Finite Group Databasebeta

← #15671936

Subgroups — #15671936

Order 2944.

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

normal subgroups only

This group has 222 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#13092951C211yesmaximal, characteristic
2#13092283C211yesmaximal, characteristic, complemented
3#13092155C212yesmaximal, complemented
4#13092152C212yesmaximal
5C23×#432C211yesmaximal, characteristic, complemented
6C2×C42×C23C2211yescharacteristic
7#10625101C2211yescharacteristic
8#10625100—21no—
9C4×C22⋊D23—21no—
10C2×C4⋊Dic23—21no—
11#10625095C2211yescharacteristic
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—
20C23×#97—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⋊Dic23—42no—
42C4⋊Dic23C2×C411yescharacteristic
43C4⋊Dic23C2×C411yescharacteristic
44Dic23⋊C4—21no—
45Dic23⋊C4—21no—
46Dic23⋊C4—21no—
47Dic23⋊C4—21no—
48C4×Dic23—21no—
49C23×C23C2×D411yescharacteristic
50C22×D23—21no—
51C2×C4×C23—21no—
52C2×C4×C23—21no—
53C2×C4×C23—41no—
54C2×C4×C23—41no—
55C2×C4×C23C22⋊C411yescharacteristic
56C2×C4×C23C22⋊C411yescharacteristic
57C2×C4×C23C22⋊C411yescharacteristic
58C2×C4×C23C22⋊C411yescharacteristic
59C2×C4×C23C22×C411yescharacteristic
60C2×C4×C23C2×D411yescharacteristic
61C22⋊D23—41no—
62C22⋊D23—41no—
63C2×Dic23—21no—
64C2×Dic23—21no—
65C2×Dic23—21no—
66C2×Dic23—42no—
67C2×Dic23—42no—
68C2×Dic23—42no—
69D92—41no—
70C4×D23—42no—
71Dic46—41no—
72C8×C23—42no—
73#1512—231nomaximal, Sylow
74C22×C23—21no—
75C22×C23—21no—
76C22×C23C2×C22⋊C411yescharacteristic
77C22×C23AGL(1,ℤ/8)11yescharacteristic
78C22×C23#13711yescharacteristic
79C2×D23—41no—
80C2×D23—41no—
81C2×D23—41no—
82C4×C23—21no—
83C4×C23—21no—
84C4×C23—21no—
85C4×C23—21no—
86C4×C23—21no—
87C4×C23—21no—
88Dic23—41no—
89Dic23—41no—
90Dic23—41no—
91Dic23—82no—
92#529—231no—
93#432D2311yescharacteristic, complemented
94#382—231no—
95#328—232no—
96#327—232no—
97C2×C23—21no—
98C2×C23—21no—
99C2×C23#41011yescharacteristic
100C2×C23#41711yescharacteristic
101C2×C23#42111yescharacteristic
102D23—81no—
103#126—461no—
104#125—231no—
105#124—231no—
106#123—461no—
107C22⋊Q8—231no—
108#121—231no—
109C4×Q8—231no—
110C4×D4—231no—
111C4×D4—461no—
112#117—461no—
113C2×C4⋊C4—461no—
114C2×C42C2×D2311yescharacteristic
115C4⋊C8—21no—
116C22⋊C8C2×D2312yes—
117#97—21no—
118#95—232no—
119#95—461no—
120C23#151211yescharacteristic, complemented, Sylow
121C2×Q8—231no—
122C2×D4—231no—
123C2×D4—461no—
124C22×C4—461no—
125C22×C4—462no—
126C22×C4D9211yescharacteristic
127C22×C4D9211yescharacteristic
128C22×C4C22×D2311yescharacteristic
129C2×C8—22no—
130C4⋊C4—231no—
131C4⋊C4—231no—
132C4⋊C4—461no—
133C4⋊C4—461no—
134C4⋊C4—461no—
135C4⋊C4—461no—
136C4⋊C4—922no—
137C22⋊C4—461no—
138C22⋊C4—461no—
139C22⋊C4—461no—
140C22⋊C4—461no—
141C22⋊C4—461no—
142C42—461no—
143C42C4×D2311yescharacteristic
144C42C4×D2311yescharacteristic
145C42C22⋊D2311yescharacteristic
146C42C22⋊D2311yescharacteristic
147C23—461no—
148C23C2×D9211yescharacteristic
149Q8—921no—
150D4—921no—
151D4—921no—
152D4—921no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—461no—
158C2×C4—461no—
159C2×C4—461no—
160C2×C4—922no—
161C2×C4—922no—
162C2×C4—922no—
163C2×C4—922no—
164C2×C4(C2×D23)⋊C411yescharacteristic
165C2×C4(C2×D23)⋊C411yescharacteristic
166C2×C4(C2×D23)⋊C411yescharacteristic
167C2×C4(C2×D23)⋊C411yescharacteristic
168C2×C4C2×C4×D2311yescharacteristic
169C2×C4C2×C22⋊D2311yescharacteristic
170C8—42no—
171C22—21no—
172C22—21no—
173C22—921no—
174C22—921no—
175C22—921no—
176C22#1062507911yescharacteristic
177C22#1062508011yescharacteristic
178C22C2×(C2×D23)⋊C411yescharacteristic
179C4—21no—
180C4—21no—
181C4—21no—
182C4—21no—
183C4—21no—
184C4—21no—
185C4—921no—
186C4—921no—
187C4—921no—
188C4—1842no—
189C2—21no—
190C2—21no—
191C2—1841no—
192C2#1309239011yescharacteristic
193C2#1309241911yescharacteristic
194C2#1309243311yescharacteristic
subgroupG/H
centerC22C2×(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#432C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#432D23
hypocenterC23#1512
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. #13092283C2semidirect
3. #13092155C2semidirect
5. C23×#432C2semidirect
13. #10625046C4semidirect
14. C4×D92C4semidirect
16. #10625041C4semidirect
17. C4×Dic46C4semidirect
93. #432D23semidirect
120. C23#1512semidirect

Maximal subgroups

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

subgroupindex
#130929512
#130922832
#130921552
#130921522
C23×#4322
#151223