Finite Group Databasebeta

← #34071112

Subgroups — #34071112

Order 19328.

270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752955C211yesmaximal, characteristic, complemented
2#23752400C211yesmaximal, characteristic, complemented
3#23752398C211yesmaximal, characteristic, complemented
4#23752392C211yesmaximal, characteristic, complemented
5#23752006C211yesmaximal, characteristic, complemented
6#23752000C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic
9#18012772—21no—
10#18012726—21no—
11#18012726C2211yescharacteristic
12#18012725—21no—
13#18012725—21no—
14#18012725—21no—
15#18012709—21no—
16#18012708—21no—
17#18012708—21no—
18#18012707—21no—
19#18012707C2211yescharacteristic
20#18012665—21no—
21#18012654C2211yescharacteristic
22#18012653—21no—
23#18012653—21no—
24#120×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27C23×D151D411yescharacteristic, complemented
28#14559004—21no—
29#14559003—41no—
30C2×Dic302—21no—
31C2×Dic302D411yescharacteristic, complemented
32C2×D604—41no—
33C2×C22⋊D151—21no—
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36C2×C22⋊D151—21no—
37C2×C22⋊D151—21no—
38C2×C22⋊D151—41no—
39D4×D151—41no—
40Dic604—41no—
41#14558993—41no—
42C22⋊Dic151—21no—
43C22⋊Dic151—21no—
44C22⋊Dic151—21no—
45C22⋊Dic151—21no—
46C22⋊Dic151—21no—
47C22⋊Dic151—41no—
48C22⋊Dic151D411yescharacteristic, complemented
49(C2×D151)⋊C4—21no—
50(C2×D151)⋊C4—21no—
51(C2×D151)⋊C4—21no—
52(C2×D151)⋊C4—41no—
53C4×Dic151—21no—
54C4×Dic151D411yescharacteristic, complemented
55C24×C151D411yescharacteristic, complemented
56C2×D4×C151—21no—
57C2×D4×C151C2311yescharacteristic
58M16×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151D411yescharacteristic, complemented
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65C22×D151—41no—
66C22×D151—81no—
67Dic302—21no—
68Dic302—41no—
69Dic302—81no—
70D604—21no—
71D604—82no—
72C22⋊D151—41no—
73C22⋊D151—41no—
74C22⋊D151—41no—
75C22⋊D151—81no—
76C22⋊D151—81no—
77C22⋊D151—81no—
78C22⋊D151—82no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—21no—
82C2×Dic151—21no—
83C2×Dic151—21no—
84C2×Dic151—41no—
85C4×D151—41no—
86C23×C151—21no—
87C23×C151—41no—
88C23×C151—81no—
89C23×C151C2×D411yescharacteristic
90C23×C151C2×D411yescharacteristic
91D4×C151—41no—
92D4×C151—81no—
93C2×C4×C151—21no—
94C2×C4×C151—41no—
95C2×C4×C151C2×D411yescharacteristic
96C8×C151—41no—
97C22×C151—21no—
98C22×C151—21no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151—42no—
104C22×C151—41no—
105C22×C151—81no—
106C22×C151#12011yescharacteristic
107C2×D151—41no—
108C2×D151—41no—
109C2×D151—42no—
110C2×D151—41no—
111C2×D151—41no—
112C2×D151—81no—
113C2×D151—81no—
114C2×D151—81no—
115C4×C151—21no—
116C4×C151—41no—
117C4×C151—81no—
118Dic151—41no—
119Dic151—41no—
120Dic151—41no—
121Dic151—41no—
122Dic151—81no—
123C2×C151—21no—
124C2×C151—41no—
125C2×C151—41no—
126C2×C151—81no—
127C2×C151B(4,𝔽2)11yescharacteristic
128D151—81no—
129D151—81no—
130C151#219911yescharacteristic, complemented, Sylow
131#2199—1511nomaximal, Sylow
132H(3,𝔽4)—1511no—
133B(4,𝔽2)—1511no—
134B(4,𝔽2)—1511no—
