Finite Group Databasebeta

← #35197162

Subgroups — #35197162

Order 20224.

7900 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777922C218yesmaximal, complemented
2#23777805C212yesmaximal, complemented
3#23777800C211yesmaximal, characteristic, complemented
4#23777762C218yesmaximal, complemented
5#23777638C214yesmaximal, complemented
6#23777433C214yesmaximal, complemented
7#23777431C214yesmaximal, complemented
8#23777308C214yesmaximal, complemented
9#23777272C214yesmaximal, complemented
10#23777250C214yesmaximal, complemented
11#23777177C214yesmaximal, complemented
12#23777158C214yesmaximal, complemented
13#23777064C218yesmaximal, complemented
14#23776697C211yesmaximal, characteristic, complemented
15#532×D79C212yesmaximal, complemented
16C79×#3548C211yesmaximal, characteristic, complemented
17C2×#14579207C2218yescomplemented
18C2×#41×D79C2214yescomplemented
19#19099311C2214yescomplemented
20#19099305C2218yescomplemented
21#19099301C22116yescomplemented
22#19099297C22116yescomplemented
23#19099284C2218yescomplemented
24#19099279C2214yescomplemented
25#19099278C2214yescomplemented
26#19099278C2214yescomplemented
27#19099273C2214yescomplemented
28#19099266C2218yescomplemented
29#19099263C2218yescomplemented
30#19099261C2218yescomplemented
31#19099260C2218yescomplemented
32#19099235C2214yescomplemented
33#19099232C2218yescomplemented
34#19099231C22116yescomplemented
35#19099223C22116yescomplemented
36#19099216C2214yescomplemented
37#19099214C2218yescomplemented
38#19099205C22116yescomplemented
39#19099204C22116yescomplemented
40#19099204C2218yescomplemented
41#19099202C22116yescomplemented
42#19099202C22116yescomplemented
43#19099201C2218yescomplemented
44D4×D316C2214yescomplemented
45D4×D316C2214yescomplemented
46D4×D316C2218yescomplemented
47#19099198C2214yescomplemented
48#19099198C2218yescomplemented
49#19099197C22116yescomplemented
50#19099197C22116yescomplemented
51#19099197C2218yescomplemented
52#19099183C22116yescomplemented
53#19099169C2214yescomplemented
54#19099168C2214yescomplemented
55#19099167C2214yescomplemented
56#19099153C22116yescomplemented
57#19099149C22116yescomplemented
58#19099145C22116yescomplemented
59#19099143C2218yescomplemented
60#19099143C2218yescomplemented
61#19099129C2218yescomplemented
62#19099129C2218yescomplemented
63#19099129C2218yescomplemented
64#19099129C22116yescomplemented
65#19099127C2218yescomplemented
66#19099124C22116yescomplemented
67#19099119C2214yescomplemented
68#19099118C2212yescomplemented
69#19099114C2212yescomplemented
70#19099114C2212yescomplemented
71#19099113C2212yescomplemented
72#19099113C2211yescharacteristic, complemented
73#19099112C2214yescomplemented
74#19099111C2212yescomplemented
75#19099110C2214yescomplemented
76#19099110C2218yescomplemented
77#19099110C2214yescomplemented
78#19099109C2214yescomplemented
79#19099108C2214yescomplemented
80#19099108C2214yescomplemented
81C4⋊Q8×D79C2212yescomplemented
82#127×D79C2212yescomplemented
83#127×D79C2214yescomplemented
84#19099100C2214yescomplemented
85#19099099C2214yescomplemented
86#19099098C2214yescomplemented
87#124×D79C2214yescomplemented
