Finite Group Databasebeta

← #35197157

Subgroups — #35197157

Order 20224.

7050 conjugacy classes of subgroups.

The subgroup lattice has 1174 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777842C214yesmaximal, complemented
2#23777838C214yesmaximal, complemented
3#23777832C218yesmaximal, complemented
4#23777736C218yesmaximal, complemented
5#23777310C214yesmaximal, complemented
6#23777301C214yesmaximal, complemented
7#23777286C211yesmaximal, characteristic, complemented
8#23777285C212yesmaximal, complemented
9#23777284C211yesmaximal, characteristic, complemented
10#23777216C214yesmaximal, complemented
11#23777211C214yesmaximal, complemented
12#23777181C212yesmaximal, complemented
13#23777180C211yesmaximal, characteristic, complemented
14#23777102C218yesmaximal, complemented
15#23777049C212yesmaximal, complemented
16#23777048C212yesmaximal, complemented
17#23776695C211yesmaximal, characteristic, complemented
18#23776693C211yesmaximal, characteristic, complemented
19C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
20C79×#3499C211yesmaximal, characteristic, complemented
21C2×#14579208C2212yes—
22C22×Q8×D79C2212yes—
23#19099316C22116yescomplemented
24#19099314C22116yescomplemented
25#19099293C2218yescomplemented
26#19099291C2214yescomplemented
27#19099288C2214yescomplemented
28#19099288C2218yescomplemented
29#19099287C2214yescomplemented
30#19099283C2214yescomplemented
31#19099282C2218yescomplemented
32#19099277C2218yescomplemented
33#19099274C2218yes—
34#19099272C2218yescomplemented
35#19099268C2218yes—
36#19099268C2218yescomplemented
37#19099267C22116yes—
38#19099263C2218yes—
39#19099260C2218yes—
40#19099258C22116yes—
41#19099253C2218yes—
42#19099250C22116yes—
43#19099248C2218yes—
44D4×Dic158C2214yescomplemented
45#19099228C2218yes—
46Q8×C22⋊D79C2218yes—
47Q8×C22⋊D79C2218yes—
48Q8×C22⋊D79C2218yescomplemented
49#19099226C2218yes—
50#19099223C2218yes—
51#19099221C2218yes—
52#19099220C2218yes—
53#19099220C2218yes—
54#19099218C2214yescomplemented
55#19099213C2218yes—
56#19099212C22116yes—
57#19099212C2218yescomplemented
58#19099194C2218yescomplemented
59#19099192C22116yescomplemented
60#19099190C2218yes—
61#19099190C2218yescomplemented
62#19099181C22116yescomplemented
63#19099180C2218yescomplemented
64#19099178C2218yescomplemented
65#19099175C2214yescomplemented
66#19099174C2214yescomplemented
67#19099173C2218yescomplemented
68#19099159C22116yes—
69#19099156C22116yes—
70#19099142C2218yes—
71#19099137C2212yes—
72#19099137C2214yescomplemented
73#19099135C2218yes—
74#19099134C2212yes—
75#19099134C2212yes—
76#19099134C2218yes—
77#19099134C2214yescomplemented
78#19099133C2214yescomplemented
79#19099120C2211yescharacteristic
80#19099120C2214yescomplemented
81#19099118C2212yes—
82#19099118C2214yescomplemented
83#19099117C2212yes—
84#19099116C2211yescharacteristic
85#19099115C2218yescomplemented
86#19099111C2212yes—
87#19099111C2212yescomplemented
88#19099110C2212yes—
89#19099109C2211yescharacteristic
90#19099109C2214yescomplemented
91C2×#14579161C2211yescharacteristic
92C2×#14579160C2214yes—
93C2×#14579159C2212yes—
94C2×#14579159C2214yescomplemented
95C4⋊Q8×D79C2214yes—
96C4⋊Q8×D79C2214yes—
97C4⋊Q8×D79C2214yes—
98C4⋊Q8×D79C2214yes—
99C4⋊Q8×D79C2212yescomplemented
100#19099100C2212yes—
101#19099095C2212yes—
102#19099095C2214yes—
103#19099094C2214yes—
104#19099093C2214yes—
