Finite Group Databasebeta

← #35196428

Subgroups — #35196428

Order 20224.

7230 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777468C218yesmaximal, complemented
2#23777378C214yesmaximal, complemented
3#23777361C214yesmaximal, complemented
4#23777265C212yesmaximal, complemented
5#23777239C214yesmaximal, complemented
6#23777203C211yesmaximal, characteristic, complemented
7#23777164C211yesmaximal, characteristic, complemented
8#23777120C212yesmaximal, complemented
9#23777098C214yesmaximal, complemented
10#23777044C212yesmaximal, complemented
11#23777015C214yesmaximal, complemented
12#23777010C214yesmaximal, complemented
13#23776962C218yesmaximal, complemented
14#23776833C212yesmaximal, complemented
15#23776809C214yesmaximal, complemented
16#23776696C212yesmaximal, complemented
17C2×#19099097C214yesmaximal, complemented
18C4×#14579206C212yesmaximal, complemented
19C2×C4×#41×C79C211yesmaximal, characteristic, complemented
20C2×#14579206C2212yes—
21#19099298C2214yescomplemented
22#19099291C2214yescomplemented
23#19099286C2214yescomplemented
24#19099285C2218yescomplemented
25#19099281C2218yescomplemented
26#19099276C2218yescomplemented
27#19099273C2214yescomplemented
28#19099272C2218yescomplemented
29#19099270C2214yescomplemented
30#19099262C22116yescomplemented
31#19099259C2218yescomplemented
32#19099257C2218yescomplemented
33#19099254C2218yescomplemented
34#19099253C2218yescomplemented
35#19099252C2218yescomplemented
36#19099246C22116yescomplemented
37#19099246C22116yescomplemented
38#19099242C22116yescomplemented
39#19099237C22116yescomplemented
40#19099237C22116yescomplemented
41D4×Dic158C2214yescomplemented
42#19099222C2218yescomplemented
43#19099217C2214yescomplemented
44#19099212C2218yescomplemented
45#19099212C2218yescomplemented
46#19099209C2218yescomplemented
47#19099208C2218yescomplemented
48#19099201C2218yescomplemented
49#19099201C2218yescomplemented
50D4×D316C2214yescomplemented
51#19099194C2212yescomplemented
52#19099189C2214yescomplemented
53#19099185C2218yescomplemented
54#19099171C2218yescomplemented
55#19099160C2218yescomplemented
56#19099160C2218yescomplemented
57#19099155C22116yescomplemented
58#19099151C2218yescomplemented
59#19099146C22116yescomplemented
60#19099144C2212yes—
61#19099137C2214yescomplemented
62#19099125C2214yes—
63#19099122C2218yescomplemented
64#19099120C2212yescomplemented
65#19099120C2212yescomplemented
66#19099120C2212yescomplemented
67#19099117C2218yescomplemented
68#19099113C2212yes—
69#19099113C2212yescomplemented
70#19099113C2212yescomplemented
71#19099100C2218yescomplemented
72#19099097C2218yescomplemented
73#19099097C2214yescomplemented
74#19099097C2218yescomplemented
75#19099097C2218yescomplemented
76#19099097C2214yescomplemented
77#19099097C2214yescomplemented
78#19099097C2218yescomplemented
79#19099097C2218yescomplemented
80#19099097C2218yescomplemented
81#19099097C2218yescomplemented
82#19099097C2214yescomplemented
83#19099097C2214yescomplemented
84#19099097C2214yescomplemented
85#19099093C22116yescomplemented
86C2×#14579155C2218yescomplemented
87C2×#14579153C2214yescomplemented
88C2×#14579149C2214yescomplemented
89#19099074C2214yescomplemented
90#19099074C2214yescomplemented
91#19099074C2214yescomplemented
92#19099072C22116yescomplemented
93C2×#14579144C2218yescomplemented
94C2×#14579140C2214yescomplemented
95C2×#14579135C2214yes—
96#19099044C2214yescomplemented
97#19099042C2218yescomplemented
98#19099038C2212yes—
99#19099036C2218yescomplemented
100#19099035C2218yescomplemented
101C4×#11929624C2214yescomplemented
102C4×#11929624C2214yescomplemented
