Finite Group Databasebeta

← #35197275

Subgroups — #35197275

Order 20224.

6624 conjugacy classes of subgroups.

The subgroup lattice has 976 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778096C218yesmaximal, complemented
2#23777814C211yesmaximal, characteristic, complemented
3#23777811C212yesmaximal, complemented
4#23777805C211yesmaximal, characteristic, complemented
5#23777675C214yesmaximal, complemented
6#23777668C218yesmaximal, complemented
7#23777417C214yesmaximal, complemented
8#23777415C214yesmaximal, complemented
9#23777409C214yesmaximal, complemented
10#23777363C214yesmaximal, complemented
11#23777361C214yesmaximal, complemented
12#23777356C214yesmaximal, complemented
13#23777296C214yesmaximal, complemented
14#23777289C218yesmaximal, complemented
15#23776696C212yesmaximal, complemented
16C79×#3444C211yesmaximal, characteristic, complemented
17#19099317C2218yescomplemented
18#19099313C2214yescomplemented
19#19099306C2218yescomplemented
20#19099305C2214yescomplemented
21#19099302C2218yescomplemented
22#19099299C2212yescomplemented
23#19099298C2214yescomplemented
24#19099297C2218yescomplemented
25#19099296C22116yescomplemented
26Q8×Dic158C2214yescomplemented
27#19099293C2212yescomplemented
28#19099287C2214yescomplemented
29#19099286C2214yescomplemented
30#19099285C22116yescomplemented
31#19099284C2218yescomplemented
32#19099283C2214yescomplemented
33#19099283C2218yescomplemented
34#19099281C22116yescomplemented
35#19099281C2218yescomplemented
36#19099280C22116yescomplemented
37#19099279C2212yescomplemented
38#19099278C2214yescomplemented
39#19099278C2218yescomplemented
40#19099277C2218yescomplemented
41#19099276C2218yescomplemented
42#19099242C22116yescomplemented
43#19099242C22116yescomplemented
44#19099241C2218yescomplemented
45#19099238C22116yescomplemented
46#19099237C22116yescomplemented
47Q8×D316C2214yescomplemented
48D4×Dic158C2214yescomplemented
49#19099228C2214yescomplemented
50#19099223C2218yescomplemented
51#19099222C2218yescomplemented
52#19099220C2218yescomplemented
53#19099210C2218yescomplemented
54#19099209C2218yescomplemented
55#19099201C2218yescomplemented
56D4×D316C2214yescomplemented
57#19099198C2212yescomplemented
58#19099186C2218yescomplemented
59#19099185C2218yescomplemented
60#19099184C2218yescomplemented
61#19099184C2218yescomplemented
62#19099183C22116yescomplemented
63#19099181C22116yescomplemented
64#19099180C2218yescomplemented
65#19099178C2218yescomplemented
66#19099178C22116yescomplemented
67#19099149C22116yescomplemented
68#19099146C22116yescomplemented
69#19099145C22116yescomplemented
70#19099136C2218yescomplemented
71#19099134C2214yescomplemented
72#19099129C2218yes—
73#19099127C2214yes—
74#19099120C2214yescomplemented
75#19099120C2212yescomplemented
76#19099120C2212yescomplemented
77#19099120C2212yescomplemented
78#19099119C2218yescomplemented
79#19099113C2212yes—
80#19099113C2212yes—
81#19099113C2212yes—
82#19099098C2218yescomplemented
83#19099097C2214yescomplemented
84#19099097C2214yescomplemented
85#19099097C2218yescomplemented
