Finite Group Databasebeta

← #35197418

Subgroups — #35197418

Order 20224.

7086 conjugacy classes of subgroups.

The subgroup lattice has 1264 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777322C214yesmaximal, complemented
2#23777317C214yesmaximal, complemented
3#23777311C214yesmaximal, complemented
4#23777303C214yesmaximal, complemented
5#23777230C218yesmaximal, complemented
6#23777152C214yesmaximal, complemented
7#23777142C214yesmaximal, complemented
8#23777135C214yesmaximal, complemented
9#23777125C214yesmaximal, complemented
10#23777113C214yesmaximal, complemented
11#23777103C214yesmaximal, complemented
12#23776827C214yesmaximal, complemented
13#23776816C214yesmaximal, complemented
14C2×#19099191C211yesmaximal, characteristic, complemented
15#23776733C211yesmaximal, characteristic, complemented
16#23776729C211yesmaximal, characteristic, complemented
17C2×#19099141C211yesmaximal, characteristic, complemented
18#23776601C211yesmaximal, characteristic, complemented
19C2×#19099043C211yesmaximal, characteristic, complemented
20C79×#3428C211yesmaximal, characteristic, complemented
21C22×#11929624C2211yescharacteristic
22C22×#11929624C2211yescharacteristic
23#19099286C2218yescomplemented
24#19099281C2218yescomplemented
25#19099278C2218yescomplemented
26#19099276C2218yescomplemented
27#19099273C2218yescomplemented
28#19099268C2218yescomplemented
29#19099263C2218yescomplemented
30#19099263C2218yescomplemented
31#19099262C22116yescomplemented
32#19099262C22116yescomplemented
33#19099261C2218yescomplemented
34#19099259C22116yescomplemented
35#19099257C2218yescomplemented
36#19099254C2218yescomplemented
37#19099254C2218yescomplemented
38#19099252C2218yescomplemented
39#19099248C2218yescomplemented
40#19099246C22116yescomplemented
41#19099239C22116yescomplemented
42#19099237C22116yescomplemented
43#19099222C22116yescomplemented
44#19099218C2218yescomplemented
45#19099214C2218yescomplemented
46#19099203C22116yescomplemented
47#19099191C2214yescomplemented
48#19099191C2214yescomplemented
49#19099191C2214yescomplemented
50#19099191C2214yescomplemented
51#19099185C2218yescomplemented
52#19099184C2218yescomplemented
53#19099184C2218yescomplemented
54#19099178C2218yescomplemented
55#19099175C2218yescomplemented
56#19099171C2218yescomplemented
57#19099168C2218yescomplemented
58#19099164C2218yescomplemented
59#19099155C22116yescomplemented
60#19099146C22116yescomplemented
61#19099144C2212yescomplemented
62#19099144C2212yescomplemented
63#19099141C2214yes—
64#19099141C2214yes—
65#19099141C2214yescomplemented
66#19099141C2212yescomplemented
67#19099141C2214yescomplemented
68#19099141C2212yescomplemented
69#19099139C2212yes—
70#19099139C2212yescomplemented
71#19099137C2212yes—
72#19099134C2212yescomplemented
73#19099132C2212yes—
74#19099132C2212yescomplemented
75#19099130C2212yes—
76#19099127C2212yescomplemented
77#19099125C2214yes—
78#19099122C2214yes—
79#19099120C2218yescomplemented
80#19099117C2218yescomplemented
81#19099113C2214yescomplemented
82#19099113C2218yescomplemented
83#19099110C2218yescomplemented
84#19099109C2214yescomplemented
85C2×#14579161C2212yescomplemented
86C2×#14579160C2212yescomplemented
87#19099100C2218yescomplemented
88#19099097C2218yescomplemented
89#19099097C2218yescomplemented
90#19099095C2218yescomplemented
91#19099093C22116yescomplemented
92C2×#14579153C2212yescomplemented
93C2×#14579152C2212yescomplemented
94#19099075C2214yes—
95#19099075C2214yescomplemented
96#19099074C2214yes—
97#19099072C22116yescomplemented
98#19099070C2214yescomplemented
99C2×#14579140C2212yescomplemented
100C2×#14579138C2214yes—
101C2×#14579137C2212yescomplemented
102C2×#14579135C2212yescomplemented
103C2×#14579133C2214yes—
104C2×#14579132C2212yescomplemented
105#19099044C2212yescomplemented
106#19099044C2212yescomplemented
107#19099043C2214yes—
108#19099043C2214yes—
109#19099043C2214yescomplemented
110#19099043C2212yescomplemented
111#19099043C2214yescomplemented
