Finite Group Databasebeta

← #34258449

Subgroups — #34258449

Order 20224.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23773424C211yesmaximal, characteristic
2#23772548C211yesmaximal, characteristic, complemented
3#23772510C211yesmaximal, characteristic, complemented
4#23762272C211yesmaximal, characteristic, complemented
5#23762263C211yesmaximal, characteristic, complemented
6#23762240C211yesmaximal, characteristic, complemented
7#23762239C211yesmaximal, characteristic, complemented
8#23762225C211yesmaximal, characteristic, complemented
9C8×#11929611C211yesmaximal, characteristic, complemented
10C8×#11929611C211yesmaximal, characteristic, complemented
11#23762169C211yesmaximal, characteristic, complemented
12#23761838C211yesmaximal, characteristic, complemented
13#23761812C211yesmaximal, characteristic, complemented
14#23761696C211yesmaximal, characteristic, complemented
15C79×#1579C211yesmaximal, characteristic, complemented
16#19099100C2211yescharacteristic
17C4×#11929625C2211yescharacteristic
18#19098903C411yescharacteristic
19#19098890C411yescharacteristic
20#19098872C411yescharacteristic
21#19098866C411yescharacteristic
22#19098787C411yescharacteristic
23#19098781C411yescharacteristic
24#19098724C411yescharacteristic
25#19098711C411yescharacteristic
26#19098694C2211yescharacteristic
27Q8×C79⋊C8C2211yescharacteristic
28C4×#11929611C2211yescharacteristic
29C4×#11929611C2211yescharacteristic
30C4×D632C2211yescharacteristic
31#19098642—21no—
32#19098640C2211yescharacteristic
33#19098633—21no—
34C8×D316—21no—
35C8×D316C2211yescharacteristic
36C8×D316C2211yescharacteristic
37#19098628—21no—
38#19098628C2211yescharacteristic
39#19098622—21no—
40#19098614—21no—
41#19098614C2211yescharacteristic
42#19098614C2211yescharacteristic
43#19098588—21no—
44#19098585C2211yescharacteristic
45C4⋊C8×D79—21no—
46C4⋊C8×D79C2211yescharacteristic
47C4×#11929607C2211yescharacteristic
48#19098314C2211yescharacteristic
49#19098313C2211yescharacteristic
50#19098313C2211yescharacteristic
51Q8⋊(C79⋊C8)C2211yescharacteristic
52Q8⋊(C79⋊C8)C2211yescharacteristic
53#19098292C2211yescharacteristic
54#19098292C2211yescharacteristic
55#19098290C2211yescharacteristic
56#19098290C2211yescharacteristic
57#19098285C2211yescharacteristic
58#19098285C2211yescharacteristic
59C8×C79⋊C8C2211yescharacteristic
60C8×Q8×C79C2211yescharacteristic
61C8×Q8×C79C2211yescharacteristic
62C4×Q16×C79C2211yescharacteristic
63#334×C79C2211yescharacteristic
64Q8⋊C8×C79C2211yescharacteristic
65Q8⋊C8×C79C2211yescharacteristic
66#322×C79C2211yescharacteristic
67C2×#11929625C2×C411yescharacteristic
68C2×#11929611C2×C411yescharacteristic
69C2×#11929611C2×C411yescharacteristic
70C2×D632C2×C411yescharacteristic
71C2×#11929607—21no—
72C2×#11929607—21no—
73C2×#11929607—21no—
74C2×C8×D79—21no—
75C2×C8×D79—21no—
76C2×C8×D79—21no—
77C2×C8×D79—21no—
78#14579156—21no—