105#19099092C2214yes—
106#19099091C2214yes—
107#19099075C2211yescharacteristic
108#19099073C2214yes—
109#19099072C2214yes—
110#19099071C2218yes—
111#19099070C2211yescharacteristic
112#19099070C2212yes—
113#19099070C2218yes—
114#19099044C2218yes—
115#19099042C2218yes—
116#19099041C2212yes—
117#19099040C2212yes—
118#41×Dic79C2212yes—
119C4×#11929624C2211yescharacteristic
120C4×#11929624C2214yes—
121C4×#11929623C2214yes—
122C2×C4⋊C4×D79C2214yes—
123C2×C42×D79C2211yescharacteristic
124C2×2−1+4×C79C2212yes—
125D4×Q8×C79C2214yescomplemented
126#547×C79C2218yes—
127#547×C79C2214yescomplemented
128#536×C79C2212yes—
129#536×C79C2214yescomplemented
130#532×C79C2211yescharacteristic
131#532×C79C2212yescomplemented
132C2×C4⋊Q8×C79C2211yescharacteristic
133C2×C4⋊Q8×C79C2212yescomplemented
134C4×#41×C79C2211yescharacteristic
135#14579208—48no—
136C2×#11929624C2311yescharacteristic
137C2×#11929624C2314yes—
138C2×#11929624C2314yes—
139C2×#11929623C2314yes—
140C2×#11929623C2318yes—
141C2×#11929623C2314yes—
142C22×Dic158C2312yes—
143C22×Dic158C2314yes—
144C22×Dic158C2314yes—
145C2×Q8×D79—48no—
146C2×Q8×D79C2314yes—
147C2×Q8×D79C2318yes—
148C2×Q8×D79C2318yes—
149C22×C4×D79C2312yes—
150C22×C4×D79C2311yescharacteristic
151C22×C4×D79C2314yes—
152#14579161C2312yes—
153#14579161C2314yes—
154#14579161C2312yes—
155#14579161C2312yes—
156#14579160C2318yes—
157#14579160C2318yes—
158#14579160C2318yes—
159#14579160C23116yes—
160#14579160C2318yes—
161#14579160C2318yes—
162#14579160C2312yes—
163#14579159C2314yes—
164#14579159C2314yes—
165#14579159C2314yes—
166#14579159C23116yes—
167#14579159C23116yes—
168#14579159C2318yes—
169#14579159C2314yes—
170#14579159C2314yes—
171#14579159C2311yescharacteristic
172#14579157C2311yescharacteristic
173#14579156C23116yes—
174#14579156C2314yes—
175#14579154C23116yes—
176#14579154C23116yes—
177#14579154C23116yes—
178#14579154C2318yes—
179#14579154C2314yes—
180#14579153C2312yes—
181#14579153C2318yes—
182#14579152C23116yes—
183#14579152C2312yes—
184#14579152C2318yes—
185#14579152C2314yes—
186#14579151C23116yes—
187#14579151C23116yes—
188#14579151C23116yes—
189#14579151C23116yes—
190#14579151C2314yes—
191#14579150C2314yes—
192#14579150C2311yescharacteristic
193#14579148C2314yes—
194#14579148C23116yes—
195#14579148C2314yes—
196#14579148C2314yes—
197#14579148C2311yescharacteristic
198#14579147C23116yes—
199#14579147C2314yes—
200#14579146C2314yes—
201#14579145C2312yes—
202#14579144C2318yes—
203#14579144C23116yes—
204#14579143C2314yes—
205#14579143C2318yes—
206#14579143C23116yes—
207#14579142C23116yes—
208#14579142C2318yes—
209#14579142C2318yes—
210#14579142C2312yes—
211#14579142C2314yes—
212#14579141C2318yes—
213#14579141C2312yes—
214#14579141C2314yes—
215#14579140C2318yes—
216#14579140C23116yes—
217#14579140C2318yes—
218#14579140C2318yes—
219#14579140C23116yes—
220#14579140C23116yes—
221#14579140C2314yes—
222#14579139C23116yes—
223#14579139C23116yes—
224#14579139C2314yes—
225#14579138C23116yes—
226#14579138C23116yes—
227#14579138C23116yes—
228#14579138C2314yes—
229#14579137C2318yes—
230#14579137C23116yes—
231#14579137C23116yes—
232#14579137C2312yes—
233#14579137C2314yes—
234#14579136C2312yes—
235#14579134C23116yes—
236#14579134C2314yes—
237#14579133C23116yes—
238#14579133C2314yes—
239#14579132C23116yes—
240#14579132C2318yes—
241#14579132C2312yes—
242#14579132C2314yes—
243#14579132C2314yes—
