Finite Group Databasebeta

← #34071059

Subgroups — #34071059

Order 19328.

216 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 47 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#23753009C211yesmaximal, characteristic
2#23752653C211yesmaximal, characteristic, complemented
3#23752467C211yesmaximal, characteristic, complemented
4#23752023C211yesmaximal, characteristic, complemented
5#23752022C211yesmaximal, characteristic, complemented
6#23751993C211yesmaximal, characteristic, complemented
7#510×C151C211yesmaximal, characteristic, complemented
8#41×D151—21no—
9#18012771—21no—
10#18012768—21no—
11#18012766—21no—
12#18012763—21no—
13#18012761C2211yescharacteristic
14#18012759—21no—
15C2×#14558987C2211yescharacteristic
16#18012715—21no—
17#18012685—21no—
18#18012682—21no—
19#18012679C2211yescharacteristic, complemented
20#18012671C2211yescharacteristic, complemented
21#18012663—21no—
22#135×C151C2211yescharacteristic
23C2×Q16×C151C2211yescharacteristic, complemented
24Q32×C151—21no—
25SD32×C151—21no—
26M32×C151C2211yescharacteristic, complemented
27#14559005—21no—
28#14559004—21no—
29#14559004—41no—
30#14559003—21no—
31#14559003—41no—
32Q8×D151—21no—
33D4×D151—21no—
34D4×D151—41no—
35C2×C4×D151—41no—
36C2×C4×D151D411yescharacteristic
37Dic604D411yescharacteristic
38#14558994—21no—
39#14558993—21no—
40#14558992—21no—
41#14558991—21no—
42D1208D411yescharacteristic
43#14558989—21no—
44#14558987—21no—
45#14558987—21no—
46C2×C151⋊C8D411yescharacteristic
47C4⋊Dic151—21no—
48Dic151⋊C4—41no—
49(C2×D151)⋊C4—41no—
50C151⋊C16—21no—
51#41×C151—21no—
52C2×Q8×C151—21no—
53Q16×C151—21no—
54Q16×C151—21no—
55Q16×C151D411yescharacteristic
56SD16×C151—21no—
57D8×C151D411yescharacteristic
58C2×C8×C151C2311yescharacteristic
59C16×C151—21no—
60C22×D151—41no—
61C22×D151D811yescharacteristic
62Dic302—21no—
63Dic302—41no—
64D604—21no—
65D604—41no—
66C22⋊D151—41no—
67C22⋊D151—41no—
68C22⋊D151—41no—
69C2×Dic151—41no—
70C2×Dic151—41no—
71C2×Dic151D811yescharacteristic
72C4×D151—21no—
73C4×D151—21no—
74C4×D151—41no—
75C4×D151—41no—
76C4×D151—41no—
77C151⋊C8—21no—
78Q8×C151—21no—
79Q8×C151—41no—
80Q8×C151—41no—
81D4×C151—21no—
82D4×C151—41no—
83C2×C4×C151—41no—
84C2×C4×C151—41no—
85C2×C4×C151C2×D411yescharacteristic
86C8×C151C2×D411yescharacteristic
87C8×C151C2×D411yescharacteristic
88C22×C151—41no—
89C22×C151C2×D811yescharacteristic
90C2×D151—21no—
91C2×D151—41no—
92C2×D151—41no—
93C2×D151—82no—
94C4×C151—41no—
95C4×C151—81no—
96C4×C151#12011yescharacteristic
97C4×C151AGL(1,ℤ/8)11yescharacteristic
98Dic151—21no—
99Dic151—41no—
100Dic151—81no—
101C2×C151—21no—
102C2×C151—81no—
103C2×C151#44711yescharacteristic
104D151—41no—
105D151—81no—
106C151#219111yescharacteristic, complemented, Sylow
107#2191—1511nomaximal, Sylow
108#575—1511no—
109#510—1511no—
110#510D15111yescharacteristic, complemented
111#470—1511no—
112#360—1511no—
113#360—1511no—
114#349—1511no—
115C2×#41—3021no—
116#137—3021no—
117#137—3021no—
118AGL(1,ℤ/8)—3021no—
119AGL(1,ℤ/8)—3021no—
120#135—3021no—
121#135—1511no—
122#135C2×D15111yescharacteristic
123C2×Q16C2×D15111yescharacteristic, complemented
124C2×M16—1511no—
125C22⋊Q8—3021no—
126Q32—21no—
127Q32—3021no—
128SD32—21no—
129SD32—3021no—
130M32—1511no—
131M32C2×D15111yescharacteristic, complemented
132#106—1511no—
133#103—3021no—
134#41—21no—
135#41—3021no—
136#41—3021no—
137#41—3021no—
138#41—6041no—
139#41—6041no—
140C2×Q8—21no—
141C2×Q8—3021no—
142C2×D4—3021no—
143C2×D4—6041no—
144C22×C4—6041no—
145C22×C4—1511no—
146Q16—21no—
147Q16—21no—
148Q16—3021no—
149Q16—1511no—
150Q16C22⋊D15111yescharacteristic
151SD16—21no—
152SD16—3021no—
153SD16—3021no—
154SD16—3021no—
155D8—3021no—
156D8—1511no—
157D8C22⋊D15111yescharacteristic
158M16—3021no—
159M16—3021no—
160C2×C8—1511no—
161C2×C8C22×D15111yescharacteristic
162C4⋊C4—3021no—
163C4⋊C4—6041no—
164C22⋊C4—6041no—
165C16—21no—
166C16—3021no—
167C23—6041no—
168C23—1511no—
169Q8—21no—
170Q8—41no—
171Q8—41no—
172Q8—3021no—
173Q8—6041no—
174D4—21no—
175D4—41no—
176D4—3021no—
177D4—6041no—
178D4—6041no—
179D4—6041no—
180D4—6041no—
181C2×C4—41no—
182C2×C4—41no—
183C2×C4—3021no—
184C2×C4—3021no—
185C2×C4—6041no—
186C2×C4—6041no—
187C2×C4—6041no—
188C2×C4—6041no—
189C2×C4—6041no—
190C2×C4—1511no—
191C2×C4D4×D15111yescharacteristic
192C8—3021no—
193C8D4×D15111yescharacteristic
194C8C2×C22⋊D15111yescharacteristic
195C22—41no—
196C22—3021no—
197C22—6041no—
198C22—6041no—
199C22—12082no—
200C22D8×D15111yescharacteristic
201C4—41no—
202C4—81no—
203C4—3021no—
204C4—6041no—
205C4—12081no—
206C4#1801270711yescharacteristic
207C4#1801276311yescharacteristic
208C2—21no—
209C2—81no—
210C2—6041no—
211C2—12081no—
212C2#2375234411yescharacteristic
subgroupG/H
centerC2#23752344
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#510×C151C2
socleC2×C151#447
prime radical#23753009C2
hypercenter#510D151
hypocenterC151#2191
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #510

Complements

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

NH ≅ G/Ntype
2. #23752653C2semidirect
3. #23752467C2semidirect
4. #23752023C2semidirect
5. #23752022C2semidirect
6. #23751993C2semidirect
7. #510×C151C2semidirect
19. #18012679C22semidirect
20. #18012671C22semidirect
23. C2×Q16×C151C22semidirect
26. M32×C151C22semidirect
106. C151#2191semidirect
110. #510D151semidirect
123. C2×Q16C2×D151semidirect
131. M32C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530092
#237526532
#237524672
#237520232
#237520222
#237519932
#510×C1512
#2191151