79#14579152C2×C411yescharacteristic
80#14579150C2×C411yescharacteristic
81#14579146—21no—
82#14579137C2×C411yescharacteristic
83#14579136C2×C411yescharacteristic
84Q8×Dic79C2×C411yescharacteristic
85C4×D316—21no—
86C4×D316—21no—
87C4×D316C2311yescharacteristic
88C4×D316C2311yescharacteristic
89#14579123—21no—
90#14579123C2×C411yescharacteristic
91#14579119—21no—
92#14579119C2×C411yescharacteristic
93#14579118—21no—
94C42×D79—21no—
95C42×D79C2311yescharacteristic
96#14579095C2×C411yescharacteristic
97#14579092C2×C411yescharacteristic
98#14579092C2×C411yescharacteristic
99C4⋊(C79⋊C8)—21no—
100C4⋊(C79⋊C8)—21no—
101C4⋊(C79⋊C8)C2311yescharacteristic
102C4⋊(C79⋊C8)C2311yescharacteristic
103Dic79⋊C8—21no—
104Dic79⋊C8—21no—
105Dic79⋊C8C2×C411yescharacteristic
106Dic79⋊C8C2×C411yescharacteristic
107Dic79⋊C8D411yescharacteristic
108Dic79⋊C8D411yescharacteristic
109#14579085C2×C411yescharacteristic
110#14579085C2×C411yescharacteristic
111#14579083C2×C411yescharacteristic
112#14579083C2×C411yescharacteristic
113#14579081C2×C411yescharacteristic
114#14579081C2×C411yescharacteristic
115(C2×D79)⋊C8—21no—
116(C2×D79)⋊C8—21no—
117(C2×D79)⋊C8—21no—
118(C2×D79)⋊C8—21no—
119(C2×D79)⋊C8C2×C411yescharacteristic
120(C2×D79)⋊C8C2×C411yescharacteristic
121(C2×D79)⋊C8D411yescharacteristic
122(C2×D79)⋊C8D411yescharacteristic
123#14579072—21no—
124#14579071—21no—
125C4×C79⋊C8—21no—
126C4×C79⋊C8C2311yescharacteristic
127C4×C79⋊C8C2311yescharacteristic
128C4×C79⋊C8C2311yescharacteristic
129C2×Q16×C79C2×C411yescharacteristic
130C4×Q8×C79C2311yescharacteristic
131C4×Q8×C79C2311yescharacteristic
132#107×C79C2×C411yescharacteristic
133C4⋊C8×C79—21no—
134C4⋊C8×C79—21no—
135C4⋊C8×C79C2311yescharacteristic
136C4⋊C8×C79C2311yescharacteristic
137#103×C79C2×C411yescharacteristic
138#103×C79C2×C411yescharacteristic
139C4×C8×C79—21no—
140C4×C8×C79—21no—
141C4×C8×C79C2311yescharacteristic
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144#11929625—22no—
145#11929625—22no—
146C2×D316—21no—
147C2×D316—21no—
148C2×D316C22×C411yescharacteristic
149C2×D316C22×C411yescharacteristic
150C2×C4×D79—21no—
151C2×C4×D79—21no—
152C2×C4×D79—21no—
153C2×C4×D79—21no—
154C2×C4×D79C22×C411yescharacteristic
155C2×C4×D79C2×D411yescharacteristic
156C2×C4×D79#4111yescharacteristic
157#11929611—22no—
158#11929611—22no—
159D632—22no—
160#11929607—42no—
161#11929607—81no—
162#11929607—81no—
163C2×C79⋊C8—21no—
164C2×C79⋊C8—21no—
165C2×C79⋊C8—21no—
166C2×C79⋊C8C22×C411yescharacteristic
167C2×C79⋊C8C22×C411yescharacteristic
168C2×C79⋊C8C2×D411yescharacteristic
169C2×C79⋊C8C2×D411yescharacteristic
170C8×D79—81no—
171C8×D79—81no—
172C8×D79—81no—
173C8×D79—81no—
174C4⋊Dic79—21no—
175C4⋊Dic79—21no—
176C4⋊Dic79C22×C411yescharacteristic
177C4⋊Dic79C22×C411yescharacteristic
178Dic79⋊C4—21no—
179Dic79⋊C4—21no—
180(C2×D79)⋊C4—21no—
181(C2×D79)⋊C4—21no—
182(C2×D79)⋊C4—21no—
183(C2×D79)⋊C4—21no—