103C4×#11929624C2214yescomplemented
104C4×#11929623C2218yescomplemented
105C2×C4×Dic158C2214yescomplemented
106C2×C4×D316C2214yescomplemented
107C2×C4×C22⋊D79C2218yescomplemented
108C4×D4×D79C2218yescomplemented
109C2×#14579118C2218yescomplemented
110C22×#41×C79C2211yescharacteristic
111C4×#41×C79C2214yescomplemented
112C4×#41×C79C2214yescomplemented
113C4×#41×C79C2214yescomplemented
114C4×#41×C79C2214yescomplemented
115C2×C4×Q8×C79C2211yescharacteristic, complemented
116C2×C4×Q8×C79C2211yescharacteristic, complemented
117C2×C4×D4×C79C2211yescharacteristic
118C2×C4×D4×C79C2211yescharacteristic
119C2×C4×D4×C79C2212yescomplemented
120C2×C4×D4×C79C2212yescomplemented
121C2×#117×C79C2212yescomplemented
122C2×#117×C79C2211yescharacteristic, complemented
123C22×C42×C79C2212yescomplemented
124C22×C42×C79C2211yescharacteristic, complemented
125#14579206—216no—
126C2×#11929624C2314yes—
127C2×#11929624C2314yes—
128C2×#11929624C2314yes—
129C2×#11929623C2318yes—
130C22×Dic158C2314yes—
131C22×D316C2314yes—
132C22×C22⋊D79C2318yes—
133C2×D4×D79C2318yes—
134C22×C4×D79C2318yes—
135#14579161C2312yes—
136#14579161C2312yes—
137#14579161C2312yes—
138#14579160C2318yes—
139#14579159C2318yes—
140#14579158C2312yes—
141#14579156C23116yes—
142#14579156C23116yes—
143#14579155C23116yes—
144#14579155C2318yes—
145#14579155C23116yes—
146#14579155C23116yes—
147#14579155C2318yes—
148#14579154C23116yes—
149#14579153C2318yes—
150#14579153C2314yes—
151#14579153C2318yes—
152#14579153C2318yes—
153#14579153C2314yes—
154#14579153C2314yes—
155#14579152C2318yes—
156#14579151C23116yes—
157#14579151C23116yes—
158#14579150C2318yes—
159#14579149C2318yes—
160#14579149C2314yes—
161#14579149C2318yes—
162#14579149C2314yes—
163#14579149C2318yes—
164#14579149C2314yes—
165#14579147C23116yes—
166#14579146C23116yes—
167#14579146C23116yes—
168#14579145C23116yes—
169#14579144C23116yes—
170#14579144C2318yes—
171#14579144C23116yes—
172#14579144C23116yes—
173#14579144C2318yes—
174#14579144C2318yes—
175#14579143C23116yes—
176#14579142C23116yes—
177#14579141C2318yes—
178#14579140C2318yes—
179#14579140C2314yes—
180#14579140C2314yes—
181#14579140C2318yes—
182#14579140C2314yes—
183#14579140C2314yes—
184#14579140C2314yes—
185#14579140C2318yes—
186#14579140C2314yes—
187#14579139C23116yes—
188#14579139C23116yes—
189#14579138C23116yes—
190#14579138C23116yes—
191#14579137C2318yes—
192#14579137C2318yes—
193#14579136C2318yes—
194#14579135C2318yes—
195#14579135C2314yes—
196#14579135C2314yes—
197#14579135C2318yes—
198#14579135C2314yes—
199#14579135C2314yes—
200#14579135C2318yes—
201#14579135C2314yes—
202#14579135C2314yes—
203#14579134C23116yes—
204#14579133C23116yes—
205#14579133C23116yes—
206#14579131C23116yes—
207#14579130C2318yes—
208#14579129C23116yes—
209C4×Dic158C2314yes—
210C4×Dic158C2318yes—
211C4×Dic158C2314yes—
212C4×Dic158C2314yes—
213C4×Dic158C2318yes—
214C4×Dic158C2314yes—
215C4×Dic158C2314yes—
216C4×Dic158C2318yes—
217C4×Dic158C2314yes—
218#14579126C2318yes—
219C4×D316C2314yes—
220C4×D316C2314yes—
221C4×D316C2314yes—
222C4×D316C2318yes—
223C4×D316C2314yes—
224C4×D316C2318yes—
225C4×D316C2314yes—
226C4×D316C2314yes—
227C4×D316C2318yes—
228D4×Dic79C2318yes—
229D4×Dic79C2318yes—
230#14579123C2318yes—
231C4×C22⋊D79C23116yes—
232C4×C22⋊D79C23116yes—
233C4×C22⋊D79C2318yes—
234C4×C22⋊D79C2318yes—
235C4×C22⋊D79C2318yes—
236C4×C22⋊D79C2318yes—
237C4×C22⋊D79C23116yes—
238C4×C22⋊D79C2318yes—
239C4×C22⋊D79C2318yes—
240(C22⋊D79)⋊C4C23116yes—
241(C22⋊D79)⋊C4C23116yes—
242#14579120C2314yes—
243#14579120C2314yes—
244#14579120C2314yes—
245#14579119C2318yes—
246#14579118C2318yes—
247#14579118C2318yes—
