Finite Group Databasebeta

← #3548×D79 #35196058

Subgroups — #3548×D79 #35196058

Order 20224.

7810 conjugacy classes of subgroups.

The subgroup lattice has 1016 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777800C211yesmaximal, characteristic, complemented
2#23777799C214yesmaximal, complemented
3#23777798C212yesmaximal, complemented
4#23777797C214yesmaximal, complemented
5#23777796C214yesmaximal, complemented
6#23777795C218yesmaximal, complemented
7#23777794C214yesmaximal, complemented
8#23777793C214yesmaximal, complemented
9#562×D79C214yesmaximal, complemented
10#554×D79C214yesmaximal, complemented
11#550×D79C214yesmaximal, complemented
12#547×D79C214yesmaximal, complemented
13#540×D79C214yesmaximal, complemented
14#537×D79C218yesmaximal, complemented
15#533×D79C211yesmaximal, characteristic, complemented
16#532×D79C212yesmaximal, complemented
17C79×#3548C211yesmaximal, characteristic, complemented
18C2×#41×D79C2218yes—
19C2×#41×D79C2214yes—
20#19099311C2214yescomplemented
21#19099310C22116yescomplemented
22#19099309C22116yescomplemented
23#19099308C22116yescomplemented
24#19099307C2218yescomplemented
25#19099274C2214yescomplemented
26#19099273C2214yescomplemented
27#19099272C2218yescomplemented
28#19099271C2218yescomplemented
29#19099270C2214yescomplemented
30#19099269C2218yescomplemented
31#19099268C2218yescomplemented
32#19099267C22116yescomplemented
33#19099235C2214yescomplemented
34#19099234C2218yescomplemented
35#19099234C2214yescomplemented
36#19099233C2218yescomplemented
37#19099233C2214yescomplemented
38#19099232C2218yescomplemented
39#19099231C22116yescomplemented
40#19099231C2218yescomplemented
41#19099218C2214yescomplemented
42#19099217C2214yescomplemented
43#19099216C2214yescomplemented
44#19099215C2218yescomplemented
45#19099214C2218yescomplemented
46#19099213C2218yescomplemented
47#19099212C2218yescomplemented
48#19099211C22116yescomplemented
49#19099169C2214yescomplemented
50#19099168C2214yescomplemented
51#19099167C2214yescomplemented
52#19099166C2218yescomplemented
53#19099165C22116yescomplemented
54#19099164C2218yescomplemented
55#19099163C22116yescomplemented
56#19099144C2218yescomplemented
57#19099143C2218yescomplemented
58#19099143C22116yescomplemented
59#19099143C2218yescomplemented
60#19099142C2218yescomplemented
61#19099142C22116yescomplemented
62#19099142C2218yescomplemented
63#19099141C2218yescomplemented
64#19099141C2218yescomplemented
65#19099140C22116yescomplemented
66#19099140C22116yescomplemented
67#19099120C2211yescharacteristic, complemented
68#19099119C2212yescomplemented
69#19099118C2212yescomplemented
70#19099117C2214yescomplemented
71#19099116C2212yescomplemented
72#19099115C2214yescomplemented
73#19099114C2212yescomplemented
74#19099113C2212yescomplemented
75#19099112C2214yescomplemented
76#19099111C2212yescomplemented
77#19099110C2214yescomplemented
78#19099110C2214yescomplemented
79#19099109C2214yescomplemented
80#19099108C2214yescomplemented
81#19099108C2214yescomplemented
82C4⋊Q8×D79C2212yes—
83C4⋊Q8×D79C2212yes—
84#127×D79C2212yes—
