Finite Group Databasebeta

← #29570140

Subgroups — #29570140

Order 15616.

604 conjugacy classes of subgroups; only the 151 normal subgroups are shown.

normal subgroups only

This group has 604 conjugacy classes of subgroups — too many to draw. Only its 151 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#21454448C211yesmaximal, characteristic
2#21448213C212yesmaximal
3#21443705C212yesmaximal
4#21443704C211yesmaximal, characteristic
5C61×#1297C211yesmaximal, characteristic
6C22×C4×Dic61C2211yescharacteristic
7#16839816—22no—
8#16839812—22no—
9#16839785C412yescomplemented
10#16839726C2211yescharacteristic
11M16×Dic61C412yescomplemented
12#16839629C414yescomplemented
13#16839626C414yescomplemented
14#16839623—22no—
15#16839620—22no—
16C4×#11758196—22no—
17C4×C22⋊Dic61C2212yes—
18#16839608—22no—
19C61×#407C2211yescharacteristic
20C4×C22⋊C4×C61C2212yes—
21C23×Dic61D412yes—
22C2×#11758194C2×C412yes—
23C2×#11758196—24no—
24C2×C22⋊Dic61—22no—
25C2×C4×Dic61—22no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61C2×C411yescharacteristic
28C2×C4×Dic61C2×C412yes—
29C2×C4×Dic61C2×C412yes—
30C2×C4×Dic61D412yes—
31C2×C4×Dic61D412yes—
32C2×C4×Dic61Q812yes—
33#14519706—24no—
34C22⋊#92418—22no—
35#14519687—22no—
36C8×Dic61—22no—
37#14519684—24no—
38#14519684—24no—
39#14519684—24no—
40#14519684C2×C414yes—
41C23×C4×C61C2311yescharacteristic
42C2×M16×C61C2×C412yes—
43C2×C22⋊C4×C61—22no—
44C2×C42×C61—22no—
45C22⋊C8×C61—22no—
46#95×C61C2×C414yes—
47C24×C61C2×D411yescharacteristic
48C22×C4×C61—24no—
49C22×C4×C61—42no—
50C22×C4×C61C22×C411yescharacteristic
51C22×C4×C61C22×C412yes—
52C22×C4×C61C2×D412yes—
53C22×C4×C61C2×Q811yescharacteristic
54C22×Dic61—24no—
55C22×Dic61—44no—
56C22×Dic61C22⋊C412yes—
57C22×Dic61C22⋊C412yes—
58C22×Dic61C22⋊C412yes—
59C22×Dic61C22⋊C412yes—
60C22×Dic61C4⋊C412yes—
61C22×Dic61C4⋊C412yes—
62M16×C61—42no—
63C2×C8×C61—22no—
64C22⋊C4×C61—44no—
65C42×C61—44no—
66C22⋊Dic61—44no—
67#11758196—48no—
68C4×Dic61—44no—
69C4×Dic61C4212yes—
70C4×Dic61C4211yescharacteristic
71C4×Dic61C4211yescharacteristic
72C4×Dic61C22⋊C411yescharacteristic
73C4×Dic61C22⋊C411yescharacteristic
74C4×Dic61C22⋊C412yes—
75C4×Dic61C4⋊C412yes—
76C4×Dic61C4⋊C412yes—
77C4×Dic61C4⋊C412yes—
78C4×Dic61C4⋊C412yes—
79#11758194—42no—
80C2×#92418—22no—
81C23×C61—24no—
82C23×C61—41no—
83C23×C61C2×C22⋊C412yes—
84C23×C61C2×C4⋊C411yescharacteristic
85C2×C4×C61—22no—
86C2×C4×C61—24no—
87C2×C4×C61—42no—
88C2×C4×C61—41no—
89C2×C4×C61—44no—
90C2×C4×C61—44no—
91C2×C4×C61—44no—
92C2×C4×C61C2×C4211yescharacteristic
93C2×C4×C61C2×C22⋊C411yescharacteristic
94C2×C4×C61C2×C4⋊C412yes—
95C2×Dic61—24no—
96C2×Dic61—24no—
97C2×Dic61—42no—
98C2×Dic61—42no—
99C2×Dic61—42no—
100C2×Dic61—42no—
101C2×Dic61—44no—
102C2×Dic61—44no—
103C2×Dic61—44no—
104C2×Dic61#9512yes—
105C2×Dic61#9512yes—
106C2×Dic61#9512yes—
107C2×Dic61#9512yes—
108C8×C61—42no—
109#92418—42no—
110#8050—611nomaximal, Sylow
111C22×C61—22no—
112C22×C61—22no—
113C22×C61—22no—
114C22×C61—21no—
115C22×C61—44no—
116C22×C61C2×#9511yescharacteristic
117C22×C61#42114yes—
118C4×C61—21no—
119C4×C61—22no—
120C4×C61—84no—
121C4×C61#41012yes—
122Dic61—22no—
123Dic61—22no—
