Finite Group Databasebeta

← #25000668

Subgroups — #25000668

Order 11008.

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

normal subgroups only

This group has 408 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#19134748C211yesmaximal, 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
11C2×Dic43⋊C8—22no—
12#14582745C2211yescharacteristic
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—
31Dic43⋊C8—44no—
32#13063247—24no—
33C43⋊#95—21no—
34C43⋊#95D412yes—
35C22×C8×C43D412yes—
36C2×C42×C43C2311yescharacteristic
37C4⋊C8×C43—22no—
38C4⋊C8×C43—22no—
39C22⋊C8×C43—22no—
40#97×C43—22no—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43#4111yescharacteristic
44C2×C22⋊D43—42no—
45C22×Dic43—22no—
46#10621898—84no—
47C2×D172—22no—
48C2×D172—22no—
49C2×D172—22no—
50C2×C4×D43—42no—
51C2×Dic86—22no—
52C2×C8×C43—22no—
53C2×C8×C43—42no—
54C2×C8×C43—42no—
55C42×C43C2×D412yes—
56C42×C43#4112yes—
57(C2×D43)⋊C4—42no—
58(C2×D43)⋊C4—42no—
59C4⋊Dic43—22no—
60C4⋊Dic43—22no—
61C4×Dic43—22no—
62C4×Dic43—22no—
63C2×C43⋊C8—42no—
64C2×C43⋊C8—41no—
65D344—82no—
66C23×C43#12111yescharacteristic
67C22×D43—42no—
68C2×C4×C43—22no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—41no—
72C2×C4×C43#12011yescharacteristic
73C2×C4×C43#12112yes—
74C2×C4×C43#12312yes—
75C2×C4×C43#12411yescharacteristic
76C22⋊D43—84no—
77C2×Dic43—24no—
78C2×Dic43—42no—
79C2×Dic43—42no—
80C2×Dic43—42no—
81D172—42no—
82D172—42no—
83D172—82no—
84D172—82no—
85C4×D43—84no—
86Dic86—82no—
87C8×C43—42no—
88C8×C43—82no—
89C43⋊C8—81no—
90#10512—431nomaximal, Sylow
91C22×C43—21no—
92C22×C43—21no—
93C22×C43#39411yescharacteristic
94C22×C43#47212yes—
95C2×D43—82no—
96C2×D43—82no—
97C2×D43—82no—
98C4×C43—22no—
99C4×C43—21no—
100C4×C43—22no—
101C4×C43#45311yescharacteristic
102C4×C43#45611yescharacteristic
103Dic43—44no—
104Dic43—82no—
105#3245—431no—
106#1843—431no—
107#1551—432no—
108#1505—432no—
109#1290D4311yescharacteristic, complemented
110C2×C43—22no—
111C2×C43#203911yescharacteristic
112C2×C43#204511yescharacteristic
113C2×C43#205311yescharacteristic
114D43—162no—
115#532—432no—
116#474—862no—
117#466—862no—
118#459—862no—
119#432C2×D4312yes—
120C2×C4⋊C8—431no—
121C2×C4⋊C8—862no—
122C2×C4⋊C8C2×D4311yescharacteristic
123#376—431no—
124#333—862no—
125#331—862no—
126#327—864no—
127C43#1051211yescharacteristic, complemented, Sylow
128C2×#41—862no—
129C2×D8—862no—
130C22×C8—861no—
131C22×C8D17212yes—
132C4⋊Q8—432no—
133#127—432no—
134#124—862no—
135#121—862no—
136#121—862no—
137C4×D4—862no—
138C4×D4—862no—
139C2×C42—861no—
140C2×C42C22×D4311yescharacteristic
141#107—862no—
142C4⋊C8—22no—
143C4⋊C8—22no—
144C4⋊C8—862no—
145C4⋊C8—1724no—
146#102—864no—
147C22⋊C8—22no—
148#97—22no—
149#95—432no—
150#95—861no—
151#41—3444no—
152C2×Q8—862no—
153C2×D4—862no—
154C2×D4—862no—
155C2×D4—862no—
156C2×D4—1722no—
157C22×C4—862no—
158C22×C4—1722no—
159C22×C4C2×D17211yescharacteristic
160C22×C4D4×D4311yescharacteristic
161C22×C4#1062190211yescharacteristic
162D8—3442no—
163C2×C8—22no—
164C2×C8—42no—
165C2×C8—42no—
166C2×C8—1722no—
167C2×C8—1721no—
168C4⋊C4—862no—
169C4⋊C4—862no—
170C22⋊C4—1722no—
171C22⋊C4—1722no—
172C42—862no—
173C42—862no—
174C42#1062189812yes—
175C42D4×D4312yes—
176C23—1722no—
177C23#1306330011yescharacteristic
178Q8—3442no—
179D4—3442no—
180D4—3442no—
181D4—3444no—
182D4—1722no—
183D4—1722no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—864no—
189C2×C4—3444no—
190C2×C4—1722no—
191C2×C4—1722no—
192C2×C4—1722no—
193C2×C4#1306329511yescharacteristic
194C2×C4#1306329812yes—
195C2×C4#1306331012yes—
196C2×C4#1306331311yescharacteristic
197C8—42no—
198C8—82no—
199C8—3441no—
200C22—21no—
201C22—21no—
202C22—3442no—
203C22—3442no—
204C22—3442no—
205C22#1458281711yescharacteristic
206C22#1458317012yes—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—3442no—
211C4—1724no—
212C4#1458306911yescharacteristic
213C4#1458308411yescharacteristic
214C2—22no—
215C2—6882no—
216C2#1913582011yescharacteristic
217C2#1913585211yescharacteristic
218C2#1913590211yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#394
prime radical#19145905C2
hypercenter#1290D43
hypocenterC43#10512
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. #19134748C2semidirect
3. #19133291C2semidirect
4. #19133104C2semidirect
5. C43×#1290C2semidirect
109. #1290D43semidirect
127. C43#10512semidirect

Maximal subgroups

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

subgroupindex
#191459052
#191347482
#191332912
#191331042
C43×#12902
#1051243