Finite Group Databasebeta

← C79×#18845 #34130534

Subgroups — C79×#18845 #34130534

Order 20224.

876 conjugacy classes of subgroups.

The subgroup lattice has 622 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3515C211yesmaximal, characteristic
2C79×#3229C211yesmaximal, characteristic, complemented
3C79×#3218C211yesmaximal, characteristic, complemented
4C79×#3079C211yesmaximal, characteristic, complemented
5C79×#1654C212yesmaximal, complemented
6C79×#1653C212yesmaximal, complemented
7C79×#1644C212yesmaximal, complemented
8C79×#1643C212yesmaximal, complemented
9C79×#1559C211yesmaximal, characteristic, complemented
10C79×#1495C211yesmaximal, characteristic, complemented
11C79×#1488C211yesmaximal, characteristic, complemented
12#557×C79C2211yescharacteristic
13#554×C79C2211yescharacteristic
14#554×C79C2211yescharacteristic
15#553×C79—21no—
16#552×C79—21no—
17#552×C79—22no—
18#552×C79—21no—
19#547×C79—21no—
20#547×C79C2211yescharacteristic
21#541×C79—21no—
22#539×C79—22no—
23#533×C79C2211yescharacteristic
24C2×C4⋊Q8×C79C2211yescharacteristic
25#529×C79—21no—
26#529×C79C2211yescharacteristic
27C2×#125×C79—21no—
28#520×C79—21no—
29C4×#41×C79C2211yescharacteristic
30#498×C79C2212yes—
31#497×C79—21no—
32#491×C79—21no—
33#487×C79C2212yes—
34#483×C79—22no—
35#477×C79—21no—
36#476×C79—21no—
37#475×C79—22no—
38#475×C79C2212yes—
39#474×C79C2212yes—
40#462×C79C2212yes—
41#461×C79C2212yes—
42#451×C79—21no—
43#448×C79—21no—
44#432×C79C2211yescharacteristic
45#431×C79C2211yescharacteristic
46#428×C79—21no—
47#423×C79C2211yescharacteristic
48#417×C79—21no—
49#333×C79C2212yes—
50#332×C79C2212yes—
51Q8⋊C8×C79C2212yes—
52Q8⋊C8×C79C2212yes—
53D4⋊C8×C79C2212yes—
54D4⋊C8×C79C2212yes—
55C2×#41×C79—21no—
56C2×#41×C79D411yescharacteristic
57C22×Q8×C79—21no—
58C2×Q16×C79—22no—
59C2×SD16×C79—22no—
60C2×M16×C79—21no—
61C4⋊Q8×C79—21no—
62C4⋊Q8×C79—21no—
63C4⋊Q8×C79—21no—
64C4⋊Q8×C79—21no—
65C4⋊Q8×C79C2312yes—
66C4⋊Q8×C79C2311yescharacteristic
67C4⋊Q8×C79C2311yescharacteristic
68#126×C79—22no—
69#126×C79—22no—
70#126×C79—22no—
71#126×C79—21no—
72#125×C79—22no—
73#125×C79—22no—
74#125×C79—22no—
75#125×C79—21no—
76#125×C79—21no—
77#125×C79—22no—
78#125×C79—21no—
79#125×C79—21no—
80#125×C79D411yescharacteristic
81#124×C79D411yescharacteristic
82#123×C79—22no—
83#123×C79—22no—
84#123×C79—22no—
85#123×C79—21no—
86#123×C79—22no—
87C22⋊Q8×C79—21no—
88C22⋊Q8×C79—22no—
89C22⋊Q8×C79—22no—
90C22⋊Q8×C79—21no—
91C22⋊Q8×C79—21no—
92C22⋊Q8×C79—21no—
93C22⋊Q8×C79D411yescharacteristic
94C22⋊Q8×C79D412yes—
95#121×C79—22no—
96#121×C79—21no—
97#121×C79D411yescharacteristic
98C4×Q8×C79—21no—
99C4×Q8×C79—21no—
100C4×Q8×C79—21no—
101C4×Q8×C79D412yes—
102C4×Q8×C79D411yescharacteristic
103C4×Q8×C79C2311yescharacteristic
104C4×Q8×C79C2311yescharacteristic
105C4×D4×C79—22no—
106C4×D4×C79—22no—
