Finite Group Databasebeta

← #15671921

Subgroups — #15671921

Order 2944.

242 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 63 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#13092953C211yesmaximal, characteristic
2#13092471C211yesmaximal, characteristic, complemented
3#13092268C211yesmaximal, characteristic, complemented
4#13092154C211yesmaximal, characteristic, complemented
5#13092152C211yesmaximal, characteristic
6#13092150C211yesmaximal, characteristic
7C23×#328C211yesmaximal, characteristic, complemented
8C23×C22⋊Q8C2211yescharacteristic
9#10625118C411yescharacteristic, complemented
10Q8×Dic23C411yescharacteristic, complemented
11#10625101C2211yescharacteristic
12C2×Dic23⋊C4—21no—
13C2×C4×Dic23—21no—
14C2×C4×Dic23C2211yescharacteristic
15#10625069—21no—
16#10625064C411yescharacteristic, complemented
17#10625063—21no—
18#10625061C411yescharacteristic, complemented
19#10625057—21no—
20(C22⋊D23)⋊C4—21no—
21C23×C22⋊C8C2211yescharacteristic
22C23×#95C2211yescharacteristic
23C23⋊#95C2211yescharacteristic
24C22⋊(C23⋊C8)C2211yescharacteristic
25#10624997—21no—
26Dic23⋊C8—21no—
27C2×Q8×C23C2×C411yescharacteristic
28C22×C4×C23—21no—
29C22×C4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C22×Dic23—21no—
32C22×Dic23D411yescharacteristic
33C22×Dic23D411yescharacteristic
34C2×D92C2×C411yescharacteristic
35C2×C4×D23—21no—
36C2×C8×C23—21no—
37C4⋊C4×C23—21no—
38C4⋊C4×C23C2×C411yescharacteristic
39C22⋊C4×C23—21no—
40(C2×D23)⋊C4—21no—
41(C2×D23)⋊C4—21no—
42(C2×D23)⋊C4—21no—
43(C2×D23)⋊C4—21no—
44C4⋊Dic23—21no—
45C4⋊Dic23—21no—
46C4⋊Dic23C2×C411yescharacteristic
47Dic23⋊C4—24no—
48Dic23⋊C4—21no—
49C4×Dic23—21no—
50C4×Dic23—42no—
51C4×Dic23C2×C411yescharacteristic
52C4×Dic23C2×C411yescharacteristic
53C4×Dic23D411yescharacteristic
54C4×Dic23D411yescharacteristic
55C2×C23⋊C8—21no—
56C23×C23C2×D411yescharacteristic
57C22×D23—21no—
58Q8×C23—41no—
59C2×C4×C23—22no—
60C2×C4×C23—21no—
61C2×C4×C23—21no—
62C2×C4×C23—41no—
63C2×C4×C23—41no—
64C2×C4×C23—41no—
65C2×C4×C23C22×C411yescharacteristic
66C2×C4×C23C2×D411yescharacteristic
67C22⋊D23—41no—
68C22⋊D23—41no—
69C2×Dic23—21no—
70C2×Dic23—21no—
71C2×Dic23—22no—
72C2×Dic23—22no—
73C2×Dic23—21no—
74C2×Dic23—41no—
75C2×Dic23—41no—
76C2×Dic23C22⋊C411yescharacteristic
77C2×Dic23C22⋊C411yescharacteristic
78C2×Dic23C22⋊C411yescharacteristic
79C2×Dic23C22⋊C411yescharacteristic
80D92—41no—
81C4×D23—42no—
82C8×C23—41no—
83C23⋊C8—41no—
84#1509—231nomaximal, Sylow
85C22×C23—21no—
86C22×C23—21no—
87C22×C23C2×C22⋊C411yescharacteristic
88C22×C23AGL(1,ℤ/8)11yescharacteristic
89C22×C23#13711yescharacteristic
90C2×D23—41no—
91C2×D23—41no—
92C2×D23—41no—
93C4×C23—21no—
94C4×C23—21no—
95C4×C23—42no—
96C4×C23—41no—
97C4×C23—41no—
98Dic23—21no—
99Dic23—21no—
100Dic23—21no—
101Dic23—42no—
102Dic23—41no—
103Dic23#10412yes—
104#529—231no—
105#432—231no—
106C4×C4⋊C4—231no—
