Finite Group Databasebeta

← #35197215

Subgroups — #35197215

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#23777990C218yesmaximal, complemented
2#23777859C214yesmaximal, complemented
3#23777760C214yesmaximal, complemented
4#23777702C218yesmaximal, complemented
5#23777401C214yesmaximal, complemented
6#23777360C214yesmaximal, complemented
7#23777341C218yesmaximal, complemented
8#23777307C214yesmaximal, complemented
9#23777291C212yesmaximal, complemented
10#23777287C211yesmaximal, characteristic, complemented
11#23777269C214yesmaximal, complemented
12#23777192C212yesmaximal, complemented
13#23777185C211yesmaximal, characteristic, complemented
14#23777176C211yesmaximal, characteristic, complemented
15#23777056C212yesmaximal, complemented
16#23777045C212yesmaximal, complemented
17#23776697C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×#19099111C211yesmaximal, characteristic, complemented
20C79×#3508C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yescomplemented
22C2×#14579206C2212yes—
23C22×#11929623C2212yescomplemented
24#19099310C22116yescomplemented
25#19099301C22116yescomplemented
26#19099296C2218yescomplemented
27#19099295C2218yescomplemented
28#19099292C2214yescomplemented
29#19099286C2214yescomplemented
30#19099283C2218yescomplemented
31#19099278C2218yescomplemented
32#19099270C2218yescomplemented
33#19099265C2218yescomplemented
34#19099265C2218yescomplemented
35#19099265C22116yescomplemented
36#19099255C2218yescomplemented
37#19099239C22116yescomplemented
38#19099236C22116yescomplemented
39#19099233C2218yescomplemented
40#19099233C2214yescomplemented
41#19099232C2218yescomplemented
42#19099231C2218yescomplemented
43Q8×D316C2214yescomplemented
44#19099221C2218yescomplemented
45#19099219C2218yescomplemented
46#19099219C2218yescomplemented
47#19099217C2218yescomplemented
48#19099217C2218yescomplemented
49#19099217C2218yescomplemented
50#19099217C2214yescomplemented
51#19099210C2218yescomplemented
52#19099208C2218yescomplemented
53#19099208C2218yescomplemented
54#19099206C2218yescomplemented
55#19099201C2218yescomplemented
56#19099200C22116yescomplemented
57#19099198C2214yescomplemented
58D4×C22⋊D79C2218yes—
59#19099182C2218yescomplemented
60#19099182C2218yescomplemented
61#19099178C2218yescomplemented
62#19099176C2214yescomplemented
63#19099166C2218yescomplemented
64#19099166C22116yescomplemented
65#19099164C2218yescomplemented
66#19099157C22116yescomplemented
67#19099150C22116yescomplemented
68#19099149C22116yescomplemented
69#19099141C2218yescomplemented
70#19099139C2212yes—
71#19099139C2212yescomplemented
72#19099139C2214yescomplemented
73#19099133C2214yescomplemented
74#19099130C2212yes—
75#19099129C2218yescomplemented
76#19099128C2218yescomplemented
77#19099126C2214yescomplemented
78#19099126C2214yescomplemented
79#19099125C2218yescomplemented
80#19099118C2214yescomplemented
81#19099118C2212yescomplemented
82#19099117C2212yescomplemented
83#19099116C2211yescharacteristic, complemented
84#19099114C2212yescomplemented
85#19099113C2211yescharacteristic
86#19099113C2212yescomplemented
87#19099111C2212yescomplemented
88#19099111C2214yescomplemented
89#19099111C2214yescomplemented
90#19099111C2214yescomplemented
91#19099111C2214yescomplemented
92#19099111C2214yescomplemented
93#19099110C2212yescomplemented
94#19099109C2211yescharacteristic
95C2×#14579161C2211yescharacteristic, complemented
96C2×#14579161C2212yescomplemented
97#127×D79C2212yescomplemented
98#19099100C2214yescomplemented
99#19099100C2212yescomplemented
100#19099099C2214yescomplemented
101#19099098C2214yescomplemented
102#19099095C2218yescomplemented
103#19099095C2212yescomplemented
104#19099093C2214yescomplemented
