Finite Group Databasebeta

← #34067732

Subgroups — #34067732

Order 19328.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D151C211yesmaximal, characteristic
2#23752267C212yesmaximal, complemented
3#23751952C211yesmaximal, characteristic, complemented
4#23751951C212yesmaximal, complemented
5#329×C151C211yesmaximal, characteristic, complemented
6C2×Q8×D151C411yescharacteristic
7C2×D4×D151C411yescharacteristic
8#18012728C411yescharacteristic
9#18012727C2211yescharacteristic
10#18012726C411yescharacteristic
11#18012725—22no—
12C22⋊C4×D151—22no—
13C42×D151C2211yescharacteristic
14Dic151⋊C8—22no—
15(C2×D151)⋊C8—22no—
16#18012650C2212yescomplemented
17#124×C151C2211yescharacteristic
18#97×C151C2212yescomplemented
19C23×D151—21no—
20C2×Dic302—21no—
21C2×Dic302C2×C411yescharacteristic
22Q8×D151—42no—
23C2×D604C2×C411yescharacteristic
24C2×C22⋊D151—21no—
25D4×D151—42no—
26C2×C4×D151—21no—
27C2×C4×D151C2×C411yescharacteristic
28C2×C4×D151D412yes—
29C2×C151⋊C8—22no—
30C22⋊Dic151—22no—
31(C2×D151)⋊C4—22no—
32(C2×D151)⋊C4—22no—
33C4×Dic151C2×C411yescharacteristic
34C4×Dic151D412yes—
35C2×Q8×C151C2×C411yescharacteristic
36C2×D4×C151C2×C411yescharacteristic
37C2×C8×C151—22no—
38C22⋊C4×C151—22no—
39C42×C151C2311yescharacteristic
40C22×D151—21no—
41C22×D151—44no—
42C22×D151—42no—
43C22×D151C22⋊C411yescharacteristic
44Dic302—42no—
45Dic302—41no—
46D604—41no—
47C22⋊D151—42no—
48C2×Dic151—21no—
49C2×Dic151C22⋊C412yes—
50C2×Dic151C22⋊C411yescharacteristic
51C4×D151—22no—
52C4×D151—42no—
53C4×D151—42no—
54C151⋊C8—42no—
55C23×C151—21no—
56Q8×C151—41no—
57D4×C151—41no—
58C2×C4×C151—21no—
59C2×C4×C151C22×C411yescharacteristic
60C2×C4×C151C2×D412yes—
61C8×C151—42no—
62C22×C151—41no—
63C22×C151—42no—
64C22×C151C2×C22⋊C411yescharacteristic
65C2×D151—22no—
66C2×D151—41no—
67C2×D151—42no—
68C2×D151—84no—
69C2×D151#10012yes—
70C4×C151—21no—
71C4×C151—22no—
72C4×C151—41no—
73Dic151—21no—
74Dic151—22no—
75Dic151—41no—
76C2×C151—81no—
77C2×C151C2×#10011yescharacteristic
78C2×C151#42112yes—
79D151—22no—
80D151—81no—
81C151#153311yescharacteristic, complemented, Sylow
82#1533—1511nomaximal, Sylow
83C2×#124—1511no—
84#432—1512no—
85#329—1511no—
86#329—1512no—
87#329D15111yescharacteristic, complemented
88C22×Q8—1511no—
89C22×D4—1511no—
90#124—3022no—
91#124—1511no—
92#124—1511no—
93#124—1511no—
94#124C2×D15111yescharacteristic
95C2×C22⋊C4—3022no—
96C2×C42—1511no—
97C4⋊C8—3022no—
98C22⋊C8—3022no—
99#97—1512no—
100#97C2×D15112yescomplemented
101C24—3021no—
102C2×Q8—3021no—
103C2×Q8—6042no—
104C2×Q8—1511no—
105C2×Q8C4×D15111yescharacteristic
106C2×D4—3021no—
107C2×D4—6042no—
108C2×D4—1511no—
109C2×D4C4×D15111yescharacteristic
110C22×C4—3021no—
111C22×C4—1511no—
112C22×C4—1512no—
113C2×C8—22no—
114C2×C8—3022no—
115C22⋊C4—22no—
116C22⋊C4—3022no—
117C22⋊C4—3022no—
118C22⋊C4—3022no—
119C42—1511no—
120C42—1512no—
121C42C22×D15111yescharacteristic
122C23—21no—
123C23—3021no—
124C23—6044no—
125C23—6042no—
126C23—1511no—
127Q8—41no—
128Q8—6041no—
129Q8—6042no—
130D4—41no—
131D4—6041no—
132D4—6042no—
133C2×C4—21no—
134C2×C4—3022no—
135C2×C4—3021no—
136C2×C4—6042no—
137C2×C4—6042no—
138C2×C4—1512no—
139C2×C4—1511no—
140C2×C4C2×C4×D15111yescharacteristic
141C2×C4D4×D15112yes—
142C8—42no—
143C8—6042no—
144C22—42no—
145C22—41no—
146C22—3022no—
147C22—6042no—
148C22—6041no—
149C22—1512no—
150C22—12084no—
151C22C22⋊C4×D15111yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—3022no—
156C4—3021no—
157C4—6041no—
158C2—81no—
159C2—3022no—
160C2—12081no—
161C2#100×D15111yescharacteristic
162C2#2375222712yes—
subgroupG/H
centerC22C22⋊C4×D151
commutatorC2×C4×C151C22×C4
FrattiniC42C22×D151
Fitting#329×C151C2
socleC22×C151C2×C22⋊C4
prime radicalC2×D4×D151C4
cosocleC42×C151C23
hypercenter#329D151
hypocenterC151#1533
LCSG ▷ C2×C4×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #23752267C2semidirect
3. #23751952C2semidirect
4. #23751951C2semidirect
5. #329×C151C2semidirect
16. #18012650C22semidirect
18. #97×C151C22semidirect
81. C151#1533semidirect
87. #329D151semidirect
100. #97C2×D151semidirect

Maximal subgroups

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

subgroupindex
#124×D1512
#237522672
#237519522
#237519512
#329×C1512
#1533151