Finite Group Databasebeta

← C151×#11740 #50316665

Subgroups — C151×#11740 #50316665

Order 38656.

358 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 102 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#2634×C151C211yesmaximal, characteristic
2C4×#101×C151C211yesmaximal, characteristic
3#1461×C151C211yesmaximal, characteristic
4#1353×C151C212yesmaximal
5#1346×C151C212yesmaximal
6C2×#125×C151C411yescharacteristic
7C2×C4×Q8×C151C2211yescharacteristic
8#431×C151—21no—
9C2×#101×C151—21no—
10C4×M16×C151—21no—
11#400×C151—21no—
12#400×C151C411yescharacteristic
13#400×C151C2211yescharacteristic
14#398×C151C411yescharacteristic
15#398×C151C2211yescharacteristic
16#395×C151—21no—
17#387×C151—21no—
18#387×C151—21no—
19#383×C151C411yescharacteristic
20#343×C151C2212yes—
21#324×C151—21no—
22#324×C151C2212yes—
23C22×Q8×C151D411yescharacteristic
24C2×M16×C151—22no—
25#125×C151—41no—
26#125×C151—41no—
27C4×Q8×C151—41no—
28C4×Q8×C151—41no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—21no—
33C2×C4⋊C4×C151C2×C411yescharacteristic
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151C2×C411yescharacteristic
36C2×C4⋊C4×C151D411yescharacteristic
37C2×C4⋊C4×C151C2311yescharacteristic
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C4⋊C8×C151—41no—
42#101×C151—24no—
43C22⋊C8×C151—22no—
44#97×C151—41no—
45C4×C8×C151—41no—
46C4×C8×C151—41no—
47#95×C151—21no—
48#95×C151—21no—
49#95×C151—21no—
50#95×C151—21no—
51#95×C151—21no—
52#95×C151—21no—
53#95×C151—21no—
54#95×C151—21no—
55#95×C151C2×C411yescharacteristic
56#95×C151C2×C411yescharacteristic
57C2×Q8×C151—22no—
58C2×Q8×C151—22no—
59C2×Q8×C151—41no—
60C22×C4×C151—21no—
61C22×C4×C151—21no—
62C22×C4×C151—21no—
63C22×C4×C151—21no—
64C22×C4×C151C22⋊C411yescharacteristic
65C22×C4×C151C22⋊C411yescharacteristic
66C22×C4×C151C22⋊C411yescharacteristic
67C22×C4×C151C22⋊C411yescharacteristic
68C22×C4×C151C22×C411yescharacteristic
69C22×C4×C151C2×D411yescharacteristic
70C22×C4×C151C2×D411yescharacteristic
71M16×C151—24no—
72M16×C151—42no—
73C2×C8×C151—42no—
74C2×C8×C151—42no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—41no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—42no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—41no—
83C4⋊C4×C151—42no—
84C4⋊C4×C151—42no—
85C42×C151—21no—
86C42×C151—21no—
87C42×C151—21no—
88C42×C151—21no—
89C42×C151—21no—
90C42×C151—21no—
91C23×C151C2×C22⋊C411yescharacteristic
92Q8×C151—44no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—21no—
98C2×C4×C151—21no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—41no—
106C2×C4×C151—41no—
107C2×C4×C151—41no—
108C2×C4×C151—41no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—42no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—41no—
118C2×C4×C151#9911yescharacteristic
119C2×C4×C151#9911yescharacteristic
120C2×C4×C151#10412yes—
121C2×C4×C151#13512yes—
122C8×C151—44no—
123C8×C151—82no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151C2×#9911yescharacteristic
127C22×C151#41611yescharacteristic
128C22×C151C2×#10411yescharacteristic
129C4×C151—21no—
130C4×C151—21no—
131C4×C151—22no—
132C4×C151—22no—
133C4×C151—41no—
134C4×C151—41no—
135C4×C151—41no—
136C4×C151—41no—
137C4×C151—81no—
138C4×C151—81no—
139C4×C151—81no—
140C4×C151—81no—
141C2×C151—21no—
142C2×C151—21no—
