Finite Group Databasebeta

← C151×#13522 #50318447

Subgroups — C151×#13522 #50318447

Order 38656.

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

normal subgroups only

This group has 240 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
1C2×#365×C151C211yesmaximal, characteristic
2#2153×C151C211yesmaximal, characteristic
3#1953×C151C211yesmaximal, characteristic
4#1951×C151C211yesmaximal, characteristic
5#1388×C151C211yesmaximal, characteristic
6#1388×C151C211yesmaximal, characteristic
7#1383×C151C211yesmaximal, characteristic
8C2×M32×C151C2211yescharacteristic
9C2×M32×C151C2211yescharacteristic
10#430×C151—21no—
11C2×#108×C151C2211yescharacteristic
12C2×#108×C151C2211yescharacteristic
13C2×#108×C151C2211yescharacteristic
14#428×C151—21no—
15C2×#106×C151C2211yescharacteristic
16#405×C151C2211yescharacteristic
17#365×C151—22no—
18#364×C151—22no—
19#344×C151—21no—
20#343×C151—21no—
21C2×M16×C151—21no—
22C2×M16×C151—21no—
23C2×M16×C151—21no—
24C2×M16×C151D411yescharacteristic
25C22×C8×C151C2311yescharacteristic
26#117×C151D411yescharacteristic
27C2×C4⋊C4×C151—21no—
28M32×C151—21no—
29M32×C151—21no—
30M32×C151—21no—
31M32×C151D412yes—
32C2×C16×C151—21no—
33C2×C16×C151—21no—
34#108×C151—21no—
35#108×C151—21no—
36#108×C151—21no—
37#108×C151—21no—
38#108×C151—42no—
39#108×C151Q812yes—
40#108×C151Q812yes—
41#107×C151—41no—
42#106×C151—21no—
43#106×C151—21no—
44#106×C151—41no—
45#97×C151—21no—
46C4×C8×C151—21no—
47C22×C4×C151—41no—
48C22×C4×C151C2×D411yescharacteristic
49M16×C151—21no—
50M16×C151—22no—
51M16×C151—22no—
52M16×C151—41no—
53M16×C151—41no—
54M16×C151—41no—
55M16×C151—41no—
56M16×C151SD1612yes—
57C2×C8×C151—21no—
58C2×C8×C151—41no—
59C2×C8×C151—41no—
60C2×C8×C151—41no—
61C2×C8×C151C2×D411yescharacteristic
62C2×C8×C151C2×Q811yescharacteristic
63C2×C8×C151C2×Q811yescharacteristic
64C2×C8×C151#4111yescharacteristic
65C2×C8×C151#4111yescharacteristic
66C2×C8×C151#4111yescharacteristic
67C4⋊C4×C151—21no—
68C4⋊C4×C151—41no—
69C4⋊C4×C151—41no—
70C22⋊C4×C151—21no—
71C42×C151—21no—
72C16×C151—22no—
73C16×C151—41no—
74C23×C151#13711yescharacteristic
75C2×C4×C151—41no—
76C2×C4×C151—81no—
77C2×C4×C151—161no—
78C2×C4×C151#12111yescharacteristic
79C2×C4×C151C22⋊Q811yescharacteristic
80C2×C4×C151C22⋊Q811yescharacteristic
81C2×C4×C151C2×SD1611yescharacteristic
82C2×C4×C151#13511yescharacteristic
83C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
84C8×C151—22no—
85C8×C151—42no—
86C8×C151—42no—
87C8×C151—81no—
88C8×C151#12311yescharacteristic
89C8×C151#12511yescharacteristic
90C8×C151#12511yescharacteristic
91C8×C151C4⋊Q811yescharacteristic
92C22×C151—41no—
93C22×C151#46811yescharacteristic
94C22×C151#47511yescharacteristic
95C22×C151#47911yescharacteristic
96C4×C151—81no—
97C4×C151—161no—
98C4×C151#39811yescharacteristic
99C4×C151#46511yescharacteristic
100C4×C151#47611yescharacteristic
101C4×C151#47811yescharacteristic
102C2×C151—21no—
103C2×C151—21no—
104C2×C151—21no—
105C2×C151#208811yescharacteristic
