Finite Group Databasebeta

← #35196101

Subgroups — #35196101

Order 20224.

7270 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777829C214yesmaximal, complemented
2#23777805C211yesmaximal, characteristic, complemented
3#23777800C212yesmaximal, complemented
4#23777785C214yesmaximal, complemented
5#23777775C214yesmaximal, complemented
6#23777758C214yesmaximal, complemented
7#23777745C212yesmaximal, complemented
8#23777734C212yesmaximal, complemented
9#23777712C218yesmaximal, complemented
10#23777541C214yesmaximal, complemented
11#23777027C212yesmaximal, complemented
12#23777009C212yesmaximal, complemented
13#23776961C214yesmaximal, complemented
14D4×#11929625C214yesmaximal, complemented
15#23776820C218yesmaximal, complemented
16#23776732C214yesmaximal, complemented
17#23776697C212yesmaximal, complemented
18#532×D79C211yesmaximal, characteristic, complemented
19C79×#3550C211yesmaximal, characteristic, complemented
20C22×#11929625C2214yescomplemented
21C2×#41×D79C2212yescomplemented
22#19099312C2218yescomplemented
23#19099311C2218yescomplemented
24#19099309C22116yescomplemented
25#19099305C2214yescomplemented
26#19099304C22116yescomplemented
27#19099303C2218yescomplemented
28#19099279C2212yescomplemented
29#19099279C2218yescomplemented
30#19099279C2218yescomplemented
31#19099278C2214yescomplemented
32#19099273C2214yescomplemented
33#19099273C2214yescomplemented
34#19099263C2218yescomplemented
35#19099257C2218yescomplemented
36#19099254C2218yescomplemented
37#19099247C2218yescomplemented
38#19099241C2218yescomplemented
39#19099238C22116yescomplemented
40#19099235C2214yescomplemented
41#19099235C2218yescomplemented
42#19099235C2214yescomplemented
43#19099224C2218yescomplemented
44#19099216C2214yescomplemented
45#19099216C2214yescomplemented
46#19099216C2218yescomplemented
47#19099206C2218yescomplemented
48#19099206C2218yescomplemented
49#19099204C2218yescomplemented
50#19099204C22116yescomplemented
51D4×D316C2214yescomplemented
52D4×D316C2218yescomplemented
53#19099198C2212yescomplemented
54#19099190C2218yescomplemented
55#19099185C2218yescomplemented
56#19099183C22116yescomplemented
57#19099168C2218yescomplemented
58#19099165C22116yescomplemented
59#19099164C2218yescomplemented
60#19099152C22116yescomplemented
61#19099147C22116yescomplemented
62#19099143C2218yescomplemented
63#19099143C2218yescomplemented
64#19099143C2218yescomplemented
65#19099138C2218yescomplemented
66#19099137C2214yescomplemented
67#19099132C2214yescomplemented
68#19099131C2218yescomplemented
69#19099131C2218yescomplemented
70#19099129C2218yescomplemented
71#19099127C2214yescomplemented
72#19099124C2218yescomplemented
73#19099124C2218yescomplemented
74#19099118C2212yescomplemented
75#19099118C2212yescomplemented
76#19099114C2212yes—
77#19099114C2211yescharacteristic, complemented
78#19099114C2218yescomplemented
79#19099114C2218yescomplemented
80#19099114C2212yescomplemented
81#19099113C2211yescharacteristic, complemented
82#19099113C2212yescomplemented
83#19099112C2212yescomplemented
84#19099112C2218yescomplemented
85#19099111C2211yescharacteristic
86#19099110C2214yescomplemented
87#19099109C2212yescomplemented
88#19099108C2214yescomplemented
89C4⋊Q8×D79C2211yescharacteristic, complemented
90#127×D79C2211yescharacteristic
91#19099100C2214yescomplemented
92#19099100C2214yescomplemented
93#19099099C2214yescomplemented
94#19099099C2214yescomplemented
95#19099098C2214yescomplemented
96#19099098C2214yescomplemented
