Finite Group Databasebeta

← #35202006

Subgroups — #35202006

Order 20224.

6496 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778097C215yesmaximal, complemented
2#23778096C215yesmaximal, complemented
3#23777968C215yesmaximal, complemented
4#23777965C215yesmaximal, complemented
5#23777962C215yesmaximal, complemented
6#23777922C215yesmaximal, complemented
7#23777810C215yesmaximal, complemented
8#23777758C215yesmaximal, complemented
9#23777752C215yesmaximal, complemented
10#23777548C211yesmaximal, characteristic, complemented
11#23777548C211yesmaximal, characteristic, complemented
12#23777409C215yesmaximal, complemented
13#23777349C215yesmaximal, complemented
14#23777289C215yesmaximal, complemented
15C79×#3531C211yesmaximal, characteristic, complemented
16#19099317C2215yescomplemented
17#19099317C2215yescomplemented
18#19099317C2215yescomplemented
19#19099317C2215yescomplemented
20#19099317C2215yescomplemented
21#19099313C2215yescomplemented
22#19099311C2215yescomplemented
23#19099311C2215yescomplemented
24#19099311C2215yescomplemented
25#19099307C2215yescomplemented
26#19099305C2215yescomplemented
27#19099305C2215yescomplemented
28#19099297C22110yescomplemented
29#19099296C2215yescomplemented
30#19099293C2215yescomplemented
31#19099287C2215yescomplemented
32#19099285C22110yescomplemented
33#19099285C2215yescomplemented
34#19099284C22110yescomplemented
35#19099281C2215yescomplemented
36#19099281C2215yescomplemented
37#19099280C22110yescomplemented
38#19099280C22110yescomplemented
39#19099279C2215yescomplemented
40#19099276C2215yescomplemented
41#19099276C2215yescomplemented
42#19099242C22110yescomplemented
43#19099241C22110yescomplemented
44#19099240C22110yescomplemented
45#19099238C22110yescomplemented
46#19099238C22110yescomplemented
47#19099237C22110yescomplemented
48#19099237C22110yescomplemented
49#19099236C22110yescomplemented
50#19099228C2215yescomplemented
51#19099226C2215yescomplemented
52#19099226C22110yescomplemented
53#19099225C2215yescomplemented
54#19099223C22110yescomplemented
55#19099219C2215yescomplemented
56#19099208C2215yescomplemented
57#19099205C22110yescomplemented
58#19099204C2215yescomplemented
59#19099204C22110yescomplemented
60#19099202C22110yescomplemented
61#19099197C2215yescomplemented
62#19099188C22110yescomplemented
63#19099187C22110yescomplemented
64#19099186C2215yescomplemented
65#19099185C2215yescomplemented
66#19099185C22110yescomplemented
67#19099183C22110yescomplemented
68#19099183C22110yescomplemented
69#19099183C22110yescomplemented
70#19099181C22110yescomplemented
71#19099180C2215yescomplemented
72#19099179C22110yescomplemented
73#19099179C22110yescomplemented
74#19099178C2215yescomplemented
75#19099153C22110yescomplemented
76#19099152C22110yescomplemented
77#19099152C22110yescomplemented
78#19099149C22110yescomplemented
79#19099146C22110yescomplemented
80#19099145C22110yescomplemented
81#19099138C22110yescomplemented
82#19099136C2215yescomplemented
83#19099135C22110yescomplemented