112#19099043C2212yescomplemented
113#19099040C2212yescomplemented
114#19099037C2212yescomplemented
115#19099036C2214yes—
116C4×#11929624C2214yescomplemented
117#19099031C2214yescomplemented
118C2×C4×Dic158C2212yescomplemented
119C2×C4×D316C2212yescomplemented
120C2×(C22⋊D79)⋊C4C2214yes—
121C2×#14579120C2211yescharacteristic
122C2×#14579119C2212yescomplemented
123#117×D79C2214yescomplemented
124C22×C4⋊Dic79C2211yescharacteristic
125C2×C4⋊C4×D79C2212yescomplemented
126C22×#41×C79C2211yescharacteristic
127#520×C79C2212yescomplemented
128#520×C79C2212yescomplemented
129#520×C79C2212yescomplemented
130#520×C79C2212yescomplemented
131#519×C79C2212yescomplemented
132#518×C79C2214yes—
133#518×C79C2212yescomplemented
134C4×#41×C79C2214yescomplemented
135C4×#41×C79C2214yescomplemented
136C2×#117×C79C2211yescharacteristic
137C2×#117×C79C2211yescharacteristic
138C2×#117×C79C2214yescomplemented
139C2×#11929624—28no—
140C2×#11929624—28no—
141C2×#11929624C2312yes—
142C2×#11929624C2312yes—
143C2×#11929624C2312yes—
144C2×#11929624C2312yes—
145C2×#11929624C2312yes—
146C2×#11929624C2312yes—
147C2×#11929624C2312yes—
148C2×#11929624C2312yes—
149C2×#11929624C23116yes—
150C22×Dic158C2311yescharacteristic
151C22×Dic158C2311yescharacteristic
152C22×Dic158C2314yes—
153C22×D316C2311yescharacteristic
154C22×D316C2311yescharacteristic
155C22×C22⋊D79C2312yes—
156C22×C22⋊D79C2312yes—
157C22×C22⋊D79C2314yes—
158C23×Dic79C2312yes—
159C22×C4×D79C2312yes—
160C22×C4×D79C2312yes—
161C22×C4×D79C2314yes—
162#14579161C2314yes—
163#14579161C2318yes—
164#14579161C2318yes—
165#14579160C2318yes—
166#14579160C2318yes—
167#14579159C2314yes—
168#14579158C2314yes—
169#14579157C2314yes—
170#14579156C23116yes—
171#14579156C23116yes—
172#14579155C23116yes—
173#14579155C23116yes—
174#14579154C23116yes—
175#14579154C23116yes—
176#14579153C23116yes—
177#14579153C2318yes—
178#14579153C2318yes—
179#14579152C2318yes—
180#14579152C2318yes—
181#14579151C23116yes—
182#14579151C23116yes—
183#14579150C2314yes—
184#14579149C2314yes—
185#14579149C2314yes—
186#14579149C23116yes—
187#14579148C2314yes—
188#14579147C23116yes—
189#14579147C23116yes—
190#14579146C23116yes—
191#14579146C23116yes—
192#14579145C2318yes—
193#14579145C2318yes—
194#14579144C2318yes—
195#14579144C23116yes—
196#14579144C23116yes—
197#14579143C23116yes—
198#14579143C23116yes—
199#14579142C2318yes—
200#14579141C2314yes—
201#14579141C2314yes—
202#14579141C2314yes—
203#14579141C2314yes—
204#14579140C2318yes—
205#14579140C2318yes—
206#14579140C2314yes—
207#14579140C2314yes—
208#14579140C23116yes—
209#14579139C23116yes—
210#14579139C23116yes—
211#14579138C23116yes—
212#14579138C23116yes—
213#14579137C2314yes—
214#14579137C2314yes—
215#14579137C2318yes—
216#14579137C2318yes—
217#14579136C2314yes—
218#14579136C2314yes—
219#14579136C2314yes—
220#14579136C2314yes—
221#14579135C2318yes—
222#14579135C2318yes—
223#14579135C2314yes—
224#14579135C2314yes—
225#14579135C2318yes—
226#14579135C2318yes—
227#14579135C23116yes—
228#14579134C23116yes—
229#14579134C23116yes—
230#14579133C23116yes—
231#14579133C23116yes—
232#14579133C2318yes—
233#14579133C2318yes—
234#14579132C2318yes—
235#14579132C2318yes—
236#14579132C2314yes—
237#14579132C2314yes—
238#14579131C2318yes—
239#14579131C2318yes—
240#14579130C2318yes—
241#14579129C2318yes—
242C4×Dic158C2318yes—
243C4×Dic158C2314yes—
244C4×Dic158C2318yes—
245C4×Dic158C2314yes—
246C4×Dic158C23116yes—
247#14579126C2314yes—
248#14579126C2314yes—
249C4×D316C2318yes—
250C4×D316C2314yes—
251C4×D316C2318yes—
252C4×D316C2314yes—
253C4×D316C2318yes—
254C4×D316C23116yes—
255C4×D316C2318yes—
256#14579123C2314yes—
257#14579123C2314yes—
258C4×C22⋊D79C2318yes—
259C4×C22⋊D79C2318yes—
260C4×C22⋊D79C23116yes—
261C4×C22⋊D79C2318yes—
262C4×C22⋊D79C23116yes—
263C4×C22⋊D79C2318yes—
264(C22⋊D79)⋊C4C23116yes—
265(C22⋊D79)⋊C4C2318yes—
266(C22⋊D79)⋊C4C23116yes—
267(C22⋊D79)⋊C4C2318yes—
268#14579120C2312yes—
269#14579120C2312yes—
270#14579120C2312yes—
