Finite Group Databasebeta

← #35174340

Subgroups — #35174340

Order 20224.

2282 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777627C211yesmaximal, characteristic, complemented
2#23775481C212yesmaximal, complemented
3#23775361C212yesmaximal, complemented
4#23775224C212yesmaximal, complemented
5#23775213C212yesmaximal, complemented
6#23775103C212yesmaximal, complemented
7#23775081C212yesmaximal, complemented
8#23774891C212yesmaximal, complemented
9#23774876C212yesmaximal, complemented
10#23774494C212yesmaximal, complemented
11#23774252C212yesmaximal, complemented
12#23774177C211yesmaximal, characteristic, complemented
13#23774161C211yesmaximal, characteristic, complemented
14#23773584C212yesmaximal, complemented
15#23772704C212yesmaximal, complemented
16C2×#19098714C211yesmaximal, characteristic, complemented
17C2×#19098697C211yesmaximal, characteristic, complemented
18#23772456C211yesmaximal, characteristic, complemented
19C79×#3484C211yesmaximal, characteristic, complemented
20C2×#14579187C2212yescomplemented
21C2×#14579181C2212yescomplemented
22C22×#11929612C2212yescomplemented
23C22×#11929609C2212yescomplemented
24#19099310—22no—
25#19099270C2212yescomplemented
26#19099222C2212yescomplemented
27#19099217C2212yescomplemented
28#19099209C2212yescomplemented
29#19099200—22no—
30#19099188—21no—
31#19099184C2212yescomplemented
32#19099162—21no—
33#19099150—21no—
34#19099141C2212yescomplemented
35#19099140—21no—
36C2×#14579140C2211yescharacteristic, complemented
37C2×#14579135C2211yescharacteristic, complemented
38#19098950C2212yescomplemented
39#19098945C2212yescomplemented
40#19098922C2212yescomplemented
41#19098909C2212yescomplemented
42#19098904C2212yescomplemented
43#19098896C2211yescharacteristic, complemented
44#19098891C2211yescharacteristic, complemented
45#19098887C2212yescomplemented
46#19098879C2211yescharacteristic, complemented
47#19098879C2212yescomplemented
48#19098874C2211yescharacteristic, complemented
49#19098874C2212yescomplemented
50#19098853C2212yescomplemented
51#19098843C2212yescomplemented
52#19098814C2212yescomplemented
53#19098807C2212yescomplemented
54#19098802C2212yescomplemented
55#19098797C2212yescomplemented
56#19098797C2212yescomplemented
57#19098794C2212yescomplemented
58#19098790C2212yescomplemented
59#19098790C2212yescomplemented
60#19098782C2212yescomplemented
61#19098778C2212yescomplemented
62#19098778C2212yescomplemented
63#19098775C2212yescomplemented
64#19098760C2212yescomplemented
65#19098755C2212yescomplemented
66#19098725C2212yescomplemented
67#19098725C2212yescomplemented
68#19098718C2211yescharacteristic, complemented
69#19098714C2212yescomplemented
70#19098714C2212yescomplemented
71#19098714C2212yescomplemented
72#19098714C2212yescomplemented
73#19098714C2212yescomplemented
74#19098713C2211yescharacteristic, complemented
75#19098708C2212yescomplemented
76#19098708C2212yescomplemented
77#19098706C2212yescomplemented
78#19098706C2212yescomplemented
79#19098701C2211yescharacteristic, complemented
80#19098697C2212yes—
81#19098697C2212yescomplemented
82#19098697C2212yescomplemented
83#19098697C2212yescomplemented
84#19098697C2212yescomplemented
85#19098696C2211yescharacteristic, complemented
86#19098673C2212yescomplemented
87#19098663C2212yescomplemented
88C4×#11929612C2212yescomplemented
89C4×#11929609C2212yescomplemented
90#19098635C2212yescomplemented
91#19098635C2212yescomplemented
92D4×C79⋊C8C2212yescomplemented
93D4×C79⋊C8C2212yescomplemented
94#19098624C2212yescomplemented
95#19098564C2212yescomplemented
96C2×#14579082C2212yescomplemented
97C2×#14579082C2212yescomplemented
98C2×#14579082C2212yescomplemented
99#19098530C2212yescomplemented
100C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