86#19099097C2214yescomplemented
87#19099097C2214yescomplemented
88#19099097C2214yescomplemented
89#19099097C2214yescomplemented
90#19099092C2218yescomplemented
91C2×#14579149C2214yescomplemented
92#124×D79C2218yescomplemented
93#19099074C2214yescomplemented
94#19099074C2214yescomplemented
95#19099074C2214yescomplemented
96#19099040C2214yescomplemented
97#19099039C2218yescomplemented
98#19099037C2214yescomplemented
99#19099035C2218yescomplemented
100C4×#11929624C2214yescomplemented
101C4×#11929624C2214yescomplemented
102C4×#11929624C2214yescomplemented
103#533×C79C2211yescharacteristic, complemented
104#533×C79C2212yescomplemented
105#532×C79C2211yescharacteristic
106#532×C79C2212yes—
107#529×C79C2214yescomplemented
108#529×C79C2214yescomplemented
109#529×C79C2214yescomplemented
110#525×C79C2214yescomplemented
111#525×C79C2212yescomplemented
112C4×#41×C79C2212yescomplemented
113C4×#41×C79C2214yescomplemented
114C22×C42×C79C2211yescharacteristic, complemented
115C2×#11929624C2314yes—
116C2×#11929624C2314yes—
117C2×#11929624C2314yes—
118C22×Dic158C2314yes—
119C2×Q8×D79C2318yes—
120C22×D316C2314yes—
121C2×D4×D79C2318yes—
122#14579161C2318yes—
123#14579161C2312yes—
124#14579161C2312yes—
125#14579161C2312yes—
126#14579160C23116yes—
127#14579160C2318yes—
128#14579160C2318yes—
129#14579159C2318yes—
130#14579158C2312yes—
131#14579157C2318yes—
132#14579156C23116yes—
133#14579156C23116yes—
134#14579156C23116yes—
135#14579155C23116yes—
136#14579155C2318yes—
137#14579155C2318yes—
138#14579154C23116yes—
139#14579154C23116yes—
140#14579154C23116yes—
141#14579153C2314yes—
142#14579153C2314yes—
143#14579153C2314yes—
144#14579150C2318yes—
145#14579150C2318yes—
146#14579149C23116yes—
147#14579149C2318yes—
148#14579149C2314yes—
149#14579149C2314yes—
150#14579149C2314yes—
151#14579148C23116yes—
152#14579148C2318yes—
153#14579148C2318yes—
154#14579147C23116yes—
155#14579147C23116yes—
156#14579147C23116yes—
157#14579147C23116yes—
158#14579147C23116yes—
159#14579147C23116yes—
160#14579146C23116yes—
161#14579146C23116yes—
162#14579144C2318yes—
163#14579144C2318yes—
164#14579144C23116yes—
165#14579144C2318yes—
166#14579143C23116yes—
167#14579143C23116yes—
168#14579142C2318yes—
169#14579142C2318yes—
170#14579141C2318yes—
171#14579141C23116yes—
172#14579140C2314yes—
173#14579140C2314yes—
174#14579140C23116yes—
175#14579140C2314yes—
176#14579140C2314yes—
177#14579140C2318yes—
178#14579140C2314yes—
179#14579140C2314yes—
180#14579139C23116yes—
181#14579139C23116yes—
182#14579139C23116yes—
183#14579138C23116yes—
184#14579137C2318yes—
185#14579136C2318yes—
186#14579135C2314yes—
187#14579135C2314yes—
188#14579135C2314yes—
189#14579135C2318yes—
190#14579135C2314yes—
191#14579135C2314yes—
192#14579135C2314yes—
193#14579134C23116yes—
194#14579133C23116yes—
195#14579132C23116yes—
196#14579132C2318yes—
197#14579131C23116yes—
198#14579130C2318yes—
199#14579129C2318yes—
200#14579129C23116yes—
201#14579129C2318yes—
202Q8×Dic79C2318yes—
203C4×Dic158C2314yes—
204C4×Dic158C23116yes—
205C4×Dic158C2314yes—
206C4×Dic158C2318yes—
