Finite Group Databasebeta

← C151×#11951 #50316876

Subgroups — C151×#11951 #50316876

Order 38656.

340 conjugacy classes of subgroups; only the 118 normal subgroups are shown.

normal subgroups only

This group has 340 conjugacy classes of subgroups — too many to draw. Only its 118 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#3169×C151C211yesmaximal, characteristic
2#2163×C151C211yesmaximal, characteristic, complemented
3#1564×C151C211yesmaximal, characteristic, complemented
4#1364×C151C212yesmaximal, complemented
5#1361×C151C212yesmaximal, complemented
6#532×C151—21no—
7#500×C151C2211yescharacteristic
8#493×C151C2211yescharacteristic
9#486×C151—21no—
10#466×C151—21no—
11#466×C151C412yes—
12C4×D8×C151—21no—
13C4×D8×C151C412yes—
14#431×C151—21no—
15C2×C4×C8×C151C2211yescharacteristic
16C4⋊C16×C151C2212yes—
17C22⋊C16×C151—21no—
18#346×C151—21no—
19#335×C151C2212yes—
20#334×C151—21no—
21C2×#41×C151—41no—
22C2×D8×C151—21no—
23C2×D8×C151C2×C412yes—
24C22×C8×C151C2×C411yescharacteristic
25C22×C8×C151D411yescharacteristic
26C4⋊Q8×C151—21no—
27#127×C151—21no—
28#124×C151—41no—
29#121×C151—22no—
30#121×C151—41no—
31C4×D4×C151—22no—
32C4×D4×C151—41no—
33C2×C42×C151D411yescharacteristic
34C2×C16×C151—22no—
35#107×C151—21no—
36#107×C151C2×C412yes—
37C4⋊C8×C151—22no—
38#102×C151—22no—
39#102×C151—22no—
40C22⋊C8×C151—41no—
41C4×C8×C151—41no—
42C4×C8×C151C2×C411yescharacteristic
43C4×C8×C151D411yescharacteristic
44C4×C8×C151D411yescharacteristic
45C4×C8×C151C2311yescharacteristic
46#41×C151—84no—
47C2×Q8×C151—41no—
48C2×D4×C151—22no—
49C2×D4×C151—42no—
50C2×D4×C151—41no—
51C2×D4×C151—41no—
52C22×C4×C151—42no—
53C22×C4×C151C22⋊C411yescharacteristic
54C22×C4×C151D811yescharacteristic
55C22×C4×C151SD1611yescharacteristic
56D8×C151—42no—
57D8×C151—42no—
58C2×C8×C151—22no—
59C2×C8×C151—41no—
60C2×C8×C151—42no—
61C2×C8×C151C22⋊C411yescharacteristic
62C2×C8×C151C22⋊C411yescharacteristic
63C2×C8×C151C22×C411yescharacteristic
64C2×C8×C151C2×D411yescharacteristic
65C4⋊C4×C151—22no—
66C4⋊C4×C151—41no—
67C22⋊C4×C151—42no—
68C22⋊C4×C151—42no—
69C42×C151C22⋊C411yescharacteristic
70C42×C151D811yescharacteristic
71C42×C151SD1611yescharacteristic
72C42×C151C2×D411yescharacteristic
73C16×C151—42no—
74C23×C151—42no—
75C23×C151#10211yescharacteristic
76Q8×C151—82no—
77D4×C151—42no—
78D4×C151—42no—
79D4×C151—82no—
80D4×C151—84no—
81D4×C151—82no—
82C2×C4×C151—21no—
83C2×C4×C151—21no—
84C2×C4×C151—22no—
85C2×C4×C151—41no—
86C2×C4×C151—42no—
87C2×C4×C151—84no—
88C2×C4×C151#10211yescharacteristic
89C2×C4×C151#10211yescharacteristic
90C2×C4×C151#10211yescharacteristic
91C2×C4×C151C2×C22⋊C411yescharacteristic
92C2×C4×C151C2×D811yescharacteristic
93C2×C4×C151C2×SD1611yescharacteristic
94C8×C151—21no—
95C8×C151—21no—
96C8×C151—21no—
97C8×C151—82no—
98C8×C151#13512yes—
99C22×C151—21no—
100C22×C151—21no—
101C22×C151—21no—
102C22×C151—82no—
103C22×C151—82no—
104C22×C151—82no—
105C22×C151C2×#10211yescharacteristic
106C4×C151—21no—
107C4×C151—21no—
108C4×C151—21no—
109C4×C151—21no—
110C4×C151—82no—
111C4×C151#41311yescharacteristic
112C4×C151#41611yescharacteristic
113C4×C151#50912yes—
114C2×C151—41no—
115C2×C151—162no—
116C2×C151#154011yescharacteristic
117C2×C151#214011yescharacteristic
118C2×C151#214811yescharacteristic
119#11951C15111yesmaximal, characteristic, direct product factor, Sylow
