Finite Group Databasebeta

← #34068319

Subgroups — #34068319

Order 19328.

208 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 57 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#23752919C211yesmaximal, characteristic
2#23752563C211yesmaximal, characteristic, complemented
3#23752498C211yesmaximal, characteristic, complemented
4#23752417C211yesmaximal, characteristic
5#23751960C211yesmaximal, characteristic, complemented
6#23751944C211yesmaximal, characteristic, complemented
7D4⋊C8×C151C211yesmaximal, characteristic
8C2×#14558992—21no—
9#18012739C2211yescharacteristic
10#18012739C2211yescharacteristic
11#18012730—21no—
12#18012718—21no—
13#18012716—22no—
14C4×Dic302C2211yescharacteristic
15D4×Dic151—21no—
16C2×C4⋊Dic151—21no—
17#18012671—21no—
18C4⋊(C151⋊C8)C2211yescharacteristic
19#18012664—21no—
20#18012664—22no—
21#18012662—21no—
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4×C8×C151C2211yescharacteristic
25C2×Dic302—21no—
26C2×Dic302D411yescharacteristic
27C2×Dic302D412yes—
28C22×Dic151—22no—
29#14558992—42no—
30C2×C151⋊C8—21no—
31C4⋊Dic151—22no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151—21no—
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—22no—
38Dic151⋊C4—21no—
39C22⋊Dic151—22no—
40C4×Dic151—21no—
41C2×D4×C151D411yescharacteristic
42C22×C4×C151—21no—
43C2×C8×C151—21no—
44C2×C8×C151—21no—
45C4⋊C4×C151D411yescharacteristic
46C22⋊C4×C151—21no—
47C42×C151C2311yescharacteristic
48Dic302—21no—
49Dic302—21no—
50Dic302—42no—
51Dic302—41no—
52Dic302—41no—
53C2×Dic151—21no—
54C2×Dic151—21no—
55C2×Dic151—22no—
56C2×Dic151—41no—
57C2×Dic151—82no—
58C151⋊C8—41no—
59C23×C151—21no—
60D4×C151—21no—
61D4×C151SD1612yes—
62C2×C4×C151—21no—
63C2×C4×C151—41no—
64C2×C4×C151—41no—
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151C2×D411yescharacteristic
67C2×C4×C151C2×D411yescharacteristic
68C8×C151—41no—
69C8×C151—41no—
70C22×C151—22no—
71C22×C151—41no—
72C22×C151—41no—
73C22×C151#12011yescharacteristic
74C4×C151—21no—
75C4×C151—41no—
76C4×C151C2×SD1611yescharacteristic
77C4×C151#13511yescharacteristic
78C4×C151#13711yescharacteristic
79C4×C151#13711yescharacteristic
80Dic151—41no—
81Dic151—41no—
82Dic151—42no—
83Dic151—81no—
84C2×C151—42no—
85C2×C151#44811yescharacteristic
86C2×C151#45211yescharacteristic
87C2×C151#45511yescharacteristic
88C151#164311yescharacteristic, complemented, Sylow
89#1643—1511nomaximal, Sylow
90#554—1511no—
91#487—1511no—
92#475—1511no—
93#461—1511no—
94#333—1511no—
95Q8⋊C8—1511no—
96D4⋊C8D15111yescharacteristic
97C2×SD16—3021no—
98C4⋊Q8—1511no—
99C4⋊Q8—1511no—
100#125—3021no—
101C22⋊Q8—3022no—
102C22⋊Q8—3021no—
103C4×Q8—1511no—
104C4×D4—3021no—
105C4×D4C2×D15111yescharacteristic
106C2×C4⋊C4—3021no—
107#106—3021no—
108C4⋊C8—1511no—
109C4⋊C8C2×D15111yescharacteristic
110#103—3021no—
111#103—3022no—
112#103—3021no—
113C4×C8C2×D15111yescharacteristic
114C2×Q8—3021no—
115C2×Q8—1511no—
116C2×Q8—1512no—
117C2×D4D60411yescharacteristic
118C22×C4—21no—
119C22×C4—3022no—
120SD16—6042no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—3021no—
124C4⋊C4—3022no—
125C4⋊C4—3022no—
126C4⋊C4—3021no—
127C4⋊C4—3021no—
128C4⋊C4—3021no—
129C4⋊C4—3021no—
130C4⋊C4—3021no—
131C4⋊C4—1511no—
132C4⋊C4D60411yescharacteristic
133C22⋊C4—21no—
134C22⋊C4—3022no—
135C42—3021no—
136C42C22×D15111yescharacteristic
137C23—21no—
138Q8—3021no—
139Q8—3021no—
140Q8—6042no—
141Q8—6041no—
142Q8—6041no—
143D4—21no—
144D4#1455899312yes—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—3021no—
149C2×C4—3021no—
150C2×C4—3022no—
151C2×C4—6041no—
152C2×C4—12082no—
153C2×C4D4×D15111yescharacteristic
154C2×C4D4×D15111yescharacteristic
155C2×C4C2×D60411yescharacteristic
156C8—41no—
157C8—41no—
158C8—6041no—
159C22—22no—
160C22—41no—
161C22—41no—
162C22#1801270911yescharacteristic
163C4—21no—
164C4—41no—
165C4—6041no—
166C4—6041no—
167C4—6042no—
168C4—12081no—
169C4C2×#1455899311yescharacteristic
170C4#1801275811yescharacteristic
171C4#1801276811yescharacteristic
172C4#1801277211yescharacteristic
173C2—42no—
174C2#2375235311yescharacteristic
175C2#2375237511yescharacteristic
176C2#2375239111yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
FittingD4⋊C8×C151C2
socleC22×C151#120
prime radicalC2×D4×C151D4
hypercenterD4⋊C8D151
hypocenterC151#1643
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #23752563C2semidirect
3. #23752498C2semidirect
5. #23751960C2semidirect
6. #23751944C2semidirect
88. C151#1643semidirect

Maximal subgroups

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

subgroupindex
#237529192
#237525632
#237524982
#237524172
#237519602
#237519442
D4⋊C8×C1512
#1643151