Finite Group Databasebeta

← #35197336

Subgroups — #35197336

Order 20224.

7106 conjugacy classes of subgroups.

The subgroup lattice has 1000 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777471C218yesmaximal, complemented
2#23777450C218yesmaximal, complemented
3#23777379C218yesmaximal, complemented
4#23777343C218yesmaximal, complemented
5#23777267C212yesmaximal, complemented
6#23777241C214yesmaximal, complemented
7#23777164C211yesmaximal, characteristic, complemented
8#23777110C212yesmaximal, complemented
9#23777099C214yesmaximal, complemented
10#23777045C212yesmaximal, complemented
11#23776834C212yesmaximal, complemented
12#23776812C214yesmaximal, complemented
13#23776792C212yesmaximal, complemented
14C2×#19099162C214yesmaximal, complemented
15#23776604C212yesmaximal, complemented
16C2×#19099042C211yesmaximal, characteristic, complemented
17C79×#3501C211yesmaximal, characteristic, complemented
18C2×#14579206C2212yes—
19C22×#11929623C2211yescharacteristic
20#19099298C2214yescomplemented
21#19099292C2214yescomplemented
22#19099287C2214yescomplemented
23#19099286C2218yescomplemented
24#19099274C2218yescomplemented
25#19099274C2214yescomplemented
26#19099266C2218yescomplemented
27#19099261C22116yescomplemented
28#19099261C2218yescomplemented
29#19099255C22116yescomplemented
30#19099255C22116yescomplemented
31#19099255C2218yescomplemented
32#19099251C2218yescomplemented
33#19099251C2218yescomplemented
34#19099240C22116yescomplemented
35#19099240C22116yescomplemented
36#19099240C22116yescomplemented
37#19099224C2218yescomplemented
38#19099217C2218yescomplemented
39#19099217C2218yescomplemented
40#19099217C2214yescomplemented
41#19099216C2218yescomplemented
42#19099208C2218yescomplemented
43#19099208C2218yescomplemented
44#19099208C2218yescomplemented
45#19099204C2218yescomplemented
46D4×D316C2214yescomplemented
47#19099187C2214yescomplemented
48#19099187C2214yescomplemented
49#19099187C2218yescomplemented
50#19099176C2214yescomplemented
51#19099176C2218yescomplemented
52#19099169C2214yescomplemented
53#19099162C2214yescomplemented
54#19099162C2214yescomplemented
55#19099162C2218yescomplemented
56#19099162C22116yescomplemented
57#19099162C22116yescomplemented
58#19099162C2218yescomplemented
59#19099162C22116yescomplemented
60#19099162C2218yescomplemented
61#19099153C2214yescomplemented
62#19099153C2214yescomplemented
63#19099153C22116yescomplemented
64#19099144C2212yes—
65#19099139C2214yescomplemented
66#19099125C2214yes—
67#19099125C2218yescomplemented
68#19099118C2218yescomplemented
69#19099113C2212yes—
70#19099100C2218yescomplemented
71#19099100C2218yescomplemented
72#19099099C2218yescomplemented
73#19099099C22116yescomplemented
74#19099099C2218yescomplemented
75#19099098C2218yescomplemented
76C2×#14579156C2218yescomplemented
77C2×#14579152C2218yescomplemented
78#19099076C22116yescomplemented
79#19099076C2218yescomplemented
80#19099075C2214yescomplemented
81C2×#14579146C2218yescomplemented
82C2×#14579145C2218yescomplemented
83C2×#14579137C2218yescomplemented
84C2×#14579135C2214yes—
85#19099043C2214yescomplemented
86#19099042C2218yescomplemented
87#19099042C2218yescomplemented
