Finite Group Databasebeta

← C151×#10512 #50315437

Subgroups — C151×#10512 #50315437

Order 38656.

408 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 94 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#3245×C151C211yesmaximal, characteristic
2#1843×C151C211yesmaximal, characteristic, complemented
3#1551×C151C212yesmaximal, complemented
4#1505×C151C212yesmaximal, complemented
5#1290×C151C211yesmaximal, characteristic, complemented
6#532×C151C2212yes—
7#474×C151—22no—
8#466×C151—22no—
9#459×C151—22no—
10#432×C151C2212yes—
11C2×C4⋊C8×C151—22no—
12C2×C4⋊C8×C151C2211yescharacteristic
13C2×C4⋊C8×C151C2211yescharacteristic
14#376×C151C2211yescharacteristic
15#333×C151—22no—
16#331×C151—22no—
17#327×C151—24no—
18C2×#41×C151—22no—
19C2×D8×C151—22no—
20C22×C8×C151—21no—
21C22×C8×C151D412yes—
22C4⋊Q8×C151D412yes—
23#127×C151D412yes—
24#124×C151—22no—
25#121×C151—22no—
26#121×C151—22no—
27C4×D4×C151—22no—
28C4×D4×C151—22no—
29C2×C42×C151—21no—
30C2×C42×C151C2311yescharacteristic
31#107×C151—22no—
32C4⋊C8×C151—22no—
33C4⋊C8×C151—22no—
34C4⋊C8×C151—22no—
35C4⋊C8×C151—44no—
36#102×C151—24no—
37C22⋊C8×C151—22no—
38#97×C151—22no—
39#95×C151—21no—
40#95×C151D412yes—
41#41×C151—84no—
42C2×Q8×C151—22no—
43C2×D4×C151—22no—
44C2×D4×C151—22no—
45C2×D4×C151—22no—
46C2×D4×C151—42no—
47C22×C4×C151—22no—
48C22×C4×C151—42no—
49C22×C4×C151C2×D411yescharacteristic
50C22×C4×C151C2×D411yescharacteristic
51C22×C4×C151#4111yescharacteristic
52D8×C151—82no—
53C2×C8×C151—22no—
54C2×C8×C151—42no—
55C2×C8×C151—42no—
56C2×C8×C151—41no—
57C2×C8×C151—42no—
58C4⋊C4×C151—22no—
59C4⋊C4×C151—22no—
60C22⋊C4×C151—42no—
61C22⋊C4×C151—42no—
62C42×C151—22no—
63C42×C151—22no—
64C42×C151C2×D412yes—
65C42×C151#4112yes—
66C23×C151—42no—
67C23×C151#12111yescharacteristic
68Q8×C151—82no—
69D4×C151—42no—
70D4×C151—42no—
71D4×C151—82no—
72D4×C151—82no—
73D4×C151—84no—
74C2×C4×C151—22no—
75C2×C4×C151—21no—
76C2×C4×C151—21no—
77C2×C4×C151—24no—
78C2×C4×C151—41no—
79C2×C4×C151—42no—
80C2×C4×C151—42no—
81C2×C4×C151—42no—
82C2×C4×C151—84no—
83C2×C4×C151#12011yescharacteristic
84C2×C4×C151#12112yes—
85C2×C4×C151#12312yes—
86C2×C4×C151#12411yescharacteristic
87C8×C151—42no—
88C8×C151—82no—
89C8×C151—81no—
90C22×C151—21no—
91C22×C151—21no—
92C22×C151—82no—
93C22×C151—82no—
94C22×C151—82no—
95C22×C151#39411yescharacteristic
96C22×C151#47212yes—
97C4×C151—22no—
98C4×C151—21no—
99C4×C151—22no—
100C4×C151—44no—
101C4×C151—82no—
102C4×C151#45311yescharacteristic
103C4×C151#45611yescharacteristic
104C2×C151—22no—
105C2×C151—162no—
106C2×C151#203911yescharacteristic
107C2×C151#204511yescharacteristic
108C2×C151#205311yescharacteristic
109#10512C15111yesmaximal, characteristic, direct product factor, Sylow
110C151#1051211yescharacteristic, direct product factor, Sylow
111#3245C2×C15111yescharacteristic
112#1843C2×C15111yescharacteristic, complemented
113#1551C2×C15112yescomplemented
114#1505C2×C15112yescomplemented
115#1290C2×C15111yescharacteristic, complemented
116#532C22×C15112yes—
117#474—22no—
118#466—22no—
119#459—22no—
120#432C22×C15112yes—
121C2×C4⋊C8—22no—
122C2×C4⋊C8C22×C15111yescharacteristic
123C2×C4⋊C8C22×C15111yescharacteristic
124#376C22×C15111yescharacteristic
125#333—22no—
126#331—22no—
127#327—24no—
128C2×#41—22no—
129C2×D8—22no—
130C22×C8—21no—
131C22×C8D4×C15112yes—
132C4⋊Q8D4×C15112yes—
133#127D4×C15112yes—
134#124—22no—
135#121—22no—
136#121—22no—
137C4×D4—22no—
138C4×D4—22no—
139C2×C42—21no—
140C2×C42C23×C15111yescharacteristic
141#107—22no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—22no—
145C4⋊C8—44no—
146#102—24no—
147C22⋊C8—22no—
148#97—22no—
149#95—21no—
150#95D4×C15112yes—
151#41—84no—
152C2×Q8—22no—
153C2×D4—22no—
154C2×D4—22no—
155C2×D4—22no—
156C2×D4—42no—
157C22×C4—22no—
158C22×C4—42no—
159C22×C4C2×D4×C15111yescharacteristic
160C22×C4C2×D4×C15111yescharacteristic
161C22×C4#41×C15111yescharacteristic
162D8—82no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—41no—
167C2×C8—42no—
168C4⋊C4—22no—
169C4⋊C4—22no—
170C22⋊C4—42no—
171C22⋊C4—42no—
172C42—22no—
173C42—22no—
174C42C2×D4×C15112yes—
175C42#41×C15112yes—
176C23—42no—
177C23#121×C15111yescharacteristic
178Q8—82no—
179D4—42no—
180D4—42no—
181D4—82no—
182D4—82no—
183D4—84no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—24no—
188C2×C4—41no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—84no—
193C2×C4#120×C15111yescharacteristic
194C2×C4#121×C15112yes—
195C2×C4#123×C15112yes—
196C2×C4#124×C15111yescharacteristic
197C8—42no—
198C8—82no—
199C8—81no—
200C22—21no—
201C22—21no—
202C22—82no—
203C22—82no—
204C22—82no—
205C22#394×C15111yescharacteristic
206C22#472×C15112yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—44no—
211C4—82no—
212C4#453×C15111yescharacteristic
213C4#456×C15111yescharacteristic
214C2—22no—
215C2—162no—
216C2#2039×C15111yescharacteristic
217C2#2045×C15111yescharacteristic
218C2#2053×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#394
commutator, Frattini, cosocleC2×C42C23×C151
prime radical#3245×C151C2
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #1843×C151C2semidirect
3. #1551×C151C2semidirect
4. #1505×C151C2semidirect
5. #1290×C151C2semidirect
109. #10512C151direct (N × H)
110. C151#10512direct (N × H)
112. #1843C2×C151semidirect
113. #1551C2×C151semidirect
114. #1505C2×C151semidirect
115. #1290C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3245×C1512
#1843×C1512
#1551×C1512
#1505×C1512
#1290×C1512
#10512151