Finite Group Databasebeta

← #35196961

Subgroups — #35196961

Order 20224.

7274 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777956C218yesmaximal, complemented
2#23777938C214yesmaximal, complemented
3#23777923C214yesmaximal, complemented
4#23777757C214yesmaximal, complemented
5#23777744C212yesmaximal, complemented
6#23777733C212yesmaximal, complemented
7#23777477C214yesmaximal, complemented
8#23777427C214yesmaximal, complemented
9#23777340C218yesmaximal, complemented
10#23777234C214yesmaximal, complemented
11#23777157C214yesmaximal, complemented
12#23777130C218yesmaximal, complemented
13#23777044C214yesmaximal, complemented
14C2×#19099097C212yesmaximal, complemented
15C2×#532×C79C211yesmaximal, characteristic, complemented
16C2×#14579206C2214yescomplemented
17#19099313C2214yescomplemented
18#19099312C2218yescomplemented
19#19099307C2218yescomplemented
20#19099305C2214yescomplemented
21#19099300C2218yescomplemented
22#19099299C2212yescomplemented
23#19099296C2218yescomplemented
24#19099293C2212yescomplemented
25#19099279C2212yescomplemented
26#19099275C2218yescomplemented
27#19099274C2214yescomplemented
28#19099272C2218yescomplemented
29#19099265C2218yescomplemented
30#19099263C2218yescomplemented
31#19099262C22116yescomplemented
32#19099256C22116yescomplemented
33#19099248C2218yescomplemented
34#19099243C2218yescomplemented
35#19099242C22116yescomplemented
36#19099239C22116yescomplemented
37#19099233C2214yescomplemented
38#19099219C2218yescomplemented
39#19099214C2218yescomplemented
40#19099213C2218yescomplemented
41#19099212C22116yescomplemented
42#19099212C22116yescomplemented
43#19099208C2218yescomplemented
44#19099207C2218yescomplemented
45#19099203C22116yescomplemented
46#19099202C22116yescomplemented
47#19099201C22116yescomplemented
48#19099201C22116yescomplemented
49#19099198C2212yescomplemented
50#19099197C2218yescomplemented
51D4×C22⋊D79C2218yescomplemented
52#19099190C2218yescomplemented
53#19099187C2218yescomplemented
54#19099178C2218yescomplemented
55#19099177C22116yescomplemented
56#19099167C2218yescomplemented
57#19099164C2218yescomplemented
58#19099158C2218yescomplemented
59#19099155C22116yescomplemented
60#19099150C2218yescomplemented
61#19099147C22116yescomplemented
62#19099146C22116yescomplemented
63#19099140C2218yescomplemented
64#19099137C2218yescomplemented
65#19099126C2218yescomplemented
66#19099122C2218yescomplemented
67#19099122C2218yescomplemented
68#19099121C2218yescomplemented
69#19099108C2218yescomplemented
70#19099097C2214yescomplemented
71#19099097C2214yescomplemented
72#19099097C2214yescomplemented
73#19099097C2214yescomplemented
74#19099097C2214yescomplemented
75#19099097C2214yescomplemented
76#19099097C2214yescomplemented
77#19099097C2214yescomplemented
78#19099094C2218yescomplemented
79C2×#14579155C2214yescomplemented
80C2×#14579153C2212yescomplemented
81C2×#14579149C2212yescomplemented
82#19099074C2218yescomplemented
83#19099073C2218yescomplemented
84C2×#14579144C2214yescomplemented
85C2×#14579144C2218yescomplemented
