Finite Group Databasebeta

← #3509×D79 #35196703

Subgroups — #3509×D79 #35196703

Order 20224.

7022 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23777287C211yesmaximal, characteristic, complemented
2#23777286C211yesmaximal, characteristic, complemented
3#23777285C212yesmaximal, complemented
4#23777284C211yesmaximal, characteristic, complemented
5#23777283C214yesmaximal, complemented
6#23777282C214yesmaximal, complemented
7#23777281C212yesmaximal, complemented
8#23777280C214yesmaximal, complemented
9#23777279C214yesmaximal, complemented
10#23777278C218yesmaximal, complemented
11#557×D79C214yesmaximal, complemented
12#556×D79C214yesmaximal, complemented
13#552×D79C218yesmaximal, complemented
14#541×D79C214yesmaximal, complemented
15#536×D79C212yesmaximal
16#533×D79C211yesmaximal, characteristic, complemented
17#533×D79C214yesmaximal, complemented
18C2×C4⋊Q8×D79C211yesmaximal, characteristic, complemented
19#519×D79C212yesmaximal, complemented
20C4×#41×D79C211yesmaximal, characteristic
21C79×#3509C211yesmaximal, characteristic, complemented
22C2×#41×D79C2211yescharacteristic
23C22×Q8×D79C2212yes—
24#19099292C2214yescomplemented
25#19099291C2218yescomplemented
26#19099291C2214yescomplemented
27#19099290C22116yescomplemented
28#19099290C2218yescomplemented
29#19099289C2218yescomplemented
30#19099288C2214yescomplemented
31#19099288C2218yescomplemented
32#19099287C2214yescomplemented
33#19099286C2214yescomplemented
34#19099285C2218yescomplemented
35#19099284C2218yescomplemented
36#19099283C2214yescomplemented
37#19099282C2218yescomplemented
38#19099281C2218yescomplemented
39#19099280C22116yescomplemented
40#19099255C2218yescomplemented
41#19099254C2218yescomplemented
42#19099253C2218yescomplemented
43#19099252C2218yescomplemented
44#19099251C2218yescomplemented
45#19099250C22116yescomplemented
46#19099249C22116yescomplemented
47#19099248C2218yescomplemented
48#19099247C2218yescomplemented
49#19099246C22116yescomplemented
50#19099245C22116yescomplemented
51#19099176C2214yescomplemented
52#19099175C2214yescomplemented
53#19099174C2214yescomplemented
54#19099173C2218yescomplemented
55#19099172C22116yescomplemented
56#19099171C2218yescomplemented
57#19099170C22116yescomplemented
58#19099139C2212yes—
59#19099138C2214yes—
60#19099137C2212yes—
61#19099136C2218yes—
62#19099135C2218yes—
63#19099134C2212yes—
64#19099133C2214yes—
65#19099120C2211yescharacteristic, complemented
66#19099120C2214yescomplemented
67#19099119C2212yescomplemented
68#19099119C2218yescomplemented
69#19099118C2214yescomplemented
70#19099118C2214yescomplemented
71#19099118C2212yescomplemented
72#19099117C2214yescomplemented
73#19099117C2218yescomplemented
74#19099117C2218yescomplemented
75#19099116C2218yescomplemented
76#19099116C2212yescomplemented
77#19099115C2218yescomplemented
78#19099115C2218yescomplemented
79#19099115C2214yescomplemented
80C2×#14579161C2211yescharacteristic, complemented
81C2×#14579160C2214yescomplemented
82C2×#14579159C2212yescomplemented
83C4⋊Q8×D79C2212yes—
84C4⋊Q8×D79C2214yes—
85C4⋊Q8×D79C2212yes—
86C4⋊Q8×D79C2212yes—
87C4⋊Q8×D79C2214yes—
88C4⋊Q8×D79C2214yescomplemented
89C4⋊Q8×D79C2212yescomplemented
90C4⋊Q8×D79C2212yescomplemented
91#126×D79C22116yes—
92#125×D79C2218yes—
93#125×D79C22116yes—
94#125×D79C2212yes—
95#124×D79C2214yes—
96#123×D79C2218yes—
97C22⋊Q8×D79C2214yes—
98C22⋊Q8×D79C2218yes—
99C22⋊Q8×D79C2218yes—
100#19099041C2212yescomplemented
101#19099040C2212yescomplemented
102#19099040C2212yescomplemented
103#19099040C2218yescomplemented
104#19099039C2218yescomplemented
105#19099039C2218yescomplemented
