Finite Group Databasebeta

← #35197420

Subgroups — #35197420

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777321C214yesmaximal, complemented
2#23777320C214yesmaximal, complemented
3#23777309C214yesmaximal, complemented
4#23777307C214yesmaximal, complemented
5#23777237C218yesmaximal, complemented
6#23777154C214yesmaximal, complemented
7#23777149C214yesmaximal, complemented
8#23777137C214yesmaximal, complemented
9#23777132C214yesmaximal, complemented
10#23777117C214yesmaximal, complemented
11#23777106C214yesmaximal, complemented
12#23776824C214yesmaximal, complemented
13#23776813C214yesmaximal, complemented
14C2×#19099191C211yesmaximal, characteristic, complemented
15#23776729C211yesmaximal, characteristic, complemented
16C2×#19099141C211yesmaximal, characteristic, complemented
17#23776603C211yesmaximal, characteristic, complemented
18#23776601C211yesmaximal, characteristic, complemented
19C2×#19099046C211yesmaximal, characteristic, complemented
20C79×#3449C211yesmaximal, characteristic, complemented
21C22×#11929624C2211yescharacteristic
22#19099284C2218yescomplemented
23#19099283C2218yescomplemented
24#19099278C2218yescomplemented
25#19099277C2218yescomplemented
26#19099271C2218yescomplemented
27#19099270C2218yescomplemented
28#19099265C22116yescomplemented
29#19099265C2218yescomplemented
30#19099260C2218yescomplemented
31#19099259C2218yescomplemented
32#19099259C2218yescomplemented
33#19099256C22116yescomplemented
34#19099256C22116yescomplemented
35#19099255C2218yescomplemented
36#19099253C2218yescomplemented
37#19099253C2218yescomplemented
38#19099250C22116yescomplemented
39#19099247C2218yescomplemented
40#19099244C22116yescomplemented
41#19099236C22116yescomplemented
42#19099219C22116yescomplemented
43#19099217C2218yescomplemented
44#19099213C2218yescomplemented
45#19099200C22116yescomplemented
46#19099191C2214yescomplemented
47#19099191C2214yescomplemented
48#19099191C2214yescomplemented
49#19099191C2214yescomplemented
50#19099186C2218yescomplemented
51#19099182C2218yescomplemented
52#19099182C2218yescomplemented
53#19099180C2218yescomplemented
54#19099174C2218yescomplemented
55#19099173C2218yescomplemented
56#19099167C2218yescomplemented
57#19099166C2218yescomplemented
58#19099157C22116yescomplemented
59#19099148C22116yescomplemented
60#19099141C2214yes—
61#19099141C2214yes—
62#19099141C2212yescomplemented
63#19099141C2214yescomplemented
64#19099141C2214yescomplemented
65#19099141C2212yescomplemented
66#19099137C2212yescomplemented
67#19099134C2212yes—
68#19099130C2212yescomplemented
69#19099127C2212yes—
70#19099122C2214yes—
71#19099118C2218yescomplemented
72#19099115C2218yescomplemented
73#19099111C2218yescomplemented
74#19099109C2214yescomplemented
75#19099108C2218yescomplemented
76C2×#14579161C2212yescomplemented
77C2×#14579160C2212yescomplemented
78#19099099C2218yescomplemented
79#19099094C2218yescomplemented
80#19099092C2218yescomplemented
81#19099092C2218yescomplemented
82#19099090C22116yescomplemented
83C2×#14579153C2212yescomplemented
84C2×#14579152C2212yescomplemented
85#19099074C2214yescomplemented
86#19099070C2214yes—
87#19099069C22116yescomplemented
88C2×#14579140C2212yescomplemented
89C2×#14579138C2214yes—
90C2×#14579137C2212yescomplemented
91C2×#14579135C2212yescomplemented
92C2×#14579133C2214yes—
93C2×#14579132C2212yescomplemented
94#19099046C2214yes—
95#19099046C2214yes—
96#19099046C2212yescomplemented
97#19099046C2214yescomplemented
98#19099046C2214yescomplemented
99#19099046C2212yescomplemented
100#19099046C2212yescomplemented
101#19099046C2212yescomplemented
102#19099044C2212yescomplemented
103#19099044C2212yescomplemented
104#19099043C2212yescomplemented
105#19099043C2212yescomplemented
106#19099041C2212yescomplemented
107#19099040C2212yescomplemented
108#19099038C2214yes—
109#19099038C2212yescomplemented
110#19099037C2212yescomplemented
111#19099036C2214yes—
