Finite Group Databasebeta

← #35196857

Subgroups — #35196857

Order 20224.

7210 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777321C214yesmaximal, complemented
2#23777309C214yesmaximal, complemented
3#23777299C212yesmaximal, complemented
4#23777295C212yesmaximal, complemented
5#23777285C212yesmaximal, complemented
6#23777275C212yesmaximal, complemented
7#23777264C214yesmaximal, complemented
8#23777251C214yesmaximal, complemented
9#23777237C218yesmaximal, complemented
10#23776997C218yesmaximal, complemented
11#23776960C218yesmaximal, complemented
12#23776788C214yesmaximal, complemented
13#23776729C211yesmaximal, characteristic, complemented
14#23776692C214yesmaximal, complemented
15C2×#19099116C211yesmaximal, characteristic, complemented
16C2×#19099109C211yesmaximal, characteristic, complemented
17#23776603C211yesmaximal, characteristic, complemented
18#23776601C211yesmaximal, characteristic, complemented
19C2×#41×Dic79C211yesmaximal, characteristic, complemented
20C79×#3449C211yesmaximal, characteristic, complemented
21C22×#11929624C2211yescharacteristic
22#19099299C2218yescomplemented
23#19099295C2218yescomplemented
24#19099295C2218yescomplemented
25#19099288C2218yescomplemented
26#19099287C2218yescomplemented
27#19099284C2218yescomplemented
28#19099282C2218yescomplemented
29#19099282C2218yescomplemented
30#19099277C2218yescomplemented
31#19099271C2218yescomplemented
32#19099265C2218yescomplemented
33#19099265C22116yescomplemented
34#19099260C2218yescomplemented
35#19099256C22116yescomplemented
36#19099256C22116yescomplemented
37#19099255C2218yescomplemented
38#19099250C22116yescomplemented
39#19099247C2218yescomplemented
40#19099244C22116yescomplemented
41#19099236C22116yescomplemented
42#19099233C2218yescomplemented
43#19099219C22116yescomplemented
44#19099213C2218yescomplemented
45#19099200C22116yescomplemented
46#19099186C2218yescomplemented
47#19099180C2218yescomplemented
48#19099173C2218yescomplemented
49#19099166C2218yescomplemented
50#19099157C22116yescomplemented
51#19099148C22116yescomplemented
52#19099141C2214yescomplemented
53#19099137C2212yescomplemented
54#19099134C2212yes—
55#19099130C2212yescomplemented
56#19099127C2212yes—
57#19099122C2214yes—
58#19099116C2212yescomplemented
59#19099116C2212yescomplemented
60#19099116C2212yescomplemented
61#19099116C2212yescomplemented
62#19099116C2214yescomplemented
63#19099116C2214yescomplemented
64#19099115C2218yescomplemented
65#19099109C2212yes—
66#19099109C2212yes—
67#19099109C2214yes—
68#19099109C2212yescomplemented
69#19099109C2212yescomplemented
70#19099109C2214yescomplemented
71#19099109C2214yescomplemented
72#19099108C2218yescomplemented
73C2×#14579160C2212yescomplemented
74C2×#14579159C2211yescharacteristic, complemented
75C2×#14579157C2211yescharacteristic, complemented
76#19099099C2218yescomplemented
77#19099095C22116yescomplemented
78#19099094C2218yescomplemented
79#19099093C22116yescomplemented
80#19099093C22116yescomplemented
81#19099090C22116yescomplemented
82C2×#14579152C2212yescomplemented
83C2×#14579150C2211yescharacteristic, complemented
84C2×#14579148C2211yescharacteristic, complemented
85#19099074C2214yescomplemented
86#19099070C2214yes—
87#19099069C22116yescomplemented
88C2×#14579138C2214yes—
89C2×#14579133C2214yes—
90#19099046C2214yescomplemented
91#19099046C2214yescomplemented
92#19099044C2214yescomplemented
93#19099043C2214yescomplemented
94#19099041C2212yescomplemented
95#19099040C2212yescomplemented
96#19099038C2214yes—
97#19099038C2212yescomplemented
98#19099037C2212yescomplemented
99#19099036C2214yes—
100#41×Dic79C2212yes—
101#41×Dic79C2212yes—
102#41×Dic79C2214yes—
103#41×Dic79C2214yescomplemented
104#41×Dic79C2212yescomplemented
105#41×Dic79C2212yescomplemented
106#41×Dic79C2214yescomplemented
