Finite Group Databasebeta

← #35197004

Subgroups — #35197004

Order 20224.

6670 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778028C216yesmaximal, complemented
2#23778018C216yesmaximal, complemented
3#23777956C216yesmaximal, complemented
4#23777946C216yesmaximal, complemented
5#23777468C2112yesmaximal, complemented
6#23777454C2112yesmaximal, complemented
7#23777101C216yesmaximal, complemented
8#23777083C216yesmaximal, complemented
9#23776696C211yesmaximal, characteristic, complemented
10C22×#14579155C211yesmaximal, characteristic, complemented
11C79×#3444C211yesmaximal, characteristic, complemented
12#19099315C22112yescomplemented
13#19099312C22112yescomplemented
14#19099304C2214yescomplemented
15#19099300C2214yescomplemented
16#19099285C22112yescomplemented
17#19099281C22112yescomplemented
18#19099272C22112yescomplemented
19#19099267C22112yescomplemented
20#19099262C22112yescomplemented
21#19099262C22112yescomplemented
22#19099257C22112yescomplemented
23#19099256C22112yescomplemented
24#19099254C22112yescomplemented
25#19099250C22112yescomplemented
26#19099246C22112yescomplemented
27#19099246C22112yescomplemented
28#19099242C22112yescomplemented
29#19099242C22112yescomplemented
30#19099240C22112yescomplemented
31#19099237C22112yescomplemented
32#19099237C22112yescomplemented
33#19099236C22112yescomplemented
34#19099212C22112yescomplemented
35#19099211C22112yescomplemented
36#19099208C22112yescomplemented
37#19099205C22112yescomplemented
38#19099202C22112yescomplemented
39#19099201C22112yescomplemented
40#19099192C2216yescomplemented
41#19099188C2216yescomplemented
42#19099185C22112yescomplemented
43#19099177C22112yescomplemented
44#19099172C22112yescomplemented
45#19099171C22112yescomplemented
46#19099162C2216yescomplemented
47#19099161C22112yescomplemented
48#19099158C2216yescomplemented
49#19099155C22112yescomplemented
50#19099155C22112yescomplemented
51#19099153C2216yes—
52#19099150C2216yes—
53#19099147C22112yescomplemented
54#19099146C22112yes—
55#19099146C22112yescomplemented
56#19099140C2216yescomplemented
57#19099121C2216yescomplemented
58#19099120C2213yescomplemented
59#19099113C2213yescomplemented
60#19099097C2216yescomplemented
61#19099097C2216yescomplemented
62#19099097C22112yescomplemented
63#19099096C22112yescomplemented
64C2×#14579155C2216yescomplemented
65C2×#14579155C2216yescomplemented
66C2×#14579155C2216yescomplemented
67C2×#14579155C2216yescomplemented
68C2×#14579155C2214yescomplemented
69#126×D79C2214yescomplemented
70#19099074C2216yescomplemented
71#19099069C22112yescomplemented
72#120×D79C2214yes—
73#19099042C22112yescomplemented
74#19099035C22112yescomplemented
75C4×#11929624C2216yescomplemented
76C22×Dic79⋊C4C2213yescomplemented
