Finite Group Databasebeta

← #30601923

Subgroups — #30601923

Order 15616.

462 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 462 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21461475C211yesmaximal, characteristic, complemented
2#21461380C211yesmaximal, characteristic, complemented
3#21461290C212yesmaximal, complemented
4#21461210C212yesmaximal, complemented
5#21456399C211yesmaximal, characteristic
6#16840784C2212yes—
7#16840721C2211yescharacteristic
8C2×#14519831—21no—
9C2×C8×#6923—21no—
10#16840698C2211yescharacteristic
11#16840625—21no—
12#16840623—21no—
13#16840618—24no—
14#16840614—24no—
15#16840313C2212yes—
16#16840139C411yescharacteristic, complemented
17#16840110C412yescomplemented
18#16839999—21no—
19#16839999—21no—
20#16839844—21no—
21#16839844—21no—
22C4×C8×D61C2211yescharacteristic
23C61×#500C411yescharacteristic, complemented
24C2×D61⋊C8—21no—
25C2×C4×#6923—21no—
26C4⋊#92420—22no—
27#14519834—22no—
28#14519832—22no—
29#14519832—21no—
30#14519832D412yes—
31#14519831—24no—
32C8×#6923—24no—
33(C2×#6923)⋊C4—21no—
34(C2×#6923)⋊C4D412yes—
35C2×#11758226—22no—
36C2×D488—21no—
37C2×D488—21no—
38C2×C8×D61D411yescharacteristic
39C2×C8×D61D411yescharacteristic
40#14519774C2×C412yes—
41#14519766—22no—
42#14519752—22no—
43#14519752—22no—
44#14519739—22no—
45#14519739—22no—
46C42×D61C2311yescharacteristic
47#14519697—22no—
48#14519697—22no—
49C4×#92418C2×C411yescharacteristic
50C8×Dic61D411yescharacteristic
51C8×Dic61D411yescharacteristic
52C4⋊Q8×C61C2×C412yes—
53#107×C61—21no—
54#107×C61—21no—
55C4×C8×C61C2×C411yescharacteristic
56C22×#6923—22no—
57C2×Q8×C61—22no—
58#11758226—84no—
59C2×D244—22no—
60C2×D244—22no—
61C2×D244—22no—
62C2×D244—42no—
63C2×C4×D61—42no—
64C2×C4×D61C2×D411yescharacteristic
65C2×C4×D61C2×D411yescharacteristic
66C2×C4×D61#4111yescharacteristic
67C2×#92420—22no—
68C2×#92420—42no—
69C4×#6923—22no—
70C4×#6923—22no—
71D61⋊C8—22no—
72D61⋊C8—22no—
73C2×C8×C61C22⋊C411yescharacteristic
74C2×C8×C61C22⋊C411yescharacteristic
75C4⋊C4×C61—22no—
76C4⋊C4×C61—22no—
77C42×C61C22×C411yescharacteristic
78#11758198—42no—
79#11758198—42no—
80C4×Dic61C2×D411yescharacteristic
81C4×Dic61C2×D411yescharacteristic
82C4×Dic61#4111yescharacteristic
83C2×#92418C22⋊C411yescharacteristic
84C2×#92418C22⋊C411yescharacteristic
85D488—42no—
86D488—42no—
87C8×D61—22no—
88C8×D61—22no—
89C22×D61—42no—
90C22×D61#12111yescharacteristic
91C2×#6923—24no—
92C2×#6923—42no—
93C2×#6923—42no—
94Q8×C61—82no—
95C2×C4×C61—42no—
96C2×C4×C61C2×C22⋊C411yescharacteristic
97C2×C4×C61C4×D411yescharacteristic
98C2×C4×C61C4×D411yescharacteristic
99C2×Dic61#12111yescharacteristic
100C2×Dic61#12411yescharacteristic
101C2×Dic61#12711yescharacteristic
102D244—42no—
103D244—42no—
104D244—82no—
105D244—82no—
106D244—84no—
107C4×D61—22no—
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—41no—
111C4×D61—84no—
112#92420—24no—
113#92420—82no—
114C8×C61#10412yes—
115C8×C61#10412yes—
116#92418—21no—
117#92418—21no—
118#9762—611nomaximal, Sylow
119C22×C61#39011yescharacteristic
120C2×D61—21no—
121C2×D61—21no—
122C2×D61—82no—
123C2×D61—82no—
124C2×D61—82no—
125C2×D61#47212yes—
126#6923—44no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—82no—
130C4×C61C2×#10411yescharacteristic
131C4×C61C2×#10411yescharacteristic
132Dic61—21no—
133Dic61—21no—
134Dic61—21no—
135#3169—611no—
