Finite Group Databasebeta

← C151×#12474 #50317399

Subgroups — C151×#12474 #50317399

Order 38656.

218 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 78 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#2241×C151C211yesmaximal, characteristic, complemented
2#2169×C151C211yesmaximal, characteristic
3#1673×C151C211yesmaximal, characteristic
4#1669×C151C211yesmaximal, characteristic
5#1371×C151C211yesmaximal, characteristic, complemented
6#1364×C151C211yesmaximal, characteristic, complemented
7#1362×C151C211yesmaximal, characteristic, complemented
8C2×M32×C151—21no—
9#500×C151C2211yescharacteristic
10#494×C151C2211yescharacteristic
11#474×C151—21no—
12#461×C151—21no—
13C8×D4×C151C2211yescharacteristic
14C4⋊C16×C151C2211yescharacteristic
15#358×C151—21no—
16#358×C151—21no—
17C22⋊C16×C151—21no—
18C4×C16×C151C2211yescharacteristic
19#335×C151C2211yescharacteristic
20#335×C151C2211yescharacteristic
21#332×C151—21no—
22#332×C151—21no—
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×SD16×C151—41no—
26C22×C8×C151—21no—
27C4⋊Q8×C151—21no—
28C4⋊Q8×C151—21no—
29C4×D4×C151D411yescharacteristic
30M32×C151—42no—
31C2×C16×C151—21no—
32C2×C16×C151D411yescharacteristic
33C2×C16×C151D411yescharacteristic
34#107×C151—21no—
35#107×C151—21no—
36#107×C151—41no—
37C4⋊C8×C151—21no—
38C4⋊C8×C151—21no—
39C4⋊C8×C151D411yescharacteristic
40#103×C151—41no—
41#102×C151—41no—
42C22⋊C8×C151—21no—
43C4×C8×C151C2311yescharacteristic
44C2×Q8×C151—41no—
45C2×Q8×C151—41no—
46C2×D4×C151D811yescharacteristic
47C22×C4×C151—21no—
48Q16×C151—41no—
49Q16×C151—41no—
50Q16×C151—81no—
51SD16×C151—82no—
52C2×C8×C151—21no—
53C2×C8×C151—41no—
54C2×C8×C151—41no—
55C2×C8×C151—41no—
56C2×C8×C151—41no—
57C2×C8×C151C2×D411yescharacteristic
58C2×C8×C151#4111yescharacteristic
59C4⋊C4×C151—41no—
60C4⋊C4×C151—41no—
61C4⋊C4×C151—41no—
62C4⋊C4×C151—41no—
63C4⋊C4×C151D811yescharacteristic
64C22⋊C4×C151—21no—
65C42×C151C2×D411yescharacteristic
66C16×C151—21no—
67C16×C151—21no—
68C16×C151—41no—
69C23×C151—21no—
70Q8×C151—81no—
71Q8×C151—81no—
72Q8×C151—81no—
73Q8×C151—81no—
74D4×C151—21no—
75D4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—41no—
78C2×C4×C151—41no—
79C2×C4×C151—81no—
80C2×C4×C151—81no—
81C2×C4×C151#12111yescharacteristic
82C2×C4×C151C2×D811yescharacteristic
83C2×C4×C151#13511yescharacteristic
84C8×C151—21no—
85C8×C151—41no—
86C8×C151—81no—
87C8×C151—81no—
88C8×C151#13511yescharacteristic
89C8×C151AGL(1,ℤ/8)11yescharacteristic
90C22×C151—41no—
91C22×C151—41no—
92C22×C151—41no—
93C22×C151#46611yescharacteristic
94C4×C151—21no—
95C4×C151—41no—
96C4×C151—161no—
97C4×C151—161no—
98C4×C151#46311yescharacteristic
99C4×C151#47111yescharacteristic
100C4×C151#50911yescharacteristic
101C4×C151#51011yescharacteristic
102C2×C151—81no—
103C2×C151#168111yescharacteristic
104C2×C151#222011yescharacteristic
105C2×C151#222211yescharacteristic
106#12474C15111yesmaximal, characteristic, direct product factor, Sylow
