Finite Group Databasebeta

← C151×#12080 #50317005

Subgroups — C151×#12080 #50317005

Order 38656.

218 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 90 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#2175×C151C211yesmaximal, characteristic
2#1594×C151C211yesmaximal, characteristic
3#1579×C151C211yesmaximal, characteristic, complemented
4#1368×C151C211yesmaximal, characteristic, complemented
5#1334×C151C211yesmaximal, characteristic, complemented
6#1333×C151C211yesmaximal, characteristic
7#1313×C151C211yesmaximal, characteristic, complemented
8C2×SD32×C151C411yescharacteristic
9C8×Q8×C151—21no—
10C4×Q16×C151C2211yescharacteristic
11C4×D8×C151C2211yescharacteristic
12#436×C151—21no—
13#366×C151C411yescharacteristic
14#358×C151C411yescharacteristic
15#357×C151C411yescharacteristic
16#346×C151C2211yescharacteristic
17#346×C151C2211yescharacteristic
18#334×C151C2211yescharacteristic
19#334×C151C2211yescharacteristic
20Q8⋊C8×C151—21no—
21D4⋊C8×C151—21no—
22#322×C151C2211yescharacteristic
23C2×Q16×C151C2×C411yescharacteristic
24C2×D8×C151C2×C411yescharacteristic
25C2×M16×C151—41no—
26C4×Q8×C151—21no—
27C4×D4×C151—21no—
28SD32×C151—22no—
29C2×C16×C151—21no—
30C2×C16×C151C2×C411yescharacteristic
31C2×C16×C151C2×C411yescharacteristic
32#107×C151C2×C411yescharacteristic
33#107×C151C2×C411yescharacteristic
34C4⋊C8×C151—21no—
35C4⋊C8×C151—21no—
36C4⋊C8×C151—41no—
37#103×C151—21no—
38#102×C151—21no—
39C22⋊C8×C151—41no—
40C4×C8×C151—41no—
41C4×C8×C151D411yescharacteristic
42C4×C8×C151D411yescharacteristic
43C4×C8×C151C2311yescharacteristic
44C2×Q8×C151—21no—
45C2×D4×C151—21no—
46C22×C4×C151—41no—
47Q16×C151—21no—
48Q16×C151M1612yescomplemented
49D8×C151—21no—
50D8×C151—21no—
51M16×C151—82no—
52C2×C8×C151—21no—
53C2×C8×C151—21no—
54C2×C8×C151—41no—
55C2×C8×C151—41no—
56C2×C8×C151C22×C411yescharacteristic
57C2×C8×C151#4111yescharacteristic
58C4⋊C4×C151—21no—
59C4⋊C4×C151—21no—
60C4⋊C4×C151—41no—
61C22⋊C4×C151—41no—
62C42×C151—41no—
63C42×C151C2×D411yescharacteristic
64C16×C151—22no—
65C16×C151—21no—
66C16×C151—21no—
67C23×C151—41no—
68Q8×C151—22no—
69Q8×C151—41no—
70D4×C151—41no—
71D4×C151—41no—
72C2×C4×C151—41no—
73C2×C4×C151—41no—
74C2×C4×C151—41no—
75C2×C4×C151—81no—
76C2×C4×C151—81no—
77C2×C4×C151C4×D411yescharacteristic
78C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
79C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
80C8×C151—21no—
81C8×C151—41no—
82C8×C151—41no—
83C8×C151—81no—
84C8×C151—81no—
85C8×C151C2×M1611yescharacteristic
86C8×C151#13111yescharacteristic
87C22×C151—81no—
88C22×C151—81no—
89C22×C151—81no—
90C22×C151#44211yescharacteristic
91C4×C151—21no—
92C4×C151—21no—
93C4×C151—42no—
94C4×C151—81no—
95C4×C151—81no—
96C4×C151#43511yescharacteristic
97C4×C151#44311yescharacteristic
98C2×C151—161no—
99C2×C151#158611yescharacteristic
100C2×C151#218011yescharacteristic
101C2×C151AGL(1,ℤ/16)11yescharacteristic
102#12080C15111yesmaximal, characteristic, direct product factor, Sylow
103C151#1208011yescharacteristic, direct product factor, Sylow
104#2175C2×C15111yescharacteristic
105#1594C2×C15111yescharacteristic