106#13522C15111yesmaximal, characteristic, direct product factor, Sylow
107C151#1352211yescharacteristic, direct product factor, Sylow
108C2×#365C2×C15111yescharacteristic
109#2153C2×C15111yescharacteristic
110#1953C2×C15111yescharacteristic
111#1951C2×C15111yescharacteristic
112#1388C2×C15111yescharacteristic
113#1388C2×C15111yescharacteristic
114#1383C2×C15111yescharacteristic
115C2×M32C22×C15111yescharacteristic
116C2×M32C22×C15111yescharacteristic
117#430—21no—
118C2×#108C22×C15111yescharacteristic
119C2×#108C22×C15111yescharacteristic
120C2×#108C22×C15111yescharacteristic
121#428—21no—
122C2×#106C22×C15111yescharacteristic
123#405C22×C15111yescharacteristic
124#365—22no—
125#364—22no—
126#344—21no—
127#343—21no—
128C2×M16—21no—
129C2×M16—21no—
130C2×M16—21no—
131C2×M16D4×C15111yescharacteristic
132C22×C8C23×C15111yescharacteristic
133#117D4×C15111yescharacteristic
134C2×C4⋊C4—21no—
135M32—21no—
136M32—21no—
137M32—21no—
138M32D4×C15112yes—
139C2×C16—21no—
140C2×C16—21no—
141#108—21no—
142#108—21no—
143#108—21no—
144#108—21no—
145#108—42no—
146#108Q8×C15112yes—
147#108Q8×C15112yes—
148#107—41no—
149#106—21no—
150#106—21no—
151#106—41no—
152#97—21no—
153C4×C8—21no—
154C22×C4—41no—
155C22×C4C2×D4×C15111yescharacteristic
156M16—21no—
157M16—22no—
158M16—22no—
159M16—41no—
160M16—41no—
161M16—41no—
162M16—41no—
163M16SD16×C15112yes—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8—41no—
167C2×C8—41no—
168C2×C8C2×D4×C15111yescharacteristic
169C2×C8C2×Q8×C15111yescharacteristic
170C2×C8C2×Q8×C15111yescharacteristic
171C2×C8#41×C15111yescharacteristic
172C2×C8#41×C15111yescharacteristic
173C2×C8#41×C15111yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C22⋊C4—21no—
178C42—21no—
179C16—22no—
180C16—41no—
181C23#137×C15111yescharacteristic
182C2×C4—41no—
183C2×C4—81no—
184C2×C4—161no—
185C2×C4#121×C15111yescharacteristic
186C2×C4C22⋊Q8×C15111yescharacteristic
187C2×C4C22⋊Q8×C15111yescharacteristic
188C2×C4C2×SD16×C15111yescharacteristic
189C2×C4#135×C15111yescharacteristic
190C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
191C8—22no—
192C8—42no—
193C8—42no—
194C8—81no—
195C8#123×C15111yescharacteristic
196C8#125×C15111yescharacteristic
197C8#125×C15111yescharacteristic
198C8C4⋊Q8×C15111yescharacteristic
199C22—41no—
200C22#468×C15111yescharacteristic
201C22#475×C15111yescharacteristic
202C22#479×C15111yescharacteristic
203C4—81no—
204C4—161no—
205C4#398×C15111yescharacteristic
206C4#465×C15111yescharacteristic
207C4#476×C15111yescharacteristic
208C4#478×C15111yescharacteristic
209C2—21no—
210C2—21no—
211C2—21no—
212C2#2088×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2088
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC23×C151#137
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G

Complements

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

NH ≅ G/Ntype
106. #13522C151direct (N × H)
107. C151#13522direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#365×C1512
#2153×C1512
#1953×C1512
#1951×C1512
#1388×C1512
#1383×C1512
#13522151