Finite Group Databasebeta

← C151×#12078 #50317003

Subgroups — C151×#12078 #50317003

Order 38656.

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

normal subgroups only

This group has 234 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#2177×C151C211yesmaximal, characteristic
2#1594×C151C211yesmaximal, characteristic, complemented
3#1580×C151C211yesmaximal, characteristic, complemented
4#1368×C151C211yesmaximal, characteristic, complemented
5#1333×C151C211yesmaximal, characteristic, complemented
6#1333×C151C211yesmaximal, characteristic, complemented
7#1313×C151C211yesmaximal, characteristic, complemented
8C2×D16×C151C411yescharacteristic
9C4×D8×C151C2211yescharacteristic
10C4×D8×C151C2211yescharacteristic
11#436×C151—21no—
12C8×D4×C151—21no—
13#367×C151C411yescharacteristic
14#357×C151C411yescharacteristic
15#357×C151C411yescharacteristic
16#346×C151C2211yescharacteristic
17#346×C151C2211yescharacteristic
18#334×C151C2211yescharacteristic
19#334×C151C2211yescharacteristic
20D4⋊C8×C151—21no—
21D4⋊C8×C151—21no—
22#322×C151C2211yescharacteristic
23C2×D8×C151C2×C411yescharacteristic
24C2×D8×C151C2×C411yescharacteristic
25C2×M16×C151—41no—
26C22×C8×C151—41no—
27C4×D4×C151—21no—
28C4×D4×C151—21no—
29D16×C151—22no—
30C2×C16×C151—21no—
31C2×C16×C151C2×C411yescharacteristic
32C2×C16×C151C2×C411yescharacteristic
33#107×C151C2×C411yescharacteristic
34#107×C151C2×C411yescharacteristic
35C4⋊C8×C151—21no—
36C4⋊C8×C151—21no—
37#102×C151—21no—
38#102×C151—21no—
39C22⋊C8×C151—41no—
40C22⋊C8×C151—41no—
41C4×C8×C151D411yescharacteristic
42C4×C8×C151D411yescharacteristic
43C4×C8×C151C2311yescharacteristic
44C2×D4×C151—21no—
45C2×D4×C151—21no—
46C22×C4×C151—41no—
47C22×C4×C151—41no—
48D8×C151—21no—
49D8×C151—21no—
50D8×C151—21no—
51D8×C151M1612yescomplemented
52M16×C151—82no—
53C2×C8×C151—21no—
54C2×C8×C151—21no—
55C2×C8×C151—41no—
56C2×C8×C151—41no—
57C2×C8×C151—82no—
58C2×C8×C151C22×C411yescharacteristic
59C2×C8×C151#4111yescharacteristic
60C4⋊C4×C151—21no—
61C4⋊C4×C151—21no—
62C22⋊C4×C151—41no—
63C22⋊C4×C151—41no—
64C42×C151C2×D411yescharacteristic
65C16×C151—22no—
66C16×C151—21no—
67C16×C151—21no—
68C23×C151—41no—
69C23×C151—41no—
70D4×C151—22no—
71D4×C151—41no—
72D4×C151—41no—
73D4×C151—41no—
74C2×C4×C151—41no—
75C2×C4×C151—41no—
76C2×C4×C151—81no—
77C2×C4×C151—81no—
78C2×C4×C151—81no—
79C2×C4×C151—81no—
80C2×C4×C151C4×D411yescharacteristic
81C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
82C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
83C8×C151—21no—
84C8×C151—41no—
85C8×C151—41no—
86C8×C151—81no—
87C8×C151—81no—
88C8×C151C2×M1611yescharacteristic
89C8×C151#13111yescharacteristic
90C22×C151—42no—
91C22×C151—81no—
92C22×C151—81no—
93C22×C151—81no—
94C22×C151—81no—
95C22×C151—81no—
96C22×C151#44211yescharacteristic
97C4×C151—21no—
98C4×C151—21no—
99C4×C151—81no—
100C4×C151—81no—
101C4×C151#43511yescharacteristic
102C4×C151#44311yescharacteristic
103C2×C151—82no—
104C2×C151—161no—
105C2×C151#158611yescharacteristic
106C2×C151AGL(1,ℤ/16)11yescharacteristic
107C2×C151AGL(1,ℤ/16)11yescharacteristic
108#12078C15111yesmaximal, characteristic, direct product factor, Sylow
109C151#1207811yescharacteristic, direct product factor, Sylow
110#2177C2×C15111yescharacteristic
111#1594C2×C15111yescharacteristic, complemented
