Finite Group Databasebeta

← #29662557

Subgroups — #29662557

Order 15616.

662 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21456330C211yesmaximal, characteristic, complemented
2#21455829C212yesmaximal
3#436×D61C211yesmaximal, characteristic
4#21445339C211yesmaximal, characteristic, complemented
5#21445333C211yesmaximal, characteristic, complemented
6#21445332C211yesmaximal, characteristic, complemented
7#21445321C212yesmaximal, complemented
8#21445320C212yesmaximal, complemented
9#21444564C211yesmaximal, characteristic, complemented
10#21444473C212yesmaximal, complemented
11C61×#1695C211yesmaximal, characteristic, complemented
12C2×M16×D61—21no—
13#16840317C2212yes—
14C4×D4×D61C2211yescharacteristic
15#16840167C2211yescharacteristic, complemented
16#16840163—21no—
17#16840163—21no—
18#16840158C2212yescomplemented
19#16840094—22no—
20#16840049C2212yes—
21#16839968C2212yes—
22#16839967C2212yes—
23#16839914—22no—
24#16839853—22no—
25#16839849—22no—
26#16839841C2211yescharacteristic
27#16839840C2211yescharacteristic
28#16839839C2211yescharacteristic
29#16839838—21no—
30#16839837—21no—
31#16839814C2212yes—
32#16839799—21no—
33#16839799—21no—
34C4⋊C8×D61C2211yescharacteristic
35C22⋊C8×D61—21no—
36C4×C8×D61C2211yescharacteristic
37#16839514C2212yescomplemented
38#16839513C2211yescharacteristic, complemented
39#16839511C2212yescomplemented
40#16839509C2212yescomplemented
41#16839507C2212yescomplemented
42C61×#500C2211yescharacteristic, complemented
43C61×#476C2212yes—
44C61×#436C2211yescharacteristic
45C61×#334C2211yescharacteristic, complemented
46C61×#333C2212yescomplemented
47C2×D4×D61D411yescharacteristic
48C22×C4×D61—21no—
49C2×#11758190—22no—
50C2×#11758200—22no—
51C2×#11758194—21no—
52C2×#11758189—21no—
53C2×#11758189—21no—
54M16×D61—44no—
55C2×C8×D61—21no—
56C2×C8×D61D411yescharacteristic
57C2×C8×D61D411yescharacteristic
58#14519777C2312yes—
59#14519768—22no—
60#14519757—22no—
61#14519753—22no—
62Q8×Dic61—22no—
63#14519742—22no—
64C4×D244C2311yescharacteristic
65D4×Dic61D411yescharacteristic
66#14519739D411yescharacteristic
67C4×C22⋊D61—21no—
68#14519737—21no—
69#14519735—22no—
70C4⋊C4×D61D411yescharacteristic
71C22⋊C4×D61—21no—
72C42×D61C2311yescharacteristic
73#14519711—21no—
74#14519711—21no—
75#14519708—22no—
76#14519708—22no—
77#14519708—22no—
78C4⋊#92418C2312yes—
79C4⋊#92418C2311yescharacteristic
80#14519706—21no—
81#14519702—22no—
82#14519700—22no—
83#14519697—22no—
84C22⋊#92418—21no—
85#14519689—22no—
86#14519689—21no—
87#14519689—21no—
88C4×#92418C2311yescharacteristic
89C8×Dic61—22no—
90C8×Dic61D411yescharacteristic
91C8×Dic61D411yescharacteristic
92C2×M16×C61—21no—
93C4⋊Q8×C61C2312yes—
94C4×D4×C61C2311yescharacteristic
95#107×C61—21no—
