Finite Group Databasebeta

← #34259286

Subgroups — #34259286

Order 20224.

608 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#23773412C211yesmaximal, characteristic
2#23772418C211yesmaximal, characteristic, complemented
3#23762312C211yesmaximal, characteristic, complemented
4#23762300C211yesmaximal, characteristic, complemented
5#23762278C211yesmaximal, characteristic, complemented
6#23762276C211yesmaximal, characteristic, complemented
7#23762269C211yesmaximal, characteristic, complemented
8#23762264C211yesmaximal, characteristic, complemented
9#23762217C211yesmaximal, characteristic, complemented
10#23762212C211yesmaximal, characteristic, complemented
11#23762178C211yesmaximal, characteristic, complemented
12#23761860C211yesmaximal, characteristic, complemented
13#23761780C211yesmaximal, characteristic, complemented
14#23761687C211yesmaximal, characteristic, complemented
15C79×#2969C211yesmaximal, characteristic, complemented
16C4×#11929624C2211yescharacteristic
17#19098901C411yescharacteristic
18#19098884C411yescharacteristic
19#19098867C411yescharacteristic
20#19098860C411yescharacteristic
21#19098782C411yescharacteristic
22#19098775C411yescharacteristic
23#19098723C411yescharacteristic
24#19098706C411yescharacteristic
25C8×Dic158C2211yescharacteristic
26C8×Dic158C2211yescharacteristic
27C4×#11929614C2211yescharacteristic
28C4×#11929611C2211yescharacteristic
29C4×#11929612C2211yescharacteristic
30C4×#11929609C2211yescharacteristic
31#19098642C2211yescharacteristic
32#19098642C2211yescharacteristic
33#19098639—21no—
34#19098639—21no—
35#19098620C2211yescharacteristic
36#19098618—21no—
37#19098616C2211yescharacteristic
38#19098515—21no—
39C2×C4×C79⋊C8C2211yescharacteristic
40#19098315C2211yescharacteristic
41#19098315C2211yescharacteristic
42#19098313C2211yescharacteristic
43#19098313C2211yescharacteristic
44Q8⋊(C79⋊C8)C2211yescharacteristic
45Q8⋊(C79⋊C8)C2211yescharacteristic
46#19098293C2211yescharacteristic
47#19098293C2211yescharacteristic
48D4⋊(C79⋊C8)C2211yescharacteristic
49D4⋊(C79⋊C8)C2211yescharacteristic
50#19098290C2211yescharacteristic
51#19098290C2211yescharacteristic
52#19098285C2211yescharacteristic
53#19098285C2211yescharacteristic
54#19098285C2211yescharacteristic
55#19098285C2211yescharacteristic
56#529×C79C2211yescharacteristic
57#446×C79C2211yescharacteristic
58C8×Q8×C79C2211yescharacteristic
59#436×C79—21no—
60#436×C79C2211yescharacteristic
61#435×C79—21no—
62C8×D4×C79C2211yescharacteristic
63#433×C79—21no—
64#431×C79C2211yescharacteristic
65#405×C79—21no—
66C4×M16×C79C2211yescharacteristic
67C2×#11929624C2×C411yescharacteristic
68C2×#11929614C2×C411yescharacteristic
69C2×#11929612C2×C411yescharacteristic
70C2×#11929611C2×C411yescharacteristic
71C2×#11929609C2×C411yescharacteristic
72C2×#11929607—21no—
73C2×#11929607—21no—
74C22×C79⋊C8—21no—
75C4×Dic158C2×C411yescharacteristic
76C4×Dic158C2311yescharacteristic
