—
886C22×C4—792no—
887C22×C4—792no—
888C22×C4—792no—
889C22×C4—792no—
890C22×C4—798no—
891C22×C4—1588no—
892C22×C4C23×D7911yescharacteristic
893C22×C4C23×D7912yes—
894C22×C4C23×D7914yes—
895C22×C4C23×D7918yes—
896C4⋊C4—798no—
897C4⋊C4—798no—
898C4⋊C4—7916no—
899C4⋊C4—798no—
900C4⋊C4—798no—
901C4⋊C4—794no—
902C4⋊C4—794no—
903C4⋊C4—794no—
904C4⋊C4—7916no—
905C4⋊C4—798no—
906C4⋊C4—794no—
907C4⋊C4C23×D7914yes—
908C4⋊C4C23×D7914yes—
909C4⋊C4C23×D7914yes—
910C22⋊C4—798no—
911C22⋊C4—798no—
912C22⋊C4—798no—
913C22⋊C4—7916no—
914C22⋊C4—798no—
915C22⋊C4—798no—
916C22⋊C4—794no—
917C22⋊C4—798no—
918C22⋊C4—7916no—
919C22⋊C4—798no—
920C22⋊C4—798no—
921C22⋊C4—798no—
922C22⋊C4—798no—
923C22⋊C4—7916no—
924C22⋊C4C23×D7918yes—
925C22⋊C4C23×D7918yes—
926C22⋊C4C23×D7918yes—
927C22⋊C4C23×D7918yes—
928C22⋊C4C23×D79116yes—
929C42—791no—
930C42—791no—
931C42—792no—
932C42—792no—
933C42—792no—
934C42—792no—
935C42—792no—
936C42—794no—
937C42—798no—
938C42—798no—
939C42C23×D7911yescharacteristic
940C42C23×D7912yes—
941C42C23×D7911yescharacteristic
942C42C23×D7918yes—
943C23—416no—
944C23—48no—
945C23—3161no—
946C23—3168no—
947C23—3168no—
948C23—31616no—
949C23—3168no—
950C23—792no—
951C23—798no—
952C23—1584no—
953C23—15816no—
954C23C24×D7914yes—
955C23C24×D7918yes—
956C23C24×D7911yescharacteristic
957Q8—44no—
958Q8—42no—
959Q8—3164no—
960Q8—15816no—
961Q8—1588no—
962D4—28no—
963D4—28no—
964D4—28no—
965D4—416no—
966D4—48no—
967D4—48no—
968D4—44no—
969D4—42no—
970D4—44no—
971D4—3164no—
972D4—3168no—
973D4—31616no—
974D4—31616no—
975D4—31616no—
976D4—3168no—
977D4—3168no—
978D4—15816no—
979D4—15816no—
980D4—15816no—
981D4—15816no—
982D4—15816no—
983D4—1588no—
984D4—1588no—
985C2×C4—216no—
986C2×C4—24no—
987C2×C4—22no—
988C2×C4—28no—
989C2×C4—3168no—
990C2×C4—3168no—
991C2×C4—3162no—
992C2×C4—31616no—
993C2×C4—3168no—
994C2×C4—3161no—
995C2×C4—31616no—
996C2×C4—792no—
997C2×C4—798no—
998C2×C4—792no—
999C2×C4—792no—
1000C2×C4—798no—
1001C2×C4—798no—
1002C2×C4—1584no—
1003C2×C4—1584no—
1004C2×C4—1584no—
1005C2×C4—15816no—
1006C2×C4—1584no—
1007C2×C4—15816no—
1008C2×C4—1584no—
1009C2×C4C24×D7914yes—
1010C2×C4C24×D7911yescharacteristic
1011C2×C4C24×D7912yes—
1012C2×C4C24×D7918yes—
1013C2×C4C24×D7912yes—
1014C2×C4C24×D7911yescharacteristic
1015C22—28no—
1016C22—22no—
1017C22—28no—
1018C22—28no—
1019C22—21no—
1020C22—24no—
1021C22—28no—
1022C22—168no—
1023C22—3164no—
1024C22—794no—
1025C22—63216no—
1026C22—1588no—
1027C22—1588no—
1028C22—1588no—
1029C22—1582no—
1030C22—1582no—
1031C22—12648no—
1032C22C25×D7911yescharacteristic
1033C4—28no—
1034C4—22no—
1035C4—21no—
1036C4—24no—
1037C4—794no—
1038C4—1582no—
1039C4—1588no—
1040C4—1588no—
1041C4—1582no—
1042C4H(5,𝔽2)×D7914yes—
1043C4#1909939812yes—
1044C2—48no—
1045C2—44no—
1046C2—41no—
1047C2—3168no—
1048C2—1584no—
1049C2C2×H(5,𝔽2)×D7912yes—
1050C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3549C2
hypercenter#3549D79
hypocenterC79#62834
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3549

