Finite Group Databasebeta

← #30599221

Subgroups — #30599221

Order 15616.

530 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 108 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#21461709C212yesmaximal
2#21460657C214yesmaximal
3C2×#16839626C211yesmaximal, characteristic
4C2×C22⋊#92420C2214yes—
5#16840628—22no—
6#16840628—22no—
7C22×#11758196C412yes—
8C22×C4×Dic61C2211yescharacteristic
9#16839626—22no—
10#16839626—22no—
11C2×#14519684C411yescharacteristic
12C2×#14519684C2212yes—
13C2×#95×C61C411yescharacteristic
14C22×#92420—24no—
15C22⋊#92420—28no—
16C23×Dic61C2×C411yescharacteristic
17C23×Dic61C2×C412yes—
18C23×Dic61C2311yescharacteristic
19C2×#11758196—22no—
20C2×#11758196—22no—
21C2×#11758196—44no—
22C2×C4×Dic61—24no—
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25#14519684—22no—
26#14519684—24no—
27C23×C4×C61C2×C412yes—
28C23×C4×C61C2×C411yescharacteristic
29#95×C61—22no—
30C24×C61C22×C411yescharacteristic
31C22×C4×C61—22no—
32C22×C4×C61—24no—
33C22×C4×C61—22no—
34C22×C4×C61—24no—
35C22×C4×C61—42no—
36C22×C4×C61—42no—
37C22×C4×C61C22⋊C412yes—
38C22×Dic61—22no—
39C22×Dic61—22no—
40C22×Dic61—22no—
41C22×Dic61—22no—
42C22×Dic61—24no—
43C22×Dic61—42no—
44C22×Dic61—42no—
45C22×Dic61—42no—
46C22×Dic61C22⋊C411yescharacteristic
47C22×Dic61C22⋊C411yescharacteristic
48C22×Dic61C2×D412yes—
49C22×Dic61#4114yes—
50C2×#92420—48no—
51C2×#92420—44no—
52#11758196—44no—
53#11758196—44no—
54C4×Dic61—24no—
55C4×Dic61—24no—
56C23×C61—22no—
57C23×C61—21no—
58C23×C61—21no—
59C23×C61C2×C22⋊C411yescharacteristic
60C23×C61#11712yes—
61C23×C61#13114yes—
62C2×C4×C61—22no—
63C2×C4×C61—24no—
64C2×C4×C61—44no—
65C2×C4×C61—42no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61—84no—
69C2×Dic61—28no—
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—24no—
73C2×Dic61—21no—
74C2×Dic61—21no—
75C2×Dic61—44no—
76C2×Dic61—42no—
77C2×Dic61—42no—
78C2×Dic61—42no—
79C2×Dic61—84no—
80C2×Dic61#10012yes—
81C2×Dic61#10112yes—
82C2×Dic61#12314yes—
83#92420—84no—
84#8703—611nomaximal, Sylow
85C22×C61—22no—
86C22×C61—22no—
87C22×C61—24no—
88C22×C61—24no—
89C22×C61#38111yescharacteristic
90C22×C61#40812yes—
91C22×C61#41012yes—
92C22×C61C2×#10011yescharacteristic
93C22×C61C2×#10111yescharacteristic
94C22×C61#43314yes—
95C4×C61—42no—
96C4×C61—82no—
97Dic61—24no—
98Dic61—22no—
99Dic61—22no—
100Dic61—82no—
101C2×#382—611no—
102#1817—612no—
103#1280—614no—
104C2×C61—24no—
105C2×C61#146912yes—
106C2×C61#147012yes—
107C2×C61#181811yescharacteristic
108C2×C61#182011yescharacteristic
109C2×C61#182111yescharacteristic
110C22×C4⋊C4—612no—
111C22×C42—611no—
112C2×C22⋊C8—614no—
113#382—1222no—
114#382—1222no—
115C2×#95—612no—
116C2×#95—611no—
117C2×#95#692311yescharacteristic
118#336—1222no—
119#336—1222no—
120C61#870311yescharacteristic, complemented, Sylow
121C23×C4—611no—
122C23×C4—611no—
123C23×C4—612no—
124C23×C4C2×#692312yes—
125C23×C4C2×#692311yescharacteristic
126C22×C8—1224no—
127C2×C4⋊C4—1222no—
128C2×C4⋊C4—1222no—
129C2×C4⋊C4—2444no—
130C2×C42—612no—
131C2×C42—612no—
132C2×C42—1224no—
133C22⋊C8—1228no—
134#95—22no—
135#95—1224no—
136#95—1222no—
137C24C22×#692311yescharacteristic
138C22×C4—22no—
139C22×C4—24no—
140C22×C4—22no—
141C22×C4—24no—
142C22×C4—42no—
143C22×C4—42no—
144C22×C4—612no—
145C22×C4—611no—
146C22×C4—611no—
147C22×C4—614no—
148C22×C4—1222no—
149C22×C4—1222no—
150C22×C4—1222no—
151C22×C4—1224no—
152C22×C4—1222no—
153C22×C4—2442no—
154C22×C4—2442no—
155C22×C4—2442no—
156C22×C4C22⋊#692312yes—
157C2×C8—2444no—
158C2×C8—2448no—
159C4⋊C4—2444no—
160C4⋊C4—2444no—
161C42—1224no—
162C42—1224no—
163C23—22no—
164C23—21no—
165C23—21no—
166C23C2×C22⋊#692311yescharacteristic
167C23#1451985612yes—
168C23#1451986414yes—
169C2×C4—22no—
170C2×C4—24no—
171C2×C4—44no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—84no—
176C2×C4—614no—
177C2×C4—612no—
178C2×C4—612no—
179C2×C4—1228no—
180C2×C4—1221no—
181C2×C4—1221no—
182C2×C4—1224no—
183C2×C4—1221no—
184C2×C4—1221no—
185C2×C4—4884no—
186C2×C4—2444no—
187C2×C4—2442no—
188C2×C4—2442no—
189C2×C4—2442no—
190C8—4884no—
191C22—24no—
192C22—24no—
193C22—22no—
194C22—22no—
195C22#1684070511yescharacteristic
196C22#1684073512yes—
197C22#1684074112yes—
198C22D61⋊#10011yescharacteristic
199C22D61⋊#10111yescharacteristic
200C22#1684078614yes—
201C4—42no—
202C4—82no—
203C4—1224no—
204C4—1222no—
205C4—1222no—
206C4—4882no—
207C2—24no—
208C2#2146108812yes—
209C2#2146109112yes—
210C2#2146171211yescharacteristic
211C2#2146171611yescharacteristic
212C2#2146171911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutator, prime radicalC24×C61C22×C4
FrattiniC24C22×#6923
FittingC2×#95×C61C4
socleC23×C61C2×C22⋊C4
cosocleC23×Dic61C23
hypercenterC2×#95#6923
hypocenterC61#8703
LCSG ▷ C24×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#95

Complements

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

NH ≅ G/Ntype
120. C61#8703semidirect

Maximal subgroups

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

subgroupindex
#214617092
#214606572
C2×#168396262
#870361