Finite Group Databasebeta

← C151×#12486 #50317411

Subgroups — C151×#12486 #50317411

Order 38656.

234 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 78 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#2227×C151C211yesmaximal, characteristic, complemented
2#2207×C151C211yesmaximal, characteristic
3#1706×C151C211yesmaximal, characteristic
4#1591×C151C211yesmaximal, characteristic, complemented
5#1370×C151C211yesmaximal, characteristic, complemented
6#1365×C151C211yesmaximal, characteristic, complemented
7#1361×C151C211yesmaximal, characteristic
8C2×SD32×C151—21no—
9#500×C151C2211yescharacteristic
10#493×C151C2211yescharacteristic
11#492×C151—21no—
12#486×C151—21no—
13#446×C151—21no—
14C4×Q16×C151C2211yescharacteristic
15#366×C151—21no—
16C4⋊C16×C151C2211yescharacteristic
17C4⋊C16×C151C2211yescharacteristic
18#358×C151—21no—
19#357×C151—21no—
20#335×C151C2211yescharacteristic
21Q8⋊C8×C151—21no—
22C82×C151C2211yescharacteristic
23C2×Q16×C151D411yescharacteristic
24C2×SD16×C151—42no—
25C2×D8×C151—21no—
26C2×D8×C151—21no—
27C4⋊Q8×C151—21no—
28#127×C151—21no—
29C4×Q8×C151—21no—
30SD32×C151—42no—
31C2×C16×C151—21no—
32C2×C16×C151—21no—
33#107×C151—21no—
34#107×C151—21no—
35#107×C151D411yescharacteristic
36C4⋊C8×C151—21no—
37C4⋊C8×C151—41no—
38#103×C151—21no—
39#102×C151—41no—
40#102×C151—41no—
41#97×C151—41no—
42C4×C8×C151D411yescharacteristic
43C4×C8×C151D411yescharacteristic
44C4×C8×C151C2311yescharacteristic
45C2×Q8×C151—21no—
46C2×Q8×C151—41no—
47C2×D4×C151—41no—
48C2×D4×C151—41no—
49C2×D4×C151—41no—
50Q16×C151—21no—
51Q16×C151—21no—
52SD16×C151—84no—
53D8×C151—41no—
54D8×C151—41no—
55D8×C151—81no—
56C2×C8×C151—21no—
57C2×C8×C151—41no—
58C2×C8×C151D811yescharacteristic
59C2×C8×C151D811yescharacteristic
60C2×C8×C151C2×D411yescharacteristic
61C2×C8×C151#4111yescharacteristic
62C4⋊C4×C151—21no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—41no—
65C4⋊C4×C151—41no—
66C42×C151—41no—
67C42×C151C2×D411yescharacteristic
68C16×C151—41no—
69C16×C151—41no—
70C23×C151—81no—
71Q8×C151—41no—
72Q8×C151—41no—
73Q8×C151—82no—
74D4×C151—82no—
75D4×C151—81no—
76D4×C151—81no—
77D4×C151—81no—
78D4×C151—81no—
79C2×C4×C151—41no—
80C2×C4×C151—41no—
81C2×C4×C151—81no—
82C2×C4×C151#12111yescharacteristic
83C2×C4×C151C2×D811yescharacteristic
84C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
85C8×C151—22no—
86C8×C151—21no—
87C8×C151—21no—
88C8×C151—21no—
89C8×C151—81no—
90C8×C151AGL(1,ℤ/8)11yescharacteristic
91C8×C151#13711yescharacteristic
92C22×C151—161no—
93C22×C151—161no—
94C22×C151—161no—
95C22×C151#45911yescharacteristic
96C4×C151—21no—
97C4×C151—81no—
98C4×C151—81no—
99C4×C151—161no—
100C4×C151#46811yescharacteristic
101C4×C151#47111yescharacteristic
102C4×C151#50811yescharacteristic
103C4×C151#51011yescharacteristic
104C2×C151—321no—
105C2×C151#168511yescharacteristic
106C2×C151#221111yescharacteristic
107C2×C151#221311yescharacteristic
108#12486C15111yesmaximal, characteristic, direct product factor, Sylow
109C151#1248611yescharacteristic, direct product factor, Sylow
