Finite Group Databasebeta

← #35196664

Subgroups — #35196664

Order 20224.

7856 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777486C212yesmaximal, complemented
2#23777433C216yesmaximal, complemented
3#23777407C212yesmaximal, complemented
4#23777362C216yesmaximal, complemented
5#23777313C213yesmaximal, complemented
6#23777277C213yesmaximal, complemented
7#23777178C211yesmaximal, characteristic, complemented
8#23777138C216yesmaximal, complemented
9#23777070C212yesmaximal, complemented
10#23777027C212yesmaximal, complemented
11#23777011C216yesmaximal, complemented
12#23777000C212yesmaximal, complemented
13D4×#11929625C216yesmaximal, complemented
14#23776823C216yesmaximal, complemented
15#23776697C213yesmaximal, complemented
16C2×#19099114C213yesmaximal, complemented
17#23776606C212yesmaximal, complemented
18C4×#41×D79C211yesmaximal, characteristic, complemented
19C79×#3503C211yesmaximal, characteristic, complemented
20C2×#14579207C2212yes—
21C22×#11929625C2216yescomplemented
22C2×#41×D79C2211yescharacteristic
23#19099298C2216yescomplemented
24#19099298C2216yescomplemented
25#19099287C2216yescomplemented
26#19099279C2216yescomplemented
27#19099279C22112yescomplemented
28#19099274C2216yescomplemented
29#19099266C22112yescomplemented
30#19099266C22112yescomplemented
31#19099261C22112yescomplemented
32#19099240C22124yescomplemented
33#19099235C2214yescomplemented
34#19099235C2216yescomplemented
35#19099235C2212yescomplemented
36#19099235C2216yescomplemented
37#19099235C2212yescomplemented
38#19099225C2214yescomplemented
39#19099224C22112yescomplemented
40#19099216C2216yescomplemented
41#19099216C22112yescomplemented
42#19099208C22112yescomplemented
43#19099204C22112yescomplemented
44#19099204C22124yescomplemented
45#19099204C22112yescomplemented
46D4×D316C22112yescomplemented
47D4×D316C2216yescomplemented
48D4×D316C2216yescomplemented
49#19099187C22112yescomplemented
50#19099187C22112yescomplemented
51#19099169C22112yescomplemented
52#19099169C22112yescomplemented
53#19099153C22124yescomplemented
54#19099144C2216yescomplemented
55#19099132C2216yescomplemented
56#19099132C2216yescomplemented
57#19099118C2213yescomplemented
58#19099118C2211yescharacteristic, complemented
59#19099114C22112yescomplemented
60#19099114C2216yescomplemented
61#19099114C2216yescomplemented
62#19099114C2216yescomplemented
63#19099114C2216yescomplemented
64#19099114C2216yescomplemented
65#19099114C2216yescomplemented
66#19099114C2216yescomplemented
67#19099114C2213yescomplemented
68#19099114C2213yescomplemented
69#19099113C2213yescomplemented
70C2×#14579158C2213yescomplemented
71#19099100C2216yescomplemented
72#19099100C2216yescomplemented
73#19099099C2216yescomplemented
74#19099099C2216yescomplemented
75#19099098C2216yescomplemented
76#19099098C22112yescomplemented
77#19099098C2216yescomplemented
78C2×#14579150C2216yescomplemented
79#19099076C22124yescomplemented
80#19099076C2216yescomplemented
81#19099076C2216yescomplemented
82#19099075C2216yescomplemented
83C2×#14579136C2216yescomplemented
84C2×#14579136C2216yescomplemented
85#19099045C2214yescomplemented
86#19099044C2216yescomplemented
87#19099037C2216yescomplemented
88#19099035C22112yescomplemented
89#41×Dic79C2211yescharacteristic
90C4×#11929625C2211yescharacteristic, complemented
91C4×#11929625C2214yescomplemented