85#127×D79C2214yes—
86#125×D79C2214yes—
87#125×D79C2212yes—
88#124×D79C2214yes—
89#123×D79C22116yes—
90C22⋊Q8×D79C2218yes—
91C22⋊Q8×D79C22116yes—
92C22⋊Q8×D79C2214yes—
93#121×D79C2218yes—
94#121×D79C22116yes—
95#121×D79C2214yes—
96#121×D79C2214yes—
97#121×D79C22116yes—
98C4×Q8×D79C2214yes—
99C4×D4×D79C2214yes—
100C4×D4×D79C2214yes—
101C4×D4×D79C2218yes—
102#117×D79C2212yes—
103C2×C4⋊C4×D79C2218yes—
104C2×C42×D79C2211yescharacteristic
105#562×C79C2214yescomplemented
106#554×C79C2214yescomplemented
107#550×C79C2214yescomplemented
108#547×C79C2214yescomplemented
109#540×C79C2214yescomplemented
110#537×C79C2218yescomplemented
111#533×C79C2211yescharacteristic, complemented
112#532×C79C2212yescomplemented
113C2×#11929625C2314yes—
114C2×#11929625C2318yes—
115C2×#11929624C2318yes—
116C2×#11929624C2318yes—
117C2×#11929624C2314yes—
118C2×#11929624C23116yes—
119C2×#11929623C2314yes—
120C2×#11929623C2318yes—
121C2×#11929623C23116yes—
122C2×#11929623C2318yes—
123#41×D79—416no—
124#41×D79—432no—
125C2×Q8×D79C2314yes—
126C2×Q8×D79C2314yes—
127C2×D4×D79C2314yes—
128C2×D4×D79C2314yes—
129C2×D4×D79C2318yes—
130C2×D4×D79C23116yes—
131C2×D4×D79C2314yes—
132C22×C4×D79C2311yescharacteristic
133C22×C4×D79C2312yes—
134C22×C4×D79C2318yes—
135C22×C4×D79C23116yes—
136#14579161C2312yes—
137#14579161C2312yes—
138#14579160C2314yes—
139#14579160C2314yes—
140#14579160C2314yes—
141#14579160C2314yes—
142#14579159C2314yes—
143#14579159C2314yes—
144#14579158C2314yes—
145#14579158C2312yes—
146#14579157C23116yes—
147#14579157C2318yes—
148#14579157C2314yes—
149#14579157C2314yes—
150#14579157C2314yes—
151#14579153C2314yes—
152#14579153C2312yes—
153#14579152C2318yes—
154#14579152C2314yes—
155#14579151C23116yes—
156#14579151C2318yes—
157#14579150C2314yes—
158#14579149C2314yes—
159#14579148C2314yes—
160#14579147C2318yes—
161#14579147C2318yes—
162#14579146C23116yes—
163#14579146C23116yes—
164#14579145C23116yes—
165#14579144C23116yes—
166#14579143C23116yes—
167#14579143C23116yes—
168#14579142C23116yes—
169#14579141C2314yes—
170#14579141C2318yes—
171#14579141C23116yes—
172#14579140C2314yes—
173#14579140C2318yes—
174#14579140C23116yes—
175#14579139C2318yes—
176#14579139C23116yes—
177#14579139C23116yes—
178#14579139C23116yes—
179#14579138C2318yes—
180#14579138C23116yes—
181#14579138C23116yes—
182#14579138C23116yes—
183#14579137C2314yes—
184#14579137C2318yes—
185#14579137C23116yes—
186#14579136C23116yes—
187#14579136C2314yes—
188#14579136C23116yes—
189#14579136C2318yes—
190#14579136C2314yes—
191#14579135C23116yes—
192#14579135C23116yes—
193#14579135C2314yes—
194#14579135C2318yes—
195#14579135C2314yes—
196#14579134C2318yes—
197#14579134C23116yes—
198#14579134C23116yes—
199#14579134C23116yes—
200#14579134C23116yes—
201#14579134C23116yes—
202#14579134C2318yes—
203#14579133C23116yes—
204#14579133C23116yes—
205#14579133C2318yes—
206#14579133C23116yes—
207#14579133C23116yes—
208#14579133C23116yes—
209#14579133C2318yes—
210#14579132C2314yes—
211#14579132C23116yes—
212#14579132C2318yes—
213#14579132C23116yes—
214#14579132C2314yes—
215Q8×Dic79C2314yes—