136#1726—611no—
137#1568—611no—
138#1530—612no—
139#1505—612no—
140C2×C61#196211yescharacteristic
141C2×C61#197611yescharacteristic
142C2×C61#197811yescharacteristic
143D61—22no—
144D61—162no—
145#532—612no—
146#500#692311yescharacteristic, complemented
147#493—611no—
148#486—612no—
149#466—1221no—
150#466—1221no—
151C4×D8—1221no—
152C4×D8—1221no—
153#432—612no—
154C2×#97—611no—
155C2×#97—1221no—
156C2×C4×C8—611no—
157C2×C4×C8—1221no—
158#376—611no—
159#335—1221no—
160#334—1221no—
161#329—1224no—
162#327—1224no—
163C61#976211yescharacteristic, complemented, Sylow
164C2×#41—1222no—
165C2×D8—1221no—
166C2×D8—1221no—
167C22×C8—611no—
168C22×C8—611no—
169C22×C8—1221no—
170C4⋊Q8C2×#692312yes—
171#127—612no—
172#124—1222no—
173#121—1222no—
174#121—1222no—
175C4×D4—1222no—
176C4×D4—1222no—
177C2×C42—611no—
178C2×C42—1221no—
179#107—21no—
180#107—21no—
181C4⋊C8—1222no—
182#102—1222no—
183#102—1222no—
184C22⋊C8—1222no—
185#97—612no—
186#97—1221no—
187#97—1222no—
188#97—1224no—
189C4×C8—611no—
190C4×C8—611no—
191C4×C8—611no—
192C4×C8—1224no—
193C4×C8C2×#692311yescharacteristic
194#95—612no—
195#95—1221no—
196#41—4884no—
197C2×Q8—22no—
198C2×D4—1222no—
199C2×D4—1222no—
200C2×D4—1222no—
201C2×D4—2442no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1222no—
206C22×C4—2442no—
207D8—2442no—
208D8—2442no—
209C2×C8—611no—
210C2×C8—611no—
211C2×C8—1222no—
212C2×C8—1222no—
213C2×C8—1222no—
214C2×C8—1222no—
215C2×C8—1222no—
216C2×C8—2442no—
217C2×C8C22⋊#692311yescharacteristic
218C2×C8C22⋊#692311yescharacteristic
219C4⋊C4—22no—
220C4⋊C4—22no—
221C22⋊C4—2442no—
222C22⋊C4—2442no—
223C42—611no—
224C42—611no—
225C42—611no—
226C42—1222no—
227C42—1222no—
228C42C22×#692311yescharacteristic
229C23—611no—
230C23—2442no—
231Q8—82no—
232D4—4882no—
233D4—4882no—
234D4—4884no—
235D4—2442no—
236D4—2442no—
237C2×C4—42no—
238C2×C4—611no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—1222no—
242C2×C4—1221no—
243C2×C4—1221no—
244C2×C4—1224no—
245C2×C4—4884no—
246C2×C4—2441no—
247C2×C4—2442no—
248C2×C4—2442no—
249C2×C4C2×C22⋊#692311yescharacteristic
250C2×C4D4×#692311yescharacteristic
251C2×C4D4×#692311yescharacteristic
252C8—1224no—
253C8—1221no—
254C8—1221no—
255C8—4882no—
256C8#1451984212yes—
257C8#1451984212yes—
258C22—612no—
259C22—1221no—
260C22—1221no—
261C22—4882no—
262C22—4882no—
263C22—4882no—
264C22#1684071411yescharacteristic
265C4—21no—
266C4—21no—
267C4—82no—
268C4—1221no—
269C4—1221no—
270C4—1221no—
271C4—2444no—
272C4C2×#1451984211yescharacteristic
273C4C2×#1451984211yescharacteristic
274C2—1222no—
275C2—9762no—
276C2#2146195211yescharacteristic
277C2#2146197811yescharacteristic
278C2#2146198011yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#500C4
socleC22×C61#390
prime radical#21456399C2
cosocleC42×D61C23
hypercenter#500#6923
hypocenterC61#9762
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #500

Complements

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

NH ≅ G/Ntype
1. #21461475C2semidirect
2. #21461380C2semidirect
3. #21461290C2semidirect
4. #21461210C2semidirect
16. #16840139C4semidirect
17. #16840110C4semidirect
23. C61×#500C4semidirect
146. #500#6923semidirect
163. C61#9762semidirect

Maximal subgroups

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

subgroupindex
#214614752
#214613802
#214612902
#214612102
#214563992
#976261