Finite Group Databasebeta

← C151×#23566 #50328491

Subgroups — C151×#23566 #50328491

Order 38656.

1118 conjugacy classes of subgroups; only the 366 normal subgroups are shown.

normal subgroups only

This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 366 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#3458×C151C211yesmaximal, characteristic
2#2317×C151C213yesmaximal
3#2062×C151C218yesmaximal
4#1740×C151C213yesmaximal
5#544×C151—23no—
6#544×C151—23no—
7#543×C151C2214yes—
8#533×C151—26no—
9C2×#117×C151C2213yes—
10C2×#117×C151C2213yes—
11C22×C4⋊C4×C151C2211yescharacteristic
12#389×C151—26no—
13#385×C151C22112yes—
14#384×C151—23no—
15#382×C151—23no—
16#342×C151C22112yes—
17C23×C4×C151C2312yes—
18C23×C4×C151C2311yescharacteristic
19C4⋊Q8×C151—26no—
20C4⋊Q8×C151—26no—
21#125×C151—212no—
22C22⋊Q8×C151—212no—
23C22⋊Q8×C151—212no—
24C4×Q8×C151—24no—
25C4×Q8×C151—24no—
26#117×C151—26no—
27#117×C151—26no—
28#117×C151—26no—
29#117×C151Q8112yescomplemented
30C2×C4⋊C4×C151—23no—
31C2×C4⋊C4×C151—23no—
32C2×C4⋊C4×C151—23no—
33C2×C4⋊C4×C151—212no—
34C2×C4⋊C4×C151D413yes—
35C2×C4⋊C4×C151D413yes—
36C2×C22⋊C4×C151C2316yes—
37C2×C22⋊C4×C151C2316yes—
38C2×C42×C151—23no—
39C2×C42×C151D416yes—
40#95×C151—212no—
41C24×C151C2411yescharacteristic
42C2×Q8×C151—24no—
43C2×Q8×C151—24no—
44C22×C4×C151—26no—
45C22×C4×C151—26no—
46C22×C4×C151—82no—
47C22×C4×C151C2×D416yes—
48C22×C4×C151C2×D416yes—
49C22×C4×C151C2×D413yes—
50C22×C4×C151C2×D413yes—
51C22×C4×C151C2×Q816yes—
52C22×C4×C151#4112yes—
53C4⋊C4×C151—212no—
54C4⋊C4×C151—212no—
55C4⋊C4×C151—26no—
56C4⋊C4×C151—26no—
57C4⋊C4×C151—212no—
58C4⋊C4×C151—41no—
59C4⋊C4×C151—43no—
60C4⋊C4×C151—812no—
61C22⋊C4×C151—212no—
62C22⋊C4×C151—26no—
63C22⋊C4×C151C2×Q8112yes—
64C42×C151—26no—
65C42×C151—26no—
66C42×C151—212no—
67C23×C151—41no—
68C23×C151—41no—
69C23×C151C22×D413yes—
70C23×C151C22×Q813yes—
71C23×C151C2×#4111yescharacteristic
72Q8×C151—84no—
73Q8×C151—84no—
74C2×C4×C151—26no—
75C2×C4×C151—26no—
76C2×C4×C151—212no—
77C2×C4×C151—46no—
78C2×C4×C151—46no—
79C2×C4×C151—46no—
80C2×C4×C151—46no—
81C2×C4×C151—412no—
82C2×C4×C151—42no—
83C2×C4×C151#12011yescharacteristic
84C2×C4×C151#12013yes—
85C2×C4×C151C22⋊Q816yes—
86C2×C4×C151C22⋊Q816yes—
87C2×C4×C151C4⋊Q816yes—
88C2×C4×C151C4⋊Q816yes—
89C22×C151—23no—
90C22×C151—23no—
91C22×C151—43no—
92C22×C151—41no—
93C22×C151C2×#12011yescharacteristic
94C22×C151C2×C22⋊Q813yes—
95C22×C151C2×C4⋊Q813yes—
96C4×C151—412no—
97C4×C151—46no—
98C4×C151—46no—
99C4×C151—82no—
100C4×C151#39512yes—
101C4×C151#39516yes—
102C2×C151—23no—
103C2×C151—23no—
104C2×C151C2×#39511yescharacteristic
105C2×C151#302711yescharacteristic
106C2×C151#302811yescharacteristic
