Finite Group Databasebeta

← #24999701

Subgroups — #24999701

Order 11008.

400 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 97 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#19142958C211yesmaximal, characteristic
2#19135572C211yesmaximal, characteristic
3#19133160C212yesmaximal
4#19132454C212yesmaximal
5C43×#1276C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7C2×#13063317—21no—
8#14582923C2211yescharacteristic
9#14582797—24no—
10#14582769—21no—
11#14582765C2212yes—
12#14582659—21no—
13#14582659—21no—
14#14582637—24no—
15C43×#431C2212yes—
16C43×C43C2211yescharacteristic
17C2×#10621877—21no—
18#13063325Q812yes—
19#13063317—21no—
20#13063317—42no—
21#13063317—42no—
22#13063304—22no—
23C4×Dic86—22no—
24#13063284—21no—
25C2×C4⋊Dic43—24no—
26C2×C4⋊Dic43—22no—
27C2×Dic43⋊C4—24no—
28C4⋊(C43⋊C8)—22no—
29C43⋊#95—22no—
30C43⋊#95D414yes—
31C2×C42×C43—22no—
32C2×C42×C43D411yescharacteristic
33C2×C42×C43D411yescharacteristic
34C2×C42×C43C2311yescharacteristic
35C4⋊C8×C43—22no—
36C22⋊C8×C43—22no—
37C4×C8×C43—22no—
38C22×C4×C43—21no—
39C22×C4×C43—21no—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43C2×D412yes—
42C22×Dic43—24no—
43C2×Dic86—22no—
44C2×C8×C43—42no—
45C42×C43—21no—
46C42×C43—21no—
47C42×C43—44no—
48C42×C43SD1612yes—
49C42×C43Q1612yes—
50C42×C43C2×Q811yescharacteristic
51C42×C43#4112yes—
52C42×C43#4111yescharacteristic
53C22⋊Dic43—41no—
54C4⋊Dic43—22no—
55C4⋊Dic43—22no—
56C4⋊Dic43—48no—
57C4⋊Dic43—42no—
58C4⋊Dic43—42no—
59Dic43⋊C4—48no—
60Dic43⋊C4—42no—
61C4×Dic43—41no—
62#10621877—41no—
63#10621877—41no—
64C2×C43⋊C8—41no—
65C23×C43#12011yescharacteristic
66C2×C4×C43—24no—
67C2×C4×C43—22no—
68C2×C4×C43—22no—
69C2×C4×C43—42no—
70C2×C4×C43—42no—
71C2×C4×C43C22⋊Q812yes—
72C2×C4×C43C22⋊Q811yescharacteristic
73C2×C4×C43#12412yes—
74C2×C4×C43#12411yescharacteristic
75C2×C4×C43C2×SD1611yescharacteristic
76C2×C4×C43C2×Q1611yescharacteristic
77C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
78C2×C4×C43#13711yescharacteristic
79C2×Dic43—48no—
80C2×Dic43—42no—
81C2×Dic43—44no—
82Dic86—82no—
83C8×C43—82no—
84C43⋊C8—81no—
85#10365—431nomaximal, Sylow
86C22×C43—22no—
87C22×C43#39311yescharacteristic
88C22×C43#45011yescharacteristic
89C22×C43#45111yescharacteristic
90C4×C43—24no—
91C4×C43—22no—
92C4×C43—22no—
93C4×C43—42no—
94C4×C43#47511yescharacteristic
95C4×C43#47711yescharacteristic
96C4×C43#48711yescharacteristic
97C4×C43#48911yescharacteristic
98Dic43—84no—
99Dic43—82no—
100#2859—431no—
101#1994—431no—
102#1518—432no—
103#1286—432no—
104#1276D4311yescharacteristic
105C2×C43—21no—
106C2×C43—21no—
107C2×C43#202411yescharacteristic
108C2×C43#203112yes—
109#533—431no—
110C2×#125—861no—
111#431C2×D4312yes—
112#423—431no—
113#389—864no—
114#384—861no—
115#382—432no—
116C43C2×D4311yescharacteristic
117#339—861no—
118#339—861no—
119#328—864no—
120C43#1036511yescharacteristic, complemented, Sylow
121C2×M16—861no—
122C4⋊Q8—432no—
123#125—861no—
124#125—1722no—
125#125—1722no—
126C22⋊Q8—862no—
127C4×Q8—862no—
128#117—861no—
129C2×C4⋊C4—864no—
130C2×C4⋊C4—864no—
131C2×C4⋊C4—862no—
132C2×C42—22no—
133C2×C42D17211yescharacteristic
134C2×C42D17211yescharacteristic
135C2×C42C22×D4311yescharacteristic
136C4⋊C8—22no—
137C4⋊C8—862no—
138C22⋊C8—22no—
139C4×C8—22no—
140#95—434no—
141#95—862no—
142C2×Q8—862no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—864no—
146C22×C4C2×D17211yescharacteristic
147C22×C4D4×D4312yes—
148M16—1721no—
149M16—1721no—
150C2×C8—42no—
151C2×C8—1721no—
152C4⋊C4—862no—
153C4⋊C4—862no—
154C4⋊C4—1728no—
155C4⋊C4—1728no—
156C4⋊C4—1722no—
157C4⋊C4—1722no—
158C4⋊C4—1722no—
159C22⋊C4—1721no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—1721no—
164C42#1062187312yes—
165C42Dic17212yes—
166C42#1062189812yes—
167C42#1062190011yescharacteristic
168C42Q8×D4311yescharacteristic
169C23#1306329511yescharacteristic
170Q8—3442no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—1728no—
177C2×C4—1724no—
178C2×C4—1722no—
179C2×C4#1306330312yes—
180C2×C4#1306330511yescharacteristic
181C2×C4#1306331112yes—
182C2×C4#1306331311yescharacteristic
183C2×C4C2×#1062187311yescharacteristic
184C2×C4C2×Dic17211yescharacteristic
185C2×C4#1306335311yescharacteristic
186C2×C4#1306335811yescharacteristic
187C8—82no—
188C8—3441no—
189C22—22no—
190C22#1458281211yescharacteristic
191C22#1458305211yescharacteristic
192C22#1458305711yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—3444no—
198C4—3442no—
199C4#1458318511yescharacteristic
200C4#1458319511yescharacteristic
201C4#1458325011yescharacteristic
202C4#1458325911yescharacteristic
203C2—21no—
204C2—21no—
205C2#1913573711yescharacteristic
206C2#1913576812yes—
subgroupG/H
centerC22#14582812
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1276C2
socleC22×C43#393
prime radicalC23×C43#120
hypercenter#1276D43
hypocenterC43#10365
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

Complements

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

NH ≅ G/Ntype
120. C43#10365semidirect

Maximal subgroups

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

subgroupindex
#191429582
#191355722
#191331602
#191324542
C43×#12762
#1036543