Finite Group Databasebeta

← #15675039

Subgroups — #15675039

Order 2944.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#13092924C211yesmaximal, characteristic
2#13092391C211yesmaximal, characteristic, complemented
3#13092208C212yesmaximal, complemented
4#13092205C212yesmaximal, complemented
5C23×#413C211yesmaximal, characteristic, complemented
6C2×#41×C23C2211yescharacteristic
7C22×C4×D23C411yescharacteristic, complemented
8C2×M16×C23—21no—
9#10625117—21no—
10#10625109—21no—
11#10625108C411yescharacteristic, complemented
12#10625108C2211yescharacteristic
13#10625106C411yescharacteristic, complemented
14#10625106C2211yescharacteristic
15C4×C22⋊D23—21no—
16C4×C22⋊D23—21no—
17#10625097—21no—
18#10625097C411yescharacteristic, complemented
19C23×#101—21no—
20C23×#100C2212yes—
21#10625016—21no—
22#10625016C2212yes—
23C23×D23C2×C411yescharacteristic
24#41×C23—41no—
25#41×C23—41no—
26C2×Q8×C23D411yescharacteristic
27C2×D4×C23C2×C411yescharacteristic
28C2×D4×C23D411yescharacteristic
29C2×D4×C23C2311yescharacteristic
30C22×C4×C23C2×C411yescharacteristic
31C22×C4×C23D411yescharacteristic
32C22×C4×C23D411yescharacteristic
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C22×Dic23C2×C411yescharacteristic
36C2×C4×D23—21no—
37C2×C4×D23—21no—
38C2×C4×D23—41no—
39C2×C4×D23—41no—
40M16×C23—22no—
41M16×C23—41no—
42C2×C8×C23—41no—
43C22⋊Dic23—21no—
44C22⋊Dic23—21no—
45C22⋊Dic23—22no—
46C22⋊Dic23C2×C411yescharacteristic
47C22⋊Dic23C2×C411yescharacteristic
48(C2×D23)⋊C4—21no—
49(C2×D23)⋊C4—21no—
50C4⋊Dic23—21no—
51C4⋊Dic23—41no—
52Dic23⋊C4—21no—
53Dic23⋊C4—21no—
54C4×Dic23—21no—
55C4×Dic23—41no—
56C23×C23C22⋊C411yescharacteristic
57C23×C23C22×C411yescharacteristic
58C23×C23C2×D411yescharacteristic
59C22×D23—21no—
60C22×D23—42no—
61C22×D23—41no—
62Q8×C23—41no—
63D4×C23—41no—
64D4×C23—41no—
65D4×C23—41no—
66C2×C4×C23—21no—
67C2×C4×C23—21no—
68C2×C4×C23—21no—
69C2×C4×C23—21no—
70C2×C4×C23—21no—
71C2×C4×C23—21no—
72C2×C4×C23C22⋊C411yescharacteristic
73C2×C4×C23C22⋊C411yescharacteristic
74C2×C4×C23C22⋊C411yescharacteristic
75C2×C4×C23C2×D411yescharacteristic
76C22⋊D23—42no—
77C22⋊D23—42no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81C2×Dic23—41no—
82C2×Dic23—42no—
83C4×D23—42no—
84C4×D23—41no—
85C4×D23—41no—
86C8×C23—42no—
87#2120—231nomaximal, Sylow
88C22×C23—21no—
89C22×C23—21no—
90C22×C23—21no—
91C22×C23—41no—
92C22×C23—41no—
93C22×C23—41no—
94C22×C23C2×C22⋊C411yescharacteristic
95C2×D23—22no—
96C2×D23—41no—
97C2×D23—42no—
98C2×D23—41no—
99C2×D23—42no—
100C4×C23—21no—
101C4×C23—21no—
102C4×C23—21no—
103C4×C23#9911yescharacteristic
104C4×C23#9911yescharacteristic
105Dic23—41no—
106Dic23—41no—
107Dic23—41no—
108Dic23—82no—
109#525—231no—
110#413D2311yescharacteristic, complemented
111#410—231no—
112#352—232no—
113AΣL(1,𝔽16)—232no—
114C2×C23—21no—
115C2×C23—41no—
116C2×C23—41no—
117C2×C23—41no—
118C2×C23C2×#9911yescharacteristic
119D23—42no—
120C2×#41C2×D2311yescharacteristic
121C23×C4—231no—
122C2×M16—21no—
123#123—231no—
124#123—231no—
125C22⋊Q8—461no—
126#121—461no—
127#120—231no—
128#120—231no—
129C4×D4—461no—
130C4×D4—461no—
131#117—231no—
132#117—461no—
133#101—21no—
134#100C2×D2312yes—
135#99—232no—
136#99—461no—
137C23#212011yescharacteristic, complemented, Sylow
138C24—231no—
139#41—41no—
140#41—41no—
141C2×Q8C22⋊D2311yescharacteristic
142C2×D4—461no—
143C2×D4—461no—
144C2×D4C4×D2311yescharacteristic
145C2×D4D9211yescharacteristic
146C2×D4C22×D2311yescharacteristic
147C22×C4—231no—
148C22×C4—461no—
149C22×C4—461no—
150C22×C4—921no—
151C22×C4—921no—
152C22×C4C4×D2311yescharacteristic
153C22×C4D9211yescharacteristic
154C22×C4C22⋊D2311yescharacteristic
155M16—22no—
156M16—41no—
157C2×C8—41no—
158C4⋊C4—461no—
159C4⋊C4—461no—
160C4⋊C4—461no—
161C4⋊C4—921no—
162C22⋊C4—231no—
163C22⋊C4—231no—
164C22⋊C4—461no—
165C22⋊C4—461no—
166C22⋊C4—461no—
167C22⋊C4—461no—
168C22⋊C4—462no—
169C42—461no—
170C42—921no—
171C23—461no—
172C23—921no—
173C23—922no—
174C23(C2×D23)⋊C411yescharacteristic
175C23C2×C4×D2311yescharacteristic
176C23C2×D9211yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—922no—
182D4—922no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—461no—
190C2×C4—461no—
191C2×C4—461no—
192C2×C4—922no—
193C2×C4—921no—
194C2×C4—921no—
195C2×C4—921no—
196C2×C4—922no—
197C2×C4(C2×D23)⋊C411yescharacteristic
198C2×C4(C2×D23)⋊C411yescharacteristic
199C2×C4(C2×D23)⋊C411yescharacteristic
200C2×C4C2×C22⋊D2311yescharacteristic
201C8—42no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—462no—
209C22—921no—
210C22—922no—
211C22—922no—
212C22—921no—
213C22C2×(C2×D23)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—921no—
218C4—921no—
219C4—921no—
220C4—1842no—
221C4#1062498811yescharacteristic
222C4#1062498811yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—922no—
228C2C2×#1062498811yescharacteristic
subgroupG/H
centerC4#10624988
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×#413C2
socleC2×C23C2×#99
prime radical#13092924C2
cosocleC2×D4×C23C23
hypercenter#413D23
hypocenterC23#2120
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #413

Complements

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

NH ≅ G/Ntype
2. #13092391C2semidirect
3. #13092208C2semidirect
4. #13092205C2semidirect
5. C23×#413C2semidirect
7. C22×C4×D23C4semidirect
11. #10625108C4semidirect
13. #10625106C4semidirect
18. #10625097C4semidirect
110. #413D23semidirect
137. C23#2120semidirect

Maximal subgroups

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

subgroupindex
#130929242
#130923912
#130922082
#130922052
C23×#4132
#212023