244#14579131C2312yes—
245#14579129C2312yes—
246#14579129C2314yes—
247Q8×Dic79C2318yes—
248Q8×Dic79C2318yes—
249Q8×Dic79C2314yes—
250C4×Dic158C2318yes—
251C4×Dic158C2318yes—
252C4×Dic158C2312yes—
253C4×Dic158C2314yes—
254C4×Dic158C2314yes—
255C4×Dic158C2314yes—
256#14579126C2318yes—
257#14579126C2318yes—
258#14579126C23116yes—
259#14579126C2314yes—
260C4×D316C2312yes—
261C4×D316C2314yes—
262C4×D316C2314yes—
263D4×Dic79C2318yes—
264D4×Dic79C2318yes—
265D4×Dic79C2314yes—
266D4×Dic79C2314yes—
267#14579123C23116yes—
268C4×C22⋊D79C23116yes—
269C4×C22⋊D79C23116yes—
270C4×C22⋊D79C23116yes—
271C4×C22⋊D79C2314yes—
272C4×C22⋊D79C2314yes—
273C4×C22⋊D79C2314yes—
274C4×C22⋊D79C2318yes—
275C4×C22⋊D79C2314yes—
276C4×C22⋊D79C2314yes—
277(C22⋊D79)⋊C4C23116yes—
278(C22⋊D79)⋊C4C2318yes—
279#14579120C2312yes—
280#14579120C2314yes—
281#14579120C2314yes—
282#14579120C2318yes—
283#14579120C2318yes—
284#14579120C2311yescharacteristic
285#14579119C2314yes—
286#14579119C2318yes—
287#14579118C2312yes—
288#14579118C2314yes—
289#14579118C2314yes—
290#14579117C2318yes—
291#14579117C23116yes—
292#14579117C2318yes—
293C2×C4⋊Dic79C2314yes—
294C2×Dic79⋊C4C23116yes—
295C2×Dic79⋊C4C2318yes—
296C4⋊C4×D79C2318yes—
297C4⋊C4×D79C2318yes—
298C4⋊C4×D79C2318yes—
299C4⋊C4×D79C2318yes—
300C4⋊C4×D79C2318yes—
301C2×C4×Dic79C2311yescharacteristic
302C2×C4×Dic79C2312yes—
303C2×C4×Dic79C2314yes—
304C42×D79C2312yes—
305C42×D79C2312yes—
306C42×D79C2312yes—
307C42×D79C2312yes—
308C42×D79C2312yes—
3092−1+4×C79—48no—
310C2×#41×C79C2312yes—
311C2×#41×C79C2311yescharacteristic
312C2×#41×C79C2318yes—
313C2×#41×C79C2314yes—
314C2×#41×C79C2314yes—
315C22×Q8×C79C2312yes—
316C22×Q8×C79C2314yes—
317C22×Q8×C79C2314yes—
318C4⋊Q8×C79C2312yes—
319C4⋊Q8×C79C2318yes—
320C4⋊Q8×C79C2314yes—
321C4⋊Q8×C79C2312yes—
322C4⋊Q8×C79C2314yes—
323C4⋊Q8×C79C2311yescharacteristic
324#127×C79C2311yescharacteristic
325#124×C79C2314yes—
326#124×C79C2312yes—
327#123×C79C23116yes—
328#123×C79C2318yes—
329C22⋊Q8×C79C23116yes—
330C22⋊Q8×C79C2318yes—
331#121×C79C2318yes—
332#121×C79C2314yes—
333C4×Q8×C79C2312yes—
334C4×D4×C79C2318yes—
335C4×D4×C79C2314yes—
336C4×D4×C79C2314yes—
337C4×D4×C79C2312yes—
338#117×C79C2312yes—
339#117×C79C2311yescharacteristic
340C2×C4⋊C4×C79C2318yes—
341C2×C4⋊C4×C79C2314yes—
342C2×C42×C79C2311yescharacteristic
343C2×C42×C79C2312yes—
344C23×D79C2411yescharacteristic
345#11929624—216no—
346#11929624—24no—
347#11929624—48no—
348#11929623—216no—
349#11929623—416no—
350#11929623—48no—
351C2×Dic158—28no—
352C2×Dic158—48no—
353C2×Dic158—48no—
354C2×Dic158C2414yes—
355C2×Dic158C2414yes—
356C2×Dic158C2411yescharacteristic
357C2×Dic158C2414yes—
358C2×Dic158C2414yes—
359C2×Dic158C24116yes—
360C2×Dic158C2418yes—
361Q8×D79—416no—
362Q8×D79—416no—
363Q8×D79—48no—
364C2×D316C2411yescharacteristic
365C2×D316C2414yes—
366C2×C22⋊D79C2412yes—
367C2×C22⋊D79C2418yes—
368C2×C22⋊D79C2414yes—
369C2×C22⋊D79C2414yes—
370C2×C22⋊D79C2418yes—
371C22×Dic79C2411yescharacteristic
372C22×Dic79C2414yes—
373C22×Dic79C2418yes—
374C22×Dic79C2412yes—
375C22×Dic79C2418yes—
376C2×C4×D79—28no—
377C2×C4×D79—24no—
378C2×C4×D79—48no—
379C2×C4×D79C2412yes—
380C2×C4×D79C2412yes—
381C2×C4×D79C2412yes—
382C2×C4×D79C2414yes—
383C2×C4×D79C2412yes—
384C2×C4×D79C2412yes—
385C2×C4×D79C2412yes—
386C2×C4×D79C24116yes—
387C2×C4×D79C2418yes—
388C2×C4×D79C2412yes—
389C4⋊Dic79C2418yes—
