Finite Group Databasebeta

← #15673855

Subgroups — #15673855

Order 2944.

378 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 93 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×#10625100C211yesmaximal, characteristic
2C2×#10624988C212yesmaximal
3#13092280C211yesmaximal, characteristic, complemented
4#13092183C212yesmaximal, complemented
5C2×C23×#117C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C22×C22⋊D23C2211yescharacteristic
8C23×#117—24no—
9C2×C4⋊C4×C23—21no—
10C2×C22⋊C4×C23C2212yes—
11C2×C42×C23—21no—
12C2×C22⋊Dic23C2212yes—
13C2×C22⋊Dic23C2211yescharacteristic
14#10625100—22no—
15#10625100—21no—
16#10625100—21no—
17C2×(C2×D23)⋊C4C412yescomplemented
18C2×Dic23⋊C4C412yescomplemented
19C23⋊#95—22no—
20#10624988—24no—
21C24×C23C2311yescharacteristic
22C23×D23C2×C411yescharacteristic
23C22×C4×C23—22no—
24C22×C4×C23—22no—
25C22×C4×C23—22no—
26C22×C4×C23C2×C412yes—
27C22×C4×C23D412yes—
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C2×C22⋊D23—21no—
31C2×C22⋊D23—21no—
32C2×C22⋊D23—22no—
33C2×C22⋊D23—22no—
34C22×Dic23—22no—
35C22×Dic23C2×C411yescharacteristic
36C22×Dic23C2×C412yes—
37C4⋊C4×C23—24no—
38C22⋊C4×C23—22no—
39C22⋊C4×C23D414yes—
40C42×C23—24no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—22no—
44C22⋊Dic23—22no—
45(C2×D23)⋊C4—22no—
46(C2×D23)⋊C4—22no—
47Dic23⋊C4—22no—
48Dic23⋊C4—22no—
49C23×C23—42no—
50C23×C23C22×C411yescharacteristic
51C23×C23C2×D411yescharacteristic
52C23×C23C2×D411yescharacteristic
53C23×C23C2×D412yes—
54C23×C23#4112yes—
55C22×D23—21no—
56C22×D23—22no—
57C22×D23—42no—
58C2×C4×C23—24no—
59C2×C4×C23—21no—
60C2×C4×C23—21no—
61C2×C4×C23—24no—
62C2×C4×C23—21no—
63C2×C4×C23—21no—
64C2×C4×C23—24no—
65C2×C4×C23—44no—
66C2×C4×C23C22⋊C412yes—
67C2×C4×C23C22⋊C412yes—
68C22⋊D23—41no—
69C22⋊D23—42no—
70C22⋊D23—41no—
71C2×Dic23—21no—
72C2×Dic23—22no—
73C2×Dic23—22no—
74C2×Dic23—42no—
75C2×Dic23—44no—
76C2×Dic23—42no—
77#1899—231nomaximal, Sylow
78C22×C23—22no—
79C22×C23—22no—
80C22×C23—22no—
81C22×C23—42no—
82C22×C23—42no—
83C22×C23C2×C22⋊C411yescharacteristic
84C22×C23C4×D412yes—
85C22×C23#12011yescharacteristic
86C22×C23#12112yes—
87C22×C23#12311yescharacteristic
88C2×D23—41no—
89C2×D23—42no—
90C2×D23—82no—
91C4×C23—22no—
92C4×C23—22no—
93C4×C23—44no—
94Dic23—41no—
95Dic23—42no—
96Dic23—82no—
97C2×#123—231no—
98C2×#117D2311yescharacteristic, complemented
99C2×#99—232no—
100#381—231no—
101#342—232no—
102C2×C23—22no—
103C2×C23—21no—
104C2×C23—22no—
105C2×C23—21no—
106C2×C23#38611yescharacteristic
107C2×C23#41012yes—
108D23—81no—
109C22×D4—231no—
110C23×C4C2×D2311yescharacteristic
111#123—462no—
112#123—461no—
113#123—461no—
114#117—24no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—232no—
117C2×C22⋊C4—231no—
118C2×C22⋊C4—232no—
119C2×C22⋊C4—232no—
120C2×C22⋊C4C2×D2312yes—
121C2×C42—21no—
122#99—464no—
123#95—462no—
124C23#189911yescharacteristic, complemented, Sylow
125C24—231no—
126C24C22×D2311yescharacteristic
127C2×D4—461no—
128C2×D4—462no—
129C2×D4—462no—
130C2×D4—461no—
131C22×C4—22no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—231no—
135C22×C4—232no—
136C22×C4—462no—
137C22×C4C4×D2312yes—
138C22×C4D9212yes—
139C22×C4C22⋊D2311yescharacteristic
140C22×C4C22⋊D2311yescharacteristic
141C4⋊C4—24no—
142C4⋊C4—462no—
143C4⋊C4—462no—
144C22⋊C4—22no—
145C22⋊C4—461no—
146C22⋊C4—461no—
147C22⋊C4—462no—
148C22⋊C4—462no—
149C22⋊C4—462no—
150C22⋊C4—462no—
151C22⋊C4C22⋊D2314yes—
152C42—24no—
153C23—42no—
154C23—461no—
155C23—462no—
156C23—922no—
157C23C2×C4×D2311yescharacteristic
158C23C2×D9211yescharacteristic
159C23#6728812yes—
160C23C2×C22⋊D2311yescharacteristic
161C23C2×C22⋊D2312yes—
162D4—921no—
163D4—922no—
164D4—921no—
165C2×C4—24no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—24no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—24no—
172C2×C4—44no—
173C2×C4—462no—
174C2×C4—461no—
175C2×C4—462no—
176C2×C4—922no—
177C2×C4—924no—
178C2×C4—922no—
179C2×C4(C2×D23)⋊C412yes—
180C2×C4(C2×D23)⋊C412yes—
181C22—22no—
182C22—22no—
183C22—22no—
184C22—42no—
185C22—42no—
186C22—922no—
187C22—921no—
188C22—1842no—
189C22C2×(C2×D23)⋊C411yescharacteristic
190C22C4×C22⋊D2312yes—
191C22#1062510011yescharacteristic
192C22#1062510112yes—
193C22#1062512411yescharacteristic
194C4—22no—
195C4—22no—
196C4—44no—
197C4—922no—
198C4—921no—
199C4—1842no—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2—1841no—
205C2#1309229611yescharacteristic
206C2#1309239012yes—
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC2×C23×#117C2
socleC22×C23C2×C22⋊C4
prime radicalC22×C22⋊D23C22
cosocleC24×C23C23
hypercenterC2×#117D23
hypocenterC23#1899
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
3. #13092280C2semidirect
4. #13092183C2semidirect
5. C2×C23×#117C2semidirect
17. C2×(C2×D23)⋊C4C4semidirect
18. C2×Dic23⋊C4C4semidirect
98. C2×#117D23semidirect
124. C23#1899semidirect

Maximal subgroups

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

subgroupindex
C2×#106251002
C2×#106249882
#130922802
#130921832
C2×C23×#1172
#189923