96#107×C61—21no—
97#106×C61—22no—
98C4⋊C8×C61C2312yes—
99C4⋊C8×C61C2311yescharacteristic
100#102×C61—22no—
101C22⋊C8×C61—21no—
102C4×C8×C61C2311yescharacteristic
103C23×D61—21no—
104C2×Q8×C61—22no—
105C2×D4×C61C2×D411yescharacteristic
106C22×C4×C61—21no—
107C2×C22⋊D61—21no—
108C22×Dic61—21no—
109D4×D61—42no—
110C2×D244C2×D411yescharacteristic
111C2×C4×D61—21no—
112C2×C4×D61—21no—
113C2×C4×D61—21no—
114C2×C4×D61—42no—
115C2×C4×D61—42no—
116C2×C4×D61C2×D411yescharacteristic
117C2×C4×D61C2×D411yescharacteristic
118C2×C4×D61#4111yescharacteristic
119C2×Dic122—22no—
120M16×C61—42no—
121C2×C8×C61—21no—
122C2×C8×C61—22no—
123C2×C8×C61C2×D411yescharacteristic
124C2×C8×C61C2×D411yescharacteristic
125C4⋊C4×C61—22no—
126C4⋊C4×C61—22no—
127C4⋊C4×C61C2×D411yescharacteristic
128C22⋊C4×C61—21no—
129C42×C61C2411yescharacteristic
130C22⋊Dic61—21no—
131#11758200—44no—
132#11758198—21no—
133#11758198—21no—
134#11758198—42no—
135C4⋊Dic61—22no—
136C4⋊Dic61—22no—
137C4⋊Dic61—42no—
138C4⋊Dic61C2×D411yescharacteristic
139#11758196—21no—
140#11758196—42no—
141C4×Dic61—42no—
142C4×Dic61C2×D411yescharacteristic
143C4×Dic61C2×D411yescharacteristic
144C4×Dic61#4111yescharacteristic
145#11758194—42no—
146C2×#92418—22no—
147C2×#92418—21no—
148C2×#92418C2×D411yescharacteristic
149C2×#92418C2×D411yescharacteristic
150#11758190—44no—
151#11758189—42no—
152#11758189—42no—
153C8×D61—22no—
154C8×D61—42no—
155C8×D61SD1614yescomplemented
156C23×C61—21no—
157C22×D61—21no—
158C22×D61—42no—
159C22×D61—42no—
160C22×D61—42no—
161C22×D61#12111yescharacteristic
162Q8×C61—82no—
163D4×C61—22no—
164C2×C4×C61—21no—
165C2×C4×C61—41no—
166C2×C4×C61—41no—
167C2×C4×C61—42no—
168C2×C4×C61C22×D411yescharacteristic
169C2×C4×C61C22×D411yescharacteristic
170C2×C4×C61C2×#4111yescharacteristic
171C22⋊D61—42no—
172C2×Dic61—21no—
173C2×Dic61—42no—
174C2×Dic61—42no—
175C2×Dic61#12111yescharacteristic
176C2×Dic61#12111yescharacteristic
177C2×Dic61#12111yescharacteristic
178D244—22no—
179C4×D61—22no—
180C4×D61—41no—
181C4×D61—42no—
182C4×D61—41no—
183C4×D61—41no—
184C4×D61—42no—
185C4×D61C2×SD1612yes—
186C4×D61#13712yes—
187Dic122—42no—
188Dic122—42no—
189C8×C61—21no—
190C8×C61—41no—
191C8×C61—42no—
192C8×C61C2×SD1612yes—
193#92418—21no—
194#92418—41no—
195#92418—42no—
196#92418C2×SD1612yes—
197#19137—611nomaximal, Sylow
198C22×C61—41no—
199C22×C61—41no—
200C22×C61—41no—
201C22×C61C2×#12111yescharacteristic
202C2×D61—21no—
203C2×D61—21no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—84no—
208C2×D61#46112yes—
209C4×C61—21no—
210C4×C61—41no—
211C4×C61—82no—
212C4×C61C22×SD1611yescharacteristic
213C4×C61C2×#13711yescharacteristic
214C4×C61#57512yes—
215Dic61—21no—
216Dic61—21no—
217Dic61—41no—
218Dic61—82no—