112#1580C2×C15111yescharacteristic, complemented
113#1368C2×C15111yescharacteristic, complemented
114#1333C2×C15111yescharacteristic, complemented
115#1333C2×C15111yescharacteristic, complemented
116#1313C2×C15111yescharacteristic, complemented
117C2×D16C4×C15111yescharacteristic
118C4×D8C22×C15111yescharacteristic
119C4×D8C22×C15111yescharacteristic
120#436—21no—
121C8×D4—21no—
122#367C4×C15111yescharacteristic
123#357C4×C15111yescharacteristic
124#357C4×C15111yescharacteristic
125#346C22×C15111yescharacteristic
126#346C22×C15111yescharacteristic
127#334C22×C15111yescharacteristic
128#334C22×C15111yescharacteristic
129D4⋊C8—21no—
130D4⋊C8—21no—
131#322C22×C15111yescharacteristic
132C2×D8C2×C4×C15111yescharacteristic
133C2×D8C2×C4×C15111yescharacteristic
134C2×M16—41no—
135C22×C8—41no—
136C4×D4—21no—
137C4×D4—21no—
138D16—22no—
139C2×C16—21no—
140C2×C16C2×C4×C15111yescharacteristic
141C2×C16C2×C4×C15111yescharacteristic
142#107C2×C4×C15111yescharacteristic
143#107C2×C4×C15111yescharacteristic
144C4⋊C8—21no—
145C4⋊C8—21no—
146#102—21no—
147#102—21no—
148C22⋊C8—41no—
149C22⋊C8—41no—
150C4×C8D4×C15111yescharacteristic
151C4×C8D4×C15111yescharacteristic
152C4×C8C23×C15111yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C22×C4—41no—
156C22×C4—41no—
157D8—21no—
158D8—21no—
159D8—21no—
160D8M16×C15112yescomplemented
161M16—82no—
162C2×C8—21no—
163C2×C8—21no—
164C2×C8—41no—
165C2×C8—41no—
166C2×C8—82no—
167C2×C8C22×C4×C15111yescharacteristic
168C2×C8#41×C15111yescharacteristic
169C4⋊C4—21no—
170C4⋊C4—21no—
171C22⋊C4—41no—
172C22⋊C4—41no—
173C42C2×D4×C15111yescharacteristic
174C16—22no—
175C16—21no—
176C16—21no—
177C23—41no—
178C23—41no—
179D4—22no—
180D4—41no—
181D4—41no—
182D4—41no—
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—81no—
186C2×C4—81no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4C4×D4×C15111yescharacteristic
190C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
191C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
192C8—21no—
193C8—41no—
194C8—41no—
195C8—81no—
196C8—81no—
197C8C2×M16×C15111yescharacteristic
198C8#131×C15111yescharacteristic
199C22—42no—
200C22—81no—
201C22—81no—
202C22—81no—
203C22—81no—
204C22—81no—
205C22#442×C15111yescharacteristic
206C4—21no—
207C4—21no—
208C4—81no—
209C4—81no—
210C4#435×C15111yescharacteristic
211C4#443×C15111yescharacteristic
212C2—82no—
213C2—161no—
214C2#1586×C15111yescharacteristic
215C2AGL(1,ℤ/16)×C15111yescharacteristic
216C2AGL(1,ℤ/16)×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#442
commutatorC2×C8C22×C4×C151
Frattini, cosocleC4×C8C23×C151
prime radicalC2×D16×C151C4
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
2. #1594×C151C2semidirect
3. #1580×C151C2semidirect
4. #1368×C151C2semidirect
5. #1333×C151C2semidirect
6. #1333×C151C2semidirect
7. #1313×C151C2semidirect
51. D8×C151M16semidirect
108. #12078C151direct (N × H)
109. C151#12078direct (N × H)
111. #1594C2×C151semidirect
112. #1580C2×C151semidirect
113. #1368C2×C151semidirect
114. #1333C2×C151semidirect
115. #1333C2×C151semidirect
116. #1313C2×C151semidirect
160. D8M16×C151semidirect

Maximal subgroups

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

subgroupindex
#2177×C1512
#1594×C1512
#1580×C1512
#1368×C1512
#1333×C1512
#1313×C1512
#12078151