Finite Group Databasebeta

← #29663537

Subgroups — #29663537

Order 15616.

704 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21457135C211yesmaximal, characteristic, complemented
2#21456193C211yesmaximal, characteristic, complemented
3#21454563C211yesmaximal, characteristic, complemented
4#21445378C212yesmaximal, complemented
5#21445350C212yesmaximal, complemented
6#21445254C212yesmaximal, complemented
7#21445226C212yesmaximal, complemented
8#21444572C211yesmaximal, characteristic, complemented
9#21444474C211yesmaximal, characteristic, complemented
10C2×#16839506C211yesmaximal, characteristic, complemented
11C61×#3205C211yesmaximal, characteristic
12C2×#14519784—21no—
13#16840319C2211yescharacteristic
14#16840126—22no—
15#16840108C2212yes—
16#16840108C2212yes—
17#16840052C2212yescomplemented
18#16840044—21no—
19#16839989—22no—
20#16839967C2212yescomplemented
21#16839959—21no—
22#16839840C2212yescomplemented
23#16839834—22no—
24D4×#92418C2212yescomplemented
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27#16839767—21no—
28#16839767—21no—
29#16839729—21no—
30C4×#11758194C2211yescharacteristic
31#16839514C2212yescomplemented
32#16839512C2212yescomplemented
33#16839510C2211yescharacteristic, complemented
34#16839510C2211yescharacteristic, complemented
35#16839509C2211yescharacteristic, complemented
36#16839509C2211yescharacteristic, complemented
37#16839506C2212yes—
38#16839506C2212yes—
39C61×#532C2211yescharacteristic
40C2×#127×C61C2211yescharacteristic
41C61×#493—21no—
42C61×#486—21no—
43C61×#459C2212yes—
44C61×#459C2212yes—
45C61×#447—22no—
46C61×#431C2211yescharacteristic
47C2×#11758200—22no—
48#14519784—44no—
49C2×#11758194—22no—
50C2×#11758194D411yescharacteristic
51C2×#11758194D411yescharacteristic
52C22×#92418—21no—
53C22×#92418—21no—
54C22×#92418—22no—
55#14519777C2311yescharacteristic
56#14519777C2311yescharacteristic
57#14519769—21no—
58#14519756—21no—
59#14519756—21no—
60C4×Dic122—21no—
61C4×Dic122—21no—
62#14519736—21no—
63#14519708—22no—
64C4⋊#92418—21no—
65C4⋊#92418—21no—
66C4⋊#92418C2312yes—
67C4⋊#92418C2311yescharacteristic
68C4⋊#92418C2311yescharacteristic
69#14519700—22no—
70#14519698—22no—
71#14519698—22no—
72#14519698—22no—
73#14519698—22no—
74#14519698—22no—
75C22⋊#92418—22no—
76C22⋊#92418—22no—
77#14519688D412yes—
78C4×#92418C2312yes—
79C2×#41×C61—21no—
80C22×D4×C61—21no—
81C22×D4×C61—21no—
82C22×D4×C61—21no—
83C2×D8×C61—22no—
84C2×D8×C61—22no—
85C4⋊Q8×C61D411yescharacteristic
86#127×C61—21no—
87#127×C61—21no—
88#127×C61—21no—
89#127×C61D411yescharacteristic
90#127×C61C2312yes—
91#124×C61—21no—
92#121×C61—21no—
93#121×C61D412yes—
94C4×D4×C61—21no—
95C4×D4×C61C2312yes—
96C2×C42×C61C2311yescharacteristic
97C4⋊C8×C61C2311yescharacteristic
98C4⋊C8×C61C2311yescharacteristic