106#41×Dic79C2211yescharacteristic
107C4×#11929625C2212yes—
108C4×#11929624C2211yescharacteristic
109C4×#11929624C2212yes—
110#19099031C2211yescharacteristic
111#19099031C2212yes—
112C4×#11929623C2212yes—
113C4×#11929623C2214yes—
114C4×Q8×D79C2212yes—
115C4×Q8×D79C2218yes—
116C4×Q8×D79C2218yes—
117C4×Q8×D79C2218yes—
118C4×Q8×D79C2214yes—
119C4×D4×D79C2214yes—
120C4×D4×D79C2212yes—
121#117×D79C2211yescharacteristic
122#117×D79C2212yes—
123#117×D79C2218yes—
124#117×D79C2212yes—
125#117×D79C2218yes—
126C2×C4⋊C4×D79C2214yes—
127C2×C42×D79C2211yescharacteristic
128C2×C42×D79C2212yes—
129#557×C79C2214yescomplemented
130#556×C79C2214yescomplemented
131#552×C79C2218yescomplemented
132#541×C79C2214yescomplemented
133#536×C79C2212yes—
134#533×C79C2211yescharacteristic, complemented
135#533×C79C2214yescomplemented
136C2×C4⋊Q8×C79C2211yescharacteristic, complemented
137#519×C79C2212yescomplemented
138C4×#41×C79C2211yescharacteristic
139C2×#11929625C2311yescharacteristic
140C2×#11929624C2312yes—
141C2×#11929624C2311yescharacteristic
142C2×#11929623C2311yescharacteristic
143C2×#11929623C2312yes—
144#41×D79—28no—
145C22×Dic158C2312yes—
146C22×Dic158C2314yes—
147C2×Q8×D79—216no—
148C2×Q8×D79C2314yes—
149C2×Q8×D79C2314yes—
150C2×Q8×D79C2314yes—
151C2×Q8×D79C2314yes—
152C2×Q8×D79C2314yes—
153C2×Q8×D79C2311yescharacteristic
154C2×D4×D79C2312yes—
155C2×D4×D79C2311yescharacteristic
156C22×C4×D79C2312yes—
157C22×C4×D79C2314yes—
158C22×C4×D79C2312yes—
159C22×C4×D79C2314yes—
160C22×C4×D79C2311yescharacteristic
161#14579161C2314yes—
162#14579161C2312yes—
163#14579161C2314yes—
164#14579161C2312yes—
165#14579161C2312yes—
166#14579160C23116yes—
167#14579160C2318yes—
168#14579160C2318yes—
169#14579160C2318yes—
170#14579160C2318yes—
171#14579160C2314yes—
172#14579160C2314yes—
173#14579159C2314yes—
174#14579159C2314yes—
175#14579159C2314yes—
176#14579159C2318yes—
177#14579159C2314yes—
178#14579159C2314yes—
179#14579156C23116yes—
180#14579156C23116yes—
181#14579156C23116yes—
182#14579155C23116yes—
183#14579154C23116yes—
184#14579154C23116yes—
185#14579154C23116yes—
186#14579153C23116yes—
187#14579153C2312yes—
188#14579153C2318yes—
189#14579152C23116yes—
190#14579152C2314yes—
191#14579152C23116yes—
192#14579152C2318yes—
193#14579152C2318yes—
194#14579151C2318yes—
195#14579151C23116yes—
196#14579151C23116yes—
197#14579151C23116yes—
198#14579151C23116yes—
199#14579151C23116yes—
200#14579151C23116yes—
201#14579150C2314yes—
202#14579149C2314yes—
203#14579148C2314yes—
204#14579147C23116yes—
205#14579146C23116yes—
206#14579145C2318yes—
207#14579144C2318yes—
208#14579143C23116yes—
209#14579142C2318yes—
210#14579141C2318yes—
211#14579141C2318yes—
212#14579141C2314yes—
213#14579140C2318yes—
214#14579140C2314yes—
215#14579140C2318yes—
216#14579139C23116yes—
217#14579139C2318yes—
218#14579139C23116yes—
219#14579138C23116yes—
220#14579138C2318yes—
221#14579138C23116yes—
222#14579137C2318yes—
223#14579137C2314yes—
224#14579137C2318yes—
225Q8×Dic79C2318yes—
226Q8×Dic79C2318yes—
227Q8×Dic79C2318yes—
228Q8×Dic79C2314yes—
229Q8×Dic79C2312yes—
230C4×Dic158C23116yes—
231C4×Dic158C2318yes—
232C4×Dic158C23116yes—
233C4×Dic158C2318yes—
234C4×Dic158C23116yes—
235C4×Dic158C2318yes—
236C4×Dic158C2318yes—
237C4×Dic158C2314yes—
238C4×Dic158C2312yes—
239C4×Dic158C2314yes—
240#14579126C23116yes—
241#14579126C2318yes—
242#14579126C23116yes—
243#14579126C2318yes—
244#14579126C2318yes—
245#14579126C23116yes—
246#14579126C2314yes—
247#14579126C2318yes—
248#14579126C2314yes—
249#14579126C2312yes—
250C4×D316C2314yes—
251C4×D316C2312yes—
252D4×Dic79C2314yes—
253D4×Dic79C2312yes—
