Finite Group Databasebeta

← #35196429

Subgroups — #35196429

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#23777471C218yesmaximal, complemented
2#23777379C214yesmaximal, complemented
3#23777362C214yesmaximal, complemented
4#23777267C212yesmaximal, complemented
5#23777241C214yesmaximal, complemented
6#23777164C211yesmaximal, characteristic, complemented
7#23777121C212yesmaximal, complemented
8#23777099C214yesmaximal, complemented
9#23777045C212yesmaximal, complemented
10#23777021C214yesmaximal, complemented
11#23777011C214yesmaximal, complemented
12#23776966C218yesmaximal, complemented
13#23776834C212yesmaximal, complemented
14#23776812C214yesmaximal, complemented
15#23776697C212yesmaximal, complemented
16C2×#19099099C214yesmaximal, complemented
17#23776604C212yesmaximal, complemented
18C2×C4×#11929623C211yesmaximal, characteristic, complemented
19C79×#3501C211yesmaximal, characteristic, complemented
20C2×#14579206C2212yes—
21C22×#11929623C2211yescharacteristic
22#19099298C2214yescomplemented
23#19099292C2214yescomplemented
24#19099287C2214yescomplemented
25#19099287C2218yescomplemented
26#19099286C2218yescomplemented
27#19099279C2218yescomplemented
28#19099274C2214yescomplemented
29#19099266C2218yescomplemented
30#19099261C2218yescomplemented
31#19099261C22116yescomplemented
32#19099255C22116yescomplemented
33#19099255C22116yescomplemented
34#19099255C2218yescomplemented
35#19099251C2218yescomplemented
36#19099251C2218yescomplemented
37#19099240C22116yescomplemented
38#19099240C22116yescomplemented
39#19099240C22116yescomplemented
40#19099224C2218yescomplemented
41#19099217C2218yescomplemented
42#19099217C2218yescomplemented
43#19099217C2214yescomplemented
44#19099208C2218yescomplemented
45#19099208C2218yescomplemented
46#19099208C2218yescomplemented
47#19099204C2218yescomplemented
48D4×D316C2214yescomplemented
49#19099187C2218yescomplemented
50#19099176C2218yescomplemented
51#19099162C2218yescomplemented
52#19099162C22116yescomplemented
53#19099162C2218yescomplemented
54#19099153C22116yescomplemented
55#19099153C2218yescomplemented
56#19099144C2212yes—
57#19099139C2214yescomplemented
58#19099125C2214yes—
59#19099125C2218yescomplemented
60#19099118C2218yescomplemented
61#19099118C2212yescomplemented
62#19099118C2212yescomplemented
63#19099114C2212yescomplemented
64#19099114C2212yescomplemented
65#19099113C2212yes—
66#19099100C2214yescomplemented
67#19099100C2214yescomplemented
68#19099099C2218yescomplemented
69#19099099C22116yescomplemented
70#19099099C2214yescomplemented
71#19099099C2218yescomplemented
72#19099099C2218yescomplemented
73#19099099C2214yescomplemented
74#19099099C2218yescomplemented
75#19099099C2218yescomplemented
76#19099099C2218yescomplemented
77#19099099C2218yescomplemented
78#19099098C2218yescomplemented
79#19099098C2214yescomplemented
80#19099098C2214yescomplemented
81C2×#14579156C2218yescomplemented
82C2×#14579152C2214yescomplemented
83C2×#14579150C2214yescomplemented
84#19099076C2214yescomplemented
85#19099076C22116yescomplemented
86#19099076C2214yescomplemented
87#19099075C2214yescomplemented
88C2×#14579145C2218yescomplemented
89C2×#14579135C2214yes—
90#19099043C2214yescomplemented
91#19099042C2218yescomplemented
92#19099036C2218yescomplemented
93#19099035C2218yescomplemented
94C4×#11929625C2214yescomplemented
95C4×#11929625C2214yescomplemented
96#19099031C2214yescomplemented
97C4×#11929623C2214yescomplemented