112#41×Dic79C2214yescomplemented
113#41×Dic79C2214yescomplemented
114C4×#11929624C2214yescomplemented
115#19099031C2214yescomplemented
116C2×Q8×Dic79C2212yescomplemented
117C2×D4×Dic79C2214yes—
118C2×D4×Dic79C2212yescomplemented
119C2×#14579120C2211yescharacteristic
120C2×#14579120C2211yescharacteristic
121C2×#14579120C2212yescomplemented
122C2×#14579120C2214yescomplemented
123#117×D79C2214yescomplemented
124C22×C4⋊Dic79C2211yescharacteristic
125C22×C4⋊Dic79C2212yescomplemented
126C22×#41×C79C2211yescharacteristic
127C22×#41×C79C2211yescharacteristic
128#537×C79C2212yescomplemented
129#537×C79C2212yescomplemented
130#536×C79C2212yes—
131#536×C79C2212yescomplemented
132#535×C79C2212yes—
133#535×C79C2212yescomplemented
134#534×C79C2214yes—
135#532×C79C2214yescomplemented
136#525×C79C2214yes—
137#525×C79C2214yescomplemented
138C2×#117×C79C2211yescharacteristic
139C2×#11929624—28no—
140C2×#11929624C2312yes—
141C2×#11929624C2312yes—
142C2×#11929624C2312yes—
143C2×#11929624C2312yes—
144C2×#11929623C23116yes—
145C22×Dic158C2311yescharacteristic
146C22×Dic158C2314yes—
147C22×D316C2311yescharacteristic
148C22×C22⋊D79C2312yes—
149C22×C22⋊D79C2314yes—
150C23×Dic79C2312yes—
151C23×Dic79C2314yes—
152C22×C4×D79C2312yes—
153#14579161C2318yes—
154#14579161C2318yes—
155#14579160C2318yes—
156#14579160C2318yes—
157#14579159C2314yes—
158#14579157C2314yes—
159#14579156C23116yes—
160#14579156C23116yes—
161#14579154C23116yes—
162#14579154C23116yes—
163#14579154C23116yes—
164#14579154C23116yes—
165#14579153C2318yes—
166#14579153C2318yes—
167#14579152C23116yes—
168#14579152C2318yes—
169#14579152C2318yes—
170#14579151C23116yes—
171#14579151C23116yes—
172#14579150C2314yes—
173#14579148C23116yes—
174#14579148C2314yes—
175#14579147C23116yes—
176#14579147C23116yes—
177#14579145C23116yes—
178#14579145C23116yes—
179#14579144C2318yes—
180#14579143C23116yes—
181#14579143C23116yes—
182#14579142C23116yes—
183#14579142C23116yes—
184#14579142C2318yes—
185#14579141C23116yes—
186#14579140C2318yes—
187#14579140C2318yes—
188#14579140C2314yes—
189#14579140C2314yes—
190#14579138C23116yes—
191#14579138C23116yes—
192#14579138C23116yes—
193#14579138C23116yes—
194#14579137C2314yes—
195#14579137C2314yes—
196#14579137C2318yes—
197#14579137C2318yes—
198#14579135C2318yes—
199#14579135C2318yes—
200#14579135C2314yes—
201#14579135C2314yes—
202#14579133C23116yes—
203#14579133C23116yes—
204#14579133C2318yes—
205#14579133C2318yes—
206#14579133C23116yes—
207#14579133C23116yes—
208#14579132C2318yes—
209#14579132C2318yes—
210#14579132C2314yes—
211#14579132C2314yes—
212#14579132C23116yes—
213#14579130C2318yes—
214#14579129C2318yes—
215Q8×Dic79C2318yes—
216Q8×Dic79C2314yes—
217Q8×Dic79C2318yes—
218Q8×Dic79C2314yes—
219Q8×Dic79C2314yes—
220Q8×Dic79C2314yes—
221C4×Dic158C2314yes—
222C4×Dic158C2314yes—
223#14579126C2314yes—
224#14579126C2314yes—
225#14579126C23116yes—
226C4×D316C2314yes—
227C4×D316C2314yes—
228D4×Dic79C2318yes—
229D4×Dic79C2318yes—
230D4×Dic79C2318yes—
231D4×Dic79C2314yes—
232D4×Dic79C2318yes—
233D4×Dic79C2314yes—
234D4×Dic79C23116yes—
235D4×Dic79C2314yes—
236D4×Dic79C2318yes—
237D4×Dic79C23116yes—
238D4×Dic79C23116yes—
239D4×Dic79C2318yes—
240D4×Dic79C2314yes—
241#14579123C2314yes—
242#14579123C2314yes—
243C4×C22⋊D79C2318yes—
244C4×C22⋊D79C2318yes—
245C4×C22⋊D79C2318yes—
246C4×C22⋊D79C2318yes—
247(C22⋊D79)⋊C4C2318yes—
248(C22⋊D79)⋊C4C2318yes—
249(C22⋊D79)⋊C4C23116yes—
250(C22⋊D79)⋊C4C23116yes—
251#14579120C2312yes—
252#14579120C2318yes—
253#14579120C2312yes—
254#14579120C2312yes—
255#14579120C2312yes—
256#14579120C2318yes—
257#14579120C2318yes—
258#14579120C2314yes—
259#14579120C2318yes—
260#14579120C2312yes—
261#14579120C2312yes—
262#14579120C2312yes—
263#14579120C2312yes—
264#14579120C2314yes—
265#14579119C23116yes—
266#14579119C2314yes—
267#14579119C2314yes—
268#14579118C2318yes—
269#14579117C2318yes—
270#14579117C23116yes—
271#14579117C23116yes—
