Finite Group Databasebeta

← #2043×C151 #34065375

Subgroups — #2043×C151 #34065375

Order 19328.

298 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 108 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×C4⋊Q8×C151C211yesmaximal, characteristic
2C2×#103×C151C212yesmaximal
3C2×#103×C151C212yesmaximal
4#389×C151C211yesmaximal, characteristic
5#336×C151C211yesmaximal, characteristic
6C22×Q8×C151C2212yes—
7C22×C8×C151C2212yes—
8C4⋊Q8×C151—24no—
9C2×C4⋊C4×C151—21no—
10C2×C4⋊C4×C151—21no—
11C2×C4⋊C4×C151—21no—
12C2×C4⋊C4×C151C2211yescharacteristic
13C2×C4⋊C4×C151C2211yescharacteristic
14C2×C42×C151C2211yescharacteristic
15#103×C151—24no—
16#103×C151—24no—
17#95×C151—21no—
18C2×Q8×C151—22no—
19C2×Q8×C151—22no—
20C2×Q8×C151—22no—
21C2×Q8×C151—22no—
22C2×Q8×C151—22no—
23C2×Q8×C151D414yes—
24C22×C4×C151—21no—
25C22×C4×C151—22no—
26C22×C4×C151—21no—
27C22×C4×C151D411yescharacteristic
28C22×C4×C151D411yescharacteristic
29C22×C4×C151C2311yescharacteristic
30C2×C8×C151—22no—
31C2×C8×C151—22no—
32C2×C8×C151—22no—
33C4⋊C4×C151—24no—
34C4⋊C4×C151—24no—
35C4⋊C4×C151—21no—
36C4⋊C4×C151—22no—
37C4⋊C4×C151—42no—
38C4⋊C4×C151D412yes—
39C42×C151—22no—
40C23×C151C2×D411yescharacteristic
41Q8×C151—24no—
42Q8×C151—24no—
43Q8×C151—42no—
44Q8×C151—42no—
45C2×C4×C151—21no—
46C2×C4×C151—21no—
47C2×C4×C151—21no—
48C2×C4×C151—21no—
49C2×C4×C151—24no—
50C2×C4×C151—22no—
51C2×C4×C151—42no—
52C2×C4×C151—42no—
53C2×C4×C151—41no—
54C2×C4×C151—41no—
55C2×C4×C151—41no—
56C2×C4×C151—41no—
57C2×C4×C151—41no—
58C2×C4×C151SD1612yes—
59C2×C4×C151Q1612yes—
60C2×C4×C151C2×D411yescharacteristic
61C2×C4×C151C2×D412yes—
62C2×C4×C151#4112yes—
63C2×C4×C151#4111yescharacteristic
64C8×C151—42no—
65C22×C151#12011yescharacteristic
66C22×C151#12111yescharacteristic
67C22×C151#12411yescharacteristic
68C22×C151C2×SD1611yescharacteristic
69C22×C151C2×Q1611yescharacteristic
70C22×C151#13711yescharacteristic
71C22×C151#13711yescharacteristic
72C4×C151—22no—
73C4×C151—22no—
74C4×C151—44no—
75C4×C151—42no—
76C4×C151—81no—
77C4×C151#12112yes—
78C4×C151#12312yes—
79C2×C151#39411yescharacteristic
80C2×C151#44811yescharacteristic
81C2×C151#45111yescharacteristic
82C2×C151#46111yescharacteristic
83C2×C151#46211yescharacteristic
84C2×C151#48711yescharacteristic
85C2×C151#49111yescharacteristic
86C151#204311yescharacteristic, direct product factor, Sylow
87#2043C15111yesmaximal, characteristic, direct product factor, Sylow
88C2×C4⋊Q8C2×C15111yescharacteristic
89C2×#103C2×C15112yes—
90C2×#103C2×C15112yes—
91#389C2×C15111yescharacteristic
92#336C2×C15111yescharacteristic
93C22×Q8C22×C15112yes—
94C22×C8C22×C15112yes—
95C4⋊Q8—24no—
96C2×C4⋊C4—21no—
97C2×C4⋊C4—21no—
98C2×C4⋊C4—21no—
99C2×C4⋊C4C22×C15111yescharacteristic
100C2×C4⋊C4C22×C15111yescharacteristic
101C2×C42C22×C15111yescharacteristic
102#103—24no—
103#103—24no—
104#95—21no—
105C2×Q8—22no—
106C2×Q8—22no—
107C2×Q8—22no—
108C2×Q8—22no—
109C2×Q8—22no—
110C2×Q8D4×C15114yes—
111C22×C4—21no—
112C22×C4—22no—
113C22×C4—21no—
114C22×C4D4×C15111yescharacteristic
115C22×C4D4×C15111yescharacteristic
116C22×C4C23×C15111yescharacteristic
117C2×C8—22no—
118C2×C8—22no—
119C2×C8—22no—
120C4⋊C4—24no—
121C4⋊C4—24no—
122C4⋊C4—21no—
123C4⋊C4—22no—
124C4⋊C4—42no—
125C4⋊C4D4×C15112yes—
126C42—22no—
127C23C2×D4×C15111yescharacteristic
128Q8—24no—
129Q8—24no—
130Q8—42no—
131Q8—42no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—24no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—41no—
141C2×C4—41no—
142C2×C4—41no—
143C2×C4—41no—
144C2×C4—41no—
145C2×C4SD16×C15112yes—
146C2×C4Q16×C15112yes—
147C2×C4C2×D4×C15111yescharacteristic
148C2×C4C2×D4×C15112yes—
149C2×C4#41×C15112yes—
150C2×C4#41×C15111yescharacteristic
151C8—42no—
152C22#120×C15111yescharacteristic
153C22#121×C15111yescharacteristic
154C22#124×C15111yescharacteristic
155C22C2×SD16×C15111yescharacteristic
156C22C2×Q16×C15111yescharacteristic
157C22#137×C15111yescharacteristic
158C22#137×C15111yescharacteristic
159C4—22no—
160C4—22no—
161C4—44no—
162C4—42no—
163C4—81no—
164C4#121×C15112yes—
165C4#123×C15112yes—
166C2#394×C15111yescharacteristic
167C2#448×C15111yescharacteristic
168C2#451×C15111yescharacteristic
169C2#461×C15111yescharacteristic
170C2#462×C15111yescharacteristic
171C2#487×C15111yescharacteristic
172C2#491×C15111yescharacteristic
subgroupG/H
center, socle, prime radicalC23×C151C2×D4
commutator, Frattini, cosocleC22×C4C23×C151
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C151 ◁ C2×C42×C151 ◁ G

Complements

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

NH ≅ G/Ntype
86. C151#2043direct (N × H)
87. #2043C151direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4⋊Q8×C1512
C2×#103×C1512
#389×C1512
#336×C1512
#2043151