88#19099042C2218yescomplemented
89#19099036C2218yescomplemented
90#19099035C2218yescomplemented
91#19099031C2214yescomplemented
92C4×#11929623C2218yescomplemented
93C2×C4×Dic158C2211yescharacteristic, complemented
94C2×#14579126C2211yescharacteristic, complemented
95C2×D4×Dic79C2211yescharacteristic
96C2×C4×C22⋊D79C2212yescomplemented
97C2×(C22⋊D79)⋊C4C2212yescomplemented
98C2×(C22⋊D79)⋊C4C2218yescomplemented
99C4×D4×D79C2218yescomplemented
100C2×#14579118C2211yescharacteristic, complemented
101C2×#14579117C2212yescomplemented
102C22×Dic79⋊C4C2212yescomplemented
103C2×C4⋊C4×D79C2211yescharacteristic, complemented
104#554×C79C2218yescomplemented
105#554×C79C2214yescomplemented
106D4×Q8×C79C2214yescomplemented
107#544×C79C2212yescomplemented
108#543×C79C2214yescomplemented
109#533×C79C2212yescomplemented
110C2×C22⋊Q8×C79C2214yescomplemented
111#518×C79C2212yes—
112C2×C4×D4×C79C2211yescharacteristic
113#14579206—216no—
114C2×#11929625C2318yes—
115C2×#11929624C2314yes—
116C2×#11929623—28no—
117C2×#11929623C2318yes—
118C2×#11929623C2318yes—
119C22×Dic158C2311yescharacteristic
120C22×D316C2314yes—
121C22×C22⋊D79C2318yes—
122C22×C22⋊D79C2312yes—
123C2×D4×D79C2318yes—
124C23×Dic79C2312yes—
125C23×Dic79C2312yes—
126C22×C4×D79C2311yescharacteristic
127C22×C4×D79C2312yes—
128C22×C4×D79C2318yes—
129#14579161C2318yes—
130#14579161C2312yes—
131#14579158C2312yes—
132#14579156C23116yes—
133#14579156C2318yes—
134#14579156C23116yes—
135#14579156C2318yes—
136#14579156C2318yes—
137#14579156C23116yes—
138#14579156C23116yes—
139#14579156C2318yes—
140#14579156C23116yes—
141#14579152C2318yes—
142#14579152C23116yes—
143#14579152C23116yes—
144#14579152C23116yes—
145#14579152C2318yes—
146#14579152C2318yes—
147#14579152C2318yes—
148#14579150C2318yes—
149#14579150C2318yes—
150#14579150C2318yes—
151#14579150C2318yes—
152#14579149C2318yes—
153#14579149C2314yes—
154#14579146C23116yes—
155#14579146C2318yes—
156#14579146C23116yes—
157#14579146C2318yes—
158#14579146C2318yes—
159#14579146C23116yes—
160#14579146C23116yes—
161#14579146C2318yes—
162#14579145C23116yes—
163#14579145C2318yes—
164#14579145C23116yes—
165#14579145C23116yes—
166#14579145C23116yes—
167#14579145C23116yes—
168#14579141C2318yes—
169#14579141C2318yes—
170#14579141C2318yes—
171#14579141C2314yes—
172#14579141C2314yes—
173#14579137C2318yes—
174#14579137C23116yes—
175#14579137C23116yes—
176#14579137C23116yes—
177#14579137C2318yes—
178#14579137C2318yes—
179#14579136C2318yes—
180#14579136C2318yes—
181#14579136C2318yes—
182#14579136C2318yes—
183#14579136C2314yes—
184#14579136C2314yes—
185#14579135C2318yes—
186#14579135C2314yes—
187#14579135C2314yes—
188#14579135C23116yes—
189#14579135C2318yes—
190#14579135C2318yes—
191#14579135C23116yes—
192#14579131C2318yes—
193#14579131C23116yes—
194#14579131C23116yes—
195Q8×Dic79C2318yes—
196Q8×Dic79C2318yes—
197C4×Dic158C2314yes—
198C4×Dic158C2318yes—
199C4×Dic158C2314yes—
200#14579126C2314yes—
201#14579126C2318yes—
202#14579126C2314yes—
203C4×D316C2314yes—
204C4×D316C2314yes—
205C4×D316C2318yes—
206C4×D316C2318yes—
207C4×D316C2318yes—
208D4×Dic79C2318yes—
209#14579123C2314yes—
210#14579123C2314yes—
211#14579123C2318yes—