272C2×C4⋊Dic79C2312yes—
273C2×C4⋊Dic79C2312yes—
274C2×C4⋊Dic79C2312yes—
275C2×C4⋊Dic79C2312yes—
276C2×C4⋊Dic79C2311yescharacteristic
277C2×C4⋊Dic79C2311yescharacteristic
278C2×C4⋊Dic79C2314yes—
279C2×C4⋊Dic79C2312yes—
280C2×C4⋊Dic79C2312yes—
281C2×C4⋊Dic79C2318yes—
282C2×C4⋊Dic79C2314yes—
283C2×C4⋊Dic79C2318yes—
284C2×C4⋊Dic79C2314yes—
285C2×C4⋊Dic79C2314yes—
286C2×C4⋊Dic79C2311yescharacteristic
287C2×C4⋊Dic79C2311yescharacteristic
288C2×Dic79⋊C4C2314yes—
289C2×Dic79⋊C4C2314yes—
290C2×Dic79⋊C4C2314yes—
291C4⋊C4×D79C2314yes—
292C4⋊C4×D79C2314yes—
293C2×C22⋊Dic79C2314yes—
294C2×C22⋊Dic79C2318yes—
295C2×C22⋊Dic79C2314yes—
296C2×C22⋊Dic79C2312yes—
297C2×C22⋊Dic79C2312yes—
298C2×(C2×D79)⋊C4C2314yes—
299C22⋊C4×D79C2318yes—
300C2×C4×Dic79C2312yes—
301C2×C4×Dic79C2312yes—
302C2×C4×Dic79C2314yes—
303C2×C4×Dic79C2318yes—
304C42×D79C2318yes—
305C2×#41×C79—28no—
306C2×#41×C79—28no—
307C2×#41×C79C2312yes—
308C2×#41×C79C2312yes—
309C2×#41×C79C2312yes—
310C2×#41×C79C2312yes—
311C2×#41×C79C2312yes—
312C2×#41×C79C2312yes—
313C2×#41×C79C2312yes—
314C2×#41×C79C2312yes—
315C22×Q8×C79C2311yescharacteristic
316C22×Q8×C79C2311yescharacteristic
317C22×D4×C79C2312yes—
318C22×D4×C79C2312yes—
319C22×D4×C79C2311yescharacteristic
320C22×D4×C79C2311yescharacteristic
321C23×C4×C79C2312yes—
322C23×C4×C79C2312yes—
323C23×C4×C79C2311yescharacteristic
324C4⋊Q8×C79C2314yes—
325#127×C79C2314yes—
326#124×C79C2314yes—
327#124×C79C2314yes—
328#123×C79C2318yes—
329#123×C79C2318yes—
330C22⋊Q8×C79C2314yes—
331C22⋊Q8×C79C2314yes—
332C22⋊Q8×C79C2314yes—
333C22⋊Q8×C79C2314yes—
334#121×C79C2314yes—
335#121×C79C2314yes—
336#121×C79C2314yes—
337#121×C79C2318yes—
338#121×C79C2314yes—
339#121×C79C2318yes—
340#120×C79C2318yes—
341#120×C79C2318yes—
342C4×D4×C79C2318yes—
343C4×D4×C79C2318yes—
344#117×C79C2312yes—
345#117×C79C2312yes—
346#117×C79C2312yes—
347#117×C79C2312yes—
348C2×C4⋊C4×C79C2311yescharacteristic
349C2×C4⋊C4×C79C2311yescharacteristic
350C2×C22⋊C4×C79C2312yes—
351C2×C42×C79C2312yes—
352C23×D79C2412yes—
353#11929624—28no—
354#11929624—28no—
355#11929624—28no—
356#11929624—28no—
357#11929623—816no—
358C2×Dic158—24no—
359C2×Dic158—84no—
360C2×Dic158C2412yes—
361C2×Dic158C2412yes—
362C2×Dic158C24116yes—
363C2×D316—24no—
364C2×D316C2412yes—
365C2×D316C2412yes—
366C2×C22⋊D79—28no—
367C2×C22⋊D79—84no—
368C2×C22⋊D79C2414yes—
369C2×C22⋊D79C2414yes—
370C2×C22⋊D79C2418yes—
371C2×C22⋊D79C24116yes—
372C2×C22⋊D79C2418yes—
373C22×Dic79—82no—
374C22×Dic79—84no—
375C22×Dic79C2412yes—
376C22×Dic79C2412yes—
377C22×Dic79C2414yes—
378C22×Dic79C2418yes—
379C22×Dic79C24116yes—
380C22×Dic79C2412yes—
381C22×Dic79C2412yes—
382C22×Dic79C2412yes—
383C22×Dic79C2414yes—
384C22×Dic79C2418yes—
385C22×Dic79C2414yes—
386C2×C4×D79—28no—
387C2×C4×D79C2414yes—
388C2×C4×D79C2414yes—
389C2×C4×D79C2418yes—
390C2×C4×D79C2418yes—
391C4⋊Dic79C2412yes—
392C4⋊Dic79C2412yes—
393C4⋊Dic79C2412yes—
394C4⋊Dic79C2414yes—
395C4⋊Dic79C2414yes—
396C4⋊Dic79C2412yes—
397C4⋊Dic79C2412yes—
398C4⋊Dic79C2412yes—
399C4⋊Dic79C2414yes—
400C4⋊Dic79C2414yes—
401C4⋊Dic79C24116yes—
402C4⋊Dic79C24116yes—
403C4⋊Dic79C2412yes—
404C4⋊Dic79C2412yes—
405C4⋊Dic79C2418yes—
406C4⋊Dic79C2418yes—
407Dic79⋊C4C2418yes—
408Dic79⋊C4C2418yes—
409Dic79⋊C4C24116yes—
410Dic79⋊C4C24116yes—
411Dic79⋊C4C24116yes—
412Dic79⋊C4C2418yes—
413Dic79⋊C4C2418yes—
414C22⋊Dic79C2414yes—
415C22⋊Dic79C2414yes—
416C22⋊Dic79C24116yes—
417C22⋊Dic79C2414yes—
418C22⋊Dic79C2414yes—
419C22⋊Dic79C2418yes—
420C22⋊Dic79C24116yes—
421C22⋊Dic79C2418yes—
422C22⋊Dic79C2418yes—
423C22⋊Dic79C2418yes—
424(C2×D79)⋊C4C2418yes—
425(C2×D79)⋊C4C2418yes—
426(C2×D79)⋊C4C24116yes—
427(C2×D79)⋊C4C2418yes—
428(C2×D79)⋊C4C2418yes—
429C4×Dic79C2414yes—
430C4×Dic79C2418yes—
431C4×Dic79C2418yes—
432C4×Dic79C2414yes—
433C4×Dic79C2414yes—
434C4×Dic79C2418yes—
435C4×Dic79C24116yes—
436C4×Dic79C2418yes—
437C4×Dic79C2414yes—
438C24×C79C2412yes—
439C24×C79C2412yes—