271#14579120C2312yes—
272#14579120C23116yes—
273#14579119C2318yes—
274#14579119C2314yes—
275#14579119C2318yes—
276#14579119C2314yes—
277#14579118C2318yes—
278#14579118C23116yes—
279#14579118C23116yes—
280#14579117C2318yes—
281C2×C4⋊Dic79C2312yes—
282C2×C4⋊Dic79C2312yes—
283C2×C4⋊Dic79C2312yes—
284C2×C4⋊Dic79C2312yes—
285C2×C4⋊Dic79C2311yescharacteristic
286C2×C4⋊Dic79C2311yescharacteristic
287C2×C4⋊Dic79C2312yes—
288C2×C4⋊Dic79C2312yes—
289C2×C4⋊Dic79C2314yes—
290C2×Dic79⋊C4C2314yes—
291C2×Dic79⋊C4C2314yes—
292C2×Dic79⋊C4C2314yes—
293C2×Dic79⋊C4C2314yes—
294C4⋊C4×D79C2318yes—
295C4⋊C4×D79C2314yes—
296C4⋊C4×D79C2318yes—
297C4⋊C4×D79C2314yes—
298C2×C22⋊Dic79C2314yes—
299C2×C22⋊Dic79C2312yes—
300C2×(C2×D79)⋊C4C2314yes—
301C2×(C2×D79)⋊C4C2314yes—
302C22⋊C4×D79C2318yes—
303C2×C4×Dic79C2314yes—
304C2×C4×Dic79C2312yes—
305C42×D79C2318yes—
306C2×#41×C79—28no—
307C2×#41×C79C2312yes—
308C2×#41×C79C2312yes—
309C2×#41×C79C2312yes—
310C2×#41×C79C2312yes—
311C22×Q8×C79C2311yescharacteristic
312C22×D4×C79C2312yes—
313C22×D4×C79C2311yescharacteristic
314C23×C4×C79C2312yes—
315C23×C4×C79C2311yescharacteristic
316C4×Q8×C79C2314yes—
317C4×Q8×C79C2314yes—
318C4×Q8×C79C2314yes—
319C4×Q8×C79C2314yes—
320C4×D4×C79C2318yes—
321C4×D4×C79C2318yes—
322C4×D4×C79C2314yes—
323C4×D4×C79C2314yes—
324C4×D4×C79C2314yes—
325C4×D4×C79C2318yes—
326C4×D4×C79C2318yes—
327C4×D4×C79C2314yes—
328#117×C79C2312yes—
329#117×C79C2312yes—
330#117×C79C2318yes—
331#117×C79C2312yes—
332#117×C79C2312yes—
333#117×C79C2312yes—
334#117×C79C2312yes—
335#117×C79C2312yes—
336#117×C79C2312yes—
337#117×C79C2318yes—
338#117×C79C2314yes—
339#117×C79C2314yes—
340C2×C4⋊C4×C79C2311yescharacteristic
341C2×C4⋊C4×C79C2311yescharacteristic
342C2×C4⋊C4×C79C2314yes—
343C2×C4⋊C4×C79C2311yescharacteristic
344C2×C4⋊C4×C79C2311yescharacteristic
345C2×C4⋊C4×C79C2314yes—
346C2×C22⋊C4×C79C2318yes—
347C2×C22⋊C4×C79C2312yes—
348C2×C22⋊C4×C79C2312yes—
349C2×C42×C79C2312yes—
350C2×C42×C79C2312yes—
351C2×C42×C79C2318yes—
352C23×D79C2412yes—
353C23×D79C2412yes—
354#11929624—28no—
355#11929624—28no—
356#11929624—28no—
357#11929624—28no—
358#11929624—28no—
359#11929624—28no—
360#11929624—28no—
361#11929624—28no—
362#11929624—816no—
363C2×Dic158—24no—
364C2×Dic158—24no—
365C2×Dic158—84no—
366C2×Dic158C2412yes—
367C2×Dic158C2412yes—
368C2×Dic158C2412yes—
369C2×Dic158C2412yes—
370C2×Dic158C24116yes—
371C2×D316—24no—
372C2×D316—24no—
373C2×D316C2412yes—
374C2×D316C2412yes—
375C2×D316C2412yes—
376C2×D316C2412yes—
377C2×D316C2418yes—
378C2×D316C2418yes—
379C2×C22⋊D79—28no—
380C2×C22⋊D79—28no—
381C2×C22⋊D79—84no—
382C2×C22⋊D79C2414yes—
383C2×C22⋊D79C2414yes—
384C2×C22⋊D79C2414yes—
385C2×C22⋊D79C2414yes—
386C2×C22⋊D79C2418yes—
387C2×C22⋊D79C24116yes—
388C2×C22⋊D79C2418yes—
389C22×Dic79—82no—
390C22×Dic79C2412yes—
391C22×Dic79C2412yes—
392C22×Dic79C2412yes—
393C22×Dic79C2414yes—
394C22×Dic79C2414yes—
395C22×Dic79C2412yes—
396C22×Dic79C2414yes—
397C2×C4×D79—28no—
398C2×C4×D79—28no—
399C2×C4×D79—84no—
400C2×C4×D79C2414yes—
401C2×C4×D79C2414yes—
402C2×C4×D79C2414yes—
403C2×C4×D79C2414yes—
404C2×C4×D79C2418yes—
405C2×C4×D79C24116yes—
406C2×C4×D79C2418yes—
407C4⋊Dic79C2414yes—
408C4⋊Dic79C2414yes—
409C4⋊Dic79C2412yes—
410C4⋊Dic79C2412yes—
411C4⋊Dic79C2414yes—
412C4⋊Dic79C2414yes—
413C4⋊Dic79C2412yes—
414C4⋊Dic79C2412yes—
415C4⋊Dic79C24116yes—
416C4⋊Dic79C2418yes—
417C4⋊Dic79C2418yes—
418Dic79⋊C4C24116yes—
419Dic79⋊C4C2418yes—
420Dic79⋊C4C2418yes—
421Dic79⋊C4C24116yes—
422Dic79⋊C4C24116yes—
423Dic79⋊C4C24116yes—
424Dic79⋊C4C2418yes—
425Dic79⋊C4C2418yes—
426C22⋊Dic79C2414yes—
427C22⋊Dic79C2414yes—
428C22⋊Dic79C24116yes—
429C22⋊Dic79C2418yes—
430C22⋊Dic79C2418yes—
431(C2×D79)⋊C4C2418yes—
432(C2×D79)⋊C4C2418yes—
433(C2×D79)⋊C4C24116yes—
434(C2×D79)⋊C4C24116yes—
435(C2×D79)⋊C4C2418yes—
436(C2×D79)⋊C4C2418yes—
437(C2×D79)⋊C4C2418yes—
438(C2×D79)⋊C4C2418yes—
439(C2×D79)⋊C4C2418yes—
440(C2×D79)⋊C4C2418yes—
441C4×Dic79C2414yes—
442C4×Dic79C2418yes—
