Finite Group Databasebeta

← #29590246

Subgroups — #29590246

Order 15616.

504 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21447430C211yesmaximal, characteristic, complemented
2C2×#16839525C211yesmaximal, characteristic, complemented
3#21443831C212yesmaximal, complemented
4#21443828C212yesmaximal, complemented
5C61×#3050C211yesmaximal, characteristic
6C22×C4⋊Dic61—21no—
7C2×#14519717—21no—
8C22⋊#11758185—21no—
9C22⋊#11758185C2212yes—
10#16839525—21no—
11#16839525C2212yes—
12C2×#135×C61C411yescharacteristic, complemented
13C23×C8×C61C2211yescharacteristic
14C61×#525—21no—
15C61×#467C411yescharacteristic, complemented
16C61×#467C2211yescharacteristic
17C61×#466C411yescharacteristic, complemented
18C61×#466C2211yescharacteristic
19C61×#465—21no—
20C61×#465—21no—
21C61×#427C411yescharacteristic, complemented
22C61×#416—21no—
23C23×Dic61—41no—
24C2×C4⋊Dic61—24no—
25C2×C4⋊Dic61—22no—
26C2×C4⋊Dic61—42no—
27C2×C4⋊Dic61—41no—
28#14519717—42no—
29C2×#11758185—22no—
30C2×#41×C61—21no—
31C23×C4×C61D411yescharacteristic
32#135×C61—42no—
33C2×Q16×C61C2×C411yescharacteristic, complemented
34C2×SD16×C61—21no—
35C2×D8×C61C2×C411yescharacteristic, complemented
36C22×C8×C61—42no—
37C22×C8×C61C2×C411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39C22×C8×C61D411yescharacteristic
40C22×C8×C61D411yescharacteristic
41C22×C8×C61D411yescharacteristic
42C22×C8×C61C2311yescharacteristic
43#123×C61—41no—
44C22⋊Q8×C61—21no—
45C22⋊Q8×C61—21no—
46#121×C61—21no—
47#121×C61—21no—
48#120×C61—41no—
49C4×D4×C61—41no—
50C4×D4×C61—41no—
51#117×C61—21no—
52#107×C61C2×C411yescharacteristic, complemented
53#107×C61C2×C411yescharacteristic, complemented
54#106×C61—21no—
55#103×C61—21no—
56#103×C61—21no—
57#102×C61—21no—
58#102×C61—21no—
59C24×C61D811yescharacteristic
60#41×C61—42no—
61#41×C61—42no—
62C2×Q8×C61—21no—
63C2×D4×C61—21no—
64C2×D4×C61—41no—
65C2×D4×C61—41no—
66C2×D4×C61—41no—
67C22×C4×C61—22no—
68C22×C4×C61—22no—
69C22×C4×C61—41no—
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22⋊C411yescharacteristic
72C22×C4×C61D811yescharacteristic
73C22×C4×C61SD1611yescharacteristic
74C22×C4×C61SD1611yescharacteristic
75C22×C4×C61C2×D411yescharacteristic
76C22×Dic61—44no—
77C22×Dic61—42no—
78C22×Dic61—82no—
79C22×Dic61—82no—
80Q16×C61—41no—
81SD16×C61—42no—
82D8×C61—41no—
83C2×C8×C61—22no—
84C2×C8×C61—22no—
85C2×C8×C61—41no—
86C2×C8×C61—41no—
87C2×C8×C61—41no—
88C2×C8×C61—41no—
89C2×C8×C61C22⋊C411yescharacteristic
90C2×C8×C61C22⋊C411yescharacteristic
91C2×C8×C61C22×C411yescharacteristic
92C2×C8×C61C2×D411yescharacteristic
93C4⋊C4×C61—21no—
94C4⋊C4×C61—21no—
95C4⋊C4×C61—41no—
96C4⋊C4×C61—41no—
97C22⋊C4×C61—41no—
98C22⋊C4×C61—41no—
99C22⋊C4×C61—41no—
100C22⋊C4×C61—41no—
101C22⋊C4×C61—41no—
102C42×C61—41no—
103C4⋊Dic61—24no—
104C4⋊Dic61—44no—
105C4⋊Dic61—42no—
106#11758185—42no—
107C23×C61—22no—
108C23×C61—22no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—41no—
112C23×C61#10211yescharacteristic
113C23×C61#10211yescharacteristic
114C23×C61C2×D811yescharacteristic
115Q8×C61—41no—
116Q8×C61—41no—
117D4×C61—41no—
118D4×C61—41no—
119D4×C61—82no—
