Finite Group Databasebeta

← #15674553

Subgroups — #15674553

Order 2944.

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

normal subgroups only

This group has 282 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#13093048C211yesmaximal, characteristic, complemented
2#13092422C212yesmaximal
3#13092186C211yesmaximal, characteristic, complemented
4#13092177C212yesmaximal, complemented
5C23×#390C211yesmaximal, characteristic
6C22×D4×C23C2211yescharacteristic
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×C22⋊C4×C23—22no—
9C2×C42×C23C2211yescharacteristic
10#10625097C2212yes—
11#10625095—22no—
12C2×#67267C2212yes—
13#10625061—22no—
14#10625059—22no—
15#10625014—22no—
16#10625014—22no—
17C24×C23—21no—
18C2×D4×C23—22no—
19C2×D4×C23—22no—
20C2×D4×C23—21no—
21C2×D4×C23Q812yescomplemented
22C22×C4×C23—21no—
23C22×C4×C23D412yes—
24C22×C4×C23C2311yescharacteristic
25C2×Dic46—22no—
26C4⋊C4×C23—22no—
27C22⋊C4×C23—44no—
28C42×C23—22no—
29C22⋊Dic23—22no—
30C4⋊Dic23—22no—
31C4⋊Dic23D412yes—
32C4⋊Dic23D412yes—
33Dic23⋊C4—24no—
34C4×Dic23—22no—
35#67267—22no—
36#67267—22no—
37C2×C23⋊C8—22no—
38C23×C23—22no—
39C23×C23—42no—
40C23×C23—42no—
41C23×C23—41no—
42C23×C23—41no—
43C23×C23C2×D411yescharacteristic
44D4×C23—24no—
45D4×C23—42no—
46C2×C4×C23—22no—
47C2×C4×C23—22no—
48C2×C4×C23—41no—
49C2×C4×C23—41no—
50C2×C4×C23—42no—
51C2×C4×C23C2×D412yes—
52C2×C4×C23C2×Q811yescharacteristic
53C2×C4×C23#4111yescharacteristic
54C2×C4×C23#4112yes—
55C2×Dic23—22no—
56C2×Dic23—22no—
57Dic46—82no—
58C23⋊C8—42no—
59#2027—231nomaximal, Sylow
60C22×C23—21no—
61C22×C23—21no—
62C22×C23—44no—
63C22×C23—42no—
64C22×C23—82no—
65C22×C23—81no—
66C22×C23—81no—
67C22×C23#12011yescharacteristic
68C22×C23C22⋊Q811yescharacteristic
69C22×C23#12411yescharacteristic
70C4×C23—42no—
71C4×C23—42no—
72C4×C23C22⋊Q812yes—
73C4×C23#12412yes—
74Dic23—42no—
75Dic23—42no—
76#544—231no—
77#418—232no—
78#390D2311yescharacteristic
79#343—231no—
80#339—232no—
81C2×C23—21no—
82C2×C23—21no—
83C2×C23—82no—
84C2×C23#39311yescharacteristic
85C2×C23#45311yescharacteristic
86C2×C23#45411yescharacteristic
87C22×D4C2×D2311yescharacteristic
88C2×M16—232no—
89C4⋊Q8—462no—
90#125—462no—
91C22⋊Q8—462no—
92#117—232no—
93C2×C4⋊C4C2×D2311yescharacteristic
94C2×C22⋊C4—22no—
95C2×C42C2×D2311yescharacteristic
96#102—462no—
97#102—462no—
98C23#202711yescharacteristic, complemented, Sylow
99C24—21no—
100C2×Q8—462no—
101C2×D4—21no—
102C2×D4—22no—
103C2×D4—22no—
104C2×D4Dic4612yescomplemented
105C22×C4—21no—
106C22×C4C22⋊D2312yes—
107C22×C4C22×D2311yescharacteristic
108M16—462no—
109M16—462no—
110C2×C8—462no—
111C4⋊C4—22no—
112C4⋊C4—232no—
113C4⋊C4—232no—
114C4⋊C4—462no—
115C4⋊C4—464no—
116C22⋊C4—44no—
117C22⋊C4—462no—
118C42—22no—
119C42—462no—
120C23—22no—
121C23—42no—
122C23—42no—
123C23—41no—
124C23—41no—
125C23C2×C22⋊D2311yescharacteristic
126Q8—1842no—
127D4—24no—
128D4—42no—
129C2×C4—22no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—42no—
134C2×C4—462no—
135C2×C4—462no—
136C2×C4C2×Dic4611yescharacteristic
137C2×C4#6728811yescharacteristic
138C2×C4D4×D2312yes—
139C2×C4#6729012yes—
140C8—922no—
141C22—21no—
142C22—21no—
143C22—44no—
144C22—42no—
145C22—82no—
146C22—81no—
147C22—81no—
148C22#1062509511yescharacteristic
149C22#1062510711yescharacteristic
150C22#1062510811yescharacteristic
151C4—42no—
152C4—42no—
153C4—922no—
154C4—922no—
155C4#1062504912yes—
156C4#1062505612yes—
157C2—21no—
158C2—21no—
159C2—82no—
160C2#1309232911yescharacteristic
161C2#1309258411yescharacteristic
162C2#1309258911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#390C2
socleC22×C23#120
prime radicalC22×D4×C23C22
hypercenter#390D23
hypocenterC23#2027
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. #13093048C2semidirect
3. #13092186C2semidirect
4. #13092177C2semidirect
21. C2×D4×C23Q8semidirect
98. C23#2027semidirect
104. C2×D4Dic46semidirect

Maximal subgroups

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

subgroupindex
#130930482
#130924222
#130921862
#130921772
C23×#3902
#202723