97#19099096C22116yescomplemented
98#19099092C2218yescomplemented
99#124×D79C2212yescomplemented
100#19099076C22116yescomplemented
101#19099076C2218yescomplemented
102#19099076C2214yescomplemented
103#19099076C2214yescomplemented
104#19099075C2214yescomplemented
105#19099071C2218yescomplemented
106#19099071C2218yescomplemented
107#121×D79C2214yescomplemented
108C4×#11929625C2218yescomplemented
109C4×#11929625C2214yescomplemented
110C4×#11929625C2214yescomplemented
111#19099031C2214yescomplemented
112C4×D4×D79C2218yescomplemented
113C4×D4×D79C2214yescomplemented
114#117×D79C2214yescomplemented
115C2×C42×D79C2211yescharacteristic, complemented
116#563×C79C2214yescomplemented
117#559×C79C2212yescomplemented
118Q82×C79C2212yescomplemented
119#556×C79C2214yescomplemented
120D4×Q8×C79C2214yescomplemented
121#542×C79C2218yescomplemented
122#536×C79C2214yescomplemented
123#533×C79C2212yescomplemented
124#532×C79C2211yescharacteristic
125C2×#11929625—416no—
126C2×#11929625C2314yes—
127C2×#11929625C2318yes—
128C2×#11929625C2318yes—
129C2×#11929625C2318yes—
130C2×#11929625C2314yes—
131C2×#11929625C2318yes—
132C2×#11929625C2312yes—
133C2×#11929624C2314yes—
134C2×#11929624C2312yes—
135C2×#11929624C2314yes—
136C2×#11929623C2312yes—
137C2×#11929623C2314yes—
138#41×D79—48no—
139C2×Q8×D79C2312yes—
140C22×D316C2318yes—
141C22×D316C2314yes—
142C2×D4×D79C2318yes—
143C2×D4×D79C2314yes—
144C2×D4×D79C2314yes—
145C2×D4×D79C2312yes—
146C22×C4×D79C2311yescharacteristic
147C22×C4×D79C2314yes—
148C22×C4×D79C2312yes—
149C22×C4×D79C2318yes—
150#14579161C2311yescharacteristic
151#14579161C2312yes—
152#14579160C2314yes—
153#14579159C2318yes—
154#14579159C2312yes—
155#14579158C2318yes—
156#14579158C2312yes—
157#14579158C2311yescharacteristic
158#14579158C2318yes—
159#14579157C2314yes—
160#14579157C2318yes—
161#14579157C2312yes—
162#14579156C2318yes—
163#14579156C2318yes—
164#14579155C23116yes—
165#14579154C23116yes—
166#14579153C2318yes—
167#14579152C2314yes—
168#14579152C2314yes—
169#14579151C23116yes—
170#14579150C2318yes—
171#14579150C2318yes—
172#14579150C23116yes—
173#14579150C2314yes—
174#14579150C2314yes—
175#14579150C2312yes—
176#14579149C2318yes—
177#14579149C2314yes—
178#14579149C2312yes—
179#14579148C2312yes—
180#14579147C2318yes—
181#14579147C23116yes—
182#14579146C2318yes—
183#14579146C23116yes—
184#14579146C23116yes—
185#14579146C23116yes—
186#14579146C23116yes—
187#14579146C2318yes—
188#14579145C2318yes—
189#14579144C2318yes—
190#14579144C2318yes—
191#14579143C23116yes—
192#14579143C23116yes—
193#14579141C2314yes—
194#14579141C2314yes—
195#14579139C23116yes—
196#14579139C23116yes—
197#14579139C23116yes—
198#14579137C2314yes—
199#14579137C2318yes—
200#14579137C2318yes—
201#14579137C23116yes—
202#14579137C2314yes—
203#14579136C2314yes—
204#14579136C23116yes—
205#14579136C2318yes—
206#14579136C2318yes—
207#14579136C23116yes—
208#14579136C23116yes—
209#14579136C23116yes—
210#14579136C2318yes—
211#14579136C2314yes—
212#14579136C2314yes—
213#14579136C2314yes—
214#14579136C2314yes—
215#14579135C2314yes—
216#14579135C2314yes—
217#14579135C2318yes—
218#14579135C23116yes—
219#14579135C2314yes—
220#14579134C23116yes—
221#14579134C23116yes—
222#14579134C23116yes—
223#14579134C23116yes—
224#14579134C23116yes—
225#14579134C2318yes—
226#14579133C2318yes—
227#14579132C2318yes—
228#14579132C2314yes—
229#14579131C23116yes—
230#14579131C2318yes—
231#14579131C23116yes—
232#14579131C23116yes—
233#14579131C2318yes—