207C4×Dic158C2314yes—
208C4×Dic158C2314yes—
209C4×Dic158C2314yes—
210C4×Dic158C2314yes—
211#14579126C2318yes—
212#14579126C23116yes—
213#14579126C23116yes—
214C4×D316C2314yes—
215C4×D316C2318yes—
216C4×D316C2314yes—
217C4×D316C2314yes—
218C4×D316C2314yes—
219C4×D316C2314yes—
220C4×D316C2314yes—
221D4×Dic79C2318yes—
222#14579123C23116yes—
223#14579123C2318yes—
224C4×C22⋊D79C2318yes—
225C4×C22⋊D79C23116yes—
226C4×C22⋊D79C2318yes—
227C4×C22⋊D79C2318yes—
228C4×C22⋊D79C2318yes—
229C4×C22⋊D79C2318yes—
230C4×C22⋊D79C2318yes—
231(C22⋊D79)⋊C4C23116yes—
232#14579120C2314yes—
233#14579120C2314yes—
234#14579120C2314yes—
235#14579120C2314yes—
236#14579120C2314yes—
237#14579119C2318yes—
238#14579119C23116yes—
239#14579119C2318yes—
240#14579118C2318yes—
241#14579118C23116yes—
242#14579118C2318yes—
243#14579118C2318yes—
244#14579117C23116yes—
245C2×(C2×D79)⋊C4C23116yes—
246C22⋊C4×D79C23116yes—
247C22⋊C4×D79C23116yes—
248C42×D79C2318yes—
249C2×#41×C79C2314yes—
250C2×#41×C79C2312yes—
251C23×C4×C79C2311yescharacteristic
252C23×C4×C79C2312yes—
253C4⋊Q8×C79C2312yes—
254C4⋊Q8×C79C2311yescharacteristic
255#127×C79C2311yescharacteristic
256#126×C79C2318yes—
257#125×C79C2312yes—
258#125×C79C2314yes—
259#124×C79C2312yes—
260#124×C79C2314yes—
261#123×C79C2318yes—
262#123×C79C2314yes—
263C22⋊Q8×C79C2314yes—
264C22⋊Q8×C79C2314yes—
265C22⋊Q8×C79C2314yes—
266#121×C79C2314yes—
267#121×C79C2314yes—
268#121×C79C2314yes—
269#120×C79C2314yes—
270C4×Q8×C79C2314yes—
271C4×Q8×C79C2314yes—
272C4×Q8×C79C2314yes—
273C4×D4×C79C2318yes—
274C4×D4×C79C2314yes—
275C4×D4×C79C2314yes—
276C4×D4×C79C2318yes—
277C4×D4×C79C2314yes—
278C4×D4×C79C2318yes—
279#117×C79C2312yes—
280#117×C79C2314yes—
281#117×C79C2318yes—
282#117×C79C2314yes—
283C2×C42×C79C2311yescharacteristic
284C2×C42×C79C2312yes—
285C2×C42×C79C2312yes—
286C2×C42×C79C2312yes—
287C2×C42×C79C2312yes—
288C2×C42×C79C2312yes—
289C2×C42×C79C2311yescharacteristic
290C2×C42×C79C2314yes—
291C23×D79C2418yes—
292#11929624—48no—
293#11929624—48no—
294#11929624—48no—
295C2×Dic158—48no—
296C2×Dic158C2414yes—
297C2×Dic158C2414yes—
298C2×Dic158C24116yes—
299C2×Dic158C2418yes—
300C2×Dic158C2414yes—
301Q8×D79—416no—
302C2×D316—48no—
303C2×D316C2414yes—
304C2×D316C2414yes—
305C2×D316C2414yes—
306C2×D316C2418yes—
307C2×C22⋊D79C2418yes—
308C2×C22⋊D79C2418yes—
309C2×C22⋊D79C2418yes—
310C2×C22⋊D79C24116yes—
311D4×D79—416no—
312C22×Dic79C2418yes—
313C2×C4×D79C2418yes—
314C2×C4×D79C24116yes—
315C2×C4×D79C2418yes—
316C2×C4×D79C2418yes—
317C4⋊Dic79C2414yes—
318C4⋊Dic79C2414yes—
319C4⋊Dic79C24116yes—
320C4⋊Dic79C2414yes—
321C4⋊Dic79C2414yes—
322C4⋊Dic79C2414yes—
323C4⋊Dic79C2414yes—
324Dic79⋊C4C2418yes—
325Dic79⋊C4C24116yes—
326Dic79⋊C4C2418yes—
327Dic79⋊C4C2418yes—
328Dic79⋊C4C2418yes—
329Dic79⋊C4C2418yes—
330Dic79⋊C4C2418yes—
331Dic79⋊C4C24116yes—
332C22⋊Dic79C2418yes—
333C22⋊Dic79C24116yes—
334C22⋊Dic79C2418yes—
335C22⋊Dic79C2418yes—
336C22⋊Dic79C2418yes—
337C22⋊Dic79C2418yes—
338(C2×D79)⋊C4C2418yes—
339(C2×D79)⋊C4C2418yes—
340(C2×D79)⋊C4C24116yes—
341(C2×D79)⋊C4C24116yes—
342(C2×D79)⋊C4C2418yes—
