Finite Group Databasebeta

← #34068392

Subgroups — #34068392

Order 19328.

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

normal subgroups only

This group has 240 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#23752867C211yesmaximal, characteristic
2#23752608C211yesmaximal, characteristic, complemented
3#23752489C211yesmaximal, characteristic, complemented
4#23751957C211yesmaximal, characteristic, complemented
5D4⋊(C151⋊C8)C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#461×C151C211yesmaximal, characteristic, complemented
8C2×#14559004—21no—
9#18012739C2211yescharacteristic
10#18012721—22no—
11#18012718—21no—
12#18012710—21no—
13C4×D604C2211yescharacteristic
14C4⋊C4×D151—21no—
15#18012672—21no—
16#18012670—22no—
17C4⋊(C151⋊C8)C2211yescharacteristic
18#18012659—21no—
19C4×C151⋊C8C2211yescharacteristic
20C2×SD16×C151—21no—
21C4⋊Q8×C151C2211yescharacteristic
22C4×D4×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24#103×C151—21no—
25#14559004—42no—
26#14559004—42no—
27C2×Dic302—21no—
28C2×D604D411yescharacteristic
29C2×C22⋊D151—22no—
30C2×C4×D151—22no—
31C2×C4×D151—21no—
32C2×C151⋊C8—21no—
33C2×C151⋊C8—21no—
34C4⋊Dic151—21no—
35C4⋊Dic151D411yescharacteristic
36C4⋊Dic151D412yes—
37Dic151⋊C4—22no—
38C22⋊Dic151—22no—
39(C2×D151)⋊C4—21no—
40C2×Q8×C151—21no—
41C2×D4×C151D411yescharacteristic
42C22×C4×C151—21no—
43SD16×C151—42no—
44C2×C8×C151—21no—
45C4⋊C4×C151—21no—
46C4⋊C4×C151—21no—
47C4⋊C4×C151D411yescharacteristic
48C22⋊C4×C151—21no—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51Dic302—41no—
52Dic302—41no—
53D604—21no—
54D604SD1612yescomplemented
55C22⋊D151—44no—
56C2×Dic151—21no—
57C2×Dic151—22no—
58C4×D151—44no—
59C4×D151—41no—
60C4×D151—41no—
61C151⋊C8—22no—
62C151⋊C8—41no—
63C23×C151—21no—
64Q8×C151—41no—
65Q8×C151—41no—
66D4×C151—21no—
67D4×C151—21no—
68C2×C4×C151—21no—
69C2×C4×C151—41no—
70C2×C4×C151—41no—
71C2×C4×C151—41no—
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C2×C4×C151C2×D411yescharacteristic
75C8×C151—41no—
76C22×C151—41no—
77C22×C151—41no—
78C22×C151—41no—
79C22×C151#12011yescharacteristic
80C2×D151—22no—
81C2×D151—41no—
82C2×D151—41no—
83C4×C151—21no—
84C4×C151—41no—
85C4×C151—81no—
86C4×C151C2×SD1611yescharacteristic
87C4×C151#13511yescharacteristic
88C4×C151AGL(1,ℤ/8)11yescharacteristic
89C4×C151AGL(1,ℤ/8)11yescharacteristic
90Dic151—41no—
91Dic151—42no—
92C2×C151—81no—
93C2×C151#44911yescharacteristic
94C2×C151#45011yescharacteristic
95C2×C151#45611yescharacteristic
96D151—42no—
97C151#165411yescharacteristic, complemented, Sylow
98#1654—1511nomaximal, Sylow
99#547—1511no—
100#498—1511no—
101#474—1511no—
102#461D15111yescharacteristic, complemented
103#332—1511no—
104D4⋊C8—1511no—
105D4⋊C8—1511no—
106C2×#41—3021no—
107C2×SD16—21no—
108C4⋊Q8—1511no—
109C4⋊Q8C2×D15111yescharacteristic
110#123—3022no—
111C22⋊Q8—3021no—
112#121—3021no—
113C4×D4—1511no—
114C4×D4C2×D15111yescharacteristic
115C2×C4⋊C4—3021no—
116#107—3021no—
117#106—3022no—
118C4⋊C8—1511no—
119C4⋊C8C2×D15111yescharacteristic
120#103—21no—
121#102—3021no—
122C4×C8—1511no—
123#41—6042no—
124#41—6042no—
125C2×Q8—21no—
126C2×Q8—3021no—
127C2×D4—3022no—
128C2×D4—1511no—
129C2×D4C22⋊D15111yescharacteristic
130C22×C4—21no—
131C22×C4—3022no—
132C22×C4—3021no—
133SD16—42no—
134C2×C8—21no—
135C2×C8—3021no—
136C2×C8—3021no—
137C4⋊C4—21no—
138C4⋊C4—21no—
139C4⋊C4—3022no—
140C4⋊C4—3021no—
141C4⋊C4—1512no—
142C4⋊C4—1511no—
143C4⋊C4C22⋊D15111yescharacteristic
144C22⋊C4—21no—
145C22⋊C4—3022no—
146C22⋊C4—3021no—
147C42C22×D15111yescharacteristic
148C23—21no—
149C23—3021no—
150Q8—41no—
151Q8—41no—
152Q8—6041no—
153Q8—6041no—
154D4—21no—
155D4—21no—
156D4—3021no—
157D4—6044no—
158D4—1512no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—3021no—
164C2×C4—3022no—
165C2×C4—6044no—
166C2×C4—6041no—
167C2×C4—6041no—
168C2×C4D4×D15111yescharacteristic
169C2×C4D4×D15111yescharacteristic
170C2×C4C2×C22⋊D15111yescharacteristic
171C8—41no—
172C8—3022no—
173C8—6041no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22—3022no—
178C22—6041no—
179C22—6041no—
180C22#1801270711yescharacteristic
181C4—21no—
182C4—41no—
183C4—81no—
184C4—6041no—
185C4—6042no—
186C4SD16×D15111yescharacteristic
187C4#1801275911yescharacteristic
188C4#1801276511yescharacteristic
189C4#1801276611yescharacteristic
190C2—81no—
191C2—6042no—
192C2#2375235511yescharacteristic
193C2#2375236111yescharacteristic
194C2#2375239311yescharacteristic
subgroupG/H
centerC22#18012707
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#461×C151C2
socleC22×C151#120
prime radical#23752867C2
hypercenter#461D151
hypocenterC151#1654
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
2. #23752608C2semidirect
3. #23752489C2semidirect
4. #23751957C2semidirect
5. D4⋊(C151⋊C8)C2semidirect
6. #23751939C2semidirect
7. #461×C151C2semidirect
54. D604SD16semidirect
97. C151#1654semidirect
102. #461D151semidirect

Maximal subgroups

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

subgroupindex
#237528672
#237526082
#237524892
#237519572
D4⋊(C151⋊C8)2
#237519392
#461×C1512
#1654151