Finite Group Databasebeta

← C151×#13415 #50318340

Subgroups — C151×#13415 #50318340

Order 38656.

436 conjugacy classes of subgroups; only the 114 normal subgroups are shown.

normal subgroups only

This group has 436 conjugacy classes of subgroups — too many to draw. Only its 114 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
1C2×#494×C151C211yesmaximal, characteristic
2C2×#362×C151C212yesmaximal
3#2141×C151C212yesmaximal
4#1945×C151C211yesmaximal, characteristic
5#1376×C151C211yesmaximal, characteristic
6C22×Q16×C151—21no—
7C22×Q16×C151C2212yes—
8C2×C4⋊Q8×C151—21no—
9C2×M32×C151C2212yes—
10#494×C151—24no—
11C2×#108×C151C2211yescharacteristic
12#427×C151C2211yescharacteristic
13#424×C151—21no—
14C2×C4×C8×C151C2211yescharacteristic
15#362×C151—24no—
16#358×C151—24no—
17#339×C151—21no—
18C22×Q8×C151—22no—
19C2×Q16×C151—24no—
20C2×Q16×C151—22no—
21C2×Q16×C151—22no—
22C2×Q16×C151—22no—
23C2×Q16×C151—22no—
24C2×Q16×C151—22no—
25C2×Q16×C151—42no—
26C2×Q16×C151—42no—
27C2×Q16×C151D414yes—
28C2×M16×C151—21no—
29C22×C8×C151D411yescharacteristic
30C22×C8×C151C2311yescharacteristic
31C4⋊Q8×C151—24no—
32C4⋊Q8×C151—42no—
33#117×C151—21no—
34C2×C4⋊C4×C151—42no—
35C2×C42×C151D411yescharacteristic
36M32×C151—22no—
37M32×C151—22no—
38C2×C16×C151—22no—
39#108×C151—22no—
40#107×C151D412yes—
41#106×C151—21no—
42C4⋊C8×C151—42no—
43C4×C8×C151—22no—
44C2×Q8×C151—24no—
45C2×Q8×C151—42no—
46C2×Q8×C151—42no—
47C2×Q8×C151—42no—
48C2×Q8×C151—42no—
49C2×Q8×C151—42no—
50C22×C4×C151—21no—
51C22×C4×C151—42no—
52C22×C4×C151C2×D411yescharacteristic
53Q16×C151—24no—
54Q16×C151—24no—
55Q16×C151—48no—
56Q16×C151—42no—
57Q16×C151—42no—
58M16×C151—41no—
59M16×C151—41no—
60C2×C8×C151—21no—
61C2×C8×C151—21no—
62C2×C8×C151—41no—
63C2×C8×C151D812yes—
64C2×C8×C151C2×D411yescharacteristic
65C2×C8×C151C2×D412yes—
66C2×C8×C151#4112yes—
67C2×C8×C151#4111yescharacteristic
68C4⋊C4×C151—22no—
69C4⋊C4×C151—48no—
70C22⋊C4×C151—41no—
71C42×C151—21no—
72C42×C151—41no—
73C42×C151SD1612yes—
74C16×C151—42no—
75C23×C151AGL(1,ℤ/8)11yescharacteristic
76Q8×C151—44no—
77Q8×C151—44no—
78Q8×C151—82no—
79Q8×C151—82no—
80C2×C4×C151—24no—
81C2×C4×C151—22no—
82C2×C4×C151—44no—
83C2×C4×C151—42no—
84C2×C4×C151—82no—
85C2×C4×C151—82no—
86C2×C4×C151#12011yescharacteristic
87C2×C4×C151#12111yescharacteristic
88C2×C4×C151#12411yescharacteristic
89C2×C4×C151C2×D811yescharacteristic
90C2×C4×C151C2×SD1611yescharacteristic
91C2×C4×C151AGL(1,ℤ/8)11yescharacteristic
92C8×C151—22no—
93C8×C151—81no—
94C8×C151#12112yes—
95C8×C151#12312yes—
96C22×C151—22no—
97C22×C151#45011yescharacteristic
98C22×C151#45911yescharacteristic
99C22×C151#49011yescharacteristic
100C4×C151—24no—
101C4×C151—82no—
102C4×C151—84no—
103C4×C151#39411yescharacteristic
104C4×C151#44711yescharacteristic
105C4×C151#46011yescharacteristic
106C4×C151#48611yescharacteristic
107C2×C151—21no—
108C2×C151—21no—
109C2×C151#204111yescharacteristic
110C2×C151#221412yes—
