Finite Group Databasebeta

← #15674564

Subgroups — #15674564

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#13093043C211yesmaximal, characteristic
2#13092280C212yesmaximal
3#13092184C211yesmaximal, characteristic
4#13092183C212yesmaximal
5C23×#381C211yesmaximal, characteristic
6C23×C4×C23C2211yescharacteristic
7C2×C22⋊C4×C23C2211yescharacteristic
8C2×C22⋊C4×C23C2211yescharacteristic
9C2×C22⋊Dic23C2212yes—
10C2×C22⋊Dic23C2212yes—
11#10625095—22no—
12#10625049—24no—
13C23×#95—22no—
14C23⋊#95—24no—
15C24×C23C2311yescharacteristic
16C22×C4×C23—22no—
17C22×C4×C23—21no—
18C22×C4×C23—21no—
19C22×C4×C23—22no—
20C22×C4×C23—21no—
21C22×C4×C23D412yes—
22C22×C4×C23Q812yescomplemented
23C22×Dic23—22no—
24C22×Dic23D414yes—
25C2×Dic46—22no—
26C22⋊C4×C23—22no—
27C22⋊C4×C23—22no—
28C22⋊Dic23—22no—
29C22⋊Dic23—22no—
30C22⋊Dic23—22no—
31C22⋊Dic23—22no—
32C4⋊Dic23—22no—
33Dic23⋊C4—24no—
34C23×C23—42no—
35C23×C23C2×D412yes—
36C23×C23C2×D411yescharacteristic
37C23×C23C2×Q811yescharacteristic
38C23×C23#4111yescharacteristic
39C23×C23#4112yes—
40C2×C4×C23—22no—
41C2×C4×C23—24no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23—42no—
45C2×C4×C23—41no—
46C2×C4×C23—42no—
47C2×C4×C23—42no—
48C2×C4×C23—41no—
49C2×Dic23—24no—
50C2×Dic23—44no—
51C2×Dic23—44no—
52C2×Dic23—42no—
53Dic46—82no—
54#2030—231nomaximal, Sylow
55C22×C23—24no—
56C22×C23—22no—
57C22×C23—41no—
58C22×C23—41no—
59C22×C23—42no—
60C22×C23#12011yescharacteristic
61C22×C23C22⋊Q812yes—
62C22×C23C22⋊Q811yescharacteristic
63C22×C23#12412yes—
64C22×C23#12411yescharacteristic
65C4×C23—42no—
66C4×C23—42no—
67C4×C23—81no—
68Dic23—44no—
69Dic23—82no—
70#543—231no—
71#381—232no—
72#381D2311yescharacteristic
73#342—232no—
74#342—231no—
75C2×C23—22no—
76C2×C23—21no—
77C2×C23—22no—
78C2×C23—21no—
79C2×C23#39311yescharacteristic
80C2×C23#45812yes—
81C23×C4C2×D2311yescharacteristic
82C22⋊Q8—464no—
83C22⋊Q8—462no—
84C2×C22⋊C4—232no—
85C2×C22⋊C4—232no—
86C2×C22⋊C4C2×D2311yescharacteristic
87C2×C22⋊C4C2×D2311yescharacteristic
88#95—22no—
89#95—464no—
90C23#203011yescharacteristic, complemented, Sylow
91C24C22×D2311yescharacteristic
92C2×Q8—462no—
93C22×C4—21no—
94C22×C4—22no—
95C22×C4—22no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4—234no—
99C22×C4—462no—
100C22×C4Dic4612yescomplemented
101C22×C4C22⋊D2312yes—
102C4⋊C4—464no—
103C4⋊C4—462no—
104C22⋊C4—22no—
105C22⋊C4—22no—
106C22⋊C4—462no—
107C22⋊C4—462no—
108C22⋊C4—462no—
109C22⋊C4—462no—
110C23—42no—
111C23C2×Dic4611yescharacteristic
112C23#6728811yescharacteristic
113C23D4×D2312yes—
114C23#6729012yes—
115C23C2×C22⋊D2311yescharacteristic
116Q8—1842no—
117C2×C4—24no—
118C2×C4—22no—
119C2×C4—22no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—42no—
124C2×C4—42no—
125C2×C4—41no—
126C2×C4—464no—
127C2×C4—924no—
128C2×C4—924no—
129C2×C4—922no—
130C22—22no—
131C22—24no—
132C22—41no—
133C22—41no—
134C22—42no—
135C22#1062504912yes—
136C22#1062505612yes—
137C22#1062509511yescharacteristic
138C22#1062510711yescharacteristic
139C22#1062510811yescharacteristic
140C4—42no—
141C4—42no—
142C4—81no—
143C4—924no—
144C4—1842no—
145C2—21no—
146C2—22no—
147C2—22no—
148C2—21no—
149C2#1309232911yescharacteristic
150C2#1309260612yes—
subgroupG/H
centerC22#10625108
commutator, prime radical, cosocleC24×C23C23
FrattiniC24C22×D23
FittingC23×#381C2
socleC22×C23#120
hypercenter#381D23
hypocenterC23#2030
LCSG ▷ C24×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C24 ◁ #381

Complements

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

NH ≅ G/Ntype
22. C22×C4×C23Q8semidirect
90. C23#2030semidirect
100. C22×C4Dic46semidirect

Maximal subgroups

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

subgroupindex
#130930432
#130922802
#130921842
#130921832
C23×#3812
#203023