Finite Group Databasebeta

← C151×#10576 #50315501

Subgroups — C151×#10576 #50315501

Order 38656.

406 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 146 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#2571×C151C211yesmaximal, characteristic
2#1948×C151C212yesmaximal
3#1845×C151C211yesmaximal, characteristic
4#1296×C151C211yesmaximal, characteristic
5#1279×C151C212yesmaximal
6C2×#107×C151—22no—
7C2×#106×C151—22no—
8C2×C4⋊C8×C151C2212yes—
9C2×C4×C8×C151C2211yescharacteristic
10#400×C151—22no—
11#389×C151—22no—
12#384×C151C2211yescharacteristic
13#384×C151C2211yescharacteristic
14#382×C151—22no—
15C4×C4⋊C4×C151C2212yes—
16#340×C151—22no—
17C22×C8×C151—21no—
18C22×C8×C151—22no—
19C2×C4⋊C4×C151—22no—
20C2×C4⋊C4×C151—22no—
21C2×C4⋊C4×C151—21no—
22C2×C4⋊C4×C151—22no—
23C2×C4⋊C4×C151D412yes—
24C2×C4⋊C4×C151D412yes—
25C2×C4⋊C4×C151D412yes—
26C2×C42×C151—22no—
27C2×C42×C151C2311yescharacteristic
28#107×C151—44no—
29#106×C151—44no—
30C4⋊C8×C151—22no—
31C4⋊C8×C151Q814yes—
32C4×C8×C151—21no—
33C4×C8×C151Q812yes—
34#95×C151—22no—
35#95×C151—24no—
36#95×C151—22no—
37C22×C4×C151—22no—
38C22×C4×C151—22no—
39C22×C4×C151—22no—
40C22×C4×C151—41no—
41C22×C4×C151C2×D411yescharacteristic
42C22×C4×C151C2×D412yes—
43C2×C8×C151—22no—
44C2×C8×C151—22no—
45C2×C8×C151—22no—
46C2×C8×C151—24no—
47C2×C8×C151—42no—
48C2×C8×C151—42no—
49C4⋊C4×C151—22no—
50C4⋊C4×C151—22no—
51C4⋊C4×C151—22no—
52C4⋊C4×C151—22no—
53C4⋊C4×C151—42no—
54C4⋊C4×C151—42no—
55C4⋊C4×C151—42no—
56C4⋊C4×C151—42no—
57C4⋊C4×C151—42no—
58C4⋊C4×C151—42no—
59C4⋊C4×C151—82no—
60C42×C151—42no—
61C42×C151—42no—
62C42×C151C2×Q811yescharacteristic
63C42×C151C2×Q812yes—
64C42×C151#4111yescharacteristic
65C23×C151#12011yescharacteristic
66C2×C4×C151—21no—
67C2×C4×C151—21no—
68C2×C4×C151—42no—
69C2×C4×C151—44no—
70C2×C4×C151—42no—
71C2×C4×C151—42no—
72C2×C4×C151—42no—
73C2×C4×C151—42no—
74C2×C4×C151—42no—
75C2×C4×C151—42no—
76C2×C4×C151—82no—
77C2×C4×C151—81no—
78C2×C4×C151C22⋊Q811yescharacteristic
79C2×C4×C151C22⋊Q812yes—
80C2×C4×C151C4⋊Q811yescharacteristic
81C2×C4×C151C4⋊Q812yes—
82C2×C4×C151#13512yes—
83C2×C4×C151#13512yes—
84C2×C4×C151AGL(1,ℤ/8)12yes—
85C2×C4×C151#13712yes—
86C8×C151—24no—
87C8×C151—44no—
88C22×C151#39511yescharacteristic
89C22×C151#44912yes—
90C22×C151#45212yes—
91C22×C151#45311yescharacteristic
92C22×C151#45611yescharacteristic
93C4×C151—21no—
94C4×C151—21no—
95C4×C151—82no—
96C4×C151—82no—
97C4×C151—82no—
98C4×C151—161no—
99C4×C151#47812yes—
100C4×C151#47912yes—
101C4×C151#49912yes—
102C4×C151#50112yes—
103C2×C151#162011yescharacteristic
104C2×C151#163411yescharacteristic
105C2×C151#165012yes—
106C2×C151#205912yes—
107C2×C151#206011yescharacteristic