86C2×#14579140C2212yescomplemented
87C2×#14579135C2212yes—
88#121×D79C2218yescomplemented
89#19099042C2218yescomplemented
90#19099038C2214yescomplemented
91#19099035C2218yescomplemented
92C2×C4×Dic158C2212yescomplemented
93C2×C4×D316C2212yescomplemented
94C2×C4×C22⋊D79C2214yescomplemented
95C2×#14579118C2214yescomplemented
96C22×#41×C79C2212yescomplemented
97#532×C79C2214yescomplemented
98#532×C79C2214yescomplemented
99#532×C79C2214yescomplemented
100#532×C79C2214yescomplemented
101C2×C4⋊Q8×C79C2211yescharacteristic, complemented
102C2×#127×C79C2211yescharacteristic, complemented
103C2×#124×C79C2212yescomplemented
104C2×#121×C79C2214yescomplemented
105C2×C4×D4×C79C2214yescomplemented
106C22×C42×C79C2211yescharacteristic, complemented
107#14579206—416no—
108C2×#11929624C2318yes—
109C2×#11929623C23116yes—
110C2×#11929623C2318yes—
111C22×Dic158C2312yes—
112C22×D316C2312yes—
113C22×C22⋊D79C2314yes—
114C22×C22⋊D79C2318yes—
115C2×D4×D79C23116yes—
116C2×D4×D79C2318yes—
117C22×C4×D79C2314yes—
118#14579160C2318yes—
119#14579159C2318yes—
120#14579159C2318yes—
121#14579157C2318yes—
122#14579156C23116yes—
123#14579155C2318yes—
124#14579155C2318yes—
125#14579155C2318yes—
126#14579155C2318yes—
127#14579154C23116yes—
128#14579154C23116yes—
129#14579153C2314yes—
130#14579153C2314yes—
131#14579153C2314yes—
132#14579153C2314yes—
133#14579152C2318yes—
134#14579151C23116yes—
135#14579150C2318yes—
136#14579150C2318yes—
137#14579149C2314yes—
138#14579149C2314yes—
139#14579149C2314yes—
140#14579149C2314yes—
141#14579148C2318yes—
142#14579147C23116yes—
143#14579147C23116yes—
144#14579146C23116yes—
145#14579145C23116yes—
146#14579144C2318yes—
147#14579144C23116yes—
148#14579144C23116yes—
149#14579144C23116yes—
150#14579144C2318yes—
151#14579144C2318yes—
152#14579144C2318yes—
153#14579143C23116yes—
154#14579143C23116yes—
155#14579142C23116yes—
156#14579142C23116yes—
157#14579142C2318yes—
158#14579142C2318yes—
159#14579141C2318yes—
160#14579140C2314yes—
161#14579140C23116yes—
162#14579140C2314yes—
163#14579140C2314yes—
164#14579140C2314yes—
165#14579139C23116yes—
166#14579138C23116yes—
167#14579138C23116yes—
168#14579137C23116yes—
169#14579137C23116yes—
170#14579136C2318yes—
171#14579135C2314yes—
172#14579135C23116yes—
173#14579135C2314yes—
174#14579135C2314yes—
175#14579135C2314yes—
176#14579134C23116yes—
177#14579134C23116yes—
178#14579133C23116yes—
179#14579133C23116yes—
180#14579133C23116yes—
181#14579133C23116yes—
182#14579133C23116yes—
183#14579133C23116yes—
184#14579132C2318yes—
185#14579132C2318yes—
186#14579131C23116yes—
187#14579130C23116yes—
188#14579129C23116yes—
189#14579129C2318yes—
190#14579129C23116yes—
191#14579129C2318yes—
192C4×Dic158C2314yes—
193C4×Dic158C2314yes—
194C4×Dic158C2314yes—
195C4×Dic158C2314yes—
196#14579126C2318yes—
197C4×D316C2314yes—
198C4×D316C2314yes—
199C4×D316C2314yes—
200C4×D316C2314yes—
201D4×Dic79C23116yes—
202D4×Dic79C23116yes—
203D4×Dic79C2318yes—
204D4×Dic79C2318yes—
205#14579123C2318yes—
206C4×C22⋊D79C23116yes—
207C4×C22⋊D79C23116yes—
208C4×C22⋊D79C2318yes—