234#14579131C2318yes—
235#14579129C2318yes—
236#14579129C2318yes—
237Q8×Dic79C2314yes—
238Q8×Dic79C2314yes—
239#14579126C2314yes—
240#14579126C2314yes—
241C4×D316C23116yes—
242C4×D316C2318yes—
243C4×D316C2318yes—
244C4×D316C2314yes—
245C4×D316C2318yes—
246C4×D316C2314yes—
247C4×D316C2318yes—
248C4×D316C2314yes—
249D4×Dic79C2314yes—
250#14579123C2314yes—
251#14579123C2318yes—
252#14579123C2314yes—
253#14579123C2314yes—
254#14579123C2314yes—
255#14579123C2314yes—
256#14579123C2318yes—
257#14579123C23116yes—
258C4×C22⋊D79C23116yes—
259C4×C22⋊D79C2318yes—
260(C22⋊D79)⋊C4C2318yes—
261(C22⋊D79)⋊C4C23116yes—
262(C22⋊D79)⋊C4C2318yes—
263(C22⋊D79)⋊C4C2318yes—
264#14579120C2314yes—
265#14579119C23116yes—
266#14579119C2318yes—
267#14579119C2318yes—
268#14579119C2314yes—
269#14579119C2314yes—
270#14579119C2318yes—
271#14579118C2318yes—
272#14579118C2318yes—
273#14579117C2318yes—
274C4⋊C4×D79C2318yes—
275C4⋊C4×D79C2318yes—
276C4⋊C4×D79C2314yes—
277C22⋊C4×D79C23116yes—
278C22⋊C4×D79C2318yes—
279C22⋊C4×D79C2318yes—
280C2×C4×Dic79C2312yes—
281C2×C4×Dic79C2311yescharacteristic
282C42×D79C2312yes—
283C42×D79C2311yescharacteristic
284C42×D79C2311yescharacteristic
285C42×D79C2311yescharacteristic
286C42×D79C2311yescharacteristic
287C42×D79C2312yes—
288C42×D79C2318yes—
289C42×D79C2318yes—
290C2×#41×C79C2312yes—
291C22×Q8×C79C2314yes—
292C4⋊Q8×C79C2318yes—
293C4⋊Q8×C79C2318yes—
294C4⋊Q8×C79C2312yes—
295C4⋊Q8×C79C2312yes—
296C4⋊Q8×C79C2311yescharacteristic
297#127×C79C2311yescharacteristic
298#126×C79C23116yes—
299#125×C79C2314yes—
300#124×C79C2318yes—
301#124×C79C2318yes—
302#124×C79C2312yes—
303#123×C79C2318yes—
304#123×C79C2318yes—
305C22⋊Q8×C79C2314yes—
306C22⋊Q8×C79C2314yes—
307C22⋊Q8×C79C2318yes—
308C22⋊Q8×C79C23116yes—
309#121×C79C2314yes—
310C4×Q8×C79C2318yes—
311C4×Q8×C79C2314yes—
312C4×Q8×C79C2314yes—
313C4×D4×C79C2318yes—
314C4×D4×C79C2314yes—
315#117×C79C2314yes—
316#117×C79C2314yes—
317C2×C42×C79C2311yescharacteristic
318C23×D79C2414yes—
319C23×D79C2411yescharacteristic
320C23×D79C2418yes—
321#11929625—216no—
322#11929625—416no—
323#11929625—48no—
324#11929625—416no—
325#11929625—44no—
326#11929625—416no—
327#11929625—416no—
328#11929624—48no—
329#11929624—44no—
330#11929624—48no—
331#11929623—44no—
332#11929623—48no—
333C2×Dic158C2412yes—
334C2×Dic158C2414yes—
335C2×Dic158C2414yes—
336Q8×D79—44no—
337C2×D316—48no—
338C2×D316—416no—
339C2×D316C2418yes—
340C2×D316C2414yes—
341C2×D316C2414yes—
342C2×D316C2414yes—
343C2×D316C2414yes—
344C2×D316C2412yes—
345C2×D316C2414yes—
346C2×D316C2418yes—
347C2×D316C24116yes—
348C2×D316C24116yes—
349C2×D316C2418yes—
350C2×C22⋊D79C2414yes—
351C2×C22⋊D79C2414yes—
352C2×C22⋊D79C2414yes—
353C2×C22⋊D79C2418yes—
354C2×C22⋊D79C24116yes—
355C2×C22⋊D79C2418yes—
356D4×D79—48no—
357D4×D79—416no—
358D4×D79—48no—
359D4×D79—44no—
360C22×Dic79C2411yescharacteristic
361C22×Dic79C2414yes—
362C22×Dic79C2412yes—
363C2×C4×D79—24no—
364C2×C4×D79—216no—
365C2×C4×D79—44no—
366C2×C4×D79—416no—
367C2×C4×D79C2411yescharacteristic
368C2×C4×D79C2414yes—
369C2×C4×D79C2411yescharacteristic
370C2×C4×D79C2414yes—
371C2×C4×D79C2411yescharacteristic
372C2×C4×D79C2414yes—
373C2×C4×D79C2418yes—
374C2×C4×D79C2418yes—
375C2×C4×D79C2412yes—
376C2×C4×D79C2412yes—
377C2×C4×D79C24116yes—
378C2×C4×D79C2418yes—
379C2×C4×D79C24116yes—
380C2×C4×D79C2412yes—
381C2×C4×D79C2412yes—
382C2×C4×D79C2411yescharacteristic
383C4⋊Dic79C2414yes—
384C4⋊Dic79C2414yes—
385C4⋊Dic79C2414yes—
386C4⋊Dic79C2418yes—
387C4⋊Dic79C2418yes—
