Finite Group Databasebeta

← C151×#9807 #50314732

Subgroups — C151×#9807 #50314732

Order 38656.

466 conjugacy classes of subgroups; only the 150 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 150 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
2#1997×C151C212yesmaximal
3#1566×C151C211yesmaximal, characteristic
4#1548×C151C212yesmaximal
5#1451×C151C211yesmaximal, characteristic
6C22×Q16×C151C414yes—
7C2×C4⋊Q8×C151C2212yes—
8#494×C151—21no—
9#494×C151—21no—
10#494×C151—22no—
11#431×C151C2211yescharacteristic
12#423×C151C2212yes—
13C4×M16×C151C2211yescharacteristic
14C2×C4×C8×C151C2211yescharacteristic
15#343×C151—24no—
16#334×C151—22no—
17#333×C151—24no—
18#322×C151—21no—
19#322×C151—21no—
20C22×Q8×C151C2×C414yes—
21C2×Q16×C151—24no—
22C2×Q16×C151—24no—
23C2×Q16×C151—48no—
24C2×M16×C151—22no—
25C2×M16×C151D412yes—
26C22×C8×C151C2×C412yes—
27C4⋊Q8×C151—22no—
28C4⋊Q8×C151—22no—
29C4⋊Q8×C151—22no—
30C4⋊Q8×C151—22no—
31C2×C4⋊C4×C151—22no—
32C2×C4⋊C4×C151—22no—
33C2×C42×C151C2311yescharacteristic
34C4⋊C8×C151—22no—
35C4⋊C8×C151—22no—
36C4⋊C8×C151D412yes—
37C22⋊C8×C151—21no—
38#97×C151—21no—
39C4×C8×C151—21no—
40C4×C8×C151—21no—
41C4×C8×C151D411yescharacteristic
42C4×C8×C151D411yescharacteristic
43C4×C8×C151D412yes—
44C2×Q8×C151—24no—
45C2×Q8×C151—24no—
46C2×Q8×C151—48no—
47C22×C4×C151—24no—
48C22×C4×C151C22×C411yescharacteristic
49C22×C4×C151C2×D411yescharacteristic
50C22×C4×C151#4111yescharacteristic
51Q16×C151—48no—
52Q16×C151—48no—
53M16×C151—24no—
54M16×C151—44no—
55C2×C8×C151—24no—
56C2×C8×C151—22no—
57C2×C8×C151—22no—
58C2×C8×C151—42no—
59C2×C8×C151C22⋊C412yes—
60C2×C8×C151C22⋊C412yes—
61C4⋊C4×C151—42no—
62C4⋊C4×C151—42no—
63C4⋊C4×C151—42no—
64C4⋊C4×C151—42no—
65C42×C151C2×D411yescharacteristic
66C42×C151C2×D411yescharacteristic
67C42×C151C2×D411yescharacteristic
68C42×C151#4111yescharacteristic
69C23×C151C4×D411yescharacteristic
70Q8×C151—48no—
71Q8×C151—84no—
72C2×C4×C151—22no—
73C2×C4×C151—22no—
74C2×C4×C151—44no—
75C2×C4×C151—84no—
76C2×C4×C151C2×C22⋊C411yescharacteristic
77C2×C4×C151C4×D411yescharacteristic
78C2×C4×C151#12111yescharacteristic
79C2×C4×C151#12111yescharacteristic
80C2×C4×C151#12411yescharacteristic
81C2×C4×C151#12711yescharacteristic
82C2×C4×C151#13714yes—
83C8×C151—22no—
84C8×C151—42no—
85C8×C151—42no—
86C8×C151—82no—
87C8×C151#10014yes—
88C22×C151—21no—
89C22×C151—21no—
90C22×C151#39011yescharacteristic
91C22×C151#44112yes—
92C4×C151—21no—
93C4×C151—21no—
94C4×C151—84no—
95C4×C151C2×#10012yes—
96C4×C151#47012yes—
97C4×C151#47312yes—
98C4×C151#49712yes—
99C2×C151—22no—
100C2×C151#196511yescharacteristic
101C2×C151#197111yescharacteristic
102C2×C151#197911yescharacteristic
