Finite Group Databasebeta

← C151×#10631 #50315556

Subgroups — C151×#10631 #50315556

Order 38656.

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

normal subgroups only

This group has 362 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#1961×C151C211yesmaximal, characteristic
2#1849×C151C211yesmaximal, characteristic, complemented
3#1545×C151C212yesmaximal
4#1286×C151C212yesmaximal, complemented
5#1281×C151C211yesmaximal, characteristic, complemented
6C2×#127×C151C2211yescharacteristic
7#431×C151C2212yes—
8C2×#108×C151—21no—
9C2×#108×C151—21no—
10#423×C151C2212yes—
11C2×#102×C151—21no—
12C2×#102×C151—21no—
13C2×#97×C151C2211yescharacteristic
14#382×C151C2211yescharacteristic
15#331×C151—24no—
16C22×D4×C151—21no—
17C22×D4×C151—22no—
18C2×M16×C151—22no—
19C22×C8×C151D411yescharacteristic
20C22×C8×C151D411yescharacteristic
21#127×C151—21no—
22#127×C151—22no—
23#127×C151D412yes—
24C2×C4⋊C4×C151—21no—
25C2×C42×C151C2311yescharacteristic
26#108×C151—42no—
27#108×C151—42no—
28C4⋊C8×C151—22no—
29C4⋊C8×C151—22no—
30C4⋊C8×C151—22no—
31#102×C151—42no—
32#102×C151—42no—
33C22⋊C8×C151—22no—
34#97×C151—22no—
35C4×C8×C151—22no—
36#95×C151—22no—
37C24×C151—41no—
38C2×D4×C151—22no—
39C2×D4×C151—24no—
40C2×D4×C151—41no—
41C2×D4×C151—42no—
42C2×D4×C151—41no—
43C2×D4×C151—41no—
44C2×D4×C151—41no—
45C2×D4×C151—41no—
46C2×D4×C151—84no—
47C22×C4×C151—41no—
48C22×C4×C151C2×D411yescharacteristic
49C22×C4×C151#4112yes—
50M16×C151—42no—
51M16×C151—42no—
52C2×C8×C151—21no—
53C2×C8×C151—21no—
54C2×C8×C151—21no—
55C2×C8×C151—21no—
56C2×C8×C151—42no—
57C2×C8×C151—42no—
58C2×C8×C151D812yes—
59C2×C8×C151SD1612yes—
60C4⋊C4×C151—41no—
61C4⋊C4×C151—41no—
62C42×C151C2×D411yescharacteristic
63C42×C151#4111yescharacteristic
64C42×C151#4112yes—
65C23×C151—42no—
66C23×C151—84no—
67C23×C151—81no—
68C23×C151—81no—
69C23×C151#12411yescharacteristic
70D4×C151—42no—
71D4×C151—42no—
72D4×C151—84no—
73D4×C151—84no—
74D4×C151—81no—
75D4×C151—81no—
76C2×C4×C151—42no—
77C2×C4×C151—82no—
78C2×C4×C151—81no—
79C2×C4×C151#12111yescharacteristic
80C2×C4×C151#12312yes—
81C2×C4×C151#12311yescharacteristic
82C2×C4×C151#12612yes—
83C2×C4×C151C2×D811yescharacteristic
84C2×C4×C151C2×SD1611yescharacteristic
85C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
86C2×C4×C151#13711yescharacteristic
87C8×C151—22no—
88C8×C151—22no—
89C8×C151—82no—
90C8×C151—82no—
91C22×C151—22no—
92C22×C151—82no—
93C22×C151—84no—
94C22×C151—162no—
95C22×C151—162no—
96C22×C151#39711yescharacteristic
97C22×C151#48611yescharacteristic
98C22×C151#48911yescharacteristic
99C4×C151—22no—
100C4×C151—22no—
101C4×C151—161no—
102C4×C151#45911yescharacteristic
103C4×C151#46111yescharacteristic
104C4×C151#48011yescharacteristic
105C4×C151#48111yescharacteristic
106C2×C151—21no—
107C2×C151—21no—
108C2×C151—162no—
109C2×C151#207111yescharacteristic
110C2×C151#208112yes—
111#10631C15111yesmaximal, characteristic, direct product factor, Sylow
