Finite Group Databasebeta

← #34068378

Subgroups — #34068378

Order 19328.

200 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 53 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#23752935C211yesmaximal, characteristic
2#23752608C211yesmaximal, characteristic, complemented
3#23752489C211yesmaximal, characteristic
4#23751957C211yesmaximal, characteristic, complemented
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic
7#462×C151C211yesmaximal, characteristic, complemented
8#18012739C2211yescharacteristic
9#18012734—22no—
10#18012727—21no—
11#18012715—21no—
12C4×Dic302—21no—
13C4×D604C2211yescharacteristic
14#18012697—21no—
15#18012672—21no—
16#18012670—22no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18#18012659—21no—
19C4×C151⋊C8C2211yescharacteristic
20C2×Q16×C151—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4×Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25C2×Dic302—21no—
26C2×D604D411yescharacteristic
27C2×C4×D151—21no—
28C2×C151⋊C8—21no—
29C2×C151⋊C8—21no—
30C4⋊Dic151—21no—
31C4⋊Dic151D411yescharacteristic
32C4⋊Dic151D412yes—
33Dic151⋊C4—22no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36(C2×D151)⋊C4—21no—
37C4×Dic151—22no—
38C2×Q8×C151—21no—
39C2×Q8×C151D411yescharacteristic
40Q16×C151—42no—
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—41no—
50Dic302—41no—
51D604—21no—
52D604—21no—
53C2×Dic151—21no—
54C2×Dic151—22no—
55C4×D151—41no—
56C4×D151—41no—
57C151⋊C8—22no—
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—41no—
72C2×D151—41no—
73C2×D151—41no—
74C4×C151—21no—
75C4×C151—41no—
76C4×C151—41no—
77C4×C151—81no—
78C4×C151#13511yescharacteristic
79C4×C151#13511yescharacteristic
80C4×C151AGL(1,ℤ/8)11yescharacteristic
81C4×C151#13711yescharacteristic
82Dic151—41no—
83Dic151—42no—
84C2×C151#44911yescharacteristic
85C2×C151#45211yescharacteristic
86C2×C151#45611yescharacteristic
87D151—81no—
88C151#165211yescharacteristic, complemented, Sylow
89#1652—1511nomaximal, Sylow
90#556—1511no—
91#498—1511no—
92#474—1511no—
93#462D15111yescharacteristic, complemented
94#332—1511no—
95Q8⋊C8—1511no—
96D4⋊C8—1511no—
97C2×Q16—21no—
98C4⋊Q8—1511no—
99C4⋊Q8C2×D15111yescharacteristic
100#126—3022no—
101#124—3021no—
102C22⋊Q8—3021no—
103C4×Q8—3021no—
104C4×Q8C2×D15111yescharacteristic
105C4×D4—1511no—
106#117—3021no—
107#107—3021no—
108#106—3022no—
109C4⋊C8—1511no—
110C4⋊C8C2×D15111yescharacteristic
111#103—21no—
112#102—3021no—
113C4×C8—1511no—
114C2×Q8—21no—
115C2×Q8—3021no—
116C2×Q8C22⋊D15111yescharacteristic
117C2×D4—1511no—
118C22×C4—3021no—
119Q16—42no—
120C2×C8—21no—
121C2×C8—3021no—
122C2×C8—3021no—
123C4⋊C4—21no—
124C4⋊C4—21no—
125C4⋊C4—21no—
126C4⋊C4—3022no—
127C4⋊C4—3021no—
128C4⋊C4—1512no—
129C4⋊C4—1511no—
130C4⋊C4C22⋊D15111yescharacteristic
131C22⋊C4—3022no—
132C22⋊C4—3022no—
133C22⋊C4—3021no—
134C42—21no—
135C42—3022no—
136C42C22×D15111yescharacteristic
137C23—3021no—
138Q8—21no—
139Q8—21no—
140Q8—41no—
141Q8—41no—
142Q8—6041no—
143Q8—6041no—
144D4—3021no—
145D4—3021no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—41no—
149C2×C4—3021no—
150C2×C4—3022no—
151C2×C4—6041no—
152C2×C4—6041no—
153C2×C4D4×D15111yescharacteristic
154C2×C4D4×D15111yescharacteristic
155C2×C4C2×C22⋊D15111yescharacteristic
156C8—41no—
157C8—3022no—
158C8—6041no—
159C22—6041no—
160C22—6041no—
161C22—6041no—
162C22#1801270711yescharacteristic
163C4—21no—
164C4—41no—
165C4—41no—
166C4—81no—
167C4—6041no—
168C4—6042no—
169C4#1801275911yescharacteristic
170C4#1801276211yescharacteristic
171C4#1801276511yescharacteristic
172C4#1801277111yescharacteristic
173C2—12081no—
174C2#2375235511yescharacteristic
175C2#2375237311yescharacteristic
176C2#2375239311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#462×C151C2
socleC22×C151#120
prime radicalC2×D604D4
hypercenter#462D151
hypocenterC151#1652
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
2. #23752608C2semidirect
4. #23751957C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
7. #462×C151C2semidirect
88. C151#1652semidirect
93. #462D151semidirect

Maximal subgroups

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

subgroupindex
#237529352
#237526082
#237524892
#237519572
Q8⋊(C151⋊C8)2
#237519392
#462×C1512
#1652151