106#1579C2×C15111yescharacteristic, complemented
107#1368C2×C15111yescharacteristic, complemented
108#1334C2×C15111yescharacteristic, complemented
109#1333C2×C15111yescharacteristic
110#1313C2×C15111yescharacteristic, complemented
111C2×SD32C4×C15111yescharacteristic
112C8×Q8—21no—
113C4×Q16C22×C15111yescharacteristic
114C4×D8C22×C15111yescharacteristic
115#436—21no—
116#366C4×C15111yescharacteristic
117#358C4×C15111yescharacteristic
118#357C4×C15111yescharacteristic
119#346C22×C15111yescharacteristic
120#346C22×C15111yescharacteristic
121#334C22×C15111yescharacteristic
122#334C22×C15111yescharacteristic
123Q8⋊C8—21no—
124D4⋊C8—21no—
125#322C22×C15111yescharacteristic
126C2×Q16C2×C4×C15111yescharacteristic
127C2×D8C2×C4×C15111yescharacteristic
128C2×M16—41no—
129C4×Q8—21no—
130C4×D4—21no—
131SD32—22no—
132C2×C16—21no—
133C2×C16C2×C4×C15111yescharacteristic
134C2×C16C2×C4×C15111yescharacteristic
135#107C2×C4×C15111yescharacteristic
136#107C2×C4×C15111yescharacteristic
137C4⋊C8—21no—
138C4⋊C8—21no—
139C4⋊C8—41no—
140#103—21no—
141#102—21no—
142C22⋊C8—41no—
143C4×C8—41no—
144C4×C8D4×C15111yescharacteristic
145C4×C8D4×C15111yescharacteristic
146C4×C8C23×C15111yescharacteristic
147C2×Q8—21no—
148C2×D4—21no—
149C22×C4—41no—
150Q16—21no—
151Q16M16×C15112yescomplemented
152D8—21no—
153D8—21no—
154M16—82no—
155C2×C8—21no—
156C2×C8—21no—
157C2×C8—41no—
158C2×C8—41no—
159C2×C8C22×C4×C15111yescharacteristic
160C2×C8#41×C15111yescharacteristic
161C4⋊C4—21no—
162C4⋊C4—21no—
163C4⋊C4—41no—
164C22⋊C4—41no—
165C42—41no—
166C42C2×D4×C15111yescharacteristic
167C16—22no—
168C16—21no—
169C16—21no—
170C23—41no—
171Q8—22no—
172Q8—41no—
173D4—41no—
174D4—41no—
175C2×C4—41no—
176C2×C4—41no—
177C2×C4—41no—
178C2×C4—81no—
179C2×C4—81no—
180C2×C4C4×D4×C15111yescharacteristic
181C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
182C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
183C8—21no—
184C8—41no—
185C8—41no—
186C8—81no—
187C8—81no—
188C8C2×M16×C15111yescharacteristic
189C8#131×C15111yescharacteristic
190C22—81no—
191C22—81no—
192C22—81no—
193C22#442×C15111yescharacteristic
194C4—21no—
195C4—21no—
196C4—42no—
197C4—81no—
198C4—81no—
199C4#435×C15111yescharacteristic
200C4#443×C15111yescharacteristic
201C2—161no—
202C2#1586×C15111yescharacteristic
203C2#2180×C15111yescharacteristic
204C2AGL(1,ℤ/16)×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#442
commutatorC2×C8C22×C4×C151
Frattini, cosocleC4×C8C23×C151
prime radicalC2×D8×C151C2×C4
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ #322×C151 ◁ G

Complements

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

NH ≅ G/Ntype
3. #1579×C151C2semidirect
4. #1368×C151C2semidirect
5. #1334×C151C2semidirect
7. #1313×C151C2semidirect
48. Q16×C151M16semidirect
102. #12080C151direct (N × H)
103. C151#12080direct (N × H)
106. #1579C2×C151semidirect
107. #1368C2×C151semidirect
108. #1334C2×C151semidirect
110. #1313C2×C151semidirect
151. Q16M16×C151semidirect

Maximal subgroups

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

subgroupindex
#2175×C1512
#1594×C1512
#1579×C1512
#1368×C1512
#1334×C1512
#1333×C1512
#1313×C1512
#12080151