Finite Group Databasebeta

← C151×#12293 #50317218

Subgroups — C151×#12293 #50317218

Order 38656.

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

normal subgroups only

This group has 316 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#3250×C151C211yesmaximal, characteristic
2#2236×C151C211yesmaximal, characteristic, complemented
3#2233×C151C211yesmaximal, characteristic
4#2087×C151C211yesmaximal, characteristic, complemented
5#1348×C151C211yesmaximal, characteristic, complemented
6#1347×C151C211yesmaximal, characteristic
7#1322×C151C211yesmaximal, characteristic, complemented
8#529×C151—21no—
9#479×C151—21no—
10#478×C151—21no—
11#467×C151C2211yescharacteristic
12#466×C151C2211yescharacteristic
13#465×C151—21no—
14#464×C151—21no—
15#463×C151—21no—
16C2×#107×C151C2211yescharacteristic
17C2×C4⋊C8×C151C2211yescharacteristic
18#389×C151—21no—
19#367×C151—21no—
20#366×C151—21no—
21#358×C151—21no—
22#357×C151—21no—
23C22⋊C16×C151C2211yescharacteristic
24C22⋊C16×C151C2211yescharacteristic
25#340×C151—21no—
26#340×C151C2211yescharacteristic
27C2×Q16×C151D411yescharacteristic
28C2×SD16×C151—21no—
29C2×D8×C151D411yescharacteristic
30C22×C8×C151D411yescharacteristic
31C22×C8×C151C2311yescharacteristic
32#126×C151—41no—
33#125×C151—21no—
34#124×C151—21no—
35#123×C151—41no—
36C22⋊Q8×C151—21no—
37#121×C151—21no—
38C4×Q8×C151—21no—
39C4×D4×C151—21no—
40C4×D4×C151—41no—
41#117×C151—41no—
42C2×C4⋊C4×C151—21no—
43C2×C4⋊C4×C151—21no—
44C2×C4⋊C4×C151—41no—
45C2×C42×C151D411yescharacteristic
46C2×C16×C151—21no—
47C2×C16×C151—21no—
48#107×C151—21no—
49#107×C151—21no—
50#107×C151D411yescharacteristic
51#107×C151D411yescharacteristic
52#106×C151—21no—
53C4⋊C8×C151—21no—
54C4⋊C8×C151—21no—
55#103×C151—21no—
56#103×C151—21no—
57#102×C151—21no—
58#102×C151—21no—
59#95×C151—41no—
60C2×Q8×C151—21no—
61C2×D4×C151—21no—
62C2×D4×C151—41no—
63C22×C4×C151—41no—
64C22×C4×C151—41no—
65C22×C4×C151—41no—
66C22×C4×C151D811yescharacteristic
67C22×C4×C151D811yescharacteristic
68C22×C4×C151C2×D411yescharacteristic
69Q16×C151—41no—
70SD16×C151—81no—
71D8×C151—41no—
72C2×C8×C151—21no—
73C2×C8×C151—41no—
74C2×C8×C151—41no—
75C2×C8×C151C2×D411yescharacteristic
76C2×C8×C151C2×D411yescharacteristic
77C4⋊C4×C151—22no—
78C4⋊C4×C151—21no—
79C4⋊C4×C151—21no—
80C4⋊C4×C151—41no—
81C4⋊C4×C151—41no—
82C4⋊C4×C151—41no—
83C4⋊C4×C151—41no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151—41no—
86C4⋊C4×C151—41no—
87C4⋊C4×C151—82no—
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—21no—
95C42×C151—41no—
96C16×C151—41no—
97C16×C151—41no—
98C23×C151—41no—
99C23×C151C2×D811yescharacteristic
100Q8×C151—41no—
101Q8×C151—41no—
102D4×C151—41no—
103D4×C151—41no—
104D4×C151—81no—
105D4×C151—81no—
106C2×C4×C151—21no—
107C2×C4×C151—21no—
108C2×C4×C151—21no—
109C2×C4×C151—21no—
110C2×C4×C151—21no—
111C2×C4×C151—21no—
112C2×C4×C151—41no—
113C2×C4×C151—42no—
114C2×C4×C151—41no—
115C2×C4×C151—41no—
116C2×C4×C151—41no—
117C2×C4×C151—82no—
118C2×C4×C151—81no—
119C2×C4×C151—81no—
120C2×C4×C151—81no—
121C2×C4×C151—81no—
122C2×C4×C151—81no—
123C2×C4×C151#12011yescharacteristic
124C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
125C8×C151—21no—
126C8×C151—21no—
127C8×C151—41no—
128C22×C151—21no—
129C22×C151—21no—
130C22×C151—81no—
131C22×C151—81no—
132C22×C151—81no—
133C22×C151#44711yescharacteristic
134C22×C151#50811yescharacteristic
135C22×C151#51011yescharacteristic
136C4×C151—21no—
137C4×C151—41no—
138C4×C151—41no—
139C4×C151—82no—
140C4×C151—81no—
141C4×C151—81no—
142C4×C151—81no—
143C4×C151—161no—
144C4×C151#45611yescharacteristic
145C4×C151#45811yescharacteristic
146C2×C151—21no—
147C2×C151—21no—
148C2×C151—161no—
149C2×C151#161011yescharacteristic
150C2×C151#218911yescharacteristic
151C2×C151#219011yescharacteristic
