Finite Group Databasebeta

← #24984228

Subgroups — #24984228

Order 11008.

198 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 41 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#19135940C211yesmaximal, characteristic
2#19132478C211yesmaximal, characteristic
3C43×#1325C211yesmaximal, characteristic
4#14583530C411yescharacteristic
5#14582939—21no—
6C2×C4⋊(C43⋊C8)—21no—
7#14582668C411yescharacteristic
8#14582659—21no—
9C43×#384C2211yescharacteristic
10C43×#324—21no—
11C2×#10621877—21no—
12C22×C43⋊C8—41no—
13#13063324—41no—
14#13063316—41no—
15#13063304—41no—
16#13063284—21no—
17#13063258—41no—
18#13063256—41no—
19C4⋊(C43⋊C8)—22no—
20C4⋊(C43⋊C8)—41no—
21C2×C4⋊C4×C43—41no—
22C2×C4⋊C4×C43C2×C411yescharacteristic
23C2×C4⋊C4×C43D411yescharacteristic
24C2×C42×C43D411yescharacteristic
25C22⋊C8×C43—41no—
26C22×C4×C43—21no—
27C22×C4×C43—21no—
28C22×C4×C43—21no—
29C22×C4×C43C22⋊C411yescharacteristic
30C2×Dic86—41no—
31C2×C8×C43—81no—
32C4⋊C4×C43—41no—
33C4⋊C4×C43—41no—
34C4⋊C4×C43—81no—
35C4⋊C4×C43—81no—
36C42×C43—21no—
37C42×C43SD1611yescharacteristic
38C42×C43Q1611yescharacteristic
39C22⋊Dic43—41no—
40C4⋊Dic43—21no—
41C4⋊Dic43—21no—
42C4⋊Dic43—41no—
43Dic43⋊C4—42no—
44C4×Dic43—41no—
45#10621877—22no—
46#10621877—41no—
47C2×C43⋊C8—41no—
48C2×C43⋊C8—42no—
49C2×C43⋊C8—81no—
50C2×C43⋊C8—81no—
51C23×C43#9911yescharacteristic
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—21no—
55C2×C4×C43—21no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—21no—
59C2×C4×C43—21no—
60C2×C4×C43—41no—
61C2×C4×C43—41no—
62C2×C4×C43—81no—
63C2×C4×C43—81no—
64C2×C4×C43#10311yescharacteristic
65C2×C4×C43#10411yescharacteristic
66C2×Dic43—41no—
67C2×Dic43—41no—
68Dic86—161no—
69C8×C43—161no—
70C43⋊C8—42no—
71C43⋊C8—82no—
72#7443—431nomaximal, Sylow
73C22×C43—21no—
74C22×C43—21no—
75C22×C43#32811yescharacteristic
76C22×C43AΣL(1,𝔽16)11yescharacteristic
77C22×C43#35611yescharacteristic
78C4×C43—21no—
79C4×C43—21no—
80C4×C43—21no—
81C4×C43—21no—
82C4×C43—21no—
83C4×C43—21no—
84C4×C43—81no—
85C4×C43—81no—
86Dic43—81no—
87Dic43—81no—
88#2060—431no—
89#1325D4311yescharacteristic
90#1296—431no—
91C2×C43—21no—
92C2×C43—21no—
93C2×C43#135411yescharacteristic
94C2×C43#140211yescharacteristic
95C2×C43#140511yescharacteristic
96#544—431no—
97#428—861no—
98C2×C4⋊C8—861no—
99#384C2×D4311yescharacteristic
100#343—431no—
101#339—861no—
102#324—21no—
103C43#744311yescharacteristic, complemented, Sylow
104C2×M16—861no—
105C22×C8—1721no—
106C4⋊Q8—1721no—
107#125—1721no—
108C22⋊Q8—1721no—
109#117—861no—
110C2×C4⋊C4—41no—
111C2×C4⋊C4C4×D4311yescharacteristic
112C2×C4⋊C4C22⋊D4311yescharacteristic
113C2×C42D17211yescharacteristic
114#107—1721no—
115#106—1721no—
116C4⋊C8—862no—
117C4⋊C8—1721no—
118C22⋊C8—41no—
119C2×Q8—1721no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—21no—
123C22×C4(C2×D43)⋊C411yescharacteristic
124M16—862no—
125M16—1721no—
126C2×C8—81no—
127C2×C8—3441no—
128C2×C8—3441no—
129C2×C8—1722no—
130C2×C8—1721no—
131C4⋊C4—41no—
132C4⋊C4—41no—
133C4⋊C4—81no—
134C4⋊C4—81no—
135C4⋊C4—861no—
136C4⋊C4—861no—
137C4⋊C4—1721no—
138C4⋊C4—1722no—
139C22⋊C4—1721no—
140C42—21no—
141C42—1721no—
142C42#1062187311yescharacteristic
143C42Dic17211yescharacteristic
144C23#1306323911yescharacteristic
145Q8—6881no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—21no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—21no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—41no—
155C2×C4—41no—
156C2×C4—81no—
157C2×C4—81no—
158C2×C4—1721no—
159C2×C4—1721no—
160C2×C4#1306325011yescharacteristic
161C2×C4#1306325111yescharacteristic
162C8—161no—
163C8—3442no—
164C8—1722no—
165C22—21no—
166C22—21no—
167C22#1458263711yescharacteristic
168C22#1458268511yescharacteristic
169C22#1458269711yescharacteristic
170C4—21no—
171C4—21no—
172C4—21no—
173C4—21no—
174C4—21no—
175C4—21no—
176C4—81no—
177C4—81no—
178C4—3441no—
179C4—3441no—
180C2—21no—
181C2—21no—
182C2#1913262611yescharacteristic
183C2#1913273911yescharacteristic
184C2#1913274811yescharacteristic
subgroupG/H
centerC22#14582685
commutatorC2×C4⋊C4×C43C2×C4
Frattini#384C2×D43
FittingC43×#1325C2
socleC22×C43AΣL(1,𝔽16)
prime radicalC23×C43#99
cosocleC43×#384C22
hypercenter#1325D43
hypocenterC43#7443
LCSG ▷ C2×C4⋊C4×C43 ▷ C22×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #384 ◁ #1325

Complements

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

NH ≅ G/Ntype
103. C43#7443semidirect

Maximal subgroups

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

subgroupindex
#191359402
#191324782
C43×#13252
#744343