Finite Group Databasebeta

← #15671884

Subgroups — #15671884

Order 2944.

238 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 238 conjugacy classes of subgroups — too many to draw. Only its 73 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#13092951C211yesmaximal, characteristic
2#13092263C211yesmaximal, characteristic, complemented
3#13092155C212yesmaximal, complemented
4#13092152C212yesmaximal
5C23×#431C211yesmaximal, characteristic, complemented
6C2×C42×C23C2211yescharacteristic
7#10625101C2211yescharacteristic
8#10625100—21no—
9C4×C22⋊D23—21no—
10#10625095C2211yescharacteristic
11C2×C4×Dic23—21no—
12#10625047—21no—
13#10625046C411yescharacteristic, complemented
14C4×D92C411yescharacteristic, complemented
15#10625043—21no—
16#10625041C411yescharacteristic, complemented
17C4×Dic46C411yescharacteristic, complemented
18C23×C4⋊C8—21no—
19C23×C22⋊C8C2212yes—
20C4×C8×C23—21no—
21C23⋊#95—21no—
22C23⋊#95C2212yes—
23C22×C4×C23D411yescharacteristic
24C22×C4×C23D411yescharacteristic
25C22×C4×C23C2311yescharacteristic
26C2×C22⋊D23—21no—
27C22×Dic23—22no—
28C2×D92C2×C411yescharacteristic
29C2×C4×D23—21no—
30C2×Dic46C2×C411yescharacteristic
31C2×C8×C23—22no—
32C42×C23C2×C411yescharacteristic
33C42×C23C2×C411yescharacteristic
34C42×C23D411yescharacteristic
35C42×C23D411yescharacteristic
36C22⋊Dic23—21no—
37(C2×D23)⋊C4—21no—
38(C2×D23)⋊C4—21no—
39(C2×D23)⋊C4—21no—
40(C2×D23)⋊C4—21no—
41C4⋊Dic23C2×C411yescharacteristic
42C4⋊Dic23C2×C411yescharacteristic
43Dic23⋊C4—21no—
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47C4×Dic23—24no—
48C4×Dic23—21no—
49C23×C23C2×D411yescharacteristic
50C22×D23—21no—
51C2×C4×C23—22no—
52C2×C4×C23—22no—
53C2×C4×C23—41no—
54C2×C4×C23C22⋊C411yescharacteristic
55C2×C4×C23C22⋊C411yescharacteristic
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22×C411yescharacteristic
59C2×C4×C23C2×D411yescharacteristic
60C22⋊D23—42no—
61C2×Dic23—24no—
62C2×Dic23—21no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—42no—
66C2×Dic23—42no—
67D92—41no—
68C4×D23—42no—
69Dic46—41no—
70C8×C23—42no—
71#1500—231nomaximal, Sylow
72C22×C23—21no—
73C22×C23—21no—
74C22×C23C2×C22⋊C411yescharacteristic
75C22×C23#13512yes—
76C2×D23—41no—
77C2×D23—41no—
78C2×D23—41no—
79C4×C23—21no—
80C4×C23—21no—
81C4×C23—21no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23#10412yes—
85Dic23—44no—
86Dic23—41no—
87Dic23—41no—
88Dic23—41no—
89#529—231no—
90#431D2311yescharacteristic, complemented
91#376—231no—
92#328—232no—
93#327—232no—
94C2×C23—22no—
95C2×C23#41011yescharacteristic
96C2×C23#41611yescharacteristic
97C2×C23C2×#10411yescharacteristic
98D23—81no—
99#126—461no—
100#125—231no—
101#124—231no—
102#123—461no—
103C22⋊Q8—231no—
104#121—231no—
105C4×Q8—231no—
106C4×D4—231no—
107C4×D4—461no—
108#117—461no—
109C2×C42—461no—
110C2×C42C2×D2311yescharacteristic
111C4⋊C8—21no—
112C22⋊C8C2×D2312yes—
113C4×C8—21no—
114#95—232no—
115#95—461no—
116C23#150011yescharacteristic, complemented, Sylow
117C2×Q8—231no—
118C2×D4—231no—
119C2×D4—461no—
120C22×C4—462no—
121C22×C4—461no—
122C22×C4D9211yescharacteristic
123C22×C4D9211yescharacteristic
124C22×C4C22×D2311yescharacteristic
125C2×C8—22no—
126C4⋊C4—231no—
127C4⋊C4—231no—
128C4⋊C4—461no—
129C4⋊C4—461no—
130C4⋊C4—461no—
131C4⋊C4—461no—
132C22⋊C4—461no—
133C22⋊C4—461no—
134C22⋊C4—461no—
135C22⋊C4—461no—
136C22⋊C4—461no—
137C42—464no—
138C42—461no—
139C42C4×D2311yescharacteristic
140C42C4×D2311yescharacteristic
141C42C22⋊D2311yescharacteristic
142C42C22⋊D2311yescharacteristic
143C23—461no—
144C23C2×D9211yescharacteristic
145Q8—921no—
146D4—921no—
147D4—922no—
148C2×C4—22no—
149C2×C4—22no—
150C2×C4—41no—
151C2×C4—464no—
152C2×C4—461no—
153C2×C4—461no—
154C2×C4—461no—
155C2×C4—922no—
156C2×C4—922no—
157C2×C4—922no—
158C2×C4(C2×D23)⋊C411yescharacteristic
159C2×C4(C2×D23)⋊C411yescharacteristic
160C2×C4(C2×D23)⋊C411yescharacteristic
161C2×C4(C2×D23)⋊C411yescharacteristic
162C2×C4C2×C4×D2311yescharacteristic
163C2×C4C2×C22⋊D2311yescharacteristic
164C8—42no—
165C22—21no—
166C22—21no—
167C22—921no—
168C22—921no—
169C22—921no—
170C22#1062507512yes—
171C22C2×(C2×D23)⋊C411yescharacteristic
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—21no—
177C4—924no—
178C4—921no—
179C4—921no—
180C4—921no—
181C4#1062500712yes—
182C2—22no—
183C2—1841no—
184C2#1309239011yescharacteristic
185C2#1309241411yescharacteristic
186C2C2×#1062500711yescharacteristic
subgroupG/H
centerC2×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#431C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#431D23
hypocenterC23#1500
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. #13092263C2semidirect
3. #13092155C2semidirect
5. C23×#431C2semidirect
13. #10625046C4semidirect
14. C4×D92C4semidirect
16. #10625041C4semidirect
17. C4×Dic46C4semidirect
90. #431D23semidirect
116. C23#1500semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130922632
#130921552
#130921522
C23×#4312
#150023