77C22×(C2×D79)⋊C4C2213yes—
78#533×C79C2213yescomplemented
79#532×C79C2213yescomplemented
80#529×C79C2216yescomplemented
81#529×C79C2216yescomplemented
82#525×C79C2216yescomplemented
83C4×#41×C79C2216yescomplemented
84C22×C42×C79C2211yescharacteristic, complemented
85C24×D79C2311yescharacteristic
86C2×#11929624C2316yes—
87C2×#11929623C23112yes—
88C2×D4×D79C23112yes—
89C23×Dic79C2313yes—
90#14579161C2313yescomplemented
91#14579160C23112yescomplemented
92#14579159C23112yescomplemented
93#14579158C2311yescharacteristic, complemented
94#14579156C23112yes—
95#14579156C23112yes—
96#14579156C23112yes—
97#14579156C23112yescomplemented
98#14579155C23112yes—
99#14579155C23112yes—
100#14579155C23112yes—
101#14579155C23112yes—
102#14579155C23112yes—
103#14579155C2314yes—
104#14579155C2314yes—
105#14579155C2314yes—
106#14579155C2314yes—
107#14579155C23112yescomplemented
108#14579155C2314yescomplemented
109#14579155C2314yescomplemented
110#14579154C23112yescomplemented
111#14579154C23112yescomplemented
112#14579153C2316yescomplemented
113#14579153C23112yescomplemented
114#14579152C23112yescomplemented
115#14579151C23112yescomplemented
116#14579151C23112yescomplemented
117#14579151C23112yescomplemented
118#14579151C23112yescomplemented
119#14579150C23112yes—
120#14579149C23112yes—
121#14579149C2316yescomplemented
122#14579147C23112yes—
123#14579147C23112yes—
124#14579146C23112yes—
125#14579146C23112yes—
126#14579146C23112yes—
127#14579146C23112yescomplemented
128#14579145C23112yes—
129#14579145C23112yes—
130#14579144C23112yes—
131#14579144C23112yes—
132#14579144C23112yescomplemented
133#14579143C23112yes—
134#14579143C23112yescomplemented
135#14579142C23112yes—
136#14579142C23112yescomplemented
137#14579141C23112yes—
138#14579140C2316yes—
139#14579140C2316yes—
140#14579140C23112yescomplemented
141#14579139C23112yes—
142#14579139C23112yes—
143#14579139C23112yescomplemented
144#14579139C23112yescomplemented
145#14579138C23112yes—
146#14579138C23112yes—
147#14579138C23112yescomplemented
148#14579138C23112yescomplemented
149#14579137C23112yes—
150#14579137C23112yescomplemented
151#14579136C23112yes—
152#14579135C2316yes—
153#14579135C23112yes—
154#14579135C2316yes—
155#14579134C23112yes—
156#14579134C23112yescomplemented
157#14579133C23112yes—
158#14579133C23112yes—
159#14579133C23112yes—
160#14579133C23112yescomplemented
161#14579131C23112yes—
162#14579131C23112yes—
163#14579130C2314yes—
164#14579129C23112yes—
165#14579129C23112yes—
166C4×Dic158C23112yescomplemented
167C4×Dic158C2316yescomplemented
168C4×Dic158C2316yescomplemented
169#14579126C23112yescomplemented
170C4×D316C23112yes—
171C4×D316C2316yescomplemented
172C4×D316C2316yescomplemented
173D4×Dic79C23112yes—
174D4×Dic79C23112yes—
175#14579123C23112yes—