88#19099076C2214yescomplemented
89#19099076C2218yescomplemented
90#19099075C2212yescomplemented
91#19099070C2218yescomplemented
92C2×#14579136C2218yescomplemented
93#121×D79C2214yescomplemented
94#121×D79C2218yescomplemented
95#121×D79C2214yescomplemented
96#19099044C2218yescomplemented
97#19099035C2218yescomplemented
98C4×#11929625C2214yescomplemented
99#19099031C2212yescomplemented
100C4×D4×D79C2214yescomplemented
101C4×D4×D79C2214yescomplemented
102C2×C42×D79C2211yescharacteristic, complemented
103#562×C79C2214yescomplemented
104#554×C79C2214yescomplemented
105#550×C79C2214yescomplemented
106#547×C79C2214yescomplemented
107#540×C79C2214yescomplemented
108#537×C79C2218yescomplemented
109#533×C79C2211yescharacteristic, complemented
110#532×C79C2212yescomplemented
111#14579207—432no—
112C2×#11929625C2314yes—
113C2×#11929625C2318yes—
114C2×#11929625C2314yes—
115C2×#11929624C2318yes—
116C2×#11929624C23116yes—
117C2×#11929624C2314yes—
118C2×#11929624C2312yes—
119C2×#11929623C2314yes—
120C2×#11929623C2318yes—
121#41×D79—416no—
122C2×Q8×D79C2314yes—
123C22×D316C23116yes—
124C22×D316C2318yes—
125C2×D4×D79C2314yes—
126C2×D4×D79C23116yes—
127C2×D4×D79C23116yes—
128C2×D4×D79C2318yes—
129C2×D4×D79C2318yes—
130C2×D4×D79C2314yes—
131C2×D4×D79C2314yes—
132C2×D4×D79C2318yes—
133C22×C4×D79C2312yes—
134C22×C4×D79C2311yescharacteristic
135C22×C4×D79C2318yes—
136#14579161C2312yes—
137#14579161C2311yescharacteristic
138#14579160C2314yes—
139#14579160C2314yes—
140#14579159C2314yes—
141#14579158C2314yes—
142#14579158C2311yescharacteristic
143#14579158C2312yes—
144#14579157C2314yes—
145#14579157C23116yes—
146#14579157C23116yes—
147#14579157C2314yes—
148#14579157C2314yes—
149#14579156C2318yes—
150#14579156C23116yes—
151#14579154C23116yes—
152#14579153C2314yes—
153#14579152C2314yes—
154#14579150C2314yes—
155#14579150C23116yes—
156#14579150C2314yes—
157#14579149C2312yes—
158#14579149C2314yes—
159#14579148C2314yes—
160#14579147C23116yes—
161#14579147C23116yes—
162#14579147C2318yes—
163#14579147C23116yes—
164#14579147C2318yes—
165#14579146C23116yes—
166#14579146C23116yes—
167#14579146C23116yes—
168#14579146C2318yes—
169#14579145C2314yes—
170#14579144C23116yes—
171#14579142C23116yes—
172#14579141C2314yes—
173#14579139C23116yes—
174#14579139C23116yes—
175#14579137C2318yes—
176#14579137C2314yes—
177#14579136C23116yes—
178#14579136C23116yes—
179#14579136C2318yes—
180#14579136C2318yes—
181#14579136C23116yes—
182#14579136C2318yes—
183#14579136C2314yes—
184#14579136C2314yes—
185#14579136C2314yes—
186#14579136C2314yes—
187#14579135C2314yes—
188#14579135C2318yes—
189#14579135C23116yes—
190#14579135C2314yes—
191#14579135C2318yes—
192#14579135C2314yes—
193#14579134C23116yes—
194#14579134C23116yes—
195#14579134C23116yes—
196#14579134C2318yes—
197#14579134C2318yes—
198#14579133C23116yes—
199#14579133C2318yes—
200#14579133C2318yes—
201#14579132C23116yes—
202#14579132C2318yes—
203#14579132C2314yes—
204#14579132C2318yes—
205#14579132C2314yes—
206#14579131C23116yes—
207#14579131C23116yes—
208#14579131C23116yes—
209#14579131C2314yes—
210#14579131C23116yes—
211#14579129C23116yes—