107C4×D4×C79—21no—
108C4×D4×C79—21no—
109C4×D4×C79—21no—
110C4×D4×C79—21no—
111C4×D4×C79—21no—
112C4×D4×C79D411yescharacteristic
113C4×D4×C79C2311yescharacteristic
114C4×D4×C79C2311yescharacteristic
115#117×C79—22no—
116#117×C79—22no—
117#117×C79—21no—
118#117×C79—21no—
119#117×C79—21no—
120#117×C79D411yescharacteristic
121C2×C4⋊C4×C79—22no—
122C2×C4⋊C4×C79—22no—
123C2×C4⋊C4×C79—21no—
124C2×C4⋊C4×C79—21no—
125C2×C4⋊C4×C79—21no—
126C2×C4⋊C4×C79—21no—
127C2×C4⋊C4×C79—21no—
128C2×C42×C79—21no—
129C2×C42×C79C2311yescharacteristic
130#107×C79—22no—
131#106×C79—22no—
132#106×C79—24no—
133C4⋊C8×C79—21no—
134C4⋊C8×C79—21no—
135C4⋊C8×C79C2312yes—
136C4⋊C8×C79C2312yes—
137#103×C79—22no—
138#103×C79—24no—
139#103×C79—22no—
140#103×C79—22no—
141#102×C79—22no—
142C22⋊C8×C79—21no—
143C22⋊C8×C79—21no—
144#97×C79—21no—
145C4×C8×C79C2312yes—
146#41×C79—22no—
147#41×C79—41no—
148#41×C79—42no—
149#41×C79—42no—
150C2×Q8×C79—21no—
151C2×Q8×C79—22no—
152C2×Q8×C79—41no—
153C2×Q8×C79—82no—
154C2×Q8×C79C2×D411yescharacteristic
155C2×Q8×C79C2×D411yescharacteristic
156C2×Q8×C79C2×D412yes—
157C2×D4×C79—22no—
158C2×D4×C79—21no—
159C2×D4×C79—21no—
160C2×D4×C79C2×D411yescharacteristic
161C2×D4×C79C2×D411yescharacteristic
162C22×C4×C79—22no—
163C22×C4×C79—22no—
164C22×C4×C79—22no—
165C22×C4×C79—21no—
166C22×C4×C79—21no—
167C22×C4×C79—21no—
168C22×C4×C79—21no—
169C22×C4×C79—41no—
170C22×C4×C79C2×D411yescharacteristic
171C22×C4×C79C2×D411yescharacteristic
172C22×C4×C79C2×D411yescharacteristic
173Q16×C79—82no—
174SD16×C79—82no—
175M16×C79—42no—
176C2×C8×C79—22no—
177C2×C8×C79—22no—
178C2×C8×C79—22no—
179C4⋊C4×C79—22no—
180C4⋊C4×C79—22no—
181C4⋊C4×C79—22no—
182C4⋊C4×C79—22no—
183C4⋊C4×C79—22no—
184C4⋊C4×C79—22no—
185C4⋊C4×C79—22no—
186C4⋊C4×C79—22no—
187C4⋊C4×C79—21no—
188C4⋊C4×C79—21no—
189C4⋊C4×C79—22no—
190C4⋊C4×C79—22no—
191C4⋊C4×C79—21no—
192C4⋊C4×C79—21no—
193C4⋊C4×C79—21no—
194C4⋊C4×C79—21no—
195C4⋊C4×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79—22no—
199C4⋊C4×C79—22no—
200C4⋊C4×C79—41no—
201C4⋊C4×C79—41no—
202C4⋊C4×C79C2×D411yescharacteristic
203C4⋊C4×C79C2×D411yescharacteristic
204C4⋊C4×C79C2×D411yescharacteristic
205C4⋊C4×C79C2×D412yes—
206C4⋊C4×C79C2×D411yescharacteristic
207C22⋊C4×C79—22no—
208C22⋊C4×C79—22no—
209C22⋊C4×C79—22no—
210C22⋊C4×C79—22no—
211C22⋊C4×C79—21no—
212C22⋊C4×C79—21no—
213C22⋊C4×C79—21no—
214C22⋊C4×C79—21no—
215C22⋊C4×C79—21no—
216C22⋊C4×C79—21no—
217C22⋊C4×C79—21no—
218C22⋊C4×C79—21no—
219C42×C79—22no—
220C42×C79—21no—
221C42×C79—21no—
222C42×C79—22no—
223C42×C79—21no—
224C42×C79—21no—
225C42×C79C2×D411yescharacteristic
226C42×C79C2×D411yescharacteristic
227C42×C79C2×D411yescharacteristic
228C42×C79C2411yescharacteristic
229C23×C79—21no—
230C23×C79—21no—
231C23×C79#12011yescharacteristic
232Q8×C79—21no—
233Q8×C79—21no—
234Q8×C79—22no—