84#19099129C2215yes—
85#19099124C22110yescomplemented
86#19099119C2215yescomplemented
87#19099119C2215yescomplemented
88#19099119C2215yescomplemented
89#19099112C2215yes—
90#19099098C2215yescomplemented
91#19099098C2215yescomplemented
92#19099098C2215yescomplemented
93#19099098C2215yescomplemented
94#19099098C2215yescomplemented
95#19099097C2215yescomplemented
96#19099097C2215yescomplemented
97#19099092C2215yescomplemented
98C2×#14579149C2215yescomplemented
99#124×D79C2215yescomplemented
100#124×D79C2215yescomplemented
101#19099039C2215yescomplemented
102#19099035C2215yescomplemented
103C4×#11929624C2215yescomplemented
104#564×C79C2211yescharacteristic, complemented
105#563×C79C2215yescomplemented
106#563×C79C2215yescomplemented
107#562×C79C2215yescomplemented
108#533×C79C2215yescomplemented
109#529×C79C2215yescomplemented
110#529×C79C2215yescomplemented
111C2×#11929625C2315yes—
112C2×#11929624C2315yes—
113C2×#11929623C2315yes—
114C22×Dic158C2315yes—
115C2×Q8×D79C2315yes—
116C2×Q8×D79C2315yes—
117C22×D316C2315yes—
118C2×D4×D79C2315yes—
119C2×D4×D79C2315yes—
120#14579160C2315yes—
121#14579160C2315yes—
122#14579160C2315yes—
123#14579160C23110yes—
124#14579160C2315yes—
125#14579160C2315yes—
126#14579160C2315yes—
127#14579159C23110yes—
128#14579159C2315yes—
129#14579157C2315yes—
130#14579156C23110yes—
131#14579156C23110yes—
132#14579156C23110yes—
133#14579156C23110yes—
134#14579156C23110yes—
135#14579156C23110yes—
136#14579156C23110yes—
137#14579155C23110yes—
138#14579155C23110yes—
139#14579154C23110yes—
140#14579154C23110yes—
141#14579154C23110yes—
142#14579153C2315yes—
143#14579153C2315yes—
144#14579150C23110yes—
145#14579150C2315yes—
146#14579150C23110yes—
147#14579150C2315yes—
148#14579149C23110yes—
149#14579149C23110yes—
150#14579149C2315yes—
151#14579149C2315yes—
152#14579149C2315yes—
153#14579149C2315yes—
154#14579149C2315yes—
155#14579149C2315yes—
156#14579148C2315yes—
157#14579148C2315yes—
158#14579147C23110yes—
159#14579147C23110yes—
160#14579147C23110yes—
161#14579147C23110yes—
162#14579147C23110yes—
163#14579147C23110yes—
164#14579147C23110yes—
165#14579147C23110yes—
166#14579146C23110yes—
167#14579146C23110yes—
168#14579146C23110yes—
169#14579146C23110yes—
170#14579146C23110yes—
171#14579146C23110yes—
172#14579146C23110yes—
173#14579146C23110yes—
174#14579145C23110yes—
175#14579144C23110yes—
176#14579144C23110yes—
177#14579143C23110yes—
178#14579143C23110yes—
179#14579142C23110yes—
180#14579141C2315yes—
181#14579141C2315yes—
182#14579141C2315yes—
183#14579141C23110yes—
184#14579141C2315yes—
185#14579141C2315yes—
186#14579140C2315yes—
187#14579140C2315yes—
188#14579139C23110yes—
189#14579139C23110yes—
190#14579139C23110yes—
191#14579139C23110yes—
192#14579139C23110yes—
193#14579139C23110yes—
194#14579139C23110yes—
195#14579139C23110yes—
196#14579139C23110yes—
197#14579138C23110yes—
198#14579138C23110yes—
199#14579138C23110yes—
200#14579137C2315yes—
201#14579137C23110yes—
202#14579136C2315yes—
