Finite Group Databasebeta

← C151×#11712 #50316637

Subgroups — C151×#11712 #50316637

Order 38656.

440 conjugacy classes of subgroups.

The subgroup lattice has 290 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#467×C151C211yesmaximal, characteristic
2#2112×C151C211yesmaximal, characteristic
3C2×#341×C151C211yesmaximal, characteristic
4#1350×C151C214yesmaximal, complemented
5C22×Q16×C151C411yescharacteristic
6C22×M16×C151—21no—
7C23×C8×C151C2211yescharacteristic
8C2×C22⋊Q8×C151—21no—
9C2×M32×C151—21no—
10#467×C151—21no—
11#467×C151—21no—
12#467×C151C412yes—
13#467×C151C2212yes—
14C2×#107×C151C411yescharacteristic
15C2×#103×C151—21no—
16C22⋊C16×C151—21no—
17C22⋊C16×C151C2212yes—
18#341×C151—21no—
19#341×C151C2212yes—
20C22×Q8×C151—21no—
21C23×C4×C151D411yescharacteristic
22C2×Q16×C151—21no—
23C2×Q16×C151—42no—
24C2×Q16×C151C2×C412yes—
25C2×M16×C151—24no—
26C2×M16×C151—22no—
27C2×M16×C151—42no—
28C2×M16×C151—41no—
29C22×C8×C151—42no—
30C22×C8×C151—41no—
31C22×C8×C151C2×C411yescharacteristic
32C22×C8×C151C2×C411yescharacteristic
33C22×C8×C151D411yescharacteristic
34C22×C8×C151D411yescharacteristic
35C22×C8×C151D411yescharacteristic
36C22×C8×C151C2311yescharacteristic
37C22⋊Q8×C151—22no—
38C22⋊Q8×C151—22no—
39C22⋊Q8×C151—41no—
40C22⋊Q8×C151—41no—
41C2×C4⋊C4×C151—21no—
42C2×C4⋊C4×C151—41no—
43C2×C22⋊C4×C151—41no—
44M32×C151—42no—
45C2×C16×C151—22no—
46#107×C151—21no—
47#107×C151C2×C412yes—
48#103×C151—22no—
49#103×C151—22no—
50C24×C151SD1611yescharacteristic
51C2×Q8×C151—22no—
52C2×Q8×C151—41no—
53C2×Q8×C151—42no—
54C2×Q8×C151—42no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—41no—
58C22×C4×C151—41no—
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151D811yescharacteristic
62C22×C4×C151D811yescharacteristic
63C22×C4×C151SD1611yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65Q16×C151—42no—
66Q16×C151—42no—
67M16×C151—24no—
68M16×C151—44no—
69M16×C151—42no—
70C2×C8×C151—22no—
71C2×C8×C151—22no—
72C2×C8×C151—41no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151—41no—
76C2×C8×C151—44no—
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—
84C4⋊C4×C151—42no—
85C4⋊C4×C151—42no—
86C22⋊C4×C151—42no—
87C22⋊C4×C151—42no—
88C16×C151—42no—
89C23×C151—22no—
90C23×C151—22no—
91C23×C151—41no—
92C23×C151#10211yescharacteristic
93C23×C151#10211yescharacteristic
94C23×C151C2×SD1611yescharacteristic
95Q8×C151—42no—
96Q8×C151—42no—
97Q8×C151—82no—
98C2×C4×C151—22no—
99C2×C4×C151—22no—
100C2×C4×C151—22no—
101C2×C4×C151—21no—
102C2×C4×C151—21no—
103C2×C4×C151—21no—
104C2×C4×C151—21no—
105C2×C4×C151—42no—
106C2×C4×C151—42no—
107C2×C4×C151—82no—
108C2×C4×C151—82no—
109C2×C4×C151#9912yes—
110C2×C4×C151#10211yescharacteristic
111C2×C4×C151#10211yescharacteristic
112C2×C4×C151#10412yes—
113C2×C4×C151C2×C22⋊C411yescharacteristic
114C2×C4×C151C2×D811yescharacteristic
115C8×C151—21no—
116C8×C151—21no—
117C8×C151—21no—
118C8×C151—21no—
119C8×C151—44no—
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#32712yes—
129C22×C151#36212yes—
130C22×C151C2×#10211yescharacteristic
131C4×C151—21no—
132C4×C151—21no—
133C4×C151—82no—
134C4×C151—82no—
135C4×C151#32712yes—
136C4×C151C2×#9911yescharacteristic
137C4×C151C2×#10411yescharacteristic
138C2×C151—22no—
139C2×C151—22no—
140C2×C151—41no—
141C2×C151C2×#32711yescharacteristic
142C2×C151#214311yescharacteristic
143C2×C151C2×#36211yescharacteristic
144#11712C15111yesmaximal, characteristic, direct product factor, Sylow