92C4×#11929625C2216yescomplemented
93C4×#11929625C2211yescharacteristic, complemented
94C4×#11929625C2216yescomplemented
95C4×#11929624C2213yescomplemented
96#19099031C2213yescomplemented
97#19099031C2216yescomplemented
98C4×#11929623C2213yescomplemented
99C4×#11929623C2213yescomplemented
100C4×Q8×D79C2211yescharacteristic, complemented
101C4×Q8×D79C2211yescharacteristic, complemented
102C2×#14579123C2216yescomplemented
103C2×#14579123C2216yescomplemented
104C4×D4×D79C2213yescomplemented
105C4×D4×D79C2213yescomplemented
106C4×D4×D79C22112yescomplemented
107#117×D79C2213yescomplemented
108C2×C42×D79C2213yescomplemented
109Q82×C79C2212yescomplemented
110#557×C79C2212yescomplemented
111#554×C79C2216yescomplemented
112D4×Q8×C79C2216yescomplemented
113#544×C79C2216yescomplemented
114#533×C79C2213yescomplemented
115C2×C4⋊Q8×C79C2213yescomplemented
116#520×C79C2212yes—
117C4×#41×C79C2211yescharacteristic
118#14579207—216no—
119C2×#11929625—424no—
120C2×#11929625C2314yes—
121C2×#11929625C2311yescharacteristic
122C2×#11929625C2316yes—
123C2×#11929625C23112yes—
124C2×#11929625C2316yes—
125C2×#11929625C23112yes—
126C2×#11929625C23112yes—
127C2×#11929624C2316yes—
128C2×#11929624C2313yes—
129C2×#11929623C2313yes—
130#41×D79—28no—
131C2×Q8×D79C2311yescharacteristic
132C22×D316C2316yes—
133C22×D316C2316yes—
134C22×D316C23112yes—
135C22×D316C2316yes—
136C2×D4×D79C23112yes—
137C2×D4×D79C2313yes—
138C22×C4×D79C2313yes—
139C22×C4×D79C2313yes—
140C22×C4×D79C2313yes—
141C22×C4×D79C23112yes—
142#14579161C2311yescharacteristic
143#14579158C2316yes—
144#14579158C23112yes—
145#14579158C2316yes—
146#14579158C2316yes—
147#14579158C2313yes—
148#14579156C23112yes—
149#14579156C23124yes—
150#14579156C23112yes—
151#14579152C2316yes—
152#14579152C2312yes—
153#14579150C23112yes—
154#14579150C23124yes—
155#14579150C2316yes—
156#14579150C23112yes—
157#14579150C23112yes—
158#14579150C2316yes—
159#14579149C2316yes—
160#14579149C23112yes—
161#14579146C23112yes—
162#14579146C23124yes—
163#14579146C23124yes—
164#14579146C23124yes—
165#14579146C23112yes—
166#14579145C23112yes—
167#14579141C2316yes—
168#14579141C23112yes—
169#14579141C2312yes—
170#14579137C23124yes—
171#14579137C2316yes—
172#14579137C2312yes—
173#14579136C23112yes—
174#14579136C23112yes—
175#14579136C23112yes—
176#14579136C23124yes—
177#14579136C23124yes—
178#14579136C2316yes—
179#14579136C23112yes—
180#14579136C23112yes—
181#14579136C23112yes—
182#14579136C2316yes—
183#14579136C23112yes—
184#14579136C23112yes—
185#14579136C23112yes—
186#14579136C2316yes—
187#14579136C2316yes—
188#14579135C23124yes—
189#14579135C2316yes—
190#14579135C2316yes—
191#14579131C23124yes—
192#14579131C23124yes—
193#14579131C23112yes—
194Q8×Dic79C2316yes—
195Q8×Dic79C2311yescharacteristic
196Q8×Dic79C2311yescharacteristic
197Q8×Dic79C2312yes—
198C4×Dic158C2313yes—
199C4×Dic158C2313yes—
200#14579126C2313yes—
201#14579126C2316yes—
202#14579126C2313yes—
203#14579126C2312yes—
204C4×D316C23112yes—
205C4×D316C2316yes—
206C4×D316C2316yes—
207C4×D316C23112yes—
208C4×D316C2313yes—
209C4×D316C23112yes—
210C4×D316C2313yes—
211C4×D316C23112yes—
212D4×Dic79C2313yes—
213D4×Dic79C2313yes—
214#14579123C2313yes—
215#14579123C2316yes—
216#14579123C23112yes—
217#14579123C23112yes—
218#14579123C23112yes—
219#14579123C2316yes—
220#14579123C23112yes—
