Finite Group Databasebeta

← #34068294

Subgroups — #34068294

Order 19328.

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

normal subgroups only

This group has 212 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#23752947C211yesmaximal, characteristic
2#23752560C211yesmaximal, characteristic
3#23752494C211yesmaximal, characteristic, complemented
4#23751955C211yesmaximal, characteristic
5Q8⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751942C211yesmaximal, characteristic, complemented
7#462×C151C211yesmaximal, characteristic, complemented
8#18012736C2211yescharacteristic
9#18012728—21no—
10#18012727—21no—
11#18012724—22no—
12C4×Dic302C2211yescharacteristic
13C4×D604—21no—
14#18012701—21no—
15#18012670—21no—
16C4⋊(C151⋊C8)C2211yescharacteristic
17#18012662—21no—
18#18012659—22no—
19C4×C151⋊C8C2211yescharacteristic
20C2×Q16×C151—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4×Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25C2×Dic302D411yescharacteristic
26C2×D604—21no—
27C2×D604—21no—
28C2×D604D412yes—
29C2×C4×D151—22no—
30C2×C151⋊C8—21no—
31C2×C151⋊C8—21no—
32C4⋊Dic151D411yescharacteristic
33Dic151⋊C4—21no—
34(C2×D151)⋊C4—22no—
35(C2×D151)⋊C4—22no—
36(C2×D151)⋊C4—22no—
37C4×Dic151—21no—
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—22no—
49Dic302—21no—
50Dic302—21no—
51D604—42no—
52D604—41no—
53D604—41no—
54D604—41no—
55D604—41no—
56C2×Dic151—21no—
57C2×Dic151—21no—
58C4×D151—82no—
59C151⋊C8—41no—
60C151⋊C8—41no—
61Q8×C151—21no—
62Q8×C151—21no—
63Q8×C151—41no—
64Q8×C151—41no—
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—42no—
74C2×D151—42no—
75C2×D151—42no—
76C4×C151—21no—
77C4×C151—41no—
78C4×C151—41no—
79C4×C151—81no—
80C4×C151#13511yescharacteristic
81C4×C151#13511yescharacteristic
82C4×C151AGL(1,ℤ/8)11yescharacteristic
83C4×C151#13711yescharacteristic
84Dic151—41no—
85Dic151—41no—
86C2×C151#44911yescharacteristic
87C2×C151#45211yescharacteristic
88C2×C151#45511yescharacteristic
89D151—82no—
90C151#164011yescharacteristic, complemented, Sylow
91#1640—1511nomaximal, Sylow
92#559—1511no—
93#486—1511no—
94#475—1511no—
95#462D15111yescharacteristic, complemented
96#331—1511no—
97Q8⋊C8—1511no—
98Q8⋊C8—1511no—
99C2×Q16—21no—
100C4⋊Q8C2×D15111yescharacteristic
101#127—1511no—
102#124—3021no—
103#124—3021no—
104#123—3022no—
105C4×Q8—1511no—
106C4×Q8C2×D15111yescharacteristic
107C4×D4—3021no—
108C4×D4—3021no—
109#106—3021no—
110C4⋊C8—1511no—
111C4⋊C8C2×D15111yescharacteristic
112#103—21no—
113#103—3021no—
114#102—3022no—
115C4×C8—1511no—
116C2×Q8—21no—
117C2×Q8—1511no—
118C2×Q8C22⋊D15111yescharacteristic
119C2×D4—3021no—
120C2×D4—3021no—
121C2×D4—1512no—
122C22×C4—3022no—
123Q16—42no—
124C2×C8—21no—
125C2×C8—3021no—
126C2×C8—3021no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—21no—
130C4⋊C4—3021no—
131C4⋊C4—1511no—
132C4⋊C4C22⋊D15111yescharacteristic
133C22⋊C4—3022no—
134C22⋊C4—3022no—
135C22⋊C4—3022no—
136C42—21no—
137C42—3021no—
138C42C22×D15111yescharacteristic
139C23—3022no—
140Q8—21no—
141Q8—21no—
142Q8—41no—
143Q8—41no—
144Q8—3021no—
145Q8—3021no—
146D4—6042no—
147D4—6041no—
148D4—6041no—
149D4—6041no—
150D4—6041no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—41no—
154C2×C4—3021no—
155C2×C4—3021no—
156C2×C4—12082no—
157C2×C4D4×D15111yescharacteristic
158C2×C4D4×D15111yescharacteristic
159C2×C4C2×C22⋊D15111yescharacteristic
160C8—41no—
161C8—6041no—
162C8—6041no—
163C22—6042no—
164C22—6042no—
165C22—6042no—
166C22#1801270711yescharacteristic
167C4—21no—
168C4—41no—
169C4—41no—
170C4—81no—
171C4—6041no—
172C4—6041no—
173C4#1801275911yescharacteristic
174C4#1801276211yescharacteristic
175C4#1801276511yescharacteristic
176C4#1801277111yescharacteristic
177C2—12082no—
178C2#2375235511yescharacteristic
179C2#2375237311yescharacteristic
180C2#2375238811yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#462×C151C2
socleC22×C151#120
prime radical#18012736C22
hypercenter#462D151
hypocenterC151#1640
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #462

Complements

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

NH ≅ G/Ntype
3. #23752494C2semidirect
5. Q8⋊(C151⋊C8)C2semidirect
6. #23751942C2semidirect
7. #462×C151C2semidirect
90. C151#1640semidirect
95. #462D151semidirect

Maximal subgroups

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

subgroupindex
#237529472
#237525602
#237524942
#237519552
Q8⋊(C151⋊C8)2
#237519422
#462×C1512
#1640151