212#14579123C2318yes—
213#14579123C23116yes—
214C4×C22⋊D79C2318yes—
215C4×C22⋊D79C2318yes—
216C4×C22⋊D79C23116yes—
217C4×C22⋊D79C23116yes—
218(C22⋊D79)⋊C4C23116yes—
219(C22⋊D79)⋊C4C2318yes—
220(C22⋊D79)⋊C4C23116yes—
221(C22⋊D79)⋊C4C2318yes—
222(C22⋊D79)⋊C4C23116yes—
223(C22⋊D79)⋊C4C23116yes—
224#14579119C23116yes—
225#14579119C23116yes—
226#14579119C2318yes—
227#14579119C2318yes—
228#14579118C2314yes—
229#14579118C2318yes—
230#14579118C2314yes—
231#14579117C23116yes—
232#14579117C23116yes—
233C2×C4⋊Dic79C2314yes—
234C2×C4⋊Dic79C2318yes—
235C2×C4⋊Dic79C2318yes—
236C2×C4⋊Dic79C2311yescharacteristic
237C2×Dic79⋊C4C2312yes—
238C2×Dic79⋊C4C2311yescharacteristic
239C2×Dic79⋊C4C2312yes—
240C2×Dic79⋊C4C2312yes—
241C2×Dic79⋊C4C2311yescharacteristic
242C2×Dic79⋊C4C2318yes—
243C2×Dic79⋊C4C2318yes—
244C2×Dic79⋊C4C2318yes—
245C4⋊C4×D79C2318yes—
246C4⋊C4×D79C2318yes—
247C2×C22⋊Dic79C2312yes—
248C2×(C2×D79)⋊C4C2311yescharacteristic
249C2×(C2×D79)⋊C4C2311yescharacteristic
250C2×(C2×D79)⋊C4C2318yes—
251C2×(C2×D79)⋊C4C2318yes—
252C2×(C2×D79)⋊C4C2318yes—
253C2×(C2×D79)⋊C4C2318yes—
254C22⋊C4×D79C23116yes—
255C2×C4×Dic79C2312yes—
256C2×C4×Dic79C2312yes—
257C2×C4×Dic79C2311yescharacteristic
258C2×C4×Dic79C2318yes—
259C42×D79C2318yes—
260C22×Q8×C79C2314yes—
261C22×D4×C79C2311yescharacteristic
262C23×C4×C79C2312yes—
263C4⋊Q8×C79C2312yes—
264C4⋊Q8×C79C2312yes—
265C4⋊Q8×C79C2318yes—
266#125×C79C2314yes—
267#125×C79C2318yes—
268C22⋊Q8×C79C2314yes—
269C22⋊Q8×C79C2314yes—
270C22⋊Q8×C79C23116yes—
271C22⋊Q8×C79C2318yes—
272C22⋊Q8×C79C2318yes—
273C22⋊Q8×C79C2318yes—
274C22⋊Q8×C79C23116yes—
275C4×Q8×C79C2314yes—
276C4×Q8×C79C2314yes—
277C4×D4×C79C2314yes—
278C4×D4×C79C2314yes—
279C4×D4×C79C2318yes—
280C4×D4×C79C2318yes—
281#117×C79C2314yes—
282C2×C4⋊C4×C79C2311yescharacteristic
283C2×C4⋊C4×C79C2318yes—
284C2×C4⋊C4×C79C2314yes—
285C2×C22⋊C4×C79C2312yes—
286C2×C22⋊C4×C79C2318yes—
287C2×C42×C79C2311yescharacteristic
288C23×D79C2418yes—
289C23×D79C2411yescharacteristic
290#11929625—88no—
291#11929624—216no—
292#11929623—232no—
293#11929623—232no—
294C2×Dic158—24no—
295C2×Dic158C2414yes—
296C2×Dic158C2414yes—
297C2×D316—84no—
298C2×D316C2414yes—
299C2×D316C2418yes—
300C2×D316C2418yes—
301C2×D316C2414yes—
302C2×D316C2418yes—
303C2×D316C2414yes—
304C2×C22⋊D79—28no—
305C2×C22⋊D79—232no—
306C2×C22⋊D79C2418yes—
307C2×C22⋊D79C24116yes—
308C2×C22⋊D79C2418yes—
309D4×D79—232no—
310C22×Dic79—28no—
311C22×Dic79—82no—
312C22×Dic79C2412yes—
313C22×Dic79C2418yes—
314C22×Dic79C2418yes—
315C22×Dic79C2411yescharacteristic
316C22×Dic79C2411yescharacteristic
317C22×Dic79C2411yescharacteristic
318C22×Dic79C2418yes—
319C22×Dic79C2412yes—
320C2×C4×D79—24no—
321C2×C4×D79—82no—
322C2×C4×D79—88no—
323C2×C4×D79C2414yes—
324C2×C4×D79C2418yes—
325C2×C4×D79C24116yes—
326C2×C4×D79C2418yes—
327C2×C4×D79C2418yes—
328C2×C4×D79C2418yes—
329C4⋊Dic79C2414yes—
330C4⋊Dic79C2414yes—
331C4⋊Dic79C2418yes—
332C4⋊Dic79C2418yes—
333C4⋊Dic79C2418yes—
334C4⋊Dic79C24116yes—
335C4⋊Dic79C24116yes—
336C4⋊Dic79C2414yes—
337Dic79⋊C4C2418yes—
338Dic79⋊C4C24116yes—
339Dic79⋊C4C2412yes—
340Dic79⋊C4C2412yes—
341Dic79⋊C4C2418yes—
342Dic79⋊C4C2414yes—
343Dic79⋊C4C2414yes—
344Dic79⋊C4C2418yes—