254#14579123C2314yes—
255#14579123C2312yes—
256C4×C22⋊D79C2314yes—
257C4×C22⋊D79C2314yes—
258C4×C22⋊D79C2314yes—
259(C22⋊D79)⋊C4C2314yes—
260(C22⋊D79)⋊C4C2314yes—
261(C22⋊D79)⋊C4C2314yes—
262#14579120C2312yes—
263#14579120C2312yes—
264#14579120C2318yes—
265#14579120C2318yes—
266#14579120C2311yescharacteristic
267#14579119C2314yes—
268#14579119C2314yes—
269#14579119C23116yes—
270#14579119C2318yes—
271#14579119C2318yes—
272#14579119C2312yes—
273#14579118C2314yes—
274#14579118C2312yes—
275#14579118C2312yes—
276#14579118C23116yes—
277#14579118C23116yes—
278#14579118C2312yes—
279#14579117C2314yes—
280#14579117C2318yes—
281#14579117C23116yes—
282#14579117C2318yes—
283#14579117C2312yes—
284#14579117C2314yes—
285C2×C4⋊Dic79C2314yes—
286C2×Dic79⋊C4C2318yes—
287C4⋊C4×D79C2318yes—
288C4⋊C4×D79C2318yes—
289C4⋊C4×D79C2318yes—
290C4⋊C4×D79C2318yes—
291C4⋊C4×D79C2314yes—
292C4⋊C4×D79C2312yes—
293C4⋊C4×D79C2314yes—
294C4⋊C4×D79C2314yes—
295C4⋊C4×D79C23116yes—
296C4⋊C4×D79C23116yes—
297C4⋊C4×D79C2318yes—
298C22⋊C4×D79C2312yes—
299C22⋊C4×D79C2314yes—
300C22⋊C4×D79C2314yes—
301C22⋊C4×D79C23116yes—
302C2×C4×Dic79C2312yes—
303C2×C4×Dic79C2314yes—
304C2×C4×Dic79C2311yescharacteristic
305C2×C4×Dic79C2312yes—
306C42×D79C2311yescharacteristic
307C42×D79C2312yes—
308C42×D79C2311yescharacteristic
309C42×D79C2314yes—
310C42×D79C2312yes—
311C42×D79C2312yes—
312C42×D79C2314yes—
313C42×D79C2311yescharacteristic
314C42×D79C2312yes—
315C42×D79C2311yescharacteristic
316C42×D79C2312yes—
317C42×D79C23116yes—
318C42×D79C2314yes—
319C2×#41×C79C2311yescharacteristic
320C22×Q8×C79C2312yes—
321C4⋊Q8×C79C2314yes—
322C4⋊Q8×C79C2312yes—
323C4⋊Q8×C79C2312yes—
324C4⋊Q8×C79C2314yes—
325C4⋊Q8×C79C2312yes—
326#126×C79C23116yes—
327#125×C79C23116yes—
328#125×C79C2312yes—
329#125×C79C2318yes—
330#124×C79C2314yes—
331#123×C79C2318yes—
332C22⋊Q8×C79C2318yes—
333C22⋊Q8×C79C2318yes—
334C22⋊Q8×C79C2314yes—
335C4×Q8×C79C2318yes—
336C4×Q8×C79C2312yes—
337C4×Q8×C79C2318yes—
338C4×Q8×C79C2318yes—
339C4×Q8×C79C2314yes—
340C4×D4×C79C2314yes—
341C4×D4×C79C2312yes—
342#117×C79C2312yes—
343#117×C79C2312yes—
344#117×C79C2311yescharacteristic
345#117×C79C2318yes—
346#117×C79C2318yes—
347C2×C4⋊C4×C79C2314yes—
348C2×C42×C79C2311yescharacteristic
349C2×C42×C79C2312yes—
350C23×D79C2412yes—
351C23×D79C2411yescharacteristic
352#11929625—24no—
353#11929624—28no—
354#11929624—24no—
355#11929623—28no—
356#11929623—24no—
357C2×Dic158—216no—
358C2×Dic158—28no—
359C2×Dic158C2418yes—
360C2×Dic158C2414yes—
361C2×Dic158C2418yes—
362C2×Dic158C2414yes—
363C2×Dic158C2411yescharacteristic
364C2×Dic158C2412yes—
365C2×Dic158C2418yes—
366C2×Dic158C2414yes—
367Q8×D79—216no—
368Q8×D79—216no—
369Q8×D79—216no—
370Q8×D79—216no—
371Q8×D79—24no—
372Q8×D79—216no—
373C2×D316C2412yes—
374C2×D316C2411yescharacteristic
375C2×C22⋊D79C2412yes—
376C2×C22⋊D79C2412yes—
377C2×C22⋊D79C2412yes—
378D4×D79—24no—
379D4×D79—28no—
380C22×Dic79C2414yes—
381C22×Dic79C2412yes—
382C22×Dic79C2412yes—
383C22×Dic79C2414yes—
384C22×Dic79C2411yescharacteristic
385C2×C4×D79—28no—
386C2×C4×D79—28no—
387C2×C4×D79—216no—
388C2×C4×D79—216no—
389C2×C4×D79#4118yes—
390C2×C4×D79C2418yes—
391C2×C4×D79C2418yes—
392C2×C4×D79C2418yes—
393C2×C4×D79C2412yes—
394C2×C4×D79C2412yes—
395C2×C4×D79C2412yes—
396C2×C4×D79C2414yes—
397C2×C4×D79C2412yes—
398C2×C4×D79C2412yes—
399C2×C4×D79C2412yes—
400C2×C4×D79C2414yes—
401C2×C4×D79C2414yes—
402C2×C4×D79C2411yescharacteristic
403C2×C4×D79C2411yescharacteristic
404C2×C4×D79C2411yescharacteristic
405C2×C4×D79C2411yescharacteristic
406C2×C4×D79C2412yes—
407C4⋊Dic79C2418yes—
408C4⋊Dic79C2418yes—
409C4⋊Dic79C2414yes—