120C151#1195111yescharacteristic, direct product factor, Sylow
121#3169C2×C15111yescharacteristic
122#2163C2×C15111yescharacteristic, complemented
123#1564C2×C15111yescharacteristic, complemented
124#1364C2×C15112yescomplemented
125#1361C2×C15112yescomplemented
126#532—21no—
127#500C22×C15111yescharacteristic
128#493C22×C15111yescharacteristic
129#486—21no—
130#466—21no—
131#466C4×C15112yes—
132C4×D8—21no—
133C4×D8C4×C15112yes—
134#431—21no—
135C2×C4×C8C22×C15111yescharacteristic
136C4⋊C16C22×C15112yes—
137C22⋊C16—21no—
138#346—21no—
139#335C22×C15112yes—
140#334—21no—
141C2×#41—41no—
142C2×D8—21no—
143C2×D8C2×C4×C15112yes—
144C22×C8C2×C4×C15111yescharacteristic
145C22×C8D4×C15111yescharacteristic
146C4⋊Q8—21no—
147#127—21no—
148#124—41no—
149#121—22no—
150#121—41no—
151C4×D4—22no—
152C4×D4—41no—
153C2×C42D4×C15111yescharacteristic
154C2×C16—22no—
155#107—21no—
156#107C2×C4×C15112yes—
157C4⋊C8—22no—
158#102—22no—
159#102—22no—
160C22⋊C8—41no—
161C4×C8—41no—
162C4×C8C2×C4×C15111yescharacteristic
163C4×C8D4×C15111yescharacteristic
164C4×C8D4×C15111yescharacteristic
165C4×C8C23×C15111yescharacteristic
166#41—84no—
167C2×Q8—41no—
168C2×D4—22no—
169C2×D4—42no—
170C2×D4—41no—
171C2×D4—41no—
172C22×C4—42no—
173C22×C4C22⋊C4×C15111yescharacteristic
174C22×C4D8×C15111yescharacteristic
175C22×C4SD16×C15111yescharacteristic
176D8—42no—
177D8—42no—
178C2×C8—22no—
179C2×C8—41no—
180C2×C8—42no—
181C2×C8C22⋊C4×C15111yescharacteristic
182C2×C8C22⋊C4×C15111yescharacteristic
183C2×C8C22×C4×C15111yescharacteristic
184C2×C8C2×D4×C15111yescharacteristic
185C4⋊C4—22no—
186C4⋊C4—41no—
187C22⋊C4—42no—
188C22⋊C4—42no—
189C42C22⋊C4×C15111yescharacteristic
190C42D8×C15111yescharacteristic
191C42SD16×C15111yescharacteristic
192C42C2×D4×C15111yescharacteristic
193C16—42no—
194C23—42no—
195C23#102×C15111yescharacteristic
196Q8—82no—
197D4—42no—
198D4—42no—
199D4—82no—
200D4—84no—
201D4—82no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—22no—
205C2×C4—41no—
206C2×C4—42no—
207C2×C4—84no—
208C2×C4#102×C15111yescharacteristic
209C2×C4#102×C15111yescharacteristic
210C2×C4#102×C15111yescharacteristic
211C2×C4C2×C22⋊C4×C15111yescharacteristic
212C2×C4C2×D8×C15111yescharacteristic
213C2×C4C2×SD16×C15111yescharacteristic
214C8—21no—
215C8—21no—
216C8—21no—
217C8—82no—
218C8#135×C15112yes—
219C22—21no—
220C22—21no—
221C22—21no—
222C22—82no—
223C22—82no—
224C22—82no—
225C22C2×#102×C15111yescharacteristic
226C4—21no—
227C4—21no—
228C4—21no—
229C4—21no—
230C4—82no—
231C4#413×C15111yescharacteristic
232C4#416×C15111yescharacteristic
233C4#509×C15112yes—
234C2—41no—
235C2—162no—
236C2#1540×C15111yescharacteristic
237C2#2140×C15111yescharacteristic
238C2#2148×C15111yescharacteristic
subgroupG/H
center, socleC22×C151C2×#102
commutatorC2×C8C22×C4×C151
Frattini, cosocleC4×C8C23×C151
prime radical#3169×C151C2
LCSG ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
2. #2163×C151C2semidirect
3. #1564×C151C2semidirect
4. #1364×C151C2semidirect
5. #1361×C151C2semidirect
119. #11951C151direct (N × H)
120. C151#11951direct (N × H)
122. #2163C2×C151semidirect
123. #1564C2×C151semidirect
124. #1364C2×C151semidirect
125. #1361C2×C151semidirect

Maximal subgroups

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

subgroupindex
#3169×C1512
#2163×C1512
#1564×C1512
#1364×C1512
#1361×C1512
#11951151