143C2×C151#150111yescharacteristic
144C2×C151#212311yescharacteristic
145C2×C151#213311yescharacteristic
146#11740C15111yesmaximal, characteristic, direct product factor, Sylow
147C151#1174011yescharacteristic, direct product factor, Sylow
148#2634C2×C15111yescharacteristic
149C4×#101C2×C15111yescharacteristic
150#1461C2×C15111yescharacteristic
151#1353C2×C15112yes—
152#1346C2×C15112yes—
153C2×#125C4×C15111yescharacteristic
154C2×C4×Q8C22×C15111yescharacteristic
155#431—21no—
156C2×#101—21no—
157C4×M16—21no—
158#400—21no—
159#400C4×C15111yescharacteristic
160#400C22×C15111yescharacteristic
161#398C4×C15111yescharacteristic
162#398C22×C15111yescharacteristic
163#395—21no—
164#387—21no—
165#387—21no—
166#383C4×C15111yescharacteristic
167#343C22×C15112yes—
168#324—21no—
169#324C22×C15112yes—
170C22×Q8D4×C15111yescharacteristic
171C2×M16—22no—
172#125—41no—
173#125—41no—
174C4×Q8—41no—
175C4×Q8—41no—
176C2×C4⋊C4—21no—
177C2×C4⋊C4—21no—
178C2×C4⋊C4—21no—
179C2×C4⋊C4—21no—
180C2×C4⋊C4C2×C4×C15111yescharacteristic
181C2×C4⋊C4C2×C4×C15111yescharacteristic
182C2×C4⋊C4C2×C4×C15111yescharacteristic
183C2×C4⋊C4D4×C15111yescharacteristic
184C2×C4⋊C4C23×C15111yescharacteristic
185C2×C42C2×C4×C15111yescharacteristic
186C2×C42D4×C15111yescharacteristic
187C2×C42D4×C15111yescharacteristic
188C4⋊C8—41no—
189#101—24no—
190C22⋊C8—22no—
191#97—41no—
192C4×C8—41no—
193C4×C8—41no—
194#95—21no—
195#95—21no—
196#95—21no—
197#95—21no—
198#95—21no—
199#95—21no—
200#95—21no—
201#95—21no—
202#95C2×C4×C15111yescharacteristic
203#95C2×C4×C15111yescharacteristic
204C2×Q8—22no—
205C2×Q8—22no—
206C2×Q8—41no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—21no—
211C22×C4C22⋊C4×C15111yescharacteristic
212C22×C4C22⋊C4×C15111yescharacteristic
213C22×C4C22⋊C4×C15111yescharacteristic
214C22×C4C22⋊C4×C15111yescharacteristic
215C22×C4C22×C4×C15111yescharacteristic
216C22×C4C2×D4×C15111yescharacteristic
217C22×C4C2×D4×C15111yescharacteristic
218M16—24no—
219M16—42no—
220C2×C8—42no—
221C2×C8—42no—
222C4⋊C4—41no—
223C4⋊C4—41no—
224C4⋊C4—41no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—41no—
229C4⋊C4—41no—
230C4⋊C4—42no—
231C4⋊C4—42no—
232C42—21no—
233C42—21no—
234C42—21no—
235C42—21no—
236C42—21no—
237C42—21no—
238C23C2×C22⋊C4×C15111yescharacteristic
239Q8—44no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—41no—
253C2×C4—41no—
254C2×C4—41no—
255C2×C4—41no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—41no—
263C2×C4—41no—
264C2×C4—41no—
265C2×C4#99×C15111yescharacteristic
266C2×C4#99×C15111yescharacteristic
267C2×C4#104×C15112yes—
268C2×C4#135×C15112yes—
269C8—44no—
270C8—82no—
271C22—21no—
272C22—21no—
273C22C2×#99×C15111yescharacteristic
274C22#416×C15111yescharacteristic
275C22C2×#104×C15111yescharacteristic
276C4—21no—
277C4—21no—
278C4—22no—
279C4—22no—
280C4—41no—
281C4—41no—
282C4—41no—
283C4—41no—
284C4—81no—
285C4—81no—
286C4—81no—
287C4—81no—
288C2—21no—
289C2—21no—
290C2#1501×C15111yescharacteristic
291C2#2123×C15111yescharacteristic
292C2#2133×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
146. #11740C151direct (N × H)
147. C151#11740direct (N × H)

Maximal subgroups

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

subgroupindex
#2634×C1512
C4×#101×C1512
#1461×C1512
#1353×C1512
#1346×C1512
#11740151