248#14579118C23116yes—
249#14579118C23116yes—
250#14579118C2318yes—
251#14579118C23116yes—
252#14579117C23116yes—
253C2×C4⋊Dic79C2314yes—
254C2×C4⋊Dic79C2314yes—
255C2×Dic79⋊C4C2318yes—
256C2×Dic79⋊C4C2318yes—
257C2×Dic79⋊C4C2318yes—
258C2×Dic79⋊C4C2318yes—
259C4⋊C4×D79C2318yes—
260C2×C22⋊Dic79C2318yes—
261C2×(C2×D79)⋊C4C2318yes—
262C2×(C2×D79)⋊C4C2318yes—
263C2×(C2×D79)⋊C4C2318yes—
264C2×(C2×D79)⋊C4C2318yes—
265C22⋊C4×D79C23116yes—
266C2×C4×Dic79C2318yes—
267C42×D79C2318yes—
268C2×#41×C79—28no—
269C2×#41×C79C2314yes—
270C2×#41×C79C2314yes—
271C22×Q8×C79C2311yescharacteristic
272C22×D4×C79C2312yes—
273C22×D4×C79C2311yescharacteristic
274C23×C4×C79C2312yes—
275C23×C4×C79C2311yescharacteristic
276C23×C4×C79C2312yes—
277C23×C4×C79C2312yes—
278C23×C4×C79C2311yescharacteristic
279C23×C4×C79C2311yescharacteristic
280C4×Q8×C79C2314yes—
281C4×Q8×C79C2314yes—
282C4×Q8×C79C2314yes—
283C4×Q8×C79C2314yes—
284C4×D4×C79C2318yes—
285C4×D4×C79C2314yes—
286C4×D4×C79C2314yes—
287C4×D4×C79C2318yes—
288C4×D4×C79C2314yes—
289C4×D4×C79C2314yes—
290C4×D4×C79C2318yes—
291C4×D4×C79C2318yes—
292#117×C79C2318yes—
293#117×C79C2318yes—
294#117×C79C2314yes—
295#117×C79C2314yes—
296C2×C4⋊C4×C79C2311yescharacteristic
297C2×C4⋊C4×C79C2312yes—
298C2×C4⋊C4×C79C2312yes—
299C2×C4⋊C4×C79C2311yescharacteristic
300C2×C22⋊C4×C79C2312yes—
301C2×C22⋊C4×C79C2312yes—
302C2×C22⋊C4×C79C2312yes—
303C2×C42×C79C2311yescharacteristic
304C2×C42×C79C2312yes—
305C2×C42×C79C2311yescharacteristic
306C2×C42×C79C2311yescharacteristic
307C2×C42×C79C2311yescharacteristic
308C2×C42×C79C2312yes—
309C2×C42×C79C2312yes—
310C2×C42×C79C2314yes—
311C2×C42×C79C2314yes—
312C2×C42×C79C2312yes—
313C2×C42×C79C2312yes—
314C2×C42×C79C2314yes—
315C2×C42×C79C2314yes—
316C2×C42×C79C2312yes—
317C2×C42×C79C2312yes—
318C23×D79C2418yes—
319#11929624—216no—
320#11929624—48no—
321#11929624—48no—
322#11929623—232no—
323C2×Dic158—48no—
324C2×Dic158C2414yes—
325C2×Dic158C2414yes—
326C2×Dic158C2418yes—
327C2×Dic158C2414yes—
328C2×D316—48no—
329C2×D316C2414yes—
330C2×D316C2414yes—
331C2×D316C2414yes—
332C2×D316C2418yes—
333C2×C22⋊D79—232no—
334C2×C22⋊D79C24116yes—
335C2×C22⋊D79C2418yes—
336C2×C22⋊D79C2418yes—
337C2×C22⋊D79C2418yes—
338D4×D79—232no—
339C22×Dic79C2418yes—
340C22×Dic79C2418yes—
341C22×Dic79C2418yes—
342C2×C4×D79—416no—
343C2×C4×D79C2418yes—
344C2×C4×D79C2418yes—
345C2×C4×D79C2418yes—
346C2×C4×D79C24116yes—
347C4⋊Dic79C2414yes—
348C4⋊Dic79C2414yes—
349C4⋊Dic79C2414yes—
350C4⋊Dic79C2418yes—
351C4⋊Dic79C2418yes—
352C4⋊Dic79C2414yes—
353C4⋊Dic79C2414yes—
354C4⋊Dic79C2414yes—
355Dic79⋊C4C24116yes—
356Dic79⋊C4C2418yes—
357Dic79⋊C4C2418yes—
358Dic79⋊C4C2418yes—
359Dic79⋊C4C2418yes—
360Dic79⋊C4C24116yes—
361Dic79⋊C4C24116yes—
362Dic79⋊C4C24116yes—
363Dic79⋊C4C2418yes—
364Dic79⋊C4C2418yes—
365C22⋊Dic79C24116yes—
366C22⋊Dic79C2418yes—
367C22⋊Dic79C2418yes—
368C22⋊Dic79C2418yes—
369(C2×D79)⋊C4C2418yes—
370(C2×D79)⋊C4C24116yes—
371(C2×D79)⋊C4C2418yes—
372(C2×D79)⋊C4C2418yes—
373(C2×D79)⋊C4C2418yes—
374(C2×D79)⋊C4C2418yes—
375(C2×D79)⋊C4C24116yes—
376(C2×D79)⋊C4C24116yes—
377(C2×D79)⋊C4C24116yes—
378(C2×D79)⋊C4C2418yes—
379C4×Dic79C2418yes—
380C4×Dic79C2418yes—
381C4×Dic79C2418yes—
382C4×Dic79C24116yes—
383C24×C79C2411yescharacteristic
384C24×C79C2412yes—
385#41×C79—216no—
386#41×C79—216no—
387C2×Q8×C79—24no—
388C2×Q8×C79C2414yes—
389C2×D4×C79—28no—
390C2×D4×C79#4118yescomplemented
391C2×D4×C79C2418yes—
392C2×D4×C79C2414yes—
393C22×C4×C79—28no—
394C22×C4×C79—24no—
395C22×C4×C79—44no—
396C22×C4×C79—44no—
397C22×C4×C79—42no—
398C22×C4×C79—42no—
399C22×C4×C79C2414yes—
400C22×C4×C79C2412yes—
401C22×C4×C79C2412yes—