101C2×C22⋊(C79⋊C8)C2211yescharacteristic, complemented
102C2×H(5,𝔽2)×C79C2211yescharacteristic, complemented
103C23×D4×C79C2211yescharacteristic
104#546×C79—21no—
105#546×C79—21no—
106#546×C79C2212yes—
107#546×C79C2212yescomplemented
108D42×C79—21no—
109D42×C79—21no—
110D42×C79C2212yes—
111D42×C79C2212yescomplemented
112#535×C79C2211yescharacteristic, complemented
113#535×C79C2211yescharacteristic, complemented
114#534×C79—22no—
115#525×C79C2211yescharacteristic
116#525×C79C2211yescharacteristic
117C2×#120×C79—22no—
118#518×C79C2211yescharacteristic, complemented
119C2×#11929624C2312yescomplemented
120C2×#11929623—22no—
121C22×Dic158C2311yescharacteristic
122C22×D316C2311yescharacteristic
123C22×C22⋊D79—21no—
124#14579187—44no—
125#14579181—44no—
126C2×#11929614C2312yescomplemented
127C2×#11929612—44no—
128C2×#11929612C2312yes—
129C2×#11929612C2312yes—
130C2×#11929612C2312yes—
131C2×#11929612C2312yes—
132C2×#11929612C2312yescomplemented
133C2×#11929611C2312yescomplemented
134C2×#11929609—44no—
135C2×#11929609C2312yes—
136C2×#11929609C2312yes—
137C2×#11929609C2312yes—
138C2×#11929609C2312yes—
139C2×#11929609C2312yescomplemented
140C2×#11929608C2312yescomplemented
141C22×C79⋊C8C2312yes—
142C22×C79⋊C8C2312yes—
143C22×C79⋊C8C2312yescomplemented
144#14579161C2312yescomplemented
145#14579156—22no—
146#14579152—22no—
147#14579149C2312yescomplemented
148#14579147—22no—
149#14579147—22no—
150#14579146—22no—
151#14579145—22no—
152#14579145—22no—
153#14579143—22no—
154#14579141—22no—
155#14579140—21no—
156#14579140—21no—
157#14579140C2312yes—
158#14579140C2312yes—
159#14579140C2312yescomplemented
160#14579139—22no—
161#14579139—22no—
162#14579138—22no—
163#14579138—22no—
164#14579137—22no—
165#14579135—21no—
166#14579135—21no—
167#14579135C2312yes—
168#14579135C2312yes—
169#14579135C2312yescomplemented
170#14579134—22no—
171#14579133—22no—
172#14579133—22no—
173#14579133—22no—
174#14579132—22no—
175#14579129—22no—
176C4×Dic158C2312yescomplemented
177C4×D316C2312yescomplemented
178D4×Dic79—22no—
179(C22⋊D79)⋊C4—22no—
180C2×C4⋊Dic79C2311yescharacteristic
181C2×C4⋊Dic79C2311yescharacteristic
182C2×C4⋊Dic79C2312yescomplemented
183C2×Dic79⋊C4—21no—
184C2×C22⋊Dic79—21no—
185C2×(C2×D79)⋊C4—21no—
186C22⋊C4×D79—22no—
187#14579094C2312yescomplemented
188#14579094C2312yescomplemented
189#14579092C2312yescomplemented
190#14579092C2312yescomplemented
191C4⋊(C79⋊C8)C2312yescomplemented
192C4⋊(C79⋊C8)C2312yescomplemented
193#14579085C2312yescomplemented
194#14579085C2312yescomplemented
195#14579084C2312yescomplemented
196#14579084C2312yescomplemented
197#14579082C2312yes—
198#14579082C2312yes—
199#14579082C2312yes—
200#14579082C2312yes—
201#14579082C2312yes—
202#14579082C2312yes—
203#14579082C2312yes—
204#14579082C2312yes—
205#14579082C2312yescomplemented
206#14579082C2312yescomplemented
207#14579081C2312yescomplemented
208#14579081C2312yescomplemented
209C22⋊(C79⋊C8)C2312yes—
210C22⋊(C79⋊C8)C2312yes—
211C22⋊(C79⋊C8)C2311yescharacteristic
212C22⋊(C79⋊C8)C2311yescharacteristic
213C22⋊(C79⋊C8)C2311yescharacteristic
214C22⋊(C79⋊C8)C2311yescharacteristic
215C22⋊(C79⋊C8)C2312yescomplemented
216C22⋊(C79⋊C8)C2312yescomplemented
217#14579072C2312yescomplemented
218C4×C79⋊C8C2312yescomplemented
219C25×C79—21no—
220H(5,𝔽2)×C79—44no—
221C2×#41×C79—21no—
222C2×#41×C79C2312yes—
223C2×#41×C79C2311yescharacteristic
224C2×#41×C79C2311yescharacteristic
225C22×D4×C79—22no—
226C22×D4×C79—21no—
227C22×D4×C79—22no—
228C22×D4×C79—22no—
229C22×D4×C79—21no—
230C22×D4×C79—21no—
231C22×D4×C79—21no—
232C22×D4×C79—44no—
233C22×D4×C79C2311yescharacteristic
234C22×D4×C79C2312yes—
235C22×D4×C79C2312yes—
236C22×D4×C79C2312yes—
237C22×D4×C79C2311yescharacteristic
238C23×C4×C79C2311yescharacteristic
239#127×C79—21no—
