Finite Group Databasebeta

← #35196722

Subgroups — #35196722

Order 20224.

7104 conjugacy classes of subgroups.

The subgroup lattice has 1350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777490C212yesmaximal, complemented
2#23777439C216yesmaximal, complemented
3#23777411C212yesmaximal, complemented
4#23777368C216yesmaximal, complemented
5#23777303C213yesmaximal, complemented
6#23777281C213yesmaximal, complemented
7#23777213C211yesmaximal, characteristic, complemented
8#23777181C211yesmaximal, characteristic, complemented
9#23777153C213yesmaximal, complemented
10#23777142C213yesmaximal, complemented
11#23777081C211yesmaximal, characteristic, complemented
12#23777073C211yesmaximal, characteristic, complemented
13#23777017C212yesmaximal, complemented
14#23777015C216yesmaximal, complemented
15Q8×#11929624C212yesmaximal, complemented
16#23776962C216yesmaximal, complemented
17#23776833C213yesmaximal, complemented
18#23776827C213yesmaximal, complemented
19#23776693C213yesmaximal, complemented
20C2×#19099117C213yesmaximal, complemented
21C4×#14579208C211yesmaximal, characteristic, complemented
22C4×#41×D79C211yesmaximal, characteristic, complemented
23C4×2−1+4×C79C211yesmaximal, characteristic, complemented
24C2×#14579208C2211yescharacteristic
25C2×#41×D79C2211yescharacteristic
26Q8×Dic158C2212yescomplemented
27#19099291C2216yescomplemented
28#19099291C2216yescomplemented
29#19099289C2212yescomplemented
30#19099286C2216yescomplemented
31#19099285C2216yescomplemented
32#19099285C2216yescomplemented
33#19099281C2216yescomplemented
34#19099281C2216yescomplemented
35#19099276C2216yescomplemented
36#19099273C2216yes—
37#19099272C2216yescomplemented
38#19099268C2216yes—
39#19099268C2216yescomplemented
40#19099262C22112yescomplemented
41#19099254C2216yes—
42#19099254C2216yescomplemented
43#19099253C22112yescomplemented
44#19099252C2216yes—
45#19099248C2216yescomplemented
46#19099246C22112yescomplemented
47#19099246C22112yescomplemented
48#19099246C22112yescomplemented
49#19099242C22112yes—
50#19099237C22112yes—
51Q8×D316C2212yes—
52D4×Dic158C2216yescomplemented
53Q8×C22⋊D79C2212yes—
54Q8×C22⋊D79C2212yescomplemented
55Q8×C22⋊D79C2212yescomplemented
56#19099225C2212yes—
57#19099224C2212yes—
58#19099222C22112yescomplemented
59#19099217C2216yes—
60#19099214C2216yescomplemented
61#19099212C2216yes—
62#19099212C2216yescomplemented
63#19099212C2216yescomplemented
64#19099208C2216yes—
65#19099201C2216yes—
66#19099194C2213yescomplemented
67#19099191C2213yescomplemented
68#19099185C2216yescomplemented
69#19099185C2216yescomplemented
70#19099184C2216yescomplemented
71#19099178C2216yescomplemented
72#19099175C2216yescomplemented
73#19099171C2216yescomplemented
74#19099171C2216yescomplemented
75#19099171C2216yescomplemented
76#19099160C22112yescomplemented
77#19099155C22112yescomplemented
78#19099144C2213yes—
79#19099141C2213yes—
80#19099139C2213yes—
81#19099137C2213yes—
82#19099137C2213yescomplemented
83#19099134C2213yescomplemented
84#19099120C2216yescomplemented
85#19099117C2216yes—
86#19099117C2216yes—
87#19099117C2213yes—
88#19099117C2216yes—
89#19099117C2213yescomplemented
90#19099117C2216yescomplemented
91#19099117C2216yescomplemented
92#19099117C2216yescomplemented
93#19099117C2216yescomplemented
94#19099117C2216yescomplemented
95#19099116C2213yescomplemented
96#19099110C2211yescharacteristic
97#19099110C2213yescomplemented
98#19099109C2213yescomplemented
99C2×#14579160C2213yescomplemented
100C2×#14579159C2213yescomplemented
101#19099100C2213yes—
102#19099100C2213yescomplemented
103#19099100C2216yescomplemented
104#19099097C2216yescomplemented
105#19099097C22112yescomplemented
106#19099095C2213yes—
107#19099095C2213yescomplemented
108#19099093C22112yescomplemented
109#19099093C2216yescomplemented
110#19099093C2216yescomplemented
111#19099091C2216yes—
112#19099091C2216yescomplemented
113C2×#14579151C2216yescomplemented
114#19099075C2213yes—
115#19099072C2216yes—
116#19099072C2216yes—
117#19099070C2213yes—
118C2×#14579141C2213yes—
119C2×#14579139C2216yes—
120C2×#14579137C2213yes—
121#19099046C2211yescharacteristic