235Q8×C79—42no—
236Q8×C79—41no—
237Q8×C79—41no—
238Q8×C79—42no—
239Q8×C79—42no—
240Q8×C79—82no—
241D4×C79—21no—
242D4×C79—22no—
243D4×C79—42no—
244D4×C79—44no—
245D4×C79—81no—
246D4×C79#13712yes—
247C2×C4×C79—21no—
248C2×C4×C79—21no—
249C2×C4×C79—22no—
250C2×C4×C79—21no—
251C2×C4×C79—21no—
252C2×C4×C79—21no—
253C2×C4×C79—21no—
254C2×C4×C79—22no—
255C2×C4×C79—22no—
256C2×C4×C79—21no—
257C2×C4×C79—21no—
258C2×C4×C79—41no—
259C2×C4×C79—42no—
260C2×C4×C79—44no—
261C2×C4×C79—41no—
262C2×C4×C79—41no—
263C2×C4×C79—42no—
264C2×C4×C79—42no—
265C2×C4×C79—81no—
266C2×C4×C79—82no—
267C2×C4×C79—82no—
268C2×C4×C79—82no—
269C2×C4×C79#12011yescharacteristic
270C2×C4×C79#12011yescharacteristic
271C2×C4×C79#12011yescharacteristic
272C2×C4×C79C22×D411yescharacteristic
273C2×C4×C79C22×D411yescharacteristic
274C2×C4×C79C22×D411yescharacteristic
275C8×C79—42no—
276C8×C79—42no—
277C8×C79—42no—
278C22×C79—21no—
279C22×C79—22no—
280C22×C79—21no—
281C22×C79—21no—
282C22×C79—41no—
283C22×C79—41no—
284C22×C79—41no—
285C22×C79—41no—
286C22×C79—41no—
287C22×C79C2×#12011yescharacteristic
288C4×C79—21no—
289C4×C79—21no—
290C4×C79—21no—
291C4×C79—21no—
292C4×C79—41no—
293C4×C79—41no—
294C4×C79—42no—
295C4×C79—41no—
296C4×C79—41no—
297C4×C79—41no—
298C4×C79—41no—
299C4×C79—42no—
300C4×C79—82no—
301C4×C79C2×#13711yescharacteristic
302C4×C79#57511yescharacteristic
303C4×C79#57712yes—
304#18845C7911yesmaximal, characteristic, direct product factor, Sylow
305C2×C79—41no—
306C2×C79—42no—
307C2×C79—81no—
308C2×C79#300711yescharacteristic
309C2×C79#301011yescharacteristic
310C2×C79#302211yescharacteristic
311#3515C2×C7911yescharacteristic
312#3229C2×C7911yescharacteristic, complemented
313#3218C2×C7911yescharacteristic, complemented
314#3079C2×C7911yescharacteristic, complemented
315#1654C2×C7912yescomplemented
316#1653C2×C7912yescomplemented
317#1644C2×C7912yescomplemented
318#1643C2×C7912yescomplemented
319#1559C2×C7911yescharacteristic, complemented
320#1495C2×C7911yescharacteristic, complemented
321#1488C2×C7911yescharacteristic, complemented
322C79#1884511yescharacteristic, direct product factor, Sylow
323#557C22×C7911yescharacteristic
324#554C22×C7911yescharacteristic
325#554C22×C7911yescharacteristic
326#553—21no—
327#552—21no—
328#552—22no—
329#552—21no—
330#547—21no—
331#547C22×C7911yescharacteristic
332#541—21no—
333#539—22no—
334#533C22×C7911yescharacteristic
335C2×C4⋊Q8C22×C7911yescharacteristic
336#529—21no—
337#529C22×C7911yescharacteristic
338C2×#125—21no—
339#520—21no—
340C4×#41C22×C7911yescharacteristic
341#498C22×C7912yes—
342#497—21no—
343#491—21no—
344#487C22×C7912yes—
345#483—22no—
346#477—21no—
347#476—21no—
348#475—22no—
349#475C22×C7912yes—
350#474C22×C7912yes—
351#462C22×C7912yes—
352#461C22×C7912yes—
353#451—21no—
354#448—21no—
355#432C22×C7911yescharacteristic
