Finite Group Databasebeta

← C79×#19848 #34131537

Subgroups — C79×#19848 #34131537

Order 20224.

556 conjugacy classes of subgroups.

The subgroup lattice has 542 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C79×#3369C211yesmaximal, characteristic
2C79×#3364C211yesmaximal, characteristic
3C79×#3363C211yesmaximal, characteristic, complemented
4C79×#3342C211yesmaximal, characteristic
5C79×#1718C211yesmaximal, characteristic, complemented
6C79×#1700C211yesmaximal, characteristic, complemented
7C79×#1684C211yesmaximal, characteristic, complemented
8C79×#1683C211yesmaximal, characteristic
9C79×#1674C211yesmaximal, characteristic, complemented
10C79×#1653C211yesmaximal, characteristic, complemented
11C79×#1652C211yesmaximal, characteristic
12C79×#1645C211yesmaximal, characteristic, complemented
13C79×#1638C211yesmaximal, characteristic
14C79×#1584C211yesmaximal, characteristic, complemented
15C79×SD16⋊C8C211yesmaximal, characteristic
16Q82×C79C2211yescharacteristic
17#557×C79C2211yescharacteristic
18#556×C79C2211yescharacteristic
19#556×C79C2211yescharacteristic
20#500×C79C2211yescharacteristic
21#498×C79C2211yescharacteristic
22#489×C79—21no—
23#488×C79—21no—
24#487×C79—21no—
25#487×C79C2211yescharacteristic
26#487×C79C2211yescharacteristic
27#487×C79C2211yescharacteristic
28#487×C79C2211yescharacteristic
29#485×C79—21no—
30#485×C79—21no—
31#479×C79—21no—
32#477×C79—21no—
33#477×C79C2211yescharacteristic
34#476×C79C2211yescharacteristic
35#475×C79—21no—
36#475×C79C2211yescharacteristic
37#475×C79C2211yescharacteristic
38#474×C79C2211yescharacteristic
39#467×C79—21no—
40#464×C79—21no—
41#464×C79—21no—
42#462×C79—21no—
43#462×C79C2211yescharacteristic
44#462×C79C2211yescharacteristic
45#462×C79C2211yescharacteristic
46#446×C79C2211yescharacteristic
47C8×Q8×C79C2211yescharacteristic
48C8×Q8×C79C2211yescharacteristic
49#441×C79—21no—
50C4×Q16×C79—21no—
51C4×Q16×C79—21no—
52C4×Q16×C79C2211yescharacteristic
53C4×SD16×C79C2211yescharacteristic
54C8×D4×C79C2211yescharacteristic
55#427×C79—21no—
56#335×C79C2211yescharacteristic
57#335×C79C2211yescharacteristic
58#333×C79C2211yescharacteristic
59#332×C79C2211yescharacteristic
60#332×C79C2211yescharacteristic
61#332×C79C2211yescharacteristic
62Q8⋊C8×C79C2211yescharacteristic
63Q8⋊C8×C79C2211yescharacteristic
64Q8⋊C8×C79C2211yescharacteristic
65D4⋊C8×C79C2211yescharacteristic
66#322×C79C2211yescharacteristic
67C2×Q16×C79—21no—
68C2×Q16×C79—21no—
69C2×Q16×C79—21no—
70C2×Q16×C79D411yescharacteristic
71C2×SD16×C79D411yescharacteristic
72C22×C8×C79—21no—
73C4⋊Q8×C79—21no—
74C4⋊Q8×C79—21no—
75C4⋊Q8×C79—21no—
76C4⋊Q8×C79—41no—
77C4⋊Q8×C79C2311yescharacteristic
78C4⋊Q8×C79C2311yescharacteristic
79C4⋊Q8×C79C2311yescharacteristic