176C4×C22⋊D79C23112yes—
177C4×C22⋊D79C23112yes—
178C4×C22⋊D79C23112yes—
179C4×C22⋊D79C23112yescomplemented
180(C22⋊D79)⋊C4C23112yes—
181(C22⋊D79)⋊C4C23112yes—
182(C22⋊D79)⋊C4C23112yes—
183(C22⋊D79)⋊C4C23112yescomplemented
184#14579120C2316yes—
185#14579119C23112yes—
186#14579118C23112yes—
187#14579118C23112yescomplemented
188#14579118C23112yescomplemented
189#14579117C23112yes—
190#14579117C23112yescomplemented
191C2×Dic79⋊C4C2316yes—
192C2×Dic79⋊C4C2316yes—
193C2×Dic79⋊C4C2316yes—
194C2×Dic79⋊C4C2316yes—
195C2×Dic79⋊C4C2316yes—
196C2×Dic79⋊C4C2316yes—
197C2×Dic79⋊C4C23112yescomplemented
198C4⋊C4×D79C23112yescomplemented
199C2×(C2×D79)⋊C4C2316yes—
200C2×(C2×D79)⋊C4C23112yes—
201C2×(C2×D79)⋊C4C2316yes—
202C2×(C2×D79)⋊C4C2316yes—
203C2×(C2×D79)⋊C4C2316yes—
204C2×(C2×D79)⋊C4C2316yes—
205C2×(C2×D79)⋊C4C2316yes—
206C22⋊C4×D79C23112yes—
207C22⋊C4×D79C23112yes—
208C42×D79C2314yescomplemented
209C2×#41×C79C2316yes—
210C23×C4×C79C2313yes—
211C4⋊Q8×C79C2313yescomplemented
212#127×C79C2311yescharacteristic, complemented
213#126×C79C2314yescomplemented
214#126×C79C2314yescomplemented
215#125×C79C2316yescomplemented
216#124×C79C2316yescomplemented
217#123×C79C23112yes—
218C22⋊Q8×C79C2316yes—
219C22⋊Q8×C79C2316yes—
220#121×C79C2316yes—
221#121×C79C2316yes—
222#120×C79C2314yes—
223C4×Q8×C79C2316yescomplemented
224C4×Q8×C79C2316yescomplemented
225C4×D4×C79C23112yes—
226C4×D4×C79C23112yes—
227C4×D4×C79C2316yescomplemented
228C4×D4×C79C2316yescomplemented
229#117×C79C2316yes—
230#117×C79C23112yescomplemented
231C2×C42×C79C2313yes—
232C2×C42×C79C2313yes—
233C2×C42×C79C2313yes—
234C2×C42×C79C2313yes—
235C2×C42×C79C2314yescomplemented
236C23×D79—46no—
237C23×D79C2416yes—
238C23×D79C2414yes—
239#11929624—412no—
240#11929623—424no—
241C2×Dic158C24112yes—
242C2×Dic158C2416yes—
243C2×D316C2416yes—
244C2×D316C24112yes—
245C2×C22⋊D79C24112yes—
246C2×C22⋊D79C24112yes—
247C2×C22⋊D79C24112yes—
248D4×D79—424no—
249C22×Dic79—46no—
250C22×Dic79C2416yes—
251C22×Dic79C24112yes—
252C22×Dic79C2416yes—
253C22×Dic79C2416yes—
254C2×C4×D79C24112yes—
255C2×C4×D79C24112yes—
256C2×C4×D79C24112yes—
257C4⋊Dic79C24112yes—
258C4⋊Dic79C24112yes—
259C4⋊Dic79C2416yes—
260C4⋊Dic79C2416yes—
261Dic79⋊C4C24112yes—
262Dic79⋊C4C24112yes—
263Dic79⋊C4C24112yes—
264Dic79⋊C4C24112yes—
265Dic79⋊C4C24112yes—
266Dic79⋊C4C24112yes—
267Dic79⋊C4C24112yes—
268Dic79⋊C4C24112yes—
269Dic79⋊C4C24112yes—
270Dic79⋊C4C24112yes—
271C22⋊Dic79C24112yes—
272C22⋊Dic79C24112yes—
273C22⋊Dic79C24112yes—
274(C2×D79)⋊C4C24112yes—
275(C2×D79)⋊C4C24112yes—
276(C2×D79)⋊C4C24112yes—
277(C2×D79)⋊C4C24112yes—
278(C2×D79)⋊C4C24112yes—
279(C2×D79)⋊C4C24112yes—
280(C2×D79)⋊C4C24112yes—
281(C2×D79)⋊C4C24112yes—
282(C2×D79)⋊C4C24112yes—
283(C2×D79)⋊C4C24112yes—