120D4×C61—82no—
121D4×C61—81no—
122D4×C61—81no—
123C2×C4×C61—22no—
124C2×C4×C61—22no—
125C2×C4×C61—22no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—21no—
129C2×C4×C61—21no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—82no—
134C2×C4×C61#9912yes—
135C2×C4×C61#10211yescharacteristic
136C2×C4×C61#10211yescharacteristic
137C2×C4×C61#10412yes—
138C2×C4×C61C2×C22⋊C411yescharacteristic
139C2×C4×C61C2×SD1611yescharacteristic
140C2×Dic61—44no—
141C2×Dic61—88no—
142C2×Dic61—82no—
143C2×Dic61—82no—
144C8×C61—21no—
145C8×C61—21no—
146C8×C61—21no—
147C8×C61—21no—
148#11704—611nomaximal, Sylow
149C22×C61—24no—
150C22×C61—24no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—21no—
156C22×C61—21no—
157C22×C61—81no—
158C22×C61—81no—
159C22×C61—81no—
160C22×C61#32712yes—
161C22×C61#36012yes—
162C22×C61C2×#10211yescharacteristic
163C22×C61#50911yescharacteristic
164C22×C61#51011yescharacteristic
165C4×C61—21no—
166C4×C61—21no—
167C4×C61—81no—
168C4×C61—81no—
169C4×C61—81no—
170C4×C61#32712yes—
171C4×C61C2×#9911yescharacteristic
172C4×C61C2×#10411yescharacteristic
173Dic61—84no—
174#3050D6111yescharacteristic
175#2112—611no—
176C2×#340—611no—
177#1348—612no—
178#1347—612no—
179C2×C61—21no—
180C2×C61—22no—
181C2×C61—22no—
182C2×C61—21no—
183C2×C61—161no—
184C2×C61C2×#32711yescharacteristic
185C2×C61#213911yescharacteristic
186C2×C61C2×#36011yescharacteristic
187C2×#135Dic6111yescharacteristic, complemented
188C23×C8C2×D6111yescharacteristic
189#525—21no—
190C22×C4⋊C4—1221no—
191C2×M32—1221no—
192#467Dic6111yescharacteristic, complemented
193#467C2×D6111yescharacteristic
194#466Dic6111yescharacteristic, complemented
195#466C2×D6111yescharacteristic
196#465—21no—
197#465—21no—
198#427Dic6111yescharacteristic, complemented
199#416—21no—
200C22⋊C16—612no—
201C22⋊C16—1221no—
202#340—612no—
203#340—1221no—
204C61#1170411yescharacteristic, complemented, Sylow
205C2×#41—21no—
206C23×C4—2441no—
207C23×C4C22⋊D6111yescharacteristic
208#135—42no—
209C2×Q16C2×Dic6111yescharacteristic, complemented
210C2×SD16—21no—
211C2×D8C2×Dic6111yescharacteristic, complemented
212C22×C8—42no—
213C22×C8C2×Dic6111yescharacteristic
214C22×C8C2×Dic6111yescharacteristic
215C22×C8C22⋊D6111yescharacteristic
216C22×C8C22⋊D6111yescharacteristic
217C22×C8C22⋊D6111yescharacteristic
218C22×C8C22×D6111yescharacteristic
219#123—41no—
220C22⋊Q8—21no—
221C22⋊Q8—21no—
222#121—21no—
223#121—21no—
224#120—41no—
225C4×D4—41no—
226C4×D4—41no—
227#117—21no—
228C2×C4⋊C4—1224no—
229C2×C4⋊C4—1222no—
230C2×C4⋊C4—2442no—
231C2×C4⋊C4—2441no—
232M32—2442no—
233C2×C16—1222no—
234#107C2×Dic6111yescharacteristic, complemented
235#107C2×Dic6111yescharacteristic, complemented
236#106—21no—
237#103—21no—
238#103—21no—
239#102—21no—
240#102—21no—
241C24#1175819911yescharacteristic
242#41—42no—
243#41—42no—
244C2×Q8—21no—
245C2×D4—21no—
246C2×D4—41no—
247C2×D4—41no—
248C2×D4—41no—
249C22×C4—22no—
250C22×C4—22no—
251C22×C4—41no—
252C22×C4—4882no—
253C22×C4—4882no—
254C22×C4—2444no—
255C22×C4—2442no—
256C22×C4#1175819911yescharacteristic
257C22×C4#1175820011yescharacteristic