105#19099091C2214yescomplemented
106C2×#14579148C2212yescomplemented
107#124×D79C2214yescomplemented
108#19099076C2214yescomplemented
109#19099075C2211yescharacteristic
110#19099075C2212yescomplemented
111#19099072C2214yescomplemented
112#19099070C2211yescharacteristic, complemented
113#19099069C2218yescomplemented
114C2×#14579145C2218yescomplemented
115C2×#14579132C2214yescomplemented
116#19099046C2218yescomplemented
117#19099040C2212yescomplemented
118#19099035C2218yescomplemented
119C4×#11929625C2214yescomplemented
120C4×#11929624C2211yescharacteristic
121C4×#11929624C2214yescomplemented
122#19099031C2212yescomplemented
123C2×D4×Dic79C2214yescomplemented
124C2×C42×D79C2211yescharacteristic, complemented
125#559×C79C2214yescomplemented
126#550×C79C2214yescomplemented
127#546×C79C2218yescomplemented
128#540×C79C2214yescomplemented
129#535×C79C2212yescomplemented
130#533×C79C2211yescharacteristic, complemented
131#532×C79C2214yescomplemented
132C2×#127×C79C2211yescharacteristic
133#518×C79C2212yescomplemented
134C4×#41×C79C2211yescharacteristic, complemented
135#14579208—48no—
136#14579206—48no—
137C2×#11929625C2314yes—
138C2×#11929624C2311yescharacteristic
139C2×#11929624C2312yes—
140C2×#11929624C2314yes—
141C2×#11929624C2314yes—
142C2×#11929623—48no—
143C2×#11929623C2314yes—
144C2×#11929623C2314yes—
145C2×#11929623C2318yes—
146C2×#11929623C2314yes—
147C2×#11929623C2318yes—
148C2×#11929623C2318yes—
149C22×Dic158C2312yes—
150C22×Dic158C2314yes—
151C2×Q8×D79C2314yes—
152C22×C22⋊D79C2318yes—
153C22×C22⋊D79C2314yes—
154C2×D4×D79C2314yes—
155C2×D4×D79C2314yes—
156C2×D4×D79C2318yes—
157C23×Dic79C2314yes—
158C22×C4×D79C2311yescharacteristic
159C22×C4×D79C2312yes—
160#14579161C2314yes—
161#14579161C2312yes—
162#14579161C2314yes—
163#14579161C2318yes—
164#14579161C2314yes—
165#14579161C2311yescharacteristic
166#14579161C2312yes—
167#14579160C2312yes—
168#14579159C2311yescharacteristic
169#14579158C2311yescharacteristic
170#14579157C2318yes—
171#14579157C23116yes—
172#14579157C2314yes—
173#14579157C2311yescharacteristic
174#14579156C23116yes—
175#14579156C2318yes—
176#14579156C2314yes—
177#14579154C23116yes—
178#14579154C23116yes—
179#14579154C2314yes—
180#14579152C23116yes—
181#14579152C2318yes—
182#14579152C2314yes—
183#14579152C2312yes—
184#14579151C2314yes—
185#14579150C2314yes—
186#14579150C2311yescharacteristic
187#14579149C2314yes—
188#14579149C2314yes—
189#14579149C2312yes—
190#14579148C2314yes—
191#14579148C2318yes—
192#14579148C2314yes—
193#14579148C2314yes—
194#14579148C2311yescharacteristic
195#14579147C23116yes—
196#14579147C23116yes—
197#14579147C2314yes—
198#14579147C23116yes—
199#14579146C2314yes—
200#14579146C2318yes—
201#14579145C2318yes—
202#14579145C23116yes—
203#14579145C2318yes—
204#14579145C23116yes—
205#14579145C23116yes—
206#14579145C23116yes—
207#14579145C2312yes—
208#14579145C2314yes—
209#14579144C23116yes—
210#14579143C23116yes—
211#14579143C2314yes—
212#14579143C23116yes—
213#14579142C2312yes—
214#14579141C2318yes—
215#14579141C23116yes—
216#14579141C2318yes—
217#14579141C2312yes—
218#14579141C2314yes—
219#14579140C23116yes—
220#14579139C2314yes—
221#14579138C23116yes—
222#14579138C23116yes—
223#14579138C2314yes—
224#14579137C2314yes—
225#14579137C2318yes—
226#14579137C2312yes—
227#14579136C2314yes—
228#14579136C2312yes—
229#14579136C2314yes—
230#14579135C23116yes—
231#14579135C23116yes—
232#14579135C2318yes—
233#14579135C2314yes—
234#14579134C23116yes—
235#14579134C2314yes—
236#14579133C23116yes—
237#14579133C23116yes—
238#14579133C23116yes—
239#14579133C23116yes—
240#14579133C2314yes—
241#14579132C2318yes—
242#14579132C2318yes—
243#14579132C2318yes—
244#14579132C23116yes—