343(C2×D79)⋊C4C2418yes—
344(C2×D79)⋊C4C24116yes—
345(C2×D79)⋊C4C24116yes—
346(C2×D79)⋊C4C2418yes—
347(C2×D79)⋊C4C2418yes—
348C4×Dic79C2418yes—
349C4×Dic79C2418yes—
350C4×Dic79C2418yes—
351C4×Dic79C24116yes—
352C4×Dic79C2418yes—
353C4×Dic79C2418yes—
354C24×C79C2411yescharacteristic
355#41×C79—44no—
356#41×C79—48no—
357C2×Q8×C79C2414yes—
358C2×Q8×C79C2412yes—
359C2×D4×C79C2414yes—
360C2×D4×C79C2418yes—
361C2×D4×C79C2414yes—
362C2×D4×C79C2412yes—
363C22×C4×C79—44no—
364C22×C4×C79—42no—
365C22×C4×C79C2414yes—
366C22×C4×C79C2412yes—
367C22×C4×C79C2412yes—
368C22×C4×C79C2412yes—
369C22×C4×C79C2412yes—
370C22×C4×C79C2411yescharacteristic
371C22×C4×C79C2412yes—
372C22×C4×C79C2412yes—
373C22×C4×C79C2412yes—
374C22×C4×C79C2411yescharacteristic
375C22×C4×C79C2412yes—
376C22×C4×C79C2418yes—
377C4⋊C4×C79C2414yes—
378C4⋊C4×C79C2414yes—
379C4⋊C4×C79C2414yes—
380C4⋊C4×C79C2418yes—
381C4⋊C4×C79C2418yes—
382C4⋊C4×C79C2418yes—
383C22⋊C4×C79C2418yes—
384C22⋊C4×C79C2414yes—
385C22⋊C4×C79C2418yes—
386C22⋊C4×C79C2418yes—
387C22⋊C4×C79C2418yes—
388C42×C79C2411yescharacteristic
389C42×C79C2411yescharacteristic
390C42×C79C2412yes—
391C42×C79C2412yes—
392C42×C79C2412yes—
393C42×C79C2412yes—
394C42×C79C2412yes—
395C42×C79C2411yescharacteristic
396C42×C79C2412yes—
397C42×C79C2411yescharacteristic
398C42×C79C2418yes—
399C42×C79C2414yes—
400C23×C79—42no—
401C23×C79—41no—
402C23×C79C2514yes—
403C23×C79C2512yes—
404C23×C79C2511yescharacteristic
405C22×D79—416no—
406C22×D79—48no—
407C22×D79C2518yes—
408Q8×C79—28no—
409Q8×C79—42no—
410D4×C79—28no—
411D4×C79—42no—
412D4×C79—44no—
413D4×C79—48no—
414C2×C4×C79—28no—
415C2×C4×C79—24no—
416C2×C4×C79—24no—
417C2×C4×C79—24no—
418C2×C4×C79—24no—
419C2×C4×C79—22no—
420C2×C4×C79—42no—
421C2×C4×C79—42no—
422C2×C4×C79—42no—
423C2×C4×C79—42no—
424C2×C4×C79—41no—
425C2×C4×C79—48no—
426C2×C4×C79C2512yes—
427C2×C4×C79C2512yes—
428C2×C4×C79C2514yes—
429C2×C4×C79C2518yes—
430C2×C4×C79C2512yes—
431C2×C4×C79C2511yescharacteristic
432C2×C4×C79C2512yes—
433C2×C4×C79C2512yes—
434C2×C4×C79C2511yescharacteristic
435C22⋊D79—416no—
436C22⋊D79—48no—
437C22⋊D79—48no—
438C22⋊D79—48no—
439C2×Dic79—48no—
440C2×Dic79C2518yes—
441C2×Dic79C2518yes—
442C2×Dic79C2518yes—
443D316—28no—
444D316—28no—
445D316—48no—
446D316—44no—
447C4×D79—216no—
448C4×D79—416no—
449C4×D79—48no—
450C4×D79—48no—
451Dic158—28no—
452Dic158—28no—
453Dic158—416no—
454Dic158—48no—
455Dic158—44no—
456C22×C79—22no—
457C22×C79—22no—
458C22×C79—22no—
459C22×C79—28no—
460C22×C79—22no—
461C22×C79—21no—
462C22×C79—24no—
463C22×C79—44no—
464C22×C79C2611yescharacteristic
465C2×D79—28no—
466C2×D79—28no—
467C2×D79—28no—
468C2×D79—168no—
469C4×C79—22no—
470C4×C79—21no—
471C4×C79—22no—
472C4×C79—22no—
473C4×C79—22no—
474C4×C79—24no—
475C4×C79—28no—
476C4×C79#58512yes—
477C4×C79#58514yes—
478Dic79—28no—
479Dic79—28no—
480Dic79—28no—
481#62841—791nomaximal, Sylow
482C2×C79—44no—
483C2×C79—41no—
484C2×C79—42no—
485C2×C79C2×#58512yes—
486C2×C79C2×#58511yescharacteristic
487D79—48no—
488#3568—798no—
489#3550—792no—
490#3550—791no—
491#3549—791no—