443C4×Dic79C2418yes—
444C4×Dic79C24116yes—
445C4×Dic79C2414yes—
446C24×C79C2412yes—
447C24×C79C2411yescharacteristic
448#41×C79—28no—
449#41×C79—28no—
450#41×C79—28no—
451#41×C79—28no—
452C2×Q8×C79—24no—
453C2×Q8×C79C2412yes—
454C2×Q8×C79C2412yes—
455C2×D4×C79—28no—
456C2×D4×C79—24no—
457C2×D4×C79C2414yes—
458C2×D4×C79C2412yes—
459C2×D4×C79C2412yes—
460C2×D4×C79C2414yes—
461C22×C4×C79—28no—
462C22×C4×C79#4118yescomplemented
463C22×C4×C79C2414yes—
464C22×C4×C79C2414yes—
465C22×C4×C79C2412yes—
466C22×C4×C79C2412yes—
467C22×C4×C79C2418yes—
468C22×C4×C79C2412yes—
469C22×C4×C79C2412yes—
470C22×C4×C79C2412yes—
471C22×C4×C79C2418yes—
472C22×C4×C79C2411yescharacteristic
473C22×C4×C79C2411yescharacteristic
474C22×C4×C79C2411yescharacteristic
475C22×C4×C79C2411yescharacteristic
476C22×C4×C79C2411yescharacteristic
477C22×C4×C79C2411yescharacteristic
478C4⋊C4×C79C2412yes—
479C4⋊C4×C79C2412yes—
480C4⋊C4×C79C2412yes—
481C4⋊C4×C79C2412yes—
482C4⋊C4×C79C2412yes—
483C4⋊C4×C79C2412yes—
484C4⋊C4×C79C2412yes—
485C4⋊C4×C79C2412yes—
486C4⋊C4×C79C2418yes—
487C4⋊C4×C79C2418yes—
488C22⋊C4×C79C2414yes—
489C22⋊C4×C79C2414yes—
490C22⋊C4×C79C2414yes—
491C22⋊C4×C79C2414yes—
492C22⋊C4×C79C2418yes—
493C22⋊C4×C79C2418yes—
494C42×C79C2414yes—
495C42×C79C2414yes—
496C42×C79C2414yes—
497C42×C79C2418yes—
498C42×C79C2418yes—
499C42×C79C2414yes—
500C23×C79—24no—
501C23×C79—41no—
502C23×C79—41no—
503C23×C79—42no—
504C23×C79—42no—
505C23×C79C2×#4114yes—
506C23×C79C2514yes—
507C23×C79C2511yescharacteristic
508C23×C79C2511yescharacteristic
509C23×C79C2511yescharacteristic
510C22×D79—24no—
511C22×D79—24no—
512C22×D79—42no—
513C22×D79—42no—
514C22×D79—42no—
515C22×D79—42no—
516C22×D79C2514yes—
517C22×D79C2514yes—
518Q8×C79—24no—
519Q8×C79—24no—
520D4×C79—28no—
521D4×C79—28no—
522D4×C79—24no—
523D4×C79—24no—
524C2×C4×C79—24no—
525C2×C4×C79—28no—
526C2×C4×C79—28no—
527C2×C4×C79—42no—
528C2×C4×C79—42no—
529C2×C4×C79—48no—
530C2×C4×C79—42no—
531C2×C4×C79—48no—
532C2×C4×C79—42no—
533C2×C4×C79C2×#4114yes—
534C2×C4×C79C2×#4114yes—
535C2×C4×C79C2×#4114yes—
536C2×C4×C79C2×#4114yes—
537C2×C4×C79C2×#4114yes—
538C2×C4×C79C2×#4114yes—
539C2×C4×C79C2514yes—
540C2×C4×C79C2514yes—
541C2×C4×C79C2514yes—
542C2×C4×C79C2514yes—
543C2×C4×C79C2514yes—
544C2×C4×C79C2511yescharacteristic
545C2×C4×C79C2511yescharacteristic
546C2×C4×C79C2511yescharacteristic
547C2×C4×C79C2511yescharacteristic
548C22⋊D79—28no—
549C22⋊D79—28no—
550C22⋊D79—28no—
551C22⋊D79—28no—
552C22⋊D79—416no—
553C22⋊D79—48no—
554C22⋊D79—48no—
555C2×Dic79—24no—
556C2×Dic79—24no—
557C2×Dic79—44no—
558C2×Dic79—44no—
559C2×Dic79—44no—
560C2×Dic79—42no—
561C2×Dic79—42no—
562C2×Dic79C2514yes—
563C2×Dic79C2514yes—
564C2×Dic79C2514yes—
565C2×Dic79C2514yes—
566C2×Dic79C2518yes—
567D316—24no—
568D316—24no—
569D316—24no—
570D316—24no—
571D316—48no—
572D316—48no—
573C4×D79—28no—
574C4×D79—28no—
575C4×D79—28no—
576C4×D79—28no—
577C4×D79—416no—
578C4×D79—48no—
579C4×D79—48no—
580Dic158—24no—
581Dic158—24no—
582Dic158—24no—
583Dic158—24no—
584Dic158—416no—
585C22×C79—21no—
586C22×C79—21no—
587C22×C79—21no—
588C22×C79—21no—
589C22×C79—21no—
590C22×C79—21no—
591C22×C79—24no—
592C22×C79—24no—
593C22×C79—24no—
594C22×C79—44no—
595C22×C79—84no—
596C22×C79C22×#4112yes—
597C22×C79C22×#4112yes—
598C22×C79C22×#4112yes—
599C22×C79C2611yescharacteristic
600C2×D79—24no—
601C2×D79—24no—
602C2×D79—24no—
603C2×D79—24no—
604C2×D79—24no—
605C2×D79—24no—
606C2×D79—48no—
607C2×D79—84no—
608C4×C79—24no—
609C4×C79—24no—
610C4×C79—24no—
611C4×C79—24no—
612C4×C79—24no—
613C4×C79C22×#4112yes—
614C4×C79C22×#4112yes—
615C4×C79C22×#4112yes—
616C4×C79C22×#4112yes—
617Dic79—24no—
618Dic79—24no—
619Dic79—24no—
620Dic79—28no—
621Dic79—24no—
622#62856—791nomaximal, Sylow
623C2×C79—22no—
624C2×C79—22no—
625C2×C79—22no—
626C2×C79—44no—
627C2×C79C23×#4111yescharacteristic
628C2×C79H(7,𝔽2)11yescharacteristic
629C2×C792−1+611yescharacteristic
630D79—44no—
631D79—44no—
632#3512—794no—
633#3512—794no—
634#3511—794no—