184(C2×D79)⋊C4—21no—
185(C2×D79)⋊C4—21no—
186(C2×D79)⋊C4—21no—
187(C2×D79)⋊C4—21no—
188C4×Dic79—21no—
189C4×Dic79—21no—
190C4×Dic79C22×C411yescharacteristic
191C4×Dic79C2×D411yescharacteristic
192C4×Dic79#4111yescharacteristic
193C2×Q8×C79C22×C411yescharacteristic
194C2×Q8×C79C22×C411yescharacteristic
195Q16×C79—22no—
196C2×C8×C79—21no—
197C2×C8×C79—21no—
198C2×C8×C79—21no—
199C2×C8×C79C22×C411yescharacteristic
200C2×C8×C79C22×C411yescharacteristic
201C2×C8×C79C2×D411yescharacteristic
202C2×C8×C79C2×D411yescharacteristic
203C4⋊C4×C79—21no—
204C4⋊C4×C79—21no—
205C4⋊C4×C79C22×C411yescharacteristic
206C4⋊C4×C79C22×C411yescharacteristic
207C42×C79—21no—
208C42×C79—21no—
209C42×C79C2411yescharacteristic
210C22×D79—21no—
211C22×D79—21no—
212C22×D79C4×D411yescharacteristic
213Q8×C79—21no—
214Q8×C79—21no—
215Q8×C79—21no—
216Q8×C79#13112yes—
217C2×C4×C79—21no—
218C2×C4×C79—21no—
219C2×C4×C79—21no—
220C2×C4×C79—21no—
221C2×C4×C79C23×C411yescharacteristic
222C2×C4×C79C22×D411yescharacteristic
223C2×C4×C79C2×#4111yescharacteristic
224C2×Dic79—21no—
225C2×Dic79—21no—
226C2×Dic79C4×D411yescharacteristic
227C2×Dic79C4×D411yescharacteristic
228C2×Dic79C4×D411yescharacteristic
229D316—24no—
230D316—21no—
231D316—21no—
232D316—21no—
233D316—81no—
234D316#13112yes—
235C4×D79—24no—
236C4×D79—21no—
237C4×D79—21no—
238C4×D79—21no—
239C4×D79—21no—
240C4×D79—41no—
241C4×D79—41no—
242C4×D79—41no—
243C4×D79—41no—
244C4×D79—41no—
245C4×D79—81no—
246C8×C79—21no—
247C8×C79—21no—
248C8×C79—21no—
249C8×C79—21no—
250C8×C79—41no—
251C8×C79—41no—
252C8×C79—41no—
253C79⋊C8—22no—
254C79⋊C8—21no—
255C79⋊C8—21no—
256C79⋊C8—21no—
257C79⋊C8—21no—
258C79⋊C8—41no—
259C79⋊C8—41no—
260C22×C79C2×C4×D411yescharacteristic
261C2×D79—22no—
262C2×D79—21no—
263C2×D79—21no—
264C2×D79—21no—
265C2×D79—41no—
266C2×D79—41no—
267C2×D79—41no—
268C2×D79—41no—
269C2×D79—41no—
270C4×C79—22no—
271C4×C79—21no—
272C4×C79—41no—
273C4×C79—41no—
274C4×C79—41no—
275C4×C79C2×#13111yescharacteristic
276C4×C79C2×#13111yescharacteristic
277C4×C79#57711yescharacteristic
278C4×C79#57711yescharacteristic
279Dic79—21no—
280Dic79—21no—
281Dic79—21no—
282Dic79—41no—
283Dic79—41no—
284#17927—791nomaximal, Sylow
285C2×C79#292911yescharacteristic
286C2×C79#295211yescharacteristic
287C2×C79#295611yescharacteristic
288D79—41no—
289D79—42no—
290D79—81no—
291#3102—791no—
292#2993—791no—
293#2988—791no—
294#1587—791no—
295#1586—791no—
296#1583—791no—
297#1582—791no—
298#1580—791no—
299#1579D7911yescharacteristic, complemented
300C8×SD16—791no—
301C8×SD16—791no—
302#1570—791no—
303#1489—791no—
304#1483—791no—
305#1453—791no—
306C79#1792711yescharacteristic, complemented, Sylow
307#529—791no—
308C4×#41—791no—
309#485—791no—
310#482—791no—
311#479—791no—
312#478—791no—
313#464—791no—
314#463—791no—
315#452—791no—
316#449—791no—
317#446—791no—
318C8×Q8—791no—
319C8×Q8C2×D7911yescharacteristic
