Finite Group Databasebeta

← C151×#11891 #50316816

Subgroups — C151×#11891 #50316816

Order 38656.

448 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 448 conjugacy classes of subgroups — too many to draw. Only its 122 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
1C2×#466×C151C211yesmaximal, characteristic
2C2×C22⋊C16×C151C211yesmaximal, characteristic, complemented
3#1810×C151C211yesmaximal, characteristic, complemented
4#1349×C151C214yesmaximal, complemented
5C22×D8×C151C411yescharacteristic
6C23×C8×C151C2211yescharacteristic
7C2×#121×C151—21no—
8C22×C16×C151—21no—
9#466×C151—21no—
10#466×C151—21no—
11#466×C151C412yes—
12#466×C151C2212yes—
13C2×#108×C151—21no—
14C2×#107×C151C411yescharacteristic
15C2×#102×C151—21no—
16#407×C151—21no—
17C22⋊C16×C151—21no—
18C22⋊C16×C151C2212yescomplemented
19#341×C151C2212yescomplemented
20C22×D4×C151—21no—
21C22×D4×C151—41no—
22C23×C4×C151D411yescharacteristic
23C2×D8×C151—21no—
24C2×D8×C151—42no—
25C2×D8×C151C2×C412yes—
26C2×M16×C151—22no—
27C22×C8×C151—42no—
28C22×C8×C151C2×C411yescharacteristic
29C22×C8×C151C2×C411yescharacteristic
30C22×C8×C151D411yescharacteristic
31C22×C8×C151D411yescharacteristic
32C22×C8×C151D411yescharacteristic
33C22×C8×C151C2311yescharacteristic
34#121×C151—22no—
35#121×C151—22no—
36#121×C151—41no—
37#121×C151—41no—
38C2×C4⋊C4×C151—21no—
39C2×C22⋊C4×C151—41no—
40C2×C16×C151—22no—
41C2×C16×C151—42no—
42#108×C151—42no—
43#107×C151—21no—
44#107×C151C2×C412yes—
45#102×C151—22no—
46#102×C151—22no—
47C22⋊C8×C151—41no—
48C22⋊C8×C151—41no—
49C24×C151—41no—
50C24×C151SD1611yescharacteristic
51C2×D4×C151—22no—
52C2×D4×C151—42no—
53C2×D4×C151—42no—
54C2×D4×C151—42no—
55C2×D4×C151—42no—
56C2×D4×C151—41no—
57C2×D4×C151—84no—
58C22×C4×C151—41no—
59C22×C4×C151—41no—
60C22×C4×C151—41no—
61C22×C4×C151C22⋊C411yescharacteristic
62C22×C4×C151C22⋊C411yescharacteristic
63C22×C4×C151D811yescharacteristic
64C22×C4×C151D811yescharacteristic
65C22×C4×C151SD1611yescharacteristic
66C22×C4×C151C2×D411yescharacteristic
67D8×C151—42no—
68D8×C151—42no—
69M16×C151—42no—
70M16×C151—42no—
71C2×C8×C151—22no—
72C2×C8×C151—22no—
73C2×C8×C151—22no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C2×C8×C151—41no—
77C2×C8×C151—42no—
78C2×C8×C151C22⋊C411yescharacteristic
79C2×C8×C151C22⋊C411yescharacteristic
80C2×C8×C151C22×C411yescharacteristic
81C2×C8×C151C2×D411yescharacteristic
82C4⋊C4×C151—22no—
83C4⋊C4×C151—41no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C16×C151—42no—
87C23×C151—22no—
88C23×C151—22no—
89C23×C151—41no—
90C23×C151—42no—
91C23×C151—82no—
92C23×C151—82no—
93C23×C151—82no—
94C23×C151#10211yescharacteristic
95C23×C151#10211yescharacteristic
96C23×C151C2×SD1611yescharacteristic
97D4×C151—42no—
98D4×C151—42no—
99D4×C151—82no—
100D4×C151—84no—
101D4×C151—84no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—41no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—42no—
112C2×C4×C151—82no—
113C2×C4×C151#10211yescharacteristic
114C2×C4×C151#10211yescharacteristic
115C2×C4×C151C2×C22⋊C411yescharacteristic
116C2×C4×C151C2×D811yescharacteristic
117C8×C151—21no—
118C8×C151—21no—
119C8×C151—21no—
120C8×C151—82no—
121C8×C151#9912yes—
122C22×C151—21no—
123C22×C151—21no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—44no—
130C22×C151—82no—
131C22×C151—82no—
132C22×C151—82no—
133C22×C151—164no—
134C22×C151#35912yes—
135C22×C151#36112yes—
136C22×C151C2×#10211yescharacteristic
137C4×C151—21no—
138C4×C151—21no—
139C4×C151—21no—
140C4×C151—82no—
141C4×C151C2×#9911yescharacteristic
142C4×C151#42111yescharacteristic
143C2×C151—22no—
144C2×C151—22no—
145C2×C151—41no—
146C2×C151—162no—
147C2×C151#151911yescharacteristic
148C2×C151C2×#35911yescharacteristic
149C2×C151C2×#36111yescharacteristic