390C4⋊Dic79C2418yes—
391C4⋊Dic79C2414yes—
392C4⋊Dic79C2414yes—
393C4⋊Dic79C2418yes—
394C4⋊Dic79C2412yes—
395C4⋊Dic79C2414yes—
396C4⋊Dic79C2414yes—
397C4⋊Dic79C24116yes—
398Dic79⋊C4C24116yes—
399Dic79⋊C4C24116yes—
400Dic79⋊C4C24116yes—
401Dic79⋊C4C2414yes—
402Dic79⋊C4C24116yes—
403Dic79⋊C4C24116yes—
404Dic79⋊C4C2414yes—
405Dic79⋊C4C2418yes—
406Dic79⋊C4C2418yes—
407Dic79⋊C4C24116yes—
408Dic79⋊C4C2414yes—
409Dic79⋊C4C2414yes—
410Dic79⋊C4C2414yes—
411C22⋊Dic79C2414yes—
412C22⋊Dic79C24116yes—
413C22⋊Dic79C2418yes—
414C22⋊Dic79C2412yes—
415C22⋊Dic79C24116yes—
416C22⋊Dic79C2414yes—
417C22⋊Dic79C2414yes—
418C22⋊Dic79C2418yes—
419(C2×D79)⋊C4C2414yes—
420(C2×D79)⋊C4C2414yes—
421(C2×D79)⋊C4C2414yes—
422(C2×D79)⋊C4C2414yes—
423(C2×D79)⋊C4C2414yes—
424(C2×D79)⋊C4C2418yes—
425(C2×D79)⋊C4C24116yes—
426C4×Dic79C2411yescharacteristic
427C4×Dic79C2412yes—
428C4×Dic79C2412yes—
429C4×Dic79C2411yescharacteristic
430C4×Dic79C2412yes—
431C4×Dic79C2412yes—
432C4×Dic79C2412yes—
433C4×Dic79C2414yes—
434C4×Dic79C2412yes—
435C4×Dic79C2418yes—
436C4×Dic79C2414yes—
437C4×Dic79C24116yes—
438C4×Dic79C24116yes—
439#41×C79—28no—
440#41×C79—24no—
441#41×C79—416no—
442#41×C79—48no—
443#41×C79—48no—
444C2×Q8×C79—28no—
445C2×Q8×C79—48no—
446C2×Q8×C79—48no—
447C2×Q8×C79C2414yes—
448C2×Q8×C79C2414yes—
449C2×Q8×C79C2412yes—
450C2×Q8×C79C2411yescharacteristic
451C2×Q8×C79C2418yes—
452C2×D4×C79C2414yes—
453C2×D4×C79C2412yes—
454C2×D4×C79C2414yes—
455C2×D4×C79C2412yes—
456C2×D4×C79C2411yescharacteristic
457C2×D4×C79C2418yes—
458C22×C4×C79C2414yes—
459C22×C4×C79C2414yes—
460C22×C4×C79C2414yes—
461C22×C4×C79C2412yes—
462C22×C4×C79C2412yes—
463C22×C4×C79C2418yes—
464C22×C4×C79C2418yes—
465C22×C4×C79C2411yescharacteristic
466C4⋊C4×C79C2414yes—
467C4⋊C4×C79C2418yes—
468C4⋊C4×C79C2418yes—
469C4⋊C4×C79C24116yes—
470C4⋊C4×C79C2412yes—
471C4⋊C4×C79C2414yes—
472C22⋊C4×C79C2412yes—
473C22⋊C4×C79C2414yes—
474C22⋊C4×C79C24116yes—
475C22⋊C4×C79C2418yes—
476C42×C79C2411yescharacteristic
477C42×C79C2411yescharacteristic
478C42×C79C2412yes—
479C42×C79C2412yes—
480C42×C79C2414yes—
481C23×C79C2512yes—
482C23×C79C2514yes—
483C23×C79C2511yescharacteristic
484C22×D79—22no—
485C22×D79—24no—
486C22×D79C2512yes—
487C22×D79C2512yes—
488Q8×C79—28no—
489Q8×C79—28no—
490Q8×C79—24no—
491Q8×C79—22no—
492Q8×C79—48no—
493D4×C79—28no—
494D4×C79—24no—
495D4×C79—24no—
496D4×C79—22no—
497D4×C79—28no—
498D4×C79—48no—
499C2×C4×C79—28no—
500C2×C4×C79—28no—
501C2×C4×C79—24no—
502C2×C4×C79—24no—
503C2×C4×C79—28no—
504C2×C4×C79—48no—
505C2×C4×C79—48no—
506C2×C4×C79H(5,𝔽2)14yes—
507C2×C4×C79C2514yes—
508C2×C4×C79C2512yes—
509C2×C4×C79C2514yes—
510C2×C4×C79C2518yes—
511C2×C4×C79C2512yes—
512C2×C4×C79C2511yescharacteristic
513C2×C4×C79C2511yescharacteristic
514C2×C4×C79C2512yes—
515C22⋊D79—24no—
516C22⋊D79—216no—
517C22⋊D79—28no—
518C22⋊D79—28no—
519C22⋊D79—48no—
520C2×Dic79—22no—
521C2×Dic79—28no—
522C2×Dic79—24no—
523C2×Dic79—216no—
524C2×Dic79—48no—
525C2×Dic79C2518yes—
526C2×Dic79C2514yes—
527C2×Dic79C2512yes—
528C2×Dic79C2512yes—
529C2×Dic79C2512yes—
530C2×Dic79C2518yes—
531C2×Dic79C2512yes—
532D316—28no—
533D316—22no—
534C4×D79—24no—
535C4×D79—24no—
536C4×D79—24no—
537C4×D79—24no—
538C4×D79—24no—
539C4×D79—28no—
540C4×D79—24no—
541C4×D79—416no—
542C4×D79—48no—
543C4×D792−1+418yescomplemented
544Dic158—28no—
545Dic158—28no—
546Dic158—22no—
547Dic158—28no—
