Finite Group Databasebeta

← C151×#7824 #50312749

Subgroups — C151×#7824 #50312749

Order 38656.

418 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 98 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#2724×C151C211yesmaximal, characteristic
2#2100×C151C212yesmaximal, complemented
3#2094×C151C211yesmaximal, characteristic
4#1271×C151C212yesmaximal, complemented
5#1270×C151C211yesmaximal, characteristic
6C2×#123×C151—21no—
7C2×#106×C151—21no—
8C2×#102×C151—21no—
9#398×C151—21no—
10#397×C151—22no—
11#390×C151C2211yescharacteristic
12#389×C151C2212yes—
13#385×C151—22no—
14#384×C151C2211yescharacteristic
15#340×C151—22no—
16#340×C151—22no—
17#336×C151C2211yescharacteristic
18#336×C151C2212yes—
19C22×D4×C151D411yescharacteristic
20C23×C4×C151—21no—
21C22×C8×C151—21no—
22C22×C8×C151—22no—
23#123×C151—42no—
24#123×C151—42no—
25C2×C4⋊C4×C151—22no—
26C2×C4⋊C4×C151—22no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151D412yes—
30C2×C4⋊C4×C151D412yes—
31C2×C4⋊C4×C151D411yescharacteristic
32C2×C22⋊C4×C151—22no—
33C2×C22⋊C4×C151—21no—
34C2×C22⋊C4×C151—22no—
35C2×C42×C151C2311yescharacteristic
36#106×C151—42no—
37#102×C151—42no—
38#95×C151—22no—
39#95×C151—21no—
40#95×C151—22no—
41C24×C151—21no—
42C2×D4×C151—21no—
43C2×D4×C151—41no—
44C2×D4×C151—41no—
45C2×D4×C151SD1612yes—
46C22×C4×C151—22no—
47C22×C4×C151—21no—
48C22×C4×C151—22no—
49C22×C4×C151—42no—
50C22×C4×C151—41no—
51C22×C4×C151—81no—
52C22×C4×C151—81no—
53C22×C4×C151C2×D411yescharacteristic
54C22×C4×C151C2×D412yes—
55C2×C8×C151—22no—
56C2×C8×C151—41no—
57C2×C8×C151—41no—
58C2×C8×C151—42no—
59C2×C8×C151—42no—
60C2×C8×C151—42no—
61C4⋊C4×C151—22no—
62C4⋊C4×C151—22no—
63C4⋊C4×C151—41no—
64C4⋊C4×C151—42no—
65C4⋊C4×C151—41no—
66C4⋊C4×C151—41no—
67C4⋊C4×C151—44no—
68C4⋊C4×C151—42no—
69C4⋊C4×C151—42no—
70C4⋊C4×C151—81no—
71C22⋊C4×C151—42no—
72C22⋊C4×C151—44no—
73C22⋊C4×C151—42no—
74C22⋊C4×C151—42no—
75C42×C151—41no—
76C23×C151—22no—
77C23×C151—42no—
78C23×C151—41no—
79C23×C151—42no—
80C23×C151—41no—
81C23×C151#12011yescharacteristic
82D4×C151—42no—
83D4×C151—81no—
84C2×C4×C151—21no—
85C2×C4×C151—22no—
86C2×C4×C151—22no—
87C2×C4×C151—21no—
88C2×C4×C151—42no—
89C2×C4×C151—42no—
90C2×C4×C151—42no—
91C2×C4×C151—42no—
92C2×C4×C151—41no—
93C2×C4×C151—42no—
94C2×C4×C151—42no—
95C2×C4×C151—42no—
96C2×C4×C151—84no—
97C2×C4×C151—81no—
98C2×C4×C151—82no—
99C2×C4×C151C2×SD1611yescharacteristic
100C2×C4×C151#13512yes—
101C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
102C2×C4×C151#13712yes—
103C8×C151—42no—
104C8×C151—82no—
105C22×C151—42no—
106C22×C151—44no—
107C22×C151—82no—
108C22×C151—81no—
109C22×C151—81no—
110C22×C151#45011yescharacteristic
111C22×C151#45212yes—
112C22×C151#45311yescharacteristic
113C22×C151#45412yes—
114C22×C151#45811yescharacteristic
115C4×C151—21no—
116C4×C151—21no—
117C4×C151—22no—
118C4×C151—22no—
119C4×C151—82no—
120C4×C151—81no—
121C4×C151—82no—
122C4×C151—161no—
123C2×C151—82no—
124C2×C151#161311yescharacteristic
125C2×C151#161512yes—
126C2×C151#163011yescharacteristic
127C2×C151#163512yes—
128C2×C151#165711yescharacteristic
