Finite Group Databasebeta

← #34071062

Subgroups — #34071062

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#23752655C211yesmaximal, characteristic, complemented
3#23752652C211yesmaximal, characteristic, complemented
4#23752471C211yesmaximal, characteristic, complemented
5#23752021C211yesmaximal, characteristic, complemented
6#23751993C211yesmaximal, characteristic, complemented
7#360×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×Dic604C2211yescharacteristic, complemented
16C2×#14558987C2211yescharacteristic
17#18012719—21no—
18Dic1208—21no—
19#18012685—21no—
20#18012684—21no—
21#18012683—21no—
22#18012679C2211yescharacteristic, complemented
23#18012662—21no—
24#135×C151C2211yescharacteristic
25M32×C151C2211yescharacteristic, complemented
26#106×C151C2211yescharacteristic, complemented
27#14559005—21no—
28#14559004—21no—
29#14559004—41no—
30#14559003—21no—
31#14559003—41no—
32C2×Dic302—21no—
33Q8×D151—21no—
34D4×D151—21no—
35D4×D151—41no—
36C2×C4×D151—41no—
37C2×C4×D151D411yescharacteristic
38Dic604—21no—
39Dic604—21no—
40Dic604D411yescharacteristic
41#14558994—21no—
42#14558993—21no—
43#14558992—21no—
44#14558991—21no—
45D1208D411yescharacteristic
46#14558989—21no—
47#14558987—21no—
48#14558987—21no—
49C2×C151⋊C8D411yescharacteristic
50C4⋊Dic151—41no—
51(C2×D151)⋊C4—41no—
52C151⋊C16—21no—
53#41×C151—21no—
54Q16×C151D411yescharacteristic
55SD16×C151—21no—
56D8×C151D411yescharacteristic
57C2×C8×C151C2311yescharacteristic
58C4⋊C4×C151—21no—
59C16×C151—21no—
60C22×D151—41no—
61C22×D151D811yescharacteristic
62Dic302—21no—
63Dic302—41no—
64Dic302—41no—
65Dic302—41no—
66D604—21no—
67D604—41no—
68C22⋊D151—41no—
69C22⋊D151—41no—
70C22⋊D151—41no—
71C2×Dic151—41no—
72C2×Dic151—41no—
73C2×Dic151D811yescharacteristic
74C4×D151—21no—
75C4×D151—21no—
76C4×D151—41no—
77C4×D151—41no—
78C4×D151—41no—
79C151⋊C8—21no—
80Q8×C151—21no—
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#510—1511no—
111#470—1511no—
112#360—1511no—
113#360D15111yescharacteristic, complemented
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×Q16—1511no—
124C2×M16—1511no—
125C22⋊Q8—3021no—
126Q32—3021no—
127Q32—3021no—
128SD32—3021no—
129SD32—3021no—
130M32—1511no—
131M32C2×D15111yescharacteristic, complemented
132#106C2×D15111yescharacteristic, complemented
133#103—3021no—
134#41—21no—
135#41—3021no—
136#41—3021no—
137#41—3021no—
138#41—6041no—
139#41—6041no—
140C2×Q8—3021no—
141C2×Q8—3021no—
142C2×D4—3021no—
143C2×D4—6041no—
144C22×C4—6041no—
145C22×C4—1511no—
146Q16—3021no—
147Q16—3021no—
148Q16—3021no—
149Q16—1511no—
150Q16D60411yescharacteristic
151SD16—21no—
152SD16—3021no—
153SD16—3021no—
154SD16—3021no—
155D8—3021no—
156D8—1511no—
157D8D60411yescharacteristic
158M16—3021no—
159M16—3021no—
160C2×C8—1511no—
161C2×C8C22×D15111yescharacteristic
162C4⋊C4—21no—
163C4⋊C4—6041no—
164C22⋊C4—6041no—
165C16—21no—
166C16—3021no—
167C23—6041no—
168C23—1511no—
169Q8—21no—
170Q8—3021no—
171Q8—6041no—
172Q8—6041no—
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×D60411yescharacteristic
195C22—41no—
196C22—3021no—
197C22—6041no—
198C22—6041no—
199C22—12082no—
200C22D8×D15111yescharacteristic
201C4—41no—
202C4—81no—
203C4—3021no—
204C4—6041no—
205C4—12081no—
206C4#1801270911yescharacteristic
207C4#1801276611yescharacteristic
208C2—21no—
209C2—81no—
210C2—6041no—
211C2—12081no—
212C2#2375234711yescharacteristic
subgroupG/H
centerC2#23752347
commutator, cosocleC2×C8×C151C23
FrattiniC2×C8C22×D151
Fitting#360×C151C2
socleC2×C151#447
prime radical#23753009C2
hypercenter#360D151
hypocenterC151#2191
LCSG ▷ C2×C8×C151 ▷ C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #360

Complements

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

NH ≅ G/Ntype
2. #23752655C2semidirect
3. #23752652C2semidirect
4. #23752471C2semidirect
5. #23752021C2semidirect
6. #23751993C2semidirect
7. #360×C151C2semidirect
15. C2×Dic604C22semidirect
22. #18012679C22semidirect
25. M32×C151C22semidirect
26. #106×C151C22semidirect
106. C151#2191semidirect
113. #360D151semidirect
131. M32C2×D151semidirect
132. #106C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237530092
#237526552
#237526522
#237524712
#237520212
#237519932
#360×C1512
#2191151