98C4×#11929623C2214yescomplemented
99C4×#11929623C2214yescomplemented
100C4×#11929623C2214yescomplemented
101C4×#11929623C2218yescomplemented
102C2×Q8×Dic79C2214yescomplemented
103C2×C4×Dic158C2211yescharacteristic, complemented
104C2×#14579126C2211yescharacteristic, complemented
105C2×D4×Dic79C2211yescharacteristic
106C2×#14579123C2214yescomplemented
107C2×C4×C22⋊D79C2212yescomplemented
108C2×(C22⋊D79)⋊C4C2212yescomplemented
109C2×(C22⋊D79)⋊C4C2218yescomplemented
110C4×D4×D79C2218yescomplemented
111C2×#14579119C2211yescharacteristic, complemented
112C2×#14579119C2218yescomplemented
113C2×#14579117C2212yescomplemented
114C22×C4×Dic79C2212yescomplemented
115C2×C42×D79C2211yescharacteristic, complemented
116#554×C79C2214yescomplemented
117#554×C79C2218yescomplemented
118D4×Q8×C79C2214yescomplemented
119#544×C79C2212yescomplemented
120#543×C79C2214yescomplemented
121#533×C79C2212yescomplemented
122C2×C22⋊Q8×C79C2214yescomplemented
123#518×C79C2212yes—
124C2×C4×D4×C79C2211yescharacteristic
125#14579206—216no—
126C2×#11929625C2314yes—
127C2×#11929625C2314yes—
128C2×#11929624C2314yes—
129C2×#11929623—28no—
130C2×#11929623C2318yes—
131C2×#11929623C2314yes—
132C2×#11929623C2314yes—
133C22×Dic158C2311yescharacteristic
134C22×D316C2314yes—
135C22×C22⋊D79C2318yes—
136C22×C22⋊D79C2312yes—
137C2×D4×D79C2318yes—
138C23×Dic79C2312yes—
139C23×Dic79C2312yes—
140C22×C4×D79C2311yescharacteristic
141C22×C4×D79C2311yescharacteristic
142C22×C4×D79C2311yescharacteristic
143C22×C4×D79C2318yes—
144#14579161C2318yes—
145#14579161C2312yes—
146#14579158C2312yes—
147#14579156C23116yes—
148#14579156C23116yes—
149#14579156C23116yes—
150#14579156C23116yes—
151#14579156C2318yes—
152#14579156C23116yes—
153#14579156C23116yes—
154#14579156C2318yes—
155#14579152C2318yes—
156#14579152C23116yes—
157#14579152C23116yes—
158#14579152C2318yes—
159#14579152C2314yes—
160#14579152C2318yes—
161#14579152C2314yes—
162#14579150C2318yes—
163#14579150C23116yes—
164#14579150C2318yes—
165#14579150C2314yes—
166#14579150C2318yes—
167#14579150C2314yes—
168#14579149C2318yes—
169#14579149C2314yes—
170#14579146C2318yes—
171#14579146C23116yes—
172#14579146C23116yes—
173#14579146C23116yes—
174#14579146C2318yes—
175#14579145C23116yes—
176#14579145C23116yes—
177#14579145C23116yes—
178#14579145C23116yes—
179#14579145C23116yes—
180#14579145C2318yes—
181#14579141C2318yes—
182#14579141C2318yes—
183#14579141C2318yes—
184#14579141C2314yes—
185#14579141C2314yes—
186#14579137C2314yes—
187#14579137C23116yes—
188#14579137C23116yes—
189#14579137C2314yes—
190#14579136C2318yes—
191#14579136C2314yes—
192#14579136C23116yes—
193#14579136C2314yes—
194#14579136C2314yes—
195#14579136C2314yes—
196#14579135C2318yes—
197#14579135C23116yes—
198#14579135C2314yes—
199#14579135C23116yes—
200#14579135C2318yes—
201#14579135C2318yes—
202#14579135C2314yes—
203#14579131C2318yes—
204#14579131C23116yes—
205#14579131C23116yes—
206Q8×Dic79C2318yes—
207Q8×Dic79C2314yes—
208Q8×Dic79C2318yes—
209Q8×Dic79C2314yes—
210Q8×Dic79C2318yes—
211C4×Dic158C2314yes—
212C4×Dic158C2318yes—
213C4×Dic158C2314yes—
214#14579126C2314yes—
215#14579126C2314yes—
216#14579126C2314yes—
217#14579126C2314yes—
218C4×D316C2314yes—
219C4×D316C2314yes—
220C4×D316C2318yes—
221C4×D316C2318yes—
222C4×D316C2318yes—
223D4×Dic79C2314yes—
224D4×Dic79C2314yes—
225#14579123C2314yes—
226#14579123C2318yes—
227#14579123C2314yes—
228#14579123C2318yes—
229#14579123C2318yes—
230#14579123C2314yes—
