Finite Group Databasebeta

← #34069657

Subgroups — #34069657

Order 19328.

340 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 89 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#23752776C211yesmaximal, characteristic
2#23752196C211yesmaximal, characteristic, complemented
3C2×#18012655C212yesmaximal, complemented
4#23751984C212yesmaximal, complemented
5#568×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7C2×#14558988C2212yes—
8#18012735—21no—
9#18012728—21no—
10#18012713—22no—
11#18012707C414yes—
12#18012698C2211yescharacteristic
13#18012658—21no—
14#18012656—21no—
15#18012655—24no—
16C2×#41×C151C2211yescharacteristic
17#131×C151—24no—
18C2×M16×C151—22no—
19C2×M16×C151C2212yes—
20C23×D151C2×C412yes—
21C2×D604—21no—
22C2×D604—21no—
23C2×D604—22no—
24C2×D604—22no—
25C2×C22⋊D151—24no—
26#14558988—22no—
27#14558988—22no—
28C2×C151⋊C8—22no—
29C4⋊Dic151—21no—
30C22⋊Dic151C2×C412yes—
31(C2×D151)⋊C4—24no—
32C4×Dic151—21no—
33#41×C151—22no—
34#41×C151—22no—
35C2×Q8×C151D411yescharacteristic
36C2×D4×C151C2×C412yes—
37C2×D4×C151D411yescharacteristic
38C22×C4×C151D412yes—
39C22×C4×C151C2311yescharacteristic
40M16×C151—24no—
41M16×C151—22no—
42M16×C151D414yescomplemented
43C2×C8×C151—24no—
44C2×C8×C151—22no—
45C22×D151—22no—
46C22×D151—24no—
47C22×D151—82no—
48D604—41no—
49D604—42no—
50D604—41no—
51C22⋊D151—84no—
52C2×Dic151—22no—
53C151⋊C8—42no—
54C23×C151C22⋊C412yes—
55C23×C151C22×C411yescharacteristic
56Q8×C151—22no—
57D4×C151—24no—
58D4×C151—22no—
59C2×C4×C151—22no—
60C2×C4×C151—22no—
61C2×C4×C151C22⋊C412yes—
62C2×C4×C151C2×D412yes—
63C2×C4×C151C2×D411yescharacteristic
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151#4112yes—
66C8×C151—24no—
67C22×C151—22no—
68C22×C151—41no—
69C22×C151—42no—
70C22×C151C2×C22⋊C411yescharacteristic
71C22×C151C4×D412yes—
72C2×D151—44no—
73C2×D151—42no—
74C2×D151—84no—
75C4×C151—22no—
76C4×C151#12011yescharacteristic
77C4×C151#12112yes—
78C4×C151#12311yescharacteristic
79Dic151—42no—
80C2×C151—21no—
81C2×C151—22no—
82C2×C151—42no—
83C2×C151#38611yescharacteristic
84D151—82no—
85C151#191411yescharacteristic, complemented, Sylow
86#1914—1511nomaximal, Sylow
87#568D15111yescharacteristic, complemented
88#535—1511no—
89#413—1511no—
90C2×#100—1512no—
91#344—1512no—
92C2×#41C2×D15111yescharacteristic
93C22×D4—1511no—
94#131—24no—
95C2×M16—22no—
96C2×M16—1512no—
97C2×M16C2×D15112yes—
98#127—3021no—
99#124—3021no—
100#121—3022no—
101#120—1514no—
102#117—1511no—
103#101—3021no—
104#100—3021no—
105#100—3024no—
106C24—1512no—
107#41—22no—
108#41—22no—
109C2×Q8D60411yescharacteristic
110C2×D4—3024no—
111C2×D4—3022no—
112C2×D4—3021no—
113C2×D4—3021no—
114C2×D4—3022no—
115C2×D4C4×D15112yes—
116C2×D4D60411yescharacteristic
117C22×C4C22⋊D15112yes—
118C22×C4C22×D15111yescharacteristic
119M16—24no—
120M16—22no—
121M16—3022no—
122M16—3022no—
123M16C22⋊D15114yescomplemented
124C2×C8—24no—
125C2×C8—22no—
126C2×C8—3022no—
127C4⋊C4—3021no—
128C22⋊C4—3024no—
129C22⋊C4—1512no—
130C42—3021no—
131C23—3022no—
132C23—3024no—
133C23—12082no—
134C23(C2×D151)⋊C412yes—
135C23C2×C4×D15111yescharacteristic
136Q8—22no—
137D4—24no—
138D4—22no—
139D4—6041no—
140D4—6042no—
141D4—6041no—
142D4—12084no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—3022no—
146C2×C4(C2×D151)⋊C412yes—
147C2×C4C2×C22⋊D15112yes—
148C2×C4C2×C22⋊D15111yescharacteristic
149C2×C4C2×D60411yescharacteristic
150C2×C4#1455900412yes—
151C8—24no—
152C8—6042no—
153C22—22no—
154C22—41no—
155C22—42no—
156C22—6044no—
157C22—6042no—
158C22—12084no—
159C22C2×(C2×D151)⋊C411yescharacteristic
160C22C4×C22⋊D15112yes—
161C4—22no—
162C4—6042no—
163C4#1801270811yescharacteristic
164C4#1801271312yes—
165C4#1801272211yescharacteristic
166C2—21no—
167C2—22no—
168C2—42no—
169C2—12082no—
170C2#2375209111yescharacteristic
subgroupG/H
centerC2#23752091
commutatorC23×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#568×C151C2
socleC2×C151#386
prime radical#23752776C2
cosocleC22×C4×C151C23
hypercenter#568D151
hypocenterC151#1914
LCSG ▷ C23×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #23752196C2semidirect
3. C2×#18012655C2semidirect
4. #23751984C2semidirect
5. #568×C151C2semidirect
42. M16×C151D4semidirect
85. C151#1914semidirect
87. #568D151semidirect
123. M16C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527762
#237521962
C2×#180126552
#237519842
#568×C1512
#1914151