240#127×C79C2312yes—
241#124×C79—21no—
242#124×C79C2312yes—
243#123×C79—21no—
244#123×C79—22no—
245#123×C79—22no—
246#123×C79D412yes—
247C22⋊Q8×C79D411yescharacteristic
248C22⋊Q8×C79D411yescharacteristic
249C22⋊Q8×C79C2311yescharacteristic
250C22⋊Q8×C79C2311yescharacteristic
251#121×C79—22no—
252#121×C79—22no—
253#121×C79—21no—
254#121×C79—21no—
255#121×C79—22no—
256#121×C79—22no—
257#121×C79D411yescharacteristic
258#121×C79D411yescharacteristic
259#121×C79C2311yescharacteristic
260#121×C79C2311yescharacteristic
261#121×C79C2312yes—
262#121×C79C2312yes—
263#120×C79—21no—
264#120×C79—22no—
265#120×C79—22no—
266#120×C79—22no—
267#120×C79—22no—
268#120×C79—22no—
269#120×C79—22no—
270#120×C79—22no—
271#120×C79—22no—
272#120×C79D412yes—
273C4×D4×C79—21no—
274C4×D4×C79—21no—
275C4×D4×C79—21no—
276C4×D4×C79—21no—
277C4×D4×C79C2312yes—
278C4×D4×C79C2312yes—
279C4×D4×C79C2312yes—
280C4×D4×C79C2312yes—
281#117×C79C2311yescharacteristic
282#117×C79C2311yescharacteristic
283C2×C22⋊C4×C79—22no—
284C2×C22⋊C4×C79—22no—
285C2×C22⋊C4×C79—22no—
286C23×D79—21no—
287#11929624—42no—
288#11929624—42no—
289#11929623—84no—
290C2×Dic158—21no—
291C2×Dic158—22no—
292C2×Dic158—42no—
293C2×Dic158C2412yes—
294C2×D316—21no—
295C2×D316—42no—
296C2×D316C2412yes—
297C2×C22⋊D79—22no—
298C2×C22⋊D79—22no—
299C2×C22⋊D79—22no—
300C2×C22⋊D79—22no—
301C2×C22⋊D79—82no—
302C22×Dic79—21no—
303C22×Dic79—21no—
304C22×Dic79—22no—
305C22×Dic79—21no—
306C2×C4×D79—22no—
307C2×C4×D79—22no—
308#11929614—42no—
309#11929612—24no—
310#11929612—24no—
311#11929612—42no—
312#11929612—42no—
313#11929612—42no—
314#11929611—42no—
315#11929609—24no—
316#11929609—24no—
317#11929609—42no—
318#11929609—42no—
319#11929609—42no—
320#11929608—42no—
321C2×C79⋊C8—42no—
322C2×C79⋊C8—42no—
323C2×C79⋊C8—42no—
324C2×C79⋊C8C2412yes—
325C2×C79⋊C8C2412yes—
326C2×C79⋊C8C2412yes—
327C2×C79⋊C8C2412yes—
328C4⋊Dic79—21no—
329C4⋊Dic79—21no—
330C4⋊Dic79—22no—
331C4⋊Dic79—22no—
332C4⋊Dic79C2412yes—
333C4⋊Dic79C2412yes—
334Dic79⋊C4—22no—
335Dic79⋊C4—22no—
336Dic79⋊C4—22no—
337Dic79⋊C4—22no—
338C22⋊Dic79—22no—
339C22⋊Dic79—22no—
340C22⋊Dic79—22no—
341(C2×D79)⋊C4—22no—
342(C2×D79)⋊C4—22no—
343(C2×D79)⋊C4—22no—
344(C2×D79)⋊C4—22no—
345(C2×D79)⋊C4—22no—
346(C2×D79)⋊C4—22no—
347C4×Dic79—22no—
348C24×C79—21no—
349C24×C79—22no—
350C24×C79—22no—
351C24×C79—21no—
352C24×C79—22no—
353C24×C79—44no—
354C24×C79—82no—
355C24×C79—82no—
356C24×C79C2×D411yescharacteristic
357#41×C79—24no—
358#41×C79—42no—
359#41×C79—42no—
360#41×C79—42no—
361#41×C79—44no—
362C2×Q8×C79C2×D411yescharacteristic
363C2×Q8×C79C2411yescharacteristic
364C2×D4×C79—24no—
365C2×D4×C79—24no—
366C2×D4×C79—24no—
367C2×D4×C79—24no—
368C2×D4×C79—21no—
369C2×D4×C79—21no—
370C2×D4×C79—21no—
371C2×D4×C79—22no—
372C2×D4×C79—22no—
373C2×D4×C79—22no—
374C2×D4×C79—21no—
375C2×D4×C79—22no—
376C2×D4×C79—22no—
377C2×D4×C79—22no—
378C2×D4×C79—21no—
379C2×D4×C79—22no—
380C2×D4×C79—22no—
381C2×D4×C79—42no—
382C2×D4×C79—42no—
383C2×D4×C79—42no—
384C2×D4×C79—42no—
385C2×D4×C79—44no—
386C2×D4×C79—44no—
387C2×D4×C79—44no—
388C2×D4×C79—44no—
389C2×D4×C79—48no—
390C2×D4×C79—84no—
391C2×D4×C79—84no—
392C2×D4×C79C2×D412yes—
393C2×D4×C79C2×D412yes—
394C2×D4×C79C2×D412yes—
395C2×D4×C79C2×D411yescharacteristic
396C2×D4×C79C2412yes—
397C2×D4×C79C2411yescharacteristic
398C2×D4×C79C2412yes—
399C22×C4×C79—22no—
400C22×C4×C79—21no—
401C22×C4×C79—22no—
402C22×C4×C79—22no—
403C22×C4×C79—42no—
404C22×C4×C79C2×D411yescharacteristic
405C22×C4×C79C2×D411yescharacteristic
406C22×C4×C79C2×D411yescharacteristic
407C22×C4×C79C2411yescharacteristic
408C22×C4×C79C2412yes—
409C22×C4×C79C2411yescharacteristic
410C22×C4×C79C2411yescharacteristic
411C4⋊C4×C79—21no—
412C4⋊C4×C79—21no—
413C4⋊C4×C79C2×D411yescharacteristic
