Finite Group Databasebeta

← #15675035

Subgroups — #15675035

Order 2944.

264 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 55 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#13092923C211yesmaximal, characteristic
2#13092398C211yesmaximal, characteristic, complemented
3#13092389C211yesmaximal, characteristic, complemented
4#13092208C211yesmaximal, characteristic, complemented
5#13092206C211yesmaximal, characteristic, complemented
6#13092204C211yesmaximal, characteristic, complemented
7C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C23×Dic23C411yescharacteristic, complemented
9C2×#67290C2211yescharacteristic
10C23×#120C2211yescharacteristic
11#10625124C411yescharacteristic, complemented
12#10625110—21no—
13#10625106C2211yescharacteristic
14D4×Dic23—21no—
15M16×D23—21no—
16#10625057C411yescharacteristic, complemented
17(C22⋊D23)⋊C4—21no—
18#10625049—21no—
19#10625048—21no—
20#10625048C411yescharacteristic, complemented
21C23×#100C2211yescharacteristic
22C23×#99C2211yescharacteristic
23#10625016C2211yescharacteristic
24#10625015C2211yescharacteristic
25#10625006—21no—
26#10624988—21no—
27C24×C23C2×C411yescharacteristic
28C2×D4×C23—21no—
29C2×D4×C23C2311yescharacteristic
30C2×C22⋊D23—21no—
31C2×C22⋊D23C2×C411yescharacteristic
32C2×C22⋊D23D411yescharacteristic
33C22×Dic23—21no—
34C22×Dic23—21no—
35C22×Dic23—41no—
36C22×Dic23—41no—
37C22×Dic23C2×C411yescharacteristic
38C22×Dic23C2×C411yescharacteristic
39C22×Dic23D411yescharacteristic
40#67290—41no—
41#67290—41no—
42C2×C4×D23D411yescharacteristic
43C2×Dic46D411yescharacteristic
44M16×C23—21no—
45C22⋊C4×C23—21no—
46C22⋊C4×C23—21no—
47C22⋊C4×C23C2×C411yescharacteristic
48C22⋊Dic23—21no—
49C22⋊Dic23—21no—
50C22⋊Dic23—21no—
51C22⋊Dic23C2×C411yescharacteristic
52(C2×D23)⋊C4—21no—
53C4⋊Dic23—21no—
54Dic23⋊C4—21no—
55Dic23⋊C4—21no—
56Dic23⋊C4—41no—
57C4×Dic23—21no—
58C4×Dic23—41no—
59#67267—21no—
60#67262—41no—
61C8×D23—41no—
62C23×C23—21no—
63C23×C23—41no—
64C23×C23—42no—
65C23×C23C22×C411yescharacteristic
66C23×C23C2×D411yescharacteristic
67C22×D23C22⋊C411yescharacteristic
68D4×C23—41no—
69D4×C23—42no—
70C2×C4×C23—21no—
71C2×C4×C23—41no—
72C2×C4×C23C2×D411yescharacteristic
73C22⋊D23—41no—
74C22⋊D23—41no—
75C22⋊D23—42no—
76C2×Dic23—21no—
77C2×Dic23—21no—
78C2×Dic23—21no—
79C2×Dic23—21no—
80C2×Dic23—21no—
81C2×Dic23—21no—
82C2×Dic23—42no—
83C2×Dic23—41no—
84C2×Dic23—41no—
85C2×Dic23—41no—
86C2×Dic23—41no—
87C2×Dic23C22⋊C411yescharacteristic
88C2×Dic23C22⋊C411yescharacteristic
89C2×Dic23C22⋊C411yescharacteristic
90C4×D23—21no—
91C4×D23—21no—
92Dic46—41no—
93C8×C23—41no—
94C23⋊C8—41no—
95#2120—231nomaximal, Sylow
96C22×C23—22no—
97C22×C23—21no—
98C22×C23—21no—
99C22×C23—41no—
100C22×C23—41no—
101C22×C23—41no—
102C22×C23—42no—
103C22×C23—42no—
104C22×C23—41no—
105C22×C23C2×C22⋊C411yescharacteristic
106C2×D23—21no—
107C2×D23—41no—
108C4×C23—21no—
109C4×C23—41no—
110C4×C23—81no—
111Dic23—21no—
112Dic23—21no—
113Dic23—41no—
114Dic23—41no—
115Dic23—81no—
116Dic23#9911yescharacteristic
