Finite Group Databasebeta

← #3487×D79 #35196509

Subgroups — #3487×D79 #35196509

Order 20224.

11510 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D79C211yesmaximal, characteristic, complemented
2C22×#41×D79C211yesmaximal, characteristic, complemented
3#23777059C211yesmaximal, characteristic, complemented
4#23777058C211yesmaximal, characteristic, complemented
5#23777057C218yesmaximal, complemented
6#23777056C216yesmaximal, complemented
7#23777055C211yesmaximal, characteristic, complemented
8#23777054C216yesmaximal, complemented
9#23777053C218yesmaximal, complemented
10#550×D79C218yesmaximal, complemented
11#548×D79C218yesmaximal, complemented
12#535×D79C216yesmaximal, complemented
13#525×D79C216yesmaximal, complemented
14#519×D79C211yesmaximal, characteristic, complemented
15C79×#3487C211yesmaximal, characteristic, complemented
16C2×#14579209C2214yescomplemented
17C2×#14579209C2211yescharacteristic, complemented
18C2×#14579208C2214yescomplemented
19C2×#14579208C2216yescomplemented
202−1+4×D79—216no—
21C22×#11929625C2211yescharacteristic, complemented
22C22×#11929624C2213yescomplemented
23C22×#11929623C2213yescomplemented
24C2×#41×D79—216no—
25C2×#41×D79C2218yes—
26C2×#41×D79C2216yes—
27C2×#41×D79C2218yescomplemented
28C2×#41×D79C2214yescomplemented
29C22×Q8×D79C2211yescharacteristic
30C22×Q8×D79C2214yescomplemented
31C22×D4×D79C2213yes—
32C23×C4×D79C2213yes—
33#19099235C2218yescomplemented
34#19099234C22124yescomplemented
35#19099233C22124yescomplemented
36#19099232C2218yescomplemented
37#19099232C2218yescomplemented
38#19099231C22124yescomplemented
39#19099231C22124yescomplemented
40#19099225C2218yescomplemented
41#19099224C2218yescomplemented
42#19099223C22124yescomplemented
43#19099222C22124yescomplemented
44#19099221C22124yescomplemented
45#19099220C2218yescomplemented
46#19099219C22124yescomplemented
47#19099132C2216yescomplemented
48#19099131C22112yescomplemented
49#19099130C2216yescomplemented
50#19099129C22124yescomplemented
51#19099128C22124yescomplemented
52#19099127C2216yescomplemented
53#19099126C22112yescomplemented
54#127×D79C22112yescomplemented
55#124×D79C22112yescomplemented
56#19099076C22112yescomplemented
57#19099075C2216yescomplemented
58#19099074C2216yescomplemented
59#19099073C22112yescomplemented
60#19099072C22124yescomplemented
61#19099071C22112yescomplemented
62#19099070C2216yescomplemented
63#19099069C22112yescomplemented
64#123×D79C2214yes—
65C22⋊Q8×D79C22112yescomplemented
66#121×D79C22124yescomplemented
67#121×D79C22112yescomplemented
68#120×D79C22112yes—
69#19099041C2211yescharacteristic, complemented
70#19099040C2216yescomplemented
71#19099039C2218yescomplemented
72C4×Q8×D79C2218yescomplemented
73C4×D4×D79C22124yescomplemented
74#117×D79C2216yes—
75C2×2−1+4×C79C2211yescharacteristic, complemented