77C4×D316C2×C411yescharacteristic
78C4×D316C2311yescharacteristic
79C4×C22⋊D79—21no—
80C4×C22⋊D79—21no—
81#14579120C2×C411yescharacteristic
82#14579118—21no—
83C42×D79—21no—
84#14579094C2×C411yescharacteristic
85#14579094C2×C411yescharacteristic
86#14579092C2×C411yescharacteristic
87#14579092C2×C411yescharacteristic
88C4⋊(C79⋊C8)C2×C411yescharacteristic
89C4⋊(C79⋊C8)C2×C411yescharacteristic
90C4⋊(C79⋊C8)C2311yescharacteristic
91C4⋊(C79⋊C8)C2311yescharacteristic
92Dic79⋊C8—21no—
93Dic79⋊C8—21no—
94#14579085C2×C411yescharacteristic
95#14579085C2×C411yescharacteristic
96#14579084C2×C411yescharacteristic
97#14579084C2×C411yescharacteristic
98#14579082C2×C411yescharacteristic
99#14579082C2×C411yescharacteristic
100#14579081C2×C411yescharacteristic
101#14579081C2×C411yescharacteristic
102C22⋊(C79⋊C8)—21no—
103C22⋊(C79⋊C8)C2×C411yescharacteristic
104C22⋊(C79⋊C8)C2×C411yescharacteristic
105(C2×D79)⋊C8—21no—
106(C2×D79)⋊C8—21no—
107#14579072—21no—
108C4×C79⋊C8—21no—
109C4×C79⋊C8C2311yescharacteristic
110C4×C79⋊C8C2311yescharacteristic
111C4×C79⋊C8C2311yescharacteristic
112C4×C79⋊C8C2311yescharacteristic
113C8×Dic79—21no—
114C8×Dic79—21no—
115C2×M16×C79—21no—
116C2×M16×C79D411yescharacteristic
117C2×M16×C79D411yescharacteristic
118C22×C8×C79—21no—
119#126×C79—21no—
120#125×C79C2×C411yescharacteristic
121#124×C79C2×C411yescharacteristic
122#123×C79—21no—
123C22⋊Q8×C79C2×C411yescharacteristic
124#121×C79C2×C411yescharacteristic
125C4×Q8×C79C2311yescharacteristic
126C4×D4×C79—21no—
127C4×D4×C79C2311yescharacteristic
128#117×C79—21no—
129C2×C42×C79C2311yescharacteristic
130C4⋊C8×C79—21no—
131C4⋊C8×C79—21no—
132C4⋊C8×C79C2311yescharacteristic
133C4⋊C8×C79C2311yescharacteristic
134C22⋊C8×C79—21no—
135C22⋊C8×C79—21no—
136C22⋊C8×C79—21no—
137#97×C79—21no—
138#97×C79D411yescharacteristic
139#97×C79D411yescharacteristic
140C4×C8×C79—21no—
141C4×C8×C79—21no—
142C4×C8×C79C2311yescharacteristic
143C4×C8×C79C2311yescharacteristic
144#11929624—22no—
145#11929624—41no—
146C2×Dic158C22×C411yescharacteristic
147C2×D316C22×C411yescharacteristic
148C2×C22⋊D79—21no—
149C2×C4×D79—21no—
150C2×C4×D79—21no—
151C2×C4×D79—21no—
152#11929614—22no—
153#11929612—22no—
154#11929611—41no—
155#11929609—41no—
156#11929607—42no—
157#11929607—42no—
158C2×C79⋊C8—21no—
159C2×C79⋊C8—21no—
160C2×C79⋊C8—21no—
161C2×C79⋊C8—21no—
162C2×C79⋊C8—42no—
163C2×C79⋊C8C22×C411yescharacteristic
164C2×C79⋊C8C22×C411yescharacteristic
165C2×C79⋊C8C22×C411yescharacteristic
166C2×C79⋊C8C22×C411yescharacteristic
167C4⋊Dic79C22×C411yescharacteristic
168C4⋊Dic79C22×C411yescharacteristic
169Dic79⋊C4—21no—
170Dic79⋊C4—21no—
171C22⋊Dic79—21no—
172(C2×D79)⋊C4—21no—
173(C2×D79)⋊C4—21no—
174C4×Dic79—21no—
175C4×Dic79—21no—
176C4×Dic79—21no—
177C2×Q8×C79C22×C411yescharacteristic
178C2×D4×C79—21no—
179C2×D4×C79C22×C411yescharacteristic
180C22×C4×C79—21no—
181C22×C4×C79C22×C411yescharacteristic