108#10576C15111yesmaximal, characteristic, direct product factor, Sylow
109C151#1057611yescharacteristic, direct product factor, Sylow
110#2571C2×C15111yescharacteristic
111#1948C2×C15112yes—
112#1845C2×C15111yescharacteristic
113#1296C2×C15111yescharacteristic
114#1279C2×C15112yes—
115C2×#107—22no—
116C2×#106—22no—
117C2×C4⋊C8C22×C15112yes—
118C2×C4×C8C22×C15111yescharacteristic
119#400—22no—
120#389—22no—
121#384C22×C15111yescharacteristic
122#384C22×C15111yescharacteristic
123#382—22no—
124C4×C4⋊C4C22×C15112yes—
125#340—22no—
126C22×C8—21no—
127C22×C8—22no—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—21no—
131C2×C4⋊C4—22no—
132C2×C4⋊C4D4×C15112yes—
133C2×C4⋊C4D4×C15112yes—
134C2×C4⋊C4D4×C15112yes—
135C2×C42—22no—
136C2×C42C23×C15111yescharacteristic
137#107—44no—
138#106—44no—
139C4⋊C8—22no—
140C4⋊C8Q8×C15114yes—
141C4×C8—21no—
142C4×C8Q8×C15112yes—
143#95—22no—
144#95—24no—
145#95—22no—
146C22×C4—22no—
147C22×C4—22no—
148C22×C4—22no—
149C22×C4—41no—
150C22×C4C2×D4×C15111yescharacteristic
151C22×C4C2×D4×C15112yes—
152C2×C8—22no—
153C2×C8—22no—
154C2×C8—22no—
155C2×C8—24no—
156C2×C8—42no—
157C2×C8—42no—
158C4⋊C4—22no—
159C4⋊C4—22no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—42no—
163C4⋊C4—42no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C42—42no—
170C42—42no—
171C42C2×Q8×C15111yescharacteristic
172C42C2×Q8×C15112yes—
173C42#41×C15111yescharacteristic
174C23#120×C15111yescharacteristic
175C2×C4—21no—
176C2×C4—21no—
177C2×C4—42no—
178C2×C4—44no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—81no—
187C2×C4C22⋊Q8×C15111yescharacteristic
188C2×C4C22⋊Q8×C15112yes—
189C2×C4C4⋊Q8×C15111yescharacteristic
190C2×C4C4⋊Q8×C15112yes—
191C2×C4#135×C15112yes—
192C2×C4#135×C15112yes—
193C2×C4AGL(1,ℤ/8)×C15112yes—
194C2×C4#137×C15112yes—
195C8—24no—
196C8—44no—
197C22#395×C15111yescharacteristic
198C22#449×C15112yes—
199C22#452×C15112yes—
200C22#453×C15111yescharacteristic
201C22#456×C15111yescharacteristic
202C4—21no—
203C4—21no—
204C4—82no—
205C4—82no—
206C4—82no—
207C4—161no—
208C4#478×C15112yes—
209C4#479×C15112yes—
210C4#499×C15112yes—
211C4#501×C15112yes—
212C2#1620×C15111yescharacteristic
213C2#1634×C15111yescharacteristic
214C2#1650×C15112yes—
215C2#2059×C15112yes—
216C2#2060×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151#120
commutator, Frattini, cosocleC2×C42C23×C151
LCSG ▷ C2×C42 ▷ C22 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
108. #10576C151direct (N × H)
109. C151#10576direct (N × H)

Maximal subgroups

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

subgroupindex
#2571×C1512
#1948×C1512
#1845×C1512
#1296×C1512
#1279×C1512
#10576151