107#328—231no—
108#328D2311yescharacteristic, complemented
109#327—231no—
110#327—231no—
111C2×C23—21no—
112C2×C23—21no—
113C2×C23#41011yescharacteristic
114C2×C23#41711yescharacteristic
115C2×C23C2×#10411yescharacteristic
116D23—81no—
117#126—461no—
118#125—231no—
119#124—231no—
120#123—461no—
121C22⋊Q8C2×D2311yescharacteristic
122#121—231no—
123C4×Q8—231no—
124C4×D4—231no—
125C4×D4—461no—
126#117—461no—
127C2×C4⋊C4—461no—
128C2×C42—231no—
129C2×C42—461no—
130C4⋊C8—461no—
131C22⋊C8—231no—
132C22⋊C8C2×D2311yescharacteristic
133#97—461no—
134#95—231no—
135#95C2×D2311yescharacteristic
136C23#150911yescharacteristic, complemented, Sylow
137C2×Q8C4×D2311yescharacteristic
138C2×D4—231no—
139C2×D4—461no—
140C22×C4—21no—
141C22×C4—231no—
142C22×C4—231no—
143C22×C4—461no—
144C22×C4—461no—
145C22×C4C22×D2311yescharacteristic
146C2×C8—21no—
147C2×C8—461no—
148C4⋊C4—21no—
149C4⋊C4—231no—
150C4⋊C4—461no—
151C4⋊C4—461no—
152C4⋊C4—461no—
153C4⋊C4—464no—
154C4⋊C4C4×D2311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—461no—
157C22⋊C4—461no—
158C22⋊C4—461no—
159C22⋊C4—461no—
160C42—231no—
161C42—231no—
162C42—231no—
163C42—231no—
164C42—461no—
165C42—922no—
166C23—461no—
167C23D4×D2311yescharacteristic
168Q8—41no—
169D4—921no—
170D4—921no—
171D4—921no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—21no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—231no—
179C2×C4—231no—
180C2×C4—231no—
181C2×C4—231no—
182C2×C4—462no—
183C2×C4—461no—
184C2×C4—461no—
185C2×C4—462no—
186C2×C4—461no—
187C2×C4—922no—
188C2×C4—921no—
189C2×C4—921no—
190C2×C4C2×C4×D2311yescharacteristic
191C2×C4D4×D2311yescharacteristic
192C8—41no—
193C8—921no—
194C22—21no—
195C22—21no—
196C22—921no—
197C22—921no—
198C22—921no—
199C22C22⋊C4×D2311yescharacteristic
200C22#1062508511yescharacteristic
201C22#1062508911yescharacteristic
202C4—21no—
203C4—21no—
204C4—42no—
205C4—41no—
206C4—41no—
207C4—232no—
208C4—461no—
209C4—461no—
210C4—461no—
211C4—922no—
212C4—921no—
213C2—21no—
214C2—21no—
215C2—1841no—
216C2#1309238911yescharacteristic
217C2#1309241711yescharacteristic
218C2#104×D2311yescharacteristic
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC23×#328C2
socleC22×C23C2×C22⋊C4
prime radical#10625101C22
cosocleC22×C4×C23C23
hypercenter#328D23
hypocenterC23#1509
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ #328

Complements

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

NH ≅ G/Ntype
2. #13092471C2semidirect
3. #13092268C2semidirect
4. #13092154C2semidirect
7. C23×#328C2semidirect
9. #10625118C4semidirect
10. Q8×Dic23C4semidirect
16. #10625064C4semidirect
18. #10625061C4semidirect
108. #328D23semidirect
136. C23#1509semidirect

Maximal subgroups

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

subgroupindex
#130929532
#130924712
#130922682
#130921542
#130921522
#130921502
C23×#3282
#150923