Finite Group Databasebeta

← C151×#8620 #50313545

Subgroups — C151×#8620 #50313545

Order 38656.

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

normal subgroups only

This group has 450 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×D4×C151C211yesmaximal, characteristic
2#1568×C151C212yesmaximal, complemented
3#1466×C151C212yesmaximal
4#1290×C151C212yesmaximal, complemented
5C23×C8×C151C412yes—
6C2×C4×D4×C151C2211yescharacteristic
7C8×D4×C151—22no—
8C8×D4×C151—22no—
9#432×C151C2214yes—
10C2×C4⋊C8×C151C2211yescharacteristic
11C2×C22⋊C8×C151C412yes—
12C2×C4×C8×C151C2211yescharacteristic
13#335×C151—22no—
14#334×C151—22no—
15#323×C151—24no—
16C22×D4×C151Q811yescharacteristic
17C23×C4×C151C2×C412yes—
18C22×C8×C151—22no—
19C22×C8×C151—22no—
20C22×C8×C151—44no—
21C22×C8×C151C2×C411yescharacteristic
22C22×C8×C151C2×C412yes—
23C22×C8×C151C2×C411yescharacteristic
24C4×D4×C151—22no—
25C4×D4×C151—22no—
26C2×C4⋊C4×C151Q811yescharacteristic
27C2×C22⋊C4×C151D412yes—
28C2×C42×C151C2311yescharacteristic
29C4⋊C8×C151—22no—
30C4⋊C8×C151—24no—
31C22⋊C8×C151—24no—
32C22⋊C8×C151—24no—
33#97×C151—24no—
34C4×C8×C151D412yes—
35C4×C8×C151D412yes—
36C24×C151C4⋊C412yes—
37C2×D4×C151—24no—
38C2×D4×C151—22no—
39C22×C4×C151—22no—
40C22×C4×C151—22no—
41C22×C4×C151—42no—
42C22×C4×C151—42no—
43C22×C4×C151C4⋊C412yes—
44C22×C4×C151C22×C411yescharacteristic
45C22×C4×C151C2×D411yescharacteristic
46C22×C4×C151C2×Q811yescharacteristic
47C2×C8×C151—22no—
48C2×C8×C151—22no—
49C2×C8×C151—41no—
50C2×C8×C151—44no—
51C2×C8×C151—44no—
52C2×C8×C151—42no—
53C2×C8×C151—44no—
54C2×C8×C151C22⋊C412yes—
55C2×C8×C151C22⋊C411yescharacteristic
56C2×C8×C151C22⋊C411yescharacteristic
57C4⋊C4×C151—22no—
58C22⋊C4×C151—24no—
59C42×C151C2×D412yes—
60C42×C151#4112yes—
61C23×C151—22no—
62C23×C151—22no—
63C23×C151—42no—
64C23×C151—42no—
65C23×C151#10814yes—
66C23×C151C2×C4⋊C411yescharacteristic
67D4×C151—28no—
68C2×C4×C151—22no—
69C2×C4×C151—21no—
70C2×C4×C151—21no—
71C2×C4×C151—22no—
72C2×C4×C151—41no—
73C2×C4×C151—44no—
74C2×C4×C151—42no—
75C2×C4×C151—42no—
76C2×C4×C151—42no—
77C2×C4×C151C2×C22⋊C411yescharacteristic
78C2×C4×C151#11711yescharacteristic
79C2×C4×C151#12112yes—
80C2×C4×C151C22⋊Q812yes—
81C8×C151—21no—
82C8×C151—22no—
83C8×C151—42no—
84C8×C151—84no—
85C8×C151#10012yes—
86C22×C151—21no—
87C22×C151—21no—
88C22×C151—24no—
89C22×C151—44no—
90C22×C151—44no—
91C22×C151—42no—
92C22×C151—42no—
93C22×C151#38011yescharacteristic
94C22×C151C2×#10812yes—
95C4×C151—21no—
96C4×C151—22no—
97C4×C151—22no—
98C4×C151—42no—
99C4×C151C2×#10011yescharacteristic
100C4×C151#41311yescharacteristic
101C2×C151—22no—
102C2×C151—44no—
103C2×C151#180011yescharacteristic
104C2×C151#181011yescharacteristic
105C2×C151#181211yescharacteristic
106#8620C15111yesmaximal, characteristic, direct product factor, Sylow