212#14579129C23116yes—
213#14579129C23116yes—
214#14579129C23116yes—
215Q8×Dic79C2314yes—
216#14579126C23116yes—
217#14579126C2314yes—
218C4×D316C2318yes—
219C4×D316C2318yes—
220C4×D316C2314yes—
221C4×D316C2314yes—
222C4×D316C2314yes—
223D4×Dic79C2314yes—
224D4×Dic79C2314yes—
225#14579123C23116yes—
226#14579123C2314yes—
227#14579123C2314yes—
228#14579123C2318yes—
229#14579123C2314yes—
230#14579123C2314yes—
231C4×C22⋊D79C23116yes—
232C4×C22⋊D79C23116yes—
233C4×C22⋊D79C23116yes—
234C4×C22⋊D79C2318yes—
235C4×C22⋊D79C2318yes—
236(C22⋊D79)⋊C4C2318yes—
237(C22⋊D79)⋊C4C23116yes—
238(C22⋊D79)⋊C4C2318yes—
239(C22⋊D79)⋊C4C2318yes—
240#14579120C2318yes—
241#14579119C2318yes—
242#14579119C2318yes—
243#14579119C2318yes—
244#14579119C2314yes—
245#14579118C2314yes—
246C4⋊C4×D79C2314yes—
247C4⋊C4×D79C2318yes—
248C4⋊C4×D79C2314yes—
249C2×(C2×D79)⋊C4C23116yes—
250C22⋊C4×D79C23116yes—
251C22⋊C4×D79C2318yes—
252C22⋊C4×D79C2318yes—
253C2×C4×Dic79C2311yescharacteristic
254C2×C4×Dic79C2312yes—
255C42×D79C2312yes—
256C42×D79C2312yes—
257C42×D79C2312yes—
258C42×D79C2312yes—
259C42×D79C2314yes—
260C2×#41×C79C2318yes—
261C2×#41×C79C2314yes—
262C4⋊Q8×C79C2312yes—
263C4⋊Q8×C79C2312yes—
264#127×C79C2314yes—
265#127×C79C2312yes—
266#125×C79C2314yes—
267#125×C79C2312yes—
268#124×C79C2314yes—
269#123×C79C23116yes—
270C22⋊Q8×C79C2314yes—
271C22⋊Q8×C79C2318yes—
272C22⋊Q8×C79C23116yes—
273#121×C79C23116yes—
274#121×C79C23116yes—
275#121×C79C2318yes—
276#121×C79C2314yes—
277#121×C79C2314yes—
278C4×Q8×C79C2314yes—
279C4×D4×C79C2314yes—
280C4×D4×C79C2314yes—
281C4×D4×C79C2318yes—
282#117×C79C2312yes—
283C2×C4⋊C4×C79C2318yes—
284C2×C42×C79C2311yescharacteristic
285C23×D79C2411yescharacteristic
286C23×D79C2418yes—
287C23×D79C24116yes—
288#11929625—216no—
289#11929625—416no—
290#11929625—48no—
291#11929624—232no—
292#11929624—432no—
293#11929624—48no—
294#11929624—44no—
295#11929623—48no—
296#11929623—416no—
297C2×Dic158C2418yes—
298C2×Dic158C2414yes—
299C2×Dic158C2412yes—
300Q8×D79—48no—
301C2×D316—416no—
302C2×D316—432no—
303C2×D316C2418yes—
304C2×D316C2414yes—
305C2×D316C2418yes—
306C2×D316C2414yes—
307C2×D316C2414yes—
308C2×D316C2414yes—
309C2×D316C2412yes—
310C2×D316C24116yes—
311C2×D316C24116yes—
312C2×C22⋊D79C2418yes—
313C2×C22⋊D79C2418yes—
314C2×C22⋊D79C2418yes—
315C2×C22⋊D79C2418yes—
316C2×C22⋊D79C2414yes—
317C2×C22⋊D79C24116yes—
318C2×C22⋊D79C2418yes—
319C2×C22⋊D79C24116yes—
320D4×D79—216no—
321D4×D79—48no—
322D4×D79—432no—
323D4×D79—416no—
324D4×D79—432no—
325D4×D79—416no—
326D4×D79—48no—
327D4×D79—416no—
328C22×Dic79C2412yes—
329C22×Dic79C2418yes—
330C22×Dic79C2411yescharacteristic
331C2×C4×D79—28no—
332C2×C4×D79—416no—
333C2×C4×D79—42no—
334C2×C4×D79C2412yes—
335C2×C4×D79C2412yes—
336C2×C4×D79C2418yes—
337C2×C4×D79C2418yes—
338C2×C4×D79C2414yes—
339C2×C4×D79C2412yes—
340C2×C4×D79C2412yes—
341C2×C4×D79C2418yes—
342C2×C4×D79C2418yes—
343C2×C4×D79C24116yes—
344C2×C4×D79C2412yes—
345C2×C4×D79C2412yes—
346C4⋊Dic79C2414yes—
347C4⋊Dic79C2414yes—
348C4⋊Dic79C2414yes—
349C4⋊Dic79C2418yes—
350Dic79⋊C4C2418yes—
351Dic79⋊C4C2418yes—
352Dic79⋊C4C24116yes—
353Dic79⋊C4C2418yes—
