Finite Group Databasebeta

← #35197241

Subgroups — #35197241

Order 20224.

6518 conjugacy classes of subgroups.

The subgroup lattice has 1380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23778048C214yesmaximal, complemented
2#23778035C214yesmaximal, complemented
3#23777877C214yesmaximal, complemented
4#23777778C214yesmaximal, complemented
5#23777678C218yesmaximal, complemented
6#23777415C214yesmaximal, complemented
7#23777384C218yesmaximal, complemented
8#23777366C214yesmaximal, complemented
9#23777320C211yesmaximal, characteristic, complemented
10#23777309C212yesmaximal, complemented
11#23777302C214yesmaximal, complemented
12#23777278C214yesmaximal, complemented
13#23777226C211yesmaximal, characteristic, complemented
14#23777224C211yesmaximal, characteristic, complemented
15#23777213C212yesmaximal, complemented
16#23777119C212yesmaximal, complemented
17#23777113C212yesmaximal, complemented
18#23776695C211yesmaximal, characteristic, complemented
19#23776693C211yesmaximal, characteristic, complemented
20C2×#19099119C211yesmaximal, characteristic, complemented
21C79×#3512C211yesmaximal, characteristic, complemented
22#19099317C2218yes—
23#19099315C2218yes—
24#19099310C2218yes—
25#19099308C2218yes—
26Q8×Dic158C2214yescomplemented
27#19099290C2218yescomplemented
28#19099290C2214yescomplemented
29#19099289C2214yescomplemented
30#19099289C2214yescomplemented
31#19099286C2214yes—
32#19099284C2214yes—
33#19099284C2214yes—
34#19099284C2214yescomplemented
35#19099283C2218yescomplemented
36#19099281C2214yes—
37#19099280C2218yes—
38#19099280C2218yescomplemented
39#19099280C2218yescomplemented
40#19099278C2214yes—
41#19099277C2214yes—
42#19099277C2214yes—
43#19099277C2214yescomplemented
44#19099276C2214yes—
45#19099272C2218yes—
46#19099272C2218yes—
47#19099272C2214yescomplemented
48#19099272C2214yescomplemented
49#19099271C2214yescomplemented
50#19099269C2214yescomplemented
51#19099268C2218yes—
52#19099265C2214yes—
53#19099265C2214yes—
54#19099263C2214yes—
55#19099261C2214yes—
56#19099259C2214yescomplemented
57#19099256C2218yes—
58#19099256C2218yes—
59#19099255C2214yes—
60#19099255C2214yes—
61#19099254C2214yes—
62#19099253C2214yescomplemented
63#19099252C2218yescomplemented
64#19099250C2218yescomplemented
65#19099250C2218yescomplemented
66#19099248C2214yes—
67#19099246C2218yes—
68D4×Dic158C2218yes—
69D4×Dic158C2214yescomplemented
70#19099222C2218yes—
71#19099219C2218yes—
72#19099219C2218yescomplemented
73#19099213C2214yescomplemented
74#19099211C2218yes—
75#19099194C2212yes—
76#19099194C2214yescomplemented
77#19099193C2214yescomplemented
78#19099191C2212yes—
79#19099191C2214yescomplemented
80#19099191C2214yescomplemented
81#19099186C2214yescomplemented
82#19099184C2218yes—
83#19099181C2218yes—
84#19099181C2218yescomplemented
85#19099181C2218yescomplemented
86#19099180C2214yescomplemented
87#19099180C2218yescomplemented
88#19099179C2218yes—
89#19099176C2218yescomplemented
90#19099174C2212yescomplemented
91#19099172C2218yes—
92#19099170C2218yescomplemented
93#19099170C2218yescomplemented
94#19099167C2212yescomplemented
95#19099155C2218yes—
96#19099154C2218yes—
97#19099150C2218yes—
98#19099146C2218yes—
99#19099141C2212yes—
100#19099140C2218yes—
101#19099135C2218yes—
102#19099120C2211yescharacteristic
103#19099120C2212yescomplemented
104#19099119C2214yes—
105#19099119C2214yes—
106#19099119C2214yes—
107#19099119C2214yes—
108#19099119C2212yescomplemented
109#19099118C2212yes—
110#19099117C2212yes—
111#19099116C2211yescharacteristic
112#19099116C2214yescomplemented
113#19099115C2214yescomplemented
114#19099111C2212yes—
115#19099110C2212yes—
116#19099109C2211yescharacteristic
117#19099108C2214yescomplemented
118C2×#14579160C2212yes—
119C2×#14579160C2214yescomplemented
120#19099100C2212yes—
121#19099095C2214yes—
122#19099095C2212yes—
123#19099094C2218yes—
124#19099094C2214yes—
125#19099093C2218yes—
126#19099093C2214yes—
127#19099092C2212yes—
