Finite Group Databasebeta

← C151×#12489 #50317414

Subgroups — C151×#12489 #50317414

Order 38656.

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

normal subgroups only

This group has 226 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#2224×C151C211yesmaximal, characteristic
2#2208×C151C211yesmaximal, characteristic
3#1707×C151C211yesmaximal, characteristic, complemented
4#1589×C151C211yesmaximal, characteristic
5#1370×C151C211yesmaximal, characteristic, complemented
6#1364×C151C211yesmaximal, characteristic, complemented
7#1362×C151C211yesmaximal, characteristic, complemented
8C2×SD32×C151—21no—
9#500×C151C2211yescharacteristic
10#498×C151—21no—
11#494×C151C2211yescharacteristic
12#487×C151—21no—
13C4×D8×C151C2211yescharacteristic
14#436×C151—21no—
15#366×C151—21no—
16C4⋊C16×C151C2211yescharacteristic
17C4⋊C16×C151C2211yescharacteristic
18#358×C151—21no—
19#357×C151—21no—
20#335×C151C2211yescharacteristic
21D4⋊C8×C151—21no—
22C82×C151C2211yescharacteristic
23C2×Q16×C151—21no—
24C2×Q16×C151—21no—
25C2×D8×C151D411yescharacteristic
26C2×M16×C151—41no—
27C4⋊Q8×C151—21no—
28C4⋊Q8×C151—21no—
29C4×D4×C151—21no—
30SD32×C151—42no—
31C2×C16×C151—21no—
32C2×C16×C151—21no—
33#107×C151—21no—
34#107×C151—21no—
35#107×C151D411yescharacteristic
36#106×C151—42no—
37C4⋊C8×C151—21no—
38#103×C151—41no—
39#103×C151—41no—
40#102×C151—21no—
41C22⋊C8×C151—41no—
42C4×C8×C151D411yescharacteristic
43C4×C8×C151D411yescharacteristic
44C4×C8×C151C2311yescharacteristic
45C2×Q8×C151—41no—
46C2×Q8×C151—41no—
47C2×D4×C151—21no—
48C22×C4×C151—41no—
49Q16×C151—41no—
50Q16×C151—41no—
51Q16×C151—81no—
52D8×C151—21no—
53D8×C151—21no—
54M16×C151—82no—
55C2×C8×C151—21no—
56C2×C8×C151—41no—
57C2×C8×C151D811yescharacteristic
58C2×C8×C151D811yescharacteristic
59C2×C8×C151C2×D411yescharacteristic
60C2×C8×C151#4111yescharacteristic
61C4⋊C4×C151—21no—
62C4⋊C4×C151—41no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—41no—
65C4⋊C4×C151—41no—
66C22⋊C4×C151—41no—
67C42×C151C2×D411yescharacteristic
68C16×C151—41no—
69C16×C151—41no—
70C23×C151—41no—
71Q8×C151—81no—
72Q8×C151—81no—
73Q8×C151—81no—
74Q8×C151—81no—
75D4×C151—41no—
76D4×C151—41no—
77C2×C4×C151—41no—
78C2×C4×C151—81no—
79C2×C4×C151—81no—
80C2×C4×C151—81no—
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—81no—
93C22×C151—81no—
94C22×C151—81no—
95C22×C151#45911yescharacteristic
96C4×C151—21no—
97C4×C151—81no—
98C4×C151—161no—
99C4×C151—161no—
100C4×C151#46811yescharacteristic
101C4×C151#47111yescharacteristic
102C4×C151#50811yescharacteristic
103C4×C151#50911yescharacteristic
104C2×C151—161no—
105C2×C151#168511yescharacteristic
106C2×C151#221011yescharacteristic
107C2×C151#221411yescharacteristic
108#12489C15111yesmaximal, characteristic, direct product factor, Sylow
109C151#1248911yescharacteristic, direct product factor, Sylow
110#2224C2×C15111yescharacteristic
111#2208C2×C15111yescharacteristic
112#1707C2×C15111yescharacteristic, complemented
113#1589C2×C15111yescharacteristic
114#1370C2×C15111yescharacteristic, complemented
115#1364C2×C15111yescharacteristic, complemented
116#1362C2×C15111yescharacteristic, complemented
117C2×SD32—21no—
118#500C22×C15111yescharacteristic
119#498—21no—
120#494C22×C15111yescharacteristic
121#487—21no—
122C4×D8C22×C15111yescharacteristic
123#436—21no—
124#366—21no—
125C4⋊C16C22×C15111yescharacteristic
126C4⋊C16C22×C15111yescharacteristic
127#358—21no—
128#357—21no—
129#335C22×C15111yescharacteristic
130D4⋊C8—21no—
131C82C22×C15111yescharacteristic
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8D4×C15111yescharacteristic
135C2×M16—41no—
136C4⋊Q8—21no—
137C4⋊Q8—21no—
138C4×D4—21no—
139SD32—42no—
140C2×C16—21no—
141C2×C16—21no—
142#107—21no—
143#107—21no—
144#107D4×C15111yescharacteristic
145#106—42no—
146C4⋊C8—21no—
147#103—41no—
148#103—41no—
149#102—21no—
150C22⋊C8—41no—
151C4×C8D4×C15111yescharacteristic
152C4×C8D4×C15111yescharacteristic
153C4×C8C23×C15111yescharacteristic
154C2×Q8—41no—
155C2×Q8—41no—
156C2×D4—21no—
157C22×C4—41no—
158Q16—41no—
159Q16—41no—
160Q16—81no—
161D8—21no—
162D8—21no—
163M16—82no—
164C2×C8—21no—
165C2×C8—41no—
166C2×C8D8×C15111yescharacteristic
167C2×C8D8×C15111yescharacteristic
168C2×C8C2×D4×C15111yescharacteristic
169C2×C8#41×C15111yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—41no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C22⋊C4—41no—
176C42C2×D4×C15111yescharacteristic
177C16—41no—
178C16—41no—
179C23—41no—
180Q8—81no—
181Q8—81no—
182Q8—81no—
183Q8—81no—
184D4—41no—
185D4—41no—
186C2×C4—41no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—81no—
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—81no—
202C22—81no—
203C22—81no—
204C22#459×C15111yescharacteristic
205C4—21no—
206C4—81no—
207C4—161no—
208C4—161no—
209C4#468×C15111yescharacteristic
210C4#471×C15111yescharacteristic
211C4#508×C15111yescharacteristic
212C4#509×C15111yescharacteristic
213C2—161no—
214C2#1685×C15111yescharacteristic
215C2#2210×C15111yescharacteristic
216C2#2214×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#459
commutator, Frattini, cosocleC4×C8C23×C151
prime radicalC2×D8×C151D4
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
3. #1707×C151C2semidirect
5. #1370×C151C2semidirect
6. #1364×C151C2semidirect
7. #1362×C151C2semidirect
108. #12489C151direct (N × H)
109. C151#12489direct (N × H)
112. #1707C2×C151semidirect
114. #1370C2×C151semidirect
115. #1364C2×C151semidirect
116. #1362C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2224×C1512
#2208×C1512
#1707×C1512
#1589×C1512
#1370×C1512
#1364×C1512
#1362×C1512
#12489151