Finite Group Databasebeta

← #34071113

Subgroups — #34071113

Order 19328.

270 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 41 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#23752954C211yesmaximal, characteristic, complemented
2#23752400C212yesmaximal, complemented
3#23752389C211yesmaximal, characteristic, complemented
4#23751998C212yesmaximal, complemented
5#354×C151C211yesmaximal, characteristic, complemented
6#18012784C2211yescharacteristic
7#18012770—21no—
8#18012728—21no—
9#18012727—21no—
10#18012725—22no—
11#18012709—22no—
12#18012709—22no—
13#18012707C2212yes—
14#18012667—21no—
15#18012656C2211yescharacteristic
16#18012653—22no—
17#124×C151C2211yescharacteristic
18#99×C151C2212yes—
19C23×D151D412yescomplemented
20#14559004—21no—
21#14559003—41no—
22C2×Dic302—21no—
23C2×D604—21no—
24C2×D604—21no—
25C2×D604—42no—
26C2×C22⋊D151—22no—
27C2×C22⋊D151—22no—
28D4×D151—41no—
29#14558994—41no—
30#14558991—41no—
31#14558988—21no—
32C22⋊Dic151D412yescomplemented
33(C2×D151)⋊C4—22no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36(C2×D151)⋊C4—42no—
37C4×Dic151—21no—
38C2×Q8×C151D411yescharacteristic, complemented
39C2×D4×C151C2311yescharacteristic
40C22⋊C4×C151—22no—
41C22⋊C4×C151—22no—
42C42×C151D411yescharacteristic, complemented
43C22×D151—22no—
44C22×D151—22no—
45C22×D151—42no—
46C22×D151—82no—
47Dic302—21no—
48Dic302—81no—
49D604—21no—
50D604—81no—
51D604—81no—
52D604—84no—
53C22⋊D151—42no—
54C22⋊D151—41no—
55C22⋊D151—82no—
56C2×Dic151—22no—
57C2×Dic151—22no—
58C4×D151—41no—
59C151⋊C8—41no—
60C23×C151C2×D412yes—
61Q8×C151—41no—
62D4×C151—41no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—42no—
66C2×C4×C151C2×D411yescharacteristic
67C22×C151—22no—
68C22×C151—42no—
69C22×C151#12011yescharacteristic
70C2×D151—42no—
71C2×D151—42no—
72C2×D151—44no—
73C2×D151—41no—
74C2×D151—42no—
75C2×D151—82no—
76C2×D151—82no—
77C4×C151—21no—
78C4×C151—41no—
79C4×C151—41no—
80C4×C151—82no—
81Dic151—42no—
82Dic151—41no—
83C2×C151—21no—
84C2×C151—42no—
85C2×C151B(4,𝔽2)11yescharacteristic
86D151—82no—
87D151—81no—
88C151#219911yescharacteristic, complemented, Sylow
89#2199—1511nomaximal, Sylow
90H(3,𝔽4)—1511no—
91B(4,𝔽2)—1512no—
92#455—1511no—
93#354D15111yescharacteristic, complemented
94AΣL(1,𝔽16)—1512no—
95H(5,𝔽2)—1511no—
96#137—3021no—
97#124—3022no—
98#124—3021no—
99#124—3021no—
100#124C2×D15111yescharacteristic
101#120—3022no—
102#120—3022no—
103#120—1512no—
104#104—3021no—
105#100—1511no—
106#99—3022no—
107#99C2×D15112yes—
108C24—1512no—
109#41—3021no—
110#41—6041no—
111C2×Q8—3021no—
112C2×Q8D60411yescharacteristic, complemented
113C2×D4—3021no—
114C2×D4—3021no—
115C2×D4—3022no—
116C2×D4—3022no—
117C2×D4—6042no—
118C2×D4—6041no—
119C2×D4C22×D15111yescharacteristic
120Q16—6041no—
121SD16—6041no—
122M16—3021no—
123C22⋊C4—22no—
124C22⋊C4—22no—
125C22⋊C4—3022no—
126C22⋊C4—3022no—
127C22⋊C4—3022no—
128C22⋊C4—6042no—
129C22⋊C4—1512no—
130C42—3021no—
131C42D60411yescharacteristic, complemented
132C23—3022no—
133C23—3022no—
134C23—6042no—
135C23—12082no—
136C23D4×D15112yes—
137Q8—41no—
138Q8—3021no—
139Q8—12081no—
140D4—41no—
141D4—3021no—
142D4—6042no—
143D4—6041no—
144D4—12081no—
145D4—12081no—
146D4—12084no—
147D4—12082no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—42no—
151C2×C4—3022no—
152C2×C4—3022no—
153C2×C4—6041no—
154C2×C4C2×D60411yescharacteristic
155C8—6041no—
156C22—22no—
157C22—42no—
158C22—6042no—
159C22—6042no—
160C22—6044no—
161C22—6041no—
162C22—6042no—
163C22—12082no—
164C22—12082no—
165C22#1801270911yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—82no—
170C4—6042no—
171C4—6041no—
172C2—21no—
173C2—42no—
174C2—12082no—
175C2—12081no—
176C2#2375240011yescharacteristic
subgroupG/H
centerC2#23752400
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#354×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#354D151
hypocenterC151#2199
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #354

Complements

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

NH ≅ G/Ntype
1. #23752954C2semidirect
2. #23752400C2semidirect
3. #23752389C2semidirect
4. #23751998C2semidirect
5. #354×C151C2semidirect
19. C23×D151D4semidirect
32. C22⋊Dic151D4semidirect
38. C2×Q8×C151D4semidirect
42. C42×C151D4semidirect
88. C151#2199semidirect
93. #354D151semidirect
112. C2×Q8D604semidirect
131. C42D604semidirect

Maximal subgroups

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

subgroupindex
#237529542
#237524002
#237523892
#237519982
#354×C1512
#2199151