99#102×C61—22no—
100#102×C61—22no—
101C22⋊C8×C61—21no—
102C4×C8×C61—21no—
103C24×C61—41no—
104#41×C61—42no—
105#41×C61—42no—
106C2×Q8×C61—21no—
107C2×D4×C61—22no—
108C2×D4×C61—21no—
109C2×D4×C61—21no—
110C2×D4×C61—22no—
111C2×D4×C61—22no—
112C2×D4×C61—22no—
113C2×D4×C61—41no—
114C2×D4×C61—41no—
115C2×D4×C61—41no—
116C2×D4×C61—42no—
117C2×D4×C61—42no—
118C2×D4×C61—81no—
119C2×D4×C61—81no—
120C2×D4×C61—82no—
121C2×D4×C61C2×D412yes—
122C22×C4×C61—22no—
123C22×C4×C61C2×D411yescharacteristic
124C22×C4×C61C2×D411yescharacteristic
125C22×C4×C61#4111yescharacteristic
126C2×Dic122—21no—
127C2×Dic122—21no—
128D8×C61—82no—
129D8×C61—82no—
130C2×C8×C61—21no—
131C2×C8×C61—21no—
132C4⋊C4×C61—21no—
133C4⋊C4×C61C2×D412yes—
134C22⋊C4×C61—22no—
135C22⋊C4×C61—22no—
136C42×C61C2×D411yescharacteristic
137C42×C61C2×D411yescharacteristic
138C42×C61#4111yescharacteristic
139C42×C61C2411yescharacteristic
140C22⋊Dic61—41no—
141#11758200—82no—
142C4⋊Dic61—21no—
143C4⋊Dic61—21no—
144C4⋊Dic61—21no—
145C4⋊Dic61—21no—
146#11758196—41no—
147#11758196—41no—
148C4×Dic61—41no—
149#11758194—22no—
150#11758194—22no—
151#11758194—44no—
152C2×#92418—21no—
153C2×#92418—21no—
154C2×#92418—22no—
155C2×#92418—44no—
156C2×#92418—42no—
157C2×#92418—81no—
158C2×#92418C2×D412yes—
159C2×#92418C2×D412yes—
160C23×C61—22no—
161C23×C61—42no—
162C23×C61—82no—
163C23×C61—82no—
164C23×C61—82no—
165C23×C61#12111yescharacteristic
166Q8×C61—42no—
167D4×C61—22no—
168D4×C61—22no—
169D4×C61—44no—
170D4×C61—42no—
171D4×C61—42no—
172D4×C61—42no—
173D4×C61—42no—
174D4×C61—42no—
175D4×C61—81no—
176D4×C61—82no—
177D4×C61—82no—
178D4×C61—82no—
179D4×C61—82no—
180C2×C4×C61—21no—
181C2×C4×C61—21no—
182C2×C4×C61—22no—
183C2×C4×C61—41no—
184C2×C4×C61—42no—
185C2×C4×C61—42no—
186C2×C4×C61#12111yescharacteristic
187C2×C4×C61#12111yescharacteristic
188C2×C4×C61#12111yescharacteristic
189C2×C4×C61#13512yes—
190C2×C4×C61AGL(1,ℤ/8)12yes—
191C2×C4×C61C22×D411yescharacteristic
192C2×C4×C61C22×D411yescharacteristic
193C2×C4×C61C2×#4111yescharacteristic
194C2×Dic61—41no—
195C2×Dic61—41no—
196Dic122—41no—
197Dic122—41no—
198Dic122—81no—
199C8×C61—41no—
200C8×C61—41no—
201#92418—22no—
202#92418—22no—
203#92418—41no—
204#92418—41no—
205#92418—42no—
206#19234—611nomaximal, Sylow
207C22×C61—21no—
208C22×C61—21no—
209C22×C61—42no—
210C22×C61—42no—
211C22×C61—42no—
212C22×C61—82no—
213C22×C61—82no—
214C22×C61—82no—
215C22×C61—164no—
216C22×C61#46312yes—
217C22×C61C2×#12111yescharacteristic
218C4×C61—21no—
219C4×C61—21no—
220C4×C61—21no—
221C4×C61—42no—
222C4×C61#46312yes—
223C4×C61C2×#13511yescharacteristic
224C4×C61C2×AGL(1,ℤ/8)11yescharacteristic
225C4×C61#57611yescharacteristic
226C4×C61#57711yescharacteristic
227Dic61—81no—
228Dic61—81no—
229#3246—611no—
230#3205D6111yescharacteristic
