Finite Group Databasebeta

← C151×#11883 #50316808

Subgroups — C151×#11883 #50316808

Order 38656.

408 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 118 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
1#2546×C151C211yesmaximal, characteristic
2#1801×C151C211yesmaximal, characteristic
3#1461×C151C211yesmaximal, characteristic
4#1346×C151C214yesmaximal
5C2×C4⋊Q8×C151—21no—
6C2×C4⋊Q8×C151C411yescharacteristic
7C2×C4×Q8×C151C2211yescharacteristic
8#431×C151—21no—
9#423×C151—21no—
10C2×#101×C151—21no—
11#398×C151C412yes—
12#398×C151C2212yes—
13#391×C151—21no—
14#389×C151—21no—
15#389×C151—21no—
16C4×C4⋊C4×C151C411yescharacteristic
17#343×C151C2212yes—
18#324×C151—21no—
19#324×C151C2212yes—
20C22×Q8×C151—21no—
21C22×Q8×C151D411yescharacteristic
22C2×M16×C151—22no—
23C4⋊Q8×C151—41no—
24C4⋊Q8×C151—41no—
25C4⋊Q8×C151—42no—
26C4⋊Q8×C151—42no—
27C4×Q8×C151—41no—
28C4×Q8×C151—41no—
29C2×C4⋊C4×C151—21no—
30C2×C4⋊C4×C151—22no—
31C2×C4⋊C4×C151—21no—
32C2×C4⋊C4×C151—22no—
33C2×C4⋊C4×C151C2×C412yes—
34C2×C4⋊C4×C151C2×C411yescharacteristic
35C2×C4⋊C4×C151D411yescharacteristic
36C2×C4⋊C4×C151C2311yescharacteristic
37C2×C42×C151—21no—
38C2×C42×C151C2×C411yescharacteristic
39C2×C42×C151D411yescharacteristic
40C2×C42×C151D411yescharacteristic
41C4⋊C8×C151—41no—
42C4⋊C8×C151—41no—
43C4⋊C8×C151—41no—
44#101×C151—42no—
45C22⋊C8×C151—22no—
46C4×C8×C151—41no—
47#95×C151—22no—
48#95×C151—22no—
49#95×C151C2×C412yes—
50C2×Q8×C151—41no—
51C2×Q8×C151—41no—
52C2×Q8×C151—42no—
53C2×Q8×C151—42no—
54C2×Q8×C151—42no—
55C2×Q8×C151D812yes—
56C2×Q8×C151SD1612yes—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151C22⋊C411yescharacteristic
60C22×C4×C151C22⋊C411yescharacteristic
61C22×C4×C151C22⋊C411yescharacteristic
62C22×C4×C151C22⋊C411yescharacteristic
63C22×C4×C151C22×C411yescharacteristic
64C22×C4×C151C2×D411yescharacteristic
65C22×C4×C151C2×D411yescharacteristic
66M16×C151—42no—
67M16×C151—42no—
68C2×C8×C151—42no—
69C2×C8×C151—42no—
70C4⋊C4×C151—24no—
71C4⋊C4×C151—41no—
72C4⋊C4×C151—41no—
73C4⋊C4×C151—41no—
74C4⋊C4×C151—42no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151—41no—
77C4⋊C4×C151—44no—
78C4⋊C4×C151—42no—
79C4⋊C4×C151—42no—
80C42×C151—21no—
81C42×C151—21no—
82C42×C151—21no—
83C42×C151—21no—
84C42×C151—21no—
85C42×C151—21no—
86C42×C151—42no—
87C23×C151C2×C22⋊C411yescharacteristic
88Q8×C151—42no—
89Q8×C151—42no—
90Q8×C151—84no—
91C2×C4×C151—21no—
92C2×C4×C151—21no—
93C2×C4×C151—21no—
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—21no—
97C2×C4×C151—22no—
98C2×C4×C151—24no—
99C2×C4×C151—21no—
100C2×C4×C151—21no—
101C2×C4×C151—21no—
102C2×C4×C151—42no—
103C2×C4×C151—42no—
104C2×C4×C151—41no—
105C2×C4×C151—41no—
106C2×C4×C151—41no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151#9911yescharacteristic
111C2×C4×C151#9911yescharacteristic
112C2×C4×C151#10212yes—
113C2×C4×C151#10212yes—
114C2×C4×C151C2×D811yescharacteristic
115C2×C4×C151C2×SD1611yescharacteristic
116C8×C151—82no—
117C8×C151—82no—
118C22×C151—21no—
119C22×C151—21no—
120C22×C151C2×#9911yescharacteristic
121C22×C151C2×#10211yescharacteristic
122C22×C151#42111yescharacteristic
123C4×C151—21no—
124C4×C151—21no—
125C4×C151—22no—
126C4×C151—22no—
127C4×C151—21no—
128C4×C151—44no—
129C4×C151—41no—
130C4×C151—41no—
131C4×C151—41no—
132C4×C151—82no—
133C4×C151#35612yes—
134C2×C151—21no—
135C2×C151—21no—
136C2×C151#151911yescharacteristic