284C4×Dic79C24112yes—
285C4×Dic79C24112yes—
286C4×Dic79C24112yes—
287C24×C79C2411yescharacteristic
288#41×C79—412no—
289C2×Q8×C79C2416yes—
290C2×D4×C79C24112yes—
291C2×D4×C79C2416yes—
292C22×C4×C79—46no—
293C22×C4×C79C2413yes—
294C22×C4×C79C2413yes—
295C22×C4×C79C2413yes—
296C22×C4×C79C2413yes—
297C22×C4×C79C2413yes—
298C22×C4×C79C2413yes—
299C22×C4×C79C24112yes—
300C4⋊C4×C79C2416yes—
301C4⋊C4×C79C2416yes—
302C4⋊C4×C79C24112yes—
303C4⋊C4×C79C24112yes—
304C22⋊C4×C79C24112yes—
305C22⋊C4×C79C24112yes—
306C22⋊C4×C79C24112yes—
307C42×C79C2411yescharacteristic
308C42×C79C2413yes—
309C42×C79C2413yes—
310C42×C79C2413yes—
311C42×C79C2413yes—
312C42×C79C2411yescharacteristic
313C42×C79C2411yescharacteristic
314C42×C79C2411yescharacteristic
315C42×C79C24112yes—
316C23×C79—26no—
317C23×C79C2514yes—
318C23×C79C2513yes—
319C22×D79—212no—
320C22×D79—46no—
321C22×D79—46no—
322C22×D79—412no—
323C22×D79—88no—
324C22×D79C2514yes—
325C22×D79C2514yes—
326Q8×C79—46no—
327D4×C79—224no—
328D4×C79—46no—
329C2×C4×C79—26no—
330C2×C4×C79—26no—
331C2×C4×C79—43no—
332C2×C4×C79—43no—
333C2×C4×C79—43no—
334C2×C4×C79—43no—
335C2×C4×C79—412no—
336C2×C4×C79C2513yes—
337C2×C4×C79C25112yes—
338C2×C4×C79C2513yes—
339C2×C4×C79C2513yes—
340C2×C4×C79C2513yes—
341C22⋊D79—224no—
342C22⋊D79—412no—
343C22⋊D79—412no—
344C2×Dic79—212no—
345C2×Dic79—46no—
346C2×Dic79—46no—
347C2×Dic79—412no—
348C2×Dic79C25112yes—
349C2×Dic79C25112yes—
350D316—412no—
351D316—46no—
352C4×D79—412no—
353C4×D79—412no—
354C4×D79—412no—
355Dic158—412no—
356Dic158—46no—
357C22×C79—28no—
358C22×C79—23no—
359C22×C79—23no—
360C22×C79—212no—
361C22×C79#58516yes—
362C22×C79C2611yescharacteristic
363C2×D79—212no—
364C2×D79—212no—
365C2×D79—812no—
366C2×D79—164no—
367C4×C79—23no—
368C4×C79—23no—
369C4×C79—23no—
370C4×C79—23no—
371C4×C79—212no—
372Dic79—212no—
373Dic79—212no—
374#62826—791nomaximal, Sylow
375C2×C79—26no—
376C2×C79—44no—
377C2×C79C2×#58513yes—
378D79—44no—
379D79—44no—
380#3564—796no—
381#3564—796no—
382#3560—796no—
383#3560—796no—
384#3521—7912no—
385#3521—7912no—
386#3492—796no—
387#3490—796no—
388#3444—791no—
389#3444D7911yescharacteristic, complemented
390C22×#126—791no—
391C79#6282611yescharacteristic, complemented, Sylow
392#563—7912no—
393#563—7912no—
394#560—794no—
395#560—794no—
396#556—7912no—
397#556—7912no—
398#554—7912no—
399#554—7912no—
400#553—7912no—
401#553—7912no—
402#553—7912no—
403#553—7912no—
404#552—7912no—
405#552—7912no—
406#552—7912no—
407#552—7912no—
408#551—7912no—
409#551—7912no—
410#551—7912no—
411#551—7912no—
412#551—7912no—
413#551—7912no—
414#547—7912no—
415#547—7912no—
416#546—7912no—
417#546—7912no—
418#546—7912no—
419#546—7912no—
420#544—796no—
421#543—796no—
422#542—7912no—
423#542—7912no—
424#541—7912no—