231#14579123C2314yes—
232#14579123C2318yes—
233#14579123C2318yes—
234C4×C22⋊D79C2318yes—
235C4×C22⋊D79C23116yes—
236C4×C22⋊D79C2318yes—
237C4×C22⋊D79C23116yes—
238(C22⋊D79)⋊C4C2318yes—
239(C22⋊D79)⋊C4C23116yes—
240(C22⋊D79)⋊C4C23116yes—
241(C22⋊D79)⋊C4C2318yes—
242(C22⋊D79)⋊C4C23116yes—
243(C22⋊D79)⋊C4C2318yes—
244(C22⋊D79)⋊C4C2318yes—
245#14579119C2318yes—
246#14579119C23116yes—
247#14579119C23116yes—
248#14579119C2314yes—
249#14579119C2318yes—
250#14579119C2314yes—
251#14579119C2314yes—
252#14579119C2318yes—
253#14579119C23116yes—
254#14579119C2314yes—
255#14579118C2318yes—
256#14579117C2318yes—
257#14579117C2318yes—
258#14579117C23116yes—
259C2×C4⋊Dic79C2318yes—
260C2×C4⋊Dic79C2314yes—
261C2×C4⋊Dic79C2318yes—
262C2×C4⋊Dic79C2311yescharacteristic
263C2×Dic79⋊C4C2312yes—
264C2×Dic79⋊C4C2312yes—
265C2×Dic79⋊C4C2318yes—
266C4⋊C4×D79C2318yes—
267C2×C22⋊Dic79C2312yes—
268C2×(C2×D79)⋊C4C2312yes—
269C2×(C2×D79)⋊C4C2318yes—
270C2×(C2×D79)⋊C4C2318yes—
271C2×(C2×D79)⋊C4C2318yes—
272C2×(C2×D79)⋊C4C2318yes—
273C22⋊C4×D79C23116yes—
274C2×C4×Dic79C2311yescharacteristic
275C2×C4×Dic79C2311yescharacteristic
276C2×C4×Dic79C2311yescharacteristic
277C2×C4×Dic79C2312yes—
278C2×C4×Dic79C2314yes—
279C2×C4×Dic79C2312yes—
280C2×C4×Dic79C2312yes—
281C2×C4×Dic79C2314yes—
282C2×C4×Dic79C2314yes—
283C2×C4×Dic79C2314yes—
284C2×C4×Dic79C2318yes—
285C42×D79C2312yes—
286C42×D79C2312yes—
287C42×D79C2312yes—
288C42×D79C2312yes—
289C42×D79C2318yes—
290C22×Q8×C79C2314yes—
291C22×D4×C79C2311yescharacteristic
292C23×C4×C79C2312yes—
293C4⋊Q8×C79C2318yes—
294C4⋊Q8×C79C2312yes—
295C4⋊Q8×C79C2312yes—
296#125×C79C2318yes—
297#125×C79C2314yes—
298C22⋊Q8×C79C2318yes—
299C22⋊Q8×C79C23116yes—
300C22⋊Q8×C79C2314yes—
301C22⋊Q8×C79C23116yes—
302C22⋊Q8×C79C2318yes—
303C22⋊Q8×C79C2318yes—
304C22⋊Q8×C79C2314yes—
305C4×Q8×C79C2314yes—
306C4×Q8×C79C2314yes—
307C4×D4×C79C2314yes—
308C4×D4×C79C2314yes—
309C4×D4×C79C2318yes—
310C4×D4×C79C2318yes—
311#117×C79C2314yes—
312C2×C4⋊C4×C79C2311yescharacteristic
313C2×C4⋊C4×C79C2318yes—
314C2×C4⋊C4×C79C2314yes—
315C2×C22⋊C4×C79C2312yes—
316C2×C22⋊C4×C79C2318yes—
317C2×C42×C79C2311yescharacteristic
318C23×D79C2418yes—
319C23×D79C2411yescharacteristic
320#11929625—48no—
321#11929625—48no—
322#11929624—216no—
323#11929623—216no—
324#11929623—216no—
325#11929623—232no—
326C2×Dic158—24no—
327C2×Dic158C2414yes—
328C2×Dic158C2414yes—
329C2×D316—48no—
330C2×D316C2414yes—
331C2×D316C2414yes—
332C2×D316C2414yes—
333C2×D316C2418yes—
334C2×D316C2418yes—
335C2×D316C2418yes—
336C2×C22⋊D79—28no—
337C2×C22⋊D79—232no—
338C2×C22⋊D79C2418yes—
339C2×C22⋊D79C24116yes—
340C2×C22⋊D79C2418yes—
341D4×D79—232no—
342C22×Dic79—28no—
343C22×Dic79—44no—
344C22×Dic79C2412yes—
345C22×Dic79C2414yes—
346C22×Dic79C2414yes—
347C22×Dic79C2418yes—
348C22×Dic79C2411yescharacteristic
349C22×Dic79C2414yes—
350C22×Dic79C2411yescharacteristic
351C22×Dic79C2414yes—
352C22×Dic79C2412yes—
353C22×Dic79C2411yescharacteristic
354C2×C4×D79—24no—
355C2×C4×D79—42no—
356C2×C4×D79—42no—
357C2×C4×D79—416no—
358C2×C4×D79C2412yes—
359C2×C4×D79C2412yes—
360C2×C4×D79C2418yes—
361C2×C4×D79C2412yes—
362C2×C4×D79C2412yes—
363C2×C4×D79C2418yes—
364C2×C4×D79C2418yes—
365C2×C4×D79C2412yes—
366C2×C4×D79C2412yes—
367C2×C4×D79C24116yes—
368C4⋊Dic79C2414yes—
369C4⋊Dic79C2418yes—
370C4⋊Dic79C2414yes—
371C4⋊Dic79C2418yes—
372C4⋊Dic79C24116yes—
373C4⋊Dic79C2418yes—
374C4⋊Dic79C24116yes—
375C4⋊Dic79C2414yes—
376Dic79⋊C4C24116yes—
377Dic79⋊C4C2418yes—