345Dic79⋊C4C2414yes—
346Dic79⋊C4C2418yes—
347C22⋊Dic79C2418yes—
348(C2×D79)⋊C4C2418yes—
349(C2×D79)⋊C4C24116yes—
350(C2×D79)⋊C4C2418yes—
351(C2×D79)⋊C4C2418yes—
352(C2×D79)⋊C4C2418yes—
353(C2×D79)⋊C4C2418yes—
354(C2×D79)⋊C4C2414yes—
355(C2×D79)⋊C4C2412yes—
356(C2×D79)⋊C4C2412yes—
357(C2×D79)⋊C4C24116yes—
358(C2×D79)⋊C4C24116yes—
359(C2×D79)⋊C4C24116yes—
360(C2×D79)⋊C4C2418yes—
361(C2×D79)⋊C4C2418yes—
362(C2×D79)⋊C4C2418yes—
363C4×Dic79C2414yes—
364C4×Dic79C2418yes—
365C4×Dic79C2418yes—
366C4×Dic79C2418yes—
367C4×Dic79C2418yes—
368C4×Dic79C24116yes—
369C24×C79C2412yes—
370C2×Q8×C79—84no—
371C2×Q8×C79C2418yes—
372C2×Q8×C79C2414yes—
373C2×Q8×C79C2414yes—
374C2×D4×C79#4118yescomplemented
375C2×D4×C79C2414yes—
376C22×C4×C79—82no—
377C22×C4×C79C2411yescharacteristic
378C22×C4×C79C2411yescharacteristic
379C22×C4×C79C2418yes—
380C22×C4×C79C2418yes—
381C22×C4×C79C2412yes—
382C22×C4×C79C2414yes—
383C22×C4×C79C2414yes—
384C22×C4×C79C2411yescharacteristic
385C4⋊C4×C79C2418yes—
386C4⋊C4×C79C2414yes—
387C4⋊C4×C79C2414yes—
388C4⋊C4×C79C2418yes—
389C4⋊C4×C79C24116yes—
390C4⋊C4×C79C2414yes—
391C4⋊C4×C79C2414yes—
392C4⋊C4×C79C2418yes—
393C4⋊C4×C79C2414yes—
394C22⋊C4×C79C2418yes—
395C22⋊C4×C79C24116yes—
396C22⋊C4×C79C2418yes—
397C42×C79C2412yes—
398C42×C79C2412yes—
399C42×C79C2418yes—
400C23×C79—42no—
401C23×C79—42no—
402C23×C79C2×#4118yes—
403C23×C79C2514yes—
404C23×C79C2511yescharacteristic
405C22×D79—22no—
406C22×D79—216no—
407C22×D79—41no—
408C22×D79—41no—
409C22×D79—48no—
410C22×D79—48no—
411C22×D79C2518yes—
412C22×D79C2512yes—
413Q8×C79—48no—
414Q8×C79—44no—
415Q8×C79—44no—
416D4×C79C2×#41116yes—
417C2×C4×C79—42no—
418C2×C4×C79—48no—
419C2×C4×C79—44no—
420C2×C4×C79—41no—
421C2×C4×C79—44no—
422C2×C4×C79—48no—
423C2×C4×C79—41no—
424C2×C4×C79C2×#4114yes—
425C2×C4×C79C2512yes—
426C2×C4×C79C2518yes—
427C2×C4×C79C2514yes—
428C2×C4×C79C2518yes—
429C2×C4×C79C2511yescharacteristic
430C2×C4×C79C2511yescharacteristic
431C2×C4×C79C2512yes—
432C22⋊D79—232no—
433C22⋊D79—216no—
434C22⋊D79—216no—
435C2×Dic79—22no—
436C2×Dic79—24no—
437C2×Dic79—216no—
438C2×Dic79—216no—
439C2×Dic79—42no—
440C2×Dic79—48no—
441C2×Dic79—41no—
442C2×Dic79—41no—
443C2×Dic79C2512yes—
444C2×Dic79C2512yes—
445C2×Dic79C2514yes—
446C2×Dic79C2514yes—
447C2×Dic79C2518yes—
448C2×Dic79C2512yes—
449D316—28no—
450D316—44no—
451D316—48no—
452D316—48no—
453D316—44no—
454D316—48no—
455C4×D79—28no—
456C4×D79—216no—
457C4×D79—48no—
458C4×D79—48no—
459C4×D79—416no—
460C4×D79—48no—
461Dic158—28no—
462Dic158—28no—
463C22×C79—24no—
464C22×C79—21no—
465C22×C79—24no—
466C22×C79—21no—
467C22×C79—48no—
468C22×C79C22×#4112yes—
469C22×C79C22×#4118yes—
470C22×C79C2611yescharacteristic
471C2×D79—22no—
472C2×D79—28no—
473C2×D79—28no—
474C2×D79—22no—
475C2×D79—28no—
476C2×D79—22no—
477C2×D79—44no—
478C2×D79—816no—
479C4×C79—21no—
480C4×C79—21no—
481C4×C79—24no—
482C4×C79—28no—
483C4×C79—28no—
484C4×C79—22no—
485C4×C79C22×#4114yes—
486Dic79—28no—
487Dic79—24no—
488Dic79—22no—
489Dic79—24no—
490Dic79—22no—
491Dic79—22no—
492#62847—791nomaximal, Sylow
493C2×C79—22no—
494C2×C79—28no—
495C2×C79C23×#4111yescharacteristic
496C2×C79H(7,𝔽2)11yescharacteristic