221#14579123C23112yes—
222#14579123C23112yes—
223#14579123C2313yes—
224#14579123C2316yes—
225#14579123C2316yes—
226#14579123C23112yes—
227#14579123C23112yes—
228C4×C22⋊D79C2316yes—
229C4×C22⋊D79C2316yes—
230C4×C22⋊D79C23124yes—
231(C22⋊D79)⋊C4C2316yes—
232(C22⋊D79)⋊C4C23112yes—
233(C22⋊D79)⋊C4C23112yes—
234(C22⋊D79)⋊C4C2316yes—
235#14579120C2313yes—
236#14579119C23112yes—
237#14579119C2316yes—
238#14579119C2313yes—
239#14579119C23112yes—
240#14579119C2313yes—
241#14579119C2312yes—
242#14579119C23112yes—
243#14579118C2316yes—
244#14579118C23112yes—
245#14579117C2316yes—
246C4⋊C4×D79C2313yes—
247C4⋊C4×D79C23112yes—
248C4⋊C4×D79C2313yes—
249C2×(C2×D79)⋊C4C23112yes—
250C2×(C2×D79)⋊C4C23112yes—
251C22⋊C4×D79C2316yes—
252C22⋊C4×D79C23124yes—
253C2×C4×Dic79C2313yes—
254C2×C4×Dic79C2313yes—
255C2×C4×Dic79C2313yes—
256C42×D79C2311yescharacteristic
257C42×D79C2313yes—
258C42×D79C2313yes—
259C42×D79C2313yes—
260C42×D79C2313yes—
261C42×D79C2313yes—
262C42×D79C2313yes—
263C42×D79C2313yes—
264C42×D79C23112yes—
265C2×#41×C79C2311yescharacteristic
266C22×Q8×C79C2316yes—
267C4⋊Q8×C79C2316yes—
268C4⋊Q8×C79C23112yes—
269C4⋊Q8×C79C2316yes—
270C4⋊Q8×C79C2313yes—
271C4⋊Q8×C79C2316yes—
272C4⋊Q8×C79C2311yescharacteristic
273#125×C79C2316yes—
274#125×C79C23112yes—
275C22⋊Q8×C79C23124yes—
276C22⋊Q8×C79C2316yes—
277C22⋊Q8×C79C2316yes—
278C4×Q8×C79C2314yes—
279C4×Q8×C79C2311yescharacteristic
280C4×Q8×C79C2311yescharacteristic
281C4×Q8×C79C2316yes—
282C4×Q8×C79C2316yes—
283C4×D4×C79C2313yes—
284C4×D4×C79C2313yes—
285C4×D4×C79C23112yes—
286#117×C79C2313yes—
287#117×C79C2316yes—
288C2×C4⋊C4×C79C2316yes—
289C2×C4⋊C4×C79C2316yes—
290C2×C42×C79C2313yes—
291C23×D79C2413yes—
292C23×D79C24112yes—
293#11929625—224no—
294#11929625—24no—
295#11929625—216no—
296#11929625—424no—
297#11929625—412no—
298#11929625—424no—
299#11929625—424no—
300#11929624—212no—
301#11929624—224no—
302#11929623—212no—
303C2×Dic158C2413yes—
304C2×Dic158C2412yes—
305Q8×D79—24no—
306C2×D316—224no—
307C2×D316—412no—
308C2×D316—412no—
309C2×D316—424no—
310C2×D316C2413yes—
311C2×D316C2416yes—
312C2×D316C24112yes—
313C2×D316C2416yes—
314C2×D316C2416yes—
315C2×D316C24112yes—
316C2×D316C24112yes—
317C2×D316C24124yes—
318C2×D316C24112yes—
319C2×D316C24112yes—
320C2×C22⋊D79C2416yes—
321C2×C22⋊D79C24112yes—
322D4×D79—212no—
323D4×D79—248no—
324C22×Dic79C2413yes—
325C22×Dic79C2413yes—
326C22×Dic79C2413yes—
327C2×C4×D79—212no—
328C2×C4×D79—212no—
329C2×C4×D79—46no—
330C2×C4×D79—424no—
331C2×C4×D79C2413yes—
332C2×C4×D79C2413yes—
333C2×C4×D79C2413yes—
334C2×C4×D79C24112yes—
335C2×C4×D79C2413yes—
336C2×C4×D79C2413yes—
337C2×C4×D79C2413yes—
338C2×C4×D79C24112yes—
339C2×C4×D79C2413yes—
340C2×C4×D79C2411yescharacteristic
341C2×C4×D79C2411yescharacteristic
342C2×C4×D79C24124yes—
343C2×C4×D79C24112yes—
344C2×C4×D79C2413yes—
345C2×C4×D79C2413yes—
346C2×C4×D79C2411yescharacteristic
347C4⋊Dic79C2413yes—
348C4⋊Dic79C2413yes—
349C4⋊Dic79C2412yes—
350C4⋊Dic79C2414yes—
351C4⋊Dic79C2412yes—
352C4⋊Dic79C24112yes—
353Dic79⋊C4C24112yes—
354Dic79⋊C4C2416yes—
355Dic79⋊C4C2416yes—
356Dic79⋊C4C2414yes—
357C22⋊Dic79C2416yes—
358(C2×D79)⋊C4C24112yes—
359(C2×D79)⋊C4C24124yes—
360(C2×D79)⋊C4C2416yes—
361(C2×D79)⋊C4C2416yes—
362(C2×D79)⋊C4C24112yes—
363(C2×D79)⋊C4C24112yes—
364(C2×D79)⋊C4C24124yes—
365(C2×D79)⋊C4C2414yes—
366(C2×D79)⋊C4C24112yes—
367(C2×D79)⋊C4C24112yes—