548Dic158—28no—
549Dic158—416no—
550Dic158—48no—
551C22×C79—22no—
552C22×C79—24no—
553C22×C79—22no—
554C22×C79—24no—
555C22×C79—28no—
556C22×C79C2×H(5,𝔽2)12yes—
557C22×C79C2611yescharacteristic
558C2×D79—28no—
559C2×D79—22no—
560C2×D79—22no—
561C2×D79—22no—
562C2×D79—24no—
563C2×D79C2×2−1+414yes—
564C4×C79—22no—
565C4×C79—24no—
566C4×C79—28no—
567C4×C79—24no—
568C4×C79—22no—
569C4×C79C2×H(5,𝔽2)12yes—
570C4×C79C2×H(5,𝔽2)12yes—
571C4×C79C2×2−1+414yes—
572Dic79—22no—
573Dic79—28no—
574Dic79—22no—
575Dic79—24no—
576Dic79—28no—
577Dic79—22no—
578Dic79C2×2−1+414yes—
579#62833—791nomaximal, Sylow
580C2×C79—22no—
581C2×C79—44no—
582C2×C79—42no—
583C2×C79C22×H(5,𝔽2)11yescharacteristic
584C2×C79C22×2−1+412yes—
585D79—24no—
586D79—42no—
587#3552—794no—
588#3552—794no—
589#3552—798no—
590#3544—798no—
591#3511—794no—
592#3511—794no—
593#3509—792no—
594#3509—791no—
595#3509—791no—
596#3503—794no—
597#3503—794no—
598#3499—792no—
599#3499—791no—
600#3499D7911yescharacteristic, complemented
601#3492—798no—
602#3486—792no—
603#3486—792no—
604#3444—791no—
605#3444—791no—
606C22×C4⋊Q8—791no—
607C79#6283311yescharacteristic, complemented, Sylow
608C2×2−1+4—792no—
609C2×2−1+4C2×D7912yes—
610C23×Q8—792no—
611#563—7916no—
612#563—7916no—
613Q82—798no—
614#557—798no—
615#557—794no—
616#557—794no—
617#556—794no—
618#556—798no—
619#556—794no—
620#555—798no—
621#554—798no—
622#554—7916no—
623#554—798no—
624#554—798no—
625#554—798no—
626#553—7916no—
627#553—798no—
628#553—798no—
629#552—7916no—
630#552—798no—
631#552—798no—
632D4×Q8—798no—
633D4×Q8—798no—
634D4×Q8—798no—
635D4×Q8—798no—
636D4×Q8—798no—
637D4×Q8—794no—
638D4×Q8C2×D7914yescomplemented
639#548—798no—
640#548—798no—
641#548—798no—
642#548—798no—
643#547—7916no—
644#547—798no—
645#547—798no—
646#547—794no—
647#547C2×D7918yes—
648#547C2×D7914yescomplemented
649#544—798no—
650#544—798no—
651#544—7916no—
652#544—798no—
653#542—7916no—
654#542—798no—
655#542—798no—
656#541—794no—
657#541—798no—
658#541—794no—
659#539—7916no—
660#539—7916no—
661#537—798no—
662#536—792no—
663#536—792no—
664#536—798no—
665#536—794no—
666#536—792no—
667#536—794no—
668#536—794no—
669#536—798no—
670#536C2×D7912yes—
671#536C2×D7914yescomplemented
672#533—792no—
673#533—794no—
674#533—798no—
675#533—792no—
676#533—791no—
677#533—791no—
678#533—794no—
679#532—791no—
680#532—794no—
681#532—792no—
682#532—792no—
683#532—792no—
684#532C2×D7911yescharacteristic
685#532C2×D7912yescomplemented
686C2×C4⋊Q8—792no—
687C2×C4⋊Q8—794no—
688C2×C4⋊Q8—794no—
689C2×C4⋊Q8—794no—
690C2×C4⋊Q8—794no—
691C2×C4⋊Q8—794no—
692C2×C4⋊Q8—792no—
693C2×C4⋊Q8—794no—
694C2×C4⋊Q8—791no—
695C2×C4⋊Q8C2×D7911yescharacteristic
696C2×C4⋊Q8C2×D7912yescomplemented
697#529—794no—
698#529—794no—
699#529—792no—
700#529—794no—
701#529—794no—
702#529—792no—
703#529—794no—
704#525—792no—
705#525—791no—
706#525—798no—
707#525—798no—
708#525—794no—
709#525—794no—
710#525—791no—
711#520—798no—
712#520—798no—
713#519—792no—
714#519—792no—
715C4×#41—792no—
716C4×#41—794no—
717C4×#41—791no—
718C4×#41—794no—
719C4×#41C2×D7911yescharacteristic
720C22×C4⋊C4—794no—
721C22×C42—791no—
7222−1+4—48no—
7232−1+4—3168no—
724C2×#41—798no—
725C2×#41—794no—
726C2×#41—794no—
727C2×#41—794no—
728C2×#41—794no—
729C2×#41—791no—
730C2×#41C22×D7912yes—
731C2×#41C22×D7911yescharacteristic
732C2×#41C22×D7918yes—
733C2×#41C22×D7914yes—