103#9807C15111yesmaximal, characteristic, direct product factor, Sylow
104C151#980711yescharacteristic, direct product factor, Sylow
105C2×#494C2×C15111yescharacteristic
106#1997C2×C15112yes—
107#1566C2×C15111yescharacteristic
108#1548C2×C15112yes—
109#1451C2×C15111yescharacteristic
110C22×Q16C4×C15114yes—
111C2×C4⋊Q8C22×C15112yes—
112#494—21no—
113#494—21no—
114#494—22no—
115#431C22×C15111yescharacteristic
116#423C22×C15112yes—
117C4×M16C22×C15111yescharacteristic
118C2×C4×C8C22×C15111yescharacteristic
119#343—24no—
120#334—22no—
121#333—24no—
122#322—21no—
123#322—21no—
124C22×Q8C2×C4×C15114yes—
125C2×Q16—24no—
126C2×Q16—24no—
127C2×Q16—48no—
128C2×M16—22no—
129C2×M16D4×C15112yes—
130C22×C8C2×C4×C15112yes—
131C4⋊Q8—22no—
132C4⋊Q8—22no—
133C4⋊Q8—22no—
134C4⋊Q8—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C42C23×C15111yescharacteristic
138C4⋊C8—22no—
139C4⋊C8—22no—
140C4⋊C8D4×C15112yes—
141C22⋊C8—21no—
142#97—21no—
143C4×C8—21no—
144C4×C8—21no—
145C4×C8D4×C15111yescharacteristic
146C4×C8D4×C15111yescharacteristic
147C4×C8D4×C15112yes—
148C2×Q8—24no—
149C2×Q8—24no—
150C2×Q8—48no—
151C22×C4—24no—
152C22×C4C22×C4×C15111yescharacteristic
153C22×C4C2×D4×C15111yescharacteristic
154C22×C4#41×C15111yescharacteristic
155Q16—48no—
156Q16—48no—
157M16—24no—
158M16—44no—
159C2×C8—24no—
160C2×C8—22no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8C22⋊C4×C15112yes—
164C2×C8C22⋊C4×C15112yes—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C42C2×D4×C15111yescharacteristic
170C42C2×D4×C15111yescharacteristic
171C42C2×D4×C15111yescharacteristic
172C42#41×C15111yescharacteristic
173C23C4×D4×C15111yescharacteristic
174Q8—48no—
175Q8—84no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—44no—
179C2×C4—84no—
180C2×C4C2×C22⋊C4×C15111yescharacteristic
181C2×C4C4×D4×C15111yescharacteristic
182C2×C4#121×C15111yescharacteristic
183C2×C4#121×C15111yescharacteristic
184C2×C4#124×C15111yescharacteristic
185C2×C4#127×C15111yescharacteristic
186C2×C4#137×C15114yes—
187C8—22no—
188C8—42no—
189C8—42no—
190C8—82no—
191C8#100×C15114yes—
192C22—21no—
193C22—21no—
194C22#390×C15111yescharacteristic
195C22#441×C15112yes—
196C4—21no—
197C4—21no—
198C4—84no—
199C4C2×#100×C15112yes—
200C4#470×C15112yes—
201C4#473×C15112yes—
202C4#497×C15112yes—
203C2—22no—
204C2#1965×C15111yescharacteristic
205C2#1971×C15111yescharacteristic
206C2#1979×C15111yescharacteristic
subgroupG/H
center, socleC22×C151#390
commutatorC22×C4C22×C4×C151
Frattini, cosocleC2×C42C23×C151
prime radicalC23×C151C4×D4
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
103. #9807C151direct (N × H)
104. C151#9807direct (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
#1997×C1512
#1566×C1512
#1548×C1512
#1451×C1512
#9807151