135#455—1511no—
136#354—1511no—
137AΣL(1,𝔽16)—1511no—
138AΣL(1,𝔽16)D15111yescharacteristic, complemented
139H(5,𝔽2)—1511no—
140#137—3021no—
141#124—3021no—
142#124—3021no—
143#124—3021no—
144#124—3021no—
145#124—1511no—
146#120—3021no—
147#120—3021no—
148#120—3021no—
149#120—3021no—
150#120—1511no—
151#120C2×D15111yescharacteristic
152#104—3021no—
153#100C2×D15111yescharacteristic
154#99—3021no—
155#99—3021no—
156#99—1511no—
157#99C2×D15111yescharacteristic
158C24—1511no—
159C24D60411yescharacteristic, complemented
160#41—3021no—
161#41—6041no—
162C2×Q8—3021no—
163C2×Q8—1511no—
164C2×D4—21no—
165C2×D4—3021no—
166C2×D4—3021no—
167C2×D4—3021no—
168C2×D4—3021no—
169C2×D4—3021no—
170C2×D4—6041no—
171C2×D4—6041no—
172C2×D4—6041no—
173C2×D4C22×D15111yescharacteristic
174Q16—6041no—
175SD16—6041no—
176M16—21no—
177C22⋊C4—21no—
178C22⋊C4—21no—
179C22⋊C4—3021no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—3021no—
185C22⋊C4—3021no—
186C22⋊C4—3021no—
187C22⋊C4—6041no—
188C22⋊C4—6041no—
189C22⋊C4—1511no—
190C22⋊C4D60411yescharacteristic, complemented
191C42—3021no—
192C42—1511no—
193C23—21no—
194C23—41no—
195C23—81no—
196C23—3021no—
197C23—3021no—
198C23—3021no—
199C23—6041no—
200C23—12081no—
201C23D4×D15111yescharacteristic
202C23C2×D60411yescharacteristic
203Q8—3021no—
204Q8—6041no—
205Q8—12081no—
206D4—41no—
207D4—81no—
208D4—3021no—
209D4—6041no—
210D4—6041no—
211D4—6041no—
212D4—12082no—
213D4—12081no—
214D4—12081no—
215D4—12081no—
216D4—12082no—
217C2×C4—21no—
218C2×C4—41no—
219C2×C4—3021no—
220C2×C4—3021no—
221C2×C4—3021no—
222C2×C4—3021no—
223C2×C4—3021no—
224C2×C4—6041no—
225C2×C4—6041no—
226C2×C4D4×D15111yescharacteristic
227C8—41no—
228C22—21no—
229C22—21no—
230C22—41no—
231C22—41no—
232C22—41no—
233C22—41no—
234C22—42no—
235C22—41no—
236C22—81no—
237C22—6041no—
238C22—6041no—
239C22—6042no—
240C22—6041no—
241C22—6041no—
242C22—12081no—
243C22—12081no—
244C22—12081no—
245C22#1801270911yescharacteristic
246C4—21no—
247C4—41no—
248C4—81no—
249C4—6041no—
250C4—6041no—
251C4—6041no—
252C4—6041no—
253C4—12081no—
254C2—21no—
255C2—41no—
256C2—41no—
257C2—81no—
258C2—12081no—
259C2—12081no—
260C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
FittingAΣL(1,𝔽16)×C151C2
socleC2×C151B(4,𝔽2)
hypercenterAΣL(1,𝔽16)D151
hypocenterC151#2199
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ AΣL(1,𝔽16)

Complements

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

NH ≅ G/Ntype
1. #23752955C2semidirect
2. #23752400C2semidirect
3. #23752398C2semidirect
4. #23752392C2semidirect
5. #23752006C2semidirect
6. #23752000C2semidirect
7. AΣL(1,𝔽16)×C151C2semidirect
27. C23×D151D4semidirect
31. C2×Dic302D4semidirect
48. C22⋊Dic151D4semidirect
54. C4×Dic151D4semidirect
55. C24×C151D4semidirect
61. C22⋊C4×C151D4semidirect
130. C151#2199semidirect
138. AΣL(1,𝔽16)D151semidirect
159. C24D604semidirect
190. C22⋊C4D604semidirect

Maximal subgroups

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

subgroupindex
#237529552
#237524002
#237523982
#237523922
#237520062
#237520002
AΣL(1,𝔽16)×C1512
#2199151