Finite Group Databasebeta

← C151×#11794 #50316719

Subgroups — C151×#11794 #50316719

Order 38656.

378 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 106 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#2568×C151C211yesmaximal, characteristic
2C4×#101×C151C211yesmaximal, characteristic
3#1467×C151C211yesmaximal, characteristic
4#1353×C151C214yesmaximal
5C2×C4⋊Q8×C151C411yescharacteristic
6C2×C4×Q8×C151C2211yescharacteristic
7#432×C151—21no—
8C2×#101×C151—21no—
9C4×M16×C151—21no—
10#400×C151C412yes—
11#400×C151C2212yes—
12#391×C151—21no—
13#391×C151—21no—
14#391×C151—21no—
15#382×C151—21no—
16C4×C4⋊C4×C151C411yescharacteristic
17#343×C151C2212yes—
18#324×C151—21no—
19#324×C151C2212yes—
20C22×Q8×C151—21no—
21C22×Q8×C151D411yescharacteristic
22C2×M16×C151—22no—
23C4⋊Q8×C151—41no—
24C4⋊Q8×C151—41no—
25C4×Q8×C151—41no—
26C4×Q8×C151—41no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151C2×C412yes—
30C2×C4⋊C4×C151C2×C411yescharacteristic
31C2×C4⋊C4×C151D411yescharacteristic
32C2×C4⋊C4×C151C2311yescharacteristic
33C2×C42×C151—21no—
34C2×C42×C151C2×C411yescharacteristic
35C2×C42×C151D411yescharacteristic
36C2×C42×C151D411yescharacteristic
37C4⋊C8×C151—41no—
38#101×C151—24no—
39C22⋊C8×C151—22no—
40#97×C151—41no—
41#97×C151—41no—
42C4×C8×C151—41no—
43#95×C151—22no—
44#95×C151—22no—
45#95×C151—22no—
46#95×C151—22no—
47#95×C151C2×C412yes—
48C2×Q8×C151—22no—
49C2×Q8×C151—22no—
50C2×Q8×C151—41no—
51C2×Q8×C151—44no—
52C2×Q8×C151—41no—
53C2×Q8×C151—41no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151C22⋊C411yescharacteristic
57C22×C4×C151C22⋊C411yescharacteristic
58C22×C4×C151C22⋊C411yescharacteristic
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22×C411yescharacteristic
61C22×C4×C151C2×D411yescharacteristic
62C22×C4×C151C2×D411yescharacteristic
63M16×C151—24no—
64M16×C151—42no—
65C2×C8×C151—42no—
66C2×C8×C151—42no—
67C4⋊C4×C151—41no—
68C4⋊C4×C151—41no—
69C4⋊C4×C151—41no—
70C4⋊C4×C151—42no—
71C4⋊C4×C151—42no—
72C4⋊C4×C151—42no—
73C42×C151—21no—
74C42×C151—21no—
75C42×C151—21no—
76C42×C151—21no—
77C42×C151—21no—
78C42×C151—21no—
79C42×C151—42no—
80C23×C151C2×C22⋊C411yescharacteristic
81Q8×C151—44no—
82Q8×C151—82no—
83Q8×C151—82no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—21no—
88C2×C4×C151—22no—
89C2×C4×C151—21no—
90C2×C4×C151—21no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—41no—
96C2×C4×C151—41no—
97C2×C4×C151—41no—
98C2×C4×C151—44no—
99C2×C4×C151—42no—
100C2×C4×C151—42no—
101C2×C4×C151—42no—
102C2×C4×C151—42no—
103C2×C4×C151#9911yescharacteristic
104C2×C4×C151#9911yescharacteristic
105C2×C4×C151#10412yes—
106C2×C4×C151#13712yes—
107C8×C151—44no—
108C8×C151—82no—
109C22×C151—21no—
110C22×C151—21no—
111C22×C151C2×#9911yescharacteristic
112C22×C151#41911yescharacteristic
113C22×C151C2×#10411yescharacteristic
114C4×C151—21no—
115C4×C151—22no—
116C4×C151—22no—
117C4×C151—41no—
118C4×C151—41no—
119C4×C151—41no—
120C4×C151—41no—
121C4×C151—82no—
122C4×C151—82no—
123C4×C151#35512yes—
124C2×C151—21no—
125C2×C151—21no—
126C2×C151#150811yescharacteristic
127C2×C151#212311yescharacteristic
128C2×C151C2×#35511yescharacteristic
129#11794C15111yesmaximal, characteristic, direct product factor, Sylow
130C151#1179411yescharacteristic, direct product factor, Sylow
131#2568C2×C15111yescharacteristic
132C4×#101C2×C15111yescharacteristic
133#1467C2×C15111yescharacteristic
134#1353C2×C15114yes—
135C2×C4⋊Q8C4×C15111yescharacteristic
136C2×C4×Q8C22×C15111yescharacteristic
137#432—21no—
138C2×#101—21no—
139C4×M16—21no—
140#400C4×C15112yes—
141#400C22×C15112yes—
142#391—21no—
143#391—21no—
144#391—21no—
145#382—21no—
146C4×C4⋊C4C4×C15111yescharacteristic
147#343C22×C15112yes—
148#324—21no—
149#324C22×C15112yes—
150C22×Q8—21no—
151C22×Q8D4×C15111yescharacteristic
152C2×M16—22no—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×C4×C15112yes—
160C2×C4⋊C4C2×C4×C15111yescharacteristic
161C2×C4⋊C4D4×C15111yescharacteristic
162C2×C4⋊C4C23×C15111yescharacteristic
163C2×C42—21no—
164C2×C42C2×C4×C15111yescharacteristic
165C2×C42D4×C15111yescharacteristic
166C2×C42D4×C15111yescharacteristic
167C4⋊C8—41no—
168#101—24no—
169C22⋊C8—22no—
170#97—41no—
171#97—41no—
172C4×C8—41no—
173#95—22no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95C2×C4×C15112yes—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—44no—
182C2×Q8—41no—
183C2×Q8—41no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊C4×C15111yescharacteristic
187C22×C4C22⋊C4×C15111yescharacteristic
188C22×C4C22⋊C4×C15111yescharacteristic
189C22×C4C22⋊C4×C15111yescharacteristic
190C22×C4C22×C4×C15111yescharacteristic
191C22×C4C2×D4×C15111yescharacteristic
192C22×C4C2×D4×C15111yescharacteristic
193M16—24no—
194M16—42no—
195C2×C8—42no—
196C2×C8—42no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—42no—
210C23C2×C22⋊C4×C15111yescharacteristic
211Q8—44no—
212Q8—82no—
213Q8—82no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4#99×C15111yescharacteristic
234C2×C4#99×C15111yescharacteristic
235C2×C4#104×C15112yes—
236C2×C4#137×C15112yes—
237C8—44no—
238C8—82no—
239C22—21no—
240C22—21no—
241C22C2×#99×C15111yescharacteristic
242C22#419×C15111yescharacteristic
243C22C2×#104×C15111yescharacteristic
244C4—21no—
245C4—22no—
246C4—22no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—82no—
252C4—82no—
253C4#355×C15112yes—
254C2—21no—
255C2—21no—
256C2#1508×C15111yescharacteristic
257C2#2123×C15111yescharacteristic
258C2C2×#355×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC23×C151C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
129. #11794C151direct (N × H)
130. C151#11794direct (N × H)

Maximal subgroups

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

subgroupindex
#2568×C1512
C4×#101×C1512
#1467×C1512
#1353×C1512
#11794151