Finite Group Databasebeta

← C151×#11888 #50316813

Subgroups — C151×#11888 #50316813

Order 38656.

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

normal subgroups only

This group has 464 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
2#2112×C151C211yesmaximal, characteristic, complemented
3#1807×C151C211yesmaximal, characteristic, complemented
4#1347×C151C214yesmaximal, complemented
5C22×D8×C151C411yescharacteristic, complemented
6C23×C8×C151C2211yescharacteristic
7C2×#121×C151—21no—
8C2×M32×C151—21no—
9#466×C151—21no—
10#466×C151—21no—
11#466×C151C412yescomplemented
12#466×C151C2212yes—
13C2×#107×C151C411yescharacteristic, complemented
14C2×#106×C151—21no—
15C2×#102×C151—21no—
16#380×C151—21no—
17C22⋊C16×C151—21no—
18C22⋊C16×C151C2212yescomplemented
19#340×C151C2212yescomplemented
20C22×D4×C151—21no—
21C22×D4×C151—41no—
22C23×C4×C151D411yescharacteristic
23C2×D8×C151—21no—
24C2×D8×C151—42no—
25C2×D8×C151C2×C412yes—
26C22×C8×C151—42no—
27C22×C8×C151C2×C411yescharacteristic
28C22×C8×C151C2×C411yescharacteristic
29C22×C8×C151D411yescharacteristic
30C22×C8×C151D411yescharacteristic
31C22×C8×C151D411yescharacteristic
32C22×C8×C151C2311yescharacteristic
33#121×C151—22no—
34#121×C151—22no—
35#121×C151—41no—
36#121×C151—41no—
37C2×C4⋊C4×C151—21no—
38C2×C4⋊C4×C151—22no—
39C2×C22⋊C4×C151—41no—
40C2×C22⋊C4×C151—41no—
41M32×C151—42no—
42C2×C16×C151—22no—
43#107×C151—21no—
44#107×C151C2×C412yes—
45#106×C151—42no—
46#102×C151—22no—
47#102×C151—22no—
48#95×C151—41no—
49C24×C151—41no—
50C24×C151D811yescharacteristic
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×C151—42no—
62C22×C4×C151C22⋊C411yescharacteristic
63C22×C4×C151C22⋊C411yescharacteristic
64C22×C4×C151D811yescharacteristic
65C22×C4×C151SD1611yescharacteristic
66C22×C4×C151SD1611yescharacteristic
67C22×C4×C151C2×D411yescharacteristic
68D8×C151—42no—
69D8×C151—42no—
70C2×C8×C151—22no—
71C2×C8×C151—22no—
72C2×C8×C151—22no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C2×C8×C151C22⋊C411yescharacteristic
77C2×C8×C151C22⋊C411yescharacteristic
78C2×C8×C151C22×C411yescharacteristic
79C2×C8×C151C2×D411yescharacteristic
80C4⋊C4×C151—22no—
81C4⋊C4×C151—42no—
82C4⋊C4×C151—42no—
83C4⋊C4×C151—41no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—42no—
86C22⋊C4×C151—82no—
87C16×C151—42no—
88C23×C151—22no—
89C23×C151—22no—
90C23×C151—41no—
91C23×C151—42no—
92C23×C151—82no—
93C23×C151—82no—
94C23×C151—82no—
95C23×C151#10211yescharacteristic
96C23×C151#10211yescharacteristic
97C23×C151C2×D811yescharacteristic
98D4×C151—42no—
99D4×C151—42no—
100D4×C151—82no—
101D4×C151—84no—
102D4×C151—84no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—21no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—41no—
110C2×C4×C151—41no—
111C2×C4×C151—41no—
112C2×C4×C151—42no—
113C2×C4×C151—82no—
114C2×C4×C151—82no—
115C2×C4×C151—82no—
116C2×C4×C151—82no—
117C2×C4×C151#10211yescharacteristic
118C2×C4×C151#10211yescharacteristic
119C2×C4×C151C2×C22⋊C411yescharacteristic
120C2×C4×C151C2×SD1611yescharacteristic
121C8×C151—21no—
122C8×C151—21no—
123C8×C151—21no—
124C8×C151#9912yes—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—44no—
133C22×C151—82no—
134C22×C151—82no—
135C22×C151—82no—
136C22×C151—164no—
137C22×C151#36012yes—
138C22×C151C2×#10211yescharacteristic
139C22×C151#50912yes—
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—21no—
143C4×C151—82no—
144C4×C151—162no—
145C4×C151C2×#9911yescharacteristic
146C4×C151#42111yescharacteristic
147C2×C151—22no—
148C2×C151—22no—
149C2×C151—41no—
150C2×C151—162no—
151C2×C151#151911yescharacteristic
152C2×C151#214011yescharacteristic
153C2×C151C2×#36011yescharacteristic
154#11888C15111yesmaximal, characteristic, direct product factor, Sylow
155C151#1188811yescharacteristic, direct product factor, Sylow