378Dic79⋊C4C2418yes—
379Dic79⋊C4C2418yes—
380Dic79⋊C4C2418yes—
381C22⋊Dic79C2418yes—
382(C2×D79)⋊C4C2418yes—
383(C2×D79)⋊C4C24116yes—
384(C2×D79)⋊C4C2418yes—
385(C2×D79)⋊C4C2418yes—
386(C2×D79)⋊C4C2418yes—
387(C2×D79)⋊C4C2418yes—
388(C2×D79)⋊C4C2418yes—
389(C2×D79)⋊C4C24116yes—
390(C2×D79)⋊C4C24116yes—
391(C2×D79)⋊C4C24116yes—
392(C2×D79)⋊C4C2418yes—
393(C2×D79)⋊C4C2418yes—
394(C2×D79)⋊C4C2418yes—
395C4×Dic79C2412yes—
396C4×Dic79C2411yescharacteristic
397C4×Dic79C2411yescharacteristic
398C4×Dic79C2411yescharacteristic
399C4×Dic79C2411yescharacteristic
400C4×Dic79C2412yes—
401C4×Dic79C2412yes—
402C4×Dic79C2412yes—
403C4×Dic79C2418yes—
404C4×Dic79C2418yes—
405C4×Dic79C2414yes—
406C4×Dic79C2414yes—
407C4×Dic79C2414yes—
408C4×Dic79C2414yes—
409C4×Dic79C2414yes—
410C4×Dic79C2414yes—
411C4×Dic79C24116yes—
412C24×C79C2412yes—
413C2×Q8×C79—48no—
414C2×Q8×C79C2414yes—
415C2×Q8×C79C2414yes—
416C2×Q8×C79C2418yes—
417C2×D4×C79#4118yescomplemented
418C2×D4×C79C2414yes—
419C22×C4×C79—44no—
420C22×C4×C79C2411yescharacteristic
421C22×C4×C79C2414yes—
422C22×C4×C79C2411yescharacteristic
423C22×C4×C79C2418yes—
424C22×C4×C79C2418yes—
425C22×C4×C79C2412yes—
426C22×C4×C79C2414yes—
427C22×C4×C79C2411yescharacteristic
428C4⋊C4×C79C2418yes—
429C4⋊C4×C79C2414yes—
430C4⋊C4×C79C2414yes—
431C4⋊C4×C79C2418yes—
432C4⋊C4×C79C24116yes—
433C4⋊C4×C79C2414yes—
434C4⋊C4×C79C2414yes—
435C4⋊C4×C79C2418yes—
436C4⋊C4×C79C2414yes—
437C22⋊C4×C79C2418yes—
438C22⋊C4×C79C24116yes—
439C22⋊C4×C79C2418yes—
440C42×C79C2412yes—
441C42×C79C2412yes—
442C42×C79C2418yes—
443C23×C79—42no—
444C23×C79—42no—
445C23×C79C2×#4118yes—
446C23×C79C2514yes—
447C23×C79C2511yescharacteristic
448C22×D79—22no—
449C22×D79—216no—
450C22×D79—41no—
451C22×D79—41no—
452C22×D79—48no—
453C22×D79—48no—
454C22×D79C2518yes—
455C22×D79C2512yes—
456Q8×C79—28no—
457Q8×C79—44no—
458Q8×C79—48no—
459D4×C79C2×#41116yes—
460C2×C4×C79—22no—
461C2×C4×C79—28no—
462C2×C4×C79—48no—
463C2×C4×C79—41no—
464C2×C4×C79—44no—
465C2×C4×C79—42no—
466C2×C4×C79—48no—
467C2×C4×C79C2×#4114yes—
468C2×C4×C79C2511yescharacteristic
469C2×C4×C79C2514yes—
470C2×C4×C79C2518yes—
471C2×C4×C79C2512yes—
472C2×C4×C79C2518yes—
473C2×C4×C79C2512yes—
474C2×C4×C79C2511yescharacteristic
475C22⋊D79—232no—
476C22⋊D79—216no—
477C22⋊D79—216no—
478C2×Dic79—22no—
479C2×Dic79—24no—
480C2×Dic79—28no—
481C2×Dic79—28no—
482C2×Dic79—216no—
483C2×Dic79—28no—
484C2×Dic79—22no—
485C2×Dic79—41no—
486C2×Dic79—42no—
487C2×Dic79—44no—
488C2×Dic79C2511yescharacteristic
489C2×Dic79C2511yescharacteristic
490C2×Dic79C2511yescharacteristic
491C2×Dic79C2514yes—
492C2×Dic79C2512yes—
493C2×Dic79C2514yes—
494C2×Dic79C2518yes—
495C2×Dic79C2511yescharacteristic
496D316—28no—
497D316—28no—
498D316—48no—
499D316—48no—
500D316—48no—
501D316—44no—
502C4×D79—24no—
503C4×D79—24no—
504C4×D79—216no—
505C4×D79—24no—
506C4×D79—216no—
507C4×D79—24no—
508C4×D79—42no—
509C4×D79—416no—
510C4×D79—42no—
511C4×D79—48no—
512Dic158—28no—
513Dic158—28no—
514C22×C79—24no—
515C22×C79—21no—
516C22×C79—24no—
517C22×C79—21no—
518C22×C79—48no—
519C22×C79C22×#4112yes—
520C22×C79C22×#4118yes—
521C22×C79C2611yescharacteristic
522C2×D79—22no—
523C2×D79—28no—
524C2×D79—28no—
525C2×D79—28no—
526C2×D79—22no—
527C2×D79—22no—
528C2×D79—44no—
529C2×D79—816no—
530C4×C79—21no—
531C4×C79—24no—
532C4×C79—28no—
533C4×C79—28no—
534C4×C79—22no—
535C4×C79C22×#4114yes—
536C4×C79#58512yes—
537Dic79—28no—
538Dic79—24no—
539Dic79—21no—
540Dic79—21no—