425#541—7912no—
426#539—7912no—
427#539—796no—
428#539—796no—
429#539—7912no—
430#539—7912no—
431#538—7912no—
432#538—796no—
433#538—796no—
434#538—7912no—
435#538—7912no—
436#537—796no—
437#534—796no—
438#533—793no—
439#533C2×D7913yescomplemented
440#532—793no—
441#532C2×D7913yescomplemented
442#529—7912no—
443#529—796no—
444#529—796no—
445#529—7912no—
446#529C2×D7916yescomplemented
447#529C2×D7916yescomplemented
448C2×#126—794no—
449C2×#126—796no—
450C2×#126—796no—
451C2×#126—796no—
452C2×#126—796no—
453C2×#126—794no—
454#525—796no—
455#525—7912no—
456#525C2×D7916yescomplemented
457C2×#120—794no—
458#520—7912no—
459#518—7912no—
460C4×#41—796no—
461C4×#41C2×D7916yescomplemented
462C22×C4⋊C4—793no—
463C22×C22⋊C4—793no—
464C22×C42C2×D7911yescharacteristic, complemented
465C25—791no—
466C2×#41—7912no—
467C2×#41—796no—
468C2×#41C22×D7916yes—
469C22×D4—7912no—
470C23×C4—793no—
471C23×C4C22×D7913yes—
472C4⋊Q8—7912no—
473C4⋊Q8—7912no—
474C4⋊Q8—793no—
475C4⋊Q8C22×D7913yescomplemented
476#127—791no—
477#127C22×D7911yescharacteristic, complemented
478#126—7912no—
479#126—7912no—
480#126—7912no—
481#126—7912no—
482#126—7912no—
483#126—7912no—
484#126—794no—
485#126—794no—
486#126—7912no—
487#126—7912no—
488#126—7912no—
489#126—7912no—
490#126—794no—
491#126—794no—
492#126—794no—
493#126—7912no—
494#126—7912no—
495#126—794no—
496#126C22×D7914yescomplemented
497#126C22×D7914yescomplemented
498#125—7912no—
499#125—7912no—
500#125—7912no—
501#125—7912no—
502#125—7912no—
503#125—796no—
504#125—7912no—
505#125C22×D7916yescomplemented
506#124—7912no—
507#124—7912no—
508#124—7912no—
509#124—796no—
510#124—7912no—
511#124C22×D7916yescomplemented
512#123—7912no—
513#123—7912no—
514#123—7912no—
515#123—7912no—
516#123—7912no—
517#123—7912no—
518#123—7912no—
519#123—7912no—
520#123—7912no—
521#123—7912no—
522#123—7912no—
523#123—7912no—
524#123—7912no—
525#123C22×D79112yes—
526C22⋊Q8—7912no—
527C22⋊Q8—7912no—
528C22⋊Q8—796no—
529C22⋊Q8—796no—
530C22⋊Q8—7912no—
531C22⋊Q8—7912no—
532C22⋊Q8—7912no—
533C22⋊Q8—7912no—
534C22⋊Q8—7912no—
535C22⋊Q8—7912no—
536C22⋊Q8—7912no—
537C22⋊Q8—7912no—
538C22⋊Q8—7912no—
539C22⋊Q8—7912no—
540C22⋊Q8C22×D7916yes—
541C22⋊Q8C22×D7916yes—
542#121—7912no—
543#121—7912no—
544#121—7912no—
545#121—7912no—
546#121—796no—
547#121—796no—
548#121—7912no—
549#121—7912no—
550#121—7912no—
551#121—7912no—
552#121C22×D7916yes—
553#121C22×D7916yes—
554#120—794no—
555#120—7912no—
556#120—7912no—
557#120—7912no—
558#120—7912no—
559#120C22×D7914yes—
560C4×Q8—7912no—
561C4×Q8—796no—
562C4×Q8—796no—
563C4×Q8—7912no—
564C4×Q8C22×D7916yescomplemented
565C4×Q8C22×D7916yescomplemented
566C4×D4—7912no—
567C4×D4—7912no—
568C4×D4—7912no—
569C4×D4—7912no—
570C4×D4—7912no—
571C4×D4—7912no—