388Dic79⋊C4C24116yes—
389Dic79⋊C4C2418yes—
390Dic79⋊C4C24116yes—
391Dic79⋊C4C2418yes—
392Dic79⋊C4C2418yes—
393C22⋊Dic79C2418yes—
394C22⋊Dic79C2418yes—
395(C2×D79)⋊C4C2418yes—
396(C2×D79)⋊C4C2418yes—
397(C2×D79)⋊C4C2418yes—
398(C2×D79)⋊C4C24116yes—
399(C2×D79)⋊C4C2418yes—
400(C2×D79)⋊C4C2418yes—
401(C2×D79)⋊C4C2418yes—
402(C2×D79)⋊C4C2418yes—
403(C2×D79)⋊C4C24116yes—
404(C2×D79)⋊C4C2418yes—
405(C2×D79)⋊C4C2418yes—
406(C2×D79)⋊C4C2418yes—
407(C2×D79)⋊C4C24116yes—
408C4×Dic79C2412yes—
409C4×Dic79C2418yes—
410C4×Dic79C2412yes—
411C4×Dic79C2411yescharacteristic
412C4×Dic79C2412yes—
413C4×Dic79C2412yes—
414C4×Dic79C2412yes—
415C4×Dic79C2411yescharacteristic
416C4×Dic79C2418yes—
417C4×Dic79C2418yes—
418#41×C79—44no—
419C2×Q8×C79—48no—
420C2×Q8×C79C2414yes—
421C2×Q8×C79C2414yes—
422C2×Q8×C79C2412yes—
423C2×Q8×C79C2418yes—
424C2×D4×C79C2414yes—
425C2×D4×C79C2414yes—
426C2×D4×C79C2412yes—
427C22×C4×C79C2412yes—
428C22×C4×C79C2411yescharacteristic
429C22×C4×C79C2414yes—
430C22×C4×C79C2418yes—
431C4⋊C4×C79C2414yes—
432C4⋊C4×C79C2414yes—
433C4⋊C4×C79C2414yes—
434C4⋊C4×C79C2414yes—
435C4⋊C4×C79C2414yes—
436C4⋊C4×C79C2418yes—
437C4⋊C4×C79C24116yes—
438C4⋊C4×C79C2418yes—
439C22⋊C4×C79C2418yes—
440C22⋊C4×C79C2418yes—
441C22⋊C4×C79C2418yes—
442C22⋊C4×C79C24116yes—
443C42×C79C2412yes—
444C42×C79C2411yescharacteristic
445C42×C79C2411yescharacteristic
446C42×C79C2418yes—
447C42×C79C2418yes—
448C23×C79C2514yes—
449C23×C79C2511yescharacteristic
450C22×D79—22no—
451C22×D79—28no—
452C22×D79—42no—
453C22×D79—48no—
454C22×D79—48no—
455C22×D79—416no—
456C22×D79C2518yes—
457C22×D79C2511yescharacteristic
458C22×D79C2514yes—
459C22×D79C2511yescharacteristic
460Q8×C79—28no—
461Q8×C79—28no—
462Q8×C79—42no—
463Q8×C79—48no—
464D4×C79—28no—
465D4×C79—42no—
466D4×C79—44no—
467C2×C4×C79—28no—
468C2×C4×C79—22no—
469C2×C4×C79—24no—
470C2×C4×C79—48no—
471C2×C4×C79C2512yes—
472C2×C4×C79C2511yescharacteristic
473C2×C4×C79C2514yes—
474C2×C4×C79C2518yes—
475C2×C4×C79C2518yes—
476C2×C4×C79C2511yescharacteristic
477C2×C4×C79C2512yes—
478C22⋊D79—48no—
479C22⋊D79—416no—
480C22⋊D79—44no—
481C22⋊D79—44no—
482C22⋊D79—44no—
483C22⋊D79—48no—
484C2×Dic79—28no—
485C2×Dic79—22no—
486C2×Dic79—42no—
487C2×Dic79C2512yes—
488C2×Dic79C2518yes—
489C2×Dic79C2512yes—
490C2×Dic79C2511yescharacteristic
491C2×Dic79C2514yes—
492C2×Dic79C2511yescharacteristic
493D316—216no—
494D316—28no—
495D316—28no—
496D316—28no—
497D316—42no—
498D316—44no—
499D316—48no—
500D316—416no—
501D316—44no—
502D316—48no—
503D316—416no—
504C4×D79—22no—
505C4×D79—28no—
506C4×D79—22no—
507C4×D79—28no—
508C4×D79—24no—
509C4×D79—24no—
510C4×D79—216no—
511C4×D79—22no—
512C4×D79—28no—
513C4×D79—216no—
514C4×D79—42no—
515C4×D79—42no—
516C4×D79—416no—
517C4×D79—416no—
518C4×D79—48no—
519C4×D79H(5,𝔽2)14yes—
520Dic158—44no—
521Dic158—42no—
522Dic158—44no—
523C22×C79—21no—
524C22×C79—24no—
525C22×C79—22no—
526C22×C79—28no—
527C22×C79C2611yescharacteristic
528C2×D79—22no—
529C2×D79—21no—
530C2×D79—24no—
531C2×D79—28no—
532C2×D79—28no—
533C2×D79—28no—
534C2×D79—28no—
535C2×D79—22no—
536C2×D79—44no—
537C2×D79—88no—
538C2×D79—816no—
539C2×D79C2×H(5,𝔽2)12yes—
540C4×C79—21no—
541C4×C79—24no—
542C4×C79—28no—
543C4×C79—22no—
544C4×C79—28no—
545C4×C79C2×H(5,𝔽2)12yes—
546C4×C79#58514yes—
547Dic79—21no—
548Dic79—24no—
549Dic79—22no—
550Dic79—28no—
551Dic79—22no—
552Dic79C2×H(5,𝔽2)12yes—
553#62759—791nomaximal, Sylow
554C2×C79—41no—
555C2×C79—44no—
556C2×C79C22×H(5,𝔽2)11yescharacteristic