440C24×C79C2411yescharacteristic
441#41×C79—28no—
442#41×C79—28no—
443#41×C79—28no—
444#41×C79—28no—
445#41×C79—28no—
446#41×C79—28no—
447#41×C79—28no—
448#41×C79—28no—
449C2×Q8×C79—24no—
450C2×Q8×C79—24no—
451C2×Q8×C79C2412yes—
452C2×Q8×C79C2412yes—
453C2×Q8×C79C2412yes—
454C2×Q8×C79C2412yes—
455C2×D4×C79—28no—
456C2×D4×C79—28no—
457C2×D4×C79—24no—
458C2×D4×C79—24no—
459C2×D4×C79C2414yes—
460C2×D4×C79C2414yes—
461C2×D4×C79C2412yes—
462C2×D4×C79C2414yes—
463C2×D4×C79C2414yes—
464C2×D4×C79C2412yes—
465C2×D4×C79C2412yes—
466C2×D4×C79C2412yes—
467C2×D4×C79C2418yes—
468C2×D4×C79C2418yes—
469C22×C4×C79—28no—
470C22×C4×C79—28no—
471C22×C4×C79#4118yescomplemented
472C22×C4×C79C2414yes—
473C22×C4×C79C2414yes—
474C22×C4×C79C2414yes—
475C22×C4×C79C2414yes—
476C22×C4×C79C2412yes—
477C22×C4×C79C2412yes—
478C22×C4×C79C2412yes—
479C22×C4×C79C2412yes—
480C22×C4×C79C2411yescharacteristic
481C22×C4×C79C2411yescharacteristic
482C22×C4×C79C2411yescharacteristic
483C22×C4×C79C2411yescharacteristic
484C22×C4×C79C2411yescharacteristic
485C22×C4×C79C2411yescharacteristic
486C4⋊C4×C79C2412yes—
487C4⋊C4×C79C2412yes—
488C4⋊C4×C79C2412yes—
489C4⋊C4×C79C2412yes—
490C4⋊C4×C79C2418yes—
491C4⋊C4×C79C2418yes—
492C22⋊C4×C79C2414yes—
493C22⋊C4×C79C2414yes—
494C22⋊C4×C79C2418yes—
495C22⋊C4×C79C2418yes—
496C22⋊C4×C79C2418yes—
497C22⋊C4×C79C2418yes—
498C42×C79C2414yes—
499C42×C79C2414yes—
500C23×C79—24no—
501C23×C79—24no—
502C23×C79—41no—
503C23×C79—42no—
504C23×C79—41no—
505C23×C79—42no—
506C23×C79—42no—
507C23×C79—42no—
508C23×C79C2×#4114yes—
509C23×C79C2514yes—
510C23×C79C2514yes—
511C23×C79C2511yescharacteristic
512C23×C79C2511yescharacteristic
513C23×C79C2511yescharacteristic
514C22×D79—24no—
515C22×D79—42no—
516C22×D79—42no—
517C22×D79C2514yes—
518Q8×C79—24no—
519Q8×C79—24no—
520Q8×C79—24no—
521Q8×C79—24no—
522D4×C79—28no—
523D4×C79—28no—
524D4×C79—28no—
525D4×C79—28no—
526D4×C79—24no—
527D4×C79—24no—
528D4×C79—24no—
529D4×C79—24no—
530D4×C79—48no—
531D4×C79—48no—
532C2×C4×C79—24no—
533C2×C4×C79—24no—
534C2×C4×C79—28no—
535C2×C4×C79—28no—
536C2×C4×C79—28no—
537C2×C4×C79—28no—
538C2×C4×C79—42no—
539C2×C4×C79—42no—
540C2×C4×C79C2×#4114yes—
541C2×C4×C79C2×#4114yes—
542C2×C4×C79C2×#4114yes—
543C2×C4×C79C2×#4114yes—
544C2×C4×C79C2×#4114yes—
545C2×C4×C79C2×#4114yes—
546C2×C4×C79C2514yes—
547C2×C4×C79C2514yes—
548C2×C4×C79C2514yes—
549C2×C4×C79C2514yes—
550C2×C4×C79C2511yescharacteristic
551C2×C4×C79C2511yescharacteristic
552C2×C4×C79C2511yescharacteristic
553C2×C4×C79C2511yescharacteristic
554C22⋊D79—28no—
555C22⋊D79—28no—
556C22⋊D79—416no—
557C22⋊D79—48no—
558C22⋊D79—48no—
559C2×Dic79—24no—
560C2×Dic79—44no—
561C2×Dic79—42no—
562C2×Dic79—44no—
563C2×Dic79—44no—
564C2×Dic79—416no—
565C2×Dic79—42no—
566C2×Dic79—48no—
567C2×Dic79—42no—
568C2×Dic79—42no—
569C2×Dic79—48no—
570C2×Dic79C2514yes—
571C2×Dic79C2514yes—
572C2×Dic79C2514yes—
573C2×Dic79C2514yes—
574C2×Dic79C2514yes—
575C2×Dic79C2518yes—
576D316—24no—
577D316—24no—
578C4×D79—28no—
579C4×D79—28no—
580C4×D79—48no—
581C4×D79—48no—
582Dic158—24no—
583Dic158—24no—
584Dic158—416no—
585C22×C79—21no—
586C22×C79—21no—
587C22×C79—21no—
588C22×C79—21no—
589C22×C79—21no—
590C22×C79—21no—
591C22×C79—24no—
592C22×C79—24no—
593C22×C79—24no—
594C22×C79—24no—
595C22×C79—24no—
596C22×C79—24no—
597C22×C79—44no—
598C22×C79—48no—
599C22×C79—84no—
600C22×C79C22×#4112yes—
601C22×C79C22×#4112yes—
602C22×C79C22×#4112yes—
603C22×C79C2611yescharacteristic
604C2×D79—24no—
605C2×D79—24no—
606C2×D79—24no—
607C2×D79—84no—
608C4×C79—24no—
609C4×C79—24no—
610C4×C79—24no—
611C4×C79—24no—
612C4×C79C22×#4112yes—
613C4×C79C22×#4112yes—
614C4×C79C22×#4112yes—
615C4×C79C22×#4112yes—
616Dic79—24no—
617Dic79—24no—
618Dic79—28no—
619Dic79—24no—
620Dic79—24no—
621Dic79—24no—
622#62856—791nomaximal, Sylow
623C2×C79—22no—
624C2×C79—22no—
625C2×C79—22no—
626C2×C79—44no—
627C2×C79—44no—
628C2×C79C23×#4111yescharacteristic
