Finite Group Databasebeta

← #29837669

Subgroups — #29837669

Order 15616.

486 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458804C211yesmaximal, characteristic, complemented
2#21458683C211yesmaximal, characteristic, complemented
3#21448049C211yesmaximal, characteristic, complemented
4#21448045C211yesmaximal, characteristic, complemented
5#21447981C211yesmaximal, characteristic, complemented
6#21447980C211yesmaximal, characteristic, complemented
7#21447964C211yesmaximal, characteristic, complemented
8#21447873C211yesmaximal, characteristic
9#21447871C211yesmaximal, characteristic
10#21447863C211yesmaximal, characteristic, complemented
11C16×Dic122C211yesmaximal, characteristic, complemented
12C4×#14519722C211yesmaximal, characteristic, complemented
13#21447668C211yesmaximal, characteristic, complemented
14#21447663C211yesmaximal, characteristic
15C61×#2242C211yesmaximal, characteristic, complemented
16#16840481—21no—
17#16840468—21no—
18C2×#14519722C2211yescharacteristic
19C2×#14519720C2211yescharacteristic
20C2×#14519718C2211yescharacteristic
21#16840166C2211yescharacteristic
22#16840163C2211yescharacteristic
23#16840145C2211yescharacteristic
24#16840140C2211yescharacteristic
25#16840061—21no—
26#16840059—21no—
27#16840051—21no—
28#16839982—21no—
29#16839981—21no—
30#16839965—21no—
31C8×Dic122C2211yescharacteristic
32C4×Dic244C2211yescharacteristic
33Q16×Dic61C2211yescharacteristic
34C4×D488C2211yescharacteristic
35D8×Dic61C2211yescharacteristic
36#16839844C2211yescharacteristic
37#16839844C2211yescharacteristic
38#16839590C2211yescharacteristic
39#16839589C2211yescharacteristic
40#16839587C2211yescharacteristic
41C4⋊#11758185C2211yescharacteristic
42#16839580C2211yescharacteristic
43#16839580C2211yescharacteristic
44#16839567C2211yescharacteristic
45#16839566C2211yescharacteristic
46#16839565C2211yescharacteristic
47#16839565C2211yescharacteristic
48#16839564C2211yescharacteristic
49#16839563C2211yescharacteristic
50C16×Dic61C2211yescharacteristic
51C16×Dic61C2211yescharacteristic
52C61×#499C2211yescharacteristic
53C61×#495C2211yescharacteristic
54C61×#358C2211yescharacteristic
55C61×#358C2211yescharacteristic
56C61×#357C2211yescharacteristic
57C61×#357C2211yescharacteristic
58C4×C16×C61C2211yescharacteristic
59C2×Dic244C2311yescharacteristic
60C2×#11758202—21no—
61C2×#11758200—21no—
62C2×D488C2311yescharacteristic
63#14519776—21no—
64#14519775—21no—
65#14519770—41no—
66#14519770—41no—
67#14519768—21no—
68#14519764—21no—
69#14519757—41no—
70#14519755—41no—
71#14519755—41no—
72#14519754—41no—
73Q8×Dic61—21no—
74C4×Dic122—21no—
75C4×Dic122D411yescharacteristic
76C4×D244—21no—
77D4×Dic61—21no—
78#14519739—21no—
79#14519739—21no—
80#14519733—41no—
81C4⋊C4×D61—41no—
82#14519722—22no—
83#14519720—22no—
84#14519718—22no—
85C2×#11758185C2311yescharacteristic
