Finite Group Databasebeta

← C151×#19733 #50324658

Subgroups — C151×#19733 #50324658

Order 38656.

712 conjugacy classes of subgroups; only the 230 normal subgroups are shown.

normal subgroups only

This group has 712 conjugacy classes of subgroups — too many to draw. Only its 230 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#3231×C151C213yesmaximal, complemented
2#3208×C151C213yesmaximal
3#1719×C151C213yesmaximal, complemented
4#1714×C151C213yesmaximal, complemented
5#1711×C151C211yesmaximal, characteristic, complemented
6#1705×C151C211yesmaximal, characteristic, complemented
7#1454×C151C211yesmaximal, characteristic, complemented
8#533×C151C2213yes—
9C2×#127×C151C2211yescharacteristic
10#500×C151C2213yescomplemented
11#498×C151C2213yescomplemented
12#492×C151C2213yes—
13#492×C151C2213yes—
14#487×C151C2213yescomplemented
15#487×C151C2213yescomplemented
16#486×C151C2213yes—
17#486×C151C2213yes—
18#485×C151—26no—
19#479×C151—26no—
20#460×C151—26no—
21#450×C151—26no—
22#431×C151C2213yes—
23#322×C151C2213yescomplemented
24C82×C151C2211yescharacteristic, complemented
25C22×D4×C151—23no—
26C2×SD16×C151—26no—
27C2×SD16×C151—26no—
28C4⋊Q8×C151C2313yes—
29C4⋊Q8×C151C2313yes—
30#127×C151—23no—
31#127×C151C2311yescharacteristic
32#127×C151C2311yescharacteristic
33#125×C151—23no—
34C22⋊Q8×C151—23no—
35C22⋊Q8×C151—23no—
36C4×Q8×C151—23no—
37C4×Q8×C151—23no—
38#117×C151—23no—
39C2×C42×C151C2311yescharacteristic
40#107×C151—26no—
41#106×C151—26no—
42C4⋊C8×C151D416yes—
43#103×C151—26no—
44#103×C151—26no—
45#102×C151—26no—
46#102×C151—26no—
47C22⋊C8×C151D416yes—
48C4×C8×C151C2313yes—
49C4×C8×C151C2313yes—
50C24×C151—41no—
51C2×Q8×C151—23no—
52C2×Q8×C151—23no—
53C2×D4×C151—23no—
54C2×D4×C151—23no—
55C2×D4×C151—43no—
56C2×D4×C151—86no—
57C22×C4×C151C2×D413yes—
58SD16×C151—86no—
59SD16×C151—86no—
60C2×C8×C151C2×D416yes—
61C2×C8×C151C2×D416yes—
62C4⋊C4×C151—23no—
63C4⋊C4×C151—23no—
64C4⋊C4×C151—23no—
65C4⋊C4×C151—23no—
66C4⋊C4×C151—43no—
67C4⋊C4×C151—43no—
68C22⋊C4×C151—43no—
69C42×C151—43no—
70C42×C151C2×D413yes—
71C42×C151C2411yescharacteristic
72C23×C151—41no—
73C23×C151—41no—
74C23×C151—86no—
75C23×C151#12711yescharacteristic
76Q8×C151—46no—
77Q8×C151—46no—
78D4×C151—46no—
79D4×C151—46no—
80D4×C151—86no—
81C2×C4×C151—26no—
82C2×C4×C151—43no—
83C2×C4×C151—43no—
84C2×C4×C151#12713yes—
85C2×C4×C151C22×D413yes—
86C8×C151—26no—
87C8×C151—26no—
88C22×C151—23no—
89C22×C151—83no—
90C22×C151—83no—
91C22×C151—164no—
92C22×C151C2×#12711yescharacteristic
93C4×C151—23no—
94C4×C151—83no—
95C4×C151—83no—
96C4×C151#57716yes—
97C2×C151—41no—
98C2×C151—161no—
99C2×C151—161no—
100C2×C151#315413yes—
101#19733C15111yesmaximal, characteristic, direct product factor, Sylow
102C151#1973311yescharacteristic, direct product factor, Sylow
103#3231C2×C15113yescomplemented
104#3208C2×C15113yes—
105#1719C2×C15113yescomplemented
106#1714C2×C15113yescomplemented
107#1711C2×C15111yescharacteristic, complemented
