Finite Group Databasebeta

← #34069642

Subgroups — #34069642

Order 19328.

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

normal subgroups only

This group has 362 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#23752779C211yesmaximal, characteristic
2#23752230C212yesmaximal, complemented
3C2×#18012656C211yesmaximal, characteristic, complemented
4#23751968C212yesmaximal, complemented
5#518×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2211yescharacteristic
7C2×#14558988C2212yes—
8#18012735C412yescomplemented
9#18012726C412yescomplemented
10#18012710—22no—
11#18012708—22no—
12#18012698C2211yescharacteristic
13#18012667—24no—
14#18012656—22no—
15C22×D4×C151C2211yescharacteristic
16C4×D4×C151—24no—
17#117×C151C2212yes—
18C2×C22⋊C4×C151—22no—
19#14559004—22no—
20#14559004—22no—
21C2×Dic302C2×C411yescharacteristic, complemented
22C2×D604C2×C411yescharacteristic, complemented
23C2×C22⋊D151—24no—
24C2×C22⋊D151—21no—
25C2×C4×D151—21no—
26#14558988—22no—
27#14558988—22no—
28C2×C151⋊C8—22no—
29C4⋊Dic151—21no—
30C22⋊Dic151—24no—
31C22⋊Dic151—21no—
32C4×Dic151C2×C412yescomplemented
33C24×C151D412yes—
34C2×D4×C151—22no—
35C2×D4×C151—22no—
36C2×D4×C151C2×C412yes—
37C2×D4×C151D412yes—
38C22×C4×C151—24no—
39C22×C4×C151C2311yescharacteristic
40C4⋊C4×C151—22no—
41C22⋊C4×C151—24no—
42C22⋊C4×C151—22no—
43C42×C151D414yescomplemented
44C22×D151—21no—
45Dic302—22no—
46D604—22no—
47C22⋊D151—41no—
48C22⋊D151—41no—
49C22⋊D151—84no—
50C2×Dic151—22no—
51C2×Dic151—21no—
52C4×D151—42no—
53C151⋊C8—42no—
54C23×C151—22no—
55C23×C151—22no—
56C23×C151—82no—
57C23×C151C22⋊C414yes—
58C23×C151C2×D411yescharacteristic
59D4×C151—24no—
60D4×C151—24no—
61C2×C4×C151—24no—
62C2×C4×C151—84no—
63C2×C4×C151C22×C411yescharacteristic
64C2×C4×C151C2×D412yes—
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151#4112yes—
67C22×C151—24no—
68C22×C151—41no—
69C22×C151—44no—
70C22×C151—44no—
71C22×C151—82no—
72C22×C151C2×C22⋊C411yescharacteristic
73C22×C151#12011yescharacteristic
74C22×C151#12311yescharacteristic
75C2×D151—42no—
76C2×D151—41no—
77C4×C151—44no—
78C4×C151C4×D412yes—
79C4×C151#12112yes—
80Dic151—42no—
81Dic151—41no—
82C2×C151—21no—
83C2×C151—21no—
84C2×C151—21no—
85C2×C151—44no—
86C2×C151#38611yescharacteristic
87D151—81no—
88C151#191111yescharacteristic, complemented, Sylow
89#1911—1511nomaximal, Sylow
90#535—1511no—
91#518D15111yescharacteristic, complemented
92#421—1512no—
93C2×#100—1511no—
94H(3,ℤ/4)—1512no—
95C2×#41—1511no—
96C22×D4C2×D15111yescharacteristic
97C2×M16—1512no—
98#127—1512no—
99#124—1512no—
100#121—3022no—
101#120—3022no—
102C4×D4—24no—
103#117—1511no—
104#117C2×D15112yes—
105C2×C22⋊C4—22no—
106#104—3024no—
107#100—3022no—
108C24C22⋊D15112yes—
109#41—3022no—
110#41—3022no—
111C2×Q8—1511no—
112C2×D4—22no—
113C2×D4—22no—
114C2×D4—3021no—
115C2×D4—3024no—
116C2×D4—1511no—
117C2×D4C4×D15112yes—
118C2×D4D60412yes—
119C22×C4—24no—
120C22×C4—3021no—
121C22×C4C22×D15111yescharacteristic
122M16—3022no—
123M16—3022no—
124C2×C8—3022no—
125C4⋊C4—22no—
126C4⋊C4—3021no—
127C22⋊C4—24no—
128C22⋊C4—22no—
129C22⋊C4—3024no—
130C22⋊C4—3021no—
131C42—1512no—
132C42C22⋊D15114yescomplemented
133C23—22no—
134C23—22no—
135C23—82no—
136C23—3021no—
137C23(C2×D151)⋊C414yes—
138C23C2×C22⋊D15111yescharacteristic
139Q8—3022no—
140D4—24no—
141D4—24no—
142D4—3022no—
143D4—6041no—
144D4—6041no—
145D4—12084no—
146C2×C4—24no—
147C2×C4—84no—
148C2×C4—3022no—
149C2×C4—3021no—
150C2×C4—6042no—
151C2×C4C2×C4×D15111yescharacteristic
152C2×C4C2×C22⋊D15112yes—
153C2×C4C2×D60411yescharacteristic
154C2×C4#1455900412yes—
155C8—6042no—
156C22—24no—
157C22—41no—
158C22—44no—
159C22—44no—
160C22—82no—
161C22—6042no—
162C22—6041no—
163C22C2×(C2×D151)⋊C411yescharacteristic
164C22#1801270811yescharacteristic
165C22#1801272211yescharacteristic
166C4—44no—
167C4—6042no—
168C4—6041no—
169C4C4×C22⋊D15112yes—
170C4#1801271312yes—
171C2—21no—
172C2—21no—
173C2—21no—
174C2—44no—
175C2—12081no—
176C2#2375209111yescharacteristic
subgroupG/H
centerC2#23752091
commutatorC2×C4×C151C22×C4
FrattiniC22×C4C22×D151
Fitting#518×C151C2
socleC2×C151#386
prime radical#23752779C2
cosocleC22×C4×C151C23
hypercenter#518D151
hypocenterC151#1911
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #23752230C2semidirect
3. C2×#18012656C2semidirect
4. #23751968C2semidirect
5. #518×C151C2semidirect
8. #18012735C4semidirect
9. #18012726C4semidirect
21. C2×Dic302C2×C4semidirect
22. C2×D604C2×C4semidirect
32. C4×Dic151C2×C4semidirect
43. C42×C151D4semidirect
88. C151#1911semidirect
91. #518D151semidirect
132. C42C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237527792
#237522302
C2×#180126562
#237519682
#518×C1512
#1911151