410C4⋊Dic79C2412yes—
411C4⋊Dic79C2414yes—
412C4⋊Dic79C2414yes—
413C4⋊Dic79C24116yes—
414C4⋊Dic79C24116yes—
415C4⋊Dic79C2418yes—
416Dic79⋊C4C24116yes—
417Dic79⋊C4C24116yes—
418Dic79⋊C4C2418yes—
419Dic79⋊C4C2414yes—
420Dic79⋊C4C2414yes—
421Dic79⋊C4C2414yes—
422Dic79⋊C4C24116yes—
423Dic79⋊C4C2418yes—
424Dic79⋊C4C24116yes—
425Dic79⋊C4C24116yes—
426Dic79⋊C4C2418yes—
427Dic79⋊C4C24116yes—
428Dic79⋊C4C2418yes—
429C22⋊Dic79C2412yes—
430C22⋊Dic79C2414yes—
431C22⋊Dic79C2414yes—
432C22⋊Dic79C24116yes—
433(C2×D79)⋊C4C2414yes—
434(C2×D79)⋊C4C2418yes—
435(C2×D79)⋊C4C2414yes—
436(C2×D79)⋊C4C2414yes—
437(C2×D79)⋊C4C24116yes—
438(C2×D79)⋊C4C24116yes—
439C4×Dic79C2411yescharacteristic
440C4×Dic79C2412yes—
441C4×Dic79C2414yes—
442C4×Dic79C2412yes—
443C4×Dic79C2412yes—
444C4×Dic79C2411yescharacteristic
445C4×Dic79C2412yes—
446C4×Dic79C2414yes—
447C4×Dic79C2414yes—
448C4×Dic79C2412yes—
449C4×Dic79C2414yes—
450C4×Dic79C2412yes—
451C4×Dic79C24116yes—
452C4×Dic79C24116yes—
453C4×Dic79C24116yes—
454C4×Dic79C2418yes—
455C4×Dic79C2414yes—
456#41×C79—24no—
457C2×Q8×C79—28no—
458C2×Q8×C79C2414yes—
459C2×Q8×C79C2414yes—
460C2×Q8×C79C2411yescharacteristic
461C2×Q8×C79C2414yes—
462C2×D4×C79C2412yes—
463C2×D4×C79C2411yescharacteristic
464C22×C4×C79C2414yes—
465C22×C4×C79C2412yes—
466C22×C4×C79C2412yes—
467C22×C4×C79C2414yes—
468C22×C4×C79C2411yescharacteristic
469C4⋊C4×C79C2418yes—
470C4⋊C4×C79C2418yes—
471C4⋊C4×C79C2414yes—
472C4⋊C4×C79C2412yes—
473C4⋊C4×C79C2414yes—
474C4⋊C4×C79C2414yes—
475C4⋊C4×C79C24116yes—
476C4⋊C4×C79C24116yes—
477C4⋊C4×C79C2418yes—
478C22⋊C4×C79C2412yes—
479C22⋊C4×C79C2414yes—
480C22⋊C4×C79C2414yes—
481C22⋊C4×C79C24116yes—
482C42×C79C2411yescharacteristic
483C42×C79C2412yes—
484C42×C79C2411yescharacteristic
485C42×C79C2414yes—
486C42×C79C2412yes—
487C42×C79C24116yes—
488C42×C79C2414yes—
489C23×C79C2512yes—
490C23×C79C2511yescharacteristic
491C22×D79—24no—
492C22×D79—24no—
493C22×D79—28no—
494C22×D79C2×#4114yes—
495C22×D79C2512yes—
496C22×D79C2511yescharacteristic
497C22×D79C2511yescharacteristic
498Q8×C79—28no—
499Q8×C79—28no—
500Q8×C79—22no—
501Q8×C79—28no—
502D4×C79—24no—
503D4×C79—22no—
504C2×C4×C79—28no—
505C2×C4×C79—24no—
506C2×C4×C79—24no—
507C2×C4×C79—28no—
508C2×C4×C79C2×#4114yes—
509C2×C4×C79C2514yes—
510C2×C4×C79C2518yes—
511C2×C4×C79C2512yes—
512C2×C4×C79C2518yes—
513C2×C4×C79C2512yes—
514C2×C4×C79C2511yescharacteristic
515C2×C4×C79C2511yescharacteristic
516C2×C4×C79C2512yes—
517C22⋊D79—24no—
518C22⋊D79—24no—
519C22⋊D79—24no—
520C2×Dic79—28no—
521C2×Dic79—24no—
522C2×Dic79—24no—
523C2×Dic79—28no—
524C2×Dic79C2×#4114yes—
525C2×Dic79C2514yes—
526C2×Dic79C2518yes—
527C2×Dic79C2512yes—
528C2×Dic79C2518yes—
529C2×Dic79C2512yes—
530C2×Dic79C2511yescharacteristic
531C2×Dic79C2511yescharacteristic
532C2×Dic79C2512yes—
533D316—24no—
534D316—22no—
535C4×D79—24no—
536C4×D79—216no—
537C4×D79—216no—
538C4×D79—28no—
539C4×D79—24no—
540C4×D79—216no—
541C4×D79—24no—
542C4×D79—24no—
543C4×D79—28no—
544C4×D79—24no—
545C4×D79—24no—
546C4×D79—28no—
547C4×D79C2×#4114yes—
548C4×D79C2×#4114yes—
549C4×D79C2×#4114yes—
550C4×D79C2×#4114yes—
551C4×D792−1+418yes—
552Dic158—28no—
553Dic158—28no—
554Dic158—22no—
555Dic158—28no—
556Dic158—216no—
557Dic158—216no—
558Dic158—24no—
559Dic158—216no—
560C22×C79—22no—
561C22×C79—22no—
562C22×C79—24no—
563C22×C79C22×#4112yes—
564C22×C79C2611yescharacteristic
565C2×D79—22no—
566C2×D79—28no—
567C2×D79—22no—
568C2×D79—24no—
569C2×D79—48no—
570C2×D79C22×#4112yes—
571C2×D79C22×#4112yes—
572C2×D79C2×2−1+414yes—
573C4×C79—22no—
574C4×C79—28no—
575C4×C79—24no—
576C4×C79—22no—
577C4×C79—28no—