107C151#862011yescharacteristic, direct product factor, Sylow
108C2×C8×D4C2×C15111yescharacteristic
109#1568C2×C15112yescomplemented
110#1466C2×C15112yes—
111#1290C2×C15112yescomplemented
112C23×C8C4×C15112yes—
113C2×C4×D4C22×C15111yescharacteristic
114C8×D4—22no—
115C8×D4—22no—
116#432C22×C15114yes—
117C2×C4⋊C8C22×C15111yescharacteristic
118C2×C22⋊C8C4×C15112yes—
119C2×C4×C8C22×C15111yescharacteristic
120#335—22no—
121#334—22no—
122#323—24no—
123C22×D4Q8×C15111yescharacteristic
124C23×C4C2×C4×C15112yes—
125C22×C8—22no—
126C22×C8—22no—
127C22×C8—44no—
128C22×C8C2×C4×C15111yescharacteristic
129C22×C8C2×C4×C15112yes—
130C22×C8C2×C4×C15111yescharacteristic
131C4×D4—22no—
132C4×D4—22no—
133C2×C4⋊C4Q8×C15111yescharacteristic
134C2×C22⋊C4D4×C15112yes—
135C2×C42C23×C15111yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—24no—
138C22⋊C8—24no—
139C22⋊C8—24no—
140#97—24no—
141C4×C8D4×C15112yes—
142C4×C8D4×C15112yes—
143C24C4⋊C4×C15112yes—
144C2×D4—24no—
145C2×D4—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—42no—
149C22×C4—42no—
150C22×C4C4⋊C4×C15112yes—
151C22×C4C22×C4×C15111yescharacteristic
152C22×C4C2×D4×C15111yescharacteristic
153C22×C4C2×Q8×C15111yescharacteristic
154C2×C8—22no—
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—44no—
158C2×C8—44no—
159C2×C8—42no—
160C2×C8—44no—
161C2×C8C22⋊C4×C15112yes—
162C2×C8C22⋊C4×C15111yescharacteristic
163C2×C8C22⋊C4×C15111yescharacteristic
164C4⋊C4—22no—
165C22⋊C4—24no—
166C42C2×D4×C15112yes—
167C42#41×C15112yes—
168C23—22no—
169C23—22no—
170C23—42no—
171C23—42no—
172C23#108×C15114yes—
173C23C2×C4⋊C4×C15111yescharacteristic
174D4—28no—
175C2×C4—22no—
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—41no—
180C2×C4—44no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4C2×C22⋊C4×C15111yescharacteristic
185C2×C4#117×C15111yescharacteristic
186C2×C4#121×C15112yes—
187C2×C4C22⋊Q8×C15112yes—
188C8—21no—
189C8—22no—
190C8—42no—
191C8—84no—
192C8#100×C15112yes—
193C22—21no—
194C22—21no—
195C22—24no—
196C22—44no—
197C22—44no—
198C22—42no—
199C22—42no—
200C22#380×C15111yescharacteristic
201C22C2×#108×C15112yes—
202C4—21no—
203C4—22no—
204C4—22no—
205C4—42no—
206C4C2×#100×C15111yescharacteristic
207C4#413×C15111yescharacteristic
208C2—22no—
209C2—44no—
210C2#1800×C15111yescharacteristic
211C2#1810×C15111yescharacteristic
212C2#1812×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#380
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151Q8
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
2. #1568×C151C2semidirect
4. #1290×C151C2semidirect
106. #8620C151direct (N × H)
107. C151#8620direct (N × H)
109. #1568C2×C151semidirect
111. #1290C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×C8×D4×C1512
#1568×C1512
#1466×C1512
#1290×C1512
#8620151