258C22×C4#1175820011yescharacteristic
259C22×C4C22⋊Dic6111yescharacteristic
260C22×C4C22⋊Dic6111yescharacteristic
261C22×C4C2×C22⋊D6111yescharacteristic
262Q16—41no—
263SD16—42no—
264D8—41no—
265C2×C8—22no—
266C2×C8—22no—
267C2×C8—41no—
268C2×C8—41no—
269C2×C8—41no—
270C2×C8—41no—
271C2×C8C22⋊Dic6111yescharacteristic
272C2×C8C22⋊Dic6111yescharacteristic
273C2×C8C22×Dic6111yescharacteristic
274C2×C8C2×C22⋊D6111yescharacteristic
275C4⋊C4—21no—
276C4⋊C4—21no—
277C4⋊C4—41no—
278C4⋊C4—41no—
279C4⋊C4—1224no—
280C4⋊C4—2442no—
281C4⋊C4—2444no—
282C22⋊C4—41no—
283C22⋊C4—41no—
284C22⋊C4—41no—
285C22⋊C4—41no—
286C22⋊C4—41no—
287C42—41no—
288C16—2442no—
289C23—21no—
290C23—21no—
291C23—22no—
292C23—22no—
293C23—41no—
294C23#1451969811yescharacteristic
295C23#1451969811yescharacteristic
296C23C2×#1175819911yescharacteristic
297Q8—41no—
298Q8—41no—
299D4—41no—
300D4—41no—
301D4—81no—
302D4—81no—
303D4—82no—
304D4—82no—
305C2×C4—22no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—41no—
313C2×C4—41no—
314C2×C4—41no—
315C2×C4—82no—
316C2×C4—4888no—
317C2×C4—4882no—
318C2×C4—4882no—
319C2×C4—2444no—
320C2×C4#1451969212yes—
321C2×C4#1451969811yescharacteristic
322C2×C4#1451969811yescharacteristic
323C2×C4#1451970412yes—
324C2×C4C2×C22⋊Dic6111yescharacteristic
325C2×C4C2×#1175820011yescharacteristic
326C8—21no—
327C8—21no—
328C8—21no—
329C8—21no—
330C22—24no—
331C22—24no—
332C22—21no—
333C22—21no—
334C22—21no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—81no—
339C22—81no—
340C22—81no—
341C22#1683949612yes—
342C22#1683957212yes—
343C22C2×#1451969811yescharacteristic
344C22#1684019711yescharacteristic
345C22#1684020211yescharacteristic
346C4—21no—
347C4—21no—
348C4—81no—
349C4—81no—
350C4—81no—
351C4—4884no—
352C4#1683949612yes—
353C4C2×#1451969211yescharacteristic
354C4C2×#1451970411yescharacteristic
355C2—21no—
356C2—21no—
357C2—22no—
358C2—22no—
359C2—161no—
360C2C2×#1683949611yescharacteristic
361C2#2144753111yescharacteristic
362C2C2×#1683957211yescharacteristic
subgroupG/H
centerC22C2×#14519698
commutatorC2×C8×C61C22×C4
FrattiniC22×C8C22×D61
Fitting, prime radicalC61×#3050C2
socleC22×C61C2×#102
cosocleC22×C8×C61C23
hypercenter#3050D61
hypocenterC61#11704
LCSG ▷ C2×C8×C61 ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C23×C8 ◁ #3050

Complements

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

NH ≅ G/Ntype
1. #21447430C2semidirect
2. C2×#16839525C2semidirect
3. #21443831C2semidirect
4. #21443828C2semidirect
12. C2×#135×C61C4semidirect
15. C61×#467C4semidirect
17. C61×#466C4semidirect
21. C61×#427C4semidirect
33. C2×Q16×C61C2×C4semidirect
35. C2×D8×C61C2×C4semidirect
52. #107×C61C2×C4semidirect
53. #107×C61C2×C4semidirect
187. C2×#135Dic61semidirect
192. #467Dic61semidirect
194. #466Dic61semidirect
198. #427Dic61semidirect
204. C61#11704semidirect
209. C2×Q16C2×Dic61semidirect
211. C2×D8C2×Dic61semidirect
234. #107C2×Dic61semidirect
235. #107C2×Dic61semidirect

Maximal subgroups

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

subgroupindex
#214474302
C2×#168395252
#214438312
#214438282
C61×#30502
#1170461