Finite Group Databasebeta

← #15675081

Subgroups — #15675081

Order 2944.

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

normal subgroups only

This group has 250 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#13092968C211yesmaximal, characteristic
2#13092400C212yesmaximal, complemented
3#13092216C211yesmaximal, characteristic, complemented
4#13092213C212yesmaximal, complemented
5C23×#356C211yesmaximal, characteristic, complemented
6C2×#67292C411yescharacteristic
7C2×#67292C2211yescharacteristic
8C23×C4⋊Q8C2211yescharacteristic
9#10625118C411yescharacteristic
10#10625118C2211yescharacteristic
11M16×D23—22no—
12#10625066—22no—
13#10625064—22no—
14#10625045C411yescharacteristic
15C42×D23C411yescharacteristic
16C23×#101C2212yes—
17#10625018C2212yes—
18#10625005—22no—
19C2×Q8×C23C2×C411yescharacteristic
20C2×Q8×C23C2311yescharacteristic
21#67292—41no—
22#67292—41no—
23#67292—41no—
24#67292—41no—
25C2×D92—22no—
26C2×D92—21no—
27C2×D92C2×C411yescharacteristic
28C2×D92C2×C411yescharacteristic
29C2×D92D412yes—
30C2×C4×D23—21no—
31C2×C4×D23—21no—
32C2×C4×D23C2×C411yescharacteristic
33C2×C4×D23D412yes—
34M16×C23—22no—
35C4⋊C4×C23—22no—
36C42×C23C2×C411yescharacteristic
37(C2×D23)⋊C4—22no—
38(C2×D23)⋊C4—22no—
39C4×Dic23—21no—
40C4×Dic23C2×C411yescharacteristic
41#67267—22no—
42#67262—42no—
43C8×D23—42no—
44C22×D23—21no—
45C22×D23C22⋊C412yes—
46C22×D23C22⋊C411yescharacteristic
47Q8×C23—41no—
48Q8×C23—41no—
49C2×C4×C23—21no—
50C2×C4×C23—21no—
51C2×C4×C23C22×C411yescharacteristic
52C2×C4×C23C2×D412yes—
53C2×Dic23—21no—
54C2×Dic23C22⋊C411yescharacteristic
55D92—41no—
56D92—42no—
57D92—41no—
58D92—44no—
59D92—42no—
60C4×D23—22no—
61C4×D23—22no—
62C4×D23—21no—
63C4×D23—21no—
64C4×D23—42no—
65C4×D23—41no—
66C4×D23—41no—
67C8×C23—42no—
68C23⋊C8—42no—
69#2132—231nomaximal, Sylow
70C22×C23C2×C22⋊C411yescharacteristic
71C2×D23—21no—
72C2×D23—22no—
73C2×D23—41no—
74C2×D23—42no—
75C2×D23—42no—
76C2×D23—41no—
77C4×C23—22no—
78C4×C23—22no—
79C4×C23—21no—
80C4×C23—41no—
81Dic23—41no—
82Dic23#9911yescharacteristic
83Dic23#9911yescharacteristic
84#532—231no—
85#413—232no—
86#356—231no—
87#356D2311yescharacteristic, complemented
88#355—232no—
89C2×C23—21no—
90C2×C23C2×#9911yescharacteristic
91D23—41no—
92D23—42no—
93D23—81no—
94C2×#41—231no—
95C2×#41—231no—
96C2×M16—462no—
97C4⋊Q8C2×D2311yescharacteristic
98#127—231no—
99#124—231no—
100#124—231no—
101#121—462no—
102C4×D4—462no—
103C2×C42—231no—
104#101—232no—
105#101C2×D2312yes—
106#100—462no—
107C23#213211yescharacteristic, complemented, Sylow
108#41—921no—
109#41—921no—
110#41—921no—
111#41—921no—
112C2×Q8C4×D2311yescharacteristic
113C2×Q8C22×D2311yescharacteristic
114C2×D4—231no—
115C2×D4—231no—
116C2×D4—232no—
117C2×D4—462no—
118C2×D4—461no—
119C22×C4—231no—
120C22×C4—232no—
121C22×C4—461no—
122C22×C4—461no—
123M16—22no—
124M16—462no—
125M16—922no—
126C2×C8—922no—
127C4⋊C4—22no—
128C22⋊C4—462no—
129C22⋊C4—462no—
130C42—231no—
131C42—461no—
132C42C4×D2311yescharacteristic
133C23—232no—
134C23—231no—
135C23—461no—
136Q8—41no—
137Q8—41no—
138D4—922no—
139D4—921no—
140D4—921no—
141D4—924no—
142D4—922no—
143C2×C4—21no—
144C2×C4—21no—
145C2×C4—231no—
146C2×C4—462no—
147C2×C4—462no—
148C2×C4—461no—
149C2×C4—461no—
150C2×C4—461no—
151C2×C4—922no—
152C2×C4—921no—
153C2×C4—921no—
154C2×C4C2×C4×D2311yescharacteristic
155C2×C4D4×D2312yes—
156C8—42no—
157C8—922no—
158C22—461no—
159C22—462no—
160C22—921no—
161C22—922no—
162C22—922no—
163C22—921no—
164C22C22⋊C4×D2311yescharacteristic
165C4—22no—
166C4—22no—
167C4—21no—
168C4—41no—
169C4—231no—
170C4—231no—
171C4—921no—
172C2—21no—
173C2—921no—
174C2—922no—
175C2—1841no—
176C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC2×C4×C23C22×C4
FrattiniC2×Q8C22×D23
FittingC23×#356C2
socleC2×C23C2×#99
prime radical#13092968C2
cosocleC2×Q8×C23C23
hypercenter#356D23
hypocenterC23#2132
LCSG ▷ C2×C4×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
2. #13092400C2semidirect
3. #13092216C2semidirect
4. #13092213C2semidirect
5. C23×#356C2semidirect
87. #356D23semidirect
107. C23#2132semidirect

Maximal subgroups

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

subgroupindex
#130929682
#130924002
#130922162
#130922132
C23×#3562
#213223