219Dic61#46112yes—
220#3160—611no—
221#3101—612no—
222C2×#436—611no—
223#1695—611no—
224#1695D6111yescharacteristic, complemented
225#1693—611no—
226#1693—611no—
227#1691—612no—
228#1691—612no—
229#1564—611no—
230#1542—612no—
231C2×C61—81no—
232C2×C61C2×#46111yescharacteristic
233C2×C61#305411yescharacteristic
234C2×C61#306711yescharacteristic
235D61—22no—
236D61—81no—
237C22×M16—1221no—
238#533—612no—
239C2×C4×D4—611no—
240#500—611no—
241#500C2×D6111yescharacteristic, complemented
242#499—1221no—
243#499—1221no—
244#498—612no—
245#483—1222no—
246#476—612no—
247#476C2×D6112yes—
248#461—612no—
249#461—612no—
250#450—1222no—
251C4×SD16—1222no—
252C4×SD16—1222no—
253#436—611no—
254#436—611no—
255#436—611no—
256#436—1221no—
257#436—1221no—
258#436C2×D6111yescharacteristic
259#431—612no—
260#427—1221no—
261#427—1221no—
262C2×C4⋊C8—611no—
263C2×C22⋊C8—1221no—
264C2×C4×C8—611no—
265#335—612no—
266#334—611no—
267#334C2×D6111yescharacteristic, complemented
268#333—612no—
269#333C2×D6112yescomplemented
270#332—612no—
271#332—612no—
272C61#1913711yescharacteristic, complemented, Sylow
273C22×D4—611no—
274C23×C4—1221no—
275C2×SD16—1222no—
276C2×SD16—1222no—
277C2×M16—21no—
278C2×M16—1221no—
279C2×M16—1221no—
280C2×M16—1221no—
281C2×M16—2444no—
282C22×C8—611no—
283C22×C8—611no—
284C22×C8—1221no—
285C4⋊Q8—612no—
286C4⋊Q8C22×D6112yes—
287#125—1222no—
288C22⋊Q8—1222no—
289C22⋊Q8—1222no—
290C4×Q8—1222no—
291C4×Q8—1222no—
292C4×D4—611no—
293C4×D4—611no—
294C4×D4—611no—
295C4×D4—1221no—
296C4×D4—1221no—
297C4×D4C22×D6111yescharacteristic
298#117—1222no—
299C2×C4⋊C4—611no—
300C2×C22⋊C4—1221no—
301C2×C42—611no—
302#107—21no—
303#107—21no—
304#107—1221no—
305#107—1221no—
306#106—22no—
307#106—1222no—
308#106—1222no—
309#106—1222no—
310C4⋊C8—611no—
311C4⋊C8—612no—
312C4⋊C8—1221no—
313C4⋊C8C22×D6111yescharacteristic
314C4⋊C8C22×D6112yes—
315#103—1222no—
316#103—1222no—
317#102—22no—
318#102—1222no—
319C22⋊C8—21no—
320C22⋊C8—1221no—
321C22⋊C8—1222no—
322C22⋊C8—1221no—
323C22⋊C8—1221no—
324C4×C8—611no—
325C4×C8—611no—
326C4×C8—611no—
327C4×C8—1222no—
328C4×C8C22×D6111yescharacteristic
329C24—1221no—
330C2×Q8—22no—
331C2×Q8—1222no—
332C2×D4—611no—
333C2×D4—1221no—
334C2×D4—2442no—
335C2×D4D4×D6111yescharacteristic
336C22×C4—21no—
337C22×C4—611no—
338C22×C4—611no—
339C22×C4—611no—
340C22×C4—1221no—
341C22×C4—1221no—
342C22×C4—1221no—
343C22×C4—1221no—
344C22×C4—2442no—
345C22×C4—2442no—
346SD16—2444no—
347SD16—2444no—
348M16—42no—
349M16—2442no—
350M16—2442no—
351M16—2442no—
352C2×C8—22no—
353C2×C8—21no—
354C2×C8—611no—
355C2×C8—614no—
356C2×C8—611no—
357C2×C8—1222no—
358C2×C8—1222no—
359C2×C8—1221no—
360C2×C8—2442no—
361C2×C8D4×D6111yescharacteristic
362C2×C8D4×D6111yescharacteristic
363C4⋊C4—22no—
