Finite Group Databasebeta

← #34070251

Subgroups — #34070251

Order 19328.

290 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 93 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
1C2×#18012739C211yesmaximal, characteristic
2C2×#18012663C212yesmaximal
3#23751974C212yesmaximal
4#23751967C211yesmaximal, characteristic
5#391×C151C211yesmaximal, characteristic
6C22×Dic302—21no—
7C22×C151⋊C8C2212yes—
8#18012739—24no—
9C2×C4⋊Dic151—21no—
10C2×C4⋊Dic151C2212yes—
11#18012663—24no—
12C22×Q8×C151C2211yescharacteristic
13C2×C4⋊C4×C151C2211yescharacteristic
14C2×C42×C151C2211yescharacteristic
15#95×C151—21no—
16#95×C151—21no—
17C2×Dic302—24no—
18C2×Dic302—42no—
19C2×Dic302—42no—
20C22×Dic151—22no—
21C2×C151⋊C8—22no—
22C2×C151⋊C8—22no—
23C2×C151⋊C8—22no—
24C4⋊Dic151—24no—
25C4⋊Dic151—22no—
26C4⋊Dic151D414yes—
27C2×Q8×C151—21no—
28C2×Q8×C151—22no—
29C2×Q8×C151—22no—
30C2×Q8×C151Q812yescomplemented
31C22×C4×C151—21no—
32C22×C4×C151—21no—
33C22×C4×C151D411yescharacteristic
34C22×C4×C151D411yescharacteristic
35C22×C4×C151C2311yescharacteristic
36C4⋊C4×C151—22no—
37C42×C151—22no—
38Dic302—48no—
39C2×Dic151—24no—
40C2×Dic151—42no—
41C2×Dic151—42no—
42C151⋊C8—42no—
43C23×C151C2×D411yescharacteristic
44Q8×C151—24no—
45Q8×C151—42no—
46C2×C4×C151—21no—
47C2×C4×C151—21no—
48C2×C4×C151—21no—
49C2×C4×C151—21no—
50C2×C4×C151—22no—
51C2×C4×C151—41no—
52C2×C4×C151—41no—
53C2×C4×C151—41no—
54C2×C4×C151—41no—
55C2×C4×C151—41no—
56C2×C4×C151SD1612yes—
57C2×C4×C151Q1612yes—
58C2×C4×C151C2×D412yes—
59C2×C4×C151C2×Q811yescharacteristic
60C2×C4×C151#4112yes—
61C2×C4×C151#4111yescharacteristic
62C22×C151#12011yescharacteristic
63C22×C151C22⋊Q811yescharacteristic
64C22×C151#12411yescharacteristic
65C22×C151C2×SD1611yescharacteristic
66C22×C151C2×Q1611yescharacteristic
67C22×C151AGL(1,ℤ/8)11yescharacteristic
68C22×C151#13711yescharacteristic
69C4×C151—22no—
70C4×C151—22no—
71C4×C151—42no—
72C4×C151—81no—
73C4×C151C22⋊Q812yes—
74C4×C151#12412yes—
75Dic151—44no—
76C2×C151#39311yescharacteristic
77C2×C151#45011yescharacteristic
78C2×C151#45111yescharacteristic
79C2×C151#47511yescharacteristic
80C2×C151#47711yescharacteristic
81C2×C151#48711yescharacteristic
82C2×C151#48911yescharacteristic
83C151#202411yescharacteristic, complemented, Sylow
84#2024—1511nomaximal, Sylow
85C2×C4⋊Q8—1511no—
86C2×#103—1512no—
87#391D15111yescharacteristic
88#340—1512no—
89#336—1511no—
90C22×Q8—3021no—
91C22×Q8C2×D15111yescharacteristic
92C22×C8—1512no—
93C4⋊Q8—3024no—
94C2×C4⋊C4—3021no—
95C2×C4⋊C4—1512no—
96C2×C4⋊C4C2×D15111yescharacteristic
97C2×C42C2×D15111yescharacteristic
98#103—3024no—
99#95—21no—
100#95—21no—
101C2×Q8—21no—
102C2×Q8—22no—
103C2×Q8—22no—
104C2×Q8—3024no—
105C2×Q8—6042no—
106C2×Q8—6042no—
107C2×Q8Dic30212yescomplemented
108C22×C4—21no—
109C22×C4—21no—
110C22×C4—3022no—
111C22×C4C22⋊D15111yescharacteristic
112C22×C4C22⋊D15111yescharacteristic
113C22×C4C22×D15111yescharacteristic
114C2×C8—3022no—
115C2×C8—3022no—
116C2×C8—3022no—
117C4⋊C4—22no—
118C4⋊C4—3024no—
119C4⋊C4—3022no—
120C4⋊C4—1514no—
121C42—22no—
122C23C2×C22⋊D15111yescharacteristic
123Q8—24no—
124Q8—42no—
125Q8—6048no—
126C2×C4—21no—
127C2×C4—21no—
128C2×C4—21no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—41no—
132C2×C4—41no—
133C2×C4—41no—
134C2×C4—41no—
135C2×C4—41no—
136C2×C4—3024no—
137C2×C4—6042no—
138C2×C4—6042no—
139C2×C4#1455899112yes—
140C2×C4#1455899412yes—
141C2×C4D4×D15112yes—
142C2×C4C2×Dic30211yescharacteristic
143C2×C4#1455900312yes—
144C2×C4#1455900411yescharacteristic
145C8—6042no—
146C22#1801270711yescharacteristic
147C22#1801271811yescharacteristic
148C22#1801272611yescharacteristic
149C22C2×#1455899111yescharacteristic
150C22C2×#1455899411yescharacteristic
151C22#1801276411yescharacteristic
152C22#1801276911yescharacteristic
153C4—22no—
154C4—22no—
155C4—42no—
156C4—81no—
157C4—6044no—
158C4#1801271612yes—
159C4#1801272512yes—
160C2#2375212411yescharacteristic
161C2#2375236211yescharacteristic
162C2#2375236711yescharacteristic
163C2#2375249711yescharacteristic
164C2#2375250711yescharacteristic
165C2#2375256211yescharacteristic
166C2#2375257111yescharacteristic
subgroupG/H
centerC23C2×C22⋊D151
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
Fitting#391×C151C2
socle, prime radicalC23×C151C2×D4
hypercenter#391D151
hypocenterC151#2024
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C23 ◁ C2×C42 ◁ #391

Complements

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

NH ≅ G/Ntype
30. C2×Q8×C151Q8semidirect
83. C151#2024semidirect
107. C2×Q8Dic302semidirect

Maximal subgroups

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

subgroupindex
C2×#180127392
C2×#180126632
#237519742
#237519672
#391×C1512
#2024151