Finite Group Databasebeta

← #15672019

Subgroups — #15672019

Order 2944.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D23C211yesmaximal, characteristic
2#13092472C212yesmaximal, complemented
3#13092157C211yesmaximal, characteristic, complemented
4#13092156C212yesmaximal, complemented
5C23×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D23C411yescharacteristic
7C2×D4×D23C411yescharacteristic
8C23×#124C2211yescharacteristic
9#10625118C411yescharacteristic
10#10625107C411yescharacteristic
11#10625056—22no—
12C22⋊C4×D23—22no—
13#10625046C2211yescharacteristic
14C42×D23C2211yescharacteristic
15C23×#97C2212yescomplemented
16(C2×D23)⋊C8—22no—
17Dic23⋊C8—22no—
18#10624985C2212yescomplemented
19C23×D23—21no—
20C2×Q8×C23C2×C411yescharacteristic
21C2×D4×C23C2×C411yescharacteristic
22C2×C22⋊D23—21no—
23Q8×D23—42no—
24D4×D23—42no—
25C2×D92C2×C411yescharacteristic
26C2×C4×D23—21no—
27C2×C4×D23C2×C411yescharacteristic
28C2×C4×D23D412yes—
29C2×Dic46—21no—
30C2×Dic46C2×C411yescharacteristic
31C2×C8×C23—22no—
32C22⋊C4×C23—22no—
33C42×C23C2311yescharacteristic
34C22⋊Dic23—22no—
35(C2×D23)⋊C4—22no—
36(C2×D23)⋊C4—22no—
37C4×Dic23C2×C411yescharacteristic
38C4×Dic23D412yes—
39C2×C23⋊C8—22no—
40C23×C23—21no—
41C22×D23—21no—
42C22×D23—44no—
43C22×D23—42no—
44C22×D23C22⋊C411yescharacteristic
45Q8×C23—41no—
46D4×C23—41no—
47C2×C4×C23—21no—
48C2×C4×C23C22×C411yescharacteristic
49C2×C4×C23C2×D412yes—
50C22⋊D23—42no—
51C2×Dic23—21no—
52C2×Dic23C22⋊C412yes—
53C2×Dic23C22⋊C411yescharacteristic
54D92—41no—
55C4×D23—22no—
56C4×D23—42no—
57C4×D23—42no—
58Dic46—42no—
59Dic46—41no—
60C8×C23—42no—
61C23⋊C8—42no—
62#1533—231nomaximal, Sylow
63C22×C23—41no—
64C22×C23—42no—
65C22×C23C2×C22⋊C411yescharacteristic
66C2×D23—22no—
67C2×D23—41no—
68C2×D23—42no—
69C2×D23—84no—
70C2×D23#10012yes—
71C4×C23—21no—
72C4×C23—22no—
73C4×C23—41no—
74Dic23—21no—
75Dic23—22no—
76Dic23—41no—
77C2×#124—231no—
78#432—232no—
79#329—231no—
80#329—232no—
81#329D2311yescharacteristic, complemented
82C2×C23—81no—
83C2×C23C2×#10011yescharacteristic
84C2×C23#42112yes—
85D23—22no—
86D23—81no—
87C22×Q8—231no—
88C22×D4—231no—
89#124—231no—
90#124—231no—
91#124—231no—
92#124—462no—
93#124C2×D2311yescharacteristic
94C2×C22⋊C4—462no—
95C2×C42—231no—
96C4⋊C8—462no—
97C22⋊C8—462no—
98#97—232no—
99#97C2×D2312yescomplemented
100C23#153311yescharacteristic, complemented, Sylow
101C24—461no—
102C2×Q8—231no—
103C2×Q8—461no—
104C2×Q8—922no—
105C2×Q8C4×D2311yescharacteristic
106C2×D4—231no—
107C2×D4—461no—
108C2×D4—922no—
109C2×D4C4×D2311yescharacteristic
110C22×C4—231no—
111C22×C4—232no—
112C22×C4—461no—
113C2×C8—22no—
114C2×C8—462no—
115C22⋊C4—22no—
116C22⋊C4—462no—
117C22⋊C4—462no—
118C22⋊C4—462no—
119C42—231no—
120C42—232no—
121C42C22×D2311yescharacteristic
122C23—21no—
123C23—231no—
124C23—461no—
125C23—922no—
126C23—924no—
127Q8—41no—
128Q8—921no—
129Q8—922no—
130D4—41no—
131D4—921no—
132D4—922no—
133C2×C4—21no—
134C2×C4—232no—
135C2×C4—231no—
136C2×C4—462no—
137C2×C4—461no—
138C2×C4—922no—
139C2×C4—922no—
140C2×C4C2×C4×D2311yescharacteristic
141C2×C4D4×D2312yes—
142C8—42no—
143C8—922no—
144C22—41no—
145C22—42no—
146C22—232no—
147C22—462no—
148C22—921no—
149C22—922no—
150C22—1844no—
151C22C22⋊C4×D2311yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—461no—
156C4—462no—
157C4—921no—
158C2—81no—
159C2—462no—
160C2—1841no—
161C2#100×D2311yescharacteristic
162C2#1309243212yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#329C2
socleC22×C23C2×C22⋊C4
prime radicalC2×D4×D23C4
cosocleC42×C23C23
hypercenter#329D23
hypocenterC23#1533
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #13092472C2semidirect
3. #13092157C2semidirect
4. #13092156C2semidirect
5. C23×#329C2semidirect
15. C23×#97C22semidirect
18. #10624985C22semidirect
81. #329D23semidirect
99. #97C2×D23semidirect
100. C23#1533semidirect

Maximal subgroups

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

subgroupindex
#124×D232
#130924722
#130921572
#130921562
C23×#3292
#153323