128#19099092C2212yes—
129#19099092C2214yescomplemented
130#19099091C2214yes—
131C2×#14579153C2211yescharacteristic
132C2×#14579153C2212yescomplemented
133#125×D79C2212yescomplemented
134#19099075C2211yescharacteristic
135#19099073C2214yes—
136#19099072C2214yes—
137#19099070C2212yes—
138#19099070C2211yescharacteristic
139C2×#14579139C2214yes—
140#19099046C2212yes—
141#19099046C2212yes—
142#19099044C2212yes—
143#19099042C2218yescomplemented
144#19099040C2218yescomplemented
145#41×Dic79C2212yes—
146C4×#11929624C2211yescharacteristic
147C4×#11929624C2214yes—
148C4×#11929623C2214yes—
149C2×#14579126C2214yes—
150C2×#14579119C2212yes—
151C2×C42×D79C2211yescharacteristic
152#553×C79C2218yes—
153#553×C79C2214yescomplemented
154#552×C79C2214yescomplemented
155#541×C79C2212yescomplemented
156#540×C79C2212yescomplemented
157#537×C79C2212yes—
158#532×C79C2211yescharacteristic
159#529×C79C2214yescomplemented
160C2×#125×C79C2211yescharacteristic
161#520×C79C2212yes—
162C4×#41×C79C2211yescharacteristic
163C2×#11929624C2311yescharacteristic
164C2×#11929624C2314yes—
165C2×#11929623C2314yes—
166C2×#11929623C2318yes—
167C22×Dic158C2314yes—
168C22×Dic158C2318yes—
169C22×C4×D79C2311yescharacteristic
170C22×C4×D79C2312yes—
171#14579161C2318yes—
172#14579161C2314yes—
173#14579161C2312yes—
174#14579160C2318yes—
175#14579160C2318yes—
176#14579160C2318yes—
177#14579160C2314yes—
178#14579160C2318yes—
179#14579160C2318yes—
180#14579160C2314yes—
181#14579160C2314yes—
182#14579160C2314yes—
183#14579160C2314yes—
184#14579160C2314yes—
185#14579160C2314yes—
186#14579160C2312yes—
187#14579159C2311yescharacteristic
188#14579157C2311yescharacteristic
189#14579156C2318yes—
190#14579156C2318yes—
191#14579156C2318yes—
192#14579156C2318yes—
193#14579156C2314yes—
194#14579156C2318yes—
195#14579156C2318yes—
196#14579155C2318yes—
197#14579154C2318yes—
198#14579154C2314yes—
199#14579154C2318yes—
200#14579154C2318yes—
201#14579154C2318yes—
202#14579154C2318yes—
203#14579154C2314yes—
204#14579154C2314yes—
205#14579153C2318yes—
206#14579153C2318yes—
207#14579153C2312yes—
208#14579153C2314yes—
209#14579153C2314yes—
210#14579153C2311yescharacteristic
211#14579153C2312yes—
212#14579153C2311yescharacteristic
213#14579152C2318yes—
214#14579152C2314yes—
215#14579152C2318yes—
216#14579152C2318yes—
217#14579152C2314yes—
218#14579152C2312yes—
219#14579152C2314yes—
220#14579152C2314yes—
221#14579151C2318yes—
222#14579151C2318yes—
223#14579151C2318yes—
224#14579151C2318yes—
225#14579151C2318yes—
226#14579151C2314yes—
227#14579150C2311yescharacteristic
228#14579149C2318yes—
229#14579148C2311yescharacteristic
230#14579148C2318yes—
231#14579148C2314yes—
232#14579148C2318yes—
233#14579147C2318yes—
234#14579147C2318yes—
235#14579147C2318yes—
236#14579147C2318yes—
237#14579147C2318yes—
238#14579147C2318yes—
239#14579147C2314yes—
240#14579146C2318yes—
241#14579146C2314yes—
242#14579145C2318yes—
243#14579145C2318yes—
244#14579145C2312yes—
245#14579144C2318yes—
246#14579143C2314yes—
247#14579143C2318yes—
248#14579143C2314yes—
249#14579143C2318yes—
250#14579143C2314yes—
251#14579142C2318yes—
252#14579142C2318yes—
253#14579142C2314yes—
254#14579142C2312yes—
255#14579141C2318yes—
256#14579141C2318yes—
257#14579141C2312yes—
258#14579141C2314yes—
259#14579140C2314yes—
260#14579140C2318yes—
261#14579140C2318yes—
262#14579140C2318yes—
263#14579140C2318yes—
264#14579140C2314yes—
265#14579139C2318yes—
266#14579139C2318yes—
267#14579139C2318yes—
268#14579139C2314yes—
269#14579139C2318yes—
270#14579139C2318yes—
271#14579139C2318yes—
272#14579138C2318yes—
273#14579138C2318yes—
274#14579138C2318yes—
275#14579138C2318yes—
276#14579138C2318yes—
277#14579138C2318yes—
278#14579138C2318yes—
279#14579138C2318yes—
280#14579138C2318yes—
281#14579138C2314yes—
282#14579137C2314yes—
283#14579137C2312yes—
284#14579137C2312yes—
285#14579137C2312yes—
286#14579136C2312yes—
287#14579135C2318yes—
288#14579135C2314yes—