557C2×C79C2×#58512yes—
558D79—22no—
559D79—41no—
560D79—44no—
561D79—48no—
562#3551—794no—
563#3550D7911yescharacteristic, complemented
564#3549—791no—
565#3548—792no—
566#3547—794no—
567#3546—794no—
568#3545—794no—
569#3544—792no—
570#3543—792no—
571#3542—798no—
572#3529—794no—
573#3483—792no—
574#3481—792no—
575#3475—794no—
576D4×#41—794no—
577#3460—798no—
578#3449—794no—
579#3444—792no—
580C2×#532—791no—
581C79#6275911yescharacteristic, complemented, Sylow
582C22×#41—792no—
583C22×#41—794no—
584#563—798no—
585#563C2×D7914yescomplemented
586#562—798no—
587#562—7916no—
588H(3,𝔽4)—794no—
589#560—7916no—
590#560—798no—
591#559C2×D7912yescomplemented
592Q82C2×D7912yescomplemented
593#556C2×D7914yescomplemented
594#555—798no—
595#555—792no—
596#555—798no—
597#555—794no—
598#554—794no—
599#554—794no—
600#553—798no—
601#553—798no—
602#552—798no—
603#552—798no—
604#551—7916no—
605#551—798no—
606#550—794no—
607#550—798no—
608#550—794no—
609D4×Q8C2×D7914yescomplemented
610#548—798no—
611#547—798no—
612#547—794no—
613#547—794no—
614#546—798no—
615#546—798no—
616#546—7916no—
617#546—798no—
618D42—792no—
619D42—798no—
620D42—794no—
621#544—798no—
622#542—7916no—
623#542—798no—
624#542C2×D7918yescomplemented
625#540—7916no—
626#540—798no—
627#540—798no—
628#538—7916no—
629#538—7916no—
630#537—798no—
631#537—798no—
632#537—798no—
633#536—794no—
634#536—798no—
635#536C2×D7914yescomplemented
636#535—794no—
637#535—798no—
638#535—798no—
639#535—798no—
640#535—794no—
641#534—798no—
642#534—798no—
643#533—792no—
644#533—792no—
645#533C2×D7912yescomplemented
646#532—792no—
647#532—791no—
648#532—792no—
649#532—792no—
650#532—798no—
651#532—798no—
652#532—791no—
653#532—792no—
654#532—798no—
655#532—794no—
656#532—794no—
657#532—791no—
658#532—792no—
659#532C2×D7911yescharacteristic
660C2×C4⋊Q8—791no—
661C2×#127—791no—
662#529—7916no—
663#529—794no—
664#529—794no—
665#529—798no—
666#529—794no—
667#529—794no—
668#529—794no—
669#529—794no—
670C2×#124—792no—
671#525—798no—
672#525—798no—
673#525—794no—
674#525—794no—
675#525—798no—
676#525—7916no—
677#525—794no—
678C2×#121—794no—
679C4×#41—794no—
680C4×#41—794no—
681C4×#41—798no—
682C4×#41—794no—
683C2×C4×D4—794no—
684C2×C4×D4—798no—
685C2×#117—794no—
686C22×C42—791no—
687C2×#41—31616no—
688C2×#41—3168no—
689C2×#41—794no—
690C2×#41—798no—
691C2×#41—798no—
692C2×#41—792no—
693C2×#41—798no—
694C2×#41—798no—
695C2×#41—794no—
696C2×#41—792no—
697C2×#41—794no—
698C2×#41—794no—
699C2×#41—794no—
700C2×#41—792no—
701C2×#41C22×D7912yes—
702C22×Q8—792no—
703C22×Q8C22×D7914yes—
704C22×D4—794no—
705C22×D4—798no—
706C22×D4—794no—
707C22×D4—792no—
708C22×D4—798no—
709C22×D4—794no—
710C23×C4—798no—
711C23×C4—792no—
712C23×C4—794no—
713C23×C4—791no—
714C4⋊Q8—792no—
715C4⋊Q8—798no—
716C4⋊Q8—794no—
717C4⋊Q8—791no—
718C4⋊Q8—792no—
719C4⋊Q8C22×D7911yescharacteristic
720C4⋊Q8C22×D7912yes—
721C4⋊Q8C22×D7912yes—
722C4⋊Q8C22×D7918yes—
723C4⋊Q8C22×D7918yes—
724#127—794no—
725#127—792no—
726#127—798no—
727#127—791no—
728#127—792no—
729#127—798no—
730#127—798no—
731#127C22×D7911yescharacteristic
732#126—798no—
733#126—798no—
734#126—7916no—
735#126—7916no—
736#126C22×D79116yes—
737#125—794no—
738#125—794no—
739#125—7916no—
740#125—798no—
741#125C22×D7914yes—
742#124—792no—
743#124—794no—
744#124—794no—
745#124—798no—
746#124—798no—
747#124—7916no—
748#124—792no—
749#124—798no—
750#124—7916no—
751#124—792no—
752#124—794no—
753#124—798no—
754#124C22×D7912yes—
755#124C22×D7918yes—
756#124C22×D7918yes—
