Finite Group Databasebeta

← #15674381

Subgroups — #15674381

Order 2944.

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

normal subgroups only

This group has 324 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×#10625095C211yesmaximal, characteristic
2C4×C22⋊Dic23C211yesmaximal, characteristic
3#13092183C214yesmaximal
4C23×#380C211yesmaximal, characteristic
5C23×C4×C23C2211yescharacteristic
6C22×Dic46C411yescharacteristic, complemented
7C2×C4⋊C4×C23—21no—
8C2×C22⋊C4×C23C2212yes—
9C2×C22⋊Dic23C2212yes—
10C2×C22⋊Dic23C2212yes—
11C2×C4⋊Dic23C411yescharacteristic, complemented
12#10625095—21no—
13#10625095—21no—
14#10625095—21no—
15#10625095—21no—
16C2×Dic23⋊C4C412yescomplemented
17C2×C4×Dic23—21no—
18C23×#95—21no—
19C23⋊#95—21no—
20C24×C23C2311yescharacteristic
21C22×C4×C23—22no—
22C22×C4×C23—42no—
23C22×C4×C23C2×C411yescharacteristic
24C22×C4×C23C2×C411yescharacteristic
25C22×C4×C23D411yescharacteristic
26C22×C4×C23D411yescharacteristic
27C22×C4×C23D411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×Dic23—22no—
30C22×Dic23C2×C412yes—
31C22×Dic23C2×C412yes—
32C2×Dic46—21no—
33C2×Dic46—21no—
34C2×Dic46—42no—
35C4⋊C4×C23—42no—
36C22⋊C4×C23—24no—
37C22⋊Dic23—22no—
38C22⋊Dic23—22no—
39C22⋊Dic23—22no—
40C22⋊Dic23Q814yescomplemented
41C4⋊Dic23—21no—
42C4⋊Dic23—21no—
43Dic23⋊C4—22no—
44Dic23⋊C4—22no—
45C4×Dic23—42no—
46C23×C23—41no—
47C23×C23—41no—
48C23×C23C22×C411yescharacteristic
49C23×C23C2×D411yescharacteristic
50C23×C23C2×D411yescharacteristic
51C23×C23C2×Q812yes—
52C23×C23#4112yes—
53C2×C4×C23—22no—
54C2×C4×C23—22no—
55C2×C4×C23—22no—
56C2×C4×C23—41no—
57C2×C4×C23—41no—
58C2×C4×C23—41no—
59C2×C4×C23—42no—
60C2×C4×C23—42no—
61C2×C4×C23—42no—
62C2×C4×C23C22⋊C411yescharacteristic
63C2×C4×C23C22⋊C411yescharacteristic
64C2×C4×C23C22⋊C411yescharacteristic
65C2×C4×C23C22⋊C411yescharacteristic
66C2×Dic23—22no—
67C2×Dic23—22no—
68C2×Dic23—24no—
69C2×Dic23—42no—
70C2×Dic23—42no—
71C2×Dic23—42no—
72C2×Dic23—42no—
73Dic46—42no—
74Dic46—42no—
75#1996—231nomaximal, Sylow
76C22×C23—21no—
77C22×C23—21no—
78C22×C23—21no—
79C22×C23—21no—
80C22×C23—21no—
81C22×C23—21no—
82C22×C23—42no—
83C22×C23—42no—
84C22×C23C2×C22⋊C411yescharacteristic
85C22×C23C4×Q812yes—
86C22×C23C22⋊Q812yes—
87C22×C23#12411yescharacteristic
88C22×C23C4⋊Q811yescharacteristic
89C4×C23—21no—
90C4×C23—21no—
91C4×C23—21no—
92C4×C23—82no—
93C4×C23#9912yes—
94Dic23—44no—
95Dic23—42no—
96Dic23—42no—
97C2×C22⋊Q8—231no—
98#380D2311yescharacteristic
99C4×C22⋊C4—231no—
100#342—234no—
101C2×C23—22no—
102C2×C23—21no—
103C2×C23—22no—
104C2×C23—21no—
105C2×C23#39111yescharacteristic
106C2×C23C2×#9911yescharacteristic