356#431C22×C7911yescharacteristic
357#428—21no—
358#423C22×C7911yescharacteristic
359#417—21no—
360#333C22×C7912yes—
361#332C22×C7912yes—
362Q8⋊C8C22×C7912yes—
363Q8⋊C8C22×C7912yes—
364D4⋊C8C22×C7912yes—
365D4⋊C8C22×C7912yes—
366C2×#41—21no—
367C2×#41D4×C7911yescharacteristic
368C22×Q8—21no—
369C2×Q16—22no—
370C2×SD16—22no—
371C2×M16—21no—
372C4⋊Q8—21no—
373C4⋊Q8—21no—
374C4⋊Q8—21no—
375C4⋊Q8—21no—
376C4⋊Q8C23×C7912yes—
377C4⋊Q8C23×C7911yescharacteristic
378C4⋊Q8C23×C7911yescharacteristic
379#126—22no—
380#126—22no—
381#126—22no—
382#126—21no—
383#125—22no—
384#125—22no—
385#125—22no—
386#125—21no—
387#125—21no—
388#125—22no—
389#125—21no—
390#125—21no—
391#125D4×C7911yescharacteristic
392#124D4×C7911yescharacteristic
393#123—22no—
394#123—22no—
395#123—22no—
396#123—21no—
397#123—22no—
398C22⋊Q8—21no—
399C22⋊Q8—22no—
400C22⋊Q8—22no—
401C22⋊Q8—21no—
402C22⋊Q8—21no—
403C22⋊Q8—21no—
404C22⋊Q8D4×C7911yescharacteristic
405C22⋊Q8D4×C7912yes—
406#121—22no—
407#121—21no—
408#121D4×C7911yescharacteristic
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—21no—
412C4×Q8D4×C7911yescharacteristic
413C4×Q8D4×C7912yes—
414C4×Q8C23×C7911yescharacteristic
415C4×Q8C23×C7911yescharacteristic
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—21no—
419C4×D4—21no—
420C4×D4—21no—
421C4×D4—21no—
422C4×D4—21no—
423C4×D4D4×C7911yescharacteristic
424C4×D4C23×C7911yescharacteristic
425C4×D4C23×C7911yescharacteristic
426#117—22no—
427#117—22no—
428#117—21no—
429#117—21no—
430#117—21no—
431#117D4×C7911yescharacteristic
432C2×C4⋊C4—22no—
433C2×C4⋊C4—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C42—21no—
440C2×C42C23×C7911yescharacteristic
441#107—22no—
442#106—22no—
443#106—24no—
444C4⋊C8—21no—
445C4⋊C8—21no—
446C4⋊C8C23×C7912yes—
447C4⋊C8C23×C7912yes—
448#103—22no—
449#103—24no—
450#103—22no—
451#103—22no—
452#102—22no—
453C22⋊C8—21no—
454C22⋊C8—21no—
455#97—21no—
456C4×C8C23×C7912yes—
457#41—22no—
458#41—41no—
459#41—42no—
460#41—42no—
461C2×Q8—21no—
462C2×Q8—22no—
463C2×Q8—41no—
464C2×Q8—82no—
465C2×Q8C2×D4×C7911yescharacteristic
466C2×Q8C2×D4×C7911yescharacteristic
467C2×Q8C2×D4×C7912yes—
468C2×D4—22no—
469C2×D4—21no—
470C2×D4—21no—
471C2×D4C2×D4×C7911yescharacteristic
472C2×D4C2×D4×C7911yescharacteristic
473C22×C4—22no—
474C22×C4—22no—
475C22×C4—22no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—41no—
481C22×C4C2×D4×C7911yescharacteristic
482C22×C4C2×D4×C7911yescharacteristic
483C22×C4C2×D4×C7911yescharacteristic
484Q16—82no—
485SD16—82no—
486M16—42no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—22no—
490C4⋊C4—22no—
491C4⋊C4—22no—
492C4⋊C4—22no—
493C4⋊C4—22no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—22no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—22no—
510C4⋊C4—22no—
511C4⋊C4—41no—
512C4⋊C4—41no—
513C4⋊C4C2×D4×C7911yescharacteristic
