Finite Group Databasebeta

← #30595483

Subgroups — #30595483

Order 15616.

408 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 110 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#21461734C212yesmaximal
2#21460638C214yesmaximal
3#21448374C211yesmaximal, characteristic
4C2×C4⋊#92420—22no—
5#16840628—22no—
6#16840628C2214yes—
7C2×#14519769C411yescharacteristic
8#16839658C2212yes—
9#16839644—22no—
10C4⋊C4×Dic61C412yes—
11#16839613—22no—
12C42×Dic61C2211yescharacteristic
13C61×#382C411yescharacteristic
14C22×#92420—24no—
15C4⋊#92420—44no—
16#14519769—22no—
17#14519769C814yescomplemented
18C2×C4⋊Dic61C2×C412yes—
19C2×#11758196—22no—
20C2×#11758196—22no—
21C2×C4×Dic61—22no—
22C2×C4×Dic61C2×C411yescharacteristic
23C2×C4×Dic61D412yes—
24C2×C4×Dic61D412yes—
25C2×C4×Dic61C2311yescharacteristic
26#14519684—22no—
27#14519684—22no—
28C2×C4⋊C4×C61C2×C412yes—
29C2×C42×C61C2×C411yescharacteristic
30#95×C61—22no—
31C22×C4×C61—22no—
32C22×C4×C61C22⋊C412yes—
33C22×C4×C61C22×C411yescharacteristic
34C22×Dic61—22no—
35C22×Dic61C22⋊C411yescharacteristic
36C22×Dic61C22⋊C411yescharacteristic
37C22×Dic61C2×D412yes—
38C2×#92420—44no—
39C2×#92420—44no—
40C2×#92420—44no—
41C4⋊C4×C61—42no—
42C42×C61C2×C812yes—
43C42×C61M1612yes—
44C4⋊Dic61—22no—
45C4⋊Dic61C2×C814yes—
46#11758196—28no—
47#11758196—42no—
48#11758196—42no—
49C4×Dic61—22no—
50C4×Dic61—22no—
51C4×Dic61—22no—
52C4×Dic61—42no—
53C4×Dic61—41no—
54C4×Dic61—44no—
55C23×C61C2×C22⋊C411yescharacteristic
56C2×C4×C61—21no—
57C2×C4×C61—21no—
58C2×C4×C61—22no—
59C2×C4×C61—22no—
60C2×C4×C61—42no—
61C2×C4×C61—42no—
62C2×C4×C61—42no—
63C2×C4×C61C22⋊C814yes—
64C2×C4×C61C22×C811yescharacteristic
65C2×C4×C61C2×M1611yescharacteristic
66C2×Dic61—22no—
67C2×Dic61—22no—
68C2×Dic61—22no—
69C2×Dic61—24no—
70C2×Dic61—21no—
71C2×Dic61—22no—
72C2×Dic61—42no—
73C2×Dic61—42no—
74C2×Dic61#10112yes—
75C2×Dic61AGL(1,ℤ/8)12yes—
76C2×Dic61#13712yes—
77#92420—84no—
78#7602—611nomaximal, Sylow
79C22×C61C2×C22⋊C811yescharacteristic
80C22×C61#41011yescharacteristic
81C22×C61C2×#10111yescharacteristic
82C22×C61#41712yes—
83C22×C61#42112yes—
84C4×C61—21no—
85C4×C61—21no—
86C4×C61—24no—
87C4×C61—82no—
88Dic61—22no—
89Dic61—22no—
90Dic61—22no—
91Dic61—41no—
92Dic61—44no—
93C4×#125—611no—
94#1831—612no—
95#1271—614no—
96C2×C61#146111yescharacteristic
97C2×C61#147712yes—
98C2×C61#151212yes—
99C2×C61#153411yescharacteristic
100C2×C61#156111yescharacteristic
101C2×#125—611no—
102C2×C4⋊C8—1222no—
103#389—612no—
104#387—1222no—
105#382#692311yescharacteristic
106C4×C4⋊C4—612no—
107C4×C4⋊C4—1222no—
108C43—611no—
109#336—614no—
110#336—1222no—
111C61#760211yescharacteristic, complemented, Sylow
112C22×C8—1224no—
113#125—614no—
114#125—1222no—
115C2×C4⋊C4—612no—
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—22no—
127#95—1222no—
128#95—1222no—
129C22×C4—22no—
130C22×C4—612no—
131C22×C4—611no—
132C22×C4—611no—
133C22×C4—1222no—
134C22×C4C22⋊#692312yes—
135C22×C4C22×#692311yescharacteristic
136C2×C8—2444no—
137C2×C8—2444no—
138C2×C8—2444no—
139C4⋊C4—42no—
140C4⋊C4—614no—
141C4⋊C4—1228no—
142C4⋊C4—1222no—
143C4⋊C4—2442no—
144C4⋊C4—2442no—
145C42—1222no—
146C42—1222no—
147C42—1222no—
148C42—2441no—
149C42—2442no—
150C42—2444no—
151C42D61⋊C812yes—
152C42#1175821312yes—
153C23C2×C22⋊#692311yescharacteristic
154C2×C4—21no—
155C2×C4—21no—
156C2×C4—22no—
157C2×C4—22no—
158C2×C4—42no—
159C2×C4—42no—
160C2×C4—42no—
161C2×C4—612no—
162C2×C4—612no—
163C2×C4—612no—
164C2×C4—1222no—
165C2×C4—1222no—
166C2×C4—1222no—
167C2×C4—1224no—
168C2×C4—1221no—
169C2×C4—1222no—
170C2×C4—2442no—
171C2×C4—2442no—
172C2×C4#1451983414yes—
173C2×C4C2×D61⋊C811yescharacteristic
174C2×C4C2×#1175821311yescharacteristic
175C8—4884no—
176C22C2×#1451983411yescharacteristic
177C22#1684074211yescharacteristic
178C22D61⋊#10111yescharacteristic
179C22#1684075312yes—
180C22#1684075912yes—
181C4—21no—
182C4—21no—
183C4—24no—
184C4—82no—
185C4—1222no—
186C4—1222no—
187C4—1222no—
188C4—2441no—
189C4—2444no—
190C2#2146106311yescharacteristic
191C2#2146111612yes—
192C2#2146123112yes—
193C2#2146130211yescharacteristic
194C2#2146135911yescharacteristic
subgroupG/H
centerC23C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC22×C4C22×#6923
FittingC61×#382C4
socle, prime radicalC23×C61C2×C22⋊C4
cosocleC2×C4×Dic61C23
hypercenter#382#6923
hypocenterC61#7602
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #382

Complements

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

NH ≅ G/Ntype
17. #14519769C8semidirect
111. C61#7602semidirect

Maximal subgroups

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

subgroupindex
#214617342
#214606382
#214483742
#760261