Finite Group Databasebeta

← C83×#7432 #35235256

Subgroups — C83×#7432 #35235256

Order 21248.

210 conjugacy classes of subgroups; only the 42 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 42 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
1C83×#2091C211yesmaximal, characteristic
2C83×#1320C211yesmaximal, characteristic
3C83×#1297C211yesmaximal, characteristic
4#430×C83—21no—
5#430×C83C411yescharacteristic, complemented
6#407×C83—21no—
7#407×C83C2211yescharacteristic
8C4×C22⋊C4×C83—21no—
9#349×C83—21no—
10#338×C83C411yescharacteristic, complemented
11C23×C4×C83D411yescharacteristic
12C2×M16×C83—21no—
13C2×M16×C83—21no—
14C2×M16×C83C2×C411yescharacteristic
15C2×M16×C83D411yescharacteristic
16C2×C22⋊C4×C83—41no—
17C2×C42×C83—41no—
18M32×C83—41no—
19#108×C83—41no—
20#108×C83—42no—
21C22⋊C8×C83—41no—
22C22⋊C8×C83—42no—
23#95×C83—22no—
24C24×C83SD1611yescharacteristic
25C22×C4×C83—21no—
26C22×C4×C83—21no—
27C22×C4×C83—41no—
28C22×C4×C83—41no—
29C22×C4×C83—42no—
30C22×C4×C83C22⋊C411yescharacteristic
31C22×C4×C83Q1611yescharacteristic
32M16×C83—41no—
33M16×C83—41no—
34M16×C83—41no—
35M16×C83—41no—
36M16×C83—41no—
37M16×C83—41no—
38C2×C8×C83—22no—
39C2×C8×C83—21no—
40C2×C8×C83—21no—
41C2×C8×C83—41no—
42C22⋊C4×C83—44no—
43C42×C83—81no—
44C42×C83—81no—
45C16×C83—81no—
46C23×C83—21no—
47C23×C83—42no—
48C23×C83—41no—
49C23×C83#10311yescharacteristic
50C2×C4×C83—21no—
51C2×C4×C83—21no—
52C2×C4×C83—21no—
53C2×C4×C83—41no—
54C2×C4×C83—41no—
55C2×C4×C83—41no—
56C2×C4×C83—44no—
57C2×C4×C83—81no—
58C2×C4×C83—82no—
59C2×C4×C83—82no—
60C2×C4×C83#9911yescharacteristic
61C2×C4×C83#10411yescharacteristic
62C8×C83—42no—
63C8×C83—41no—
64C8×C83—41no—
65C8×C83—81no—
66C22×C83—22no—
67C22×C83—21no—
68C22×C83—41no—
69C22×C83—41no—
70C22×C83—42no—
71C22×C83—41no—
72C22×C83—81no—
73C22×C83#32811yescharacteristic
74C4×C83—21no—
75C4×C83—41no—
76C4×C83—84no—
77C4×C83#35211yescharacteristic
78C4×C83#35311yescharacteristic
79#7432C8311yesmaximal, characteristic, direct product factor, Sylow
80C2×C83—21no—
81C2×C83—42no—
82C2×C83—41no—
83C2×C83#135211yescharacteristic
84#2091C2×C8311yescharacteristic
85#1320C2×C8311yescharacteristic
86#1297C2×C8311yescharacteristic
87C83#743211yescharacteristic, direct product factor, Sylow
88#430—21no—
89#430C4×C8311yescharacteristic, complemented
90#407—21no—
91#407C22×C8311yescharacteristic
92C4×C22⋊C4—21no—
93#349—21no—
94#338C4×C8311yescharacteristic, complemented
95C23×C4D4×C8311yescharacteristic
96C2×M16—21no—
97C2×M16—21no—
98C2×M16C2×C4×C8311yescharacteristic
99C2×M16D4×C8311yescharacteristic
100C2×C22⋊C4—41no—
101C2×C42—41no—
102M32—41no—
103#108—41no—
104#108—42no—
105C22⋊C8—41no—
106C22⋊C8—42no—
107#95—22no—
108C24SD16×C8311yescharacteristic
109C22×C4—21no—
110C22×C4—21no—
111C22×C4—41no—
112C22×C4—41no—
113C22×C4—42no—
114C22×C4C22⋊C4×C8311yescharacteristic
115C22×C4Q16×C8311yescharacteristic
116M16—41no—
117M16—41no—
118M16—41no—
119M16—41no—
120M16—41no—
121M16—41no—
122C2×C8—22no—
123C2×C8—21no—
124C2×C8—21no—
125C2×C8—41no—
126C22⋊C4—44no—
127C42—81no—
128C42—81no—
129C16—81no—
130C23—21no—
131C23—42no—
132C23—41no—
133C23#103×C8311yescharacteristic
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—21no—
137C2×C4—41no—
138C2×C4—41no—
139C2×C4—41no—
140C2×C4—44no—
141C2×C4—81no—
142C2×C4—82no—
143C2×C4—82no—
144C2×C4#99×C8311yescharacteristic
145C2×C4#104×C8311yescharacteristic
146C8—42no—
147C8—41no—
148C8—41no—
149C8—81no—
150C22—22no—
151C22—21no—
152C22—41no—
153C22—41no—
154C22—42no—
155C22—41no—
156C22—81no—
157C22#328×C8311yescharacteristic
158C4—21no—
159C4—41no—
160C4—84no—
161C4#352×C8311yescharacteristic
162C4#353×C8311yescharacteristic
163C2—21no—
164C2—42no—
165C2—41no—
166C2C83×#135211yescharacteristic
subgroupG/H
centerC4×C83#353
commutatorC2×M16C2×C4×C83
Frattini, cosocle#407C22×C83
socleC2×C83#1352
prime radicalC24×C83SD16
LCSG ▷ C2×M16 ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C4×C83 ◁ C2×C4×C83 ◁ C22×C4×C83 ◁ #407×C83 ◁ G

Complements

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

NH ≅ G/Ntype
5. #430×C83C4semidirect
10. #338×C83C4semidirect
79. #7432C83direct (N × H)
87. C83#7432direct (N × H)
89. #430C4×C83semidirect
94. #338C4×C83semidirect

Maximal subgroups

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

subgroupindex
C83×#20912
C83×#13202
C83×#12972
#743283