216C4×Dic158C2318yes—
217C4×Dic158C2314yes—
218#14579126C2318yes—
219#14579126C2314yes—
220C4×D316C2318yes—
221C4×D316C2314yes—
222C4×D316C2314yes—
223D4×Dic79C2318yes—
224D4×Dic79C2314yes—
225D4×Dic79C2314yes—
226#14579123C2318yes—
227#14579123C2314yes—
228#14579123C2314yes—
229C4×C22⋊D79C23116yes—
230C4×C22⋊D79C2318yes—
231C4×C22⋊D79C2318yes—
232(C22⋊D79)⋊C4C23116yes—
233(C22⋊D79)⋊C4C2318yes—
234(C22⋊D79)⋊C4C2318yes—
235#14579120C2312yes—
236#14579119C2314yes—
237#14579118C2314yes—
238#14579117C2314yes—
239C2×C4⋊Dic79C2318yes—
240C2×Dic79⋊C4C23116yes—
241C4⋊C4×D79C23116yes—
242C4⋊C4×D79C2318yes—
243C4⋊C4×D79C2318yes—
244C4⋊C4×D79C2314yes—
245C4⋊C4×D79C2314yes—
246C4⋊C4×D79C23116yes—
247C4⋊C4×D79C2314yes—
248C4⋊C4×D79C2314yes—
249C4⋊C4×D79C2318yes—
250C22⋊C4×D79C2314yes—
251C22⋊C4×D79C23116yes—
252C22⋊C4×D79C2318yes—
253C22⋊C4×D79C2318yes—
254C2×C4×Dic79C2311yescharacteristic
255C2×C4×Dic79C2312yes—
256C42×D79C2311yescharacteristic
257C42×D79C2312yes—
258C42×D79C2311yescharacteristic
259C42×D79C2311yescharacteristic
260C42×D79C2312yes—
261C42×D79C2311yescharacteristic
262C42×D79C2314yes—
263C2×#41×C79C2314yes—
264C2×#41×C79C2318yes—
265C4⋊Q8×C79C2312yes—
266C4⋊Q8×C79C2312yes—
267#127×C79C2314yes—
268#127×C79C2312yes—
269#125×C79C2314yes—
270#125×C79C2312yes—
271#124×C79C2314yes—
272#123×C79C23116yes—
273C22⋊Q8×C79C2314yes—
274C22⋊Q8×C79C2318yes—
275C22⋊Q8×C79C23116yes—
276#121×C79C23116yes—
277#121×C79C23116yes—
278#121×C79C2314yes—
279#121×C79C2318yes—
280#121×C79C2314yes—
281C4×Q8×C79C2314yes—
282C4×D4×C79C2318yes—
283C4×D4×C79C2314yes—
284C4×D4×C79C2314yes—
285#117×C79C2312yes—
286C2×C4⋊C4×C79C2318yes—
287C2×C42×C79C2311yescharacteristic
288C23×D79C2411yescharacteristic
289C23×D79C2418yes—
290#11929625—416no—
291#11929625—48no—
292#11929624—432no—
293#11929624—416no—
294#11929624—48no—
295#11929624—416no—
296#11929623—432no—
297#11929623—416no—
298#11929623—48no—
299#11929623—416no—
300C2×Dic158C2418yes—
301C2×Dic158C2414yes—
302C2×Dic158C2414yes—
303C2×Dic158C2418yes—
304Q8×D79—216no—
305Q8×D79—48no—
306C2×D316C2414yes—
307C2×D316C2414yes—
308C2×D316C2418yes—
309C2×D316C2414yes—
310C2×D316C24116yes—
311C2×C22⋊D79C2418yes—
312C2×C22⋊D79C2418yes—
313C2×C22⋊D79C2418yes—
314C2×C22⋊D79C2418yes—
315C2×C22⋊D79C24116yes—
316C2×C22⋊D79C2418yes—
317C2×C22⋊D79C24116yes—
318D4×D79—216no—
319D4×D79—216no—
320D4×D79—416no—
321D4×D79—48no—
322D4×D79—432no—
323C22×Dic79C2412yes—
324C22×Dic79C2418yes—
325C22×Dic79C2411yescharacteristic
326C22×Dic79C24116yes—
327C2×C4×D79—232no—
328C2×C4×D79—28no—
329C2×C4×D79—24no—
330C2×C4×D79—432no—
331C2×C4×D79C2412yes—
332C2×C4×D79C2418yes—
333C2×C4×D79C2418yes—
334C2×C4×D79C2412yes—
335C2×C4×D79C2418yes—
336C2×C4×D79C2418yes—
337C2×C4×D79C2412yes—
338C2×C4×D79C2411yescharacteristic
339C2×C4×D79C2411yescharacteristic
340C2×C4×D79C2411yescharacteristic
341C2×C4×D79C24116yes—
342C2×C4×D79C24116yes—
343C2×C4×D79C2412yes—
344C2×C4×D79C2411yescharacteristic
345C4⋊Dic79C2414yes—
346C4⋊Dic79C2414yes—
347C4⋊Dic79C24116yes—
348C4⋊Dic79C2414yes—
349C4⋊Dic79C2414yes—