354C22⋊Dic79C2418yes—
355C22⋊Dic79C2418yes—
356C22⋊Dic79C24116yes—
357(C2×D79)⋊C4C2418yes—
358(C2×D79)⋊C4C2418yes—
359(C2×D79)⋊C4C24116yes—
360(C2×D79)⋊C4C2418yes—
361(C2×D79)⋊C4C2418yes—
362(C2×D79)⋊C4C2418yes—
363(C2×D79)⋊C4C24116yes—
364(C2×D79)⋊C4C2418yes—
365(C2×D79)⋊C4C24116yes—
366(C2×D79)⋊C4C2418yes—
367(C2×D79)⋊C4C2418yes—
368C4×Dic79C2411yescharacteristic
369C4×Dic79C2411yescharacteristic
370C4×Dic79C2412yes—
371C4×Dic79C2412yes—
372C4×Dic79C2412yes—
373C4×Dic79C2412yes—
374C4×Dic79C2412yes—
375C4×Dic79C2418yes—
376C4×Dic79C24116yes—
377#41×C79—48no—
378#41×C79—416no—
379C2×Q8×C79C2414yes—
380C2×Q8×C79C2414yes—
381C2×D4×C79C2414yes—
382C2×D4×C79C2414yes—
383C2×D4×C79C2418yes—
384C2×D4×C79C2414yes—
385C2×D4×C79C24116yes—
386C22×C4×C79C2411yescharacteristic
387C22×C4×C79C2412yes—
388C22×C4×C79C2418yes—
389C22×C4×C79C24116yes—
390C4⋊C4×C79C2414yes—
391C4⋊C4×C79C2414yes—
392C4⋊C4×C79C24116yes—
393C4⋊C4×C79C2414yes—
394C4⋊C4×C79C2414yes—
395C4⋊C4×C79C2418yes—
396C22⋊C4×C79C2414yes—
397C22⋊C4×C79C24116yes—
398C22⋊C4×C79C2418yes—
399C22⋊C4×C79C2418yes—
400C42×C79C2411yescharacteristic
401C42×C79C2412yes—
402C42×C79C2411yescharacteristic
403C42×C79C2414yes—
404C23×C79C2518yes—
405C23×C79C2511yescharacteristic
406C22×D79—24no—
407C22×D79—216no—
408C22×D79—41no—
409C22×D79—48no—
410C22×D79—48no—
411C22×D79—416no—
412C22×D79—416no—
413C22×D79—416no—
414C22×D79C2514yes—
415C22×D79C2518yes—
416C22×D79C2512yes—
417Q8×C79—28no—
418Q8×C79—44no—
419D4×C79—28no—
420D4×C79—28no—
421D4×C79—416no—
422D4×C79—48no—
423D4×C79—44no—
424C2×C4×C79—24no—
425C2×C4×C79—216no—
426C2×C4×C79—22no—
427C2×C4×C79—416no—
428C2×C4×C79C2511yescharacteristic
429C2×C4×C79C2512yes—
430C2×C4×C79C2518yes—
431C2×C4×C79C2518yes—
432C2×C4×C79C2512yes—
433C2×C4×C79C2511yescharacteristic
434C22⋊D79—216no—
435C22⋊D79—216no—
436C22⋊D79—216no—
437C22⋊D79—416no—
438C22⋊D79—416no—
439C22⋊D79—48no—
440C22⋊D79—48no—
441C22⋊D79—44no—
442C2×Dic79—24no—
443C2×Dic79—41no—
444C2×Dic79—48no—
445C2×Dic79C2514yes—
446C2×Dic79C2512yes—
447C2×Dic79C2512yes—
448C2×Dic79C2518yes—
449C2×Dic79C2512yes—
450D316—216no—
451D316—216no—
452D316—28no—
453D316—28no—
454D316—28no—
455D316—416no—
456D316—44no—
457D316—416no—
458D316—42no—
459C4×D79—24no—
460C4×D79—24no—
461C4×D79—216no—
462C4×D79—24no—
463C4×D79—28no—
464C4×D79—24no—
465C4×D79—216no—
466C4×D79—42no—
467C4×D79—48no—
468C4×D79—48no—
469C4×D79—416no—
470C4×D79H(5,𝔽2)18yescomplemented
471Dic158—216no—
472Dic158—44no—
473Dic158—42no—
474C22×C79—28no—
475C22×C79—28no—
476C22×C79—22no—
477C22×C79—21no—
478C22×C79—28no—
479C22×C79C2611yescharacteristic
480C2×D79—22no—
481C2×D79—22no—
482C2×D79—28no—
483C2×D79—28no—
484C2×D79—28no—
485C2×D79—28no—
486C2×D79—24no—
487C2×D79—44no—
488C2×D79—816no—
489C2×D79—1616no—
490C2×D79C2×H(5,𝔽2)14yes—
491C4×C79—28no—
492C4×C79—22no—
493C4×C79—28no—
494C4×C79—21no—
495C4×C79C2×H(5,𝔽2)14yes—
496C4×C79#58512yes—
497Dic79—28no—
498Dic79—22no—
499Dic79—24no—
500Dic79—22no—
501Dic79C2×H(5,𝔽2)14yes—
502#62834—791nomaximal, Sylow
503C2×C79—41no—
504C2×C79—48no—
505C2×C79C22×H(5,𝔽2)12yes—
506C2×C79C2×#58511yescharacteristic