107#41×Dic79C2214yescomplemented
108C4×#11929624C2214yescomplemented
109#19099031C2214yescomplemented
110C4×#11929623C22116yescomplemented
111C2×Q8×Dic79C2212yescomplemented
112C2×C4×Dic158C2214yescomplemented
113C2×D4×Dic79C2214yes—
114C2×D4×Dic79C2212yescomplemented
115C2×C4×C22⋊D79C2214yescomplemented
116C2×#14579120C2211yescharacteristic
117C2×#14579120C2211yescharacteristic
118C2×#14579120C2212yescomplemented
119C2×#14579120C2214yescomplemented
120#117×D79C2214yescomplemented
121C22×C4×Dic79C2211yescharacteristic
122C22×C4×Dic79C2212yescomplemented
123C22×#41×C79C2211yescharacteristic
124C22×#41×C79C2211yescharacteristic
125#537×C79C2214yescomplemented
126#536×C79C2212yes—
127#536×C79C2212yescomplemented
128#535×C79C2212yes—
129#535×C79C2212yescomplemented
130#534×C79C2214yes—
131#532×C79C2214yescomplemented
132#525×C79C2214yes—
133#525×C79C2214yescomplemented
134C2×#117×C79C2211yescharacteristic
135C2×#11929624—28no—
136C2×#11929624C2312yes—
137C2×#11929624C2312yes—
138C2×#11929624C2312yes—
139C2×#11929624C2312yes—
140C2×#11929623C23116yes—
141C22×Dic158C2311yescharacteristic
142C22×Dic158C2314yes—
143C22×D316C2311yescharacteristic
144C22×C22⋊D79C2312yes—
145C22×C22⋊D79C2314yes—
146C23×Dic79C2312yes—
147C23×Dic79C2314yes—
148C22×C4×D79C2312yes—
149#14579160C2314yes—
150#14579160C2314yes—
151#14579160C2314yes—
152#14579160C2314yes—
153#14579159C2314yes—
154#14579159C2312yes—
155#14579159C2314yes—
156#14579159C2312yes—
157#14579157C2312yes—
158#14579157C2314yes—
159#14579157C2314yes—
160#14579157C2312yes—
161#14579156C23116yes—
162#14579156C23116yes—
163#14579154C23116yes—
164#14579154C23116yes—
165#14579154C23116yes—
166#14579154C23116yes—
167#14579152C23116yes—
168#14579152C2314yes—
169#14579152C2314yes—
170#14579152C2314yes—
171#14579152C2314yes—
172#14579151C23116yes—
173#14579151C23116yes—
174#14579150C2314yes—
175#14579150C2312yes—
176#14579150C2314yes—
177#14579150C2312yes—
178#14579148C23116yes—
179#14579148C2312yes—
180#14579148C2314yes—
181#14579148C2314yes—
182#14579148C2312yes—
183#14579147C23116yes—
184#14579147C23116yes—
185#14579145C23116yes—
186#14579145C23116yes—
187#14579144C2318yes—
188#14579143C23116yes—
189#14579143C23116yes—
190#14579142C23116yes—
191#14579142C2318yes—
192#14579142C23116yes—
193#14579141C23116yes—
194#14579140C2318yes—
195#14579138C2318yes—
196#14579138C23116yes—
197#14579138C2318yes—
198#14579138C23116yes—
199#14579138C2318yes—
200#14579138C2318yes—
201#14579137C2318yes—
202#14579135C2318yes—
203#14579133C23116yes—
204#14579133C2318yes—
205#14579133C23116yes—
206#14579133C23116yes—
207#14579133C2318yes—
208#14579133C2318yes—
209#14579133C2318yes—
210#14579132C2318yes—
211#14579132C23116yes—
212#14579130C2318yes—
213#14579129C2318yes—
214Q8×Dic79C2318yes—
215Q8×Dic79C2314yes—
216Q8×Dic79C2314yes—
217Q8×Dic79C2314yes—
218Q8×Dic79C2318yes—
219Q8×Dic79C2314yes—
220C4×Dic158C2318yes—
221C4×Dic158C2318yes—
222C4×Dic158C2318yes—
223C4×Dic158C2318yes—
224C4×Dic158C2318yes—
225#14579126C2318yes—
226#14579126C23116yes—
227C4×D316C2318yes—
228D4×Dic79C23116yes—
229D4×Dic79C2318yes—
230D4×Dic79C2318yes—
231D4×Dic79C2314yes—
232D4×Dic79C2318yes—
233D4×Dic79C23116yes—
234D4×Dic79C2314yes—
235D4×Dic79C2318yes—
236D4×Dic79C2318yes—
237D4×Dic79C23116yes—
238D4×Dic79C2318yes—
239D4×Dic79C2314yes—
240D4×Dic79C2314yes—
241#14579123C2318yes—
242C4×C22⋊D79C2318yes—
243C4×C22⋊D79C23116yes—
244C4×C22⋊D79C2318yes—
245C4×C22⋊D79C2318yes—
246C4×C22⋊D79C2318yes—
247C4×C22⋊D79C23116yes—
248(C22⋊D79)⋊C4C23116yes—
249(C22⋊D79)⋊C4C23116yes—
250(C22⋊D79)⋊C4C23116yes—
251#14579120C2312yes—
252#14579120C2314yes—
253#14579120C2314yes—
254#14579120C2318yes—
255#14579120C2318yes—
256#14579120C2312yes—
257#14579120C2312yes—
258#14579120C2312yes—