350C4⋊Dic79C2418yes—
351Dic79⋊C4C2418yes—
352Dic79⋊C4C2418yes—
353Dic79⋊C4C24116yes—
354Dic79⋊C4C24116yes—
355Dic79⋊C4C2418yes—
356Dic79⋊C4C2418yes—
357Dic79⋊C4C2418yes—
358Dic79⋊C4C2418yes—
359C22⋊Dic79C2414yes—
360C22⋊Dic79C24116yes—
361C22⋊Dic79C2418yes—
362C22⋊Dic79C2418yes—
363(C2×D79)⋊C4C2418yes—
364(C2×D79)⋊C4C2418yes—
365(C2×D79)⋊C4C24116yes—
366(C2×D79)⋊C4C2418yes—
367(C2×D79)⋊C4C24116yes—
368(C2×D79)⋊C4C2418yes—
369(C2×D79)⋊C4C2418yes—
370C4×Dic79C2411yescharacteristic
371C4×Dic79C2412yes—
372C4×Dic79C2412yes—
373C4×Dic79C2412yes—
374C4×Dic79C2412yes—
375C4×Dic79C2411yescharacteristic
376C4×Dic79C2412yes—
377C4×Dic79C2418yes—
378C4×Dic79C2414yes—
379#41×C79—48no—
380#41×C79—416no—
381C2×Q8×C79C2414yes—
382C2×Q8×C79C2414yes—
383C2×D4×C79C2414yes—
384C2×D4×C79C2414yes—
385C2×D4×C79C2418yes—
386C2×D4×C79C24116yes—
387C2×D4×C79C2414yes—
388C22×C4×C79C2412yes—
389C22×C4×C79C2418yes—
390C22×C4×C79C2411yescharacteristic
391C22×C4×C79C24116yes—
392C4⋊C4×C79C2414yes—
393C4⋊C4×C79C2414yes—
394C4⋊C4×C79C24116yes—
395C4⋊C4×C79C2414yes—
396C4⋊C4×C79C2414yes—
397C4⋊C4×C79C2418yes—
398C22⋊C4×C79C2414yes—
399C22⋊C4×C79C24116yes—
400C22⋊C4×C79C2418yes—
401C22⋊C4×C79C2418yes—
402C42×C79C2411yescharacteristic
403C42×C79C2412yes—
404C42×C79C2411yescharacteristic
405C42×C79C2414yes—
406C23×C79C2518yes—
407C23×C79C2511yescharacteristic
408C22×D79—216no—
409C22×D79—24no—
410C22×D79—216no—
411C22×D79—22no—
412C22×D79—216no—
413C22×D79C2518yes—
414C22×D79C2511yescharacteristic
415C22×D79C2511yescharacteristic
416Q8×C79—28no—
417Q8×C79—44no—
418D4×C79—28no—
419D4×C79—28no—
420D4×C79—48no—
421D4×C79—44no—
422D4×C79—416no—
423C2×C4×C79—216no—
424C2×C4×C79—24no—
425C2×C4×C79—22no—
426C2×C4×C79—416no—
427C2×C4×C79C2511yescharacteristic
428C2×C4×C79C2512yes—
429C2×C4×C79C2518yes—
430C2×C4×C79C2518yes—
431C2×C4×C79C2512yes—
432C2×C4×C79C2511yescharacteristic
433C22⋊D79—216no—
434C22⋊D79—216no—
435C22⋊D79—416no—
436C22⋊D79—416no—
437C22⋊D79—48no—
438C22⋊D79—48no—
439C22⋊D79—48no—
440C2×Dic79—24no—
441C2×Dic79—216no—
442C2×Dic79—22no—
443C2×Dic79—416no—
444C2×Dic79C2511yescharacteristic
445C2×Dic79C2512yes—
446C2×Dic79C2518yes—
447C2×Dic79C2518yes—
448C2×Dic79C2512yes—
449C2×Dic79C2511yescharacteristic
450D316—28no—
451D316—28no—
452D316—48no—
453D316—44no—
454D316—416no—
455C4×D79—216no—
456C4×D79—24no—
457C4×D79—216no—
458C4×D79—22no—
459C4×D79—216no—
460C4×D79—24no—
461C4×D79—22no—
462C4×D79—24no—
463C4×D79—216no—
464C4×D79—22no—
465C4×D79—416no—
466C4×D79—416no—
467C4×D79H(5,𝔽2)18yes—
468C4×D792−1+414yes—
469Dic158—28no—
470Dic158—216no—
471Dic158—48no—
472Dic158—44no—
473C22×C79—28no—
474C22×C79—28no—
475C22×C79—22no—
476C22×C79—28no—
477C22×C79—21no—
478C22×C79C2611yescharacteristic
479C2×D79—28no—
480C2×D79—28no—
481C2×D79—22no—
482C2×D79—28no—
483C2×D79—21no—
484C2×D79—44no—
485C2×D79—432no—
486C2×D79C2×H(5,𝔽2)14yes—
487C2×D79C2×2−1+412yes—
488C4×C79—28no—
489C4×C79—22no—
490C4×C79—28no—
491C4×C79—21no—
492C4×C79C2×H(5,𝔽2)14yes—
493C4×C79C2×2−1+412yes—
494Dic79—28no—
495Dic79—22no—
496Dic79—28no—
497Dic79—21no—
