Finite Group Databasebeta

← #29663196

Subgroups — #29663196

Order 15616.

660 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457131C211yesmaximal, characteristic, complemented
2#21457126C211yesmaximal, characteristic
3#21454532C211yesmaximal, characteristic, complemented
4#21445363C212yesmaximal, complemented
5#21445349C212yesmaximal, complemented
6#21445267C212yesmaximal, complemented
7#21445253C212yesmaximal, complemented
8C2×#16839515C211yesmaximal, characteristic, complemented
9#21444509C211yesmaximal, characteristic, complemented
10#21444496C211yesmaximal, characteristic, complemented
11C61×#3131C211yesmaximal, characteristic, complemented
12C2×#14519783—21no—
13#16840312C2211yescharacteristic
14#16840049C2212yes—
15#16840047—21no—
16#16840042—21no—
17#16840039C2212yes—
18#16839996—22no—
19#16839993—22no—
20#16839964C2212yes—
21#16839962—21no—
22#16839957—21no—
23#16839954C2212yes—
24#16839841—21no—
25#16839841C2212yes—
26C8×D244—21no—
27C8×D244C2212yes—
28#16839786C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31#16839728—21no—
32#16839515C2212yes—
33#16839515C2212yes—
34#16839511C2212yes—
35#16839508C2212yes—
36#16839508C2212yes—
37#16839506C2212yes—
38C61×#533C2211yescharacteristic
39C61×#532C2211yescharacteristic
40C61×#488—21no—
41C61×#488—21no—
42C61×#487C2211yescharacteristic
43C61×#487C2211yescharacteristic
44C61×#486C2211yescharacteristic
45C61×#486C2211yescharacteristic
46C61×#416—21no—
47C61×#416—21no—
48C2×C4×C8×C61C2211yescharacteristic
49C2×#11758222—21no—
50C2×#11758201—22no—
51C2×#11758199—22no—
52#14519783—44no—
53C2×#11758194—21no—
54C2×#11758189—22no—
55C22×#92418—21no—
56C22×#92418—21no—
57C2×C8×D61—22no—
58#14519777D411yescharacteristic
59#14519774D411yescharacteristic
60#14519765—21no—
61#14519751—21no—
62#14519751D412yes—
63C4×D244—21no—
64C4×D244C2312yes—
65#14519710—22no—
66#14519708—22no—
67C4⋊#92418—21no—
68C4⋊#92418—21no—
69C4⋊#92418—21no—
70C4⋊#92418C2312yes—
71C4⋊#92418C2312yes—
72C4⋊#92418C2312yes—
73#14519701—22no—
74#14519698—22no—
75#14519697—22no—
76#14519697—22no—
77#14519689—22no—
78#14519689—22no—
79C2×#41×C61—21no—
80C22×C8×C61D411yescharacteristic
81C22×C8×C61D411yescharacteristic
82C4⋊Q8×C61C2311yescharacteristic
83C4⋊Q8×C61C2311yescharacteristic
84C4⋊Q8×C61C2311yescharacteristic
85#127×C61C2311yescharacteristic
86#125×C61—21no—
87#124×C61—21no—
88C22⋊Q8×C61—21no—
89C22⋊Q8×C61—21no—
90#121×C61—21no—
91#121×C61—21no—
92C4×Q8×C61—21no—
93C4×Q8×C61—21no—
94C4×D4×C61—21no—
95C4×D4×C61—21no—
96#117×C61—21no—
97C2×C42×C61C2311yescharacteristic
98#103×C61—21no—
99#103×C61—21no—
100#103×C61—21no—
101#103×C61—21no—
102#102×C61—21no—
103#102×C61—21no—
104#102×C61—21no—
105#102×C61—21no—
106C4×C8×C61D411yescharacteristic
107C4×C8×C61D411yescharacteristic