259#14579120C2312yes—
260#14579120C2312yes—
261#14579120C2312yes—
262#14579120C2312yes—
263#14579120C2318yes—
264#14579120C2318yes—
265#14579119C23116yes—
266#14579119C2318yes—
267#14579118C2318yes—
268#14579117C2318yes—
269#14579117C23116yes—
270#14579117C23116yes—
271C2×C4⋊Dic79C2312yes—
272C2×C4⋊Dic79C2314yes—
273C2×C4⋊Dic79C2318yes—
274C2×C4⋊Dic79C2314yes—
275C2×C4⋊Dic79C2312yes—
276C2×Dic79⋊C4C2314yes—
277C2×Dic79⋊C4C2314yes—
278C2×Dic79⋊C4C2314yes—
279C4⋊C4×D79C2318yes—
280C2×C22⋊Dic79C2314yes—
281C2×C22⋊Dic79C2318yes—
282C2×C22⋊Dic79C2314yes—
283C2×C22⋊Dic79C2312yes—
284C2×C22⋊Dic79C2312yes—
285C2×(C2×D79)⋊C4C2314yes—
286C22⋊C4×D79C2318yes—
287C2×C4×Dic79C2311yescharacteristic
288C2×C4×Dic79C2311yescharacteristic
289C2×C4×Dic79C2312yes—
290C2×C4×Dic79C2312yes—
291C2×C4×Dic79C2312yes—
292C2×C4×Dic79C2311yescharacteristic
293C2×C4×Dic79C2311yescharacteristic
294C2×C4×Dic79C2311yescharacteristic
295C2×C4×Dic79C2311yescharacteristic
296C2×C4×Dic79C2312yes—
297C2×C4×Dic79C2314yes—
298C2×C4×Dic79C2318yes—
299C2×C4×Dic79C2314yes—
300C2×C4×Dic79C2314yes—
301C2×C4×Dic79C2312yes—
302C2×C4×Dic79C2318yes—
303C42×D79C2318yes—
304C2×#41×C79—28no—
305C2×#41×C79—28no—
306C2×#41×C79C2312yes—
307C2×#41×C79C2312yes—
308C2×#41×C79C2312yes—
309C2×#41×C79C2312yes—
310C2×#41×C79C2312yes—
311C2×#41×C79C2312yes—
312C2×#41×C79C2312yes—
313C2×#41×C79C2312yes—
314C22×Q8×C79C2311yescharacteristic
315C22×Q8×C79C2311yescharacteristic
316C22×D4×C79C2312yes—
317C22×D4×C79C2312yes—
318C22×D4×C79C2311yescharacteristic
319C22×D4×C79C2311yescharacteristic
320C23×C4×C79C2312yes—
321C23×C4×C79C2312yes—
322C23×C4×C79C2311yescharacteristic
323C4⋊Q8×C79C2314yes—
324#127×C79C2314yes—
325#124×C79C2314yes—
326#124×C79C2314yes—
327#123×C79C2318yes—
328#123×C79C2318yes—
329C22⋊Q8×C79C2318yes—
330C22⋊Q8×C79C2318yes—
331#121×C79C2318yes—
332#121×C79C2318yes—
333#121×C79C23116yes—
334#120×C79C2318yes—
335#120×C79C2318yes—
336C4×D4×C79C23116yes—
337#117×C79C2312yes—
338#117×C79C2312yes—
339#117×C79C2312yes—
340#117×C79C2312yes—
341C2×C4⋊C4×C79C2312yes—
342C2×C22⋊C4×C79C2312yes—
343C2×C42×C79C2312yes—
344C23×D79C2412yes—
345#11929624—28no—
346#11929624—28no—
347#11929624—28no—
348#11929624—28no—
349#11929623—432no—
350C2×Dic158—24no—
351C2×Dic158—48no—
352C2×Dic158C2418yes—
353C2×Dic158C2412yes—
354C2×Dic158C2412yes—
355C2×Dic158C2418yes—
356C2×D316—24no—
357C2×D316C2412yes—
358C2×D316C2412yes—
359C2×C22⋊D79—28no—
360C2×C22⋊D79—48no—
361C2×C22⋊D79C2418yes—
362C2×C22⋊D79C2414yes—
363C2×C22⋊D79C2414yes—
364C2×C22⋊D79C24116yes—
365C2×C22⋊D79C2418yes—
366C22×Dic79—44no—
367C22×Dic79—48no—
368C22×Dic79C2412yes—
369C22×Dic79C2412yes—
370C22×Dic79C2418yes—
371C22×Dic79C2412yes—
372C22×Dic79C2412yes—
373C22×Dic79C2414yes—
374C22×Dic79C24116yes—
375C22×Dic79C2412yes—
376C22×Dic79C2414yes—
377C22×Dic79C2412yes—
378C22×Dic79C2412yes—
379C22×Dic79C2418yes—
380C2×C4×D79—28no—
381C2×C4×D79C2414yes—
382C2×C4×D79C2414yes—
383C2×C4×D79C24116yes—
384C4⋊Dic79C2414yes—
385C4⋊Dic79C2414yes—
386C4⋊Dic79C2418yes—
387C4⋊Dic79C2414yes—
388C4⋊Dic79C2414yes—
389C4⋊Dic79C2418yes—
390C4⋊Dic79C24116yes—
391C4⋊Dic79C2418yes—
392C4⋊Dic79C2418yes—
393Dic79⋊C4C24116yes—
394Dic79⋊C4C2418yes—
395Dic79⋊C4C2418yes—
396Dic79⋊C4C2418yes—
397Dic79⋊C4C2418yes—
398Dic79⋊C4C2418yes—
399Dic79⋊C4C2418yes—
400Dic79⋊C4C24116yes—
401C22⋊Dic79C2414yes—
402C22⋊Dic79C2414yes—
403C22⋊Dic79C2418yes—
404C22⋊Dic79C2414yes—
405C22⋊Dic79C2414yes—
406C22⋊Dic79C2418yes—
407C22⋊Dic79C24116yes—
408C22⋊Dic79C2418yes—
409C22⋊Dic79C2418yes—
410C22⋊Dic79C24116yes—
411(C2×D79)⋊C4C24116yes—
412(C2×D79)⋊C4C2418yes—
413(C2×D79)⋊C4C2418yes—
414(C2×D79)⋊C4C24116yes—
415C4×Dic79C2414yes—
416C4×Dic79C24116yes—
417C4×Dic79C2412yes—
418C4×Dic79C2411yescharacteristic
419C4×Dic79C2411yescharacteristic
