Finite Group Databasebeta

← #34079240

Subgroups — #34079240

Order 19328.

380 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 133 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#23752769C211yesmaximal, characteristic
2#23752542C212yesmaximal
3#23752497C212yesmaximal, complemented
4#23752422C212yesmaximal, complemented
5#23752368C212yesmaximal
6#23752317C214yesmaximal, complemented
7#23752269C211yesmaximal, characteristic
8C2×C4×Q8×C151C211yesmaximal, characteristic
9C2×#14558994C2214yes—
10#18012739C2211yescharacteristic
11#18012739C2211yescharacteristic
12#18012731—21no—
13#18012718—21no—
14#18012718C2212yes—
15C4×Dic302—21no—
16C4×Dic302C2212yes—
17#18012698—21no—
18#18012670C2214yes—
19C4⋊(C151⋊C8)C2212yes—
20#18012663C2214yes—
21#18012662C2214yes—
22C22⋊(C151⋊C8)C2212yes—
23#18012650C2212yes—
24C22×Q8×C151C2211yescharacteristic
25C4×Q8×C151—21no—
26C4×Q8×C151—21no—
27C4×Q8×C151C2212yes—
28C4×Q8×C151C2212yes—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151C2211yescharacteristic
31C2×C42×C151—21no—
32C2×C42×C151C2211yescharacteristic
33C2×Dic302—21no—
34C2×Dic302C2312yes—
35#14558994—28no—
36C2×C151⋊C8C2314yes—
37C4⋊Dic151—21no—
38C4⋊Dic151—21no—
39C4⋊Dic151—21no—
40C4⋊Dic151C2312yes—
41Dic151⋊C4—22no—
42Dic151⋊C4—22no—
43C22⋊Dic151—22no—
44C4×Dic151—22no—
45C2×Q8×C151—24no—
46C2×Q8×C151—21no—
47C2×Q8×C151C2312yes—
48C22×C4×C151—21no—
49C22×C4×C151—21no—
50C22×C4×C151D411yescharacteristic
51C22×C4×C151D411yescharacteristic
52C22×C4×C151C2311yescharacteristic
53C4⋊C4×C151—22no—
54C4⋊C4×C151—22no—
55C4⋊C4×C151—21no—
56C4⋊C4×C151C2312yes—
57C42×C151—22no—
58C42×C151—22no—
59C42×C151D411yescharacteristic
60C42×C151D411yescharacteristic
61C42×C151C2311yescharacteristic
62C42×C151C2311yescharacteristic
63Dic302—24no—
64Dic302—42no—
65C2×Dic151—22no—
66C2×Dic151—22no—
67C151⋊C8—24no—
68C23×C151C2×D411yescharacteristic
69Q8×C151—24no—
70Q8×C151—22no—
71Q8×C151#4114yes—
72C2×C4×C151—24no—
73C2×C4×C151—22no—
74C2×C4×C151—22no—
75C2×C4×C151—22no—
76C2×C4×C151—22no—
77C2×C4×C151—22no—
78C2×C4×C151—42no—
79C2×C4×C151C2×D411yescharacteristic
80C2×C4×C151C2×D411yescharacteristic
81C2×C4×C151C2×D411yescharacteristic
82C2×C4×C151C2×D411yescharacteristic
83C2×C4×C151C2×D411yescharacteristic
84C2×C4×C151C2411yescharacteristic
85C22×C151—21no—
86C22×C151—21no—
87C22×C151#13712yes—
88C22×C151C22×D411yescharacteristic
89C4×C151—24no—
90C4×C151—21no—
91C4×C151—21no—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—42no—
95C4×C151#13712yes—
96C4×C151C2×#4112yes—
97Dic151—42no—
98Dic151—42no—
99C2×C151—22no—
100C2×C151#52511yescharacteristic
101C2×C151C2×#13711yescharacteristic
102C2×C151C2×#13711yescharacteristic