209C4×C22⋊D79C2318yes—
210C4×C22⋊D79C2318yes—
211C4×C22⋊D79C2318yes—
212(C22⋊D79)⋊C4C23116yes—
213(C22⋊D79)⋊C4C23116yes—
214#14579120C2318yes—
215#14579119C2318yes—
216#14579118C2318yes—
217#14579118C2318yes—
218#14579118C2318yes—
219#14579118C2318yes—
220#14579117C23116yes—
221C2×C4⋊Dic79C2312yes—
222C2×C4⋊Dic79C2312yes—
223C2×Dic79⋊C4C2314yes—
224C2×Dic79⋊C4C23116yes—
225C2×Dic79⋊C4C2314yes—
226C2×Dic79⋊C4C2314yes—
227C2×Dic79⋊C4C2314yes—
228C4⋊C4×D79C2318yes—
229C2×C22⋊Dic79C2318yes—
230C2×C22⋊Dic79C2314yes—
231C2×(C2×D79)⋊C4C23116yes—
232C2×(C2×D79)⋊C4C2314yes—
233C2×(C2×D79)⋊C4C2314yes—
234C2×(C2×D79)⋊C4C2314yes—
235C2×(C2×D79)⋊C4C2314yes—
236C22⋊C4×D79C23116yes—
237C2×C4×Dic79C2314yes—
238C2×#41×C79—48no—
239C2×#41×C79C2318yes—
240C2×#41×C79C2318yes—
241C22×Q8×C79C2312yes—
242C22×D4×C79C2314yes—
243C22×D4×C79C2314yes—
244C22×D4×C79C2312yes—
245C23×C4×C79C2311yescharacteristic
246C23×C4×C79C2312yes—
247C23×C4×C79C2314yes—
248C4⋊Q8×C79C2314yes—
249C4⋊Q8×C79C2312yes—
250C4⋊Q8×C79C2312yes—
251#127×C79C2314yes—
252#127×C79C2312yes—
253#127×C79C2312yes—
254#124×C79C2318yes—
255#124×C79C2314yes—
256#124×C79C2314yes—
257#121×C79C2318yes—
258#121×C79C2318yes—
259#121×C79C2318yes—
260#121×C79C2318yes—
261C4×D4×C79C2318yes—
262C4×D4×C79C2318yes—
263C4×D4×C79C2318yes—
264C4×D4×C79C2318yes—
265C2×C4⋊C4×C79C2314yes—
266C2×C22⋊C4×C79C2318yes—
267C2×C42×C79C2312yes—
268C2×C42×C79C2311yescharacteristic
269C2×C42×C79C2311yescharacteristic
270C2×C42×C79C2312yes—
271C2×C42×C79C2312yes—
272C2×C42×C79C2312yes—
273C2×C42×C79C2312yes—
274C23×D79C2414yes—
275C23×D79C2418yes—
276#11929624—416no—
277#11929623—432no—
278#11929623—416no—
279C2×Dic158—44no—
280C2×Dic158C2414yes—
281C2×Dic158C2414yes—
282C2×Dic158C2418yes—
283C2×D316—44no—
284C2×D316C2414yes—
285C2×D316C2418yes—
286C2×D316C2414yes—
287C2×C22⋊D79—216no—
288C2×C22⋊D79—416no—
289C2×C22⋊D79C2418yes—
290C2×C22⋊D79C2418yes—
291C2×C22⋊D79C24116yes—
292C2×C22⋊D79C24116yes—
293C2×C22⋊D79C24116yes—
294D4×D79—432no—
295D4×D79—416no—
296C22×Dic79C2414yes—
297C22×Dic79C2414yes—
298C22×Dic79C2418yes—
299C22×Dic79C24116yes—
300C22×Dic79C2414yes—
301C2×C4×D79—48no—
302C2×C4×D79C2418yes—
303C2×C4×D79C24116yes—
304C2×C4×D79C2418yes—
305C4⋊Dic79C2414yes—
306C4⋊Dic79C2414yes—
307C4⋊Dic79C2414yes—
308C4⋊Dic79C2414yes—
309C4⋊Dic79C24116yes—
310Dic79⋊C4C24116yes—
311Dic79⋊C4C2418yes—
312Dic79⋊C4C2418yes—
313Dic79⋊C4C2418yes—
314Dic79⋊C4C2418yes—
315Dic79⋊C4C2418yes—
316Dic79⋊C4C24116yes—
317Dic79⋊C4C2418yes—
318Dic79⋊C4C2418yes—
319Dic79⋊C4C2418yes—
320C22⋊Dic79C24116yes—
321C22⋊Dic79C2418yes—
322C22⋊Dic79C2418yes—
323C22⋊Dic79C2418yes—
324C22⋊Dic79C2418yes—
325C22⋊Dic79C24116yes—
326(C2×D79)⋊C4C2418yes—
327(C2×D79)⋊C4C24116yes—
328(C2×D79)⋊C4C2418yes—
329(C2×D79)⋊C4C2418yes—
330(C2×D79)⋊C4C2418yes—
331(C2×D79)⋊C4C2418yes—
332(C2×D79)⋊C4C24116yes—
333(C2×D79)⋊C4C2418yes—
334(C2×D79)⋊C4C2418yes—
335(C2×D79)⋊C4C2418yes—
336C4×Dic79C2418yes—
337C4×Dic79C2418yes—
338C4×Dic79C2418yes—
339C4×Dic79C2418yes—
340C24×C79C2414yes—
341C24×C79C2411yescharacteristic
