Finite Group Databasebeta

← #34068441

Subgroups — #34068441

Order 19328.

184 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 45 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#23752966C211yesmaximal, characteristic
2#23752618C211yesmaximal, characteristic, complemented
3#23752574C211yesmaximal, characteristic
4#23751954C211yesmaximal, characteristic, complemented
5#23751953C211yesmaximal, characteristic, complemented
6#23751951C211yesmaximal, characteristic
7#491×C151C211yesmaximal, characteristic, complemented
8#18012738—21no—
9#18012734—21no—
10#18012734—21no—
11#18012731C2211yescharacteristic
12#18012727C2211yescharacteristic
13#18012724—21no—
14#18012719—21no—
15#18012717—21no—
16#18012672—21no—
17#18012670—21no—
18#18012662—21no—
19#18012659—21no—
20#18012650C2211yescharacteristic
21#18012650C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23#125×C151C2211yescharacteristic
24#103×C151—21no—
25#103×C151—21no—
26#97×C151C2211yescharacteristic
27C2×Dic302—21no—
28C2×Dic302D411yescharacteristic
29C2×D604D411yescharacteristic
30C2×C4×D151—21no—
31C2×C151⋊C8—21no—
32C2×C151⋊C8—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151D411yescharacteristic
35C4⋊Dic151D411yescharacteristic
36Dic151⋊C4—21no—
37Dic151⋊C4—21no—
38Dic151⋊C4—21no—
39(C2×D151)⋊C4—21no—
40(C2×D151)⋊C4—21no—
41(C2×D151)⋊C4—21no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44C4×Dic151—21no—
45C2×Q8×C151—21no—
46C2×C8×C151—21no—
47C4⋊C4×C151—21no—
48C4⋊C4×C151—21no—
49C4⋊C4×C151—21no—
50C4⋊C4×C151—21no—
51C4⋊C4×C151D411yescharacteristic
52C4⋊C4×C151D411yescharacteristic
53C42×C151C2311yescharacteristic
54C22×D151—21no—
55Dic302—41no—
56Dic302—81no—
57D604—41no—
58C2×Dic151—21no—
59C2×Dic151—21no—
60C2×Dic151—21no—
61C4×D151—81no—
62C151⋊C8—22no—
63C151⋊C8—41no—
64Q8×C151—42no—
65C2×C4×C151—21no—
66C2×C4×C151—21no—
67C2×C4×C151—41no—
68C2×C4×C151C2×D411yescharacteristic
69C2×C4×C151C2×D411yescharacteristic
70C2×C4×C151C2×D411yescharacteristic
71C8×C151—41no—
72C22×C151#12011yescharacteristic
73C2×D151—41no—
74C2×D151—41no—
75C2×D151—41no—
76C4×C151—21no—
77C4×C151—21no—
78C4×C151—21no—
79C4×C151—41no—
80C4×C151—41no—
81C4×C151—81no—
82Dic151—41no—
83Dic151—41no—
84Dic151—41no—
85C2×C151#45411yescharacteristic
86C2×C151#45511yescharacteristic
87C2×C151#45611yescharacteristic
88D151—81no—
89C151#166411yescharacteristic, complemented, Sylow
90#1664—1511nomaximal, Sylow
91#563—1511no—
92#501—1511no—
93#491D15111yescharacteristic, complemented
94#489—1511no—
95#330—1511no—
96#330—1511no—
97#329—1511no—
98C4⋊Q8—3021no—
99C4⋊Q8C2×D15111yescharacteristic
100#126—3021no—
101#126—3021no—
102#125—1511no—
103#125C2×D15111yescharacteristic
104#124—1511no—
105#123—3021no—
106C22⋊Q8—3021no—
107C22⋊Q8—3021no—
108#107—3021no—
109#106—3021no—
110#103—21no—
111#103—21no—
112#103—3021no—
113#102—3021no—
114#97—1511no—
115#97—1511no—
116#97C2×D15111yescharacteristic
117C2×Q8—21no—
118C2×Q8—3021no—
119C2×Q8—1511no—
120C2×D4—1511no—
121C22×C4—3021no—
122C2×C8—21no—
123C2×C8—3021no—
124C2×C8—3021no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—3021no—
130C4⋊C4—3021no—
131C4⋊C4—3021no—
132C4⋊C4—3021no—
133C4⋊C4—1511no—
134C4⋊C4—1511no—
135C4⋊C4C22⋊D15111yescharacteristic
136C4⋊C4C22⋊D15111yescharacteristic
137C22⋊C4—3021no—
138C22⋊C4—3021no—
139C22⋊C4—3021no—
140C22⋊C4—3021no—
141C22⋊C4—3021no—
142C42—3021no—
143C42C22×D15111yescharacteristic
144C23—3021no—
145Q8—42no—
146Q8—6041no—
147Q8—12081no—
148D4—6041no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—3021no—
153C2×C4—3021no—
154C2×C4—3021no—
155C2×C4—12081no—
156C2×C4D4×D15111yescharacteristic
157C2×C4D4×D15111yescharacteristic
158C2×C4C2×C22⋊D15111yescharacteristic
159C8—41no—
160C8—3022no—
161C8—6041no—
162C22—6041no—
163C22—6041no—
164C22—6041no—
165C22#1801270711yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—6041no—
173C4—6041no—
174C4—6041no—
175C2—12081no—
176C2#2375238411yescharacteristic
177C2#2375238811yescharacteristic
178C2#2375239311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#491×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#491D151
hypocenterC151#1664
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #23752618C2semidirect
4. #23751954C2semidirect
5. #23751953C2semidirect
7. #491×C151C2semidirect
89. C151#1664semidirect
93. #491D151semidirect

Maximal subgroups

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

subgroupindex
#237529662
#237526182
#237525742
#237519542
#237519532
#237519512
#491×C1512
#1664151