Finite Group Databasebeta

← C151×#13691 #50318616

Subgroups — C151×#13691 #50318616

Order 38656.

200 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 70 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#2264×C151C211yesmaximal, characteristic, complemented
2#2263×C151C211yesmaximal, characteristic
3#2249×C151C211yesmaximal, characteristic, complemented
4#2178×C151C211yesmaximal, characteristic, complemented
5#1422×C151C211yesmaximal, characteristic, complemented
6#1420×C151C211yesmaximal, characteristic, complemented
7#1419×C151C211yesmaximal, characteristic, complemented
8#508×C151C2211yescharacteristic
9C2×Q32×C151C2211yescharacteristic
10C2×SD32×C151—21no—
11C2×D16×C151C2211yescharacteristic
12#495×C151—21no—
13#443×C151—21no—
14Q64×C151—21no—
15SD64×C151—21no—
16SD64×C151—21no—
17D32×C151—21no—
18M64×C151C2211yescharacteristic
19M64×C151C2211yescharacteristic
20#368×C151C2211yescharacteristic
21#359×C151—21no—
22C4×C16×C151C2211yescharacteristic
23#135×C151—21no—
24C2×Q16×C151—21no—
25C2×SD16×C151—41no—
26C2×D8×C151—21no—
27#131×C151—41no—
28#124×C151—41no—
29Q32×C151—21no—
30Q32×C151—21no—
31Q32×C151D411yescharacteristic
32SD32×C151—21no—
33SD32×C151—42no—
34D16×C151—21no—
35D16×C151—21no—
36D16×C151D411yescharacteristic
37C2×C16×C151D411yescharacteristic
38C2×C16×C151C2311yescharacteristic
39#108×C151—21no—
40#104×C151—41no—
41C4×C8×C151D411yescharacteristic
42C32×C151—21no—
43C32×C151—21no—
44#41×C151—41no—
45C2×Q8×C151—41no—
46C2×D4×C151—41no—
47Q16×C151—21no—
48Q16×C151—41no—
49Q16×C151—41no—
50SD16×C151—41no—
51SD16×C151—81no—
52SD16×C151—81no—
53D8×C151—21no—
54D8×C151—41no—
55D8×C151—41no—
56M16×C151—41no—
57M16×C151—81no—
58C2×C8×C151—81no—
59C2×C8×C151D811yescharacteristic
60C2×C8×C151C2×D411yescharacteristic
61C22⋊C4×C151—82no—
62C42×C151D811yescharacteristic
63C16×C151—21no—
64C16×C151C2×D411yescharacteristic
65C16×C151#4111yescharacteristic
66C23×C151—81no—
67Q8×C151—41no—
68Q8×C151—81no—
69Q8×C151—81no—
70D4×C151—41no—
71D4×C151—81no—
72D4×C151—81no—
73D4×C151—81no—
74C2×C4×C151—21no—
75C2×C4×C151—81no—
76C2×C4×C151—81no—
77C2×C4×C151C2×D811yescharacteristic
78C8×C151—81no—
79C8×C151D1611yescharacteristic
80C8×C151D1611yescharacteristic
81C8×C151#12111yescharacteristic
82C8×C151AGL(1,ℤ/8)11yescharacteristic
83C22×C151—81no—
84C22×C151—162no—
85C22×C151—161no—
86C22×C151#50911yescharacteristic
87C4×C151—41no—
88C4×C151—81no—
89C4×C151—161no—
90C4×C151#45911yescharacteristic
91C4×C151C2×D1611yescharacteristic
92C2×C151—21no—
93C2×C151—161no—
94C2×C151—321no—
95C2×C151#220611yescharacteristic
96#13691C15111yesmaximal, characteristic, direct product factor, Sylow
97C151#1369111yescharacteristic, direct product factor, Sylow
98#2264C2×C15111yescharacteristic, complemented
99#2263C2×C15111yescharacteristic
100#2249C2×C15111yescharacteristic, complemented
101#2178C2×C15111yescharacteristic, complemented
102#1422C2×C15111yescharacteristic, complemented
103#1420C2×C15111yescharacteristic, complemented
104#1419C2×C15111yescharacteristic, complemented
105#508C22×C15111yescharacteristic
106C2×Q32C22×C15111yescharacteristic
107C2×SD32—21no—
108C2×D16C22×C15111yescharacteristic
109#495—21no—
110#443—21no—
111Q64—21no—
112SD64—21no—
113SD64—21no—
114D32—21no—
115M64C22×C15111yescharacteristic
116M64C22×C15111yescharacteristic
117#368C22×C15111yescharacteristic
118#359—21no—
119C4×C16C22×C15111yescharacteristic
120#135—21no—
121C2×Q16—21no—
122C2×SD16—41no—
123C2×D8—21no—
124#131—41no—
125#124—41no—
126Q32—21no—
127Q32—21no—
128Q32D4×C15111yescharacteristic
129SD32—21no—
130SD32—42no—
131D16—21no—
132D16—21no—
133D16D4×C15111yescharacteristic
134C2×C16D4×C15111yescharacteristic
135C2×C16C23×C15111yescharacteristic
136#108—21no—
137#104—41no—
138C4×C8D4×C15111yescharacteristic
139C32—21no—
140C32—21no—
141#41—41no—
142C2×Q8—41no—
143C2×D4—41no—
144Q16—21no—
145Q16—41no—
146Q16—41no—
147SD16—41no—
148SD16—81no—
149SD16—81no—
150D8—21no—
151D8—41no—
152D8—41no—
153M16—41no—
154M16—81no—
155C2×C8—81no—
156C2×C8D8×C15111yescharacteristic
157C2×C8C2×D4×C15111yescharacteristic
158C22⋊C4—82no—
159C42D8×C15111yescharacteristic
160C16—21no—
161C16C2×D4×C15111yescharacteristic
162C16#41×C15111yescharacteristic
163C23—81no—
164Q8—41no—
165Q8—81no—
166Q8—81no—
167D4—41no—
168D4—81no—
169D4—81no—
170D4—81no—
171C2×C4—21no—
172C2×C4—81no—
173C2×C4—81no—
174C2×C4C2×D8×C15111yescharacteristic
175C8—81no—
176C8D16×C15111yescharacteristic
177C8D16×C15111yescharacteristic
178C8#121×C15111yescharacteristic
179C8AGL(1,ℤ/8)×C15111yescharacteristic
180C22—81no—
181C22—162no—
182C22—161no—
183C22#509×C15111yescharacteristic
184C4—41no—
185C4—81no—
186C4—161no—
187C4#459×C15111yescharacteristic
188C4C2×D16×C15111yescharacteristic
189C2—21no—
190C2—161no—
191C2—321no—
192C2#2206×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2206
commutator, Frattini, cosocleC2×C16C23×C151
prime radical#2263×C151C2
LCSG ▷ C2×C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C4×C8×C151 ◁ C4×C16×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2264×C151C2semidirect
3. #2249×C151C2semidirect
4. #2178×C151C2semidirect
5. #1422×C151C2semidirect
6. #1420×C151C2semidirect
7. #1419×C151C2semidirect
96. #13691C151direct (N × H)
97. C151#13691direct (N × H)
98. #2264C2×C151semidirect
100. #2249C2×C151semidirect
101. #2178C2×C151semidirect
102. #1422C2×C151semidirect
103. #1420C2×C151semidirect
104. #1419C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2264×C1512
#2263×C1512
#2249×C1512
#2178×C1512
#1422×C1512
#1420×C1512
#1419×C1512
#13691151