578C4×C79C22×#4112yes—
579C4×C79C22×#4112yes—
580C4×C79C2×2−1+414yes—
581Dic79—22no—
582Dic79—28no—
583Dic79—28no—
584Dic79—24no—
585Dic79—22no—
586Dic79C22×#4112yes—
587Dic79C22×#4112yes—
588Dic79C2×2−1+414yes—
589C2×#3509—791nomaximal, Sylow
590C2×C79—22no—
591C2×C79—42no—
592C2×C79C23×#4111yescharacteristic
593C2×C79C22×2−1+412yes—
594D79—22no—
595D79—42no—
596D79#350914yesdirect product factor
597#3509—794no—
598#3509—794no—
599#3509—798no—
600#3509—794no—
601#3509—792no—
602#3509—791no—
603#3509—794no—
604#3509—791no—
605#3509—792no—
606#3509—791no—
607#3509D7911yescharacteristic, direct product factor
608C2×#557—794no—
609C2×#556—794no—
610C2×#552—798no—
611C2×#541—794no—
612C2×#536—792no—
613C2×#533—791no—
614C2×#533—794no—
615C22×C4⋊Q8—791no—
616C2×#519—792no—
617C2×C4×#41—791no—
618C79C2×#350911yescharacteristic, complemented, Sylow
619C22×#41—791no—
620C23×Q8—792no—
621#557—798no—
622#557—794no—
623#557—7916no—
624#557—798no—
625#557—798no—
626#557—798no—
627#557—794no—
628#557—794no—
629#557C2×D7914yescomplemented
630#556—794no—
631#556—7916no—
632#556—798no—
633#556—798no—
634#556—798no—
635#556—794no—
636#556—794no—
637#556—798no—
638#556C2×D7914yescomplemented
639#552—7916no—
640#552—7916no—
641#552—798no—
642#552—7916no—
643#552—798no—
644#552—798no—
645#552—798no—
646#552—798no—
647#552—7916no—
648#552—798no—
649#552—798no—
650#552C2×D7918yescomplemented
651#541—794no—
652#541—7916no—
653#541—7916no—
654#541—794no—
655#541—798no—
656#541—798no—
657#541—794no—
658#541C2×D7914yescomplemented
659#536—792no—
660#536—792no—
661#536—794no—
662#536—794no—
663#536—798no—
664#536—798no—
665#536—792no—
666#536C2×D7912yes—
667#533—792no—
668#533—794no—
669#533—794no—
670#533—792no—
671#533—798no—
672#533—794no—
673#533—798no—
674#533—798no—
675#533—794no—
676#533—798no—
677#533—798no—
678#533—792no—
679#533—798no—
680#533—791no—
681#533—794no—
682#533C2×D7911yescharacteristic, complemented
683#533C2×D7914yescomplemented
684C2×C4⋊Q8—792no—
685C2×C4⋊Q8—792no—
686C2×C4⋊Q8—792no—
687C2×C4⋊Q8—794no—
688C2×C4⋊Q8—792no—
689C2×C4⋊Q8—792no—
690C2×C4⋊Q8—794no—
691C2×C4⋊Q8—792no—
692C2×C4⋊Q8—794no—
693C2×C4⋊Q8—794no—
694C2×C4⋊Q8—791no—
695C2×C4⋊Q8C2×D7911yescharacteristic, complemented
696C2×#126—7916no—
697C2×#125—792no—
698C2×#125—798no—
699C2×#125—7916no—
700C2×#124—794no—
701C2×#123—798no—
702C2×C22⋊Q8—798no—
703C2×C22⋊Q8—794no—
704C2×C22⋊Q8—798no—
705#519—792no—
706#519—798no—
707#519—798no—
708#519—792no—
709#519—792no—
710#519—798no—
711#519C2×D7912yescomplemented
712C4×#41—791no—
713C4×#41—792no—
714C4×#41—794no—
715C4×#41—792no—
716C4×#41—791no—
717C4×#41—792no—
718C4×#41—792no—
719C4×#41—791no—
720C4×#41C2×D7911yescharacteristic
721C2×C4×Q8—792no—
722C2×C4×Q8—798no—
723C2×C4×Q8—798no—
724C2×C4×Q8—798no—
725C2×C4×Q8—794no—
726C2×C4×D4—794no—
727C2×C4×D4—792no—
728C2×#117—791no—
729C2×#117—792no—
730C2×#117—792no—
731C2×#117—798no—
732C2×#117—798no—
733C22×C4⋊C4—794no—
734C22×C42—791no—
735C22×C42—792no—
736C2×#41—791no—
737C2×#41—792no—
738C2×#41—791no—
739C2×#41—792no—
740C2×#41—791no—
741C2×#41—1588no—
742C2×#41C22×D7911yescharacteristic
743C22×Q8—794no—
744C22×Q8—794no—
745C22×Q8—794no—
746C22×Q8—791no—
747C22×Q8—794no—
748C22×Q8—794no—
749C22×Q8—794no—
750C22×Q8—792no—
751C22×Q8—15816no—
752C22×Q8C22×D7912yes—
753C22×D4—792no—
754C22×D4—791no—
755C23×C4—791no—
756C23×C4—794no—
757C23×C4—792no—
758C23×C4—794no—
759C23×C4—792no—
760C4⋊Q8—794no—
761C4⋊Q8—794no—
762C4⋊Q8—798no—
763C4⋊Q8—794no—
764C4⋊Q8—794no—
765C4⋊Q8—794no—
766C4⋊Q8—798no—
767C4⋊Q8—798no—
768C4⋊Q8—798no—
769C4⋊Q8—798no—
770C4⋊Q8—794no—
771C4⋊Q8—794no—