122#19099043C2213yescomplemented
123#19099042C2216yescomplemented
124#19099040C2213yescomplemented
125#19099039C2212yescomplemented
126#41×Dic79C2211yescharacteristic
127C4×#11929625C2211yescharacteristic
128C4×#11929625C2211yescharacteristic
129C4×#11929624C2213yes—
130C4×#11929624C2216yes—
131C4×#11929624C2213yescomplemented
132C4×#11929624C2216yescomplemented
133#19099031C2213yes—
134C4×#11929623C2213yes—
135C4×#11929623C2213yes—
136C4×#11929623C2216yescomplemented
137C2×C4×Dic158C2213yescomplemented
138C2×C4×Dic158C2216yescomplemented
139C4×Q8×D79C2211yescharacteristic
140C4×Q8×D79C2211yescharacteristic
141C4×Q8×D79C2212yescomplemented
142C4×D4×D79C2213yes—
143C4×D4×D79C2213yes—
144C2×#14579118C2216yes—
145#117×D79C2213yes—
146C2×C42×D79C2213yes—
147C2×2−1+4×C79C2211yescharacteristic
148#520×C79C2211yescharacteristic
149#520×C79C2213yescomplemented
150#520×C79C2216yescomplemented
151#519×C79C2213yescomplemented
152#519×C79C2212yescomplemented
153C4×#41×C79C2211yescharacteristic
154C4×#41×C79C2213yescomplemented
155C4×#41×C79C2216yescomplemented
156C2×C4×Q8×C79C2213yescomplemented
157C2×C4×Q8×C79C2212yescomplemented
158#14579208—28no—
159C2×#11929625C2311yescharacteristic
160C2×#11929624C2313yes—
161C2×#11929624C2313yes—
162C2×#11929624C2312yes—
163C2×#11929624C2316yes—
164C2×#11929623C2316yes—
165C2×#11929623C2313yes—
166#41×D79—28no—
167C22×Dic158C2313yes—
168C22×Dic158C2316yes—
169C2×Q8×D79C2312yes—
170C2×Q8×D79C2311yescharacteristic
171C2×D4×D79C2313yes—
172C22×C4×D79C2313yes—
173C22×C4×D79C2313yes—
174C22×C4×D79C2313yes—
175#14579161C2316yes—
176#14579161C2316yes—
177#14579160C2316yes—
178#14579160C2316yes—
179#14579160C2316yes—
180#14579160C2316yes—
181#14579160C2313yes—
182#14579160C2311yescharacteristic
183#14579159C2316yes—
184#14579159C2316yes—
185#14579159C2316yes—
186#14579159C2316yes—
187#14579159C2313yes—
188#14579157C2311yescharacteristic
189#14579156C2316yes—
190#14579156C23112yes—
191#14579156C23112yes—
192#14579156C2316yes—
193#14579155C23112yes—
194#14579155C23112yes—
195#14579155C23112yes—
196#14579154C2316yes—
197#14579154C23112yes—
198#14579154C2316yes—
199#14579153C23112yes—
200#14579153C23112yes—
201#14579153C2316yes—
202#14579152C2313yes—
203#14579152C2313yes—
204#14579152C2316yes—
205#14579151C23112yes—
206#14579151C23112yes—
207#14579151C23112yes—
208#14579151C2316yes—
209#14579151C23112yes—
210#14579151C23112yes—
211#14579151C2316yes—
212#14579150C2316yes—
213#14579150C2313yes—
214#14579149C2316yes—
215#14579149C23112yes—
216#14579148C2313yes—
217#14579147C23112yes—
218#14579147C2316yes—
219#14579147C2312yes—
220#14579146C2316yes—
221#14579146C23112yes—
222#14579146C2316yes—
223#14579145C23112yes—
224#14579145C2316yes—
225#14579144C23112yes—
226#14579144C23112yes—
227#14579144C23112yes—
228#14579143C2316yes—
229#14579143C2316yes—
230#14579142C23112yes—
231#14579142C2316yes—
232#14579141C2313yes—
233#14579141C2316yes—
234#14579141C2316yes—
235#14579141C2316yes—
236#14579141C2316yes—
237#14579141C2313yes—
238#14579140C2316yes—
239#14579140C23112yes—
240#14579140C23112yes—
241#14579140C2316yes—
242#14579140C2316yes—
243#14579139C23112yes—
244#14579139C23112yes—
245#14579139C23112yes—
246#14579139C23112yes—
247#14579139C2316yes—
248#14579139C2316yes—
249#14579138C23112yes—
250#14579138C2316yes—
251#14579138C2316yes—
252#14579137C2313yes—
253#14579137C2316yes—
254#14579137C2316yes—
255#14579137C2316yes—
256#14579137C2316yes—
257#14579137C2316yes—
258#14579137C2313yes—
259#14579136C2313yes—
260#14579136C2316yes—
261#14579136C2311yescharacteristic
262#14579135C2316yes—
263#14579135C23112yes—
264#14579134C2316yes—
265#14579134C2312yes—
266#14579133C23112yes—
267#14579133C2316yes—
268#14579133C2316yes—
269#14579132C2313yes—
270#14579132C2311yescharacteristic
271#14579131C2316yes—
272#14579129C2316yes—
273Q8×Dic79C2312yes—
274Q8×Dic79C2311yescharacteristic
275Q8×Dic79C2311yescharacteristic
276C4×Dic158C2313yes—
277C4×Dic158C2313yes—
278C4×Dic158C2316yes—
279C4×Dic158C2316yes—
280C4×Dic158C23112yes—
281C4×Dic158C2316yes—
282C4×Dic158C2316yes—
283C4×Dic158C23112yes—
284C4×Dic158C2316yes—