289#14579134C2314yes—
290#14579134C2318yes—
291#14579133C2318yes—
292#14579133C2318yes—
293#14579133C2318yes—
294#14579133C2318yes—
295#14579133C2318yes—
296#14579133C2314yes—
297#14579132C2314yes—
298#14579132C2312yes—
299#14579132C2312yes—
300#14579132C2312yes—
301#14579132C2314yes—
302#14579131C2312yes—
303#14579129C2314yes—
304#14579129C2312yes—
305Q8×Dic79C2314yes—
306Q8×Dic79C2314yes—
307Q8×Dic79C2312yes—
308Q8×Dic79C2312yes—
309C4×Dic158C2314yes—
310C4×Dic158C2318yes—
311C4×Dic158C2318yes—
312C4×Dic158C2318yes—
313C4×Dic158C2318yes—
314C4×Dic158C2314yes—
315C4×Dic158C2312yes—
316C4×Dic158C2314yes—
317#14579126C2318yes—
318#14579126C2318yes—
319#14579126C2318yes—
320#14579126C2318yes—
321#14579126C2314yes—
322#14579126C2318yes—
323#14579126C2318yes—
324#14579126C2318yes—
325#14579126C2314yes—
326C4×D316C2314yes—
327C4×D316C2314yes—
328C4×D316C2312yes—
329D4×Dic79C2318yes—
330D4×Dic79C2318yes—
331D4×Dic79C2314yes—
332D4×Dic79C2318yes—
333D4×Dic79C2314yes—
334D4×Dic79C2312yes—
335D4×Dic79C2314yes—
336D4×Dic79C2314yes—
337D4×Dic79C2314yes—
338D4×Dic79C2312yes—
339#14579123C2314yes—
340C4×C22⋊D79C2318yes—
341C4×C22⋊D79C2314yes—
342C4×C22⋊D79C2314yes—
343C4×C22⋊D79C2318yes—
344C4×C22⋊D79C2314yes—
345C4×C22⋊D79C2314yes—
346C4×C22⋊D79C2314yes—
347C4×C22⋊D79C2314yes—
348C4×C22⋊D79C2314yes—
349(C22⋊D79)⋊C4C2318yes—
350(C22⋊D79)⋊C4C2318yes—
351(C22⋊D79)⋊C4C2314yes—
352(C22⋊D79)⋊C4C2314yes—
353#14579120C2314yes—
354#14579120C2318yes—
355#14579120C2312yes—
356#14579120C2314yes—
357#14579120C2311yescharacteristic
358#14579120C2314yes—
359#14579120C2314yes—
360#14579119C2314yes—
361#14579119C2314yes—
362#14579119C2314yes—
363#14579119C2314yes—
364#14579119C2314yes—
365#14579119C2314yes—
366#14579118C2312yes—
367#14579118C2318yes—
368#14579118C2314yes—
369#14579118C2314yes—
370#14579117C2314yes—
371#14579117C2318yes—
372#14579117C2318yes—
373#14579117C2314yes—
374#14579117C2318yes—
375#14579117C2318yes—
376C2×C4⋊Dic79C2312yes—
377C2×C4⋊Dic79C2314yes—
378C2×C4⋊Dic79C2314yes—
379C2×Dic79⋊C4C2318yes—
380C2×Dic79⋊C4C2318yes—
381C2×Dic79⋊C4C2314yes—
382C2×Dic79⋊C4C2314yes—
383C4⋊C4×D79C2318yes—
384C4⋊C4×D79C2314yes—
385C2×(C2×D79)⋊C4C2314yes—
386C2×C4×Dic79C2312yes—
387C2×C4×Dic79C2311yescharacteristic
388C2×C4×Dic79C2314yes—
389C2×C4×Dic79C2314yes—
390C42×D79C2312yes—
391C42×D79C2312yes—
392C42×D79C2312yes—
393C42×D79C2312yes—
394C42×D79C2312yes—
395C2×#41×C79C2312yes—
396C2×#41×C79C2311yescharacteristic
397C4⋊Q8×C79C2311yescharacteristic
398#127×C79C2311yescharacteristic
399#126×C79C2318yes—
400#126×C79C2318yes—
401#125×C79C2318yes—
402#125×C79C2312yes—
403#125×C79C2312yes—
404#125×C79C2314yes—
405#124×C79C2312yes—
406#123×C79C2318yes—
407#123×C79C2318yes—
408C22⋊Q8×C79C2314yes—
409C22⋊Q8×C79C2314yes—
410#121×C79C2318yes—
411#121×C79C2318yes—
412#121×C79C2314yes—
413#121×C79C2314yes—
414#121×C79C2314yes—
415C4×Q8×C79C2312yes—
416C4×Q8×C79C2314yes—
417C4×D4×C79C2318yes—
418C4×D4×C79C2318yes—
419C4×D4×C79C2314yes—
420C4×D4×C79C2314yes—
421C4×D4×C79C2312yes—
422C4×D4×C79C2314yes—
423#117×C79C2318yes—
424#117×C79C2311yescharacteristic
425#117×C79C2312yes—
426#117×C79C2314yes—
427C2×C4⋊C4×C79C2312yes—
428C2×C4⋊C4×C79C2314yes—
429C2×C4⋊C4×C79C2314yes—
430C2×C42×C79C2311yescharacteristic
431C2×C42×C79C2312yes—
432C23×D79C2411yescharacteristic
433#11929624—24no—
434#11929624—48no—
435#11929623—416no—
436#11929623—48no—
437C2×Dic158—48no—
438C2×Dic158—416no—
439C2×Dic158C2418yes—
440C2×Dic158C2414yes—
441C2×Dic158C2411yescharacteristic
442C2×Dic158C2418yes—
443C2×Dic158C2418yes—
444C2×Dic158C2418yes—
445C2×Dic158C2414yes—
446C2×D316C2411yescharacteristic
447C2×D316C2414yes—
448C2×C22⋊D79C2414yes—
449C2×C22⋊D79C2412yes—
450C2×C22⋊D79C2414yes—
451C2×C22⋊D79C2414yes—
452C2×C22⋊D79C2418yes—
453C2×C22⋊D79C2414yes—
454C22×Dic79C2414yes—
455C22×Dic79C2412yes—
456C22×Dic79C2414yes—
457C22×Dic79C2411yescharacteristic
458C22×Dic79C2414yes—
459C22×Dic79C2418yes—