245#14579132C2318yes—
246#14579132C2318yes—
247#14579132C2312yes—
248#14579132C2318yes—
249#14579131C23116yes—
250#14579131C2312yes—
251#14579131C2314yes—
252#14579130C2318yes—
253#14579129C23116yes—
254#14579129C23116yes—
255#14579129C2312yes—
256Q8×Dic79C2314yes—
257Q8×Dic79C2318yes—
258C4×Dic158C2318yes—
259C4×Dic158C2312yes—
260C4×Dic158C2314yes—
261C4×Dic158C2314yes—
262#14579126C2318yes—
263#14579126C2314yes—
264C4×D316C2318yes—
265C4×D316C2312yes—
266C4×D316C2314yes—
267C4×D316C2314yes—
268C4×D316C2314yes—
269C4×D316C2318yes—
270D4×Dic79C2318yes—
271D4×Dic79C23116yes—
272D4×Dic79C2318yes—
273D4×Dic79C23116yes—
274D4×Dic79C2318yes—
275D4×Dic79C2318yes—
276D4×Dic79C2318yes—
277#14579123C2318yes—
278#14579123C2314yes—
279#14579123C2314yes—
280C4×C22⋊D79C23116yes—
281C4×C22⋊D79C2314yes—
282C4×C22⋊D79C2314yes—
283C4×C22⋊D79C2314yes—
284C4×C22⋊D79C2314yes—
285C4×C22⋊D79C2314yes—
286(C22⋊D79)⋊C4C23116yes—
287(C22⋊D79)⋊C4C2318yes—
288#14579120C2314yes—
289#14579120C23116yes—
290#14579120C2311yescharacteristic
291#14579119C2318yes—
292#14579119C2318yes—
293#14579119C2314yes—
294#14579118C2314yes—
295#14579118C2312yes—
296#14579118C2314yes—
297#14579118C2314yes—
298#14579117C2318yes—
299C2×C4⋊Dic79C2318yes—
300C2×C4⋊Dic79C23116yes—
301C2×C4⋊Dic79C2314yes—
302C2×C22⋊Dic79C2318yes—
303C2×(C2×D79)⋊C4C23116yes—
304C22⋊C4×D79C23116yes—
305C2×C4×Dic79C2312yes—
306C2×C4×Dic79C2311yescharacteristic
307C42×D79C2312yes—
308C42×D79C2312yes—
309C42×D79C2312yes—
310C42×D79C2312yes—
311C42×D79C2314yes—
312C42×D79C2312yes—
313C2×#41×C79C2311yescharacteristic
314C2×#41×C79C2318yes—
315C22×D4×C79C2312yes—
316C22×D4×C79C2314yes—
317C4⋊Q8×C79C2312yes—
318#127×C79C2314yes—
319#127×C79C2314yes—
320#127×C79C2312yes—
321#127×C79C2312yes—
322#125×C79C2312yes—
323#124×C79C2318yes—
324#124×C79C2314yes—
325#123×C79C23116yes—
326C22⋊Q8×C79C2314yes—
327#121×C79C23116yes—
328#121×C79C2318yes—
329#121×C79C2318yes—
330#120×C79C2318yes—
331C4×Q8×C79C2312yes—
332C4×Q8×C79C2314yes—
333C4×D4×C79C2318yes—
334C4×D4×C79C2318yes—
335C4×D4×C79C2318yes—
336C4×D4×C79C2314yes—
337C4×D4×C79C2312yes—
338#117×C79C2312yes—
339#117×C79C2311yescharacteristic
340#117×C79C2312yes—
341C2×C22⋊C4×C79C2318yes—
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2411yescharacteristic
345C23×D79C2418yes—
346#11929625—48no—
347#11929624—24no—
348#11929624—28no—
349#11929624—48no—
350#11929624—48no—
351#11929623—416no—
352#11929623—416no—
353#11929623—416no—
354#11929623—48no—
355#11929623—48no—
356#11929623—48no—
357C2×Dic158—28no—
358C2×Dic158—48no—
359C2×Dic158C2414yes—
360C2×Dic158C2414yes—
361C2×Dic158C2412yes—
362C2×Dic158C2411yescharacteristic
363C2×Dic158C2418yes—
364C2×Dic158C2414yes—
365Q8×D79—48no—
366C2×D316C2412yes—
367C2×D316C2411yescharacteristic
368C2×D316C2414yes—
369C2×D316C2414yes—
370C2×D316C2418yes—
371C2×C22⋊D79—416no—
372C2×C22⋊D79—48no—
373C2×C22⋊D79C2414yes—
374C2×C22⋊D79C2412yes—
375C2×C22⋊D79C2418yes—
376C2×C22⋊D79C24116yes—
377C2×C22⋊D79C2418yes—
378C2×C22⋊D79C2418yes—
379C2×C22⋊D79C2414yes—
380C2×C22⋊D79C2414yes—
381C2×C22⋊D79C24116yes—
382D4×D79—48no—
383D4×D79—48no—
384D4×D79—416no—
385C22×Dic79—48no—
386C22×Dic79C2414yes—
387C22×Dic79C2411yescharacteristic
388C22×Dic79C2418yes—
389C22×Dic79C24116yes—
390C22×Dic79C2418yes—
391C22×Dic79C2412yes—
392C2×C4×D79—24no—
393C2×C4×D79—44no—
394C2×C4×D79C2414yes—
395C2×C4×D79C2412yes—
396C2×C4×D79C2412yes—
397C2×C4×D79C2412yes—
398C2×C4×D79C2412yes—
399C2×C4×D79C2414yes—
400C2×C4×D79C2412yes—
401C2×C4×D79C2418yes—
402C2×C4×D79C2418yes—
403C2×C4×D79C2412yes—
404C2×C4×D79C2412yes—
405C4⋊Dic79C2414yes—
406C4⋊Dic79C2414yes—
407C4⋊Dic79C2418yes—
408C4⋊Dic79C2418yes—
409C4⋊Dic79C24116yes—