320C8×Q8C2×D7911yescharacteristic
321C4×Q16C2×D7911yescharacteristic
322C4×SD16—791no—
323C4×SD16—791no—
324C4×D8—791no—
325#436—791no—
326#436—1581no—
327#435—1581no—
328C8×D4—791no—
329C8×D4—791no—
330C8×D4—791no—
331C8×D4—1581no—
332C8×D4—1581no—
333#433—1581no—
334#431—791no—
335#431—791no—
336#431—1581no—
337#424—1581no—
338#423—791no—
339C2×C4⋊C8—791no—
340C2×C4⋊C8—1581no—
341C4×M16—791no—
342#334—791no—
343#334—791no—
344#334—791no—
345#334C2×D7911yescharacteristic
346Q8⋊C8—791no—
347Q8⋊C8—791no—
348Q8⋊C8C2×D7911yescharacteristic
349Q8⋊C8C2×D7911yescharacteristic
350D4⋊C8—791no—
351D4⋊C8—791no—
352D4⋊C8—791no—
353D4⋊C8—791no—
354#322—791no—
355#322—791no—
356#322C2×D7911yescharacteristic
357C82—791no—
358C2×#41—791no—
359C2×Q16C4×D7911yescharacteristic
360C2×SD16—791no—
361C2×SD16—791no—
362C2×D8—791no—
363C2×M16—1581no—
364C2×M16—1581no—
365C2×M16—1581no—
366C22×C8—1581no—
367C22×C8—1581no—
368C22×C8—1581no—
369C22×C8—1581no—
370#126—1581no—
371#125—791no—
372#124—791no—
373#123—1581no—
374C22⋊Q8—791no—
375#121—791no—
376C4×Q8—791no—
377C4×Q8C22×D7911yescharacteristic
378C4×Q8C22×D7911yescharacteristic
379C4×D4—791no—
380C4×D4—791no—
381C4×D4—791no—
382C4×D4—1581no—
383C4×D4—1581no—
384C4×D4—1581no—
385#117—791no—
386#117—1581no—
387#117—1581no—
388C2×C42—791no—
389C2×C42—1581no—
390#107—791no—
391#107C4×D7911yescharacteristic
392#106—791no—
393#106—791no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—791no—
397C4⋊C8—791no—
398C4⋊C8—791no—
399C4⋊C8—791no—
400C4⋊C8—791no—
401C4⋊C8—791no—
402C4⋊C8—1581no—
403C4⋊C8—1581no—
404C4⋊C8—1581no—
405C4⋊C8—1581no—
406C4⋊C8C22×D7911yescharacteristic
407C4⋊C8C22×D7911yescharacteristic
408#103—791no—
409#103—791no—
410#103C4×D7911yescharacteristic
411#103C4×D7911yescharacteristic
412#102—791no—
413#102—791no—
414#102—791no—
415#102—791no—
416C22⋊C8—791no—
417C22⋊C8—791no—
418C22⋊C8—791no—
419C22⋊C8—791no—
420C22⋊C8—1581no—
421C22⋊C8—1581no—
422C22⋊C8—1581no—
423C22⋊C8—1581no—
424#97—1581no—
425#97—1581no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—791no—
429C4×C8—791no—
430C4×C8—791no—
431C4×C8—1581no—
432C4×C8C22×D7911yescharacteristic
433C4×C8C22×D7911yescharacteristic
434C4×C8C22×D7911yescharacteristic
435#41—1582no—
436#41—1582no—
437C2×Q8C2×C4×D7911yescharacteristic
438C2×Q8C2×C4×D7911yescharacteristic
439C2×D4—791no—
440C2×D4—791no—
441C2×D4—1581no—
442C2×D4—1581no—
443C22×C4—791no—
444C22×C4—791no—
445C22×C4—791no—
446C22×C4—1581no—
447C22×C4—1581no—
448C22×C4—1581no—
449C22×C4—1581no—
450Q16—22no—
451SD16—1582no—
452SD16—1582no—
453D8—1582no—
454M16—3162no—
455M16—6321no—
456M16—6321no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—791no—
461C2×C8—791no—
462C2×C8—791no—
463C2×C8—791no—
464C2×C8—6321no—
465C2×C8—6321no—
466C2×C8—6321no—
467C2×C8—6321no—
468C2×C8—1581no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8C2×C4×D7911yescharacteristic