342#41×C79—416no—
343#41×C79—416no—
344C2×Q8×C79—44no—
345C2×Q8×C79C2414yes—
346C2×Q8×C79C2414yes—
347C2×D4×C79—216no—
348C2×D4×C79—48no—
349C2×D4×C79—44no—
350C2×D4×C79C2418yes—
351C2×D4×C79C24116yes—
352C2×D4×C79C2418yes—
353C2×D4×C79C2414yes—
354C2×D4×C79C2414yes—
355C22×C4×C79—24no—
356C22×C4×C79—44no—
357C22×C4×C79—48no—
358C22×C4×C79C2412yes—
359C22×C4×C79C2414yes—
360C22×C4×C79C2412yes—
361C22×C4×C79C2412yes—
362C22×C4×C79C2411yescharacteristic
363C22×C4×C79C2411yescharacteristic
364C22×C4×C79C2412yes—
365C22×C4×C79C2412yes—
366C22×C4×C79C2412yes—
367C22×C4×C79C2412yes—
368C22×C4×C79C2412yes—
369C22×C4×C79C24116yes—
370C4⋊C4×C79C2418yes—
371C4⋊C4×C79C2418yes—
372C22⋊C4×C79C24116yes—
373C22⋊C4×C79C24116yes—
374C42×C79C2412yes—
375C42×C79C2412yes—
376C42×C79C2412yes—
377C42×C79C2412yes—
378C42×C79C2411yescharacteristic
379C42×C79C2412yes—
380C42×C79C2411yescharacteristic
381C42×C79C2412yes—
382C42×C79C2411yescharacteristic
383C42×C79C2411yescharacteristic
384C23×C79—28no—
385C23×C79—42no—
386C23×C79—48no—
387C23×C79H(5,𝔽2)14yes—
388C23×C79C2518yes—
389C23×C79C2511yescharacteristic
390C23×C79C2512yes—
391C22×D79—28no—
392C22×D79—44no—
393C22×D79—44no—
394C22×D79—48no—
395C22×D79—416no—
396C22×D79C2518yes—
397Q8×C79—44no—
398Q8×C79—44no—
399D4×C79—232no—
400D4×C79—216no—
401D4×C79—48no—
402D4×C79—44no—
403D4×C79—44no—
404C2×C4×C79—28no—
405C2×C4×C79—22no—
406C2×C4×C79—22no—
407C2×C4×C79—24no—
408C2×C4×C79—24no—
409C2×C4×C79—24no—
410C2×C4×C79—24no—
411C2×C4×C79—24no—
412C2×C4×C79—42no—
413C2×C4×C79—42no—
414C2×C4×C79—42no—
415C2×C4×C79—416no—
416C2×C4×C79C2512yes—
417C2×C4×C79C2518yes—
418C2×C4×C79C2512yes—
419C2×C4×C79C2512yes—
420C2×C4×C79C2511yescharacteristic
421C2×C4×C79C2511yescharacteristic
422C2×C4×C79C2512yes—
423C2×C4×C79C2512yes—
424C22⋊D79—216no—
425C22⋊D79—216no—
426C22⋊D79—416no—
427C22⋊D79—416no—
428C22⋊D79—416no—
429C2×Dic79—28no—
430C2×Dic79—44no—
431C2×Dic79—48no—
432C2×Dic79—44no—
433C2×Dic79—416no—
434C2×Dic79C2518yes—
435C2×Dic79C2518yes—
436C2×Dic79C2518yes—
437D316—28no—
438D316—48no—
439D316—44no—
440C4×D79—216no—
441C4×D79—48no—
442C4×D79—416no—
443Dic158—28no—
444Dic158—44no—
445Dic158—48no—
446C22×C79—22no—
447C22×C79—22no—
448C22×C79—22no—
449C22×C79—28no—
450C22×C79—216no—
451C22×C79—44no—
452C22×C79—88no—
453C22×C79C2×H(5,𝔽2)12yes—
454C22×C79C2×H(5,𝔽2)14yes—
455C22×C79C2611yescharacteristic
456C2×D79—28no—
457C2×D79—28no—
458C2×D79—28no—
459C2×D79—88no—
460C2×D79—168no—
461C4×C79—22no—
462C4×C79—21no—
463C4×C79—21no—
464C4×C79—28no—
465C4×C79—22no—
466C4×C79—22no—
467C4×C79—22no—
468C4×C79#58514yes—
469Dic79—28no—
470Dic79—28no—
471Dic79—28no—
472#62822—791nomaximal, Sylow
473C2×C79—24no—
474C2×C79—22no—
475C2×C79—48no—
476C2×C79C22×H(5,𝔽2)11yescharacteristic
477C2×C79C2×#58512yes—
478D79—48no—
479#3560—798no—
480#3559—794no—
481#3558—794no—
482#3545—794no—
483#3544—792no—
484#3543—792no—
485#3522—794no—
486#3519—794no—
487#3513—798no—
488#3505—794no—
489#3496—794no—
490#3494—798no—
491#3485—794no—
492C2×#532D7911yescharacteristic, complemented
