Finite Group Databasebeta

← #34069019

Subgroups — #34069019

Order 19328.

852 conjugacy classes of subgroups; only the 153 normal subgroups are shown.

normal subgroups only

This group has 852 conjugacy classes of subgroups — too many to draw. Only its 153 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
1C23×C4×D151C211yesmaximal, characteristic
2C2×C22⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
3C2×(C2×D151)⋊C8C214yesmaximal, complemented
4C2×C22⋊C8×C151C211yesmaximal, characteristic, complemented
5C24×D151C411yescharacteristic
6C23×Dic151C411yescharacteristic
7C22×C4×D151—22no—
8C22×C4×D151—22no—
9C22×C4×D151—28no—
10C22×C4×D151C412yes—
11C22×C4×D151C2212yes—
12C22×C151⋊C8C2212yescomplemented
13C22⋊(C151⋊C8)—22no—
14(C2×D151)⋊C8—28no—
15C23×C4×C151C2211yescharacteristic
16C22×C8×C151C2212yescomplemented
17C22⋊C8×C151—22no—
18C23×D151—24no—
19C23×D151—24no—
20C23×D151—22no—
21C23×D151—22no—
22C23×D151C814yescomplemented
23C23×D151C2×C412yes—
24C22×Dic151—24no—
25C22×Dic151—22no—
26C22×Dic151C2×C412yes—
27C2×C4×D151—216no—
28C2×C4×D151—216no—
29C2×C4×D151—24no—
30C2×C4×D151—24no—
31C2×C4×D151—24no—
32C2×C4×D151—24no—
33C2×C4×D151—22no—
34C2×C4×D151—22no—
35C2×C4×D151D418yes—
36C2×C151⋊C8—24no—
37C2×C151⋊C8—22no—
38C24×C151C2×C411yescharacteristic
39C22×C4×C151—24no—
40C22×C4×C151C2×C411yescharacteristic
41C22×C4×C151D412yes—
42C22×C4×C151D412yes—
43C22×C4×C151C2311yescharacteristic
44C2×C8×C151—22no—
45C2×C8×C151—24no—
46C22×D151—28no—
47C22×D151—216no—
48C22×D151—28no—
49C22×D151—28no—
50C22×D151—22no—
51C22×D151—22no—
52C22×D151—22no—
53C22×D151—22no—
54C22×D151—216no—
55C22×D151C22⋊C414yes—
56C22×D151C2×C814yes—
57C22×D151M1614yes—
58C2×Dic151—28no—
59C2×Dic151—22no—
60C2×Dic151—22no—
61C2×Dic151C22⋊C414yes—
62C4×D151—216no—
63C4×D151—28no—
64C4×D151—28no—
65C151⋊C8—42no—
66C23×C151—22no—
67C23×C151—22no—
68C23×C151C22⋊C412yes—
69C23×C151C2×C812yes—
70C23×C151M1612yes—
71C23×C151C22×C411yescharacteristic
72C2×C4×C151—22no—
73C2×C4×C151—24no—
74C2×C4×C151—24no—
75C2×C4×C151C22⋊C412yes—
76C2×C4×C151C2×D414yes—
77C2×C4×C151C2×D411yescharacteristic
78C2×C4×C151C2×D411yescharacteristic
79C8×C151—42no—
80C22×C151—22no—
81C22×C151—24no—
82C22×C151—22no—
83C22×C151—24no—
84C22×C151C22⋊C814yescomplemented
85C22×C151C2×C22⋊C412yes—
86C22×C151C2×C22⋊C411yescharacteristic
87C22×C151C22×C811yescharacteristic
88C22×C151C2×M1612yes—
89C22×C151C2×M1611yescharacteristic
90C2×D151—232no—
91C2×D151—24no—
92C2×D151—24no—
93C2×D151—24no—
94C2×D151—24no—
95C2×D151—24no—
96C2×D151—24no—
97C2×D151C22⋊C818yescomplemented
98C4×C151—22no—
99C4×C151#12012yes—
100C4×C151#12012yes—
101Dic151—24no—
102C2×C151—24no—
103C2×C151#37911yescharacteristic
104C2×C151C2×C22⋊C812yes—
105C2×C151C2×C22⋊C811yescharacteristic
106C2×C151#40712yes—
107C2×C151#40711yescharacteristic
108D151—28no—
109C151#177911yescharacteristic, complemented, Sylow
110#1779—1511nomaximal, Sylow
