Finite Group Databasebeta

← #30604111

Subgroups — #30604111

Order 15616.

510 conjugacy classes of subgroups; only the 76 normal subgroups are shown.

normal subgroups only

This group has 510 conjugacy classes of subgroups — too many to draw. Only its 76 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#21460750C214yesmaximal, complemented
3#21448403C211yesmaximal, characteristic
4#16840782—22no—
5#16840607C2214yes—
6#16840605—22no—
7C23×Dic122C411yescharacteristic
8C2×#14519736C2211yescharacteristic
9#16839668C412yes—
10#16839668C2212yes—
11#16839667—22no—
12#16839623—22no—
13C2×#117×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17C22×Dic122—21no—
18C22×Dic122—24no—
19C22×Dic122—42no—
20C22×Dic122—42no—
21C22×Dic122C2×C412yes—
22C23×Dic61—21no—
23#14519736—42no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2311yescharacteristic
26C2×C22⋊Dic61D412yes—
27C2×C4×Dic61D412yes—
28#14519684—24no—
29#14519684—24no—
30C23×C4×C61C2×C411yescharacteristic
31#117×C61—42no—
32C2×C4⋊C4×C61—21no—
33C2×C22⋊C4×C61—21no—
34C2×C42×C61C2×C412yes—
35C24×C61C22⋊C411yescharacteristic
36C22×C4×C61—22no—
37C22×C4×C61—22no—
38C22×C4×C61—22no—
39C22×C4×C61—22no—
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C22×C411yescharacteristic
42C22×Dic61—24no—
43C22×Dic61—22no—
44C22×Dic61—42no—
45C22×Dic61—42no—
46C22×Dic61C22⋊C412yes—
47C22×Dic61C2×D412yes—
48C2×Dic122—24no—
49C2×Dic122—22no—
50C2×Dic122—42no—
51C2×Dic122—416no—
52C2×Dic122—42no—
53C2×Dic122—42no—
54C2×Dic122—42no—
55C2×Dic122M1614yes—
56C2×#92420—44no—
57C4⋊C4×C61—42no—
58C22⋊C4×C61—42no—
59C42×C61—42no—
60C22⋊Dic61—42no—
61C4⋊Dic61—41no—
62C4⋊Dic61—41no—
63C4×Dic61—22no—
64C4×Dic61—22no—
65C23×C61—21no—
66C23×C61—21no—
67C23×C61—41no—
68C23×C61—41no—
69C23×C61#10012yes—
70C23×C61C2×C22⋊C411yescharacteristic
71C2×C4×C61—28no—
72C2×C4×C61—21no—
73C2×C4×C61—21no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—42no—
77C2×C4×C61—42no—
78C2×C4×C61—42no—
79C2×C4×C61#9912yes—
80C2×C4×C61C2×M1612yes—
81C2×Dic61—24no—
82C2×Dic61—22no—
83C2×Dic61—22no—
84C2×Dic61—48no—
85C2×Dic61—42no—
86C2×Dic61—42no—
87C2×Dic61—42no—
88C2×Dic61—42no—
89Dic122—48no—
90Dic122—44no—
91Dic122—44no—
92#92420—84no—
93#11510—611nomaximal, Sylow
94C22×C61—21no—
95C22×C61—21no—
96C22×C61—22no—
97C22×C61—42no—
98C22×C61—42no—
99C22×C61—41no—
100C22×C61—41no—
101C22×C61#40711yescharacteristic
102C22×C61C2×#9911yescharacteristic
103C22×C61C2×#10011yescharacteristic
104C4×C61—22no—
105C4×C61—22no—
106C4×C61—82no—
107Dic61—42no—
108Dic61—42no—
109Dic61—44no—
110#2310—611no—
111#1464—612no—
112#1319—614no—
113C2×C61—21no—
114C2×C61—21no—
115C2×C61—42no—
116C2×C61#146211yescharacteristic
117C2×C61#212911yescharacteristic
118C2×C61#213511yescharacteristic
119C23×Q8—611no—
120C2×#117—611no—
121C2×#117#692311yescharacteristic
122#432—1222no—
123#391—612no—
124#391—612no—
125#391—1222no—
126#381—1222no—
127#324—614no—
128#323—1222no—
129C61#1151011yescharacteristic, complemented, Sylow
130C22×Q8—612no—
131C22×Q8—1224no—
132C22×Q8—1221no—
133C22×Q8—2442no—
134C22×Q8—2442no—
135C23×C4—1221no—
136C23×C4C2×#692311yescharacteristic
137#117—42no—
138#117—2442no—
139C2×C4⋊C4—21no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4—611no—
142C2×C22⋊C4—21no—
143C2×C22⋊C4—612no—
144C2×C42—612no—
145C2×C42C2×#692312yes—
146C4⋊C8—2442no—
147C22⋊C8—1224no—
148#97—2442no—
149#95—1224no—
150#95—1224no—
151C24C22⋊#692311yescharacteristic
152C2×Q8—614no—
153C2×Q8—1224no—
154C2×Q8—1222no—
155C2×Q8—24416no—
156C2×Q8—2442no—
157C2×Q8—2442no—
158C2×Q8—2442no—
159C2×Q8—2442no—
160C22×C4—22no—
161C22×C4—22no—
162C22×C4—22no—
163C22×C4—22no—
164C22×C4—612no—
165C22×C4—612no—
166C22×C4—1224no—
167C22×C4—1222no—
168C22×C4—2442no—
169C22×C4—2442no—
170C22×C4C22⋊#692311yescharacteristic
171C22×C4C22×#692311yescharacteristic
172C2×C8—2444no—
173C4⋊C4—42no—
174C4⋊C4—2441no—
175C4⋊C4—2441no—
176C22⋊C4—42no—
177C22⋊C4—2442no—
178C42—42no—
179C42—1222no—
180C42—1222no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23#1451983712yes—
186C23C2×C22⋊#692311yescharacteristic
187Q8—2444no—
188Q8—2448no—
189Q8—2444no—
190C2×C4—28no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—42no—
198C2×C4—1224no—
199C2×C4—1222no—
200C2×C4—1222no—
201C2×C4—2448no—
202C2×C4—2442no—
203C2×C4—2442no—
204C2×C4—2442no—
205C2×C4—2442no—
206C2×C4#1451983612yes—
207C2×C4D61⋊M1612yes—
208C8—4884no—
209C22—21no—
210C22—21no—
211C22—22no—
212C22—42no—
213C22—42no—
214C22—41no—
215C22—41no—
216C22#1684073411yescharacteristic
217C22C2×#1451983611yescharacteristic
218C22C2×#1451983711yescharacteristic
219C4—22no—
220C4—22no—
221C4—82no—
222C4—2444no—
223C4—2442no—
224C4—2442no—
225C2—21no—
226C2—21no—
227C2—42no—
228C2#2146106611yescharacteristic
229C2#2146210311yescharacteristic
230C2#2146212311yescharacteristic
subgroupG/H
centerC22C2×#14519836
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
prime radicalC24×C61C22⋊C4
cosocleC2×C4⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11510
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460750C2semidirect
129. C61#11510semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607502
#214484032
#1151061