Finite Group Databasebeta

← #34071119

Subgroups — #34071119

Order 19328.

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

normal subgroups only

This group has 260 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#23752951C211yesmaximal, characteristic, complemented
2#23752403C211yesmaximal, characteristic, complemented
3#23752398C211yesmaximal, characteristic, complemented
4#23752382C211yesmaximal, characteristic, complemented
5#23752004C211yesmaximal, characteristic, complemented
6#23752003C211yesmaximal, characteristic, complemented
7AΣL(1,𝔽16)×C151C211yesmaximal, characteristic, complemented
8#18012784C2211yescharacteristic
9#18012767—21no—
10#18012735C2211yescharacteristic
11#18012732—21no—
12#18012723—21no—
13#18012721—21no—
14#18012720C2211yescharacteristic
15#18012712—21no—
16#18012711—21no—
17#18012710—21no—
18#18012708—21no—
19#18012708—21no—
20#18012665—21no—
21#18012654C2211yescharacteristic
22#18012653—21no—
23#18012653—21no—
24#120×C151C2211yescharacteristic
25#100×C151C2211yescharacteristic
26#99×C151C2211yescharacteristic
27#14559004—21no—
28#14559003—41no—
29C2×D604D411yescharacteristic, complemented
30C2×C22⋊D151—21no—
31C2×C22⋊D151—21no—
32C2×C22⋊D151—21no—
33C2×C22⋊D151—21no—
34C2×C22⋊D151—21no—
35C2×C22⋊D151—21no—
36C2×C22⋊D151—41no—
37D4×D151—41no—
38C22×Dic151D411yescharacteristic, complemented
39C2×C4×D151—21no—
40#14558993—41no—
41D1208—41no—
42C4⋊Dic151—21no—
43C4⋊Dic151—41no—
44Dic151⋊C4—21no—
45Dic151⋊C4—21no—
46C22⋊Dic151—21no—
47C22⋊Dic151—21no—
48C22⋊Dic151—21no—
49C22⋊Dic151—21no—
50C22⋊Dic151—41no—
51C22⋊Dic151D411yescharacteristic, complemented
52(C2×D151)⋊C4—21no—
53(C2×D151)⋊C4—41no—
54C4×Dic151D411yescharacteristic, complemented
55C24×C151D411yescharacteristic
56C2×D4×C151—21no—
57C2×D4×C151C2311yescharacteristic
58M16×C151—21no—
59C22⋊C4×C151—21no—
60C22⋊C4×C151—21no—
61C22⋊C4×C151D411yescharacteristic
62C22×D151—21no—
63C22×D151—21no—
64C22×D151—21no—
65Dic302—21no—
66D604—21no—
67D604—41no—
68C22⋊D151—41no—
69C22⋊D151—41no—
70C22⋊D151—41no—
71C22⋊D151—81no—
72C22⋊D151—81no—
73C22⋊D151—81no—
74C22⋊D151—81no—
75C22⋊D151—82no—
76C2×Dic151—21no—
77C2×Dic151—21no—
78C2×Dic151—21no—
79C2×Dic151—21no—
80C2×Dic151—21no—
81C2×Dic151—41no—
82C2×Dic151—41no—
83C4×D151—41no—
84C4×D151—81no—
85C23×C151—21no—
86C23×C151—41no—
87C23×C151—81no—
88C23×C151C2×D411yescharacteristic
89C23×C151C2×D411yescharacteristic
90D4×C151—41no—
91D4×C151—81no—
92C2×C4×C151—21no—
93C2×C4×C151—41no—
94C2×C4×C151C2×D411yescharacteristic
95C8×C151—41no—
96C22×C151—21no—
97C22×C151—21no—
98C22×C151—41no—
99C22×C151—41no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—42no—
103C22×C151—41no—
104C22×C151—81no—
105C22×C151#12011yescharacteristic
106C2×D151—41no—
107C2×D151—41no—
108C2×D151—41no—
109C2×D151—41no—
110C2×D151—81no—
111C2×D151—81no—
112C4×C151—21no—
113C4×C151—41no—
114C4×C151—81no—
115Dic151—41no—
116Dic151—41no—
117Dic151—41no—
118Dic151—41no—
119Dic151—81no—
120C2×C151—21no—
