Finite Group Databasebeta

← #30604089

Subgroups — #30604089

Order 15616.

510 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 80 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#21461070C212yesmaximal
2#21460745C214yesmaximal
3#21448405C211yesmaximal, characteristic
4#16840782—22no—
5#16840607—22no—
6#16840605C2214yes—
7C2×#14519736C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839669—22no—
10#16839669—22no—
11#16839625C412yes—
12#16839625C2212yes—
13C23×Q8×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17#14519736—41no—
18#14519736—41no—
19#14519736—42no—
20C2×C4⋊Dic61—21no—
21C2×C4⋊Dic61D412yes—
22C2×C22⋊Dic61C2×C412yes—
23C2×C22⋊Dic61C2×C411yescharacteristic
24C2×C22⋊Dic61C2311yescharacteristic
25C2×C4×Dic61—21no—
26C2×C4×Dic61D412yes—
27#14519684—24no—
28#14519684—24no—
29C22×Q8×C61—21no—
30C22×Q8×C61—21no—
31C22×Q8×C61—24no—
32C22×Q8×C61—41no—
33C22×Q8×C61—41no—
34C22×Q8×C61—42no—
35C23×C4×C61C2×C412yes—
36C23×C4×C61C2×C411yescharacteristic
37C24×C61C22×C411yescharacteristic
38C2×Q8×C61—24no—
39C2×Q8×C61—24no—
40C2×Q8×C61—48no—
41C2×Q8×C61—48no—
42C2×Q8×C61—42no—
43C2×Q8×C61—42no—
44C2×Q8×C61—41no—
45C2×Q8×C61—41no—
46C2×Q8×C61—42no—
47C22×C4×C61—22no—
48C22×C4×C61—21no—
49C22×C4×C61—21no—
50C22×C4×C61—22no—
51C22×C4×C61—22no—
52C22×C4×C61—22no—
53C22×C4×C61—42no—
54C22×C4×C61—42no—
55C22×C4×C61C22⋊C411yescharacteristic
56C22×C4×C61C22⋊C411yescharacteristic
57C22×C4×C61M1614yes—
58C22×Dic61—22no—
59C22×Dic61C22⋊C412yes—
60C22×Dic61C2×D412yes—
61C2×#92420—44no—
62C22⋊Dic61—41no—
63C22⋊Dic61—41no—
64C22⋊Dic61—42no—
65C4⋊Dic61—42no—
66C4⋊Dic61—42no—
67C4×Dic61—22no—
68C4×Dic61—22no—
69C4×Dic61—42no—
70C23×C61—21no—
71C23×C61—21no—
72C23×C61—42no—
73C23×C61C2×C22⋊C411yescharacteristic
74C23×C61C2×M1612yes—
75Q8×C61—44no—
76Q8×C61—44no—
77Q8×C61—48no—
78C2×C4×C61—24no—
79C2×C4×C61—24no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—24no—
85C2×C4×C61—44no—
86C2×C4×C61—42no—
87C2×C4×C61—42no—
88C2×C4×C61—44no—
89C2×C4×C61#9911yescharacteristic
90C2×C4×C61#9911yescharacteristic
91C2×C4×C61#10012yes—
92C2×Dic61—22no—
93C2×Dic61—22no—
94C2×Dic61—42no—
95C2×Dic61—42no—
96C2×Dic61—44no—
97C2×Dic61—42no—
98#92420—84no—
99#11504—611nomaximal, Sylow
100C22×C61—22no—
101C22×C61—22no—
102C22×C61—42no—
103C22×C61—42no—
104C22×C61—42no—
105C22×C61#40711yescharacteristic
106C22×C61C2×#9911yescharacteristic
107C22×C61C2×#10011yescharacteristic
108C4×C61—21no—
109C4×C61—21no—
110C4×C61—22no—
111C4×C61—44no—
112Dic61—42no—
113Dic61—42no—
114Dic61—82no—
115#2310—611no—
116#1464—612no—
117#1317—614no—
118C2×C61—21no—
119C2×C61—21no—
120C2×C61—42no—
121C2×C61#146211yescharacteristic
122C2×C61#212312yes—
123C23×Q8#692311yescharacteristic
124C2×#117—611no—
125C2×#117—611no—
126#432—1222no—
127#391—1222no—
128#391—1222no—
129#381—612no—
130#381—612no—
131#324—1222no—
132#323—614no—
133C61#1150411yescharacteristic, complemented, Sylow
134C22×Q8—24no—
135C22×Q8—21no—
136C22×Q8—21no—
137C22×Q8—41no—
138C22×Q8—41no—
139C22×Q8—42no—
140C23×C4C2×#692312yes—
141C23×C4C2×#692311yescharacteristic
142#117—2441no—
143#117—2441no—
144#117—2442no—
145C2×C4⋊C4—612no—
146C2×C4⋊C4—1221no—
147C2×C22⋊C4—611no—
148C2×C22⋊C4—611no—
149C2×C22⋊C4—612no—
150C2×C42—612no—
151C2×C42—1221no—
152C4⋊C8—2442no—
153C22⋊C8—1224no—
154#97—2442no—
155#95—1224no—
156#95—1224no—
157C24C22×#692311yescharacteristic
158C2×Q8—24no—
159C2×Q8—24no—
160C2×Q8—48no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—42no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—42no—
174C22×C4—42no—
175C22×C4—612no—
176C22×C4—612no—
177C22×C4—1222no—
178C22×C4#1175821714yes—
179C22×C4C22⋊#692311yescharacteristic
180C22×C4C22⋊#692311yescharacteristic
181C2×C8—2444no—
182C4⋊C4—2442no—
183C4⋊C4—2442no—
184C22⋊C4—2441no—
185C22⋊C4—2441no—
186C22⋊C4—2442no—
187C42—1222no—
188C42—1222no—
189C42—2442no—
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×C22⋊#692311yescharacteristic
194C23C2×#1175821712yes—
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—44no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—44no—
209C2×C4—1222no—
210C2×C4—1222no—
211C2×C4—2444no—
212C2×C4—2442no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4#1451983511yescharacteristic
216C2×C4#1451983511yescharacteristic
217C2×C4#1451983712yes—
218C8—4884no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#1684073211yescharacteristic
225C22C2×#1451983511yescharacteristic
226C22C2×#1451983711yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—44no—
231C4—4882no—
232C4—2442no—
233C4—2442no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2#2146106411yescharacteristic
238C2#2146208112yes—
subgroupG/H
centerC22C2×#14519835
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC23×Q8×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC23×Q8#6923
hypocenterC61#11504
LCSG ▷ C24×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C23×Q8

Complements

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

NH ≅ G/Ntype
133. C61#11504semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607452
#214484052
#1150461