Finite Group Databasebeta

← C151×#12508 #50317433

Subgroups — C151×#12508 #50317433

Order 38656.

280 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 102 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#2252×C151C211yesmaximal, characteristic, complemented
2#2248×C151C211yesmaximal, characteristic
3#2241×C151C211yesmaximal, characteristic, complemented
4#2240×C151C211yesmaximal, characteristic
5#1707×C151C211yesmaximal, characteristic, complemented
6#1706×C151C211yesmaximal, characteristic
7#1311×C151C211yesmaximal, characteristic, complemented
8C2×SD32×C151—22no—
9#500×C151C2211yescharacteristic
10#500×C151C2211yescharacteristic
11#498×C151—21no—
12#494×C151C2211yescharacteristic
13#493×C151C2211yescharacteristic
14#492×C151—21no—
15#487×C151—21no—
16#486×C151—21no—
17#366×C151—22no—
18#358×C151—22no—
19#357×C151—22no—
20C4×C16×C151C2211yescharacteristic
21C4×C16×C151C2211yescharacteristic
22C82×C151C2211yescharacteristic
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×SD16×C151—42no—
26C2×D8×C151—21no—
27C2×D8×C151—21no—
28C4⋊Q8×C151—21no—
29C4⋊Q8×C151—21no—
30C4⋊Q8×C151—21no—
31#127×C151—21no—
32SD32×C151—44no—
33C2×C16×C151D412yes—
34C2×C16×C151D412yes—
35#107×C151—21no—
36#107×C151—21no—
37#107×C151—21no—
38#107×C151—21no—
39#106×C151—42no—
40#103×C151—42no—
41#102×C151—42no—
42C4×C8×C151D411yescharacteristic
43C4×C8×C151D411yescharacteristic
44C4×C8×C151C2311yescharacteristic
45C2×Q8×C151—41no—
46C2×Q8×C151—41no—
47C2×Q8×C151—41no—
48C2×D4×C151—41no—
49C2×D4×C151—41no—
50C2×D4×C151—41no—
51Q16×C151—42no—
52Q16×C151—42no—
53SD16×C151—84no—
54D8×C151—42no—
55D8×C151—42no—
56C2×C8×C151D812yes—
57C2×C8×C151D812yes—
58C2×C8×C151C2×D411yescharacteristic
59C2×C8×C151C2×D411yescharacteristic
60C4⋊C4×C151—41no—
61C4⋊C4×C151—41no—
62C4⋊C4×C151—41no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—41no—
65C4⋊C4×C151—41no—
66C42×C151C2×D411yescharacteristic
67C16×C151—22no—
68C16×C151SD1614yescomplemented
69C23×C151—81no—
70Q8×C151—81no—
71Q8×C151—81no—
72Q8×C151—82no—
73Q8×C151—82no—
74D4×C151—81no—
75D4×C151—81no—
76D4×C151—82no—
77D4×C151—82no—
78C2×C4×C151—81no—
79C2×C4×C151—81no—
80C2×C4×C151—81no—
81C2×C4×C151#12711yescharacteristic
82C2×C4×C151C2×D811yescharacteristic
83C2×C4×C151C2×D811yescharacteristic
84C8×C151—22no—
85C8×C151—22no—
86C8×C151C2×SD1612yes—
87C8×C151#13512yes—
88C22×C151—161no—
89C22×C151—161no—
90C22×C151—161no—
91C22×C151#49311yescharacteristic
92C4×C151—161no—
93C4×C151—161no—
94C4×C151—161no—
95C4×C151#49211yescharacteristic
96C4×C151#49511yescharacteristic
97C4×C151#50912yes—
98C4×C151#51012yes—
99C2×C151—321no—
100C2×C151#170611yescharacteristic
101C2×C151#225011yescharacteristic
102C2×C151#225111yescharacteristic
103#12508C15111yesmaximal, characteristic, direct product factor, Sylow
104C151#1250811yescharacteristic, direct product factor, Sylow
