Finite Group Databasebeta

← #35197211

Subgroups — #35197211

Order 20224.

7254 conjugacy classes of subgroups.

The subgroup lattice has 1202 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777992C218yesmaximal, complemented
2#23777865C214yesmaximal, complemented
3#23777766C214yesmaximal, complemented
4#23777720C218yesmaximal, complemented
5#23777398C214yesmaximal, complemented
6#23777356C214yesmaximal, complemented
7#23777340C218yesmaximal, complemented
8#23777301C214yesmaximal, complemented
9#23777294C212yesmaximal, complemented
10#23777284C211yesmaximal, characteristic, complemented
11#23777274C211yesmaximal, characteristic, complemented
12#23777269C214yesmaximal, complemented
13#23777190C212yesmaximal, complemented
14#23777183C211yesmaximal, characteristic, complemented
15#23777176C211yesmaximal, characteristic, complemented
16#23777058C212yesmaximal, complemented
17#23777044C212yesmaximal, complemented
18#23776696C211yesmaximal, characteristic, complemented
19#23776696C211yesmaximal, characteristic, complemented
20C2×#532×C79C211yesmaximal, characteristic, complemented
21C2×#14579209C2212yescomplemented
22C2×#14579206C2212yes—
23#19099308C22116yescomplemented
24#19099301C22116yescomplemented
25#19099299C2214yescomplemented
26#19099296C2218yescomplemented
27#19099295C2218yescomplemented
28#19099288C2214yescomplemented
29#19099287C2214yescomplemented
30#19099282C2218yescomplemented
31#19099277C2218yescomplemented
32#19099272C2218yescomplemented
33#19099263C2218yescomplemented
34#19099262C22116yescomplemented
35#19099260C2218yescomplemented
36#19099248C2218yescomplemented
37#19099242C22116yescomplemented
38#19099239C22116yescomplemented
39#19099233C2214yescomplemented
40#19099233C2214yescomplemented
41#19099232C2218yescomplemented
42#19099232C2218yescomplemented
43#19099231C2218yescomplemented
44#19099228C2214yescomplemented
45#19099221C2218yescomplemented
46#19099220C2218yescomplemented
47#19099220C2218yescomplemented
48#19099216C2214yescomplemented
49#19099214C2218yescomplemented
50#19099212C2218yescomplemented
51#19099212C2218yescomplemented
52#19099210C2218yescomplemented
53#19099208C2218yescomplemented
54#19099207C2218yescomplemented
55#19099206C2218yescomplemented
56#19099203C22116yescomplemented
57#19099201C2218yescomplemented
58#19099201C2218yescomplemented
59#19099198C2214yescomplemented
60D4×C22⋊D79C2218yes—
61#19099182C2218yescomplemented
62#19099180C2218yescomplemented
63#19099178C2218yescomplemented
64#19099174C2214yescomplemented
65#19099167C2214yescomplemented
66#19099166C2218yescomplemented
67#19099164C2218yescomplemented
68#19099163C22116yescomplemented
69#19099155C22116yescomplemented
70#19099146C22116yescomplemented
71#19099145C22116yescomplemented
72#19099142C2218yescomplemented
73#19099138C2214yescomplemented
74#19099137C2212yes—
75#19099137C2212yescomplemented
76#19099133C2214yescomplemented
77#19099131C2214yescomplemented
78#19099130C2212yes—
79#19099130C2212yescomplemented
80#19099130C2218yescomplemented
81#19099129C2218yescomplemented
82#19099126C2214yescomplemented
83#19099122C2218yescomplemented
84#19099120C2211yescharacteristic, complemented
85#19099120C2211yescharacteristic, complemented
86#19099120C2212yescomplemented
87#19099120C2212yescomplemented
88#19099118C2214yescomplemented
89#19099114C2212yescomplemented
90#19099113C2211yescharacteristic
91#19099113C2211yescharacteristic
92#19099113C2212yescomplemented
93#19099113C2212yescomplemented
94#19099112C2214yescomplemented
95#19099111C2212yescomplemented
96#19099111C2214yescomplemented
97C4⋊Q8×D79C2212yescomplemented
98#127×D79C2212yescomplemented
99#19099097C2214yescomplemented
100#19099097C2214yescomplemented
101#19099097C2214yescomplemented