757#123—798no—
758#123—798no—
759#123—798no—
760#123—798no—
761#123—7916no—
762#123—7916no—
763#123—7916no—
764#123—7916no—
765#123—798no—
766#123—7916no—
767#123—7916no—
768#123C22×D7918yes—
769#123C22×D7918yes—
770C22⋊Q8—794no—
771C22⋊Q8—794no—
772C22⋊Q8—798no—
773C22⋊Q8—7916no—
774C22⋊Q8—798no—
775C22⋊Q8—794no—
776C22⋊Q8—794no—
777C22⋊Q8—7916no—
778C22⋊Q8—7916no—
779C22⋊Q8—7916no—
780C22⋊Q8C22×D7914yes—
781C22⋊Q8C22×D7914yes—
782C22⋊Q8C22×D7918yes—
783C22⋊Q8C22×D79116yes—
784#121—798no—
785#121—794no—
786#121—798no—
787#121—794no—
788#121—794no—
789#121—794no—
790#121—798no—
791#121—7916no—
792#121—794no—
793#121—794no—
794#121—794no—
795#121—794no—
796#121—794no—
797#121—798no—
798#121—7916no—
799#121—7916no—
800#121—7916no—
801#121—798no—
802#121—798no—
803#121—7916no—
804#121—798no—
805#121—7916no—
806#121—7916no—
807#121—7916no—
808#121—7916no—
809#121—7916no—
810#121C22×D7914yes—
811#120—798no—
812#120—798no—
813#120—798no—
814#120—798no—
815#120—7916no—
816#120—798no—
817#120—7916no—
818#120—7916no—
819C4×Q8—794no—
820C4×Q8—794no—
821C4×Q8—794no—
822C4×Q8—794no—
823C4×Q8C22×D7914yes—
824C4×Q8C22×D7914yes—
825C4×Q8C22×D7918yes—
826C4×D4—794no—
827C4×D4—798no—
828C4×D4—7916no—
829C4×D4—794no—
830C4×D4—794no—
831C4×D4—794no—
832C4×D4—798no—
833C4×D4—7916no—
834C4×D4—798no—
835C4×D4—794no—
836C4×D4—794no—
837C4×D4—7916no—
838C4×D4—798no—
839C4×D4—798no—
840C4×D4—798no—
841C4×D4—794no—
842C4×D4—798no—
843C4×D4—798no—
844C4×D4—798no—
845C4×D4—794no—
846C4×D4—794no—
847C4×D4—7916no—
848C4×D4—798no—
849C4×D4C22×D7914yes—
850C4×D4C22×D7918yes—
851#117—794no—
852#117—794no—
853#117—798no—
854#117—794no—
855#117—798no—
856#117—798no—
857#117—7916no—
858#117—798no—
859#117—798no—
860#117—798no—
861#117C22×D7914yes—
862#117C22×D7914yes—
863C2×C4⋊C4—798no—
864C2×C4⋊C4—794no—
865C2×C4⋊C4—798no—
866C2×C22⋊C4—798no—
867C2×C22⋊C4—798no—
868C2×C22⋊C4—7916no—
869C2×C42—792no—
870C2×C42—791no—
871C2×C42—798no—
872C2×C42—792no—
873C2×C42—798no—
874C2×C42—791no—
875C2×C42—791no—
876C2×C42—791no—
877C2×C42—791no—
878C2×C42—792no—
879C2×C42C22×D7911yescharacteristic
880C24—798no—
881C24—794no—
882C24—791no—
883#41—44no—
884#41—3168no—
885#41—3164no—
886#41—3168no—
887#41—31616no—
888#41—3168no—
889#41—31616no—
890#41—31616no—
891#41—3164no—
892#41—3168no—
893#41—31616no—
894#41—3164no—
895#41—15816no—
896C2×Q8—48no—
897C2×Q8—3164no—
898C2×Q8—794no—
899C2×Q8—792no—
900C2×Q8—794no—
901C2×Q8C23×D7914yes—
902C2×Q8C23×D7914yes—
903C2×Q8C23×D7918yes—
904C2×Q8C23×D7912yes—
905C2×D4—3168no—
906C2×D4—31616no—
907C2×D4—3168no—
908C2×D4—31616no—
909C2×D4—3164no—
910C2×D4—3168no—
911C2×D4—7916no—
912C2×D4—798no—
913C2×D4—798no—
914C2×D4—794no—
915C2×D4—794no—
916C2×D4—794no—
917C2×D4—794no—
918C2×D4—798no—
919C2×D4—7916no—
920C2×D4—798no—
921C2×D4—7916no—
922C2×D4—792no—
923C2×D4—794no—
924C2×D4—794no—
925C2×D4—794no—
926C2×D4—798no—
927C2×D4—794no—
928C2×D4C23×D7914yes—
929C2×D4C23×D7912yes—
930C2×D4C23×D7914yes—
931C22×C4—3164no—
932C22×C4—31616no—
933C22×C4—792no—
934C22×C4—792no—
935C22×C4—792no—
936C22×C4—798no—
937C22×C4—7916no—
938C22×C4—7916no—
939C22×C4—791no—
940C22×C4—791no—
941C22×C4—794no—
942C22×C4—792no—
943C22×C4—792no—
944C22×C4—791no—
945C22×C4—794no—
946C22×C4—791no—
947C22×C4—791no—
948C22×C4—798no—
949C22×C4—798no—
950C22×C4—794no—
951C22×C4—794no—
952C22×C4—15816no—
953C22×C4—1584no—
954C22×C4C23×D7912yes—
955C22×C4C23×D7911yescharacteristic
956C22×C4C23×D7914yes—
957C22×C4C23×D7918yes—