80C4⋊Q8×C79C2311yescharacteristic
81#126×C79—41no—
82#126×C79—41no—
83#125×C79—21no—
84#125×C79—41no—
85#124×C79—21no—
86#124×C79—21no—
87C22⋊Q8×C79—21no—
88C22⋊Q8×C79—21no—
89C4×Q8×C79—21no—
90C4×Q8×C79—21no—
91C4×Q8×C79—21no—
92C4×Q8×C79—21no—
93C4×Q8×C79—21no—
94C4×Q8×C79—21no—
95C4×Q8×C79C2311yescharacteristic
96C4×Q8×C79C2311yescharacteristic
97C4×Q8×C79C2311yescharacteristic
98C4×D4×C79C2311yescharacteristic
99#117×C79—21no—
100#117×C79—21no—
101#107×C79—21no—
102#107×C79—21no—
103#107×C79—21no—
104#107×C79—21no—
105#107×C79D411yescharacteristic
106#106×C79—21no—
107#106×C79—21no—
108#106×C79—21no—
109#106×C79—41no—
110#106×C79D411yescharacteristic
111C4⋊C8×C79—21no—
112C4⋊C8×C79—21no—
113C4⋊C8×C79—21no—
114C4⋊C8×C79C2311yescharacteristic
115C4⋊C8×C79C2311yescharacteristic
116C4⋊C8×C79C2311yescharacteristic
117C4⋊C8×C79C2311yescharacteristic
118#103×C79—21no—
119#103×C79—21no—
120#103×C79—21no—
121#103×C79—21no—
122#103×C79—21no—
123#103×C79—21no—
124#103×C79—21no—
125#103×C79—21no—
126#103×C79—21no—
127#103×C79—21no—
128#103×C79—21no—
129#103×C79—21no—
130#103×C79—41no—
131#103×C79D411yescharacteristic
132#103×C79D411yescharacteristic
133#103×C79D411yescharacteristic
134#102×C79—21no—
135#102×C79—21no—
136#102×C79D411yescharacteristic
137C22⋊C8×C79—21no—
138#97×C79—21no—
139C4×C8×C79—21no—
140C4×C8×C79—21no—
141C4×C8×C79C2311yescharacteristic
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144C2×Q8×C79—21no—
145C2×Q8×C79—21no—
146C2×Q8×C79—21no—
147C2×Q8×C79—21no—
148C2×Q8×C79—41no—
149C2×Q8×C79C2×D411yescharacteristic
150C2×Q8×C79C2×D411yescharacteristic
151C2×Q8×C79C2×D411yescharacteristic
152C2×D4×C79C2×D411yescharacteristic
153C22×C4×C79—21no—
154Q16×C79—41no—
155Q16×C79—42no—
156Q16×C79—42no—
157Q16×C79—42no—
158SD16×C79—22no—
159C2×C8×C79—21no—
160C2×C8×C79—21no—
161C2×C8×C79—21no—
162C2×C8×C79—21no—
163C2×C8×C79—21no—
164C2×C8×C79—42no—
165C2×C8×C79C2×D411yescharacteristic
166C2×C8×C79C2×D411yescharacteristic
167C2×C8×C79C2×D411yescharacteristic
168C2×C8×C79C2×D411yescharacteristic
169C4⋊C4×C79—21no—
170C4⋊C4×C79—21no—
171C4⋊C4×C79—21no—
172C4⋊C4×C79—21no—
173C4⋊C4×C79—21no—
174C4⋊C4×C79—21no—
175C4⋊C4×C79—21no—
176C4⋊C4×C79—21no—
177C4⋊C4×C79—21no—
178C4⋊C4×C79—21no—
179C4⋊C4×C79—21no—
180C4⋊C4×C79—41no—
181C4⋊C4×C79—41no—
182C4⋊C4×C79—41no—
183C4⋊C4×C79—41no—
184C4⋊C4×C79—41no—
185C4⋊C4×C79—41no—
186C4⋊C4×C79—41no—
187C4⋊C4×C79C2×D411yescharacteristic
188C4⋊C4×C79C2×D411yescharacteristic
189C4⋊C4×C79C2×D411yescharacteristic
190C4⋊C4×C79C2×D411yescharacteristic
191C22⋊C4×C79—21no—
192C22⋊C4×C79—41no—
193C22⋊C4×C79—41no—
194C22⋊C4×C79—41no—
195C22⋊C4×C79—41no—
196C42×C79—21no—
197C42×C79—21no—
198C42×C79—21no—
199C42×C79—41no—
