Finite Group Databasebeta

← #30594772

Subgroups — #30594772

Order 15616.

244 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 50 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#21461070C211yesmaximal, characteristic
2#21461070C211yesmaximal, characteristic
3#21445888C211yesmaximal, characteristic
4#16840782—21no—
5#16840782—21no—
6#16840607C412yes—
7#16840607C412yes—
8#16840605—21no—
9#16840605—21no—
10C2×#14519736C2211yescharacteristic
11C2×C22⋊#92418C411yescharacteristic
12#16839516—21no—
13#16839516—21no—
14C2×C22⋊C8×C61C411yescharacteristic
15#14519844—41no—
16#14519844—41no—
17C22⋊#92420—22no—
18C22⋊#92420—22no—
19#14519832—41no—
20#14519832—41no—
21C22×#92418—21no—
22#14519736—41no—
23#14519736—41no—
24C2×C4⋊Dic61C2×C411yescharacteristic
25C2×C4⋊Dic61C2×C411yescharacteristic
26C2×C22⋊Dic61D411yescharacteristic
27C2×C22⋊Dic61Q811yescharacteristic
28C2×C4×Dic61D411yescharacteristic
29C2×C4×Dic61D411yescharacteristic
30C22⋊#92418—41no—
31C23×C4×C61C2×C411yescharacteristic
32C22×C8×C61—21no—
33C22⋊C8×C61—41no—
34C24×C61C4⋊C411yescharacteristic
35C22×C4×C61—21no—
36C22×C4×C61—21no—
37C22×C4×C61—42no—
38C22×C4×C61C4211yescharacteristic
39C22×C4×C61C22⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C22×Dic61C4⋊C411yescharacteristic
44C2×#92420—42no—
45C2×#92420—42no—
46C2×C8×C61—42no—
47C2×C8×C61—41no—
48C22⋊Dic61—41no—
49C22⋊Dic61—41no—
50C4⋊Dic61—41no—
51C4⋊Dic61—41no—
52C4×Dic61—21no—
53C4×Dic61—21no—
54C4×Dic61—21no—
55C4×Dic61—21no—
56C2×#92418—42no—
57C2×#92418—41no—
58C23×C61—21no—
59C23×C61—22no—
60C23×C61—41no—
61C23×C61—41no—
62C23×C61#9511yescharacteristic
63C2×C4×C61—22no—
64C2×C4×C61—21no—
65C2×C4×C61—22no—
66C2×C4×C61—42no—
67C2×C4×C61—42no—
68C2×C4×C61#9911yescharacteristic
69C2×C4×C61#9911yescharacteristic
70C2×Dic61—21no—
71C2×Dic61—21no—
72C2×Dic61—21no—
73C2×Dic61—21no—
74C2×Dic61—41no—
75C2×Dic61—41no—
76C2×Dic61—41no—
77C2×Dic61—41no—
78#92420—82no—
79#92420—82no—
80C8×C61—81no—
81#92418—81no—
82#7327—611nomaximal, Sylow
83C22×C61—21no—
84C22×C61—21no—
85C22×C61—41no—
86C22×C61—41no—
87C22×C61—41no—
88C22×C61—82no—
89C22×C61#34211yescharacteristic
90C22×C61#34412yes—
91C4×C61—21no—
92C4×C61—21no—
93C4×C61—41no—
94Dic61—41no—
95Dic61—41no—
96Dic61—41no—
97Dic61—41no—
98#1818—611no—
99#1464—611no—
100#1464—611no—
101C2×C61—22no—
102C2×C61—81no—
103C2×C61#130611yescharacteristic
104C2×C61#139511yescharacteristic
105C2×C61#139511yescharacteristic
106C2×#117—611no—
107#432—1221no—
108#432—1221no—
109C2×C22⋊C8—611no—
110C2×C22⋊C8#692311yescharacteristic
111#336—1221no—
112#336—1221no—
113#324—612no—
114#324—612no—
115#323—1221no—
116#323—1221no—
117C61#732711yescharacteristic, complemented, Sylow
118C23×C4C2×#692311yescharacteristic
119C22×C8—21no—
120C22×C8—1221no—
121#117—2441no—
122#117—2441no—
123C2×C4⋊C4—611no—
124C2×C4⋊C4—611no—
125C2×C22⋊C4—611no—
126C2×C22⋊C4—611no—
127C2×C42—611no—
128C2×C42—611no—
129C4⋊C8—2441no—
130C4⋊C8—2441no—
131C22⋊C8—41no—
132C22⋊C8—1222no—
133C22⋊C8—1222no—
134C22⋊C8—2441no—
135#97—2441no—
136#97—2441no—
137C24C4⋊#692311yescharacteristic
138C22×C4—21no—
139C22×C4—21no—
140C22×C4—42no—
141C22×C4—611no—
142C22×C4—611no—
143C22×C4—611no—
144C22×C4—611no—
145C22×C4C4×#692311yescharacteristic
146C22×C4C22⋊#692311yescharacteristic
147C2×C8—42no—
148C2×C8—41no—
149C2×C8—2442no—
150C2×C8—2442no—
151C2×C8—2442no—
152C2×C8—2441no—
153C4⋊C4—2441no—
154C4⋊C4—2441no—
155C22⋊C4—2441no—
156C22⋊C4—2441no—
157C42—1221no—
158C42—1221no—
159C42—1221no—
160C42—1221no—
161C23—21no—
162C23—22no—
163C23—41no—
164C23—41no—
165C23(C2×#6923)⋊C411yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—1221no—
172C2×C4—1221no—
173C2×C4—1221no—
174C2×C4—1221no—
175C2×C4—2441no—
176C2×C4—2441no—
177C2×C4—2441no—
178C2×C4—2441no—
179C2×C4#1451983511yescharacteristic
180C2×C4#1451983611yescharacteristic
181C8—81no—
182C8—4881no—
183C8—4882no—
184C8—4882no—
185C22—21no—
186C22—21no—
187C22—41no—
188C22—41no—
189C22—41no—
190C22—82no—
191C22#1684064011yescharacteristic
192C22#1684064312yes—
193C4—21no—
194C4—21no—
195C4—41no—
196C4—2441no—
197C4—2441no—
198C4—2441no—
199C4—2441no—
200C2—22no—
201C2—81no—
202C2#2146072211yescharacteristic
203C2#2146091911yescharacteristic
204C2#2146092011yescharacteristic
subgroupG/H
centerC22#16840640
commutatorC22×C4×C61C42
FrattiniC23×C4C2×#6923
FittingC2×C22⋊C8×C61C4
socleC22×C61#342
prime radicalC24×C61C4⋊C4
cosocleC2×#14519736C22
hypercenterC2×C22⋊C8#6923
hypocenterC61#7327
LCSG ▷ C22×C4×C61 ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C23×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
117. C61#7327semidirect

Maximal subgroups

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

subgroupindex
#214610702
#214458882
#732761