137C2×C151#212311yescharacteristic
138C2×C151C2×#35611yescharacteristic
139#11883C15111yesmaximal, characteristic, direct product factor, Sylow
140C151#1188311yescharacteristic, direct product factor, Sylow
141#2546C2×C15111yescharacteristic
142#1801C2×C15111yescharacteristic
143#1461C2×C15111yescharacteristic
144#1346C2×C15114yes—
145C2×C4⋊Q8—21no—
146C2×C4⋊Q8C4×C15111yescharacteristic
147C2×C4×Q8C22×C15111yescharacteristic
148#431—21no—
149#423—21no—
150C2×#101—21no—
151#398C4×C15112yes—
152#398C22×C15112yes—
153#391—21no—
154#389—21no—
155#389—21no—
156C4×C4⋊C4C4×C15111yescharacteristic
157#343C22×C15112yes—
158#324—21no—
159#324C22×C15112yes—
160C22×Q8—21no—
161C22×Q8D4×C15111yescharacteristic
162C2×M16—22no—
163C4⋊Q8—41no—
164C4⋊Q8—41no—
165C4⋊Q8—42no—
166C4⋊Q8—42no—
167C4×Q8—41no—
168C4×Q8—41no—
169C2×C4⋊C4—21no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—22no—
173C2×C4⋊C4C2×C4×C15112yes—
174C2×C4⋊C4C2×C4×C15111yescharacteristic
175C2×C4⋊C4D4×C15111yescharacteristic
176C2×C4⋊C4C23×C15111yescharacteristic
177C2×C42—21no—
178C2×C42C2×C4×C15111yescharacteristic
179C2×C42D4×C15111yescharacteristic
180C2×C42D4×C15111yescharacteristic
181C4⋊C8—41no—
182C4⋊C8—41no—
183C4⋊C8—41no—
184#101—42no—
185C22⋊C8—22no—
186C4×C8—41no—
187#95—22no—
188#95—22no—
189#95C2×C4×C15112yes—
190C2×Q8—41no—
191C2×Q8—41no—
192C2×Q8—42no—
193C2×Q8—42no—
194C2×Q8—42no—
195C2×Q8D8×C15112yes—
196C2×Q8SD16×C15112yes—
197C22×C4—22no—
198C22×C4—22no—
199C22×C4C22⋊C4×C15111yescharacteristic
200C22×C4C22⋊C4×C15111yescharacteristic
201C22×C4C22⋊C4×C15111yescharacteristic
202C22×C4C22⋊C4×C15111yescharacteristic
203C22×C4C22×C4×C15111yescharacteristic
204C22×C4C2×D4×C15111yescharacteristic
205C22×C4C2×D4×C15111yescharacteristic
206M16—42no—
207M16—42no—
208C2×C8—42no—
209C2×C8—42no—
210C4⋊C4—24no—
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—42no—
215C4⋊C4—41no—
216C4⋊C4—41no—
217C4⋊C4—44no—
218C4⋊C4—42no—
219C4⋊C4—42no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—21no—
224C42—21no—
225C42—21no—
226C42—42no—
227C23C2×C22⋊C4×C15111yescharacteristic
228Q8—42no—
229Q8—42no—
230Q8—84no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—22no—
238C2×C4—24no—
239C2×C4—21no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—42no—
243C2×C4—42no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—42no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4#99×C15111yescharacteristic
251C2×C4#99×C15111yescharacteristic
252C2×C4#102×C15112yes—
253C2×C4#102×C15112yes—
254C2×C4C2×D8×C15111yescharacteristic
255C2×C4C2×SD16×C15111yescharacteristic
256C8—82no—
257C8—82no—
258C22—21no—
259C22—21no—
260C22C2×#99×C15111yescharacteristic
261C22C2×#102×C15111yescharacteristic
262C22#421×C15111yescharacteristic
263C4—21no—
264C4—21no—
265C4—22no—
266C4—22no—
267C4—21no—
268C4—44no—
269C4—41no—
270C4—41no—
271C4—41no—
272C4—82no—
273C4#356×C15112yes—
274C2—21no—
275C2—21no—
276C2#1519×C15111yescharacteristic
277C2#2123×C15111yescharacteristic
278C2C2×#356×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC23×C151C2×C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×Q8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
139. #11883C151direct (N × H)
140. C151#11883direct (N × H)

Maximal subgroups

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

subgroupindex
#2546×C1512
#1801×C1512
#1461×C1512
#1346×C1512
#11883151