410C4⋊Dic79C2418yes—
411C4⋊Dic79C24116yes—
412C4⋊Dic79C2414yes—
413C4⋊Dic79C2412yes—
414Dic79⋊C4C24116yes—
415Dic79⋊C4C2414yes—
416Dic79⋊C4C2418yes—
417Dic79⋊C4C2414yes—
418Dic79⋊C4C2414yes—
419Dic79⋊C4C2414yes—
420Dic79⋊C4C2414yes—
421C22⋊Dic79C24116yes—
422C22⋊Dic79C24116yes—
423C22⋊Dic79C2412yes—
424C22⋊Dic79C2414yes—
425C22⋊Dic79C2414yes—
426C22⋊Dic79C24116yes—
427(C2×D79)⋊C4C2414yes—
428(C2×D79)⋊C4C24116yes—
429(C2×D79)⋊C4C2414yes—
430(C2×D79)⋊C4C2418yes—
431(C2×D79)⋊C4C24116yes—
432(C2×D79)⋊C4C2418yes—
433(C2×D79)⋊C4C2414yes—
434(C2×D79)⋊C4C2414yes—
435(C2×D79)⋊C4C2414yes—
436(C2×D79)⋊C4C2418yes—
437(C2×D79)⋊C4C2418yes—
438C4×Dic79C2411yescharacteristic
439C4×Dic79C2411yescharacteristic
440C4×Dic79C2412yes—
441C4×Dic79C2412yes—
442C4×Dic79C2412yes—
443C4×Dic79C2412yes—
444C4×Dic79C2412yes—
445C4×Dic79C2414yes—
446C4×Dic79C2412yes—
447C4×Dic79C2418yes—
448C4×Dic79C24116yes—
449C24×C79C2414yes—
450#41×C79—24no—
451#41×C79—416no—
452C2×Q8×C79C2411yescharacteristic
453C2×Q8×C79C2414yes—
454C2×D4×C79—28no—
455C2×D4×C79—48no—
456C2×D4×C79C2412yes—
457C2×D4×C79C2411yescharacteristic
458C2×D4×C79C2414yes—
459C2×D4×C79C2414yes—
460C2×D4×C79C2418yes—
461C2×D4×C79C24116yes—
462C2×D4×C79C2418yes—
463C22×C4×C79C2412yes—
464C22×C4×C79C2414yes—
465C22×C4×C79C2412yes—
466C22×C4×C79C24116yes—
467C22×C4×C79C2411yescharacteristic
468C4⋊C4×C79C2412yes—
469C4⋊C4×C79C2414yes—
470C4⋊C4×C79C2414yes—
471C4⋊C4×C79C2414yes—
472C4⋊C4×C79C2418yes—
473C22⋊C4×C79C2412yes—
474C22⋊C4×C79C2414yes—
475C22⋊C4×C79C24116yes—
476C22⋊C4×C79C2414yes—
477C22⋊C4×C79C24116yes—
478C42×C79C2411yescharacteristic
479C42×C79C2412yes—
480C42×C79C2411yescharacteristic
481C42×C79C2414yes—
482C42×C79C2412yes—
483C42×C79C2414yes—
484C23×C79—28no—
485C23×C79—48no—
486C23×C79C2518yes—
487C23×C79C2512yes—
488C23×C79C2511yescharacteristic
489C22×D79—22no—
490C22×D79—42no—
491C22×D79—48no—
492C22×D79—416no—
493C22×D79C2512yes—
494C22×D79C2514yes—
495C22×D79C2512yes—
496Q8×C79—22no—
497Q8×C79—28no—
498D4×C79—24no—
499D4×C79—28no—
500D4×C79—28no—
501D4×C79—22no—
502D4×C79—216no—
503D4×C79—48no—
504D4×C79—416no—
505C2×C4×C79—24no—
506C2×C4×C79—24no—
507C2×C4×C79—28no—
508C2×C4×C79—416no—
509C2×C4×C79H(5,𝔽2)14yes—
510C2×C4×C79C2518yes—
511C2×C4×C79C2512yes—
512C2×C4×C79C2514yes—
513C2×C4×C79C2512yes—
514C2×C4×C79C2511yescharacteristic
515C2×C4×C79C2511yescharacteristic
516C2×C4×C79C2512yes—
517C22⋊D79—24no—
518C22⋊D79—28no—
519C22⋊D79—48no—
520C22⋊D79—48no—
521C22⋊D79—416no—
522C22⋊D79—416no—
523C22⋊D79—48no—
524C22⋊D79—44no—
525C22⋊D79—44no—
526C2×Dic79—22no—
527C2×Dic79—28no—
528C2×Dic79—42no—
529C2×Dic79—416no—
530C2×Dic79—48no—
531C2×Dic79—48no—
532C2×Dic79C2512yes—
533C2×Dic79C2514yes—
534C2×Dic79C2512yes—
535C2×Dic79C2512yes—
536C2×Dic79C2514yes—
537C2×Dic79C2518yes—
538C2×Dic79C2512yes—
539D316—22no—
540D316—24no—
541D316—28no—
542D316—44no—
543D316—48no—
544C4×D79—24no—
545C4×D79—24no—
546C4×D79—24no—
547C4×D79—28no—
548C4×D79—24no—
549C4×D79—24no—
550C4×D79—28no—
551C4×D79—42no—
552C4×D79—42no—
553C4×D79—48no—
554C4×D79—48no—
555Dic158—28no—
556Dic158—28no—
557Dic158—24no—
558Dic158—22no—
559Dic158—48no—
560Dic158—44no—
561C22×C79—22no—
562C22×C79—22no—
563C22×C79—28no—
564C22×C79—24no—
565C22×C79—216no—
566C22×C79—88no—
567C22×C79C2×H(5,𝔽2)12yes—
568C22×C79C2611yescharacteristic
569C2×D79—22no—
570C2×D79—24no—
571C2×D79—22no—
572C2×D79—28no—
573C2×D79—22no—
574C2×D79—24no—
575C2×D79—22no—
576C2×D79—44no—
577C2×D79—168no—
578C4×C79—22no—
579C4×C79—24no—
580C4×C79—22no—
581C4×C79—28no—
582C4×C79C2×H(5,𝔽2)12yes—
583C4×C79C2×H(5,𝔽2)12yes—
584C4×C79#58514yes—
585Dic79—22no—
586Dic79—24no—
587Dic79—28no—
588Dic79—22no—
589Dic79—24no—
590Dic79—22no—