629C2×C79H(7,𝔽2)11yescharacteristic
630C2×C792−1+611yescharacteristic
631D79—44no—
632#3512—794no—
633#3512—794no—
634#3511—794no—
635#3511—794no—
636#3505—798no—
637#3495—794no—
638#3495—794no—
639#3494—794no—
640#3494—794no—
641#3493—794no—
642#3492—794no—
643#3461—794no—
644#3460—794no—
645C2×#544—791no—
646#3449—791no—
647#3449D7911yescharacteristic, complemented
648C2×#537—791no—
649#3428—791no—
650#3428—791no—
651C2×#520—791no—
652C79#6285611yescharacteristic, complemented, Sylow
653C22×#41—791no—
654C22×#41C2×D7911yescharacteristic
655C22×#41C2×D7911yescharacteristic
656#556—798no—
657#556—798no—
658#555—798no—
659#555—798no—
660#554—798no—
661#554—798no—
662#553—7916no—
663#553—7916no—
664#553—798no—
665#553—798no—
666#553—7916no—
667#553—798no—
668#553—798no—
669#552—7916no—
670#552—798no—
671#552—798no—
672#552—798no—
673#552—798no—
674#551—7916no—
675#551—7916no—
676#548—7916no—
677#547—798no—
678#547—798no—
679#546—7916no—
680#544—794no—
681#544—794no—
682#544—794no—
683#544—794no—
684#542—798no—
685#542—798no—
686#542—798no—
687#542—798no—
688#541—798no—
689#541—798no—
690#540—798no—
691#540—798no—
692#539—7916no—
693#538—7916no—
694#537—794no—
695#537—794no—
696#537—794no—
697#537—794no—
698#537—792no—
699#537—792no—
700#537C2×D7912yescomplemented
701#537C2×D7912yescomplemented
702#536—792no—
703#536—792no—
704#536C2×D7912yes—
705#536C2×D7912yescomplemented
706#535—792no—
707#535—792no—
708#535C2×D7912yes—
709#535C2×D7912yescomplemented
710#534—794no—
711#534C2×D7914yes—
712#533—798no—
713#533—798no—
714#532—794no—
715#532—798no—
716#532—798no—
717#532C2×D7914yescomplemented
718C2×C4⋊Q8—792no—
719C2×C4⋊Q8—792no—
720#529—798no—
721#529—798no—
722#529—7916no—
723#529—798no—
724#529—798no—
725C2×#125—792no—
726C2×#125—792no—
727#525—794no—
728#525—794no—
729#525—7916no—
730#525C2×D7914yes—
731#525C2×D7914yescomplemented
732C2×C22⋊Q8—792no—
733C2×C22⋊Q8—792no—
734C2×C22⋊Q8—794no—
735C2×#121—792no—
736C2×#121—794no—
737C2×#121—792no—
738#520—794no—
739#520—794no—
740#520—794no—
741#520—794no—
742#520—792no—
743#520—792no—
744#520—792no—
745#520—792no—
746#520—792no—
747#520—792no—
748#520—792no—
749#520—792no—
750#519—792no—
751#519—792no—
752#518—794no—
753#518—792no—
754#518—792no—
755#518—794no—
756C4×#41—794no—
757C4×#41—794no—
758C4×#41—794no—
759C4×#41—794no—
760C2×C4×Q8—792no—
761C2×C4×D4—792no—
762C2×C4×D4—794no—
763C2×#117—791no—
764C2×#117—792no—
765C2×#117—791no—
766C2×#117—794no—
767C2×#117—794no—
768C2×#117C2×D7911yescharacteristic
769C22×C4⋊C4—791no—
770C22×C4⋊C4—792no—
771C2×#41—28no—
772C2×#41—28no—
773C2×#41—7916no—
774C2×#41—792no—
775C2×#41—792no—
776C2×#41—792no—
777C2×#41—792no—
778C2×#41—1588no—
779C2×#41C22×D7912yes—
780C2×#41C22×D7912yes—
781C2×#41C22×D7912yes—
782C2×#41C22×D7912yes—
783C2×#41C22×D7912yes—
784C2×#41C22×D7912yes—
785C2×#41C22×D7912yes—
786C2×#41C22×D7912yes—
787C22×Q8—794no—
788C22×Q8—791no—
789C22×Q8C22×D7911yescharacteristic
790C22×Q8C22×D7911yescharacteristic
791C22×D4—794no—
792C22×D4—792no—
793C22×D4—791no—
794C22×D4C22×D7912yes—
795C22×D4C22×D7911yescharacteristic
796C22×D4C22×D7912yes—
797C22×D4C22×D7911yescharacteristic
798C23×C4—792no—
799C23×C4—794no—
800C23×C4—792no—
801C23×C4C22×D7912yes—
802C23×C4C22×D7912yes—
803C23×C4C22×D7911yescharacteristic
804C4⋊Q8—794no—
805C4⋊Q8—798no—
806C4⋊Q8—798no—
807C4⋊Q8—798no—
808C4⋊Q8—798no—
809C4⋊Q8C22×D7914yes—
810#127—794no—
811#127C22×D7914yes—
812#126—7916no—
813#126—7916no—
814#126—7916no—
815#126—7916no—
816#126—7916no—
817#126—7916no—
818#125—798no—
819#125—798no—
820#125—7916no—
821#125—7916no—
822#125—7916no—
823#125—798no—
824#125—798no—
825#124—794no—
826#124—794no—
827#124—7916no—
828#124—7916no—
829#124—7916no—
830#124C22×D7914yes—
831#124C22×D7914yes—
832#123—798no—
833#123—7916no—
834#123—7916no—
835#123—798no—
836#123—7916no—
837#123—7916no—
838#123—7916no—
839#123—7916no—
840#123C22×D7918yes—