203#14579136C2315yes—
204#14579136C23110yes—
205#14579136C23110yes—
206#14579136C2315yes—
207#14579136C2315yes—
208#14579136C2315yes—
209#14579135C2315yes—
210#14579135C2315yes—
211#14579134C23110yes—
212#14579134C23110yes—
213#14579134C23110yes—
214#14579133C23110yes—
215#14579132C2315yes—
216#14579131C23110yes—
217#14579131C23110yes—
218#14579131C23110yes—
219#14579131C23110yes—
220#14579129C23110yes—
221#14579129C23110yes—
222Q8×Dic79C2315yes—
223C4×Dic158C2315yes—
224C4×Dic158C2315yes—
225C4×Dic158C2315yes—
226C4×Dic158C2315yes—
227#14579126C2315yes—
228#14579126C23110yes—
229#14579126C2315yes—
230#14579126C23110yes—
231#14579126C2315yes—
232#14579126C2315yes—
233#14579126C2315yes—
234C4×D316C2315yes—
235C4×D316C2315yes—
236C4×D316C2315yes—
237C4×D316C2315yes—
238D4×Dic79C2315yes—
239#14579123C23110yes—
240#14579123C2315yes—
241#14579123C2315yes—
242#14579123C2315yes—
243#14579123C2315yes—
244#14579123C2315yes—
245C4×C22⋊D79C23110yes—
246C4×C22⋊D79C2315yes—
247C4×C22⋊D79C23110yes—
248C4×C22⋊D79C2315yes—
249C4×C22⋊D79C2315yes—
250C4×C22⋊D79C2315yes—
251(C22⋊D79)⋊C4C23110yes—
252(C22⋊D79)⋊C4C23110yes—
253(C22⋊D79)⋊C4C23110yes—
254#14579120C2315yes—
255#14579119C2315yes—
256#14579119C2315yes—
257#14579119C2315yes—
258#14579119C2315yes—
259#14579119C23110yes—
260#14579119C2315yes—
261#14579119C2315yes—
262#14579118C23110yes—
263#14579118C2315yes—
264#14579118C23110yes—
265#14579118C2315yes—
266#14579117C23110yes—
267C2×(C2×D79)⋊C4C23110yes—
268C2×(C2×D79)⋊C4C23110yes—
269C22⋊C4×D79C23110yes—
270C22⋊C4×D79C23110yes—
271C22⋊C4×D79C23110yes—
272C22⋊C4×D79C23110yes—
273C42×D79C2315yes—
274C42×D79C2315yes—
275C4⋊Q8×C79C2315yes—
276C4⋊Q8×C79C2315yes—
277#126×C79C23110yes—
278#126×C79C23110yes—
279#125×C79C2315yes—
280#125×C79C2315yes—
281#125×C79C2315yes—
282#125×C79C2315yes—
283#124×C79C2315yes—
284#124×C79C2315yes—
285#123×C79C23110yes—
286#123×C79C23110yes—
287C22⋊Q8×C79C2315yes—
288C22⋊Q8×C79C23110yes—
289C22⋊Q8×C79C2315yes—
290C22⋊Q8×C79C23110yes—
291#121×C79C2315yes—
292#121×C79C2315yes—
293C4×Q8×C79C2315yes—
294C4×Q8×C79C2315yes—
295C4×D4×C79C2315yes—
296C4×D4×C79C2315yes—
297#117×C79C2315yes—
298#117×C79C2315yes—
299C2×C42×C79C2315yes—
300C23×D79C24110yes—
301#11929625—85no—
302#11929624—410no—
303#11929623—85no—
304C2×Dic158—85no—
305C2×Dic158C2415yes—
306C2×Dic158C2415yes—
307C2×Dic158C24110yes—
308C2×Dic158C2415yes—
309C2×Dic158C2415yes—
310C2×Dic158C2415yes—
311Q8×D79—410no—
312Q8×D79—85no—
313C2×D316—85no—
314C2×D316C2415yes—
315C2×D316C24110yes—
316C2×D316C2415yes—
317C2×D316C2415yes—
318C2×D316C2415yes—
319C2×D316C2415yes—
320C2×C22⋊D79C2415yes—
321C2×C22⋊D79C24110yes—
322C2×C22⋊D79C2415yes—
323C2×C22⋊D79C24110yes—
324D4×D79—410no—
325D4×D79—85no—
326C22×Dic79C24110yes—
327C2×C4×D79C2415yes—
328C2×C4×D79C24110yes—
329C2×C4×D79C2415yes—
330C2×C4×D79C24110yes—
331C2×C4×D79C2415yes—
332C2×C4×D79C2415yes—
333C2×C4×D79C2415yes—
334C2×C4×D79C2415yes—
335C4⋊Dic79C2415yes—
336C4⋊Dic79C2415yes—
337C4⋊Dic79C2415yes—
338C4⋊Dic79C2415yes—
