Finite Group Databasebeta

← C151×#13541 #50318466

Subgroups — C151×#13541 #50318466

Order 38656.

254 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 254 conjugacy classes of subgroups — too many to draw. Only its 106 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#1944×C151C211yesmaximal, characteristic
2#1849×C151C211yesmaximal, characteristic
3#1387×C151C212yesmaximal
4#1383×C151C212yesmaximal
5#1377×C151C211yesmaximal, characteristic
6C2×M32×C151C2212yes—
7C2×#108×C151—21no—
8C2×#108×C151C2212yes—
9C2×#107×C151C2211yescharacteristic
10C2×#106×C151C2211yescharacteristic
11#423×C151—21no—
12C2×#97×C151C2211yescharacteristic
13#389×C151—21no—
14#340×C151—21no—
15C2×M16×C151—22no—
16C22×C8×C151D411yescharacteristic
17C22×C8×C151C2311yescharacteristic
18C2×C4⋊C4×C151—21no—
19C2×C4⋊C4×C151—21no—
20C2×C4⋊C4×C151—41no—
21C2×C42×C151D411yescharacteristic
22M32×C151—22no—
23M32×C151—22no—
24C2×C16×C151—22no—
25#108×C151—24no—
26#108×C151—42no—
27#107×C151—22no—
28#106×C151—21no—
29#106×C151Q812yes—
30C4⋊C8×C151—42no—
31#97×C151—22no—
32#95×C151—41no—
33C22×C4×C151—41no—
34C22×C4×C151—41no—
35C22×C4×C151SD1611yescharacteristic
36C22×C4×C151SD1611yescharacteristic
37C22×C4×C151C2×D411yescharacteristic
38M16×C151—42no—
39M16×C151—42no—
40C2×C8×C151—21no—
41C2×C8×C151—21no—
42C2×C8×C151—42no—
43C2×C8×C151Q1612yes—
44C2×C8×C151C2×Q811yescharacteristic
45C2×C8×C151#4112yes—
46C2×C8×C151#4112yes—
47C2×C8×C151#4111yescharacteristic
48C4⋊C4×C151—22no—
49C4⋊C4×C151—41no—
50C4⋊C4×C151—41no—
51C4⋊C4×C151—41no—
52C4⋊C4×C151—82no—
53C42×C151—21no—
54C42×C151—21no—
55C16×C151—42no—
56C23×C151C2×SD1611yescharacteristic
57C2×C4×C151—21no—
58C2×C4×C151—21no—
59C2×C4×C151—41no—
60C2×C4×C151—41no—
61C2×C4×C151—42no—
62C2×C4×C151—81no—
63C2×C4×C151—81no—
64C2×C4×C151—81no—
65C2×C4×C151—81no—
66C2×C4×C151—81no—
67C2×C4×C151C22⋊Q811yescharacteristic
68C2×C4×C151#12311yescharacteristic
69C2×C4×C151#12411yescharacteristic
70C2×C4×C151C2×Q1611yescharacteristic
71C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
72C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
73C8×C151—22no—
74C8×C151—82no—
75C8×C151#12512yes—
76C8×C151#12612yes—
77C22×C151—21no—
78C22×C151—21no—
79C22×C151#47611yescharacteristic
80C22×C151#48111yescharacteristic
81C22×C151#48711yescharacteristic
82C4×C151—41no—
83C4×C151—41no—
84C4×C151—82no—
85C4×C151—161no—
86C4×C151#40011yescharacteristic
87C4×C151#47711yescharacteristic
88C4×C151#48411yescharacteristic
89C4×C151#49011yescharacteristic
90C2×C151—21no—
91C2×C151—21no—
92C2×C151#210011yescharacteristic
93C2×C151#223811yescharacteristic
94C2×C151#223911yescharacteristic
95#13541C15111yesmaximal, characteristic, direct product factor, Sylow
96C151#1354111yescharacteristic, direct product factor, Sylow
97#1944C2×C15111yescharacteristic
98#1849C2×C15111yescharacteristic
99#1387C2×C15112yes—
100#1383C2×C15112yes—
101#1377C2×C15111yescharacteristic
102C2×M32C22×C15112yes—
103C2×#108—21no—
104C2×#108C22×C15112yes—
105C2×#107C22×C15111yescharacteristic
106C2×#106C22×C15111yescharacteristic
107#423—21no—
108C2×#97C22×C15111yescharacteristic
109#389—21no—
110#340—21no—
111C2×M16—22no—
112C22×C8D4×C15111yescharacteristic
113C22×C8C23×C15111yescharacteristic
114C2×C4⋊C4—21no—
115C2×C4⋊C4—21no—
116C2×C4⋊C4—41no—
117C2×C42D4×C15111yescharacteristic
118M32—22no—
119M32—22no—
120C2×C16—22no—
121#108—24no—
122#108—42no—
123#107—22no—
124#106—21no—
125#106Q8×C15112yes—
126C4⋊C8—42no—
127#97—22no—
128#95—41no—
129C22×C4—41no—
130C22×C4—41no—
131C22×C4SD16×C15111yescharacteristic
132C22×C4SD16×C15111yescharacteristic
133C22×C4C2×D4×C15111yescharacteristic
134M16—42no—
135M16—42no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—42no—
139C2×C8Q16×C15112yes—
140C2×C8C2×Q8×C15111yescharacteristic
141C2×C8#41×C15112yes—
142C2×C8#41×C15112yes—
143C2×C8#41×C15111yescharacteristic
144C4⋊C4—22no—
145C4⋊C4—41no—
146C4⋊C4—41no—
147C4⋊C4—41no—
148C4⋊C4—82no—
149C42—21no—
150C42—21no—
151C16—42no—
152C23C2×SD16×C15111yescharacteristic
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—41no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4—81no—
159C2×C4—81no—
160C2×C4—81no—
161C2×C4—81no—
162C2×C4—81no—
163C2×C4C22⋊Q8×C15111yescharacteristic
164C2×C4#123×C15111yescharacteristic
165C2×C4#124×C15111yescharacteristic
166C2×C4C2×Q16×C15111yescharacteristic
167C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
168C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
169C8—22no—
170C8—82no—
171C8#125×C15112yes—
172C8#126×C15112yes—
173C22—21no—
174C22—21no—
175C22#476×C15111yescharacteristic
176C22#481×C15111yescharacteristic
177C22#487×C15111yescharacteristic
178C4—41no—
179C4—41no—
180C4—82no—
181C4—161no—
182C4#400×C15111yescharacteristic
183C4#477×C15111yescharacteristic
184C4#484×C15111yescharacteristic
185C4#490×C15111yescharacteristic
186C2—21no—
187C2—21no—
188C2#2100×C15111yescharacteristic
189C2#2238×C15111yescharacteristic
190C2#2239×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#481
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC23×C151C2×SD16
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×#97×C151 ◁ G

Complements

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

NH ≅ G/Ntype
95. #13541C151direct (N × H)
96. C151#13541direct (N × H)

Maximal subgroups

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

subgroupindex
#1944×C1512
#1849×C1512
#1387×C1512
#1383×C1512
#1377×C1512
#13541151