231#3138—611no—
232#2935—611no—
233#1701—612no—
234#1697—612no—
235#1681—612no—
236#1677—612no—
237#1565—611no—
238#1542—611no—
239C2×#331—611no—
240C2×C61—22no—
241C2×C61—82no—
242C2×C61—162no—
243C2×C61C2×#46311yescharacteristic
244C2×C61#306211yescharacteristic
245C2×C61#306811yescharacteristic
246C2×#131—1221no—
247#533—611no—
248#532C2×D6111yescharacteristic
249C2×#127C2×D6111yescharacteristic
250#493—21no—
251#490—1222no—
252#486—21no—
253#486—612no—
254#486—612no—
255#476—612no—
256#475—1221no—
257#465—1222no—
258#461—612no—
259#460—1221no—
260#459C2×D6112yes—
261#459C2×D6112yes—
262#447—22no—
263#436—612no—
264#435—1222no—
265C8×D4—612no—
266#431C2×D6111yescharacteristic
267C2×C4⋊C8—611no—
268C2×C4⋊C8—611no—
269#418—1221no—
270#418—1221no—
271#408—1221no—
272C4×M16—611no—
273#335—612no—
274#334—612no—
275#333—611no—
276#333—611no—
277#332—611no—
278#332—611no—
279#331—612no—
280#331—612no—
281C61#1923411yescharacteristic, complemented, Sylow
282C2×#41—21no—
283C22×D4—21no—
284C22×D4—21no—
285C22×D4—21no—
286C2×SD16—1222no—
287C2×D8—22no—
288C2×D8—22no—
289#131—2444no—
290C2×M16—611no—
291C2×M16—611no—
292C2×M16—1222no—
293C22×C8—1222no—
294C22×C8—1221no—
295C22×C8—1221no—
296C4⋊Q8—611no—
297C4⋊Q8—611no—
298C4⋊Q8C22⋊D6111yescharacteristic
299#127—21no—
300#127—21no—
301#127—21no—
302#127C22⋊D6111yescharacteristic
303#127C22×D6112yes—
304#125—1221no—
305#124—21no—
306C22⋊Q8—1221no—
307C22⋊Q8—1221no—
308#121—21no—
309#121C22⋊D6112yes—
310C4×Q8—1221no—
311C4×Q8—1221no—
312C4×D4—21no—
313C4×D4C22×D6112yes—
314#117—1221no—
315C2×C42C22×D6111yescharacteristic
316#106—1222no—
317C4⋊C8—611no—
318C4⋊C8—611no—
319C4⋊C8—612no—
320C4⋊C8—1221no—
321C4⋊C8—1221no—
322C4⋊C8C22×D6111yescharacteristic
323C4⋊C8C22×D6111yescharacteristic
324#103—1222no—
325#102—22no—
326#102—22no—
327#102—1222no—
328#102—1222no—
329#102—1222no—
330#102—1222no—
331#102—1222no—
332C22⋊C8—21no—
333C22⋊C8—1222no—
334C22⋊C8—1222no—
335#97—612no—
336C4×C8—21no—
337C4×C8—612no—
338C24—41no—
339#41—42no—
340#41—42no—
341C2×Q8—21no—
342C2×Q8—1221no—
343C2×Q8—1221no—
344C2×D4—22no—
345C2×D4—22no—
346C2×D4—22no—
347C2×D4—22no—
348C2×D4—21no—
349C2×D4—21no—
350C2×D4—41no—
351C2×D4—41no—
352C2×D4—41no—
353C2×D4—42no—
354C2×D4—42no—
355C2×D4—81no—
356C2×D4—81no—
357C2×D4—82no—
358C2×D4C2×C22⋊D6112yes—
359C22×C4—22no—
360C22×C4D4×D6111yescharacteristic
361C22×C4#1175822411yescharacteristic
362C22×C4C2×C22⋊D6111yescharacteristic
363SD16—4882no—
364D8—82no—
365D8—82no—
366M16—1222no—
367M16—1222no—
368M16—2444no—
369C2×C8—21no—
370C2×C8—21no—
371C2×C8—612no—
372C2×C8—612no—
373C2×C8—1221no—
374C2×C8—1221no—
375C2×C8—1222no—
376C2×C8—4881no—
377C2×C8—2444no—
378C2×C8—2442no—
379C4⋊C4—21no—
380C4⋊C4—1221no—
381C4⋊C4—1221no—
382C4⋊C4—1221no—