107#23566C15111yesmaximal, characteristic, direct product factor, Sylow
108C151#2356611yescharacteristic, direct product factor, Sylow
109#3458C2×C15111yescharacteristic
110#2317C2×C15113yes—
111#2062C2×C15118yes—
112#1740C2×C15113yes—
113#544—23no—
114#544—23no—
115#543C22×C15114yes—
116#533—26no—
117C2×#117C22×C15113yes—
118C2×#117C22×C15113yes—
119C22×C4⋊C4C22×C15111yescharacteristic
120#389—26no—
121#385C22×C151112yes—
122#384—23no—
123#382—23no—
124#342C22×C151112yes—
125C23×C4C23×C15112yes—
126C23×C4C23×C15111yescharacteristic
127C4⋊Q8—26no—
128C4⋊Q8—26no—
129#125—212no—
130C22⋊Q8—212no—
131C22⋊Q8—212no—
132C4×Q8—24no—
133C4×Q8—24no—
134#117—26no—
135#117—26no—
136#117—26no—
137#117Q8×C151112yescomplemented
138C2×C4⋊C4—23no—
139C2×C4⋊C4—23no—
140C2×C4⋊C4—23no—
141C2×C4⋊C4—212no—
142C2×C4⋊C4D4×C15113yes—
143C2×C4⋊C4D4×C15113yes—
144C2×C22⋊C4C23×C15116yes—
145C2×C22⋊C4C23×C15116yes—
146C2×C42—23no—
147C2×C42D4×C15116yes—
148#95—212no—
149C24C24×C15111yescharacteristic
150C2×Q8—24no—
151C2×Q8—24no—
152C22×C4—26no—
153C22×C4—26no—
154C22×C4—82no—
155C22×C4C2×D4×C15116yes—
156C22×C4C2×D4×C15116yes—
157C22×C4C2×D4×C15113yes—
158C22×C4C2×D4×C15113yes—
159C22×C4C2×Q8×C15116yes—
160C22×C4#41×C15112yes—
161C4⋊C4—212no—
162C4⋊C4—212no—
163C4⋊C4—26no—
164C4⋊C4—26no—
165C4⋊C4—212no—
166C4⋊C4—41no—
167C4⋊C4—43no—
168C4⋊C4—812no—
169C22⋊C4—212no—
170C22⋊C4—26no—
171C22⋊C4C2×Q8×C151112yes—
172C42—26no—
173C42—26no—
174C42—212no—
175C23—41no—
176C23—41no—
177C23C22×D4×C15113yes—
178C23C22×Q8×C15113yes—
179C23C2×#41×C15111yescharacteristic
180Q8—84no—
181Q8—84no—
182C2×C4—26no—
183C2×C4—26no—
184C2×C4—212no—
185C2×C4—46no—
186C2×C4—46no—
187C2×C4—46no—
188C2×C4—46no—
189C2×C4—412no—
190C2×C4—42no—
191C2×C4#120×C15111yescharacteristic
192C2×C4#120×C15113yes—
193C2×C4C22⋊Q8×C15116yes—
194C2×C4C22⋊Q8×C15116yes—
195C2×C4C4⋊Q8×C15116yes—
196C2×C4C4⋊Q8×C15116yes—
197C22—23no—
198C22—23no—
199C22—43no—
200C22—41no—
201C22C2×#120×C15111yescharacteristic
202C22C2×C22⋊Q8×C15113yes—
203C22C2×C4⋊Q8×C15113yes—
204C4—412no—
205C4—46no—
206C4—46no—
207C4—82no—
208C4#395×C15112yes—
209C4#395×C15116yes—
210C2—23no—
211C2—23no—
212C2C2×#395×C15111yescharacteristic
213C2#3027×C15111yescharacteristic
214C2#3028×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#120
commutator, Frattini, cosocleC24C24×C151
prime radicalC24×C151C24
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
29. #117×C151Q8semidirect
107. #23566C151direct (N × H)
108. C151#23566direct (N × H)
137. #117Q8×C151semidirect

Maximal subgroups

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

subgroupindex
#3458×C1512
#2317×C1512
#2062×C1512
#1740×C1512
#23566151