591Dic79—22no—
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#3508D7911yescharacteristic, complemented
613#3500—792no—
614#3499—791no—
615#3498—791no—
616#3487—792no—
617#3485—792no—
618#3444—791no—
619#3444—791no—
620C2×#532—791no—
621C79#6283611yescharacteristic, complemented, Sylow
622C2×2−1+4—792no—
623C2×H(5,𝔽2)—792no—
624C22×#41—792no—
625#562—7916no—
626#560—7916no—
627#559—798no—
628#559—798no—
629#559C2×D7914yescomplemented
630#557—794no—
631#556—794no—
632#556—798no—
633#555—798no—
634#554—798no—
635#553—798no—
636#553—798no—
637#553—7916no—
638#552—798no—
639#551—7916no—
640#551—7916no—
641#550—798no—
642#550—798no—
643#550—794no—
644#550—798no—
645#550C2×D7914yescomplemented
646D4×Q8—794no—
647#548—798no—
648#548—798no—
649#548—798no—
650#547—798no—
651#547—798no—
652#547—798no—
653#547—794no—
654#546—798no—
655#546—798no—
656#546—798no—
657#546—7916no—
658#546—798no—
659#546—798no—
660#546C2×D7918yescomplemented
661D42—798no—
662D42—794no—
663#542—798no—
664#542—798no—
665#542—798no—
666#541—794no—
667#540—798no—
668#540—7916no—
669#540—798no—
670#540C2×D7914yescomplemented
671#539—7916no—
672#538—7916no—
673#538—7916no—
674#537—798no—
675#536—794no—
676#536—792no—
677#536—792no—
678#536—794no—
679#535—792no—
680#535—794no—
681#535—794no—
682#535—798no—
683#535—798no—
684#535C2×D7912yescomplemented
685#534—798no—
686#533—792no—
687#533—794no—
688#533—792no—
689#533—791no—
690#533C2×D7911yescharacteristic, complemented
691#532—791no—
692#532—792no—
693#532—794no—
694#532—794no—
695#532—794no—
696#532—794no—
697#532—792no—
698#532—794no—
699#532—792no—
700#532—791no—
701#532—792no—
702#532C2×D7914yescomplemented
703C2×C4⋊Q8—791no—
704C2×C4⋊Q8—792no—
705C2×#127—792no—
706C2×#127C2×D7911yescharacteristic
707#529—794no—
708#529—794no—
709#529—792no—
710#529—794no—
711#529—794no—
712#529—792no—
713#529—798no—
714#529—794no—
715C2×#124—792no—
716C2×#124—794no—
717#525—791no—
718#525—794no—
719#525—798no—
720#525—794no—
721#525—791no—
722#525—792no—
723C2×#123—798no—
724C2×#121—794no—
725#520—798no—
726#519—792no—
727#518—798no—
728#518C2×D7912yescomplemented
729C4×#41—794no—
730C4×#41—792no—
731C4×#41—791no—
732C4×#41—794no—
733C4×#41C2×D7911yescharacteristic, complemented
734C2×C4×D4—794no—
735C22×C42—791no—
7362−1+4—3168no—
737H(5,𝔽2)—3168no—
738C2×#41—3168no—
739C2×#41—794no—
740C2×#41—798no—
741C2×#41—798no—
742C2×#41—798no—
743C2×#41—794no—
744C2×#41—794no—
745C2×#41—794no—
746C2×#41—794no—
747C2×#41—794no—
748C2×#41—792no—
749C2×#41—791no—
750C2×#41C22×D7911yescharacteristic
751C2×#41C22×D7918yes—
752C22×Q8—794no—
753C22×Q8—794no—
754C22×Q8—792no—
755C22×D4—794no—
756C22×D4—798no—
757C22×D4—798no—
758C22×D4—794no—
759C22×D4—794no—
760C22×D4C22×D7912yes—
761C22×D4C22×D7914yes—
762C23×C4—794no—
763C23×C4—792no—
764C23×C4—791no—
765C4⋊Q8—791no—
766C4⋊Q8—792no—
767C4⋊Q8—792no—
768C4⋊Q8—791no—
769C4⋊Q8—792no—
770C4⋊Q8—794no—
771C4⋊Q8—794no—
772C4⋊Q8—798no—
773C4⋊Q8—794no—
774C4⋊Q8C22×D7912yes—
775#127—794no—
776#127—798no—
777#127—791no—
778#127—7916no—
779#127—791no—
780#127C22×D7912yes—
781#127C22×D7912yes—
782#127C22×D7914yes—
783#127C22×D7914yes—
784#126—798no—
785#126—794no—
786#126—7916no—
787#126—794no—
788#126—7916no—
789#126—7916no—
790#125—792no—
791#125—794no—
792#125—794no—
793#125—798no—
794#125—7916no—
795#125C22×D7912yes—
796#124—791no—
797#124—794no—
798#124—794no—
799#124—794no—
800#124—798no—
801#124—791no—
802#124—794no—
803#124—7916no—
804#124—794no—
805#124—7916no—
806#124—7916no—
807#124—794no—
808#124—792no—
809#124—794no—
810#124C22×D7914yes—
811#124C22×D7918yes—
812#123—792no—
813#123—7916no—
814#123—794no—
815#123—798no—
816#123—792no—
817#123—794no—