414C4⋊C4×C79C2×D411yescharacteristic
415C4⋊C4×C79C2×D412yes—
416C4⋊C4×C79C2×D412yes—
417C4⋊C4×C79C2411yescharacteristic
418C4⋊C4×C79C2411yescharacteristic
419C22⋊C4×C79—21no—
420C22⋊C4×C79—21no—
421C22⋊C4×C79—21no—
422C22⋊C4×C79—22no—
423C22⋊C4×C79—22no—
424C22⋊C4×C79—22no—
425C22⋊C4×C79—22no—
426C22⋊C4×C79—22no—
427C22⋊C4×C79—22no—
428C22⋊C4×C79—21no—
429C22⋊C4×C79—21no—
430C22⋊C4×C79C2×D412yes—
431C22⋊C4×C79C2×D412yes—
432C22⋊C4×C79C2×D412yes—
433C22⋊C4×C79C2×D412yes—
434C22⋊C4×C79C2×D412yes—
435C42×C79—21no—
436C42×C79C2412yes—
437C23×C79—24no—
438C23×C79—22no—
439C23×C79—22no—
440C23×C79—22no—
441C23×C79—22no—
442C23×C79—21no—
443C23×C79—41no—
444C23×C79—44no—
445C23×C79—44no—
446C23×C79—44no—
447C23×C79—42no—
448C23×C79—44no—
449C23×C79—44no—
450C23×C79—82no—
451C23×C79—82no—
452C23×C79—81no—
453C23×C79—81no—
454C23×C79—81no—
455C23×C79—81no—
456C23×C79—82no—
457C23×C79—82no—
458C23×C79—816no—
459C23×C79C22×D411yescharacteristic
460C23×C79C22×D412yes—
461C23×C79C22×D411yescharacteristic
462C23×C79C22×D411yescharacteristic
463C22×D79—22no—
464C22×D79—42no—
465C22×D79—81no—
466C22×D79—81no—
467Q8×C79—22no—
468Q8×C79—41no—
469D4×C79—24no—
470D4×C79—24no—
471D4×C79—24no—
472D4×C79—22no—
473D4×C79—22no—
474D4×C79—22no—
475D4×C79—22no—
476D4×C79—41no—
477D4×C79—42no—
478D4×C79—44no—
479D4×C79—44no—
480D4×C79—44no—
481D4×C79—42no—
482D4×C79—44no—
483D4×C79—42no—
484D4×C79—42no—
485D4×C79—42no—
486D4×C79—82no—
487D4×C79—82no—
488D4×C79—82no—
489D4×C79—82no—
490D4×C79H(5,𝔽2)14yes—
491C2×C4×C79—22no—
492C2×C4×C79—22no—
493C2×C4×C79—22no—
494C2×C4×C79—22no—
495C2×C4×C79—22no—
496C2×C4×C79—21no—
497C2×C4×C79—21no—
498C2×C4×C79—21no—
499C2×C4×C79—41no—
500C2×C4×C79—41no—
501C2×C4×C79—41no—
502C2×C4×C79—44no—
503C2×C4×C79—42no—
504C2×C4×C79—82no—
505C2×C4×C79—82no—
506C2×C4×C79C22×D412yes—
507C2×C4×C79C22×D411yescharacteristic
508C2×C4×C79C22×D411yescharacteristic
509C2×C4×C79C22×D412yes—
510C2×C4×C79C22×D412yes—
511C2×C4×C79C22×D411yescharacteristic
512C2×C4×C79C2511yescharacteristic
513C22⋊D79—44no—
514C22⋊D79—82no—
515C22⋊D79—82no—
516C22⋊D79—82no—
517C2×Dic79—22no—
518C2×Dic79—22no—
519C2×Dic79—22no—
520C2×Dic79—42no—
521C2×Dic79—81no—
522C2×Dic79—81no—
523C2×Dic79—82no—
524D316—22no—
525D316—22no—
526D316—81no—
527C4×D79—82no—
528C4×D79—82no—
529Dic158—22no—
530Dic158—22no—
531Dic158—81no—
532Dic158—82no—
533C79⋊C8—22no—
534C79⋊C8—22no—
535C79⋊C8—22no—
536C79⋊C8—22no—
537C22×C79—21no—
538C22×C79—21no—
539C22×C79—21no—
540C22×C79—21no—
541C22×C79—22no—
542C22×C79—21no—
543C22×C79—24no—
544C22×C79—21no—
545C22×C79—22no—
546C22×C79—22no—
547C22×C79—21no—
548C22×C79—44no—
549C22×C79—42no—
550C22×C79—42no—
551C22×C79—41no—
552C22×C79—42no—
553C22×C79—41no—
554C22×C79—42no—
555C22×C79—41no—
556C22×C79—42no—
557C22×C79—88no—
558C22×C79—88no—
559C22×C79—84no—
560C22×C79—84no—
561C22×C79—164no—
562C22×C79#57612yes—
563C22×C79#57712yes—
564C22×C79C23×D411yescharacteristic
565C2×D79—42no—
566C2×D79—42no—
567C2×D79—42no—
568C2×D79—162no—
569C4×C79—21no—
570C4×C79—21no—
571C4×C79—21no—
572C4×C79—22no—
573C4×C79—22no—
574C4×C79—22no—
575C4×C79—41no—
576C4×C79—41no—
577C4×C79—41no—
578C4×C79C2×H(5,𝔽2)12yes—
579Dic79—42no—
580Dic79—42no—
581Dic79—42no—
582#61629—791nomaximal, Sylow
583C2×C79—22no—
584C2×C79—22no—
585C2×C79—41no—
586C2×C79—42no—
587C2×C79—44no—
588C2×C79—82no—
589C2×C79—81no—
590C2×C79#348411yescharacteristic
591C2×C79C2×#57611yescharacteristic
592C2×C79C2×#57711yescharacteristic
593D79—82no—
594#3536—791no—
595#3484D7911yescharacteristic, complemented
596#3314—792no—
597#3306—792no—
598#3295—792no—
599#3294—792no—
600#3282—792no—
601#3280—792no—
602#3265—792no—
603#3264—792no—
604#3224—792no—
605#3198—792no—
606#3190—791no—
607#3188—791no—
608#3118—792no—
