Finite Group Databasebeta

← C151×#7496 #50312421

Subgroups — C151×#7496 #50312421

Order 38656.

274 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 66 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#2132×C151C211yesmaximal, characteristic
2#1884×C151C211yesmaximal, characteristic
3#1560×C151C211yesmaximal, characteristic
4#568×C151C411yescharacteristic
5#532×C151C2211yescharacteristic
6#423×C151—21no—
7#421×C151—21no—
8#413×C151—21no—
9#410×C151C411yescharacteristic
10#356×C151—21no—
11#355×C151C412yescomplemented
12#339×C151—21no—
13#333×C151—21no—
14#331×C151C412yescomplemented
15C2×#41×C151C2×C411yescharacteristic
16C2×#41×C151D411yescharacteristic
17#131×C151—42no—
18C2×M16×C151—21no—
19C2×M16×C151—41no—
20C2×M16×C151—41no—
21C2×M16×C151—41no—
22C4⋊Q8×C151D411yescharacteristic
23#127×C151C2×C411yescharacteristic
24#124×C151C2×C411yescharacteristic
25#124×C151Q811yescharacteristic
26#121×C151—41no—
27C4×D4×C151—41no—
28#117×C151—21no—
29C2×C42×C151D411yescharacteristic
30C4⋊C8×C151—22no—
31C4⋊C8×C151—41no—
32#104×C151—42no—
33#101×C151—22no—
34#100×C151—41no—
35#99×C151—41no—
36#41×C151—41no—
37#41×C151—41no—
38#41×C151—41no—
39#41×C151—41no—
40C2×Q8×C151C22⋊C411yescharacteristic
41C2×Q8×C151C4⋊C411yescharacteristic
42C2×D4×C151—21no—
43C2×D4×C151—21no—
44C2×D4×C151—41no—
45C2×D4×C151C4211yescharacteristic
46C2×D4×C151C4⋊C411yescharacteristic
47C22×C4×C151—21no—
48C22×C4×C151—21no—
49C22×C4×C151—21no—
50C22×C4×C151C22⋊C411yescharacteristic
51M16×C151—22no—
52M16×C151—41no—
53M16×C151—42no—
54M16×C151—42no—
55M16×C151—82no—
56M16×C151—81no—
57C2×C8×C151—41no—
58C2×C8×C151—42no—
59C2×C8×C151—42no—
60C2×C8×C151—81no—
61C4⋊C4×C151—41no—
62C4⋊C4×C151—41no—
63C22⋊C4×C151—41no—
64C22⋊C4×C151—41no—
65C22⋊C4×C151—41no—
66C42×C151—21no—
67C42×C151—41no—
68C42×C151C22⋊C411yescharacteristic
69C42×C151C4⋊C411yescharacteristic
70C23×C151—21no—
71C23×C151—21no—
72C23×C151#9911yescharacteristic
73Q8×C151—41no—
74Q8×C151—41no—
75D4×C151—41no—
76D4×C151—41no—
77D4×C151—42no—
78D4×C151—81no—
79D4×C151—81no—
80D4×C151—81no—
81C2×C4×C151—21no—
82C2×C4×C151—21no—
83C2×C4×C151—21no—
84C2×C4×C151—21no—
85C2×C4×C151—21no—
86C2×C4×C151—21no—
87C2×C4×C151—41no—
88C2×C4×C151—41no—
89C2×C4×C151—41no—
90C2×C4×C151—41no—
91C2×C4×C151—41no—
92C2×C4×C151—41no—
93C2×C4×C151—81no—
94C2×C4×C151#9511yescharacteristic
95C2×C4×C151#9911yescharacteristic
96C8×C151—42no—
97C8×C151—82no—
98C8×C151—82no—
99C22×C151—21no—
100C22×C151—41no—
101C22×C151—41no—
102C22×C151—41no—
103C22×C151—81no—
104C22×C151—81no—
105C22×C151#34211yescharacteristic
106C4×C151—21no—
107C4×C151—21no—
108C4×C151—21no—
109C4×C151—41no—
110C4×C151—41no—
111C4×C151—41no—
112C4×C151—161no—
113C4×C151AΣL(1,𝔽16)11yescharacteristic
114C4×C151#35211yescharacteristic
115C2×C151—21no—
116C2×C151—41no—
117C2×C151—81no—
118C2×C151—81no—
119C2×C151#139011yescharacteristic
120#7496C15111yesmaximal, characteristic, direct product factor, Sylow