772C4⋊Q8—7916no—
773C4⋊Q8—792no—
774C4⋊Q8—792no—
775C4⋊Q8—794no—
776C4⋊Q8—792no—
777C4⋊Q8—794no—
778C4⋊Q8C22×D7912yes—
779C4⋊Q8C22×D7912yes—
780C4⋊Q8C22×D7914yes—
781C4⋊Q8C22×D7912yes—
782C4⋊Q8C22×D7914yes—
783#126—7916no—
784#126—7916no—
785#126—7916no—
786#126—7916no—
787#126—7916no—
788#126—7916no—
789#126—7916no—
790#126C22×D79116yes—
791#125—798no—
792#125—794no—
793#125—7916no—
794#125—7916no—
795#125—798no—
796#125—798no—
797#125—7916no—
798#125—7916no—
799#125—7916no—
800#125—7916no—
801#125—7916no—
802#125—7916no—
803#125—792no—
804#125—798no—
805#125—7916no—
806#125C22×D7912yes—
807#125C22×D7918yes—
808#125C22×D79116yes—
809#124—794no—
810#124—794no—
811#124—7916no—
812#124—794no—
813#124C22×D7914yes—
814#123—798no—
815#123—798no—
816#123—7916no—
817#123—7916no—
818#123—798no—
819#123C22×D7918yes—
820C22⋊Q8—798no—
821C22⋊Q8—794no—
822C22⋊Q8—798no—
823C22⋊Q8—798no—
824C22⋊Q8—794no—
825C22⋊Q8—798no—
826C22⋊Q8—7916no—
827C22⋊Q8—798no—
828C22⋊Q8—798no—
829C22⋊Q8—794no—
830C22⋊Q8—7916no—
831C22⋊Q8—798no—
832C22⋊Q8—7916no—
833C22⋊Q8—798no—
834C22⋊Q8—7916no—
835C22⋊Q8C22×D7918yes—
836C22⋊Q8C22×D7914yes—
837C22⋊Q8C22×D7918yes—
838C4×Q8—792no—
839C4×Q8—798no—
840C4×Q8—798no—
841C4×Q8—798no—
842C4×Q8—794no—
843C4×Q8—794no—
844C4×Q8—792no—
845C4×Q8—7916no—
846C4×Q8—798no—
847C4×Q8—7916no—
848C4×Q8—798no—
849C4×Q8—7916no—
850C4×Q8—798no—
851C4×Q8—798no—
852C4×Q8—794no—
853C4×Q8—792no—
854C4×Q8—794no—
855C4×Q8—7916no—
856C4×Q8—798no—
857C4×Q8—798no—
858C4×Q8—7916no—
859C4×Q8—7916no—
860C4×Q8—798no—
861C4×Q8—798no—
862C4×Q8—794no—
863C4×Q8C22×D7912yes—
864C4×Q8C22×D7918yes—
865C4×Q8C22×D7918yes—
866C4×Q8C22×D7918yes—
867C4×Q8C22×D7914yes—
868C4×D4—794no—
869C4×D4—792no—
870C4×D4—794no—
871C4×D4—794no—
872C4×D4—794no—
873C4×D4—794no—
874C4×D4—792no—
875C4×D4—794no—
876C4×D4—794no—
877C4×D4—794no—
878C4×D4—794no—
879C4×D4—792no—
880C4×D4C22×D7914yes—
881C4×D4C22×D7912yes—
882#117—791no—
883#117—792no—
884#117—792no—
885#117—798no—
886#117—798no—
887#117—792no—
888#117—794no—
889#117—794no—
890#117—7916no—
891#117—798no—
892#117—798no—
893#117—792no—
894#117—794no—
895#117—794no—
896#117—798no—
897#117—798no—
898#117—7916no—
899#117—792no—
900#117—792no—
901#117—792no—
902#117—794no—
903#117—7916no—
904#117—7916no—
905#117C22×D7911yescharacteristic
906#117C22×D7912yes—
907#117C22×D7912yes—
908#117C22×D7918yes—
909#117C22×D7918yes—
910C2×C4⋊C4—798no—
911C2×C4⋊C4—794no—
912C2×C4⋊C4—798no—
913C2×C4⋊C4—798no—
914C2×C4⋊C4—798no—
915C2×C4⋊C4—798no—
916C2×C4⋊C4—794no—
917C2×C4⋊C4—792no—
918C2×C4⋊C4—794no—
919C2×C4⋊C4—794no—
920C2×C4⋊C4—7916no—
921C2×C4⋊C4—7916no—
922C2×C4⋊C4—798no—
923C2×C4⋊C4C22×D7914yes—
924C2×C22⋊C4—792no—
925C2×C22⋊C4—794no—
926C2×C22⋊C4—794no—
927C2×C22⋊C4—7916no—
928C2×C42—792no—
929C2×C42—791no—
930C2×C42—792no—
931C2×C42—794no—
932C2×C42—792no—
933C2×C42—7916no—
934C2×C42—791no—
935C2×C42—794no—
936C2×C42—794no—
937C2×C42—792no—
938C2×C42—792no—
939C2×C42—791no—
940C2×C42—791no—
941C2×C42—794no—
942C2×C42—792no—
943C2×C42—792no—
944C2×C42—791no—
945C2×C42C22×D7911yescharacteristic
946C2×C42C22×D7912yes—
947C24—791no—
948C24—792no—
949#41—24no—
950#41—1588no—
951#41—1588no—
952#41—1584no—
953#41—1584no—
954#41—1584no—
955C2×Q8—28no—
956C2×Q8—798no—
957C2×Q8—794no—
958C2×Q8—798no—
959C2×Q8—794no—
960C2×Q8—798no—
961C2×Q8—794no—
962C2×Q8—792no—
963C2×Q8—791no—
964C2×Q8—15816no—
965C2×Q8—15816no—
966C2×Q8—15816no—
967C2×Q8—15816no—
968C2×Q8—15816no—
969C2×Q8—15816no—
970C2×Q8—1584no—
971C2×Q8—1588no—
972C2×Q8C23×D7914yes—
973C2×Q8C23×D7914yes—
974C2×Q8C23×D7914yes—
975C2×Q8C23×D7911yescharacteristic