105#2252C2×C15111yescharacteristic, complemented
106#2248C2×C15111yescharacteristic
107#2241C2×C15111yescharacteristic, complemented
108#2240C2×C15111yescharacteristic
109#1707C2×C15111yescharacteristic, complemented
110#1706C2×C15111yescharacteristic
111#1311C2×C15111yescharacteristic, complemented
112C2×SD32—22no—
113#500C22×C15111yescharacteristic
114#500C22×C15111yescharacteristic
115#498—21no—
116#494C22×C15111yescharacteristic
117#493C22×C15111yescharacteristic
118#492—21no—
119#487—21no—
120#486—21no—
121#366—22no—
122#358—22no—
123#357—22no—
124C4×C16C22×C15111yescharacteristic
125C4×C16C22×C15111yescharacteristic
126C82C22×C15111yescharacteristic
127C2×Q16—21no—
128C2×Q16—21no—
129C2×SD16—42no—
130C2×D8—21no—
131C2×D8—21no—
132C4⋊Q8—21no—
133C4⋊Q8—21no—
134C4⋊Q8—21no—
135#127—21no—
136SD32—44no—
137C2×C16D4×C15112yes—
138C2×C16D4×C15112yes—
139#107—21no—
140#107—21no—
141#107—21no—
142#107—21no—
143#106—42no—
144#103—42no—
145#102—42no—
146C4×C8D4×C15111yescharacteristic
147C4×C8D4×C15111yescharacteristic
148C4×C8C23×C15111yescharacteristic
149C2×Q8—41no—
150C2×Q8—41no—
151C2×Q8—41no—
152C2×D4—41no—
153C2×D4—41no—
154C2×D4—41no—
155Q16—42no—
156Q16—42no—
157SD16—84no—
158D8—42no—
159D8—42no—
160C2×C8D8×C15112yes—
161C2×C8D8×C15112yes—
162C2×C8C2×D4×C15111yescharacteristic
163C2×C8C2×D4×C15111yescharacteristic
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C42C2×D4×C15111yescharacteristic
171C16—22no—
172C16SD16×C15114yescomplemented
173C23—81no—
174Q8—81no—
175Q8—81no—
176Q8—82no—
177Q8—82no—
178D4—81no—
179D4—81no—
180D4—82no—
181D4—82no—
182C2×C4—81no—
183C2×C4—81no—
184C2×C4—81no—
185C2×C4#127×C15111yescharacteristic
186C2×C4C2×D8×C15111yescharacteristic
187C2×C4C2×D8×C15111yescharacteristic
188C8—22no—
189C8—22no—
190C8C2×SD16×C15112yes—
191C8#135×C15112yes—
192C22—161no—
193C22—161no—
194C22—161no—
195C22#493×C15111yescharacteristic
196C4—161no—
197C4—161no—
198C4—161no—
199C4#492×C15111yescharacteristic
200C4#495×C15111yescharacteristic
201C4#509×C15112yes—
202C4#510×C15112yes—
203C2—321no—
204C2#1706×C15111yescharacteristic
205C2#2250×C15111yescharacteristic
206C2#2251×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#493
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#493×C151C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C82×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2252×C151C2semidirect
3. #2241×C151C2semidirect
5. #1707×C151C2semidirect
7. #1311×C151C2semidirect
68. C16×C151SD16semidirect
103. #12508C151direct (N × H)
104. C151#12508direct (N × H)
105. #2252C2×C151semidirect
107. #2241C2×C151semidirect
109. #1707C2×C151semidirect
111. #1311C2×C151semidirect
172. C16SD16×C151semidirect

Maximal subgroups

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

subgroupindex
#2252×C1512
#2248×C1512
#2241×C1512
#2240×C1512
#1707×C1512
#1706×C1512
#1311×C1512
#12508151