Finite Group Databasebeta

← C151×#13525 #50318450

Subgroups — C151×#13525 #50318450

Order 38656.

294 conjugacy classes of subgroups.

The subgroup lattice has 282 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#2158×C151C211yesmaximal, characteristic, complemented
2#2155×C151C211yesmaximal, characteristic, complemented
3#2145×C151C211yesmaximal, characteristic
4C2×#359×C151C211yesmaximal, characteristic
5#1976×C151C211yesmaximal, characteristic
6#1833×C151C211yesmaximal, characteristic, complemented
7#1379×C151C211yesmaximal, characteristic, complemented
8C2×#135×C151C2211yescharacteristic
9C2×M32×C151C2211yescharacteristic
10C22×C16×C151C2211yescharacteristic
11C2×#108×C151C2211yescharacteristic
12#427×C151C2211yescharacteristic
13#427×C151C2211yescharacteristic
14#421×C151—21no—
15#410×C151—21no—
16#405×C151C2211yescharacteristic
17#367×C151—21no—
18#366×C151—21no—
19#365×C151—22no—
20#360×C151—22no—
21#359×C151—21no—
22#359×C151—21no—
23#344×C151—21no—
24H(3,ℤ/4)×C151—21no—
25C2×#41×C151—21no—
26#135×C151—21no—
27#135×C151—21no—
28#135×C151—21no—
29#135×C151—21no—
30C2×Q16×C151Q811yescharacteristic
31C2×SD16×C151—21no—
32C2×D8×C151Q811yescharacteristic
33C2×M16×C151—21no—
34C2×M16×C151D411yescharacteristic
35C22×C8×C151C2311yescharacteristic
36#117×C151—21no—
37#117×C151—21no—
38#117×C151D411yescharacteristic
39M32×C151—21no—
40M32×C151D412yes—
41C2×C16×C151—21no—
42C2×C16×C151—21no—
43C2×C16×C151—21no—
44C2×C16×C151D411yescharacteristic
45C2×C16×C151D411yescharacteristic
46#108×C151—21no—
47#108×C151—21no—
48#107×C151—21no—
49#107×C151—21no—
50#106×C151—21no—
51#106×C151—21no—
52#104×C151—42no—
53#99×C151—42no—
54#97×C151—21no—
55C4×C8×C151—21no—
56#41×C151—41no—
57#41×C151—41no—
58#41×C151—41no—
59#41×C151—41no—
60C2×Q8×C151—21no—
61C2×D4×C151—21no—
62C2×D4×C151—41no—
63C22×C4×C151—41no—
64C22×C4×C151C2×D411yescharacteristic
65Q16×C151—21no—
66Q16×C151—21no—
67SD16×C151—41no—
68SD16×C151—41no—
69D8×C151—21no—
70D8×C151—21no—
71M16×C151—21no—
72M16×C151—21no—
73M16×C151—41no—
74M16×C151—41no—
75C2×C8×C151—21no—
76C2×C8×C151—41no—
77C2×C8×C151C2×D411yescharacteristic
78C2×C8×C151C2×D411yescharacteristic
79C2×C8×C151C2×Q811yescharacteristic
80C2×C8×C151#4111yescharacteristic
81C2×C8×C151#4111yescharacteristic
82C2×C8×C151#4111yescharacteristic
83C4⋊C4×C151—21no—
84C4⋊C4×C151—41no—
85C4⋊C4×C151—41no—
86C22⋊C4×C151—21no—
87C22⋊C4×C151—41no—
88C22⋊C4×C151—41no—
89C42×C151—21no—
90C42×C151—41no—
91C42×C151—41no—
92C16×C151—21no—
93C16×C151—21no—
94C16×C151—22no—
95C23×C151—41no—
96C23×C151AGL(1,ℤ/8)11yescharacteristic
97Q8×C151—41no—
98Q8×C151—41no—
99D4×C151—41no—
100D4×C151—41no—
101D4×C151—81no—
102D4×C151—81no—
103C2×C4×C151—41no—
104C2×C4×C151—41no—
105C2×C4×C151—81no—
106C2×C4×C151—81no—
107C2×C4×C151—81no—
108C2×C4×C151—81no—
109C2×C4×C151C22⋊Q811yescharacteristic
110C2×C4×C151#12311yescharacteristic
111C2×C4×C151#12711yescharacteristic
112C2×C4×C151#13511yescharacteristic
113C2×C4×C151#13511yescharacteristic
114C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
115C8×C151—41no—
116C8×C151—81no—
117C8×C151C22⋊Q811yescharacteristic
118C8×C151C22⋊Q811yescharacteristic
119C8×C151#12311yescharacteristic
120C8×C151#12311yescharacteristic
121C22×C151—41no—
122C22×C151—81no—
123C22×C151—161no—
124C22×C151#47811yescharacteristic
125C22×C151#48211yescharacteristic
126C22×C151#49611yescharacteristic
127C4×C151—81no—
128C4×C151—81no—
129C4×C151—161no—
130C4×C151—161no—
131C4×C151#39911yescharacteristic
132C4×C151#47811yescharacteristic
133C4×C151#48211yescharacteristic
134C4×C151#49511yescharacteristic
135C2×C151—21no—
136C2×C151—21no—
137C2×C151—21no—
138C2×C151—161no—
139C2×C151#209211yescharacteristic
140#13525C15111yesmaximal, characteristic, direct product factor, Sylow