339C4⋊Dic79C2415yes—
340C4⋊Dic79C2415yes—
341Dic79⋊C4C24110yes—
342Dic79⋊C4C24110yes—
343Dic79⋊C4C2411yescharacteristic
344Dic79⋊C4C2415yes—
345Dic79⋊C4C2415yes—
346Dic79⋊C4C2415yes—
347Dic79⋊C4C24110yes—
348Dic79⋊C4C24110yes—
349Dic79⋊C4C24110yes—
350Dic79⋊C4C24110yes—
351C22⋊Dic79C2415yes—
352C22⋊Dic79C24110yes—
353C22⋊Dic79C24110yes—
354C22⋊Dic79C2415yes—
355(C2×D79)⋊C4C2415yes—
356(C2×D79)⋊C4C24110yes—
357(C2×D79)⋊C4C24110yes—
358(C2×D79)⋊C4C24110yes—
359(C2×D79)⋊C4C24110yes—
360(C2×D79)⋊C4C24110yes—
361(C2×D79)⋊C4C24110yes—
362(C2×D79)⋊C4C24110yes—
363(C2×D79)⋊C4C2415yes—
364(C2×D79)⋊C4C2415yes—
365(C2×D79)⋊C4C24110yes—
366(C2×D79)⋊C4C24110yes—
367(C2×D79)⋊C4C24110yes—
368(C2×D79)⋊C4C24110yes—
369(C2×D79)⋊C4C2415yes—
370(C2×D79)⋊C4C24110yes—
371C4×Dic79C2415yes—
372C4×Dic79C2415yes—
373C4×Dic79C2415yes—
374C4×Dic79C2415yes—
375C4×Dic79C2415yes—
376C4×Dic79C2415yes—
377C4×Dic79C24110yes—
378C4×Dic79C24110yes—
379C2×Q8×C79C2415yes—
380C2×Q8×C79C2415yes—
381C2×D4×C79C2415yes—
382C2×D4×C79C2415yes—
383C22×C4×C79C2415yes—
384C22×C4×C79C2415yes—
385C22×C4×C79C2415yes—
386C4⋊C4×C79C2415yes—
387C4⋊C4×C79C2415yes—
388C4⋊C4×C79C2415yes—
389C4⋊C4×C79C2415yes—
390C4⋊C4×C79C2415yes—
391C4⋊C4×C79C2415yes—
392C4⋊C4×C79C2415yes—
393C4⋊C4×C79C2415yes—
394C4⋊C4×C79C24110yes—
395C4⋊C4×C79C24110yes—
396C22⋊C4×C79C24110yes—
397C22⋊C4×C79C24110yes—
398C22⋊C4×C79C24110yes—
399C22⋊C4×C79C24110yes—
400C42×C79C2415yes—
401C42×C79C2415yes—
402C42×C79C2415yes—
403C42×C79C2415yes—
404C23×C79C2515yes—
405C22×D79—410no—
406C22×D79—410no—
407C22×D79—410no—
408C22×D79C2515yes—
409C22×D79C2515yes—
410Q8×C79—45no—
411Q8×C79—45no—
412D4×C79—45no—
413D4×C79—45no—
414C2×C4×C79—45no—
415C2×C4×C79—45no—
416C2×C4×C79—45no—
417C2×C4×C79C2515yes—
418C2×C4×C79C2515yes—
419C2×C4×C79C2515yes—
420C2×C4×C79C2515yes—
421C2×C4×C79C2515yes—
422C2×C4×C79C2511yescharacteristic
423C22⋊D79—210no—
424C22⋊D79—410no—
425C22⋊D79—410no—
426C22⋊D79—45no—
427C2×Dic79—410no—
428C2×Dic79C2511yescharacteristic
429C2×Dic79C2515yes—
430C2×Dic79C2515yes—
431C2×Dic79C2515yes—
432C2×Dic79C2515yes—
433C2×Dic79C2511yescharacteristic
434D316—45no—
435D316—45no—
436D316—45no—
437D316—410no—
438D316—45no—
439D316—45no—
440C4×D79—210no—
441C4×D79—45no—
442C4×D79—45no—
443C4×D79—45no—
444C4×D79—410no—
445C4×D79—410no—
446C4×D79—45no—
447C4×D79—45no—
448Dic158—210no—
449Dic158—45no—
450Dic158—410no—
451Dic158—45no—
452Dic158—45no—
453Dic158—45no—
454C22×C79—25no—
455C22×C79—25no—
456C22×C79—25no—
457C22×C79C2611yescharacteristic
458C2×D79—25no—
459C2×D79—25no—
460C2×D79—25no—
461C2×D79—25no—
462C2×D79—25no—
463C2×D79—25no—
464C2×D79—1610no—
465C4×C79—25no—
466C4×C79—25no—
467C4×C79—25no—
468C4×C79—25no—
469C4×C79—21no—
470C4×C79—25no—
471Dic79—25no—
472Dic79—25no—
473Dic79—25no—
474Dic79—25no—
475Dic79—21no—
476Dic79#58512yes—
477#63069—791nomaximal, Sylow
478C2×C79—45no—
479C2×C79C2×#58511yescharacteristic
480C2×C79H(7,𝔽2)11yescharacteristic
481C2×C792−1+611yescharacteristic
