Finite Group Databasebeta

← #25008115

Subgroups — #25008115

Order 11008.

292 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 79 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#19145245C211yesmaximal, characteristic
2#19136361C211yesmaximal, characteristic, complemented
3#19132655C212yesmaximal, complemented
4#19132631C212yesmaximal, complemented
5C43×#2166C211yesmaximal, characteristic, complemented
6#14583504C412yes—
7C2×#13063265—21no—
8#14583301C2211yescharacteristic
9#14583276C2211yescharacteristic
10#14583264C412yes—
11#14583152—21no—
12#14583135—21no—
13#14583012—21no—
14C4×D344—21no—
15#14582720—21no—
16#14582720C2212yes—
17C43×#405C2211yescharacteristic
18C43×#364C2212yes—
19C43×#349—21no—
20C43×#347—21no—
21C2×D344—21no—
22C2×D344—21no—
23#13063322C2×C412yes—
24#13063317C2×C412yes—
25#13063310—42no—
26#13063299—22no—
27#13063298—42no—
28C4×D172—22no—
29#13063265—22no—
30#13063265—41no—
31C2×C43⋊C16—41no—
32#13063259—21no—
33#13063257—21no—
34#13063247—22no—
35#13063247—22no—
36C2×M16×C43D411yescharacteristic
37C22×C8×C43D411yescharacteristic
38#117×C43C2×C411yescharacteristic
39M32×C43—22no—
40#97×C43C2×C411yescharacteristic
41#97×C43D411yescharacteristic
42C4×C8×C43D411yescharacteristic
43C4×C8×C43C2311yescharacteristic
44C22×C4×C43C22⋊C411yescharacteristic
45C2×C22⋊D43—42no—
46C2×D172—22no—
47C2×D172—42no—
48C2×C4×D43—42no—
49M16×C43—22no—
50C2×C8×C43—21no—
51C2×C8×C43—21no—
52C2×C8×C43C22⋊C411yescharacteristic
53C2×C8×C43C22⋊C411yescharacteristic
54C2×C8×C43C2×D411yescharacteristic
55C2×C8×C43C2×D411yescharacteristic
56C4⋊C4×C43—21no—
57C22⋊C4×C43—21no—
58C42×C43C22⋊C411yescharacteristic
59C42×C43C22×C411yescharacteristic
60(C2×D43)⋊C4—42no—
61(C2×D43)⋊C4—42no—
62C4⋊Dic43—22no—
63Dic43⋊C4—42no—
64D344—42no—
65D344—41no—
66D344—41no—
67C16×C43—42no—
68C43⋊C16—42no—
69C23×C43#10011yescharacteristic
70C22×D43—42no—
71C2×C4×C43—21no—
72C2×C4×C43—21no—
73C2×C4×C43—21no—
74C2×C4×C43—21no—
75C2×C4×C43#10011yescharacteristic
76C2×C4×C43C2×C22⋊C411yescharacteristic
77C22⋊D43—162no—
78C2×Dic43—42no—
79D172—42no—
80D172—42no—
81D172—162no—
82C4×D43—162no—
83C8×C43—21no—
84C8×C43—21no—
85C8×C43#13512yes—
86C8×C43AGL(1,ℤ/8)11yescharacteristic
87C8×C43#13711yescharacteristic
88#11989—431nomaximal, Sylow
89C22×C43—21no—
90C22×C43—41no—
91C22×C43C2×#10011yescharacteristic
92C2×D43—82no—
93C2×D43—82no—
94C2×D43—82no—
95C4×C43—21no—
96C4×C43—41no—
97C4×C43—41no—
98C4×C43#41611yescharacteristic
99C4×C43#41711yescharacteristic
100Dic43—82no—
101#3176—431no—
102#2166D4311yescharacteristic, complemented
103#2153—431no—
104#1366—432no—
105#1357—432no—
106C2×C43—21no—
107C2×C43—41no—
108C2×C43#155111yescharacteristic
109D43—162no—
110#540—432no—
111C2×M32—861no—
112#499—431no—
113#493—431no—
114#490—432no—
115#469—861no—
116#466—861no—
117#442—861no—
118C4×D8—861no—
119#405C2×D4311yescharacteristic
120#364—432no—
121#364—861no—
122#364C2×D4312yes—
123#349—21no—
124#347—21no—
125C43#1198911yescharacteristic, complemented, Sylow
126C2×D8—861no—
127C2×D8—861no—
128C2×M16C22⋊D4311yescharacteristic
129C22×C8D17211yescharacteristic
130#127—432no—
131#125—432no—
132#123—1722no—
133#121—862no—
134#121—1722no—
135C4×D4—862no—
136#117C4×D4311yescharacteristic
137M32—22no—
138M32—862no—
139M32—1721no—
140C2×C16—1721no—
141#107—861no—
142#106—861no—
143#102—862no—
144#102—862no—
145#97C4×D4311yescharacteristic
146#97C22⋊D4311yescharacteristic
147C4×C8D17211yescharacteristic
148C4×C8C22×D4311yescharacteristic
149C2×D4—862no—
150C2×D4—1722no—
151C2×D4—1722no—
152C22×C4—1722no—
153C22×C4(C2×D43)⋊C411yescharacteristic
154D8—1722no—
155D8—1721no—
156D8—1721no—
157M16—22no—
158C2×C8—21no—
159C2×C8—21no—
160C2×C8(C2×D43)⋊C411yescharacteristic
161C2×C8(C2×D43)⋊C411yescharacteristic
162C2×C8C2×D17211yescharacteristic
163C2×C8C2×C22⋊D4311yescharacteristic
164C4⋊C4—21no—
165C4⋊C4—862no—
166C4⋊C4—1722no—
167C22⋊C4—21no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C42(C2×D43)⋊C411yescharacteristic
171C42C2×C4×D4311yescharacteristic
172C16—42no—
173C16—1722no—
174C23—1722no—
175C23#1306324111yescharacteristic
176D4—1722no—
177D4—1722no—
178D4—6882no—
179D4—6882no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—1722no—
185C2×C4—6882no—
186C2×C4#1306324111yescharacteristic
187C2×C4C2×(C2×D43)⋊C411yescharacteristic
188C8—21no—
189C8—21no—
190C8#1306334512yes—
191C8#1306335311yescharacteristic
192C8#1306335811yescharacteristic
193C22—21no—
194C22—41no—
195C22—3442no—
196C22—3442no—
197C22—3442no—
198C22C2×#1306324111yescharacteristic
199C4—21no—
200C4—41no—
201C4—41no—
202C4—3442no—
203C4#1458289311yescharacteristic
204C4#1458290111yescharacteristic
205C2—21no—
206C2—41no—
207C2—6882no—
208C2#1913329111yescharacteristic
subgroupG/H
centerC2#19133291
commutatorC42×C43C22×C4
FrattiniC4×C8C22×D43
FittingC43×#2166C2
socleC2×C43#1551
prime radical#19145245C2
cosocleC4×C8×C43C23
hypercenter#2166D43
hypocenterC43#11989
LCSG ▷ C42×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
2. #19136361C2semidirect
3. #19132655C2semidirect
4. #19132631C2semidirect
5. C43×#2166C2semidirect
102. #2166D43semidirect
125. C43#11989semidirect

Maximal subgroups

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

subgroupindex
#191452452
#191363612
#191326552
#191326312
C43×#21662
#1198943