734C2×#41C22×D7914yes—
735C22×Q8—3168no—
736C22×Q8—798no—
737C22×Q8—798no—
738C22×Q8—794no—
739C22×Q8—794no—
740C22×Q8—794no—
741C22×Q8—792no—
742C22×Q8C22×D7912yes—
743C22×Q8C22×D7914yes—
744C22×Q8C22×D7914yes—
745C23×C4—794no—
746C23×C4—792no—
747C23×C4—791no—
748C4⋊Q8—794no—
749C4⋊Q8—791no—
750C4⋊Q8—794no—
751C4⋊Q8—798no—
752C4⋊Q8—794no—
753C4⋊Q8—794no—
754C4⋊Q8—794no—
755C4⋊Q8—7916no—
756C4⋊Q8—7916no—
757C4⋊Q8—798no—
758C4⋊Q8—798no—
759C4⋊Q8—798no—
760C4⋊Q8—798no—
761C4⋊Q8—798no—
762C4⋊Q8—792no—
763C4⋊Q8—7916no—
764C4⋊Q8—792no—
765C4⋊Q8—792no—
766C4⋊Q8—794no—
767C4⋊Q8—792no—
768C4⋊Q8C22×D7912yes—
769C4⋊Q8C22×D7912yes—
770C4⋊Q8C22×D7914yes—
771C4⋊Q8C22×D7911yescharacteristic
772C4⋊Q8C22×D7914yes—
773C4⋊Q8C22×D7918yes—
774#127—791no—
775#127C22×D7911yescharacteristic
776#126—794no—
777#126—7916no—
778#126—794no—
779#126—798no—
780#126—7916no—
781#126—7916no—
782#126—7916no—
783#125—792no—
784#125—794no—
785#125—794no—
786#125—7916no—
787#125—798no—
788#125—7916no—
789#125—7916no—
790#125—7916no—
791#125—7916no—
792#125—792no—
793#125—798no—
794#124—791no—
795#124—794no—
796#124—791no—
797#124—794no—
798#124—794no—
799#124—794no—
800#124—7916no—
801#124—794no—
802#124—7916no—
803#124C22×D7912yes—
804#124C22×D7914yes—
805#123—794no—
806#123—792no—
807#123—798no—
808#123—798no—
809#123—7916no—
810#123—798no—
811#123—7916no—
812#123—794no—
813#123—792no—
814#123—794no—
815#123—798no—
816#123—7916no—
817#123C22×D7918yes—
818#123C22×D79116yes—
819C22⋊Q8—794no—
820C22⋊Q8—792no—
821C22⋊Q8—7916no—
822C22⋊Q8—798no—
823C22⋊Q8—7916no—
824C22⋊Q8—794no—
825C22⋊Q8—798no—
826C22⋊Q8—798no—
827C22⋊Q8—798no—
828C22⋊Q8—7916no—
829C22⋊Q8—7916no—
830C22⋊Q8—7916no—
831C22⋊Q8—792no—
832C22⋊Q8—794no—
833C22⋊Q8—794no—
834C22⋊Q8—7916no—
835C22⋊Q8—798no—
836C22⋊Q8—7916no—
837C22⋊Q8—794no—
838C22⋊Q8—7916no—
839C22⋊Q8—7916no—
840C22⋊Q8—7916no—
841C22⋊Q8C22×D7918yes—
842C22⋊Q8C22×D79116yes—
843#121—794no—
844#121—794no—
845#121—792no—
846#121—794no—
847#121—7916no—
848#121—798no—
849#121—7916no—
850#121—792no—
851#121—794no—
852#121—7916no—
853#121C22×D7914yes—
854#121C22×D7918yes—
855#120—794no—
856#120—792no—
857#120—792no—
858C4×Q8—794no—
859C4×Q8—798no—
860C4×Q8—798no—
861C4×Q8—794no—
862C4×Q8—798no—
863C4×Q8—7916no—
864C4×Q8—798no—
865C4×Q8—792no—
866C4×Q8—794no—
867C4×Q8—794no—
868C4×Q8—794no—
869C4×Q8—798no—
870C4×Q8—798no—
871C4×Q8C22×D7912yes—
872C4×D4—798no—
873C4×D4—794no—
874C4×D4—794no—
875C4×D4—798no—
876C4×D4—794no—
877C4×D4—798no—
878C4×D4—794no—
879C4×D4—794no—
880C4×D4—794no—
881C4×D4—794no—
882C4×D4—7916no—
883C4×D4—7916no—
884C4×D4—7916no—
885C4×D4—7916no—
886C4×D4—798no—
887C4×D4—7916no—
888C4×D4—794no—
889C4×D4—794no—
890C4×D4—792no—
891C4×D4C22×D7914yes—
892C4×D4C22×D7914yes—
893C4×D4C22×D7912yes—
894C4×D4C22×D7918yes—
895#117—792no—
896#117—791no—
897#117—794no—
898#117—794no—
899#117—798no—
900#117—798no—
901#117—794no—
902#117—798no—
903#117—798no—
904#117—798no—
905#117—7916no—
906#117—794no—
907#117—792no—
908#117—794no—
909#117C22×D7911yescharacteristic
910#117C22×D7912yes—
911C2×C4⋊C4—798no—
912C2×C4⋊C4—794no—
913C2×C4⋊C4—7916no—
914C2×C4⋊C4—798no—
915C2×C4⋊C4—798no—
916C2×C4⋊C4—798no—
917C2×C4⋊C4—798no—
918C2×C4⋊C4—798no—
919C2×C4⋊C4C22×D7914yes—
920C2×C4⋊C4C22×D7918yes—
921C2×C42—794no—
922C2×C42—791no—
923C2×C42—792no—
924C2×C42—792no—
925C2×C42—792no—
926C2×C42—792no—