107C2×C23#41011yescharacteristic
108C22×Q8—231no—
109C23×C4C2×D2311yescharacteristic
110C22⋊Q8—461no—
111C22⋊Q8—461no—
112C22⋊Q8—461no—
113C22⋊Q8—461no—
114C2×C4⋊C4—21no—
115C2×C4⋊C4—232no—
116C2×C4⋊C4—231no—
117C2×C22⋊C4—232no—
118C2×C22⋊C4—232no—
119C2×C22⋊C4C2×D2312yes—
120C2×C42—461no—
121#95—21no—
122#95—461no—
123C23#199611yescharacteristic, complemented, Sylow
124C24C22×D2311yescharacteristic
125C2×Q8—461no—
126C2×Q8—461no—
127C2×Q8—922no—
128C22×C4—22no—
129C22×C4—42no—
130C22×C4—232no—
131C22×C4—232no—
132C22×C4—462no—
133C22×C4C4×D2311yescharacteristic
134C22×C4C4×D2311yescharacteristic
135C22×C4D9211yescharacteristic
136C22×C4D9211yescharacteristic
137C22×C4C22⋊D2311yescharacteristic
138C22×C4C22⋊D2311yescharacteristic
139C4⋊C4—42no—
140C4⋊C4—462no—
141C4⋊C4—462no—
142C4⋊C4—461no—
143C4⋊C4—461no—
144C22⋊C4—24no—
145C22⋊C4—234no—
146C22⋊C4—462no—
147C22⋊C4—462no—
148C22⋊C4—462no—
149C42—922no—
150C23—41no—
151C23—41no—
152C23C2×C4×D2311yescharacteristic
153C23C2×D9211yescharacteristic
154C23#6729012yes—
155C23Q8×D2312yes—
156C23C2×C22⋊D2311yescharacteristic
157Q8—922no—
158Q8—922no—
159C2×C4—22no—
160C2×C4—22no—
161C2×C4—22no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—464no—
169C2×C4—462no—
170C2×C4—462no—
171C2×C4—922no—
172C2×C4—922no—
173C2×C4—922no—
174C2×C4—922no—
175C2×C4(C2×D23)⋊C411yescharacteristic
176C2×C4(C2×D23)⋊C411yescharacteristic
177C2×C4(C2×D23)⋊C411yescharacteristic
178C2×C4(C2×D23)⋊C411yescharacteristic
179C22—21no—
180C22—21no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22—21no—
185C22—42no—
186C22—42no—
187C22#1062505812yes—
188C22#1062506812yes—
189C22C2×(C2×D23)⋊C411yescharacteristic
190C22#1062510711yescharacteristic
191C22#1062511511yescharacteristic
192C4—21no—
193C4—21no—
194C4—21no—
195C4—82no—
196C4—924no—
197C4—922no—
198C4—922no—
199C4#1062498812yes—
200C2—21no—
201C2—22no—
202C2—22no—
203C2—21no—
204C2#1309232211yescharacteristic
205C2C2×#1062498811yescharacteristic
206C2#1309239011yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC23×C23C22×C4
FrattiniC24C22×D23
FittingC23×#380C2
socleC22×C23C2×C22⋊C4
prime radical, cosocleC24×C23C23
hypercenter#380D23
hypocenterC23#1996
LCSG ▷ C23×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C23×C4 ◁ #380

Complements

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

NH ≅ G/Ntype
6. C22×Dic46C4semidirect
11. C2×C4⋊Dic23C4semidirect
16. C2×Dic23⋊C4C4semidirect
40. C22⋊Dic23Q8semidirect
123. C23#1996semidirect

Maximal subgroups

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

subgroupindex
C2×#106250952
C4×C22⋊Dic232
#130921832
C23×#3802
#199623