141C151#1352511yescharacteristic, direct product factor, Sylow
142#2158C2×C15111yescharacteristic, complemented
143#2155C2×C15111yescharacteristic, complemented
144#2145C2×C15111yescharacteristic
145C2×#359C2×C15111yescharacteristic
146#1976C2×C15111yescharacteristic
147#1833C2×C15111yescharacteristic, complemented
148#1379C2×C15111yescharacteristic, complemented
149C2×#135C22×C15111yescharacteristic
150C2×M32C22×C15111yescharacteristic
151C22×C16C22×C15111yescharacteristic
152C2×#108C22×C15111yescharacteristic
153#427C22×C15111yescharacteristic
154#427C22×C15111yescharacteristic
155#421—21no—
156#410—21no—
157#405C22×C15111yescharacteristic
158#367—21no—
159#366—21no—
160#365—22no—
161#360—22no—
162#359—21no—
163#359—21no—
164#344—21no—
165H(3,ℤ/4)—21no—
166C2×#41—21no—
167#135—21no—
168#135—21no—
169#135—21no—
170#135—21no—
171C2×Q16Q8×C15111yescharacteristic
172C2×SD16—21no—
173C2×D8Q8×C15111yescharacteristic
174C2×M16—21no—
175C2×M16D4×C15111yescharacteristic
176C22×C8C23×C15111yescharacteristic
177#117—21no—
178#117—21no—
179#117D4×C15111yescharacteristic
180M32—21no—
181M32D4×C15112yes—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—21no—
185C2×C16D4×C15111yescharacteristic
186C2×C16D4×C15111yescharacteristic
187#108—21no—
188#108—21no—
189#107—21no—
190#107—21no—
191#106—21no—
192#106—21no—
193#104—42no—
194#99—42no—
195#97—21no—
196C4×C8—21no—
197#41—41no—
198#41—41no—
199#41—41no—
200#41—41no—
201C2×Q8—21no—
202C2×D4—21no—
203C2×D4—41no—
204C22×C4—41no—
205C22×C4C2×D4×C15111yescharacteristic
206Q16—21no—
207Q16—21no—
208SD16—41no—
209SD16—41no—
210D8—21no—
211D8—21no—
212M16—21no—
213M16—21no—
214M16—41no—
215M16—41no—
216C2×C8—21no—
217C2×C8—41no—
218C2×C8C2×D4×C15111yescharacteristic
219C2×C8C2×D4×C15111yescharacteristic
220C2×C8C2×Q8×C15111yescharacteristic
221C2×C8#41×C15111yescharacteristic
222C2×C8#41×C15111yescharacteristic
223C2×C8#41×C15111yescharacteristic
224C4⋊C4—21no—
225C4⋊C4—41no—
226C4⋊C4—41no—
227C22⋊C4—21no—
228C22⋊C4—41no—
229C22⋊C4—41no—
230C42—21no—
231C42—41no—
232C42—41no—
233C16—21no—
234C16—21no—
235C16—22no—
236C23—41no—
237C23AGL(1,ℤ/8)×C15111yescharacteristic
238Q8—41no—
239Q8—41no—
240D4—41no—
241D4—41no—
242D4—81no—
243D4—81no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—81no—
247C2×C4—81no—
248C2×C4—81no—
249C2×C4—81no—
250C2×C4C22⋊Q8×C15111yescharacteristic
251C2×C4#123×C15111yescharacteristic
252C2×C4#127×C15111yescharacteristic
253C2×C4#135×C15111yescharacteristic
254C2×C4#135×C15111yescharacteristic
255C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
256C8—41no—
257C8—81no—
258C8C22⋊Q8×C15111yescharacteristic
259C8C22⋊Q8×C15111yescharacteristic
260C8#123×C15111yescharacteristic
261C8#123×C15111yescharacteristic
262C22—41no—
263C22—81no—
264C22—161no—
265C22#478×C15111yescharacteristic
266C22#482×C15111yescharacteristic
267C22#496×C15111yescharacteristic
268C4—81no—
269C4—81no—
270C4—161no—
271C4—161no—
272C4#399×C15111yescharacteristic
273C4#478×C15111yescharacteristic
274C4#482×C15111yescharacteristic
275C4#495×C15111yescharacteristic
276C2—21no—
277C2—21no—
278C2—21no—
279C2—161no—
280C2#2092×C15111yescharacteristic
subgroupG/H
centerC4×C151#482
commutator, Frattini, cosocleC22×C8C23×C151
socleC2×C151#2092
prime radicalC2×#135×C151C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C4×C151 ◁ C22×C4×C151 ◁ #405×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2158×C151C2semidirect
2. #2155×C151C2semidirect
6. #1833×C151C2semidirect
7. #1379×C151C2semidirect
140. #13525C151direct (N × H)
141. C151#13525direct (N × H)
142. #2158C2×C151semidirect
143. #2155C2×C151semidirect
147. #1833C2×C151semidirect
148. #1379C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2158×C1512
#2155×C1512
#2145×C1512
C2×#359×C1512
#1976×C1512
#1833×C1512
#1379×C1512
#13525151