102#19099097C2212yescomplemented
103#19099097C2212yescomplemented
104#19099097C2214yescomplemented
105#19099097C2214yescomplemented
106#19099092C2218yescomplemented
107#124×D79C2214yescomplemented
108#19099074C2211yescharacteristic
109#19099074C2212yescomplemented
110#19099074C2211yescharacteristic, complemented
111#19099074C2218yescomplemented
112#19099074C2214yescomplemented
113#19099074C2214yescomplemented
114C2×#14579144C2218yescomplemented
115#19099042C2218yescomplemented
116#19099041C2212yescomplemented
117#19099038C2212yescomplemented
118#19099035C2218yescomplemented
119C4×#11929624C2211yescharacteristic
120C4×#11929624C2212yescomplemented
121C4×#11929624C2214yescomplemented
122C4×#11929624C2214yescomplemented
123C4×#11929624C2211yescharacteristic, complemented
124C22×#41×C79C2212yescomplemented
125#532×C79C2214yescomplemented
126#532×C79C2214yescomplemented
127#532×C79C2214yescomplemented
128#532×C79C2214yescomplemented
129C2×C4⋊Q8×C79C2211yescharacteristic, complemented
130C2×#127×C79C2211yescharacteristic
131C2×#124×C79C2212yescomplemented
132C2×#121×C79C2214yescomplemented
133C2×C4×D4×C79C2214yescomplemented
134C22×C42×C79C2211yescharacteristic, complemented
135#14579209—48no—
136#14579206—48no—
137C2×#11929625C2314yes—
138C2×#11929625C2314yes—
139C2×#11929624C2311yescharacteristic
140C2×#11929624C2312yes—
141C2×#11929624C2311yescharacteristic
142C2×#11929624C2318yes—
143C2×#11929624C2314yes—
144C2×#11929624C2314yes—
145C2×#11929623C2314yes—
146C2×#11929623C2314yes—
147C2×#11929623C2318yes—
148C2×Q8×D79C2314yes—
149C2×Q8×D79C2314yes—
150C22×C22⋊D79C2318yes—
151C2×D4×D79C2314yes—
152C2×D4×D79C2314yes—
153C2×D4×D79C2318yes—
154#14579161C2312yes—
155#14579161C2311yescharacteristic
156#14579161C2312yes—
157#14579161C2311yescharacteristic
158#14579160C2318yes—
159#14579159C2314yes—
160#14579159C2314yes—
161#14579158C2311yescharacteristic
162#14579158C2311yescharacteristic
163#14579157C23116yes—
164#14579157C2318yes—
165#14579157C2314yes—
166#14579157C2314yes—
167#14579156C23116yes—
168#14579155C2318yes—
169#14579155C2314yes—
170#14579155C2314yes—
171#14579154C23116yes—
172#14579154C23116yes—
173#14579153C2314yes—
174#14579153C2312yes—
175#14579153C2314yes—
176#14579153C2312yes—
177#14579152C2318yes—
178#14579151C23116yes—
179#14579150C2314yes—
180#14579150C2314yes—
181#14579149C2312yes—
182#14579149C2314yes—
183#14579149C2314yes—
184#14579149C2311yescharacteristic
185#14579149C2311yescharacteristic
186#14579148C23116yes—
187#14579148C2318yes—
188#14579148C2314yes—
189#14579148C2314yes—
190#14579147C23116yes—
191#14579147C23116yes—
192#14579146C23116yes—
193#14579145C23116yes—
194#14579144C2318yes—
195#14579144C2318yes—
196#14579144C2314yes—
197#14579144C23116yes—
198#14579144C23116yes—
199#14579144C2314yes—
200#14579144C2318yes—
201#14579144C2312yes—
202#14579144C2314yes—
203#14579144C2312yes—
204#14579143C23116yes—
205#14579143C23116yes—
206#14579142C23116yes—
207#14579142C23116yes—
208#14579141C2318yes—
209#14579140C2314yes—
210#14579140C23116yes—
211#14579140C2314yes—
212#14579140C2312yes—
213#14579140C2314yes—
214#14579140C2312yes—
215#14579140C2314yes—
216#14579140C2314yes—
217#14579139C23116yes—
218#14579138C23116yes—
219#14579138C23116yes—
220#14579137C2318yes—
221#14579137C2318yes—
222#14579136C2318yes—
223#14579135C23116yes—
224#14579135C2314yes—
225#14579135C2314yes—
226#14579135C2312yes—
227#14579135C2314yes—
228#14579135C2314yes—
229#14579135C2312yes—
230#14579135C2314yes—
231#14579134C23116yes—
232#14579134C23116yes—
233#14579133C23116yes—
234#14579133C23116yes—
235#14579133C23116yes—
236#14579133C23116yes—
237#14579132C23116yes—
238#14579132C2318yes—
239#14579132C23116yes—
240#14579132C2318yes—
241#14579132C2318yes—
242#14579132C2318yes—
