Finite Group Databasebeta

← C151×#12396 #50317321

Subgroups — C151×#12396 #50317321

Order 38656.

318 conjugacy classes of subgroups; only the 86 normal subgroups are shown.

normal subgroups only

This group has 318 conjugacy classes of subgroups — too many to draw. Only its 86 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#3334×C151C211yesmaximal, characteristic
2#2254×C151C211yesmaximal, characteristic, complemented
3#2226×C151C211yesmaximal, characteristic, complemented
4#1675×C151C211yesmaximal, characteristic, complemented
5#1364×C151C211yesmaximal, characteristic, complemented
6#1331×C151C211yesmaximal, characteristic, complemented
7D4⋊C16×C151C211yesmaximal, characteristic, complemented
8#547×C151—21no—
9#500×C151C2211yescharacteristic
10#500×C151C2211yescharacteristic
11#480×C151—22no—
12#476×C151—21no—
13#474×C151—21no—
14#466×C151—21no—
15C4×D8×C151C2211yescharacteristic
16C8×D4×C151C2211yescharacteristic
17C2×#107×C151—21no—
18#367×C151—21no—
19#367×C151—22no—
20C4⋊C16×C151C2211yescharacteristic
21#357×C151—21no—
22C4×C16×C151C2211yescharacteristic
23#335×C151C2211yescharacteristic
24#333×C151—21no—
25C2×#41×C151—41no—
26C2×D8×C151D411yescharacteristic
27C22×C8×C151—21no—
28C4⋊Q8×C151—21no—
29C4⋊Q8×C151—21no—
30#123×C151—42no—
31C22⋊Q8×C151—41no—
32#121×C151—22no—
33C4×D4×C151—21no—
34C4×D4×C151D411yescharacteristic
35C2×C4⋊C4×C151—22no—
36C2×C16×C151—21no—
37C2×C16×C151—21no—
38#107×C151—22no—
39#107×C151—21no—
40#107×C151—21no—
41#107×C151—21no—
42#107×C151D411yescharacteristic
43#107×C151D412yes—
44#106×C151—41no—
45C4⋊C8×C151—21no—
46C4⋊C8×C151D411yescharacteristic
47#102×C151—22no—
48#102×C151—21no—
49#102×C151—41no—
50C22⋊C8×C151—21no—
51C4×C8×C151C2311yescharacteristic
52#41×C151—82no—
53#41×C151—82no—
54C2×Q8×C151—41no—
55C2×Q8×C151—41no—
56C2×D4×C151—21no—
57C2×D4×C151—42no—
58C2×D4×C151D811yescharacteristic
59C22×C4×C151—21no—
60C22×C4×C151—42no—
61C22×C4×C151—41no—
62D8×C151—21no—
63D8×C151—21no—
64C2×C8×C151—21no—
65C2×C8×C151—41no—
66C2×C8×C151—41no—
67C2×C8×C151—41no—
68C2×C8×C151C2×D411yescharacteristic
69C2×C8×C151C2×D411yescharacteristic
70C4⋊C4×C151—21no—
71C4⋊C4×C151—22no—
72C4⋊C4×C151—42no—
73C4⋊C4×C151—41no—
74C4⋊C4×C151—41no—
75C4⋊C4×C151—41no—
76C4⋊C4×C151D811yescharacteristic
77C22⋊C4×C151—21no—
78C22⋊C4×C151—42no—
79C22⋊C4×C151—41no—
80C42×C151C2×D411yescharacteristic
81C16×C151—22no—
82C16×C151—41no—
83C23×C151—21no—
84C23×C151—41no—
85Q8×C151—81no—
86Q8×C151—81no—
87Q8×C151—161no—
88D4×C151—21no—
89D4×C151—41no—
90D4×C151—41no—
91D4×C151—84no—
92D4×C151SD3212yes—
93C2×C4×C151—21no—
94C2×C4×C151—41no—
95C2×C4×C151—41no—
96C2×C4×C151—42no—
97C2×C4×C151—41no—
98C2×C4×C151—84no—
99C2×C4×C151—81no—
100C2×C4×C151—81no—
101C2×C4×C151—81no—
102C2×C4×C151#12011yescharacteristic
103C2×C4×C151C2×D811yescharacteristic
104C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
105C8×C151—21no—
106C8×C151—41no—
107C8×C151—81no—
108C8×C151#13511yescharacteristic
109C8×C151#13711yescharacteristic
110C22×C151—22no—
111C22×C151—41no—
112C22×C151—41no—
113C22×C151—81no—
114C22×C151—81no—
115C22×C151—81no—
116C22×C151#44711yescharacteristic
117C4×C151—21no—
118C4×C151—41no—
119C4×C151—81no—
120C4×C151—82no—
121C4×C151—161no—
122C4×C151#45211yescharacteristic
123C4×C151#45611yescharacteristic
124C4×C151C2×SD3211yescharacteristic
125C4×C151#50911yescharacteristic
126C2×C151—42no—
127C2×C151—161no—
128C2×C151#164711yescharacteristic
129C2×C151#218711yescharacteristic
130C2×C151#219311yescharacteristic
131#12396C15111yesmaximal, characteristic, direct product factor, Sylow