402C22×C4×C79C2411yescharacteristic
403C22×C4×C79C2411yescharacteristic
404C22×C4×C79C2411yescharacteristic
405C22×C4×C79C2412yes—
406C22×C4×C79C2414yes—
407C22×C4×C79C2414yes—
408C22×C4×C79C2412yes—
409C22×C4×C79C2412yes—
410C22×C4×C79C2414yes—
411C22×C4×C79C2411yescharacteristic
412C22×C4×C79C2412yes—
413C22×C4×C79C2411yescharacteristic
414C22×C4×C79C2412yes—
415C22×C4×C79C2414yes—
416C22×C4×C79C2414yes—
417C22×C4×C79C2412yes—
418C22×C4×C79C2412yes—
419C22×C4×C79C2411yescharacteristic
420C4⋊C4×C79C2414yes—
421C4⋊C4×C79C2414yes—
422C4⋊C4×C79C2418yes—
423C4⋊C4×C79C2418yes—
424C22⋊C4×C79C2418yes—
425C22⋊C4×C79C2418yes—
426C22⋊C4×C79C2418yes—
427C42×C79C2411yescharacteristic
428C42×C79C2411yescharacteristic
429C42×C79C2411yescharacteristic
430C42×C79C2411yescharacteristic
431C42×C79C2414yes—
432C42×C79C2412yes—
433C42×C79C2414yes—
434C42×C79C2412yes—
435C42×C79C2412yes—
436C42×C79C2412yes—
437C42×C79C2414yes—
438C42×C79C2414yes—
439C42×C79C2414yes—
440C42×C79C2412yes—
441C42×C79C2412yes—
442C42×C79C2414yes—
443C23×C79—22no—
444C23×C79—42no—
445C23×C79—42no—
446C23×C79—41no—
447C23×C79—41no—
448C23×C79C2×#4118yes—
449C23×C79C2512yes—
450C23×C79C2511yescharacteristic
451C23×C79C2514yes—
452C22×D79—216no—
453C22×D79—48no—
454C22×D79—48no—
455C22×D79C2518yes—
456Q8×C79—28no—
457D4×C79—216no—
458D4×C79C2×#41116yes—
459C2×C4×C79—22no—
460C2×C4×C79—24no—
461C2×C4×C79—28no—
462C2×C4×C79—28no—
463C2×C4×C79—24no—
464C2×C4×C79—24no—
465C2×C4×C79—28no—
466C2×C4×C79—28no—
467C2×C4×C79—24no—
468C2×C4×C79—24no—
469C2×C4×C79—22no—
470C2×C4×C79—22no—
471C2×C4×C79—44no—
472C2×C4×C79—42no—
473C2×C4×C79—44no—
474C2×C4×C79—42no—
475C2×C4×C79—42no—
476C2×C4×C79—41no—
477C2×C4×C79—42no—
478C2×C4×C79—41no—
479C2×C4×C79C2×#4114yes—
480C2×C4×C79C2512yes—
481C2×C4×C79C2514yes—
482C2×C4×C79C2511yescharacteristic
483C2×C4×C79C2511yescharacteristic
484C2×C4×C79C2511yescharacteristic
485C2×C4×C79C2511yescharacteristic
486C2×C4×C79C2514yes—
487C2×C4×C79C2514yes—
488C2×C4×C79C2512yes—
489C2×C4×C79C2512yes—
490C2×C4×C79C2511yescharacteristic
491C2×C4×C79C2511yescharacteristic
492C22⋊D79—232no—
493C22⋊D79—216no—
494C22⋊D79—48no—
495C22⋊D79—48no—
496C2×Dic79—216no—
497C2×Dic79—48no—
498C2×Dic79—48no—
499C2×Dic79C2518yes—
500C2×Dic79C2518yes—
501C2×Dic79C2518yes—
502D316—28no—
503D316—28no—
504D316—48no—
505D316—44no—
506C4×D79—216no—
507C4×D79—216no—
508C4×D79—416no—
509C4×D79—48no—
510Dic158—28no—
511Dic158—28no—
512Dic158—48no—
513Dic158—44no—
514C22×C79—21no—
515C22×C79—21no—
516C22×C79—24no—
517C22×C79—24no—
518C22×C79—22no—
519C22×C79—22no—
520C22×C79—22no—
521C22×C79—48no—
522C22×C79—44no—
523C22×C79C22×#4112yes—
524C22×C79C22×#4118yes—
525C22×C79C2611yescharacteristic
526C2×D79—28no—
527C2×D79—28no—
528C2×D79—28no—
529C2×D79—816no—
530C4×C79—21no—
531C4×C79—21no—
532C4×C79—24no—
533C4×C79—21no—
534C4×C79—21no—
535C4×C79—24no—
536C4×C79—22no—
537C4×C79—24no—
538C4×C79—22no—
539C4×C79C22×#4114yes—
540C4×C79#58512yes—
541C4×C79#58512yes—
542Dic79—28no—
543Dic79—28no—
544Dic79—28no—
545#62781—791nomaximal, Sylow
546C2×C79—28no—
547C2×C79—22no—
548C2×C79—42no—
549C2×C79C23×#4111yescharacteristic
550C2×C79C2×#58511yescharacteristic
551C2×C79C2×#58511yescharacteristic
552D79—48no—
553#3521—798no—
554#3515—794no—
555#3514—794no—
556#3507—792no—
557#3505—794no—
558#3501—791no—
559#3496—791no—
560#3493—792no—
561#3491—794no—
562#3485—792no—
563#3482—794no—
564#3481—794no—
565#3475—798no—
566#3461—792no—
567#3459—794no—
568#3444—792no—
569C2×#529—794no—
570C4×H(5,𝔽2)—792no—
571C2×C4×#41D7911yescharacteristic, complemented
572C79#6278111yescharacteristic, complemented, Sylow