112C151#1063111yescharacteristic, direct product factor, Sylow
113#1961C2×C15111yescharacteristic
114#1849C2×C15111yescharacteristic, complemented
115#1545C2×C15112yes—
116#1286C2×C15112yescomplemented
117#1281C2×C15111yescharacteristic, complemented
118C2×#127C22×C15111yescharacteristic
119#431C22×C15112yes—
120C2×#108—21no—
121C2×#108—21no—
122#423C22×C15112yes—
123C2×#102—21no—
124C2×#102—21no—
125C2×#97C22×C15111yescharacteristic
126#382C22×C15111yescharacteristic
127#331—24no—
128C22×D4—22no—
129C22×D4—21no—
130C2×M16—22no—
131C22×C8D4×C15111yescharacteristic
132C22×C8D4×C15111yescharacteristic
133#127—21no—
134#127—22no—
135#127D4×C15112yes—
136C2×C4⋊C4—21no—
137C2×C42C23×C15111yescharacteristic
138#108—42no—
139#108—42no—
140C4⋊C8—22no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143#102—42no—
144#102—42no—
145C22⋊C8—22no—
146#97—22no—
147C4×C8—22no—
148#95—22no—
149C24—41no—
150C2×D4—22no—
151C2×D4—24no—
152C2×D4—41no—
153C2×D4—42no—
154C2×D4—41no—
155C2×D4—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—84no—
159C22×C4—41no—
160C22×C4C2×D4×C15111yescharacteristic
161C22×C4#41×C15112yes—
162M16—42no—
163M16—42no—
164C2×C8—21no—
165C2×C8—21no—
166C2×C8—21no—
167C2×C8—21no—
168C2×C8—42no—
169C2×C8—42no—
170C2×C8D8×C15112yes—
171C2×C8SD16×C15112yes—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C42C2×D4×C15111yescharacteristic
175C42#41×C15111yescharacteristic
176C42#41×C15112yes—
177C23—42no—
178C23—84no—
179C23—81no—
180C23—81no—
181C23#124×C15111yescharacteristic
182D4—42no—
183D4—42no—
184D4—84no—
185D4—84no—
186D4—81no—
187D4—81no—
188C2×C4—42no—
189C2×C4—82no—
190C2×C4—81no—
191C2×C4#121×C15111yescharacteristic
192C2×C4#123×C15112yes—
193C2×C4#123×C15111yescharacteristic
194C2×C4#126×C15112yes—
195C2×C4C2×D8×C15111yescharacteristic
196C2×C4C2×SD16×C15111yescharacteristic
197C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
198C2×C4#137×C15111yescharacteristic
199C8—22no—
200C8—22no—
201C8—82no—
202C8—82no—
203C22—22no—
204C22—84no—
205C22—82no—
206C22—162no—
207C22—162no—
208C22#397×C15111yescharacteristic
209C22#486×C15111yescharacteristic
210C22#489×C15111yescharacteristic
211C4—22no—
212C4—22no—
213C4—161no—
214C4#459×C15111yescharacteristic
215C4#461×C15111yescharacteristic
216C4#480×C15111yescharacteristic
217C4#481×C15111yescharacteristic
218C2—21no—
219C2—21no—
220C2—162no—
221C2#2071×C15111yescharacteristic
222C2#2081×C15112yes—
subgroupG/H
center, socleC22×C151#397
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC2×#127×C151C22
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1849×C151C2semidirect
4. #1286×C151C2semidirect
5. #1281×C151C2semidirect
111. #10631C151direct (N × H)
112. C151#10631direct (N × H)
114. #1849C2×C151semidirect
116. #1286C2×C151semidirect
117. #1281C2×C151semidirect

Maximal subgroups

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

subgroupindex
#1961×C1512
#1849×C1512
#1545×C1512
#1286×C1512
#1281×C1512
#10631151