Finite Group Databasebeta

← #15671886

Subgroups — #15671886

Order 2944.

304 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 77 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#13092928C211yesmaximal, characteristic
2C2×C22⋊(C23⋊C8)C211yesmaximal, characteristic, complemented
3#13092153C212yesmaximal, complemented
4#13092150C212yesmaximal, complemented
5C4×C22⋊C4×C23C211yesmaximal, characteristic, complemented
6C23×C4×C23C2211yescharacteristic
7C2×#67288C411yescharacteristic, complemented
8C2×C22⋊C4×C23—21no—
9C2×C42×C23—21no—
10#10625124—21no—
11#10625101C411yescharacteristic, complemented
12#10625101C2211yescharacteristic
13#10625100—21no—
14C4×C22⋊D23—21no—
15C4×C22⋊D23—21no—
16#10625097C411yescharacteristic, complemented
17#10625095C411yescharacteristic, complemented
18#10625095C2211yescharacteristic
19C22×C23⋊C8—21no—
20C23×#95C2212yes—
21C22⋊(C23⋊C8)—21no—
22C22⋊(C23⋊C8)C2212yes—
23C24×C23D411yescharacteristic
24C22×C4×C23—22no—
25C22×C4×C23—42no—
26C22×C4×C23C2×C411yescharacteristic
27C22×C4×C23C2×C411yescharacteristic
28C22×C4×C23D411yescharacteristic
29C22×C4×C23D411yescharacteristic
30C22×C4×C23D411yescharacteristic
31C22×C4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35#67288—42no—
36C2×D92C2×C411yescharacteristic
37C2×C4×D23—21no—
38C2×Dic46C2×C411yescharacteristic
39C22⋊C4×C23—24no—
40C42×C23—42no—
41C22⋊Dic23—21no—
42C22⋊Dic23—21no—
43C22⋊Dic23—21no—
44(C2×D23)⋊C4—21no—
45(C2×D23)⋊C4—21no—
46C4⋊Dic23C2×C411yescharacteristic
47C4⋊Dic23C2×C411yescharacteristic
48Dic23⋊C4—21no—
49Dic23⋊C4—21no—
50C4×Dic23—21no—
51C2×C23⋊C8—22no—
52C2×C23⋊C8—42no—
53C23×C23—22no—
54C23×C23—22no—
55C23×C23—41no—
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22⋊C411yescharacteristic
58C23×C23C2×D411yescharacteristic
59C22×D23—21no—
60C2×C4×C23—22no—
61C2×C4×C23—22no—
62C2×C4×C23—22no—
63C2×C4×C23—24no—
64C2×C4×C23—41no—
65C2×C4×C23—41no—
66C2×C4×C23—41no—
67C2×C4×C23—42no—
68C2×C4×C23—42no—
69C2×C4×C23C22⋊C411yescharacteristic
70C2×C4×C23C22⋊C411yescharacteristic
71C2×C4×C23C22×C411yescharacteristic
72C2×C4×C23C2×D411yescharacteristic
73C22⋊D23—42no—
74C22⋊D23—42no—
75C22⋊D23—42no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79D92—41no—
80C4×D23—42no—
81Dic46—41no—
82C23⋊C8—42no—
83#1501—231nomaximal, Sylow
84C22×C23—21no—
85C22×C23—21no—
86C22×C23—21no—
87C22×C23—21no—
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—44no—
92C22×C23#10412yes—
93C22×C23C2×C22⋊C411yescharacteristic
94C22×C23#13512yes—
95C2×D23—41no—
96C2×D23—41no—
97C2×D23—41no—
98C4×C23—21no—
99C4×C23—21no—
100C4×C23—21no—
101C4×C23—44no—
102C4×C23#9912yes—
103Dic23—41no—
104Dic23—41no—
105Dic23—41no—
106#525—231no—
107C2×C22⋊C8—231no—
108C4×C22⋊C4D2311yescharacteristic, complemented
109#328—232no—
110#327—232no—
111C2×C23—22no—
112C2×C23—22no—
113C2×C23—41no—