86C2×#11758185C2311yescharacteristic
87#14519711C2311yescharacteristic
88#14519711C2311yescharacteristic
89#14519710—21no—
90#14519708—21no—
91C4⋊#92418D411yescharacteristic
92#14519706D411yescharacteristic
93#14519706D411yescharacteristic
94#14519702—21no—
95#14519701—21no—
96#14519699—21no—
97#14519698—21no—
98#14519697—21no—
99#14519697—21no—
100C8×Dic61C2311yescharacteristic
101C8×Dic61C2311yescharacteristic
102C2×Q16×C61C2311yescharacteristic
103C2×SD16×C61—21no—
104C2×D8×C61C2311yescharacteristic
105#125×C61—21no—
106#124×C61—21no—
107C2×C16×C61C2311yescharacteristic
108C2×C16×C61C2311yescharacteristic
109#107×C61C2311yescharacteristic
110#107×C61C2311yescharacteristic
111#106×C61—21no—
112C4×C8×C61C2311yescharacteristic
113C2×Q8×C61—21no—
114C2×D4×C61—21no—
115C22×Dic61—41no—
116C2×D244—21no—
117C2×C4×D61—41no—
118C2×C4×D61—41no—
119C2×C4×D61—41no—
120C2×Dic122—21no—
121C2×Dic122—41no—
122C2×Dic122D811yescharacteristic
123Q16×C61—21no—
124Q16×C61—21no—
125SD16×C61—81no—
126D8×C61—21no—
127D8×C61—21no—
128C2×C8×C61C2×D411yescharacteristic
129C2×C8×C61C2411yescharacteristic
130C4⋊C4×C61—21no—
131C4⋊C4×C61—21no—
132C4⋊C4×C61—41no—
133C4⋊C4×C61—41no—
134C22⋊C4×C61—41no—
135C22⋊C4×C61—41no—
136C42×C61C2×D411yescharacteristic
137C22⋊Dic61—41no—
138C22⋊Dic61—41no—
139C22⋊Dic61—41no—
140#11758202—81no—
141#11758200—81no—
142#11758198—41no—
143#11758198—41no—
144#11758198—41no—
145C4⋊Dic61—21no—
146C4⋊Dic61—21no—
147C4⋊Dic61—41no—
148C4⋊Dic61—41no—
149C4⋊Dic61D811yescharacteristic
150#11758196—41no—
151#11758196—41no—
152#11758196—41no—
153#11758196—41no—
154#11758196—41no—
155#11758196D811yescharacteristic
156#11758196D811yescharacteristic
157C4×Dic61—41no—
158C4×Dic61—41no—
159C4×Dic61C2×D411yescharacteristic
160C4×Dic61C2×D411yescharacteristic
161C2×#92418C2×D411yescharacteristic
162C2×#92418C2×D411yescharacteristic
163Dic244—21no—
164Dic244—21no—
165D488—21no—
166D488#4112yes—
167C16×C61—21no—
168C16×C61—21no—
169#11758185—21no—
170#11758185—21no—
171C23×C61—41no—
172C22×D61—41no—
173Q8×C61—41no—
174Q8×C61—41no—
175D4×C61—41no—
176D4×C61—41no—
177C2×C4×C61—41no—
178C2×C4×C61—41no—
179C2×C4×C61—41no—
180C2×C4×C61C2×D811yescharacteristic
181C2×C4×C61C2×D811yescharacteristic
182C2×C4×C61C22×D411yescharacteristic
183C2×Dic61—41no—
184C2×Dic61—41no—
185C2×Dic61—41no—
186C2×Dic61—82no—
187C2×Dic61C2×D811yescharacteristic
188C2×Dic61C2×D811yescharacteristic
189C2×Dic61C2×D811yescharacteristic
190C2×Dic61C2×D811yescharacteristic
191D244—22no—
192D244—41no—
193C4×D61—82no—
194C4×D61—161no—
195C4×D61—161no—
196Dic122—22no—
197Dic122—41no—
198Dic122—41no—
199Dic122—161no—
200C8×C61—21no—
201C8×C61C2×#4111yescharacteristic
202C8×C612−1+411yescharacteristic
203#92418—21no—
204#92418—21no—
205#33927—611nomaximal, Sylow
206C22×C61—81no—
207C22×C61—81no—
208C22×C61—81no—