482D79—45no—
483D79—45no—
484#3568—795no—
485#3568—795no—
486#3561—795no—
487#3561—795no—
488#3561—795no—
489#3558—795no—
490#3550—795no—
491#3545—795no—
492#3545—795no—
493#3531—791no—
494#3531—791no—
495#3531D7911yescharacteristic, complemented
496#3518—795no—
497#3514—795no—
498#3510—795no—
499C79#6306911yescharacteristic, complemented, Sylow
500#564C2×D7911yescharacteristic, complemented
501#563—795no—
502#563—795no—
503#563—795no—
504#563—795no—
505#563—795no—
506#563—795no—
507#563C2×D7915yescomplemented
508#563C2×D7915yescomplemented
509#562—795no—
510#562—795no—
511#562—795no—
512#562—795no—
513#562C2×D7915yescomplemented
514H(3,𝔽4)—795no—
515H(3,𝔽4)—795no—
516#559—7910no—
517#559—795no—
518Q82—795no—
519#556—795no—
520#556—7910no—
521#556—7910no—
522#556—7910no—
523#556—795no—
524#556—7910no—
525#556—795no—
526#556—795no—
527#555—795no—
528#555—795no—
529#555—795no—
530#551—7910no—
531#551—7910no—
532#551—7910no—
533#551—7910no—
534#551—7910no—
535#551—7910no—
536#551—7910no—
537#551—7910no—
538D4×Q8—795no—
539D4×Q8—795no—
540D4×Q8—7910no—
541#548—7910no—
542#548—795no—
543#548—795no—
544#546—7910no—
545#546—795no—
546#546—7910no—
547#546—7910no—
548#546—795no—
549D42—795no—
550#543—7910no—
551#542—7910no—
552#542—7910no—
553#542—7910no—
554#542—7910no—
555#542—7910no—
556#542—7910no—
557#542—7910no—
558#542—795no—
559#542—795no—
560#542—795no—
561#542—7910no—
562#542—795no—
563#538—7910no—
564#538—7910no—
565#538—7910no—
566#538—7910no—
567#538—7910no—
568#538—7910no—
569#536—7910no—
570#536—7910no—
571#536—795no—
572#535—795no—
573#534—7910no—
574#533—795no—
575#533—795no—
576#533—795no—
577#533C2×D7915yescomplemented
578#532—795no—
579#529—795no—
580#529—795no—
581#529—795no—
582#529—795no—
583#529—795no—
584#529—795no—
585#529—795no—
586#529—795no—
587#529C2×D7915yescomplemented
588#529C2×D7915yescomplemented
589C2×#124—795no—
590C2×#124—795no—
591C2×#124—795no—
592#519—795no—
593#518—795no—
594C4×#41—795no—
595C2×#41—795no—
596C2×#41—795no—
597C2×#41—795no—
598C22×Q8—795no—
599C22×Q8—795no—
600C22×Q8—795no—
601C22×D4—795no—
602C22×D4—795no—
603C22×D4—795no—
604C4⋊Q8—795no—
605C4⋊Q8—7910no—
606C4⋊Q8—795no—
607C4⋊Q8—795no—
608C4⋊Q8—795no—
609C4⋊Q8—795no—
610C4⋊Q8—795no—
611C4⋊Q8—795no—
612C4⋊Q8—7910no—
613C4⋊Q8C22×D7915yes—
614C4⋊Q8C22×D7915yes—
615#127—795no—
616#126—7910no—
617#126—7910no—
618#126—7910no—
619#126—7910no—
620#126—7910no—
621#126—7910no—
622#126—7910no—
623#126—7910no—
624#126—7910no—
625#126—7910no—
626#126—7910no—
627#126—7910no—
628#126C22×D79110yes—
629#126C22×D79110yes—
630#125—795no—
631#125—795no—
632#125C22×D7915yes—
633#125C22×D7915yes—
634#125C22×D7915yes—
635#125C22×D7915yes—
636#124—795no—
637#124—795no—
638#124—7910no—
639#124—7910no—
640#124—795no—
641#124—795no—
642#124—7910no—
643#124—7910no—
644#124—7910no—
645#124—7910no—
646#124—7910no—
647#124—7910no—
648#124—7910no—
649#124—7910no—
650#124—795no—
651#124—795no—
652#124—795no—
653#124—7910no—
654#124—7910no—
655#124—795no—