498Dic79C2×H(5,𝔽2)14yes—
499Dic79C2×2−1+412yes—
500C2×#3548—791nomaximal, Sylow
501C2×C79—48no—
502C2×C79—41no—
503C2×C79C22×H(5,𝔽2)12yes—
504C2×C79C22×2−1+411yescharacteristic
505D79—48no—
506D79—41no—
507D79#354814yesdirect product factor
508#3548—794no—
509#3548—794no—
510#3548—794no—
511#3548—794no—
512#3548—794no—
513#3548—798no—
514#3548—791no—
515#3548—792no—
516#3548D7911yescharacteristic, direct product factor
517C2×#562—794no—
518C2×#554—794no—
519C2×#550—794no—
520C2×#547—794no—
521C2×#540—794no—
522C2×#537—798no—
523C2×#533—791no—
524C2×#532—792no—
525C79C2×#354811yescharacteristic, complemented, Sylow
526C22×#41—794no—
527C22×#41—798no—
528#562—794no—
529#562—798no—
530#562—7916no—
531#562—7916no—
532#562—7916no—
533#562C2×D7914yescomplemented
534#554—794no—
535#554—798no—
536#554—7916no—
537#554—798no—
538#554—794no—
539#554—794no—
540#554—798no—
541#554—798no—
542#554C2×D7914yescomplemented
543#550—798no—
544#550—798no—
545#550—794no—
546#550—798no—
547#550—7916no—
548#550—794no—
549#550—798no—
550#550—794no—
551#550C2×D7914yescomplemented
552#547—798no—
553#547—794no—
554#547—7916no—
555#547—798no—
556#547—798no—
557#547—794no—
558#547—794no—
559#547—798no—
560#547C2×D7914yescomplemented
561#540—794no—
562#540—794no—
563#540—7916no—
564#540—7916no—
565#540—798no—
566#540—798no—
567#540—794no—
568#540C2×D7914yescomplemented
569#537—798no—
570#537—798no—
571#537—798no—
572#537—7916no—
573#537—798no—
574#537—7916no—
575#537—7916no—
576#537—798no—
577#537—7916no—
578#537—798no—
579#537—798no—
580#537C2×D7918yescomplemented
581#533—792no—
582#533—792no—
583#533—794no—
584#533—794no—
585#533—792no—
586#533—791no—
587#533C2×D7911yescharacteristic, complemented
588#532—794no—
589#532—792no—
590#532—792no—
591#532—794no—
592#532—794no—
593#532—794no—
594#532—794no—
595#532—794no—
596#532—792no—
597#532C2×D7912yescomplemented
598C2×C4⋊Q8—792no—
599C2×C4⋊Q8—792no—
600C2×#127—792no—
601C2×#127—794no—
602C2×#125—792no—
603C2×#125—794no—
604C2×#124—794no—
605C2×#123—7916no—
606C2×C22⋊Q8—794no—
607C2×C22⋊Q8—798no—
608C2×C22⋊Q8—7916no—
609C2×#121—794no—
610C2×#121—794no—
611C2×#121—7916no—
612C2×#121—798no—
613C2×#121—7916no—
614C2×C4×Q8—794no—
615C2×C4×D4—794no—
616C2×C4×D4—794no—
617C2×C4×D4—798no—
618C2×#117—792no—
619C22×C4⋊C4—798no—
620C22×C42—791no—
621C2×#41—31632no—
622C2×#41—31616no—
623C2×#41—794no—
624C2×#41—798no—
625C2×#41—798no—
626C2×#41—794no—
627C2×#41—798no—
628C2×#41—7916no—
629C2×#41—798no—
630C2×#41—794no—
631C2×#41—798no—
632C2×#41—7916no—
633C2×#41C22×D7914yes—
634C2×#41C22×D7918yes—
635C22×Q8—794no—
636C22×Q8—794no—
637C22×D4—798no—
638C22×D4—7916no—
639C22×D4—794no—
640C22×D4—794no—
641C22×D4—794no—
642C23×C4—7916no—
643C23×C4—798no—
644C23×C4—791no—
645C23×C4—792no—
646C4⋊Q8—794no—
647C4⋊Q8—794no—
648C4⋊Q8—794no—
649C4⋊Q8—794no—
650C4⋊Q8—794no—
651C4⋊Q8—794no—
652C4⋊Q8—792no—
653C4⋊Q8—792no—
654C4⋊Q8C22×D7912yes—
655C4⋊Q8C22×D7912yes—
656#127—794no—
657#127—794no—
658#127—794no—
659#127—798no—
660#127—7916no—
661#127—792no—
662#127—794no—
663#127C22×D7912yes—
