Finite Group Databasebeta

← #30604135

Subgroups — #30604135

Order 15616.

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

normal subgroups only

This group has 446 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#21460763C214yesmaximal
3#21448303C211yesmaximal, characteristic
4#16840782—22no—
5#16840607—22no—
6#16840605C2214yes—
7C2×#14519736C2211yescharacteristic
8C22×C4×Dic61C411yescharacteristic
9#16839661—22no—
10#16839637C412yes—
11#16839637C2212yes—
12C4×C4⋊Dic61—22no—
13C2×#117×C61C411yescharacteristic
14#14519844—42no—
15C22⋊#92420—24no—
16#14519832—42no—
17C23×Dic61C2×C412yes—
18#14519736—42no—
19C2×C4⋊Dic61—22no—
20C2×C4⋊Dic61—22no—
21C2×C4⋊Dic61D412yes—
22C2×C22⋊Dic61C2×C411yescharacteristic
23C2×C22⋊Dic61C2311yescharacteristic
24C2×C4×Dic61—21no—
25C2×C4×Dic61—21no—
26C2×C4×Dic61—42no—
27C2×C4×Dic61D412yes—
28#14519684—22no—
29#14519684—22no—
30C23×C4×C61C2×C411yescharacteristic
31#117×C61—24no—
32C2×C4⋊C4×C61—21no—
33C2×C22⋊C4×C61C2×C412yes—
34C2×C42×C61—21no—
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—22no—
43C22×Dic61—44no—
44C22×Dic61—42no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C2×D412yes—
47C2×#92420—44no—
48C4⋊C4×C61—24no—
49C22⋊C4×C61—22no—
50C22⋊C4×C61M1614yes—
51C42×C61—24no—
52C22⋊Dic61—41no—
53C22⋊Dic61—41no—
54C4⋊Dic61—42no—
55C4⋊Dic61—44no—
56C4⋊Dic61—44no—
57C4×Dic61—22no—
58C4×Dic61—22no—
59C4×Dic61—42no—
60C4×Dic61—42no—
61C23×C61—21no—
62C23×C61—21no—
63C23×C61—42no—
64C23×C61C2×C22⋊C411yescharacteristic
65C23×C61C2×M1612yes—
66C2×C4×C61—28no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—24no—
72C2×C4×C61—42no—
73C2×C4×C61—42no—
74C2×C4×C61#9912yes—
75C2×C4×C61#10112yes—
76C2×Dic61—24no—
77C2×Dic61—22no—
78C2×Dic61—22no—
79C2×Dic61—42no—
80C2×Dic61—44no—
81C2×Dic61—42no—
82C2×Dic61—42no—
83C2×Dic61—42no—
84C2×Dic61—44no—
85#92420—84no—
86#11518—611nomaximal, Sylow
87C22×C61—22no—
88C22×C61—22no—
89C22×C61—42no—
90C22×C61—42no—
91C22×C61—42no—
92C22×C61#40711yescharacteristic
93C22×C61C2×#9911yescharacteristic
94C22×C61C2×#10111yescharacteristic
95C4×C61—22no—
96C4×C61—22no—
97C4×C61—44no—
98Dic61—42no—
99Dic61—42no—
100Dic61—44no—
101#2296—611no—
102#1464—612no—
103#1326—614no—
104C2×C61—21no—
105C2×C61—21no—
106C2×C61—42no—
107C2×C61#146311yescharacteristic
108C2×C61#212012yes—
109C2×#117—611no—
110C2×#117#692311yescharacteristic
111C22×C42—611no—
112#432—1222no—
113#389—1222no—
114#385—612no—
115#385—612no—
116C4×C4⋊C4—1222no—
117#324—1222no—
118#323—614no—
119C61#1151811yescharacteristic, complemented, Sylow
120C23×C4—612no—
121C23×C4C2×#692311yescharacteristic
122#117—24no—
123#117—2442no—
124C2×C4⋊C4—21no—
125C2×C4⋊C4—612no—
126C2×C4⋊C4—1222no—
127C2×C4⋊C4—1222no—
128C2×C22⋊C4—611no—
129C2×C22⋊C4—611no—
130C2×C22⋊C4C2×#692312yes—
131C2×C42—21no—
132C2×C42—612no—
133C2×C42—1221no—
134C2×C42—1221no—
135C2×C42—2442no—
136C4⋊C8—2442no—
137C22⋊C8—1224no—
138#97—2442no—
139#95—1222no—
140#95—1222no—
141C24C22×#692311yescharacteristic
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—612no—
147C22×C4—612no—
148C22×C4—1222no—
149C22×C4—2444no—
150C22×C4—2442no—
151C22×C4C22⋊#692311yescharacteristic
152C22×C4C22⋊#692311yescharacteristic
153C2×C8—2444no—
154C4⋊C4—24no—
155C4⋊C4—2442no—
156C4⋊C4—2444no—
157C4⋊C4—2444no—
158C22⋊C4—22no—
159C22⋊C4—2441no—
160C22⋊C4—2441no—
161C22⋊C4#1175821714yes—
162C42—24no—
163C42—1222no—
164C42—1222no—
165C42—2442no—
166C42—2442no—
167C23—21no—
168C23—21no—
169C23—42no—
170C23C2×C22⋊#692311yescharacteristic
171C23C2×#1175821712yes—
172C2×C4—28no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—24no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—1224no—
181C2×C4—1222no—
182C2×C4—1222no—
183C2×C4—2442no—
184C2×C4—2444no—
185C2×C4—2442no—
186C2×C4—2442no—
187C2×C4—2442no—
188C2×C4—2444no—
189C2×C4#1451983612yes—
190C2×C4#1451983812yes—
191C8—4884no—
192C22—22no—
193C22—22no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22#1684073211yescharacteristic
198C22C2×#1451983611yescharacteristic
199C22C2×#1451983811yescharacteristic
200C4—22no—
201C4—22no—
202C4—44no—
203C4—2442no—
204C4—2442no—
205C4—2444no—
206C2—21no—
207C2—21no—
208C2—42no—
209C2#2146106711yescharacteristic
210C2#2146207212yes—
subgroupG/H
centerC22C2×#14519836
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#117×C61C4
socleC22×C61C2×#99
cosocleC2×C22⋊Dic61C23
hypercenterC2×#117#6923
hypocenterC61#11518
LCSG ▷ C24×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
119. C61#11518semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214607632
#214483032
#1151861