Finite Group Databasebeta

← #34068395

Subgroups — #34068395

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#23752865C211yesmaximal, characteristic
2#23752608C211yesmaximal, characteristic, complemented
3#23752493C211yesmaximal, characteristic, complemented
4#23752418C211yesmaximal, characteristic, complemented
5#23751939C211yesmaximal, characteristic, complemented
6#23751939C211yesmaximal, characteristic, complemented
7#332×C151C211yesmaximal, characteristic, complemented
8C2×#14559005—21no—
9C2×#14558993—21no—
10#18012739C2211yescharacteristic
11#18012724—22no—
12#18012715—21no—
13#18012714—21no—
14C4×D604C2211yescharacteristic
15C4×D604C2211yescharacteristic
16C4⋊C4×D151—21no—
17#18012673—21no—
18#18012670—22no—
19#18012664—21no—
20#18012661—21no—
21C4×C151⋊C8C2211yescharacteristic
22C4⋊Q8×C151C2211yescharacteristic
23C4⋊C8×C151C2211yescharacteristic
24C4⋊C8×C151C2211yescharacteristic
25#14559005—42no—
26#14559005—42no—
27C2×Dic302—21no—
28C2×D604—22no—
29C2×D604D411yescharacteristic
30C2×D604D411yescharacteristic
31C2×C4×D151—22no—
32C2×C4×D151—21no—
33C2×C4×D151—21no—
34#14558993—42no—
35C2×C151⋊C8—21no—
36C4⋊Dic151—21no—
37C4⋊Dic151—21no—
38C4⋊Dic151D411yescharacteristic
39C4⋊Dic151D411yescharacteristic
40Dic151⋊C4—22no—
41(C2×D151)⋊C4—22no—
42(C2×D151)⋊C4—21no—
43(C2×D151)⋊C4—21no—
44C2×Q8×C151—21no—
45C2×C8×C151—21no—
46C2×C8×C151—21no—
47C4⋊C4×C151—21no—
48C4⋊C4×C151D412yes—
49C42×C151C2311yescharacteristic
50C22×D151—21no—
51C22×D151—21no—
52Dic302—41no—
53Dic302—41no—
54D604—21no—
55D604—21no—
56D604—21no—
57D604—44no—
58D604SD1612yescomplemented
59C2×Dic151—21no—
60C2×Dic151—21no—
61C2×Dic151—41no—
62C4×D151—44no—
63C4×D151—41no—
64C4×D151—41no—
65C4×D151—41no—
66C4×D151—41no—
67C151⋊C8—22no—
68Q8×C151—41no—
69Q8×C151—41no—
70C2×C4×C151—22no—
71C2×C4×C151C2×D411yescharacteristic
72C2×C4×C151C2×D411yescharacteristic
73C2×C4×C151C2×D411yescharacteristic
74C8×C151—41no—
75C8×C151—41no—
76C22×C151#12011yescharacteristic
77C2×D151—22no—
78C2×D151—41no—
79C2×D151—41no—
80C2×D151—41no—
81C2×D151—41no—
82C2×D151—41no—
83C4×C151—21no—
84C4×C151—42no—
85C4×C151C2×SD1611yescharacteristic
86C4×C151#13511yescharacteristic
87C4×C151AGL(1,ℤ/8)11yescharacteristic
88C4×C151AGL(1,ℤ/8)11yescharacteristic
89Dic151—41no—
90Dic151—41no—
91Dic151—81no—
92C2×C151#44911yescharacteristic
93C2×C151#45011yescharacteristic
94C2×C151#45611yescharacteristic
95D151—42no—
96D151—81no—
97C151#165411yescharacteristic, complemented, Sylow
98#1654—1511nomaximal, Sylow
99#547—1511no—
100#498—1511no—
101#474—1511no—
102#461—1511no—
103#332D15111yescharacteristic, complemented
104D4⋊C8—1511no—
105D4⋊C8—1511no—
106C2×#41—3021no—
107C2×SD16—3021no—
108C4⋊Q8—1511no—
109C4⋊Q8C2×D15111yescharacteristic
110#123—3022no—
111C22⋊Q8—3021no—
112#121—3021no—
113C4×D4—1511no—
114C4×D4—1511no—
115C2×C4⋊C4—3021no—
116#107—3021no—
117#106—3022no—
118C4⋊C8C2×D15111yescharacteristic
119C4⋊C8C2×D15111yescharacteristic
120#103—3021no—
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×D4—1511no—
130C22×C4—3022no—
131C22×C4—3021no—
132C22×C4—3021no—
133SD16—6042no—
134C2×C8—21no—
135C2×C8—21no—
136C2×C8—3021no—
137C4⋊C4—21no—
138C4⋊C4—3022no—
139C4⋊C4—3021no—
140C4⋊C4—3021no—
141C4⋊C4—1511no—
142C4⋊C4—1511no—
143C4⋊C4D60412yes—
144C22⋊C4—3022no—
145C22⋊C4—3021no—
146C22⋊C4—3021no—
147C42C22×D15111yescharacteristic
148C23—3021no—
149C23—3021no—
150Q8—41no—
151Q8—41no—
152Q8—6041no—
153Q8—6041no—
154D4—3021no—
155D4—3021no—
156D4—3021no—
157D4—6044no—
158D4—1512no—
159C2×C4—22no—
160C2×C4—3021no—
161C2×C4—3021no—
162C2×C4—6044no—
163C2×C4—6041no—
164C2×C4—6041no—
165C2×C4—6041no—
166C2×C4—6041no—
167C2×C4—6041no—
168C2×C4D4×D15111yescharacteristic
169C2×C4D4×D15111yescharacteristic
170C2×C4C2×D60411yescharacteristic
171C8—41no—
172C8—41no—
173C8—3022no—
174C22—3022no—
175C22—6041no—
176C22—6041no—
177C22—6041no—
178C22—6041no—
179C22—6041no—
180C22#1801270911yescharacteristic
181C4—21no—
182C4—42no—
183C4—6041no—
184C4—6041no—
185C4—12081no—
186C4SD16×D15111yescharacteristic
187C4#1801276211yescharacteristic
188C4#1801276311yescharacteristic
189C4#1801276611yescharacteristic
190C2—6042no—
191C2—12081no—
192C2#2375236011yescharacteristic
193C2#2375236411yescharacteristic
194C2#2375239711yescharacteristic
subgroupG/H
centerC22#18012709
commutator, cosocleC42×C151C23
FrattiniC42C22×D151
Fitting#332×C151C2
socleC22×C151#120
prime radical#23752865C2
hypercenter#332D151
hypocenterC151#1654
LCSG ▷ C42×C151 ▷ C22×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #23752608C2semidirect
3. #23752493C2semidirect
4. #23752418C2semidirect
5. #23751939C2semidirect
6. #23751939C2semidirect
7. #332×C151C2semidirect
58. D604SD16semidirect
97. C151#1654semidirect
103. #332D151semidirect

Maximal subgroups

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

subgroupindex
#237528652
#237526082
#237524932
#237524182
#237519392
#332×C1512
#1654151