Finite Group Databasebeta

← #15675040

Subgroups — #15675040

Order 2944.

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

normal subgroups only

This group has 280 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#13092977C211yesmaximal, characteristic
2#100×D23C211yesmaximal, characteristic, complemented
3#99×D23C211yesmaximal, characteristic, complemented
4#13092208C211yesmaximal, characteristic, complemented
5#13092206C211yesmaximal, characteristic, complemented
6#13092204C211yesmaximal, characteristic, complemented
7C23×AΣL(1,𝔽16)C211yesmaximal, characteristic, complemented
8C22×C22⋊D23C411yescharacteristic, complemented
9C2×D4×D23C2211yescharacteristic
10C23×#120C2211yescharacteristic
11#10625124C411yescharacteristic, complemented
12#10625109—21no—
13#10625108—21no—
14#10625106C2211yescharacteristic
15M16×D23—21no—
16#10625057C411yescharacteristic, complemented
17#10625055—21no—
18#10625054—21no—
19C22⋊C4×D23—21no—
20C22⋊C4×D23C411yescharacteristic, complemented
21C23×#100C2211yescharacteristic
22C23×#99C2211yescharacteristic
23#10625016C2211yescharacteristic
24#10625015C2211yescharacteristic
25#10625005—21no—
26#10624988—21no—
27C24×C23C2×C411yescharacteristic, complemented
28C23×D23C2×C411yescharacteristic
29C23×D23D411yescharacteristic
30C2×D4×C23—21no—
31C2×D4×C23C2311yescharacteristic
32C2×C22⋊D23—21no—
33C2×C22⋊D23—21no—
34C2×C22⋊D23—21no—
35C2×C22⋊D23—41no—
36C2×C22⋊D23—41no—
37C2×C22⋊D23C2×C411yescharacteristic
38C2×C22⋊D23D411yescharacteristic
39C22×Dic23C2×C411yescharacteristic, complemented
40D4×D23—41no—
41D4×D23—41no—
42C2×D92D411yescharacteristic
43C2×C4×D23—21no—
44C2×C4×D23—41no—
45C2×C4×D23D411yescharacteristic
46M16×C23—21no—
47C22⋊C4×C23—21no—
48C22⋊C4×C23—21no—
49C22⋊C4×C23C2×C411yescharacteristic, complemented
50C22⋊Dic23—21no—
51C22⋊Dic23—21no—
52C22⋊Dic23—21no—
53C22⋊Dic23C2×C411yescharacteristic, complemented
54(C2×D23)⋊C4—21no—
55(C2×D23)⋊C4—21no—
56(C2×D23)⋊C4—41no—
57C4⋊Dic23—21no—
58Dic23⋊C4—21no—
59#67267—21no—
60#67262—41no—
61C8×D23—41no—
62C23×C23—21no—
63C23×C23—41no—
64C23×C23—81no—
65C23×C23C22×C411yescharacteristic
66C23×C23C2×D411yescharacteristic
67C22×D23—21no—
68C22×D23—21no—
69C22×D23—21no—
70C22×D23—21no—
71C22×D23—81no—
72C22×D23—81no—
73C22×D23C22⋊C411yescharacteristic
74C22×D23C22⋊C411yescharacteristic
75C22×D23C22⋊C411yescharacteristic
76D4×C23—41no—
77D4×C23—81no—
78C2×C4×C23—21no—
79C2×C4×C23—41no—
80C2×C4×C23C2×D411yescharacteristic
81C22⋊D23—41no—
82C22⋊D23—41no—
83C22⋊D23—42no—
84C22⋊D23—41no—
85C22⋊D23—41no—
86C22⋊D23—81no—
87C2×Dic23—21no—
88C2×Dic23—21no—
89C2×Dic23—41no—
90C2×Dic23—41no—
91C2×Dic23C22⋊C411yescharacteristic
92D92—41no—
93C4×D23—21no—
94C4×D23—21no—
95C4×D23—81no—
96C4×D23—82no—
97C8×C23—41no—
98C23⋊C8—41no—
99#2121—231nomaximal, Sylow
100C22×C23—21no—
101C22×C23—21no—
102C22×C23—41no—
103C22×C23—41no—
104C22×C23—41no—
105C22×C23—41no—
106C22×C23—41no—
107C22×C23—82no—
108C22×C23C2×C22⋊C411yescharacteristic
109C2×D23—21no—
110C2×D23—21no—
111C2×D23—41no—
112C2×D23—42no—
113C2×D23—41no—
114C2×D23—41no—
115C2×D23—81no—
116C2×D23—81no—
117C2×D23—81no—
118C2×D23#9911yescharacteristic
119C2×D23#9911yescharacteristic
120C4×C23—21no—
121C4×C23—41no—
122C4×C23—81no—
123Dic23—21no—
124Dic23—41no—
125Dic23—41no—
126Dic23—81no—
127#534—231no—
128C2×#100—231no—
129C2×#99—231no—