514C4⋊C4C2×D4×C7911yescharacteristic
515C4⋊C4C2×D4×C7911yescharacteristic
516C4⋊C4C2×D4×C7912yes—
517C4⋊C4C2×D4×C7911yescharacteristic
518C22⋊C4—22no—
519C22⋊C4—22no—
520C22⋊C4—22no—
521C22⋊C4—22no—
522C22⋊C4—21no—
523C22⋊C4—21no—
524C22⋊C4—21no—
525C22⋊C4—21no—
526C22⋊C4—21no—
527C22⋊C4—21no—
528C22⋊C4—21no—
529C22⋊C4—21no—
530C42—22no—
531C42—21no—
532C42—21no—
533C42—22no—
534C42—21no—
535C42—21no—
536C42C2×D4×C7911yescharacteristic
537C42C2×D4×C7911yescharacteristic
538C42C2×D4×C7911yescharacteristic
539C42C24×C7911yescharacteristic
540C23—21no—
541C23—21no—
542C23#120×C7911yescharacteristic
543Q8—21no—
544Q8—21no—
545Q8—22no—
546Q8—42no—
547Q8—41no—
548Q8—41no—
549Q8—42no—
550Q8—42no—
551Q8—82no—
552D4—21no—
553D4—22no—
554D4—42no—
555D4—44no—
556D4—81no—
557D4#137×C7912yes—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—41no—
570C2×C4—42no—
571C2×C4—44no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—42no—
575C2×C4—42no—
576C2×C4—81no—
577C2×C4—82no—
578C2×C4—82no—
579C2×C4—82no—
580C2×C4#120×C7911yescharacteristic
581C2×C4#120×C7911yescharacteristic
582C2×C4#120×C7911yescharacteristic
583C2×C4C22×D4×C7911yescharacteristic
584C2×C4C22×D4×C7911yescharacteristic
585C2×C4C22×D4×C7911yescharacteristic
586C8—42no—
587C8—42no—
588C8—42no—
589C22—21no—
590C22—21no—
591C22—22no—
592C22—21no—
593C22—41no—
594C22—41no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22C2×#120×C7911yescharacteristic
599C4—21no—
600C4—21no—
601C4—21no—
602C4—21no—
603C4—41no—
604C4—41no—
605C4—42no—
606C4—41no—
607C4—41no—
608C4—42no—
609C4—41no—
610C4—41no—
611C4—82no—
612C4C2×#137×C7911yescharacteristic
613C4#575×C7911yescharacteristic
614C4#577×C7912yes—
615C2—41no—
616C2—42no—
617C2—81no—
618C2C79×#300711yescharacteristic
619C2C79×#301011yescharacteristic
620C2C79×#302211yescharacteristic
subgroupG/H
center, socleC22×C79C2×#120
commutator, Frattini, cosocleC42C24×C79
prime radicalC79×#3515C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C2×C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
2. C79×#3229C2semidirect
3. C79×#3218C2semidirect
4. C79×#3079C2semidirect
5. C79×#1654C2semidirect
6. C79×#1653C2semidirect
7. C79×#1644C2semidirect
8. C79×#1643C2semidirect
9. C79×#1559C2semidirect
10. C79×#1495C2semidirect
11. C79×#1488C2semidirect
304. #18845C79direct (N × H)
312. #3229C2×C79semidirect
313. #3218C2×C79semidirect
314. #3079C2×C79semidirect
315. #1654C2×C79semidirect
316. #1653C2×C79semidirect
317. #1644C2×C79semidirect
318. #1643C2×C79semidirect
319. #1559C2×C79semidirect
320. #1495C2×C79semidirect
321. #1488C2×C79semidirect
322. C79#18845direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#35152
C79×#32292
C79×#32182
C79×#30792
C79×#16542
C79×#16532
C79×#16442
C79×#16432
C79×#15592
C79×#14952
C79×#14882
#1884579