243#14579131C23116yes—
244#14579130C2318yes—
245#14579130C2318yes—
246#14579130C2312yes—
247#14579130C2314yes—
248#14579130C2312yes—
249#14579129C23116yes—
250#14579129C23116yes—
251Q8×Dic79C2318yes—
252Q8×Dic79C2318yes—
253C4×Dic158C2314yes—
254C4×Dic158C2314yes—
255C4×Dic158C2312yes—
256C4×Dic158C2312yes—
257C4×Dic158C2314yes—
258C4×Dic158C2314yes—
259C4×Dic158C2314yes—
260#14579126C2318yes—
261C4×D316C2314yes—
262C4×D316C2312yes—
263C4×D316C2314yes—
264C4×D316C2314yes—
265C4×D316C2314yes—
266C4×D316C2314yes—
267C4×D316C2312yes—
268D4×Dic79C2318yes—
269D4×Dic79C2318yes—
270D4×Dic79C2318yes—
271D4×Dic79C2318yes—
272#14579123C2318yes—
273C4×C22⋊D79C2318yes—
274C4×C22⋊D79C23116yes—
275C4×C22⋊D79C23116yes—
276C4×C22⋊D79C2314yes—
277C4×C22⋊D79C2314yes—
278C4×C22⋊D79C2318yes—
279C4×C22⋊D79C2318yes—
280C4×C22⋊D79C2314yes—
281C4×C22⋊D79C2314yes—
282C4×C22⋊D79C2314yes—
283C4×C22⋊D79C2314yes—
284(C22⋊D79)⋊C4C23116yes—
285(C22⋊D79)⋊C4C23116yes—
286#14579120C2312yes—
287#14579120C2311yescharacteristic
288#14579120C2314yes—
289#14579120C2318yes—
290#14579120C2314yes—
291#14579120C2311yescharacteristic
292#14579119C2318yes—
293#14579118C2312yes—
294#14579118C2314yes—
295#14579118C2312yes—
296#14579118C2314yes—
297#14579118C2314yes—
298#14579118C2318yes—
299#14579117C23116yes—
300C2×Dic79⋊C4C23116yes—
301C4⋊C4×D79C2318yes—
302C2×C22⋊Dic79C2318yes—
303C2×(C2×D79)⋊C4C23116yes—
304C22⋊C4×D79C23116yes—
305C42×D79C2312yes—
306C42×D79C2314yes—
307C42×D79C2312yes—
308C2×#41×C79—48no—
309C2×#41×C79C2318yes—
310C2×#41×C79C2318yes—
311C22×Q8×C79C2312yes—
312C22×D4×C79C2312yes—
313C22×D4×C79C2314yes—
314C22×D4×C79C2314yes—
315C23×C4×C79C2311yescharacteristic
316C23×C4×C79C2312yes—
317C23×C4×C79C2314yes—
318C4⋊Q8×C79C2312yes—
319C4⋊Q8×C79C2314yes—
320C4⋊Q8×C79C2312yes—
321#127×C79C2312yes—
322#127×C79C2314yes—
323#127×C79C2312yes—
324#124×C79C2314yes—
325#124×C79C2318yes—
326#124×C79C2314yes—
327#121×C79C2318yes—
328#121×C79C2318yes—
329#121×C79C2318yes—
330#121×C79C2318yes—
331C4×D4×C79C2318yes—
332C4×D4×C79C2318yes—
333C4×D4×C79C2318yes—
334C4×D4×C79C2318yes—
335C2×C4⋊C4×C79C2314yes—
336C2×C22⋊C4×C79C2318yes—
337C2×C42×C79C2312yes—
338C2×C42×C79C2311yescharacteristic
339C2×C42×C79C2311yescharacteristic
340C2×C42×C79C2312yes—
341C2×C42×C79C2312yes—
342C2×C42×C79C2312yes—
343C2×C42×C79C2312yes—
344C23×D79C2418yes—
345#11929625—48no—
346#11929625—48no—
347#11929624—24no—
348#11929624—28no—
349#11929624—24no—
350#11929624—416no—
351#11929624—48no—
352#11929624—48no—
353#11929623—416no—
354#11929623—48no—
355#11929623—48no—
356C2×Dic158C2411yescharacteristic
357C2×Dic158C2412yes—
358C2×Dic158C2411yescharacteristic
359C2×Dic158C2414yes—
360C2×Dic158C2418yes—
361C2×Dic158C2414yes—
362Q8×D79—48no—
363Q8×D79—48no—
364C2×D316C2411yescharacteristic
365C2×D316C2412yes—
366C2×D316C2414yes—
367C2×D316C2411yescharacteristic
368C2×D316C2418yes—
369C2×D316C2414yes—
370C2×C22⋊D79—416no—
371C2×C22⋊D79C2412yes—
372C2×C22⋊D79C2414yes—
373C2×C22⋊D79C2412yes—
374C2×C22⋊D79C24116yes—
375C2×C22⋊D79C2418yes—
376C2×C22⋊D79C2418yes—
377C2×C22⋊D79C2414yes—
378C2×C22⋊D79C2418yes—
379C2×C22⋊D79C2414yes—
380C2×C22⋊D79C24116yes—
381D4×D79—48no—
382D4×D79—48no—
383D4×D79—416no—
384C22×Dic79C2418yes—
385C22×Dic79C24116yes—
386C2×C4×D79C2412yes—
387C2×C4×D79C2414yes—
388C2×C4×D79C2414yes—
389C2×C4×D79C2412yes—
390C2×C4×D79C2414yes—
391C2×C4×D79C2418yes—
392C2×C4×D79C2418yes—
393C2×C4×D79C2418yes—
394C4⋊Dic79C2414yes—
395C4⋊Dic79C2414yes—
396C4⋊Dic79C2412yes—
397C4⋊Dic79C2414yes—
398C4⋊Dic79C2412yes—
399C4⋊Dic79C2414yes—
400C4⋊Dic79C2414yes—
401C4⋊Dic79C24116yes—
402Dic79⋊C4C24116yes—
403Dic79⋊C4C2414yes—
404Dic79⋊C4C2418yes—
405Dic79⋊C4C24116yes—
406Dic79⋊C4C2414yes—