818#123—798no—
819#123—798no—
820#123—7916no—
821#123—7916no—
822#123—794no—
823#123—7916no—
824#123—7916no—
825#123—7916no—
826#123—7916no—
827#123C22×D79116yes—
828C22⋊Q8—794no—
829C22⋊Q8—792no—
830C22⋊Q8—798no—
831C22⋊Q8—7916no—
832C22⋊Q8—792no—
833C22⋊Q8—794no—
834C22⋊Q8—794no—
835C22⋊Q8—798no—
836C22⋊Q8—798no—
837C22⋊Q8—7916no—
838C22⋊Q8—794no—
839C22⋊Q8—7916no—
840C22⋊Q8—7916no—
841C22⋊Q8C22×D7914yes—
842#121—798no—
843#121—798no—
844#121—798no—
845#121—798no—
846#121—794no—
847#121—792no—
848#121—7916no—
849#121—798no—
850#121—798no—
851#121—7916no—
852#121—7916no—
853#121—7916no—
854#121—7916no—
855#121—794no—
856#121—798no—
857#121—7916no—
858#121—7916no—
859#121—794no—
860#121—792no—
861#121—794no—
862#121—794no—
863#121—7916no—
864#121C22×D7918yes—
865#121C22×D7918yes—
866#121C22×D79116yes—
867#120—798no—
868#120—792no—
869#120—7916no—
870#120—7916no—
871#120—792no—
872#120—794no—
873#120—7916no—
874#120C22×D7918yes—
875C4×Q8—794no—
876C4×Q8—798no—
877C4×Q8—794no—
878C4×Q8—798no—
879C4×Q8—792no—
880C4×Q8—794no—
881C4×Q8—794no—
882C4×Q8—798no—
883C4×Q8C22×D7914yes—
884C4×Q8C22×D7912yes—
885C4×D4—798no—
886C4×D4—798no—
887C4×D4—798no—
888C4×D4—798no—
889C4×D4—7916no—
890C4×D4—7916no—
891C4×D4—798no—
892C4×D4—794no—
893C4×D4—794no—
894C4×D4—794no—
895C4×D4—794no—
896C4×D4—794no—
897C4×D4—7916no—
898C4×D4—794no—
899C4×D4—798no—
900C4×D4—794no—
901C4×D4—798no—
902C4×D4—7916no—
903C4×D4—794no—
904C4×D4—794no—
905C4×D4—798no—
906C4×D4—792no—
907C4×D4—794no—
908C4×D4—798no—
909C4×D4C22×D7914yes—
910C4×D4C22×D7912yes—
911C4×D4C22×D7918yes—
912C4×D4C22×D7918yes—
913C4×D4C22×D7918yes—
914#117—791no—
915#117—794no—
916#117—7916no—
917#117—794no—
918#117—798no—
919#117—798no—
920#117—798no—
921#117—794no—
922#117—794no—
923#117—792no—
924#117—794no—
925#117C22×D7912yes—
926#117C22×D7911yescharacteristic
927#117C22×D7912yes—
928C2×C4⋊C4—794no—
929C2×C4⋊C4—7916no—
930C2×C4⋊C4—798no—
931C2×C22⋊C4—798no—
932C2×C22⋊C4—7916no—
933C2×C22⋊C4—7916no—
934C2×C22⋊C4C22×D7918yes—
935C2×C42—792no—
936C2×C42—791no—
937C2×C42—794no—
938C2×C42—792no—
939C2×C42—792no—
940C2×C42—792no—
941C2×C42—792no—
942C2×C42—792no—
943C2×C42C22×D7912yes—
944C2×C42C22×D7911yescharacteristic
945C24—798no—
946C24—791no—
947C24C23×D7914yes—
948#41—24no—
949#41—416no—
950#41—3168no—
951#41—3168no—
952#41—31616no—
953#41—31616no—
954#41—3168no—
955#41—3168no—
956#41—3168no—
957#41—31616no—
958#41—3168no—
959#41—1584no—
960#41—1588no—
961C2×Q8—3168no—
962C2×Q8—3168no—
963C2×Q8—794no—
964C2×Q8—798no—
965C2×Q8—792no—
966C2×Q8—794no—
967C2×Q8—794no—
968C2×Q8—791no—
969C2×Q8—1588no—
970C2×Q8C23×D7914yes—
971C2×Q8C23×D7911yescharacteristic
972C2×D4—28no—
973C2×D4—48no—
974C2×D4—31616no—
975C2×D4—31616no—
976C2×D4—3168no—
977C2×D4—3168no—
978C2×D4—3168no—
979C2×D4—794no—
980C2×D4—7916no—
981C2×D4—794no—
982C2×D4—798no—
983C2×D4—798no—
984C2×D4—7916no—
985C2×D4—798no—
986C2×D4—794no—
987C2×D4—792no—
988C2×D4—794no—
989C2×D4—798no—
990C2×D4—794no—
991C2×D4—791no—
992C2×D4—792no—
993C2×D4C23×D7918yes—
994C2×D4C23×D7912yes—
995C2×D4C23×D7914yes—
996C2×D4C23×D7911yescharacteristic
997C2×D4C23×D7914yes—
998C2×D4C23×D7918yes—
999C2×D4C23×D79116yes—
1000C22×C4—3164no—
1001C22×C4—3168no—
1002C22×C4—792no—
1003C22×C4—7916no—
1004C22×C4—798no—
1005C22×C4—798no—
1006C22×C4—792no—
1007C22×C4—792no—
1008C22×C4—798no—
1009C22×C4—798no—
1010C22×C4—791no—
1011C22×C4—794no—
1012C22×C4—792no—
1013C22×C4—792no—
1014C22×C4—792no—
1015C22×C4—792no—
1016C22×C4—794no—
1017C22×C4—794no—
1018C22×C4—792no—
1019C22×C4—1584no—
1020C22×C4C23×D7912yes—
1021C22×C4C23×D7914yes—
1022C22×C4C23×D7912yes—
1023C22×C4C23×D79116yes—
1024C22×C4C23×D7911yescharacteristic
