Finite Group Databasebeta

← #15673932

Subgroups — #15673932

Order 2944.

314 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 85 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#13092991C211yesmaximal, characteristic
2#13092895C211yesmaximal, characteristic, complemented
3#13092433C212yesmaximal
4#13092174C212yesmaximal, complemented
5C2×C23×#101C211yesmaximal, characteristic, complemented
6C22×Q8×C23C2211yescharacteristic
7C2×#67288C2211yescharacteristic
8C2×M16×C23C2212yes—
9#10625118C412yescomplemented
10#10625117—22no—
11Q8×Dic23—24no—
12#10625115C412yescomplemented
13#10625100—22no—
14#10625097—22no—
15#10625097C2211yescharacteristic
16#10625097C2212yes—
17C23×#101—22no—
18#10625007—24no—
19C2×Q8×C23—22no—
20C2×Q8×C23—22no—
21C2×Q8×C23C2×C412yes—
22C2×Q8×C23D412yes—
23C22×C4×C23D412yes—
24C22×C4×C23C2311yescharacteristic
25C2×C22⋊D23—21no—
26#67288—22no—
27#67288—22no—
28C2×D92C2×C411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46C2×C411yescharacteristic
31M16×C23—22no—
32M16×C23—22no—
33C2×C8×C23—22no—
34C22⋊Dic23—22no—
35C22⋊Dic23—21no—
36(C2×D23)⋊C4—24no—
37C4⋊Dic23—24no—
38C4⋊Dic23—22no—
39C4⋊Dic23—21no—
40Dic23⋊C4—24no—
41C4×Dic23—24no—
42C4×Dic23C2×C412yes—
43C4×Dic23D414yes—
44C23×C23C2×D411yescharacteristic
45C22×D23—21no—
46Q8×C23—24no—
47Q8×C23—24no—
48C2×C4×C23—22no—
49C2×C4×C23—22no—
50C2×C4×C23C22⋊C414yes—
51C2×C4×C23C22×C411yescharacteristic
52C2×C4×C23C2×D412yes—
53C2×C4×C23C2×D411yescharacteristic
54C2×C4×C23#4112yes—
55C22⋊D23—41no—
56C22⋊D23—41no—
57C2×Dic23—22no—
58C2×Dic23—21no—
59C2×Dic23—24no—
60D92—22no—
61C4×D23—42no—
62Dic46—22no—
63C8×C23—42no—
64#1912—231nomaximal, Sylow
65C22×C23—41no—
66C22×C23C2×C22⋊C411yescharacteristic
67C22×C23#12011yescharacteristic
68C22×C23#12311yescharacteristic
69C2×D23—42no—
70C2×D23—41no—
71C4×C23—24no—
72C4×C23C4×D412yes—
73C4×C23#12112yes—
74Dic23—44no—
75Dic23—42no—
76Dic23—41no—
77#536—231no—
78#519—231no—
79#421—232no—
80C2×#101D2311yescharacteristic, complemented
81H(3,ℤ/4)—232no—
82C2×C23—21no—
83C2×C23—21no—
84C2×C23—21no—
85C2×C23#38611yescharacteristic
86D23—81no—
87C2×#41—231no—
88C22×Q8C2×D2311yescharacteristic
89C2×M16C2×D2312yes—
90C4⋊Q8—232no—
91#124—232no—
92#123—462no—
93C22⋊Q8—462no—
94C4×Q8—464no—
95#117—232no—
96#117—231no—
97#117—462no—
98#104—464no—
99#101—22no—
100C23#191211yescharacteristic, complemented, Sylow
101#41—462no—
102#41—462no—
103C2×Q8—22no—
104C2×Q8—22no—
105C2×Q8—231no—
106C2×Q8C4×D2312yes—
107C2×Q8C22⋊D2312yes—
108C2×D4—231no—
109C2×D4—461no—
110C22×C4—461no—
111C22×C4D9212yes—
112C22×C4C22×D2311yescharacteristic
113M16—22no—
114M16—22no—
115C2×C8—22no—
116C4⋊C4—464no—
117C4⋊C4—464no—
118C4⋊C4—462no—
119C4⋊C4—461no—
120C22⋊C4—462no—
121C22⋊C4—461no—
122C22⋊C4—464no—
123C42—232no—
124C42—234no—
125C42—464no—
126C23—461no—
127C23C2×D9211yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—462no—
131D4—462no—
132D4—921no—
133D4—921no—
134C2×C4—22no—
135C2×C4—22no—
136C2×C4—464no—
137C2×C4—462no—
138C2×C4—461no—
139C2×C4—922no—
140C2×C4(C2×D23)⋊C414yes—
141C2×C4C2×C4×D2311yescharacteristic
142C2×C4D4×D2312yes—
143C2×C4#6729012yes—
144C2×C4C2×C22⋊D2311yescharacteristic
145C8—42no—
146C22—41no—
147C22—922no—
148C22—921no—
149C22#1062505311yescharacteristic
150C22#1062505711yescharacteristic
151C22C2×(C2×D23)⋊C411yescharacteristic
152C4—24no—
153C4—924no—
154C4—922no—
155C4—921no—
156C4(C22⋊D23)⋊C412yes—
157C4#1062511012yes—
158C2—21no—
159C2—21no—
160C2—21no—
161C2—1841no—
162C2#1309229411yescharacteristic
subgroupG/H
centerC2#13092294
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#101C2
socleC2×C23#386
prime radicalC2×#67288C22
cosocleC22×C4×C23C23
hypercenterC2×#101D23
hypocenterC23#1912
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
2. #13092895C2semidirect
4. #13092174C2semidirect
5. C2×C23×#101C2semidirect
9. #10625118C4semidirect
12. #10625115C4semidirect
80. C2×#101D23semidirect
100. C23#1912semidirect

Maximal subgroups

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

subgroupindex
#130929912
#130928952
#130924332
#130921742
C2×C23×#1012
#191223