76C22×#41×C79C2211yescharacteristic, complemented
77#550×C79C2218yescomplemented
78#548×C79C2218yescomplemented
79#535×C79C2216yescomplemented
80#525×C79C2216yescomplemented
81#519×C79C2211yescharacteristic, complemented
82C24×D79C2313yes—
83#14579209—28no—
84#14579209—232no—
85#14579208—248no—
86#14579208—232no—
87C2×#11929625—28no—
88C2×#11929625C2316yes—
89C2×#11929625C2318yes—
90C2×#11929625C2314yescomplemented
91C2×#11929624—224no—
92C2×#11929624C23112yes—
93C2×#11929624C2316yes—
94C2×#11929624C23124yes—
95C2×#11929624C23112yescomplemented
96C2×#11929623—224no—
97C2×#11929623C23112yes—
98C2×#11929623C2316yes—
99C2×#11929623C23124yes—
100C2×#11929623C23112yescomplemented
101#41×D79—232no—
102#41×D79—264no—
103#41×D79—264no—
104#41×D79—248no—
105C22×Dic158C2313yes—
106C22×Dic158C23112yescomplemented
107C2×Q8×D79—232no—
108C2×Q8×D79D4116yescomplemented
109C2×Q8×D79C2316yes—
110C2×Q8×D79C2314yes—
111C2×Q8×D79C2314yes—
112C2×Q8×D79C2314yescomplemented
113C2×Q8×D79C23112yescomplemented
114C22×D316C2313yes—
115C22×C22⋊D79C2316yes—
116C2×D4×D79—224no—
117C2×D4×D79C2314yes—
118C2×D4×D79C23112yes—
119C2×D4×D79C2316yes—
120C2×D4×D79C23112yes—
121C2×D4×D79C23124yes—
122C23×Dic79C2313yes—
123C22×C4×D79—224no—
124C22×C4×D79C23112yes—
125C22×C4×D79C23112yes—
126C22×C4×D79C2311yescharacteristic
127C22×C4×D79C2313yes—
128C22×C4×D79C2313yes—
129C22×C4×D79C23112yes—
130C22×C4×D79C2313yes—
131#14579158C23112yescomplemented
132#14579157C23112yescomplemented
133#14579157C23112yescomplemented
134#14579157C23148yescomplemented
135#14579150C23112yescomplemented
136#14579149C23112yescomplemented
137#14579148C23112yescomplemented
138#14579147C23148yescomplemented
139#14579146C2318yes—
140#14579145C2314yes—
141#14579144C2314yes—
142#14579143C2318yes—
143#14579142C2314yes—
144#14579141C23112yescomplemented
145#14579140C23112yescomplemented
146#14579139C23124yescomplemented
147#14579138C23124yescomplemented
148#14579137C23112yescomplemented
149#14579136C23124yescomplemented
150#14579136C23112yescomplemented
151#14579135C23124yescomplemented
152#14579135C23112yescomplemented
153#14579134C23148yescomplemented
154#14579134C23124yescomplemented
155#14579133C23148yescomplemented
156#14579133C23124yescomplemented
157#14579132C23124yescomplemented
158#14579132C23112yescomplemented
159#14579131C23112yes—
160#14579131C23124yes—
161#14579130C23112yes—
162#14579129C23112yes—
163#14579129C23124yes—
164Q8×Dic79C2318yescomplemented
165C4×Dic158C23124yescomplemented
166#14579126C23124yescomplemented
167C4×D316C23124yescomplemented
168D4×Dic79C23124yescomplemented
169#14579123C23124yescomplemented
170C4×C22⋊D79C23124yescomplemented
171C4×C22⋊D79C23124yescomplemented
172(C22⋊D79)⋊C4C23124yescomplemented
173(C22⋊D79)⋊C4C23124yescomplemented
174#14579120C2316yes—
175#14579119C23112yes—
176#14579118C23112yes—