1025C4⋊C4—794no—
1026C4⋊C4—794no—
1027C4⋊C4—794no—
1028C4⋊C4—798no—
1029C4⋊C4—794no—
1030C4⋊C4—794no—
1031C4⋊C4—7916no—
1032C4⋊C4—794no—
1033C4⋊C4—798no—
1034C4⋊C4—794no—
1035C4⋊C4—798no—
1036C4⋊C4—7916no—
1037C4⋊C4—798no—
1038C4⋊C4—7916no—
1039C4⋊C4—794no—
1040C4⋊C4—792no—
1041C4⋊C4C23×D7914yes—
1042C4⋊C4C23×D7918yes—
1043C4⋊C4C23×D7914yes—
1044C4⋊C4C23×D7912yes—
1045C4⋊C4C23×D7914yes—
1046C22⋊C4—7916no—
1047C22⋊C4—7916no—
1048C22⋊C4—792no—
1049C22⋊C4—794no—
1050C22⋊C4—794no—
1051C22⋊C4—7916no—
1052C22⋊C4—794no—
1053C22⋊C4—794no—
1054C22⋊C4—798no—
1055C22⋊C4—7916no—
1056C22⋊C4—7916no—
1057C22⋊C4—794no—
1058C22⋊C4—798no—
1059C22⋊C4—798no—
1060C22⋊C4—794no—
1061C22⋊C4—798no—
1062C22⋊C4—794no—
1063C22⋊C4C23×D79116yes—
1064C22⋊C4C23×D7912yes—
1065C22⋊C4C23×D7914yes—
1066C22⋊C4C23×D79116yes—
1067C22⋊C4C23×D7914yes—
1068C42—791no—
1069C42—792no—
1070C42—792no—
1071C42—791no—
1072C42—792no—
1073C42—792no—
1074C42—792no—
1075C42—798no—
1076C42—794no—
1077C42—792no—
1078C42—7916no—
1079C42C23×D7911yescharacteristic
1080C42C23×D7911yescharacteristic
1081C42C23×D7912yes—
1082C42C23×D7914yes—
1083C42C23×D7914yes—
1084C42C23×D7912yes—
1085C23—28no—
1086C23—48no—
1087C23—3162no—
1088C23—3168no—
1089C23—31616no—
1090C23—792no—
1091C23—794no—
1092C23—792no—
1093C23—1582no—
1094C23C24×D7918yes—
1095C23C24×D7912yes—
1096C23C24×D7911yescharacteristic
1097Q8—22no—
1098Q8—28no—
1099Q8—3168no—
1100Q8—3164no—
1101Q8—1584no—
1102Q8—1588no—
1103Q8—1588no—
1104Q8—1582no—
1105D4—24no—
1106D4—28no—
1107D4—28no—
1108D4—22no—
1109D4—216no—
1110D4—48no—
1111D4—416no—
1112D4—3164no—
1113D4—3168no—
1114D4—3168no—
1115D4—3168no—
1116D4—31616no—
1117D4—31616no—
1118D4—3164no—
1119D4—3164no—
1120D4—3168no—
1121D4—1584no—
1122D4—1588no—
1123D4—1582no—
1124D4—1584no—
1125D4—1588no—
1126C2×C4—24no—
1127C2×C4—24no—
1128C2×C4—28no—
1129C2×C4—416no—
1130C2×C4—3162no—
1131C2×C4—3162no—
1132C2×C4—3168no—
1133C2×C4—3168no—
1134C2×C4—31616no—
1135C2×C4—3162no—
1136C2×C4—3168no—
1137C2×C4—3168no—
1138C2×C4—792no—
1139C2×C4—794no—
1140C2×C4—792no—
1141C2×C4—792no—
1142C2×C4—798no—
1143C2×C4—794no—
1144C2×C4—792no—
1145C2×C4—1582no—
1146C2×C4—1588no—
1147C2×C4—1584no—
1148C2×C4—1584no—
1149C2×C4—1584no—
1150C2×C4—1588no—
1151C2×C4—1584no—
1152C2×C4—1584no—
1153C2×C4—1588no—
1154C2×C4#1457920714yes—
1155C2×C4C24×D7918yes—
1156C2×C4C24×D7912yes—
1157C2×C4C24×D7914yes—
1158C2×C4C24×D7912yes—
1159C2×C4C24×D7911yescharacteristic
1160C2×C4C24×D7911yescharacteristic
1161C2×C4C24×D7912yes—
1162C22—22no—
1163C22—22no—
1164C22—28no—
1165C22—24no—
1166C22—216no—
1167C22—88no—
1168C22—3164no—
1169C22—1584no—
1170C22—1582no—
1171C22—1582no—
1172C22—1582no—
1173C22—1582no—
1174C22—1588no—
1175C22—1584no—
1176C22—12648no—
1177C22C2×#1457920712yes—
1178C22C25×D7911yescharacteristic
1179C4—22no—
1180C4—24no—
1181C4—22no—
1182C4—28no—
1183C4—1582no—
1184C4—1582no—
1185C4—1588no—
1186C4—1584no—
1187C4—1582no—
1188C4—1582no—
1189C4—1584no—
1190C4C2×#1457920712yes—
1191C4C2×#1457920712yes—
1192C4#1909939814yes—
1193C2—22no—
1194C2—48no—
1195C2—42no—
1196C2—3162no—
1197C2—3162no—
1198C2—3164no—
1199C2C22×#1457920711yescharacteristic
1200C2C2×#1909939812yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3508C2
hypercenter#3508D79
hypocenterC79#62836
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3508

Complements

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

NH ≅ G/Ntype
1. #23777990C2semidirect
2. #23777859C2semidirect
3. #23777760C2semidirect
4. #23777702C2semidirect
5. #23777401C2semidirect
6. #23777360C2semidirect
7. #23777341C2semidirect
8. #23777307C2semidirect
9. #23777291C2semidirect
10. #23777287C2semidirect
11. #23777269C2semidirect