285C4×Dic158C2313yes—
286C4×Dic158C2316yes—
287C4×Dic158C2316yes—
288C4×Dic158C2313yes—
289C4×Dic158C23112yes—
290#14579126C2316yes—
291#14579126C2316yes—
292#14579126C2313yes—
293#14579126C2313yes—
294C4×D316C2313yes—
295C4×D316C2313yes—
296C4×D316C2316yes—
297C4×D316C2316yes—
298C4×D316C2316yes—
299C4×D316C2313yes—
300C4×D316C2311yescharacteristic
301C4×D316C2316yes—
302D4×Dic79C2316yes—
303D4×Dic79C2313yes—
304D4×Dic79C2313yes—
305#14579123C2313yes—
306#14579123C2313yes—
307C4×C22⋊D79C2316yes—
308C4×C22⋊D79C2316yes—
309C4×C22⋊D79C2316yes—
310C4×C22⋊D79C2316yes—
311C4×C22⋊D79C2316yes—
312C4×C22⋊D79C2316yes—
313C4×C22⋊D79C2316yes—
314C4×C22⋊D79C2316yes—
315C4×C22⋊D79C2316yes—
316C4×C22⋊D79C2316yes—
317C4×C22⋊D79C2312yes—
318C4×C22⋊D79C2316yes—
319(C22⋊D79)⋊C4C2316yes—
320(C22⋊D79)⋊C4C23112yes—
321(C22⋊D79)⋊C4C2316yes—
322#14579120C2313yes—
323#14579120C2313yes—
324#14579120C2316yes—
325#14579120C2316yes—
326#14579119C2313yes—
327#14579119C2316yes—
328#14579119C2313yes—
329#14579118C2316yes—
330#14579118C2316yes—
331#14579118C23112yes—
332#14579118C2316yes—
333#14579118C2316yes—
334#14579118C23112yes—
335#14579118C2316yes—
336#14579118C23112yes—
337#14579118C2316yes—
338#14579117C23112yes—
339#14579117C2316yes—
340C2×C4⋊Dic79C2313yes—
341C2×C4⋊Dic79C2316yes—
342C2×Dic79⋊C4C2316yes—
343C2×Dic79⋊C4C2316yes—
344C2×Dic79⋊C4C2316yes—
345C2×Dic79⋊C4C2316yes—
346C2×Dic79⋊C4C2316yes—
347C4⋊C4×D79C2316yes—
348C4⋊C4×D79C2313yes—
349C4⋊C4×D79C2313yes—
350C2×(C2×D79)⋊C4C2316yes—
351C2×(C2×D79)⋊C4C2316yes—
352C22⋊C4×D79C2316yes—
353C2×C4×Dic79C2313yes—
354C2×C4×Dic79C2313yes—
355C2×C4×Dic79C2313yes—
356C2×C4×Dic79C2316yes—
357C42×D79C2311yescharacteristic
358C42×D79C2313yes—
359C42×D79C2313yes—
360C42×D79C2313yes—
361C42×D79C2313yes—
362C42×D79C2313yes—
363C42×D79C2313yes—
364C42×D79C2313yes—
365C42×D79C2316yes—
3662−1+4×C79—28no—
367C2×#41×C79C2313yes—
368C2×#41×C79C2316yes—
369C2×#41×C79C2311yescharacteristic
370C22×Q8×C79C2313yes—
371C22×Q8×C79C2312yes—
372C4×Q8×C79C2313yes—
373C4×Q8×C79C2316yes—
374C4×Q8×C79C2316yes—
375C4×Q8×C79C2312yes—
376C4×Q8×C79C2311yescharacteristic
377C4×Q8×C79C2313yes—
378C4×Q8×C79C2316yes—
379C4×Q8×C79C2316yes—
380C4×Q8×C79C2311yescharacteristic
381C4×Q8×C79C2316yes—
382C4×D4×C79C2316yes—
383C4×D4×C79C2313yes—
384C4×D4×C79C2316yes—
385C4×D4×C79C23112yes—
386C4×D4×C79C2313yes—
387C4×D4×C79C2313yes—
388C4×D4×C79C2316yes—
389C4×D4×C79C2311yescharacteristic
390#117×C79C2313yes—
391#117×C79C2316yes—
392#117×C79C2313yes—
393#117×C79C23112yes—
394#117×C79C2316yes—
395C2×C4⋊C4×C79C2313yes—
396C2×C4⋊C4×C79C2316yes—
397C2×C4⋊C4×C79C2316yes—
398C2×C42×C79C2313yes—
399C2×C42×C79C2316yes—
400C2×C42×C79C2316yes—
401C23×D79C2413yes—
402#11929625—24no—
403#11929624—28no—
404#11929624—212no—
405#11929624—212no—
406#11929624—412no—
407#11929623—212no—
408#11929623—224no—
409C2×Dic158—212no—
410C2×Dic158—412no—
411C2×Dic158C2416yes—
412C2×Dic158C2413yes—
413C2×Dic158C2416yes—
414C2×Dic158C2413yes—
415C2×Dic158C2412yes—
416C2×Dic158C24112yes—
417Q8×D79—24no—
418Q8×D79—28no—
419C2×D316C2411yescharacteristic
420C2×D316C2413yes—
421C2×D316C2412yes—
422C2×D316C2416yes—
423C2×C22⋊D79C2416yes—
424C2×C22⋊D79C2416yes—
425C2×C22⋊D79C2412yes—
426C2×C22⋊D79C2412yes—
427C2×C22⋊D79C2412yes—
428C2×C22⋊D79C2416yes—
429D4×D79—212no—
430C22×Dic79C2413yes—
431C22×Dic79C2416yes—
432C22×Dic79C2413yes—
433C22×Dic79C2413yes—
434C22×Dic79C2416yes—
435C2×C4×D79—212no—
436C2×C4×D79—212no—
437C2×C4×D79—46no—
438C2×C4×D79C2416yes—
439C2×C4×D79C2413yes—
440C2×C4×D79C2413yes—
441C2×C4×D79C2413yes—
442C2×C4×D79C2413yes—
443C2×C4×D79C2412yes—
444C2×C4×D79C2411yescharacteristic
445C2×C4×D79C2411yescharacteristic
446C2×C4×D79C2413yes—
447C2×C4×D79C2413yes—
448C2×C4×D79C2413yes—
449C2×C4×D79C2416yes—
450C2×C4×D79C2413yes—
451C2×C4×D79C2413yes—
452C2×C4×D79C2411yescharacteristic
453C4⋊Dic79C2416yes—
454C4⋊Dic79C2413yes—
455C4⋊Dic79C2413yes—
456C4⋊Dic79C2413yes—
457C4⋊Dic79C2416yes—
458C4⋊Dic79C24112yes—
459C4⋊Dic79C2411yescharacteristic
460C4⋊Dic79C2416yes—
461C4⋊Dic79C2416yes—
462C4⋊Dic79C2416yes—
463Dic79⋊C4C24112yes—
464Dic79⋊C4C2416yes—