656#124—795no—
657#124—795no—
658#124C22×D7915yes—
659#124C22×D7915yes—
660#123—7910no—
661#123—7910no—
662#123—7910no—
663#123—7910no—
664#123—7910no—
665#123—7910no—
666#123—7910no—
667#123—7910no—
668#123—7910no—
669#123—7910no—
670#123—7910no—
671#123—7910no—
672#123—7910no—
673#123—7910no—
674#123C22×D79110yes—
675#123C22×D79110yes—
676C22⋊Q8—795no—
677C22⋊Q8—7910no—
678C22⋊Q8—795no—
679C22⋊Q8—795no—
680C22⋊Q8—795no—
681C22⋊Q8—795no—
682C22⋊Q8—795no—
683C22⋊Q8—795no—
684C22⋊Q8—795no—
685C22⋊Q8—7910no—
686C22⋊Q8—7910no—
687C22⋊Q8—7910no—
688C22⋊Q8—7910no—
689C22⋊Q8—7910no—
690C22⋊Q8—7910no—
691C22⋊Q8—7910no—
692C22⋊Q8—7910no—
693C22⋊Q8—7910no—
694C22⋊Q8—7910no—
695C22⋊Q8—7910no—
696C22⋊Q8—7910no—
697C22⋊Q8—7910no—
698C22⋊Q8C22×D7915yes—
699C22⋊Q8C22×D7915yes—
700C22⋊Q8C22×D79110yes—
701C22⋊Q8C22×D79110yes—
702#121—795no—
703#121—7910no—
704#121—795no—
705#121—795no—
706#121—795no—
707#121—795no—
708#121—795no—
709#121—795no—
710#121—795no—
711#121—7910no—
712#121—7910no—
713#121—7910no—
714#121—7910no—
715#121—7910no—
716#121C22×D7915yes—
717#121C22×D7915yes—
718#120—7910no—
719#120—7910no—
720#120—7910no—
721#120—7910no—
722#120—7910no—
723#120—7910no—
724C4×Q8—795no—
725C4×Q8—795no—
726C4×Q8—7910no—
727C4×Q8—795no—
728C4×Q8—795no—
729C4×Q8—795no—
730C4×Q8—795no—
731C4×Q8—7910no—
732C4×Q8—795no—
733C4×Q8—795no—
734C4×Q8—795no—
735C4×Q8—795no—
736C4×Q8C22×D7915yes—
737C4×Q8C22×D7915yes—
738C4×D4—795no—
739C4×D4—795no—
740C4×D4—795no—
741C4×D4—795no—
742C4×D4—795no—
743C4×D4—7910no—
744C4×D4—7910no—
745C4×D4—795no—
746C4×D4—795no—
747C4×D4—795no—
748C4×D4—795no—
749C4×D4—795no—
750C4×D4—7910no—
751C4×D4—7910no—
752C4×D4—7910no—
753C4×D4—7910no—
754C4×D4—795no—
755C4×D4—795no—
756C4×D4—795no—
757C4×D4—795no—
758C4×D4C22×D7915yes—
759C4×D4C22×D7915yes—
760#117—795no—
761#117—795no—
762#117—795no—
763#117—7910no—
764#117—795no—
765#117—795no—
766#117—795no—
767#117—795no—
768#117—7910no—
769#117—795no—
770#117—795no—
771#117—7910no—
772#117—7910no—
773#117C22×D7915yes—
774#117C22×D7915yes—
775C2×C22⋊C4—7910no—
776C2×C22⋊C4—7910no—
777C2×C22⋊C4—7910no—
778C2×C22⋊C4—7910no—
779C2×C22⋊C4—7910no—
780C2×C22⋊C4—7910no—
781C2×C42—795no—
782C2×C42—795no—
783C2×C42C22×D7915yes—
784C24—7910no—
785#41—31610no—
786#41—6325no—
787#41—6325no—
788C2×Q8—31610no—
789C2×Q8—795no—
790C2×Q8—795no—
791C2×Q8—795no—
792C2×Q8—7910no—
793C2×Q8—795no—
794C2×Q8—795no—
795C2×Q8—6325no—
796C2×Q8—6325no—
797C2×Q8C23×D7915yes—
798C2×Q8C23×D7915yes—
799C2×D4—31610no—
800C2×D4—7910no—
801C2×D4—795no—
802C2×D4—7910no—
803C2×D4—795no—
804C2×D4—795no—
805C2×D4—795no—
806C2×D4—795no—
807C2×D4—7910no—
808C2×D4—795no—
809C2×D4—795no—
810C2×D4—6325no—
811C2×D4—6325no—
812C2×D4C23×D7915yes—
813C2×D4C23×D7915yes—
814C22×C4—7910no—
815C22×C4—795no—
816C22×C4—795no—
817C22×C4—795no—
818C22×C4—795no—
819C22×C4—795no—
820C22×C4—7910no—
821C22×C4—7910no—
822C22×C4—795no—
823C22×C4C23×D7915yes—
824C22×C4C23×D7915yes—
825C22×C4C23×D7915yes—
826C4⋊C4—791no—
827C4⋊C4—795no—