664#127C22×D7914yes—
665#125—798no—
666#125—794no—
667#125—7916no—
668#125—798no—
669#125—792no—
670#125—794no—
671#125C22×D7912yes—
672#125C22×D7914yes—
673#124—794no—
674#124—794no—
675#124—798no—
676#124—798no—
677#124—794no—
678#124C22×D7914yes—
679#123—7916no—
680#123—7916no—
681#123—7916no—
682#123—7916no—
683#123—7916no—
684#123—7916no—
685#123—7916no—
686#123C22×D79116yes—
687C22⋊Q8—794no—
688C22⋊Q8—798no—
689C22⋊Q8—7916no—
690C22⋊Q8—794no—
691C22⋊Q8—798no—
692C22⋊Q8—7916no—
693C22⋊Q8—798no—
694C22⋊Q8—794no—
695C22⋊Q8—7916no—
696C22⋊Q8—798no—
697C22⋊Q8—7916no—
698C22⋊Q8—7916no—
699C22⋊Q8—7916no—
700C22⋊Q8—798no—
701C22⋊Q8—7916no—
702C22⋊Q8—7916no—
703C22⋊Q8—7916no—
704C22⋊Q8C22×D7914yes—
705C22⋊Q8C22×D7918yes—
706C22⋊Q8C22×D79116yes—
707#121—794no—
708#121—798no—
709#121—794no—
710#121—798no—
711#121—7916no—
712#121—7916no—
713#121—7916no—
714#121—798no—
715#121—7916no—
716#121—7916no—
717#121—7916no—
718#121—7916no—
719#121—794no—
720#121—794no—
721#121—7916no—
722#121—798no—
723#121—7916no—
724#121—794no—
725#121—794no—
726#121—7916no—
727#121—798no—
728#121—7916no—
729#121—798no—
730#121—798no—
731#121—7916no—
732#121—7916no—
733#121—7916no—
734#121—7916no—
735#121—7916no—
736#121C22×D7914yes—
737#121C22×D7914yes—
738#121C22×D79116yes—
739#121C22×D7918yes—
740#121C22×D79116yes—
741C4×Q8—794no—
742C4×Q8—798no—
743C4×Q8—794no—
744C4×Q8—798no—
745C4×Q8—794no—
746C4×Q8C22×D7914yes—
747C4×D4—794no—
748C4×D4—794no—
749C4×D4—798no—
750C4×D4—798no—
751C4×D4—798no—
752C4×D4—7916no—
753C4×D4—794no—
754C4×D4—794no—
755C4×D4—798no—
756C4×D4—798no—
757C4×D4—798no—
758C4×D4—7916no—
759C4×D4—794no—
760C4×D4—794no—
761C4×D4—798no—
762C4×D4C22×D7914yes—
763C4×D4C22×D7914yes—
764C4×D4C22×D7918yes—
765#117—792no—
766#117—794no—
767#117—794no—
768#117—794no—
769#117C22×D7912yes—
770C2×C4⋊C4—7916no—
771C2×C4⋊C4—798no—
772C2×C4⋊C4—794no—
773C2×C4⋊C4—794no—
774C2×C4⋊C4—7916no—
775C2×C4⋊C4—7916no—
776C2×C4⋊C4—798no—
777C2×C4⋊C4—798no—
778C2×C4⋊C4—794no—
779C2×C4⋊C4—794no—
780C2×C4⋊C4—798no—
781C2×C4⋊C4C22×D7918yes—
782C2×C22⋊C4—794no—
783C2×C22⋊C4—7916no—
784C2×C22⋊C4—798no—
785C2×C22⋊C4—798no—
786C2×C42—792no—
787C2×C42—791no—
788C2×C42—794no—
789C2×C42—791no—
790C2×C42—792no—
791C2×C42—791no—
792C2×C42—791no—
793C2×C42—792no—
794C2×C42—791no—
795C2×C42C22×D7911yescharacteristic
796C24—798no—
797C24—791no—
798#41—48no—
799#41—416no—
800#41—31616no—
801#41—31616no—
802#41—3168no—
803#41—31632no—
804#41—31616no—
805#41—31632no—
806#41—31616no—
807#41—31616no—
808#41—3168no—
809#41—3168no—
810C2×Q8—3168no—
811C2×Q8—798no—
812C2×Q8—794no—
813C2×Q8—798no—
814C2×Q8—794no—
815C2×Q8—15816no—
816C2×Q8C23×D7914yes—
817C2×Q8C23×D7914yes—
818C2×D4—31616no—
819C2×D4—31632no—
820C2×D4—3168no—
821C2×D4—798no—
822C2×D4—798no—
823C2×D4—7916no—
824C2×D4—7916no—
825C2×D4—798no—
826C2×D4—798no—
827C2×D4—798no—
828C2×D4—798no—
829C2×D4—7916no—
830C2×D4—794no—
831C2×D4—794no—
832C2×D4—794no—
833C2×D4—15816no—
834C2×D4—15816no—
835C2×D4C23×D7914yes—
836C2×D4C23×D7914yes—
837C2×D4C23×D7918yes—
838C2×D4C23×D79116yes—
839C2×D4C23×D7914yes—