200C42×C79—41no—
201C42×C79—41no—
202C42×C79—41no—
203C42×C79C2411yescharacteristic
204C23×C79—21no—
205Q8×C79—21no—
206Q8×C79—21no—
207Q8×C79—21no—
208Q8×C79—21no—
209Q8×C79—21no—
210Q8×C79—41no—
211Q8×C79—41no—
212Q8×C79—41no—
213Q8×C79—41no—
214Q8×C79—41no—
215Q8×C79—41no—
216Q8×C79—81no—
217Q8×C79—161no—
218Q8×C79#13512yes—
219D4×C79—21no—
220D4×C79—21no—
221C2×C4×C79—21no—
222C2×C4×C79—21no—
223C2×C4×C79—21no—
224C2×C4×C79—21no—
225C2×C4×C79—21no—
226C2×C4×C79—21no—
227C2×C4×C79—21no—
228C2×C4×C79—41no—
229C2×C4×C79—41no—
230C2×C4×C79—41no—
231C2×C4×C79—41no—
232C2×C4×C79—41no—
233C2×C4×C79—41no—
234C2×C4×C79C22×D411yescharacteristic
235C2×C4×C79C22×D411yescharacteristic
236C2×C4×C79H(5,𝔽2)11yescharacteristic
237C8×C79—21no—
238C8×C79—21no—
239C8×C79—21no—
240C8×C79—21no—
241C8×C79—41no—
242C8×C79—41no—
243C8×C79—41no—
244C8×C79—41no—
245C8×C79—41no—
246C22×C79—41no—
247C22×C79—41no—
248C22×C79—41no—
249C22×C79D4211yescharacteristic
250C4×C79—22no—
251C4×C79—21no—
252C4×C79—41no—
253C4×C79—41no—
254C4×C79—41no—
255C4×C79—41no—
256C4×C79—41no—
257C4×C79—41no—
258C4×C79—81no—
259C4×C79—81no—
260C4×C79—81no—
261C4×C79—81no—
262C4×C79C2×#13511yescharacteristic
263C4×C79#57511yescharacteristic
264C4×C79#57811yescharacteristic
265C4×C79#57811yescharacteristic
266#19848C7911yesmaximal, characteristic, direct product factor, Sylow
267C2×C79—81no—
268C2×C79#326911yescharacteristic
269C2×C79#328511yescharacteristic
270C2×C79#328911yescharacteristic
271#3369C2×C7911yescharacteristic
272#3364C2×C7911yescharacteristic
273#3363C2×C7911yescharacteristic, complemented
274#3342C2×C7911yescharacteristic
275#1718C2×C7911yescharacteristic, complemented
276#1700C2×C7911yescharacteristic, complemented
277#1684C2×C7911yescharacteristic, complemented
278#1683C2×C7911yescharacteristic
279#1674C2×C7911yescharacteristic, complemented
280#1653C2×C7911yescharacteristic, complemented
281#1652C2×C7911yescharacteristic
282#1645C2×C7911yescharacteristic, complemented
283#1638C2×C7911yescharacteristic
284#1584C2×C7911yescharacteristic, complemented
285SD16⋊C8C2×C7911yescharacteristic
286C79#1984811yescharacteristic, direct product factor, Sylow
287Q82C22×C7911yescharacteristic
288#557C22×C7911yescharacteristic
289#556C22×C7911yescharacteristic
290#556C22×C7911yescharacteristic
291#500C22×C7911yescharacteristic
292#498C22×C7911yescharacteristic
293#489—21no—
294#488—21no—
295#487—21no—
296#487C22×C7911yescharacteristic
297#487C22×C7911yescharacteristic
298#487C22×C7911yescharacteristic
299#487C22×C7911yescharacteristic
300#485—21no—
301#485—21no—
302#479—21no—
303#477—21no—
304#477C22×C7911yescharacteristic
305#476C22×C7911yescharacteristic
306#475—21no—
307#475C22×C7911yescharacteristic
