Finite Group Databasebeta

← #34070178

Subgroups — #34070178

Order 19328.

394 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 71 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#23753012C211yesmaximal, characteristic, complemented
2#23752724C212yesmaximal, complemented
3#23752230C212yesmaximal, complemented
4#23752175C211yesmaximal, characteristic, complemented
5H(3,ℤ/4)×C151C211yesmaximal, characteristic, complemented
6C2×#14559004C2212yes—
7C22×C4×D151C2211yescharacteristic
8#18012772—22no—
9#18012767—22no—
10#18012761—22no—
11C2×#14558988C2211yescharacteristic
12#18012723—22no—
13#18012719—22no—
14#18012714—22no—
15#18012709—22no—
16C4×D604—24no—
17#18012667—24no—
18(C2×D151)⋊C8—22no—
19C2×M16×C151C2211yescharacteristic
20#117×C151C2212yes—
21C23×D151D411yescharacteristic
22#14559004—22no—
23#14559004—22no—
24#14559004—22no—
25#14559004—22no—
26C2×Dic302D412yescomplemented
27C2×D604—24no—
28C2×D604D412yescomplemented
29C2×C22⋊D151—22no—
30C22×Dic151D411yescharacteristic
31C2×C4×D151—22no—
32C2×C4×D151—22no—
33C2×C4×D151—22no—
34C2×C4×D151—21no—
35C2×C4×D151—21no—
36Dic604—22no—
37#14558993—24no—
38D1208—22no—
39#14558988—22no—
40C2×C151⋊C8—21no—
41C4⋊Dic151—24no—
42(C2×D151)⋊C4—24no—
43(C2×D151)⋊C4—24no—
44C22×C4×C151C2311yescharacteristic
45M16×C151—22no—
46C2×C8×C151D412yescomplemented
47C4⋊C4×C151—22no—
48C22⋊C4×C151—22no—
49C42×C151D414yescomplemented
50C22×D151—22no—
51C22×D151—21no—
52C22×D151—22no—
53C22×D151—42no—
54Dic302—22no—
55Dic302—22no—
56D604—22no—
57D604—22no—
58D604—48no—
59C22⋊D151—42no—
60C22⋊D151—42no—
61C2×Dic151—22no—
62C2×Dic151—22no—
63C2×Dic151—21no—
64C4×D151—41no—
65C4×D151—42no—
66C4×D151—42no—
67C4×D151—41no—
68C4×D151—42no—
69C151⋊C8—41no—
70C23×C151C2×D411yescharacteristic
71C2×C4×C151—24no—
72C2×C4×C151C2×D412yes—
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D412yes—
75C2×C4×C151#4111yescharacteristic
76C8×C151—22no—
77C22×C151—41no—
78C22×C151#12012yes—
79C22×C151#12111yescharacteristic
80C2×D151—24no—
81C2×D151—22no—
82C2×D151—42no—
83C2×D151—41no—
84C2×D151—41no—
85C2×D151—44no—
86C2×D151—42no—
87C4×C151—44no—
88C4×C151#12011yescharacteristic
89C4×C151#12112yes—
90C4×C151#12711yescharacteristic
91Dic151—41no—
92Dic151—42no—
93C2×C151—22no—
94C2×C151—21no—
95C2×C151#39211yescharacteristic
96D151—42no—
97D151—82no—
98C151#201011yescharacteristic, complemented, Sylow
99#2010—1511nomaximal, Sylow
100#575—1511no—
101#525—1512no—
102#421—1512no—
103#407—1511no—
104H(3,ℤ/4)D15111yescharacteristic, complemented
105C2×#41—1512no—
106C23×C4—1511no—
107#137—3022no—
108AGL(1,ℤ/8)—3022no—
109#135—3022no—
110C2×M16—1511no—
111C2×M16C2×D15111yescharacteristic
112#123—3022no—
113C22⋊Q8—3022no—
114#121—3022no—
115#120—3022no—
116C4×D4—3024no—
117#117C2×D15112yes—
118#104—3024no—
119C22⋊C8—3022no—
120C24—1511no—
121#41—3022no—
122#41—3022no—
123#41—3022no—
124#41—3022no—
125C2×Q8—1512no—
126C2×D4—3024no—
127C2×D4—3022no—
128C2×D4—1512no—
129C22×C4—3022no—
130C22×C4—3021no—
131C22×C4—3022no—
132C22×C4—3022no—
133C22×C4—3021no—
134C22×C4—1511no—
135C22×C4C22×D15111yescharacteristic
136Q16—3022no—
137SD16—3024no—
138D8—3022no—
139M16—22no—
140M16—3022no—
141C2×C8—3021no—
142C2×C8D60412yescomplemented
143C4⋊C4—22no—
144C4⋊C4—3024no—
145C22⋊C4—22no—
146C22⋊C4—3024no—
147C22⋊C4—3024no—
148C42D60414yescomplemented
149C23—3022no—
150C23—3021no—
151C23—3022no—
152C23—6042no—
153C23D4×D15111yescharacteristic
154Q8—3022no—
155Q8—3022no—
156D4—3022no—
157D4—3022no—
158D4—6048no—
159D4—6042no—
160D4—6042no—
161C2×C4—24no—
162C2×C4—3022no—
163C2×C4—3022no—
164C2×C4—3021no—
165C2×C4—6041no—
166C2×C4—6042no—
167C2×C4—6042no—
168C2×C4—6041no—
169C2×C4—6042no—
170C2×C4D4×D15112yes—
171C2×C4C2×D60411yescharacteristic
172C2×C4C2×D60412yes—
173C2×C4#1455900511yescharacteristic
174C8—22no—
175C8—6041no—
176C22—41no—
177C22—3024no—
178C22—3022no—
179C22—6042no—
180C22—6041no—
181C22—6044no—
182C22—6041no—
183C22—6042no—
184C22#1801270912yes—
185C22#1801271411yescharacteristic
186C4—44no—
187C4—6041no—
188C4—6042no—
189C4#1801270911yescharacteristic
190C4#1801271412yes—
191C4#1801273611yescharacteristic
192C2—22no—
193C2—21no—
194C2—6042no—
195C2—12082no—
196C2#2375212211yescharacteristic
subgroupG/H
centerC4#18012736
commutator, cosocleC22×C4×C151C23
FrattiniC22×C4C22×D151
FittingH(3,ℤ/4)×C151C2
socleC2×C151#392
hypercenterH(3,ℤ/4)D151
hypocenterC151#2010
LCSG ▷ C22×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C4 ◁ C22×C4 ◁ H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
1. #23753012C2semidirect
2. #23752724C2semidirect
3. #23752230C2semidirect
4. #23752175C2semidirect
5. H(3,ℤ/4)×C151C2semidirect
26. C2×Dic302D4semidirect
28. C2×D604D4semidirect
46. C2×C8×C151D4semidirect
49. C42×C151D4semidirect
98. C151#2010semidirect
104. H(3,ℤ/4)D151semidirect
142. C2×C8D604semidirect
148. C42D604semidirect

Maximal subgroups

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

subgroupindex
#237530122
#237527242
#237522302
#237521752
H(3,ℤ/4)×C1512
#2010151