609#3012—792no—
610C2×#450—791no—
611C2×#447—791no—
612#2977—791no—
613C79#6162911yescharacteristic, complemented, Sylow
614C2×H(5,𝔽2)C2×D7911yescharacteristic, complemented
615C23×D4C2×D7911yescharacteristic
616C2×AGL(1,ℤ/8)—792no—
617C2×#135—792no—
618C22×SD16—792no—
619C22×D8—792no—
620#562—1582no—
621#554—792no—
622#548—792no—
623#547—792no—
624#546—21no—
625#546—21no—
626#546—792no—
627#546—1582no—
628#546C2×D7912yes—
629#546C2×D7912yescomplemented
630D42—21no—
631D42—21no—
632D42C2×D7912yes—
633D42C2×D7912yescomplemented
634#543—1581no—
635#542—792no—
636#539—1581no—
637#538—1581no—
638#537—792no—
639#537—1581no—
640#535C2×D7911yescharacteristic, complemented
641#535C2×D7911yescharacteristic, complemented
642#534—22no—
643#525C2×D7911yescharacteristic
644#525C2×D7911yescharacteristic
645C2×C22⋊Q8—791no—
646C2×#121—791no—
647C2×#120—22no—
648#518C2×D7911yescharacteristic, complemented
649#496—792no—
650#495—792no—
651#489—792no—
652#486—792no—
653#485—792no—
654#484—791no—
655#483—791no—
656#482—792no—
657#481—791no—
658#481—792no—
659#480—791no—
660#480—792no—
661#476—792no—
662#474—792no—
663#469—792no—
664#468—792no—
665#467—792no—
666#466—792no—
667#466—792no—
668#465—792no—
669#465—792no—
670#465—792no—
671#464—792no—
672#463—792no—
673#463—792no—
674#463—792no—
675#460—792no—
676#459—792no—
677#452—792no—
678#452—792no—
679#451—791no—
680#450—792no—
681#450—792no—
682#450—792no—
683#450—792no—
684#450—792no—
685#450—791no—
686#449—792no—
687#449—792no—
688#449—792no—
689#449—792no—
690#448—791no—
691#447—792no—
692#447—792no—
693#447—792no—
694#447—792no—
695#447—792no—
696#447—791no—
697#442—792no—
698#440—792no—
699C4×SD16—792no—
700C4×D8—792no—
701#435—792no—
702#435—792no—
703C8×D4—792no—
704C8×D4—792no—
705#433—792no—
706#417—792no—
707C2×#102—792no—
708C2×#102—792no—
709C2×#102—792no—
710#408—792no—
711C2×C22⋊C8—791no—
712C2×C22⋊C8—791no—
713C25—21no—
714H(5,𝔽2)—44no—
715C2×#41—21no—
716C2×#41—792no—
717C2×#41—1582no—
718C2×#41C22×D7912yes—
719C2×#41C22×D7911yescharacteristic
720C2×#41C22×D7911yescharacteristic
721C22×Q8—791no—
722C22×D4—22no—
723C22×D4—21no—
724C22×D4—22no—
725C22×D4—22no—
726C22×D4—21no—
727C22×D4—21no—
728C22×D4—21no—
729C22×D4—44no—
730C22×D4—791no—
731C22×D4—1581no—
732C22×D4C22×D7911yescharacteristic
733C22×D4C22×D7912yes—
734C22×D4C22×D7912yes—
735C22×D4C22×D7912yes—
736C22×D4C22×D7911yescharacteristic
737C23×C4C22×D7911yescharacteristic
738AGL(1,ℤ/8)—3164no—
739#135—3164no—
740C2×Q16—792no—
741C2×SD16—3164no—
742C2×SD16—792no—
743C2×SD16—792no—
744C2×SD16—792no—
745C2×SD16—792no—
746C2×SD16—792no—
747C2×SD16—792no—
748C2×D8—3164no—
749C2×D8—792no—
750C2×D8—792no—
751C2×D8—792no—
752C2×D8—792no—
753C2×D8—792no—
754C2×M16—792no—
755C22×C8—792no—
756C22×C8—792no—
757C22×C8—792no—
758C4⋊Q8—792no—
759#127—21no—
760#127C22×D7912yes—
761#126—1582no—
762#125—1582no—
763#124—21no—
764#124—792no—
765#124—1582no—
766#124—1582no—
767#124C22×D7912yes—
768#123—21no—
769#123—22no—
770#123—22no—
771#123—1582no—
772#123—1582no—
773#123—1582no—
774#123—1582no—
775#123C22⋊D7912yes—
776C22⋊Q8—792no—
777C22⋊Q8—792no—
778C22⋊Q8—792no—
779C22⋊Q8—1582no—
780C22⋊Q8—1581no—
781C22⋊Q8—1581no—
782C22⋊Q8—1582no—
783C22⋊Q8—1582no—
784C22⋊Q8—1582no—
785C22⋊Q8—1582no—
786C22⋊Q8—1582no—
787C22⋊Q8C22⋊D7911yescharacteristic
788C22⋊Q8C22⋊D7911yescharacteristic
789C22⋊Q8C22×D7911yescharacteristic
790C22⋊Q8C22×D7911yescharacteristic
791#121—22no—
792#121—22no—
793#121—21no—
794#121—21no—
795#121—22no—
796#121—22no—
797#121—792no—
798#121—792no—
799#121—792no—
800#121—1582no—
801#121—1582no—
802#121—1582no—
803#121—1582no—
804#121—1581no—
805#121—1581no—
806#121—1582no—
807#121C22⋊D7911yescharacteristic
808#121C22⋊D7911yescharacteristic
