Finite Group Databasebeta

← C151×#11889 #50316814

Subgroups — C151×#11889 #50316814

Order 38656.

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

normal subgroups only

This group has 412 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×#467×C151C211yesmaximal, characteristic
2#2112×C151C211yesmaximal, characteristic
3#1807×C151C211yesmaximal, characteristic
4#1348×C151C214yesmaximal, complemented
5C22×Q16×C151C411yescharacteristic, complemented
6C23×C8×C151C2211yescharacteristic
7C2×C22⋊Q8×C151—21no—
8C2×M32×C151—21no—
9#467×C151—21no—
10#467×C151—21no—
11#467×C151C412yescomplemented
12#467×C151C2212yes—
13C2×#107×C151C411yescharacteristic, complemented
14C2×#106×C151—21no—
15C2×#103×C151—21no—
16#380×C151—21no—
17C22⋊C16×C151—21no—
18C22⋊C16×C151C2212yes—
19#340×C151C2212yes—
20C22×Q8×C151—21no—
21C23×C4×C151D411yescharacteristic
22C2×Q16×C151—21no—
23C2×Q16×C151—42no—
24C2×Q16×C151C2×C412yes—
25C22×C8×C151—42no—
26C22×C8×C151C2×C411yescharacteristic
27C22×C8×C151C2×C411yescharacteristic
28C22×C8×C151D411yescharacteristic
29C22×C8×C151D411yescharacteristic
30C22×C8×C151D411yescharacteristic
31C22×C8×C151C2311yescharacteristic
32C22⋊Q8×C151—22no—
33C22⋊Q8×C151—22no—
34C22⋊Q8×C151—41no—
35C22⋊Q8×C151—41no—
36C2×C4⋊C4×C151—21no—
37C2×C4⋊C4×C151—22no—
38C2×C4⋊C4×C151—41no—
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#103×C151—22no—
47#103×C151—22no—
48#95×C151—41no—
49C24×C151D811yescharacteristic
50C2×Q8×C151—22no—
51C2×Q8×C151—42no—
52C2×Q8×C151—42no—
53C2×Q8×C151—41no—
54C22×C4×C151—41no—
55C22×C4×C151—41no—
56C22×C4×C151—41no—
57C22×C4×C151—41no—
58C22×C4×C151—42no—
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151D811yescharacteristic
62C22×C4×C151SD1611yescharacteristic
63C22×C4×C151SD1611yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65Q16×C151—42no—
66Q16×C151—42no—
67C2×C8×C151—22no—
68C2×C8×C151—22no—
69C2×C8×C151—22no—
70C2×C8×C151—41no—
71C2×C8×C151—41no—
72C2×C8×C151—41no—
73C2×C8×C151C22⋊C411yescharacteristic
74C2×C8×C151C22⋊C411yescharacteristic
75C2×C8×C151C22×C411yescharacteristic
76C2×C8×C151C2×D411yescharacteristic
77C4⋊C4×C151—22no—
78C4⋊C4×C151—42no—
79C4⋊C4×C151—42no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—42no—
82C4⋊C4×C151—42no—
83C22⋊C4×C151—42no—
84C22⋊C4×C151—42no—
85C22⋊C4×C151—82no—
86C16×C151—42no—
87C23×C151—22no—
88C23×C151—22no—
89C23×C151—41no—
90C23×C151#10211yescharacteristic
91C23×C151#10211yescharacteristic
92C23×C151C2×D811yescharacteristic
93Q8×C151—42no—
94Q8×C151—42no—
95Q8×C151—82no—
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—41no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—42no—
106C2×C4×C151—42no—
107C2×C4×C151—82no—
108C2×C4×C151—82no—
109C2×C4×C151—82no—
110C2×C4×C151—82no—
111C2×C4×C151—82no—
112C2×C4×C151#10211yescharacteristic
113C2×C4×C151#10211yescharacteristic
114C2×C4×C151C2×C22⋊C411yescharacteristic
115C2×C4×C151C2×SD1611yescharacteristic
116C8×C151—21no—
117C8×C151—21no—
118C8×C151—21no—
119C8×C151#9912yes—
120C22×C151—21no—
121C22×C151—21no—
122C22×C151—21no—
123C22×C151—21no—
124C22×C151—21no—
125C22×C151—21no—
126C22×C151—21no—
127C22×C151—44no—
128C22×C151#36012yes—
129C22×C151C2×#10211yescharacteristic
130C22×C151#51012yes—
131C4×C151—21no—
132C4×C151—21no—
133C4×C151—21no—
134C4×C151—82no—
135C4×C151—82no—
136C4×C151—162no—
137C4×C151C2×#9911yescharacteristic
138C4×C151#42111yescharacteristic
139C2×C151—22no—
140C2×C151—22no—
141C2×C151—41no—
142C2×C151#151911yescharacteristic
143C2×C151#214111yescharacteristic
144C2×C151C2×#36011yescharacteristic
145#11889C15111yesmaximal, characteristic, direct product factor, Sylow