635#3511—794no—
636#3505—798no—
637#3495—794no—
638#3495—794no—
639#3494—794no—
640#3494—794no—
641#3493—794no—
642#3492—794no—
643#3461—794no—
644#3460—794no—
645C2×#544—791no—
646#3449—791no—
647#3449—791no—
648C2×#537—791no—
649#3428—791no—
650#3428D7911yescharacteristic, complemented
651C2×#520—791no—
652C79#6285611yescharacteristic, complemented, Sylow
653C22×#41—791no—
654C22×#41—791no—
655C22×#41C2×D7911yescharacteristic
656#556—798no—
657#556—798no—
658#555—798no—
659#555—798no—
660#554—798no—
661#554—798no—
662#553—7916no—
663#553—7916no—
664#553—7916no—
665#553—798no—
666#553—798no—
667#553—798no—
668#553—798no—
669#552—798no—
670#552—798no—
671#552—7916no—
672#552—798no—
673#552—798no—
674#551—7916no—
675#551—7916no—
676#548—7916no—
677#547—798no—
678#547—798no—
679#546—7916no—
680#544—794no—
681#544—794no—
682#544—794no—
683#544—794no—
684#542—798no—
685#542—798no—
686#542—798no—
687#542—798no—
688#541—798no—
689#541—798no—
690#540—798no—
691#540—798no—
692#539—7916no—
693#538—7916no—
694#537—794no—
695#537—794no—
696#537—794no—
697#537—794no—
698#537—792no—
699#537—792no—
700#537—792no—
701#537—792no—
702#536—792no—
703#536—792no—
704#536—792no—
705#536—792no—
706#535—792no—
707#535—792no—
708#535—792no—
709#535—792no—
710#534—794no—
711#534—794no—
712#533—798no—
713#533—798no—
714#532—794no—
715#532—798no—
716#532—794no—
717#532—798no—
718C2×C4⋊Q8—792no—
719C2×C4⋊Q8—792no—
720#529—798no—
721#529—7916no—
722#529—798no—
723#529—798no—
724#529—798no—
725C2×#125—792no—
726C2×#125—792no—
727#525—794no—
728#525—794no—
729#525—7916no—
730#525—794no—
731#525—794no—
732C2×C22⋊Q8—792no—
733C2×C22⋊Q8—792no—
734C2×C22⋊Q8—794no—
735C2×#121—792no—
736C2×#121—794no—
737C2×#121—792no—
738#520—794no—
739#520—794no—
740#520—794no—
741#520—794no—
742#520—792no—
743#520—792no—
744#520—792no—
745#520—792no—
746#520C2×D7912yescomplemented
747#520C2×D7912yescomplemented
748#520C2×D7912yescomplemented
749#520C2×D7912yescomplemented
750#519—792no—
751#519C2×D7912yescomplemented
752#518—792no—
753#518—794no—
754#518C2×D7914yes—
755#518C2×D7912yescomplemented
756C4×#41—794no—
757C4×#41—794no—
758C4×#41C2×D7914yescomplemented
759C4×#41C2×D7914yescomplemented
760C2×C4×Q8—792no—
761C2×C4×D4—794no—
762C2×C4×D4—792no—
763C2×#117—791no—
764C2×#117—794no—
765C2×#117—792no—
766C2×#117C2×D7911yescharacteristic
767C2×#117C2×D7911yescharacteristic
768C2×#117C2×D7914yescomplemented
769C22×C4⋊C4—791no—
770C22×C4⋊C4—792no—
771C2×#41—28no—
772C2×#41—7916no—
773C2×#41—792no—
774C2×#41—792no—
775C2×#41—792no—
776C2×#41—792no—
777C2×#41—792no—
778C2×#41—792no—
779C2×#41—792no—
780C2×#41—792no—
781C2×#41—1588no—
782C2×#41—1588no—
783C2×#41C22×D7912yes—
784C2×#41C22×D7912yes—
785C2×#41C22×D7912yes—
786C2×#41C22×D7912yes—
787C22×Q8—794no—
788C22×Q8—791no—
789C22×Q8—791no—
790C22×Q8C22×D7911yescharacteristic
791C22×D4—794no—
792C22×D4—792no—
793C22×D4—792no—
794C22×D4—791no—
795C22×D4—791no—
796C22×D4C22×D7912yes—
797C22×D4C22×D7911yescharacteristic
798C23×C4—792no—
799C23×C4—794no—
800C23×C4—792no—
801C23×C4—792no—
802C23×C4C22×D7912yes—
803C23×C4C22×D7911yescharacteristic
804C4⋊Q8—794no—
805C4⋊Q8—798no—
806C4⋊Q8—798no—
807C4⋊Q8—798no—
808C4⋊Q8—798no—
809C4⋊Q8—794no—
810#127—794no—
811#127—794no—
812#126—7916no—
813#126—7916no—
814#126—7916no—
815#126—7916no—
816#126—7916no—
817#126—7916no—
818#125—798no—
819#125—798no—
820#125—7916no—
821#125—7916no—
822#125—798no—
823#125—798no—
824#125—7916no—
825#124—794no—
826#124—794no—
827#124—7916no—
828#124—7916no—
829#124—794no—
830#124—794no—
831#124—7916no—
832#123—798no—
833#123—798no—
834#123—7916no—
835#123—7916no—
836#123—7916no—
837#123—7916no—
838#123—798no—
839#123—798no—
840#123—7916no—
841#123—7916no—
842C22⋊Q8—798no—
843C22⋊Q8—798no—
844C22⋊Q8—794no—
845C22⋊Q8—794no—
846C22⋊Q8—798no—
847C22⋊Q8—798no—
848C22⋊Q8—794no—
849C22⋊Q8—794no—
850C22⋊Q8—7916no—
851C22⋊Q8—794no—
852C22⋊Q8—794no—
853C22⋊Q8—794no—
854C22⋊Q8—794no—
855C22⋊Q8—7916no—