182C22×C4×C79C2×D411yescharacteristic
183C22×C4×C79#4111yescharacteristic
184M16×C79—41no—
185M16×C79—41no—
186M16×C79—42no—
187C2×C8×C79—21no—
188C2×C8×C79—21no—
189C2×C8×C79—42no—
190C2×C8×C79C2×D411yescharacteristic
191C2×C8×C79C2×D411yescharacteristic
192C2×C8×C79C2×D411yescharacteristic
193C2×C8×C79C2×D411yescharacteristic
194C4⋊C4×C79—21no—
195C4⋊C4×C79—21no—
196C4⋊C4×C79—21no—
197C4⋊C4×C79—21no—
198C4⋊C4×C79C22×C411yescharacteristic
199C4⋊C4×C79C22×C411yescharacteristic
200C22⋊C4×C79—21no—
201C22⋊C4×C79—21no—
202C22⋊C4×C79—21no—
203C22⋊C4×C79—21no—
204C22⋊C4×C79—21no—
205C42×C79—21no—
206C42×C79C22×C411yescharacteristic
207C42×C79C2×D411yescharacteristic
208C42×C79#4111yescharacteristic
209C42×C79C2411yescharacteristic
210C23×C79—21no—
211C23×C79C4×D411yescharacteristic
212C22×D79—21no—
213Q8×C79—21no—
214Q8×C79—21no—
215D4×C79—21no—
216D4×C79—21no—
217D4×C79—81no—
218C2×C4×C79—21no—
219C2×C4×C79—21no—
220C2×C4×C79—21no—
221C2×C4×C79—21no—
222C2×C4×C79—21no—
223C2×C4×C79—21no—
224C2×C4×C79—21no—
225C2×C4×C79—41no—
226C2×C4×C79—41no—
227C2×C4×C79—41no—
228C2×C4×C79C4×D411yescharacteristic
229C2×C4×C79C4×D411yescharacteristic
230C2×C4×C79C4×D411yescharacteristic
231C2×C4×C79C23×C411yescharacteristic
232C2×C4×C79C22×D411yescharacteristic
233C2×C4×C79C2×#4111yescharacteristic
234C22⋊D79—42no—
235C2×Dic79—21no—
236C2×Dic79—21no—
237C2×Dic79—21no—
238D316—21no—
239D316—21no—
240C4×D79—42no—
241C4×D79—41no—
242C4×D79—41no—
243C4×D79—81no—
244Dic158—21no—
245Dic158#13112yes—
246C8×C79—21no—
247C8×C79—21no—
248C8×C79—21no—
249C8×C79—21no—
250C8×C79—41no—
251C8×C79—41no—
252C79⋊C8—22no—
253C79⋊C8—21no—
254C79⋊C8—21no—
255C79⋊C8—21no—
256C79⋊C8—21no—
257C79⋊C8—41no—
258C79⋊C8—41no—
259C79⋊C8—41no—
260C22×C79—21no—
261C22×C79—21no—
262C22×C79—21no—
263C22×C79—41no—
264C22×C79—41no—
265C22×C79—41no—
266C22×C79C2×C4×D411yescharacteristic
267C2×D79—41no—
268C2×D79—41no—
269C2×D79—41no—
270C4×C79—21no—
271C4×C79—21no—
272C4×C79—21no—
273C4×C79—21no—
274C4×C79—41no—
275C4×C79—41no—
276C4×C79—41no—
277C4×C79C2×#13111yescharacteristic
278C4×C79#56811yescharacteristic
279C4×C79#57511yescharacteristic
280C4×C79#57511yescharacteristic
281Dic79—22no—
282Dic79—41no—
283Dic79—41no—
284#18005—791nomaximal, Sylow
285C2×C79—41no—
286C2×C79—81no—
287C2×C79#293311yescharacteristic
288C2×C79#294311yescharacteristic
289C2×C79#295611yescharacteristic
290D79—81no—
291#3102—791no—
292#2971—791no—
293#2969D7911yescharacteristic, complemented
294#1594—791no—
295#1592—791no—
296#1588—791no—
297#1588—791no—
298#1587—791no—
299#1586—791no—
300#1579—791no—
301SD16⋊C8—791no—
302#1572—791no—
303#1494—791no—
304#1476—791no—
305#1451—791no—
306C79#1800511yescharacteristic, complemented, Sylow
307#529C2×D7911yescharacteristic
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#446C2×D7911yescharacteristic
318C8×Q8—791no—
319C8×Q8—791no—
320C8×Q8C2×D7911yescharacteristic
