Finite Group Databasebeta

← #15675428

Subgroups — #15675428

Order 2944.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#13093147C211yesmaximal, characteristic, complemented
2#13092602C212yesmaximal
3#13092599C211yesmaximal, characteristic
4#13092215C212yesmaximal, complemented
5C23×#356C211yesmaximal, characteristic, complemented
6#10625158C2211yescharacteristic
7C23×C4⋊Q8C2211yescharacteristic
8#10625115—21no—
9#10625115C2212yes—
10#10625113—21no—
11#10625080—22no—
12#10625059—22no—
13#10625058—22no—
14C4×Dic46—21no—
15C23×#101C2212yes—
16#10625018C2211yescharacteristic
17#10625007—22no—
18#10624987—21no—
19C2×Q8×C23D411yescharacteristic
20C2×Q8×C23C2311yescharacteristic
21#67292—41no—
22Q8×D23—41no—
23#67288—22no—
24#67288—21no—
25C2×Dic46—21no—
26C2×Dic46—21no—
27C2×Dic46D412yes—
28M16×C23—22no—
29C4⋊C4×C23—22no—
30C42×C23D411yescharacteristic
31#67275—41no—
32#67274—41no—
33C4⋊Dic23—21no—
34Dic23⋊C4—22no—
35Dic23⋊C4—22no—
36Dic23⋊C4—22no—
37C4×Dic23—22no—
38C4×Dic23—21no—
39C4×Dic23D412yes—
40#67267—21no—
41Dic92—42no—
42#67263—42no—
43Q8×C23—41no—
44Q8×C23—41no—
45C2×C4×C23—21no—
46C2×C4×C23—21no—
47C2×C4×C23C2×D411yescharacteristic
48C2×C4×C23C2×D412yes—
49C22⋊D23—41no—
50C2×Dic23—22no—
51C2×Dic23—22no—
52D92—22no—
53D92—21no—
54C4×D23—41no—
55C4×D23—42no—
56Dic46—24no—
57Dic46—22no—
58Dic46—21no—
59Dic46—42no—
60Dic46—81no—
61C8×C23—42no—
62C23⋊C8—41no—
63#2205—231nomaximal, Sylow
64C22×C23#12011yescharacteristic
65C2×D23—41no—
66C4×C23—22no—
67C4×C23—21no—
68C4×C23—22no—
69C4×C23—41no—
70Dic23—24no—
71Dic23—41no—
72Dic23—42no—
73Q82—231no—
74#456—231no—
75#456—232no—
76#356—232no—
77#356D2311yescharacteristic, complemented
78C2×C23—21no—
79C2×C23B(4,𝔽2)11yescharacteristic
80D23—81no—
812−1+4—231no—
82#137—462no—
83#137—461no—
84C4⋊Q8—232no—
85C4⋊Q8—462no—
86C4⋊Q8—461no—
87C4⋊Q8C2×D2311yescharacteristic
88C4×Q8—462no—
89C4×Q8—461no—
90#104—462no—
91#104—461no—
92#101—231no—
93#101C2×D2312yes—
94C23#220511yescharacteristic, complemented, Sylow
95#41—461no—
96#41—462no—
97#41—921no—
98C2×Q8—232no—
99C2×Q8—461no—
100C2×Q8—461no—
101C2×Q8—921no—
102C2×Q8D9211yescharacteristic
103C2×Q8C22×D2311yescharacteristic
104Q16—922no—
105Q16—921no—
106SD16—922no—
107SD16—921no—
108M16—22no—
109M16—461no—
110C4⋊C4—22no—
111C4⋊C4—462no—
112C4⋊C4—461no—
113C4⋊C4—462no—
114C4⋊C4—462no—
115C42—232no—
116C42—462no—
117C42—461no—
118C42D9211yescharacteristic
119Q8—41no—
120Q8—41no—
121Q8—464no—
122Q8—462no—
123Q8—461no—
124Q8—922no—
125Q8—1841no—
126D4—462no—
127D4—461no—
128D4—921no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—462no—
132C2×C4—462no—
133C2×C4—922no—
134C2×C4—921no—
135C2×C4C2×D9211yescharacteristic
136C2×C4D4×D2312yes—
137C8—42no—
138C8—921no—
139C22—921no—
140C22#1062505311yescharacteristic
141C4—22no—
142C4—22no—
143C4—21no—
144C4—41no—
145C4—464no—
146C4—922no—
147C4—921no—
148C2—21no—
149C2—1841no—
150C2#1309260511yescharacteristic
subgroupG/H
centerC2#13092605
commutator, cosocleC2×Q8×C23C23
FrattiniC2×Q8C22×D23
FittingC23×#356C2
socleC2×C23B(4,𝔽2)
prime radical#10625158C22
hypercenter#356D23
hypocenterC23#2205
LCSG ▷ C2×Q8×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
1. #13093147C2semidirect
4. #13092215C2semidirect
5. C23×#356C2semidirect
77. #356D23semidirect
94. C23#2205semidirect

Maximal subgroups

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

subgroupindex
#130931472
#130926022
#130925992
#130922152
C23×#3562
#220523