572C4×D4—7912no—
573C4×D4—7912no—
574C4×D4—7912no—
575C4×D4—7912no—
576C4×D4—7912no—
577C4×D4—796no—
578C4×D4—796no—
579C4×D4—7912no—
580C4×D4C22×D79112yes—
581C4×D4C22×D79112yes—
582C4×D4C22×D7916yescomplemented
583C4×D4C22×D7916yescomplemented
584#117—796no—
585#117—7912no—
586#117—7912no—
587#117—7912no—
588#117—7912no—
589#117—7912no—
590#117—7912no—
591#117C22×D7916yes—
592#117C22×D79112yescomplemented
593C2×C4⋊C4—796no—
594C2×C4⋊C4—796no—
595C2×C4⋊C4—796no—
596C2×C4⋊C4—796no—
597C2×C4⋊C4—796no—
598C2×C4⋊C4—796no—
599C2×C4⋊C4—7912no—
600C2×C4⋊C4—7912no—
601C2×C22⋊C4—796no—
602C2×C22⋊C4—796no—
603C2×C22⋊C4—796no—
604C2×C22⋊C4—796no—
605C2×C22⋊C4—796no—
606C2×C22⋊C4—796no—
607C2×C22⋊C4—7912no—
608C2×C22⋊C4—7912no—
609C2×C22⋊C4—7912no—
610C2×C42—794no—
611C2×C42C22×D7913yes—
612C2×C42C22×D7913yes—
613C2×C42C22×D7913yes—
614C2×C42C22×D7913yes—
615C2×C42C22×D7914yescomplemented
616C24—3166no—
617C24—794no—
618C24—796no—
619C24C23×D7911yescharacteristic
620#41—412no—
621#41—31612no—
622#41—31624no—
623C2×Q8—7912no—
624C2×Q8—796no—
625C2×Q8C23×D7916yes—
626C2×D4—31624no—
627C2×D4—7912no—
628C2×D4—7912no—
629C2×D4—7912no—
630C2×D4—7912no—
631C2×D4—796no—
632C2×D4C23×D79112yes—
633C2×D4C23×D7916yes—
634C22×C4—46no—
635C22×C4—3166no—
636C22×C4—796no—
637C22×C4—796no—
638C22×C4—7912no—
639C22×C4—7912no—
640C22×C4—7912no—
641C22×C4—7912no—
642C22×C4—796no—
643C22×C4C23×D7913yes—
644C22×C4C23×D7913yes—
645C22×C4C23×D7913yes—
646C22×C4C23×D7913yes—
647C22×C4C23×D7913yes—
648C22×C4C23×D7913yes—
649C22×C4C23×D79112yes—
650C4⋊C4—7912no—
651C4⋊C4—7912no—
652C4⋊C4—7912no—
653C4⋊C4—7912no—
654C4⋊C4—7912no—
655C4⋊C4—7912no—
656C4⋊C4—7912no—
657C4⋊C4—7912no—
658C4⋊C4—7912no—
659C4⋊C4—7912no—
660C4⋊C4—7912no—
661C4⋊C4—7912no—
662C4⋊C4—796no—
663C4⋊C4—796no—
664C4⋊C4C23×D79112yes—
665C4⋊C4C23×D7916yes—
666C4⋊C4C23×D7916yes—
667C4⋊C4C23×D79112yes—
668C22⋊C4—7912no—
669C22⋊C4—7912no—
670C22⋊C4—7912no—
671C22⋊C4—7912no—
672C22⋊C4—7912no—
673C22⋊C4—7912no—
674C22⋊C4—7912no—
675C22⋊C4—7912no—
676C22⋊C4—7912no—
677C22⋊C4—7912no—
678C22⋊C4—7912no—
679C22⋊C4—7912no—
680C22⋊C4—7912no—
681C22⋊C4C23×D79112yes—
682C22⋊C4C23×D79112yes—
683C22⋊C4C23×D79112yes—
684C42—7912no—
685C42—7912no—
686C42—7912no—
687C42C23×D7911yescharacteristic
688C42C23×D7911yescharacteristic
689C42C23×D7913yes—
690C42C23×D7913yes—
691C42C23×D7913yes—
692C42C23×D7913yes—
693C42C23×D7911yescharacteristic
694C42C23×D7911yescharacteristic
695C42C23×D79112yes—
696C23—26no—
697C23—3166no—
698C23—3166no—
699C23—31612no—
700C23—794no—
701C23—794no—
702C23—6328no—
703C23—15812no—
704C23C24×D7914yes—
705C23C24×D7913yes—
706Q8—46no—
707Q8—3166no—
708Q8—31612no—
709D4—224no—
710D4—46no—
711D4—31612no—
712D4—3166no—
713D4—31612no—
714D4—31612no—