Complements

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

NH ≅ G/Ntype
1. #23777913C2semidirect
2. #23777805C2semidirect
3. #23777798C2semidirect
4. #23777770C2semidirect
5. #23777633C2semidirect
6. #23777435C2semidirect
7. #23777423C2semidirect
8. #23777300C2semidirect
9. #23777275C2semidirect
10. #23777242C2semidirect
11. #23777172C2semidirect
12. #23777156C2semidirect
13. #23777067C2semidirect
14. #23776695C2semidirect
15. #532×D79C2semidirect
16. C79×#3549C2semidirect
17. C2×#14579206C22semidirect
18. C2×#41×D79C22semidirect
19. #19099307C22semidirect
20. #19099305C22semidirect
21. #19099302C22semidirect
22. #19099300C22semidirect
23. #19099295C22semidirect
24. #19099281C22semidirect
25. #19099279C22semidirect
26. #19099278C22semidirect
27. #19099274C22semidirect
28. #19099270C22semidirect
29. #19099265C22semidirect
30. #19099260C22semidirect
31. #19099257C22semidirect
32. #19099257C22semidirect
33. #19099234C22semidirect
34. #19099233C22semidirect
35. #19099233C22semidirect
36. #19099231C22semidirect
37. #19099221C22semidirect
38. #19099218C22semidirect
39. #19099217C22semidirect
40. #19099213C22semidirect
41. #19099210C22semidirect
42. #19099207C22semidirect
43. #19099206C22semidirect
44. #19099200C22semidirect
45. #19099200C22semidirect
46. #19099200C22semidirect
47. D4×D316C22semidirect
48. #19099198C22semidirect
49. #19099198C22semidirect
50. #19099197C22semidirect
51. D4×C22⋊D79C22semidirect
52. D4×C22⋊D79C22semidirect
53. #19099195C22semidirect
54. #19099195C22semidirect
55. #19099177C22semidirect
56. #19099166C22semidirect
57. #19099166C22semidirect
58. #19099148C22semidirect
59. #19099147C22semidirect
60. #19099147C22semidirect
61. #19099142C22semidirect
62. #19099142C22semidirect
63. #19099141C22semidirect
64. #19099129C22semidirect
65. #19099129C22semidirect
66. #19099128C22semidirect
67. #19099127C22semidirect
68. #19099123C22semidirect
69. #19099120C22semidirect
70. #19099118C22semidirect
71. #19099116C22semidirect
72. #19099114C22semidirect
73. #19099113C22semidirect
74. #19099112C22semidirect
75. #19099111C22semidirect
76. #19099111C22semidirect
77. #19099110C22semidirect
78. #19099110C22semidirect
79. #19099109C22semidirect
80. #19099108C22semidirect
81. #19099108C22semidirect
82. #19099108C22semidirect
83. C4⋊Q8×D79C22semidirect
84. C2×#14579157C22semidirect
85. #127×D79C22semidirect
86. #19099095C22semidirect
87. #19099094C22semidirect
88. #19099092C22semidirect
89. #124×D79C22semidirect
90. #19099075C22semidirect
91. #19099073C22semidirect
92. #19099073C22semidirect
93. #19099070C22semidirect
94. C2×#14579132C22semidirect
95. #121×D79C22semidirect
96. #121×D79C22semidirect
97. #121×D79C22semidirect
98. #19099043C22semidirect
99. #19099038C22semidirect
100. #19099037C22semidirect
101. #41×Dic79C22semidirect
102. C4×#11929623C22semidirect
103. C4×D4×D79C22semidirect
104. C4×D4×D79C22semidirect
105. C2×C42×D79C22semidirect
106. H(3,𝔽4)×C79C22semidirect
107. #555×C79C22semidirect
108. #555×C79C22semidirect
109. D42×C79C22semidirect
110. D42×C79C22semidirect
111. #535×C79C22semidirect
112. #535×C79C22semidirect
113. #532×C79C22semidirect
114. #532×C79C22semidirect
485. C4×D79H(5,𝔽2)semidirect
528. #3549D79semidirect
542. C79#62834semidirect
547. H(3,𝔽4)C2×D79semidirect
554. #555C2×D79semidirect
555. #555C2×D79semidirect
584. D42C2×D79semidirect
585. D42C2×D79semidirect
599. #535C2×D79semidirect
600. #535C2×D79semidirect
616. #532C2×D79semidirect
617. #532C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779132
#237778052
#237777982
#237777702
#237776332
#237774352
#237774232
#237773002
#237772752
#237772422
#237771722
#237771562
#237770672
#237766952
#532×D792
C79×#35492
#6283479