Finite Group Databasebeta

← #30599332

Subgroups — #30599332

Order 15616.

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

normal subgroups only

This group has 450 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#21460670C214yesmaximal, complemented
3#21448301C211yesmaximal, characteristic
4#16840782C2214yes—
5#16840607—22no—
6#16840605—22no—
7C2×#14519736C2211yescharacteristic
8C22×C4×Dic61C411yescharacteristic
9#16839658—22no—
10#16839634—22no—
11C4×#11758196C412yes—
12C4×#11758196C2212yes—
13C2×#117×C61C411yescharacteristic
14#14519844—24no—
15C22⋊#92420—24no—
16#14519832—24no—
17C23×Dic61—21no—
18#14519736—24no—
19C2×C4⋊Dic61D412yes—
20C2×#11758196—22no—
21C2×#11758196—22no—
22C2×C22⋊Dic61D412yes—
23C2×C4×Dic61—21no—
24C2×C4×Dic61—42no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61C2×C412yes—
27C2×C4×Dic61C2311yescharacteristic
28#14519684—22no—
29#14519684—22no—
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—22no—
43C22×Dic61—44no—
44C22×Dic61—42no—
45C22×Dic61C22⋊C412yes—
46C22×Dic61C2×D412yes—
47C2×#92420—44no—
48C4⋊C4×C61—42no—
49C22⋊C4×C61—42no—
50C42×C61—42no—
51C22⋊Dic61—24no—
52C4⋊Dic61—24no—
53#11758196—44no—
54#11758196—44no—
55C4×Dic61—22no—
56C4×Dic61—42no—
57C4×Dic61—42no—
58C4×Dic61#4114yes—
59C23×C61—21no—
60C23×C61—21no—
61C23×C61—42no—
62C23×C61#10012yes—
63C23×C61C2×C22⋊C411yescharacteristic
64C2×C4×C61—28no—
65C2×C4×C61—21no—
66C2×C4×C61—21no—
67C2×C4×C61—21no—
68C2×C4×C61—21no—
69C2×C4×C61—42no—
70C2×C4×C61—42no—
71C2×C4×C61—42no—
72C2×C4×C61#10112yes—
73C2×C4×C61#11712yes—
74C2×Dic61—24no—
75C2×Dic61—22no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—48no—
79C2×Dic61—42no—
80C2×Dic61—42no—
81C2×Dic61#12314yes—
82#92420—84no—
83#8742—611nomaximal, Sylow
84C22×C61—22no—
85C22×C61—22no—
86C22×C61—42no—
87C22×C61—42no—
88C22×C61—42no—
89C22×C61#38111yescharacteristic
90C22×C61C2×#10011yescharacteristic
91C22×C61C2×#10111yescharacteristic
92C4×C61—22no—
93C4×C61—22no—
94C4×C61—82no—
95Dic61—24no—
96Dic61—44no—
97Dic61—42no—
98#2296—611no—
99#1464—612no—
100#1285—614no—
101C2×C61—21no—
102C2×C61—21no—
103C2×C61—42no—
104C2×C61#182111yescharacteristic
105C2×C61#182712yes—
106C2×#117—611no—
107C2×#117#692311yescharacteristic
108C22×C42—611no—
109#432—614no—
110#389—1222no—
111#385—1222no—
112C4×C4⋊C4—612no—
113C4×C4⋊C4—612no—
114#324—1222no—
115#323—1222no—
116C61#874211yescharacteristic, complemented, Sylow
117C23×C4—1221no—
118C23×C4C2×#692311yescharacteristic
119#117—42no—
120#117—1224no—
121C2×C4⋊C4—21no—
122C2×C4⋊C4—612no—
123C2×C4⋊C4—1222no—
124C2×C4⋊C4—1222no—
125C2×C22⋊C4—21no—
126C2×C22⋊C4—612no—
127C2×C42—611no—
128C2×C42—611no—
129C2×C42—612no—
130C2×C42—1221no—
131C2×C42—2442no—
132C2×C42C2×#692312yes—
133C4⋊C8—1224no—
134C22⋊C8—1224no—
135#97—1224no—
136#95—1222no—
137#95—1222no—
138C24C22⋊#692311yescharacteristic
139C22×C4—22no—
140C22×C4—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—612no—
144C22×C4—612no—
145C22×C4—1222no—
146C22×C4—2444no—
147C22×C4—2442no—
148C22×C4C22⋊#692311yescharacteristic
149C22×C4C22×#692311yescharacteristic
150C2×C8—2444no—
151C4⋊C4—42no—
152C4⋊C4—1224no—
153C4⋊C4—2444no—
154C4⋊C4—2444no—
155C22⋊C4—42no—
156C22⋊C4—1224no—
157C42—42no—
158C42—614no—
159C42—1222no—
160C42—2442no—
161C42—2442no—
162C23—21no—
163C23—21no—
164C23—42no—
165C23#1451983712yes—
166C23C2×C22⋊#692311yescharacteristic
167C2×C4—28no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—614no—
176C2×C4—1224no—
177C2×C4—1222no—
178C2×C4—2442no—
179C2×C4—2442no—
180C2×C4—2448no—
181C2×C4—2442no—
182C2×C4—2442no—
183C2×C4#1451983812yes—
184C2×C4#1451985612yes—
185C8—4884no—
186C22—22no—
187C22—22no—
188C22—42no—
189C22—42no—
190C22—42no—
191C22#1684070511yescharacteristic
192C22C2×#1451983711yescharacteristic
193C22C2×#1451983811yescharacteristic
194C4—22no—
195C4—22no—
196C4—82no—
197C4—1224no—
198C4—2444no—
199C4—2442no—
200C2—21no—
201C2—21no—
202C2—42no—
203C2#2146171811yescharacteristic
204C2#2146172912yes—
subgroupG/H
centerC22#16840705
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC2×#117×C61C4
socleC22×C61#381
prime radicalC24×C61C22⋊C4
cosocleC2×C4×Dic61C23
hypercenterC2×#117#6923
hypocenterC61#8742
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
2. #21460670C2semidirect
116. C61#8742semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214606702
#214483012
#874261