368(C2×D79)⋊C4C24112yes—
369(C2×D79)⋊C4C24112yes—
370C4×Dic79C2413yes—
371C4×Dic79C2411yescharacteristic
372C4×Dic79C2411yescharacteristic
373C4×Dic79C2411yescharacteristic
374C4×Dic79C2414yes—
375C4×Dic79C2413yes—
376C4×Dic79C2413yes—
377C4×Dic79C2413yes—
378C4×Dic79C2413yes—
379C4×Dic79C2413yes—
380C4×Dic79C2413yes—
381C4×Dic79C2413yes—
382C4×Dic79C2413yes—
383C4×Dic79C24112yes—
384#41×C79#4118yescomplemented
385C2×Q8×C79—412no—
386C2×Q8×C79C2412yes—
387C2×Q8×C79C2416yes—
388C2×Q8×C79C24112yes—
389C2×Q8×C79C2411yescharacteristic
390C2×D4×C79C2413yes—
391C22×C4×C79C2413yes—
392C22×C4×C79C2413yes—
393C22×C4×C79C24112yes—
394C22×C4×C79C2413yes—
395C4⋊C4×C79C2416yes—
396C4⋊C4×C79C2416yes—
397C4⋊C4×C79C24112yes—
398C4⋊C4×C79C24112yes—
399C4⋊C4×C79C2412yes—
400C4⋊C4×C79C2413yes—
401C4⋊C4×C79C2413yes—
402C4⋊C4×C79C2412yes—
403C4⋊C4×C79C24112yes—
404C4⋊C4×C79C24112yes—
405C22⋊C4×C79C24112yes—
406C22⋊C4×C79C2416yes—
407C42×C79C2411yescharacteristic
408C42×C79C2413yes—
409C42×C79C2413yes—
410C42×C79C2413yes—
411C42×C79C24112yes—
412C23×C79C2513yes—
413C22×D79—26no—
414C22×D79—224no—
415C22×D79—26no—
416C22×D79—43no—
417C22×D79—412no—
418C22×D79—412no—
419C22×D79C25112yes—
420C22×D79C2513yes—
421C22×D79C2511yescharacteristic
422Q8×C79—212no—
423Q8×C79—24no—
424Q8×C79—412no—
425Q8×C79C2×#4114yescomplemented
426D4×C79C2×#41112yescomplemented
427C2×C4×C79—26no—
428C2×C4×C79—26no—
429C2×C4×C79—412no—
430C2×C4×C79C2×#41112yescomplemented
431C2×C4×C79C2513yes—
432C2×C4×C79C2513yes—
433C2×C4×C79C2514yes—
434C2×C4×C79C25112yes—
435C2×C4×C79C2511yescharacteristic
436C2×C4×C79C2513yes—
437C2×C4×C79C2511yescharacteristic
438C2×C4×C79C2511yescharacteristic
439C22⋊D79—224no—
440C22⋊D79—212no—
441C2×Dic79—26no—
442C2×Dic79—26no—
443C2×Dic79—43no—
444C2×Dic79C2511yescharacteristic
445C2×Dic79C2511yescharacteristic
446C2×Dic79C2513yes—
447C2×Dic79C2513yes—
448C2×Dic79C2514yes—
449C2×Dic79C2513yes—
450C2×Dic79C2511yescharacteristic
451D316—224no—
452D316—224no—
453D316—26no—
454D316—212no—
455D316—212no—
456D316—212no—
457D316—412no—
458D316—412no—
459D316—424no—
460D316—412no—
461C4×D79—26no—
462C4×D79—22no—
463C4×D79—26no—
464C4×D79—26no—
465C4×D79—26no—
466C4×D79—224no—
467C4×D79—26no—
468C4×D79—22no—
469C4×D79—26no—
470C4×D79—26no—
471C4×D79—224no—
472C4×D79—43no—
473C4×D79—43no—
474C4×D79—424no—
475C4×D79—412no—
476C4×D79H(5,𝔽2)14yescomplemented
477Dic158—26no—
478Dic158—24no—
479C22×C79—23no—
480C22×C79—23no—
481C22×C79C22×#4116yes—
482C22×C79C2611yescharacteristic
483C2×D79—21no—
484C2×D79—21no—
485C2×D79—23no—
486C2×D79—212no—
487C2×D79—23no—
488C2×D79—212no—
489C2×D79—212no—
490C2×D79—23no—
491C2×D79—412no—
492C2×D79—824no—
493C2×D79C2×H(5,𝔽2)12yes—
494C4×C79—23no—
495C4×C79—212no—
496C4×C79—23no—
497C4×C79—24no—
498C4×C79C22×#4112yes—
499C4×C79C22×#4116yes—
500C4×C79C2×H(5,𝔽2)12yes—
501C4×C79#58512yes—
502Dic79—24no—
503Dic79—23no—
504Dic79—21no—
505Dic79—23no—
506Dic79—23no—
507Dic79—21no—
508Dic79C2×H(5,𝔽2)12yes—
509#62800—791nomaximal, Sylow
510C2×C79—26no—
511C2×C79C23×#4111yescharacteristic
512C2×C79C22×H(5,𝔽2)11yescharacteristic
513C2×C79C2×#58511yescharacteristic
514D79—22no—
515D79—43no—
516D79—412no—
517#3522—792no—
518#3519—796no—
519#3517—792no—
520#3514—796no—
521#3511—793no—
522#3508—793no—
523#3503D7911yescharacteristic, complemented