573C2×H(5,𝔽2)—792no—
574C22×#41C2×D7911yescharacteristic
575#559—794no—
576#557—794no—
577#556—798no—
578#556—794no—
579#556—798no—
580#555—798no—
581#554—794no—
582#554—794no—
583#554—798no—
584#553—798no—
585#553—7916no—
586#553—798no—
587#552—798no—
588#552—798no—
589#552—7916no—
590#552—7916no—
591#552—798no—
592#551—7916no—
593#551—7916no—
594#551—7916no—
595D4×Q8—794no—
596#548—798no—
597#547—798no—
598#547—798no—
599#547—794no—
600#546—798no—
601#546—798no—
602#546—798no—
603#546—798no—
604D42—794no—
605#544—792no—
606#543—794no—
607#542—798no—
608#541—798no—
609#539—7916no—
610#539—798no—
611#539—798no—
612#538—7916no—
613#538—798no—
614#537—792no—
615#536—794no—
616#534—798no—
617#534—794no—
618#533—798no—
619#533—792no—
620#533—792no—
621#533—792no—
622#532—792no—
623#532—792no—
624#532—792no—
625#529—798no—
626#529—7916no—
627#529—794no—
628#529—798no—
629#529—798no—
630#529—798no—
631#529—798no—
632#529—798no—
633#529—798no—
634#529—798no—
635#529—794no—
636#529—794no—
637#529—794no—
638#529—794no—
639#529—794no—
640C2×#126—798no—
641C2×#125—794no—
642C2×#124—794no—
643#525—794no—
644#525—794no—
645#525—794no—
646#525—7916no—
647C2×#123—798no—
648C2×C22⋊Q8—794no—
649C2×#121—794no—
650#520—798no—
651#520—794no—
652#518—792no—
653#518—798no—
654#518—798no—
655C4×#41—798no—
656C4×#41—794no—
657C4×#41—794no—
658C4×#41—794no—
659C4×#41C2×D7914yescomplemented
660C4×#41C2×D7914yescomplemented
661C4×#41C2×D7914yescomplemented
662C4×#41C2×D7914yescomplemented
663C2×C4×Q8—794no—
664C2×C4×Q8C2×D7911yescharacteristic, complemented
665C2×C4×Q8C2×D7911yescharacteristic, complemented
666C2×C4×D4—798no—
667C2×C4×D4—798no—
668C2×C4×D4—794no—
669C2×C4×D4C2×D7911yescharacteristic
670C2×C4×D4C2×D7911yescharacteristic
671C2×C4×D4C2×D7912yescomplemented
672C2×C4×D4C2×D7912yescomplemented
673C2×#117—798no—
674C2×#117C2×D7912yescomplemented
675C2×#117C2×D7911yescharacteristic, complemented
676C22×C42C2×D7912yescomplemented
677C22×C42C2×D7911yescharacteristic, complemented
678H(5,𝔽2)—15816no—
679C2×#41—28no—
680C2×#41—798no—
681C2×#41—794no—
682C2×#41—794no—
683C2×#41—794no—
684C2×#41C22×D7914yes—
685C2×#41C22×D7914yes—
686C22×Q8—794no—
687C22×Q8C22×D7911yescharacteristic
688C22×D4—798no—
689C22×D4—798no—
690C22×D4—794no—
691C22×D4C22×D7912yes—
692C22×D4C22×D7911yescharacteristic
693C23×C4—798no—
694C23×C4C22×D7912yes—
695C23×C4C22×D7911yescharacteristic
696C23×C4C22×D7912yes—
697C23×C4C22×D7912yes—
698C23×C4C22×D7911yescharacteristic
699C23×C4C22×D7911yescharacteristic
700C4⋊Q8—798no—
701C4⋊Q8—798no—
702C4⋊Q8—792no—
703C4⋊Q8—792no—
704C4⋊Q8—792no—
705#127—792no—
706#126—7916no—
707#126—7916no—
708#126—7916no—
709#126—798no—
710#126—7916no—
711#126—7916no—
712#126—7916no—
713#126—798no—
714#125—7916no—
715#125—798no—
716#125—7916no—
717#125—794no—
718#125—798no—
719#125—798no—
720#125—798no—
721#125—794no—
722#125—794no—
723#124—798no—
724#124—7916no—
725#124—794no—
726#124—798no—
727#124—798no—
728#124—798no—
729#124—794no—
730#124—794no—
731#123—7916no—
732#123—798no—
733#123—7916no—
734#123—7916no—
735#123—7916no—
736#123—798no—
737#123—798no—
738#123—7916no—
739#123—7916no—
740#123—7916no—
741#123—7916no—
742C22⋊Q8—798no—
743C22⋊Q8—798no—
744C22⋊Q8—794no—
745C22⋊Q8—798no—
746C22⋊Q8—798no—
747C22⋊Q8—798no—
748C22⋊Q8—794no—
749C22⋊Q8—794no—
750C22⋊Q8—794no—
751C22⋊Q8—794no—
752C22⋊Q8—794no—
753C22⋊Q8—7916no—
754C22⋊Q8—798no—
755C22⋊Q8—7916no—
756C22⋊Q8—7916no—
757C22⋊Q8—7916no—
758#121—7916no—
759#121—7916no—
760#121—794no—
761#121—798no—
762#121—798no—
763#121—798no—
764#121—794no—
765#121—794no—
766#121—794no—
