Finite Group Databasebeta

← #15674558

Subgroups — #15674558

Order 2944.

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

normal subgroups only

This group has 246 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
2#13092426C212yesmaximal
3#13092186C211yesmaximal, characteristic
4#13092177C212yesmaximal
5C23×#391C211yesmaximal, characteristic
6C22×Q8×C23C2211yescharacteristic
7C2×C4⋊C4×C23C2211yescharacteristic
8C2×C42×C23C2211yescharacteristic
9#10625097C2212yes—
10#10625095—22no—
11C2×#67267C2212yes—
12#10625061—22no—
13#10625059—22no—
14C23×#95—22no—
15#10625017—22no—
16#10625017—22no—
17C2×Q8×C23—21no—
18C2×Q8×C23—22no—
19C2×Q8×C23—22no—
20C2×Q8×C23Q812yescomplemented
21C22×C4×C23—21no—
22C22×C4×C23—21no—
23C22×C4×C23D412yes—
24C22×C4×C23C2311yescharacteristic
25C2×Dic46—22no—
26C4⋊C4×C23—22no—
27C42×C23—22no—
28C22⋊Dic23—22no—
29C4⋊Dic23—22no—
30C4⋊Dic23D412yes—
31C4⋊Dic23D412yes—
32Dic23⋊C4—24no—
33C4×Dic23—22no—
34#67267—22no—
35#67267—22no—
36C2×C23⋊C8—22no—
37C23×C23C2×D411yescharacteristic
38Q8×C23—24no—
39Q8×C23—42no—
40C2×C4×C23—22no—
41C2×C4×C23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23—41no—
45C2×C4×C23—41no—
46C2×C4×C23—41no—
47C2×C4×C23—42no—
48C2×C4×C23C2×D412yes—
49C2×C4×C23C2×Q811yescharacteristic
50C2×C4×C23#4111yescharacteristic
51C2×C4×C23#4112yes—
52C2×Dic23—22no—
53C2×Dic23—22no—
54Dic46—82no—
55C23⋊C8—42no—
56#2028—231nomaximal, Sylow
57C22×C23—21no—
58C22×C23—21no—
59C22×C23#12011yescharacteristic
60C22×C23C22⋊Q811yescharacteristic
61C22×C23#12411yescharacteristic
62C4×C23—42no—
63C4×C23—42no—
64C4×C23—42no—
65C4×C23C22⋊Q812yes—
66C4×C23#12412yes—
67Dic23—42no—
68Dic23—42no—
69#544—231no—
70#419—232no—
71#391D2311yescharacteristic
72#343—231no—
73#339—232no—
74C2×C23—21no—
75C2×C23—21no—
76C2×C23#39311yescharacteristic
77C2×C23#45511yescharacteristic
78C2×C23#45611yescharacteristic
79C22×Q8C2×D2311yescharacteristic
80C2×M16—232no—
81C4⋊Q8—462no—
82#125—462no—
83C22⋊Q8—462no—
84#117—232no—
85C2×C4⋊C4C2×D2311yescharacteristic
86C2×C42C2×D2311yescharacteristic
87#103—462no—
88#103—462no—
89#95—22no—
90C23#202811yescharacteristic, complemented, Sylow
91C2×Q8—21no—
92C2×Q8—22no—
93C2×Q8—22no—
94C2×Q8—462no—
95C2×Q8Dic4612yescomplemented
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D2312yes—
99C22×C4C22×D2311yescharacteristic
100M16—462no—
101M16—462no—
102C2×C8—462no—
103C4⋊C4—22no—
104C4⋊C4—232no—
105C4⋊C4—232no—
106C4⋊C4—462no—
107C4⋊C4—464no—
108C22⋊C4—462no—
109C42—22no—
110C42—462no—
111C23C2×C22⋊D2311yescharacteristic
112Q8—24no—
113Q8—42no—
114Q8—1842no—
115C2×C4—22no—
116C2×C4—22no—
117C2×C4—22no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—42no—
123C2×C4—462no—
124C2×C4—462no—
125C2×C4C2×Dic4611yescharacteristic
126C2×C4#6728811yescharacteristic
127C2×C4D4×D2312yes—
128C2×C4#6729012yes—
129C8—922no—
130C22—21no—
131C22—21no—
132C22#1062509511yescharacteristic
133C22#1062510711yescharacteristic
134C22#1062510811yescharacteristic
135C4—42no—
136C4—42no—
137C4—42no—
138C4—922no—
139C4—922no—
140C4#1062504912yes—
141C4#1062505612yes—
142C2—21no—
143C2—21no—
144C2#1309232911yescharacteristic
145C2#1309259411yescharacteristic
146C2#1309259911yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#391C2
socleC22×C23#120
prime radicalC23×C23C2×D4
hypercenter#391D23
hypocenterC23#2028
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
20. C2×Q8×C23Q8semidirect
90. C23#2028semidirect
95. C2×Q8Dic46semidirect

Maximal subgroups

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

subgroupindex
#130930482
#130924262
#130921862
#130921772
C23×#3912
#202823