Finite Group Databasebeta

← #25000692

Subgroups — #25000692

Order 11008.

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

normal subgroups only

This group has 364 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#19145940C211yesmaximal, characteristic
2#19134748C211yesmaximal, characteristic
3#19133296C212yesmaximal
4#19133108C212yesmaximal
5C43×#1290C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583195—22no—
8#14583140—22no—
9#14583110—22no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11C2×Dic43⋊C8—22no—
12#14582745C2211yescharacteristic
13#14582646—22no—
14#14582644—22no—
15#14582637—24no—
16C43×#432C2212yes—
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×Dic172—22no—
19C22×C43⋊C8—21no—
20#13063325D412yes—
21#13063325D412yes—
22#13063317—22no—
23#13063304—22no—
24#13063304—22no—
25C4×Dic86—22no—
26C4×Dic86—22no—
27#13063284—22no—
28C2×C4×Dic43—21no—
29#13063259—22no—
30C4⋊(C43⋊C8)—22no—
31Dic43⋊C8—44no—
32#13063250—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
44C22×Dic43—22no—
45C2×Dic86—22no—
46C2×Dic86—22no—
47C2×C8×C43—22no—
48C2×C8×C43—42no—
49C2×C8×C43—42no—
50C42×C43C2×D412yes—
51C42×C43#4112yes—
52C22⋊Dic43—42no—
53C4⋊Dic43—22no—
54C4⋊Dic43—22no—
55C4⋊Dic43—22no—
56C4⋊Dic43—22no—
57Dic43⋊C4—42no—
58Dic43⋊C4—42no—
59C4×Dic43—22no—
60C4×Dic43—22no—
61C4×Dic43—42no—
62C2×C43⋊C8—42no—
63C2×C43⋊C8—41no—
64Dic172—82no—
65C23×C43#12111yescharacteristic
66C2×C4×C43—22no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—41no—
70C2×C4×C43#12011yescharacteristic
71C2×C4×C43#12112yes—
72C2×C4×C43#12312yes—
73C2×C4×C43#12411yescharacteristic
74C2×Dic43—24no—
75C2×Dic43—42no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78C2×Dic43—42no—
79Dic86—42no—
80Dic86—42no—
81Dic86—82no—
82C8×C43—42no—
83C8×C43—82no—
84C43⋊C8—81no—
85#10516—431nomaximal, Sylow
86C22×C43—21no—
87C22×C43—21no—
88C22×C43#39411yescharacteristic
89C22×C43#47312yes—
90C4×C43—22no—
91C4×C43—21no—
92C4×C43—22no—
93C4×C43#45311yescharacteristic
94C4×C43#45611yescharacteristic
95Dic43—44no—
96Dic43—82no—
97Dic43—82no—
98#3249—431no—
99#1843—431no—
100#1552—432no—
101#1506—432no—
102#1290D4311yescharacteristic
103C2×C43—22no—
104C2×C43#203911yescharacteristic
105C2×C43#204711yescharacteristic
106C2×C43#205311yescharacteristic
107#533—432no—
108#477—862no—
109#467—862no—
110#462—862no—
111#432C2×D4312yes—
112C2×C4⋊C8—431no—
113C2×C4⋊C8—862no—
114C2×C4⋊C8C2×D4311yescharacteristic
115#376—431no—
116#332—862no—
117#332—862no—
118#328—864no—
119C43#1051611yescharacteristic, complemented, Sylow
120C2×Q16—862no—
121C22×C8—861no—
122C22×C8D17212yes—
123C4⋊Q8—432no—
124C4⋊Q8—432no—
125#125—862no—
126C22⋊Q8—862no—
127C22⋊Q8—862no—
128C4×Q8—862no—
129C4×Q8—862no—
130#117—862no—
131C2×C42—861no—
132C2×C42C22×D4311yescharacteristic
133#107—862no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—862no—
137C4⋊C8—1724no—
138#103—864no—
139C22⋊C8—22no—
140#97—22no—
141#95—432no—
142#95—861no—
143C2×Q8—862no—
144C2×Q8—862no—
145C22×C4—862no—
146C22×C4C2×D17211yescharacteristic
147C22×C4D4×D4311yescharacteristic
148C22×C4#1062190211yescharacteristic
149Q16—3442no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—1722no—
154C2×C8—1721no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—862no—
158C4⋊C4—862no—
159C4⋊C4—1722no—
160C4⋊C4—1722no—
161C22⋊C4—1722no—
162C42—862no—
163C42—862no—
164C42—1722no—
165C42#1062189812yes—
166C42D4×D4312yes—
167C23#1306330011yescharacteristic
168Q8—3442no—
169Q8—1722no—
170Q8—1722no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—864no—
176C2×C4—1722no—
177C2×C4—1722no—
178C2×C4—1722no—
179C2×C4—1722no—
180C2×C4#1306329511yescharacteristic
181C2×C4#1306329812yes—
182C2×C4#1306331012yes—
183C2×C4#1306331311yescharacteristic
184C8—42no—
185C8—82no—
186C8—3441no—
187C22—21no—
188C22—21no—
189C22#1458281711yescharacteristic
190C22#1458317512yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—3442no—
195C4—3442no—
196C4—1724no—
197C4#1458306911yescharacteristic
198C4#1458308411yescharacteristic
199C2—22no—
200C2#1913582011yescharacteristic
201C2#1913586411yescharacteristic
202C2#1913590211yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1290D43
hypocenterC43#10516
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
119. C43#10516semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191347482
#191332962
#191331082
C43×#12902
#1051643