321C4×Q16—791no—
322C4×SD16—791no—
323C4×SD16—791no—
324C4×D8—791no—
325#436—21no—
326#436—791no—
327#436—791no—
328#436—1581no—
329#436—1581no—
330#436C2×D7911yescharacteristic
331#435—21no—
332C8×D4C2×D7911yescharacteristic
333#433—21no—
334#432—791no—
335#432—1581no—
336#431—791no—
337#431C2×D7911yescharacteristic
338#405—21no—
339C4×M16—1581no—
340C4×M16C2×D7911yescharacteristic
341C2×C4×C8—791no—
342#335—791no—
343#335—791no—
344#334—791no—
345#334—791no—
346Q8⋊C8—791no—
347Q8⋊C8—791no—
348Q8⋊C8—791no—
349Q8⋊C8—791no—
350D4⋊C8—791no—
351D4⋊C8—791no—
352D4⋊C8—791no—
353D4⋊C8—791no—
354#322—791no—
355#322—791no—
356#322—791no—
357#322—791no—
358C2×#41—791no—
359C2×Q16—791no—
360C2×SD16—791no—
361C2×SD16—791no—
362C2×D8—791no—
363C2×M16—21no—
364C2×M16—1581no—
365C2×M16—1581no—
366C2×M16C22⋊D7911yescharacteristic
367C2×M16C22⋊D7911yescharacteristic
368C22×C8—21no—
369C22×C8—1581no—
370#126—21no—
371#125C4×D7911yescharacteristic
372#124C4×D7911yescharacteristic
373#123—21no—
374C22⋊Q8C4×D7911yescharacteristic
375#121C4×D7911yescharacteristic
376C4×Q8—791no—
377C4×Q8—791no—
378C4×Q8C22×D7911yescharacteristic
379C4×D4—21no—
380C4×D4—791no—
381C4×D4—791no—
382C4×D4—1581no—
383C4×D4—1581no—
384C4×D4C22×D7911yescharacteristic
385#117—21no—
386#117—791no—
387#117—1581no—
388C2×C42—1581no—
389C2×C42C22×D7911yescharacteristic
390#107—791no—
391#107—791no—
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—1581no—
401C4⋊C8—1581no—
402C4⋊C8C22×D7911yescharacteristic
403C4⋊C8C22×D7911yescharacteristic
404#103—791no—
405#103—791no—
406#103—791no—
407#103—791no—
408#102—791no—
409#102—791no—
410#102—791no—
411#102—791no—
412C22⋊C8—21no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—791no—
416C22⋊C8—791no—
417C22⋊C8—1581no—
418C22⋊C8—1581no—
419C22⋊C8—1581no—
420#97—21no—
421#97—1581no—
422#97C22⋊D7911yescharacteristic
423#97C22⋊D7911yescharacteristic
424C4×C8—21no—
425C4×C8—21no—
426C4×C8—791no—
427C4×C8—791no—
428C4×C8—791no—
429C4×C8—791no—
430C4×C8—1581no—
431C4×C8—1581no—
432C4×C8—1581no—
433C4×C8C22×D7911yescharacteristic
434C4×C8C22×D7911yescharacteristic
435#41—3161no—
436#41—1582no—
437C2×Q8—791no—
438C2×Q8C2×C4×D7911yescharacteristic
439C2×D4—21no—
440C2×D4—791no—
441C2×D4—1581no—
442C2×D4C2×C4×D7911yescharacteristic
443C22×C4—21no—
444C22×C4—1581no—
445C22×C4—1581no—
446C22×C4—1581no—
447C22×C4C2×C4×D7911yescharacteristic
448C22×C4C2×C22⋊D7911yescharacteristic
449C22×C4#1192962411yescharacteristic
450Q16—1582no—
451SD16—3161no—
452SD16—1582no—
453D8—3161no—
454M16—41no—
455M16—41no—
456M16—42no—
457M16—3162no—
458M16—3162no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—3162no—
463C2×C8—791no—
464C2×C8—791no—
465C2×C8—791no—
466C2×C8—791no—
467C2×C8—1581no—
468C2×C8—1581no—
469C2×C8—1581no—
470C2×C8—1581no—
471C2×C8C2×C22⋊D7911yescharacteristic
472C2×C8C2×C22⋊D7911yescharacteristic
