Finite Group Databasebeta

← #15675083

Subgroups — #15675083

Order 2944.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092987C211yesmaximal, characteristic
2#101×D23C212yesmaximal, complemented
3#13092215C212yesmaximal, complemented
4#13092214C211yesmaximal, characteristic, complemented
5C23×#355C211yesmaximal, characteristic, complemented
6C2×Q8×D23C2211yescharacteristic
7C2×#67290C411yescharacteristic
8C23×#124C2211yescharacteristic
9#10625115C2211yescharacteristic
10#10625107C411yescharacteristic
11M16×D23—22no—
12#10625054—22no—
13#10625049—22no—
14#10625043C411yescharacteristic
15#10625040C411yescharacteristic
16C23×#101C2212yes—
17#10625018C2212yes—
18#10625006—22no—
19C2×Q8×C23C2311yescharacteristic
20C2×D4×C23C2×C411yescharacteristic
21C2×C22⋊D23—21no—
22C22×Dic23—21no—
23Q8×D23—42no—
24#67290—42no—
25C2×C4×D23C2×C411yescharacteristic
26C2×C4×D23D412yes—
27C2×Dic46C2×C411yescharacteristic
28C2×Dic46C2×C411yescharacteristic
29C2×Dic46D412yes—
30M16×C23—22no—
31C22⋊C4×C23—22no—
32C42×C23C2×C411yescharacteristic
33C22⋊Dic23—22no—
34(C2×D23)⋊C4—21no—
35C4⋊Dic23—22no—
36Dic23⋊C4—22no—
37Dic23⋊C4—21no—
38C4×Dic23C2×C411yescharacteristic
39#67267—22no—
40#67262—42no—
41C8×D23—42no—
42C23×C23—21no—
43C22×D23C22⋊C411yescharacteristic
44Q8×C23—41no—
45D4×C23—41no—
46C2×C4×C23—21no—
47C2×C4×C23C22×C411yescharacteristic
48C2×C4×C23C2×D412yes—
49C22⋊D23—42no—
50C2×Dic23—21no—
51C2×Dic23—21no—
52C2×Dic23—42no—
53C2×Dic23C22⋊C411yescharacteristic
54C2×Dic23C22⋊C412yes—
55C4×D23—22no—
56C4×D23—22no—
57C4×D23—22no—
58Dic46—41no—
59Dic46—42no—
60Dic46—41no—
61C8×C23—42no—
62C23⋊C8—42no—
63#2133—231nomaximal, Sylow
64C22×C23—42no—
65C22×C23—41no—
66C22×C23C2×C22⋊C411yescharacteristic
67C2×D23—41no—
68C2×D23#9912yes—
69C4×C23—22no—
70C4×C23—21no—
71C4×C23—41no—
72Dic23—21no—
73Dic23—22no—
74Dic23—41no—
75Dic23—41no—
76#536—231no—
77C2×#101—232no—
78#356—232no—
79#355—231no—
80#355D2311yescharacteristic, complemented
81C2×C23—21no—
82C2×C23—81no—
83C2×C23C2×#9911yescharacteristic
84D23—22no—
85C2×#41—231no—
86C22×Q8—231no—
87C2×M16—462no—
88C4⋊Q8—231no—
89C4⋊Q8—231no—
90#124—231no—
91#124C2×D2311yescharacteristic
92#123—462no—
93C22⋊Q8—462no—
94#117—231no—
95#101—232no—
96#101—462no—
97#101C2×D2312yes—
98C23#213311yescharacteristic, complemented, Sylow
99#41—922no—
100C2×Q8—231no—
101C2×Q8—232no—
102C2×Q8—231no—
103C2×Q8—922no—
104C2×Q8C22×D2311yescharacteristic
105C2×D4—461no—
106C2×D4C4×D2311yescharacteristic
107C22×C4—231no—
108C22×C4—232no—
109C22×C4—461no—
110M16—22no—
111M16—462no—
112M16—922no—
113C2×C8—922no—
114C4⋊C4—461no—
115C4⋊C4—462no—
116C4⋊C4—462no—
117C22⋊C4—22no—
118C22⋊C4—461no—
119C22⋊C4—462no—
120C42—231no—
121C42C4×D2311yescharacteristic
122C23—21no—
123C23—231no—
124Q8—41no—
125Q8—922no—
126Q8—921no—
127Q8—921no—
128D4—41no—
129D4—922no—
130C2×C4—21no—
131C2×C4—232no—
132C2×C4—231no—
133C2×C4—462no—
134C2×C4—462no—
135C2×C4—462no—
136C2×C4—461no—
137C2×C4—461no—
138C2×C4—922no—
139C2×C4C2×C4×D2311yescharacteristic
140C2×C4D4×D2312yes—
141C8—42no—
142C8—922no—
143C22—42no—
144C22—41no—
145C22—232no—
146C22—921no—
147C22C22⋊C4×D2311yescharacteristic
148C4—22no—
149C4—21no—
150C4—41no—
151C4—461no—
152C4—462no—
153C4—921no—
154C4—921no—
155C2—21no—
156C2—81no—
157C2—462no—
158C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#355C2
socleC2×C23C2×#99
prime radicalC2×#67290C4
cosocleC2×Q8×C23C23
hypercenter#355D23
hypocenterC23#2133
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
2. #101×D23C2semidirect
3. #13092215C2semidirect
4. #13092214C2semidirect
5. C23×#355C2semidirect
80. #355D23semidirect
98. C23#2133semidirect

Maximal subgroups

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

subgroupindex
#130929872
#101×D232
#130922152
#130922142
C23×#3552
#213323