177#14579117C23112yes—
178C4⋊C4×D79C23112yes—
179C4⋊C4×D79C2318yes—
180C22⋊C4×D79C2314yes—
181C22⋊C4×D79C2318yes—
182C22⋊C4×D79C23124yes—
183C42×D79C23112yes—
1842−1+4×C79—28no—
185C2×#41×C79—28no—
186C2×#41×C79C2316yes—
187C2×#41×C79C2318yes—
188C2×#41×C79C2314yescomplemented
189C22×Q8×C79C2311yescharacteristic
190C22×Q8×C79C2314yescomplemented
191C22×D4×C79C2313yes—
192C23×C4×C79C2313yes—
193#127×C79C23112yescomplemented
194#124×C79C23112yescomplemented
195#123×C79C2314yes—
196C22⋊Q8×C79C23112yescomplemented
197#121×C79C23124yescomplemented
198#121×C79C23112yescomplemented
199#120×C79C23112yes—
200C4×Q8×C79C2318yescomplemented
201C4×D4×C79C23124yescomplemented
202#117×C79C2316yes—
203C23×D79—212no—
204C23×D79—412no—
205C23×D79C2416yes—
206C23×D79C2414yes—
207C23×D79C2411yescharacteristic
208C23×D79C2416yes—
209C23×D79C2413yes—
210#11929625—224no—
211#11929625—232no—
212#11929625—216no—
213#11929624—248no—
214#11929624—296no—
215#11929624—248no—
216#11929624—224no—
217#11929623—248no—
218#11929623—224no—
219#11929623—296no—
220#11929623—248no—
221C2×Dic158—248no—
222C2×Dic158C2×D4124yescomplemented
223C2×Dic158C24112yes—
224C2×Dic158C2416yes—
225C2×Dic158C24112yes—
226Q8×D79—224no—
227Q8×D79—248no—
228Q8×D79—216no—
229Q8×D79C2×D4132yes—
230Q8×D79C2×D4132yescomplemented
231C2×D316—212no—
232C2×D316C2414yes—
233C2×D316C24112yes—
234C2×D316C2416yes—
235C2×D316C24124yes—
236C2×C22⋊D79—224no—
237C2×C22⋊D79C2414yes—
238C2×C22⋊D79C2414yes—
239C2×C22⋊D79C24124yes—
240C2×C22⋊D79C24112yes—
241C2×C22⋊D79C24124yes—
242C2×C22⋊D79C24124yes—
243D4×D79—224no—
244D4×D79—248no—
245D4×D79—248no—
246D4×D79—216no—
247D4×D79—448no—
248C22×Dic79—212no—
249C22×Dic79C24112yes—
250C22×Dic79C24112yes—
251C22×Dic79C2411yescharacteristic
252C22×Dic79C2413yes—
253C2×C4×D79—212no—
254C2×C4×D79—248no—
255C2×C4×D79—248no—
256C2×C4×D79—248no—
257C2×C4×D79—24no—
258C2×C4×D79—212no—
259C2×C4×D79C2×D4124yes—
260C2×C4×D79C2414yes—
261C2×C4×D79C24112yes—
262C2×C4×D79C24112yes—
263C2×C4×D79C24112yes—
264C2×C4×D79C24112yes—
265C2×C4×D79C2418yes—
266C2×C4×D79C2412yes—
267C2×C4×D79C2412yes—
268C2×C4×D79C2416yes—
269C2×C4×D79C2416yes—
270C4⋊Dic79C24112yes—
271C4⋊Dic79C2418yes—
272Dic79⋊C4C24124yes—
273Dic79⋊C4C2418yes—
274Dic79⋊C4C2418yes—
275C22⋊Dic79C2414yes—
276C22⋊Dic79C2418yes—
277C22⋊Dic79C24124yes—
278(C2×D79)⋊C4C2418yes—
279(C2×D79)⋊C4C2418yes—
280(C2×D79)⋊C4C24124yes—
281(C2×D79)⋊C4C2418yes—
282(C2×D79)⋊C4C24124yes—
283C4×Dic79C24124yes—
284C4×Dic79C24112yes—
285C24×C79C2413yes—
286#41×C79—232no—
287#41×C79—216no—
288#41×C79—224no—
289C2×Q8×C79—216no—
290C2×Q8×C79C2×D418yescomplemented
291C2×Q8×C79C2416yes—
292C2×Q8×C79C2414yes—
293C2×D4×C79—212no—
294C2×D4×C79C2414yes—
295C2×D4×C79C24112yes—
296C2×D4×C79C2416yes—
297C2×D4×C79C24124yes—
298C22×C4×C79—212no—
299C22×C4×C79C24112yes—