124Dic61—22no—
125Dic61—22no—
126Dic61—84no—
127#2920—611no—
128#2283—612no—
129#1297—611no—
130#1297—612no—
131#1297D6111yescharacteristic
132C2×C61—24no—
133C2×C61—41no—
134C2×C61#173312yes—
135C2×C61#174011yescharacteristic
136C22×C42—611no—
137#432—1222no—
138#431—1222no—
139#423—612no—
140#407—611no—
141#407C2×D6111yescharacteristic
142C4×M16—612no—
143#383—614no—
144#382—614no—
145#381—1222no—
146#380—1222no—
147C4×C4⋊C4—1222no—
148C4×C22⋊C4—612no—
149C4×C22⋊C4C2×D6112yes—
150#376—1222no—
151C61#805011yescharacteristic, complemented, Sylow
152C23×C4—612no—
153C23×C4C22×D6111yescharacteristic
154C2×M16—612no—
155C2×M16C4×D6112yes—
156C2×C4⋊C4—1224no—
157C2×C22⋊C4—22no—
158C2×C22⋊C4—1222no—
159C2×C42—22no—
160C2×C42—612no—
161C2×C42—612no—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—612no—
165C2×C42—612no—
166C2×C42—612no—
167C2×C42—1222no—
168C4⋊C8—1224no—
169C22⋊C8—22no—
170C22⋊C8—1222no—
171#97—1222no—
172C4×C8—1222no—
173#95—614no—
174#95—1224no—
175#95—1224no—
176#95—1224no—
177#95C4×D6114yes—
178C24D4×D6111yescharacteristic
179C22×C4—24no—
180C22×C4—42no—
181C22×C4—612no—
182C22×C4—612no—
183C22×C4—612no—
184C22×C4—612no—
185C22×C4—612no—
186C22×C4—612no—
187C22×C4—1224no—
188C22×C4—2444no—
189C22×C4C2×C4×D6111yescharacteristic
190C22×C4C2×C4×D6112yes—
191C22×C4D4×D6112yes—
192C22×C4Q8×D6111yescharacteristic
193M16—42no—
194M16—2442no—
195C2×C8—22no—
196C2×C8—1222no—
197C4⋊C4—2448no—
198C22⋊C4—44no—
199C22⋊C4—2444no—
200C42—44no—
201C42—611no—
202C42—612no—
203C42—611no—
204C42—611no—
205C42—611no—
206C42—612no—
207C42—612no—
208C42—612no—
209C42—612no—
210C42—612no—
211C42—2444no—
212C23—24no—
213C23—41no—
214C23C22⋊C4×D6112yes—
215C23C4⋊C4×D6111yescharacteristic
216C2×C4—24no—
217C2×C4—22no—
218C2×C4—42no—
219C2×C4—41no—
220C2×C4—44no—
221C2×C4—44no—
222C2×C4—44no—
223C2×C4—612no—
224C2×C4—612no—
225C2×C4—612no—
226C2×C4—612no—
227C2×C4—1224no—
228C2×C4—1224no—
229C2×C4—2442no—
230C2×C4—2442no—
231C2×C4—2442no—
232C2×C4—2442no—
233C2×C4—2444no—
234C2×C4—2444no—
235C2×C4—2444no—
236C2×C4C42×D6111yescharacteristic
237C2×C4C22⋊C4×D6111yescharacteristic
238C2×C4C4⋊C4×D6112yes—
239C8—42no—
240C8—2442no—
241C22—22no—
242C22—22no—
243C22—22no—
244C22—21no—
245C22—44no—
246C22#95×D6111yescharacteristic
247C22#1683977714yes—
248C4—21no—
249C4—22no—
250C4—84no—
251C4—1222no—
252C4—1222no—
253C4—1222no—
254C4—1222no—
255C4—4884no—
256C4#1683973412yes—
257C2—24no—
258C2—41no—
259C2#2144552712yes—
260C2#2144555011yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D61
commutatorC2×C4×C61C2×C42
FrattiniC23×C4C22×D61
FittingC61×#1297C2
socleC22×C61C2×#95
prime radicalC24×C61C2×D4
cosocleC23×C4×C61C23
hypercenter#1297D61
hypocenterC61#8050
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ #1297

Complements

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

NH ≅ G/Ntype
9. #16839785C4semidirect
11. M16×Dic61C4semidirect
12. #16839629C4semidirect
13. #16839626C4semidirect
151. C61#8050semidirect

Maximal subgroups

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

subgroupindex
#214544482
#214482132
#214437052
#214437042
C61×#12972
#805061