308#475C22×C7911yescharacteristic
309#474C22×C7911yescharacteristic
310#467—21no—
311#464—21no—
312#464—21no—
313#462—21no—
314#462C22×C7911yescharacteristic
315#462C22×C7911yescharacteristic
316#462C22×C7911yescharacteristic
317#446C22×C7911yescharacteristic
318C8×Q8C22×C7911yescharacteristic
319C8×Q8C22×C7911yescharacteristic
320#441—21no—
321C4×Q16—21no—
322C4×Q16—21no—
323C4×Q16C22×C7911yescharacteristic
324C4×SD16C22×C7911yescharacteristic
325C8×D4C22×C7911yescharacteristic
326#427—21no—
327#335C22×C7911yescharacteristic
328#335C22×C7911yescharacteristic
329#333C22×C7911yescharacteristic
330#332C22×C7911yescharacteristic
331#332C22×C7911yescharacteristic
332#332C22×C7911yescharacteristic
333Q8⋊C8C22×C7911yescharacteristic
334Q8⋊C8C22×C7911yescharacteristic
335Q8⋊C8C22×C7911yescharacteristic
336D4⋊C8C22×C7911yescharacteristic
337#322C22×C7911yescharacteristic
338C2×Q16—21no—
339C2×Q16—21no—
340C2×Q16—21no—
341C2×Q16D4×C7911yescharacteristic
342C2×SD16D4×C7911yescharacteristic
343C22×C8—21no—
344C4⋊Q8—21no—
345C4⋊Q8—21no—
346C4⋊Q8—21no—
347C4⋊Q8—41no—
348C4⋊Q8C23×C7911yescharacteristic
349C4⋊Q8C23×C7911yescharacteristic
350C4⋊Q8C23×C7911yescharacteristic
351C4⋊Q8C23×C7911yescharacteristic
352#126—41no—
353#126—41no—
354#125—21no—
355#125—41no—
356#124—21no—
357#124—21no—
358C22⋊Q8—21no—
359C22⋊Q8—21no—
360C4×Q8—21no—
361C4×Q8—21no—
362C4×Q8—21no—
363C4×Q8—21no—
364C4×Q8—21no—
365C4×Q8—21no—
366C4×Q8C23×C7911yescharacteristic
367C4×Q8C23×C7911yescharacteristic
368C4×Q8C23×C7911yescharacteristic
369C4×D4C23×C7911yescharacteristic
370#117—21no—
371#117—21no—
372#107—21no—
373#107—21no—
374#107—21no—
375#107—21no—
376#107D4×C7911yescharacteristic
377#106—21no—
378#106—21no—
379#106—21no—
380#106—41no—
381#106D4×C7911yescharacteristic
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8C23×C7911yescharacteristic
386C4⋊C8C23×C7911yescharacteristic
387C4⋊C8C23×C7911yescharacteristic
388C4⋊C8C23×C7911yescharacteristic
389#103—21no—
390#103—21no—
391#103—21no—
392#103—21no—
393#103—21no—
394#103—21no—
395#103—21no—
396#103—21no—
397#103—21no—
398#103—21no—
399#103—21no—
400#103—21no—
401#103—41no—
402#103D4×C7911yescharacteristic
403#103D4×C7911yescharacteristic
404#103D4×C7911yescharacteristic
405#102—21no—
406#102—21no—
407#102D4×C7911yescharacteristic
408C22⋊C8—21no—
409#97—21no—
410C4×C8—21no—
411C4×C8—21no—
412C4×C8C23×C7911yescharacteristic
413C4×C8C23×C7911yescharacteristic
414C4×C8C23×C7911yescharacteristic
415C2×Q8—21no—
416C2×Q8—21no—
417C2×Q8—21no—
418C2×Q8—21no—
419C2×Q8—41no—
420C2×Q8C2×D4×C7911yescharacteristic
421C2×Q8C2×D4×C7911yescharacteristic
422C2×Q8C2×D4×C7911yescharacteristic
423C2×D4C2×D4×C7911yescharacteristic
424C22×C4—21no—
425Q16—41no—