828C4⋊C4—7910no—
829C4⋊C4—7910no—
830C4⋊C4—795no—
831C4⋊C4—795no—
832C4⋊C4—7910no—
833C4⋊C4—7910no—
834C4⋊C4—7910no—
835C4⋊C4—7910no—
836C4⋊C4—795no—
837C4⋊C4—795no—
838C4⋊C4—795no—
839C4⋊C4—795no—
840C4⋊C4—795no—
841C4⋊C4—795no—
842C4⋊C4C23×D7915yes—
843C4⋊C4C23×D7915yes—
844C4⋊C4C23×D7915yes—
845C4⋊C4C23×D7915yes—
846C4⋊C4C23×D7915yes—
847C4⋊C4C23×D7915yes—
848C4⋊C4C23×D79110yes—
849C4⋊C4C23×D7915yes—
850C4⋊C4C23×D7915yes—
851C4⋊C4C23×D79110yes—
852C22⋊C4—795no—
853C22⋊C4—7910no—
854C22⋊C4—7910no—
855C22⋊C4—795no—
856C22⋊C4—795no—
857C22⋊C4—795no—
858C22⋊C4—795no—
859C22⋊C4—7910no—
860C22⋊C4—7910no—
861C22⋊C4—7910no—
862C22⋊C4—7910no—
863C22⋊C4—7910no—
864C22⋊C4—7910no—
865C22⋊C4—7910no—
866C22⋊C4—7910no—
867C22⋊C4—7910no—
868C22⋊C4—7910no—
869C22⋊C4—7910no—
870C22⋊C4—795no—
871C22⋊C4—7910no—
872C22⋊C4C23×D79110yes—
873C22⋊C4C23×D79110yes—
874C22⋊C4C23×D79110yes—
875C22⋊C4C23×D79110yes—
876C42—795no—
877C42—795no—
878C42—795no—
879C42—795no—
880C42—795no—
881C42—795no—
882C42—7910no—
883C42—7910no—
884C42C23×D7915yes—
885C42C23×D7915yes—
886C42C23×D7915yes—
887C42C23×D7915yes—
888C23—31610no—
889C23—31610no—
890C23—31610no—
891C23—795no—
892C23—795no—
893C23C24×D7915yes—
894Q8—45no—
895Q8—45no—
896Q8—3165no—
897Q8—3165no—
898Q8—31610no—
899Q8—3165no—
900Q8—3165no—
901Q8—15810no—
902D4—45no—
903D4—45no—
904D4—3165no—
905D4—3165no—
906D4—3165no—
907D4—31610no—
908D4—3165no—
909D4—3165no—
910D4—31610no—
911D4—31610no—
912D4—3165no—
913D4—15810no—
914C2×C4—45no—
915C2×C4—45no—
916C2×C4—45no—
917C2×C4—3165no—
918C2×C4—31610no—
919C2×C4—31610no—
920C2×C4—3165no—
921C2×C4—3165no—
922C2×C4—3165no—
923C2×C4—3165no—
924C2×C4—31610no—
925C2×C4—791no—
926C2×C4—791no—
927C2×C4—795no—
928C2×C4—795no—
929C2×C4—795no—
930C2×C4—795no—
931C2×C4—15810no—
932C2×C4C24×D7915yes—
933C2×C4C24×D7915yes—
934C2×C4C24×D7915yes—
935C2×C4C24×D7915yes—
936C2×C4C24×D7915yes—
937C2×C4C24×D7911yescharacteristic
938C22—25no—
939C22—25no—
940C22—25no—
941C22—1585no—
942C22—1585no—
943C22—1585no—
944C22—1585no—
945C22—1585no—
946C22—1585no—
947C22—126410no—
948C22C25×D7911yescharacteristic
949C4—25no—
950C4—25no—
951C4—25no—
952C4—25no—
953C4—21no—
954C4—25no—
955C4—792no—
956C4—1585no—
957C4—1585no—
958C4—1585no—
959C4—1581no—
960C4—1585no—
961C2—45no—
962C2—3165no—
963C2—3165no—
964C2#585×D7911yescharacteristic
965C2#2377821111yescharacteristic
966C2#2377821211yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3531C2
hypercenter#3531D79
hypocenterC79#63069
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3531

Complements

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

NH ≅ G/Ntype
1. #23778097C2semidirect
2. #23778096C2semidirect
3. #23777968C2semidirect
4. #23777965C2semidirect
5. #23777962C2semidirect
6. #23777922C2semidirect
7. #23777810C2semidirect
8. #23777758C2semidirect
9. #23777752C2semidirect
10. #23777548C2semidirect
11. #23777548C2semidirect
12. #23777409C2semidirect
13. #23777349C2semidirect
14. #23777289C2semidirect