856C22⋊Q8—7916no—
857C22⋊Q8—7916no—
858C22⋊Q8—7916no—
859#121—7916no—
860#121—798no—
861#121—798no—
862#121—7916no—
863#121—794no—
864#121—794no—
865#121—798no—
866#121—798no—
867#121—798no—
868#121—798no—
869#121—794no—
870#121—794no—
871#121—798no—
872#121—798no—
873#121—7916no—
874#121—794no—
875#121—794no—
876#121—794no—
877#121—794no—
878#121—7916no—
879#121—7916no—
880#120—798no—
881#120—798no—
882#120—798no—
883#120—798no—
884C4×Q8—794no—
885C4×Q8—794no—
886C4×Q8—798no—
887C4×Q8—798no—
888C4×Q8—794no—
889C4×Q8—794no—
890C4×Q8—7916no—
891C4×Q8C22×D7914yes—
892C4×Q8C22×D7914yes—
893C4×Q8C22×D7914yes—
894C4×Q8C22×D7914yes—
895C4×D4—798no—
896C4×D4—798no—
897C4×D4—798no—
898C4×D4—798no—
899C4×D4—7916no—
900C4×D4—7916no—
901C4×D4—794no—
902C4×D4—794no—
903C4×D4—7916no—
904C4×D4—7916no—
905C4×D4—798no—
906C4×D4—798no—
907C4×D4—798no—
908C4×D4—798no—
909C4×D4—794no—
910C4×D4—794no—
911C4×D4—798no—
912C4×D4—798no—
913C4×D4—7916no—
914C4×D4C22×D7918yes—
915C4×D4C22×D7918yes—
916C4×D4C22×D7918yes—
917C4×D4C22×D7918yes—
918C4×D4C22×D7914yes—
919C4×D4C22×D7914yes—
920C4×D4C22×D7914yes—
921C4×D4C22×D7914yes—
922#117—792no—
923#117—792no—
924#117—792no—
925#117—792no—
926#117—7916no—
927#117—794no—
928#117—798no—
929#117—798no—
930#117—794no—
931#117—798no—
932#117—798no—
933#117—7916no—
934#117—7916no—
935#117C22×D7912yes—
936#117C22×D7912yes—
937#117C22×D7912yes—
938#117C22×D7912yes—
939#117C22×D7912yes—
940#117C22×D7912yes—
941#117C22×D7912yes—
942#117C22×D7912yes—
943#117C22×D7918yes—
944#117C22×D7918yes—
945#117C22×D7914yes—
946#117C22×D7914yes—
947C2×C4⋊C4—792no—
948C2×C4⋊C4—792no—
949C2×C4⋊C4—794no—
950C2×C4⋊C4—792no—
951C2×C4⋊C4—792no—
952C2×C4⋊C4—792no—
953C2×C4⋊C4—792no—
954C2×C4⋊C4—791no—
955C2×C4⋊C4—791no—
956C2×C4⋊C4—794no—
957C2×C4⋊C4—794no—
958C2×C4⋊C4—794no—
959C2×C4⋊C4—794no—
960C2×C4⋊C4—798no—
961C2×C4⋊C4—798no—
962C2×C4⋊C4—794no—
963C2×C4⋊C4—794no—
964C2×C4⋊C4C22×D7911yescharacteristic
965C2×C4⋊C4C22×D7911yescharacteristic
966C2×C4⋊C4C22×D7911yescharacteristic
967C2×C4⋊C4C22×D7911yescharacteristic
968C2×C4⋊C4C22×D7914yes—
969C2×C4⋊C4C22×D7914yes—
970C2×C22⋊C4—792no—
971C2×C22⋊C4—794no—
972C2×C22⋊C4—794no—
973C2×C22⋊C4—794no—
974C2×C22⋊C4—798no—
975C2×C22⋊C4C22×D7912yes—
976C2×C22⋊C4C22×D7912yes—
977C2×C22⋊C4C22×D7918yes—
978C2×C42—794no—
979C2×C42—792no—
980C2×C42—798no—
981C2×C42C22×D7912yes—
982C2×C42C22×D7912yes—
983C2×C42C22×D7918yes—
984C24—792no—
985C24—792no—
986C24C23×D7912yes—
987C24C23×D7911yescharacteristic
988#41—28no—
989#41—28no—
990#41—28no—
991#41—28no—
992#41—63216no—
993#41—1588no—
994#41—1588no—
995#41—1588no—
996#41—1588no—
997#41—1588no—
998#41—1588no—
999#41—1588no—
1000#41—1588no—
1001C2×Q8—24no—
1002C2×Q8—7916no—
1003C2×Q8—792no—
1004C2×Q8—792no—
1005C2×Q8—792no—
1006C2×Q8—792no—
1007C2×Q8—6324no—
1008C2×Q8—1584no—
1009C2×Q8—1584no—
1010C2×Q8C23×D7912yes—
1011C2×Q8C23×D7912yes—
1012C2×D4—28no—
1013C2×D4—24no—
1014C2×D4—798no—
1015C2×D4—798no—
1016C2×D4—7916no—
1017C2×D4—794no—
1018C2×D4—794no—
1019C2×D4—794no—
1020C2×D4—794no—
1021C2×D4—798no—
1022C2×D4—798no—
1023C2×D4—792no—
1024C2×D4—792no—
1025C2×D4—792no—
1026C2×D4—792no—
1027C2×D4—6324no—
1028C2×D4—1588no—
1029C2×D4—1588no—
1030C2×D4—1584no—
1031C2×D4—1584no—
1032C2×D4C23×D7914yes—
1033C2×D4C23×D7914yes—
1034C2×D4C23×D7912yes—
1035C2×D4C23×D7912yes—
1036C22×C4—28no—
1037C22×C4—792no—
1038C22×C4—792no—
1039C22×C4—794no—
1040C22×C4—794no—
1041C22×C4—794no—
1042C22×C4—798no—
1043C22×C4—798no—
1044C22×C4—7916no—
1045C22×C4—792no—
1046C22×C4—792no—
1047C22×C4—794no—
1048C22×C4—794no—
1049C22×C4—794no—
1050C22×C4—794no—
1051C22×C4—6324no—
1052C22×C4—6322no—
1053C22×C4—1588no—
1054C22×C4—1588no—
1055C22×C4#1192962418yescomplemented
1056C22×C4C23×D7914yes—
1057C22×C4C23×D7912yes—
1058C22×C4C23×D7914yes—
1059C22×C4C23×D7912yes—
1060C22×C4C23×D7912yes—
1061C22×C4C23×D7912yes—
1062C22×C4C23×D7912yes—
1063C22×C4C23×D7918yes—
1064C22×C4C23×D7918yes—
1065C22×C4C23×D7911yescharacteristic