121C151#749611yescharacteristic, direct product factor, Sylow
122#2132C2×C15111yescharacteristic
123#1884C2×C15111yescharacteristic
124#1560C2×C15111yescharacteristic
125#568C4×C15111yescharacteristic
126#532C22×C15111yescharacteristic
127#423—21no—
128#421—21no—
129#413—21no—
130#410C4×C15111yescharacteristic
131#356—21no—
132#355C4×C15112yescomplemented
133#339—21no—
134#333—21no—
135#331C4×C15112yescomplemented
136C2×#41C2×C4×C15111yescharacteristic
137C2×#41D4×C15111yescharacteristic
138#131—42no—
139C2×M16—21no—
140C2×M16—41no—
141C2×M16—41no—
142C2×M16—41no—
143C4⋊Q8D4×C15111yescharacteristic
144#127C2×C4×C15111yescharacteristic
145#124C2×C4×C15111yescharacteristic
146#124Q8×C15111yescharacteristic
147#121—41no—
148C4×D4—41no—
149#117—21no—
150C2×C42D4×C15111yescharacteristic
151C4⋊C8—22no—
152C4⋊C8—41no—
153#104—42no—
154#101—22no—
155#100—41no—
156#99—41no—
157#41—41no—
158#41—41no—
159#41—41no—
160#41—41no—
161C2×Q8C22⋊C4×C15111yescharacteristic
162C2×Q8C4⋊C4×C15111yescharacteristic
163C2×D4—21no—
164C2×D4—21no—
165C2×D4—41no—
166C2×D4C42×C15111yescharacteristic
167C2×D4C4⋊C4×C15111yescharacteristic
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4C22⋊C4×C15111yescharacteristic
172M16—22no—
173M16—41no—
174M16—42no—
175M16—42no—
176M16—82no—
177M16—81no—
178C2×C8—41no—
179C2×C8—42no—
180C2×C8—42no—
181C2×C8—81no—
182C4⋊C4—41no—
183C4⋊C4—41no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—41no—
187C42—21no—
188C42—41no—
189C42C22⋊C4×C15111yescharacteristic
190C42C4⋊C4×C15111yescharacteristic
191C23—21no—
192C23—21no—
193C23#99×C15111yescharacteristic
194Q8—41no—
195Q8—41no—
196D4—41no—
197D4—41no—
198D4—42no—
199D4—81no—
200D4—81no—
201D4—81no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—41no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—81no—
215C2×C4#95×C15111yescharacteristic
216C2×C4#99×C15111yescharacteristic
217C8—42no—
218C8—82no—
219C8—82no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—81no—
225C22—81no—
226C22#342×C15111yescharacteristic
227C4—21no—
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—41no—
233C4—161no—
234C4AΣL(1,𝔽16)×C15111yescharacteristic
235C4#352×C15111yescharacteristic
236C2—21no—
237C2—41no—
238C2—81no—
239C2—81no—
240C2#1390×C15111yescharacteristic
subgroupG/H
center, socleC2×C151#1390
commutatorC2×D4C42×C151
Frattini, cosocle#532C22×C151
prime radical#532×C151C22
LCSG ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C151 ◁ C2×C4×C151 ◁ C22×C4×C151 ◁ #532×C151 ◁ G

Complements

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

NH ≅ G/Ntype
11. #355×C151C4semidirect
14. #331×C151C4semidirect
120. #7496C151direct (N × H)
121. C151#7496direct (N × H)
132. #355C4×C151semidirect
135. #331C4×C151semidirect

Maximal subgroups

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

subgroupindex
#2132×C1512
#1884×C1512
#1560×C1512
#7496151