Finite Group Databasebeta

← #34069635

Subgroups — #34069635

Order 19328.

344 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 85 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#23752979C211yesmaximal, characteristic, complemented
2#23752776C211yesmaximal, characteristic
3#23752216C212yesmaximal, complemented
4#23751968C212yesmaximal, complemented
5#410×C151C211yesmaximal, characteristic, complemented
6C22×D604C2211yescharacteristic
7#18012746—24no—
8C2×#14558988—22no—
9C2×#14558988C2212yes—
10#18012735C412yescomplemented
11#18012728C412yescomplemented
12#18012713—22no—
13#18012707—22no—
14#18012698C2211yescharacteristic
15#18012659—24no—
16C2×#41×C151C2211yescharacteristic
17#117×C151C2212yes—
18#99×C151—22no—
19C23×D151—21no—
20C2×D604—22no—
21C2×D604—21no—
22C2×D604—22no—
23C2×D604C2×C412yes—
24C2×C22⋊D151—24no—
25#14558988—24no—
26#14558988—22no—
27#14558988—22no—
28C2×C151⋊C8—24no—
29C2×C151⋊C8D414yescomplemented
30C4⋊Dic151—21no—
31C22⋊Dic151—21no—
32(C2×D151)⋊C4—24no—
33C4×Dic151C2×C412yes—
34#41×C151—22no—
35#41×C151—22no—
36C2×Q8×C151C2×C411yescharacteristic
37C2×D4×C151C2×C411yescharacteristic
38C2×D4×C151D412yes—
39C22×C4×C151D412yes—
40C22×C4×C151C2311yescharacteristic
41C4⋊C4×C151—22no—
42C22⋊C4×C151—22no—
43C42×C151—22no—
44C22×D151—22no—
45C22×D151—42no—
46C22×D151—82no—
47D604—24no—
48D604—41no—
49D604—41no—
50C22⋊D151—84no—
51C2×Dic151—22no—
52C151⋊C8—24no—
53C23×C151C22⋊C412yes—
54C23×C151C2×D411yescharacteristic
55Q8×C151—22no—
56D4×C151—24no—
57D4×C151—22no—
58C2×C4×C151—22no—
59C2×C4×C151—22no—
60C2×C4×C151—42no—
61C2×C4×C151C22⋊C412yes—
62C2×C4×C151C22×C411yescharacteristic
63C2×C4×C151C2×D412yes—
64C2×C4×C151C2×D411yescharacteristic
65C2×C4×C151#4112yes—
66C22×C151—22no—
67C22×C151—41no—
68C22×C151—42no—
69C22×C151C2×C22⋊C411yescharacteristic
70C22×C151#12112yes—
71C2×D151—44no—
72C2×D151—42no—
73C2×D151—84no—
74C4×C151—22no—
75C4×C151—82no—
76C4×C151C4×D412yes—
77C4×C151#12011yescharacteristic
78C4×C151#12311yescharacteristic
79Dic151—42no—
80C2×C151—21no—
81C2×C151—22no—
82C2×C151—42no—
83C2×C151#38611yescharacteristic
84D151—82no—
85C151#191011yescharacteristic, complemented, Sylow
86#1910—1511nomaximal, Sylow
87#568—1511no—
88#535—1511no—
89#418—1512no—
90#410D15111yescharacteristic, complemented
91H(3,ℤ/4)—1512no—
92C2×#41C2×D15111yescharacteristic
93C22×D4—1511no—
94#131—3024no—
95C2×M16—3022no—
96C2×M16—1512no—
97#127—1512no—
98#124—1512no—
99#121—3022no—
100#120—3022no—
101#117—1511no—
102#117C2×D15112yes—
103#102—3024no—
104#99—22no—
105C24—3021no—
106#41—22no—
107#41—22no—
108C2×Q8C4×D15111yescharacteristic
109C2×D4—3024no—
110C2×D4—3022no—
111C2×D4—3021no—
112C2×D4—3022no—
113C2×D4—1512no—
114C2×D4C4×D15111yescharacteristic
115C2×D4C22⋊D15112yes—
116C22×C4D60412yes—
117C22×C4C22×D15111yescharacteristic
118M16—3024no—
119M16—3022no—
120M16—3022no—
121C2×C8—3024no—
122C2×C8—1514no—
123C4⋊C4—22no—
124C4⋊C4—3021no—
125C22⋊C4—22no—
126C22⋊C4—3021no—
127C22⋊C4—3024no—
128C42—22no—
129C42—1512no—
130C23—3022no—
131C23—6042no—
132C23—12082no—
133C23(C2×D151)⋊C412yes—
134C23C2×C22⋊D15111yescharacteristic
135Q8—22no—
136D4—24no—
137D4—22no—
138D4—3024no—
139D4—6041no—
140D4—6041no—
141D4—12084no—
142C2×C4—22no—
143C2×C4—22no—
144C2×C4—42no—
145C2×C4—3022no—
146C2×C4(C2×D151)⋊C412yes—
147C2×C4C2×C4×D15111yescharacteristic
148C2×C4D4×D15112yes—
149C2×C4C2×D60411yescharacteristic
150C2×C4#1455900312yes—
151C8—3024no—
152C22—22no—
153C22—41no—
154C22—42no—
155C22—6044no—
156C22—6042no—
157C22—12084no—
158C22C2×(C2×D151)⋊C411yescharacteristic
159C22#1801271112yes—
160C4—22no—
161C4—82no—
162C4—6042no—
163C4(C22⋊D151)⋊C412yes—
164C4#1801270911yescharacteristic
165C4#1801272311yescharacteristic
166C2—22no—
167C2—21no—
168C2—42no—
169C2—12082no—
170C2#2375208911yescharacteristic
subgroupG/H
centerC2#23752089
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#410×C151C2
socleC2×C151#386
prime radical#23752776C2
cosocleC22×C4×C151C23
hypercenter#410D151
hypocenterC151#1910
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #410

Complements

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

NH ≅ G/Ntype
1. #23752979C2semidirect
3. #23752216C2semidirect
4. #23751968C2semidirect
5. #410×C151C2semidirect
10. #18012735C4semidirect
11. #18012728C4semidirect
29. C2×C151⋊C8D4semidirect
85. C151#1910semidirect
90. #410D151semidirect

Maximal subgroups

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

subgroupindex
#237529792
#237527762
#237522162
#237519682
#410×C1512
#1910151