460C22×Dic79C2418yes—
461C2×C4×D79—24no—
462C2×C4×D79—44no—
463C2×C4×D79C2412yes—
464C2×C4×D79C2412yes—
465C2×C4×D79C2412yes—
466C2×C4×D79C2412yes—
467C2×C4×D79C2412yes—
468C2×C4×D79C2418yes—
469C2×C4×D79C2414yes—
470C2×C4×D79C2412yes—
471C2×C4×D79C2412yes—
472C4⋊Dic79C2412yes—
473C4⋊Dic79C2418yes—
474C4⋊Dic79C2414yes—
475C4⋊Dic79C2414yes—
476C4⋊Dic79C2412yes—
477C4⋊Dic79C2418yes—
478C4⋊Dic79C2418yes—
479C4⋊Dic79C2412yes—
480C4⋊Dic79C2414yes—
481C4⋊Dic79C2414yes—
482C4⋊Dic79C2414yes—
483C4⋊Dic79C2414yes—
484C4⋊Dic79C2414yes—
485C4⋊Dic79C2418yes—
486Dic79⋊C4C2414yes—
487Dic79⋊C4C2418yes—
488Dic79⋊C4C2418yes—
489Dic79⋊C4C2418yes—
490Dic79⋊C4C2418yes—
491Dic79⋊C4C2414yes—
492Dic79⋊C4C2418yes—
493Dic79⋊C4C2418yes—
494Dic79⋊C4C2418yes—
495Dic79⋊C4C2418yes—
496Dic79⋊C4C2414yes—
497Dic79⋊C4C2414yes—
498Dic79⋊C4C2414yes—
499Dic79⋊C4C2414yes—
500Dic79⋊C4C2414yes—
501Dic79⋊C4C2418yes—
502Dic79⋊C4C2418yes—
503Dic79⋊C4C2414yes—
504Dic79⋊C4C2414yes—
505C22⋊Dic79C2414yes—
506C22⋊Dic79C2414yes—
507C22⋊Dic79C2418yes—
508C22⋊Dic79C2414yes—
509C22⋊Dic79C2414yes—
510C22⋊Dic79C2412yes—
511C22⋊Dic79C2414yes—
512C22⋊Dic79C2414yes—
513C22⋊Dic79C2414yes—
514C22⋊Dic79C2418yes—
515C22⋊Dic79C2418yes—
516(C2×D79)⋊C4C2418yes—
517(C2×D79)⋊C4C2418yes—
518(C2×D79)⋊C4C2414yes—
519(C2×D79)⋊C4C2418yes—
520(C2×D79)⋊C4C2414yes—
521(C2×D79)⋊C4C2414yes—
522(C2×D79)⋊C4C2414yes—
523(C2×D79)⋊C4C2414yes—
524(C2×D79)⋊C4C2414yes—
525(C2×D79)⋊C4C2414yes—
526(C2×D79)⋊C4C2418yes—
527C4×Dic79C2411yescharacteristic
528C4×Dic79C2412yes—
529C4×Dic79C2412yes—
530C4×Dic79C2411yescharacteristic
531C4×Dic79C2412yes—
532C4×Dic79C2412yes—
533C4×Dic79C2412yes—
534C4×Dic79C2414yes—
535C4×Dic79C2412yes—
536C4×Dic79C2418yes—
537C4×Dic79C2414yes—
538C4×Dic79C2414yes—
539C4×Dic79C2418yes—
540C4×Dic79C2414yes—
541C4×Dic79C2418yes—
542C4×Dic79C2418yes—
543C4×Dic79C2418yes—
544#41×C79—28no—
545#41×C79—24no—
546C2×Q8×C79C2411yescharacteristic
547C2×Q8×C79C2412yes—
548C2×D4×C79C2414yes—
549C2×D4×C79C2412yes—
550C2×D4×C79C2411yescharacteristic
551C2×D4×C79C2412yes—
552C2×D4×C79C2418yes—
553C2×D4×C79C2414yes—
554C22×C4×C79C2412yes—
555C22×C4×C79C2414yes—
556C22×C4×C79C2414yes—
557C22×C4×C79C2418yes—
558C22×C4×C79C2414yes—
559C22×C4×C79C2412yes—
560C22×C4×C79C2411yescharacteristic
561C4⋊C4×C79C2412yes—
562C4⋊C4×C79C2414yes—
563C4⋊C4×C79C2418yes—
564C4⋊C4×C79C2414yes—
565C4⋊C4×C79C2418yes—
566C4⋊C4×C79C2418yes—
567C4⋊C4×C79C2414yes—
568C4⋊C4×C79C2418yes—
569C4⋊C4×C79C2414yes—
570C22⋊C4×C79C2414yes—
571C22⋊C4×C79C2412yes—
572C22⋊C4×C79C2414yes—
573C22⋊C4×C79C2418yes—
574C22⋊C4×C79C2418yes—
575C22⋊C4×C79C2414yes—
576C22⋊C4×C79C2418yes—
577C42×C79C2411yescharacteristic
578C42×C79C2412yes—
579C42×C79C2414yes—
580C42×C79C2411yescharacteristic
581C42×C79C2412yes—
582C42×C79C2418yes—
583C23×C79C2512yes—
584C23×C79C2514yes—
585C23×C79C2511yescharacteristic
586C22×D79—22no—
587C22×D79—42no—
588C22×D79C2512yes—
589C22×D79C2512yes—
590Q8×C79—22no—
591Q8×C79—24no—
592D4×C79—28no—
593D4×C79—24no—
594D4×C79—22no—
595D4×C79—24no—
596D4×C79—48no—
597D4×C79—44no—
598C2×C4×C79—28no—
599C2×C4×C79—24no—
600C2×C4×C79—42no—
601C2×C4×C79—48no—
602C2×C4×C79—44no—
603C2×C4×C79—44no—
604C2×C4×C792−1+414yes—
605C2×C4×C79C2514yes—
606C2×C4×C79C2512yes—
607C2×C4×C79C2512yes—
608C2×C4×C79C2518yes—
609C2×C4×C79C2512yes—
610C2×C4×C79C2514yes—
611C2×C4×C79C2511yescharacteristic
612C2×C4×C79C2511yescharacteristic
613C22⋊D79—24no—
614C22⋊D79—28no—
615C22⋊D79—48no—
616C22⋊D79—44no—
617C22⋊D79—44no—
618C22⋊D79—44no—
619C2×Dic79—22no—
620C2×Dic79—24no—
621C2×Dic79—28no—
622C2×Dic79—28no—
623C2×Dic79—48no—
624C2×Dic79—44no—
625C2×Dic79—48no—
626C2×Dic79C2512yes—
627C2×Dic79C2514yes—
628C2×Dic79C2512yes—
629C2×Dic79C2518yes—
630C2×Dic79C2512yes—
631C2×Dic79C2514yes—
632C2×Dic79C2514yes—
633C2×Dic79C2512yes—
634D316—22no—
635D316—44no—
636C4×D79—24no—
637C4×D79—24no—
638C4×D79—24no—
639C4×D79—24no—
640C4×D79—24no—
641C4×D79—42no—