407Dic79⋊C4C2414yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C2414yes—
410Dic79⋊C4C2418yes—
411Dic79⋊C4C2418yes—
412Dic79⋊C4C2414yes—
413C22⋊Dic79C24116yes—
414C22⋊Dic79C2412yes—
415C22⋊Dic79C2414yes—
416C22⋊Dic79C24116yes—
417C22⋊Dic79C24116yes—
418C22⋊Dic79C2412yes—
419C22⋊Dic79C2414yes—
420C22⋊Dic79C2418yes—
421C22⋊Dic79C2414yes—
422(C2×D79)⋊C4C2414yes—
423(C2×D79)⋊C4C24116yes—
424(C2×D79)⋊C4C2414yes—
425(C2×D79)⋊C4C2418yes—
426(C2×D79)⋊C4C24116yes—
427(C2×D79)⋊C4C2414yes—
428(C2×D79)⋊C4C2414yes—
429(C2×D79)⋊C4C2414yes—
430(C2×D79)⋊C4C2418yes—
431(C2×D79)⋊C4C2418yes—
432(C2×D79)⋊C4C2414yes—
433C4×Dic79C2418yes—
434C4×Dic79C2414yes—
435C4×Dic79C2412yes—
436C4×Dic79C2414yes—
437C4×Dic79C2414yes—
438C4×Dic79C2412yes—
439C4×Dic79C24116yes—
440C24×C79C2414yes—
441C24×C79C2411yescharacteristic
442#41×C79—416no—
443#41×C79—416no—
444C2×Q8×C79—28no—
445C2×Q8×C79C2414yes—
446C2×Q8×C79C2414yes—
447C2×D4×C79—28no—
448C2×D4×C79—48no—
449C2×D4×C79—48no—
450C2×D4×C79C2418yes—
451C2×D4×C79C2414yes—
452C2×D4×C79C2414yes—
453C2×D4×C79C2418yes—
454C2×D4×C79C24116yes—
455C22×C4×C79—24no—
456C22×C4×C79—44no—
457C22×C4×C79—48no—
458C22×C4×C79C2412yes—
459C22×C4×C79C2412yes—
460C22×C4×C79C2414yes—
461C22×C4×C79C2412yes—
462C22×C4×C79C2411yescharacteristic
463C22×C4×C79C2412yes—
464C22×C4×C79C2412yes—
465C22×C4×C79C2412yes—
466C22×C4×C79C2412yes—
467C22×C4×C79C2412yes—
468C22×C4×C79C24116yes—
469C22×C4×C79C2411yescharacteristic
470C4⋊C4×C79C2418yes—
471C4⋊C4×C79C2418yes—
472C22⋊C4×C79C24116yes—
473C22⋊C4×C79C24116yes—
474C42×C79C2412yes—
475C42×C79C2412yes—
476C42×C79C2412yes—
477C42×C79C2412yes—
478C42×C79C2411yescharacteristic
479C42×C79C2411yescharacteristic
480C42×C79C2412yes—
481C42×C79C2411yescharacteristic
482C42×C79C2411yescharacteristic
483C42×C79C2412yes—
484C23×C79—22no—
485C23×C79—28no—
486C23×C79—42no—
487C23×C79—48no—
488C23×C79C2512yes—
489C23×C79C2518yes—
490C23×C79C2511yescharacteristic
491C22×D79—48no—
492C22×D79—416no—
493C22×D79C2512yes—
494C22×D79C2514yes—
495C22×D79C2512yes—
496Q8×C79—28no—
497Q8×C79—28no—
498D4×C79—28no—
499D4×C79—28no—
500D4×C79—216no—
501D4×C79—48no—
502D4×C79—416no—
503C2×C4×C79—28no—
504C2×C4×C79—22no—
505C2×C4×C79—24no—
506C2×C4×C79—24no—
507C2×C4×C79—24no—
508C2×C4×C79—24no—
509C2×C4×C79—24no—
510C2×C4×C79—42no—
511C2×C4×C79—42no—
512C2×C4×C79—42no—
513C2×C4×C79—416no—
514C2×C4×C79H(5,𝔽2)14yes—
515C2×C4×C79C2512yes—
516C2×C4×C79C2518yes—
517C2×C4×C79C2512yes—
518C2×C4×C79C2512yes—
519C2×C4×C79C2512yes—
520C2×C4×C79C2511yescharacteristic
521C2×C4×C79C2511yescharacteristic
522C2×C4×C79C2512yes—
523C22⋊D79—24no—
524C22⋊D79—28no—
525C22⋊D79—24no—
526C22⋊D79—48no—
527C22⋊D79—48no—
528C22⋊D79—416no—
529C22⋊D79—416no—
530C22⋊D79—44no—
531C22⋊D79—48no—
532C22⋊D79—44no—
533C2×Dic79—48no—
534C2×Dic79—416no—
535C2×Dic79C2514yes—
536C2×Dic79C2518yes—
537C2×Dic79C2514yes—
538C2×Dic79C2512yes—
539C2×Dic79C2514yes—
540C2×Dic79C2512yes—
541D316—22no—
542D316—24no—
543D316—22no—
544D316—28no—
545D316—44no—
546D316—48no—
547C4×D79—24no—
548C4×D79—28no—
549C4×D79—24no—
550C4×D79—28no—
551C4×D79—28no—
552C4×D79—48no—
553C4×D79—48no—
554C4×D79—48no—
555Dic158—22no—
556Dic158—24no—
557Dic158—22no—
558Dic158—28no—
559Dic158—48no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—28no—
563C22×C79—22no—
564C22×C79—22no—
565C22×C79—22no—
566C22×C79—216no—
567C22×C79—44no—
568C22×C79—88no—
569C22×C79C2×H(5,𝔽2)12yes—
570C22×C79C2611yescharacteristic
571C2×D79—22no—
572C2×D79—24no—
573C2×D79—22no—
574C2×D79—24no—
575C2×D79—28no—
576C2×D79—24no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—28no—
580C4×C79—22no—
581C4×C79—22no—
582C4×C79—22no—
583C4×C79C2×H(5,𝔽2)12yes—
584C4×C79C2×H(5,𝔽2)12yes—
585C4×C79#58514yes—
586Dic79—22no—
587Dic79—24no—
588Dic79—22no—
589Dic79—24no—