465Dic79⋊C4C2416yes—
466Dic79⋊C4C2416yes—
467Dic79⋊C4C2416yes—
468Dic79⋊C4C2416yes—
469Dic79⋊C4C2416yes—
470Dic79⋊C4C2416yes—
471Dic79⋊C4C24112yes—
472Dic79⋊C4C24112yes—
473Dic79⋊C4C24112yes—
474Dic79⋊C4C24112yes—
475Dic79⋊C4C2416yes—
476Dic79⋊C4C2412yes—
477Dic79⋊C4C2416yes—
478Dic79⋊C4C2416yes—
479Dic79⋊C4C2416yes—
480C22⋊Dic79C2416yes—
481C22⋊Dic79C2416yes—
482C22⋊Dic79C2412yes—
483C22⋊Dic79C2416yes—
484C22⋊Dic79C2416yes—
485C22⋊Dic79C2416yes—
486(C2×D79)⋊C4C2416yes—
487(C2×D79)⋊C4C2416yes—
488(C2×D79)⋊C4C2416yes—
489(C2×D79)⋊C4C2416yes—
490(C2×D79)⋊C4C24112yes—
491(C2×D79)⋊C4C24112yes—
492(C2×D79)⋊C4C2412yes—
493(C2×D79)⋊C4C2412yes—
494(C2×D79)⋊C4C2416yes—
495(C2×D79)⋊C4C2416yes—
496(C2×D79)⋊C4C2416yes—
497(C2×D79)⋊C4C2416yes—
498(C2×D79)⋊C4C2416yes—
499(C2×D79)⋊C4C2416yes—
500C4×Dic79C2411yescharacteristic
501C4×Dic79C2411yescharacteristic
502C4×Dic79C2411yescharacteristic
503C4×Dic79C2413yes—
504C4×Dic79C2413yes—
505C4×Dic79C2413yes—
506C4×Dic79C2413yes—
507C4×Dic79C2413yes—
508C4×Dic79C2413yes—
509C4×Dic79C2413yes—
510C4×Dic79C2413yes—
511C4×Dic79C2413yes—
512C4×Dic79C2416yes—
513C4×Dic79C2416yes—
514C4×Dic79C2416yes—
515C4×Dic79C24112yes—
516#41×C79—224no—
517#41×C79—212no—
518#41×C79#4118yescomplemented
519C2×Q8×C79—28no—
520C2×Q8×C79—212no—
521C2×Q8×C79C2413yes—
522C2×Q8×C79C2416yes—
523C2×Q8×C79C2411yescharacteristic
524C2×D4×C79C2416yes—
525C2×D4×C79C2411yescharacteristic
526C2×D4×C79C2413yes—
527C22×C4×C79C2412yes—
528C22×C4×C79C2413yes—
529C22×C4×C79C2416yes—
530C22×C4×C79C2416yes—
531C22×C4×C79C2416yes—
532C22×C4×C79C2416yes—
533C22×C4×C79C2413yes—
534C22×C4×C79C2413yes—
535C4⋊C4×C79C2413yes—
536C4⋊C4×C79C2413yes—
537C4⋊C4×C79C2416yes—
538C4⋊C4×C79C2416yes—
539C4⋊C4×C79C24112yes—
540C4⋊C4×C79C2413yes—
541C4⋊C4×C79C2411yescharacteristic
542C4⋊C4×C79C2416yes—
543C22⋊C4×C79C2416yes—
544C22⋊C4×C79C2416yes—
545C22⋊C4×C79C2412yes—
546C22⋊C4×C79C2416yes—
547C42×C79C2411yescharacteristic
548C42×C79C2413yes—
549C42×C79C2416yes—
550C42×C79C2413yes—
551C42×C79C2413yes—
552C42×C79C2416yes—
553C42×C79C24112yes—
554C42×C79C2416yes—
555C23×C79C2512yes—
556C23×C79C2513yes—
557C22×D79—26no—
558C22×D79—26no—
559C22×D79—43no—
560C22×D79C2513yes—
561C22×D79C2512yes—
562C22×D79C2511yescharacteristic
563Q8×C79—212no—
564Q8×C79—26no—
565Q8×C79C2×#4114yes—
566D4×C79—212no—
567D4×C79—22no—
568D4×C79C2×#41112yes—
569C2×C4×C79—212no—
570C2×C4×C79—212no—
571C2×C4×C79—26no—
572C2×C4×C79—24no—
573C2×C4×C79—43no—
574C2×C4×C79—46no—
575C2×C4×C79—46no—
576C2×C4×C79C2×#41112yes—
577C2×C4×C79C2513yes—
578C2×C4×C79C2511yescharacteristic
579C2×C4×C79C2513yes—
580C2×C4×C79C2516yes—
581C2×C4×C79C2512yes—
582C2×C4×C79C2516yes—
583C2×C4×C79C2513yes—
584C2×C4×C79C2511yescharacteristic
585C2×C4×C79C2511yescharacteristic
586C22⋊D79—212no—
587C22⋊D79—212no—
588C22⋊D79—24no—
589C22⋊D79—24no—
590C22⋊D79—24no—
591C22⋊D79—46no—
592C2×Dic79—26no—
593C2×Dic79—212no—
594C2×Dic79—26no—
595C2×Dic79—26no—
596C2×Dic79—46no—
597C2×Dic79C2511yescharacteristic
598C2×Dic79C2512yes—
599C2×Dic79C2513yes—
600C2×Dic79C2513yes—
601C2×Dic79C2516yes—
602C2×Dic79C2516yes—
603C2×Dic79C2513yes—
604C2×Dic79C2511yescharacteristic
605C2×Dic79C2511yescharacteristic
606D316—24no—
607D316—26no—
608D316—22no—
609D316—46no—
610C4×D79—26no—
611C4×D79—22no—
612C4×D79—26no—
613C4×D79—26no—
614C4×D79—26no—
615C4×D79—212no—
616C4×D79—26no—
617C4×D79—24no—
618C4×D79—26no—
619C4×D79—22no—
620C4×D79—26no—
621C4×D79—43no—
622C4×D79—43no—
623C4×D79—46no—
624C4×D792−1+414yescomplemented
625Dic158—212no—
626Dic158—26no—
627Dic158—26no—
628Dic158—24no—
629Dic158—212no—
630Dic158—412no—
631C22×C79—23no—
632C22×C79—23no—
633C22×C79—22no—
634C22×C79—22no—
635C22×C79—22no—
636C22×C79C22×#4116yes—
637C22×C79C2611yescharacteristic
638C2×D79—21no—
639C2×D79—21no—
640C2×D79—22no—
641C2×D79—23no—
642C2×D79—22no—
643C2×D79—23no—
644C2×D79—22no—
645C2×D79—23no—
646C2×D79—412no—
647C2×D79C2×2−1+412yes—
648C4×C79—26no—
649C4×C79—22no—
650C4×C79—23no—
651C4×C79—26no—
652C4×C79—21no—
653C4×C79—23no—
654C4×C79C22×#4116yes—
655C4×C79C22×#4112yes—
656C4×C79C2×2−1+412yes—
657Dic79—23no—