473C2×C8C2×C22⋊D7911yescharacteristic
474C2×C8C2×C22⋊D7911yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—21no—
479C4⋊C4—791no—
480C4⋊C4—791no—
481C4⋊C4—1581no—
482C4⋊C4—1581no—
483C4⋊C4C2×C4×D7911yescharacteristic
484C4⋊C4C2×C4×D7911yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—21no—
489C22⋊C4—21no—
490C22⋊C4—1581no—
491C22⋊C4—1581no—
492C22⋊C4—1581no—
493C42—21no—
494C42—1581no—
495C42—1581no—
496C42—1581no—
497C42C2×C4×D7911yescharacteristic
498C42C2×C22⋊D7911yescharacteristic
499C42#1192962411yescharacteristic
500C42C23×D7911yescharacteristic
501C23—21no—
502C23—1581no—
503C23C4×C22⋊D7911yescharacteristic
504Q8—21no—
505Q8—21no—
506Q8—792no—
507Q8—1581no—
508D4—21no—
509D4—21no—
510D4—81no—
511D4—3162no—
512D4—1581no—
513D4—1581no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—3162no—
525C2×C4—3161no—
526C2×C4—3161no—
527C2×C4—6321no—
528C2×C4—1581no—
529C2×C4—1581no—
530C2×C4—1581no—
531C2×C4C4×C22⋊D7911yescharacteristic
532C2×C4C4×C22⋊D7911yescharacteristic
533C2×C4C4×C22⋊D7911yescharacteristic
534C2×C4C22×C4×D7911yescharacteristic
535C2×C4C22×C22⋊D7911yescharacteristic
536C2×C4C2×#1192962411yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—3161no—
544C8—3161no—
545C8—3161no—
546C8—1582no—
547C8—1581no—
548C8—1581no—
549C8—1581no—
550C8—1581no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—41no—
555C22—41no—
556C22—41no—
557C22—3161no—
558C22—3161no—
559C22—3161no—
560C22C2×C4×C22⋊D7911yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—41no—
566C4—41no—
567C4—41no—
568C4—3161no—
569C4—3161no—
570C4—1582no—
571C4#131×D7911yescharacteristic
572C4#1909932811yescharacteristic
573C4#1909936111yescharacteristic
574C4#1909936111yescharacteristic
575C2—41no—
576C2—81no—
577C2—6321no—
578C2#2377212211yescharacteristic
579C2#2377219811yescharacteristic
580C2#2377230711yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D79
commutatorC2×C4×C79C23×C4
FrattiniC42C23×D79
FittingC79×#2969C2
socleC22×C79C2×C4×D4
prime radical#19098706C4
cosocleC42×C79C24
hypercenter#2969D79
hypocenterC79#18005
LCSG ▷ C2×C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2×C4 ◁ C4×M16 ◁ #2969

Complements

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

NH ≅ G/Ntype
2. #23772418C2semidirect
3. #23762312C2semidirect
4. #23762300C2semidirect
5. #23762278C2semidirect
6. #23762276C2semidirect
7. #23762269C2semidirect
8. #23762264C2semidirect
9. #23762217C2semidirect
10. #23762212C2semidirect
11. #23762178C2semidirect
12. #23761860C2semidirect
13. #23761780C2semidirect
14. #23761687C2semidirect
15. C79×#2969C2semidirect
293. #2969D79semidirect
306. C79#18005semidirect

Maximal subgroups

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

subgroupindex
#237734122
#237724182
#237623122
#237623002
#237622782
#237622762
#237622692
#237622642
#237622172
#237622122
#237621782
#237618602
#237617802
#237616872
C79×#29692
#1800579