Finite Group Databasebeta

← C151×#11803 #50316728

Subgroups — C151×#11803 #50316728

Order 38656.

478 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 106 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×#398×C151C211yesmaximal, characteristic
2#1821×C151C211yesmaximal, characteristic
3#1463×C151C211yesmaximal, characteristic
4#1346×C151C214yesmaximal, complemented
5C22×C4⋊C4×C151—21no—
6C22×C4⋊C4×C151C411yescharacteristic
7C22×C4⋊C4×C151C2211yescharacteristic
8#407×C151—21no—
9#407×C151—21no—
10#398×C151—21no—
11#398×C151—21no—
12#398×C151C412yes—
13#398×C151C2212yes—
14C2×#95×C151—21no—
15C2×#95×C151C411yescharacteristic
16#343×C151—21no—
17#343×C151C2212yes—
18#324×C151—21no—
19#324×C151C2212yes—
20C23×C4×C151—21no—
21C23×C4×C151—21no—
22C23×C4×C151C2×C411yescharacteristic
23C23×C4×C151D411yescharacteristic
24C23×C4×C151D411yescharacteristic
25C2×M16×C151—22no—
26C2×M16×C151—41no—
27C2×C4⋊C4×C151—21no—
28C2×C4⋊C4×C151—22no—
29C2×C4⋊C4×C151—22no—
30C2×C4⋊C4×C151—41no—
31C2×C4⋊C4×C151—41no—
32C2×C4⋊C4×C151—41no—
33C2×C4⋊C4×C151—41no—
34C2×C4⋊C4×C151—44no—
35C2×C4⋊C4×C151C2×C412yes—
36C2×C4⋊C4×C151C2×C411yescharacteristic
37C2×C4⋊C4×C151D411yescharacteristic
38C2×C4⋊C4×C151D411yescharacteristic
39C2×C4⋊C4×C151C2311yescharacteristic
40C22⋊C8×C151—22no—
41C22⋊C8×C151—41no—
42C22⋊C8×C151—41no—
43C22⋊C8×C151—41no—
44#95×C151—22no—
45#95×C151—21no—
46#95×C151—22no—
47#95×C151C2×C412yes—
48C24×C151C22⋊C411yescharacteristic
49C22×C4×C151—24no—
50C22×C4×C151—21no—
51C22×C4×C151—21no—
52C22×C4×C151—21no—
53C22×C4×C151—21no—
54C22×C4×C151—21no—
55C22×C4×C151—22no—
56C22×C4×C151—21no—
57C22×C4×C151—22no—
58C22×C4×C151—22no—
59C22×C4×C151—41no—
60C22×C4×C151—42no—
61C22×C4×C151—42no—
62C22×C4×C151—42no—
63C22×C4×C151—42no—
64C22×C4×C151—42no—
65C22×C4×C151—42no—
66C22×C4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151C22⋊C411yescharacteristic
69C22×C4×C151C22⋊C411yescharacteristic
70C22×C4×C151C22⋊C411yescharacteristic
71C22×C4×C151C22×C411yescharacteristic
72C22×C4×C151C2×D411yescharacteristic
73C22×C4×C151C2×D411yescharacteristic
74M16×C151—42no—
75M16×C151—42no—
76M16×C151—82no—
77C2×C8×C151—42no—
78C2×C8×C151—42no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—41no—
83C4⋊C4×C151—42no—
84C4⋊C4×C151—42no—
85C4⋊C4×C151—44no—
86C4⋊C4×C151—44no—
87C23×C151—22no—
88C23×C151—22no—
89C23×C151—21no—
90C23×C151—21no—
91C23×C151#9911yescharacteristic
92C23×C151#9911yescharacteristic
93C23×C151C2×C22⋊C411yescharacteristic
94C2×C4×C151—21no—
95C2×C4×C151—21no—
96C2×C4×C151—24no—
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—42no—
105C2×C4×C151—42no—
106C2×C4×C151—48no—
107C2×C4×C151—42no—
108C2×C4×C151—42no—
109C2×C4×C151—42no—
110C2×C4×C151—42no—
111C2×C4×C151—42no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—42no—
117C2×C4×C151—42no—
118C2×C4×C151—42no—
119C2×C4×C151—81no—
120C2×C4×C151—82no—
121C2×C4×C151—82no—
122C2×C4×C151AGL(1,ℤ/8)12yes—
123C8×C151—82no—
124C8×C151—82no—
125C22×C151—24no—
126C22×C151—24no—
127C22×C151—21no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—21no—
131C22×C151—21no—
132C22×C151—21no—
133C22×C151#35212yes—
134C22×C151#35612yes—
135C22×C151C2×#9911yescharacteristic
136C22×C151#41811yescharacteristic
137C22×C151#42111yescharacteristic
138C4×C151—22no—
139C4×C151—44no—
140C4×C151—41no—
141C4×C151—41no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—41no—
145C4×C151—82no—
146C2×C151—21no—
147C2×C151—22no—
148C2×C151—22no—
149C2×C151—21no—
150C2×C151#151011yescharacteristic
151C2×C151C2×#35211yescharacteristic
152C2×C151C2×#35611yescharacteristic
153#11803C15111yesmaximal, characteristic, direct product factor, Sylow
