Finite Group Databasebeta

← #15674626

Subgroups — #15674626

Order 2944.

290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092998C211yesmaximal, characteristic
2C2×#10624987C212yesmaximal, complemented
3#13092416C212yesmaximal, complemented
4#13092186C211yesmaximal, characteristic, complemented
5C23×#382C211yesmaximal, characteristic, complemented
6C2×#67288C2212yes—
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×C4⋊C4×C23C2211yescharacteristic
9C2×C42×C23C2211yescharacteristic
10#10625101—22no—
11C2×#67267C2212yes—
12#10625068—22no—
13#10625066—22no—
14C23×#95—22no—
15#10624992—22no—
16#10624991—22no—
17#10624987—24no—
18C22×C4×C23—21no—
19C22×C4×C23—21no—
20C22×C4×C23D412yes—
21C22×C4×C23C2311yescharacteristic
22C2×C22⋊D23—22no—
23#67288—22no—
24#67288—22no—
25#67288—22no—
26#67288—22no—
27C2×D92—22no—
28C2×D92D412yes—
29C2×C4×D23—22no—
30C2×Dic46D412yes—
31C4⋊C4×C23—22no—
32C4⋊C4×C23—22no—
33C42×C23—21no—
34C42×C23D412yescomplemented
35(C2×D23)⋊C4—24no—
36C4⋊Dic23—22no—
37#67267—22no—
38#67267—22no—
39C2×C23⋊C8—22no—
40C23×C23C2×D411yescharacteristic
41C22×D23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—22no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23—42no—
47C2×C4×C23—42no—
48C2×C4×C23—41no—
49C2×C4×C23C2×D411yescharacteristic
50C2×C4×C23C2×D412yes—
51C2×C4×C23#4111yescharacteristic
52C2×C4×C23#4112yes—
53C22⋊D23—42no—
54C22⋊D23—42no—
55C2×Dic23—22no—
56D92—22no—
57D92—22no—
58D92—82no—
59C4×D23—42no—
60C4×D23—42no—
61Dic46—22no—
62Dic46—22no—
63C23⋊C8—42no—
64#2040—231nomaximal, Sylow
65C22×C23—21no—
66C22×C23—21no—
67C22×C23#12011yescharacteristic
68C22×C23#12111yescharacteristic
69C22×C23#12411yescharacteristic
70C2×D23—42no—
71C2×D23—42no—
72C2×D23—42no—
73C4×C23—42no—
74C4×C23—42no—
75C4×C23—81no—
76C4×C23#12112yes—
77C4×C23#12312yes—
78Dic23—42no—
79#537—231no—
80C2×#104—232no—
81#417—232no—
82#382D2311yescharacteristic, complemented
83#343—231no—
84C2×C23—21no—
85C2×C23—21no—
86C2×C23#39411yescharacteristic
87C2×C23#45411yescharacteristic
88C2×C23#45511yescharacteristic
89D23—82no—
90C2×#41—232no—
91C2×M16—232no—
92C22⋊Q8—462no—
93#121—462no—
94#121—462no—
95C2×C4⋊C4C2×D2311yescharacteristic
96C2×C4⋊C4C2×D2311yescharacteristic
97C2×C42C2×D2311yescharacteristic
98#104—464no—
99#103—462no—
100#102—462no—
101#95—22no—
102C23#204011yescharacteristic, complemented, Sylow
103#41—462no—
104#41—462no—
105#41—462no—
106#41—462no—
107C2×Q8—232no—
108C2×D4—232no—
109C2×D4—462no—
110C2×D4—462no—
111C22×C4—21no—
112C22×C4—21no—
113C22×C4—462no—
114C22×C4C22⋊D2312yes—
115C22×C4C22×D2311yescharacteristic
116M16—462no—
117M16—462no—
118C2×C8—462no—
119C4⋊C4—22no—
120C4⋊C4—22no—
121C4⋊C4—462no—
122C22⋊C4—464no—
123C42—21no—
124C42D9212yescomplemented
125C23—462no—
126C23C2×C22⋊D2311yescharacteristic
127Q8—462no—
128Q8—462no—
129D4—462no—
130D4—462no—
131D4—922no—
132D4—922no—
133D4—1842no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—462no—
142C2×C4—922no—
143C2×C4—922no—
144C2×C4C2×D9211yescharacteristic
145C2×C4#6728811yescharacteristic
146C2×C4D4×D2312yes—
147C2×C4#6729212yes—
148C8—922no—
149C22—21no—
150C22—21no—
151C22—922no—
152C22—922no—
153C22—922no—
154C22#1062510111yescharacteristic
155C22#1062510811yescharacteristic
156C22#1062511811yescharacteristic
157C4—42no—
158C4—42no—
159C4—81no—
160C4—922no—
161C4#1062506512yes—
162C4#1062506612yes—
163C2—21no—
164C2—21no—
165C2—1842no—
166C2#1309233411yescharacteristic
167C2#1309258911yescharacteristic
168C2#1309259411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#382C2
socleC22×C23#120
prime radical#13092998C2
hypercenter#382D23
hypocenterC23#2040
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #382

Complements

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

NH ≅ G/Ntype
2. C2×#10624987C2semidirect
3. #13092416C2semidirect
4. #13092186C2semidirect
5. C23×#382C2semidirect
34. C42×C23D4semidirect
82. #382D23semidirect
102. C23#2040semidirect
124. C42D92semidirect

Maximal subgroups

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

subgroupindex
#130929982
C2×#106249872
#130924162
#130921862
C23×#3822
#204023