497C2×C792−1+611yescharacteristic
498D79—42no—
499D79—48no—
500#3521—798no—
501#3520—798no—
502#3515—798no—
503#3513—798no—
504#3507—792no—
505#3505—794no—
506#3501D7911yescharacteristic, complemented
507#3496—791no—
508#3492—792no—
509#3491—794no—
510#3485—792no—
511#3461—792no—
512#3459—794no—
513#3455—792no—
514C2×#539—794no—
515C4×H(5,𝔽2)—792no—
516C2×#520—791no—
517C79#6284711yescharacteristic, complemented, Sylow
518C2×H(5,𝔽2)—792no—
519C22×#41—791no—
520#559—794no—
521#557—794no—
522#556—794no—
523#556—798no—
524#554—798no—
525#554—794no—
526#554C2×D7918yescomplemented
527#554C2×D7914yescomplemented
528#553—798no—
529#553—7916no—
530#553—798no—
531#552—798no—
532#552—798no—
533#552—7916no—
534#552—7916no—
535#552—798no—
536#551—7916no—
537#551—7916no—
538#551—7916no—
539D4×Q8C2×D7914yescomplemented
540#548—798no—
541#547—798no—
542#547—798no—
543#547—798no—
544#547—794no—
545#546—798no—
546#546—798no—
547#546—798no—
548#546—798no—
549D42—794no—
550#544C2×D7912yescomplemented
551#543C2×D7914yescomplemented
552#542—794no—
553#542—794no—
554#542—798no—
555#541—794no—
556#541—798no—
557#540—794no—
558#539—794no—
559#539—798no—
560#539—798no—
561#539—798no—
562#539—7916no—
563#539—7916no—
564#539—794no—
565#539—7916no—
566#538—794no—
567#538—794no—
568#538—7916no—
569#537—792no—
570#536—794no—
571#534—798no—
572#534—794no—
573#533—798no—
574#533C2×D7912yescomplemented
575#532—792no—
576#529—798no—
577#529—798no—
578#529—7916no—
579#529—798no—
580#529—798no—
581#529—798no—
582C2×#126—798no—
583C2×#125—798no—
584#525—798no—
585#525—7916no—
586#525—794no—
587C2×#123—798no—
588C2×#123—798no—
589C2×C22⋊Q8—798no—
590C2×C22⋊Q8C2×D7914yescomplemented
591C2×#121—794no—
592#520—798no—
593#520—798no—
594#520—798no—
595#520—794no—
596#518—798no—
597#518—798no—
598#518C2×D7912yes—
599C4×#41—798no—
600C4×#41—794no—
601C2×C4×Q8—791no—
602C2×C4×Q8—791no—
603C2×C4×D4—791no—
604C2×C4×D4—792no—
605C2×C4×D4—798no—
606C2×C4×D4—792no—
607C2×C4×D4—798no—
608C2×C4×D4C2×D7911yescharacteristic
609C2×#117—792no—
610C2×#117—791no—
611C22×C4⋊C4—792no—
612C22×C4⋊C4—791no—
613H(5,𝔽2)—15816no—
614C2×#41—798no—
615C2×#41—798no—
616C2×#41—798no—
617C2×#41—794no—
618C2×#41—1588no—
619C22×Q8—791no—
620C22×Q8C22×D7914yes—
621C22×D4—792no—
622C22×D4—798no—
623C22×D4—798no—
624C22×D4—794no—
625C22×D4C22×D7911yescharacteristic
626C23×C4—792no—
627C23×C4—792no—
628C23×C4—792no—
629C23×C4—798no—
630C23×C4—791no—
631C23×C4C22×D7912yes—
632C4⋊Q8—792no—
633C4⋊Q8—798no—
634C4⋊Q8C22×D7918yes—
635C4⋊Q8C22×D7912yes—
636C4⋊Q8C22×D7912yes—
637#127—792no—
638#126—798no—
639#126—7916no—
640#126—7916no—
641#126—7916no—
642#126—798no—
643#126—7916no—
644#126—798no—
645#126—798no—
646#126—7916no—
647#125—798no—
648#125—7916no—
649#125—7916no—
650#125—7916no—
651#125—798no—
652#125—798no—
653#125—798no—
654#125C22×D7918yes—
655#125C22×D7914yes—
656#124—798no—
657#124—798no—
658#124—798no—
659#124—798no—
660#124—798no—
661#124—794no—
662#123—798no—
663#123—7916no—
664#123—7916no—
665#123—7916no—
666#123—798no—
667#123—7916no—
668#123—798no—
669#123—798no—
670#123—798no—
671#123—7916no—
672#123—7916no—
673#123—7916no—
674#123—7916no—
675#123—7916no—