108C4×C8×C61C2311yescharacteristic
109C4×C8×C61C2311yescharacteristic
110#41×C61—42no—
111#41×C61—42no—
112C2×Q8×C61—21no—
113C2×Q8×C61—21no—
114C2×Q8×C61—21no—
115C2×D4×C61—21no—
116C2×D4×C61—21no—
117C2×D4×C61—21no—
118C2×D4×C61—41no—
119C22×C4×C61—41no—
120C22×C4×C61C2×D411yescharacteristic
121C22×C4×C61C2×D411yescharacteristic
122C22×C4×C61#4111yescharacteristic
123C2×C22⋊D61—22no—
124#11758222—42no—
125#11758222—42no—
126C2×D244—21no—
127C2×D244—21no—
128C2×D244C2×D412yes—
129C2×C4×D61—22no—
130C2×Dic122—21no—
131C2×C8×C61—22no—
132C2×C8×C61—22no—
133C2×C8×C61C2×D411yescharacteristic
134C2×C8×C61C2×D411yescharacteristic
135C2×C8×C61C2×D411yescharacteristic
136C2×C8×C61C2×D411yescharacteristic
137C4⋊C4×C61—21no—
138C4⋊C4×C61—21no—
139C4⋊C4×C61—21no—
140C4⋊C4×C61—21no—
141C4⋊C4×C61—21no—
142C4⋊C4×C61—21no—
143C4⋊C4×C61—41no—
144C4⋊C4×C61—41no—
145C22⋊C4×C61—41no—
146C22⋊C4×C61—41no—
147C22⋊C4×C61—41no—
148C42×C61—41no—
149C42×C61C2×D411yescharacteristic
150C42×C61C2×D411yescharacteristic
151C42×C61#4111yescharacteristic
152C42×C61C2411yescharacteristic
153#11758201—82no—
154#11758199—82no—
155#11758198—22no—
156#11758198—22no—
157C4⋊Dic61—21no—
158C4⋊Dic61C2×D412yes—
159#11758194—42no—
160C2×#92418—22no—
161C2×#92418—22no—
162C2×#92418—22no—
163C2×#92418—81no—
164C2×#92418—81no—
165#11758189—44no—
166C8×D61—44no—
167C23×C61—41no—
168C23×C61#12111yescharacteristic
169C22×D61—22no—
170Q8×C61—41no—
171Q8×C61—41no—
172Q8×C61—41no—
173Q8×C61—41no—
174Q8×C61—81no—
175D4×C61—41no—
176D4×C61—41no—
177D4×C61—41no—
178D4×C61—41no—
179D4×C61—81no—
180D4×C61—82no—
181C2×C4×C61—21no—
182C2×C4×C61—21no—
183C2×C4×C61—41no—
184C2×C4×C61—41no—
185C2×C4×C61—41no—
186C2×C4×C61—41no—
187C2×C4×C61—82no—
188C2×C4×C61#12111yescharacteristic
189C2×C4×C61#12111yescharacteristic
190C2×C4×C61#12111yescharacteristic
191C2×C4×C61#13512yes—
192C2×C4×C61AGL(1,ℤ/8)12yes—
193C2×C4×C61C22×D411yescharacteristic
194C2×C4×C61C22×D411yescharacteristic
195C2×C4×C61C2×#4111yescharacteristic
196C22⋊D61—44no—
197C2×Dic61—22no—
198D244—22no—
199D244—22no—
200D244—42no—
201D244—42no—
202C4×D61—42no—
203C4×D61—42no—
204Dic122—42no—
205C8×C61—21no—
206C8×C61—21no—
207C8×C61—21no—
208C8×C61—21no—
209#92418—42no—
210#92418—42no—
211#92418—42no—
212#19201—611nomaximal, Sylow
213C22×C61—21no—
214C22×C61—21no—
215C22×C61—81no—
216C22×C61—81no—
217C22×C61—81no—
218C22×C61#46312yes—
219C22×C61C2×#12111yescharacteristic
220C2×D61—42no—
221C2×D61—42no—
222C2×D61—42no—
223C4×C61—21no—
224C4×C61—21no—
225C4×C61—21no—
226C4×C61—81no—
227C4×C61—81no—
228C4×C61—81no—
229C4×C61#46312yes—
230C4×C61C2×#13511yescharacteristic
231C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
232C4×C61#57611yescharacteristic
233C4×C61#57811yescharacteristic
234Dic61—42no—
235#3246—611no—