642C4×D79—42no—
643C4×D79—48no—
644C4×D79—44no—
645Dic158—22no—
646Dic158—216no—
647Dic158—28no—
648Dic158—48no—
649Dic158—48no—
650Dic158—48no—
651Dic158—44no—
652C22×C79—22no—
653C22×C79—22no—
654C22×C79—24no—
655C22×C79—24no—
656C22×C79—24no—
657C22×C79—24no—
658C22×C79C2×2−1+412yes—
659C22×C79C2611yescharacteristic
660C2×D79—22no—
661C2×D79—22no—
662C2×D79—24no—
663C2×D79—22no—
664C2×D79—22no—
665C2×D79—44no—
666C4×C79—24no—
667C4×C79—22no—
668C4×C79—24no—
669C4×C79—22no—
670C4×C79—28no—
671C4×C79—22no—
672C4×C79C2×2−1+412yes—
673C4×C79C2×2−1+412yes—
674Dic79—22no—
675Dic79—22no—
676Dic79—24no—
677Dic79—28no—
678Dic79—24no—
679Dic79—24no—
680Dic79—22no—
681Dic79#58514yes—
682#62838—791nomaximal, Sylow
683C2×C79—22no—
684C2×C79—42no—
685C2×C79—44no—
686C2×C79C22×2−1+411yescharacteristic
687C2×C79C2×#58512yes—
688D79—42no—
689D79—42no—
690#3565—794no—
691#3565—794no—
692#3555—794no—
693#3547—794no—
694#3541—798no—
695#3518—794no—
696#3516—798no—
697#3515—794no—
698#3512—791no—
699#3512D7911yescharacteristic, complemented
700#3511—794no—
701#3511—792no—
702#3509—794no—
703#3504—791no—
704#3504—791no—
705#3503—792no—
706#3493—792no—
707#3493—792no—
708#3444—791no—
709#3444—791no—
710C2×#533—791no—
711C79#6283811yescharacteristic, complemented, Sylow
712#563—798no—
713#563—798no—
714#562—798no—
715#562—798no—
716Q82—794no—
717#557—794no—
718#557—798no—
719#557—794no—
720#557—794no—
721#556—798no—
722#556—798no—
723#556—798no—
724#556—794no—
725#556—794no—
726#556—794no—
727#556—794no—
728#556—798no—
729#556—794no—
730#555—794no—
731#555—794no—
732#555—794no—
733#555—794no—
734#555—794no—
735#554—794no—
736#554—794no—
737#554—798no—
738#554—798no—
739#554—794no—
740#554—794no—
741#554—798no—
742#553—798no—
743#553—798no—
744#553—794no—
745#553—794no—
746#553—794no—
747#553—794no—
748#553—794no—
749#553C2×D7918yes—
750#553C2×D7914yescomplemented
751#552—798no—
752#552—798no—
753#552—794no—
754#552—794no—
755#552—794no—
756#552—794no—
757#552—798no—
758#552—798no—
759#552—794no—
760#552C2×D7914yescomplemented
761D4×Q8—798no—
762D4×Q8—794no—
763#548—798no—
764#548—798no—
765#548—798no—
766#547—798no—
767#547—794no—
768#544—794no—
769#544—792no—
770#544—794no—
771#544—794no—
772#544—792no—
773#544—794no—
774#542—798no—
775#542—798no—
776#542—798no—
777#542—798no—
778#542—794no—
779#542—794no—
780#542—798no—
781#542—798no—
782#541—792no—
783#541—798no—
784#541—798no—
785#541—798no—
786#541—798no—
787#541C2×D7912yescomplemented
788#540—792no—
789#540C2×D7912yescomplemented
790#539—798no—
791#539—798no—
792#538—798no—
793#538—798no—
794#537—792no—
795#537—798no—
796#537C2×D7912yes—
797#536—798no—
798#533—792no—
799#533—794no—
800#533—794no—
801#533—794no—
802#533—794no—
803#533—792no—
804#533—794no—
805#533—792no—
806#533—791no—
807#533—794no—
808#533—791no—
809#533—792no—
810#532—791no—
811#532—792no—
812#532—794no—
813#532—792no—
814#532C2×D7911yescharacteristic
815C2×C4⋊Q8—792no—
816C2×C4⋊Q8—794no—
817#529—792no—
818#529—792no—
819#529—794no—
820#529—794no—
821#529—798no—
822#529—792no—
823#529—794no—
824#529—794no—
825#529—792no—
826#529—798no—
827#529—794no—
828#529C2×D7914yescomplemented
829C2×#125—792no—
830C2×#125—791no—
831C2×#125—792no—
832C2×#125C2×D7911yescharacteristic
833#525—792no—
834#525—791no—
835#525—794no—
836#525—794no—
837#525—791no—
838C2×C22⋊Q8—794no—
839#520—792no—
840#520—792no—
841#520—798no—
842#520—792no—
843#520C2×D7912yes—
844#519—798no—
845C4×#41—792no—
846C4×#41—794no—
847C4×#41—791no—
848C4×#41—794no—
849C4×#41C2×D7911yescharacteristic
850C2×C4×Q8—794no—
851C2×#117—792no—
852C22×C42—791no—
853C2×#41—794no—
854C2×#41—798no—
855C2×#41—794no—
856C2×#41—791no—
857C2×#41C22×D7912yes—
858C2×#41C22×D7911yescharacteristic
859C22×Q8—794no—
860C22×Q8—798no—
861C23×C4—792no—
862C23×C4—791no—
863C4⋊Q8—791no—
864C4⋊Q8—794no—
865C4⋊Q8—792no—
866C4⋊Q8—794no—
867C4⋊Q8—794no—
868C4⋊Q8—794no—
869C4⋊Q8—798no—
870C4⋊Q8—798no—
