Finite Group Databasebeta

← C151×#12338 #50317263

Subgroups — C151×#12338 #50317263

Order 38656.

320 conjugacy classes of subgroups; only the 78 normal subgroups are shown.

normal subgroups only

This group has 320 conjugacy classes of subgroups — too many to draw. Only its 78 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#3403×C151C211yesmaximal, characteristic
2#2251×C151C211yesmaximal, characteristic, complemented
3#2208×C151C211yesmaximal, characteristic, complemented
4#1690×C151C211yesmaximal, characteristic, complemented
5#1360×C151C211yesmaximal, characteristic, complemented
6#1338×C151C211yesmaximal, characteristic, complemented
7#1333×C151C211yesmaximal, characteristic, complemented
8#559×C151—21no—
9C2×Q32×C151—21no—
10C2×SD32×C151—21no—
11C2×SD32×C151—21no—
12#496×C151—21no—
13#495×C151C2211yescharacteristic
14#494×C151C2211yescharacteristic
15#475×C151—21no—
16#464×C151—21no—
17#463×C151—21no—
18#459×C151—21no—
19#446×C151C2211yescharacteristic
20#440×C151—21no—
21C4×D8×C151C2211yescharacteristic
22C4⋊C16×C151C2211yescharacteristic
23#358×C151—21no—
24#346×C151C2211yescharacteristic
25#334×C151C2211yescharacteristic
26#332×C151—21no—
27C2×Q16×C151—21no—
28C2×Q16×C151—21no—
29C2×Q16×C151D411yescharacteristic
30C2×SD16×C151—21no—
31C2×SD16×C151—21no—
32C2×D8×C151—21no—
33C2×D8×C151D411yescharacteristic
34C2×D8×C151D411yescharacteristic
35C4⋊Q8×C151—21no—
36#127×C151—21no—
37#124×C151—21no—
38#124×C151—21no—
39#124×C151—41no—
40#123×C151—41no—
41#123×C151—41no—
42C4×Q8×C151—21no—
43C4×Q8×C151D411yescharacteristic
44C4×D4×C151—21no—
45C4×D4×C151—21no—
46C4×D4×C151—41no—
47Q32×C151—42no—
48SD32×C151—42no—
49SD32×C151—42no—
50C2×C16×C151—21no—
51C2×C16×C151—21no—
52#107×C151D411yescharacteristic
53#106×C151—41no—
54C4⋊C8×C151—21no—
55C4⋊C8×C151—21no—
56C4⋊C8×C151D411yescharacteristic
57#103×C151—21no—
58#103×C151—41no—
59#102×C151—21no—
60#102×C151—21no—
61#97×C151—21no—
62C4×C8×C151C2311yescharacteristic
63C2×Q8×C151—21no—
64C2×Q8×C151—41no—
65C2×Q8×C151D811yescharacteristic
66C2×D4×C151—21no—
67C2×D4×C151—21no—
68C2×D4×C151—41no—
69C2×D4×C151—41no—
70C22×C4×C151—41no—
71C22×C4×C151—41no—
72Q16×C151—41no—
73Q16×C151—41no—
74Q16×C151—41no—
75Q16×C151—41no—
76Q16×C151—41no—
77SD16×C151—41no—
78SD16×C151—41no—
79SD16×C151—81no—
80D8×C151—21no—
81D8×C151—21no—
82D8×C151—41no—
83D8×C151—81no—
84C2×C8×C151—21no—
85C2×C8×C151—41no—
86C2×C8×C151C2×D411yescharacteristic
87C2×C8×C151C2×D411yescharacteristic
88C4⋊C4×C151—21no—
89C4⋊C4×C151—21no—
90C4⋊C4×C151—41no—
91C4⋊C4×C151—41no—
92C4⋊C4×C151—41no—
93C4⋊C4×C151D811yescharacteristic
94C22⋊C4×C151—41no—
95C22⋊C4×C151—41no—
96C22⋊C4×C151—41no—
97C22⋊C4×C151—41no—
98C22⋊C4×C151—41no—
99C22⋊C4×C151—41no—
100C42×C151—21no—
101C42×C151—41no—
102C42×C151C2×D411yescharacteristic
103C16×C151—22no—
104C16×C151—41no—
105C23×C151—41no—
106C23×C151—41no—
107Q8×C151—41no—
108Q8×C151—41no—
109Q8×C151—41no—
110Q8×C151—81no—
111Q8×C151—81no—
112D4×C151—41no—
113D4×C151—41no—
114D4×C151—41no—
115D4×C151—41no—
116D4×C151—82no—
117D4×C151—161no—
118C2×C4×C151—21no—
119C2×C4×C151—21no—
120C2×C4×C151—41no—
121C2×C4×C151—41no—
122C2×C4×C151—81no—
123C2×C4×C151—161no—
124C2×C4×C151—161no—
125C2×C4×C151#12011yescharacteristic
126C2×C4×C151C2×D811yescharacteristic
127C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
128C8×C151—21no—
129C8×C151—41no—
130C8×C151—81no—
131C8×C151#13511yescharacteristic
132C8×C151AGL(1,ℤ/8)11yescharacteristic
133C22×C151—81no—
134C22×C151—81no—
135C22×C151—81no—
136C22×C151—81no—
137C22×C151—81no—
138C22×C151—81no—
139C22×C151#44711yescharacteristic
140C4×C151—21no—
141C4×C151—21no—
142C4×C151—41no—
143C4×C151—41no—
144C4×C151—81no—
145C4×C151—81no—
146C4×C151—161no—
147C4×C151#44911yescharacteristic
148C4×C151#45311yescharacteristic
149C2×C151—161no—
150C2×C151—161no—
151C2×C151#162111yescharacteristic
152C2×C151#219111yescharacteristic