420C4×Dic79C2418yes—
421C4×Dic79C2412yes—
422C4×Dic79C2414yes—
423C4×Dic79C2414yes—
424C4×Dic79C2411yescharacteristic
425C4×Dic79C2411yescharacteristic
426C4×Dic79C2418yes—
427C4×Dic79C2412yes—
428C4×Dic79C2412yes—
429C4×Dic79C2412yes—
430C4×Dic79C2412yes—
431C4×Dic79C24116yes—
432C4×Dic79C2414yes—
433C24×C79C2412yes—
434C24×C79C2412yes—
435C24×C79C2411yescharacteristic
436#41×C79—28no—
437#41×C79—28no—
438#41×C79—28no—
439#41×C79—28no—
440#41×C79—28no—
441#41×C79—28no—
442#41×C79—28no—
443#41×C79—28no—
444C2×Q8×C79—24no—
445C2×Q8×C79—24no—
446C2×Q8×C79C2412yes—
447C2×Q8×C79C2412yes—
448C2×Q8×C79C2412yes—
449C2×Q8×C79C2412yes—
450C2×D4×C79—28no—
451C2×D4×C79—28no—
452C2×D4×C79—24no—
453C2×D4×C79—24no—
454C2×D4×C79C2414yes—
455C2×D4×C79C2414yes—
456C2×D4×C79C2412yes—
457C2×D4×C79C2414yes—
458C2×D4×C79C2414yes—
459C2×D4×C79C2412yes—
460C2×D4×C79C2412yes—
461C2×D4×C79C2412yes—
462C2×D4×C79C24116yes—
463C22×C4×C79—28no—
464C22×C4×C79—28no—
465C22×C4×C79#4118yescomplemented
466C22×C4×C79C2414yes—
467C22×C4×C79C2414yes—
468C22×C4×C79C2414yes—
469C22×C4×C79C2414yes—
470C22×C4×C79C2412yes—
471C22×C4×C79C2412yes—
472C22×C4×C79C2414yes—
473C22×C4×C79C2411yescharacteristic
474C22×C4×C79C2411yescharacteristic
475C22×C4×C79C2411yescharacteristic
476C22×C4×C79C2411yescharacteristic
477C22×C4×C79C2411yescharacteristic
478C22×C4×C79C2411yescharacteristic
479C4⋊C4×C79C2414yes—
480C4⋊C4×C79C2414yes—
481C4⋊C4×C79C24116yes—
482C22⋊C4×C79C2414yes—
483C22⋊C4×C79C2414yes—
484C22⋊C4×C79C24116yes—
485C22⋊C4×C79C24116yes—
486C42×C79C2414yes—
487C42×C79C2414yes—
488C23×C79—24no—
489C23×C79—24no—
490C23×C79—42no—
491C23×C79—44no—
492C23×C79—44no—
493C23×C79C2×#4114yes—
494C23×C79C2514yes—
495C23×C79C2514yes—
496C23×C79C2511yescharacteristic
497C23×C79C2511yescharacteristic
498C23×C79C2511yescharacteristic
499C22×D79—24no—
500C22×D79—44no—
501C22×D79C2514yes—
502Q8×C79—24no—
503Q8×C79—24no—
504Q8×C79—24no—
505Q8×C79—24no—
506D4×C79—28no—
507D4×C79—28no—
508D4×C79—28no—
509D4×C79—28no—
510D4×C79—24no—
511D4×C79—24no—
512D4×C79—24no—
513D4×C79—24no—
514D4×C79—416no—
515C2×C4×C79—24no—
516C2×C4×C79—24no—
517C2×C4×C79—28no—
518C2×C4×C79—28no—
519C2×C4×C79—28no—
520C2×C4×C79—28no—
521C2×C4×C79—44no—
522C2×C4×C79C2×#4114yes—
523C2×C4×C79C2×#4114yes—
524C2×C4×C79C2×#4114yes—
525C2×C4×C79C2×#4114yes—
526C2×C4×C79C2×#4114yes—
527C2×C4×C79C2×#4114yes—
528C2×C4×C79C2514yes—
529C2×C4×C79C2514yes—
530C2×C4×C79C2518yes—
531C2×C4×C79C2511yescharacteristic
532C2×C4×C79C2511yescharacteristic
533C2×C4×C79C2511yescharacteristic
534C2×C4×C79C2511yescharacteristic
535C22⋊D79—28no—
536C22⋊D79—28no—
537C22⋊D79—216no—
538C22⋊D79—48no—
539C22⋊D79—416no—
540C2×Dic79—24no—
541C2×Dic79—24no—
542C2×Dic79—24no—
543C2×Dic79—24no—
544C2×Dic79—216no—
545C2×Dic79—42no—
546C2×Dic79—42no—
547C2×Dic79—42no—
548C2×Dic79—44no—
549C2×Dic79—48no—
550C2×Dic79—44no—
551C2×Dic79—416no—
552C2×Dic79C2512yes—
553C2×Dic79C2518yes—
554C2×Dic79C2512yes—
555C2×Dic79C2518yes—
556C2×Dic79C2514yes—
557C2×Dic79C2512yes—
558C2×Dic79C2512yes—
559D316—24no—
560D316—24no—
561C4×D79—28no—
562C4×D79—28no—
563C4×D79—416no—
564Dic158—24no—
565Dic158—24no—
566Dic158—216no—
567Dic158—48no—
568C22×C79—22no—
569C22×C79—22no—
570C22×C79—22no—
571C22×C79—24no—
572C22×C79—24no—
573C22×C79—28no—
574C22×C79—28no—
575C22×C79—44no—
576C22×C79—48no—
577C22×C79—84no—
578C22×C79C22×#4112yes—
579C22×C79C22×#4112yes—
580C22×C79C22×#4112yes—
581C22×C79C2611yescharacteristic
582C2×D79—24no—
583C2×D79—28no—
584C2×D79—84no—
585C4×C79—24no—
586C4×C79—24no—
587C4×C79—28no—
588C4×C79C22×#4112yes—
589C4×C79C22×#4112yes—
590C4×C79C22×#4112yes—
591C4×C79C22×#4112yes—
592Dic79—24no—
593Dic79—22no—
594Dic79—28no—
595Dic79—22no—
596Dic79—28no—
597Dic79—22no—
598Dic79#58514yes—
599#62815—791nomaximal, Sylow