658Dic79—26no—
659Dic79—21no—
660Dic79—22no—
661Dic79—23no—
662Dic79—26no—
663Dic79—23no—
664Dic79C2×2−1+412yes—
665Dic79#58512yes—
666#62805—791nomaximal, Sylow
667C2×C79—26no—
668C2×C79—42no—
669C2×C79C23×#4111yescharacteristic
670C2×C79C22×2−1+411yescharacteristic
671C2×C79C2×#58511yescharacteristic
672D79—22no—
673D79—42no—
674D79—43no—
675#3523—792no—
676#3520—796no—
677#3518—792no—
678#3515—796no—
679#3511—793no—
680#3509—793no—
681#3503—791no—
682#3499—791no—
683#3495—793no—
684#3495—793no—
685#3489—791no—
686#3489—791no—
687#3482—796no—
688#3482—792no—
689Q8×#41—792no—
690#3475—796no—
691#3461—793no—
692#3461—793no—
693#3444—793no—
694C2×#533—793no—
695C4×2−1+4—791no—
696C4×2−1+4D7911yescharacteristic, complemented
697C2×C4×#41—791no—
698C79#6280511yescharacteristic, complemented, Sylow
699C2×2−1+4—791no—
700C2×2−1+4C2×D7911yescharacteristic
701C22×#41—791no—
702Q82—792no—
703#557—796no—
704#557—792no—
705#557—796no—
706#556—796no—
707#556—796no—
708#556—796no—
709#556—796no—
710#556—796no—
711#555—796no—
712#554—796no—
713#554—796no—
714#554—796no—
715#554—796no—
716#553—7912no—
717#552—796no—
718#552—796no—
719#552—7912no—
720#552—7912no—
721#552—7912no—
722#552—7912no—
723#552—796no—
724#552—796no—
725#551—7912no—
726#551—7912no—
727D4×Q8—792no—
728D4×Q8—792no—
729D4×Q8—792no—
730D4×Q8—792no—
731D4×Q8—796no—
732#548—792no—
733#548—792no—
734#548—7912no—
735#547—796no—
736#547—796no—
737#547—796no—
738#547—796no—
739#547—796no—
740#546—796no—
741#546—796no—
742#544—793no—
743#544—793no—
744#542—796no—
745#542—796no—
746#542—796no—
747#542—796no—
748#541—796no—
749#541—796no—
750#541—796no—
751#541—796no—
752#539—7912no—
753#539—7912no—
754#537—793no—
755#537—793no—
756#536—793no—
757#536—793no—
758#536—793no—
759#536—793no—
760#533—793no—
761#533—796no—
762#533—796no—
763#533—796no—
764#533—796no—
765#533—796no—
766#533—796no—
767#533—796no—
768#533—793no—
769#533—796no—
770#533—793no—
771#533—796no—
772#532—793no—
773#532—791no—
774#532—793no—
775C2×C4⋊Q8—793no—
776C2×C4⋊Q8—793no—
777#529—793no—
778#529—793no—
779#529—796no—
780#529—793no—
781#529—796no—
782#529—793no—
783#529—796no—
784#529—7912no—
785#529—796no—
786#529—796no—
787#529—7912no—
788#529—796no—
789C2×#125—796no—
790#525—793no—
791#525—796no—
792#525—796no—
793#525—793no—
794C2×C22⋊Q8—793no—
795C2×C22⋊Q8—793no—
796C2×C22⋊Q8—796no—
797#520—791no—
798#520—796no—
799#520—793no—
800#520C2×D7911yescharacteristic
801#520C2×D7913yescomplemented
802#520C2×D7916yescomplemented
803#519—792no—
804#519—793no—
805#519C2×D7913yescomplemented
806#519C2×D7912yescomplemented
807C4×#41—791no—
808C4×#41—791no—
809C4×#41—791no—
810C4×#41—793no—
811C4×#41—793no—
812C4×#41—796no—
813C4×#41—793no—
814C4×#41—793no—
815C4×#41—793no—
816C4×#41—796no—
817C4×#41—796no—
818C4×#41C2×D7911yescharacteristic
819C4×#41C2×D7913yescomplemented
820C4×#41C2×D7916yescomplemented
821C2×C4×Q8—791no—
822C2×C4×Q8—791no—
823C2×C4×Q8—792no—
824C2×C4×Q8—793no—
825C2×C4×Q8—796no—
826C2×C4×Q8C2×D7913yescomplemented
827C2×C4×Q8C2×D7912yescomplemented
828C2×C4×D4—793no—
829C2×C4×D4—793no—
830C2×#117—793no—
831C2×#117—796no—
832C22×C42—793no—
8332−1+4—28no—
8342−1+4—1588no—
835C2×#41—791no—
836C2×#41—793no—
837C2×#41—796no—
838C2×#41—796no—
839C2×#41—792no—
840C2×#41—793no—
841C2×#41—793no—
842C2×#41—1588no—
843C2×#41C22×D7913yes—
844C2×#41C22×D7916yes—
845C2×#41C22×D7911yescharacteristic
846C22×Q8—791no—
847C22×Q8—792no—
848C22×Q8—796no—
849C22×Q8—793no—
850C22×Q8C22×D7913yes—
851C22×Q8C22×D7912yes—
852C22×D4—793no—
853C23×C4—793no—
854C23×C4—793no—
855C23×C4—793no—
856C4⋊Q8—793no—
857C4⋊Q8—796no—
858C4⋊Q8—796no—
859C4⋊Q8—796no—
860C4⋊Q8—796no—
861C4⋊Q8—793no—
862C4⋊Q8—796no—
863C4⋊Q8—796no—
864C4⋊Q8—796no—
865C4⋊Q8—791no—
866C4⋊Q8—796no—
867C4⋊Q8—796no—
868C4⋊Q8—796no—
869#127—791no—
870#126—796no—
871#126—796no—
872#126—7912no—
873#126—7912no—
874#126—796no—
875#126—796no—
876#126—7912no—
877#126—7912no—
878#126—7912no—
879#126—7912no—
880#125—796no—
881#125—7912no—
882#125—7912no—
883#125—7912no—
884#125—793no—
885#125—793no—
886#125—796no—
887#125—7912no—
888#125—796no—