841#123C22×D7918yes—
842C22⋊Q8—798no—
843C22⋊Q8—798no—
844C22⋊Q8—794no—
845C22⋊Q8—794no—
846C22⋊Q8—798no—
847C22⋊Q8—798no—
848C22⋊Q8—794no—
849C22⋊Q8—794no—
850C22⋊Q8—7916no—
851C22⋊Q8—7916no—
852C22⋊Q8—7916no—
853C22⋊Q8—7916no—
854C22⋊Q8—7916no—
855C22⋊Q8C22×D7914yes—
856C22⋊Q8C22×D7914yes—
857C22⋊Q8C22×D7914yes—
858C22⋊Q8C22×D7914yes—
859#121—7916no—
860#121—798no—
861#121—798no—
862#121—7916no—
863#121—794no—
864#121—794no—
865#121—7916no—
866#121—798no—
867#121—798no—
868#121—7916no—
869#121—7916no—
870#121—798no—
871#121—798no—
872#121—794no—
873#121—794no—
874#121C22×D7914yes—
875#121C22×D7914yes—
876#121C22×D7914yes—
877#121C22×D7914yes—
878#121C22×D7918yes—
879#121C22×D7918yes—
880#120—798no—
881#120—798no—
882#120C22×D7918yes—
883#120C22×D7918yes—
884C4×Q8—798no—
885C4×Q8—798no—
886C4×Q8—794no—
887C4×Q8—794no—
888C4×Q8—794no—
889C4×Q8—794no—
890C4×Q8—794no—
891C4×Q8—794no—
892C4×Q8—7916no—
893C4×Q8—794no—
894C4×Q8—794no—
895C4×D4—798no—
896C4×D4—798no—
897C4×D4—7916no—
898C4×D4—7916no—
899C4×D4—798no—
900C4×D4—798no—
901C4×D4—794no—
902C4×D4—794no—
903C4×D4—794no—
904C4×D4—798no—
905C4×D4—798no—
906C4×D4—794no—
907C4×D4—7916no—
908C4×D4—798no—
909C4×D4—798no—
910C4×D4—798no—
911C4×D4—798no—
912C4×D4—794no—
913C4×D4—794no—
914C4×D4—798no—
915C4×D4—798no—
916C4×D4—7916no—
917C4×D4—7916no—
918C4×D4—794no—
919C4×D4—794no—
920C4×D4C22×D7918yes—
921C4×D4C22×D7918yes—
922#117—792no—
923#117—792no—
924#117—792no—
925#117—792no—
926#117—792no—
927#117—792no—
928#117—798no—
929#117—792no—
930#117—798no—
931#117—792no—
932#117—794no—
933#117—798no—
934#117—798no—
935#117—794no—
936#117—794no—
937#117—794no—
938#117—7916no—
939#117—798no—
940#117—7916no—
941#117—7916no—
942#117—798no—
943#117C22×D7912yes—
944#117C22×D7912yes—
945#117C22×D7912yes—
946#117C22×D7912yes—
947C2×C4⋊C4—791no—
948C2×C4⋊C4—792no—
949C2×C4⋊C4—792no—
950C2×C4⋊C4—794no—
951C2×C4⋊C4—792no—
952C2×C4⋊C4—792no—
953C2×C4⋊C4—792no—
954C2×C4⋊C4—792no—
955C2×C4⋊C4—798no—
956C2×C4⋊C4—798no—
957C2×C4⋊C4—791no—
958C2×C4⋊C4—791no—
959C2×C4⋊C4—791no—
960C2×C4⋊C4—794no—
961C2×C4⋊C4—794no—
962C2×C4⋊C4—794no—
963C2×C4⋊C4—794no—
964C2×C4⋊C4—794no—
965C2×C4⋊C4—794no—
966C2×C4⋊C4—794no—
967C2×C4⋊C4—794no—
968C2×C4⋊C4C22×D7911yescharacteristic
969C2×C4⋊C4C22×D7911yescharacteristic
970C2×C22⋊C4—792no—
971C2×C22⋊C4—794no—
972C2×C22⋊C4—792no—
973C2×C22⋊C4—798no—
974C2×C22⋊C4—794no—
975C2×C22⋊C4—794no—
976C2×C22⋊C4—798no—
977C2×C22⋊C4C22×D7912yes—
978C2×C42—792no—
979C2×C42—794no—
980C2×C42—792no—
981C2×C42—798no—
982C2×C42—798no—
983C2×C42C22×D7912yes—
984C24—792no—
985C24C23×D7912yes—
986C24C23×D7912yes—
987C24C23×D7911yescharacteristic
988#41—28no—
989#41—28no—
990#41—28no—
991#41—28no—
992#41—28no—
993#41—28no—
994#41—28no—
995#41—28no—
996#41—63216no—
997#41—1588no—
998#41—1588no—
999#41—1588no—
1000#41—1588no—
1001C2×Q8—24no—
1002C2×Q8—24no—
1003C2×Q8—7916no—
1004C2×Q8—792no—
1005C2×Q8—792no—
1006C2×Q8—6324no—
1007C2×Q8—1584no—
1008C2×Q8C23×D7912yes—
1009C2×Q8C23×D7912yes—
1010C2×Q8C23×D7912yes—
1011C2×Q8C23×D7912yes—
1012C2×D4—28no—
1013C2×D4—28no—
1014C2×D4—24no—
1015C2×D4—24no—
1016C2×D4—798no—
1017C2×D4—798no—
1018C2×D4—7916no—
1019C2×D4—794no—
1020C2×D4—794no—
1021C2×D4—792no—
1022C2×D4—792no—
1023C2×D4—6324no—
1024C2×D4—1588no—
1025C2×D4—1584no—
1026C2×D4C23×D7914yes—
1027C2×D4C23×D7914yes—
1028C2×D4C23×D7914yes—
1029C2×D4C23×D7914yes—
1030C2×D4C23×D7912yes—
1031C2×D4C23×D7912yes—
1032C2×D4C23×D7912yes—
1033C2×D4C23×D7912yes—
1034C2×D4C23×D7918yes—
1035C2×D4C23×D7918yes—
1036C22×C4—28no—
1037C22×C4—28no—
1038C22×C4—792no—
1039C22×C4—792no—
1040C22×C4—792no—
1041C22×C4—792no—
1042C22×C4—794no—
1043C22×C4—798no—
1044C22×C4—798no—
1045C22×C4—794no—
1046C22×C4—794no—
1047C22×C4—7916no—
1048C22×C4—798no—
1049C22×C4—798no—
1050C22×C4—792no—
1051C22×C4—794no—
1052C22×C4—794no—
1053C22×C4—6322no—
1054C22×C4—6324no—
1055C22×C4—1588no—