600C2×C79—22no—
601C2×C79—22no—
602C2×C79—22no—
603C2×C79—44no—
604C2×C79—44no—
605C2×C79C23×#4111yescharacteristic
606C2×C79C2×#58512yes—
607D79—44no—
608#3512—794no—
609#3511—794no—
610#3510—792no—
611#3510—792no—
612#3509—792no—
613#3508—792no—
614#3507—794no—
615#3506—794no—
616#3505—798no—
617#3480—798no—
618#3475—798no—
619#3455—794no—
620#3449—791no—
621#3449D7911yescharacteristic, complemented
622#3444—794no—
623C2×#533—791no—
624C2×#532—791no—
625#3428—791no—
626#3428—791no—
627C2×C4×#41—791no—
628C79#6281511yescharacteristic, complemented, Sylow
629C22×#41—791no—
630C22×#41C2×D7911yescharacteristic
631C22×#41C2×D7911yescharacteristic
632#559—798no—
633#559—798no—
634#559—798no—
635#557—798no—
636#556—798no—
637#556—798no—
638#556—798no—
639#556—798no—
640#555—798no—
641#554—798no—
642#553—7916no—
643#553—7916no—
644#553—798no—
645#553—798no—
646#553—7916no—
647#552—7916no—
648#552—798no—
649#552—798no—
650#551—7916no—
651#551—7916no—
652#550—798no—
653#548—7916no—
654#547—798no—
655#546—7916no—
656#542—798no—
657#542—798no—
658#541—798no—
659#540—798no—
660#539—7916no—
661#538—7916no—
662#537—794no—
663#537C2×D7914yescomplemented
664#536—792no—
665#536—792no—
666#536C2×D7912yes—
667#536C2×D7912yescomplemented
668#535—792no—
669#535—792no—
670#535C2×D7912yes—
671#535C2×D7912yescomplemented
672#534—794no—
673#534C2×D7914yes—
674#533—798no—
675#533—792no—
676#533—792no—
677#533—794no—
678#533—794no—
679#533—792no—
680#533—792no—
681#532—792no—
682#532—792no—
683#532—794no—
684#532—794no—
685#532—792no—
686#532—792no—
687#532—794no—
688#532—798no—
689#532C2×D7914yescomplemented
690C2×C4⋊Q8—791no—
691C2×C4⋊Q8—792no—
692C2×#127—791no—
693#529—7916no—
694#529—798no—
695#529—798no—
696#529—7916no—
697#529—7916no—
698#529—7916no—
699C2×#125—792no—
700C2×#124—791no—
701C2×#124—791no—
702#525—794no—
703#525—794no—
704#525—7916no—
705#525C2×D7914yes—
706#525C2×D7914yescomplemented
707C2×C22⋊Q8—794no—
708C2×#121—794no—
709#520—794no—
710#520—794no—
711#520—794no—
712#520—794no—
713#519—792no—
714#519—792no—
715#518—794no—
716#518—792no—
717#518—792no—
718#518—794no—
719C4×#41—794no—
720C4×#41—794no—
721C4×#41—792no—
722C4×#41—792no—
723C4×#41—792no—
724C4×#41—792no—
725C4×#41—794no—
726C4×#41—794no—
727C4×#41—7916no—
728C4×#41—794no—
729C4×#41—794no—
730C2×C4×Q8—792no—
731C2×C4×Q8—794no—
732C2×C4×D4—794no—
733C2×C4×D4—792no—
734C2×C4×D4—794no—
735C2×#117—791no—
736C2×#117—792no—
737C2×#117—791no—
738C2×#117—794no—
739C2×#117—794no—
740C2×#117C2×D7911yescharacteristic
741C22×C42—791no—
742C22×C42—792no—
743C2×#41—28no—
744C2×#41—28no—
745C2×#41—7916no—
746C2×#41—792no—
747C2×#41—792no—
748C2×#41—792no—
749C2×#41—792no—
750C2×#41—1588no—
751C2×#41C22×D7912yes—
752C2×#41C22×D7912yes—
753C2×#41C22×D7912yes—
754C2×#41C22×D7912yes—
755C2×#41C22×D7912yes—
756C2×#41C22×D7912yes—
757C2×#41C22×D7912yes—
758C2×#41C22×D7912yes—
759C22×Q8—794no—
760C22×Q8—791no—
761C22×Q8C22×D7911yescharacteristic
762C22×Q8C22×D7911yescharacteristic
763C22×D4—794no—
764C22×D4—792no—
765C22×D4—791no—
766C22×D4C22×D7912yes—
767C22×D4C22×D7911yescharacteristic
768C22×D4C22×D7912yes—
769C22×D4C22×D7911yescharacteristic
770C23×C4—792no—
771C23×C4—794no—
772C23×C4—792no—
773C23×C4C22×D7912yes—
774C23×C4C22×D7912yes—
775C23×C4C22×D7911yescharacteristic
776C4⋊Q8—792no—
777C4⋊Q8—792no—
778C4⋊Q8—794no—
779C4⋊Q8—794no—
780C4⋊Q8—794no—
781C4⋊Q8—794no—
782C4⋊Q8—794no—
783C4⋊Q8—794no—
784C4⋊Q8C22×D7914yes—
785#127—792no—
786#127—792no—
787#127—794no—
788#127—794no—
789#127C22×D7914yes—
790#126—7916no—
791#126—7916no—
792#126—7916no—
793#126—7916no—
794#126—7916no—
795#126—7916no—
796#125—794no—
797#125—794no—
798#125—794no—
799#125—794no—
800#125—7916no—
801#125—7916no—
802#125—7916no—
803#124—792no—
804#124—792no—