150#11891C15111yesmaximal, characteristic, direct product factor, Sylow
151C151#1189111yescharacteristic, direct product factor, Sylow
152C2×#466C2×C15111yescharacteristic
153C2×C22⋊C16C2×C15111yescharacteristic, complemented
154#1810C2×C15111yescharacteristic, complemented
155#1349C2×C15114yescomplemented
156C22×D8C4×C15111yescharacteristic
157C23×C8C22×C15111yescharacteristic
158C2×#121—21no—
159C22×C16—21no—
160#466—21no—
161#466—21no—
162#466C4×C15112yes—
163#466C22×C15112yes—
164C2×#108—21no—
165C2×#107C4×C15111yescharacteristic
166C2×#102—21no—
167#407—21no—
168C22⋊C16—21no—
169C22⋊C16C22×C15112yescomplemented
170#341C22×C15112yescomplemented
171C22×D4—21no—
172C22×D4—41no—
173C23×C4D4×C15111yescharacteristic
174C2×D8—21no—
175C2×D8—42no—
176C2×D8C2×C4×C15112yes—
177C2×M16—22no—
178C22×C8—42no—
179C22×C8C2×C4×C15111yescharacteristic
180C22×C8C2×C4×C15111yescharacteristic
181C22×C8D4×C15111yescharacteristic
182C22×C8D4×C15111yescharacteristic
183C22×C8D4×C15111yescharacteristic
184C22×C8C23×C15111yescharacteristic
185#121—22no—
186#121—22no—
187#121—41no—
188#121—41no—
189C2×C4⋊C4—21no—
190C2×C22⋊C4—41no—
191C2×C16—22no—
192C2×C16—42no—
193#108—42no—
194#107—21no—
195#107C2×C4×C15112yes—
196#102—22no—
197#102—22no—
198C22⋊C8—41no—
199C22⋊C8—41no—
200C24—41no—
201C24SD16×C15111yescharacteristic
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—42no—
206C2×D4—42no—
207C2×D4—41no—
208C2×D4—84no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C22⋊C4×C15111yescharacteristic
213C22×C4C22⋊C4×C15111yescharacteristic
214C22×C4D8×C15111yescharacteristic
215C22×C4D8×C15111yescharacteristic
216C22×C4SD16×C15111yescharacteristic
217C22×C4C2×D4×C15111yescharacteristic
218D8—42no—
219D8—42no—
220M16—42no—
221M16—42no—
222C2×C8—22no—
223C2×C8—22no—
224C2×C8—22no—
225C2×C8—41no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8—42no—
229C2×C8C22⋊C4×C15111yescharacteristic
230C2×C8C22⋊C4×C15111yescharacteristic
231C2×C8C22×C4×C15111yescharacteristic
232C2×C8C2×D4×C15111yescharacteristic
233C4⋊C4—22no—
234C4⋊C4—41no—
235C22⋊C4—42no—
236C22⋊C4—42no—
237C16—42no—
238C23—22no—
239C23—22no—
240C23—41no—
241C23—42no—
242C23—82no—
243C23—82no—
244C23—82no—
245C23#102×C15111yescharacteristic
246C23#102×C15111yescharacteristic
247C23C2×SD16×C15111yescharacteristic
248D4—42no—
249D4—42no—
250D4—82no—
251D4—84no—
252D4—84no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—41no—
262C2×C4—42no—
263C2×C4—82no—
264C2×C4#102×C15111yescharacteristic
265C2×C4#102×C15111yescharacteristic
266C2×C4C2×C22⋊C4×C15111yescharacteristic
267C2×C4C2×D8×C15111yescharacteristic
268C8—21no—
269C8—21no—
270C8—21no—
271C8—82no—
272C8#99×C15112yes—
273C22—21no—
274C22—21no—
275C22—21no—
276C22—21no—
277C22—21no—
278C22—21no—
279C22—21no—
280C22—44no—
281C22—82no—
282C22—82no—
283C22—82no—
284C22—164no—
285C22#359×C15112yes—
286C22#361×C15112yes—
287C22C2×#102×C15111yescharacteristic
288C4—21no—
289C4—21no—
290C4—21no—
291C4—82no—
292C4C2×#99×C15111yescharacteristic
293C4#421×C15111yescharacteristic
294C2—22no—
295C2—22no—
296C2—41no—
297C2—162no—
298C2#1519×C15111yescharacteristic
299C2C2×#359×C15111yescharacteristic
300C2C2×#361×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radicalC2×#466×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C23×C4×C151 ◁ C23×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊C16×C151C2semidirect
3. #1810×C151C2semidirect
4. #1349×C151C2semidirect
18. C22⋊C16×C151C22semidirect
19. #341×C151C22semidirect
150. #11891C151direct (N × H)
151. C151#11891direct (N × H)
153. C2×C22⋊C16C2×C151semidirect
154. #1810C2×C151semidirect
155. #1349C2×C151semidirect
169. C22⋊C16C22×C151semidirect
170. #341C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1512
C2×C22⋊C16×C1512
#1810×C1512
#1349×C1512
#11891151