364C4⋊C4—22no—
365C4⋊C4—611no—
366C4⋊C4—1221no—
367C4⋊C4—1222no—
368C4⋊C4—1222no—
369C4⋊C4—2442no—
370C4⋊C4—2442no—
371C4⋊C4D4×D6111yescharacteristic
372C22⋊C4—21no—
373C22⋊C4—1221no—
374C22⋊C4—1221no—
375C22⋊C4—1221no—
376C22⋊C4—2442no—
377C42—611no—
378C42—611no—
379C42—611no—
380C42—2442no—
381C42C23×D6111yescharacteristic
382C23—21no—
383C23—611no—
384C23—1221no—
385C23—2442no—
386C23—2442no—
387C23—2442no—
388Q8—82no—
389Q8—2442no—
390Q8—2442no—
391D4—22no—
392D4—1222no—
393D4—2442no—
394C2×C4—21no—
395C2×C4—41no—
396C2×C4—41no—
397C2×C4—42no—
398C2×C4—611no—
399C2×C4—612no—
400C2×C4—612no—
401C2×C4—611no—
402C2×C4—611no—
403C2×C4—1222no—
404C2×C4—1221no—
405C2×C4—2441no—
406C2×C4—2442no—
407C2×C4—2442no—
408C2×C4—2442no—
409C2×C4—2442no—
410C2×C4—2441no—
411C2×C4—2441no—
412C2×C4C2×D4×D6111yescharacteristic
413C2×C4C2×D4×D6111yescharacteristic
414C2×C4#41×D6111yescharacteristic
415C8—21no—
416C8—41no—
417C8—42no—
418C8—612no—
419C8—1221no—
420C8—2441no—
421C8—2442no—
422C8SD16×D6112yes—
423C22—41no—
424C22—41no—
425C22—41no—
426C22—612no—
427C22—1221no—
428C22—1221no—
429C22—4884no—
430C22—2441no—
431C22—2441no—
432C22—2441no—
433C22#121×D6111yescharacteristic
434C4—21no—
435C4—41no—
436C4—82no—
437C4—612no—
438C4—1221no—
439C4—1221no—
440C4—4882no—
441C4—2441no—
442C4C2×SD16×D6111yescharacteristic
443C4#137×D6111yescharacteristic
444C4#1684056112yes—
445C2—81no—
446C2—1222no—
447C2—4881no—
448C2#461×D6111yescharacteristic
449C2#2145543011yescharacteristic
450C2#2145553711yescharacteristic
subgroupG/H
centerC22#121×D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#1695C2
socleC22×C61C2×#121
prime radicalC2×D4×D61D4
hypercenter#1695D61
hypocenterC61#19137
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #1695

Complements

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

NH ≅ G/Ntype
1. #21456330C2semidirect
4. #21445339C2semidirect
5. #21445333C2semidirect
6. #21445332C2semidirect
7. #21445321C2semidirect
8. #21445320C2semidirect
9. #21444564C2semidirect
10. #21444473C2semidirect
11. C61×#1695C2semidirect
15. #16840167C22semidirect
18. #16840158C22semidirect
37. #16839514C22semidirect
38. #16839513C22semidirect
39. #16839511C22semidirect
40. #16839509C22semidirect
41. #16839507C22semidirect
42. C61×#500C22semidirect
45. C61×#334C22semidirect
46. C61×#333C22semidirect
155. C8×D61SD16semidirect
224. #1695D61semidirect
241. #500C2×D61semidirect
267. #334C2×D61semidirect
269. #333C2×D61semidirect
272. C61#19137semidirect

Maximal subgroups

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

subgroupindex
#214563302
#214558292
#436×D612
#214453392
#214453332
#214453322
#214453212
#214453202
#214445642
#214444732
C61×#16952
#1913761