156C2×#466C2×C15111yescharacteristic
157#2112C2×C15111yescharacteristic, complemented
158#1807C2×C15111yescharacteristic, complemented
159#1347C2×C15114yescomplemented
160C22×D8C4×C15111yescharacteristic, complemented
161C23×C8C22×C15111yescharacteristic
162C2×#121—21no—
163C2×M32—21no—
164#466—21no—
165#466—21no—
166#466C4×C15112yescomplemented
167#466C22×C15112yes—
168C2×#107C4×C15111yescharacteristic, complemented
169C2×#106—21no—
170C2×#102—21no—
171#380—21no—
172C22⋊C16—21no—
173C22⋊C16C22×C15112yescomplemented
174#340C22×C15112yescomplemented
175C22×D4—21no—
176C22×D4—41no—
177C23×C4D4×C15111yescharacteristic
178C2×D8—21no—
179C2×D8—42no—
180C2×D8C2×C4×C15112yes—
181C22×C8—42no—
182C22×C8C2×C4×C15111yescharacteristic
183C22×C8C2×C4×C15111yescharacteristic
184C22×C8D4×C15111yescharacteristic
185C22×C8D4×C15111yescharacteristic
186C22×C8D4×C15111yescharacteristic
187C22×C8C23×C15111yescharacteristic
188#121—22no—
189#121—22no—
190#121—41no—
191#121—41no—
192C2×C4⋊C4—21no—
193C2×C4⋊C4—22no—
194C2×C22⋊C4—41no—
195C2×C22⋊C4—41no—
196M32—42no—
197C2×C16—22no—
198#107—21no—
199#107C2×C4×C15112yes—
200#106—42no—
201#102—22no—
202#102—22no—
203#95—41no—
204C24—41no—
205C24D8×C15111yescharacteristic
206C2×D4—22no—
207C2×D4—42no—
208C2×D4—42no—
209C2×D4—42no—
210C2×D4—42no—
211C2×D4—41no—
212C2×D4—84no—
213C22×C4—41no—
214C22×C4—41no—
215C22×C4—41no—
216C22×C4—42no—
217C22×C4C22⋊C4×C15111yescharacteristic
218C22×C4C22⋊C4×C15111yescharacteristic
219C22×C4D8×C15111yescharacteristic
220C22×C4SD16×C15111yescharacteristic
221C22×C4SD16×C15111yescharacteristic
222C22×C4C2×D4×C15111yescharacteristic
223D8—42no—
224D8—42no—
225C2×C8—22no—
226C2×C8—22no—
227C2×C8—22no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8C22⋊C4×C15111yescharacteristic
232C2×C8C22⋊C4×C15111yescharacteristic
233C2×C8C22×C4×C15111yescharacteristic
234C2×C8C2×D4×C15111yescharacteristic
235C4⋊C4—22no—
236C4⋊C4—42no—
237C4⋊C4—42no—
238C4⋊C4—41no—
239C22⋊C4—42no—
240C22⋊C4—42no—
241C22⋊C4—82no—
242C16—42no—
243C23—22no—
244C23—22no—
245C23—41no—
246C23—42no—
247C23—82no—
248C23—82no—
249C23—82no—
250C23#102×C15111yescharacteristic
251C23#102×C15111yescharacteristic
252C23C2×D8×C15111yescharacteristic
253D4—42no—
254D4—42no—
255D4—82no—
256D4—84no—
257D4—84no—
258C2×C4—21no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—41no—
265C2×C4—41no—
266C2×C4—41no—
267C2×C4—42no—
268C2×C4—82no—
269C2×C4—82no—
270C2×C4—82no—
271C2×C4—82no—
272C2×C4#102×C15111yescharacteristic
273C2×C4#102×C15111yescharacteristic
274C2×C4C2×C22⋊C4×C15111yescharacteristic
275C2×C4C2×SD16×C15111yescharacteristic
276C8—21no—
277C8—21no—
278C8—21no—
279C8#99×C15112yes—
280C22—21no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22—44no—
288C22—82no—
289C22—82no—
290C22—82no—
291C22—164no—
292C22#360×C15112yes—
293C22C2×#102×C15111yescharacteristic
294C22#509×C15112yes—
295C4—21no—
296C4—21no—
297C4—21no—
298C4—82no—
299C4—162no—
300C4C2×#99×C15111yescharacteristic
301C4#421×C15111yescharacteristic
302C2—22no—
303C2—22no—
304C2—41no—
305C2—162no—
306C2#1519×C15111yescharacteristic
307C2#2140×C15111yescharacteristic
308C2C2×#360×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. #2112×C151C2semidirect
3. #1807×C151C2semidirect
4. #1347×C151C2semidirect
5. C22×D8×C151C4semidirect
11. #466×C151C4semidirect
13. C2×#107×C151C4semidirect
18. C22⋊C16×C151C22semidirect
19. #340×C151C22semidirect
154. #11888C151direct (N × H)
155. C151#11888direct (N × H)
157. #2112C2×C151semidirect
158. #1807C2×C151semidirect
159. #1347C2×C151semidirect
160. C22×D8C4×C151semidirect
166. #466C4×C151semidirect
168. C2×#107C4×C151semidirect
173. C22⋊C16C22×C151semidirect
174. #340C22×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#466×C1512
#2112×C1512
#1807×C1512
#1347×C1512
#11888151