493C2×#529—792no—
494C79#6282211yescharacteristic, complemented, Sylow
495C2×H(5,𝔽2)—794no—
496C22×#41C2×D7912yescomplemented
497#563—798no—
498#563—794no—
499#562—798no—
500H(3,𝔽4)—794no—
501#560—798no—
502#559—792no—
503#559—798no—
504Q82—792no—
505#555—792no—
506#555—798no—
507#554—794no—
508#554—798no—
509#553—7916no—
510#553—798no—
511#553—7916no—
512#553—798no—
513#552—798no—
514#551—798no—
515#551—7916no—
516#551—7916no—
517#550—794no—
518#548—798no—
519#547—7916no—
520#547—7916no—
521#547—798no—
522#547—798no—
523#546—7916no—
524#546—7916no—
525#546—798no—
526#546—7916no—
527#546—798no—
528#546—7916no—
529D42—798no—
530D42—792no—
531D42—798no—
532#544—798no—
533#542—798no—
534#542—7916no—
535#542—798no—
536#540—798no—
537#540—798no—
538#539—798no—
539#539—7916no—
540#538—7916no—
541#538—798no—
542#538—7916no—
543#537—798no—
544#536—798no—
545#535—798no—
546#534—798no—
547#534—798no—
548#534—798no—
549#532—798no—
550#532C2×D7914yescomplemented
551#532C2×D7914yescomplemented
552#532C2×D7914yescomplemented
553#532C2×D7914yescomplemented
554C2×C4⋊Q8C2×D7911yescharacteristic, complemented
555C2×#127C2×D7911yescharacteristic, complemented
556#529—798no—
557#529—794no—
558#529—794no—
559#529—794no—
560#529—794no—
561#529—794no—
562#529—794no—
563#529—794no—
564#529—794no—
565C2×#126—794no—
566C2×#125—792no—
567C2×#124—792no—
568C2×#124C2×D7912yescomplemented
569#525—798no—
570#525—798no—
571C2×#123—794no—
572C2×#123—798no—
573C2×C22⋊Q8—792no—
574C2×#121—792no—
575C2×#121—798no—
576C2×#121C2×D7914yescomplemented
577#520—798no—
578#518—794no—
579#518—798no—
580C2×C4×Q8—792no—
581C2×C4×D4—794no—
582C2×C4×D4—792no—
583C2×C4×D4C2×D7914yescomplemented
584C2×#117—794no—
585C22×C42C2×D7911yescharacteristic, complemented
586H(5,𝔽2)—31616no—
587C2×#41—48no—
588C2×#41—798no—
589C2×#41—7916no—
590C2×#41—798no—
591C2×#41C22×D7918yes—
592C2×#41C22×D7918yes—
593C22×Q8—792no—
594C22×Q8C22×D7912yes—
595C22×D4—798no—
596C22×D4—798no—
597C22×D4—7916no—
598C22×D4—794no—
599C22×D4—792no—
600C22×D4C22×D7914yes—
601C22×D4C22×D7914yes—
602C22×D4C22×D7912yes—
603C23×C4—794no—
604C23×C4C22×D7911yescharacteristic
605C23×C4C22×D7912yes—
606C23×C4C22×D7914yes—
607C4⋊Q8—798no—
608C4⋊Q8—798no—
609C4⋊Q8—798no—
610C4⋊Q8C22×D7914yes—
611C4⋊Q8C22×D7912yes—
612C4⋊Q8C22×D7912yes—
613#127—798no—
614#127C22×D7914yes—
615#127C22×D7912yes—
616#127C22×D7912yes—
617#126—7916no—
618#126—7916no—
619#126—7916no—
620#126—798no—
621#126—798no—
622#126—798no—
623#126—798no—
624#125—798no—
625#125—7916no—
626#125—794no—
627#125—794no—
628#125—794no—
629#125—794no—
630#124—798no—
631#124—798no—
632#124—798no—
633#124—7916no—
634#124—7916no—
635#124—794no—
636#124—794no—
637#124—794no—
638#124—794no—
639#124C22×D7918yes—
640#124C22×D7914yes—
641#124C22×D7914yes—
642#123—7916no—
643#123—798no—
644#123—798no—
645#123—7916no—
646#123—798no—
647#123—798no—
648#123—798no—
649#123—798no—
650#123—7916no—
651#123—7916no—
652#123—7916no—
653#123—7916no—
654#123—7916no—
655#123—7916no—
656#123—7916no—
657C22⋊Q8—7916no—
