Finite Group Databasebeta

← C151×#7707 #50312632

Subgroups — C151×#7707 #50312632

Order 38656.

500 conjugacy classes of subgroups.

The subgroup lattice has 304 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2857×C151C211yesmaximal, characteristic
2#1817×C151C211yesmaximal, characteristic
3#1749×C151C211yesmaximal, characteristic
4#1272×C151C214yesmaximal, complemented
5C2×C4⋊Q8×C151C411yescharacteristic
6C2×C22⋊Q8×C151C412yes—
7C22×C42×C151C2211yescharacteristic
8C2×C22⋊C8×C151—21no—
9C2×C22⋊C8×C151—21no—
10C2×#97×C151—21no—
11#391×C151C2212yes—
12#389×C151—21no—
13#389×C151—21no—
14#384×C151C411yescharacteristic
15#380×C151—21no—
16#380×C151—21no—
17#336×C151—21no—
18#336×C151C2212yes—
19#336×C151C2212yes—
20C22×Q8×C151C2×C412yes—
21C23×C4×C151C2×C411yescharacteristic
22C23×C4×C151D411yescharacteristic
23C23×C4×C151D411yescharacteristic
24C22×C8×C151—22no—
25C22×C8×C151—22no—
26C4⋊Q8×C151—42no—
27C22⋊Q8×C151—44no—
28C2×C4⋊C4×C151—21no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—21no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—22no—
33C2×C4⋊C4×C151C2×C412yes—
34C2×C22⋊C4×C151—22no—
35C2×C42×C151—42no—
36C2×C42×C151C2×C411yescharacteristic
37C2×C42×C151D411yescharacteristic
38C2×C42×C151D411yescharacteristic
39C2×C42×C151C2311yescharacteristic
40C22⋊C8×C151—24no—
41C22⋊C8×C151—42no—
42#97×C151—42no—
43#95×C151—22no—
44#95×C151—22no—
45C24×C151C22⋊C411yescharacteristic
46C2×Q8×C151—24no—
47C2×Q8×C151—42no—
48C2×Q8×C151—42no—
49C22×C4×C151—22no—
50C22×C4×C151—22no—
51C22×C4×C151—22no—
52C22×C4×C151—22no—
53C22×C4×C151—22no—
54C22×C4×C151—22no—
55C22×C4×C151—22no—
56C22×C4×C151—22no—
57C22×C4×C151—41no—
58C22×C4×C151—41no—
59C22×C4×C151—41no—
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151C22⋊C411yescharacteristic
62C22×C4×C151C22⋊C411yescharacteristic
63C22×C4×C151C22×C411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66C2×C8×C151—24no—
67C2×C8×C151—42no—
68C2×C8×C151—42no—
69C2×C8×C151—42no—
70C2×C8×C151—42no—
71C2×C8×C151—42no—
72C4⋊C4×C151—42no—
73C4⋊C4×C151—42no—
74C4⋊C4×C151—44no—
75C4⋊C4×C151—42no—
76C4⋊C4×C151—42no—
77C4⋊C4×C151—42no—
78C22⋊C4×C151—44no—
79C42×C151—22no—
80C42×C151—22no—
81C42×C151—41no—
82C42×C151—41no—
83C23×C151—21no—
84C23×C151—21no—
85C23×C151—21no—
86C23×C151—21no—
87C23×C151—21no—
88C23×C151—21no—
89C23×C151#10012yes—
90C23×C151C2×C22⋊C411yescharacteristic
91Q8×C151—84no—
92C2×C4×C151—21no—
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—21no—
104C2×C4×C151—21no—
105C2×C4×C151—44no—
106C2×C4×C151—44no—
107C2×C4×C151—44no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151—42no—
111C2×C4×C151—42no—
112C2×C4×C151—42no—
113C2×C4×C151—42no—
114C2×C4×C151#9912yes—
115C2×C4×C151#10412yes—
116C2×C4×C151#13112yes—
117C2×C4×C151#13712yes—
118C2×C4×C151#13712yes—
119C8×C151—44no—
120C8×C151—82no—
121C22×C151—22no—
122C22×C151—22no—
123C22×C151—22no—
124C22×C151—41no—
125C22×C151—41no—
126C22×C151—41no—
127C22×C151—41no—
128C22×C151#40811yescharacteristic
129C22×C151C2×#9911yescharacteristic
130C22×C151C2×#10011yescharacteristic
131C22×C151#41911yescharacteristic
132C22×C151#41911yescharacteristic
133C22×C151C2×#10411yescharacteristic
134C22×C151#42111yescharacteristic
135C4×C151—22no—
136C4×C151—22no—
137C4×C151—22no—
138C4×C151—22no—
139C4×C151—22no—
140C4×C151—41no—
141C4×C151—82no—
142C4×C151—82no—
143C2×C151—42no—
144C2×C151#147111yescharacteristic
145C2×C151#148511yescharacteristic
146C2×C151#149711yescharacteristic
147C2×C151#150811yescharacteristic
148C2×C151#151111yescharacteristic
149C2×C151#153011yescharacteristic