805#124—794no—
806#124—794no—
807#124—792no—
808#124—792no—
809#124—794no—
810#124—7916no—
811#124—794no—
812#124—7916no—
813#124—7916no—
814#124C22×D7914yes—
815#124C22×D7914yes—
816#123—7916no—
817#123—798no—
818#123—7916no—
819#123—798no—
820#123—7916no—
821#123—7916no—
822#123—7916no—
823#123—7916no—
824#123C22×D7918yes—
825#123C22×D7918yes—
826C22⋊Q8—798no—
827C22⋊Q8—798no—
828C22⋊Q8—7916no—
829C22⋊Q8—798no—
830C22⋊Q8—798no—
831C22⋊Q8—798no—
832C22⋊Q8—798no—
833C22⋊Q8—7916no—
834C22⋊Q8—7916no—
835C22⋊Q8C22×D7918yes—
836C22⋊Q8C22×D7918yes—
837#121—798no—
838#121—798no—
839#121—798no—
840#121—798no—
841#121—7916no—
842#121—798no—
843#121—7916no—
844#121—7916no—
845#121—7916no—
846#121—798no—
847#121C22×D7918yes—
848#121C22×D7918yes—
849#121C22×D79116yes—
850#120—798no—
851#120—798no—
852#120C22×D7918yes—
853#120C22×D7918yes—
854C4×Q8—794no—
855C4×Q8—794no—
856C4×Q8—794no—
857C4×Q8—794no—
858C4×Q8—798no—
859C4×Q8—798no—
860C4×Q8—798no—
861C4×Q8—7916no—
862C4×Q8—798no—
863C4×Q8—798no—
864C4×Q8—798no—
865C4×Q8—798no—
866C4×Q8—798no—
867C4×D4—798no—
868C4×D4—794no—
869C4×D4—798no—
870C4×D4—794no—
871C4×D4—798no—
872C4×D4—798no—
873C4×D4—794no—
874C4×D4—794no—
875C4×D4—7916no—
876C4×D4—798no—
877C4×D4—7916no—
878C4×D4—798no—
879C4×D4—7916no—
880C4×D4—798no—
881C4×D4—798no—
882C4×D4—798no—
883C4×D4—798no—
884C4×D4—7916no—
885C4×D4—7916no—
886C4×D4—798no—
887C4×D4—7916no—
888C4×D4—7916no—
889C4×D4—7916no—
890C4×D4—798no—
891C4×D4C22×D79116yes—
892#117—792no—
893#117—792no—
894#117—792no—
895#117—792no—
896#117—792no—
897#117—792no—
898#117—798no—
899#117—798no—
900#117—794no—
901#117—794no—
902#117—792no—
903#117—798no—
904#117—792no—
905#117—798no—
906#117—798no—
907#117—7916no—
908#117—798no—
909#117—7916no—
910#117—7916no—
911#117—798no—
912#117C22×D7912yes—
913#117C22×D7912yes—
914#117C22×D7912yes—
915#117C22×D7912yes—
916C2×C4⋊C4—792no—
917C2×C4⋊C4—794no—
918C2×C4⋊C4—792no—
919C2×C4⋊C4—798no—
920C2×C4⋊C4—794no—
921C2×C4⋊C4—794no—
922C2×C4⋊C4—794no—
923C2×C4⋊C4—794no—
924C2×C4⋊C4—798no—
925C2×C4⋊C4C22×D7912yes—
926C2×C22⋊C4—792no—
927C2×C22⋊C4—794no—
928C2×C22⋊C4—792no—
929C2×C22⋊C4—798no—
930C2×C22⋊C4—794no—
931C2×C22⋊C4—794no—
932C2×C22⋊C4—798no—
933C2×C22⋊C4C22×D7912yes—
934C2×C42—792no—
935C2×C42—791no—
936C2×C42—792no—
937C2×C42—798no—
938C2×C42—792no—
939C2×C42—794no—
940C2×C42—792no—
941C2×C42—792no—
942C2×C42—798no—
943C2×C42—791no—
944C2×C42—791no—
945C2×C42—794no—
946C2×C42—791no—
947C2×C42—791no—
948C2×C42—794no—
949C2×C42—791no—
950C2×C42—798no—
951C2×C42C22×D7912yes—
952C24—792no—
953C24C23×D7912yes—
954C24C23×D7912yes—
955C24C23×D7911yescharacteristic
956#41—28no—
957#41—28no—
958#41—28no—
959#41—28no—
960#41—28no—
961#41—28no—
962#41—28no—
963#41—28no—
964#41—31632no—
965#41—1588no—
966#41—1588no—
967#41—1588no—
968#41—1588no—
969C2×Q8—24no—
970C2×Q8—24no—
971C2×Q8—3168no—
972C2×Q8—798no—
973C2×Q8—798no—
974C2×Q8—792no—
975C2×Q8—792no—
976C2×Q8—1584no—
977C2×Q8C23×D7912yes—
978C2×Q8C23×D7912yes—
979C2×Q8C23×D7912yes—
980C2×Q8C23×D7912yes—
981C2×D4—28no—
982C2×D4—28no—
983C2×D4—24no—
984C2×D4—24no—
985C2×D4—3168no—
986C2×D4—7916no—
987C2×D4—798no—
988C2×D4—794no—
989C2×D4—794no—
990C2×D4—798no—
991C2×D4—792no—
992C2×D4—792no—
993C2×D4—1588no—
994C2×D4—1584no—
995C2×D4C23×D7914yes—
996C2×D4C23×D7914yes—
997C2×D4C23×D7914yes—
998C2×D4C23×D7914yes—
999C2×D4C23×D7912yes—
1000C2×D4C23×D7912yes—
1001C2×D4C23×D7912yes—
1002C2×D4C23×D7912yes—
1003C2×D4C23×D79116yes—
1004C22×C4—28no—
1005C22×C4—28no—
1006C22×C4—3164no—
1007C22×C4—3168no—
1008C22×C4—792no—
1009C22×C4—794no—
1010C22×C4—792no—
1011C22×C4—792no—
1012C22×C4—798no—
1013C22×C4—794no—
1014C22×C4—7916no—
1015C22×C4—7916no—
1016C22×C4—792no—
1017C22×C4—792no—
1018C22×C4—792no—
1019C22×C4—798no—
1020C22×C4—792no—