103C151#311311yescharacteristic, complemented, Sylow
104#3113—1511nomaximal, Sylow
105#533—1511no—
106C2×C4×Q8D15111yescharacteristic
107#483—1512no—
108#475—1512no—
109#462—1512no—
110#451—1512no—
111#441—1514no—
112#432—1511no—
113C22×Q8C2×D15111yescharacteristic
114C2×Q16—1514no—
115C4⋊Q8—1511no—
116C4⋊Q8—1511no—
117#125—3021no—
118C22⋊Q8—3021no—
119C22⋊Q8—1512no—
120C4×Q8—21no—
121C4×Q8—21no—
122C4×Q8—3021no—
123C4×Q8—1512no—
124C4×Q8C2×D15112yes—
125C4×Q8C2×D15112yes—
126#117—3021no—
127C2×C4⋊C4—21no—
128C2×C4⋊C4C2×D15111yescharacteristic
129C2×C42—21no—
130C2×C42C2×D15111yescharacteristic
131#106—1514no—
132C4⋊C8—1512no—
133#103—1514no—
134#103—1514no—
135C22⋊C8—1512no—
136#97—1512no—
137C2×Q8—24no—
138C2×Q8—21no—
139C2×Q8—3021no—
140C2×Q8—1512no—
141C2×Q8C22×D15112yes—
142C22×C4—21no—
143C22×C4—21no—
144C22×C4C22⋊D15111yescharacteristic
145C22×C4C22⋊D15111yescharacteristic
146C22×C4C22×D15111yescharacteristic
147Q16—3028no—
148C2×C8—1514no—
149C4⋊C4—22no—
150C4⋊C4—22no—
151C4⋊C4—21no—
152C4⋊C4—3022no—
153C4⋊C4—3022no—
154C4⋊C4—3021no—
155C4⋊C4—3021no—
156C4⋊C4—3021no—
157C4⋊C4—1512no—
158C4⋊C4C22×D15112yes—
159C22⋊C4—3022no—
160C42—22no—
161C42—22no—
162C42—3022no—
163C42C22⋊D15111yescharacteristic
164C42C22⋊D15111yescharacteristic
165C42C22×D15111yescharacteristic
166C42C22×D15111yescharacteristic
167C23C2×C22⋊D15111yescharacteristic
168Q8—24no—
169Q8—22no—
170Q8—3024no—
171Q8—6042no—
172Q8#1455900414yes—
173C2×C4—24no—
174C2×C4—22no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—22no—
179C2×C4—42no—
180C2×C4—3022no—
181C2×C4—3022no—
182C2×C4C2×C22⋊D15111yescharacteristic
183C2×C4C2×C22⋊D15111yescharacteristic
184C2×C4C2×C22⋊D15111yescharacteristic
185C2×C4C2×C22⋊D15111yescharacteristic
186C2×C4C2×C22⋊D15111yescharacteristic
187C2×C4C23×D15111yescharacteristic
188C8—3024no—
189C22—21no—
190C22—21no—
191C22#1801276912yes—
192C22C22×C22⋊D15111yescharacteristic
193C4—24no—
194C4—21no—
195C4—21no—
196C4—21no—
197C4—21no—
198C4—42no—
199C4—6042no—
200C4—6042no—
201C4#1801277012yes—
202C4C2×#1455900412yes—
203C2—22no—
204C2#2375272311yescharacteristic
205C2C2×#1801276911yescharacteristic
206C2C2×#1801277011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC2×C4×Q8×C151C2
socleC22×C151C22×D4
prime radicalC23×C151C2×D4
hypercenterC2×C4×Q8D151
hypocenterC151#3113
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
3. #23752497C2semidirect
4. #23752422C2semidirect
6. #23752317C2semidirect
103. C151#3113semidirect

Maximal subgroups

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

subgroupindex
#237527692
#237525422
#237524972
#237524222
#237523682
#237523172
#237522692
C2×C4×Q8×C1512
#3113151