590Dic79—28no—
591Dic79—24no—
592#62836—791nomaximal, Sylow
593C2×C79—22no—
594C2×C79—48no—
595C2×C79—42no—
596C2×C79C22×H(5,𝔽2)11yescharacteristic
597C2×C79C2×#58512yes—
598D79—42no—
599D79—44no—
600D79—42no—
601#3562—798no—
602#3554—794no—
603#3546—794no—
604#3542—798no—
605#3517—794no—
606#3514—794no—
607#3513—798no—
608#3511—794no—
609#3510—792no—
610#3509—791no—
611#3508—794no—
612#3508—791no—
613#3500—792no—
614#3499—791no—
615#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444—791no—
620C2×#532D7911yescharacteristic, complemented
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)—792no—
624C22×#41C2×D7912yescomplemented
625#562—7916no—
626#560—7916no—
627#559—794no—
628#559—798no—
629#559—798no—
630#557—794no—
631#556—794no—
632#556—798no—
633#555—798no—
634#554—798no—
635#553—798no—
636#553—7916no—
637#553—798no—
638#552—798no—
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—794no—
644#550—794no—
645#550—798no—
646D4×Q8—794no—
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—798no—
652#547—794no—
653#547—798no—
654#546—798no—
655#546—798no—
656#546—798no—
657#546—798no—
658#546—798no—
659#546—798no—
660#546—7916no—
661D42—798no—
662D42—794no—
663#542—798no—
664#542—798no—
665#542—798no—
666#541—794no—
667#540—794no—
668#540—7916no—
669#540—798no—
670#540—798no—
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—792no—
676#536—792no—
677#536—794no—
678#536—794no—
679#535—792no—
680#535—792no—
681#535—798no—
682#535—794no—
683#535—794no—
684#535—798no—
685#534—798no—
686#533—794no—
687#533—791no—
688#533—791no—
689#533—792no—
690#533—792no—
691#532—792no—
692#532—792no—
693#532—794no—
694#532—794no—
695#532—791no—
696#532—791no—
697#532—792no—
698#532—792no—
699#532C2×D7914yescomplemented
700#532C2×D7914yescomplemented
701#532C2×D7914yescomplemented
702#532C2×D7914yescomplemented
703C2×C4⋊Q8—792no—
704C2×C4⋊Q8C2×D7911yescharacteristic, complemented
705C2×#127—792no—
706C2×#127C2×D7911yescharacteristic
707#529—798no—
708#529—794no—
709#529—794no—
710#529—792no—
711#529—792no—
712#529—794no—
713#529—794no—
714#529—794no—
715C2×#124—794no—
716C2×#124C2×D7912yescomplemented
717#525—791no—
718#525—792no—
719#525—791no—
720#525—794no—
721#525—794no—
722#525—798no—
723C2×#123—798no—
724C2×#121C2×D7914yescomplemented
725#520—798no—
726#519—792no—
727#518—792no—
728#518—798no—
729C4×#41—791no—
730C4×#41—791no—
731C4×#41—792no—
732C4×#41—794no—
733C4×#41—794no—
734C2×C4×D4C2×D7914yescomplemented
735C22×C42C2×D7911yescharacteristic, complemented
7362−1+4—3168no—
737H(5,𝔽2)—3168no—
738C2×#41—48no—
739C2×#41—794no—
740C2×#41—794no—
741C2×#41—798no—
742C2×#41—794no—
743C2×#41—794no—
744C2×#41—794no—
745C2×#41—794no—
746C2×#41—798no—
747C2×#41—791no—
748C2×#41—792no—
749C2×#41—791no—
750C2×#41C22×D7918yes—
751C2×#41C22×D7918yes—
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8C22×D7912yes—
755C22×D4—798no—
756C22×D4—798no—
757C22×D4—794no—
758C22×D4—794no—
759C22×D4C22×D7912yes—
760C22×D4C22×D7914yes—
761C22×D4C22×D7914yes—
762C23×C4C22×D7911yescharacteristic
763C23×C4C22×D7914yes—
764C23×C4C22×D7912yes—
765C4⋊Q8—794no—
766C4⋊Q8—794no—
767C4⋊Q8—798no—
768C4⋊Q8—791no—
769C4⋊Q8—792no—
770C4⋊Q8—791no—
771C4⋊Q8—792no—
772C4⋊Q8C22×D7912yes—
773C4⋊Q8C22×D7912yes—
774C4⋊Q8C22×D7914yes—
775#127—794no—
776#127—798no—
777#127—794no—
778#127—7916no—
779#127—791no—
780#127—791no—
781#127C22×D7912yes—
782#127C22×D7912yes—
783#127C22×D7914yes—
784#126—7916no—
785#126—7916no—
786#126—7916no—
787#126—798no—
788#126—794no—
789#126—794no—
790#125—798no—
791#125—7916no—
792#125—792no—
793#125—794no—
794#125—792no—
795#125—794no—
796#124—794no—
797#124—794no—
798#124—794no—
799#124—794no—
800#124—798no—
801#124—7916no—
802#124—7916no—
803#124—7916no—
