Finite Group Databasebeta

← #34069320

Subgroups — #34069320

Order 19328.

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

normal subgroups only

This group has 324 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
1#23752255C212yesmaximal, complemented
2C2×#18012656C211yesmaximal, characteristic
3#23752115C211yesmaximal, characteristic
4#23751971C212yesmaximal, complemented
5#518×C151C211yesmaximal, characteristic
6C2×#14558988C2212yes—
7C2×C4⋊Dic151C2211yescharacteristic
8C2×C22⋊Dic151—22no—
9C2×C4×Dic151C2211yescharacteristic
10#18012672—22no—
11#18012670—22no—
12#18012656C414yescomplemented
13C22×D4×C151C2211yescharacteristic
14C4×D4×C151—22no—
15C4×D4×C151—22no—
16#117×C151C2212yes—
17C2×C22⋊C4×C151—22no—
18C22×Dic151—21no—
19C22×Dic151—21no—
20#14558988—22no—
21#14558988C2×C414yescomplemented
22C2×C151⋊C8—22no—
23C4⋊Dic151—22no—
24C22⋊Dic151—44no—
25C4×Dic151—22no—
26C24×C151D412yes—
27C2×D4×C151—22no—
28C2×D4×C151—22no—
29C2×D4×C151C2×C412yes—
30C2×D4×C151Q812yes—
31C22×C4×C151—22no—
32C22×C4×C151—22no—
33C22×C4×C151C2311yescharacteristic
34C4⋊C4×C151D412yes—
35C4⋊C4×C151D412yes—
36C22⋊C4×C151—24no—
37C22⋊C4×C151—22no—
38C42×C151—22no—
39C2×Dic151—22no—
40C2×Dic151—41no—
41C2×Dic151—41no—
42C2×Dic151—42no—
43C2×Dic151—41no—
44C151⋊C8—24no—
45C23×C151—22no—
46C23×C151—22no—
47C23×C151—42no—
48C23×C151—42no—
49C23×C151C4⋊C414yes—
50C23×C151C2×D411yescharacteristic
51D4×C151—24no—
52D4×C151—24no—
53C2×C4×C151—22no—
54C2×C4×C151—22no—
55C2×C4×C151—82no—
56C2×C4×C151—82no—
57C2×C4×C151C22×C411yescharacteristic
58C2×C4×C151C2×D412yes—
59C2×C4×C151C2×Q811yescharacteristic
60C2×C4×C151#4112yes—
61C22×C151—21no—
62C22×C151—21no—
63C22×C151—24no—
64C22×C151—44no—
65C22×C151—42no—
66C22×C151—42no—
67C22×C151—82no—
68C22×C151C2×C4⋊C411yescharacteristic
69C22×C151#12011yescharacteristic
70C22×C151#12311yescharacteristic
71C4×C151—42no—
72C4×C151—42no—
73C4×C151C4×D412yes—
74C4×C151C22⋊Q812yes—
75Dic151—42no—
76Dic151—81no—
77C2×C151—21no—
78C2×C151—21no—
79C2×C151—44no—
80C2×C151#38511yescharacteristic
81C2×C151#45311yescharacteristic
82C2×C151#45511yescharacteristic
83C151#185611yescharacteristic, complemented, Sylow
84#1856—1511nomaximal, Sylow
85#518D15111yescharacteristic
86#428—1512no—
87C2×#100—1511no—
88#390—1511no—
89#339—1512no—
90C22×D4C2×D15111yescharacteristic
91C2×M16—1512no—
92C4×D4—22no—
93C4×D4—22no—
94#117C2×D15112yes—
95C2×C4⋊C4—1511no—
96C2×C22⋊C4—22no—
97C2×C22⋊C4—3022no—
98C2×C42—1511no—
99#107—3022no—
100#106—3022no—
101#100—1514no—
102C24C22⋊D15112yes—
103C2×D4—22no—
104C2×D4—22no—
105C2×D4C4×D15112yes—
106C2×D4Dic30212yes—
107C22×C4—22no—
108C22×C4—22no—
109C22×C4—3021no—
110C22×C4—3021no—
111C22×C4C22×D15111yescharacteristic
112M16—3022no—
113M16—1514no—
114C2×C8—3022no—
115C4⋊C4—3022no—
116C4⋊C4C22⋊D15112yes—
117C4⋊C4C22⋊D15112yes—
118C22⋊C4—24no—
119C22⋊C4—22no—
120C22⋊C4—6044no—
121C42—22no—
122C42—3022no—
123C23—22no—
124C23—22no—
125C23—42no—
126C23—42no—
127C23Dic151⋊C414yes—
128C23C2×C22⋊D15111yescharacteristic
129D4—24no—
130D4—24no—
131C2×C4—22no—
132C2×C4—22no—
133C2×C4—82no—
134C2×C4—82no—
135C2×C4—3022no—
136C2×C4—6041no—
137C2×C4—6041no—
138C2×C4—6042no—
139C2×C4—6041no—
140C2×C4C2×C4×D15111yescharacteristic
141C2×C4C2×C22⋊D15112yes—
142C2×C4C2×Dic30211yescharacteristic
143C2×C4#1455900412yes—
144C8—3024no—
145C22—21no—
146C22—21no—
147C22—24no—
148C22—44no—
149C22—42no—
150C22—42no—
151C22—82no—
152C22C2×Dic151⋊C411yescharacteristic
153C22#1801270811yescharacteristic
154C22#1801272211yescharacteristic
155C4—42no—
156C4—42no—
157C4—6042no—
158C4—12081no—
159C4C4×C22⋊D15112yes—
160C4#1801271812yes—
161C2—21no—
162C2—21no—
163C2—44no—
164C2#2375208511yescharacteristic
165C2#2375238011yescharacteristic
166C2#2375239011yescharacteristic
subgroupG/H
centerC22#18012708
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#518×C151C2
socleC22×C151#120
prime radicalC22×D4×C151C22
cosocleC22×C4×C151C23
hypercenter#518D151
hypocenterC151#1856
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #23752255C2semidirect
4. #23751971C2semidirect
12. #18012656C4semidirect
21. #14558988C2×C4semidirect
83. C151#1856semidirect

Maximal subgroups

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

subgroupindex
#237522552
C2×#180126562
#237521152
#237519712
#518×C1512
#1856151