927C2×C42—792no—
928C2×C42—792no—
929C2×C42C22×D7912yes—
930C2×C42C22×D7911yescharacteristic
931C24—791no—
932#41—24no—
933#41—28no—
934#41—416no—
935#41—48no—
936#41—48no—
937#41—3168no—
938#41—3168no—
939#41—31616no—
940#41—15816no—
941#41—15816no—
942#41—1584no—
943C2×Q8—28no—
944C2×Q8—48no—
945C2×Q8—48no—
946C2×Q8—3168no—
947C2×Q8—3168no—
948C2×Q8—31616no—
949C2×Q8—31616no—
950C2×Q8—3168no—
951C2×Q8—798no—
952C2×Q8—7916no—
953C2×Q8—794no—
954C2×Q8—794no—
955C2×Q8—791no—
956C2×Q8—794no—
957C2×Q8—794no—
958C2×Q8—1588no—
959C2×Q8C23×D7914yes—
960C2×Q8C23×D7912yes—
961C2×Q8C23×D7914yes—
962C2×Q8C23×D7911yescharacteristic
963C2×Q8C23×D7918yes—
964C2×D4—798no—
965C2×D4—794no—
966C2×D4—798no—
967C2×D4—794no—
968C2×D4—792no—
969C2×D4—794no—
970C2×D4—791no—
971C2×D4C23×D7914yes—
972C2×D4C23×D7914yes—
973C2×D4C23×D7912yes—
974C2×D4C23×D7912yes—
975C2×D4C23×D7911yescharacteristic
976C2×D4C23×D7918yes—
977C22×C4—3168no—
978C22×C4—798no—
979C22×C4—7916no—
980C22×C4—798no—
981C22×C4—792no—
982C22×C4—792no—
983C22×C4—791no—
984C22×C4—798no—
985C22×C4—794no—
986C22×C4—792no—
987C22×C4—792no—
988C22×C4—792no—
989C22×C4—792no—
990C22×C4—792no—
991C22×C4—794no—
992C22×C4—792no—
993C22×C4—1588no—
994C22×C4—1584no—
995C22×C4C23×D7912yes—
996C22×C4C23×D7914yes—
997C22×C4C23×D7914yes—
998C22×C4C23×D7912yes—
999C22×C4C23×D7914yes—
1000C22×C4C23×D7918yes—
1001C22×C4C23×D7918yes—
1002C22×C4C23×D7911yescharacteristic
1003C4⋊C4—7916no—
1004C4⋊C4—794no—
1005C4⋊C4—7916no—
1006C4⋊C4—7916no—
1007C4⋊C4—7916no—
1008C4⋊C4—7916no—
1009C4⋊C4—794no—
1010C4⋊C4—794no—
1011C4⋊C4—798no—
1012C4⋊C4—794no—
1013C4⋊C4—798no—
1014C4⋊C4—794no—
1015C4⋊C4—7916no—
1016C4⋊C4—798no—
1017C4⋊C4—798no—
1018C4⋊C4—794no—
1019C4⋊C4—792no—
1020C4⋊C4—794no—
1021C4⋊C4—798no—
1022C4⋊C4—794no—
1023C4⋊C4—794no—
1024C4⋊C4—7916no—
1025C4⋊C4C23×D7918yes—
1026C4⋊C4C23×D7914yes—
1027C4⋊C4C23×D7918yes—
1028C4⋊C4C23×D79116yes—
1029C4⋊C4C23×D7912yes—
1030C4⋊C4C23×D7914yes—
1031C22⋊C4—794no—
1032C22⋊C4—792no—
1033C22⋊C4—7916no—
1034C22⋊C4—7916no—
1035C22⋊C4—794no—
1036C22⋊C4—794no—
1037C22⋊C4—798no—
1038C22⋊C4—798no—
1039C22⋊C4—798no—
1040C22⋊C4—794no—
1041C22⋊C4—794no—
1042C22⋊C4—7916no—
1043C22⋊C4—794no—
1044C22⋊C4—794no—
1045C22⋊C4—794no—
1046C22⋊C4C23×D7912yes—
1047C22⋊C4C23×D79116yes—
1048C22⋊C4C23×D7918yes—
1049C22⋊C4C23×D7914yes—
1050C42—791no—
1051C42—792no—
1052C42—791no—
1053C42—792no—
1054C42—792no—
1055C42—792no—
1056C42—792no—
1057C42—798no—
1058C42—794no—
1059C42—794no—
1060C42—792no—
1061C42—7916no—
1062C42—7916no—
1063C42C23×D7911yescharacteristic
1064C42C23×D7911yescharacteristic
1065C42C23×D7912yes—
1066C42C23×D7914yes—
1067C42C23×D7912yes—
1068C23—792no—
1069C23—792no—
1070C23—1584no—
1071C23—1582no—
1072C23C24×D7912yes—
1073C23C24×D7914yes—
1074C23C24×D7911yescharacteristic
1075Q8—28no—
1076Q8—28no—
1077Q8—22no—
1078Q8—24no—
1079Q8—48no—
1080Q8—31616no—
1081Q8—3168no—
1082Q8—1588no—
1083Q8—1582no—
1084Q8—1588no—
1085Q8—1588no—
1086Q8—1588no—
1087D4—24no—
1088D4—28no—
1089D4—22no—
1090D4—24no—
1091D4—28no—
1092D4—48no—
1093D4—3168no—
1094D4—1588no—
1095D4—1588no—
1096D4—1588no—
1097D4—15816no—
1098D4—1584no—
1099D4—1582no—
1100C2×C4—28no—
1101C2×C4—24no—
1102C2×C4—28no—
1103C2×C4—24no—
1104C2×C4—28no—
1105C2×C4—48no—
1106C2×C4—48no—
1107C2×C4—31616no—
1108C2×C4—3168no—
1109C2×C4—3168no—
1110C2×C4—792no—
1111C2×C4—798no—
1112C2×C4—794no—