472C2×C8C2×C4×D7911yescharacteristic
473C2×C8D4×D7911yescharacteristic
474C2×C8D4×D7911yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—791no—
478C4⋊C4—791no—
479C4⋊C4—1581no—
480C4⋊C4—1581no—
481C4⋊C4—1581no—
482C4⋊C4—1581no—
483C4⋊C4C2×C4×D7911yescharacteristic
484C4⋊C4C2×C4×D7911yescharacteristic
485C22⋊C4—1581no—
486C22⋊C4—1581no—
487C22⋊C4—1581no—
488C22⋊C4—1581no—
489C22⋊C4—1581no—
490C22⋊C4—1581no—
491C22⋊C4—1581no—
492C22⋊C4—1581no—
493C42—21no—
494C42—21no—
495C42—791no—
496C42—791no—
497C42—791no—
498C42—1581no—
499C42—1581no—
500C42C23×D7911yescharacteristic
501C23—791no—
502C23—1581no—
503C23—1581no—
504Q8—21no—
505Q8—21no—
506Q8—21no—
507Q8#1457916712yes—
508D4—792no—
509D4—6321no—
510D4—1584no—
511D4—1581no—
512D4—1581no—
513D4—1581no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—3161no—
519C2×C4—3161no—
520C2×C4—3161no—
521C2×C4—3161no—
522C2×C4—3161no—
523C2×C4—791no—
524C2×C4—791no—
525C2×C4—791no—
526C2×C4—6321no—
527C2×C4—1584no—
528C2×C4—1581no—
529C2×C4—1581no—
530C2×C4—1581no—
531C2×C4—1581no—
532C2×C4—1581no—
533C2×C4—1581no—
534C2×C4C22×C4×D7911yescharacteristic
535C2×C4C2×D4×D7911yescharacteristic
536C2×C4#41×D7911yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—3161no—
545C8—3161no—
546C8—1582no—
547C8—1581no—
548C8—1581no—
549C8—1581no—
550C8—1581no—
551C22—3161no—
552C22—3161no—
553C22—3161no—
554C22—3161no—
555C22—3161no—
556C22—1581no—
557C22—1581no—
558C22—1582no—
559C22—1581no—
560C22C4×D4×D7911yescharacteristic
561C4—21no—
562C4—22no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—3161no—
567C4—3161no—
568C4—1581no—
569C4—1581no—
570C4—1581no—
571C4#131×D7911yescharacteristic
572C4C2×#1457916711yescharacteristic
573C4#1909937211yescharacteristic
574C4#1909937211yescharacteristic
575C2—3162no—
576C2—3161no—
577C2—6321no—
578C2#2377208911yescharacteristic
579C2#2377228011yescharacteristic
580C2#2377230811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#1579C2
socleC22×C79C2×C4×D4
prime radical#19098711C4
cosocleC42×C79C24
hypercenter#1579D79
hypocenterC79#17927
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #1579

Complements

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

NH ≅ G/Ntype
2. #23772548C2semidirect
3. #23772510C2semidirect
4. #23762272C2semidirect
5. #23762263C2semidirect
6. #23762240C2semidirect
7. #23762239C2semidirect
8. #23762225C2semidirect
9. C8×#11929611C2semidirect
10. C8×#11929611C2semidirect
11. #23762169C2semidirect
12. #23761838C2semidirect
13. #23761812C2semidirect
14. #23761696C2semidirect
15. C79×#1579C2semidirect
299. #1579D79semidirect
306. C79#17927semidirect

Maximal subgroups

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

subgroupindex
#237734242
#237725482
#237725102
#237622722
#237622632
#237622402
#237622392
#237622252
C8×#119296112
#237621692
#237618382
#237618122
#237616962
C79×#15792
#1792779