804#124—791no—
805#124—791no—
806#124—792no—
807#124—794no—
808#124—794no—
809#124C22×D7914yes—
810#124C22×D7914yes—
811#124C22×D7918yes—
812#123—7916no—
813#123—7916no—
814#123—792no—
815#123—794no—
816#123—798no—
817#123—798no—
818#123—7916no—
819#123—7916no—
820#123—792no—
821#123—794no—
822#123—794no—
823#123—798no—
824#123—7916no—
825#123—7916no—
826#123—7916no—
827#123—7916no—
828C22⋊Q8—798no—
829C22⋊Q8—798no—
830C22⋊Q8—794no—
831C22⋊Q8—794no—
832C22⋊Q8—792no—
833C22⋊Q8—794no—
834C22⋊Q8—792no—
835C22⋊Q8—794no—
836C22⋊Q8—794no—
837C22⋊Q8—7916no—
838C22⋊Q8—798no—
839C22⋊Q8—7916no—
840C22⋊Q8—7916no—
841C22⋊Q8—7916no—
842#121—798no—
843#121—798no—
844#121—798no—
845#121—798no—
846#121—7916no—
847#121—7916no—
848#121—7916no—
849#121—7916no—
850#121—7916no—
851#121—7916no—
852#121—794no—
853#121—794no—
854#121—792no—
855#121—794no—
856#121—794no—
857#121—792no—
858#121—794no—
859#121—7916no—
860#121—798no—
861#121—7916no—
862#121—7916no—
863#121C22×D7918yes—
864#121C22×D7918yes—
865#121C22×D7918yes—
866#121C22×D7918yes—
867#120—792no—
868#120—794no—
869#120—792no—
870#120—798no—
871#120—798no—
872#120—7916no—
873#120—7916no—
874#120—7916no—
875C4×Q8—798no—
876C4×Q8—798no—
877C4×Q8—798no—
878C4×Q8—794no—
879C4×Q8—794no—
880C4×Q8—792no—
881C4×Q8—792no—
882C4×Q8—794no—
883C4×Q8—794no—
884C4×Q8—794no—
885C4×D4—798no—
886C4×D4—798no—
887C4×D4—798no—
888C4×D4—798no—
889C4×D4—798no—
890C4×D4—794no—
891C4×D4—794no—
892C4×D4—794no—
893C4×D4—798no—
894C4×D4—794no—
895C4×D4—798no—
896C4×D4—794no—
897C4×D4—794no—
898C4×D4—7916no—
899C4×D4—7916no—
900C4×D4—798no—
901C4×D4—7916no—
902C4×D4—7916no—
903C4×D4—794no—
904C4×D4—792no—
905C4×D4—794no—
906C4×D4—794no—
907C4×D4—794no—
908C4×D4—794no—
909C4×D4—792no—
910C4×D4C22×D7918yes—
911C4×D4C22×D7918yes—
912C4×D4C22×D7918yes—
913C4×D4C22×D7918yes—
914#117—791no—
915#117—792no—
916#117—791no—
917#117—794no—
918#117—794no—
919#117—798no—
920#117—798no—
921#117—7916no—
922#117—794no—
923#117—794no—
924#117—792no—
925#117—794no—
926#117—792no—
927#117—798no—
928C2×C4⋊C4—7916no—
929C2×C4⋊C4—798no—
930C2×C4⋊C4C22×D7914yes—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—7916no—
933C2×C22⋊C4—7916no—
934C2×C22⋊C4C22×D7918yes—
935C2×C42—794no—
936C2×C42—792no—
937C2×C42—792no—
938C2×C42C22×D7912yes—
939C2×C42C22×D7911yescharacteristic
940C2×C42C22×D7912yes—
941C2×C42C22×D7911yescharacteristic
942C2×C42C22×D7912yes—
943C2×C42C22×D7912yes—
944C2×C42C22×D7912yes—
945C24—798no—
946C24C23×D7914yes—
947C24C23×D7911yescharacteristic
948#41—416no—
949#41—416no—
950#41—3168no—
951#41—31616no—
952#41—3168no—
953#41—31616no—
954#41—3168no—
955#41—3168no—
956#41—3168no—
957#41—3168no—
958#41—1584no—
959#41—1588no—
960#41—1584no—
961C2×Q8—28no—
962C2×Q8—3168no—
963C2×Q8—3168no—
964C2×Q8—794no—
965C2×Q8—798no—
966C2×Q8—794no—
967C2×Q8—791no—
968C2×Q8—792no—
969C2×Q8—791no—
970C2×Q8C23×D7914yes—
971C2×Q8C23×D7914yes—
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—48no—
975C2×D4—31616no—
976C2×D4—31616no—
977C2×D4—3168no—
978C2×D4—3168no—
979C2×D4—794no—
980C2×D4—798no—
981C2×D4—7916no—
982C2×D4—7916no—
983C2×D4—794no—
984C2×D4—798no—
985C2×D4—798no—
986C2×D4—792no—
987C2×D4—794no—
988C2×D4—792no—
989C2×D4—794no—
990C2×D4—798no—
991C2×D4—794no—
992C2×D4—791no—
993C2×D4—792no—
994C2×D4—791no—
995C2×D4C23×D7918yes—
996C2×D4C23×D7914yes—
997C2×D4C23×D7914yes—
998C2×D4C23×D7918yes—
999C2×D4C23×D79116yes—
1000C22×C4—24no—
1001C22×C4—44no—
1002C22×C4—48no—
1003C22×C4—7916no—
1004C22×C4—798no—
1005C22×C4—798no—
1006C22×C4—798no—
1007C22×C4—798no—
1008C22×C4—794no—
1009C22×C4—794no—
1010C22×C4—792no—
1011C22×C4—794no—
1012C22×C4—792no—
1013C22×C4C23×D7912yes—
1014C22×C4C23×D7912yes—
1015C22×C4C23×D7912yes—
1016C22×C4C23×D7912yes—