1113C2×C4—798no—
1114C2×C4—792no—
1115C2×C4—792no—
1116C2×C4—798no—
1117C2×C4—792no—
1118C2×C4—1584no—
1119C2×C4—1584no—
1120C2×C4—1584no—
1121C2×C4—15816no—
1122C2×C4—1588no—
1123C2×C4—1582no—
1124C2×C4—1584no—
1125C2×C4—1584no—
1126C2×C4—1584no—
1127C2×C4—1584no—
1128C2×C4—1588no—
1129C2×C4#1457920614yes—
1130C2×C4C24×D7914yes—
1131C2×C4C24×D7912yes—
1132C2×C4C24×D7914yes—
1133C2×C4C24×D7918yes—
1134C2×C4C24×D7912yes—
1135C2×C4C24×D7911yescharacteristic
1136C2×C4C24×D7911yescharacteristic
1137C2×C4C24×D7912yes—
1138C22—22no—
1139C22—22no—
1140C22—24no—
1141C22—24no—
1142C22—28no—
1143C22—794no—
1144C22—1588no—
1145C22—1582no—
1146C22—1584no—
1147C22—1582no—
1148C22—1582no—
1149C22C2×#1457920612yes—
1150C22C25×D7911yescharacteristic
1151C4—22no—
1152C4—24no—
1153C4—28no—
1154C4—22no—
1155C4—24no—
1156C4—794no—
1157C4—1588no—
1158C4—1582no—
1159C4—1582no—
1160C4—1582no—
1161C4—1588no—
1162C4—1584no—
1163C4C2×#1457920612yes—
1164C4C2×#1457920612yes—
1165C42−1+4×D7914yes—
1166C2—22no—
1167C2—42no—
1168C2—44no—
1169C2—3162no—
1170C2—1584no—
1171C2C22×#1457920611yescharacteristic
1172C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3499C2
hypercenter#3499D79
hypocenterC79#62833
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. #23777842C2semidirect
2. #23777838C2semidirect
3. #23777832C2semidirect
4. #23777736C2semidirect
5. #23777310C2semidirect
6. #23777301C2semidirect
7. #23777286C2semidirect
8. #23777285C2semidirect
9. #23777284C2semidirect
10. #23777216C2semidirect
11. #23777211C2semidirect
12. #23777181C2semidirect
13. #23777180C2semidirect
14. #23777102C2semidirect
15. #23777049C2semidirect
16. #23777048C2semidirect
17. #23776695C2semidirect
18. #23776693C2semidirect
19. C2×C4⋊Q8×D79C2semidirect
20. C79×#3499C2semidirect
23. #19099316C22semidirect
24. #19099314C22semidirect
25. #19099293C22semidirect
26. #19099291C22semidirect
27. #19099288C22semidirect
28. #19099288C22semidirect
29. #19099287C22semidirect
30. #19099283C22semidirect
31. #19099282C22semidirect
32. #19099277C22semidirect
34. #19099272C22semidirect
36. #19099268C22semidirect
44. D4×Dic158C22semidirect
48. Q8×C22⋊D79C22semidirect
54. #19099218C22semidirect
57. #19099212C22semidirect
58. #19099194C22semidirect
59. #19099192C22semidirect
61. #19099190C22semidirect
62. #19099181C22semidirect
63. #19099180C22semidirect
64. #19099178C22semidirect
65. #19099175C22semidirect
66. #19099174C22semidirect
67. #19099173C22semidirect
72. #19099137C22semidirect
77. #19099134C22semidirect
78. #19099133C22semidirect
80. #19099120C22semidirect
82. #19099118C22semidirect
85. #19099115C22semidirect
87. #19099111C22semidirect
90. #19099109C22semidirect
94. C2×#14579159C22semidirect
99. C4⋊Q8×D79C22semidirect
125. D4×Q8×C79C22semidirect
127. #547×C79C22semidirect
129. #536×C79C22semidirect
131. #532×C79C22semidirect
133. C2×C4⋊Q8×C79C22semidirect
543. C4×D792−1+4semidirect
600. #3499D79semidirect
607. C79#62833semidirect
638. D4×Q8C2×D79semidirect
648. #547C2×D79semidirect
671. #536C2×D79semidirect
685. #532C2×D79semidirect
696. C2×C4⋊Q8C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237778422
#237778382
#237778322
#237777362
#237773102
#237773012
#237772862
#237772852
#237772842
#237772162
#237772112
#237771812
#237771802
#237771022
#237770492
#237770482
#237766952
#237766932
C2×C4⋊Q8×D792
C79×#34992
#6283379