507D79—24no—
508D79—48no—
509D79—44no—
510#3558—798no—
511#3549—792no—
512#3548—791no—
513#3548D7911yescharacteristic, complemented
514#3546—798no—
515#3537—794no—
516#3519—794no—
517#3519—794no—
518#3511—794no—
519#3508—794no—
520#3506—794no—
521#3498—794no—
522#3496—794no—
523#3488—798no—
524#3444—791no—
525C2×#532—792no—
526C79#6283411yescharacteristic, complemented, Sylow
527C2×H(5,𝔽2)—798no—
528C22×#41—794no—
529#562—794no—
530#562C2×D7914yescomplemented
531H(3,𝔽4)—798no—
532#560—7916no—
533#559—7916no—
534#556—798no—
535#555—794no—
536#555—794no—
537#555—794no—
538#554—794no—
539#554C2×D7914yescomplemented
540#553—798no—
541#553—798no—
542#553—798no—
543#553—798no—
544#550—798no—
545#550—7916no—
546#550—794no—
547#550C2×D7914yescomplemented
548#548—7916no—
549#547—794no—
550#547—798no—
551#547C2×D7914yescomplemented
552#546—798no—
553#546—7916no—
554#546—7916no—
555#546—798no—
556#546—7916no—
557#546—7916no—
558D42—798no—
559D42—794no—
560D42—7916no—
561D42—7916no—
562D42—798no—
563D42—794no—
564D42—798no—
565D42—794no—
566#542—7916no—
567#540—794no—
568#540—794no—
569#540—794no—
570#540C2×D7914yescomplemented
571#538—7916no—
572#538—7916no—
573#538—7916no—
574#537—798no—
575#537—798no—
576#537C2×D7918yescomplemented
577#535—798no—
578#535—798no—
579#535—798no—
580#535—7916no—
581#535—798no—
582#534—7916no—
583#533—792no—
584#533—794no—
585#533C2×D7911yescharacteristic, complemented
586#532—794no—
587#532—792no—
588#532—792no—
589#532—792no—
590#532—794no—
591#532—794no—
592#532—794no—
593#532—794no—
594#532—794no—
595#532—798no—
596#532—792no—
597#532—791no—
598#532C2×D7912yescomplemented
599C2×C4⋊Q8—792no—
600C2×#127—792no—
601C2×#127—794no—
602#529—794no—
603#529—794no—
604#529—794no—
605C2×#124—794no—
606#525—798no—
607#525—794no—
608#525—798no—
609#525—792no—
610C2×#121—794no—
611C2×#121—794no—
612C2×#121—798no—
613C2×#121—798no—
614#520—798no—
615#518—798no—
616C4×#41—794no—
617C4×#41—792no—
618C2×C4×D4—794no—
619C2×C4×D4—794no—
620C22×C42—791no—
621H(5,𝔽2)—31632no—
622C2×#41—31616no—
623C2×#41—798no—
624C2×#41—794no—
625C2×#41—794no—
626C2×#41—794no—
627C2×#41—798no—
628C2×#41—792no—
629C2×#41—794no—
630C2×#41—7916no—
631C2×#41—798no—
632C2×#41C22×D7918yes—
633C2×#41C22×D7914yes—
634C22×Q8—794no—
635C22×D4—794no—
636C22×D4—798no—
637C22×D4—798no—
638C22×D4—7916no—
639C22×D4—798no—
640C22×D4—794no—
641C22×D4—7916no—
642C22×D4—794no—
643C22×D4—7916no—
644C22×D4—798no—
645C23×C4—798no—
646C23×C4—791no—
647C23×C4—792no—
648C4⋊Q8—794no—
649C4⋊Q8—794no—
650C4⋊Q8—794no—
651C4⋊Q8—792no—
652C4⋊Q8—791no—
653C4⋊Q8C22×D7912yes—
654C4⋊Q8C22×D7912yes—
655#127—794no—
656#127—794no—
657#127—794no—
658#127—7916no—
659#127—7916no—
660#127—792no—
661#127—794no—
662#127—791no—
663#127C22×D7912yes—
664#127C22×D7914yes—
665#126—798no—
666#126—7916no—
667#126—7916no—
668#125—794no—
669#125—794no—
670#125C22×D7912yes—
671#125C22×D7914yes—
672#124—794no—
673#124—794no—
674#124—7916no—
675#124—794no—
676#124—798no—
677#124—798no—
678#124—7916no—
679#124—7916no—
680#124—7916no—
681#124—794no—
682#124—792no—
683#124C22×D7914yes—
684#123—7916no—
685#123—7916no—