1066C22×C4C23×D7911yescharacteristic
1067C22×C4C23×D7911yescharacteristic
1068C22×C4C23×D7911yescharacteristic
1069C22×C4C23×D7911yescharacteristic
1070C22×C4C23×D7911yescharacteristic
1071C4⋊C4—7916no—
1072C4⋊C4—798no—
1073C4⋊C4—798no—
1074C4⋊C4—7916no—
1075C4⋊C4—7916no—
1076C4⋊C4—7916no—
1077C4⋊C4—798no—
1078C4⋊C4—798no—
1079C4⋊C4—794no—
1080C4⋊C4—794no—
1081C4⋊C4—792no—
1082C4⋊C4—792no—
1083C4⋊C4—794no—
1084C4⋊C4—794no—
1085C4⋊C4—792no—
1086C4⋊C4—792no—
1087C4⋊C4—7916no—
1088C4⋊C4—798no—
1089C4⋊C4—798no—
1090C4⋊C4C23×D7912yes—
1091C4⋊C4C23×D7912yes—
1092C4⋊C4C23×D7912yes—
1093C4⋊C4C23×D7912yes—
1094C4⋊C4C23×D7912yes—
1095C4⋊C4C23×D7912yes—
1096C4⋊C4C23×D7912yes—
1097C4⋊C4C23×D7912yes—
1098C4⋊C4C23×D7918yes—
1099C4⋊C4C23×D7918yes—
1100C22⋊C4—794no—
1101C22⋊C4—794no—
1102C22⋊C4—7916no—
1103C22⋊C4—798no—
1104C22⋊C4—798no—
1105C22⋊C4—798no—
1106C22⋊C4—7916no—
1107C22⋊C4—798no—
1108C22⋊C4—7916no—
1109C22⋊C4—798no—
1110C22⋊C4—798no—
1111C22⋊C4—798no—
1112C22⋊C4—798no—
1113C22⋊C4—798no—
1114C22⋊C4—798no—
1115C22⋊C4C23×D7914yes—
1116C22⋊C4C23×D7914yes—
1117C22⋊C4C23×D7914yes—
1118C22⋊C4C23×D7914yes—
1119C22⋊C4C23×D7918yes—
1120C22⋊C4C23×D7918yes—
1121C42—794no—
1122C42—798no—
1123C42—7916no—
1124C42—798no—
1125C42—794no—
1126C42C23×D7914yes—
1127C42C23×D7914yes—
1128C42C23×D7914yes—
1129C42C23×D7918yes—
1130C42C23×D7918yes—
1131C42C23×D7914yes—
1132C23—24no—
1133C23—41no—
1134C23—41no—
1135C23—42no—
1136C23—42no—
1137C23—3162no—
1138C23—3162no—
1139C23—3162no—
1140C23—3162no—
1141C23—794no—
1142C23—794no—
1143C23—1584no—
1144C23—1584no—
1145C23C2×#1192962414yes—
1146C23C24×D7914yes—
1147C23C24×D7911yescharacteristic
1148C23C24×D7911yescharacteristic
1149C23C24×D7911yescharacteristic
1150Q8—24no—
1151Q8—24no—
1152Q8—31616no—
1153Q8—1584no—
1154Q8—1584no—
1155Q8—1584no—
1156Q8—1584no—
1157D4—28no—
1158D4—28no—
1159D4—24no—
1160D4—24no—
1161D4—3168no—
1162D4—3168no—
1163D4—3168no—
1164D4—31616no—
1165D4—3168no—
1166D4—1588no—
1167D4—1588no—
1168D4—1588no—
1169D4—1588no—
1170D4—1584no—
1171D4—1584no—
1172D4—1584no—
1173D4—1584no—
1174C2×C4—24no—
1175C2×C4—28no—
1176C2×C4—28no—
1177C2×C4—42no—
1178C2×C4—42no—
1179C2×C4—48no—
1180C2×C4—42no—
1181C2×C4—42no—
1182C2×C4—48no—
1183C2×C4—31616no—
1184C2×C4—3168no—
1185C2×C4—3168no—
1186C2×C4—3164no—
1187C2×C4—3164no—
1188C2×C4—3164no—
1189C2×C4—3162no—
1190C2×C4—3162no—
1191C2×C4—794no—
1192C2×C4—794no—
1193C2×C4—794no—
1194C2×C4—794no—
1195C2×C4—798no—
1196C2×C4—1584no—
1197C2×C4—1584no—
1198C2×C4—1588no—
1199C2×C4—1588no—
1200C2×C4—1588no—
1201C2×C4—1588no—
1202C2×C4C2×#1192962414yes—
1203C2×C4C2×#1192962414yes—
1204C2×C4C2×#1192962414yes—
1205C2×C4C2×#1192962414yes—
1206C2×C4C2×#1192962414yes—
1207C2×C4C2×#1192962414yes—
1208C2×C4C24×D7914yes—
1209C2×C4C24×D7914yes—
1210C2×C4C24×D7914yes—
1211C2×C4C24×D7914yes—
1212C2×C4C24×D7914yes—
1213C2×C4C24×D7911yescharacteristic
1214C2×C4C24×D7911yescharacteristic
1215C2×C4C24×D7911yescharacteristic
1216C2×C4C24×D7911yescharacteristic
1217C22—21no—
1218C22—21no—
1219C22—21no—
1220C22—21no—
1221C22—21no—
1222C22—21no—
1223C22—24no—
1224C22—24no—
1225C22—24no—
1226C22—44no—
1227C22—84no—
1228C22—3168no—
1229C22—6324no—
1230C22—1584no—
1231C22—1584no—
1232C22—1584no—
1233C22—1584no—
1234C22—1584no—
1235C22—1584no—
1236C22C22×#1192962412yes—
1237C22C22×#1192962412yes—
1238C22C22×#1192962412yes—
1239C22C25×D7911yescharacteristic
1240C4—24no—
1241C4—24no—
1242C4—24no—
1243C4—24no—
1244C4—24no—
1245C4—1584no—
1246C4—1584no—
1247C4—1588no—
1248C4—1584no—
1249C4—1584no—
1250C4C22×#1192962412yes—
1251C4C22×#1192962412yes—
1252C4C22×#1192962412yes—
1253C4C22×#1192962412yes—
1254C2—22no—
1255C2—22no—
1256C2—22no—
1257C2—44no—
1258C2—3164no—
1259C2—3164no—
1260C2C23×#1192962411yescharacteristic
1261C2#2377821111yescharacteristic
1262C2#2377821311yescharacteristic
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3428C2
hypercenter#3428D79
hypocenterC79#62856