541Dic79—22no—
542Dic79—24no—
543Dic79—21no—
544Dic79#58512yes—
545#62781—791nomaximal, Sylow
546C2×C79—22no—
547C2×C79—28no—
548C2×C79C23×#4111yescharacteristic
549C2×C79C2×#58511yescharacteristic
550C2×C79C2×#58511yescharacteristic
551D79—42no—
552D79—48no—
553#3521—798no—
554#3515—794no—
555#3514—794no—
556#3507—792no—
557#3505—794no—
558#3501D7911yescharacteristic, complemented
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×#41—791no—
572C79#6278111yescharacteristic, complemented, Sylow
573C2×H(5,𝔽2)—792no—
574C22×#41—791no—
575#559—794no—
576#557—794no—
577#556—798no—
578#556—794no—
579#556—798no—
580#555—798no—
581#554—794no—
582#554C2×D7918yescomplemented
583#554C2×D7914yescomplemented
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×Q8C2×D7914yescomplemented
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#544C2×D7912yescomplemented
606#543C2×D7914yescomplemented
607#542—798no—
608#541—798no—
609#539—798no—
610#539—7916no—
611#539—798no—
612#538—798no—
613#538—7916no—
614#537—792no—
615#536—794no—
616#534—798no—
617#534—794no—
618#533—792no—
619#533—792no—
620#533—798no—
621#533C2×D7912yescomplemented
622#532—792no—
623#532—792no—
624#532—792no—
625#529—794no—
626#529—794no—
627#529—798no—
628#529—794no—
629#529—798no—
630#529—798no—
631#529—798no—
632#529—798no—
633#529—798no—
634#529—798no—
635#529—798no—
636#529—794no—
637#529—7916no—
638#529—794no—
639#529—794no—
640C2×#126—798no—
641C2×#125—794no—
642C2×#124—794no—
643#525—794no—
644#525—794no—
645#525—7916no—
646#525—794no—
647C2×#123—798no—
648C2×C22⋊Q8C2×D7914yescomplemented
649C2×#121—794no—
650#520—798no—
651#520—794no—
652#518—798no—
653#518—798no—
654#518C2×D7912yes—
655C4×#41—794no—
656C4×#41—794no—
657C4×#41—794no—
658C4×#41—794no—
659C4×#41—794no—
660C4×#41—794no—
661C4×#41—798no—
662C4×#41—794no—
663C2×C4×Q8—794no—
664C2×C4×Q8—791no—
665C2×C4×Q8—791no—
666C2×C4×D4—791no—
667C2×C4×D4—792no—
668C2×C4×D4—798no—
669C2×C4×D4—794no—
670C2×C4×D4—792no—
671C2×C4×D4—798no—
672C2×C4×D4C2×D7911yescharacteristic
673C2×#117—791no—
674C2×#117—798no—
675C2×#117—792no—
676C22×C42—792no—
677C22×C42—791no—
678H(5,𝔽2)—15816no—
679C2×#41—794no—
680C2×#41—794no—
681C2×#41—794no—
682C2×#41—794no—
683C2×#41—798no—
684C2×#41—794no—
685C2×#41—1588no—
686C22×Q8—791no—
687C22×Q8C22×D7914yes—
688C22×D4—792no—
689C22×D4—798no—
690C22×D4—798no—
691C22×D4—794no—
692C22×D4C22×D7911yescharacteristic
693C23×C4—792no—
694C23×C4—798no—
695C23×C4—791no—
696C23×C4—791no—
697C23×C4—792no—
698C23×C4—791no—
699C23×C4C22×D7912yes—
700C4⋊Q8—792no—
701C4⋊Q8—798no—
702C4⋊Q8C22×D7912yes—
703C4⋊Q8C22×D7912yes—
704C4⋊Q8C22×D7918yes—
705#127—792no—
706#126—798no—
707#126—7916no—
708#126—7916no—
709#126—7916no—
710#126—798no—
711#126—7916no—
712#126—7916no—
713#126—7916no—
714#125—794no—
715#125—798no—
716#125—798no—
717#125—798no—
718#125—794no—
719#125—7916no—
720#125—7916no—
721#125C22×D7914yes—
722#125C22×D7918yes—
723#124—794no—
724#124—798no—
725#124—798no—
726#124—798no—
727#124—794no—
728#124—7916no—
729#124—794no—
730#124—798no—
731#123—798no—
732#123—798no—
733#123—7916no—
734#123—7916no—
735#123—7916no—
736#123—798no—
737#123—7916no—
738#123—7916no—
739#123—7916no—
740#123—7916no—
741#123—7916no—
742C22⋊Q8—794no—
743C22⋊Q8—794no—
744C22⋊Q8—7916no—
745C22⋊Q8—7916no—
746C22⋊Q8—794no—
747C22⋊Q8—794no—
748C22⋊Q8—798no—
749C22⋊Q8—798no—
750C22⋊Q8—798no—
751C22⋊Q8C22×D7914yes—
752C22⋊Q8C22×D7918yes—