767#121—794no—
768#121—794no—
769#121—798no—
770#121—7916no—
771#120—798no—
772#120—7916no—
773#120—7916no—
774C4×Q8—798no—
775C4×Q8—794no—
776C4×Q8—798no—
777C4×Q8—798no—
778C4×Q8—798no—
779C4×Q8—794no—
780C4×Q8—794no—
781C4×Q8—794no—
782C4×Q8—794no—
783C4×Q8—794no—
784C4×Q8C22×D7914yes—
785C4×Q8C22×D7914yes—
786C4×Q8C22×D7914yes—
787C4×Q8C22×D7914yes—
788C4×D4—798no—
789C4×D4—798no—
790C4×D4—7916no—
791C4×D4—798no—
792C4×D4—7916no—
793C4×D4—7916no—
794C4×D4—798no—
795C4×D4—798no—
796C4×D4—798no—
797C4×D4—798no—
798C4×D4—798no—
799C4×D4—798no—
800C4×D4—7916no—
801C4×D4—7916no—
802C4×D4—794no—
803C4×D4—794no—
804C4×D4—798no—
805C4×D4—798no—
806C4×D4—798no—
807C4×D4—794no—
808C4×D4—794no—
809C4×D4—794no—
810C4×D4—794no—
811C4×D4C22×D7914yes—
812C4×D4C22×D7914yes—
813C4×D4C22×D7914yes—
814C4×D4C22×D7914yes—
815C4×D4C22×D7918yes—
816C4×D4C22×D7918yes—
817C4×D4C22×D7918yes—
818C4×D4C22×D7918yes—
819#117—794no—
820#117—794no—
821#117—794no—
822#117—798no—
823#117—7916no—
824#117—798no—
825#117—7916no—
826#117—7916no—
827#117—7916no—
828#117—798no—
829#117—798no—
830#117C22×D7918yes—
831#117C22×D7918yes—
832#117C22×D7914yes—
833#117C22×D7914yes—
834C2×C4⋊C4—798no—
835C2×C4⋊C4—798no—
836C2×C4⋊C4—798no—
837C2×C4⋊C4—794no—
838C2×C4⋊C4—794no—
839C2×C4⋊C4—798no—
840C2×C4⋊C4—798no—
841C2×C4⋊C4C22×D7911yescharacteristic
842C2×C4⋊C4C22×D7911yescharacteristic
843C2×C4⋊C4C22×D7912yes—
844C2×C4⋊C4C22×D7912yes—
845C2×C22⋊C4—798no—
846C2×C22⋊C4—798no—
847C2×C22⋊C4—798no—
848C2×C22⋊C4—798no—
849C2×C22⋊C4—798no—
850C2×C22⋊C4—7916no—
851C2×C22⋊C4C22×D7912yes—
852C2×C22⋊C4C22×D7912yes—
853C2×C22⋊C4C22×D7912yes—
854C2×C42—798no—
855C2×C42—798no—
856C2×C42C22×D7914yes—
857C2×C42C22×D7911yescharacteristic
858C2×C42C22×D7912yes—
859C2×C42C22×D7914yes—
860C2×C42C22×D7911yescharacteristic
861C2×C42C22×D7911yescharacteristic
862C2×C42C22×D7912yes—
863C2×C42C22×D7912yes—
864C2×C42C22×D7912yes—
865C2×C42C22×D7912yes—
866C2×C42C22×D7914yes—
867C2×C42C22×D7914yes—
868C2×C42C22×D7912yes—
869C2×C42C22×D7912yes—
870C2×C42C22×D7911yescharacteristic
871C24—798no—
872C24C23×D7911yescharacteristic
873C24C23×D7912yes—
874#41—216no—
875#41—216no—
876#41—3168no—
877#41—3168no—
878#41—15832no—
879#41—15816no—
880C2×Q8—24no—
881C2×Q8—3168no—
882C2×Q8—794no—
883C2×Q8—798no—
884C2×Q8—794no—
885C2×Q8—794no—
886C2×Q8C23×D7914yes—
887C2×D4—28no—
888C2×D4—3168no—
889C2×D4—798no—
890C2×D4—798no—
891C2×D4—798no—
892C2×D4—7916no—
893C2×D4—794no—
894C2×D4—798no—
895C2×D4—794no—
896C2×D4—794no—
897C2×D4—15832no—
898C2×D4—15832no—
899C2×D4#1192962418yescomplemented
900C2×D4C23×D7918yes—
901C2×D4C23×D7914yes—
902C22×C4—28no—
903C22×C4—24no—
904C22×C4—44no—
905C22×C4—44no—
906C22×C4—42no—
907C22×C4—42no—
908C22×C4—31616no—
909C22×C4—798no—
910C22×C4—798no—
911C22×C4—798no—
912C22×C4—7916no—
913C22×C4—798no—
914C22×C4—798no—
915C22×C4—798no—
916C22×C4C23×D7911yescharacteristic
917C22×C4C23×D7911yescharacteristic
918C22×C4C23×D7914yes—
919C22×C4C23×D7914yes—
920C22×C4C23×D7914yes—
921C22×C4C23×D7912yes—
922C22×C4C23×D7912yes—
923C22×C4C23×D7912yes—
924C22×C4C23×D7912yes—
925C22×C4C23×D7914yes—
926C22×C4C23×D7911yescharacteristic
927C22×C4C23×D7912yes—
928C22×C4C23×D7914yes—
929C22×C4C23×D7914yes—
930C22×C4C23×D7911yescharacteristic
931C22×C4C23×D7912yes—
932C22×C4C23×D7911yescharacteristic
933C22×C4C23×D7912yes—
934C22×C4C23×D7912yes—
935C22×C4C23×D7912yes—
936C22×C4C23×D7911yescharacteristic
937C4⋊C4—798no—
938C4⋊C4—798no—
939C4⋊C4—7916no—
940C4⋊C4—798no—
941C4⋊C4—798no—
942C4⋊C4—7916no—
943C4⋊C4—7916no—
944C4⋊C4—7916no—
945C4⋊C4—798no—
946C4⋊C4—798no—
947C4⋊C4—794no—