958C4⋊C4—7916no—
959C4⋊C4—798no—
960C4⋊C4—7916no—
961C4⋊C4—798no—
962C4⋊C4—798no—
963C4⋊C4—794no—
964C4⋊C4—794no—
965C4⋊C4—794no—
966C4⋊C4—798no—
967C4⋊C4—798no—
968C4⋊C4C23×D7914yes—
969C4⋊C4C23×D7914yes—
970C4⋊C4C23×D7914yes—
971C4⋊C4C23×D7918yes—
972C4⋊C4C23×D7918yes—
973C4⋊C4C23×D79116yes—
974C4⋊C4C23×D7914yes—
975C4⋊C4C23×D7914yes—
976C22⋊C4—798no—
977C22⋊C4—798no—
978C22⋊C4—798no—
979C22⋊C4—798no—
980C22⋊C4—798no—
981C22⋊C4—7916no—
982C22⋊C4—798no—
983C22⋊C4—798no—
984C22⋊C4—798no—
985C22⋊C4—7916no—
986C22⋊C4—798no—
987C22⋊C4—798no—
988C22⋊C4—798no—
989C22⋊C4—798no—
990C22⋊C4—7916no—
991C22⋊C4C23×D7918yes—
992C22⋊C4C23×D79116yes—
993C22⋊C4C23×D7918yes—
994C22⋊C4C23×D7918yes—
995C42—792no—
996C42—791no—
997C42—798no—
998C42—792no—
999C42—792no—
1000C42—792no—
1001C42—792no—
1002C42—791no—
1003C42—798no—
1004C42—798no—
1005C42C23×D7912yes—
1006C42C23×D7911yescharacteristic
1007C42C23×D7911yescharacteristic
1008C42C23×D7918yes—
1009C42C23×D7918yes—
1010C23—3162no—
1011C23—3168no—
1012C23—31616no—
1013C23—3168no—
1014C23—791no—
1015C23—798no—
1016C23—794no—
1017C23—791no—
1018C23—1582no—
1019C23—1588no—
1020C23C24×D7914yes—
1021C23C24×D7911yescharacteristic
1022Q8—28no—
1023Q8—28no—
1024Q8—48no—
1025Q8—42no—
1026Q8—3162no—
1027Q8—3164no—
1028Q8—3164no—
1029D4—28no—
1030D4—42no—
1031D4—44no—
1032D4—3162no—
1033D4—3168no—
1034D4—3164no—
1035D4—31616no—
1036D4—3164no—
1037D4—31616no—
1038D4—3168no—
1039D4—3168no—
1040D4—31616no—
1041D4—3164no—
1042D4—3164no—
1043D4—3164no—
1044D4—3168no—
1045D4—15816no—
1046D4—1588no—
1047D4—1588no—
1048D4—1588no—
1049C2×C4—28no—
1050C2×C4—22no—
1051C2×C4—24no—
1052C2×C4—48no—
1053C2×C4—31616no—
1054C2×C4—3162no—
1055C2×C4—3162no—
1056C2×C4—3168no—
1057C2×C4—31616no—
1058C2×C4—3162no—
1059C2×C4—791no—
1060C2×C4—794no—
1061C2×C4—792no—
1062C2×C4—798no—
1063C2×C4—792no—
1064C2×C4—791no—
1065C2×C4—794no—
1066C2×C4—15816no—
1067C2×C4—1582no—
1068C2×C4—1588no—
1069C2×C4—1582no—
1070C2×C4—1588no—
1071C2×C4—1588no—
1072C2×C4—1582no—
1073C2×C4—1588no—
1074C2×C4—1582no—
1075C2×C4—1584no—
1076C2×C4—1584no—
1077C2×C4—15816no—
1078C2×C4C24×D7912yes—
1079C2×C4C24×D7911yescharacteristic
1080C2×C4C24×D7914yes—
1081C2×C4C24×D7918yes—
1082C2×C4C24×D7918yes—
1083C2×C4C24×D7911yescharacteristic
1084C2×C4C24×D7912yes—
1085C22—24no—
1086C22—21no—
1087C22—22no—
1088C22—28no—
1089C22—3164no—
1090C22—792no—
1091C22—63216no—
1092C22—6328no—
1093C22—1588no—
1094C22—1581no—
1095C22—1584no—
1096C22—1588no—
1097C22—1582no—
1098C22—1588no—
1099C22—1588no—
1100C22—1582no—
1101C22C25×D7911yescharacteristic
1102C4—21no—
1103C4—24no—
1104C4—28no—
1105C4—22no—
1106C4—28no—
1107C4—792no—
1108C4—1584no—
1109C4—1581no—
1110C4—1582no—
1111C4—1582no—
1112C4—1588no—
1113C4H(5,𝔽2)×D7912yes—
1114C4#1909940014yes—
1115C2—41no—
1116C2—44no—
1117C2—3161no—
1118C2—3168no—
1119C2—3164no—
1120C2—1582no—
1121C2C2×H(5,𝔽2)×D7911yescharacteristic
1122C2C2×#1909940012yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3550C2
hypercenter#3550D79
hypocenterC79#62759
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3550

Complements

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

NH ≅ G/Ntype
1. #23777829C2semidirect
2. #23777805C2semidirect
3. #23777800C2semidirect
4. #23777785C2semidirect
5. #23777775C2semidirect
6. #23777758C2semidirect
7. #23777745C2semidirect
8. #23777734C2semidirect
9. #23777712C2semidirect
10. #23777541C2semidirect
11. #23777027C2semidirect
12. #23777009C2semidirect