129#7824C15111yesmaximal, characteristic, direct product factor, Sylow
130C151#782411yescharacteristic, direct product factor, Sylow
131#2724C2×C15111yescharacteristic
132#2100C2×C15112yescomplemented
133#2094C2×C15111yescharacteristic
134#1271C2×C15112yescomplemented
135#1270C2×C15111yescharacteristic
136C2×#123—21no—
137C2×#106—21no—
138C2×#102—21no—
139#398—21no—
140#397—22no—
141#390C22×C15111yescharacteristic
142#389C22×C15112yes—
143#385—22no—
144#384C22×C15111yescharacteristic
145#340—22no—
146#340—22no—
147#336C22×C15111yescharacteristic
148#336C22×C15112yes—
149C22×D4D4×C15111yescharacteristic
150C23×C4—21no—
151C22×C8—21no—
152C22×C8—22no—
153#123—42no—
154#123—42no—
155C2×C4⋊C4—22no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4D4×C15112yes—
160C2×C4⋊C4D4×C15112yes—
161C2×C4⋊C4D4×C15111yescharacteristic
162C2×C22⋊C4—22no—
163C2×C22⋊C4—21no—
164C2×C22⋊C4—22no—
165C2×C42C23×C15111yescharacteristic
166#106—42no—
167#102—42no—
168#95—22no—
169#95—21no—
170#95—22no—
171C24—21no—
172C2×D4—21no—
173C2×D4—41no—
174C2×D4—41no—
175C2×D4SD16×C15112yes—
176C22×C4—22no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—42no—
180C22×C4—41no—
181C22×C4—81no—
182C22×C4—81no—
183C22×C4C2×D4×C15111yescharacteristic
184C22×C4C2×D4×C15112yes—
185C2×C8—22no—
186C2×C8—41no—
187C2×C8—41no—
188C2×C8—42no—
189C2×C8—42no—
190C2×C8—42no—
191C4⋊C4—22no—
192C4⋊C4—22no—
193C4⋊C4—41no—
194C4⋊C4—42no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—44no—
198C4⋊C4—42no—
199C4⋊C4—42no—
200C4⋊C4—81no—
201C22⋊C4—42no—
202C22⋊C4—44no—
203C22⋊C4—42no—
204C22⋊C4—42no—
205C42—41no—
206C23—22no—
207C23—42no—
208C23—41no—
209C23—42no—
210C23—41no—
211C23#120×C15111yescharacteristic
212D4—42no—
213D4—81no—
214C2×C4—21no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—21no—
218C2×C4—42no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—41no—
223C2×C4—42no—
224C2×C4—42no—
225C2×C4—42no—
226C2×C4—84no—
227C2×C4—81no—
228C2×C4—82no—
229C2×C4C2×SD16×C15111yescharacteristic
230C2×C4#135×C15112yes—
231C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
232C2×C4#137×C15112yes—
233C8—42no—
234C8—82no—
235C22—42no—
236C22—44no—
237C22—82no—
238C22—81no—
239C22—81no—
240C22#450×C15111yescharacteristic
241C22#452×C15112yes—
242C22#453×C15111yescharacteristic
243C22#454×C15112yes—
244C22#458×C15111yescharacteristic
245C4—21no—
246C4—21no—
247C4—22no—
248C4—22no—
249C4—82no—
250C4—81no—
251C4—82no—
252C4—161no—
253C2—82no—
254C2#1613×C15111yescharacteristic
255C2#1615×C15112yes—
256C2#1630×C15111yescharacteristic
257C2#1635×C15112yes—
258C2#1657×C15111yescharacteristic
subgroupG/H
center, socleC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
prime radicalC22×D4×C151D4
LCSG ▷ C2×C42 ▷ C23 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2100×C151C2semidirect
4. #1271×C151C2semidirect
129. #7824C151direct (N × H)
130. C151#7824direct (N × H)
132. #2100C2×C151semidirect
134. #1271C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2724×C1512
#2100×C1512
#2094×C1512
#1271×C1512
#1270×C1512
#7824151