840C22×C4—31632no—
841C22×C4—7916no—
842C22×C4—7916no—
843C22×C4—7916no—
844C22×C4—791no—
845C22×C4—792no—
846C22×C4—791no—
847C22×C4—792no—
848C22×C4—798no—
849C22×C4—791no—
850C22×C4—792no—
851C22×C4—791no—
852C22×C4—791no—
853C22×C4—792no—
854C22×C4—792no—
855C22×C4—798no—
856C22×C4—798no—
857C22×C4—798no—
858C22×C4—798no—
859C22×C4—1584no—
860C22×C4—15832no—
861C22×C4—1588no—
862C22×C4C23×D7911yescharacteristic
863C22×C4C23×D7912yes—
864C22×C4C23×D7918yes—
865C22×C4C23×D79116yes—
866C4⋊C4—798no—
867C4⋊C4—798no—
868C4⋊C4—7916no—
869C4⋊C4—7916no—
870C4⋊C4—798no—
871C4⋊C4—798no—
872C4⋊C4—798no—
873C4⋊C4—798no—
874C4⋊C4—794no—
875C4⋊C4—794no—
876C4⋊C4—7916no—
877C4⋊C4—794no—
878C4⋊C4—794no—
879C4⋊C4—798no—
880C4⋊C4C23×D7914yes—
881C4⋊C4C23×D7914yes—
882C4⋊C4C23×D79116yes—
883C4⋊C4C23×D7914yes—
884C4⋊C4C23×D7914yes—
885C4⋊C4C23×D7918yes—
886C22⋊C4—794no—
887C22⋊C4—7916no—
888C22⋊C4—798no—
889C22⋊C4—798no—
890C22⋊C4—798no—
891C22⋊C4—7916no—
892C22⋊C4—7916no—
893C22⋊C4—798no—
894C22⋊C4—798no—
895C22⋊C4—798no—
896C22⋊C4—798no—
897C22⋊C4C23×D7914yes—
898C22⋊C4C23×D79116yes—
899C22⋊C4C23×D7918yes—
900C22⋊C4C23×D7918yes—
901C42—791no—
902C42—792no—
903C42—792no—
904C42—792no—
905C42—792no—
906C42—792no—
907C42—791no—
908C42—798no—
909C42—794no—
910C42C23×D7911yescharacteristic
911C42C23×D7912yes—
912C42C23×D7911yescharacteristic
913C42C23×D7914yes—
914C23—791no—
915C23—798no—
916C23—791no—
917C23—15816no—
918C23—15816no—
919C23—1584no—
920C23—1582no—
921C23—15816no—
922C23C24×D7911yescharacteristic
923C23C24×D7918yes—
924Q8—28no—
925Q8—44no—
926Q8—3168no—
927Q8—3164no—
928Q8—15816no—
929Q8—1588no—
930D4—28no—
931D4—28no—
932D4—48no—
933D4—44no—
934D4—416no—
935D4—3168no—
936D4—3164no—
937D4—31616no—
938D4—3168no—
939D4—3168no—
940D4—31616no—
941D4—31616no—
942D4—3168no—
943D4—15816no—
944D4—15816no—
945D4—1588no—
946D4—1588no—
947C2×C4—216no—
948C2×C4—24no—
949C2×C4—22no—
950C2×C4—416no—
951C2×C4—31616no—
952C2×C4—31616no—
953C2×C4—31616no—
954C2×C4—791no—
955C2×C4—792no—
956C2×C4—798no—
957C2×C4—794no—
958C2×C4—791no—
959C2×C4—792no—
960C2×C4—798no—
961C2×C4—798no—
962C2×C4—15816no—
963C2×C4—1584no—
964C2×C4—1582no—
965C2×C4—15816no—
966C2×C4—15816no—
967C2×C4—1584no—
968C2×C4—1582no—
969C2×C4—15816no—
970C2×C4—1584no—
971C2×C4—1582no—
972C2×C4—15816no—
973C2×C4—1584no—
974C2×C4—1582no—
975C2×C4C24×D7911yescharacteristic
976C2×C4C24×D7912yes—
977C2×C4C24×D7918yes—
978C2×C4C24×D7918yes—
979C2×C4C24×D7912yes—
980C2×C4C24×D7911yescharacteristic
981C22—22no—
982C22—28no—
983C22—28no—
984C22—21no—
985C22—28no—
986C22—31632no—
987C22—3164no—
988C22—794no—
989C22—792no—
990C22—1588no—
991C22—1588no—
992C22—1582no—
993C22—1581no—
994C22—1588no—
995C22C25×D7911yescharacteristic
996C4—28no—
997C4—22no—
998C4—28no—
999C4—21no—
1000C4—794no—
1001C4—792no—
1002C4—1588no—
1003C4—1588no—
1004C4—1582no—
1005C4—1581no—
1006C4H(5,𝔽2)×D7914yes—
1007C42−1+4×D7912yes—
1008C2—41no—
1009C2—48no—
1010C2—3168no—
1011C2—3161no—
1012C2—794no—
1013C2C2×H(5,𝔽2)×D7912yes—
1014C2C2×2−1+4×D7911yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3548C2