492#3540—798no—
493#3540—794no—
494#3518—794no—
495#3518—794no—
496#3518—794no—
497#3514—794no—
498#3514—794no—
499#3514—794no—
500#3510—798no—
501#3510—794no—
502#3444—792no—
503#3444D7911yescharacteristic, complemented
504C79#6284111yescharacteristic, complemented, Sylow
505#563—798no—
506#563—794no—
507H(3,𝔽4)—794no—
508H(3,𝔽4)—798no—
509#560—798no—
510#559—792no—
511#559—798no—
512#559—794no—
513#559—7916no—
514Q82—792no—
515Q82—794no—
516#556—794no—
517#556—7916no—
518#556—798no—
519#556—7916no—
520#556—794no—
521#556—794no—
522#556—798no—
523#556—7916no—
524#556—798no—
525#555—792no—
526#555—798no—
527#555—798no—
528#555—794no—
529#555—798no—
530#551—7916no—
531#551—798no—
532#551—7916no—
533#551—7916no—
534#551—7916no—
535D4×Q8—794no—
536D4×Q8—794no—
537D4×Q8—794no—
538#548—798no—
539#548—798no—
540#548—798no—
541#546—798no—
542#546—798no—
543#546—798no—
544D42—792no—
545D42—794no—
546#542—7916no—
547#542—7916no—
548#542—798no—
549#542—798no—
550#542—798no—
551#542—798no—
552#542—7916no—
553#542—798no—
554#542—798no—
555#538—7916no—
556#538—7916no—
557#538—7916no—
558#536—794no—
559#536—798no—
560#535—794no—
561#535—798no—
562#533—798no—
563#533—792no—
564#533—792no—
565#533—792no—
566#533—794no—
567#533C2×D7912yescomplemented
568#533C2×D7911yescharacteristic, complemented
569#532—792no—
570#532—792no—
571#532—792no—
572#532C2×D7912yes—
573#532C2×D7911yescharacteristic
574#529—798no—
575#529—798no—
576#529—794no—
577#529—794no—
578#529—794no—
579#529—794no—
580#529—794no—
581#529—794no—
582#529—798no—
583#529C2×D7914yescomplemented
584#529C2×D7914yescomplemented
585#529C2×D7914yescomplemented
586C2×#124—798no—
587C2×#124—794no—
588#525—794no—
589#525—794no—
590#525—794no—
591#525C2×D7912yescomplemented
592#525C2×D7914yescomplemented
593#519—798no—
594#519—794no—
595#518—798no—
596#518—794no—
597C4×#41—794no—
598C4×#41—794no—
599C4×#41—794no—
600C4×#41C2×D7912yescomplemented
601C4×#41C2×D7914yescomplemented
602C22×C42C2×D7911yescharacteristic, complemented
603C2×#41—794no—
604C2×#41—794no—
605C2×#41—794no—
606C2×#41C22×D7912yes—
607C2×#41C22×D7914yes—
608C22×Q8—798no—
609C22×Q8—794no—
610C22×D4—798no—
611C22×D4—794no—
612C23×C4C22×D7912yes—
613C23×C4C22×D7911yescharacteristic
614C4⋊Q8—798no—
615C4⋊Q8—798no—
616C4⋊Q8—798no—
617C4⋊Q8—7916no—
618C4⋊Q8—792no—
619C4⋊Q8—792no—
620C4⋊Q8—792no—
621C4⋊Q8—798no—
622C4⋊Q8C22×D7912yes—
623C4⋊Q8C22×D7911yescharacteristic
624#127—798no—
625#127—792no—
626#127C22×D7911yescharacteristic
627#126—7916no—
628#126—7916no—
629#126—7916no—
630#126—7916no—
631#126—7916no—
632#126—7916no—
633#126—798no—
634#126—798no—
635#126—7916no—
636#126C22×D7918yes—
637#125—794no—
638#125—794no—
639#125—794no—
640#125C22×D7914yes—
641#125C22×D7912yes—
642#124—798no—
643#124—798no—
644#124—798no—
645#124—798no—
646#124—7916no—
647#124—7916no—
648#124—7916no—
649#124—7916no—
650#124—7916no—
651#124—7916no—
652#124—7916no—
653#124—794no—
654#124—794no—
655#124—7916no—
656#124—798no—
657#124—794no—
658#124C22×D7914yes—
659#124C22×D7912yes—
660#123—798no—
661#123—798no—