889#125—7912no—
890#125—7912no—
891#125—796no—
892#125—7912no—
893#124—793no—
894#124—796no—
895#124—793no—
896#124—792no—
897#124—796no—
898#124—7912no—
899#124—796no—
900#124—7912no—
901#123—796no—
902#123—7912no—
903#123—7912no—
904#123—7912no—
905#123—7912no—
906#123—796no—
907#123—796no—
908#123—7912no—
909#123—796no—
910#123—796no—
911#123—796no—
912#123—7912no—
913C22⋊Q8—793no—
914C22⋊Q8—796no—
915C22⋊Q8—796no—
916C22⋊Q8—796no—
917C22⋊Q8—793no—
918C22⋊Q8—796no—
919C22⋊Q8—796no—
920C22⋊Q8—796no—
921C22⋊Q8—7912no—
922C22⋊Q8—796no—
923C22⋊Q8—796no—
924C22⋊Q8—7912no—
925C22⋊Q8—796no—
926C22⋊Q8—793no—
927C22⋊Q8—796no—
928C22⋊Q8—7912no—
929C22⋊Q8—796no—
930C22⋊Q8—7912no—
931C22⋊Q8—796no—
932C22⋊Q8—7912no—
933C22⋊Q8—793no—
934C22⋊Q8—796no—
935C22⋊Q8—796no—
936C22⋊Q8—7912no—
937C22⋊Q8—796no—
938C22⋊Q8—796no—
939C22⋊Q8—7912no—
940#121—791no—
941#121—793no—
942#121—796no—
943#121—796no—
944#121—7912no—
945#121—7912no—
946#121—796no—
947#121—791no—
948#121—793no—
949#121—796no—
950#121—792no—
951#121—796no—
952#120—796no—
953#120—796no—
954C4×Q8—791no—
955C4×Q8—791no—
956C4×Q8—792no—
957C4×Q8—793no—
958C4×Q8—793no—
959C4×Q8—796no—
960C4×Q8—796no—
961C4×Q8—796no—
962C4×Q8—796no—
963C4×Q8—793no—
964C4×Q8—793no—
965C4×Q8—793no—
966C4×Q8—796no—
967C4×Q8—796no—
968C4×Q8—7912no—
969C4×Q8—7912no—
970C4×Q8—7912no—
971C4×Q8—793no—
972C4×Q8—796no—
973C4×Q8—796no—
974C4×Q8—796no—
975C4×Q8C22×D7911yescharacteristic
976C4×Q8C22×D7911yescharacteristic
977C4×Q8C22×D7913yes—
978C4×Q8C22×D7916yes—
979C4×Q8C22×D7912yes—
980C4×Q8C22×D7916yes—
981C4×Q8C22×D7916yes—
982C4×Q8C22×D7916yes—
983C4×Q8C22×D7913yes—
984C4×Q8C22×D7916yes—
985C4×D4—793no—
986C4×D4—793no—
987C4×D4—796no—
988C4×D4—796no—
989C4×D4—796no—
990C4×D4—796no—
991C4×D4—792no—
992C4×D4—796no—
993C4×D4—796no—
994C4×D4—796no—
995C4×D4—796no—
996C4×D4—796no—
997C4×D4—796no—
998C4×D4—796no—
999C4×D4—796no—
1000C4×D4—793no—
1001C4×D4—793no—
1002C4×D4—796no—
1003C4×D4—796no—
1004C4×D4—7912no—
1005C4×D4—793no—
1006C4×D4—793no—
1007C4×D4—791no—
1008C4×D4—793no—
1009C4×D4—796no—
1010C4×D4—796no—
1011C4×D4—796no—
1012C4×D4—796no—
1013C4×D4C22×D7913yes—
1014C4×D4C22×D7913yes—
1015C4×D4C22×D7916yes—
1016C4×D4C22×D7911yescharacteristic
1017C4×D4C22×D7916yes—
1018C4×D4C22×D7916yes—
1019C4×D4C22×D7913yes—
1020C4×D4C22×D79112yes—
1021#117—793no—
1022#117—793no—
1023#117—796no—
1024#117—796no—
1025#117—793no—
1026#117—793no—
1027#117—796no—
1028#117—796no—
1029#117—7912no—
1030#117—796no—
1031#117—796no—
1032#117—7912no—
1033#117—7912no—
1034#117—7912no—
1035#117—796no—
1036#117—796no—
1037#117—796no—
1038#117—796no—
1039#117C22×D7913yes—
1040#117C22×D7913yes—
1041#117C22×D7916yes—
1042#117C22×D79112yes—
1043#117C22×D7916yes—
1044C2×C4⋊C4—796no—
1045C2×C4⋊C4—796no—
1046C2×C4⋊C4—796no—
1047C2×C4⋊C4—793no—
1048C2×C4⋊C4—796no—
1049C2×C4⋊C4—796no—
1050C2×C4⋊C4—796no—
1051C2×C4⋊C4—793no—
1052C2×C4⋊C4—793no—
1053C2×C4⋊C4—796no—
1054C2×C4⋊C4C22×D7913yes—
1055C2×C4⋊C4C22×D7916yes—
1056C2×C4⋊C4C22×D7916yes—
1057C2×C22⋊C4—796no—
1058C2×C22⋊C4—796no—
1059C2×C22⋊C4—796no—
1060C2×C42—796no—
1061C2×C42—793no—
1062C2×C42—793no—
1063C2×C42—793no—
1064C2×C42—793no—
1065C2×C42—793no—
1066C2×C42—793no—
1067C2×C42—796no—
1068C2×C42—793no—
1069C2×C42—793no—
1070C2×C42—793no—
1071C2×C42—793no—
1072C2×C42—791no—
1073C2×C42C22×D7916yes—
1074C2×C42C22×D7913yes—
1075C2×C42C22×D7916yes—
1076C24—793no—
1077#41—224no—
1078#41—212no—
1079#41—31612no—
1080#41—1588no—
1081#41—1584no—
1082#41—15812no—
1083#41—15824no—
1084#41—15812no—
1085#41—15812no—
1086#41#1192962418yescomplemented
1087C2×Q8—28no—
1088C2×Q8—212no—
1089C2×Q8—31612no—
1090C2×Q8—7912no—
1091C2×Q8—792no—
1092C2×Q8—796no—
1093C2×Q8—796no—
1094C2×Q8—793no—
1095C2×Q8—793no—
1096C2×Q8—1584no—
1097C2×Q8—1588no—
1098C2×Q8—15812no—
1099C2×Q8C23×D7913yes—
1100C2×Q8C23×D7916yes—
1101C2×Q8C23×D7911yescharacteristic
1102C2×D4—796no—
1103C2×D4—792no—
1104C2×D4—792no—
1105C2×D4—796no—
1106C2×D4—796no—
1107C2×D4—792no—
1108C2×D4—796no—
1109C2×D4—792no—
1110C2×D4—793no—
1111C2×D4—791no—
1112C2×D4—15812no—
1113C2×D4C23×D7916yes—
1114C2×D4C23×D7911yescharacteristic