676C22⋊Q8—798no—
677C22⋊Q8—7916no—
678C22⋊Q8—7916no—
679C22⋊Q8—7916no—
680C22⋊Q8—798no—
681C22⋊Q8—798no—
682C22⋊Q8—794no—
683C22⋊Q8—794no—
684C22⋊Q8—798no—
685C22⋊Q8—798no—
686C22⋊Q8—798no—
687C22⋊Q8C22×D7914yes—
688C22⋊Q8C22×D7918yes—
689C22⋊Q8C22×D7918yes—
690C22⋊Q8C22×D7918yes—
691C22⋊Q8C22×D79116yes—
692C22⋊Q8C22×D7914yes—
693C22⋊Q8C22×D79116yes—
694#121—794no—
695#121—798no—
696#121—798no—
697#121—798no—
698#121—7916no—
699#121—794no—
700#121—7916no—
701#121—798no—
702#121—798no—
703#121—794no—
704#121—794no—
705#121—798no—
706#121—798no—
707#120—798no—
708#120—7916no—
709#120—7916no—
710C4×Q8—798no—
711C4×Q8—798no—
712C4×Q8—798no—
713C4×Q8—794no—
714C4×Q8—794no—
715C4×Q8—794no—
716C4×Q8—794no—
717C4×Q8—798no—
718C4×Q8C22×D7914yes—
719C4×Q8C22×D7914yes—
720C4×D4—798no—
721C4×D4—7916no—
722C4×D4—798no—
723C4×D4—798no—
724C4×D4—7916no—
725C4×D4—794no—
726C4×D4—794no—
727C4×D4—798no—
728C4×D4—7916no—
729C4×D4—798no—
730C4×D4—7916no—
731C4×D4—798no—
732C4×D4—7916no—
733C4×D4—7916no—
734C4×D4—7916no—
735C4×D4—798no—
736C4×D4—798no—
737C4×D4—798no—
738C4×D4—798no—
739C4×D4—794no—
740C4×D4—794no—
741C4×D4C22×D7918yes—
742C4×D4C22×D7914yes—
743C4×D4C22×D7914yes—
744C4×D4C22×D7918yes—
745#117—798no—
746#117—7916no—
747#117—798no—
748#117—7916no—
749#117—7916no—
750#117—7916no—
751#117—794no—
752#117—794no—
753#117—798no—
754#117C22×D7914yes—
755C2×C4⋊C4—791no—
756C2×C4⋊C4—792no—
757C2×C4⋊C4—791no—
758C2×C4⋊C4—792no—
759C2×C4⋊C4—792no—
760C2×C4⋊C4—798no—
761C2×C4⋊C4—798no—
762C2×C4⋊C4—791no—
763C2×C4⋊C4—798no—
764C2×C4⋊C4—794no—
765C2×C4⋊C4—798no—
766C2×C4⋊C4—798no—
767C2×C4⋊C4—798no—
768C2×C4⋊C4—798no—
769C2×C4⋊C4C22×D7911yescharacteristic
770C2×C4⋊C4C22×D7918yes—
771C2×C4⋊C4C22×D7914yes—
772C2×C22⋊C4—792no—
773C2×C22⋊C4—791no—
774C2×C22⋊C4—791no—
775C2×C22⋊C4—798no—
776C2×C22⋊C4—798no—
777C2×C22⋊C4—798no—
778C2×C22⋊C4—798no—
779C2×C22⋊C4—7916no—
780C2×C22⋊C4C22×D7912yes—
781C2×C22⋊C4C22×D7918yes—
782C2×C42—791no—
783C2×C42—792no—
784C2×C42—792no—
785C2×C42—798no—
786C2×C42—798no—
787C2×C42C22×D7911yescharacteristic
788C24—798no—
789C24—791no—
790C24C23×D7912yes—
791#41—6328no—
792#41—15832no—
793#41—15832no—
794#41—15816no—
795C2×Q8—84no—
796C2×Q8—794no—
797C2×Q8—794no—
798C2×Q8—1584no—
799C2×Q8C23×D7914yes—
800C2×Q8C23×D7918yes—
801C2×Q8C23×D7914yes—
802C2×D4—798no—
803C2×D4—7916no—
804C2×D4—798no—
805C2×D4—794no—
806C2×D4—798no—
807C2×D4—798no—
808C2×D4—798no—
809C2×D4—794no—
810C2×D4—794no—
811C2×D4—6324no—
812C2×D4—1588no—
813C2×D4—15832no—
814C2×D4—15832no—
815C2×D4#1192962518yescomplemented
816C2×D4C23×D7914yes—
817C22×C4—82no—
818C22×C4—791no—
819C22×C4—798no—
820C22×C4—791no—
821C22×C4—792no—
822C22×C4—798no—
823C22×C4—798no—
824C22×C4—7916no—
825C22×C4—798no—
826C22×C4—792no—
827C22×C4—798no—
828C22×C4—798no—
829C22×C4—791no—
830C22×C4—798no—
831C22×C4—794no—
832C22×C4—6322no—
833C22×C4—6328no—
834C22×C4—6322no—
835C22×C4—1588no—
836C22×C4—1584no—
837C22×C4C23×D7911yescharacteristic
838C22×C4C23×D7918yes—
839C22×C4C23×D7912yes—
840C22×C4C23×D7911yescharacteristic
841C22×C4C23×D7914yes—
842C22×C4C23×D7918yes—
843C22×C4C23×D7914yes—
844C22×C4C23×D7911yescharacteristic
845C4⋊C4—792no—
