Finite Group Databasebeta

← C151×#8621 #50313546

Subgroups — C151×#8621 #50313546

Order 38656.

362 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 142 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×C8×Q8×C151C211yesmaximal, characteristic
2#1568×C151C212yesmaximal
3#1467×C151C212yesmaximal
4#1290×C151C212yesmaximal
5C2×C4×Q8×C151C2211yescharacteristic
6C8×Q8×C151—22no—
7C8×Q8×C151—22no—
8#432×C151C2214yes—
9C2×C4⋊C8×C151C412yes—
10C2×C4⋊C8×C151C2211yescharacteristic
11C2×C4×C8×C151C412yes—
12C2×C4×C8×C151C2211yescharacteristic
13#335×C151—22no—
14#334×C151—22no—
15#324×C151—24no—
16C22×Q8×C151Q811yescharacteristic
17C22×C8×C151C2×C411yescharacteristic
18C22×C8×C151C2×C412yes—
19C22×C8×C151C2×C411yescharacteristic
20C4×Q8×C151—22no—
21C4×Q8×C151—22no—
22C2×C4⋊C4×C151D412yes—
23C2×C4⋊C4×C151Q811yescharacteristic
24C2×C42×C151C2×C412yes—
25C2×C42×C151C2311yescharacteristic
26C4⋊C8×C151—24no—
27C4⋊C8×C151—22no—
28C4⋊C8×C151—24no—
29C22⋊C8×C151—24no—
30#97×C151—24no—
31C4×C8×C151—22no—
32C4×C8×C151—22no—
33C4×C8×C151D412yes—
34C4×C8×C151D412yes—
35C2×Q8×C151—24no—
36C2×Q8×C151—22no—
37C22×C4×C151C4⋊C412yes—
38C22×C4×C151C4⋊C412yes—
39C22×C4×C151C22×C411yescharacteristic
40C22×C4×C151C2×D411yescharacteristic
41C22×C4×C151C2×Q811yescharacteristic
42C2×C8×C151—22no—
43C2×C8×C151—22no—
44C2×C8×C151—41no—
45C2×C8×C151—42no—
46C2×C8×C151—44no—
47C2×C8×C151C22⋊C411yescharacteristic
48C2×C8×C151C22⋊C412yes—
49C2×C8×C151C22⋊C411yescharacteristic
50C4⋊C4×C151—24no—
51C4⋊C4×C151—22no—
52C42×C151—22no—
53C42×C151—22no—
54C42×C151C2×D412yes—
55C42×C151#4112yes—
56C23×C151C2×C4⋊C411yescharacteristic
57Q8×C151—28no—
58C2×C4×C151—22no—
59C2×C4×C151—22no—
60C2×C4×C151—22no—
61C2×C4×C151—21no—
62C2×C4×C151—21no—
63C2×C4×C151—22no—
64C2×C4×C151—41no—
65C2×C4×C151—42no—
66C2×C4×C151#10814yes—
67C2×C4×C151C2×C22⋊C411yescharacteristic
68C2×C4×C151#11711yescharacteristic
69C2×C4×C151#12112yes—
70C2×C4×C151C22⋊Q812yes—
71C8×C151—21no—
72C8×C151—22no—
73C8×C151—42no—
74C8×C151—84no—
75C8×C151#10112yes—
76C22×C151—21no—
77C22×C151—21no—
78C22×C151#38011yescharacteristic
79C22×C151C2×#10812yes—
80C4×C151—21no—
81C4×C151—24no—
82C4×C151—22no—
83C4×C151—22no—
84C4×C151—42no—
85C4×C151C2×#10111yescharacteristic
86C4×C151#41311yescharacteristic
87C2×C151—22no—
88C2×C151#180111yescharacteristic
89C2×C151#181011yescharacteristic
90C2×C151#181211yescharacteristic
91#8621C15111yesmaximal, characteristic, direct product factor, Sylow
92C151#862111yescharacteristic, direct product factor, Sylow
93C2×C8×Q8C2×C15111yescharacteristic
94#1568C2×C15112yes—
95#1467C2×C15112yes—
96#1290C2×C15112yes—
97C2×C4×Q8C22×C15111yescharacteristic
98C8×Q8—22no—
99C8×Q8—22no—
100#432C22×C15114yes—
101C2×C4⋊C8C4×C15112yes—
102C2×C4⋊C8C22×C15111yescharacteristic
103C2×C4×C8C4×C15112yes—
104C2×C4×C8C22×C15111yescharacteristic
105#335—22no—
106#334—22no—
107#324—24no—
108C22×Q8Q8×C15111yescharacteristic
109C22×C8C2×C4×C15111yescharacteristic
110C22×C8C2×C4×C15112yes—
111C22×C8C2×C4×C15111yescharacteristic
112C4×Q8—22no—
113C4×Q8—22no—
114C2×C4⋊C4D4×C15112yes—
115C2×C4⋊C4Q8×C15111yescharacteristic
116C2×C42C2×C4×C15112yes—
117C2×C42C23×C15111yescharacteristic
118C4⋊C8—24no—
119C4⋊C8—22no—
120C4⋊C8—24no—
121C22⋊C8—24no—
122#97—24no—
123C4×C8—22no—
124C4×C8—22no—
125C4×C8D4×C15112yes—
126C4×C8D4×C15112yes—
127C2×Q8—24no—
128C2×Q8—22no—
129C22×C4C4⋊C4×C15112yes—
130C22×C4C4⋊C4×C15112yes—
131C22×C4C22×C4×C15111yescharacteristic
132C22×C4C2×D4×C15111yescharacteristic
133C22×C4C2×Q8×C15111yescharacteristic
134C2×C8—22no—
135C2×C8—22no—
136C2×C8—41no—
137C2×C8—42no—
138C2×C8—44no—
139C2×C8C22⋊C4×C15111yescharacteristic
140C2×C8C22⋊C4×C15112yes—
141C2×C8C22⋊C4×C15111yescharacteristic
142C4⋊C4—24no—
143C4⋊C4—22no—
144C42—22no—
145C42—22no—
146C42C2×D4×C15112yes—
147C42#41×C15112yes—
148C23C2×C4⋊C4×C15111yescharacteristic
149Q8—28no—
150C2×C4—22no—
151C2×C4—22no—
152C2×C4—22no—
153C2×C4—21no—
154C2×C4—21no—
155C2×C4—22no—
156C2×C4—41no—
157C2×C4—42no—
158C2×C4#108×C15114yes—
159C2×C4C2×C22⋊C4×C15111yescharacteristic
160C2×C4#117×C15111yescharacteristic
161C2×C4#121×C15112yes—
162C2×C4C22⋊Q8×C15112yes—
163C8—21no—
164C8—22no—
165C8—42no—
166C8—84no—
167C8#101×C15112yes—
168C22—21no—
169C22—21no—
170C22#380×C15111yescharacteristic
171C22C2×#108×C15112yes—
172C4—21no—
173C4—24no—
174C4—22no—
175C4—22no—
176C4—42no—
177C4C2×#101×C15111yescharacteristic
178C4#413×C15111yescharacteristic
179C2—22no—
180C2#1801×C15111yescharacteristic
181C2#1810×C15111yescharacteristic
182C2#1812×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#380
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151C2×C4⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
91. #8621C151direct (N × H)
92. C151#8621direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C8×Q8×C1512
#1568×C1512
#1467×C1512
#1290×C1512
#8621151