15. C79×#3531C2semidirect
16. #19099317C22semidirect
17. #19099317C22semidirect
18. #19099317C22semidirect
19. #19099317C22semidirect
20. #19099317C22semidirect
21. #19099313C22semidirect
22. #19099311C22semidirect
23. #19099311C22semidirect
24. #19099311C22semidirect
25. #19099307C22semidirect
26. #19099305C22semidirect
27. #19099305C22semidirect
28. #19099297C22semidirect
29. #19099296C22semidirect
30. #19099293C22semidirect
31. #19099287C22semidirect
32. #19099285C22semidirect
33. #19099285C22semidirect
34. #19099284C22semidirect
35. #19099281C22semidirect
36. #19099281C22semidirect
37. #19099280C22semidirect
38. #19099280C22semidirect
39. #19099279C22semidirect
40. #19099276C22semidirect
41. #19099276C22semidirect
42. #19099242C22semidirect
43. #19099241C22semidirect
44. #19099240C22semidirect
45. #19099238C22semidirect
46. #19099238C22semidirect
47. #19099237C22semidirect
48. #19099237C22semidirect
49. #19099236C22semidirect
50. #19099228C22semidirect
51. #19099226C22semidirect
52. #19099226C22semidirect
53. #19099225C22semidirect
54. #19099223C22semidirect
55. #19099219C22semidirect
56. #19099208C22semidirect
57. #19099205C22semidirect
58. #19099204C22semidirect
59. #19099204C22semidirect
60. #19099202C22semidirect
61. #19099197C22semidirect
62. #19099188C22semidirect
63. #19099187C22semidirect
64. #19099186C22semidirect
65. #19099185C22semidirect
66. #19099185C22semidirect
67. #19099183C22semidirect
68. #19099183C22semidirect
69. #19099183C22semidirect
70. #19099181C22semidirect
71. #19099180C22semidirect
72. #19099179C22semidirect
73. #19099179C22semidirect
74. #19099178C22semidirect
75. #19099153C22semidirect
76. #19099152C22semidirect
77. #19099152C22semidirect
78. #19099149C22semidirect
79. #19099146C22semidirect
80. #19099145C22semidirect
81. #19099138C22semidirect
82. #19099136C22semidirect
83. #19099135C22semidirect
85. #19099124C22semidirect
86. #19099119C22semidirect
87. #19099119C22semidirect
88. #19099119C22semidirect
90. #19099098C22semidirect
91. #19099098C22semidirect
92. #19099098C22semidirect
93. #19099098C22semidirect
94. #19099098C22semidirect
95. #19099097C22semidirect
96. #19099097C22semidirect
97. #19099092C22semidirect
98. C2×#14579149C22semidirect
99. #124×D79C22semidirect
100. #124×D79C22semidirect
101. #19099039C22semidirect
102. #19099035C22semidirect
103. C4×#11929624C22semidirect
104. #564×C79C22semidirect
105. #563×C79C22semidirect
106. #563×C79C22semidirect
107. #562×C79C22semidirect
108. #533×C79C22semidirect
109. #529×C79C22semidirect
110. #529×C79C22semidirect
495. #3531D79semidirect
499. C79#63069semidirect
500. #564C2×D79semidirect
507. #563C2×D79semidirect
508. #563C2×D79semidirect
513. #562C2×D79semidirect
577. #533C2×D79semidirect
587. #529C2×D79semidirect
588. #529C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780972
#237780962
#237779682
#237779652
#237779622
#237779222
#237778102
#237777582
#237777522
#237775482
#237774092
#237773492
#237772892
C79×#35312
#6306979