715D4—15824no—
716C2×C4—26no—
717C2×C4—26no—
718C2×C4—43no—
719C2×C4—43no—
720C2×C4—43no—
721C2×C4—43no—
722C2×C4—412no—
723C2×C4—31612no—
724C2×C4—31612no—
725C2×C4—31612no—
726C2×C4—3166no—
727C2×C4—3166no—
728C2×C4—31612no—
729C2×C4—7912no—
730C2×C4—7912no—
731C2×C4—15812no—
732C2×C4C24×D7913yes—
733C2×C4C24×D79112yes—
734C2×C4C24×D7913yes—
735C2×C4C24×D7913yes—
736C2×C4C24×D7913yes—
737C22—28no—
738C22—23no—
739C22—23no—
740C22—212no—
741C22—63212no—
742C22—15812no—
743C22—15812no—
744C22—12644no—
745C22#1909939916yes—
746C22C25×D7911yescharacteristic
747C4—23no—
748C4—23no—
749C4—23no—
750C4—23no—
751C4—212no—
752C4—15812no—
753C4—15812no—
754C2—26no—
755C2—44no—
756C2—3164no—
757C2—3164no—
758C2C2×#1909939913yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3444C2
hypercenter#3444D79
hypocenterC79#62826
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3444

Complements

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

NH ≅ G/Ntype
1. #23778028C2semidirect
2. #23778018C2semidirect
3. #23777956C2semidirect
4. #23777946C2semidirect
5. #23777468C2semidirect
6. #23777454C2semidirect
7. #23777101C2semidirect
8. #23777083C2semidirect
9. #23776696C2semidirect
10. C22×#14579155C2semidirect
11. C79×#3444C2semidirect
12. #19099315C22semidirect
13. #19099312C22semidirect
14. #19099304C22semidirect
15. #19099300C22semidirect
16. #19099285C22semidirect
17. #19099281C22semidirect
18. #19099272C22semidirect
19. #19099267C22semidirect
20. #19099262C22semidirect
21. #19099262C22semidirect
22. #19099257C22semidirect
23. #19099256C22semidirect
24. #19099254C22semidirect
25. #19099250C22semidirect
26. #19099246C22semidirect
27. #19099246C22semidirect
28. #19099242C22semidirect
29. #19099242C22semidirect
30. #19099240C22semidirect
31. #19099237C22semidirect
32. #19099237C22semidirect
33. #19099236C22semidirect
34. #19099212C22semidirect
35. #19099211C22semidirect
36. #19099208C22semidirect
37. #19099205C22semidirect
38. #19099202C22semidirect
39. #19099201C22semidirect
40. #19099192C22semidirect
41. #19099188C22semidirect
42. #19099185C22semidirect
43. #19099177C22semidirect
44. #19099172C22semidirect
45. #19099171C22semidirect
46. #19099162C22semidirect
47. #19099161C22semidirect
48. #19099158C22semidirect
49. #19099155C22semidirect
50. #19099155C22semidirect
53. #19099147C22semidirect
55. #19099146C22semidirect
56. #19099140C22semidirect
57. #19099121C22semidirect
58. #19099120C22semidirect
59. #19099113C22semidirect
60. #19099097C22semidirect
61. #19099097C22semidirect
62. #19099097C22semidirect
63. #19099096C22semidirect
64. C2×#14579155C22semidirect
65. C2×#14579155C22semidirect
66. C2×#14579155C22semidirect
67. C2×#14579155C22semidirect
68. C2×#14579155C22semidirect