524#3498—791no—
525#3494—796no—
526#3488—792no—
527#3483—792no—
528#3481—796no—
529#3480—792no—
530D4×#41—796no—
531#3460—796no—
532#3444—793no—
533C2×#532—793no—
534C4×H(5,𝔽2)—792no—
535C2×C4×#41—791no—
536C79#6280011yescharacteristic, complemented, Sylow
537C2×H(5,𝔽2)—792no—
538C22×#41—791no—
539C22×#41—796no—
540#559—796no—
541#559—796no—
542Q82C2×D7912yescomplemented
543#557C2×D7912yescomplemented
544#556—796no—
545#555—7912no—
546#555—796no—
547#554—796no—
548#554C2×D7916yescomplemented
549#553—7912no—
550#553—7912no—
551#553—7912no—
552#551—7924no—
553#550—796no—
554#550—792no—
555#550—794no—
556#550—792no—
557#550—796no—
558D4×Q8C2×D7916yescomplemented
559#548—7912no—
560#548—794no—
561#547—7912no—
562#547—796no—
563#546—7924no—
564#546—7912no—
565#546—7912no—
566#546—7912no—
567D42—7912no—
568D42—796no—
569D42—796no—
570#544C2×D7916yescomplemented
571#542—7912no—
572#542—7912no—
573#540—7912no—
574#540—7912no—
575#538—7924no—
576#537—796no—
577#535—796no—
578#535—796no—
579#533—791no—
580#533—793no—
581#533C2×D7913yescomplemented
582#532—793no—
583#532—796no—
584#532—796no—
585#532—796no—
586#532—796no—
587#532—796no—
588#532—796no—
589#532—796no—
590#532—793no—
591#532—7912no—
592#532—793no—
593C2×C4⋊Q8C2×D7913yescomplemented
594C2×#127—793no—
595#529—796no—
596#529—796no—
597#529—7912no—
598#529—796no—
599#529—796no—
600#529—796no—
601#529—796no—
602C2×#124—796no—
603#525—796no—
604#525—796no—
605#525—7924no—
606#525—796no—
607C2×#121—796no—
608C2×#121—796no—
609#520—794no—
610#520—796no—
611#520C2×D7912yes—
612#518—7912no—
613#518—796no—
614C4×#41—791no—
615C4×#41—791no—
616C4×#41—791no—
617C4×#41—794no—
618C4×#41—796no—
619C4×#41—796no—
620C4×#41—793no—
621C4×#41—793no—
622C4×#41—793no—
623C4×#41—796no—
624C4×#41—793no—
625C4×#41C2×D7911yescharacteristic
626C2×C4×Q8—791no—
627C2×C4×Q8—791no—
628C2×C4×D4—793no—
629C2×C4×D4—793no—
630C2×C4×D4—7912no—
631C2×C4×D4—796no—
632C2×C4×D4—796no—
633C2×#117—793no—
634C22×C42—793no—
635H(5,𝔽2)—15816no—
636C2×#41—31624no—
637C2×#41—796no—
638C2×#41—7912no—
639C2×#41—7912no—
640C2×#41—7912no—
641C2×#41—791no—
642C2×#41—794no—
643C2×#41—796no—
644C2×#41—793no—
645C2×#41—793no—
646C2×#41—796no—
647C2×#41—1588no—
648C2×#41C22×D7911yescharacteristic
649C22×Q8—791no—
650C22×Q8C22×D7916yes—
651C22×D4—793no—
652C22×D4—7912no—
653C22×D4—796no—
654C22×D4—7912no—
655C22×D4—796no—
656C22×D4—796no—
657C23×C4—7912no—
658C23×C4—793no—
659C23×C4—793no—
660C23×C4—793no—
661C4⋊Q8—791no—
662C4⋊Q8C22×D7913yes—
663C4⋊Q8C22×D7916yes—
664C4⋊Q8C22×D7916yes—
665C4⋊Q8C22×D7916yes—
666C4⋊Q8C22×D7911yescharacteristic
667C4⋊Q8C22×D79112yes—
668#127—793no—
669#127—796no—
670#127—796no—
671#127—796no—
672#127—7912no—
673#126—7912no—
674#126—7912no—
675#126—7924no—
676#125—792no—
677#125—796no—
678#125C22×D7916yes—
679#125C22×D79112yes—
680#124—796no—
681#124—7912no—
682#124—7912no—
683#124—7912no—
684#124—796no—
685#124—7924no—
686#124—796no—
687#124—7912no—
688#123—7912no—
689#123—7912no—
690#123—7924no—
691#123—7924no—
692#123—7924no—
693#123—7912no—
694C22⋊Q8—792no—
695C22⋊Q8—796no—
696C22⋊Q8—7924no—
697C22⋊Q8—792no—
698C22⋊Q8—796no—
699C22⋊Q8—7912no—
700C22⋊Q8C22×D7916yes—
701C22⋊Q8C22×D7916yes—
702C22⋊Q8C22×D79124yes—
703#121—796no—
704#121—796no—
705#121—7924no—
706#121—796no—
707#121—796no—
708#121—7912no—
709#121—7912no—
