Finite Group Databasebeta

← C151×#13488 #50318413

Subgroups — C151×#13488 #50318413

Order 38656.

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

normal subgroups only

This group has 302 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
1C2×#362×C151C212yesmaximal
2#1971×C151C211yesmaximal, characteristic
3#1849×C151C211yesmaximal, characteristic
4#1383×C151C212yesmaximal
5#1377×C151C211yesmaximal, characteristic
6C22×Q16×C151C2211yescharacteristic
7C2×M32×C151C2212yes—
8C2×#108×C151—21no—
9C2×#108×C151C2212yes—
10C2×#106×C151C2211yescharacteristic
11#423×C151—21no—
12C2×#103×C151—21no—
13C2×#97×C151C2211yescharacteristic
14#391×C151—21no—
15#362×C151—24no—
16C22×Q8×C151—21no—
17C2×Q16×C151—21no—
18C2×Q16×C151—22no—
19C2×Q16×C151—22no—
20C2×Q16×C151D412yes—
21C2×M16×C151—22no—
22C22×C8×C151D411yescharacteristic
23C22×C8×C151C2311yescharacteristic
24C2×C4⋊C4×C151—21no—
25C2×C42×C151D411yescharacteristic
26M32×C151—22no—
27M32×C151—22no—
28C2×C16×C151—22no—
29#108×C151—22no—
30#108×C151—22no—
31#108×C151—42no—
32#106×C151—22no—
33C4⋊C8×C151—42no—
34#103×C151—42no—
35#97×C151—22no—
36#95×C151—42no—
37C2×Q8×C151—22no—
38C2×Q8×C151—41no—
39C2×Q8×C151—41no—
40C2×Q8×C151—41no—
41C2×Q8×C151—41no—
42C2×Q8×C151—41no—
43C22×C4×C151—41no—
44C22×C4×C151—41no—
45C22×C4×C151SD1612yes—
46C22×C4×C151C2×D411yescharacteristic
47Q16×C151—24no—
48Q16×C151—42no—
49M16×C151—42no—
50M16×C151—42no—
51C2×C8×C151—21no—
52C2×C8×C151—21no—
53C2×C8×C151—42no—
54C2×C8×C151D812yes—
55C2×C8×C151C2×D411yescharacteristic
56C2×C8×C151#4112yes—
57C2×C8×C151#4112yes—
58C2×C8×C151#4111yescharacteristic
59C4⋊C4×C151—41no—
60C4⋊C4×C151—41no—
61C42×C151—21no—
62C42×C151—21no—
63C16×C151—42no—
64C23×C151C2×SD1611yescharacteristic
65Q8×C151—42no—
66Q8×C151—42no—
67Q8×C151—81no—
68Q8×C151—81no—
69C2×C4×C151—22no—
70C2×C4×C151—42no—
71C2×C4×C151—42no—
72C2×C4×C151—81no—
73C2×C4×C151—81no—
74C2×C4×C151—82no—
75C2×C4×C151—81no—
76C2×C4×C151#12111yescharacteristic
77C2×C4×C151#12311yescharacteristic
78C2×C4×C151#12411yescharacteristic
79C2×C4×C151C2×D811yescharacteristic
80C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
81C2×C4×C151#13711yescharacteristic
82C8×C151—22no—
83C8×C151—82no—
84C8×C151#12312yes—
85C8×C151#12612yes—
86C22×C151—22no—
87C22×C151#46111yescharacteristic
88C22×C151#48111yescharacteristic
89C22×C151#48611yescharacteristic
90C4×C151—42no—
91C4×C151—82no—
92C4×C151—161no—
93C4×C151#39711yescharacteristic
94C4×C151#45911yescharacteristic
95C4×C151#48011yescharacteristic
96C4×C151#48911yescharacteristic
97C2×C151—21no—
98C2×C151—21no—
99C2×C151#207111yescharacteristic
100C2×C151#223912yes—
101#13488C15111yesmaximal, characteristic, direct product factor, Sylow
102C151#1348811yescharacteristic, direct product factor, Sylow
103C2×#362C2×C15112yes—
104#1971C2×C15111yescharacteristic
105#1849C2×C15111yescharacteristic
106#1383C2×C15112yes—
107#1377C2×C15111yescharacteristic
108C22×Q16C22×C15111yescharacteristic
109C2×M32C22×C15112yes—
110C2×#108—21no—
111C2×#108C22×C15112yes—
112C2×#106C22×C15111yescharacteristic
113#423—21no—
114C2×#103—21no—
115C2×#97C22×C15111yescharacteristic
116#391—21no—
117#362—24no—
118C22×Q8—21no—
119C2×Q16—22no—
120C2×Q16—22no—
121C2×Q16—21no—
122C2×Q16D4×C15112yes—
123C2×M16—22no—
124C22×C8D4×C15111yescharacteristic
125C22×C8C23×C15111yescharacteristic
126C2×C4⋊C4—21no—
127C2×C42D4×C15111yescharacteristic
128M32—22no—
129M32—22no—
130C2×C16—22no—
131#108—22no—
132#108—22no—
133#108—42no—
134#106—22no—
135C4⋊C8—42no—
136#103—42no—
137#97—22no—
138#95—42no—
139C2×Q8—22no—
140C2×Q8—41no—
141C2×Q8—41no—
142C2×Q8—41no—
143C2×Q8—41no—
144C2×Q8—41no—
145C22×C4—41no—
146C22×C4—41no—
147C22×C4SD16×C15112yes—
148C22×C4C2×D4×C15111yescharacteristic
149Q16—24no—
150Q16—42no—
151M16—42no—
152M16—42no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—42no—
156C2×C8D8×C15112yes—
157C2×C8C2×D4×C15111yescharacteristic
158C2×C8#41×C15112yes—
159C2×C8#41×C15112yes—
160C2×C8#41×C15111yescharacteristic
161C4⋊C4—41no—
162C4⋊C4—41no—
163C42—21no—
164C42—21no—
165C16—42no—
166C23C2×SD16×C15111yescharacteristic
167Q8—42no—
168Q8—42no—
169Q8—81no—
170Q8—81no—
171C2×C4—22no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—81no—
175C2×C4—81no—
176C2×C4—82no—
177C2×C4—81no—
178C2×C4#121×C15111yescharacteristic
179C2×C4#123×C15111yescharacteristic
180C2×C4#124×C15111yescharacteristic
181C2×C4C2×D8×C15111yescharacteristic
182C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
183C2×C4#137×C15111yescharacteristic
184C8—22no—
185C8—82no—
186C8#123×C15112yes—
187C8#126×C15112yes—
188C22—22no—
189C22#461×C15111yescharacteristic
190C22#481×C15111yescharacteristic
191C22#486×C15111yescharacteristic
192C4—42no—
193C4—82no—
194C4—161no—
195C4#397×C15111yescharacteristic
196C4#459×C15111yescharacteristic
197C4#480×C15111yescharacteristic
198C4#489×C15111yescharacteristic
199C2—21no—
200C2—21no—
201C2#2071×C15111yescharacteristic
202C2#2239×C15112yes—
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
101. #13488C151direct (N × H)
102. C151#13488direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#362×C1512
#1971×C1512
#1849×C1512
#1383×C1512
#1377×C1512
#13488151