300C22×C4×C79C24112yes—
301C22×C4×C79C2411yescharacteristic
302C22×C4×C79C2413yes—
303C4⋊C4×C79C24112yes—
304C4⋊C4×C79C2418yes—
305C22⋊C4×C79C2414yes—
306C22⋊C4×C79C2418yes—
307C22⋊C4×C79C24124yes—
308C42×C79C24112yes—
309C23×C79—26no—
310C23×C79—46no—
311C23×C79C2516yes—
312C23×C79C2514yes—
313C23×C79C2511yescharacteristic
314C22×D79—24no—
315C22×D79—26no—
316C22×D79—28no—
317C22×D79—212no—
318C22×D79—212no—
319C22×D79—216no—
320C22×D79—224no—
321C22×D79—412no—
322C22×D79—46no—
323C22×D79—448no—
324C22×D79C22×D414yes—
325C22×D79C2516yes—
326C22×D79C2514yes—
327C22×D79C2511yescharacteristic
328C22×D79C2511yescharacteristic
329Q8×C79—212no—
330Q8×C79C22×D4116yes—
331D4×C79—28no—
332D4×C79—224no—
333D4×C79—212no—
334D4×C79—424no—
335C2×C4×C79—22no—
336C2×C4×C79—224no—
337C2×C4×C79—224no—
338C2×C4×C79C22×D4112yes—
339C2×C4×C79C2518yes—
340C2×C4×C79C2514yes—
341C2×C4×C79C2512yes—
342C2×C4×C79C2516yes—
343C22⋊D79—28no—
344C22⋊D79—28no—
345C22⋊D79—248no—
346C22⋊D79—224no—
347C22⋊D79—424no—
348C22⋊D79—424no—
349C2×Dic79—22no—
350C2×Dic79—224no—
351C2×Dic79—224no—
352C2×Dic79C22×D4112yes—
353C2×Dic79C2518yes—
354C2×Dic79C2514yes—
355C2×Dic79C2512yes—
356C2×Dic79C2516yes—
357D316—28no—
358D316—224no—
359D316—212no—
360D316—424no—
361C4×D79—24no—
362C4×D79—24no—
363C4×D79—28no—
364C4×D79—216no—
365C4×D79—224no—
366C4×D79—224no—
367C4×D79—224no—
368C4×D79—224no—
369C4×D79C22×D4124yes—
370C4×D79C22×D4124yes—
371Dic158—212no—
372Dic158—224no—
373Dic158C22×D4148yes—
374C22×C79—22no—
375C22×C79—24no—
376C22×C79—26no—
377C22×C79—28no—
378C22×C79—212no—
379C22×C79—412no—
380C22×C79C23×D412yes—
381C22×C79C2611yescharacteristic
382C2×D79—22no—
383C2×D79—28no—
384C2×D79—26no—
385C2×D79—24no—
386C2×D79—28no—
387C2×D79—212no—
388C2×D79—424no—
389C2×D79—412no—
390C2×D79—416no—
391C2×D79—424no—
392C2×D79C23×D412yes—
393C2×D79C23×D412yes—
394C2×D79#58514yes—
395C4×C79—22no—
396C4×C79—24no—
397C4×C79—28no—
398C4×C79C23×D4112yes—
399Dic79—24no—
400Dic79—22no—
401Dic79—28no—
402Dic79C23×D4112yes—
403C2×#3487—791nomaximal, Sylow
404C2×C79—22no—
405C2×C79—46no—
406C2×C79—44no—
407C2×C79C24×D411yescharacteristic
408C2×C79C2×#58512yes—
409D79—22no—
410D79—44no—
411D79—46no—
412D79#348714yesdirect product factor
413C22×2−1+4—791no—
414C23×#41—791no—
415#3487—791no—
416#3487—791no—
417#3487—798no—
418#3487—798no—
419#3487—796no—
420#3487—796no—
421#3487—791no—
422#3487D7911yescharacteristic, direct product factor
423C2×#550—798no—
424C2×#548—798no—
425C2×#535—796no—
426C2×#525—796no—
427C2×#519—791no—
428C79C2×#348711yescharacteristic, complemented, Sylow
429C2×2−1+4—796no—
430C2×2−1+4—794no—
431C2×2−1+4—791no—
432C2×2−1+4—794no—
433C2×2−1+4—15816no—
434C2×2−1+4C2×D7911yescharacteristic, complemented
435C22×#41—798no—
436C22×#41—798no—
437C22×#41—796no—
438C22×#41—794no—
439C22×#41—791no—
440C22×#41—793no—
