Finite Group Databasebeta

← #34068318

Subgroups — #34068318

Order 19328.

208 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 55 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#23752923C211yesmaximal, characteristic
2#23752562C211yesmaximal, characteristic, complemented
3#23752498C211yesmaximal, characteristic, complemented
4#23752418C211yesmaximal, characteristic
5#23751942C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#333×C151C211yesmaximal, characteristic, complemented
8C2×#14558993—21no—
9#18012739C2211yescharacteristic
10#18012730—21no—
11#18012719—21no—
12#18012715—22no—
13C4×Dic302C2211yescharacteristic
14C4×D604C2211yescharacteristic
15#18012701—21no—
16C4⋊C4×D151—21no—
17#18012671—21no—
18#18012664—21no—
19#18012664—21no—
20#18012663—22no—
21C4×C151⋊C8C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25C2×Dic302—21no—
26C2×Dic302D411yescharacteristic
27C2×D604D411yescharacteristic
28C2×C4×D151—22no—
29C2×C4×D151—21no—
30#14558993—42no—
31C2×C151⋊C8—21no—
32C4⋊Dic151—22no—
33C4⋊Dic151—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D411yescharacteristic
37Dic151⋊C4—22no—
38Dic151⋊C4—21no—
39(C2×D151)⋊C4—22no—
40(C2×D151)⋊C4—21no—
41C4×Dic151—21no—
42C2×Q8×C151D412yes—
43C2×C8×C151—21no—
44C2×C8×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C42×C151C2311yescharacteristic
48C22×D151—21no—
49Dic302—21no—
50Dic302—21no—
51Dic302—41no—
52Dic302—41no—
53D604—21no—
54D604SD1612yes—
55C2×Dic151—21no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C2×Dic151—41no—
59C4×D151—41no—
60C4×D151—41no—
61C4×D151—82no—
62C151⋊C8—41no—
63Q8×C151—42no—
64C2×C4×C151—22no—
65C2×C4×C151C2×D411yescharacteristic
66C2×C4×C151C2×D411yescharacteristic
67C2×C4×C151C2×D411yescharacteristic
68C8×C151—41no—
69C8×C151—41no—
70C22×C151#12011yescharacteristic
71C2×D151—22no—
72C2×D151—41no—
73C2×D151—41no—
74C4×C151—21no—
75C4×C151—42no—
76C4×C151C2×SD1611yescharacteristic
77C4×C151#13511yescharacteristic
78C4×C151#13711yescharacteristic
79C4×C151#13711yescharacteristic
80Dic151—41no—
81Dic151—41no—
82Dic151—41no—
83Dic151—81no—
84C2×C151#44811yescharacteristic
85C2×C151#45211yescharacteristic
86C2×C151#45511yescharacteristic
87D151—42no—
88C151#164311yescharacteristic, complemented, Sylow
89#1643—1511nomaximal, Sylow
90#554—1511no—
91#487—1511no—
92#475—1511no—
93#461—1511no—
94#333D15111yescharacteristic, complemented
95Q8⋊C8—1511no—
96D4⋊C8—1511no—
97C2×SD16—3021no—
98C4⋊Q8—1511no—
99C4⋊Q8C2×D15111yescharacteristic
100#125—3021no—
101C22⋊Q8—3021no—
102C22⋊Q8—3022no—
103C4×Q8—1511no—
104C4×D4—3021no—
105C4×D4—1511no—
106C2×C4⋊C4—3021no—
107#106—3021no—
108C4⋊C8C2×D15111yescharacteristic
109C4⋊C8C2×D15111yescharacteristic
110#103—3021no—
111#103—3022no—
112#103—3021no—
113C4×C8—1511no—
114C2×Q8—3021no—
115C2×Q8—1511no—
116C2×Q8D60412yes—
117C2×D4—1511no—
118C22×C4—3022no—
119C22×C4—3021no—
120SD16—6042no—
121C2×C8—21no—
122C2×C8—21no—
123C2×C8—3021no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3022no—
127C4⋊C4—3022no—
128C4⋊C4—3021no—
129C4⋊C4—3021no—
130C4⋊C4—3021no—
131C4⋊C4—1511no—
132C4⋊C4—1511no—
133C22⋊C4—3022no—
134C22⋊C4—3021no—
135C42—3021no—
136C42C22×D15111yescharacteristic
137C23—3021no—
138Q8—42no—
139Q8—3021no—
140Q8—3021no—
141Q8—6041no—
142Q8—6041no—
143D4—3021no—
144D4—1512no—
145C2×C4—22no—
146C2×C4—3021no—
147C2×C4—3021no—
148C2×C4—3021no—
149C2×C4—6041no—
150C2×C4—6041no—
151C2×C4—6041no—
152C2×C4—12082no—
153C2×C4D4×D15111yescharacteristic
154C2×C4D4×D15111yescharacteristic
155C2×C4C2×D60411yescharacteristic
156C8—41no—
157C8—41no—
158C8—6041no—
159C22—3022no—
160C22—6041no—
161C22—6041no—
162C22#1801270911yescharacteristic
163C4—21no—
164C4—42no—
165C4—6041no—
166C4—6041no—
167C4—6041no—
168C4—12081no—
169C4SD16×D15111yescharacteristic
170C4#1801276011yescharacteristic
171C4#1801277111yescharacteristic
172C4#1801277111yescharacteristic
173C2—6042no—
174C2#2375235211yescharacteristic
175C2#2375237711yescharacteristic
176C2#2375239211yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#333×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#333D151
hypocenterC151#1643
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #23752562C2semidirect
3. #23752498C2semidirect
5. #23751942C2semidirect
7. #333×C151C2semidirect
88. C151#1643semidirect
94. #333D151semidirect

Maximal subgroups

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

subgroupindex
#237529232
#237525622
#237524982
#237524182
#237519422
#237519392
#333×C1512
#1643151