426Q16—42no—
427Q16—42no—
428Q16—42no—
429SD16—22no—
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—42no—
436C2×C8C2×D4×C7911yescharacteristic
437C2×C8C2×D4×C7911yescharacteristic
438C2×C8C2×D4×C7911yescharacteristic
439C2×C8C2×D4×C7911yescharacteristic
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—41no—
452C4⋊C4—41no—
453C4⋊C4—41no—
454C4⋊C4—41no—
455C4⋊C4—41no—
456C4⋊C4—41no—
457C4⋊C4—41no—
458C4⋊C4C2×D4×C7911yescharacteristic
459C4⋊C4C2×D4×C7911yescharacteristic
460C4⋊C4C2×D4×C7911yescharacteristic
461C4⋊C4C2×D4×C7911yescharacteristic
462C22⋊C4—21no—
463C22⋊C4—41no—
464C22⋊C4—41no—
465C22⋊C4—41no—
466C22⋊C4—41no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—41no—
471C42—41no—
472C42—41no—
473C42—41no—
474C42C24×C7911yescharacteristic
475C23—21no—
476Q8—21no—
477Q8—21no—
478Q8—21no—
479Q8—21no—
480Q8—21no—
481Q8—41no—
482Q8—41no—
483Q8—41no—
484Q8—41no—
485Q8—41no—
486Q8—41no—
487Q8—81no—
488Q8—161no—
489Q8#135×C7912yes—
490D4—21no—
491D4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4C22×D4×C7911yescharacteristic
506C2×C4C22×D4×C7911yescharacteristic
507C2×C4H(5,𝔽2)×C7911yescharacteristic
508C8—21no—
509C8—21no—
510C8—21no—
511C8—21no—
512C8—41no—
513C8—41no—
514C8—41no—
515C8—41no—
516C8—41no—
517C22—41no—
518C22—41no—
519C22—41no—
520C22D42×C7911yescharacteristic
521C4—22no—
522C4—21no—
523C4—41no—
524C4—41no—
525C4—41no—
526C4—41no—
527C4—41no—
528C4—41no—
529C4—81no—
530C4—81no—
531C4—81no—
532C4—81no—
533C4C2×#135×C7911yescharacteristic
534C4#575×C7911yescharacteristic
535C4#578×C7911yescharacteristic
536C4#578×C7911yescharacteristic
537C2—81no—
538C2C79×#326911yescharacteristic
539C2C79×#328511yescharacteristic
540C2C79×#328911yescharacteristic
subgroupG/H
center, socleC22×C79D42
commutator, Frattini, cosocleC42C24×C79
prime radicalC2×D4×C79C2×D4
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C79 ◁ C42×C79 ◁ G

Complements

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

NH ≅ G/Ntype
3. C79×#3363C2semidirect
5. C79×#1718C2semidirect
6. C79×#1700C2semidirect
7. C79×#1684C2semidirect
9. C79×#1674C2semidirect
10. C79×#1653C2semidirect
12. C79×#1645C2semidirect
14. C79×#1584C2semidirect
266. #19848C79direct (N × H)
273. #3363C2×C79semidirect
275. #1718C2×C79semidirect
276. #1700C2×C79semidirect
277. #1684C2×C79semidirect
279. #1674C2×C79semidirect
280. #1653C2×C79semidirect
282. #1645C2×C79semidirect
284. #1584C2×C79semidirect
286. C79#19848direct (N × H)

Maximal subgroups

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

subgroupindex
C79×#33692
C79×#33642
C79×#33632
C79×#33422
C79×#17182
C79×#17002
C79×#16842
C79×#16832
C79×#16742
C79×#16532
C79×#16522
C79×#16452
C79×#16382
C79×#15842
C79×SD16⋊C82
#1984879