110#2227C2×C15111yescharacteristic, complemented
111#2207C2×C15111yescharacteristic
112#1706C2×C15111yescharacteristic
113#1591C2×C15111yescharacteristic, complemented
114#1370C2×C15111yescharacteristic, complemented
115#1365C2×C15111yescharacteristic, complemented
116#1361C2×C15111yescharacteristic
117C2×SD32—21no—
118#500C22×C15111yescharacteristic
119#493C22×C15111yescharacteristic
120#492—21no—
121#486—21no—
122#446—21no—
123C4×Q16C22×C15111yescharacteristic
124#366—21no—
125C4⋊C16C22×C15111yescharacteristic
126C4⋊C16C22×C15111yescharacteristic
127#358—21no—
128#357—21no—
129#335C22×C15111yescharacteristic
130Q8⋊C8—21no—
131C82C22×C15111yescharacteristic
132C2×Q16D4×C15111yescharacteristic
133C2×SD16—42no—
134C2×D8—21no—
135C2×D8—21no—
136C4⋊Q8—21no—
137#127—21no—
138C4×Q8—21no—
139SD32—42no—
140C2×C16—21no—
141C2×C16—21no—
142#107—21no—
143#107—21no—
144#107D4×C15111yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—41no—
147#103—21no—
148#102—41no—
149#102—41no—
150#97—41no—
151C4×C8D4×C15111yescharacteristic
152C4×C8D4×C15111yescharacteristic
153C4×C8C23×C15111yescharacteristic
154C2×Q8—21no—
155C2×Q8—41no—
156C2×D4—41no—
157C2×D4—41no—
158C2×D4—41no—
159Q16—21no—
160Q16—21no—
161SD16—84no—
162D8—41no—
163D8—41no—
164D8—81no—
165C2×C8—21no—
166C2×C8—41no—
167C2×C8D8×C15111yescharacteristic
168C2×C8D8×C15111yescharacteristic
169C2×C8C2×D4×C15111yescharacteristic
170C2×C8#41×C15111yescharacteristic
171C4⋊C4—21no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C42—41no—
176C42C2×D4×C15111yescharacteristic
177C16—41no—
178C16—41no—
179C23—81no—
180Q8—41no—
181Q8—41no—
182Q8—82no—
183D4—82no—
184D4—81no—
185D4—81no—
186D4—81no—
187D4—81no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—81no—
191C2×C4#121×C15111yescharacteristic
192C2×C4C2×D8×C15111yescharacteristic
193C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
194C8—22no—
195C8—21no—
196C8—21no—
197C8—21no—
198C8—81no—
199C8AGL(1,ℤ/8)×C15111yescharacteristic
200C8#137×C15111yescharacteristic
201C22—161no—
202C22—161no—
203C22—161no—
204C22#459×C15111yescharacteristic
205C4—21no—
206C4—81no—
207C4—81no—
208C4—161no—
209C4#468×C15111yescharacteristic
210C4#471×C15111yescharacteristic
211C4#508×C15111yescharacteristic
212C4#510×C15111yescharacteristic
213C2—321no—
214C2#1685×C15111yescharacteristic
215C2#2211×C15111yescharacteristic
216C2#2213×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#459
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#493×C151C22
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C82×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2227×C151C2semidirect
4. #1591×C151C2semidirect
5. #1370×C151C2semidirect
6. #1365×C151C2semidirect
108. #12486C151direct (N × H)
109. C151#12486direct (N × H)
110. #2227C2×C151semidirect
113. #1591C2×C151semidirect
114. #1370C2×C151semidirect
115. #1365C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2227×C1512
#2207×C1512
#1706×C1512
#1591×C1512
#1370×C1512
#1365×C1512
#1361×C1512
#12486151