69. #126×D79C22semidirect
70. #19099074C22semidirect
71. #19099069C22semidirect
73. #19099042C22semidirect
74. #19099035C22semidirect
75. C4×#11929624C22semidirect
76. C22×Dic79⋊C4C22semidirect
78. #533×C79C22semidirect
79. #532×C79C22semidirect
80. #529×C79C22semidirect
81. #529×C79C22semidirect
82. #525×C79C22semidirect
83. C4×#41×C79C22semidirect
84. C22×C42×C79C22semidirect
90. #14579161C23semidirect
91. #14579160C23semidirect
92. #14579159C23semidirect
93. #14579158C23semidirect
97. #14579156C23semidirect
107. #14579155C23semidirect
108. #14579155C23semidirect
109. #14579155C23semidirect
110. #14579154C23semidirect
111. #14579154C23semidirect
112. #14579153C23semidirect
113. #14579153C23semidirect
114. #14579152C23semidirect
115. #14579151C23semidirect
116. #14579151C23semidirect
117. #14579151C23semidirect
118. #14579151C23semidirect
121. #14579149C23semidirect
127. #14579146C23semidirect
132. #14579144C23semidirect
134. #14579143C23semidirect
136. #14579142C23semidirect
140. #14579140C23semidirect
143. #14579139C23semidirect
144. #14579139C23semidirect
147. #14579138C23semidirect
148. #14579138C23semidirect
150. #14579137C23semidirect
156. #14579134C23semidirect
160. #14579133C23semidirect
166. C4×Dic158C23semidirect
167. C4×Dic158C23semidirect
168. C4×Dic158C23semidirect
169. #14579126C23semidirect
171. C4×D316C23semidirect
172. C4×D316C23semidirect
179. C4×C22⋊D79C23semidirect
183. (C22⋊D79)⋊C4C23semidirect
187. #14579118C23semidirect
188. #14579118C23semidirect
190. #14579117C23semidirect
197. C2×Dic79⋊C4C23semidirect
198. C4⋊C4×D79C23semidirect
208. C42×D79C23semidirect
211. C4⋊Q8×C79C23semidirect
212. #127×C79C23semidirect
213. #126×C79C23semidirect
214. #126×C79C23semidirect
215. #125×C79C23semidirect
216. #124×C79C23semidirect
223. C4×Q8×C79C23semidirect
224. C4×Q8×C79C23semidirect
227. C4×D4×C79C23semidirect
228. C4×D4×C79C23semidirect
230. #117×C79C23semidirect
235. C2×C42×C79C23semidirect
389. #3444D79semidirect
391. C79#62826semidirect
439. #533C2×D79semidirect
441. #532C2×D79semidirect
446. #529C2×D79semidirect
447. #529C2×D79semidirect
456. #525C2×D79semidirect
461. C4×#41C2×D79semidirect
464. C22×C42C2×D79semidirect
475. C4⋊Q8C22×D79semidirect
477. #127C22×D79semidirect
496. #126C22×D79semidirect
497. #126C22×D79semidirect
505. #125C22×D79semidirect
511. #124C22×D79semidirect
564. C4×Q8C22×D79semidirect
565. C4×Q8C22×D79semidirect
582. C4×D4C22×D79semidirect
583. C4×D4C22×D79semidirect
592. #117C22×D79semidirect
615. C2×C42C22×D79semidirect

Maximal subgroups

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

subgroupindex
#237780282
#237780182
#237779562
#237779462
#237774682
#237774542
#237771012
#237770832
#237766962
C22×#145791552
C79×#34442
#6282679