132C151#1239611yescharacteristic, direct product factor, Sylow
133#3334C2×C15111yescharacteristic
134#2254C2×C15111yescharacteristic, complemented
135#2226C2×C15111yescharacteristic, complemented
136#1675C2×C15111yescharacteristic, complemented
137#1364C2×C15111yescharacteristic, complemented
138#1331C2×C15111yescharacteristic, complemented
139D4⋊C16C2×C15111yescharacteristic, complemented
140#547—21no—
141#500C22×C15111yescharacteristic
142#500C22×C15111yescharacteristic
143#480—22no—
144#476—21no—
145#474—21no—
146#466—21no—
147C4×D8C22×C15111yescharacteristic
148C8×D4C22×C15111yescharacteristic
149C2×#107—21no—
150#367—21no—
151#367—22no—
152C4⋊C16C22×C15111yescharacteristic
153#357—21no—
154C4×C16C22×C15111yescharacteristic
155#335C22×C15111yescharacteristic
156#333—21no—
157C2×#41—41no—
158C2×D8D4×C15111yescharacteristic
159C22×C8—21no—
160C4⋊Q8—21no—
161C4⋊Q8—21no—
162#123—42no—
163C22⋊Q8—41no—
164#121—22no—
165C4×D4—21no—
166C4×D4D4×C15111yescharacteristic
167C2×C4⋊C4—22no—
168C2×C16—21no—
169C2×C16—21no—
170#107—22no—
171#107—21no—
172#107—21no—
173#107—21no—
174#107D4×C15111yescharacteristic
175#107D4×C15112yes—
176#106—41no—
177C4⋊C8—21no—
178C4⋊C8D4×C15111yescharacteristic
179#102—22no—
180#102—21no—
181#102—41no—
182C22⋊C8—21no—
183C4×C8C23×C15111yescharacteristic
184#41—82no—
185#41—82no—
186C2×Q8—41no—
187C2×Q8—41no—
188C2×D4—21no—
189C2×D4—42no—
190C2×D4D8×C15111yescharacteristic
191C22×C4—21no—
192C22×C4—42no—
193C22×C4—41no—
194D8—21no—
195D8—21no—
196C2×C8—21no—
197C2×C8—41no—
198C2×C8—41no—
199C2×C8—41no—
200C2×C8C2×D4×C15111yescharacteristic
201C2×C8C2×D4×C15111yescharacteristic
202C4⋊C4—21no—
203C4⋊C4—22no—
204C4⋊C4—42no—
205C4⋊C4—41no—
206C4⋊C4—41no—
207C4⋊C4—41no—
208C4⋊C4D8×C15111yescharacteristic
209C22⋊C4—21no—
210C22⋊C4—42no—
211C22⋊C4—41no—
212C42C2×D4×C15111yescharacteristic
213C16—22no—
214C16—41no—
215C23—21no—
216C23—41no—
217Q8—81no—
218Q8—81no—
219Q8—161no—
220D4—21no—
221D4—41no—
222D4—41no—
223D4—84no—
224D4SD32×C15112yes—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—41no—
229C2×C4—42no—
230C2×C4—84no—
231C2×C4—81no—
232C2×C4—81no—
233C2×C4—81no—
234C2×C4#120×C15111yescharacteristic
235C2×C4C2×D8×C15111yescharacteristic
236C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
237C8—21no—
238C8—41no—
239C8—81no—
240C8#135×C15111yescharacteristic
241C8#137×C15111yescharacteristic
242C22—22no—
243C22—41no—
244C22—41no—
245C22—81no—
246C22—81no—
247C22—81no—
248C22#447×C15111yescharacteristic
249C4—21no—
250C4—41no—
251C4—81no—
252C4—82no—
253C4—161no—
254C4#452×C15111yescharacteristic
255C4#456×C15111yescharacteristic
256C4C2×SD32×C15111yescharacteristic
257C4#509×C15111yescharacteristic
258C2—42no—
259C2—161no—
260C2#1647×C15111yescharacteristic
261C2#2187×C15111yescharacteristic
262C2#2193×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#447
commutator, Frattini, cosocleC4×C8C23×C151
prime radical#3334×C151C2
LCSG ▷ C4×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C42×C151 ◁ C8×D4×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2254×C151C2semidirect
3. #2226×C151C2semidirect
4. #1675×C151C2semidirect
5. #1364×C151C2semidirect
6. #1331×C151C2semidirect
7. D4⋊C16×C151C2semidirect
131. #12396C151direct (N × H)
132. C151#12396direct (N × H)
134. #2254C2×C151semidirect
135. #2226C2×C151semidirect
136. #1675C2×C151semidirect
137. #1364C2×C151semidirect
138. #1331C2×C151semidirect
139. D4⋊C16C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3334×C1512
#2254×C1512
#2226×C1512
#1675×C1512
#1364×C1512
#1331×C1512
D4⋊C16×C1512
#12396151