Finite Group Databasebeta

← #25000673

Subgroups — #25000673

Order 11008.

388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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#19145905C211yesmaximal, characteristic
2#19134714C211yesmaximal, characteristic, complemented
3#19133291C212yesmaximal, complemented
4#19133104C212yesmaximal, complemented
5C43×#1290C211yesmaximal, characteristic, complemented
6#14583449C2212yes—
7#14583180—22no—
8#14583135—22no—
9#14583095—22no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11#14582745C2211yescharacteristic
12#14582653—22no—
13#14582647—22no—
14#14582642—22no—
15#14582634—24no—
16C43×#432C2212yes—
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×#10621898—22no—
19C2×D344—22no—
20C22×C43⋊C8—21no—
21#13063325D412yes—
22#13063322D412yes—
23#13063313—22no—
24#13063299—22no—
25#13063299—22no—
26C4×D172—22no—
27C4×D172—22no—
28C2×C4×Dic43—21no—
29#13063259—22no—
30C4⋊(C43⋊C8)—22no—
31#13063247—24no—
32C43⋊#95—21no—
33C43⋊#95D412yes—
34C22×C8×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38C22⋊C8×C43—22no—
39#97×C43—22no—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43#4111yescharacteristic
43C2×C22⋊D43—42no—
44C22×Dic43—22no—
45#10621898—84no—
46C2×D172—22no—
47C2×D172—22no—
48C2×D172—22no—
49C2×C4×D43—42no—
50C2×Dic86—22no—
51C2×C8×C43—22no—
52C2×C8×C43—42no—
53C2×C8×C43—42no—
54C42×C43C2×D412yes—
55C42×C43#4112yes—
56(C2×D43)⋊C4—42no—
57(C2×D43)⋊C4—42no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4×Dic43—41no—
61C4×Dic43—41no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—41no—
64D344—82no—
65C23×C43#12111yescharacteristic
66C22×D43—42no—
67C2×C4×C43—22no—
68C2×C4×C43—21no—
69C2×C4×C43—21no—
70C2×C4×C43—41no—
71C2×C4×C43#12011yescharacteristic
72C2×C4×C43#12112yes—
73C2×C4×C43#12312yes—
74C2×C4×C43#12411yescharacteristic
75C22⋊D43—84no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78C2×Dic43—42no—
79C2×Dic43—42no—
80D172—42no—
81D172—42no—
82D172—82no—
83D172—82no—
84C4×D43—84no—
85Dic86—82no—
86C8×C43—42no—
87C8×C43—82no—
88C43⋊C8—81no—
89#10513—431nomaximal, Sylow
90C22×C43—21no—
91C22×C43—21no—
92C22×C43#39411yescharacteristic
93C22×C43#47212yes—
94C2×D43—82no—
95C2×D43—82no—
96C2×D43—82no—
97C4×C43—22no—
98C4×C43—21no—
99C4×C43—22no—
100C4×C43#45411yescharacteristic
101C4×C43#45511yescharacteristic
102Dic43—82no—
103Dic43—82no—
104#3245—431no—
105#1832—431no—
106#1551—432no—
107#1505—432no—
108#1290D4311yescharacteristic, complemented
109C2×C43—22no—
110C2×C43#204011yescharacteristic
111C2×C43#204511yescharacteristic
112C2×C43#205311yescharacteristic
113D43—162no—
114#532—432no—
115#474—862no—
116#466—862no—
117#459—862no—
118#432C2×D4312yes—
119C2×C4⋊C8—431no—
120C2×C4⋊C8C2×D4311yescharacteristic
121#376—431no—
122#336—862no—
123#333—862no—
124#331—862no—
125#327—864no—
126C43#1051311yescharacteristic, complemented, Sylow
127C2×#41—862no—
128C2×D8—862no—
129C22×C8—861no—
130C22×C8D17212yes—
131C4⋊Q8—432no—
132#127—432no—
133#124—862no—
134#121—862no—
135#121—862no—
136C4×D4—862no—
137C4×D4—862no—
138C2×C42—861no—
139C2×C42C22×D4311yescharacteristic
140#107—862no—
141C4⋊C8—22no—
142C4⋊C8—22no—
143C4⋊C8—862no—
144#102—864no—
145C22⋊C8—22no—
146#97—22no—
147#95—432no—
148#95—861no—
149#41—3444no—
150C2×Q8—862no—
151C2×D4—862no—
152C2×D4—862no—
153C2×D4—862no—
154C2×D4—1722no—
155C22×C4—862no—
156C22×C4—1722no—
157C22×C4C2×D17211yescharacteristic
158C22×C4D4×D4311yescharacteristic
159C22×C4#1062190211yescharacteristic
160D8—3442no—
161C2×C8—22no—
162C2×C8—42no—
163C2×C8—42no—
164C2×C8—1722no—
165C2×C8—1721no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C22⋊C4—1722no—
169C22⋊C4—1722no—
170C42—1721no—
171C42—1721no—
172C42#1062189812yes—
173C42D4×D4312yes—
174C23—1722no—
175C23#1306330011yescharacteristic
176Q8—3442no—
177D4—3442no—
178D4—3442no—
179D4—3444no—
180D4—1722no—
181D4—1722no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—41no—
186C2×C4—3444no—
187C2×C4—1722no—
188C2×C4—1722no—
189C2×C4—1722no—
190C2×C4—1722no—
191C2×C4#1306329511yescharacteristic
192C2×C4#1306329812yes—
193C2×C4#1306331012yes—
194C2×C4#1306331311yescharacteristic
195C8—42no—
196C8—82no—
197C8—3441no—
198C22—21no—
199C22—21no—
200C22—3442no—
201C22—3442no—
202C22—3442no—
203C22#1458281711yescharacteristic
204C22#1458317012yes—
205C4—21no—
206C4—22no—
207C4—22no—
208C4—3442no—
209C4—3442no—
210C4#1458307411yescharacteristic
211C4#1458307911yescharacteristic
212C2—22no—
213C2—6882no—
214C2#1913582511yescharacteristic
215C2#1913585211yescharacteristic
216C2#1913590211yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#394
prime radical#19145905C2
hypercenter#1290D43
hypocenterC43#10513
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
2. #19134714C2semidirect
3. #19133291C2semidirect
4. #19133104C2semidirect
5. C43×#1290C2semidirect
108. #1290D43semidirect
126. C43#10513semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191347142
#191332912
#191331042
C43×#12902
#1051343