753C22⋊Q8C22×D7918yes—
754C22⋊Q8C22×D7918yes—
755C22⋊Q8C22×D7914yes—
756C22⋊Q8C22×D79116yes—
757C22⋊Q8C22×D79116yes—
758#121—794no—
759#121—798no—
760#121—798no—
761#121—798no—
762#121—794no—
763#121—7916no—
764#121—7916no—
765#121—794no—
766#121—794no—
767#121—794no—
768#121—794no—
769#121—7916no—
770#121—798no—
771#120—798no—
772#120—7916no—
773#120—7916no—
774C4×Q8—794no—
775C4×Q8—798no—
776C4×Q8—798no—
777C4×Q8—798no—
778C4×Q8—794no—
779C4×Q8—794no—
780C4×Q8—794no—
781C4×Q8—794no—
782C4×Q8—794no—
783C4×Q8—794no—
784C4×Q8—794no—
785C4×Q8—798no—
786C4×Q8C22×D7914yes—
787C4×Q8C22×D7914yes—
788C4×D4—794no—
789C4×D4—794no—
790C4×D4—798no—
791C4×D4—798no—
792C4×D4—7916no—
793C4×D4—7916no—
794C4×D4—794no—
795C4×D4—794no—
796C4×D4—798no—
797C4×D4—798no—
798C4×D4—798no—
799C4×D4—794no—
800C4×D4—798no—
801C4×D4—798no—
802C4×D4—794no—
803C4×D4—7916no—
804C4×D4—798no—
805C4×D4—798no—
806C4×D4—798no—
807C4×D4—7916no—
808C4×D4—7916no—
809C4×D4—798no—
810C4×D4—798no—
811C4×D4—798no—
812C4×D4—798no—
813C4×D4—794no—
814C4×D4—794no—
815C4×D4C22×D7918yes—
816C4×D4C22×D7914yes—
817C4×D4C22×D7914yes—
818C4×D4C22×D7918yes—
819#117—798no—
820#117—794no—
821#117—794no—
822#117—7916no—
823#117—7916no—
824#117—7916no—
825#117—798no—
826#117—794no—
827#117—794no—
828#117—798no—
829#117—798no—
830#117—798no—
831#117—7916no—
832#117—798no—
833#117C22×D7914yes—
834C2×C4⋊C4—791no—
835C2×C4⋊C4—792no—
836C2×C4⋊C4—792no—
837C2×C4⋊C4—798no—
838C2×C4⋊C4—798no—
839C2×C4⋊C4—794no—
840C2×C4⋊C4—798no—
841C2×C4⋊C4—798no—
842C2×C4⋊C4C22×D7911yescharacteristic
843C2×C4⋊C4C22×D7918yes—
844C2×C4⋊C4C22×D7914yes—
845C2×C22⋊C4—792no—
846C2×C22⋊C4—792no—
847C2×C22⋊C4—798no—
848C2×C22⋊C4—798no—
849C2×C22⋊C4—798no—
850C2×C22⋊C4—798no—
851C2×C22⋊C4—7916no—
852C2×C22⋊C4C22×D7912yes—
853C2×C22⋊C4C22×D7918yes—
854C2×C42—794no—
855C2×C42—792no—
856C2×C42—791no—
857C2×C42—798no—
858C2×C42—791no—
859C2×C42—794no—
860C2×C42—792no—
861C2×C42—792no—
862C2×C42—794no—
863C2×C42—794no—
864C2×C42—791no—
865C2×C42—798no—
866C2×C42—792no—
867C2×C42—792no—
868C2×C42—792no—
869C2×C42—792no—
870C2×C42C22×D7911yescharacteristic
871C24—798no—
872C24—791no—
873C24C23×D7912yes—
874#41—3168no—
875#41—3168no—
876#41—15816no—
877#41—15816no—
878#41—15832no—
879#41—15816no—
880C2×Q8—48no—
881C2×Q8—794no—
882C2×Q8—794no—
883C2×Q8—1584no—
884C2×Q8C23×D7914yes—
885C2×Q8C23×D7918yes—
886C2×Q8C23×D7914yes—
887C2×D4—3168no—
888C2×D4—798no—
889C2×D4—7916no—
890C2×D4—798no—
891C2×D4—794no—
892C2×D4—798no—
893C2×D4—798no—
894C2×D4—798no—
895C2×D4—794no—
896C2×D4—794no—
897C2×D4—1588no—
898C2×D4—15832no—
899C2×D4—15832no—
900C2×D4#1192962518yescomplemented
901C2×D4C23×D7914yes—
902C22×C4—44no—
903C22×C4—3162no—
904C22×C4—31616no—
905C22×C4—3162no—
906C22×C4—3164no—
907C22×C4—794no—
908C22×C4—792no—
909C22×C4—791no—
910C22×C4—792no—
911C22×C4—792no—
912C22×C4—798no—
913C22×C4—7916no—
914C22×C4—794no—
915C22×C4—791no—
916C22×C4—791no—
917C22×C4—794no—
918C22×C4—794no—
919C22×C4—792no—
920C22×C4—798no—
921C22×C4—792no—
922C22×C4—792no—
923C22×C4—792no—
924C22×C4—792no—
925C22×C4—798no—
926C22×C4—798no—
927C22×C4—1588no—
928C22×C4—1584no—
929C22×C4C23×D7911yescharacteristic
930C22×C4C23×D7914yes—
931C22×C4C23×D7914yes—
932C22×C4C23×D7912yes—
933C22×C4C23×D7911yescharacteristic
934C22×C4C23×D7918yes—
935C22×C4C23×D7918yes—
936C22×C4C23×D7911yescharacteristic
937C4⋊C4—7916no—
938C4⋊C4—798no—
939C4⋊C4—798no—
940C4⋊C4—798no—
941C4⋊C4—798no—