114C2×C23C2×#9911yescharacteristic
115C2×C23#41611yescharacteristic
116C2×C23C2×#10411yescharacteristic
117D23—81no—
118C2×#41—231no—
119C23×C4C2×D2311yescharacteristic
120C22×C8—461no—
121#123—461no—
122C22⋊Q8—231no—
123C22⋊Q8—231no—
124#121—231no—
125#121—231no—
126#120—461no—
127C4×D4—461no—
128C4×D4—461no—
129#117—231no—
130C2×C22⋊C4—21no—
131C2×C42—21no—
132C22⋊C8—232no—
133C22⋊C8—461no—
134#95C2×D2312yes—
135C23#150111yescharacteristic, complemented, Sylow
136C24C22⋊D2311yescharacteristic
137#41—922no—
138C2×Q8—231no—
139C2×D4—231no—
140C2×D4—461no—
141C2×D4—461no—
142C2×D4—461no—
143C22×C4—22no—
144C22×C4—42no—
145C22×C4—461no—
146C22×C4C4×D2311yescharacteristic
147C22×C4C4×D2311yescharacteristic
148C22×C4D9211yescharacteristic
149C22×C4D9211yescharacteristic
150C22×C4C22⋊D2311yescharacteristic
151C22×C4C22×D2311yescharacteristic
152C2×C8—462no—
153C2×C8—922no—
154C4⋊C4—231no—
155C4⋊C4—231no—
156C4⋊C4—461no—
157C4⋊C4—461no—
158C22⋊C4—24no—
159C22⋊C4—461no—
160C22⋊C4—461no—
161C22⋊C4—461no—
162C22⋊C4—461no—
163C22⋊C4—461no—
164C42—42no—
165C42—461no—
166C23—22no—
167C23—22no—
168C23—41no—
169C23—461no—
170C23(C2×D23)⋊C411yescharacteristic
171C23(C2×D23)⋊C411yescharacteristic
172C23C2×C22⋊D2311yescharacteristic
173Q8—921no—
174D4—921no—
175D4—922no—
176D4—922no—
177D4—922no—
178C2×C4—22no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—24no—
182C2×C4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—461no—
188C2×C4—461no—
189C2×C4—461no—
190C2×C4—922no—
191C2×C4(C2×D23)⋊C411yescharacteristic
192C2×C4(C2×D23)⋊C411yescharacteristic
193C2×C4C2×C4×D2311yescharacteristic
194C2×C4C2×D9211yescharacteristic
195C8—922no—
196C22—21no—
197C22—21no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—21no—
202C22—21no—
203C22—44no—
204C22—921no—
205C22—921no—
206C22—921no—
207C22#1062498712yes—
208C22C2×(C2×D23)⋊C411yescharacteristic
209C22#1062512112yes—
210C4—21no—
211C4—21no—
212C4—21no—
213C4—44no—
214C4—921no—
215C4—921no—
216C4—921no—
217C4#1062498812yes—
218C2—22no—
219C2—22no—
220C2—41no—
221C2—1841no—
222C2C2×#1062498811yescharacteristic
223C2#1309241111yescharacteristic
224C2C2×#1062498711yescharacteristic
subgroupG/H
centerC2×C4(C2×D23)⋊C4
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC4×C22⋊C4×C23C2
socleC22×C23C2×C22⋊C4
prime radical#13092928C2
cosocleC22×C4×C23C23
hypercenterC4×C22⋊C4D23
hypocenterC23#1501
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C23⋊C8)C2semidirect
3. #13092153C2semidirect
4. #13092150C2semidirect
5. C4×C22⋊C4×C23C2semidirect
7. C2×#67288C4semidirect
11. #10625101C4semidirect
16. #10625097C4semidirect
17. #10625095C4semidirect
108. C4×C22⋊C4D23semidirect
135. C23#1501semidirect

Maximal subgroups

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

subgroupindex
#130929282
C2×C22⋊(C23⋊C8)2
#130921532
#130921502
C4×C22⋊C4×C232
#150123