236#3245—611no—
237#3131D6111yescharacteristic, complemented
238#2931—611no—
239#1699—612no—
240#1697—612no—
241#1683—612no—
242#1681—612no—
243C2×#335—611no—
244#1550—611no—
245#1547—611no—
246C2×C61—22no—
247C2×C61—161no—
248C2×C61C2×#46311yescharacteristic
249C2×C61#306111yescharacteristic
250C2×C61#306711yescharacteristic
251D61—82no—
252C2×#131—1221no—
253#533C2×D6111yescharacteristic
254#532—611no—
255#532C2×D6111yescharacteristic
256#488—21no—
257#488—21no—
258#487C2×D6111yescharacteristic
259#487C2×D6111yescharacteristic
260#486C2×D6111yescharacteristic
261#486C2×D6111yescharacteristic
262#476—612no—
263#475—1221no—
264#474—612no—
265#474—1221no—
266#466—1222no—
267#465—1222no—
268#461—612no—
269#460—1221no—
270#459—612no—
271#459—1221no—
272#436—612no—
273#436—1221no—
274C8×D4—612no—
275C8×D4—1221no—
276#423—611no—
277C2×C4⋊C8—611no—
278C2×C4⋊C8—611no—
279#416—21no—
280#416—21no—
281#408—1221no—
282C2×C4×C8C2×D6111yescharacteristic
283#335—612no—
284#335—612no—
285#333—612no—
286#332—612no—
287#332—612no—
288#331—612no—
289C61#1920111yescharacteristic, complemented, Sylow
290C2×#41—21no—
291C2×#41—1221no—
292C2×SD16—1222no—
293C2×D8—1222no—
294#131—2444no—
295C2×M16—1221no—
296C2×M16—1222no—
297C22×C8—1221no—
298C22×C8—1221no—
299C22×C8—1222no—
300C22×C8C22⋊D6111yescharacteristic
301C22×C8C22⋊D6111yescharacteristic
302C4⋊Q8—611no—
303C4⋊Q8C22×D6111yescharacteristic
304C4⋊Q8C22×D6111yescharacteristic
305C4⋊Q8C22×D6111yescharacteristic
306#127—611no—
307#127C22×D6111yescharacteristic
308#125—21no—
309#124—21no—
310#124—1221no—
311C22⋊Q8—21no—
312C22⋊Q8—21no—
313#121—21no—
314#121—21no—
315#121—612no—
316#121—1221no—
317C4×Q8—21no—
318C4×Q8—21no—
319C4×D4—21no—
320C4×D4—21no—
321C4×D4—612no—
322C4×D4—1221no—
323#117—21no—
324C2×C42C22×D6111yescharacteristic
325#107—1222no—
326#106—1222no—
327C4⋊C8—612no—
328C4⋊C8—612no—
329C4⋊C8—612no—
330C4⋊C8—1221no—
331C4⋊C8—1221no—
332C4⋊C8—1221no—
333#103—21no—
334#103—21no—
335#103—21no—
336#103—21no—
337#103—1222no—
338#102—21no—
339#102—21no—
340#102—21no—
341#102—21no—
342#102—1222no—
343#102—1222no—
344#102—1222no—
345C22⋊C8—1222no—
346C22⋊C8—1222no—
347C4×C8C22⋊D6111yescharacteristic
348C4×C8C22⋊D6111yescharacteristic
349C4×C8C22×D6111yescharacteristic
350C4×C8C22×D6111yescharacteristic
351#41—42no—
352#41—42no—
353#41—2442no—
354#41—2442no—
355C2×Q8—21no—
356C2×Q8—21no—
357C2×Q8—21no—
358C2×Q8—1221no—
359C2×D4—21no—
360C2×D4—21no—
361C2×D4—21no—
362C2×D4—41no—
363C2×D4—612no—
364C2×D4—1222no—
365C2×D4—1221no—
366C2×D4—1221no—
367C22×C4—41no—
368C22×C4—1222no—
369C22×C4D4×D6111yescharacteristic
370C22×C4#1175822411yescharacteristic
371C22×C4C2×C22⋊D6111yescharacteristic
372SD16—4882no—
373D8—4882no—
374M16—2444no—
375M16—2442no—
376C2×C8—22no—
377C2×C8—22no—
378C2×C8—1222no—
