Finite Group Databasebeta

← #34068316

Subgroups — #34068316

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#23752922C211yesmaximal, characteristic
2#23752564C211yesmaximal, characteristic, complemented
3#23752414C211yesmaximal, characteristic
4#23751960C211yesmaximal, characteristic, complemented
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#475×C151C211yesmaximal, characteristic, complemented
8C2×#14558991—21no—
9#18012739C2211yescharacteristic
10#18012731—21no—
11#18012717—22no—
12#18012715—21no—
13C4×D604—21no—
14C4×D604C2211yescharacteristic
15C4⋊C4×D151—21no—
16C4⋊(C151⋊C8)C2211yescharacteristic
17#18012663—21no—
18#18012662—22no—
19C4×C151⋊C8C2211yescharacteristic
20C4⋊Q8×C151C2211yescharacteristic
21C4×Q8×C151C2211yescharacteristic
22#106×C151—21no—
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25C2×Dic302D412yes—
26C2×D604D411yescharacteristic
27C2×C4×D151—22no—
28C2×C4×D151—21no—
29#14558991—42no—
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C4⋊Dic151—21no—
33C4⋊Dic151—21no—
34C4⋊Dic151D411yescharacteristic
35Dic151⋊C4—22no—
36Dic151⋊C4—22no—
37(C2×D151)⋊C4—22no—
38(C2×D151)⋊C4—21no—
39C2×Q8×C151—21no—
40C2×Q8×C151D411yescharacteristic
41C2×C8×C151—21no—
42C4⋊C4×C151—21no—
43C4⋊C4×C151—21no—
44C4⋊C4×C151—21no—
45C4⋊C4×C151D411yescharacteristic
46C42×C151—21no—
47C42×C151C2311yescharacteristic
48C22×D151—21no—
49Dic302—42no—
50D604—21no—
51D604SD1612yes—
52C2×Dic151—21no—
53C2×Dic151—22no—
54C4×D151—41no—
55C4×D151—41no—
56C4×D151—82no—
57C151⋊C8—41no—
58C151⋊C8—41no—
59Q8×C151—21no—
60Q8×C151—21no—
61Q8×C151—41no—
62Q8×C151—41no—
63C2×C4×C151—21no—
64C2×C4×C151—21no—
65C2×C4×C151—41no—
66C2×C4×C151C2×D411yescharacteristic
67C2×C4×C151C2×D411yescharacteristic
68C2×C4×C151C2×D411yescharacteristic
69C8×C151—41no—
70C22×C151#12011yescharacteristic
71C2×D151—22no—
72C2×D151—41no—
73C2×D151—41no—
74C4×C151—21no—
75C4×C151—41no—
76C4×C151—41no—
77C4×C151—81no—
78C4×C151C2×SD1611yescharacteristic
79C4×C151#13511yescharacteristic
80C4×C151#13711yescharacteristic
81C4×C151#13711yescharacteristic
82Dic151—41no—
83Dic151—42no—
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#475D15111yescharacteristic, complemented
93#461—1511no—
94#333—1511no—
95Q8⋊C8—1511no—
96D4⋊C8—1511no—
97C2×SD16—3021no—
98C4⋊Q8—1511no—
99C4⋊Q8C2×D15111yescharacteristic
100#125—3021no—
101C22⋊Q8—3022no—
102C22⋊Q8—3021no—
103C4×Q8C2×D15111yescharacteristic
104C4×D4—3021no—
105C4×D4—1511no—
106C2×C4⋊C4—3021no—
107#106—21no—
108C4⋊C8—1511no—
109C4⋊C8C2×D15111yescharacteristic
110#103—21no—
111#103—3022no—
112#103—3021no—
113C4×C8—1511no—
114C2×Q8—21no—
115C2×Q8—1512no—
116C2×Q8C22⋊D15111yescharacteristic
117C2×D4—1511no—
118C22×C4—3022no—
119C22×C4—3021no—
120SD16—6042no—
121C2×C8—21no—
122C2×C8—3021no—
123C2×C8—3021no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—3022no—
128C4⋊C4—3022no—
129C4⋊C4—3021no—
130C4⋊C4—3021no—
131C4⋊C4—1511no—
132C4⋊C4C22⋊D15111yescharacteristic
133C22⋊C4—3022no—
134C22⋊C4—3021no—
135C42—21no—
136C42C22×D15111yescharacteristic
137C23—3021no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—6042no—
143D4—3021no—
144D4—1512no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—3021no—
149C2×C4—3022no—
150C2×C4—6041no—
151C2×C4—6041no—
152C2×C4—12082no—
153C2×C4D4×D15111yescharacteristic
154C2×C4D4×D15111yescharacteristic
155C2×C4C2×C22⋊D15111yescharacteristic
156C8—41no—
157C8—6041no—
158C8—6041no—
159C22—3022no—
160C22—6041no—
161C22—6041no—
162C22#1801270711yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—6041no—
168C4—6042no—
169C4SD16×D15111yescharacteristic
170C4#1801275911yescharacteristic
171C4#1801276811yescharacteristic
172C4#1801277011yescharacteristic
173C2—6042no—
174C2#2375234911yescharacteristic
175C2#2375237211yescharacteristic
176C2#2375238811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#475×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#475D151
hypocenterC151#1643
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
2. #23752564C2semidirect
4. #23751960C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
7. #475×C151C2semidirect
88. C151#1643semidirect
92. #475D151semidirect

Maximal subgroups

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

subgroupindex
#237529222
#237525642
#237524142
#237519602
Q8⋊(C151⋊C8)2
#237519392
#475×C1512
#1643151