Finite Group Databasebeta

← #30595660

Subgroups — #30595660

Order 15616.

456 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 114 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#21461735C212yesmaximal
2#21460640C214yesmaximal
3#21448386C211yesmaximal, characteristic
4C2×#14519844—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×#14519777C411yescharacteristic
8C2×#14519742C412yes—
9#16839667C2212yes—
10#16839658—22no—
11C4⋊C4×Dic61—22no—
12C42×Dic61C2211yescharacteristic
13C61×#384C411yescharacteristic
14C22×#92420—24no—
15#14519844—44no—
16C22×Dic122C2×C412yes—
17#14519777—24no—
18#14519742—44no—
19C2×C4⋊Dic61—22no—
20C2×#11758196—22no—
21C2×C4×Dic61—22no—
22C2×C4×Dic61C2×C411yescharacteristic
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26#14519684—24no—
27C2×C4⋊C4×C61—22no—
28C2×C4⋊C4×C61C2×C412yes—
29C2×C42×C61C2×C411yescharacteristic
30C22×C4×C61—22no—
31C22×C4×C61C22⋊C412yes—
32C22×C4×C61C22×C411yescharacteristic
33C22×Dic61—22no—
34C22×Dic61C22⋊C411yescharacteristic
35C22×Dic61C22⋊C411yescharacteristic
36C22×Dic61C2×D412yes—
37C2×Dic122—22no—
38C2×Dic122—42no—
39C2×Dic122—42no—
40C2×Dic122M1614yes—
41C2×#92420—44no—
42C2×#92420—44no—
43C2×#92420—44no—
44C4⋊C4×C61—44no—
45C4⋊C4×C61—42no—
46C42×C61—22no—
47C4⋊Dic61—28no—
48#11758196—44no—
49C4×Dic61—22no—
50C4×Dic61—42no—
51C4×Dic61—41no—
52C4×Dic61—44no—
53C4×Dic61SD1614yes—
54C4×Dic61Q1614yes—
55C23×C61C2×C22⋊C411yescharacteristic
56C2×C4×C61—22no—
57C2×C4×C61—21no—
58C2×C4×C61—21no—
59C2×C4×C61—22no—
60C2×C4×C61—42no—
61C2×C4×C61—44no—
62C2×C4×C61#10314yes—
63C2×C4×C61C2×M1612yes—
64C2×Dic61—22no—
65C2×Dic61—22no—
66C2×Dic61—24no—
67C2×Dic61—21no—
68C2×Dic61—22no—
69C2×Dic61—42no—
70C2×Dic61—42no—
71C2×Dic61#10012yes—
72C2×Dic61#10314yes—
73C2×Dic61C2×SD1612yes—
74C2×Dic61C2×Q1612yes—
75Dic122—44no—
76Dic122—44no—
77#92420—84no—
78#7653—611nomaximal, Sylow
79C22×C61#40711yescharacteristic
80C22×C61#41011yescharacteristic
81C22×C61C2×#10011yescharacteristic
82C22×C61C2×#10312yes—
83C22×C61#42112yes—
84C4×C61—22no—
85C4×C61—24no—
86C4×C61—82no—
87Dic61—22no—
88Dic61—22no—
89Dic61—41no—
90Dic61—44no—
91Dic61#33314yes—
92C4×C4⋊Q8—611no—
93#1831—612no—
94#1272—614no—
95C2×C61#146611yescharacteristic
96C2×C61#148712yes—
97C2×C61#151812yes—
98C2×C61#153611yescharacteristic
99C2×C61C2×#33311yescharacteristic
100C2×C4⋊Q8—611no—
101C2×C4×Q8—612no—
102C2×C4⋊C8—1222no—
103#391—612no—
104#389—1222no—
105#384#692311yescharacteristic
106C4×C4⋊C4—1222no—
107C43—611no—
108#336—614no—
109#336—1222no—
110C61#765311yescharacteristic, complemented, Sylow
111C22×Q8—612no—
112C22×C8—1224no—
113C4⋊Q8—1224no—
114C4×Q8—2444no—
115C2×C4⋊C4—22no—
116C2×C4⋊C4—1222no—
117C2×C4⋊C4—1222no—
118C2×C4⋊C4C2×#692312yes—
119C2×C42—612no—
120C2×C42—611no—
121C2×C42—612no—
122C2×C42—611no—
123C2×C42—1222no—
124C2×C42C2×#692311yescharacteristic
125C4⋊C8—2444no—
126#95—1224no—
127C2×Q8—614no—
128C2×Q8—1222no—
129C2×Q8—2442no—
130C2×Q8—2442no—
131C22×C4—22no—
132C22×C4—611no—
133C22×C4—612no—
134C22×C4—611no—
135C22×C4—1222no—
136C22×C4C22⋊#692312yes—
137C22×C4C22×#692311yescharacteristic
138C2×C8—2444no—
139C2×C8—2444no—
140C2×C8—2444no—
141C4⋊C4—42no—
142C4⋊C4—44no—
143C4⋊C4—1228no—
144C4⋊C4—2444no—
145C42—22no—
146C42—614no—
147C42—614no—
148C42—1222no—
149C42—2441no—
150C42—2442no—
151C42—2444no—
152C23C2×C22⋊#692311yescharacteristic
153Q8—2444no—
154Q8—2444no—
155C2×C4—22no—
156C2×C4—21no—
157C2×C4—21no—
158C2×C4—22no—
159C2×C4—42no—
160C2×C4—44no—
161C2×C4—612no—
162C2×C4—614no—
163C2×C4—612no—
164C2×C4—612no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1221no—
169C2×C4—1222no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4#1451984014yes—
173C2×C4D61⋊M1612yes—
174C8—4884no—
175C22#1684073411yescharacteristic
176C22#1684074311yescharacteristic
177C22D61⋊#10011yescharacteristic
178C22C2×#1451984012yes—
179C22#1684076012yes—
180C4—22no—
181C4—24no—
182C4—82no—
183C4—614no—
184C4—1222no—
185C4—1222no—
186C4—2441no—
187C4—2444no—
188C2#2146108011yescharacteristic
189C2#2146114912yes—
190C2#2146125112yes—
191C2#2146130811yescharacteristic
192C2D61⋊#33311yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#384C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#384#6923
hypocenterC61#7653
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #384

Complements

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

NH ≅ G/Ntype
110. C61#7653semidirect

Maximal subgroups

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

subgroupindex
#214617352
#214606402
#214483862
#765361