Finite Group Databasebeta

← #24998889

Subgroups — #24998889

Order 11008.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#19145736C212yesmaximal
2#19135415C211yesmaximal, characteristic
3#19133159C212yesmaximal
4#19132440C211yesmaximal, characteristic
5C43×#3162C211yesmaximal, characteristic
6C2×#13063325C2211yescharacteristic
7#14583295—22no—
8#14583249—22no—
9#14583227—24no—
10#14583184—24no—
11#14582952C2212yes—
12C2×#13063250—22no—
13#14582765C2211yescharacteristic
14#14582636—24no—
15C43×#533C2212yes—
16C43×#501—22no—
17C43×#501—22no—
18C43×#427—22no—
19C2×#97×C43C2211yescharacteristic
20C22×Dic86—21no—
21#13063325—22no—
22#13063325—21no—
23#13063325D412yes—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—21no—
26#13063256—28no—
27C4⋊(C43⋊C8)—22no—
28#13063250—44no—
29#13063249—28no—
30C22⋊(C43⋊C8)D414yes—
31C4×C43⋊C8—22no—
32C43⋊#95—22no—
33C22×C8×C43D412yes—
34C4⋊Q8×C43D412yes—
35C4⋊Q8×C43D412yes—
36#125×C43—22no—
37C22⋊Q8×C43—22no—
38C22⋊Q8×C43—22no—
39C4×Q8×C43—22no—
40C4×Q8×C43—22no—
41#117×C43—22no—
42C2×C42×C43C2311yescharacteristic
43#107×C43—24no—
44#106×C43—22no—
45#106×C43—22no—
46#97×C43—22no—
47C2×Q8×C43—22no—
48C2×Q8×C43—22no—
49C22×C4×C43C2×D412yes—
50C22×C4×C43C2×D411yescharacteristic
51C22×Dic43—41no—
52C22×Dic43—41no—
53C2×Dic86—22no—
54C2×Dic86—42no—
55C2×Dic86—42no—
56C2×Dic86—41no—
57C2×C8×C43—22no—
58C2×C8×C43—22no—
59C2×C8×C43SD1614yes—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—22no—
64C4⋊C4×C43—42no—
65C4⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C42×C43—42no—
68C42×C43C2×D411yescharacteristic
69C42×C43C2×D412yes—
70C42×C43#4111yescharacteristic
71C4⋊Dic43—24no—
72C4⋊Dic43—42no—
73C4⋊Dic43—42no—
74C2×C43⋊C8—24no—
75C23×C43#12711yescharacteristic
76Q8×C43—44no—
77Q8×C43—82no—
78C2×C4×C43—42no—
79C2×C4×C43—42no—
80C2×C4×C43—42no—
81C2×C4×C43#12012yes—
82C2×C4×C43#12011yescharacteristic
83C2×C4×C43#12111yescharacteristic
84C2×C4×C43#12112yes—
85C2×C4×C43C2×SD1612yes—
86C2×C4×C43#13712yes—
87C2×Dic43—42no—
88C2×Dic43—81no—
89C2×Dic43—81no—
90C2×Dic43—82no—
91C2×Dic43—81no—
92Dic86—44no—
93Dic86—82no—
94C8×C43—24no—
95C43⋊C8—44no—
96#10227—431nomaximal, Sylow
97C22×C43—22no—
98C22×C43#39211yescharacteristic
99C22×C43#49211yescharacteristic
100C22×C43#49711yescharacteristic
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—82no—
104C4×C43—82no—
105C4×C43#44812yes—
106C4×C43#46112yes—
107Dic43—82no—
108Dic43—161no—
109#3229—432no—
110#3162D4311yescharacteristic
111#1960—431no—
112#1518—432no—
113#1281—431no—
114C2×C43—21no—
115C2×C43—21no—
116C2×C43#200912yes—
117C2×C43#201311yescharacteristic
118#533C2×D4312yes—
119C2×C4⋊Q8—431no—
120#501—22no—
121#501—22no—
122#498—862no—
123#487—862no—
124#483—864no—
125#475—864no—
126#431—432no—
127#427—22no—
128C2×#103—862no—
129C2×#97C2×D4311yescharacteristic
130#382—431no—
131#328—864no—
132C43#1022711yescharacteristic, complemented, Sylow
133C22×Q8—861no—
134C22×C8C22⋊D4312yes—
135C4⋊Q8—432no—
136C4⋊Q8—861no—
137C4⋊Q8—862no—
138C4⋊Q8C22⋊D4312yes—
139C4⋊Q8C22⋊D4312yes—
140#125—22no—
141C22⋊Q8—22no—
142C22⋊Q8—22no—
143C4×Q8—22no—
144C4×Q8—22no—
145#117—22no—
146C2×C4⋊C4—862no—
147C2×C4⋊C4—861no—
148C2×C42C22×D4311yescharacteristic
149#107—24no—
150#106—22no—
151#106—22no—
152#106—868no—
153C4⋊C8—862no—
154#103—868no—
155#103—1724no—
156C22⋊C8—434no—
157#97—22no—
158C4×C8—862no—
159#95—862no—
160C2×Q8—22no—
161C2×Q8—22no—
162C2×Q8—862no—
163C2×Q8—1722no—
164C2×Q8—1722no—
165C2×Q8—1721no—
166C22×C4—1721no—
167C22×C4—1721no—
168C22×C4D4×D4312yes—
169C22×C4C2×C22⋊D4311yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—864no—
173C2×C8#1062188414yes—
174C4⋊C4—22no—
175C4⋊C4—22no—
176C4⋊C4—22no—
177C4⋊C4—22no—
178C4⋊C4—42no—
179C4⋊C4—42no—
180C4⋊C4—864no—
181C4⋊C4—1722no—
182C4⋊C4—1722no—
183C22⋊C4—42no—
184C42—42no—
185C42D4×D4311yescharacteristic
186C42#1062190011yescharacteristic
187C42C2×C22⋊D4312yes—
188C23#1306332111yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—3442no—
192Q8—1724no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—3441no—
197C2×C4—3441no—
198C2×C4—3442no—
199C2×C4—3441no—
200C2×C4—1722no—
201C2×C4#1306329312yes—
202C2×C4#1306329411yescharacteristic
203C2×C4#1306329611yescharacteristic
204C2×C4#1306329712yes—
205C2×C4C2×#1062188412yes—
206C2×C4#1306335612yes—
207C8—24no—
208C8—1724no—
209C22—22no—
210C22#1458280711yescharacteristic
211C22#1458327311yescharacteristic
212C22#1458329111yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—82no—
217C4—3442no—
218C4—6881no—
219C4#1458303812yes—
220C4#1458310112yes—
221C2—21no—
222C2—21no—
223C2#1913565212yes—
224C2#1913567811yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3162C2
socleC22×C43#392
prime radicalC23×C43#127
hypercenter#3162D43
hypocenterC43#10227
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3162

Complements

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

NH ≅ G/Ntype
132. C43#10227semidirect

Maximal subgroups

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

subgroupindex
#191457362
#191354152
#191331592
#191324402
C43×#31622
#1022743