686#123—798no—
687#123—7916no—
688#123—7916no—
689#123—7916no—
690#123—794no—
691#123C22×D79116yes—
692C22⋊Q8—794no—
693C22⋊Q8—798no—
694C22⋊Q8—794no—
695C22⋊Q8—7916no—
696C22⋊Q8—7916no—
697C22⋊Q8C22×D7914yes—
698C22⋊Q8C22×D7918yes—
699C22⋊Q8C22×D79116yes—
700#121—794no—
701#121—794no—
702#121—798no—
703#121—798no—
704#121—7916no—
705#121—798no—
706#121—798no—
707#121—7916no—
708#121—794no—
709#121—794no—
710#121—798no—
711#121—794no—
712#121—798no—
713#121—7916no—
714#121—794no—
715#121—794no—
716#121—794no—
717#121—7916no—
718#121—798no—
719#121—798no—
720#121—7916no—
721#121—794no—
722#121—798no—
723#121—7916no—
724#121—798no—
725#121—798no—
726#121—7916no—
727#121—7916no—
728#121—7916no—
729#121C22×D7914yes—
730#121C22×D7914yes—
731#121C22×D7918yes—
732#121C22×D79116yes—
733#121C22×D79116yes—
734#120—7916no—
735#120—7916no—
736#120—7916no—
737#120—7916no—
738#120—794no—
739#120—7916no—
740#120—7916no—
741#120—7916no—
742#120—7916no—
743C4×Q8—794no—
744C4×Q8—794no—
745C4×Q8—7916no—
746C4×Q8C22×D7914yes—
747C4×D4—794no—
748C4×D4—794no—
749C4×D4—798no—
750C4×D4—798no—
751C4×D4—7916no—
752C4×D4—7916no—
753C4×D4—7916no—
754C4×D4—794no—
755C4×D4—794no—
756C4×D4—798no—
757C4×D4—794no—
758C4×D4—794no—
759C4×D4—7916no—
760C4×D4—798no—
761C4×D4—798no—
762C4×D4—798no—
763C4×D4—7916no—
764C4×D4—794no—
765C4×D4—794no—
766C4×D4—798no—
767C4×D4—794no—
768C4×D4—798no—
769C4×D4C22×D7914yes—
770C4×D4C22×D7914yes—
771C4×D4C22×D7918yes—
772#117—798no—
773#117—794no—
774#117—798no—
775#117—798no—
776#117—798no—
777#117—794no—
778#117C22×D7912yes—
779C2×C4⋊C4—794no—
780C2×C4⋊C4—794no—
781C2×C4⋊C4—798no—
782C2×C4⋊C4C22×D7918yes—
783C2×C22⋊C4—7916no—
784C2×C22⋊C4—798no—
785C2×C22⋊C4—798no—
786C2×C22⋊C4—7916no—
787C2×C42—791no—
788C2×C42—792no—
789C2×C42—792no—
790C2×C42—792no—
791C2×C42—794no—
792C2×C42—792no—
793C2×C42—792no—
794C2×C42C22×D7911yescharacteristic
795C24—7916no—
796C24—798no—
797C24—791no—
798#41—48no—
799#41—416no—
800#41—3168no—
801#41—3164no—
802#41—31632no—
803#41—31616no—
804#41—3168no—
805#41—31616no—
806#41—3168no—
807#41—15832no—
808#41—15816no—
809C2×Q8—3168no—
810C2×Q8—792no—
811C2×Q8—794no—
812C2×Q8—798no—
813C2×Q8C23×D7914yes—
814C2×Q8C23×D7914yes—
815C2×D4—31616no—
816C2×D4—31632no—
817C2×D4—31616no—
818C2×D4—31632no—
819C2×D4—3168no—
820C2×D4—31616no—
821C2×D4—31616no—
822C2×D4—3168no—
823C2×D4—31632no—
824C2×D4—794no—
825C2×D4—798no—
826C2×D4—7916no—
827C2×D4—7916no—
828C2×D4—798no—
829C2×D4—798no—
830C2×D4—798no—
831C2×D4—798no—
832C2×D4—792no—
833C2×D4—794no—
834C2×D4—7916no—
835C2×D4—7916no—
836C2×D4—794no—
837C2×D4—798no—
838C2×D4—798no—
839C2×D4—794no—
840C2×D4—794no—
841C2×D4—15816no—
842C2×D4C23×D7914yes—
843C2×D4C23×D7914yes—
844C2×D4C23×D7914yes—
845C2×D4C23×D7918yes—
846C2×D4C23×D79116yes—
847C22×C4—3162no—
848C22×C4—31616no—
849C22×C4—791no—
850C22×C4—798no—
851C22×C4—792no—
852C22×C4—798no—
853C22×C4—798no—
854C22×C4—7916no—
855C22×C4—792no—
856C22×C4—792no—
857C22×C4—792no—
858C22×C4—792no—
859C22×C4—792no—
860C22×C4—792no—
861C22×C4—794no—
862C22×C4—798no—
863C22×C4—798no—
864C22×C4—1588no—
865C22×C4C23×D7911yescharacteristic
