Finite Group Databasebeta

← C151×#13457 #50318382

Subgroups — C151×#13457 #50318382

Order 38656.

356 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 356 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#498×C151C211yesmaximal, characteristic
2C2×#365×C151C212yesmaximal
3#1945×C151C211yesmaximal, characteristic
4#1386×C151C212yesmaximal
5#1376×C151C211yesmaximal, characteristic
6C2×C4⋊Q8×C151—21no—
7C2×M32×C151C2212yes—
8#498×C151—24no—
9C2×#108×C151C2211yescharacteristic
10#427×C151C2211yescharacteristic
11C2×#106×C151—21no—
12C2×#106×C151C2212yes—
13#424×C151—21no—
14C2×C4×C8×C151C2211yescharacteristic
15#365×C151—24no—
16#339×C151—21no—
17C22×Q8×C151—41no—
18C2×M16×C151—21no—
19C22×C8×C151D411yescharacteristic
20C22×C8×C151C2311yescharacteristic
21C4⋊Q8×C151—24no—
22C4⋊Q8×C151—42no—
23#117×C151—21no—
24C2×C4⋊C4×C151—22no—
25C2×C4⋊C4×C151—41no—
26C2×C42×C151D411yescharacteristic
27M32×C151—22no—
28M32×C151Q814yescomplemented
29C2×C16×C151—22no—
30#108×C151—22no—
31#107×C151Q812yescomplemented
32#106×C151—24no—
33#106×C151—22no—
34#106×C151—21no—
35#106×C151D414yes—
36C4⋊C8×C151—42no—
37C4×C8×C151—22no—
38C2×Q8×C151—44no—
39C2×Q8×C151—84no—
40C22×C4×C151—21no—
41C22×C4×C151—42no—
42C22×C4×C151C2×D411yescharacteristic
43M16×C151—41no—
44M16×C151—41no—
45C2×C8×C151—21no—
46C2×C8×C151—21no—
47C2×C8×C151—41no—
48C2×C8×C151SD1612yes—
49C2×C8×C151C2×D412yes—
50C2×C8×C151C2×Q812yes—
51C2×C8×C151C2×Q811yescharacteristic
52C2×C8×C151#4111yescharacteristic
53C4⋊C4×C151—24no—
54C4⋊C4×C151—22no—
55C4⋊C4×C151—44no—
56C4⋊C4×C151—42no—
57C22⋊C4×C151—41no—
58C42×C151—21no—
59C42×C151—41no—
60C42×C151SD1612yes—
61C16×C151—24no—
62C23×C151AGL(1,ℤ/8)11yescharacteristic
63Q8×C151—88no—
64C2×C4×C151—24no—
65C2×C4×C151—22no—
66C2×C4×C151—44no—
67C2×C4×C151—42no—
68C2×C4×C151—84no—
69C2×C4×C151#12011yescharacteristic
70C2×C4×C151C22⋊Q811yescharacteristic
71C2×C4×C151C4⋊Q811yescharacteristic
72C2×C4×C151C2×SD1611yescharacteristic
73C2×C4×C151C2×SD1611yescharacteristic
74C2×C4×C151#13711yescharacteristic
75C8×C151—22no—
76C8×C151—81no—
77C8×C151C22⋊Q812yes—
78C8×C151C4⋊Q812yes—
79C22×C151—22no—
80C22×C151#45011yescharacteristic
81C22×C151#47611yescharacteristic
82C22×C151#50111yescharacteristic
83C4×C151—24no—
84C4×C151—84no—
85C4×C151—82no—
86C4×C151#39511yescharacteristic
87C4×C151#44811yescharacteristic
88C4×C151#47511yescharacteristic
89C4×C151#49811yescharacteristic
90C2×C151—21no—
91C2×C151—21no—
92C2×C151#205811yescharacteristic
93C2×C151#223012yes—
94#13457C15111yesmaximal, characteristic, direct product factor, Sylow
95C151#1345711yescharacteristic, direct product factor, Sylow
96C2×#498C2×C15111yescharacteristic
97C2×#365C2×C15112yes—
98#1945C2×C15111yescharacteristic
99#1386C2×C15112yes—
100#1376C2×C15111yescharacteristic
101C2×C4⋊Q8—21no—
102C2×M32C22×C15112yes—
103#498—24no—
104C2×#108C22×C15111yescharacteristic
105#427C22×C15111yescharacteristic
106C2×#106—21no—
107C2×#106C22×C15112yes—
108#424—21no—
109C2×C4×C8C22×C15111yescharacteristic
110#365—24no—
111#339—21no—
112C22×Q8—41no—
113C2×M16—21no—
114C22×C8D4×C15111yescharacteristic
115C22×C8C23×C15111yescharacteristic
116C4⋊Q8—24no—
117C4⋊Q8—42no—
118#117—21no—
119C2×C4⋊C4—22no—
120C2×C4⋊C4—41no—
121C2×C42D4×C15111yescharacteristic
122M32—22no—
123M32Q8×C15114yescomplemented
124C2×C16—22no—
125#108—22no—
126#107Q8×C15112yescomplemented
127#106—24no—
128#106—21no—
129#106—22no—
130#106D4×C15114yes—
131C4⋊C8—42no—
132C4×C8—22no—
133C2×Q8—44no—
134C2×Q8—84no—
135C22×C4—21no—
136C22×C4—42no—
137C22×C4C2×D4×C15111yescharacteristic
138M16—41no—
139M16—41no—
140C2×C8—21no—
141C2×C8—21no—
142C2×C8—41no—
143C2×C8SD16×C15112yes—
144C2×C8C2×D4×C15112yes—
145C2×C8C2×Q8×C15112yes—
146C2×C8C2×Q8×C15111yescharacteristic
147C2×C8#41×C15111yescharacteristic
148C4⋊C4—24no—
149C4⋊C4—22no—
150C4⋊C4—44no—
151C4⋊C4—42no—
152C22⋊C4—41no—
153C42—21no—
154C42—41no—
155C42SD16×C15112yes—
156C16—24no—
157C23AGL(1,ℤ/8)×C15111yescharacteristic
158Q8—88no—
159C2×C4—24no—
160C2×C4—22no—
161C2×C4—44no—
162C2×C4—42no—
163C2×C4—84no—
164C2×C4#120×C15111yescharacteristic
165C2×C4C22⋊Q8×C15111yescharacteristic
166C2×C4C4⋊Q8×C15111yescharacteristic
167C2×C4C2×SD16×C15111yescharacteristic
168C2×C4C2×SD16×C15111yescharacteristic
169C2×C4#137×C15111yescharacteristic
170C8—22no—
171C8—81no—
172C8C22⋊Q8×C15112yes—
173C8C4⋊Q8×C15112yes—
174C22—22no—
175C22#450×C15111yescharacteristic
176C22#476×C15111yescharacteristic
177C22#501×C15111yescharacteristic
178C4—24no—
179C4—84no—
180C4—82no—
181C4#395×C15111yescharacteristic
182C4#448×C15111yescharacteristic
183C4#475×C15111yescharacteristic
184C4#498×C15111yescharacteristic
185C2—21no—
186C2—21no—
187C2#2058×C15111yescharacteristic
188C2#2230×C15112yes—
subgroupG/H
center, socleC22×C151#476
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC23×C151AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
28. M32×C151Q8semidirect
31. #107×C151Q8semidirect
94. #13457C151direct (N × H)
95. C151#13457direct (N × H)
123. M32Q8×C151semidirect
126. #107Q8×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#498×C1512
C2×#365×C1512
#1945×C1512
#1386×C1512
#1376×C1512
#13457151