146C151#1188911yescharacteristic, direct product factor, Sylow
147C2×#467C2×C15111yescharacteristic
148#2112C2×C15111yescharacteristic
149#1807C2×C15111yescharacteristic
150#1348C2×C15114yescomplemented
151C22×Q16C4×C15111yescharacteristic, complemented
152C23×C8C22×C15111yescharacteristic
153C2×C22⋊Q8—21no—
154C2×M32—21no—
155#467—21no—
156#467—21no—
157#467C4×C15112yescomplemented
158#467C22×C15112yes—
159C2×#107C4×C15111yescharacteristic, complemented
160C2×#106—21no—
161C2×#103—21no—
162#380—21no—
163C22⋊C16—21no—
164C22⋊C16C22×C15112yes—
165#340C22×C15112yes—
166C22×Q8—21no—
167C23×C4D4×C15111yescharacteristic
168C2×Q16—21no—
169C2×Q16—42no—
170C2×Q16C2×C4×C15112yes—
171C22×C8—42no—
172C22×C8C2×C4×C15111yescharacteristic
173C22×C8C2×C4×C15111yescharacteristic
174C22×C8D4×C15111yescharacteristic
175C22×C8D4×C15111yescharacteristic
176C22×C8D4×C15111yescharacteristic
177C22×C8C23×C15111yescharacteristic
178C22⋊Q8—22no—
179C22⋊Q8—22no—
180C22⋊Q8—41no—
181C22⋊Q8—41no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—41no—
185C2×C22⋊C4—41no—
186C2×C22⋊C4—41no—
187M32—42no—
188C2×C16—22no—
189#107—21no—
190#107C2×C4×C15112yes—
191#106—42no—
192#103—22no—
193#103—22no—
194#95—41no—
195C24D8×C15111yescharacteristic
196C2×Q8—22no—
197C2×Q8—42no—
198C2×Q8—42no—
199C2×Q8—41no—
200C22×C4—41no—
201C22×C4—41no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4—42no—
205C22×C4C22⋊C4×C15111yescharacteristic
206C22×C4C22⋊C4×C15111yescharacteristic
207C22×C4D8×C15111yescharacteristic
208C22×C4SD16×C15111yescharacteristic
209C22×C4SD16×C15111yescharacteristic
210C22×C4C2×D4×C15111yescharacteristic
211Q16—42no—
212Q16—42no—
213C2×C8—22no—
214C2×C8—22no—
215C2×C8—22no—
216C2×C8—41no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8C22⋊C4×C15111yescharacteristic
220C2×C8C22⋊C4×C15111yescharacteristic
221C2×C8C22×C4×C15111yescharacteristic
222C2×C8C2×D4×C15111yescharacteristic
223C4⋊C4—22no—
224C4⋊C4—42no—
225C4⋊C4—42no—
226C4⋊C4—41no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C22⋊C4—42no—
230C22⋊C4—42no—
231C22⋊C4—82no—
232C16—42no—
233C23—22no—
234C23—22no—
235C23—41no—
236C23#102×C15111yescharacteristic
237C23#102×C15111yescharacteristic
238C23C2×D8×C15111yescharacteristic
239Q8—42no—
240Q8—42no—
241Q8—82no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—41no—
249C2×C4—41no—
250C2×C4—41no—
251C2×C4—42no—
252C2×C4—42no—
253C2×C4—82no—
254C2×C4—82no—
255C2×C4—82no—
256C2×C4—82no—
257C2×C4—82no—
258C2×C4#102×C15111yescharacteristic
259C2×C4#102×C15111yescharacteristic
260C2×C4C2×C22⋊C4×C15111yescharacteristic
261C2×C4C2×SD16×C15111yescharacteristic
262C8—21no—
263C8—21no—
264C8—21no—
265C8#99×C15112yes—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—21no—
273C22—44no—
274C22#360×C15112yes—
275C22C2×#102×C15111yescharacteristic
276C22#510×C15112yes—
277C4—21no—
278C4—21no—
279C4—21no—
280C4—82no—
281C4—82no—
282C4—162no—
283C4C2×#99×C15111yescharacteristic
284C4#421×C15111yescharacteristic
285C2—22no—
286C2—22no—
287C2—41no—
288C2#1519×C15111yescharacteristic
289C2#2141×C15111yescharacteristic
290C2C2×#360×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radicalC24×C151D8
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
4. #1348×C151C2semidirect
5. C22×Q16×C151C4semidirect
11. #467×C151C4semidirect
13. C2×#107×C151C4semidirect
145. #11889C151direct (N × H)
146. C151#11889direct (N × H)
150. #1348C2×C151semidirect
151. C22×Q16C4×C151semidirect
157. #467C4×C151semidirect
159. C2×#107C4×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#467×C1512
#2112×C1512
#1807×C1512
#1348×C1512
#11889151