Finite Group Databasebeta

← #30594807

Subgroups — #30594807

Order 15616.

356 conjugacy classes of subgroups; only the 36 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 36 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#21460745C212yesmaximal, complemented
2#21445736C211yesmaximal, characteristic
3#16840605—22no—
4C22×#11758222C411yescharacteristic
5C2×#14519691—22no—
6#16839625C2211yescharacteristic
7C61×#381C411yescharacteristic
8C22⋊#92420—42no—
9C2×#11758222—41no—
10C2×#11758222—41no—
11C2×#11758222—44no—
12C22×Dic122C811yescharacteristic, complemented
13C22×D244C811yescharacteristic, complemented
14C22×C22⋊D61—21no—
15C22×C4×D61—21no—
16C2×C22⋊Dic61D412yes—
17#14519691—44no—
18#14519684—41no—
19C23×C4×C61C2×C411yescharacteristic
20C2×C22⋊C4×C61—21no—
21#95×C61—41no—
22C24×C61C22⋊C411yescharacteristic
23C23×D61—21no—
24C22×C4×C61—21no—
25C22×C4×C61—21no—
26C22×C4×C61—42no—
27C22×C4×C61—41no—
28C22×C4×C61C2×C811yescharacteristic
29C22×C4×C61M1611yescharacteristic
30C2×C22⋊D61—24no—
31C2×C22⋊D61—42no—
32C2×C22⋊D61—41no—
33C2×C22⋊D61—41no—
34C22×Dic61—21no—
35C22×Dic61—22no—
36#11758222—44no—
37#11758222—44no—
38#11758222—44no—
39#11758222—44no—
40C2×D244—41no—
41C2×D244—42no—
42C2×C4×D61—42no—
43C2×C4×D61—42no—
44C2×C4×D61—42no—
45C2×Dic122—41no—
46C2×Dic122—42no—
47C2×#92420—82no—
48C22⋊C4×C61—42no—
49C22⋊Dic61—42no—
50C23×C61—22no—
51C23×C61—81no—
52C23×C61C22⋊C811yescharacteristic
53C23×C61#9911yescharacteristic
54C23×C61#10011yescharacteristic
55C22×D61—22no—
56C22×D61—41no—
57C22×D61—41no—
58C22×D61—82no—
59C2×C4×C61—21no—
60C2×C4×C61—21no—
61C2×C4×C61—42no—
62C2×C4×C61—42no—
63C2×C4×C61—41no—
64C2×C4×C61—41no—
65C2×C4×C61—81no—
66C2×C4×C61—82no—
67C22⋊D61—44no—
68C22⋊D61—44no—
69C2×Dic61—22no—
70C2×Dic61—41no—
71C2×Dic61—41no—
72C2×Dic61—42no—
73C2×Dic61—82no—
74D244—42no—
75D244—42no—
76C4×D61—48no—
77Dic122—42no—
78Dic122—42no—
79#92420—162no—
80#7339—611nomaximal, Sylow
81C22×C61—21no—
82C22×C61—21no—
83C22×C61—41no—
84C22×C61—41no—
85C22×C61—41no—
86C22×C61—82no—
87C22×C61#32311yescharacteristic
88C22×C61AΣL(1,𝔽16)12yes—
89C2×D61—42no—
90C2×D61—82no—
91C2×D61—82no—
92C2×D61—82no—
93C4×C61—41no—
94C4×C61—41no—
95C4×C61—161no—
96Dic61—42no—
97Dic61—82no—
98#1782—611no—
99#1317—612no—
100C2×C61—22no—
101C2×C61—21no—
102C2×C61—41no—
103C2×C61—41no—
104C2×C61#131611yescharacteristic
105D61—82no—
106C22×#41—611no—
107C2×#99—1222no—
108#381—611no—
109#381#692311yescharacteristic
110#323—1222no—
111C61#733911yescharacteristic, complemented, Sylow
112C2×#41—2441no—
113C2×#41—2441no—
114C2×#41—2444no—
115C22×Q8—611no—
116C22×D4—611no—
117C22×D4—1221no—
118C23×C4—1221no—
119C23×C4C2×#692311yescharacteristic
120C2×C22⋊C4—21no—
121C2×C22⋊C4—612no—
122#99—2444no—
123C22⋊C8—2442no—
124#95—41no—
125#95—2441no—
126C24—1221no—
127C24C22⋊#692311yescharacteristic
128#41—2444no—
129#41—2444no—
130#41—2444no—
131#41—2444no—
132C2×Q8—2441no—
133C2×Q8—2442no—
134C2×D4—1224no—
135C2×D4—2441no—
136C2×D4—2442no—
137C2×D4—2442no—
138C2×D4—2441no—
139C2×D4—2441no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—42no—
143C22×C4—41no—
144C22×C4—1221no—
145C22×C4—1222no—
146C22×C4—2442no—
147C22×C4—2442no—
148C22×C4—2442no—
149C22×C4D61⋊C811yescharacteristic
150C22×C4#1175821311yescharacteristic
151C2×C8—4882no—
152C22⋊C4—42no—
153C22⋊C4—2442no—
154C23—22no—
155C23—81no—
156C23—1222no—
157C23—4882no—
158C23—2441no—
159C23—2441no—
160C23#1451983411yescharacteristic
161C23#1451983611yescharacteristic
162C23#1451983711yescharacteristic
163Q8—2442no—
164Q8—2442no—
165D4—2442no—
166D4—2442no—
167D4—2444no—
168D4—2444no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4—1222no—
178C2×C4—4882no—
179C2×C4—2448no—
180C2×C4—2442no—
181C2×C4—2441no—
182C2×C4—2441no—
183C8—9762no—
184C22—21no—
185C22—21no—
186C22—41no—
187C22—41no—
188C22—41no—
189C22—82no—
190C22—4882no—
191C22—4882no—
192C22—4882no—
193C22—2442no—
194C22#1684060611yescharacteristic
195C22#1684066312yes—
196C4—41no—
197C4—41no—
198C4—161no—
199C4—4882no—
200C4—2442no—
201C2—22no—
202C2—21no—
203C2—41no—
204C2—41no—
205C2—4882no—
206C2#2146074411yescharacteristic
subgroupG/H
centerC2#21460744
commutatorC22×C4×C61C2×C8
FrattiniC23×C4C2×#6923
FittingC61×#381C4
socleC2×C61#1316
prime radicalC22×#11758222C4
cosocle#16839625C22
hypercenter#381#6923
hypocenterC61#7339
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C23 ◁ C24 ◁ C23×C4 ◁ #381

Complements

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

NH ≅ G/Ntype
1. #21460745C2semidirect
12. C22×Dic122C8semidirect
13. C22×D244C8semidirect
111. C61#7339semidirect

Maximal subgroups

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

subgroupindex
#214607452
#214457362
#733961