658C22⋊Q8—7916no—
659C22⋊Q8—794no—
660C22⋊Q8—794no—
661C22⋊Q8—794no—
662C22⋊Q8—794no—
663C22⋊Q8—7916no—
664C22⋊Q8—798no—
665C22⋊Q8—7916no—
666C22⋊Q8—7916no—
667C22⋊Q8—7916no—
668#121—7916no—
669#121—798no—
670#121—798no—
671#121—7916no—
672#121—7916no—
673#121—7916no—
674#121—7916no—
675#121—7916no—
676#121—794no—
677#121—794no—
678#121—794no—
679#121—794no—
680#121—7916no—
681#121—798no—
682#121—7916no—
683#121—7916no—
684#121C22×D7918yes—
685#121C22×D7918yes—
686#121C22×D7918yes—
687#121C22×D7918yes—
688#120—7916no—
689#120—7916no—
690#120—798no—
691#120—7916no—
692#120—798no—
693#120—7916no—
694C4×Q8—798no—
695C4×Q8—794no—
696C4×Q8—794no—
697C4×Q8—794no—
698C4×Q8—794no—
699C4×D4—7916no—
700C4×D4—7916no—
701C4×D4—798no—
702C4×D4—798no—
703C4×D4—798no—
704C4×D4—798no—
705C4×D4—798no—
706C4×D4—798no—
707C4×D4—7916no—
708C4×D4—7916no—
709C4×D4—798no—
710C4×D4—7916no—
711C4×D4—7916no—
712C4×D4—794no—
713C4×D4—794no—
714C4×D4—794no—
715C4×D4—794no—
716C4×D4C22×D7918yes—
717C4×D4C22×D7918yes—
718C4×D4C22×D7918yes—
719C4×D4C22×D7918yes—
720#117—798no—
721#117—798no—
722#117—7916no—
723#117—798no—
724#117—798no—
725#117—798no—
726#117—798no—
727C2×C4⋊C4—794no—
728C2×C4⋊C4—794no—
729C2×C4⋊C4—792no—
730C2×C4⋊C4—794no—
731C2×C4⋊C4—792no—
732C2×C4⋊C4—794no—
733C2×C4⋊C4—7916no—
734C2×C4⋊C4—798no—
735C2×C4⋊C4C22×D7914yes—
736C2×C22⋊C4—794no—
737C2×C22⋊C4—798no—
738C2×C22⋊C4—794no—
739C2×C22⋊C4—794no—
740C2×C22⋊C4—794no—
741C2×C22⋊C4—794no—
742C2×C22⋊C4—7916no—
743C2×C22⋊C4—7916no—
744C2×C22⋊C4C22×D7918yes—
745C2×C42—794no—
746C2×C42C22×D7912yes—
747C2×C42C22×D7912yes—
748C2×C42C22×D7912yes—
749C2×C42C22×D7912yes—
750C2×C42C22×D7911yescharacteristic
751C2×C42C22×D7912yes—
752C2×C42C22×D7911yescharacteristic
753C24—798no—
754C24—794no—
755C24C23×D7914yes—
756C24C23×D7911yescharacteristic
757#41—416no—
758#41—416no—
759#41—31616no—
760#41—31616no—
761#41—31632no—
762C2×Q8—44no—
763C2×Q8—3164no—
764C2×Q8—794no—
765C2×Q8—798no—
766C2×Q8—794no—
767C2×Q8C23×D7914yes—
768C2×Q8C23×D7914yes—
769C2×D4—216no—
770C2×D4—48no—
771C2×D4—44no—
772C2×D4—3164no—
773C2×D4—31632no—
774C2×D4—31616no—
775C2×D4—31616no—
776C2×D4—7916no—
777C2×D4—7916no—
778C2×D4—7916no—
779C2×D4—798no—
780C2×D4—798no—
781C2×D4—794no—
782C2×D4—798no—
783C2×D4—794no—
784C2×D4—15816no—
785C2×D4C23×D7918yes—
786C2×D4C23×D79116yes—
787C2×D4C23×D7918yes—
788C2×D4C23×D7914yes—
789C2×D4C23×D7914yes—
790C22×C4—24no—
791C22×C4—44no—
792C22×C4—48no—
793C22×C4—3168no—
794C22×C4—794no—
795C22×C4—794no—
796C22×C4—7916no—
797C22×C4—798no—
798C22×C4—798no—
799C22×C4—7916no—
800C22×C4—794no—
801C22×C4—798no—
802C22×C4C23×D7912yes—
803C22×C4C23×D7912yes—
804C22×C4C23×D7912yes—
805C22×C4C23×D7912yes—
806C22×C4C23×D7912yes—
807C22×C4C23×D7911yescharacteristic
808C22×C4C23×D7911yescharacteristic
809C22×C4C23×D7914yes—
810C22×C4C23×D7912yes—
811C22×C4C23×D7912yes—
812C22×C4C23×D7912yes—
813C22×C4C23×D79116yes—
814C4⋊C4—798no—
815C4⋊C4—798no—
816C4⋊C4—7916no—
817C4⋊C4—798no—
818C4⋊C4—798no—
819C4⋊C4—798no—
820C4⋊C4—798no—
821C4⋊C4—798no—