1017C22×C4C23×D7912yes—
1018C22×C4C23×D7911yescharacteristic
1019C22×C4C23×D7914yes—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7912yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D79116yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—794no—
1026C4⋊C4—798no—
1027C4⋊C4—7916no—
1028C4⋊C4—7916no—
1029C4⋊C4—794no—
1030C4⋊C4—794no—
1031C4⋊C4—794no—
1032C4⋊C4—794no—
1033C4⋊C4—798no—
1034C4⋊C4—798no—
1035C4⋊C4—794no—
1036C4⋊C4—794no—
1037C4⋊C4—794no—
1038C4⋊C4—792no—
1039C4⋊C4—794no—
1040C4⋊C4—792no—
1041C4⋊C4—794no—
1042C4⋊C4—794no—
1043C4⋊C4—7916no—
1044C4⋊C4C23×D7918yes—
1045C4⋊C4C23×D7918yes—
1046C22⋊C4—792no—
1047C22⋊C4—794no—
1048C22⋊C4—7916no—
1049C22⋊C4—7916no—
1050C22⋊C4—792no—
1051C22⋊C4—7916no—
1052C22⋊C4—794no—
1053C22⋊C4—798no—
1054C22⋊C4—794no—
1055C22⋊C4—794no—
1056C22⋊C4—794no—
1057C22⋊C4—798no—
1058C22⋊C4—7916no—
1059C22⋊C4—7916no—
1060C22⋊C4—794no—
1061C22⋊C4—794no—
1062C22⋊C4—794no—
1063C22⋊C4—798no—
1064C22⋊C4—798no—
1065C22⋊C4—794no—
1066C22⋊C4C23×D79116yes—
1067C22⋊C4C23×D79116yes—
1068C42—798no—
1069C42—792no—
1070C42—794no—
1071C42—794no—
1072C42—794no—
1073C42—792no—
1074C42—7916no—
1075C42C23×D7911yescharacteristic
1076C42C23×D7911yescharacteristic
1077C42C23×D7912yes—
1078C42C23×D7912yes—
1079C42C23×D7911yescharacteristic
1080C42C23×D7911yescharacteristic
1081C42C23×D7912yes—
1082C42C23×D7912yes—
1083C42C23×D7912yes—
1084C42C23×D7912yes—
1085C23—22no—
1086C23—28no—
1087C23—42no—
1088C23—48no—
1089C23—3168no—
1090C23—31616no—
1091C23—792no—
1092C23—794no—
1093C23—792no—
1094C23C24×D7912yes—
1095C23C24×D7918yes—
1096C23C24×D7911yescharacteristic
1097Q8—28no—
1098Q8—28no—
1099Q8—3168no—
1100Q8—3164no—
1101Q8—1582no—
1102Q8—1584no—
1103Q8—1582no—
1104Q8—1588no—
1105D4—28no—
1106D4—28no—
1107D4—216no—
1108D4—48no—
1109D4—416no—
1110D4—3168no—
1111D4—3164no—
1112D4—3168no—
1113D4—3168no—
1114D4—31616no—
1115D4—3164no—
1116D4—3168no—
1117D4—31616no—
1118D4—3164no—
1119D4—1584no—
1120D4—1588no—
1121D4—1584no—
1122D4—1582no—
1123D4—1584no—
1124D4—1582no—
1125D4—1588no—
1126C2×C4—22no—
1127C2×C4—28no—
1128C2×C4—24no—
1129C2×C4—24no—
1130C2×C4—24no—
1131C2×C4—24no—
1132C2×C4—24no—
1133C2×C4—42no—
1134C2×C4—42no—
1135C2×C4—42no—
1136C2×C4—416no—
1137C2×C4—3168no—
1138C2×C4—3168no—
1139C2×C4—3168no—
1140C2×C4—3168no—
1141C2×C4—31616no—
1142C2×C4—794no—
1143C2×C4—798no—
1144C2×C4—794no—
1145C2×C4—792no—
1146C2×C4—794no—
1147C2×C4—792no—
1148C2×C4—1584no—
1149C2×C4—1588no—
1150C2×C4—1584no—
1151C2×C4—1588no—
1152C2×C4—1588no—
1153C2×C4#1457920614yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7918yes—
1156C2×C4C24×D7912yes—
1157C2×C4C24×D7912yes—
1158C2×C4C24×D7912yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—28no—
1165C22—22no—
1166C22—22no—
1167C22—216no—
1168C22—44no—
1169C22—88no—
1170C22—1582no—
1171C22—1584no—
1172C22—1582no—
1173C22—1588no—
1174C22—1584no—
1175C22—1584no—
1176C22—12648no—
1177C22C2×#1457920612yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—28no—
1181C4—22no—
1182C4—22no—
1183C4—22no—
1184C4—1582no—
1185C4—1584no—
1186C4—1582no—
1187C4—1584no—
1188C4—1588no—
1189C4—1584no—
1190C4C2×#1457920612yes—
1191C4C2×#1457920612yes—
1192C4#1909939914yes—
1193C2—22no—
1194C2—42no—
1195C2—48no—
1196C2—3162no—
1197C2—3164no—
1198C2—3162no—
1199C2C22×#1457920611yescharacteristic
1200C2C2×#1909939912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC2×#532×C79C2
hypercenterC2×#532D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777992C2semidirect
2. #23777865C2semidirect
3. #23777766C2semidirect
4. #23777720C2semidirect
5. #23777398C2semidirect
6. #23777356C2semidirect
7. #23777340C2semidirect
8. #23777301C2semidirect
9. #23777294C2semidirect
10. #23777284C2semidirect
11. #23777274C2semidirect