809#121C22×D7911yescharacteristic
810#121C22×D7911yescharacteristic
811#121C22×D7912yes—
812#121C22×D7912yes—
813#120—21no—
814#120—22no—
815#120—22no—
816#120—22no—
817#120—22no—
818#120—22no—
819#120—22no—
820#120—22no—
821#120—22no—
822#120—1582no—
823#120C22⋊D7912yes—
824C4×Q8—792no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—21no—
828C4×D4—21no—
829C4×D4—792no—
830C4×D4—1582no—
831C4×D4—1582no—
832C4×D4C22×D7912yes—
833C4×D4C22×D7912yes—
834C4×D4C22×D7912yes—
835C4×D4C22×D7912yes—
836#117C22×D7911yescharacteristic
837#117C22×D7911yescharacteristic
838C2×C4⋊C4—791no—
839C2×C4⋊C4—791no—
840C2×C4⋊C4—792no—
841C2×C4⋊C4—1581no—
842C2×C22⋊C4—22no—
843C2×C22⋊C4—22no—
844C2×C22⋊C4—22no—
845C2×C22⋊C4—1581no—
846C2×C22⋊C4—1581no—
847C2×C22⋊C4—1582no—
848#107—792no—
849#107—792no—
850#106—792no—
851#106—792no—
852C4⋊C8—792no—
853C4⋊C8—792no—
854#103—792no—
855#103—792no—
856#103—792no—
857#103—792no—
858#102—792no—
859#102—792no—
860#102—792no—
861#102—792no—
862#102—792no—
863#102—792no—
864#102—792no—
865#102—792no—
866#102—792no—
867#102—792no—
868#102—792no—
869#102—792no—
870C22⋊C8—792no—
871C22⋊C8—792no—
872C22⋊C8—791no—
873C22⋊C8—791no—
874C22⋊C8—791no—
875C22⋊C8—791no—
876C22⋊C8—792no—
877C22⋊C8—792no—
878#97—792no—
879C4×C8—792no—
880C24—21no—
881C24—22no—
882C24—22no—
883C24—21no—
884C24—22no—
885C24—44no—
886C24—82no—
887C24—82no—
888C24—1581no—
889C24C2×C22⋊D7911yescharacteristic
890#41—24no—
891#41—42no—
892#41—42no—
893#41—42no—
894#41—44no—
895#41—3162no—
896#41—3162no—
897#41—6324no—
898C2×Q8—3162no—
899C2×Q8—792no—
900C2×Q8—1581no—
901C2×Q8—1582no—
902C2×Q8C2×C22⋊D7911yescharacteristic
903C2×Q8C23×D7911yescharacteristic
904C2×D4—24no—
905C2×D4—24no—
906C2×D4—24no—
907C2×D4—24no—
908C2×D4—21no—
909C2×D4—21no—
910C2×D4—21no—
911C2×D4—22no—
912C2×D4—22no—
913C2×D4—22no—
914C2×D4—21no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—22no—
918C2×D4—21no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—42no—
922C2×D4—42no—
923C2×D4—42no—
924C2×D4—42no—
925C2×D4—44no—
926C2×D4—44no—
927C2×D4—44no—
928C2×D4—44no—
929C2×D4—48no—
930C2×D4—84no—
931C2×D4—84no—
932C2×D4—3162no—
933C2×D4—792no—
934C2×D4—6322no—
935C2×D4—1582no—
936C2×D4—1582no—
937C2×D4—1582no—
938C2×D4—1582no—
939C2×D4—1581no—
940C2×D4C2×C22⋊D7912yes—
941C2×D4C2×C22⋊D7912yes—
942C2×D4C2×C22⋊D7912yes—
943C2×D4C2×C22⋊D7911yescharacteristic
944C2×D4C23×D7912yes—
945C2×D4C23×D7911yescharacteristic
946C2×D4C23×D7912yes—
947C22×C4—22no—
948C22×C4—21no—
949C22×C4—22no—
950C22×C4—22no—
951C22×C4—42no—
952C22×C4—1581no—
953C22×C4—1581no—
954C22×C4—1581no—
955C22×C4—1582no—
956C22×C4—1582no—
957C22×C4—1582no—
958C22×C4C2×C22⋊D7911yescharacteristic
959C22×C4C2×C22⋊D7911yescharacteristic
960C22×C4C2×C22⋊D7911yescharacteristic
961C22×C4C23×D7911yescharacteristic
962C22×C4C23×D7911yescharacteristic
963C22×C4C23×D7912yes—
964C22×C4C23×D7911yescharacteristic
965Q16—3162no—
966SD16—3162no—
967SD16—3162no—
968SD16—3162no—
969SD16—3162no—
970SD16—1584no—
971SD16—1584no—
972D8—3162no—
973D8—3162no—
974D8—3162no—
975D8—1584no—
976D8—1584no—
977M16—3162no—
978C2×C8—3162no—
979C2×C8—3162no—
980C2×C8—3162no—
981C2×C8—792no—
982C2×C8—792no—
983C2×C8—792no—
984C2×C8—792no—
985C4⋊C4—21no—
986C4⋊C4—21no—
987C4⋊C4—792no—
988C4⋊C4—792no—
989C4⋊C4—1582no—
990C4⋊C4—1582no—
991C4⋊C4—1582no—
992C4⋊C4—1582no—
993C4⋊C4—1581no—
994C4⋊C4—1582no—
995C4⋊C4—1581no—
996C4⋊C4—1582no—
997C4⋊C4C2×C22⋊D7911yescharacteristic
998C4⋊C4C2×C22⋊D7911yescharacteristic
999C4⋊C4C2×C22⋊D7912yes—
1000C4⋊C4C2×C22⋊D7912yes—
1001C4⋊C4C23×D7911yescharacteristic
1002C4⋊C4C23×D7911yescharacteristic
1003C22⋊C4—21no—
1004C22⋊C4—21no—
1005C22⋊C4—21no—
1006C22⋊C4—22no—
1007C22⋊C4—22no—
1008C22⋊C4—22no—
1009C22⋊C4—22no—
1010C22⋊C4—22no—
1011C22⋊C4—22no—