948C4⋊C4—794no—
949C4⋊C4—794no—
950C4⋊C4—798no—
951C4⋊C4—798no—
952C4⋊C4—794no—
953C4⋊C4—794no—
954C4⋊C4—794no—
955C4⋊C4C23×D7914yes—
956C4⋊C4C23×D7914yes—
957C4⋊C4C23×D7918yes—
958C4⋊C4C23×D7918yes—
959C22⋊C4—798no—
960C22⋊C4—7916no—
961C22⋊C4—798no—
962C22⋊C4—798no—
963C22⋊C4—798no—
964C22⋊C4—798no—
965C22⋊C4—798no—
966C22⋊C4—798no—
967C22⋊C4—7916no—
968C22⋊C4—798no—
969C22⋊C4—7916no—
970C22⋊C4—7916no—
971C22⋊C4—7916no—
972C22⋊C4—798no—
973C22⋊C4C23×D7918yes—
974C22⋊C4C23×D7918yes—
975C22⋊C4C23×D7918yes—
976C42—798no—
977C42—7916no—
978C42—798no—
979C42—798no—
980C42C23×D7911yescharacteristic
981C42C23×D7911yescharacteristic
982C42C23×D7914yes—
983C42C23×D7912yes—
984C42C23×D7912yes—
985C42C23×D7914yes—
986C42C23×D7914yes—
987C42C23×D7912yes—
988C42C23×D7914yes—
989C42C23×D7912yes—
990C42C23×D7912yes—
991C42C23×D7914yes—
992C42C23×D7912yes—
993C42C23×D7911yescharacteristic
994C42C23×D7911yescharacteristic
995C42C23×D7914yes—
996C23—22no—
997C23—42no—
998C23—42no—
999C23—41no—
1000C23—41no—
1001C23—3168no—
1002C23—3168no—
1003C23—798no—
1004C23—15816no—
1005C23C2×#1192962418yes—
1006C23C24×D7912yes—
1007C23C24×D7911yescharacteristic
1008C23C24×D7914yes—
1009Q8—28no—
1010Q8—3168no—
1011Q8—3164no—
1012Q8—1588no—
1013Q8—1588no—
1014D4—216no—
1015D4—3168no—
1016D4—3164no—
1017D4—3168no—
1018D4—3168no—
1019D4—15816no—
1020D4—15832no—
1021D4—1588no—
1022D4—1588no—
1023D4C2×#11929624116yes—
1024C2×C4—22no—
1025C2×C4—24no—
1026C2×C4—28no—
1027C2×C4—28no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—28no—
1031C2×C4—28no—
1032C2×C4—24no—
1033C2×C4—24no—
1034C2×C4—24no—
1035C2×C4—24no—
1036C2×C4—44no—
1037C2×C4—42no—
1038C2×C4—44no—
1039C2×C4—42no—
1040C2×C4—42no—
1041C2×C4—41no—
1042C2×C4—42no—
1043C2×C4—41no—
1044C2×C4—31616no—
1045C2×C4—3168no—
1046C2×C4—3168no—
1047C2×C4—3168no—
1048C2×C4—798no—
1049C2×C4—798no—
1050C2×C4—798no—
1051C2×C4—15816no—
1052C2×C4—15816no—
1053C2×C4—15816no—
1054C2×C4C2×#1192962414yes—
1055C2×C4C24×D7912yes—
1056C2×C4C24×D7914yes—
1057C2×C4C24×D7911yescharacteristic
1058C2×C4C24×D7911yescharacteristic
1059C2×C4C24×D7911yescharacteristic
1060C2×C4C24×D7911yescharacteristic
1061C2×C4C24×D7914yes—
1062C2×C4C24×D7912yes—
1063C2×C4C24×D7914yes—
1064C2×C4C24×D7911yescharacteristic
1065C2×C4C24×D7912yes—
1066C2×C4C24×D7911yescharacteristic
1067C22—21no—
1068C22—21no—
1069C22—24no—
1070C22—24no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—48no—
1075C22—44no—
1076C22—63216no—
1077C22—1588no—
1078C22—1588no—
1079C22—1588no—
1080C22C22×#1192962412yes—
1081C22C22×#1192962418yes—
1082C22C25×D7911yescharacteristic
1083C4—21no—
1084C4—21no—
1085C4—24no—
1086C4—21no—
1087C4—21no—
1088C4—24no—
1089C4—22no—
1090C4—24no—
1091C4—22no—
1092C4—1588no—
1093C4—1588no—
1094C4—1588no—
1095C4C22×#1192962414yes—
1096C4#1909939912yes—
1097C4#1909939912yes—
1098C2—22no—
1099C2—28no—
1100C2—42no—
1101C2—3168no—
1102C2C23×#1192962411yescharacteristic
1103C2C2×#1909939911yescharacteristic
1104C2C2×#1909939911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC2×C4×#41×C79C2
hypercenterC2×C4×#41D79
hypocenterC79#62781
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C2×C4×#41

Complements

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

NH ≅ G/Ntype
1. #23777468C2semidirect
2. #23777378C2semidirect
3. #23777361C2semidirect
4. #23777265C2semidirect
5. #23777239C2semidirect
6. #23777203C2semidirect
7. #23777164C2semidirect
8. #23777120C2semidirect
9. #23777098C2semidirect
10. #23777044C2semidirect
11. #23777015C2semidirect
12. #23777010C2semidirect
13. #23776962C2semidirect
14. #23776833C2semidirect