942C4⋊C4—794no—
943C4⋊C4—798no—
944C4⋊C4—794no—
945C4⋊C4—798no—
946C4⋊C4—7916no—
947C4⋊C4—798no—
948C4⋊C4—7916no—
949C4⋊C4—794no—
950C4⋊C4C23×D7914yes—
951C4⋊C4C23×D7918yes—
952C4⋊C4C23×D7914yes—
953C4⋊C4C23×D7914yes—
954C4⋊C4C23×D79116yes—
955C4⋊C4C23×D7918yes—
956C4⋊C4C23×D7914yes—
957C4⋊C4C23×D7914yes—
958C4⋊C4C23×D7918yes—
959C22⋊C4—798no—
960C22⋊C4—798no—
961C22⋊C4—798no—
962C22⋊C4—798no—
963C22⋊C4—798no—
964C22⋊C4—7916no—
965C22⋊C4—798no—
966C22⋊C4—798no—
967C22⋊C4—7916no—
968C22⋊C4—7916no—
969C22⋊C4—7916no—
970C22⋊C4—798no—
971C22⋊C4—798no—
972C22⋊C4—798no—
973C22⋊C4C23×D79116yes—
974C22⋊C4C23×D7918yes—
975C22⋊C4C23×D7918yes—
976C42—791no—
977C42—791no—
978C42—792no—
979C42—791no—
980C42—791no—
981C42—794no—
982C42—792no—
983C42—794no—
984C42—798no—
985C42—792no—
986C42—794no—
987C42—792no—
988C42—794no—
989C42—794no—
990C42—794no—
991C42—798no—
992C42—7916no—
993C42C23×D7912yes—
994C42C23×D7912yes—
995C42C23×D7918yes—
996C23—42no—
997C23—42no—
998C23—3161no—
999C23—3161no—
1000C23—3168no—
1001C23—3168no—
1002C23—798no—
1003C23—792no—
1004C23—1582no—
1005C23—15816no—
1006C23C2×#1192962518yes—
1007C23C24×D7914yes—
1008C23C24×D7911yescharacteristic
1009Q8—28no—
1010Q8—48no—
1011Q8—44no—
1012Q8—1588no—
1013Q8—1588no—
1014D4—3168no—
1015D4—3168no—
1016D4—3164no—
1017D4—3168no—
1018D4—15832no—
1019D4—15816no—
1020D4—15816no—
1021D4—1588no—
1022D4—1588no—
1023D4C2×#11929625116yes—
1024C2×C4—22no—
1025C2×C4—28no—
1026C2×C4—44no—
1027C2×C4—42no—
1028C2×C4—48no—
1029C2×C4—41no—
1030C2×C4—48no—
1031C2×C4—31616no—
1032C2×C4—3162no—
1033C2×C4—3162no—
1034C2×C4—3168no—
1035C2×C4—3164no—
1036C2×C4—3162no—
1037C2×C4—3161no—
1038C2×C4—791no—
1039C2×C4—791no—
1040C2×C4—791no—
1041C2×C4—791no—
1042C2×C4—794no—
1043C2×C4—792no—
1044C2×C4—794no—
1045C2×C4—798no—
1046C2×C4—15816no—
1047C2×C4—1584no—
1048C2×C4—1588no—
1049C2×C4—1582no—
1050C2×C4—1582no—
1051C2×C4—1584no—
1052C2×C4—1588no—
1053C2×C4—1588no—
1054C2×C4—15816no—
1055C2×C4—1584no—
1056C2×C4—1584no—
1057C2×C4—1584no—
1058C2×C4—15816no—
1059C2×C4C2×#1192962514yes—
1060C2×C4C24×D7911yescharacteristic
1061C2×C4C24×D7914yes—
1062C2×C4C24×D7918yes—
1063C2×C4C24×D7912yes—
1064C2×C4C24×D7918yes—
1065C2×C4C24×D7911yescharacteristic
1066C2×C4C24×D7912yes—
1067C22—24no—
1068C22—21no—
1069C22—24no—
1070C22—21no—
1071C22—48no—
1072C22—3164no—
1073C22—63216no—
1074C22—1582no—
1075C22—1588no—
1076C22—1588no—
1077C22—1582no—
1078C22—1582no—
1079C22—1588no—
1080C22C22×#1192962518yes—
1081C22C22×#1192962512yes—
1082C22C25×D7911yescharacteristic
1083C4—28no—
1084C4—22no—
1085C4—21no—
1086C4—24no—
1087C4—28no—
1088C4—792no—
1089C4—1581no—
1090C4—1581no—
1091C4—1588no—
1092C4—1584no—
1093C4—1584no—
1094C4—1581no—
1095C4—1582no—
1096C4C22×#1192962514yes—
1097C4#1909939812yes—
1098C2—22no—
1099C2—28no—
1100C2—3162no—
1101C2—3168no—
1102C2C23×#1192962511yescharacteristic
1103C2#585×D7911yescharacteristic
1104C2C2×#1909939811yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3501C2
hypercenter#3501D79
hypocenterC79#62781
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #23777471C2semidirect
2. #23777379C2semidirect
3. #23777362C2semidirect
4. #23777267C2semidirect
5. #23777241C2semidirect
6. #23777164C2semidirect
7. #23777121C2semidirect
8. #23777099C2semidirect
9. #23777045C2semidirect
10. #23777021C2semidirect
11. #23777011C2semidirect
12. #23776966C2semidirect
13. #23776834C2semidirect
14. #23776812C2semidirect
15. #23776697C2semidirect