hypercenter#3548D79
hypocenterC79C2×#3548
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3548

Complements

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

NH ≅ G/Ntype
1. #23777800C2semidirect
2. #23777799C2semidirect
3. #23777798C2semidirect
4. #23777797C2semidirect
5. #23777796C2semidirect
6. #23777795C2semidirect
7. #23777794C2semidirect
8. #23777793C2semidirect
9. #562×D79C2semidirect
10. #554×D79C2semidirect
11. #550×D79C2semidirect
12. #547×D79C2semidirect
13. #540×D79C2semidirect
14. #537×D79C2semidirect
15. #533×D79C2semidirect
16. #532×D79C2semidirect
17. C79×#3548C2semidirect
20. #19099311C22semidirect
21. #19099310C22semidirect
22. #19099309C22semidirect
23. #19099308C22semidirect
24. #19099307C22semidirect
25. #19099274C22semidirect
26. #19099273C22semidirect
27. #19099272C22semidirect
28. #19099271C22semidirect
29. #19099270C22semidirect
30. #19099269C22semidirect
31. #19099268C22semidirect
32. #19099267C22semidirect
33. #19099235C22semidirect
34. #19099234C22semidirect
35. #19099234C22semidirect
36. #19099233C22semidirect
37. #19099233C22semidirect
38. #19099232C22semidirect
39. #19099231C22semidirect
40. #19099231C22semidirect
41. #19099218C22semidirect
42. #19099217C22semidirect
43. #19099216C22semidirect
44. #19099215C22semidirect
45. #19099214C22semidirect
46. #19099213C22semidirect
47. #19099212C22semidirect
48. #19099211C22semidirect
49. #19099169C22semidirect
50. #19099168C22semidirect
51. #19099167C22semidirect
52. #19099166C22semidirect
53. #19099165C22semidirect
54. #19099164C22semidirect
55. #19099163C22semidirect
56. #19099144C22semidirect
57. #19099143C22semidirect
58. #19099143C22semidirect
59. #19099143C22semidirect
60. #19099142C22semidirect
61. #19099142C22semidirect
62. #19099142C22semidirect
63. #19099141C22semidirect
64. #19099141C22semidirect
65. #19099140C22semidirect
66. #19099140C22semidirect
67. #19099120C22semidirect
68. #19099119C22semidirect
69. #19099118C22semidirect
70. #19099117C22semidirect
71. #19099116C22semidirect
72. #19099115C22semidirect
73. #19099114C22semidirect
74. #19099113C22semidirect
75. #19099112C22semidirect
76. #19099111C22semidirect
77. #19099110C22semidirect
78. #19099110C22semidirect
79. #19099109C22semidirect
80. #19099108C22semidirect
81. #19099108C22semidirect
105. #562×C79C22semidirect
106. #554×C79C22semidirect
107. #550×C79C22semidirect
108. #547×C79C22semidirect
109. #540×C79C22semidirect
110. #537×C79C22semidirect
111. #533×C79C22semidirect
112. #532×C79C22semidirect
507. D79#3548direct (N × H)
516. #3548D79direct (N × H)
525. C79C2×#3548semidirect
533. #562C2×D79semidirect
542. #554C2×D79semidirect
551. #550C2×D79semidirect
560. #547C2×D79semidirect
568. #540C2×D79semidirect
580. #537C2×D79semidirect
587. #533C2×D79semidirect
597. #532C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778002
#237777992
#237777982
#237777972
#237777962
#237777952
#237777942
#237777932
#562×D792
#554×D792
#550×D792
#547×D792
#540×D792
#537×D792
#533×D792
#532×D792
C79×#35482
C2×#354879