383C4⋊C4—1221no—
384C4⋊C4—2441no—
385C4⋊C4—2441no—
386C4⋊C4C2×C22⋊D6112yes—
387C22⋊C4—22no—
388C22⋊C4—22no—
389C22⋊C4—2441no—
390C42—2441no—
391C42D4×D6111yescharacteristic
392C42#1175822411yescharacteristic
393C42C2×C22⋊D6111yescharacteristic
394C42C23×D6111yescharacteristic
395C23—22no—
396C23—42no—
397C23—82no—
398C23—82no—
399C23—82no—
400C23#1451974911yescharacteristic
401Q8—42no—
402Q8—4881no—
403Q8—2441no—
404Q8—2441no—
405D4—22no—
406D4—22no—
407D4—44no—
408D4—42no—
409D4—42no—
410D4—42no—
411D4—42no—
412D4—42no—
413D4—81no—
414D4—82no—
415D4—82no—
416D4—82no—
417D4—82no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—22no—
421C2×C4—41no—
422C2×C4—42no—
423C2×C4—42no—
424C2×C4—2441no—
425C2×C4—2441no—
426C2×C4#1451974911yescharacteristic
427C2×C4#1451974911yescharacteristic
428C2×C4#1451974911yescharacteristic
429C2×C4#1451979612yes—
430C2×C4#1451980112yes—
431C2×C4C2×D4×D6111yescharacteristic
432C2×C4C22×C22⋊D6111yescharacteristic
433C2×C4C2×#1175822411yescharacteristic
434C8—41no—
435C8—41no—
436C8—1222no—
437C8—1222no—
438C8—2441no—
439C8—2441no—
440C8—2442no—
441C22—21no—
442C22—21no—
443C22—42no—
444C22—42no—
445C22—42no—
446C22—82no—
447C22—82no—
448C22—82no—
449C22—164no—
450C22#1683997512yes—
451C22C2×#1451974911yescharacteristic
452C4—21no—
453C4—21no—
454C4—21no—
455C4—42no—
456C4—4881no—
457C4—4881no—
458C4#1683997512yes—
459C4C2×#1451979611yescharacteristic
460C4C2×#1451980111yescharacteristic
461C4#1684056511yescharacteristic
462C4#1684057311yescharacteristic
463C2—22no—
464C2—82no—
465C2—162no—
466C2C2×#1683997511yescharacteristic
467C2#2145549511yescharacteristic
468C2#2145554411yescharacteristic
subgroupG/H
centerC22C2×#14519749
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
Fitting, prime radicalC61×#3205C2
socleC22×C61C2×#121
hypercenter#3205D61
hypocenterC61#19234
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3205

Complements

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

NH ≅ G/Ntype
1. #21457135C2semidirect
2. #21456193C2semidirect
3. #21454563C2semidirect
4. #21445378C2semidirect
5. #21445350C2semidirect
6. #21445254C2semidirect
7. #21445226C2semidirect
8. #21444572C2semidirect
9. #21444474C2semidirect
10. C2×#16839506C2semidirect
17. #16840052C22semidirect
20. #16839967C22semidirect
22. #16839840C22semidirect
24. D4×#92418C22semidirect
31. #16839514C22semidirect
32. #16839512C22semidirect
33. #16839510C22semidirect
34. #16839510C22semidirect
35. #16839509C22semidirect
36. #16839509C22semidirect
281. C61#19234semidirect

Maximal subgroups

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

subgroupindex
#214571352
#214561932
#214545632
#214453782
#214453502
#214452542
#214452262
#214445722
#214444742
C2×#168395062
C61×#32052
#1923461