145C151#1171211yescharacteristic, direct product factor, Sylow
146C2×#467C2×C15111yescharacteristic
147#2112C2×C15111yescharacteristic
148C2×#341C2×C15111yescharacteristic
149#1350C2×C15114yescomplemented
150C22×Q16C4×C15111yescharacteristic
151C22×M16—21no—
152C23×C8C22×C15111yescharacteristic
153C2×C22⋊Q8—21no—
154C2×M32—21no—
155#467—21no—
156#467—21no—
157#467C4×C15112yes—
158#467C22×C15112yes—
159C2×#107C4×C15111yescharacteristic
160C2×#103—21no—
161C22⋊C16—21no—
162C22⋊C16C22×C15112yes—
163#341—21no—
164#341C22×C15112yes—
165C22×Q8—21no—
166C23×C4D4×C15111yescharacteristic
167C2×Q16—21no—
168C2×Q16—42no—
169C2×Q16C2×C4×C15112yes—
170C2×M16—24no—
171C2×M16—22no—
172C2×M16—42no—
173C2×M16—41no—
174C22×C8—42no—
175C22×C8—41no—
176C22×C8C2×C4×C15111yescharacteristic
177C22×C8C2×C4×C15111yescharacteristic
178C22×C8D4×C15111yescharacteristic
179C22×C8D4×C15111yescharacteristic
180C22×C8D4×C15111yescharacteristic
181C22×C8C23×C15111yescharacteristic
182C22⋊Q8—22no—
183C22⋊Q8—22no—
184C22⋊Q8—41no—
185C22⋊Q8—41no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—41no—
188C2×C22⋊C4—41no—
189M32—42no—
190C2×C16—22no—
191#107—21no—
192#107C2×C4×C15112yes—
193#103—22no—
194#103—22no—
195C24SD16×C15111yescharacteristic
196C2×Q8—22no—
197C2×Q8—41no—
198C2×Q8—42no—
199C2×Q8—42no—
200C22×C4—22no—
201C22×C4—22no—
202C22×C4—41no—
203C22×C4—41no—
204C22×C4C22⋊C4×C15111yescharacteristic
205C22×C4C22⋊C4×C15111yescharacteristic
206C22×C4D8×C15111yescharacteristic
207C22×C4D8×C15111yescharacteristic
208C22×C4SD16×C15111yescharacteristic
209C22×C4C2×D4×C15111yescharacteristic
210Q16—42no—
211Q16—42no—
212M16—24no—
213M16—44no—
214M16—42no—
215C2×C8—22no—
216C2×C8—22no—
217C2×C8—41no—
218C2×C8—41no—
219C2×C8—41no—
220C2×C8—41no—
221C2×C8—44no—
222C2×C8—42no—
223C2×C8C22⋊C4×C15111yescharacteristic
224C2×C8C22⋊C4×C15111yescharacteristic
225C2×C8C22×C4×C15111yescharacteristic
226C2×C8C2×D4×C15111yescharacteristic
227C4⋊C4—22no—
228C4⋊C4—41no—
229C4⋊C4—42no—
230C4⋊C4—42no—
231C22⋊C4—42no—
232C22⋊C4—42no—
233C16—42no—
234C23—22no—
235C23—22no—
236C23—41no—
237C23#102×C15111yescharacteristic
238C23#102×C15111yescharacteristic
239C23C2×SD16×C15111yescharacteristic
240Q8—42no—
241Q8—42no—
242Q8—82no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—22no—
249C2×C4—22no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—82no—
253C2×C4—82no—
254C2×C4#99×C15112yes—
255C2×C4#102×C15111yescharacteristic
256C2×C4#102×C15111yescharacteristic
257C2×C4#104×C15112yes—
258C2×C4C2×C22⋊C4×C15111yescharacteristic
259C2×C4C2×D8×C15111yescharacteristic
260C8—21no—
261C8—21no—
262C8—21no—
263C8—21no—
264C8—44no—
265C22—21no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—21no—
271C22—21no—
272C22—44no—
273C22#327×C15112yes—
274C22#362×C15112yes—
275C22C2×#102×C15111yescharacteristic
276C4—21no—
277C4—21no—
278C4—82no—
279C4—82no—
280C4#327×C15112yes—
281C4C2×#99×C15111yescharacteristic
282C4C2×#104×C15111yescharacteristic
283C2—22no—
284C2—22no—
285C2—41no—
286C2C2×#327×C15111yescharacteristic
287C2#2143×C15111yescharacteristic
288C2C2×#362×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC22×C8C23×C151
prime radicalC24×C151SD16
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. #1350×C151C2semidirect
144. #11712C151direct (N × H)
145. C151#11712direct (N × H)
149. #1350C2×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
C2×#341×C1512
#1350×C1512
#11712151