209C22×C61C22×D811yescharacteristic
210C2×D61—42no—
211C2×D61—81no—
212C2×D61—81no—
213C4×C61—21no—
214C4×C61—21no—
215C4×C61—81no—
216C4×C61—81no—
217C4×C61—81no—
218C4×C61#54811yescharacteristic
219C4×C61#57711yescharacteristic
220Dic61—21no—
221Dic61—21no—
222Dic61—21no—
223Dic61—81no—
224Dic61—81no—
225Dic61—81no—
226Dic61#50812yes—
227#3393—611no—
228#3380—611no—
229#2242—611no—
230#2242D6111yescharacteristic, complemented
231#2241—611no—
232#2229—611no—
233#2229—611no—
234#2226—611no—
235#2210—611no—
236#2210—611no—
237#2208—611no—
238Q8×C16—611no—
239C4×SD32—611no—
240C4×SD32—611no—
241C4×D16—611no—
242C2×C61—161no—
243C2×C61#335811yescharacteristic
244C2×C61C2×#50811yescharacteristic
245C2×C61#341611yescharacteristic
246D61—82no—
247#556—1221no—
248#554—1221no—
249C2×SD32—611no—
250C2×SD32—611no—
251C2×D16—611no—
252#500—611no—
253#499—611no—
254#499C2×D6111yescharacteristic
255#495—611no—
256#495C2×D6111yescharacteristic
257#494—611no—
258#478—1221no—
259#478—1221no—
260#476—1221no—
261#464—1221no—
262#464—1221no—
263#461—1221no—
264C8×Q8—611no—
265C4×Q16—611no—
266C4×Q16—611no—
267C4×D8—611no—
268C4×D8—611no—
269C4×D8—611no—
270C4×D8—611no—
271#367—611no—
272#367—611no—
273#366—611no—
274C4⋊C16—611no—
275C4⋊C16—611no—
276C4⋊C16—611no—
277#358—611no—
278#358—611no—
279#358—611no—
280#358—611no—
281#358C2×D6111yescharacteristic
282#358C2×D6111yescharacteristic
283#357—611no—
284#357—611no—
285#357C2×D6111yescharacteristic
286#357C2×D6111yescharacteristic
287C4×C16—611no—
288C4×C16—611no—
289C4×C16C2×D6111yescharacteristic
290C61#3392711yescharacteristic, complemented, Sylow
291C2×Q16—611no—
292C2×Q16—1221no—
293C2×Q16C22×D6111yescharacteristic
294C2×SD16—21no—
295C2×SD16—1221no—
296C2×D8—611no—
297C2×D8C22×D6111yescharacteristic
298C4⋊Q8—1221no—
299C4⋊Q8—1221no—
300#126—2441no—
301#126—2441no—
302#125—21no—
303#125—1221no—
304#124—21no—
305#124—1221no—
306C22⋊Q8—2441no—
307C22⋊Q8—2441no—
308C22⋊Q8—2441no—
309C22⋊Q8—2441no—
310C4×Q8—611no—
311C4×Q8—1221no—
312C4×Q8—1221no—
313C4×D4—1221no—
314C4×D4—1221no—
315C4×D4—1221no—
316C4×D4—1221no—
317#117—2441no—
318C2×C4⋊C4—2441no—
319SD32—1222no—
320SD32—1222no—
321D16—1222no—
322C2×C16—611no—
323C2×C16—611no—
324C2×C16C22×D6111yescharacteristic
325C2×C16C22×D6111yescharacteristic
326#107—611no—
327#107—611no—
328#107—1221no—
329#107C22×D6111yescharacteristic
330#107C22×D6111yescharacteristic
331#106—21no—
332#106—1221no—
333C4⋊C8—611no—
334C4⋊C8—611no—
335C4⋊C8—611no—
336#103—1221no—
337#103—1221no—
338#102—1221no—
339#102—1221no—
340#102—1221no—
341#102—1221no—
342C4×C8—611no—
343C4×C8—611no—
344C4×C8C22×D6111yescharacteristic
345C2×Q8—21no—
346C2×Q8—611no—
347C2×Q8—1221no—
348C2×Q8—2441no—
349C2×D4—21no—
350C2×D4—1221no—
351C22×C4—2441no—
352C22×C4—2441no—
353C22×C4—2441no—
354C22×C4—2441no—
355Q16—21no—
356Q16—21no—
357Q16—1221no—
