Finite Group Databasebeta

← #15674528

Subgroups — #15674528

Order 2944.

430 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 430 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092979C211yesmaximal, characteristic
2C2×#10625100C212yesmaximal, complemented
3C2×#10624988C212yesmaximal, complemented
4#13092184C211yesmaximal, characteristic, complemented
5C23×#381C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C22×C22⋊D23C2212yes—
8C2×C22⋊C4×C23C2211yescharacteristic
9C2×C22⋊C4×C23C2211yescharacteristic
10C2×C22⋊Dic23C2212yes—
11#10625101—22no—
12#10625100—24no—
13#10625100—24no—
14C2×(C2×D23)⋊C4—22no—
15C2×Dic23⋊C4—22no—
16#10625057—22no—
17#10625053—22no—
18C23×#95—22no—
19#10624988—24no—
20C24×C23C2311yescharacteristic
21C23×D23D412yes—
22C22×C4×C23—22no—
23C22×C4×C23—22no—
24C22×C4×C23—21no—
25C22×C4×C23—21no—
26C22×C4×C23—21no—
27C22×C4×C23D412yes—
28C22×C4×C23D412yescomplemented
29C2×C22⋊D23—22no—
30C2×C22⋊D23—22no—
31C2×C22⋊D23—22no—
32C2×C22⋊D23—22no—
33C2×C22⋊D23—22no—
34C2×C22⋊D23—22no—
35C22×Dic23—22no—
36C22×Dic23D412yes—
37C2×D92—22no—
38C22⋊C4×C23—22no—
39C22⋊C4×C23—22no—
40C22⋊Dic23—22no—
41C22⋊Dic23D414yescomplemented
42(C2×D23)⋊C4—24no—
43(C2×D23)⋊C4—28no—
44C4⋊Dic23—22no—
45Dic23⋊C4—28no—
46C23×C23—42no—
47C23×C23C2×D411yescharacteristic
48C23×C23C2×D412yes—
49C23×C23C2×D412yes—
50C23×C23C2×D411yescharacteristic
51C23×C23#4111yescharacteristic
52C22×D23—22no—
53C22×D23—22no—
54C22×D23—22no—
55C22×D23—44no—
56C2×C4×C23—24no—
57C2×C4×C23—22no—
58C2×C4×C23—22no—
59C2×C4×C23—41no—
60C2×C4×C23—42no—
61C2×C4×C23—41no—
62C2×C4×C23—42no—
63C2×C4×C23—42no—
64C2×C4×C23—41no—
65C22⋊D23—42no—
66C22⋊D23—42no—
67C22⋊D23—42no—
68C22⋊D23—42no—
69C2×Dic23—22no—
70C2×Dic23—24no—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—44no—
74D92—82no—
75#2022—231nomaximal, Sylow
76C22×C23—24no—
77C22×C23—22no—
78C22×C23—41no—
79C22×C23—42no—
80C22×C23—41no—
81C22×C23#12012yes—
82C22×C23#12011yescharacteristic
83C22×C23#12112yes—
84C22×C23#12111yescharacteristic
85C22×C23#12711yescharacteristic
86C2×D23—44no—
87C2×D23—42no—
88C2×D23—44no—
89C2×D23—82no—
90C4×C23—42no—
91C4×C23—42no—
92C4×C23—81no—
93Dic23—44no—
94Dic23—42no—
95#534—231no—
96C2×#123—232no—
97C2×#99—232no—
98#381D2311yescharacteristic, complemented
99#342—231no—
100C2×C23—22no—
101C2×C23—21no—
102C2×C23—22no—
103C2×C23—21no—
104C2×C23#39211yescharacteristic
105C2×C23#45812yes—
106D23—82no—
107C22×D4—232no—
108C23×C4C2×D2311yescharacteristic
109#123—462no—
110#123—464no—
111#123—464no—
112#121—462no—
113#120—462no—
114C2×C4⋊C4—462no—
115C2×C22⋊C4—232no—
116C2×C22⋊C4—462no—
117C2×C22⋊C4C2×D2311yescharacteristic
118C2×C22⋊C4C2×D2311yescharacteristic
119#99—464no—
120#95—22no—
121C23#202211yescharacteristic, complemented, Sylow
122C24—232no—
123C24C22×D2311yescharacteristic
124C2×D4—462no—
125C2×D4—462no—
126C2×D4—462no—
127C2×D4—462no—
128C2×D4—462no—
129C2×D4—462no—
130C2×D4—462no—
131C22×C4—21no—
132C22×C4—22no—
133C22×C4—22no—
134C22×C4—21no—
135C22×C4—21no—
136C22×C4—232no—
137C22×C4—462no—
138C22×C4D9212yescomplemented
139C22×C4C22⋊D2312yes—
140C4⋊C4—468no—
141C4⋊C4—462no—
142C22⋊C4—22no—
143C22⋊C4—22no—
144C22⋊C4—234no—
145C22⋊C4—468no—
146C22⋊C4—464no—
147C22⋊C4—462no—
148C23—42no—
149C23—462no—
150C23—462no—
151C23—462no—
152C23—924no—
153C23C2×D9211yescharacteristic
154C23#6728811yescharacteristic
155C23D4×D2312yes—
156C23D4×D2312yes—
157C23C2×C22⋊D2311yescharacteristic
158D4—922no—
159D4—922no—
160D4—922no—
161D4—922no—
162D4—1842no—
163C2×C4—24no—
164C2×C4—22no—
165C2×C4—22no—
166C2×C4—42no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—41no—
172C2×C4—464no—
173C2×C4—462no—
174C2×C4—462no—
175C2×C4—462no—
176C2×C4—924no—
177C22—22no—
178C22—24no—
179C22—41no—
180C22—41no—
181C22—42no—
182C22—924no—
183C22—922no—
184C22—924no—
185C22—1842no—
186C22#1062505312yes—
187C22#1062505512yes—
188C22#1062510111yescharacteristic
189C22#1062510811yescharacteristic
190C22#1062511111yescharacteristic
191C4—42no—
192C4—42no—
193C4—81no—
194C4—924no—
195C4—922no—
196C2—21no—
197C2—22no—
198C2—22no—
199C2—21no—
200C2—1842no—
201C2#1309232611yescharacteristic
202C2#1309260612yes—
subgroupG/H
centerC22#10625108
commutator, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#381C2
socleC22×C23#120
prime radical#13092979C2
hypercenter#381D23
hypocenterC23#2022
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#10625100C2semidirect
3. C2×#10624988C2semidirect
4. #13092184C2semidirect
5. C23×#381C2semidirect
28. C22×C4×C23D4semidirect
41. C22⋊Dic23D4semidirect
98. #381D23semidirect
121. C23#2022semidirect
138. C22×C4D92semidirect

Maximal subgroups

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

subgroupindex
#130929792
C2×#106251002
C2×#106249882
#130921842
C23×#3812
#202223