13. #23776961C2semidirect
14. D4×#11929625C2semidirect
15. #23776820C2semidirect
16. #23776732C2semidirect
17. #23776697C2semidirect
18. #532×D79C2semidirect
19. C79×#3550C2semidirect
20. C22×#11929625C22semidirect
21. C2×#41×D79C22semidirect
22. #19099312C22semidirect
23. #19099311C22semidirect
24. #19099309C22semidirect
25. #19099305C22semidirect
26. #19099304C22semidirect
27. #19099303C22semidirect
28. #19099279C22semidirect
29. #19099279C22semidirect
30. #19099279C22semidirect
31. #19099278C22semidirect
32. #19099273C22semidirect
33. #19099273C22semidirect
34. #19099263C22semidirect
35. #19099257C22semidirect
36. #19099254C22semidirect
37. #19099247C22semidirect
38. #19099241C22semidirect
39. #19099238C22semidirect
40. #19099235C22semidirect
41. #19099235C22semidirect
42. #19099235C22semidirect
43. #19099224C22semidirect
44. #19099216C22semidirect
45. #19099216C22semidirect
46. #19099216C22semidirect
47. #19099206C22semidirect
48. #19099206C22semidirect
49. #19099204C22semidirect
50. #19099204C22semidirect
51. D4×D316C22semidirect
52. D4×D316C22semidirect
53. #19099198C22semidirect
54. #19099190C22semidirect
55. #19099185C22semidirect
56. #19099183C22semidirect
57. #19099168C22semidirect
58. #19099165C22semidirect
59. #19099164C22semidirect
60. #19099152C22semidirect
61. #19099147C22semidirect
62. #19099143C22semidirect
63. #19099143C22semidirect
64. #19099143C22semidirect
65. #19099138C22semidirect
66. #19099137C22semidirect
67. #19099132C22semidirect
68. #19099131C22semidirect
69. #19099131C22semidirect
70. #19099129C22semidirect
71. #19099127C22semidirect
72. #19099124C22semidirect
73. #19099124C22semidirect
74. #19099118C22semidirect
75. #19099118C22semidirect
77. #19099114C22semidirect
78. #19099114C22semidirect
79. #19099114C22semidirect
80. #19099114C22semidirect
81. #19099113C22semidirect
82. #19099113C22semidirect
83. #19099112C22semidirect
84. #19099112C22semidirect
86. #19099110C22semidirect
87. #19099109C22semidirect
88. #19099108C22semidirect
89. C4⋊Q8×D79C22semidirect
91. #19099100C22semidirect
92. #19099100C22semidirect
93. #19099099C22semidirect
94. #19099099C22semidirect
95. #19099098C22semidirect
96. #19099098C22semidirect
97. #19099096C22semidirect
98. #19099092C22semidirect
99. #124×D79C22semidirect
100. #19099076C22semidirect
101. #19099076C22semidirect
102. #19099076C22semidirect
103. #19099076C22semidirect
104. #19099075C22semidirect
105. #19099071C22semidirect
106. #19099071C22semidirect
107. #121×D79C22semidirect
108. C4×#11929625C22semidirect
109. C4×#11929625C22semidirect
110. C4×#11929625C22semidirect
111. #19099031C22semidirect
112. C4×D4×D79C22semidirect
113. C4×D4×D79C22semidirect
114. #117×D79C22semidirect
115. C2×C42×D79C22semidirect
116. #563×C79C22semidirect
117. #559×C79C22semidirect
118. Q82×C79C22semidirect
119. #556×C79C22semidirect
120. D4×Q8×C79C22semidirect
121. #542×C79C22semidirect
122. #536×C79C22semidirect
123. #533×C79C22semidirect
563. #3550D79semidirect
581. C79#62759semidirect
585. #563C2×D79semidirect
591. #559C2×D79semidirect
592. Q82C2×D79semidirect
593. #556C2×D79semidirect
609. D4×Q8C2×D79semidirect
624. #542C2×D79semidirect
635. #536C2×D79semidirect
645. #533C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778292
#237778052
#237778002
#237777852
#237777752
#237777582
#237777452
#237777342
#237777122
#237775412
#237770272
#237770092
#237769612
D4×#119296252
#237768202
#237767322
#237766972
#532×D792
C79×#35502
#6275979