866C22×C4C23×D7912yes—
867C22×C4C23×D7918yes—
868C22×C4C23×D79116yes—
869C4⋊C4—798no—
870C4⋊C4—798no—
871C4⋊C4—7916no—
872C4⋊C4—798no—
873C4⋊C4—794no—
874C4⋊C4—794no—
875C4⋊C4—794no—
876C4⋊C4—798no—
877C4⋊C4C23×D7914yes—
878C4⋊C4C23×D7914yes—
879C4⋊C4C23×D7914yes—
880C4⋊C4C23×D79116yes—
881C4⋊C4C23×D7918yes—
882C4⋊C4C23×D7914yes—
883C22⋊C4—798no—
884C22⋊C4—798no—
885C22⋊C4—7916no—
886C22⋊C4—798no—
887C22⋊C4—798no—
888C22⋊C4—7916no—
889C22⋊C4—7916no—
890C22⋊C4—798no—
891C22⋊C4—798no—
892C22⋊C4—798no—
893C22⋊C4—798no—
894C22⋊C4—798no—
895C22⋊C4—798no—
896C22⋊C4—7916no—
897C22⋊C4C23×D79116yes—
898C22⋊C4C23×D7918yes—
899C22⋊C4C23×D7918yes—
900C22⋊C4C23×D7914yes—
901C42—791no—
902C42—791no—
903C42—792no—
904C42—792no—
905C42—792no—
906C42—792no—
907C42—792no—
908C42—798no—
909C42—7916no—
910C42C23×D7911yescharacteristic
911C42C23×D7912yes—
912C42C23×D7911yescharacteristic
913C42C23×D7914yes—
914C23—3161no—
915C23—3168no—
916C23—3168no—
917C23—31616no—
918C23—31616no—
919C23—31616no—
920C23—792no—
921C23—794no—
922C23—798no—
923C23—1584no—
924C23—15816no—
925C23C24×D7918yes—
926C23C24×D7911yescharacteristic
927Q8—28no—
928Q8—44no—
929Q8—3164no—
930Q8—3162no—
931Q8—15816no—
932D4—28no—
933D4—28no—
934D4—416no—
935D4—48no—
936D4—44no—
937D4—31616no—
938D4—31616no—
939D4—3164no—
940D4—3162no—
941D4—31616no—
942D4—3168no—
943D4—31616no—
944D4—3168no—
945D4—3164no—
946D4—15816no—
947D4—15816no—
948D4—15816no—
949D4—15816no—
950D4—15816no—
951D4—1588no—
952D4—1588no—
953D4—1588no—
954C2×C4—216no—
955C2×C4—24no—
956C2×C4—22no—
957C2×C4—416no—
958C2×C4—3168no—
959C2×C4—3168no—
960C2×C4—3162no—
961C2×C4—31616no—
962C2×C4—3168no—
963C2×C4—3161no—
964C2×C4—792no—
965C2×C4—798no—
966C2×C4—794no—
967C2×C4—792no—
968C2×C4—792no—
969C2×C4—798no—
970C2×C4—1584no—
971C2×C4—15816no—
972C2×C4—1584no—
973C2×C4—1584no—
974C2×C4—1584no—
975C2×C4—15816no—
976C2×C4—1584no—
977C2×C4—1588no—
978C2×C4C24×D7911yescharacteristic
979C2×C4C24×D7912yes—
980C2×C4C24×D7918yes—
981C2×C4C24×D7918yes—
982C2×C4C24×D7912yes—
983C2×C4C24×D7911yescharacteristic
984C22—28no—
985C22—22no—
986C22—28no—
987C22—21no—
988C22—28no—
989C22—3164no—
990C22—794no—
991C22—63216no—
992C22—1588no—
993C22—1588no—
994C22—1588no—
995C22—1584no—
996C22—1588no—
997C22—1582no—
998C22—1582no—
999C22—126416no—
1000C22C25×D7911yescharacteristic
1001C4—28no—
1002C4—22no—
1003C4—28no—
1004C4—21no—
1005C4—794no—
1006C4—1582no—
1007C4—1588no—
1008C4—1582no—
1009C4—1584no—
1010C4H(5,𝔽2)×D7914yes—
1011C4#1909940012yes—
1012C2—41no—
1013C2—48no—
1014C2—3168no—
1015C2—3164no—
1016C2—1584no—
1017C2C2×H(5,𝔽2)×D7912yes—
1018C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3548C2
hypercenter#3548D79
hypocenterC79#62834
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #23777922C2semidirect
2. #23777805C2semidirect
3. #23777800C2semidirect
4. #23777762C2semidirect
5. #23777638C2semidirect
6. #23777433C2semidirect
7. #23777431C2semidirect
8. #23777308C2semidirect
9. #23777272C2semidirect
10. #23777250C2semidirect
11. #23777177C2semidirect
12. #23777158C2semidirect
13. #23777064C2semidirect
14. #23776697C2semidirect