150C2×C151#155811yescharacteristic
151#7707C15111yesmaximal, characteristic, direct product factor, Sylow
152C151#770711yescharacteristic, direct product factor, Sylow
153#2857C2×C15111yescharacteristic
154#1817C2×C15111yescharacteristic
155#1749C2×C15111yescharacteristic
156#1272C2×C15114yescomplemented
157C2×C4⋊Q8C4×C15111yescharacteristic
158C2×C22⋊Q8C4×C15112yes—
159C22×C42C22×C15111yescharacteristic
160C2×C22⋊C8—21no—
161C2×C22⋊C8—21no—
162C2×#97—21no—
163#391C22×C15112yes—
164#389—21no—
165#389—21no—
166#384C4×C15111yescharacteristic
167#380—21no—
168#380—21no—
169#336—21no—
170#336C22×C15112yes—
171#336C22×C15112yes—
172C22×Q8C2×C4×C15112yes—
173C23×C4C2×C4×C15111yescharacteristic
174C23×C4D4×C15111yescharacteristic
175C23×C4D4×C15111yescharacteristic
176C22×C8—22no—
177C22×C8—22no—
178C4⋊Q8—42no—
179C22⋊Q8—44no—
180C2×C4⋊C4—22no—
181C2×C4⋊C4—21no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—21no—
184C2×C4⋊C4—21no—
185C2×C4⋊C4C2×C4×C15112yes—
186C2×C22⋊C4—22no—
187C2×C42—42no—
188C2×C42C2×C4×C15111yescharacteristic
189C2×C42D4×C15111yescharacteristic
190C2×C42D4×C15111yescharacteristic
191C2×C42C23×C15111yescharacteristic
192C22⋊C8—24no—
193C22⋊C8—42no—
194#97—42no—
195#95—22no—
196#95—22no—
197C24C22⋊C4×C15111yescharacteristic
198C2×Q8—24no—
199C2×Q8—42no—
200C2×Q8—42no—
201C22×C4—22no—
202C22×C4—22no—
203C22×C4—22no—
204C22×C4—22no—
205C22×C4—22no—
206C22×C4—22no—
207C22×C4—22no—
208C22×C4—22no—
209C22×C4—41no—
210C22×C4—41no—
211C22×C4—41no—
212C22×C4C22⋊C4×C15111yescharacteristic
213C22×C4C22⋊C4×C15111yescharacteristic
214C22×C4C22⋊C4×C15111yescharacteristic
215C22×C4C22×C4×C15111yescharacteristic
216C22×C4C2×D4×C15111yescharacteristic
217C22×C4C2×D4×C15111yescharacteristic
218C2×C8—24no—
219C2×C8—42no—
220C2×C8—42no—
221C2×C8—42no—
222C2×C8—42no—
223C2×C8—42no—
224C4⋊C4—42no—
225C4⋊C4—44no—
226C4⋊C4—42no—
227C4⋊C4—42no—
228C4⋊C4—42no—
229C4⋊C4—42no—
230C22⋊C4—44no—
231C42—22no—
232C42—22no—
233C42—41no—
234C42—41no—
235C23—21no—
236C23—21no—
237C23—21no—
238C23—21no—
239C23—21no—
240C23—21no—
241C23#100×C15112yes—
242C23C2×C22⋊C4×C15111yescharacteristic
243Q8—84no—
244C2×C4—21no—
245C2×C4—21no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—21no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—44no—
258C2×C4—44no—
259C2×C4—44no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4#99×C15112yes—
267C2×C4#104×C15112yes—
268C2×C4#131×C15112yes—
269C2×C4#137×C15112yes—
270C2×C4#137×C15112yes—
271C8—44no—
272C8—82no—
273C22—22no—
274C22—22no—
275C22—22no—
276C22—41no—
277C22—41no—
278C22—41no—
279C22—41no—
280C22#408×C15111yescharacteristic
281C22C2×#99×C15111yescharacteristic
282C22C2×#100×C15111yescharacteristic
283C22#419×C15111yescharacteristic
284C22#419×C15111yescharacteristic
285C22C2×#104×C15111yescharacteristic
286C22#421×C15111yescharacteristic
287C4—22no—
288C4—22no—
289C4—22no—
290C4—22no—
291C4—22no—
292C4—41no—
293C4—82no—
294C4—82no—
295C2—42no—
296C2#1471×C15111yescharacteristic
297C2#1485×C15111yescharacteristic
298C2#1497×C15111yescharacteristic
299C2#1508×C15111yescharacteristic
300C2#1511×C15111yescharacteristic
301C2#1530×C15111yescharacteristic
302C2#1558×C15111yescharacteristic
subgroupG/H
center, socleC23×C151C2×C22⋊C4
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C22×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1272×C151C2semidirect
151. #7707C151direct (N × H)
152. C151#7707direct (N × H)
156. #1272C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2857×C1512
#1817×C1512
#1749×C1512
#1272×C1512
#7707151