Finite Group Databasebeta

← C151×#12488 #50317413

Subgroups — C151×#12488 #50317413

Order 38656.

212 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 212 conjugacy classes of subgroups — too many to draw. Only its 82 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#2227×C151C211yesmaximal, characteristic
2#2209×C151C211yesmaximal, characteristic
3#1707×C151C211yesmaximal, characteristic
4#1591×C151C211yesmaximal, characteristic
5#1370×C151C211yesmaximal, characteristic
6#1365×C151C211yesmaximal, characteristic
7#1362×C151C211yesmaximal, characteristic
8C2×Q32×C151—21no—
9#500×C151C2211yescharacteristic
10#498×C151—21no—
11#494×C151C2211yescharacteristic
12#487×C151—21no—
13#446×C151—21no—
14C4×Q16×C151C2211yescharacteristic
15#366×C151—21no—
16C4⋊C16×C151C2211yescharacteristic
17C4⋊C16×C151C2211yescharacteristic
18#358×C151—21no—
19#358×C151—21no—
20#335×C151C2211yescharacteristic
21Q8⋊C8×C151—21no—
22C82×C151C2211yescharacteristic
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×Q16×C151D411yescharacteristic
26C4⋊Q8×C151—21no—
27C4⋊Q8×C151—21no—
28C4×Q8×C151—21no—
29Q32×C151—42no—
30C2×C16×C151—21no—
31C2×C16×C151—21no—
32#107×C151—21no—
33#107×C151—21no—
34#107×C151D411yescharacteristic
35#106×C151—41no—
36#106×C151—41no—
37C4⋊C8×C151—21no—
38C4⋊C8×C151—41no—
39#103×C151—21no—
40#103×C151—42no—
41#97×C151—41no—
42C4×C8×C151D411yescharacteristic
43C4×C8×C151D411yescharacteristic
44C4×C8×C151C2311yescharacteristic
45C2×Q8×C151—21no—
46C2×Q8×C151—41no—
47C2×Q8×C151—41no—
48Q16×C151—21no—
49Q16×C151—21no—
50Q16×C151—41no—
51Q16×C151—41no—
52Q16×C151—81no—
53C2×C8×C151—21no—
54C2×C8×C151—41no—
55C2×C8×C151D811yescharacteristic
56C2×C8×C151D811yescharacteristic
57C2×C8×C151C2×D411yescharacteristic
58C2×C8×C151#4111yescharacteristic
59C4⋊C4×C151—21no—
60C4⋊C4×C151—41no—
61C4⋊C4×C151—41no—
62C4⋊C4×C151—41no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—41no—
65C42×C151—41no—
66C42×C151C2×D411yescharacteristic
67C16×C151—41no—
68C16×C151—41no—
69Q8×C151—41no—
70Q8×C151—41no—
71Q8×C151—82no—
72Q8×C151—81no—
73Q8×C151—81no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151—81no—
77C2×C4×C151—81no—
78C2×C4×C151#12111yescharacteristic
79C2×C4×C151C2×D811yescharacteristic
80C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
81C8×C151—21no—
82C8×C151—21no—
83C8×C151—41no—
84C8×C151—81no—
85C8×C151Q3212yescomplemented
86C8×C151AGL(1,ℤ/8)11yescharacteristic
87C8×C151#13711yescharacteristic
88C22×C151#45911yescharacteristic
89C4×C151—21no—
90C4×C151—81no—
91C4×C151—81no—
92C4×C151—161no—
93C4×C151—161no—
94C4×C151#46811yescharacteristic
95C4×C151#47111yescharacteristic
96C4×C151C2×Q3211yescharacteristic
97C4×C151#51011yescharacteristic
98C2×C151#168511yescharacteristic
99C2×C151#220911yescharacteristic
100C2×C151#221211yescharacteristic
101#12488C15111yesmaximal, characteristic, direct product factor, Sylow
102C151#1248811yescharacteristic, direct product factor, Sylow
103#2227C2×C15111yescharacteristic
104#2209C2×C15111yescharacteristic
105#1707C2×C15111yescharacteristic
106#1591C2×C15111yescharacteristic
107#1370C2×C15111yescharacteristic
108#1365C2×C15111yescharacteristic
109#1362C2×C15111yescharacteristic
110C2×Q32—21no—
111#500C22×C15111yescharacteristic
112#498—21no—
113#494C22×C15111yescharacteristic
114#487—21no—
115#446—21no—
116C4×Q16C22×C15111yescharacteristic
117#366—21no—
118C4⋊C16C22×C15111yescharacteristic
119C4⋊C16C22×C15111yescharacteristic
120#358—21no—
121#358—21no—
122#335C22×C15111yescharacteristic
123Q8⋊C8—21no—
124C82C22×C15111yescharacteristic
125C2×Q16—21no—
126C2×Q16—21no—
127C2×Q16D4×C15111yescharacteristic
128C4⋊Q8—21no—
129C4⋊Q8—21no—
130C4×Q8—21no—
131Q32—42no—
132C2×C16—21no—
133C2×C16—21no—
134#107—21no—
135#107—21no—
136#107D4×C15111yescharacteristic
137#106—41no—
138#106—41no—
139C4⋊C8—21no—
140C4⋊C8—41no—
141#103—21no—
142#103—42no—
143#97—41no—
144C4×C8D4×C15111yescharacteristic
145C4×C8D4×C15111yescharacteristic
146C4×C8C23×C15111yescharacteristic
147C2×Q8—21no—
148C2×Q8—41no—
149C2×Q8—41no—
150Q16—21no—
151Q16—21no—
152Q16—41no—
153Q16—41no—
154Q16—81no—
155C2×C8—21no—
156C2×C8—41no—
157C2×C8D8×C15111yescharacteristic
158C2×C8D8×C15111yescharacteristic
159C2×C8C2×D4×C15111yescharacteristic
160C2×C8#41×C15111yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—41no—
165C4⋊C4—41no—
166C4⋊C4—41no—
167C42—41no—
168C42C2×D4×C15111yescharacteristic
169C16—41no—
170C16—41no—
171Q8—41no—
172Q8—41no—
173Q8—82no—
174Q8—81no—
175Q8—81no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4#121×C15111yescharacteristic
181C2×C4C2×D8×C15111yescharacteristic
182C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—81no—
187C8Q32×C15112yescomplemented
188C8AGL(1,ℤ/8)×C15111yescharacteristic
189C8#137×C15111yescharacteristic
190C22#459×C15111yescharacteristic
191C4—21no—
192C4—81no—
193C4—81no—
194C4—161no—
195C4—161no—
196C4#468×C15111yescharacteristic
197C4#471×C15111yescharacteristic
198C4C2×Q32×C15111yescharacteristic
199C4#510×C15111yescharacteristic
200C2#1685×C15111yescharacteristic
201C2#2209×C15111yescharacteristic
202C2#2212×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC22×C151#459
commutator, Frattini, cosocleC4×C8C23×C151
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
85. C8×C151Q32semidirect
101. #12488C151direct (N × H)
102. C151#12488direct (N × H)
187. C8Q32×C151semidirect

Maximal subgroups

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

subgroupindex
#2227×C1512
#2209×C1512
#1707×C1512
#1591×C1512
#1370×C1512
#1365×C1512
#1362×C1512
#12488151