846C4⋊C4—798no—
847C4⋊C4—792no—
848C4⋊C4—794no—
849C4⋊C4—798no—
850C4⋊C4—794no—
851C4⋊C4—7916no—
852C4⋊C4—798no—
853C4⋊C4—794no—
854C4⋊C4—798no—
855C4⋊C4—794no—
856C4⋊C4—794no—
857C4⋊C4—798no—
858C4⋊C4—798no—
859C4⋊C4—798no—
860C4⋊C4—7916no—
861C4⋊C4—7916no—
862C4⋊C4—794no—
863C4⋊C4C23×D7914yes—
864C4⋊C4C23×D7914yes—
865C4⋊C4C23×D7918yes—
866C4⋊C4C23×D7914yes—
867C4⋊C4C23×D7918yes—
868C4⋊C4C23×D79116yes—
869C4⋊C4C23×D7914yes—
870C4⋊C4C23×D7918yes—
871C4⋊C4C23×D7914yes—
872C22⋊C4—798no—
873C22⋊C4—7916no—
874C22⋊C4—798no—
875C22⋊C4—798no—
876C22⋊C4—798no—
877C22⋊C4—798no—
878C22⋊C4—798no—
879C22⋊C4—792no—
880C22⋊C4—794no—
881C22⋊C4—792no—
882C22⋊C4—7916no—
883C22⋊C4—7916no—
884C22⋊C4—7916no—
885C22⋊C4—798no—
886C22⋊C4—798no—
887C22⋊C4—798no—
888C22⋊C4C23×D79116yes—
889C22⋊C4C23×D7918yes—
890C22⋊C4C23×D7918yes—
891C42—794no—
892C42—798no—
893C42—7916no—
894C42—798no—
895C42—798no—
896C42—798no—
897C42C23×D7918yes—
898C42C23×D7912yes—
899C42C23×D7912yes—
900C23—42no—
901C23—42no—
902C23—3161no—
903C23—3161no—
904C23—3168no—
905C23—3168no—
906C23—798no—
907C23—792no—
908C23—1582no—
909C23—15816no—
910C23C2×#1192962518yes—
911C23C24×D7914yes—
912C23C24×D7911yescharacteristic
913Q8—44no—
914Q8—48no—
915Q8—44no—
916Q8—1588no—
917Q8—1588no—
918D4—3164no—
919D4—3168no—
920D4—3168no—
921D4—3168no—
922D4—3164no—
923D4—15832no—
924D4—15816no—
925D4—15816no—
926D4—1588no—
927D4C2×#11929625116yes—
928C2×C4—41no—
929C2×C4—42no—
930C2×C4—44no—
931C2×C4—44no—
932C2×C4—48no—
933C2×C4—48no—
934C2×C4—41no—
935C2×C4—3168no—
936C2×C4—3168no—
937C2×C4—31616no—
938C2×C4—3168no—
939C2×C4—3168no—
940C2×C4—3162no—
941C2×C4—3161no—
942C2×C4—3161no—
943C2×C4—792no—
944C2×C4—792no—
945C2×C4—794no—
946C2×C4—794no—
947C2×C4—798no—
948C2×C4—792no—
949C2×C4—1582no—
950C2×C4—1584no—
951C2×C4—15816no—
952C2×C4—15816no—
953C2×C4—1588no—
954C2×C4—15816no—
955C2×C4C2×#1192962514yes—
956C2×C4C24×D7912yes—
957C2×C4C24×D7918yes—
958C2×C4C24×D7914yes—
959C2×C4C24×D7918yes—
960C2×C4C24×D7911yescharacteristic
961C2×C4C24×D7911yescharacteristic
962C2×C4C24×D7912yes—
963C22—24no—
964C22—21no—
965C22—24no—
966C22—21no—
967C22—48no—
968C22—3164no—
969C22—63216no—
970C22—1582no—
971C22—1588no—
972C22—1582no—
973C22—1588no—
974C22—1588no—
975C22—1582no—
976C22C22×#1192962518yes—
977C22C22×#1192962512yes—
978C22C25×D7911yescharacteristic
979C4—21no—
980C4—21no—
981C4—24no—
982C4—28no—
983C4—28no—
984C4—22no—
985C4—1582no—
986C4—1588no—
987C4—1584no—
988C4—1582no—
989C4—1584no—
990C4—1582no—
991C4C22×#1192962514yes—
992C2—22no—
993C2—28no—
994C2—3162no—
995C2—3168no—
996C2C23×#1192962511yescharacteristic
997C2#2377821011yescharacteristic
998C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3501C2
hypercenter#3501D79
hypocenterC79#62847
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3501

Complements

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

NH ≅ G/Ntype
1. #23777471C2semidirect
2. #23777450C2semidirect
3. #23777379C2semidirect
4. #23777343C2semidirect
5. #23777267C2semidirect
6. #23777241C2semidirect
7. #23777164C2semidirect
8. #23777110C2semidirect
9. #23777099C2semidirect
10. #23777045C2semidirect