441C22×#41—793no—
442C22×#41—15816no—
443C22×#41C2×D7911yescharacteristic, complemented
444C23×Q8—791no—
445C23×Q8—794no—
446C23×D4—793no—
447C24×C4—793no—
448#550—798no—
449#550—798no—
450#550—7924no—
451#550—7924no—
452#550—7924no—
453#550—798no—
454#550—7924no—
455#550C2×D7918yescomplemented
456#548—798no—
457#548—798no—
458#548—7924no—
459#548—7924no—
460#548—7924no—
461#548—798no—
462#548—7924no—
463#548C2×D7918yescomplemented
464#535—796no—
465#535—796no—
466#535—7912no—
467#535—7912no—
468#535—7924no—
469#535—7924no—
470#535—796no—
471#535C2×D7916yescomplemented
472C2×#127—7912no—
473C2×#124—7912no—
474#525—796no—
475#525—796no—
476#525—7912no—
477#525—7912no—
478#525—7912no—
479#525—7912no—
480#525—7924no—
481#525—796no—
482#525C2×D7916yescomplemented
483C2×#123—794no—
484C2×C22⋊Q8—7912no—
485C2×#121—7912no—
486C2×#121—7924no—
487C2×#120—7912no—
488#519—791no—
489#519—798no—
490#519—796no—
491#519C2×D7911yescharacteristic, complemented
492C2×C4×Q8—798no—
493C2×C4×D4—7924no—
494C2×#117—796no—
495C25—793no—
4962−1+4—28no—
4972−1+4—15832no—
4982−1+4—15832no—
4992−1+4—15848no—
5002−1+4—1588no—
501C2×#41—28no—
502C2×#41—796no—
503C2×#41—798no—
504C2×#41—794no—
505C2×#41—7912no—
506C2×#41—796no—
507C2×#41—7924no—
508C2×#41—7912no—
509C2×#41—7912no—
510C2×#41—796no—
511C2×#41—7924no—
512C2×#41—7912no—
513C2×#41—15824no—
514C2×#41—15848no—
515C2×#41—15824no—
516C2×#41—15864no—
517C2×#41—15864no—
518C2×#41—15832no—
519C2×#41—1588no—
520C2×#41C22×D7916yes—
521C2×#41C22×D7918yes—
522C2×#41C22×D7914yescomplemented
523C22×Q8—7916no—
524C22×Q8—794no—
525C22×Q8—794no—
526C22×Q8—796no—
527C22×Q8—7912no—
528C22×Q8—794no—
529C22×Q8—793no—
530C22×Q8—7912no—
531C22×Q8—15832no—
532C22×Q8C22×D7911yescharacteristic
533C22×Q8C22×D7914yescomplemented
534C22×D4—7924no—
535C22×D4—796no—
536C22×D4—794no—
537C22×D4—7912no—
538C22×D4—796no—
539C22×D4—7912no—
540C22×D4—793no—
541C22×D4—15824no—
542C22×D4C22×D7913yes—
543C23×C4—793no—
544C23×C4—793no—
545C23×C4—7912no—
546C23×C4—7912no—
547C23×C4—791no—
548C23×C4—793no—
549C23×C4—7912no—
550C23×C4—793no—
551C23×C4—15824no—
552C23×C4C22×D7913yes—
553#127—7912no—
554#127—7912no—
555#127—7948no—
556#127—7912no—
557#127C22×D79112yescomplemented
558#124—7912no—
559#124—7912no—
560#124—7948no—
561#124—7912no—
562#124C22×D79112yescomplemented
563#123—794no—
564#123—794no—
565#123—798no—
566#123—798no—
567#123—794no—
568#123C22×D7914yes—
569C22⋊Q8—7912no—
570C22⋊Q8—7912no—
571C22⋊Q8—7924no—
572C22⋊Q8—7912no—
573C22⋊Q8—7924no—
574C22⋊Q8C22×D79112yescomplemented
575#121—7912no—
576#121—7924no—
577#121—7924no—
578#121—7948no—
579#121—7912no—
580#121—7924no—
581#121—7912no—
582#121—7924no—
583#121—7924no—
584#121—7948no—
585#121C22×D79112yescomplemented
586#121C22×D79124yescomplemented
587#120—7912no—
588#120—7912no—
589#120—7924no—