710#121—7912no—
711#121—7912no—
712#121—7912no—
713#121—7912no—
714#121—796no—
715#121—796no—
716#121—7924no—
717#121—7912no—
718#121—7912no—
719#121—7912no—
720#121—7924no—
721#120—7912no—
722#120—7924no—
723#120—7924no—
724C4×Q8—791no—
725C4×Q8—791no—
726C4×Q8—792no—
727C4×Q8—796no—
728C4×Q8—793no—
729C4×Q8—793no—
730C4×Q8—792no—
731C4×Q8—796no—
732C4×Q8—793no—
733C4×Q8—793no—
734C4×Q8C22×D7911yescharacteristic
735C4×Q8C22×D7911yescharacteristic
736C4×Q8C22×D7914yes—
737C4×Q8C22×D7916yes—
738C4×Q8C22×D7916yes—
739C4×D4—793no—
740C4×D4—793no—
741C4×D4—796no—
742C4×D4—796no—
743C4×D4—7924no—
744C4×D4—7912no—
745C4×D4—796no—
746C4×D4—796no—
747C4×D4—793no—
748C4×D4—793no—
749C4×D4—7912no—
750C4×D4—7912no—
751C4×D4—7912no—
752C4×D4—7912no—
753C4×D4—7912no—
754C4×D4—796no—
755C4×D4—7912no—
756C4×D4—7912no—
757C4×D4—796no—
758C4×D4—7912no—
759C4×D4—796no—
760C4×D4—796no—
761C4×D4—7912no—
762C4×D4—793no—
763C4×D4—793no—
764C4×D4—7912no—
765C4×D4—7912no—
766C4×D4—7912no—
767C4×D4—7912no—
768C4×D4—796no—
769C4×D4—796no—
770C4×D4C22×D7913yes—
771C4×D4C22×D7913yes—
772C4×D4C22×D79112yes—
773#117—793no—
774#117—793no—
775#117—793no—
776#117—792no—
777#117—7912no—
778#117—7912no—
779#117—796no—
780#117—7912no—
781#117—796no—
782#117—796no—
783#117—7912no—
784#117C22×D7913yes—
785#117C22×D7916yes—
786C2×C4⋊C4—793no—
787C2×C4⋊C4—793no—
788C2×C4⋊C4—7912no—
789C2×C4⋊C4C22×D7916yes—
790C2×C4⋊C4C22×D7916yes—
791C2×C22⋊C4—7912no—
792C2×C22⋊C4—7912no—
793C2×C22⋊C4—796no—
794C2×C22⋊C4—7924no—
795C2×C42—793no—
796C2×C42—793no—
797C2×C42—793no—
798C2×C42—793no—
799C2×C42—793no—
800C2×C42—793no—
801C2×C42—7912no—
802C2×C42—793no—
803C2×C42—793no—
804C2×C42—793no—
805C2×C42—793no—
806C2×C42—791no—
807C2×C42C22×D7913yes—
808C24—7912no—
809C24—793no—
810#41—31624no—
811#41—31612no—
812#41—31624no—
813#41—31624no—
814#41—15824no—
815#41—1584no—
816#41—15816no—
817#41—15812no—
818#41—15812no—
819#41—15824no—
820#41#1192962518yescomplemented
821C2×Q8—412no—
822C2×Q8—793no—
823C2×Q8—792no—
824C2×Q8—1584no—
825C2×Q8C23×D7912yes—
826C2×Q8C23×D7916yes—
827C2×Q8C23×D79112yes—
828C2×Q8C23×D7911yescharacteristic
829C2×D4—31612no—
830C2×D4—31612no—
831C2×D4—31624no—
832C2×D4—796no—
833C2×D4—7912no—
834C2×D4—7912no—
835C2×D4—7912no—
836C2×D4—7912no—
837C2×D4—7924no—
838C2×D4—796no—
839C2×D4—796no—
840C2×D4—7912no—
841C2×D4—793no—
842C2×D4—7912no—
843C2×D4—796no—
844C2×D4—15812no—
845C2×D4—15848no—
846C2×D4—15824no—
847C2×D4C23×D7913yes—
848C22×C4—3166no—
849C22×C4—31624no—
850C22×C4—793no—
851C22×C4—793no—
852C22×C4—793no—
853C22×C4—7912no—
854C22×C4—7924no—
855C22×C4—791no—
856C22×C4—793no—
857C22×C4—793no—
858C22×C4—791no—
859C22×C4—791no—
860C22×C4—793no—
861C22×C4—793no—
862C22×C4—793no—
863C22×C4—793no—
864C22×C4—793no—
865C22×C4—793no—
866C22×C4—793no—
867C22×C4—7912no—
868C22×C4—7912no—
869C22×C4—15812no—
870C22×C4—15812no—
871C22×C4C23×D7913yes—
872C22×C4C23×D7913yes—
873C22×C4C23×D79112yes—
874C22×C4C23×D7913yes—
875C4⋊C4—7912no—
876C4⋊C4—796no—
877C4⋊C4—796no—
878C4⋊C4—794no—
879C4⋊C4—793no—
880C4⋊C4—793no—
881C4⋊C4—792no—
882C4⋊C4—794no—
883C4⋊C4—792no—
884C4⋊C4—7912no—
885C4⋊C4C23×D79112yes—
886C4⋊C4C23×D7913yes—
887C4⋊C4C23×D7913yes—
888C4⋊C4C23×D7916yes—
889C4⋊C4C23×D7916yes—
890C4⋊C4C23×D79112yes—
891C4⋊C4C23×D7912yes—
892C4⋊C4C23×D79112yes—
893C4⋊C4C23×D79112yes—