12. #23777192C2semidirect
13. #23777185C2semidirect
14. #23777176C2semidirect
15. #23777056C2semidirect
16. #23777045C2semidirect
17. #23776697C2semidirect
18. #23776693C2semidirect
19. C2×#19099111C2semidirect
20. C79×#3508C2semidirect
21. C2×#14579208C22semidirect
23. C22×#11929623C22semidirect
24. #19099310C22semidirect
25. #19099301C22semidirect
26. #19099296C22semidirect
27. #19099295C22semidirect
28. #19099292C22semidirect
29. #19099286C22semidirect
30. #19099283C22semidirect
31. #19099278C22semidirect
32. #19099270C22semidirect
33. #19099265C22semidirect
34. #19099265C22semidirect
35. #19099265C22semidirect
36. #19099255C22semidirect
37. #19099239C22semidirect
38. #19099236C22semidirect
39. #19099233C22semidirect
40. #19099233C22semidirect
41. #19099232C22semidirect
42. #19099231C22semidirect
43. Q8×D316C22semidirect
44. #19099221C22semidirect
45. #19099219C22semidirect
46. #19099219C22semidirect
47. #19099217C22semidirect
48. #19099217C22semidirect
49. #19099217C22semidirect
50. #19099217C22semidirect
51. #19099210C22semidirect
52. #19099208C22semidirect
53. #19099208C22semidirect
54. #19099206C22semidirect
55. #19099201C22semidirect
56. #19099200C22semidirect
57. #19099198C22semidirect
59. #19099182C22semidirect
60. #19099182C22semidirect
61. #19099178C22semidirect
62. #19099176C22semidirect
63. #19099166C22semidirect
64. #19099166C22semidirect
65. #19099164C22semidirect
66. #19099157C22semidirect
67. #19099150C22semidirect
68. #19099149C22semidirect
69. #19099141C22semidirect
71. #19099139C22semidirect
72. #19099139C22semidirect
73. #19099133C22semidirect
75. #19099129C22semidirect
76. #19099128C22semidirect
77. #19099126C22semidirect
78. #19099126C22semidirect
79. #19099125C22semidirect
80. #19099118C22semidirect
81. #19099118C22semidirect
82. #19099117C22semidirect
83. #19099116C22semidirect
84. #19099114C22semidirect
86. #19099113C22semidirect
87. #19099111C22semidirect
88. #19099111C22semidirect
89. #19099111C22semidirect
90. #19099111C22semidirect
91. #19099111C22semidirect
92. #19099111C22semidirect
93. #19099110C22semidirect
95. C2×#14579161C22semidirect
96. C2×#14579161C22semidirect
97. #127×D79C22semidirect
98. #19099100C22semidirect
99. #19099100C22semidirect
100. #19099099C22semidirect
101. #19099098C22semidirect
102. #19099095C22semidirect
103. #19099095C22semidirect
104. #19099093C22semidirect
105. #19099091C22semidirect
106. C2×#14579148C22semidirect
107. #124×D79C22semidirect
108. #19099076C22semidirect
110. #19099075C22semidirect
111. #19099072C22semidirect
112. #19099070C22semidirect
113. #19099069C22semidirect
114. C2×#14579145C22semidirect
115. C2×#14579132C22semidirect
116. #19099046C22semidirect
117. #19099040C22semidirect
118. #19099035C22semidirect
119. C4×#11929625C22semidirect
121. C4×#11929624C22semidirect
122. #19099031C22semidirect
123. C2×D4×Dic79C22semidirect
124. C2×C42×D79C22semidirect
125. #559×C79C22semidirect
126. #550×C79C22semidirect
127. #546×C79C22semidirect
128. #540×C79C22semidirect
129. #535×C79C22semidirect
130. #533×C79C22semidirect
131. #532×C79C22semidirect
133. #518×C79C22semidirect
134. C4×#41×C79C22semidirect
612. #3508D79semidirect
621. C79#62836semidirect
629. #559C2×D79semidirect
645. #550C2×D79semidirect
660. #546C2×D79semidirect
670. #540C2×D79semidirect
684. #535C2×D79semidirect
690. #533C2×D79semidirect
702. #532C2×D79semidirect
728. #518C2×D79semidirect
733. C4×#41C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779902
#237778592
#237777602
#237777022
#237774012
#237773602
#237773412
#237773072
#237772912
#237772872
#237772692
#237771922
#237771852
#237771762
#237770562
#237770452
#237766972
#237766932
C2×#190991112
C79×#35082
#6283679