662#123—798no—
663#123—798no—
664#123—798no—
665#123—7916no—
666#123—7916no—
667#123—7916no—
668#123—7916no—
669#123—7916no—
670#123C22×D7918yes—
671#123C22×D7914yes—
672C22⋊Q8—798no—
673C22⋊Q8—794no—
674C22⋊Q8—794no—
675C22⋊Q8—794no—
676C22⋊Q8—794no—
677C22⋊Q8—794no—
678C22⋊Q8—794no—
679C22⋊Q8—798no—
680C22⋊Q8—7916no—
681C22⋊Q8—798no—
682C22⋊Q8—7916no—
683C22⋊Q8—7916no—
684C22⋊Q8—7916no—
685C22⋊Q8—7916no—
686C22⋊Q8—7916no—
687C22⋊Q8C22×D7914yes—
688C22⋊Q8C22×D7914yes—
689C22⋊Q8C22×D7914yes—
690#121—798no—
691#121—7916no—
692#121—7916no—
693#121—794no—
694#121—794no—
695#121—794no—
696#121—794no—
697#121—794no—
698#121—794no—
699#121—798no—
700#121—798no—
701#121—7916no—
702#121C22×D7914yes—
703#121C22×D7914yes—
704#121C22×D7914yes—
705#120—798no—
706#120—798no—
707#120—798no—
708#120—7916no—
709#120—7916no—
710#120C22×D7914yes—
711C4×Q8—798no—
712C4×Q8—798no—
713C4×Q8—7916no—
714C4×Q8—7916no—
715C4×Q8—794no—
716C4×Q8—794no—
717C4×Q8—794no—
718C4×Q8—794no—
719C4×Q8—794no—
720C4×Q8—794no—
721C4×Q8—798no—
722C4×Q8—7916no—
723C4×Q8C22×D7914yes—
724C4×Q8C22×D7914yes—
725C4×Q8C22×D7914yes—
726C4×D4—798no—
727C4×D4—798no—
728C4×D4—798no—
729C4×D4—798no—
730C4×D4—798no—
731C4×D4—798no—
732C4×D4—798no—
733C4×D4—7916no—
734C4×D4—7916no—
735C4×D4—798no—
736C4×D4—7916no—
737C4×D4—794no—
738C4×D4—794no—
739C4×D4—794no—
740C4×D4—794no—
741C4×D4—794no—
742C4×D4—794no—
743C4×D4—798no—
744C4×D4C22×D7914yes—
745C4×D4C22×D7918yes—
746C4×D4C22×D7918yes—
747C4×D4C22×D7918yes—
748C4×D4C22×D7914yes—
749C4×D4C22×D7914yes—
750#117—794no—
751#117—794no—
752#117—794no—
753#117—794no—
754#117—794no—
755#117—798no—
756#117—7916no—
757#117—798no—
758#117—7916no—
759#117—798no—
760#117—798no—
761#117—798no—
762#117—7916no—
763#117C22×D7914yes—
764#117C22×D7912yes—
765#117C22×D7914yes—
766#117C22×D7918yes—
767C2×C22⋊C4—7916no—
768C2×C22⋊C4—7916no—
769C2×C22⋊C4—7916no—
770C2×C42—798no—
771C2×C42C22×D7912yes—
772C2×C42C22×D7912yes—
773C2×C42C22×D7912yes—
774C2×C42C22×D7914yes—
775C2×C42C22×D7911yescharacteristic
776C2×C42C22×D7912yes—
777C2×C42C22×D7912yes—
778C2×C42C22×D7911yescharacteristic
779C24—798no—
780C24C23×D7911yescharacteristic
781#41—44no—
782#41—48no—
783#41—3168no—
784#41—3168no—
785#41—3168no—
786C2×Q8—3168no—
787C2×Q8—31616no—
788C2×Q8—7916no—
789C2×Q8—798no—
790C2×Q8—794no—
791C2×Q8—794no—
792C2×Q8—794no—
793C2×Q8C23×D7914yes—
794C2×Q8C23×D7912yes—
795C2×D4—3168no—
796C2×D4—31616no—
797C2×D4—798no—
798C2×D4—798no—
799C2×D4—798no—
800C2×D4—7916no—
801C2×D4—794no—
802C2×D4—798no—
803C2×D4—794no—
804C2×D4—794no—
805C2×D4C23×D7914yes—
806C2×D4C23×D7912yes—
807C2×D4C23×D7918yes—
808C2×D4C23×D7914yes—
809C22×C4—44no—
810C22×C4—42no—
811C22×C4—798no—
812C22×C4—798no—
813C22×C4—798no—
814C22×C4—7916no—
815C22×C4—798no—
816C22×C4C23×D7912yes—
817C22×C4C23×D7912yes—
818C22×C4C23×D7912yes—
819C22×C4C23×D7912yes—
820C22×C4C23×D7911yescharacteristic
821C22×C4C23×D7914yes—
822C22×C4C23×D7911yescharacteristic
823C22×C4C23×D7912yes—
824C22×C4C23×D7912yes—
825C22×C4C23×D7912yes—
826C22×C4C23×D7912yes—