152#12293C15111yesmaximal, characteristic, direct product factor, Sylow
153C151#1229311yescharacteristic, direct product factor, Sylow
154#3250C2×C15111yescharacteristic
155#2236C2×C15111yescharacteristic, complemented
156#2233C2×C15111yescharacteristic
157#2087C2×C15111yescharacteristic, complemented
158#1348C2×C15111yescharacteristic, complemented
159#1347C2×C15111yescharacteristic
160#1322C2×C15111yescharacteristic, complemented
161#529—21no—
162#479—21no—
163#478—21no—
164#467C22×C15111yescharacteristic
165#466C22×C15111yescharacteristic
166#465—21no—
167#464—21no—
168#463—21no—
169C2×#107C22×C15111yescharacteristic
170C2×C4⋊C8C22×C15111yescharacteristic
171#389—21no—
172#367—21no—
173#366—21no—
174#358—21no—
175#357—21no—
176C22⋊C16C22×C15111yescharacteristic
177C22⋊C16C22×C15111yescharacteristic
178#340—21no—
179#340C22×C15111yescharacteristic
180C2×Q16D4×C15111yescharacteristic
181C2×SD16—21no—
182C2×D8D4×C15111yescharacteristic
183C22×C8D4×C15111yescharacteristic
184C22×C8C23×C15111yescharacteristic
185#126—41no—
186#125—21no—
187#124—21no—
188#123—41no—
189C22⋊Q8—21no—
190#121—21no—
191C4×Q8—21no—
192C4×D4—21no—
193C4×D4—41no—
194#117—41no—
195C2×C4⋊C4—21no—
196C2×C4⋊C4—21no—
197C2×C4⋊C4—41no—
198C2×C42D4×C15111yescharacteristic
199C2×C16—21no—
200C2×C16—21no—
201#107—21no—
202#107—21no—
203#107D4×C15111yescharacteristic
204#107D4×C15111yescharacteristic
205#106—21no—
206C4⋊C8—21no—
207C4⋊C8—21no—
208#103—21no—
209#103—21no—
210#102—21no—
211#102—21no—
212#95—41no—
213C2×Q8—21no—
214C2×D4—21no—
215C2×D4—41no—
216C22×C4—41no—
217C22×C4—41no—
218C22×C4—41no—
219C22×C4D8×C15111yescharacteristic
220C22×C4D8×C15111yescharacteristic
221C22×C4C2×D4×C15111yescharacteristic
222Q16—41no—
223SD16—81no—
224D8—41no—
225C2×C8—21no—
226C2×C8—41no—
227C2×C8—41no—
228C2×C8C2×D4×C15111yescharacteristic
229C2×C8C2×D4×C15111yescharacteristic
230C4⋊C4—22no—
231C4⋊C4—21no—
232C4⋊C4—21no—
233C4⋊C4—41no—
234C4⋊C4—41no—
235C4⋊C4—41no—
236C4⋊C4—41no—
237C4⋊C4—41no—
238C4⋊C4—41no—
239C4⋊C4—41no—
240C4⋊C4—82no—
241C22⋊C4—41no—
242C22⋊C4—41no—
243C22⋊C4—41no—
244C22⋊C4—41no—
245C22⋊C4—41no—
246C42—21no—
247C42—21no—
248C42—41no—
249C16—41no—
250C16—41no—
251C23—41no—
252C23C2×D8×C15111yescharacteristic
253Q8—41no—
254Q8—41no—
255D4—41no—
256D4—41no—
257D4—81no—
258D4—81no—
259C2×C4—21no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—21no—
264C2×C4—21no—
265C2×C4—41no—
266C2×C4—42no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—82no—
271C2×C4—81no—
272C2×C4—81no—
273C2×C4—81no—
274C2×C4—81no—
275C2×C4—81no—
276C2×C4#120×C15111yescharacteristic
277C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
278C8—21no—
279C8—21no—
280C8—41no—
281C22—21no—
282C22—21no—
283C22—81no—
284C22—81no—
285C22—81no—
286C22#447×C15111yescharacteristic
287C22#508×C15111yescharacteristic
288C22#510×C15111yescharacteristic
289C4—21no—
290C4—41no—
291C4—41no—
292C4—82no—
293C4—81no—
294C4—81no—
295C4—81no—
296C4—161no—
297C4#456×C15111yescharacteristic
298C4#458×C15111yescharacteristic
299C2—21no—
300C2—21no—
301C2—161no—
302C2#1610×C15111yescharacteristic
303C2#2189×C15111yescharacteristic
304C2#2190×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC22×C8C23×C151
prime radical#466×C151C22
LCSG ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4⋊C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2236×C151C2semidirect
4. #2087×C151C2semidirect
5. #1348×C151C2semidirect
7. #1322×C151C2semidirect
152. #12293C151direct (N × H)
153. C151#12293direct (N × H)
155. #2236C2×C151semidirect
157. #2087C2×C151semidirect
158. #1348C2×C151semidirect
160. #1322C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3250×C1512
#2236×C1512
#2233×C1512
#2087×C1512
#1348×C1512
#1347×C1512
#1322×C1512
#12293151