Finite Group Databasebeta

← C151×#13495 #50318420

Subgroups — C151×#13495 #50318420

Order 38656.

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

normal subgroups only

This group has 284 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
1C2×#366×C151C211yesmaximal, characteristic, complemented
2#2113×C151C211yesmaximal, characteristic
3#1816×C151C212yesmaximal
4#1387×C151C212yesmaximal, complemented
5#1381×C151C211yesmaximal, characteristic, complemented
6C2×#131×C151C2211yescharacteristic
7C2×M32×C151C2211yescharacteristic
8C22×C16×C151C2211yescharacteristic
9C2×#108×C151C2212yes—
10C2×#107×C151C2212yes—
11#417×C151—22no—
12#366×C151—22no—
13C22⋊C16×C151—22no—
14#343×C151—22no—
15C2×#41×C151D411yescharacteristic
16#131×C151—22no—
17#131×C151—22no—
18C2×M16×C151—21no—
19C2×M16×C151—22no—
20C2×M16×C151D411yescharacteristic
21C22×C8×C151—21no—
22C22×C8×C151C2311yescharacteristic
23C2×C4⋊C4×C151—22no—
24M32×C151—22no—
25C2×C16×C151—22no—
26C2×C16×C151—21no—
27C2×C16×C151D412yes—
28#108×C151—22no—
29#108×C151—22no—
30#107×C151—22no—
31#107×C151—22no—
32#103×C151—42no—
33#102×C151—42no—
34#41×C151—22no—
35#41×C151—22no—
36C2×Q8×C151D811yescharacteristic
37C2×D4×C151—21no—
38C2×D4×C151D811yescharacteristic
39C22×C4×C151—21no—
40C22×C4×C151—42no—
41C22×C4×C151C2×D411yescharacteristic
42M16×C151—22no—
43M16×C151—42no—
44M16×C151—42no—
45M16×C151—42no—
46C2×C8×C151—21no—
47C2×C8×C151—41no—
48C2×C8×C151—41no—
49C2×C8×C151—42no—
50C2×C8×C151C2×D411yescharacteristic
51C2×C8×C151#4112yes—
52C2×C8×C151#4112yes—
53C2×C8×C151#4111yescharacteristic
54C4⋊C4×C151—42no—
55C4⋊C4×C151—42no—
56C16×C151—22no—
57C16×C151—41no—
58C23×C151—21no—
59C23×C151#13511yescharacteristic
60Q8×C151—22no—
61D4×C151—22no—
62D4×C151—42no—
63C2×C4×C151—21no—
64C2×C4×C151—41no—
65C2×C4×C151—41no—
66C2×C4×C151—82no—
67C2×C4×C151—162no—
68C2×C4×C151#12111yescharacteristic
69C2×C4×C151#12312yes—
70C2×C4×C151C2×D811yescharacteristic
71C2×C4×C151#13712yes—
72C8×C151—41no—
73C8×C151—82no—
74C8×C151#12311yescharacteristic
75C8×C151#12411yescharacteristic
76C8×C151#12612yes—
77C22×C151—21no—
78C22×C151—21no—
79C22×C151—41no—
80C22×C151—41no—
81C22×C151—41no—
82C22×C151#46611yescharacteristic
83C22×C151#48512yes—
84C4×C151—41no—
85C4×C151—162no—
86C4×C151#39711yescharacteristic
87C4×C151#47011yescharacteristic
88C4×C151#48012yes—
89C2×C151—22no—
90C2×C151—81no—
91C2×C151#207511yescharacteristic
92C2×C151#222111yescharacteristic
93C2×C151#222211yescharacteristic
94#13495C15111yesmaximal, characteristic, direct product factor, Sylow
95C151#1349511yescharacteristic, direct product factor, Sylow
96C2×#366C2×C15111yescharacteristic, complemented
97#2113C2×C15111yescharacteristic
98#1816C2×C15112yes—
99#1387C2×C15112yescomplemented
100#1381C2×C15111yescharacteristic, complemented
101C2×#131C22×C15111yescharacteristic
102C2×M32C22×C15111yescharacteristic
103C22×C16C22×C15111yescharacteristic
104C2×#108C22×C15112yes—
105C2×#107C22×C15112yes—
106#417—22no—
107#366—22no—
108C22⋊C16—22no—
109#343—22no—
110C2×#41D4×C15111yescharacteristic
111#131—22no—
112#131—22no—
113C2×M16—21no—
114C2×M16—22no—
115C2×M16D4×C15111yescharacteristic
116C22×C8—21no—
117C22×C8C23×C15111yescharacteristic
118C2×C4⋊C4—22no—
119M32—22no—
120C2×C16—22no—
121C2×C16—21no—
122C2×C16D4×C15112yes—
123#108—22no—
124#108—22no—
125#107—22no—
126#107—22no—
127#103—42no—
128#102—42no—
129#41—22no—
130#41—22no—
131C2×Q8D8×C15111yescharacteristic
132C2×D4—21no—
133C2×D4D8×C15111yescharacteristic
134C22×C4—21no—
135C22×C4—42no—
136C22×C4C2×D4×C15111yescharacteristic
137M16—22no—
138M16—42no—
139M16—42no—
140M16—42no—
141C2×C8—21no—
142C2×C8—41no—
143C2×C8—41no—
144C2×C8—42no—
145C2×C8C2×D4×C15111yescharacteristic
146C2×C8#41×C15112yes—
147C2×C8#41×C15112yes—
148C2×C8#41×C15111yescharacteristic
149C4⋊C4—42no—
150C4⋊C4—42no—
151C16—22no—
152C16—41no—
153C23—21no—
154C23#135×C15111yescharacteristic
155Q8—22no—
156D4—22no—
157D4—42no—
158C2×C4—21no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—82no—
162C2×C4—162no—
163C2×C4#121×C15111yescharacteristic
164C2×C4#123×C15112yes—
165C2×C4C2×D8×C15111yescharacteristic
166C2×C4#137×C15112yes—
167C8—41no—
168C8—82no—
169C8#123×C15111yescharacteristic
170C8#124×C15111yescharacteristic
171C8#126×C15112yes—
172C22—21no—
173C22—21no—
174C22—41no—
175C22—41no—
176C22—41no—
177C22#466×C15111yescharacteristic
178C22#485×C15112yes—
179C4—41no—
180C4—162no—
181C4#397×C15111yescharacteristic
182C4#470×C15111yescharacteristic
183C4#480×C15112yes—
184C2—22no—
185C2—81no—
186C2#2075×C15111yescharacteristic
187C2#2221×C15111yescharacteristic
188C2#2222×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#466
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC2×#41×C151D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#366×C151C2semidirect
4. #1387×C151C2semidirect
5. #1381×C151C2semidirect
94. #13495C151direct (N × H)
95. C151#13495direct (N × H)
96. C2×#366C2×C151semidirect
99. #1387C2×C151semidirect
100. #1381C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#366×C1512
#2113×C1512
#1816×C1512
#1387×C1512
#1381×C1512
#13495151