11. #23776834C2semidirect
12. #23776812C2semidirect
13. #23776792C2semidirect
14. C2×#19099162C2semidirect
15. #23776604C2semidirect
16. C2×#19099042C2semidirect
17. C79×#3501C2semidirect
20. #19099298C22semidirect
21. #19099292C22semidirect
22. #19099287C22semidirect
23. #19099286C22semidirect
24. #19099274C22semidirect
25. #19099274C22semidirect
26. #19099266C22semidirect
27. #19099261C22semidirect
28. #19099261C22semidirect
29. #19099255C22semidirect
30. #19099255C22semidirect
31. #19099255C22semidirect
32. #19099251C22semidirect
33. #19099251C22semidirect
34. #19099240C22semidirect
35. #19099240C22semidirect
36. #19099240C22semidirect
37. #19099224C22semidirect
38. #19099217C22semidirect
39. #19099217C22semidirect
40. #19099217C22semidirect
41. #19099216C22semidirect
42. #19099208C22semidirect
43. #19099208C22semidirect
44. #19099208C22semidirect
45. #19099204C22semidirect
46. D4×D316C22semidirect
47. #19099187C22semidirect
48. #19099187C22semidirect
49. #19099187C22semidirect
50. #19099176C22semidirect
51. #19099176C22semidirect
52. #19099169C22semidirect
53. #19099162C22semidirect
54. #19099162C22semidirect
55. #19099162C22semidirect
56. #19099162C22semidirect
57. #19099162C22semidirect
58. #19099162C22semidirect
59. #19099162C22semidirect
60. #19099162C22semidirect
61. #19099153C22semidirect
62. #19099153C22semidirect
63. #19099153C22semidirect
65. #19099139C22semidirect
67. #19099125C22semidirect
68. #19099118C22semidirect
70. #19099100C22semidirect
71. #19099100C22semidirect
72. #19099099C22semidirect
73. #19099099C22semidirect
74. #19099099C22semidirect
75. #19099098C22semidirect
76. C2×#14579156C22semidirect
77. C2×#14579152C22semidirect
78. #19099076C22semidirect
79. #19099076C22semidirect
80. #19099075C22semidirect
81. C2×#14579146C22semidirect
82. C2×#14579145C22semidirect
83. C2×#14579137C22semidirect
85. #19099043C22semidirect
86. #19099042C22semidirect
87. #19099042C22semidirect
88. #19099042C22semidirect
89. #19099036C22semidirect
90. #19099035C22semidirect
91. #19099031C22semidirect
92. C4×#11929623C22semidirect
93. C2×C4×Dic158C22semidirect
94. C2×#14579126C22semidirect
96. C2×C4×C22⋊D79C22semidirect
97. C2×(C22⋊D79)⋊C4C22semidirect
98. C2×(C22⋊D79)⋊C4C22semidirect
99. C4×D4×D79C22semidirect
100. C2×#14579118C22semidirect
101. C2×#14579117C22semidirect
102. C22×Dic79⋊C4C22semidirect
103. C2×C4⋊C4×D79C22semidirect
104. #554×C79C22semidirect
105. #554×C79C22semidirect
106. D4×Q8×C79C22semidirect
107. #544×C79C22semidirect
108. #543×C79C22semidirect
109. #533×C79C22semidirect
110. C2×C22⋊Q8×C79C22semidirect
374. C2×D4×C79#41semidirect
506. #3501D79semidirect
517. C79#62847semidirect
526. #554C2×D79semidirect
527. #554C2×D79semidirect
539. D4×Q8C2×D79semidirect
550. #544C2×D79semidirect
551. #543C2×D79semidirect
574. #533C2×D79semidirect
590. C2×C22⋊Q8C2×D79semidirect
815. C2×D4#11929625semidirect

Maximal subgroups

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

subgroupindex
#237774712
#237774502
#237773792
#237773432
#237772672
#237772412
#237771642
#237771102
#237770992
#237770452
#237768342
#237768122
#237767922
C2×#190991622
#237766042
C2×#190990422
C79×#35012
#6284779