1012C22⋊C4—21no—
1013C22⋊C4—21no—
1014C22⋊C4—1582no—
1015C22⋊C4—1582no—
1016C22⋊C4—1582no—
1017C22⋊C4—1582no—
1018C22⋊C4—1582no—
1019C22⋊C4—1582no—
1020C22⋊C4—1582no—
1021C22⋊C4—1582no—
1022C22⋊C4—1582no—
1023C22⋊C4C2×C22⋊D7912yes—
1024C22⋊C4C2×C22⋊D7912yes—
1025C22⋊C4C2×C22⋊D7912yes—
1026C22⋊C4C2×C22⋊D7912yes—
1027C22⋊C4C2×C22⋊D7912yes—
1028C42—21no—
1029C42—1582no—
1030C42C23×D7912yes—
1031C23—24no—
1032C23—22no—
1033C23—22no—
1034C23—22no—
1035C23—22no—
1036C23—21no—
1037C23—41no—
1038C23—44no—
1039C23—44no—
1040C23—44no—
1041C23—42no—
1042C23—44no—
1043C23—44no—
1044C23—82no—
1045C23—82no—
1046C23—81no—
1047C23—81no—
1048C23—81no—
1049C23—81no—
1050C23—82no—
1051C23—82no—
1052C23—816no—
1053C23—3162no—
1054C23—6321no—
1055C23—6321no—
1056C23—1582no—
1057C23C22×C22⋊D7911yescharacteristic
1058C23C22×C22⋊D7912yes—
1059C23C22×C22⋊D7911yescharacteristic
1060C23C22×C22⋊D7911yescharacteristic
1061Q8—22no—
1062Q8—41no—
1063Q8—6321no—
1064Q8—6322no—
1065Q8—1582no—
1066Q8—1582no—
1067D4—24no—
1068D4—24no—
1069D4—24no—
1070D4—22no—
1071D4—22no—
1072D4—22no—
1073D4—22no—
1074D4—41no—
1075D4—42no—
1076D4—44no—
1077D4—44no—
1078D4—44no—
1079D4—42no—
1080D4—44no—
1081D4—42no—
1082D4—42no—
1083D4—42no—
1084D4—82no—
1085D4—82no—
1086D4—82no—
1087D4—82no—
1088D4—3164no—
1089D4—6321no—
1090D4—6322no—
1091D4—6322no—
1092D4—6322no—
1093D4—1582no—
1094D4—1582no—
1095D4#1457920614yes—
1096C2×C4—22no—
1097C2×C4—22no—
1098C2×C4—22no—
1099C2×C4—22no—
1100C2×C4—22no—
1101C2×C4—21no—
1102C2×C4—21no—
1103C2×C4—21no—
1104C2×C4—41no—
1105C2×C4—41no—
1106C2×C4—41no—
1107C2×C4—44no—
1108C2×C4—42no—
1109C2×C4—82no—
1110C2×C4—82no—
1111C2×C4—3162no—
1112C2×C4—6322no—
1113C2×C4—6322no—
1114C2×C4—6321no—
1115C2×C4—6321no—
1116C2×C4—6322no—
1117C2×C4—1582no—
1118C2×C4—1582no—
1119C2×C4—1582no—
1120C2×C4C22×C22⋊D7911yescharacteristic
1121C2×C4C22×C22⋊D7912yes—
1122C2×C4C22×C22⋊D7912yes—
1123C2×C4C22×C22⋊D7912yes—
1124C2×C4C22×C22⋊D7911yescharacteristic
1125C2×C4C22×C22⋊D7911yescharacteristic
1126C2×C4C24×D7911yescharacteristic
1127C8—1582no—
1128C8—1582no—
1129C8—1582no—
1130C8—1582no—
1131C22—21no—
1132C22—21no—
1133C22—21no—
1134C22—21no—
1135C22—21no—
1136C22—22no—
1137C22—24no—
1138C22—22no—
1139C22—21no—
1140C22—22no—
1141C22—21no—
1142C22—44no—
1143C22—42no—
1144C22—42no—
1145C22—41no—
1146C22—42no—
1147C22—41no—
1148C22—42no—
1149C22—41no—
1150C22—42no—
1151C22—88no—
1152C22—88no—
1153C22—84no—
1154C22—84no—
1155C22—164no—
1156C22—3162no—
1157C22—3162no—
1158C22—3162no—
1159C22—12642no—
1160C22#1909936612yes—
1161C22#1909937412yes—
1162C22C23×C22⋊D7911yescharacteristic
1163C4—21no—
1164C4—22no—
1165C4—21no—
1166C4—21no—
1167C4—22no—
1168C4—22no—
1169C4—41no—
1170C4—41no—
1171C4—41no—
1172C4—3162no—
1173C4—3162no—
1174C4—3162no—
1175C4C2×#1457920612yes—
1176C2—22no—
1177C2—22no—
1178C2—41no—
1179C2—42no—
1180C2—44no—
1181C2—82no—
1182C2—81no—
1183C2—6322no—
1184C2#2377703511yescharacteristic
1185C2C2×#1909936611yescharacteristic
1186C2C2×#1909937411yescharacteristic
subgroupG/H
centerC22C23×C22⋊D79
commutator, cosocleC2×C4×C79C25
FrattiniC2×C4C24×D79
FittingC79×#3484C2
socleC22×C79C23×D4
hypercenter#3484D79
hypocenterC79#61629
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C22 ◁ #525 ◁ #3484

Complements

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

NH ≅ G/Ntype
1. #23777627C2semidirect
2. #23775481C2semidirect
3. #23775361C2semidirect
4. #23775224C2semidirect
5. #23775213C2semidirect
6. #23775103C2semidirect
7. #23775081C2semidirect
8. #23774891C2semidirect
9. #23774876C2semidirect
10. #23774494C2semidirect
11. #23774252C2semidirect
12. #23774177C2semidirect
13. #23774161C2semidirect
14. #23773584C2semidirect
15. #23772704C2semidirect
16. C2×#19098714C2semidirect
