Finite Group Databasebeta

← C151×#12484 #50317409

Subgroups — C151×#12484 #50317409

Order 38656.

234 conjugacy classes of subgroups; only the 82 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 82 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#2225×C151C211yesmaximal, characteristic, complemented
2#2207×C151C211yesmaximal, characteristic
3#1706×C151C211yesmaximal, characteristic
4#1591×C151C211yesmaximal, characteristic, complemented
5#1370×C151C211yesmaximal, characteristic, complemented
6#1364×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#367×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—41no—
25C2×SD16×C151—41no—
26C2×D8×C151—21no—
27C2×D8×C151—21no—
28C4⋊Q8×C151—21no—
29#127×C151—21no—
30C4×Q8×C151—21no—
31SD32×C151—42no—
32C2×C16×C151—21no—
33C2×C16×C151—21no—
34#107×C151—21no—
35#107×C151—21no—
36#107×C151D411yescharacteristic
37C4⋊C8×C151—21no—
38C4⋊C8×C151—41no—
39#103×C151—21no—
40#102×C151—42no—
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—82no—
53SD16×C151—82no—
54D8×C151—41no—
55D8×C151—41no—
56D8×C151—81no—
57C2×C8×C151—21no—
58C2×C8×C151—41no—
59C2×C8×C151D811yescharacteristic
60C2×C8×C151D811yescharacteristic
61C2×C8×C151C2×D411yescharacteristic
62C2×C8×C151#4111yescharacteristic
63C4⋊C4×C151—21no—
64C4⋊C4×C151—41no—
65C4⋊C4×C151—41no—
66C4⋊C4×C151—41no—
67C42×C151—41no—
68C42×C151C2×D411yescharacteristic
69C16×C151—41no—
70C16×C151—41no—
71C23×C151—81no—
72Q8×C151—41no—
73Q8×C151—41no—
74Q8×C151—81no—
75Q8×C151—81no—
76D4×C151—82no—
77D4×C151—81no—
78D4×C151—81no—
79D4×C151—81no—
80D4×C151—81no—
81C2×C4×C151—41no—
82C2×C4×C151—41no—
83C2×C4×C151—81no—
84C2×C4×C151#12111yescharacteristic
85C2×C4×C151C2×D811yescharacteristic
86C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
87C8×C151—21no—
88C8×C151—21no—
89C8×C151—41no—
90C8×C151—81no—
91C8×C151SD3212yescomplemented
92C8×C151AGL(1,ℤ/8)11yescharacteristic
93C8×C151#13711yescharacteristic
94C22×C151—161no—
95C22×C151—161no—
96C22×C151—161no—
97C22×C151#45911yescharacteristic
98C4×C151—21no—
99C4×C151—81no—
100C4×C151—81no—
101C4×C151—161no—
102C4×C151#46811yescharacteristic
103C4×C151#47111yescharacteristic
104C4×C151C2×SD3211yescharacteristic
105C4×C151#50911yescharacteristic
106C2×C151—321no—
107C2×C151#168511yescharacteristic
108C2×C151#220711yescharacteristic
109C2×C151#221211yescharacteristic
110#12484C15111yesmaximal, characteristic, direct product factor, Sylow
111C151#1248411yescharacteristic, direct product factor, Sylow
112#2225C2×C15111yescharacteristic, complemented
113#2207C2×C15111yescharacteristic
114#1706C2×C15111yescharacteristic
115#1591C2×C15111yescharacteristic, complemented
116#1370C2×C15111yescharacteristic, complemented
117#1364C2×C15111yescharacteristic, complemented
118#1361C2×C15111yescharacteristic
119C2×SD32—21no—
120#500C22×C15111yescharacteristic
121#493C22×C15111yescharacteristic
122#492—21no—
123#486—21no—
124#446—21no—
125C4×Q16C22×C15111yescharacteristic
126#367—21no—
127C4⋊C16C22×C15111yescharacteristic
128C4⋊C16C22×C15111yescharacteristic
129#358—21no—
130#357—21no—
131#335C22×C15111yescharacteristic
132Q8⋊C8—21no—
133C82C22×C15111yescharacteristic
134C2×Q16D4×C15111yescharacteristic
135C2×SD16—41no—
136C2×SD16—41no—
137C2×D8—21no—
138C2×D8—21no—
139C4⋊Q8—21no—
140#127—21no—
141C4×Q8—21no—
142SD32—42no—
143C2×C16—21no—
144C2×C16—21no—
145#107—21no—
146#107—21no—
147#107D4×C15111yescharacteristic
148C4⋊C8—21no—
149C4⋊C8—41no—
150#103—21no—
151#102—42no—
152#97—41no—
153C4×C8D4×C15111yescharacteristic
154C4×C8D4×C15111yescharacteristic
155C4×C8C23×C15111yescharacteristic
156C2×Q8—21no—
157C2×Q8—41no—
158C2×D4—41no—
159C2×D4—41no—
160C2×D4—41no—
161Q16—21no—
162Q16—21no—
163SD16—82no—
164SD16—82no—
165D8—41no—
166D8—41no—
167D8—81no—
168C2×C8—21no—
169C2×C8—41no—
170C2×C8D8×C15111yescharacteristic
171C2×C8D8×C15111yescharacteristic
172C2×C8C2×D4×C15111yescharacteristic
173C2×C8#41×C15111yescharacteristic
174C4⋊C4—21no—
175C4⋊C4—41no—
176C4⋊C4—41no—
177C4⋊C4—41no—
178C42—41no—
179C42C2×D4×C15111yescharacteristic
180C16—41no—
181C16—41no—
182C23—81no—
183Q8—41no—
184Q8—41no—
185Q8—81no—
186Q8—81no—
187D4—82no—
188D4—81no—
189D4—81no—
190D4—81no—
191D4—81no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—81no—
195C2×C4#121×C15111yescharacteristic
196C2×C4C2×D8×C15111yescharacteristic
197C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
198C8—21no—
199C8—21no—
200C8—41no—
201C8—81no—
202C8SD32×C15112yescomplemented
203C8AGL(1,ℤ/8)×C15111yescharacteristic
204C8#137×C15111yescharacteristic
205C22—161no—
206C22—161no—
207C22—161no—
208C22#459×C15111yescharacteristic
209C4—21no—
210C4—81no—
211C4—81no—
212C4—161no—
213C4#468×C15111yescharacteristic
214C4#471×C15111yescharacteristic
215C4C2×SD32×C15111yescharacteristic
216C4#509×C15111yescharacteristic
217C2—321no—
218C2#1685×C15111yescharacteristic
219C2#2207×C15111yescharacteristic
220C2#2212×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. #2225×C151C2semidirect
4. #1591×C151C2semidirect
5. #1370×C151C2semidirect
6. #1364×C151C2semidirect
91. C8×C151SD32semidirect
110. #12484C151direct (N × H)
111. C151#12484direct (N × H)
112. #2225C2×C151semidirect
115. #1591C2×C151semidirect
116. #1370C2×C151semidirect
117. #1364C2×C151semidirect
202. C8SD32×C151semidirect

Maximal subgroups

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

subgroupindex
#2225×C1512
#2207×C1512
#1706×C1512
#1591×C1512
#1370×C1512
#1364×C1512
#1361×C1512
#12484151