871C4⋊Q8—794no—
872C4⋊Q8—794no—
873C4⋊Q8—794no—
874C4⋊Q8—798no—
875C4⋊Q8—798no—
876C4⋊Q8—798no—
877C4⋊Q8—792no—
878C4⋊Q8—794no—
879C4⋊Q8—798no—
880C4⋊Q8C22×D7911yescharacteristic
881#127—791no—
882#127C22×D7911yescharacteristic
883#126—794no—
884#126—798no—
885#126—798no—
886#126—798no—
887#126—798no—
888#126—798no—
889#126—798no—
890#126—794no—
891#126—794no—
892#126—794no—
893#126—798no—
894#126—798no—
895#126—798no—
896#126—798no—
897#126—798no—
898#126—798no—
899#126C22×D7918yes—
900#126C22×D7918yes—
901#125—798no—
902#125—794no—
903#125—794no—
904#125—792no—
905#125—794no—
906#125—798no—
907#125—798no—
908#125—798no—
909#125—794no—
910#125—794no—
911#125—798no—
912#125—798no—
913#125—798no—
914#125—798no—
915#125—791no—
916#125—792no—
917#125—792no—
918#125—794no—
919#125—798no—
920#125—794no—
921#125—791no—
922#125—798no—
923#125C22×D7912yes—
924#125C22×D7912yes—
925#125C22×D7914yes—
926#125C22×D7918yes—
927#124—791no—
928#124—791no—
929#124—794no—
930#124—798no—
931#124—798no—
932#124—794no—
933#124—798no—
934#124—798no—
935#124—798no—
936#124—798no—
937#124—798no—
938#124—798no—
939#124—798no—
940#124C22×D7912yes—
941#123—794no—
942#123—792no—
943#123—798no—
944#123—798no—
945#123—798no—
946#123—794no—
947#123—798no—
948#123—792no—
949#123—794no—
950#123—794no—
951#123—794no—
952#123—798no—
953#123—798no—
954#123—798no—
955#123—798no—
956#123C22×D7918yes—
957#123C22×D7918yes—
958C22⋊Q8—792no—
959C22⋊Q8—792no—
960C22⋊Q8—792no—
961C22⋊Q8—794no—
962C22⋊Q8—794no—
963C22⋊Q8—798no—
964C22⋊Q8—794no—
965C22⋊Q8—798no—
966C22⋊Q8—798no—
967C22⋊Q8—798no—
968C22⋊Q8—798no—
969C22⋊Q8—798no—
970C22⋊Q8—798no—
971C22⋊Q8—798no—
972C22⋊Q8—794no—
973C22⋊Q8—792no—
974C22⋊Q8—794no—
975C22⋊Q8—798no—
976C22⋊Q8—798no—
977C22⋊Q8—798no—
978C22⋊Q8—798no—
979C22⋊Q8—794no—
980C22⋊Q8—798no—
981C22⋊Q8—798no—
982C22⋊Q8—798no—
983C22⋊Q8—798no—
984C22⋊Q8—798no—
985C22⋊Q8—798no—
986C22⋊Q8—798no—
987C22⋊Q8—798no—
988C22⋊Q8—798no—
989C22⋊Q8C22×D7914yes—
990C22⋊Q8C22×D7914yes—
991#121—794no—
992#121—792no—
993#121—792no—
994#121—792no—
995#121—794no—
996#121—798no—
997#121—794no—
998#121—798no—
999#121—798no—
1000#121—798no—
1001#121—798no—
1002#121—794no—
1003#121—798no—
1004#121—792no—
1005#121—794no—
1006#121—798no—
1007#121C22×D7914yes—
1008#121C22×D7918yes—
1009#121C22×D7914yes—
1010#121C22×D7914yes—
1011#121C22×D7918yes—
1012#120—794no—
1013#120—792no—
1014#120—792no—
1015C4×Q8—792no—
1016C4×Q8—792no—
1017C4×Q8—794no—
1018C4×Q8—794no—
1019C4×Q8—798no—
1020C4×Q8—798no—
1021C4×Q8—798no—
1022C4×Q8—798no—
1023C4×Q8—794no—
1024C4×Q8—798no—
1025C4×Q8—798no—
1026C4×Q8—798no—
1027C4×Q8—794no—
1028C4×Q8—794no—
1029C4×Q8—794no—
1030C4×Q8—792no—
1031C4×Q8—794no—
1032C4×Q8—798no—
1033C4×Q8—798no—
1034C4×Q8—798no—
1035C4×Q8—798no—
1036C4×Q8C22×D7912yes—
1037C4×Q8C22×D7914yes—
1038C4×D4—794no—
1039C4×D4—794no—
1040C4×D4—792no—
1041C4×D4—794no—
1042C4×D4—792no—
1043C4×D4—798no—
1044C4×D4—798no—
1045C4×D4—794no—
1046C4×D4—798no—
1047C4×D4—794no—
1048C4×D4—794no—
1049C4×D4—794no—
1050C4×D4—794no—
1051C4×D4—794no—
1052C4×D4—794no—
1053C4×D4—794no—
1054C4×D4—794no—
1055C4×D4—798no—
1056C4×D4—798no—
1057C4×D4—794no—
1058C4×D4—794no—
1059C4×D4—794no—
1060C4×D4—798no—
1061C4×D4—798no—
1062C4×D4—794no—
1063C4×D4—794no—
1064C4×D4—792no—
1065C4×D4C22×D7914yes—
1066C4×D4C22×D7914yes—
1067C4×D4C22×D7912yes—
1068C4×D4C22×D7918yes—
1069C4×D4C22×D7918yes—
1070C4×D4C22×D7914yes—
1071#117—792no—
1072#117—791no—
1073#117—794no—
1074#117—794no—
1075#117—798no—
1076#117—794no—
1077#117—794no—
1078#117—794no—
1079#117—794no—
1080#117—794no—
1081#117—794no—
1082#117—794no—
1083#117—794no—
1084#117—794no—
1085#117—794no—
1086#117—798no—
1087#117—798no—
1088#117—798no—
1089#117—798no—
1090#117—794no—
1091#117—792no—
1092#117—794no—
1093#117—798no—
1094#117C22×D7911yescharacteristic
1095#117C22×D7912yes—
1096#117C22×D7918yes—
1097#117C22×D7914yes—
1098C2×C4⋊C4—792no—
1099C2×C4⋊C4—794no—