16. C2×#19099099C2semidirect
17. #23776604C2semidirect
18. C2×C4×#11929623C2semidirect
19. C79×#3501C2semidirect
22. #19099298C22semidirect
23. #19099292C22semidirect
24. #19099287C22semidirect
25. #19099287C22semidirect
26. #19099286C22semidirect
27. #19099279C22semidirect
28. #19099274C22semidirect
29. #19099266C22semidirect
30. #19099261C22semidirect
31. #19099261C22semidirect
32. #19099255C22semidirect
33. #19099255C22semidirect
34. #19099255C22semidirect
35. #19099251C22semidirect
36. #19099251C22semidirect
37. #19099240C22semidirect
38. #19099240C22semidirect
39. #19099240C22semidirect
40. #19099224C22semidirect
41. #19099217C22semidirect
42. #19099217C22semidirect
43. #19099217C22semidirect
44. #19099208C22semidirect
45. #19099208C22semidirect
46. #19099208C22semidirect
47. #19099204C22semidirect
48. D4×D316C22semidirect
49. #19099187C22semidirect
50. #19099176C22semidirect
51. #19099162C22semidirect
52. #19099162C22semidirect
53. #19099162C22semidirect
54. #19099153C22semidirect
55. #19099153C22semidirect
57. #19099139C22semidirect
59. #19099125C22semidirect
60. #19099118C22semidirect
61. #19099118C22semidirect
62. #19099118C22semidirect
63. #19099114C22semidirect
64. #19099114C22semidirect
66. #19099100C22semidirect
67. #19099100C22semidirect
68. #19099099C22semidirect
69. #19099099C22semidirect
70. #19099099C22semidirect
71. #19099099C22semidirect
72. #19099099C22semidirect
73. #19099099C22semidirect
74. #19099099C22semidirect
75. #19099099C22semidirect
76. #19099099C22semidirect
77. #19099099C22semidirect
78. #19099098C22semidirect
79. #19099098C22semidirect
80. #19099098C22semidirect
81. C2×#14579156C22semidirect
82. C2×#14579152C22semidirect
83. C2×#14579150C22semidirect
84. #19099076C22semidirect
85. #19099076C22semidirect
86. #19099076C22semidirect
87. #19099075C22semidirect
88. C2×#14579145C22semidirect
90. #19099043C22semidirect
91. #19099042C22semidirect
92. #19099036C22semidirect
93. #19099035C22semidirect
94. C4×#11929625C22semidirect
95. C4×#11929625C22semidirect
96. #19099031C22semidirect
97. C4×#11929623C22semidirect
98. C4×#11929623C22semidirect
99. C4×#11929623C22semidirect
100. C4×#11929623C22semidirect
101. C4×#11929623C22semidirect
102. C2×Q8×Dic79C22semidirect
103. C2×C4×Dic158C22semidirect
104. C2×#14579126C22semidirect
106. C2×#14579123C22semidirect
107. C2×C4×C22⋊D79C22semidirect
108. C2×(C22⋊D79)⋊C4C22semidirect
109. C2×(C22⋊D79)⋊C4C22semidirect
110. C4×D4×D79C22semidirect
111. C2×#14579119C22semidirect
112. C2×#14579119C22semidirect
113. C2×#14579117C22semidirect
114. C22×C4×Dic79C22semidirect
115. C2×C42×D79C22semidirect
116. #554×C79C22semidirect
117. #554×C79C22semidirect
118. D4×Q8×C79C22semidirect
119. #544×C79C22semidirect
120. #543×C79C22semidirect
121. #533×C79C22semidirect
122. C2×C22⋊Q8×C79C22semidirect
417. C2×D4×C79#41semidirect
558. #3501D79semidirect
572. C79#62781semidirect
582. #554C2×D79semidirect
583. #554C2×D79semidirect
595. D4×Q8C2×D79semidirect
605. #544C2×D79semidirect
606. #543C2×D79semidirect
621. #533C2×D79semidirect
648. C2×C22⋊Q8C2×D79semidirect
900. C2×D4#11929625semidirect

Maximal subgroups

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

subgroupindex
#237774712
#237773792
#237773622
#237772672
#237772412
#237771642
#237771212
#237770992
#237770452
#237770212
#237770112
#237769662
#237768342
#237768122
#237766972
C2×#190990992
#237766042
C2×C4×#119296232
C79×#35012
#6278179