894C4⋊C4C23×D7912yes—
895C22⋊C4—796no—
896C22⋊C4—7912no—
897C22⋊C4—7924no—
898C22⋊C4—7912no—
899C22⋊C4—7912no—
900C22⋊C4—796no—
901C22⋊C4—796no—
902C22⋊C4—7924no—
903C22⋊C4—794no—
904C22⋊C4—7912no—
905C22⋊C4—7912no—
906C22⋊C4—7912no—
907C22⋊C4—7912no—
908C22⋊C4C23×D79112yes—
909C22⋊C4C23×D7916yes—
910C42—791no—
911C42—791no—
912C42—793no—
913C42—791no—
914C42—793no—
915C42—793no—
916C42—794no—
917C42—793no—
918C42—793no—
919C42—793no—
920C42—793no—
921C42—793no—
922C42—793no—
923C42—7912no—
924C42C23×D7911yescharacteristic
925C42C23×D7913yes—
926C42C23×D7913yes—
927C42C23×D7913yes—
928C42C23×D79112yes—
929C23—3163no—
930C23—31612no—
931C23—31612no—
932C23—791no—
933C23—7912no—
934C23—793no—
935C23—1586no—
936C23—1586no—
937C23—15824no—
938C23C24×D7913yes—
939Q8—212no—
940Q8—24no—
941Q8—412no—
942Q8—1586no—
943Q8—1584no—
944Q8C2×#1192962514yescomplemented
945D4—31612no—
946D4—31624no—
947D4—31612no—
948D4—31612no—
949D4—15824no—
950D4—15824no—
951D4—15812no—
952D4—15812no—
953D4—15812no—
954D4—15824no—
955D4—15812no—
956D4—1586no—
957D4C2×#11929625112yescomplemented
958C2×C4—26no—
959C2×C4—26no—
960C2×C4—412no—
961C2×C4—31624no—
962C2×C4—3163no—
963C2×C4—3163no—
964C2×C4—31612no—
965C2×C4—3163no—
966C2×C4—791no—
967C2×C4—794no—
968C2×C4—791no—
969C2×C4—791no—
970C2×C4—793no—
971C2×C4—793no—
972C2×C4—794no—
973C2×C4—793no—
974C2×C4—15824no—
975C2×C4—1586no—
976C2×C4—1586no—
977C2×C4—1586no—
978C2×C4—1586no—
979C2×C4—1586no—
980C2×C4—1582no—
981C2×C4—1586no—
982C2×C4—1582no—
983C2×C4—1586no—
984C2×C4—1586no—
985C2×C4—1586no—
986C2×C4—15824no—
987C2×C4C2×#11929625112yescomplemented
988C2×C4C24×D7913yes—
989C2×C4C24×D7913yes—
990C2×C4C24×D7914yes—
991C2×C4C24×D79112yes—
992C2×C4C24×D7911yescharacteristic
993C2×C4C24×D7911yescharacteristic
994C2×C4C24×D7911yescharacteristic
995C2×C4C24×D7913yes—
996C22—23no—
997C22—23no—
998C22—31612no—
999C22—792no—
1000C22—63224no—
1001C22—1583no—
1002C22—15812no—
1003C22—15812no—
1004C22—1583no—
1005C22—1583no—
1006C22—15812no—
1007C22—1581no—
1008C22—1581no—
1009C22C22×#1192962516yes—
1010C22C25×D7911yescharacteristic
1011C4—23no—
1012C4—212no—
1013C4—23no—
1014C4—24no—
1015C4—792no—
1016C4—1581no—
1017C4—1584no—
1018C4—1583no—
1019C4—1583no—
1020C4—1581no—
1021C4—1583no—
1022C4C22×#1192962516yes—
1023C4C22×#1192962512yes—
1024C4H(5,𝔽2)×D7912yes—
1025C4#1909940012yes—
1026C2—26no—
1027C2—3163no—
1028C2—31612no—
1029C2—1582no—
1030C2C23×#1192962511yescharacteristic
1031C2C2×H(5,𝔽2)×D7911yescharacteristic
1032C2C2×#1909940011yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3503C2
hypercenter#3503D79
hypocenterC79#62800
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3503

Complements

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

NH ≅ G/Ntype
1. #23777486C2semidirect
2. #23777433C2semidirect
3. #23777407C2semidirect
4. #23777362C2semidirect
5. #23777313C2semidirect
6. #23777277C2semidirect
7. #23777178C2semidirect
8. #23777138C2semidirect
9. #23777070C2semidirect
10. #23777027C2semidirect
11. #23777011C2semidirect
12. #23777000C2semidirect
13. D4×#11929625C2semidirect
14. #23776823C2semidirect
15. #23776697C2semidirect
16. C2×#19099114C2semidirect
17. #23776606C2semidirect
18. C4×#41×D79C2semidirect
19. C79×#3503C2semidirect
21. C22×#11929625C22semidirect
23. #19099298C22semidirect