379C2×C8—1222no—
380C2×C8—1222no—
381C2×C8—4881no—
382C2×C8—4881no—
383C2×C8—2444no—
384C2×C8C2×C22⋊D6111yescharacteristic
385C2×C8C2×C22⋊D6111yescharacteristic
386C2×C8C2×C22⋊D6111yescharacteristic
387C2×C8C2×C22⋊D6111yescharacteristic
388C4⋊C4—21no—
389C4⋊C4—21no—
390C4⋊C4—21no—
391C4⋊C4—21no—
392C4⋊C4—21no—
393C4⋊C4—21no—
394C4⋊C4—41no—
395C4⋊C4—41no—
396C4⋊C4—612no—
397C4⋊C4—1221no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—41no—
401C22⋊C4—1222no—
402C22⋊C4—1222no—
403C42—41no—
404C42D4×D6111yescharacteristic
405C42#1175822411yescharacteristic
406C42C2×C22⋊D6111yescharacteristic
407C42C23×D6111yescharacteristic
408C23—41no—
409C23—1222no—
410C23#1451974811yescharacteristic
411Q8—41no—
412Q8—41no—
413Q8—41no—
414Q8—41no—
415Q8—81no—
416Q8—2442no—
417D4—41no—
418D4—41no—
419D4—41no—
420D4—41no—
421D4—81no—
422D4—82no—
423D4—1222no—
424D4—1222no—
425D4—2442no—
426D4—2444no—
427D4—2442no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—41no—
431C2×C4—41no—
432C2×C4—41no—
433C2×C4—41no—
434C2×C4—82no—
435C2×C4—1222no—
436C2×C4—2442no—
437C2×C4—2442no—
438C2×C4#1451974811yescharacteristic
439C2×C4#1451974811yescharacteristic
440C2×C4#1451974811yescharacteristic
441C2×C4#1451979712yes—
442C2×C4#1451980212yes—
443C2×C4C2×D4×D6111yescharacteristic
444C2×C4C22×C22⋊D6111yescharacteristic
445C2×C4C2×#1175822411yescharacteristic
446C8—21no—
447C8—21no—
448C8—21no—
449C8—21no—
450C8—2442no—
451C8—2442no—
452C8—2442no—
453C22—21no—
454C22—21no—
455C22—81no—
456C22—81no—
457C22—81no—
458C22—2442no—
459C22—2442no—
460C22—2442no—
461C22#1683997412yes—
462C22C2×#1451974811yescharacteristic
463C4—21no—
464C4—21no—
465C4—21no—
466C4—81no—
467C4—81no—
468C4—81no—
469C4—2442no—
470C4#1683997412yes—
471C4C2×#1451979711yescharacteristic
472C4C2×#1451980211yescharacteristic
473C4#1684056411yescharacteristic
474C4#1684057611yescharacteristic
475C2—22no—
476C2—161no—
477C2—4882no—
478C2C2×#1683997411yescharacteristic
479C2#2145548511yescharacteristic
480C2#2145553511yescharacteristic
subgroupG/H
centerC22C2×#14519748
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3131C2
socleC22×C61C2×#121
prime radical#21457126C2
hypercenter#3131D61
hypocenterC61#19201
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #21457131C2semidirect
3. #21454532C2semidirect
4. #21445363C2semidirect
5. #21445349C2semidirect
6. #21445267C2semidirect
7. #21445253C2semidirect
8. C2×#16839515C2semidirect
9. #21444509C2semidirect
10. #21444496C2semidirect
11. C61×#3131C2semidirect
237. #3131D61semidirect
289. C61#19201semidirect

Maximal subgroups

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

subgroupindex
#214571312
#214571262
#214545322
#214453632
#214453492
#214452672
#214452532
C2×#168395152
#214445092
#214444962
C61×#31312
#1920161