976C2×D4—792no—
977C2×D4—792no—
978C2×D4—792no—
979C2×D4—792no—
980C2×D4—791no—
981C2×D4—1584no—
982C2×D4—1588no—
983C2×D4C23×D7912yes—
984C2×D4C23×D7911yescharacteristic
985C22×C4—791no—
986C22×C4—798no—
987C22×C4—791no—
988C22×C4—792no—
989C22×C4—791no—
990C22×C4—791no—
991C22×C4—791no—
992C22×C4—792no—
993C22×C4—794no—
994C22×C4—792no—
995C22×C4—794no—
996C22×C4—794no—
997C22×C4—798no—
998C22×C4—792no—
999C22×C4—798no—
1000C22×C4—792no—
1001C22×C4—792no—
1002C22×C4—792no—
1003C22×C4—794no—
1004C22×C4—794no—
1005C22×C4—792no—
1006C22×C4—792no—
1007C22×C4—798no—
1008C22×C4—15816no—
1009C22×C4—1588no—
1010C22×C4—1588no—
1011C22×C4—15816no—
1012C22×C4C23×D7912yes—
1013C22×C4C23×D7914yes—
1014C22×C4C23×D7912yes—
1015C22×C4C23×D7914yes—
1016C22×C4C23×D7911yescharacteristic
1017C4⋊C4—7916no—
1018C4⋊C4—7916no—
1019C4⋊C4—798no—
1020C4⋊C4—794no—
1021C4⋊C4—794no—
1022C4⋊C4—794no—
1023C4⋊C4—798no—
1024C4⋊C4—7916no—
1025C4⋊C4—7916no—
1026C4⋊C4—7916no—
1027C4⋊C4—7916no—
1028C4⋊C4—798no—
1029C4⋊C4—798no—
1030C4⋊C4—798no—
1031C4⋊C4—798no—
1032C4⋊C4—794no—
1033C4⋊C4—792no—
1034C4⋊C4—794no—
1035C4⋊C4—794no—
1036C4⋊C4—7916no—
1037C4⋊C4—7916no—
1038C4⋊C4—798no—
1039C4⋊C4C23×D7918yes—
1040C4⋊C4C23×D7918yes—
1041C4⋊C4C23×D7914yes—
1042C4⋊C4C23×D7912yes—
1043C4⋊C4C23×D7914yes—
1044C4⋊C4C23×D7914yes—
1045C4⋊C4C23×D79116yes—
1046C4⋊C4C23×D79116yes—
1047C4⋊C4C23×D7918yes—
1048C22⋊C4—792no—
1049C22⋊C4—794no—
1050C22⋊C4—794no—
1051C22⋊C4—7916no—
1052C22⋊C4—794no—
1053C22⋊C4—798no—
1054C22⋊C4—794no—
1055C22⋊C4—794no—
1056C22⋊C4—7916no—
1057C22⋊C4—7916no—
1058C22⋊C4C23×D7912yes—
1059C22⋊C4C23×D7914yes—
1060C22⋊C4C23×D7914yes—
1061C22⋊C4C23×D79116yes—
1062C42—791no—
1063C42—792no—
1064C42—794no—
1065C42—792no—
1066C42—792no—
1067C42—791no—
1068C42—794no—
1069C42—794no—
1070C42—794no—
1071C42—792no—
1072C42—792no—
1073C42—792no—
1074C42—7916no—
1075C42—7916no—
1076C42—7916no—
1077C42—798no—
1078C42—794no—
1079C42C23×D7911yescharacteristic
1080C42C23×D7912yes—
1081C42C23×D7911yescharacteristic
1082C42C23×D7914yes—
1083C42C23×D7912yes—
1084C42C23×D79116yes—
1085C42C23×D7914yes—
1086C23—791no—
1087C23—791no—
1088C23—794no—
1089C23—792no—
1090C23—1584no—
1091C23—1588no—
1092C23—1584no—
1093C23C24×D7912yes—
1094C23C24×D7911yescharacteristic
1095Q8—28no—
1096Q8—28no—
1097Q8—28no—
1098Q8—22no—
1099Q8—15816no—
1100Q8—15816no—
1101Q8—1584no—
1102Q8—15816no—
1103Q8—1588no—
1104Q8—1588no—
1105Q8—1588no—
1106Q8—1582no—
1107D4—24no—
1108D4—22no—
1109D4—1584no—
1110D4—1584no—
1111D4—1584no—
1112D4—1584no—
1113D4—1582no—
1114C2×C4—28no—
1115C2×C4—24no—
1116C2×C4—28no—
1117C2×C4—24no—
1118C2×C4—791no—
1119C2×C4—792no—
1120C2×C4—791no—
1121C2×C4—794no—
1122C2×C4—798no—
1123C2×C4—794no—
1124C2×C4—794no—
1125C2×C4—794no—
1126C2×C4—794no—
1127C2×C4—794no—
1128C2×C4—798no—
1129C2×C4—792no—
1130C2×C4—798no—
1131C2×C4—792no—
1132C2×C4—1584no—
1133C2×C4—1588no—
1134C2×C4—1584no—
1135C2×C4—1584no—
1136C2×C4—15816no—
1137C2×C4—15816no—
1138C2×C4—1588no—
1139C2×C4—1584no—
1140C2×C4—15816no—
1141C2×C4—1584no—
1142C2×C4—1584no—
1143C2×C4—1588no—
1144C2×C4—1588no—
1145C2×C4—1588no—
1146C2×C4—1584no—
1147C2×C4—1584no—
1148C2×C4#41×D7914yes—
1149C2×C4C24×D7914yes—
1150C2×C4C24×D7918yes—
1151C2×C4C24×D7912yes—
1152C2×C4C24×D7918yes—
1153C2×C4C24×D7912yes—
1154C2×C4C24×D7912yes—
1155C2×C4C24×D7911yescharacteristic
1156C2×C4C24×D7911yescharacteristic
1157C22—22no—
1158C22—22no—
1159C22—24no—
1160C22—3168no—
1161C22—792no—
1162C22—794no—
1163C22—792no—
1164C22—1588no—
1165C22—1582no—
1166C22—1584no—
1167C22—1582no—
1168C22C2×#41×D7912yes—
1169C22C25×D7911yescharacteristic