1021C22×C4—794no—
1022C22×C4—794no—
1023C22×C4—1588no—
1024C22×C4#1192962318yescomplemented
1025C22×C4C23×D7912yes—
1026C22×C4C23×D7914yes—
1027C22×C4C23×D7912yes—
1028C22×C4C23×D7914yes—
1029C22×C4C23×D7914yes—
1030C22×C4C23×D7914yes—
1031C22×C4C23×D7914yes—
1032C22×C4C23×D7911yescharacteristic
1033C22×C4C23×D7911yescharacteristic
1034C22×C4C23×D7911yescharacteristic
1035C22×C4C23×D7911yescharacteristic
1036C22×C4C23×D7911yescharacteristic
1037C22×C4C23×D7911yescharacteristic
1038C4⋊C4—798no—
1039C4⋊C4—798no—
1040C4⋊C4—7916no—
1041C4⋊C4—798no—
1042C4⋊C4—798no—
1043C4⋊C4—798no—
1044C4⋊C4—798no—
1045C4⋊C4—7916no—
1046C4⋊C4—794no—
1047C4⋊C4—794no—
1048C4⋊C4—794no—
1049C4⋊C4—794no—
1050C4⋊C4—798no—
1051C4⋊C4—7916no—
1052C4⋊C4—798no—
1053C4⋊C4—798no—
1054C4⋊C4—798no—
1055C4⋊C4C23×D7914yes—
1056C4⋊C4C23×D7914yes—
1057C4⋊C4C23×D79116yes—
1058C22⋊C4—794no—
1059C22⋊C4—794no—
1060C22⋊C4—794no—
1061C22⋊C4—794no—
1062C22⋊C4—798no—
1063C22⋊C4—798no—
1064C22⋊C4—7916no—
1065C22⋊C4—798no—
1066C22⋊C4—798no—
1067C22⋊C4—7916no—
1068C22⋊C4—798no—
1069C22⋊C4—7916no—
1070C22⋊C4—798no—
1071C22⋊C4—7916no—
1072C22⋊C4C23×D7914yes—
1073C22⋊C4C23×D7914yes—
1074C22⋊C4C23×D79116yes—
1075C22⋊C4C23×D79116yes—
1076C42—791no—
1077C42—791no—
1078C42—794no—
1079C42—798no—
1080C42—791no—
1081C42—791no—
1082C42—792no—
1083C42—792no—
1084C42—798no—
1085C42—792no—
1086C42—792no—
1087C42—7916no—
1088C42—7916no—
1089C42—794no—
1090C42—794no—
1091C42—792no—
1092C42—792no—
1093C42—794no—
1094C42C23×D7914yes—
1095C42C23×D7914yes—
1096C23—24no—
1097C23—24no—
1098C23—42no—
1099C23—44no—
1100C23—44no—
1101C23—3164no—
1102C23—794no—
1103C23—1584no—
1104C23C2×#1192962314yes—
1105C23C24×D7914yes—
1106C23C24×D7914yes—
1107C23C24×D7911yescharacteristic
1108C23C24×D7911yescharacteristic
1109C23C24×D7911yescharacteristic
1110Q8—24no—
1111Q8—24no—
1112Q8—24no—
1113Q8—24no—
1114Q8—3168no—
1115Q8—15816no—
1116Q8—1584no—
1117Q8—1584no—
1118D4—28no—
1119D4—28no—
1120D4—28no—
1121D4—28no—
1122D4—24no—
1123D4—24no—
1124D4—24no—
1125D4—24no—
1126D4—416no—
1127D4—3168no—
1128D4—31616no—
1129D4—15816no—
1130D4—1588no—
1131D4—1588no—
1132D4—1584no—
1133D4—1584no—
1134C2×C4—24no—
1135C2×C4—24no—
1136C2×C4—28no—
1137C2×C4—28no—
1138C2×C4—28no—
1139C2×C4—28no—
1140C2×C4—44no—
1141C2×C4—31616no—
1142C2×C4—3164no—
1143C2×C4—3168no—
1144C2×C4—3162no—
1145C2×C4—3162no—
1146C2×C4—3162no—
1147C2×C4—3164no—
1148C2×C4—31616no—
1149C2×C4—792no—
1150C2×C4—792no—
1151C2×C4—798no—
1152C2×C4—792no—
1153C2×C4—794no—
1154C2×C4—798no—
1155C2×C4—792no—
1156C2×C4—1584no—
1157C2×C4—1584no—
1158C2×C4—1584no—
1159C2×C4—15816no—
1160C2×C4—1584no—
1161C2×C4—1588no—
1162C2×C4—1588no—
1163C2×C4C2×#1192962314yes—
1164C2×C4C2×#1192962314yes—
1165C2×C4C2×#1192962314yes—
1166C2×C4C2×#1192962314yes—
1167C2×C4C2×#1192962314yes—
1168C2×C4C2×#1192962314yes—
1169C2×C4C24×D7914yes—
1170C2×C4C24×D7914yes—
1171C2×C4C24×D7918yes—
1172C2×C4C24×D7911yescharacteristic
1173C2×C4C24×D7911yescharacteristic
1174C2×C4C24×D7911yescharacteristic
1175C2×C4C24×D7911yescharacteristic
1176C22—22no—
1177C22—22no—
1178C22—22no—
1179C22—24no—
1180C22—24no—
1181C22—28no—
1182C22—28no—
1183C22—44no—
1184C22—48no—
1185C22—84no—
1186C22—6324no—
1187C22—1584no—
1188C22—1588no—
1189C22C22×#1192962312yes—
1190C22C22×#1192962312yes—
1191C22C22×#1192962312yes—
1192C22C25×D7911yescharacteristic
1193C4—24no—
1194C4—24no—
1195C4—28no—
1196C4—794no—
1197C4—1584no—
1198C4—1588no—
1199C4—1582no—
1200C4—1588no—
1201C4—1582no—
1202C4—1582no—
1203C4C22×#1192962312yes—
1204C4C22×#1192962312yes—
1205C4C22×#1192962312yes—
1206C4C22×#1192962312yes—
1207C2—22no—
1208C2—22no—
1209C2—22no—
1210C2—44no—
1211C2—44no—
1212C2—3164no—
1213C2C23×#1192962311yescharacteristic
1214C2#585×D7912yes—