117Dic23#9911yescharacteristic
118#525—231no—
119#413—231no—
120#410—231no—
121#352—231no—
122#352—231no—
123AΣL(1,𝔽16)—231no—
124AΣL(1,𝔽16)D2311yescharacteristic, complemented
125C2×C23—21no—
126C2×C23—41no—
127C2×C23—42no—
128C2×C23—41no—
129C2×C23C2×#9911yescharacteristic
130D23—41no—
131C2×#41—231no—
132C23×C4—231no—
133C2×M16—461no—
134#123—231no—
135#123—231no—
136C22⋊Q8—461no—
137#121—461no—
138#120—231no—
139#120C2×D2311yescharacteristic
140C4×D4—461no—
141C4×D4—461no—
142#117—231no—
143#117—461no—
144#101—461no—
145#100—231no—
146#100C2×D2311yescharacteristic
147#99—231no—
148#99—461no—
149#99C2×D2311yescharacteristic
150C23#212011yescharacteristic, complemented, Sylow
151C24C4×D2311yescharacteristic
152#41—921no—
153#41—921no—
154C2×Q8—231no—
155C2×D4—21no—
156C2×D4—231no—
157C2×D4—231no—
158C2×D4—461no—
159C2×D4C22×D2311yescharacteristic
160C22×C4—231no—
161C22×C4—231no—
162C22×C4—231no—
163C22×C4—231no—
164C22×C4—461no—
165C22×C4—461no—
166C22×C4—921no—
167C22×C4—921no—
168M16—21no—
169M16—461no—
170M16—921no—
171C2×C8—921no—
172C4⋊C4—461no—
173C4⋊C4—461no—
174C4⋊C4—461no—
175C4⋊C4—921no—
176C22⋊C4—21no—
177C22⋊C4—21no—
178C22⋊C4—231no—
179C22⋊C4—461no—
180C22⋊C4—461no—
181C22⋊C4—461no—
182C22⋊C4—461no—
183C22⋊C4C4×D2311yescharacteristic
184C42—461no—
185C42—921no—
186C23—21no—
187C23—41no—
188C23—42no—
189C23—231no—
190C23C2×C4×D2311yescharacteristic
191C23D4×D2311yescharacteristic
192Q8—921no—
193D4—41no—
194D4—42no—
195D4—921no—
196D4—921no—
197D4—922no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4—231no—
201C2×C4—231no—
202C2×C4—231no—
203C2×C4—461no—
204C2×C4—461no—
205C2×C4—461no—
206C2×C4—461no—
207C2×C4—461no—
208C2×C4—461no—
209C2×C4—461no—
210C2×C4—461no—
211C2×C4—921no—
212C2×C4—921no—
213C2×C4—922no—
214C2×C4—921no—
215C2×C4—921no—
216C2×C4D4×D2311yescharacteristic
217C8—41no—
218C8—921no—
219C22—22no—
220C22—21no—
221C22—21no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22—42no—
226C22—42no—
227C22—41no—
228C22—461no—
229C22—921no—
230C22C22⋊C4×D2311yescharacteristic
231C4—21no—
232C4—41no—
233C4—81no—
234C4—231no—
235C4—231no—
236C4—461no—
237C4—461no—
238C4—921no—
239C4—921no—
240C4—1841no—
241C2—21no—
242C2—41no—
243C2—42no—
244C2—41no—
245C2—921no—
246C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×AΣL(1,𝔽16)C2
socleC2×C23C2×#99
prime radical#13092923C2
cosocleC2×D4×C23C23
hypercenterAΣL(1,𝔽16)D23
hypocenterC23#2120
LCSG ▷ C23×C23 ▷ C22×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
2. #13092398C2semidirect
3. #13092389C2semidirect
4. #13092208C2semidirect
5. #13092206C2semidirect
6. #13092204C2semidirect
7. C23×AΣL(1,𝔽16)C2semidirect
8. C23×Dic23C4semidirect
11. #10625124C4semidirect
16. #10625057C4semidirect
20. #10625048C4semidirect
124. AΣL(1,𝔽16)D23semidirect
150. C23#2120semidirect

Maximal subgroups

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

subgroupindex
#130929232
#130923982
#130923892
#130922082
#130922062
#130922042
C23×AΣL(1,𝔽16)2
#212023