24. #19099298C22semidirect
25. #19099287C22semidirect
26. #19099279C22semidirect
27. #19099279C22semidirect
28. #19099274C22semidirect
29. #19099266C22semidirect
30. #19099266C22semidirect
31. #19099261C22semidirect
32. #19099240C22semidirect
33. #19099235C22semidirect
34. #19099235C22semidirect
35. #19099235C22semidirect
36. #19099235C22semidirect
37. #19099235C22semidirect
38. #19099225C22semidirect
39. #19099224C22semidirect
40. #19099216C22semidirect
41. #19099216C22semidirect
42. #19099208C22semidirect
43. #19099204C22semidirect
44. #19099204C22semidirect
45. #19099204C22semidirect
46. D4×D316C22semidirect
47. D4×D316C22semidirect
48. D4×D316C22semidirect
49. #19099187C22semidirect
50. #19099187C22semidirect
51. #19099169C22semidirect
52. #19099169C22semidirect
53. #19099153C22semidirect
54. #19099144C22semidirect
55. #19099132C22semidirect
56. #19099132C22semidirect
57. #19099118C22semidirect
58. #19099118C22semidirect
59. #19099114C22semidirect
60. #19099114C22semidirect
61. #19099114C22semidirect
62. #19099114C22semidirect
63. #19099114C22semidirect
64. #19099114C22semidirect
65. #19099114C22semidirect
66. #19099114C22semidirect
67. #19099114C22semidirect
68. #19099114C22semidirect
69. #19099113C22semidirect
70. C2×#14579158C22semidirect
71. #19099100C22semidirect
72. #19099100C22semidirect
73. #19099099C22semidirect
74. #19099099C22semidirect
75. #19099098C22semidirect
76. #19099098C22semidirect
77. #19099098C22semidirect
78. C2×#14579150C22semidirect
79. #19099076C22semidirect
80. #19099076C22semidirect
81. #19099076C22semidirect
82. #19099075C22semidirect
83. C2×#14579136C22semidirect
84. C2×#14579136C22semidirect
85. #19099045C22semidirect
86. #19099044C22semidirect
87. #19099037C22semidirect
88. #19099035C22semidirect
90. C4×#11929625C22semidirect
91. C4×#11929625C22semidirect
92. C4×#11929625C22semidirect
93. C4×#11929625C22semidirect
94. C4×#11929625C22semidirect
95. C4×#11929624C22semidirect
96. #19099031C22semidirect
97. #19099031C22semidirect
98. C4×#11929623C22semidirect
99. C4×#11929623C22semidirect
100. C4×Q8×D79C22semidirect
101. C4×Q8×D79C22semidirect
102. C2×#14579123C22semidirect
103. C2×#14579123C22semidirect
104. C4×D4×D79C22semidirect
105. C4×D4×D79C22semidirect
106. C4×D4×D79C22semidirect
107. #117×D79C22semidirect
108. C2×C42×D79C22semidirect
109. Q82×C79C22semidirect
110. #557×C79C22semidirect
111. #554×C79C22semidirect
112. D4×Q8×C79C22semidirect
113. #544×C79C22semidirect
114. #533×C79C22semidirect
115. C2×C4⋊Q8×C79C22semidirect
384. #41×C79#41semidirect
425. Q8×C79C2×#41semidirect
426. D4×C79C2×#41semidirect
430. C2×C4×C79C2×#41semidirect
476. C4×D79H(5,𝔽2)semidirect
523. #3503D79semidirect
536. C79#62800semidirect
542. Q82C2×D79semidirect
543. #557C2×D79semidirect
548. #554C2×D79semidirect
558. D4×Q8C2×D79semidirect
570. #544C2×D79semidirect
581. #533C2×D79semidirect
593. C2×C4⋊Q8C2×D79semidirect
820. #41#11929625semidirect
944. Q8C2×#11929625semidirect
957. D4C2×#11929625semidirect
987. C2×C4C2×#11929625semidirect

Maximal subgroups

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

subgroupindex
#237774862
#237774332
#237774072
#237773622
#237773132
#237772772
#237771782
#237771382
#237770702
#237770272
#237770112
#237770002
D4×#119296252
#237768232
#237766972
C2×#190991142
#237766062
C4×#41×D792
C79×#35032
#6280079