Finite Group Databasebeta

← #34071110

Subgroups — #34071110

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#23752399C212yesmaximal, complemented
3#23752007C211yesmaximal, characteristic, complemented
4#23752000C212yesmaximal, complemented
5#455×C151C211yesmaximal, characteristic, complemented
6#18012728—21no—
7#18012727—21no—
8#18012725—22no—
9#18012709—22no—
10#18012707—22no—
11#18012707C2212yes—
12#18012654—22no—
13#18012654C2212yes—
14H(5,𝔽2)×C151C2211yescharacteristic
15#137×C151—21no—
16#124×C151C2211yescharacteristic
17#104×C151—21no—
18#100×C151C2211yescharacteristic
19C23×D151D412yescomplemented
20C2×Dic302—21no—
21C2×D604—21no—
22C2×D604—21no—
23C2×C22⋊D151—22no—
24C2×C22⋊D151—42no—
25C22⋊Dic151—22no—
26C22⋊Dic151D412yescomplemented
27(C2×D151)⋊C4—22no—
28(C2×D151)⋊C4—22no—
29(C2×D151)⋊C4—22no—
30(C2×D151)⋊C4—42no—
31C4×Dic151—21no—
32#41×C151—21no—
33#41×C151—41no—
34C2×Q8×C151D411yescharacteristic, complemented
35C2×D4×C151—22no—
36C2×D4×C151—41no—
37C2×D4×C151C2311yescharacteristic
38Q16×C151—41no—
39SD16×C151—41no—
40M16×C151—21no—
41C22⋊C4×C151—22no—
42C42×C151D411yescharacteristic, complemented
43C22×D151—22no—
44C22×D151—42no—
45C22×D151—82no—
46Dic302—81no—
47D604—81no—
48D604—81no—
49C22⋊D151—82no—
50C22⋊D151—84no—
51C2×Dic151—22no—
52C2×Dic151—42no—
53C23×C151—22no—
54C23×C151C2×D412yes—
55Q8×C151—21no—
56Q8×C151—41no—
57D4×C151—21no—
58D4×C151—41no—
59D4×C151—42no—
60D4×C151—41no—
61C2×C4×C151—22no—
62C2×C4×C151—21no—
63C2×C4×C151—21no—
64C2×C4×C151—41no—
65C2×C4×C151C2×D411yescharacteristic
66C8×C151—41no—
67C22×C151—22no—
68C22×C151—42no—
69C22×C151—41no—
70C22×C151—82no—
71C22×C151#12011yescharacteristic
72C2×D151—42no—
73C2×D151—42no—
74C2×D151—44no—
75C2×D151—42no—
76C2×D151—82no—
77C4×C151—21no—
78C4×C151—41no—
79C4×C151—41no—
80C4×C151—41no—
81Dic151—42no—
82Dic151—82no—
83C2×C151—21no—
84C2×C151—42no—
85C2×C151—81no—
86C2×C151B(4,𝔽2)11yescharacteristic
87D151—82no—
88C151#219911yescharacteristic, complemented, Sylow
89#2199—1511nomaximal, Sylow
90H(3,𝔽4)—1511no—
91B(4,𝔽2)—1512no—
92#455D15111yescharacteristic, complemented
93#354—1511no—
94AΣL(1,𝔽16)—1512no—
95H(5,𝔽2)C2×D15111yescharacteristic
96#137—21no—
97#124—3022no—
98#124—3021no—
99#124—3021no—
100#124C2×D15111yescharacteristic
101#120—3022no—
102#120—3022no—
103#120—1512no—
104#104—21no—
105#100C2×D15111yescharacteristic
106#99—3022no—
107#99—1512no—
108C24—1512no—
109#41—21no—
110#41—41no—
111C2×Q8—3021no—
112C2×Q8C22⋊D15111yescharacteristic, complemented
113C2×D4—22no—
114C2×D4—41no—
115C2×D4—3021no—
116C2×D4—3021no—
117C2×D4—3022no—
118C2×D4—6042no—
119C2×D4C22×D15111yescharacteristic
120Q16—41no—
121SD16—41no—
122M16—21no—
123C22⋊C4—22no—
124C22⋊C4—3022no—
125C22⋊C4—3022no—
126C22⋊C4—3022no—
127C22⋊C4—3022no—
128C22⋊C4—6042no—
129C22⋊C4—1512no—
130C42—3021no—
131C42C22⋊D15111yescharacteristic, complemented
132C23—22no—
133C23—3022no—
134C23—6042no—
135C23—12082no—
136C23D4×D15112yes—
137Q8—21no—
138Q8—41no—
139Q8—12081no—
140D4—21no—
141D4—41no—
142D4—42no—
143D4—41no—
144D4—12081no—
145D4—12081no—
146D4—12082no—
147D4—12084no—
148C2×C4—22no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—3022no—
153C2×C4—6042no—
154C2×C4C2×C22⋊D15111yescharacteristic
155C8—41no—
156C22—22no—
157C22—42no—
158C22—41no—
159C22—82no—
160C22—6042no—
161C22—6042no—
162C22—6044no—
163C22—6042no—
164C22—12082no—
165C22#1801270711yescharacteristic
166C4—21no—
167C4—41no—
168C4—41no—
169C4—41no—
170C4—6042no—
171C4—12082no—
172C2—21no—
173C2—42no—
174C2—81no—
175C2—12082no—
176C2#2375239811yescharacteristic
subgroupG/H
centerC2#23752398
commutator, cosocleC2×D4×C151C23
FrattiniC2×D4C22×D151
Fitting#455×C151C2
socleC2×C151B(4,𝔽2)
hypercenter#455D151
hypocenterC151#2199
LCSG ▷ C2×D4×C151 ▷ C22×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #23752954C2semidirect
2. #23752399C2semidirect
3. #23752007C2semidirect
4. #23752000C2semidirect
5. #455×C151C2semidirect
19. C23×D151D4semidirect
26. C22⋊Dic151D4semidirect
34. C2×Q8×C151D4semidirect
42. C42×C151D4semidirect
88. C151#2199semidirect
92. #455D151semidirect
112. C2×Q8C22⋊D151semidirect
131. C42C22⋊D151semidirect

Maximal subgroups

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

subgroupindex
#237529542
#237523992
#237520072
#237520002
#455×C1512
#2199151