822C4⋊C4—7916no—
823C4⋊C4—798no—
824C4⋊C4—794no—
825C4⋊C4—794no—
826C4⋊C4—794no—
827C4⋊C4—794no—
828C4⋊C4—7916no—
829C4⋊C4C23×D7918yes—
830C4⋊C4C23×D7918yes—
831C22⋊C4—798no—
832C22⋊C4—798no—
833C22⋊C4—7916no—
834C22⋊C4—798no—
835C22⋊C4—798no—
836C22⋊C4—7916no—
837C22⋊C4—798no—
838C22⋊C4—798no—
839C22⋊C4—798no—
840C22⋊C4—7916no—
841C22⋊C4—798no—
842C22⋊C4—798no—
843C22⋊C4—798no—
844C22⋊C4—798no—
845C22⋊C4—7916no—
846C22⋊C4—798no—
847C22⋊C4C23×D79116yes—
848C22⋊C4C23×D79116yes—
849C42—798no—
850C42—798no—
851C42—798no—
852C42—798no—
853C42C23×D7911yescharacteristic
854C42C23×D7912yes—
855C42C23×D7912yes—
856C42C23×D7912yes—
857C42C23×D7911yescharacteristic
858C42C23×D7912yes—
859C42C23×D7912yes—
860C42C23×D7912yes—
861C42C23×D7911yescharacteristic
862C42C23×D7911yescharacteristic
863C23—28no—
864C23—42no—
865C23—48no—
866C23—3164no—
867C23—3164no—
868C23—3168no—
869C23—31616no—
870C23—798no—
871C23—1588no—
872C23#1457920614yes—
873C23C24×D7918yes—
874C23C24×D7911yescharacteristic
875C23C24×D7912yes—
876Q8—44no—
877Q8—44no—
878Q8—3164no—
879Q8—3168no—
880Q8—1588no—
881D4—232no—
882D4—216no—
883D4—48no—
884D4—44no—
885D4—44no—
886D4—3168no—
887D4—3164no—
888D4—31616no—
889D4—31616no—
890D4—31616no—
891D4—15816no—
892D4—15816no—
893D4—1588no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—24no—
897C2×C4—24no—
898C2×C4—28no—
899C2×C4—24no—
900C2×C4—24no—
901C2×C4—24no—
902C2×C4—42no—
903C2×C4—42no—
904C2×C4—42no—
905C2×C4—416no—
906C2×C4—3168no—
907C2×C4—31616no—
908C2×C4—3164no—
909C2×C4—3168no—
910C2×C4—3164no—
911C2×C4—31616no—
912C2×C4—798no—
913C2×C4—798no—
914C2×C4—798no—
915C2×C4—1588no—
916C2×C4—15816no—
917C2×C4C24×D7912yes—
918C2×C4C24×D7918yes—
919C2×C4C24×D7912yes—
920C2×C4C24×D7912yes—
921C2×C4C24×D7911yescharacteristic
922C2×C4C24×D7911yescharacteristic
923C2×C4C24×D7912yes—
924C2×C4C24×D7912yes—
925C22—22no—
926C22—22no—
927C22—22no—
928C22—28no—
929C22—216no—
930C22—44no—
931C22—88no—
932C22—6328no—
933C22—1588no—
934C22—1588no—
935C22—1588no—
936C22—12648no—
937C22C2×#1457920612yes—
938C22C2×#1457920614yes—
939C22C25×D7911yescharacteristic
940C4—22no—
941C4—21no—
942C4—21no—
943C4—28no—
944C4—22no—
945C4—22no—
946C4—22no—
947C4—1588no—
948C4—1588no—
949C4—1588no—
950C4#1909939914yes—
951C2—22no—
952C2—24no—
953C2—48no—
954C2—3168no—
955C2C22×#1457920611yescharacteristic
956C2C2×#1909939912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC2×#532×C79C2
hypercenterC2×#532D79
hypocenterC79#62822
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C2×#532

Complements

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

NH ≅ G/Ntype
1. #23777956C2semidirect
2. #23777938C2semidirect
3. #23777923C2semidirect
4. #23777757C2semidirect
5. #23777744C2semidirect
6. #23777733C2semidirect
7. #23777477C2semidirect
8. #23777427C2semidirect
9. #23777340C2semidirect
10. #23777234C2semidirect
11. #23777157C2semidirect
12. #23777130C2semidirect
13. #23777044C2semidirect
14. C2×#19099097C2semidirect
15. C2×#532×C79C2semidirect
16. C2×#14579206C22semidirect