358Q16—1221no—
359Q16—4881no—
360SD16—81no—
361SD16—4881no—
362D8—21no—
363D8—21no—
364D8—612no—
365D8—1221no—
366C2×C8—611no—
367C2×C8—611no—
368C2×C8D4×D6111yescharacteristic
369C2×C8C23×D6111yescharacteristic
370C4⋊C4—21no—
371C4⋊C4—21no—
372C4⋊C4—41no—
373C4⋊C4—41no—
374C4⋊C4—611no—
375C4⋊C4—611no—
376C4⋊C4—611no—
377C4⋊C4—1221no—
378C4⋊C4—1221no—
379C4⋊C4—2441no—
380C4⋊C4—2441no—
381C4⋊C4—2441no—
382C4⋊C4—2441no—
383C4⋊C4—2441no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C22⋊C4—41no—
387C22⋊C4—41no—
388C22⋊C4—2441no—
389C22⋊C4—2441no—
390C22⋊C4—2441no—
391C22⋊C4—2441no—
392C22⋊C4—2441no—
393C22⋊C4—2441no—
394C42—611no—
395C42—611no—
396C42—2441no—
397C42—2441no—
398C42D4×D6111yescharacteristic
399C16—21no—
400C16—21no—
401C16—1221no—
402C16—1221no—
403C23—41no—
404C23—2441no—
405Q8—41no—
406Q8—41no—
407Q8—1222no—
408Q8—9761no—
409Q8—2441no—
410Q8—2441no—
411D4—41no—
412D4—41no—
413D4—1222no—
414D4—2441no—
415C2×C4—41no—
416C2×C4—41no—
417C2×C4—41no—
418C2×C4—611no—
419C2×C4—611no—
420C2×C4—611no—
421C2×C4—611no—
422C2×C4—9761no—
423C2×C4—9761no—
424C2×C4—4882no—
425C2×C4—4882no—
426C2×C4—2441no—
427C2×C4—2441no—
428C2×C4—2441no—
429C2×C4D8×D6111yescharacteristic
430C2×C4D8×D6111yescharacteristic
431C2×C4C2×D4×D6111yescharacteristic
432C8—21no—
433C8—1221no—
434C8—1221no—
435C8#41×D6111yescharacteristic
436C8#1451982411yescharacteristic
437C22—81no—
438C22—81no—
439C22—81no—
440C22—4881no—
441C22—4881no—
442C22—2442no—
443C22C2×D8×D6111yescharacteristic
444C4—21no—
445C4—21no—
446C4—81no—
447C4—81no—
448C4—81no—
449C4—612no—
450C4—1221no—
451C4—1221no—
452C4—1221no—
453C4—4881no—
454C4—4881no—
455C4—4881no—
456C4#1684042011yescharacteristic
457C4#1684056811yescharacteristic
458C2—161no—
459C2—4882no—
460C2#2145845111yescharacteristic
461C2#508×D6111yescharacteristic
462C2#2145896211yescharacteristic
subgroupG/H
centerC22C2×D8×D61
commutator, cosocleC2×C8×C61C24
FrattiniC2×C8C23×D61
FittingC61×#2242C2
socleC22×C61C22×D8
prime radicalC2×#14519718C22
hypercenter#2242D61
hypocenterC61#33927
LCSG ▷ C2×C8×C61 ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2242

Complements

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

NH ≅ G/Ntype
1. #21458804C2semidirect
2. #21458683C2semidirect
3. #21448049C2semidirect
4. #21448045C2semidirect
5. #21447981C2semidirect
6. #21447980C2semidirect
7. #21447964C2semidirect
10. #21447863C2semidirect
11. C16×Dic122C2semidirect
12. C4×#14519722C2semidirect
13. #21447668C2semidirect
15. C61×#2242C2semidirect
230. #2242D61semidirect
290. C61#33927semidirect

Maximal subgroups

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

subgroupindex
#214588042
#214586832
#214480492
#214480452
#214479812
#214479802
#214479642
#214478732
#214478712
#214478632
C16×Dic1222
C4×#145197222
#214476682
#214476632
C61×#22422
#3392761