1056C22×C4#1192962318yescomplemented
1057C22×C4C23×D7912yes—
1058C22×C4C23×D7914yes—
1059C22×C4C23×D7912yes—
1060C22×C4C23×D7914yes—
1061C22×C4C23×D7914yes—
1062C22×C4C23×D7914yes—
1063C22×C4C23×D7912yes—
1064C22×C4C23×D7912yes—
1065C22×C4C23×D7911yescharacteristic
1066C22×C4C23×D7911yescharacteristic
1067C22×C4C23×D7911yescharacteristic
1068C22×C4C23×D7911yescharacteristic
1069C22×C4C23×D7911yescharacteristic
1070C22×C4C23×D7911yescharacteristic
1071C4⋊C4—798no—
1072C4⋊C4—798no—
1073C4⋊C4—7916no—
1074C4⋊C4—7916no—
1075C4⋊C4—7916no—
1076C4⋊C4—798no—
1077C4⋊C4—798no—
1078C4⋊C4—792no—
1079C4⋊C4—792no—
1080C4⋊C4—794no—
1081C4⋊C4—794no—
1082C4⋊C4—792no—
1083C4⋊C4—792no—
1084C4⋊C4—792no—
1085C4⋊C4—792no—
1086C4⋊C4—794no—
1087C4⋊C4—794no—
1088C4⋊C4—7916no—
1089C4⋊C4—792no—
1090C4⋊C4—792no—
1091C4⋊C4—798no—
1092C4⋊C4—798no—
1093C4⋊C4—7916no—
1094C4⋊C4C23×D7912yes—
1095C4⋊C4C23×D7912yes—
1096C4⋊C4C23×D7912yes—
1097C4⋊C4C23×D7912yes—
1098C4⋊C4C23×D7918yes—
1099C4⋊C4C23×D7918yes—
1100C22⋊C4—794no—
1101C22⋊C4—794no—
1102C22⋊C4—794no—
1103C22⋊C4—794no—
1104C22⋊C4—798no—
1105C22⋊C4—7916no—
1106C22⋊C4—798no—
1107C22⋊C4—7916no—
1108C22⋊C4—798no—
1109C22⋊C4—798no—
1110C22⋊C4—798no—
1111C22⋊C4—798no—
1112C22⋊C4—7916no—
1113C22⋊C4—798no—
1114C22⋊C4—798no—
1115C22⋊C4C23×D7914yes—
1116C22⋊C4C23×D7914yes—
1117C22⋊C4C23×D7918yes—
1118C22⋊C4C23×D7918yes—
1119C22⋊C4C23×D7918yes—
1120C22⋊C4C23×D7918yes—
1121C42—794no—
1122C42—794no—
1123C42—794no—
1124C42—798no—
1125C42—798no—
1126C42—7916no—
1127C42—798no—
1128C42—798no—
1129C42—794no—
1130C42C23×D7914yes—
1131C42C23×D7914yes—
1132C23—24no—
1133C23—24no—
1134C23—41no—
1135C23—42no—
1136C23—41no—
1137C23—42no—
1138C23—42no—
1139C23—42no—
1140C23—3162no—
1141C23—3162no—
1142C23—794no—
1143C23—1584no—
1144C23C2×#1192962314yes—
1145C23C24×D7914yes—
1146C23C24×D7914yes—
1147C23C24×D7911yescharacteristic
1148C23C24×D7911yescharacteristic
1149C23C24×D7911yescharacteristic
1150Q8—24no—
1151Q8—24no—
1152Q8—24no—
1153Q8—24no—
1154Q8—31616no—
1155Q8—1584no—
1156Q8—1584no—
1157D4—28no—
1158D4—28no—
1159D4—28no—
1160D4—28no—
1161D4—24no—
1162D4—24no—
1163D4—24no—
1164D4—24no—
1165D4—48no—
1166D4—48no—
1167D4—3168no—
1168D4—31616no—
1169D4—3168no—
1170D4—1588no—
1171D4—1588no—
1172D4—1584no—
1173D4—1584no—
1174C2×C4—24no—
1175C2×C4—24no—
1176C2×C4—28no—
1177C2×C4—28no—
1178C2×C4—28no—
1179C2×C4—28no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—3168no—
1183C2×C4—3168no—
1184C2×C4—3162no—
1185C2×C4—3164no—
1186C2×C4—3164no—
1187C2×C4—3164no—
1188C2×C4—31616no—
1189C2×C4—3162no—
1190C2×C4—3168no—
1191C2×C4—3162no—
1192C2×C4—3168no—
1193C2×C4—3162no—
1194C2×C4—794no—
1195C2×C4—794no—
1196C2×C4—794no—
1197C2×C4—794no—
1198C2×C4—794no—
1199C2×C4—798no—
1200C2×C4—1584no—
1201C2×C4—1588no—
1202C2×C4—1588no—
1203C2×C4C2×#1192962314yes—
1204C2×C4C2×#1192962314yes—
1205C2×C4C2×#1192962314yes—
1206C2×C4C2×#1192962314yes—
1207C2×C4C2×#1192962314yes—
1208C2×C4C2×#1192962314yes—
1209C2×C4C24×D7914yes—
1210C2×C4C24×D7914yes—
1211C2×C4C24×D7914yes—
1212C2×C4C24×D7914yes—
1213C2×C4C24×D7911yescharacteristic
1214C2×C4C24×D7911yescharacteristic
1215C2×C4C24×D7911yescharacteristic
1216C2×C4C24×D7911yescharacteristic
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—24no—
1227C22—24no—
1228C22—24no—
1229C22—44no—
1230C22—48no—
1231C22—84no—
1232C22—6324no—
1233C22—1584no—
1234C22—1584no—
1235C22—1584no—
1236C22C22×#1192962312yes—
1237C22C22×#1192962312yes—
1238C22C22×#1192962312yes—
1239C22C25×D7911yescharacteristic
1240C4—24no—
1241C4—24no—
1242C4—24no—
1243C4—24no—
1244C4—1584no—
1245C4—1584no—
1246C4—1588no—
1247C4—1584no—
1248C4—1584no—
1249C4—1584no—
1250C4C22×#1192962312yes—
1251C4C22×#1192962312yes—
1252C4C22×#1192962312yes—
1253C4C22×#1192962312yes—
1254C2—22no—
1255C2—22no—
1256C2—22no—
1257C2—44no—
1258C2—44no—
1259C2—3164no—
1260C2C23×#1192962311yescharacteristic
1261C2#2377821111yescharacteristic