111C24×C4—1511no—
112C2×C22⋊C8—1511no—
113C2×C22⋊C8—1514no—
114C2×C22⋊C8D15111yescharacteristic, complemented
115C25—1511no—
116C23×C4—3028no—
117C23×C4—3022no—
118C23×C4—3022no—
119C23×C4—1511no—
120C23×C4—1512no—
121C23×C4—1512no—
122C23×C4C2×D15111yescharacteristic
123C22×C8—1512no—
124C22×C8C2×D15112yescomplemented
125C22⋊C8—22no—
126C22⋊C8—3028no—
127C22⋊C8—3022no—
128C24—3024no—
129C24—3024no—
130C24—3022no—
131C24—3022no—
132C24—1514no—
133C24—1512no—
134C24C4×D15111yescharacteristic
135C22×C4—24no—
136C22×C4—30216no—
137C22×C4—30216no—
138C22×C4—3024no—
139C22×C4—3024no—
140C22×C4—3022no—
141C22×C4—3024no—
142C22×C4—3024no—
143C22×C4—3024no—
144C22×C4—3022no—
145C22×C4—3022no—
146C22×C4—1512no—
147C22×C4—1518no—
148C22×C4C4×D15111yescharacteristic
149C22×C4C22⋊D15112yes—
150C22×C4D60412yes—
151C22×C4C22×D15111yescharacteristic
152C2×C8—24no—
153C2×C8—22no—
154C2×C8—3024no—
155C2×C8—3022no—
156C23—22no—
157C23—22no—
158C23—3028no—
159C23—30216no—
160C23—3028no—
161C23—30216no—
162C23—3022no—
163C23—3022no—
164C23—3022no—
165C23—3022no—
166C23—3028no—
167C23—1514no—
168C23—1514no—
169C23—1514no—
170C23(C2×D151)⋊C412yes—
171C23C8×D15112yes—
172C23#1455898712yes—
173C23C2×C4×D15111yescharacteristic
174C2×C4—22no—
175C2×C4—24no—
176C2×C4—24no—
177C2×C4—30216no—
178C2×C4—3028no—
179C2×C4—3022no—
180C2×C4—3022no—
181C2×C4—3028no—
182C2×C4—3028no—
183C2×C4—1514no—
184C2×C4(C2×D151)⋊C412yes—
185C2×C4D4×D15114yes—
186C2×C4C2×C22⋊D15111yescharacteristic
187C2×C4C2×D60411yescharacteristic
188C8—42no—
189C8—6042no—
190C22—22no—
191C22—24no—
192C22—24no—
193C22—22no—
194C22—30232no—
195C22—3024no—
196C22—3024no—
197C22—3024no—
198C22—3024no—
199C22—3024no—
200C22—3024no—
201C22—1518no—
202C22(C2×D151)⋊C814yescomplemented
203C22C22⋊C4×D15112yes—
204C22C2×(C2×D151)⋊C411yescharacteristic
205C22C2×C8×D15111yescharacteristic
206C22M16×D15112yes—
207C22C2×#1455898711yescharacteristic
208C4—22no—
209C4—3024no—
210C4#1801270712yes—
211C4#1801270912yes—
212C2—24no—
213C2—3028no—
214C2#2375206711yescharacteristic
215C2C22⋊C8×D15112yes—
216C2C2×(C2×D151)⋊C811yescharacteristic
217C2#2375217412yes—
218C2#2375217511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×D151
commutatorC22×C151C22×C8
FittingC2×C22⋊C8×C151C2
socleC23×C151C22×C4
prime radicalC24×D151C4
cosocleC22×C4×C151C23
hypercenterC2×C22⋊C8D151
hypocenterC151#1779
LCSG ▷ C22×C151 ▷ C151
UCSC1 ◁ C22×C4 ◁ C2×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊(C151⋊C8)C2semidirect
3. C2×(C2×D151)⋊C8C2semidirect
4. C2×C22⋊C8×C151C2semidirect
12. C22×C151⋊C8C22semidirect
16. C22×C8×C151C22semidirect
22. C23×D151C8semidirect
84. C22×C151C22⋊C8semidirect
97. C2×D151C22⋊C8semidirect
109. C151#1779semidirect
114. C2×C22⋊C8D151semidirect
124. C22×C8C2×D151semidirect
202. C22(C2×D151)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C23×C4×D1512
C2×C22⋊(C151⋊C8)2
C2×(C2×D151)⋊C82
C2×C22⋊C8×C1512
#1779151