Finite Group Databasebeta

← #15673470

Subgroups — #15673470

Order 2944.

504 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 504 conjugacy classes of subgroups — too many to draw. Only its 81 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
1C2×C22⋊C4×D23C211yesmaximal, characteristic
2#13092272C212yesmaximal
3#13092184C211yesmaximal, characteristic, complemented
4#13092183C212yesmaximal, complemented
5C23×#342C211yesmaximal, characteristic, complemented
6C24×D23C2211yescharacteristic
7C22×C4×D23C412yescomplemented
8C2×C22⋊C4×C23C2212yes—
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊Dic23C2212yes—
11C2×C22⋊Dic23C2211yescharacteristic
12C2×(C2×D23)⋊C4—24no—
13C2×(C2×D23)⋊C4C412yescomplemented
14C22⋊C4×D23—24no—
15C24×C23C2311yescharacteristic
16C23×D23—22no—
17C23×D23—21no—
18C23×D23—21no—
19C23×D23—44no—
20C23×D23C2×C411yescharacteristic
21C23×D23C2×C411yescharacteristic
22C23×D23D414yes—
23C22×C4×C23—22no—
24C22×C4×C23C2×C412yes—
25C22×Dic23—22no—
26C22×Dic23C2×C412yes—
27C2×C4×D23—22no—
28C2×C4×D23—22no—
29C2×C4×D23—44no—
30C22⋊C4×C23—22no—
31C22⋊C4×C23—22no—
32C22⋊C4×C23—22no—
33C22⋊Dic23—22no—
34C22⋊Dic23—22no—
35C22⋊Dic23—22no—
36(C2×D23)⋊C4—24no—
37(C2×D23)⋊C4—48no—
38C23×C23—42no—
39C23×C23C22×C411yescharacteristic
40C23×C23C2×D412yes—
41C23×C23#4112yes—
42C23×C23#4111yescharacteristic
43C23×C23#4111yescharacteristic
44C22×D23—21no—
45C22×D23—21no—
46C22×D23—24no—
47C22×D23—21no—
48C22×D23—21no—
49C22×D23—24no—
50C22×D23—24no—
51C22×D23—28no—
52C22×D23—42no—
53C22×D23—44no—
54C22×D23—48no—
55C22×D23—44no—
56C22×D23—44no—
57C22×D23C22⋊C412yes—
58C22×D23C22⋊C412yes—
59C2×C4×C23—22no—
60C2×C4×C23—42no—
61C2×C4×C23—44no—
62C2×C4×C23—42no—
63C2×Dic23—22no—
64C2×Dic23—42no—
65C2×Dic23—44no—
66C2×Dic23—42no—
67C4×D23—44no—
68C4×D23—44no—
69#1819—231nomaximal, Sylow
70C22×C23—22no—
71C22×C23—24no—
72C22×C23—42no—
73C22×C23—41no—
74C22×C23—41no—
75C22×C23C2×C22⋊C411yescharacteristic
76C22×C23#11711yescharacteristic
77C22×C23#11711yescharacteristic
78C22×C23#12312yes—
79C22×C23#12312yes—
80C2×D23—24no—
81C2×D23—24no—
82C2×D23—22no—
83C2×D23—22no—
84C2×D23—22no—
85C2×D23—24no—
86C2×D23—48no—
87C2×D23—48no—
88C2×D23—42no—
89C2×D23—42no—
90C2×D23#9914yes—
91C4×C23—42no—
92C4×C23—82no—
93Dic23—42no—
94Dic23—82no—
95C22×C22⋊C4—231no—
96#379—232no—
97#342—232no—
98#342—231no—
99#342D2311yescharacteristic, complemented
100C2×C23—22no—
101C2×C23—22no—
102C2×C23—21no—
103C2×C23—21no—
104C2×C23#38111yescharacteristic
105C2×C23C2×#9912yes—
106D23—24no—
107D23—42no—
108C25—231no—
109C23×C4—232no—
110C2×C22⋊C4—231no—
111C2×C22⋊C4—232no—
112C2×C22⋊C4—232no—
113C2×C22⋊C4—464no—
114C2×C22⋊C4—464no—
115C2×C22⋊C4C2×D2312yes—
116C2×C22⋊C4C2×D2311yescharacteristic
117C23#181911yescharacteristic, complemented, Sylow
118C24—231no—
119C24—234no—
120C24—231no—
121C24—462no—
122C24—461no—
123C24—461no—
124C24—924no—
125C24C22×D2311yescharacteristic
126C22×C4—22no—
127C22×C4—232no—
128C22×C4—462no—
129C22×C4—462no—
130C22×C4—462no—
131C22×C4—924no—
132C22×C4C4×D2312yes—
133C22⋊C4—22no—
134C22⋊C4—22no—
135C22⋊C4—22no—
136C22⋊C4—464no—
137C22⋊C4—462no—
138C22⋊C4—462no—
139C22⋊C4—462no—
140C22⋊C4—928no—
141C23—42no—
142C23—232no—
143C23—232no—
144C23—464no—
145C23—468no—
146C23—461no—
147C23—461no—
148C23—461no—
149C23—464no—
150C23—461no—
151C23—464no—
152C23—922no—
153C23—924no—
154C23—928no—
155C23—924no—
156C23—924no—
157C23C2×C4×D2311yescharacteristic
158C23#6728812yes—
159C23D4×D2312yes—
160C23#6729011yescharacteristic
161C23#6729211yescharacteristic
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—44no—
165C2×C4—42no—
166C2×C4—462no—
167C2×C4—924no—
168C2×C4—924no—
169C2×C4—922no—
170C2×C4—924no—
171C2×C4—922no—
172C22—22no—
173C22—24no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—234no—
178C22—464no—
179C22—464no—
180C22—462no—
181C22—462no—
182C22—464no—
183C22—462no—
184C22—928no—
185C22—928no—
186C22—922no—
187C22—922no—
188C22#1062504311yescharacteristic
189C22C22⋊C4×D2311yescharacteristic
190C22#1062505412yes—
191C22#1062506311yescharacteristic
192C22#1062506512yes—
193C4—42no—
194C4—82no—
195C4—922no—
196C4—1842no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—21no—
201C2—464no—
202C2—922no—
203C2#1309227911yescharacteristic
204C2#99×D2312yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#342C2
socleC22×C23C2×C22⋊C4
prime radicalC24×D23C22
cosocleC24×C23C23
hypercenter#342D23
hypocenterC23#1819
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #342

Complements

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

NH ≅ G/Ntype
3. #13092184C2semidirect
4. #13092183C2semidirect
5. C23×#342C2semidirect
7. C22×C4×D23C4semidirect
13. C2×(C2×D23)⋊C4C4semidirect
99. #342D23semidirect
117. C23#1819semidirect

Maximal subgroups

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

subgroupindex
C2×C22⋊C4×D232
#130922722
#130921842
#130921832
C23×#3422
#181923