130#352—231no—
131#352—231no—
132AΣL(1,𝔽16)—231no—
133AΣL(1,𝔽16)D2311yescharacteristic, complemented
134C2×C23—21no—
135C2×C23—41no—
136C2×C23—41no—
137C2×C23—81no—
138C2×C23C2×#9911yescharacteristic
139D23—21no—
140D23—21no—
141D23—41no—
142D23—41no—
143C22×D4—231no—
144C22×D4—231no—
145C2×M16—461no—
146#123—231no—
147#123—231no—
148#123—461no—
149#121—461no—
150#121—461no—
151#120—231no—
152#120—461no—
153#120C2×D2311yescharacteristic
154C2×C22⋊C4—231no—
155C2×C22⋊C4—461no—
156#100—231no—
157#100—461no—
158#100C2×D2311yescharacteristic
159#99—231no—
160#99—461no—
161#99C2×D2311yescharacteristic
162C23#212111yescharacteristic, complemented, Sylow
163C24—231no—
164C24—231no—
165C24C4×D2311yescharacteristic, complemented
166C2×D4—21no—
167C2×D4—231no—
168C2×D4—231no—
169C2×D4—231no—
170C2×D4—461no—
171C2×D4—461no—
172C2×D4—461no—
173C2×D4—921no—
174C2×D4—921no—
175C2×D4—921no—
176C2×D4—921no—
177C2×D4C22×D2311yescharacteristic
178C22×C4—231no—
179C22×C4—231no—
180C22×C4—461no—
181C22×C4—921no—
182M16—21no—
183M16—461no—
184M16—921no—
185C2×C8—921no—
186C4⋊C4—461no—
187C4⋊C4—461no—
188C22⋊C4—21no—
189C22⋊C4—21no—
190C22⋊C4—231no—
191C22⋊C4—461no—
192C22⋊C4—461no—
193C22⋊C4—461no—
194C22⋊C4—461no—
195C22⋊C4—461no—
196C22⋊C4—921no—
197C22⋊C4C4×D2311yescharacteristic, complemented
198C23—21no—
199C23—41no—
200C23—81no—
201C23—231no—
202C23—231no—
203C23—231no—
204C23—461no—
205C23—461no—
206C23—461no—
207C23—461no—
208C23—1841no—
209C23—1841no—
210C23C2×C4×D2311yescharacteristic
211C23D4×D2311yescharacteristic
212D4—41no—
213D4—81no—
214D4—921no—
215D4—921no—
216D4—921no—
217D4—921no—
218D4—921no—
219D4—922no—
220D4—1841no—
221C2×C4—21no—
222C2×C4—41no—
223C2×C4—231no—
224C2×C4—461no—
225C2×C4—461no—
226C2×C4—461no—
227C2×C4—461no—
228C2×C4—921no—
229C2×C4—921no—
230C2×C4—1841no—
231C2×C4—1842no—
232C2×C4D4×D2311yescharacteristic
233C8—41no—
234C8—921no—
235C22—21no—
236C22—21no—
237C22—41no—
238C22—41no—
239C22—41no—
240C22—41no—
241C22—41no—
242C22—82no—
243C22—231no—
244C22—231no—
245C22—461no—
246C22—461no—
247C22—921no—
248C22—921no—
249C22—921no—
250C22—922no—
251C22—1841no—
252C22—1841no—
253C22—1841no—
254C22C22⋊C4×D2311yescharacteristic
255C4—21no—
256C4—41no—
257C4—81no—
258C4—461no—
259C4—921no—
260C4—921no—
261C4—1841no—
262C2—21no—
263C2—41no—
264C2—41no—
265C2—81no—
266C2—461no—
267C2—461no—
268C2—921no—
269C2—921no—
270C2#99×D2311yescharacteristic
subgroupG/H
centerC2#99×D23
commutatorC23×C23C22×C4
FrattiniC2×D4C22×D23
FittingC23×AΣL(1,𝔽16)C2
socleC2×C23C2×#99
prime radical#13092977C2
cosocleC2×D4×C23C23
hypercenterAΣL(1,𝔽16)D23
hypocenterC23#2121
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. #100×D23C2semidirect
3. #99×D23C2semidirect
4. #13092208C2semidirect
5. #13092206C2semidirect
6. #13092204C2semidirect
7. C23×AΣL(1,𝔽16)C2semidirect
8. C22×C22⋊D23C4semidirect
11. #10625124C4semidirect
16. #10625057C4semidirect
20. C22⋊C4×D23C4semidirect
27. C24×C23C2×C4semidirect
39. C22×Dic23C2×C4semidirect
49. C22⋊C4×C23C2×C4semidirect
53. C22⋊Dic23C2×C4semidirect
133. AΣL(1,𝔽16)D23semidirect
162. C23#2121semidirect
165. C24C4×D23semidirect
197. C22⋊C4C4×D23semidirect

Maximal subgroups

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

subgroupindex
#130929772
#100×D232
#99×D232
#130922082
#130922062
#130922042
C23×AΣL(1,𝔽16)2
#212123