154C151#1180311yescharacteristic, direct product factor, Sylow
155C2×#398C2×C15111yescharacteristic
156#1821C2×C15111yescharacteristic
157#1463C2×C15111yescharacteristic
158#1346C2×C15114yescomplemented
159C22×C4⋊C4—21no—
160C22×C4⋊C4C4×C15111yescharacteristic
161C22×C4⋊C4C22×C15111yescharacteristic
162#407—21no—
163#407—21no—
164#398—21no—
165#398—21no—
166#398C4×C15112yes—
167#398C22×C15112yes—
168C2×#95—21no—
169C2×#95C4×C15111yescharacteristic
170#343—21no—
171#343C22×C15112yes—
172#324—21no—
173#324C22×C15112yes—
174C23×C4—21no—
175C23×C4—21no—
176C23×C4C2×C4×C15111yescharacteristic
177C23×C4D4×C15111yescharacteristic
178C23×C4D4×C15111yescharacteristic
179C2×M16—22no—
180C2×M16—41no—
181C2×C4⋊C4—22no—
182C2×C4⋊C4—21no—
183C2×C4⋊C4—22no—
184C2×C4⋊C4—41no—
185C2×C4⋊C4—41no—
186C2×C4⋊C4—41no—
187C2×C4⋊C4—41no—
188C2×C4⋊C4—44no—
189C2×C4⋊C4C2×C4×C15112yes—
190C2×C4⋊C4C2×C4×C15111yescharacteristic
191C2×C4⋊C4D4×C15111yescharacteristic
192C2×C4⋊C4D4×C15111yescharacteristic
193C2×C4⋊C4C23×C15111yescharacteristic
194C22⋊C8—22no—
195C22⋊C8—41no—
196C22⋊C8—41no—
197C22⋊C8—41no—
198#95—22no—
199#95—21no—
200#95—22no—
201#95C2×C4×C15112yes—
202C24C22⋊C4×C15111yescharacteristic
203C22×C4—24no—
204C22×C4—21no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—21no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—21no—
211C22×C4—22no—
212C22×C4—22no—
213C22×C4—41no—
214C22×C4—42no—
215C22×C4—42no—
216C22×C4—42no—
217C22×C4—42no—
218C22×C4—42no—
219C22×C4—42no—
220C22×C4—41no—
221C22×C4—41no—
222C22×C4C22⋊C4×C15111yescharacteristic
223C22×C4C22⋊C4×C15111yescharacteristic
224C22×C4C22⋊C4×C15111yescharacteristic
225C22×C4C22×C4×C15111yescharacteristic
226C22×C4C2×D4×C15111yescharacteristic
227C22×C4C2×D4×C15111yescharacteristic
228M16—42no—
229M16—42no—
230M16—82no—
231C2×C8—42no—
232C2×C8—42no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—42no—
238C4⋊C4—42no—
239C4⋊C4—44no—
240C4⋊C4—44no—
241C23—22no—
242C23—22no—
243C23—21no—
244C23—21no—
245C23#99×C15111yescharacteristic
246C23#99×C15111yescharacteristic
247C23C2×C22⋊C4×C15111yescharacteristic
248C2×C4—21no—
249C2×C4—21no—
250C2×C4—24no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—21no—
254C2×C4—21no—
255C2×C4—21no—
256C2×C4—21no—
257C2×C4—21no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—48no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—42no—
266C2×C4—41no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—42no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—81no—
274C2×C4—82no—
275C2×C4—82no—
276C2×C4AGL(1,ℤ/8)×C15112yes—
277C8—82no—
278C8—82no—
279C22—24no—
280C22—24no—
281C22—21no—
282C22—21no—
283C22—21no—
284C22—21no—
285C22—21no—
286C22—21no—
287C22#352×C15112yes—
288C22#356×C15112yes—
289C22C2×#99×C15111yescharacteristic
290C22#418×C15111yescharacteristic
291C22#421×C15111yescharacteristic
292C4—22no—
293C4—44no—
294C4—41no—
295C4—41no—
296C4—41no—
297C4—41no—
298C4—41no—
299C4—82no—
300C2—21no—
301C2—22no—
302C2—22no—
303C2—21no—
304C2#1510×C15111yescharacteristic
305C2C2×#352×C15111yescharacteristic
306C2C2×#356×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#99
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C4⋊C4C23×C151
prime radicalC24×C151C22⋊C4
LCSG ▷ C22×C4 ▷ C23 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C24×C151 ◁ C22×C4⋊C4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
4. #1346×C151C2semidirect
153. #11803C151direct (N × H)
154. C151#11803direct (N × H)
158. #1346C2×C151semidirect

Maximal subgroups

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

subgroupindex
C2×#398×C1512
#1821×C1512
#1463×C1512
#1346×C1512
#11803151