111#13415C15111yesmaximal, characteristic, direct product factor, Sylow
112C151#1341511yescharacteristic, direct product factor, Sylow
113C2×#494C2×C15111yescharacteristic
114C2×#362C2×C15112yes—
115#2141C2×C15112yes—
116#1945C2×C15111yescharacteristic
117#1376C2×C15111yescharacteristic
118C22×Q16—21no—
119C22×Q16C22×C15112yes—
120C2×C4⋊Q8—21no—
121C2×M32C22×C15112yes—
122#494—24no—
123C2×#108C22×C15111yescharacteristic
124#427C22×C15111yescharacteristic
125#424—21no—
126C2×C4×C8C22×C15111yescharacteristic
127#362—24no—
128#358—24no—
129#339—21no—
130C22×Q8—22no—
131C2×Q16—24no—
132C2×Q16—22no—
133C2×Q16—22no—
134C2×Q16—22no—
135C2×Q16—22no—
136C2×Q16—22no—
137C2×Q16—42no—
138C2×Q16—42no—
139C2×Q16D4×C15114yes—
140C2×M16—21no—
141C22×C8D4×C15111yescharacteristic
142C22×C8C23×C15111yescharacteristic
143C4⋊Q8—24no—
144C4⋊Q8—42no—
145#117—21no—
146C2×C4⋊C4—42no—
147C2×C42D4×C15111yescharacteristic
148M32—22no—
149M32—22no—
150C2×C16—22no—
151#108—22no—
152#107D4×C15112yes—
153#106—21no—
154C4⋊C8—42no—
155C4×C8—22no—
156C2×Q8—24no—
157C2×Q8—42no—
158C2×Q8—42no—
159C2×Q8—42no—
160C2×Q8—42no—
161C2×Q8—42no—
162C22×C4—21no—
163C22×C4—42no—
164C22×C4C2×D4×C15111yescharacteristic
165Q16—24no—
166Q16—24no—
167Q16—48no—
168Q16—42no—
169Q16—42no—
170M16—41no—
171M16—41no—
172C2×C8—21no—
173C2×C8—21no—
174C2×C8—41no—
175C2×C8D8×C15112yes—
176C2×C8C2×D4×C15111yescharacteristic
177C2×C8C2×D4×C15112yes—
178C2×C8#41×C15112yes—
179C2×C8#41×C15111yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—48no—
182C22⋊C4—41no—
183C42—21no—
184C42—41no—
185C42SD16×C15112yes—
186C16—42no—
187C23AGL(1,ℤ/8)×C15111yescharacteristic
188Q8—44no—
189Q8—44no—
190Q8—82no—
191Q8—82no—
192C2×C4—24no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—82no—
197C2×C4—82no—
198C2×C4#120×C15111yescharacteristic
199C2×C4#121×C15111yescharacteristic
200C2×C4#124×C15111yescharacteristic
201C2×C4C2×D8×C15111yescharacteristic
202C2×C4C2×SD16×C15111yescharacteristic
203C2×C4AGL(1,ℤ/8)×C15111yescharacteristic
204C8—22no—
205C8—81no—
206C8#121×C15112yes—
207C8#123×C15112yes—
208C22—22no—
209C22#450×C15111yescharacteristic
210C22#459×C15111yescharacteristic
211C22#490×C15111yescharacteristic
212C4—24no—
213C4—82no—
214C4—84no—
215C4#394×C15111yescharacteristic
216C4#447×C15111yescharacteristic
217C4#460×C15111yescharacteristic
218C4#486×C15111yescharacteristic
219C2—21no—
220C2—21no—
221C2#2041×C15111yescharacteristic
222C2#2214×C15112yes—
subgroupG/H
center, socleC22×C151#459
commutator, Frattini, cosocleC22×C8C23×C151
prime radicalC23×C151AGL(1,ℤ/8)
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C151 ◁ C22×C4×C151 ◁ C2×C4×C8×C151 ◁ G

Complements

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

NH ≅ G/Ntype
111. #13415C151direct (N × H)
112. C151#13415direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#494×C1512
C2×#362×C1512
#2141×C1512
#1945×C1512
#1376×C1512
#13415151