Finite Group Databasebeta

← C151×#12388 #50317313

Subgroups — C151×#12388 #50317313

Order 38656.

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

normal subgroups only

This group has 296 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#2243×C151C211yesmaximal, characteristic, complemented
3#2224×C151C211yesmaximal, characteristic, complemented
4#1696×C151C211yesmaximal, characteristic, complemented
5#1360×C151C211yesmaximal, characteristic, complemented
6#1338×C151C211yesmaximal, characteristic, complemented
7#1333×C151C211yesmaximal, characteristic, complemented
8#559×C151—21no—
9#500×C151C2211yescharacteristic
10#496×C151—21no—
11#495×C151C2211yescharacteristic
12#477×C151—21no—
13#464×C151—21no—
14#463×C151—21no—
15#459×C151—21no—
16#446×C151C2211yescharacteristic
17#440×C151—21no—
18C4×D8×C151C2211yescharacteristic
19#366×C151—21no—
20C4⋊C16×C151C2211yescharacteristic
21#358×C151—21no—
22#357×C151—21no—
23#357×C151—21no—
24#346×C151C2211yescharacteristic
25#334×C151C2211yescharacteristic
26#333×C151—21no—
27C2×Q16×C151D411yescharacteristic
28C2×SD16×C151—21no—
29C2×SD16×C151—21no—
30C2×D8×C151—21no—
31C2×D8×C151D411yescharacteristic
32C2×D8×C151D411yescharacteristic
33C4⋊Q8×C151—21no—
34#127×C151—21no—
35#124×C151—21no—
36#124×C151—21no—
37#124×C151—41no—
38#123×C151—41no—
39#123×C151—41no—
40C4×Q8×C151—21no—
41C4×Q8×C151D411yescharacteristic
42C4×D4×C151—21no—
43C4×D4×C151—21no—
44C4×D4×C151—41no—
45C2×C16×C151—21no—
46C2×C16×C151—21no—
47#107×C151—21no—
48#107×C151—21no—
49#107×C151—41no—
50#107×C151D411yescharacteristic
51C4⋊C8×C151—21no—
52C4⋊C8×C151—21no—
53C4⋊C8×C151D411yescharacteristic
54#103×C151—21no—
55#103×C151—41no—
56#102×C151—21no—
57#102×C151—21no—
58#97×C151—21no—
59C4×C8×C151C2311yescharacteristic
60C2×Q8×C151—21no—
61C2×Q8×C151—41no—
62C2×Q8×C151D811yescharacteristic
63C2×D4×C151—21no—
64C2×D4×C151—21no—
65C2×D4×C151—41no—
66C2×D4×C151—41no—
67C22×C4×C151—41no—
68C22×C4×C151—41no—
69Q16×C151—41no—
70SD16×C151—41no—
71SD16×C151—41no—
72SD16×C151—81no—
73D8×C151—21no—
74D8×C151—21no—
75D8×C151—41no—
76D8×C151—81no—
77C2×C8×C151—21no—
78C2×C8×C151—41no—
79C2×C8×C151C2×D411yescharacteristic
80C2×C8×C151C2×D411yescharacteristic
81C4⋊C4×C151—21no—
82C4⋊C4×C151—21no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151—41no—
86C4⋊C4×C151D811yescharacteristic
87C22⋊C4×C151—41no—
88C22⋊C4×C151—41no—
89C22⋊C4×C151—41no—
90C22⋊C4×C151—41no—
91C22⋊C4×C151—41no—
92C22⋊C4×C151—41no—
93C42×C151—21no—
94C42×C151—41no—
95C42×C151C2×D411yescharacteristic
96C16×C151—41no—
97C16×C151—41no—
98C23×C151—41no—
99C23×C151—41no—
100Q8×C151—41no—
101Q8×C151—41no—
102Q8×C151—41no—
103Q8×C151—161no—
104D4×C151—41no—
105D4×C151—41no—
106D4×C151—41no—
107D4×C151—41no—
108D4×C151—82no—
109D4×C151—161no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—41no—
113C2×C4×C151—41no—
114C2×C4×C151—81no—
115C2×C4×C151—161no—
116C2×C4×C151—161no—
117C2×C4×C151#12011yescharacteristic
118C2×C4×C151C2×D811yescharacteristic
119C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
120C8×C151—21no—
121C8×C151—41no—
122C8×C151—81no—
123C8×C151#13511yescharacteristic
124C8×C151#13711yescharacteristic
125C22×C151—81no—
126C22×C151—81no—
127C22×C151—81no—
128C22×C151—81no—
129C22×C151—81no—
130C22×C151—81no—
131C22×C151#44711yescharacteristic
132C4×C151—21no—
133C4×C151—21no—
134C4×C151—41no—
135C4×C151—41no—
136C4×C151—81no—
137C4×C151—81no—
138C4×C151—161no—
139C4×C151#45211yescharacteristic
140C4×C151#45511yescharacteristic
141C2×C151—161no—
142C2×C151—161no—
143C2×C151#164111yescharacteristic
144C2×C151#219111yescharacteristic
145C2×C151#219211yescharacteristic