15. #532×D79C2semidirect
16. C79×#3548C2semidirect
17. C2×#14579207C22semidirect
18. C2×#41×D79C22semidirect
19. #19099311C22semidirect
20. #19099305C22semidirect
21. #19099301C22semidirect
22. #19099297C22semidirect
23. #19099284C22semidirect
24. #19099279C22semidirect
25. #19099278C22semidirect
26. #19099278C22semidirect
27. #19099273C22semidirect
28. #19099266C22semidirect
29. #19099263C22semidirect
30. #19099261C22semidirect
31. #19099260C22semidirect
32. #19099235C22semidirect
33. #19099232C22semidirect
34. #19099231C22semidirect
35. #19099223C22semidirect
36. #19099216C22semidirect
37. #19099214C22semidirect
38. #19099205C22semidirect
39. #19099204C22semidirect
40. #19099204C22semidirect
41. #19099202C22semidirect
42. #19099202C22semidirect
43. #19099201C22semidirect
44. D4×D316C22semidirect
45. D4×D316C22semidirect
46. D4×D316C22semidirect
47. #19099198C22semidirect
48. #19099198C22semidirect
49. #19099197C22semidirect
50. #19099197C22semidirect
51. #19099197C22semidirect
52. #19099183C22semidirect
53. #19099169C22semidirect
54. #19099168C22semidirect
55. #19099167C22semidirect
56. #19099153C22semidirect
57. #19099149C22semidirect
58. #19099145C22semidirect
59. #19099143C22semidirect
60. #19099143C22semidirect
61. #19099129C22semidirect
62. #19099129C22semidirect
63. #19099129C22semidirect
64. #19099129C22semidirect
65. #19099127C22semidirect
66. #19099124C22semidirect
67. #19099119C22semidirect
68. #19099118C22semidirect
69. #19099114C22semidirect
70. #19099114C22semidirect
71. #19099113C22semidirect
72. #19099113C22semidirect
73. #19099112C22semidirect
74. #19099111C22semidirect
75. #19099110C22semidirect
76. #19099110C22semidirect
77. #19099110C22semidirect
78. #19099109C22semidirect
79. #19099108C22semidirect
80. #19099108C22semidirect
81. C4⋊Q8×D79C22semidirect
82. #127×D79C22semidirect
83. #127×D79C22semidirect
84. #19099100C22semidirect
85. #19099099C22semidirect
86. #19099098C22semidirect
87. #124×D79C22semidirect
88. #19099076C22semidirect
89. #19099076C22semidirect
90. #19099075C22semidirect
91. #19099070C22semidirect
92. C2×#14579136C22semidirect
93. #121×D79C22semidirect
94. #121×D79C22semidirect
95. #121×D79C22semidirect
96. #19099044C22semidirect
97. #19099035C22semidirect
98. C4×#11929625C22semidirect
99. #19099031C22semidirect
100. C4×D4×D79C22semidirect
101. C4×D4×D79C22semidirect
102. C2×C42×D79C22semidirect
103. #562×C79C22semidirect
104. #554×C79C22semidirect
105. #550×C79C22semidirect
106. #547×C79C22semidirect
107. #540×C79C22semidirect
108. #537×C79C22semidirect
109. #533×C79C22semidirect
110. #532×C79C22semidirect
470. C4×D79H(5,𝔽2)semidirect
513. #3548D79semidirect
526. C79#62834semidirect
530. #562C2×D79semidirect
539. #554C2×D79semidirect
547. #550C2×D79semidirect
551. #547C2×D79semidirect
570. #540C2×D79semidirect
576. #537C2×D79semidirect
585. #533C2×D79semidirect
598. #532C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779222
#237778052
#237778002
#237777622
#237776382
#237774332
#237774312
#237773082
#237772722
#237772502
#237771772
#237771582
#237770642
#237766972
#532×D792
C79×#35482
#6283479