12. #23777269C2semidirect
13. #23777190C2semidirect
14. #23777183C2semidirect
15. #23777176C2semidirect
16. #23777058C2semidirect
17. #23777044C2semidirect
18. #23776696C2semidirect
19. #23776696C2semidirect
20. C2×#532×C79C2semidirect
21. C2×#14579209C22semidirect
23. #19099308C22semidirect
24. #19099301C22semidirect
25. #19099299C22semidirect
26. #19099296C22semidirect
27. #19099295C22semidirect
28. #19099288C22semidirect
29. #19099287C22semidirect
30. #19099282C22semidirect
31. #19099277C22semidirect
32. #19099272C22semidirect
33. #19099263C22semidirect
34. #19099262C22semidirect
35. #19099260C22semidirect
36. #19099248C22semidirect
37. #19099242C22semidirect
38. #19099239C22semidirect
39. #19099233C22semidirect
40. #19099233C22semidirect
41. #19099232C22semidirect
42. #19099232C22semidirect
43. #19099231C22semidirect
44. #19099228C22semidirect
45. #19099221C22semidirect
46. #19099220C22semidirect
47. #19099220C22semidirect
48. #19099216C22semidirect
49. #19099214C22semidirect
50. #19099212C22semidirect
51. #19099212C22semidirect
52. #19099210C22semidirect
53. #19099208C22semidirect
54. #19099207C22semidirect
55. #19099206C22semidirect
56. #19099203C22semidirect
57. #19099201C22semidirect
58. #19099201C22semidirect
59. #19099198C22semidirect
61. #19099182C22semidirect
62. #19099180C22semidirect
63. #19099178C22semidirect
64. #19099174C22semidirect
65. #19099167C22semidirect
66. #19099166C22semidirect
67. #19099164C22semidirect
68. #19099163C22semidirect
69. #19099155C22semidirect
70. #19099146C22semidirect
71. #19099145C22semidirect
72. #19099142C22semidirect
73. #19099138C22semidirect
75. #19099137C22semidirect
76. #19099133C22semidirect
77. #19099131C22semidirect
79. #19099130C22semidirect
80. #19099130C22semidirect
81. #19099129C22semidirect
82. #19099126C22semidirect
83. #19099122C22semidirect
84. #19099120C22semidirect
85. #19099120C22semidirect
86. #19099120C22semidirect
87. #19099120C22semidirect
88. #19099118C22semidirect
89. #19099114C22semidirect
92. #19099113C22semidirect
93. #19099113C22semidirect
94. #19099112C22semidirect
95. #19099111C22semidirect
96. #19099111C22semidirect
97. C4⋊Q8×D79C22semidirect
98. #127×D79C22semidirect
99. #19099097C22semidirect
100. #19099097C22semidirect
101. #19099097C22semidirect
102. #19099097C22semidirect
103. #19099097C22semidirect
104. #19099097C22semidirect
105. #19099097C22semidirect
106. #19099092C22semidirect
107. #124×D79C22semidirect
109. #19099074C22semidirect
110. #19099074C22semidirect
111. #19099074C22semidirect
112. #19099074C22semidirect
113. #19099074C22semidirect
114. C2×#14579144C22semidirect
115. #19099042C22semidirect
116. #19099041C22semidirect
117. #19099038C22semidirect
118. #19099035C22semidirect
120. C4×#11929624C22semidirect
121. C4×#11929624C22semidirect
122. C4×#11929624C22semidirect
123. C4×#11929624C22semidirect
124. C22×#41×C79C22semidirect
125. #532×C79C22semidirect
126. #532×C79C22semidirect
127. #532×C79C22semidirect
128. #532×C79C22semidirect
129. C2×C4⋊Q8×C79C22semidirect
131. C2×#124×C79C22semidirect
132. C2×#121×C79C22semidirect
133. C2×C4×D4×C79C22semidirect
134. C22×C42×C79C22semidirect
620. C2×#532D79semidirect
621. C79#62836semidirect
624. C22×#41C2×D79semidirect
699. #532C2×D79semidirect
700. #532C2×D79semidirect
701. #532C2×D79semidirect
702. #532C2×D79semidirect
704. C2×C4⋊Q8C2×D79semidirect
716. C2×#124C2×D79semidirect
724. C2×#121C2×D79semidirect
734. C2×C4×D4C2×D79semidirect
735. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779922
#237778652
#237777662
#237777202
#237773982
#237773562
#237773402
#237773012
#237772942
#237772842
#237772742
#237772692
#237771902
#237771832
#237771762
#237770582
#237770442
#237766962
C2×#532×C792
#6283679