1115C2×D4C23×D7913yes—
1116C22×C4—3166no—
1117C22×C4—796no—
1118C22×C4—793no—
1119C22×C4—793no—
1120C22×C4—796no—
1121C22×C4—791no—
1122C22×C4—793no—
1123C22×C4—793no—
1124C22×C4—793no—
1125C22×C4—796no—
1126C22×C4—791no—
1127C22×C4—791no—
1128C22×C4—793no—
1129C22×C4—793no—
1130C22×C4—793no—
1131C22×C4—793no—
1132C22×C4—793no—
1133C22×C4—793no—
1134C22×C4—796no—
1135C22×C4—792no—
1136C22×C4—793no—
1137C22×C4—15812no—
1138C22×C4—15812no—
1139C22×C4C23×D7916yes—
1140C22×C4C23×D7916yes—
1141C22×C4C23×D7913yes—
1142C22×C4C23×D7912yes—
1143C22×C4C23×D7913yes—
1144C22×C4C23×D7916yes—
1145C22×C4C23×D7916yes—
1146C22×C4C23×D7913yes—
1147C4⋊C4—796no—
1148C4⋊C4—796no—
1149C4⋊C4—796no—
1150C4⋊C4—796no—
1151C4⋊C4—7912no—
1152C4⋊C4—796no—
1153C4⋊C4—796no—
1154C4⋊C4—796no—
1155C4⋊C4—7912no—
1156C4⋊C4—7912no—
1157C4⋊C4—7912no—
1158C4⋊C4—7912no—
1159C4⋊C4—792no—
1160C4⋊C4—796no—
1161C4⋊C4—796no—
1162C4⋊C4—796no—
1163C4⋊C4—796no—
1164C4⋊C4—796no—
1165C4⋊C4—793no—
1166C4⋊C4—796no—
1167C4⋊C4—793no—
1168C4⋊C4—793no—
1169C4⋊C4—7912no—
1170C4⋊C4—791no—
1171C4⋊C4—796no—
1172C4⋊C4—796no—
1173C4⋊C4—796no—
1174C4⋊C4C23×D7913yes—
1175C4⋊C4C23×D7913yes—
1176C4⋊C4C23×D7913yes—
1177C4⋊C4C23×D7916yes—
1178C4⋊C4C23×D7916yes—
1179C4⋊C4C23×D79112yes—
1180C4⋊C4C23×D7911yescharacteristic
1181C4⋊C4C23×D7916yes—
1182C22⋊C4—796no—
1183C22⋊C4—796no—
1184C22⋊C4—792no—
1185C22⋊C4—796no—
1186C22⋊C4—796no—
1187C22⋊C4—796no—
1188C22⋊C4—796no—
1189C22⋊C4—796no—
1190C22⋊C4—796no—
1191C22⋊C4—796no—
1192C22⋊C4—7912no—
1193C22⋊C4—7912no—
1194C22⋊C4—792no—
1195C22⋊C4—792no—
1196C22⋊C4—796no—
1197C22⋊C4—796no—
1198C22⋊C4—796no—
1199C22⋊C4—796no—
1200C22⋊C4—796no—
1201C22⋊C4—796no—
1202C22⋊C4C23×D7916yes—
1203C22⋊C4C23×D7916yes—
1204C22⋊C4C23×D7912yes—
1205C22⋊C4C23×D7916yes—
1206C42—791no—
1207C42—791no—
1208C42—793no—
1209C42—793no—
1210C42—793no—
1211C42—793no—
1212C42—793no—
1213C42—793no—
1214C42—793no—
1215C42—793no—
1216C42—796no—
1217C42—7912no—
1218C42—796no—
1219C42—791no—
1220C42—793no—
1221C42—796no—
1222C42C23×D7913yes—
1223C42C23×D7913yes—
1224C42C23×D7916yes—
1225C42C23×D79112yes—
1226C42C23×D7916yes—
1227C42C23×D7913yes—
1228C42C23×D7911yescharacteristic
1229C42C23×D7916yes—
1230C23—3163no—
1231C23—791no—
1232C23—793no—
1233C23—792no—
1234C23—1586no—
1235C23—1586no—
1236C23C24×D7912yes—
1237C23C24×D7913yes—
1238Q8—212no—
1239Q8—26no—
1240Q8—31612no—
1241Q8—15812no—
1242Q8—1584no—
1243Q8—15812no—
1244Q8—1586no—
1245Q8—1586no—
1246Q8C2×#1192962414yes—
1247D4—212no—
1248D4—22no—
1249D4—3166no—
1250D4—3166no—
1251D4—1584no—
1252D4—1584no—
1253D4—1584no—
1254D4—1584no—
1255D4—15812no—
1256D4—15812no—
1257D4—1586no—
1258D4—1582no—
1259D4C2×#11929624112yes—
1260C2×C4—212no—
1261C2×C4—26no—
1262C2×C4—24no—
1263C2×C4—212no—
1264C2×C4—43no—
1265C2×C4—46no—
1266C2×C4—46no—
1267C2×C4—3163no—
1268C2×C4—3163no—
1269C2×C4—3166no—
1270C2×C4—3166no—
1271C2×C4—791no—
1272C2×C4—791no—
1273C2×C4—794no—
1274C2×C4—791no—
1275C2×C4—792no—
1276C2×C4—793no—
1277C2×C4—793no—
1278C2×C4—796no—
1279C2×C4—796no—
1280C2×C4—793no—
1281C2×C4—1582no—
1282C2×C4—1586no—
1283C2×C4—1586no—
1284C2×C4—1586no—
1285C2×C4—1586no—
1286C2×C4—1586no—
1287C2×C4—1586no—
1288C2×C4—15812no—
1289C2×C4—1586no—
1290C2×C4—1584no—
1291C2×C4—1582no—
1292C2×C4—1586no—
1293C2×C4—1586no—
1294C2×C4—1586no—
1295C2×C4—15812no—
1296C2×C4C2×#11929624112yes—
1297C2×C4C24×D7913yes—
1298C2×C4C24×D7911yescharacteristic
1299C2×C4C24×D7913yes—
1300C2×C4C24×D7912yes—
1301C2×C4C24×D7916yes—
1302C2×C4C24×D7916yes—
1303C2×C4C24×D7913yes—
1304C2×C4C24×D7911yescharacteristic
1305C2×C4C24×D7911yescharacteristic
1306C22—23no—
1307C22—23no—
1308C22—22no—
1309C22—22no—
1310C22—22no—
1311C22—31612no—
1312C22—792no—
1313C22—1582no—
1314C22—1583no—
1315C22—1583no—
1316C22—1582no—
1317C22—1582no—
1318C22—1583no—
1319C22—1581no—
1320C22—1581no—
1321C22C22×#1192962416yes—
1322C22C25×D7911yescharacteristic
1323C4—26no—
1324C4—23no—
1325C4—22no—
1326C4—21no—
1327C4—23no—
1328C4—26no—
1329C4—792no—
1330C4—792no—
1331C4—1581no—
1332C4—1583no—
1333C4—1586no—
1334C4—1583no—
1335C4—1582no—
1336C4—1586no—
1337C4—1583no—