153C2×C151#219411yescharacteristic
154#12338C15111yesmaximal, characteristic, direct product factor, Sylow
155C151#1233811yescharacteristic, direct product factor, Sylow
156#3403C2×C15111yescharacteristic
157#2251C2×C15111yescharacteristic, complemented
158#2208C2×C15111yescharacteristic, complemented
159#1690C2×C15111yescharacteristic, complemented
160#1360C2×C15111yescharacteristic, complemented
161#1338C2×C15111yescharacteristic, complemented
162#1333C2×C15111yescharacteristic, complemented
163#559—21no—
164C2×Q32—21no—
165C2×SD32—21no—
166C2×SD32—21no—
167#496—21no—
168#495C22×C15111yescharacteristic
169#494C22×C15111yescharacteristic
170#475—21no—
171#464—21no—
172#463—21no—
173#459—21no—
174#446C22×C15111yescharacteristic
175#440—21no—
176C4×D8C22×C15111yescharacteristic
177C4⋊C16C22×C15111yescharacteristic
178#358—21no—
179#346C22×C15111yescharacteristic
180#334C22×C15111yescharacteristic
181#332—21no—
182C2×Q16—21no—
183C2×Q16—21no—
184C2×Q16D4×C15111yescharacteristic
185C2×SD16—21no—
186C2×SD16—21no—
187C2×D8—21no—
188C2×D8D4×C15111yescharacteristic
189C2×D8D4×C15111yescharacteristic
190C4⋊Q8—21no—
191#127—21no—
192#124—21no—
193#124—21no—
194#124—41no—
195#123—41no—
196#123—41no—
197C4×Q8—21no—
198C4×Q8D4×C15111yescharacteristic
199C4×D4—21no—
200C4×D4—21no—
201C4×D4—41no—
202Q32—42no—
203SD32—42no—
204SD32—42no—
205C2×C16—21no—
206C2×C16—21no—
207#107D4×C15111yescharacteristic
208#106—41no—
209C4⋊C8—21no—
210C4⋊C8—21no—
211C4⋊C8D4×C15111yescharacteristic
212#103—21no—
213#103—41no—
214#102—21no—
215#102—21no—
216#97—21no—
217C4×C8C23×C15111yescharacteristic
218C2×Q8—21no—
219C2×Q8—41no—
220C2×Q8D8×C15111yescharacteristic
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—41no—
224C2×D4—41no—
225C22×C4—41no—
226C22×C4—41no—
227Q16—41no—
228Q16—41no—
229Q16—41no—
230Q16—41no—
231Q16—41no—
232SD16—41no—
233SD16—41no—
234SD16—81no—
235D8—21no—
236D8—21no—
237D8—41no—
238D8—81no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8C2×D4×C15111yescharacteristic
242C2×C8C2×D4×C15111yescharacteristic
243C4⋊C4—21no—
244C4⋊C4—21no—
245C4⋊C4—41no—
246C4⋊C4—41no—
247C4⋊C4—41no—
248C4⋊C4D8×C15111yescharacteristic
249C22⋊C4—41no—
250C22⋊C4—41no—
251C22⋊C4—41no—
252C22⋊C4—41no—
253C22⋊C4—41no—
254C22⋊C4—41no—
255C42—21no—
256C42—41no—
257C42C2×D4×C15111yescharacteristic
258C16—22no—
259C16—41no—
260C23—41no—
261C23—41no—
262Q8—41no—
263Q8—41no—
264Q8—41no—
265Q8—81no—
266Q8—81no—
267D4—41no—
268D4—41no—
269D4—41no—
270D4—41no—
271D4—82no—
272D4—161no—
273C2×C4—21no—
274C2×C4—21no—
275C2×C4—41no—
276C2×C4—41no—
277C2×C4—81no—
278C2×C4—161no—
279C2×C4—161no—
280C2×C4#120×C15111yescharacteristic
281C2×C4C2×D8×C15111yescharacteristic
282C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
283C8—21no—
284C8—41no—
285C8—81no—
286C8#135×C15111yescharacteristic
287C8AGL(1,ℤ/8)×C15111yescharacteristic
288C22—81no—
289C22—81no—
290C22—81no—
291C22—81no—
292C22—81no—
293C22—81no—
294C22#447×C15111yescharacteristic
295C4—21no—
296C4—21no—
297C4—41no—
298C4—41no—
299C4—81no—
300C4—81no—
301C4—161no—
302C4#449×C15111yescharacteristic
303C4#453×C15111yescharacteristic
304C2—161no—
305C2—161no—
306C2#1621×C15111yescharacteristic
307C2#2191×C15111yescharacteristic
308C2#2194×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#3403×C151C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ #446×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2251×C151C2semidirect
3. #2208×C151C2semidirect
4. #1690×C151C2semidirect
5. #1360×C151C2semidirect
6. #1338×C151C2semidirect
7. #1333×C151C2semidirect
154. #12338C151direct (N × H)
155. C151#12338direct (N × H)
157. #2251C2×C151semidirect
158. #2208C2×C151semidirect
159. #1690C2×C151semidirect
160. #1360C2×C151semidirect
161. #1338C2×C151semidirect
162. #1333C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3403×C1512
#2251×C1512
#2208×C1512
#1690×C1512
#1360×C1512
#1338×C1512
#1333×C1512
#12338151