827C22×C4C23×D7918yes—
828C4⋊C4—798no—
829C4⋊C4—798no—
830C4⋊C4—798no—
831C4⋊C4—798no—
832C4⋊C4—798no—
833C4⋊C4—798no—
834C4⋊C4—7916no—
835C4⋊C4—7916no—
836C4⋊C4—794no—
837C4⋊C4—794no—
838C4⋊C4—794no—
839C4⋊C4—794no—
840C4⋊C4—794no—
841C4⋊C4—794no—
842C4⋊C4—7916no—
843C4⋊C4C23×D7914yes—
844C4⋊C4C23×D7914yes—
845C4⋊C4C23×D7918yes—
846C4⋊C4C23×D7918yes—
847C4⋊C4C23×D7914yes—
848C4⋊C4C23×D7918yes—
849C22⋊C4—798no—
850C22⋊C4—7916no—
851C22⋊C4—798no—
852C22⋊C4—798no—
853C22⋊C4—798no—
854C22⋊C4—798no—
855C22⋊C4—798no—
856C22⋊C4—798no—
857C22⋊C4—798no—
858C22⋊C4—798no—
859C22⋊C4—7916no—
860C22⋊C4—7916no—
861C22⋊C4—7916no—
862C22⋊C4—7916no—
863C22⋊C4—798no—
864C22⋊C4—798no—
865C22⋊C4C23×D7918yes—
866C22⋊C4C23×D7918yes—
867C22⋊C4C23×D7918yes—
868C22⋊C4C23×D7918yes—
869C22⋊C4C23×D7914yes—
870C42—798no—
871C42—798no—
872C42—798no—
873C42—7916no—
874C42—798no—
875C42—798no—
876C42C23×D7912yes—
877C42C23×D7911yescharacteristic
878C42C23×D7912yes—
879C42C23×D7912yes—
880C42C23×D7912yes—
881C42C23×D7911yescharacteristic
882C42C23×D7912yes—
883C42C23×D7911yescharacteristic
884C42C23×D7912yes—
885C42C23×D7911yescharacteristic
886C42C23×D7918yes—
887C42C23×D7914yes—
888C23—42no—
889C23—41no—
890C23—3168no—
891C23—31616no—
892C23—798no—
893C23C24×D7914yes—
894C23C24×D7912yes—
895C23C24×D7911yescharacteristic
896Q8—28no—
897Q8—42no—
898Q8—3168no—
899Q8—31616no—
900Q8—3164no—
901Q8—1588no—
902Q8—1588no—
903D4—28no—
904D4—42no—
905D4—44no—
906D4—48no—
907D4—3168no—
908D4—3164no—
909D4—31616no—
910D4—3168no—
911D4—3168no—
912D4—3168no—
913D4—1588no—
914D4—1588no—
915C2×C4—24no—
916C2×C4—22no—
917C2×C4—24no—
918C2×C4—24no—
919C2×C4—24no—
920C2×C4—28no—
921C2×C4—42no—
922C2×C4—42no—
923C2×C4—41no—
924C2×C4—42no—
925C2×C4—42no—
926C2×C4—48no—
927C2×C4—31616no—
928C2×C4—3168no—
929C2×C4—3168no—
930C2×C4—3168no—
931C2×C4—798no—
932C2×C4—798no—
933C2×C4—798no—
934C2×C4—15816no—
935C2×C4C24×D7912yes—
936C2×C4C24×D7912yes—
937C2×C4C24×D7914yes—
938C2×C4C24×D7918yes—
939C2×C4C24×D7912yes—
940C2×C4C24×D7911yescharacteristic
941C2×C4C24×D7912yes—
942C2×C4C24×D7912yes—
943C2×C4C24×D7911yescharacteristic
944C22—22no—
945C22—21no—
946C22—22no—
947C22—22no—
948C22—22no—
949C22—24no—
950C22—28no—
951C22—44no—
952C22—1588no—
953C22—1588no—
954C22—1588no—
955C22—12648no—
956C22C25×D7911yescharacteristic
957C4—22no—
958C4—22no—
959C4—22no—
960C4—21no—
961C4—22no—
962C4—24no—
963C4—28no—
964C4—1588no—
965C4—1588no—
966C4—1588no—
967C4#1909939912yes—
968C4#1909939914yes—
969C2—42no—
970C2—41no—
971C2—44no—
972C2—3168no—
973C2C2×#1909939912yes—
974C2C2×#1909939911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62841
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23778096C2semidirect
2. #23777814C2semidirect
3. #23777811C2semidirect
4. #23777805C2semidirect
5. #23777675C2semidirect
6. #23777668C2semidirect
7. #23777417C2semidirect
8. #23777415C2semidirect
9. #23777409C2semidirect
10. #23777363C2semidirect
11. #23777361C2semidirect
12. #23777356C2semidirect
13. #23777296C2semidirect
14. #23777289C2semidirect
15. #23776696C2semidirect