590#120—7924no—
591#120—7912no—
592#120C22×D79112yes—
593C4×Q8—798no—
594C4×Q8—7924no—
595C4×Q8—7924no—
596C4×Q8C22×D7918yescomplemented
597C4×D4—7924no—
598C4×D4—7924no—
599C4×D4—7924no—
600C4×D4—7924no—
601C4×D4—7924no—
602C4×D4—7924no—
603C4×D4—7924no—
604C4×D4C22×D79124yescomplemented
605#117—796no—
606#117—7912no—
607#117—7912no—
608#117—7912no—
609#117C22×D7916yes—
610C2×C4⋊C4—7912no—
611C2×C4⋊C4—798no—
612C2×C22⋊C4—794no—
613C2×C22⋊C4—798no—
614C2×C22⋊C4—7924no—
615C2×C42—7912no—
616C24—31612no—
617C24—796no—
618C24—793no—
619C24—791no—
620C24—796no—
621C24—794no—
622C24—15812no—
623C24C23×D7913yes—
624#41—232no—
625#41—216no—
626#41—224no—
627#41—15848no—
628#41—15896no—
629#41—15848no—
630#41—15848no—
631#41—15824no—
632#41—15824no—
633#41—15896no—
634#41—15848no—
635#41—15832no—
636#41—15816no—
637#41—15824no—
638C2×Q8—216no—
639C2×Q8—7932no—
640C2×Q8—7932no—
641C2×Q8—7912no—
642C2×Q8—7912no—
643C2×Q8—796no—
644C2×Q8—7924no—
645C2×Q8—15848no—
646C2×Q8—15824no—
647C2×Q8—15848no—
648C2×Q8—15816no—
649C2×Q8D4×D7918yescomplemented
650C2×Q8C23×D7916yes—
651C2×Q8C23×D7914yes—
652C2×D4—212no—
653C2×D4—31648no—
654C2×D4—7924no—
655C2×D4—7924no—
656C2×D4—794no—
657C2×D4—794no—
658C2×D4—7924no—
659C2×D4—7912no—
660C2×D4—7924no—
661C2×D4—794no—
662C2×D4—7912no—
663C2×D4—796no—
664C2×D4—15848no—
665C2×D4—15848no—
666C2×D4—15824no—
667C2×D4—15824no—
668C2×D4—15816no—
669C2×D4—15812no—
670C2×D4C23×D7914yes—
671C2×D4C23×D79112yes—
672C2×D4C23×D7916yes—
673C2×D4C23×D79124yes—
674C22×C4—212no—
675C22×C4—793no—
676C22×C4—796no—
677C22×C4—796no—
678C22×C4—7924no—
679C22×C4—7912no—
680C22×C4—7912no—
681C22×C4—791no—
682C22×C4—798no—
683C22×C4—794no—
684C22×C4—792no—
685C22×C4—7912no—
686C22×C4—7912no—
687C22×C4—7912no—
688C22×C4—7912no—
689C22×C4—792no—
690C22×C4—15812no—
691C22×C4—15848no—
692C22×C4—15848no—
693C22×C4—15848no—
694C22×C4—1584no—
695C22×C4—15812no—
696C22×C4—15812no—
697C22×C4C23×D79112yes—
698C22×C4C23×D79112yes—
699C22×C4C23×D7911yescharacteristic
700C22×C4C23×D7913yes—
701C4⋊C4—7924no—
702C4⋊C4—798no—
703C4⋊C4—798no—
704C4⋊C4—7912no—
705C4⋊C4—798no—
706C4⋊C4C23×D79112yes—
707C4⋊C4C23×D7918yes—
708C22⋊C4—794no—
709C22⋊C4—798no—
710C22⋊C4—7924no—
711C22⋊C4—798no—
712C22⋊C4—798no—
713C22⋊C4—798no—
714C22⋊C4—7924no—
715C22⋊C4—7924no—
716C22⋊C4C23×D7914yes—
717C22⋊C4C23×D7918yes—
718C22⋊C4C23×D79124yes—
719C42—7924no—
720C42—7912no—
721C42C23×D79112yes—
722C23—26no—
723C23—46no—
724C23—3166no—
725C23—31612no—
726C23—31648no—
727C23—791no—
728C23—791no—
729C23—794no—
730C23—796no—
731C23—794no—
732C23—1588no—
733C23—15812no—
734C23—15812no—
735C23—15816no—
736C23—15824no—
737C23—1584no—
738C23—1586no—
739C23C24×D7916yes—
740C23C24×D7914yes—
741C23C24×D7911yescharacteristic
742Q8—212no—
743Q8—7948no—
744Q8—15824no—
745Q8—15812no—
746Q8C2×D4×D79116yes—
