Finite Group Databasebeta

← C151×#13504 #50318429

Subgroups — C151×#13504 #50318429

Order 38656.

278 conjugacy classes of subgroups; only the 98 normal subgroups are shown.

normal subgroups only

This group has 278 conjugacy classes of subgroups — too many to draw. Only its 98 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#2155×C151C211yesmaximal, characteristic, complemented
2#2117×C151C211yesmaximal, characteristic
3#1815×C151C211yesmaximal, characteristic
4#1812×C151C211yesmaximal, characteristic
5#1389×C151C211yesmaximal, characteristic, complemented
6#1386×C151C211yesmaximal, characteristic, complemented
7#1386×C151C211yesmaximal, characteristic, complemented
8C2×#131×C151C2211yescharacteristic
9C2×M32×C151C2211yescharacteristic
10C2×M32×C151C2211yescharacteristic
11C2×#108×C151C2211yescharacteristic
12#427×C151C2211yescharacteristic
13#427×C151C2211yescharacteristic
14C2×#106×C151C2211yescharacteristic
15#417×C151—21no—
16#410×C151—21no—
17#365×C151—22no—
18#350×C151—22no—
19#343×C151—21no—
20H(3,ℤ/4)×C151—21no—
21C2×#41×C151D411yescharacteristic
22#131×C151—21no—
23#131×C151—21no—
24#131×C151—21no—
25#131×C151—21no—
26C2×M16×C151—21no—
27C2×M16×C151—21no—
28C2×M16×C151D411yescharacteristic
29C22×C8×C151—21no—
30C22×C8×C151C2311yescharacteristic
31#117×C151—21no—
32#117×C151—21no—
33C2×C4⋊C4×C151—21no—
34M32×C151—21no—
35M32×C151—21no—
36M32×C151—21no—
37M32×C151D412yes—
38C2×C16×C151—21no—
39C2×C16×C151—21no—
40#108×C151—21no—
41#108×C151—21no—
42#107×C151—21no—
43#107×C151—21no—
44#106×C151—21no—
45#106×C151—21no—
46#106×C151—21no—
47#106×C151—21no—
48#103×C151—41no—
49#102×C151—41no—
50#99×C151—42no—
51#41×C151—21no—
52#41×C151—21no—
53#41×C151—21no—
54#41×C151—21no—
55C2×Q8×C151SD1611yescharacteristic
56C2×D4×C151—21no—
57C2×D4×C151SD1611yescharacteristic
58C22×C4×C151—21no—
59C22×C4×C151—41no—
60C22×C4×C151C2×D411yescharacteristic
61M16×C151—21no—
62M16×C151—21no—
63M16×C151—41no—
64M16×C151—41no—
65M16×C151—41no—
66M16×C151—41no—
67C2×C8×C151—21no—
68C2×C8×C151—41no—
69C2×C8×C151—41no—
70C2×C8×C151—41no—
71C2×C8×C151C2×D411yescharacteristic
72C2×C8×C151#4111yescharacteristic
73C2×C8×C151#4111yescharacteristic
74C2×C8×C151#4111yescharacteristic
75C2×C8×C151#4111yescharacteristic
76C2×C8×C151#4111yescharacteristic
77C4⋊C4×C151—41no—
78C4⋊C4×C151—41no—
79C4⋊C4×C151—41no—
80C4⋊C4×C151—41no—
81C22⋊C4×C151—41no—
82C22⋊C4×C151—41no—
83C42×C151—41no—
84C42×C151—41no—
85C16×C151—22no—
86C16×C151—41no—
87C23×C151—21no—
88C23×C151AGL(1,ℤ/8)11yescharacteristic
89Q8×C151—21no—
90Q8×C151—21no—
91D4×C151—21no—
92D4×C151—21no—
93D4×C151—41no—
94D4×C151—41no—
95C2×C4×C151—21no—
96C2×C4×C151—41no—
97C2×C4×C151—41no—
98C2×C4×C151—81no—
99C2×C4×C151—81no—
100C2×C4×C151—81no—
101C2×C4×C151—161no—
102C2×C4×C151#12111yescharacteristic
103C2×C4×C151#12311yescharacteristic
104C2×C4×C151#12311yescharacteristic
105C2×C4×C151C2×SD1611yescharacteristic
106C2×C4×C151#13511yescharacteristic
107C2×C4×C151#13711yescharacteristic
108C8×C151—41no—
109C8×C151—81no—
110C8×C151#12311yescharacteristic
111C8×C151#12411yescharacteristic
112C8×C151#12611yescharacteristic
113C8×C151#12611yescharacteristic
114C22×C151—41no—
115C22×C151—41no—
116C22×C151—81no—
117C22×C151#46811yescharacteristic
118C22×C151#48111yescharacteristic
119C22×C151#48211yescharacteristic
120C4×C151—41no—
121C4×C151—161no—
122C4×C151—161no—
123C4×C151—161no—
124C4×C151#39711yescharacteristic
125C4×C151#46511yescharacteristic
126C4×C151#48311yescharacteristic
127C4×C151#48511yescharacteristic
128C2×C151—21no—
129C2×C151—21no—
130C2×C151—21no—
131C2×C151—81no—
132C2×C151#207711yescharacteristic
133#13504C15111yesmaximal, characteristic, direct product factor, Sylow