17. #19099313C22semidirect
18. #19099312C22semidirect
19. #19099307C22semidirect
20. #19099305C22semidirect
21. #19099300C22semidirect
22. #19099299C22semidirect
23. #19099296C22semidirect
24. #19099293C22semidirect
25. #19099279C22semidirect
26. #19099275C22semidirect
27. #19099274C22semidirect
28. #19099272C22semidirect
29. #19099265C22semidirect
30. #19099263C22semidirect
31. #19099262C22semidirect
32. #19099256C22semidirect
33. #19099248C22semidirect
34. #19099243C22semidirect
35. #19099242C22semidirect
36. #19099239C22semidirect
37. #19099233C22semidirect
38. #19099219C22semidirect
39. #19099214C22semidirect
40. #19099213C22semidirect
41. #19099212C22semidirect
42. #19099212C22semidirect
43. #19099208C22semidirect
44. #19099207C22semidirect
45. #19099203C22semidirect
46. #19099202C22semidirect
47. #19099201C22semidirect
48. #19099201C22semidirect
49. #19099198C22semidirect
50. #19099197C22semidirect
51. D4×C22⋊D79C22semidirect
52. #19099190C22semidirect
53. #19099187C22semidirect
54. #19099178C22semidirect
55. #19099177C22semidirect
56. #19099167C22semidirect
57. #19099164C22semidirect
58. #19099158C22semidirect
59. #19099155C22semidirect
60. #19099150C22semidirect
61. #19099147C22semidirect
62. #19099146C22semidirect
63. #19099140C22semidirect
64. #19099137C22semidirect
65. #19099126C22semidirect
66. #19099122C22semidirect
67. #19099122C22semidirect
68. #19099121C22semidirect
69. #19099108C22semidirect
70. #19099097C22semidirect
71. #19099097C22semidirect
72. #19099097C22semidirect
73. #19099097C22semidirect
74. #19099097C22semidirect
75. #19099097C22semidirect
76. #19099097C22semidirect
77. #19099097C22semidirect
78. #19099094C22semidirect
79. C2×#14579155C22semidirect
80. C2×#14579153C22semidirect
81. C2×#14579149C22semidirect
82. #19099074C22semidirect
83. #19099073C22semidirect
84. C2×#14579144C22semidirect
85. C2×#14579144C22semidirect
86. C2×#14579140C22semidirect
88. #121×D79C22semidirect
89. #19099042C22semidirect
90. #19099038C22semidirect
91. #19099035C22semidirect
92. C2×C4×Dic158C22semidirect
93. C2×C4×D316C22semidirect
94. C2×C4×C22⋊D79C22semidirect
95. C2×#14579118C22semidirect
96. C22×#41×C79C22semidirect
97. #532×C79C22semidirect
98. #532×C79C22semidirect
99. #532×C79C22semidirect
100. #532×C79C22semidirect
101. C2×C4⋊Q8×C79C22semidirect
102. C2×#127×C79C22semidirect
103. C2×#124×C79C22semidirect
104. C2×#121×C79C22semidirect
105. C2×C4×D4×C79C22semidirect
106. C22×C42×C79C22semidirect
492. C2×#532D79semidirect
494. C79#62822semidirect
496. C22×#41C2×D79semidirect
550. #532C2×D79semidirect
551. #532C2×D79semidirect
552. #532C2×D79semidirect
553. #532C2×D79semidirect
554. C2×C4⋊Q8C2×D79semidirect
555. C2×#127C2×D79semidirect
568. C2×#124C2×D79semidirect
576. C2×#121C2×D79semidirect
583. C2×C4×D4C2×D79semidirect
585. C22×C42C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237779562
#237779382
#237779232
#237777572
#237777442
#237777332
#237774772
#237774272
#237773402
#237772342
#237771572
#237771302
#237770442
C2×#190990972
C2×#532×C792
#6282279