1100C2×C4⋊C4—794no—
1101C2×C4⋊C4—798no—
1102C2×C4⋊C4—794no—
1103C2×C4⋊C4—798no—
1104C2×C4⋊C4—794no—
1105C2×C4⋊C4—798no—
1106C2×C4⋊C4—794no—
1107C2×C4⋊C4C22×D7912yes—
1108C2×C4⋊C4C22×D7914yes—
1109C2×C4⋊C4C22×D7914yes—
1110C2×C22⋊C4—794no—
1111C2×C42—794no—
1112C2×C42—792no—
1113C2×C42—794no—
1114C2×C42—791no—
1115C2×C42—792no—
1116C2×C42—792no—
1117C2×C42—792no—
1118C2×C42—792no—
1119C2×C42—792no—
1120C2×C42C22×D7912yes—
1121C2×C42C22×D7911yescharacteristic
1122C24—791no—
1123#41—28no—
1124#41—24no—
1125#41—3168no—
1126#41—31616no—
1127#41—3168no—
1128#41—1584no—
1129C2×Q8—3168no—
1130C2×Q8—31616no—
1131C2×Q8—798no—
1132C2×Q8—794no—
1133C2×Q8—798no—
1134C2×Q8—798no—
1135C2×Q8—791no—
1136C2×Q8—798no—
1137C2×Q8—794no—
1138C2×Q8C23×D7912yes—
1139C2×Q8C23×D7911yescharacteristic
1140C2×D4—794no—
1141C2×D4—794no—
1142C2×D4—794no—
1143C2×D4—798no—
1144C2×D4—792no—
1145C2×D4—794no—
1146C2×D4—794no—
1147C2×D4—791no—
1148C2×D4C23×D7914yes—
1149C2×D4C23×D7912yes—
1150C2×D4C23×D7912yes—
1151C2×D4C23×D7911yescharacteristic
1152C2×D4C23×D7918yes—
1153C2×D4C23×D7914yes—
1154C22×C4—3164no—
1155C22×C4—794no—
1156C22×C4—798no—
1157C22×C4—798no—
1158C22×C4—792no—
1159C22×C4—792no—
1160C22×C4—794no—
1161C22×C4—798no—
1162C22×C4—791no—
1163C22×C4—792no—
1164C22×C4—794no—
1165C22×C4—794no—
1166C22×C4—792no—
1167C22×C4—792no—
1168C22×C4—792no—
1169C22×C4—792no—
1170C22×C4—792no—
1171C22×C4—1584no—
1172C22×C4C23×D7914yes—
1173C22×C4C23×D7912yes—
1174C22×C4C23×D7912yes—
1175C22×C4C23×D7914yes—
1176C22×C4C23×D7914yes—
1177C22×C4C23×D7918yes—
1178C22×C4C23×D7911yescharacteristic
1179C4⋊C4—794no—
1180C4⋊C4—798no—
1181C4⋊C4—794no—
1182C4⋊C4—798no—
1183C4⋊C4—798no—
1184C4⋊C4—798no—
1185C4⋊C4—798no—
1186C4⋊C4—798no—
1187C4⋊C4—798no—
1188C4⋊C4—798no—
1189C4⋊C4—794no—
1190C4⋊C4—794no—
1191C4⋊C4—794no—
1192C4⋊C4—794no—
1193C4⋊C4—794no—
1194C4⋊C4—794no—
1195C4⋊C4—794no—
1196C4⋊C4—798no—
1197C4⋊C4—798no—
1198C4⋊C4—792no—
1199C4⋊C4—794no—
1200C4⋊C4—792no—
1201C4⋊C4—794no—
1202C4⋊C4—798no—
1203C4⋊C4—798no—
1204C4⋊C4—798no—
1205C4⋊C4—792no—
1206C4⋊C4—794no—
1207C4⋊C4—794no—
1208C4⋊C4—794no—
1209C4⋊C4—794no—
1210C4⋊C4—794no—
1211C4⋊C4—798no—
1212C4⋊C4C23×D7914yes—
1213C4⋊C4C23×D7918yes—
1214C4⋊C4C23×D7914yes—
1215C4⋊C4C23×D7912yes—
1216C4⋊C4C23×D7918yes—
1217C4⋊C4C23×D7918yes—
1218C4⋊C4C23×D7914yes—
1219C4⋊C4C23×D7914yes—
1220C4⋊C4C23×D7918yes—
1221C22⋊C4—794no—
1222C22⋊C4—794no—
1223C22⋊C4—798no—
1224C22⋊C4—794no—
1225C22⋊C4—792no—
1226C22⋊C4—794no—
1227C22⋊C4—798no—
1228C22⋊C4—798no—
1229C22⋊C4—794no—
1230C22⋊C4—794no—
1231C22⋊C4—794no—
1232C22⋊C4—798no—
1233C22⋊C4—798no—
1234C22⋊C4—794no—
1235C22⋊C4—794no—
1236C22⋊C4—794no—
1237C22⋊C4—794no—
1238C22⋊C4—794no—
1239C22⋊C4—794no—
1240C22⋊C4—798no—
1241C22⋊C4—798no—
1242C22⋊C4—794no—
1243C22⋊C4C23×D7914yes—
1244C22⋊C4C23×D7918yes—
1245C22⋊C4C23×D7914yes—
1246C22⋊C4C23×D7918yes—
1247C22⋊C4C23×D7912yes—
1248C22⋊C4C23×D7914yes—
1249C22⋊C4C23×D7918yes—
1250C42—791no—
1251C42—792no—
1252C42—792no—
1253C42—791no—
1254C42—792no—
1255C42—792no—
1256C42—792no—
1257C42—794no—
1258C42—798no—
1259C42—798no—
1260C42—794no—
1261C42—794no—
1262C42—792no—
1263C42—794no—
1264C42—798no—
1265C42—798no—
1266C42—798no—
1267C42C23×D7911yescharacteristic
1268C42C23×D7911yescharacteristic
1269C42C23×D7912yes—
1270C42C23×D7914yes—
1271C42C23×D7912yes—
1272C42C23×D7918yes—
1273C23—3162no—
1274C23—792no—
1275C23—792no—
1276C23—1582no—
1277C23C24×D7914yes—
1278C23C24×D7912yes—
1279C23C24×D7911yescharacteristic
1280Q8—22no—
1281Q8—24no—
1282Q8—3168no—
1283Q8—3168no—
1284Q8—3168no—
1285Q8—3164no—
1286Q8—1588no—
1287Q8—15816no—
1288Q8—1582no—
1289D4—28no—
1290D4—24no—
1291D4—22no—
1292D4—24no—
1293D4—48no—
1294D4—44no—
1295D4—3164no—
1296D4—3164no—
1297D4—3164no—
1298D4—3168no—
1299D4—3164no—
1300D4—1588no—
1301D4—1584no—
1302D4—1582no—
1303C2×C4—28no—
1304C2×C4—24no—
1305C2×C4—42no—
1306C2×C4—48no—
1307C2×C4—44no—
1308C2×C4—44no—
1309C2×C4—3162no—