1338C4C22×#1192962416yes—
1339C4C22×#1192962412yes—
1340C42−1+4×D7912yes—
1341C2—26no—
1342C2—42no—
1343C2—3163no—
1344C2—3162no—
1345C2—1582no—
1346C2C23×#1192962411yescharacteristic
1347C2C2×2−1+4×D7911yescharacteristic
1348C2#585×D7911yescharacteristic
subgroupG/H
centerC2×C4C24×D79
commutator, socle, cosocleC22×C79C26
FrattiniC22C25×D79
FittingC4×2−1+4×C79C2
hypercenterC4×2−1+4D79
hypocenterC79#62805
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×2−1+4

Complements

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

NH ≅ G/Ntype
1. #23777490C2semidirect
2. #23777439C2semidirect
3. #23777411C2semidirect
4. #23777368C2semidirect
5. #23777303C2semidirect
6. #23777281C2semidirect
7. #23777213C2semidirect
8. #23777181C2semidirect
9. #23777153C2semidirect
10. #23777142C2semidirect
11. #23777081C2semidirect
12. #23777073C2semidirect
13. #23777017C2semidirect
14. #23777015C2semidirect
15. Q8×#11929624C2semidirect
16. #23776962C2semidirect
17. #23776833C2semidirect
18. #23776827C2semidirect
19. #23776693C2semidirect
20. C2×#19099117C2semidirect
21. C4×#14579208C2semidirect
22. C4×#41×D79C2semidirect
23. C4×2−1+4×C79C2semidirect
26. Q8×Dic158C22semidirect
27. #19099291C22semidirect
28. #19099291C22semidirect
29. #19099289C22semidirect
30. #19099286C22semidirect
31. #19099285C22semidirect
32. #19099285C22semidirect
33. #19099281C22semidirect
34. #19099281C22semidirect
35. #19099276C22semidirect
37. #19099272C22semidirect
39. #19099268C22semidirect
40. #19099262C22semidirect
42. #19099254C22semidirect
43. #19099253C22semidirect
45. #19099248C22semidirect
46. #19099246C22semidirect
47. #19099246C22semidirect
48. #19099246C22semidirect
52. D4×Dic158C22semidirect
54. Q8×C22⋊D79C22semidirect
55. Q8×C22⋊D79C22semidirect
58. #19099222C22semidirect
60. #19099214C22semidirect
62. #19099212C22semidirect
63. #19099212C22semidirect
66. #19099194C22semidirect
67. #19099191C22semidirect
68. #19099185C22semidirect
69. #19099185C22semidirect
70. #19099184C22semidirect
71. #19099178C22semidirect
72. #19099175C22semidirect
73. #19099171C22semidirect
74. #19099171C22semidirect
75. #19099171C22semidirect
76. #19099160C22semidirect
77. #19099155C22semidirect
82. #19099137C22semidirect
83. #19099134C22semidirect
84. #19099120C22semidirect
89. #19099117C22semidirect
90. #19099117C22semidirect
91. #19099117C22semidirect
92. #19099117C22semidirect
93. #19099117C22semidirect
94. #19099117C22semidirect
95. #19099116C22semidirect
97. #19099110C22semidirect
98. #19099109C22semidirect
99. C2×#14579160C22semidirect
100. C2×#14579159C22semidirect
102. #19099100C22semidirect
103. #19099100C22semidirect
104. #19099097C22semidirect
105. #19099097C22semidirect
107. #19099095C22semidirect
108. #19099093C22semidirect
109. #19099093C22semidirect
110. #19099093C22semidirect
112. #19099091C22semidirect
113. C2×#14579151C22semidirect
122. #19099043C22semidirect
123. #19099042C22semidirect
124. #19099040C22semidirect
125. #19099039C22semidirect
131. C4×#11929624C22semidirect
132. C4×#11929624C22semidirect
136. C4×#11929623C22semidirect
137. C2×C4×Dic158C22semidirect
138. C2×C4×Dic158C22semidirect
141. C4×Q8×D79C22semidirect
149. #520×C79C22semidirect
150. #520×C79C22semidirect
151. #519×C79C22semidirect
152. #519×C79C22semidirect
154. C4×#41×C79C22semidirect
155. C4×#41×C79C22semidirect
156. C2×C4×Q8×C79C22semidirect
157. C2×C4×Q8×C79C22semidirect
518. #41×C79#41semidirect
624. C4×D792−1+4semidirect
696. C4×2−1+4D79semidirect
698. C79#62805semidirect
801. #520C2×D79semidirect
802. #520C2×D79semidirect
805. #519C2×D79semidirect
806. #519C2×D79semidirect
819. C4×#41C2×D79semidirect
820. C4×#41C2×D79semidirect
826. C2×C4×Q8C2×D79semidirect
827. C2×C4×Q8C2×D79semidirect
1086. #41#11929624semidirect

Maximal subgroups

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

subgroupindex
#237774902
#237774392
#237774112
#237773682
#237773032
#237772812
#237772132
#237771812
#237771532
#237771422
#237770812
#237770732
#237770172
#237770152
Q8×#119296242
#237769622
#237768332
#237768272
#237766932
C2×#190991172
C4×#145792082
C4×#41×D792
C4×2−1+4×C792
#6280579