146#12388C15111yesmaximal, characteristic, direct product factor, Sylow
147C151#1238811yescharacteristic, direct product factor, Sylow
148#3403C2×C15111yescharacteristic
149#2243C2×C15111yescharacteristic, complemented
150#2224C2×C15111yescharacteristic, complemented
151#1696C2×C15111yescharacteristic, complemented
152#1360C2×C15111yescharacteristic, complemented
153#1338C2×C15111yescharacteristic, complemented
154#1333C2×C15111yescharacteristic, complemented
155#559—21no—
156#500C22×C15111yescharacteristic
157#496—21no—
158#495C22×C15111yescharacteristic
159#477—21no—
160#464—21no—
161#463—21no—
162#459—21no—
163#446C22×C15111yescharacteristic
164#440—21no—
165C4×D8C22×C15111yescharacteristic
166#366—21no—
167C4⋊C16C22×C15111yescharacteristic
168#358—21no—
169#357—21no—
170#357—21no—
171#346C22×C15111yescharacteristic
172#334C22×C15111yescharacteristic
173#333—21no—
174C2×Q16D4×C15111yescharacteristic
175C2×SD16—21no—
176C2×SD16—21no—
177C2×D8—21no—
178C2×D8D4×C15111yescharacteristic
179C2×D8D4×C15111yescharacteristic
180C4⋊Q8—21no—
181#127—21no—
182#124—21no—
183#124—21no—
184#124—41no—
185#123—41no—
186#123—41no—
187C4×Q8—21no—
188C4×Q8D4×C15111yescharacteristic
189C4×D4—21no—
190C4×D4—21no—
191C4×D4—41no—
192C2×C16—21no—
193C2×C16—21no—
194#107—21no—
195#107—21no—
196#107—41no—
197#107D4×C15111yescharacteristic
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8D4×C15111yescharacteristic
201#103—21no—
202#103—41no—
203#102—21no—
204#102—21no—
205#97—21no—
206C4×C8C23×C15111yescharacteristic
207C2×Q8—21no—
208C2×Q8—41no—
209C2×Q8D8×C15111yescharacteristic
210C2×D4—21no—
211C2×D4—21no—
212C2×D4—41no—
213C2×D4—41no—
214C22×C4—41no—
215C22×C4—41no—
216Q16—41no—
217SD16—41no—
218SD16—41no—
219SD16—81no—
220D8—21no—
221D8—21no—
222D8—41no—
223D8—81no—
224C2×C8—21no—
225C2×C8—41no—
226C2×C8C2×D4×C15111yescharacteristic
227C2×C8C2×D4×C15111yescharacteristic
228C4⋊C4—21no—
229C4⋊C4—21no—
230C4⋊C4—41no—
231C4⋊C4—41no—
232C4⋊C4—41no—
233C4⋊C4D8×C15111yescharacteristic
234C22⋊C4—41no—
235C22⋊C4—41no—
236C22⋊C4—41no—
237C22⋊C4—41no—
238C22⋊C4—41no—
239C22⋊C4—41no—
240C42—21no—
241C42—41no—
242C42C2×D4×C15111yescharacteristic
243C16—41no—
244C16—41no—
245C23—41no—
246C23—41no—
247Q8—41no—
248Q8—41no—
249Q8—41no—
250Q8—161no—
251D4—41no—
252D4—41no—
253D4—41no—
254D4—41no—
255D4—82no—
256D4—161no—
257C2×C4—21no—
258C2×C4—21no—
259C2×C4—41no—
260C2×C4—41no—
261C2×C4—81no—
262C2×C4—161no—
263C2×C4—161no—
264C2×C4#120×C15111yescharacteristic
265C2×C4C2×D8×C15111yescharacteristic
266C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
267C8—21no—
268C8—41no—
269C8—81no—
270C8#135×C15111yescharacteristic
271C8#137×C15111yescharacteristic
272C22—81no—
273C22—81no—
274C22—81no—
275C22—81no—
276C22—81no—
277C22—81no—
278C22#447×C15111yescharacteristic
279C4—21no—
280C4—21no—
281C4—41no—
282C4—41no—
283C4—81no—
284C4—81no—
285C4—161no—
286C4#452×C15111yescharacteristic
287C4#455×C15111yescharacteristic
288C2—161no—
289C2—161no—
290C2#1641×C15111yescharacteristic
291C2#2191×C15111yescharacteristic
292C2#2192×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. #2243×C151C2semidirect
3. #2224×C151C2semidirect
4. #1696×C151C2semidirect
5. #1360×C151C2semidirect
6. #1338×C151C2semidirect
7. #1333×C151C2semidirect
146. #12388C151direct (N × H)
147. C151#12388direct (N × H)
149. #2243C2×C151semidirect
150. #2224C2×C151semidirect
151. #1696C2×C151semidirect
152. #1360C2×C151semidirect
153. #1338C2×C151semidirect
154. #1333C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3403×C1512
#2243×C1512
#2224×C1512
#1696×C1512
#1360×C1512
#1338×C1512
#1333×C1512
#12388151