1310C2×C4—3162no—
1311C2×C4—3164no—
1312C2×C4—3168no—
1313C2×C4—3164no—
1314C2×C4—3168no—
1315C2×C4—3168no—
1316C2×C4—792no—
1317C2×C4—792no—
1318C2×C4—792no—
1319C2×C4—794no—
1320C2×C4—792no—
1321C2×C4—794no—
1322C2×C4—798no—
1323C2×C4—794no—
1324C2×C4—1584no—
1325C2×C4—1584no—
1326C2×C4—1584no—
1327C2×C4—1588no—
1328C2×C4—1588no—
1329C2×C4—1582no—
1330C2×C4—1584no—
1331C2×C4—1584no—
1332C2×C4—1584no—
1333C2×C4#1457920814yes—
1334C2×C4C24×D7912yes—
1335C2×C4C24×D7914yes—
1336C2×C4C24×D7912yes—
1337C2×C4C24×D7918yes—
1338C2×C4C24×D7912yes—
1339C2×C4C24×D7914yes—
1340C2×C4C24×D7911yescharacteristic
1341C2×C4C24×D7911yescharacteristic
1342C22—22no—
1343C22—24no—
1344C22—22no—
1345C22—24no—
1346C22—24no—
1347C22—24no—
1348C22—3164no—
1349C22—1582no—
1350C22—1582no—
1351C22—1584no—
1352C22—1582no—
1353C22—1582no—
1354C22C2×#1457920812yes—
1355C22C25×D7911yescharacteristic
1356C4—24no—
1357C4—22no—
1358C4—22no—
1359C4—24no—
1360C4—28no—
1361C4—22no—
1362C4—794no—
1363C4—1582no—
1364C4—1582no—
1365C4—1584no—
1366C4—1584no—
1367C4—1588no—
1368C4—1582no—
1369C4—1584no—
1370C4C2×#1457920812yes—
1371C4C2×#1457920812yes—
1372C2—22no—
1373C2—44no—
1374C2—42no—
1375C2—3162no—
1376C2—3162no—
1377C2C22×#1457920811yescharacteristic
1378C2#585×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3512C2
hypercenter#3512D79
hypocenterC79#62838
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3512

Complements

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

NH ≅ G/Ntype
1. #23778048C2semidirect
2. #23778035C2semidirect
3. #23777877C2semidirect
4. #23777778C2semidirect
5. #23777678C2semidirect
6. #23777415C2semidirect
7. #23777384C2semidirect
8. #23777366C2semidirect
9. #23777320C2semidirect
10. #23777309C2semidirect
11. #23777302C2semidirect
12. #23777278C2semidirect
13. #23777226C2semidirect
14. #23777224C2semidirect
15. #23777213C2semidirect
16. #23777119C2semidirect
17. #23777113C2semidirect
18. #23776695C2semidirect
19. #23776693C2semidirect
20. C2×#19099119C2semidirect
21. C79×#3512C2semidirect
26. Q8×Dic158C22semidirect
27. #19099290C22semidirect
28. #19099290C22semidirect
29. #19099289C22semidirect
30. #19099289C22semidirect
34. #19099284C22semidirect
35. #19099283C22semidirect
38. #19099280C22semidirect
39. #19099280C22semidirect
43. #19099277C22semidirect
47. #19099272C22semidirect
48. #19099272C22semidirect
49. #19099271C22semidirect
50. #19099269C22semidirect
56. #19099259C22semidirect
62. #19099253C22semidirect
63. #19099252C22semidirect
64. #19099250C22semidirect
65. #19099250C22semidirect
69. D4×Dic158C22semidirect
72. #19099219C22semidirect
73. #19099213C22semidirect
76. #19099194C22semidirect
77. #19099193C22semidirect
79. #19099191C22semidirect
80. #19099191C22semidirect
81. #19099186C22semidirect
84. #19099181C22semidirect
85. #19099181C22semidirect
86. #19099180C22semidirect
87. #19099180C22semidirect
89. #19099176C22semidirect
90. #19099174C22semidirect
92. #19099170C22semidirect
93. #19099170C22semidirect
94. #19099167C22semidirect
103. #19099120C22semidirect
108. #19099119C22semidirect
112. #19099116C22semidirect
113. #19099115C22semidirect
117. #19099108C22semidirect
119. C2×#14579160C22semidirect
129. #19099092C22semidirect
132. C2×#14579153C22semidirect
133. #125×D79C22semidirect
143. #19099042C22semidirect
144. #19099040C22semidirect
153. #553×C79C22semidirect
154. #552×C79C22semidirect
155. #541×C79C22semidirect
156. #540×C79C22semidirect
159. #529×C79C22semidirect
699. #3512D79semidirect
711. C79#62838semidirect
750. #553C2×D79semidirect
760. #552C2×D79semidirect
787. #541C2×D79semidirect
789. #540C2×D79semidirect
828. #529C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237780482
#237780352
#237778772
#237777782
#237776782
#237774152
#237773842
#237773662
#237773202
#237773092
#237773022
#237772782
#237772262
#237772242
#237772132
#237771192
#237771132
#237766952
#237766932
C2×#190991192
C79×#35122
#6283879