108#1705C2×C15111yescharacteristic, complemented
109#1454C2×C15111yescharacteristic, complemented
110#533C22×C15113yes—
111C2×#127C22×C15111yescharacteristic
112#500C22×C15113yescomplemented
113#498C22×C15113yescomplemented
114#492C22×C15113yes—
115#492C22×C15113yes—
116#487C22×C15113yescomplemented
117#487C22×C15113yescomplemented
118#486C22×C15113yes—
119#486C22×C15113yes—
120#485—26no—
121#479—26no—
122#460—26no—
123#450—26no—
124#431C22×C15113yes—
125#322C22×C15113yescomplemented
126C82C22×C15111yescharacteristic, complemented
127C22×D4—23no—
128C2×SD16—26no—
129C2×SD16—26no—
130C4⋊Q8C23×C15113yes—
131C4⋊Q8C23×C15113yes—
132#127—23no—
133#127C23×C15111yescharacteristic
134#127C23×C15111yescharacteristic
135#125—23no—
136C22⋊Q8—23no—
137C22⋊Q8—23no—
138C4×Q8—23no—
139C4×Q8—23no—
140#117—23no—
141C2×C42C23×C15111yescharacteristic
142#107—26no—
143#106—26no—
144C4⋊C8D4×C15116yes—
145#103—26no—
146#103—26no—
147#102—26no—
148#102—26no—
149C22⋊C8D4×C15116yes—
150C4×C8C23×C15113yes—
151C4×C8C23×C15113yes—
152C24—41no—
153C2×Q8—23no—
154C2×Q8—23no—
155C2×D4—23no—
156C2×D4—23no—
157C2×D4—43no—
158C2×D4—86no—
159C22×C4C2×D4×C15113yes—
160SD16—86no—
161SD16—86no—
162C2×C8C2×D4×C15116yes—
163C2×C8C2×D4×C15116yes—
164C4⋊C4—23no—
165C4⋊C4—23no—
166C4⋊C4—23no—
167C4⋊C4—23no—
168C4⋊C4—43no—
169C4⋊C4—43no—
170C22⋊C4—43no—
171C42—43no—
172C42C2×D4×C15113yes—
173C42C24×C15111yescharacteristic
174C23—41no—
175C23—41no—
176C23—86no—
177C23#127×C15111yescharacteristic
178Q8—46no—
179Q8—46no—
180D4—46no—
181D4—46no—
182D4—86no—
183C2×C4—26no—
184C2×C4—43no—
185C2×C4—43no—
186C2×C4#127×C15113yes—
187C2×C4C22×D4×C15113yes—
188C8—26no—
189C8—26no—
190C22—23no—
191C22—83no—
192C22—83no—
193C22—164no—
194C22C2×#127×C15111yescharacteristic
195C4—23no—
196C4—83no—
197C4—83no—
198C4#577×C15116yes—
199C2—41no—
200C2—161no—
201C2—161no—
202C2#3154×C15113yes—
subgroupG/H
center, socleC22×C151C2×#127
commutator, Frattini, cosocleC42C24×C151
prime radicalC2×#127×C151C22
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #3231×C151C2semidirect
3. #1719×C151C2semidirect
4. #1714×C151C2semidirect
5. #1711×C151C2semidirect
6. #1705×C151C2semidirect
7. #1454×C151C2semidirect
10. #500×C151C22semidirect
11. #498×C151C22semidirect
14. #487×C151C22semidirect
15. #487×C151C22semidirect
23. #322×C151C22semidirect
24. C82×C151C22semidirect
101. #19733C151direct (N × H)
102. C151#19733direct (N × H)
103. #3231C2×C151semidirect
105. #1719C2×C151semidirect
106. #1714C2×C151semidirect
107. #1711C2×C151semidirect
108. #1705C2×C151semidirect
109. #1454C2×C151semidirect
112. #500C22×C151semidirect
113. #498C22×C151semidirect
116. #487C22×C151semidirect
117. #487C22×C151semidirect
125. #322C22×C151semidirect
126. C82C22×C151semidirect

Maximal subgroups

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

subgroupindex
#3231×C1512
#3208×C1512
#1719×C1512
#1714×C1512
#1711×C1512
#1705×C1512
#1454×C1512
#19733151