747D4—28no—
748D4—224no—
749D4—212no—
750D4—424no—
751D4—31624no—
752D4—31624no—
753D4—31624no—
754D4—1588no—
755D4—15848no—
756D4—15824no—
757D4—1588no—
758D4—1588no—
759D4—15824no—
760D4—15812no—
761C2×C4—22no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—796no—
765C2×C4—7912no—
766C2×C4—7924no—
767C2×C4—7924no—
768C2×C4—798no—
769C2×C4—794no—
770C2×C4—792no—
771C2×C4—15824no—
772C2×C4—15824no—
773C2×C4—1584no—
774C2×C4—1584no—
775C2×C4—1588no—
776C2×C4—15816no—
777C2×C4—15824no—
778C2×C4—15824no—
779C2×C4—1582no—
780C2×C4—15824no—
781C2×C4—15824no—
782C2×C4C2×D4×D79112yes—
783C2×C4C24×D7918yes—
784C2×C4C24×D7914yes—
785C2×C4C24×D7912yes—
786C2×C4C24×D7916yes—
787C22—22no—
788C22—24no—
789C22—26no—
790C22—28no—
791C22—212no—
792C22—412no—
793C22—31612no—
794C22—31624no—
795C22—31616no—
796C22—31624no—
797C22—792no—
798C22—794no—
799C22—792no—
800C22—1588no—
801C22—1584no—
802C22—1586no—
803C22—1588no—
804C22—15812no—
805C22—1582no—
806C22C22×D4×D7912yes—
807C22C25×D7911yescharacteristic
808C4—22no—
809C4—24no—
810C4—28no—
811C4—7912no—
812C4—1582no—
813C4—1584no—
814C4—1588no—
815C4C22×D4×D79112yes—
816C2—22no—
817C2—46no—
818C2—44no—
819C2—3166no—
820C2—3164no—
821C2—794no—
822C2—1582no—
823C2C23×D4×D7911yescharacteristic
824C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3487C2
hypercenter#3487D79
hypocenterC79C2×#3487
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3487

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D79C2semidirect
2. C22×#41×D79C2semidirect
3. #23777059C2semidirect
4. #23777058C2semidirect
5. #23777057C2semidirect
6. #23777056C2semidirect
7. #23777055C2semidirect
8. #23777054C2semidirect
9. #23777053C2semidirect
10. #550×D79C2semidirect
11. #548×D79C2semidirect
12. #535×D79C2semidirect
13. #525×D79C2semidirect
14. #519×D79C2semidirect
15. C79×#3487C2semidirect
16. C2×#14579209C22semidirect
17. C2×#14579209C22semidirect
18. C2×#14579208C22semidirect
19. C2×#14579208C22semidirect
21. C22×#11929625C22semidirect
22. C22×#11929624C22semidirect
23. C22×#11929623C22semidirect
27. C2×#41×D79C22semidirect
28. C2×#41×D79C22semidirect
30. C22×Q8×D79C22semidirect
33. #19099235C22semidirect
34. #19099234C22semidirect
35. #19099233C22semidirect
36. #19099232C22semidirect
37. #19099232C22semidirect
38. #19099231C22semidirect
39. #19099231C22semidirect
40. #19099225C22semidirect
41. #19099224C22semidirect
42. #19099223C22semidirect
43. #19099222C22semidirect
44. #19099221C22semidirect
45. #19099220C22semidirect
46. #19099219C22semidirect
47. #19099132C22semidirect
48. #19099131C22semidirect
49. #19099130C22semidirect
50. #19099129C22semidirect
51. #19099128C22semidirect
52. #19099127C22semidirect
53. #19099126C22semidirect
54. #127×D79C22semidirect
55. #124×D79C22semidirect
56. #19099076C22semidirect
57. #19099075C22semidirect