107C151#1247411yescharacteristic, direct product factor, Sylow
108#2241C2×C15111yescharacteristic, complemented
109#2169C2×C15111yescharacteristic
110#1673C2×C15111yescharacteristic
111#1669C2×C15111yescharacteristic
112#1371C2×C15111yescharacteristic, complemented
113#1364C2×C15111yescharacteristic, complemented
114#1362C2×C15111yescharacteristic, complemented
115C2×M32—21no—
116#500C22×C15111yescharacteristic
117#494C22×C15111yescharacteristic
118#474—21no—
119#461—21no—
120C8×D4C22×C15111yescharacteristic
121C4⋊C16C22×C15111yescharacteristic
122#358—21no—
123#358—21no—
124C22⋊C16—21no—
125C4×C16C22×C15111yescharacteristic
126#335C22×C15111yescharacteristic
127#335C22×C15111yescharacteristic
128#332—21no—
129#332—21no—
130C2×Q16—21no—
131C2×Q16—21no—
132C2×SD16—41no—
133C22×C8—21no—
134C4⋊Q8—21no—
135C4⋊Q8—21no—
136C4×D4D4×C15111yescharacteristic
137M32—42no—
138C2×C16—21no—
139C2×C16D4×C15111yescharacteristic
140C2×C16D4×C15111yescharacteristic
141#107—21no—
142#107—21no—
143#107—41no—
144C4⋊C8—21no—
145C4⋊C8—21no—
146C4⋊C8D4×C15111yescharacteristic
147#103—41no—
148#102—41no—
149C22⋊C8—21no—
150C4×C8C23×C15111yescharacteristic
151C2×Q8—41no—
152C2×Q8—41no—
153C2×D4D8×C15111yescharacteristic
154C22×C4—21no—
155Q16—41no—
156Q16—41no—
157Q16—81no—
158SD16—82no—
159C2×C8—21no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—41no—
163C2×C8—41no—
164C2×C8C2×D4×C15111yescharacteristic
165C2×C8#41×C15111yescharacteristic
166C4⋊C4—41no—
167C4⋊C4—41no—
168C4⋊C4—41no—
169C4⋊C4—41no—
170C4⋊C4D8×C15111yescharacteristic
171C22⋊C4—21no—
172C42C2×D4×C15111yescharacteristic
173C16—21no—
174C16—21no—
175C16—41no—
176C23—21no—
177Q8—81no—
178Q8—81no—
179Q8—81no—
180Q8—81no—
181D4—21no—
182D4—21no—
183C2×C4—21no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4#121×C15111yescharacteristic
189C2×C4C2×D8×C15111yescharacteristic
190C2×C4#135×C15111yescharacteristic
191C8—21no—
192C8—41no—
193C8—81no—
194C8—81no—
195C8#135×C15111yescharacteristic
196C8AGL(1,ℤ/8)×C15111yescharacteristic
197C22—41no—
198C22—41no—
199C22—41no—
200C22#466×C15111yescharacteristic
201C4—21no—
202C4—41no—
203C4—161no—
204C4—161no—
205C4#463×C15111yescharacteristic
206C4#471×C15111yescharacteristic
207C4#509×C15111yescharacteristic
208C4#510×C15111yescharacteristic
209C2—81no—
210C2#1681×C15111yescharacteristic
211C2#2220×C15111yescharacteristic
212C2#2222×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#466
commutator, Frattini, cosocleC4×C8C23×C151
prime radicalC2×D4×C151D8
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2241×C151C2semidirect
5. #1371×C151C2semidirect
6. #1364×C151C2semidirect
7. #1362×C151C2semidirect
106. #12474C151direct (N × H)
107. C151#12474direct (N × H)
108. #2241C2×C151semidirect
112. #1371C2×C151semidirect
113. #1364C2×C151semidirect
114. #1362C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2241×C1512
#2169×C1512
#1673×C1512
#1669×C1512
#1371×C1512
#1364×C1512
#1362×C1512
#12474151