1170C4—22no—
1171C4—28no—
1172C4—24no—
1173C4—22no—
1174C4—28no—
1175C4—792no—
1176C4—792no—
1177C4—794no—
1178C4—1582no—
1179C4—1588no—
1180C4—1584no—
1181C4—1582no—
1182C4—1588no—
1183C4C2×#41×D7912yes—
1184C4C2×#41×D7912yes—
1185C42−1+4×D7914yes—
1186C2—22no—
1187C2—42no—
1188C2—3162no—
1189C2—794no—
1190C2—1582no—
1191C2C22×#41×D7911yescharacteristic
1192C2C2×2−1+4×D7912yes—
subgroupG/H
center, FrattiniC22C25×D79
commutator, socle, cosocleC22×C79C26
FittingC79×#3509C2
prime radicalC2×#41×D79C22
hypercenter#3509D79
hypocenterC79C2×#3509
LCSG ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #23777287C2semidirect
2. #23777286C2semidirect
3. #23777285C2semidirect
4. #23777284C2semidirect
5. #23777283C2semidirect
6. #23777282C2semidirect
7. #23777281C2semidirect
8. #23777280C2semidirect
9. #23777279C2semidirect
10. #23777278C2semidirect
11. #557×D79C2semidirect
12. #556×D79C2semidirect
13. #552×D79C2semidirect
14. #541×D79C2semidirect
16. #533×D79C2semidirect
17. #533×D79C2semidirect
18. C2×C4⋊Q8×D79C2semidirect
19. #519×D79C2semidirect
21. C79×#3509C2semidirect
24. #19099292C22semidirect
25. #19099291C22semidirect
26. #19099291C22semidirect
27. #19099290C22semidirect
28. #19099290C22semidirect
29. #19099289C22semidirect
30. #19099288C22semidirect
31. #19099288C22semidirect
32. #19099287C22semidirect
33. #19099286C22semidirect
34. #19099285C22semidirect
35. #19099284C22semidirect
36. #19099283C22semidirect
37. #19099282C22semidirect
38. #19099281C22semidirect
39. #19099280C22semidirect
40. #19099255C22semidirect
41. #19099254C22semidirect
42. #19099253C22semidirect
43. #19099252C22semidirect
44. #19099251C22semidirect
45. #19099250C22semidirect
46. #19099249C22semidirect
47. #19099248C22semidirect
48. #19099247C22semidirect
49. #19099246C22semidirect
50. #19099245C22semidirect
51. #19099176C22semidirect
52. #19099175C22semidirect
53. #19099174C22semidirect
54. #19099173C22semidirect
55. #19099172C22semidirect
56. #19099171C22semidirect
57. #19099170C22semidirect
65. #19099120C22semidirect
66. #19099120C22semidirect
67. #19099119C22semidirect
68. #19099119C22semidirect
69. #19099118C22semidirect
70. #19099118C22semidirect
71. #19099118C22semidirect
72. #19099117C22semidirect
73. #19099117C22semidirect
74. #19099117C22semidirect
75. #19099116C22semidirect
76. #19099116C22semidirect
77. #19099115C22semidirect
78. #19099115C22semidirect
79. #19099115C22semidirect
80. C2×#14579161C22semidirect
81. C2×#14579160C22semidirect
82. C2×#14579159C22semidirect
88. C4⋊Q8×D79C22semidirect
89. C4⋊Q8×D79C22semidirect
90. C4⋊Q8×D79C22semidirect
100. #19099041C22semidirect
101. #19099040C22semidirect
102. #19099040C22semidirect
103. #19099040C22semidirect
104. #19099039C22semidirect
105. #19099039C22semidirect
129. #557×C79C22semidirect
130. #556×C79C22semidirect
131. #552×C79C22semidirect
132. #541×C79C22semidirect
134. #533×C79C22semidirect
135. #533×C79C22semidirect
136. C2×C4⋊Q8×C79C22semidirect
137. #519×C79C22semidirect
596. D79#3509direct (N × H)
607. #3509D79direct (N × H)
618. C79C2×#3509semidirect
629. #557C2×D79semidirect
638. #556C2×D79semidirect
650. #552C2×D79semidirect
658. #541C2×D79semidirect
682. #533C2×D79semidirect
683. #533C2×D79semidirect
695. C2×C4⋊Q8C2×D79semidirect
711. #519C2×D79semidirect

Maximal subgroups

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

subgroupindex
#237772872
#237772862
#237772852
#237772842
#237772832
#237772822
#237772812
#237772802
#237772792
#237772782
#557×D792
#556×D792
#552×D792
#541×D792
#536×D792
#533×D792
C2×C4⋊Q8×D792
#519×D792
C4×#41×D792
C79×#35092
C2×#350979