121C2×C151—41no—
122C2×C151—41no—
123C2×C151—81no—
124C2×C151B(4,𝔽2)11yescharacteristic
125D151—81no—
126D151—81no—
127C151#220011yescharacteristic, complemented, Sylow
128#2200—1511nomaximal, Sylow
129#560—1511no—
130#458—1511no—
131B(4,𝔽2)—1511no—
132#453—1511no—
133#353—1511no—
134#352—1511no—
135AΣL(1,𝔽16)D15111yescharacteristic, complemented
136H(5,𝔽2)—1511no—
137AGL(1,ℤ/8)—3021no—
138#127—1511no—
139#126—3021no—
140#123—3021no—
141#123—3021no—
142#123—1511no—
143#121—3021no—
144#121—3021no—
145#121—3021no—
146#120—3021no—
147#120—3021no—
148#120C2×D15111yescharacteristic
149#104—3021no—
150#100C2×D15111yescharacteristic
151#99—3021no—
152#99—3021no—
153#99—1511no—
154#99C2×D15111yescharacteristic
155C24D60411yescharacteristic
156#41—3021no—
157#41—6041no—
158C2×D4—21no—
159C2×D4—3021no—
160C2×D4—3021no—
161C2×D4—3021no—
162C2×D4—3021no—
163C2×D4—3021no—
164C2×D4—3021no—
165C2×D4—6041no—
166C2×D4—6041no—
167C2×D4—1511no—
168C2×D4C22×D15111yescharacteristic
169C22×C4—3021no—
170C22×C4—1511no—
171SD16—6041no—
172D8—6041no—
173M16—21no—
174C4⋊C4—3021no—
175C4⋊C4—3021no—
176C4⋊C4—3021no—
177C4⋊C4—6041no—
178C22⋊C4—21no—
179C22⋊C4—21no—
180C22⋊C4—3021no—
181C22⋊C4—3021no—
182C22⋊C4—3021no—
183C22⋊C4—3021no—
184C22⋊C4—3021no—
185C22⋊C4—6041no—
186C22⋊C4—6041no—
187C22⋊C4—1511no—
188C22⋊C4D60411yescharacteristic
189C42—1511no—
190C23—21no—
191C23—41no—
192C23—81no—
193C23—3021no—
194C23—3021no—
195C23—3021no—
196C23D4×D15111yescharacteristic
197C23C2×D60411yescharacteristic
198Q8—3021no—
199D4—41no—
200D4—81no—
201D4—3021no—
202D4—6041no—
203D4—6041no—
204D4—6041no—
205D4—6041no—
206D4—12081no—
207D4—12081no—
208D4—12081no—
209D4—12081no—
210D4—12082no—
211C2×C4—21no—
212C2×C4—41no—
213C2×C4—3021no—
214C2×C4—3021no—
215C2×C4—3021no—
216C2×C4—3021no—
217C2×C4—3021no—
218C2×C4—6041no—
219C2×C4—6041no—
220C2×C4—6041no—
221C2×C4—12081no—
222C2×C4D4×D15111yescharacteristic
223C8—41no—
224C22—21no—
225C22—21no—
226C22—41no—
227C22—41no—
228C22—41no—
229C22—41no—
230C22—42no—
231C22—41no—
232C22—81no—
233C22—6041no—
234C22—6041no—
235C22—6041no—
236C22—6041no—
237C22—12081no—
238C22—12081no—
239C22#1801270911yescharacteristic
240C4—21no—
241C4—41no—
242C4—81no—
243C4—6041no—
244C4—6041no—
245C4—6041no—
246C4—6041no—
247C4—12081no—
248C2—21no—
249C2—41no—
250C2—41no—
251C2—81no—
252C2—12081no—
253C2—12081no—
254C2#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#2200
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. #23752951C2semidirect
2. #23752403C2semidirect
3. #23752398C2semidirect
4. #23752382C2semidirect
5. #23752004C2semidirect
6. #23752003C2semidirect
7. AΣL(1,𝔽16)×C151C2semidirect
29. C2×D604D4semidirect
38. C22×Dic151D4semidirect
51. C22⋊Dic151D4semidirect
54. C4×Dic151D4semidirect
127. C151#2200semidirect
135. AΣL(1,𝔽16)D151semidirect

Maximal subgroups

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

subgroupindex
#237529512
#237524032
#237523982
#237523822
#237520042
#237520032
AΣL(1,𝔽16)×C1512
#2200151