1262C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3449C2
hypercenter#3449D79
hypocenterC79#62856
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #23777321C2semidirect
2. #23777320C2semidirect
3. #23777309C2semidirect
4. #23777307C2semidirect
5. #23777237C2semidirect
6. #23777154C2semidirect
7. #23777149C2semidirect
8. #23777137C2semidirect
9. #23777132C2semidirect
10. #23777117C2semidirect
11. #23777106C2semidirect
12. #23776824C2semidirect
13. #23776813C2semidirect
14. C2×#19099191C2semidirect
15. #23776729C2semidirect
16. C2×#19099141C2semidirect
17. #23776603C2semidirect
18. #23776601C2semidirect
19. C2×#19099046C2semidirect
20. C79×#3449C2semidirect
22. #19099284C22semidirect
23. #19099283C22semidirect
24. #19099278C22semidirect
25. #19099277C22semidirect
26. #19099271C22semidirect
27. #19099270C22semidirect
28. #19099265C22semidirect
29. #19099265C22semidirect
30. #19099260C22semidirect
31. #19099259C22semidirect
32. #19099259C22semidirect
33. #19099256C22semidirect
34. #19099256C22semidirect
35. #19099255C22semidirect
36. #19099253C22semidirect
37. #19099253C22semidirect
38. #19099250C22semidirect
39. #19099247C22semidirect
40. #19099244C22semidirect
41. #19099236C22semidirect
42. #19099219C22semidirect
43. #19099217C22semidirect
44. #19099213C22semidirect
45. #19099200C22semidirect
46. #19099191C22semidirect
47. #19099191C22semidirect
48. #19099191C22semidirect
49. #19099191C22semidirect
50. #19099186C22semidirect
51. #19099182C22semidirect
52. #19099182C22semidirect
53. #19099180C22semidirect
54. #19099174C22semidirect
55. #19099173C22semidirect
56. #19099167C22semidirect
57. #19099166C22semidirect
58. #19099157C22semidirect
59. #19099148C22semidirect
62. #19099141C22semidirect
63. #19099141C22semidirect
64. #19099141C22semidirect
65. #19099141C22semidirect
66. #19099137C22semidirect
68. #19099130C22semidirect
71. #19099118C22semidirect
72. #19099115C22semidirect
73. #19099111C22semidirect
74. #19099109C22semidirect
75. #19099108C22semidirect
76. C2×#14579161C22semidirect
77. C2×#14579160C22semidirect
78. #19099099C22semidirect
79. #19099094C22semidirect
80. #19099092C22semidirect
81. #19099092C22semidirect
82. #19099090C22semidirect
83. C2×#14579153C22semidirect
84. C2×#14579152C22semidirect
85. #19099074C22semidirect
87. #19099069C22semidirect
88. C2×#14579140C22semidirect
90. C2×#14579137C22semidirect
91. C2×#14579135C22semidirect
93. C2×#14579132C22semidirect
96. #19099046C22semidirect
97. #19099046C22semidirect
98. #19099046C22semidirect
99. #19099046C22semidirect
100. #19099046C22semidirect
101. #19099046C22semidirect
102. #19099044C22semidirect
103. #19099044C22semidirect
104. #19099043C22semidirect
105. #19099043C22semidirect
106. #19099041C22semidirect
107. #19099040C22semidirect
109. #19099038C22semidirect
110. #19099037C22semidirect
112. #41×Dic79C22semidirect
113. #41×Dic79C22semidirect
114. C4×#11929624C22semidirect
115. #19099031C22semidirect
116. C2×Q8×Dic79C22semidirect
118. C2×D4×Dic79C22semidirect
121. C2×#14579120C22semidirect
122. C2×#14579120C22semidirect
123. #117×D79C22semidirect
125. C22×C4⋊Dic79C22semidirect
128. #537×C79C22semidirect
129. #537×C79C22semidirect
131. #536×C79C22semidirect
133. #535×C79C22semidirect
135. #532×C79C22semidirect
137. #525×C79C22semidirect
471. C22×C4×C79#41semidirect
647. #3449D79semidirect
652. C79#62856semidirect
700. #537C2×D79semidirect
701. #537C2×D79semidirect
705. #536C2×D79semidirect
709. #535C2×D79semidirect
717. #532C2×D79semidirect
731. #525C2×D79semidirect
1056. C22×C4#11929623semidirect

Maximal subgroups

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

subgroupindex
#237773212
#237773202
#237773092
#237773072
#237772372
#237771542
#237771492
#237771372
#237771322
#237771172
#237771062
#237768242
#237768132
C2×#190991912
#237767292
C2×#190991412
#237766032
#237766012
C2×#190990462
C79×#34492
#6285679