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC79×#3449C2
hypercenter#3449D79
hypocenterC79#62815
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ #3449

Complements

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

NH ≅ G/Ntype
1. #23777321C2semidirect
2. #23777309C2semidirect
3. #23777299C2semidirect
4. #23777295C2semidirect
5. #23777285C2semidirect
6. #23777275C2semidirect
7. #23777264C2semidirect
8. #23777251C2semidirect
9. #23777237C2semidirect
10. #23776997C2semidirect
11. #23776960C2semidirect
12. #23776788C2semidirect
13. #23776729C2semidirect
14. #23776692C2semidirect
15. C2×#19099116C2semidirect
16. C2×#19099109C2semidirect
17. #23776603C2semidirect
18. #23776601C2semidirect
19. C2×#41×Dic79C2semidirect
20. C79×#3449C2semidirect
22. #19099299C22semidirect
23. #19099295C22semidirect
24. #19099295C22semidirect
25. #19099288C22semidirect
26. #19099287C22semidirect
27. #19099284C22semidirect
28. #19099282C22semidirect
29. #19099282C22semidirect
30. #19099277C22semidirect
31. #19099271C22semidirect
32. #19099265C22semidirect
33. #19099265C22semidirect
34. #19099260C22semidirect
35. #19099256C22semidirect
36. #19099256C22semidirect
37. #19099255C22semidirect
38. #19099250C22semidirect
39. #19099247C22semidirect
40. #19099244C22semidirect
41. #19099236C22semidirect
42. #19099233C22semidirect
43. #19099219C22semidirect
44. #19099213C22semidirect
45. #19099200C22semidirect
46. #19099186C22semidirect
47. #19099180C22semidirect
48. #19099173C22semidirect
49. #19099166C22semidirect
50. #19099157C22semidirect
51. #19099148C22semidirect
52. #19099141C22semidirect
53. #19099137C22semidirect
55. #19099130C22semidirect
58. #19099116C22semidirect
59. #19099116C22semidirect
60. #19099116C22semidirect
61. #19099116C22semidirect
62. #19099116C22semidirect
63. #19099116C22semidirect
64. #19099115C22semidirect
68. #19099109C22semidirect
69. #19099109C22semidirect
70. #19099109C22semidirect
71. #19099109C22semidirect
72. #19099108C22semidirect
73. C2×#14579160C22semidirect
74. C2×#14579159C22semidirect
75. C2×#14579157C22semidirect
76. #19099099C22semidirect
77. #19099095C22semidirect
78. #19099094C22semidirect
79. #19099093C22semidirect
80. #19099093C22semidirect
81. #19099090C22semidirect
82. C2×#14579152C22semidirect
83. C2×#14579150C22semidirect
84. C2×#14579148C22semidirect
85. #19099074C22semidirect
87. #19099069C22semidirect
90. #19099046C22semidirect
91. #19099046C22semidirect
92. #19099044C22semidirect
93. #19099043C22semidirect
94. #19099041C22semidirect
95. #19099040C22semidirect
97. #19099038C22semidirect
98. #19099037C22semidirect
103. #41×Dic79C22semidirect
104. #41×Dic79C22semidirect
105. #41×Dic79C22semidirect
106. #41×Dic79C22semidirect
107. #41×Dic79C22semidirect
108. C4×#11929624C22semidirect
109. #19099031C22semidirect
110. C4×#11929623C22semidirect
111. C2×Q8×Dic79C22semidirect
112. C2×C4×Dic158C22semidirect
114. C2×D4×Dic79C22semidirect
115. C2×C4×C22⋊D79C22semidirect
118. C2×#14579120C22semidirect
119. C2×#14579120C22semidirect
120. #117×D79C22semidirect
122. C22×C4×Dic79C22semidirect
125. #537×C79C22semidirect
127. #536×C79C22semidirect
129. #535×C79C22semidirect
131. #532×C79C22semidirect
133. #525×C79C22semidirect
465. C22×C4×C79#41semidirect
621. #3449D79semidirect
628. C79#62815semidirect
663. #537C2×D79semidirect
667. #536C2×D79semidirect
671. #535C2×D79semidirect
689. #532C2×D79semidirect
706. #525C2×D79semidirect
1024. C22×C4#11929623semidirect

Maximal subgroups

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

subgroupindex
#237773212
#237773092
#237772992
#237772952
#237772852
#237772752
#237772642
#237772512
#237772372
#237769972
#237769602
#237767882
#237767292
#237766922
C2×#190991162
C2×#190991092
#237766032
#237766012
C2×#41×Dic792
C79×#34492
#6281579