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3428

Complements

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

NH ≅ G/Ntype
1. #23777322C2semidirect
2. #23777317C2semidirect
3. #23777311C2semidirect
4. #23777303C2semidirect
5. #23777230C2semidirect
6. #23777152C2semidirect
7. #23777142C2semidirect
8. #23777135C2semidirect
9. #23777125C2semidirect
10. #23777113C2semidirect
11. #23777103C2semidirect
12. #23776827C2semidirect
13. #23776816C2semidirect
14. C2×#19099191C2semidirect
15. #23776733C2semidirect
16. #23776729C2semidirect
17. C2×#19099141C2semidirect
18. #23776601C2semidirect
19. C2×#19099043C2semidirect
20. C79×#3428C2semidirect
23. #19099286C22semidirect
24. #19099281C22semidirect
25. #19099278C22semidirect
26. #19099276C22semidirect
27. #19099273C22semidirect
28. #19099268C22semidirect
29. #19099263C22semidirect
30. #19099263C22semidirect
31. #19099262C22semidirect
32. #19099262C22semidirect
33. #19099261C22semidirect
34. #19099259C22semidirect
35. #19099257C22semidirect
36. #19099254C22semidirect
37. #19099254C22semidirect
38. #19099252C22semidirect
39. #19099248C22semidirect
40. #19099246C22semidirect
41. #19099239C22semidirect
42. #19099237C22semidirect
43. #19099222C22semidirect
44. #19099218C22semidirect
45. #19099214C22semidirect
46. #19099203C22semidirect
47. #19099191C22semidirect
48. #19099191C22semidirect
49. #19099191C22semidirect
50. #19099191C22semidirect
51. #19099185C22semidirect
52. #19099184C22semidirect
53. #19099184C22semidirect
54. #19099178C22semidirect
55. #19099175C22semidirect
56. #19099171C22semidirect
57. #19099168C22semidirect
58. #19099164C22semidirect
59. #19099155C22semidirect
60. #19099146C22semidirect
61. #19099144C22semidirect
62. #19099144C22semidirect
65. #19099141C22semidirect
66. #19099141C22semidirect
67. #19099141C22semidirect
68. #19099141C22semidirect
70. #19099139C22semidirect
72. #19099134C22semidirect
74. #19099132C22semidirect
76. #19099127C22semidirect
79. #19099120C22semidirect
80. #19099117C22semidirect
81. #19099113C22semidirect
82. #19099113C22semidirect
83. #19099110C22semidirect
84. #19099109C22semidirect
85. C2×#14579161C22semidirect
86. C2×#14579160C22semidirect
87. #19099100C22semidirect
88. #19099097C22semidirect
89. #19099097C22semidirect
90. #19099095C22semidirect
91. #19099093C22semidirect
92. C2×#14579153C22semidirect
93. C2×#14579152C22semidirect
95. #19099075C22semidirect
97. #19099072C22semidirect
98. #19099070C22semidirect
99. C2×#14579140C22semidirect
101. C2×#14579137C22semidirect
102. C2×#14579135C22semidirect
104. C2×#14579132C22semidirect
105. #19099044C22semidirect
106. #19099044C22semidirect
109. #19099043C22semidirect
110. #19099043C22semidirect
111. #19099043C22semidirect
112. #19099043C22semidirect
113. #19099040C22semidirect
114. #19099037C22semidirect
116. C4×#11929624C22semidirect
117. #19099031C22semidirect
118. C2×C4×Dic158C22semidirect
119. C2×C4×D316C22semidirect
122. C2×#14579119C22semidirect
123. #117×D79C22semidirect
125. C2×C4⋊C4×D79C22semidirect
127. #520×C79C22semidirect
128. #520×C79C22semidirect
129. #520×C79C22semidirect
130. #520×C79C22semidirect
131. #519×C79C22semidirect
133. #518×C79C22semidirect
134. C4×#41×C79C22semidirect
135. C4×#41×C79C22semidirect
138. C2×#117×C79C22semidirect
462. C22×C4×C79#41semidirect
650. #3428D79semidirect
652. C79#62856semidirect
746. #520C2×D79semidirect
747. #520C2×D79semidirect
748. #520C2×D79semidirect
749. #520C2×D79semidirect
751. #519C2×D79semidirect
755. #518C2×D79semidirect
758. C4×#41C2×D79semidirect
759. C4×#41C2×D79semidirect
768. C2×#117C2×D79semidirect
1055. C22×C4#11929624semidirect

Maximal subgroups

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

subgroupindex
#237773222
#237773172
#237773112
#237773032
#237772302
#237771522
#237771422
#237771352
#237771252
#237771132
#237771032
#237768272
#237768162
C2×#190991912
#237767332
#237767292
C2×#190991412
#237766012
C2×#190990432
C79×#34282
#6285679