16. C79×#3444C2semidirect
17. #19099317C22semidirect
18. #19099313C22semidirect
19. #19099306C22semidirect
20. #19099305C22semidirect
21. #19099302C22semidirect
22. #19099299C22semidirect
23. #19099298C22semidirect
24. #19099297C22semidirect
25. #19099296C22semidirect
26. Q8×Dic158C22semidirect
27. #19099293C22semidirect
28. #19099287C22semidirect
29. #19099286C22semidirect
30. #19099285C22semidirect
31. #19099284C22semidirect
32. #19099283C22semidirect
33. #19099283C22semidirect
34. #19099281C22semidirect
35. #19099281C22semidirect
36. #19099280C22semidirect
37. #19099279C22semidirect
38. #19099278C22semidirect
39. #19099278C22semidirect
40. #19099277C22semidirect
41. #19099276C22semidirect
42. #19099242C22semidirect
43. #19099242C22semidirect
44. #19099241C22semidirect
45. #19099238C22semidirect
46. #19099237C22semidirect
47. Q8×D316C22semidirect
48. D4×Dic158C22semidirect
49. #19099228C22semidirect
50. #19099223C22semidirect
51. #19099222C22semidirect
52. #19099220C22semidirect
53. #19099210C22semidirect
54. #19099209C22semidirect
55. #19099201C22semidirect
56. D4×D316C22semidirect
57. #19099198C22semidirect
58. #19099186C22semidirect
59. #19099185C22semidirect
60. #19099184C22semidirect
61. #19099184C22semidirect
62. #19099183C22semidirect
63. #19099181C22semidirect
64. #19099180C22semidirect
65. #19099178C22semidirect
66. #19099178C22semidirect
67. #19099149C22semidirect
68. #19099146C22semidirect
69. #19099145C22semidirect
70. #19099136C22semidirect
71. #19099134C22semidirect
74. #19099120C22semidirect
75. #19099120C22semidirect
76. #19099120C22semidirect
77. #19099120C22semidirect
78. #19099119C22semidirect
82. #19099098C22semidirect
83. #19099097C22semidirect
84. #19099097C22semidirect
85. #19099097C22semidirect
86. #19099097C22semidirect
87. #19099097C22semidirect
88. #19099097C22semidirect
89. #19099097C22semidirect
90. #19099092C22semidirect
91. C2×#14579149C22semidirect
92. #124×D79C22semidirect
93. #19099074C22semidirect
94. #19099074C22semidirect
95. #19099074C22semidirect
96. #19099040C22semidirect
97. #19099039C22semidirect
98. #19099037C22semidirect
99. #19099035C22semidirect
100. C4×#11929624C22semidirect
101. C4×#11929624C22semidirect
102. C4×#11929624C22semidirect
103. #533×C79C22semidirect
104. #533×C79C22semidirect
107. #529×C79C22semidirect
108. #529×C79C22semidirect
109. #529×C79C22semidirect
110. #525×C79C22semidirect
111. #525×C79C22semidirect
112. C4×#41×C79C22semidirect
113. C4×#41×C79C22semidirect
114. C22×C42×C79C22semidirect
503. #3444D79semidirect
504. C79#62841semidirect
567. #533C2×D79semidirect
568. #533C2×D79semidirect
583. #529C2×D79semidirect
584. #529C2×D79semidirect
585. #529C2×D79semidirect
591. #525C2×D79semidirect
592. #525C2×D79semidirect
600. C4×#41C2×D79semidirect
601. C4×#41C2×D79semidirect
602. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780962
#237778142
#237778112
#237778052
#237776752
#237776682
#237774172
#237774152
#237774092
#237773632
#237773612
#237773562
#237772962
#237772892
#237766962
C79×#34442
#6284179