Finite Group Databasebeta

← #24999702

Subgroups — #24999702

Order 11008.

402 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 93 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#19135423C211yesmaximal, characteristic
2#19133154C212yesmaximal
3#19132453C212yesmaximal, complemented
4#19132428C211yesmaximal, characteristic, complemented
5C43×#2864C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14582952C2212yes—
8#14582923C2211yescharacteristic
9C2×#13063253—22no—
10#14582632—24no—
11C43×#389—22no—
12C43×#387—24no—
13C43×#382C2212yes—
14C43×C43C2211yescharacteristic
15C2×#10621898—21no—
16C2×#10621877—21no—
17#13063325Q811yescharacteristic
18#13063322Q811yescharacteristic
19#13063313—21no—
20#13063299—22no—
21C4×D172—22no—
22C4⋊(C43⋊C8)—22no—
23C4⋊(C43⋊C8)—22no—
24#13063253—44no—
25C22⋊(C43⋊C8)—22no—
26C4×C43⋊C8—22no—
27C2×C4⋊C4×C43—24no—
28C2×C4⋊C4×C43—22no—
29C2×C42×C43—22no—
30C2×C42×C43D412yes—
31C2×C42×C43C2311yescharacteristic
32#95×C43—24no—
33#95×C43—22no—
34#95×C43D414yes—
35C22×C4×C43—22no—
36C22×C4×C43—24no—
37C22×C4×C43C2×D412yes—
38C22×C4×C43C2×D411yescharacteristic
39C2×C22⋊D43—41no—
40#10621898—42no—
41#10621898—42no—
42C2×D172—21no—
43C2×D172—22no—
44C2×C4×D43—41no—
45C2×Dic86—21no—
46C4⋊C4×C43—48no—
47C4⋊C4×C43—42no—
48C4⋊C4×C43—42no—
49C42×C43—22no—
50C42×C43—22no—
51C42×C43—44no—
52C42×C43C2×Q811yescharacteristic
53C42×C43#4111yescharacteristic
54C42×C43#4112yes—
55(C2×D43)⋊C4—42no—
56C4⋊Dic43—22no—
57#10621877—42no—
58C2×C43⋊C8—42no—
59C2×C43⋊C8—41no—
60C23×C43#12011yescharacteristic
61C22×D43—41no—
62C2×C4×C43—24no—
63C2×C4×C43—42no—
64C2×C4×C43—42no—
65C2×C4×C43—42no—
66C2×C4×C43—48no—
67C2×C4×C43—44no—
68C2×C4×C43C22⋊Q812yes—
69C2×C4×C43C22⋊Q811yescharacteristic
70C2×C4×C43#12412yes—
71C2×C4×C43#12411yescharacteristic
72C2×C4×C43#13512yes—
73C2×C4×C43AGL(1,ℤ/8)12yes—
74C22⋊D43—82no—
75C2×Dic43—41no—
76D172—42no—
77D172—82no—
78C4×D43—81no—
79C4×D43—81no—
80Dic86—42no—
81C43⋊C8—82no—
82C43⋊C8—81no—
83#10366—431nomaximal, Sylow
84C22×C43—22no—
85C22×C43#39311yescharacteristic
86C22×C43#44912yes—
87C2×D43—81no—
88C2×D43—82no—
89C4×C43—22no—
90C4×C43—22no—
91C4×C43—44no—
92C4×C43—84no—
93C4×C43#47812yes—
94C4×C43#48811yescharacteristic
95C4×C43#49011yescharacteristic
96Dic43—81no—
97#2864D4311yescharacteristic, complemented
98#1962—431no—
99#1517—432no—
100#1286—432no—
101#1276—431no—
102C2×C43—22no—
103C2×C43#202511yescharacteristic
104C2×C43#203112yes—
105D43—161no—
106#532—431no—
107#431—432no—
108#423—431no—
109C2×#104—862no—
110#389—22no—
111#387—24no—
112#382C2×D4312yes—
113C43C2×D4311yescharacteristic
114#327—864no—
115C43#1036611yescharacteristic, complemented, Sylow
116C2×#41—861no—
117C2×M16—861no—
118C4⋊Q8—431no—
119#127—431no—
120#124—861no—
121#121—862no—
122C4×D4—862no—
123C2×C4⋊C4—24no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D4312yes—
127C2×C42C22×D4311yescharacteristic
128C4⋊C8—862no—
129C4⋊C8—862no—
130#104—1724no—
131C22⋊C8—862no—
132C4×C8—862no—
133#95—24no—
134#95—22no—
135#95C22⋊D4314yes—
136#41—1722no—
137#41—1722no—
138C2×Q8—861no—
139C2×D4—862no—
140C2×D4—861no—
141C2×D4—1721no—
142C22×C4—22no—
143C22×C4—24no—
144C22×C4—1721no—
145C22×C4C2×C22⋊D4312yes—
146C22×C4C2×C22⋊D4311yescharacteristic
147M16—1722no—
148C2×C8—1722no—
149C2×C8—1721no—
150C4⋊C4—48no—
151C4⋊C4—42no—
152C4⋊C4—42no—
153C4⋊C4—862no—
154C22⋊C4—1722no—
155C42—22no—
156C42—22no—
157C42—44no—
158C42Q8×D4311yescharacteristic
159C42#1062190211yescharacteristic
160C42#1062190212yes—
161C23—1721no—
162C23#1306329411yescharacteristic
163Q8—1722no—
164D4—3442no—
165D4—3442no—
166D4—1722no—
167C2×C4—24no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—48no—
172C2×C4—44no—
173C2×C4—3441no—
174C2×C4—3441no—
175C2×C4—1721no—
176C2×C4#1306330112yes—
177C2×C4#1306330111yescharacteristic
178C2×C4#1306331412yes—
179C2×C4#1306331411yescharacteristic
180C2×C4#1306334512yes—
181C2×C4#1306335012yes—
182C8—3442no—
183C8—3441no—
184C22—22no—
185C22—3442no—
186C22—3441no—
187C22#1458281011yescharacteristic
188C22#1458304412yes—
189C4—22no—
190C4—22no—
191C4—44no—
192C4—84no—
193C4—3441no—
194C4#1458319612yes—
195C4#1458325611yescharacteristic
196C4#1458326511yescharacteristic
197C2—22no—
198C2—6881no—
199C2#1913573811yescharacteristic
200C2#1913576412yes—
subgroupG/H
centerC22#14582810
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2864C2
socleC22×C43#393
prime radical#14583449C22
hypercenter#2864D43
hypocenterC43#10366
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2864

Complements

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

NH ≅ G/Ntype
3. #19132453C2semidirect
4. #19132428C2semidirect
5. C43×#2864C2semidirect
97. #2864D43semidirect
115. C43#10366semidirect

Maximal subgroups

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

subgroupindex
#191354232
#191331542
#191324532
#191324282
C43×#28642
#1036643