58. #19099074C22semidirect
59. #19099073C22semidirect
60. #19099072C22semidirect
61. #19099071C22semidirect
62. #19099070C22semidirect
63. #19099069C22semidirect
65. C22⋊Q8×D79C22semidirect
66. #121×D79C22semidirect
67. #121×D79C22semidirect
69. #19099041C22semidirect
70. #19099040C22semidirect
71. #19099039C22semidirect
72. C4×Q8×D79C22semidirect
73. C4×D4×D79C22semidirect
75. C2×2−1+4×C79C22semidirect
76. C22×#41×C79C22semidirect
77. #550×C79C22semidirect
78. #548×C79C22semidirect
79. #535×C79C22semidirect
80. #525×C79C22semidirect
81. #519×C79C22semidirect
90. C2×#11929625C23semidirect
95. C2×#11929624C23semidirect
100. C2×#11929623C23semidirect
106. C22×Dic158C23semidirect
108. C2×Q8×D79D4semidirect
112. C2×Q8×D79C23semidirect
113. C2×Q8×D79C23semidirect
131. #14579158C23semidirect
132. #14579157C23semidirect
133. #14579157C23semidirect
134. #14579157C23semidirect
135. #14579150C23semidirect
136. #14579149C23semidirect
137. #14579148C23semidirect
138. #14579147C23semidirect
144. #14579141C23semidirect
145. #14579140C23semidirect
146. #14579139C23semidirect
147. #14579138C23semidirect
148. #14579137C23semidirect
149. #14579136C23semidirect
150. #14579136C23semidirect
151. #14579135C23semidirect
152. #14579135C23semidirect
153. #14579134C23semidirect
154. #14579134C23semidirect
155. #14579133C23semidirect
156. #14579133C23semidirect
157. #14579132C23semidirect
158. #14579132C23semidirect
164. Q8×Dic79C23semidirect
165. C4×Dic158C23semidirect
166. #14579126C23semidirect
167. C4×D316C23semidirect
168. D4×Dic79C23semidirect
169. #14579123C23semidirect
170. C4×C22⋊D79C23semidirect
171. C4×C22⋊D79C23semidirect
172. (C22⋊D79)⋊C4C23semidirect
173. (C22⋊D79)⋊C4C23semidirect
188. C2×#41×C79C23semidirect
190. C22×Q8×C79C23semidirect
193. #127×C79C23semidirect
194. #124×C79C23semidirect
196. C22⋊Q8×C79C23semidirect
197. #121×C79C23semidirect
198. #121×C79C23semidirect
200. C4×Q8×C79C23semidirect
201. C4×D4×C79C23semidirect
222. C2×Dic158C2×D4semidirect
230. Q8×D79C2×D4semidirect
290. C2×Q8×C79C2×D4semidirect
412. D79#3487direct (N × H)
422. #3487D79direct (N × H)
428. C79C2×#3487semidirect
434. C2×2−1+4C2×D79semidirect
443. C22×#41C2×D79semidirect
455. #550C2×D79semidirect
463. #548C2×D79semidirect
471. #535C2×D79semidirect
482. #525C2×D79semidirect
491. #519C2×D79semidirect
522. C2×#41C22×D79semidirect
533. C22×Q8C22×D79semidirect
557. #127C22×D79semidirect
562. #124C22×D79semidirect
574. C22⋊Q8C22×D79semidirect
585. #121C22×D79semidirect
586. #121C22×D79semidirect
596. C4×Q8C22×D79semidirect
604. C4×D4C22×D79semidirect
649. C2×Q8D4×D79semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D792
C22×#41×D792
#237770592
#237770582
#237770572
#237770562
#237770552
#237770542
#237770532
#550×D792
#548×D792
#535×D792
#525×D792
#519×D792
C79×#34872
C2×#348779