134C151#1350411yescharacteristic, direct product factor, Sylow
135#2155C2×C15111yescharacteristic, complemented
136#2117C2×C15111yescharacteristic
137#1815C2×C15111yescharacteristic
138#1812C2×C15111yescharacteristic
139#1389C2×C15111yescharacteristic, complemented
140#1386C2×C15111yescharacteristic, complemented
141#1386C2×C15111yescharacteristic, complemented
142C2×#131C22×C15111yescharacteristic
143C2×M32C22×C15111yescharacteristic
144C2×M32C22×C15111yescharacteristic
145C2×#108C22×C15111yescharacteristic
146#427C22×C15111yescharacteristic
147#427C22×C15111yescharacteristic
148C2×#106C22×C15111yescharacteristic
149#417—21no—
150#410—21no—
151#365—22no—
152#350—22no—
153#343—21no—
154H(3,ℤ/4)—21no—
155C2×#41D4×C15111yescharacteristic
156#131—21no—
157#131—21no—
158#131—21no—
159#131—21no—
160C2×M16—21no—
161C2×M16—21no—
162C2×M16D4×C15111yescharacteristic
163C22×C8—21no—
164C22×C8C23×C15111yescharacteristic
165#117—21no—
166#117—21no—
167C2×C4⋊C4—21no—
168M32—21no—
169M32—21no—
170M32—21no—
171M32D4×C15112yes—
172C2×C16—21no—
173C2×C16—21no—
174#108—21no—
175#108—21no—
176#107—21no—
177#107—21no—
178#106—21no—
179#106—21no—
180#106—21no—
181#106—21no—
182#103—41no—
183#102—41no—
184#99—42no—
185#41—21no—
186#41—21no—
187#41—21no—
188#41—21no—
189C2×Q8SD16×C15111yescharacteristic
190C2×D4—21no—
191C2×D4SD16×C15111yescharacteristic
192C22×C4—21no—
193C22×C4—41no—
194C22×C4C2×D4×C15111yescharacteristic
195M16—21no—
196M16—21no—
197M16—41no—
198M16—41no—
199M16—41no—
200M16—41no—
201C2×C8—21no—
202C2×C8—41no—
203C2×C8—41no—
204C2×C8—41no—
205C2×C8C2×D4×C15111yescharacteristic
206C2×C8#41×C15111yescharacteristic
207C2×C8#41×C15111yescharacteristic
208C2×C8#41×C15111yescharacteristic
209C2×C8#41×C15111yescharacteristic
210C2×C8#41×C15111yescharacteristic
211C4⋊C4—41no—
212C4⋊C4—41no—
213C4⋊C4—41no—
214C4⋊C4—41no—
215C22⋊C4—41no—
216C22⋊C4—41no—
217C42—41no—
218C42—41no—
219C16—22no—
220C16—41no—
221C23—21no—
222C23AGL(1,ℤ/8)×C15111yescharacteristic
223Q8—21no—
224Q8—21no—
225D4—21no—
226D4—21no—
227D4—41no—
228D4—41no—
229C2×C4—21no—
230C2×C4—41no—
231C2×C4—41no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4—81no—
235C2×C4—161no—
236C2×C4#121×C15111yescharacteristic
237C2×C4#123×C15111yescharacteristic
238C2×C4#123×C15111yescharacteristic
239C2×C4C2×SD16×C15111yescharacteristic
240C2×C4#135×C15111yescharacteristic
241C2×C4#137×C15111yescharacteristic
242C8—41no—
243C8—81no—
244C8#123×C15111yescharacteristic
245C8#124×C15111yescharacteristic
246C8#126×C15111yescharacteristic
247C8#126×C15111yescharacteristic
248C22—41no—
249C22—41no—
250C22—81no—
251C22#468×C15111yescharacteristic
252C22#481×C15111yescharacteristic
253C22#482×C15111yescharacteristic
254C4—41no—
255C4—161no—
256C4—161no—
257C4—161no—
258C4#397×C15111yescharacteristic
259C4#465×C15111yescharacteristic
260C4#483×C15111yescharacteristic
261C4#485×C15111yescharacteristic
262C2—21no—
263C2—21no—
264C2—21no—
265C2—81no—
266C2#2077×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#2077
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC2×#41×C151D4
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C22×C4×C151 ◁ C2×#131×C151 ◁ G

Complements

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

NH ≅ G/Ntype
1. #2155×C151C2semidirect
5. #1389×C151C2semidirect
6. #1386×C151C2semidirect
7. #1386×C151C2semidirect
133. #13504C151direct (N × H)
134. C151#13504direct (N × H)
135. #2155C2×C151semidirect
139. #1389C2×C151semidirect
140. #1386C2×C151semidirect
141. #1386C2×C151semidirect

Maximal subgroups

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

subgroupindex
#2155×C1512
#2117×C1512
#1815×C1512
#1812×C1512
#1389×C1512
#1386×C1512
#13504151