17. C2×#19098697C2semidirect
18. #23772456C2semidirect
19. C79×#3484C2semidirect
20. C2×#14579187C22semidirect
21. C2×#14579181C22semidirect
22. C22×#11929612C22semidirect
23. C22×#11929609C22semidirect
25. #19099270C22semidirect
26. #19099222C22semidirect
27. #19099217C22semidirect
28. #19099209C22semidirect
31. #19099184C22semidirect
34. #19099141C22semidirect
36. C2×#14579140C22semidirect
37. C2×#14579135C22semidirect
38. #19098950C22semidirect
39. #19098945C22semidirect
40. #19098922C22semidirect
41. #19098909C22semidirect
42. #19098904C22semidirect
43. #19098896C22semidirect
44. #19098891C22semidirect
45. #19098887C22semidirect
46. #19098879C22semidirect
47. #19098879C22semidirect
48. #19098874C22semidirect
49. #19098874C22semidirect
50. #19098853C22semidirect
51. #19098843C22semidirect
52. #19098814C22semidirect
53. #19098807C22semidirect
54. #19098802C22semidirect
55. #19098797C22semidirect
56. #19098797C22semidirect
57. #19098794C22semidirect
58. #19098790C22semidirect
59. #19098790C22semidirect
60. #19098782C22semidirect
61. #19098778C22semidirect
62. #19098778C22semidirect
63. #19098775C22semidirect
64. #19098760C22semidirect
65. #19098755C22semidirect
66. #19098725C22semidirect
67. #19098725C22semidirect
68. #19098718C22semidirect
69. #19098714C22semidirect
70. #19098714C22semidirect
71. #19098714C22semidirect
72. #19098714C22semidirect
73. #19098714C22semidirect
74. #19098713C22semidirect
75. #19098708C22semidirect
76. #19098708C22semidirect
77. #19098706C22semidirect
78. #19098706C22semidirect
79. #19098701C22semidirect
81. #19098697C22semidirect
82. #19098697C22semidirect
83. #19098697C22semidirect
84. #19098697C22semidirect
85. #19098696C22semidirect
86. #19098673C22semidirect
87. #19098663C22semidirect
88. C4×#11929612C22semidirect
89. C4×#11929609C22semidirect
90. #19098635C22semidirect
91. #19098635C22semidirect
92. D4×C79⋊C8C22semidirect
93. D4×C79⋊C8C22semidirect
94. #19098624C22semidirect
95. #19098564C22semidirect
96. C2×#14579082C22semidirect
97. C2×#14579082C22semidirect
98. C2×#14579082C22semidirect
99. #19098530C22semidirect
100. C2×C22⋊(C79⋊C8)C22semidirect
101. C2×C22⋊(C79⋊C8)C22semidirect
102. C2×H(5,𝔽2)×C79C22semidirect
107. #546×C79C22semidirect
111. D42×C79C22semidirect
112. #535×C79C22semidirect
113. #535×C79C22semidirect
118. #518×C79C22semidirect
119. C2×#11929624C23semidirect
126. C2×#11929614C23semidirect
132. C2×#11929612C23semidirect
133. C2×#11929611C23semidirect
139. C2×#11929609C23semidirect
140. C2×#11929608C23semidirect
143. C22×C79⋊C8C23semidirect
144. #14579161C23semidirect
147. #14579149C23semidirect
159. #14579140C23semidirect
169. #14579135C23semidirect
176. C4×Dic158C23semidirect
177. C4×D316C23semidirect
182. C2×C4⋊Dic79C23semidirect
187. #14579094C23semidirect
188. #14579094C23semidirect
189. #14579092C23semidirect
190. #14579092C23semidirect
191. C4⋊(C79⋊C8)C23semidirect
192. C4⋊(C79⋊C8)C23semidirect
193. #14579085C23semidirect
194. #14579085C23semidirect
195. #14579084C23semidirect
196. #14579084C23semidirect
205. #14579082C23semidirect
206. #14579082C23semidirect
207. #14579081C23semidirect
208. #14579081C23semidirect
215. C22⋊(C79⋊C8)C23semidirect
216. C22⋊(C79⋊C8)C23semidirect
217. #14579072C23semidirect
218. C4×C79⋊C8C23semidirect
595. #3484D79semidirect
613. C79#61629semidirect
614. C2×H(5,𝔽2)C2×D79semidirect
629. #546C2×D79semidirect
633. D42C2×D79semidirect
640. #535C2×D79semidirect
641. #535C2×D79semidirect
648. #518C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237776272
#237754812
#237753612
#237752242
#237752132
#237751032
#237750812
#237748912
#237748762
#237744942
#237742522
#237741772
#237741612
#237735842
#237727042
C2×#190987142
C2×#190986972
#237724562
C79×#34842
#6162979