Finite Group Databasebeta

← #15671945

Subgroups — #15671945

Order 2944.

252 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 69 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#13092967C211yesmaximal, characteristic
2#13092285C211yesmaximal, characteristic, complemented
3#13092152C214yesmaximal, complemented
4C23×#432C211yesmaximal, characteristic, complemented
5C2×#67288—21no—
6C2×C42×C23C2211yescharacteristic
7#10625101—21no—
8#10625101C2212yes—
9#10625046—21no—
10#10625045C411yescharacteristic, complemented
11C4×D92—21no—
12C4×D92C412yescomplemented
13#10625040C411yescharacteristic, complemented
14C23×C4⋊C8—21no—
15C23×C22⋊C8C2212yes—
16C23×#97—21no—
17C23⋊#95—21no—
18C23⋊#95—21no—
19C23⋊#95C2212yes—
20C22×C4×C23D411yescharacteristic
21C22×C4×C23D411yescharacteristic
22C22×C4×C23C2311yescharacteristic
23C2×C22⋊D23—22no—
24C22×Dic23—22no—
25#67288—44no—
26C2×D92—21no—
27C2×D92—21no—
28C2×D92C2×C412yes—
29C2×C4×D23—22no—
30C2×Dic46—21no—
31C2×C8×C23—22no—
32C42×C23C2×C411yescharacteristic
33C42×C23C2×C411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23D411yescharacteristic
36(C2×D23)⋊C4—22no—
37(C2×D23)⋊C4—22no—
38C4⋊Dic23—21no—
39C4⋊Dic23C2×C412yes—
40C23×C23C2×D411yescharacteristic
41C22×D23—22no—
42C2×C4×C23—22no—
43C2×C4×C23—41no—
44C2×C4×C23—41no—
45C2×C4×C23C22⋊C411yescharacteristic
46C2×C4×C23C22⋊C411yescharacteristic
47C2×C4×C23C22⋊C411yescharacteristic
48C2×C4×C23C22⋊C411yescharacteristic
49C2×C4×C23C22×C411yescharacteristic
50C2×C4×C23C2×D411yescharacteristic
51C22⋊D23—44no—
52C2×Dic23—22no—
53C2×Dic23—42no—
54C2×Dic23—42no—
55C2×Dic23—42no—
56D92—42no—
57D92—42no—
58D92—42no—
59C4×D23—44no—
60Dic46—42no—
61C8×C23—42no—
62#1514—231nomaximal, Sylow
63C22×C23—21no—
64C22×C23—21no—
65C22×C23C2×C22⋊C411yescharacteristic
66C22×C23AGL(1,ℤ/8)12yes—
67C2×D23—42no—
68C2×D23—42no—
69C2×D23—42no—
70C4×C23—21no—
71C4×C23—21no—
72C4×C23—21no—
73C4×C23—21no—
74C4×C23—21no—
75C4×C23—21no—
76Dic23—42no—
77Dic23—82no—
78#532—231no—
79#432D2311yescharacteristic, complemented
80#383—231no—
81#327—234no—
82C2×C23—22no—
83C2×C23#41011yescharacteristic
84C2×C23#41811yescharacteristic
85C2×C23#42111yescharacteristic
86D23—82no—
87C2×#41—461no—
88C4⋊Q8—231no—
89#127—231no—
90#124—461no—
91#121—232no—
92#121—461no—
93C4×D4—232no—
94C4×D4—461no—
95C2×C42C2×D2311yescharacteristic
96C4⋊C8—21no—
97C22⋊C8C2×D2312yes—
98#97—21no—
99#95—232no—
100#95—461no—
101#95—461no—
102C23#151411yescharacteristic, complemented, Sylow
103#41—924no—
104C2×Q8—461no—
105C2×D4—232no—
106C2×D4—462no—
107C2×D4—461no—
108C2×D4—461no—
109C22×C4—462no—
110C22×C4—462no—
111C22×C4D9211yescharacteristic
112C22×C4D9211yescharacteristic
113C22×C4C22×D2311yescharacteristic
114C2×C8—22no—
115C4⋊C4—232no—
116C4⋊C4—461no—
117C22⋊C4—462no—
118C22⋊C4—462no—
119C42C4×D2311yescharacteristic
120C42C4×D2311yescharacteristic
121C42C22⋊D2311yescharacteristic
122C42C22⋊D2311yescharacteristic
123C23—462no—
124C23C2×D9211yescharacteristic
125Q8—922no—
126D4—922no—
127D4—922no—
128D4—922no—
129D4—924no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—462no—
134C2×C4—924no—
135C2×C4—922no—
136C2×C4—922no—
137C2×C4—922no—
138C2×C4(C2×D23)⋊C411yescharacteristic
139C2×C4(C2×D23)⋊C411yescharacteristic
140C2×C4(C2×D23)⋊C411yescharacteristic
141C2×C4(C2×D23)⋊C411yescharacteristic
142C2×C4C2×C4×D2311yescharacteristic
143C2×C4C2×C22⋊D2311yescharacteristic
144C8—42no—
145C22—21no—
146C22—21no—
147C22—922no—
148C22—922no—
149C22—922no—
150C22#1062507912yes—
151C22C2×(C2×D23)⋊C411yescharacteristic
152C4—21no—
153C4—21no—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—922no—
159C4—1842no—
160C2—22no—
161C2—1842no—
162C2#1309239011yescharacteristic
163C2#1309242311yescharacteristic
164C2#1309243311yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radical#13092967C2
cosocleC22×C4×C23C23
hypercenter#432D23
hypocenterC23#1514
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. #13092285C2semidirect
3. #13092152C2semidirect
4. C23×#432C2semidirect
10. #10625045C4semidirect
12. C4×D92C4semidirect
13. #10625040C4semidirect
79. #432D23semidirect
102. C23#1514semidirect

Maximal subgroups

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

subgroupindex
#130929672
#130922852
#130921522
C23×#4322
#151423