15. #23776809C2semidirect
16. #23776696C2semidirect
17. C2×#19099097C2semidirect
18. C4×#14579206C2semidirect
19. C2×C4×#41×C79C2semidirect
21. #19099298C22semidirect
22. #19099291C22semidirect
23. #19099286C22semidirect
24. #19099285C22semidirect
25. #19099281C22semidirect
26. #19099276C22semidirect
27. #19099273C22semidirect
28. #19099272C22semidirect
29. #19099270C22semidirect
30. #19099262C22semidirect
31. #19099259C22semidirect
32. #19099257C22semidirect
33. #19099254C22semidirect
34. #19099253C22semidirect
35. #19099252C22semidirect
36. #19099246C22semidirect
37. #19099246C22semidirect
38. #19099242C22semidirect
39. #19099237C22semidirect
40. #19099237C22semidirect
41. D4×Dic158C22semidirect
42. #19099222C22semidirect
43. #19099217C22semidirect
44. #19099212C22semidirect
45. #19099212C22semidirect
46. #19099209C22semidirect
47. #19099208C22semidirect
48. #19099201C22semidirect
49. #19099201C22semidirect
50. D4×D316C22semidirect
51. #19099194C22semidirect
52. #19099189C22semidirect
53. #19099185C22semidirect
54. #19099171C22semidirect
55. #19099160C22semidirect
56. #19099160C22semidirect
57. #19099155C22semidirect
58. #19099151C22semidirect
59. #19099146C22semidirect
61. #19099137C22semidirect
63. #19099122C22semidirect
64. #19099120C22semidirect
65. #19099120C22semidirect
66. #19099120C22semidirect
67. #19099117C22semidirect
69. #19099113C22semidirect
70. #19099113C22semidirect
71. #19099100C22semidirect
72. #19099097C22semidirect
73. #19099097C22semidirect
74. #19099097C22semidirect
75. #19099097C22semidirect
76. #19099097C22semidirect
77. #19099097C22semidirect
78. #19099097C22semidirect
79. #19099097C22semidirect
80. #19099097C22semidirect
81. #19099097C22semidirect
82. #19099097C22semidirect
83. #19099097C22semidirect
84. #19099097C22semidirect
85. #19099093C22semidirect
86. C2×#14579155C22semidirect
87. C2×#14579153C22semidirect
88. C2×#14579149C22semidirect
89. #19099074C22semidirect
90. #19099074C22semidirect
91. #19099074C22semidirect
92. #19099072C22semidirect
93. C2×#14579144C22semidirect
94. C2×#14579140C22semidirect
96. #19099044C22semidirect
97. #19099042C22semidirect
99. #19099036C22semidirect
100. #19099035C22semidirect
101. C4×#11929624C22semidirect
102. C4×#11929624C22semidirect
103. C4×#11929624C22semidirect
104. C4×#11929623C22semidirect
105. C2×C4×Dic158C22semidirect
106. C2×C4×D316C22semidirect
107. C2×C4×C22⋊D79C22semidirect
108. C4×D4×D79C22semidirect
109. C2×#14579118C22semidirect
111. C4×#41×C79C22semidirect
112. C4×#41×C79C22semidirect
113. C4×#41×C79C22semidirect
114. C4×#41×C79C22semidirect
115. C2×C4×Q8×C79C22semidirect
116. C2×C4×Q8×C79C22semidirect
119. C2×C4×D4×C79C22semidirect
120. C2×C4×D4×C79C22semidirect
121. C2×#117×C79C22semidirect
122. C2×#117×C79C22semidirect
123. C22×C42×C79C22semidirect
124. C22×C42×C79C22semidirect
390. C2×D4×C79#41semidirect
571. C2×C4×#41D79semidirect
572. C79#62781semidirect
659. C4×#41C2×D79semidirect
660. C4×#41C2×D79semidirect
661. C4×#41C2×D79semidirect
662. C4×#41C2×D79semidirect
664. C2×C4×Q8C2×D79semidirect
665. C2×C4×Q8C2×D79semidirect
671. C2×C4×D4C2×D79semidirect
672. C2×C4×D4C2×D79semidirect
674. C2×#117C2×D79semidirect
675. C2×#117C2×D79semidirect
676. C22×C42C2×D79semidirect
677. C22×C42C2×D79semidirect
899. C2×D4#11929624semidirect

Maximal subgroups

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

subgroupindex
#237774682
#237773782
#237773612
#237772652
#237772392
#237772032
#237771642
#237771202
#237770982
#237770442
#237770152
#237770102
#237769622
#237768332
#237768092
#237766962
C2×#190990972
C4×#145792062
C2×C4×#41×C792
#6278179