Finite Group Databasebeta

← #24991921

Subgroups — #24991921

Order 11008.

426 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 103 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#19144920C211yesmaximal, characteristic
2#19143697C211yesmaximal, characteristic, complemented
3#19133013C212yesmaximal
4#19132433C212yesmaximal, complemented
5C43×#1526C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14583256—22no—
8#14583251C412yes—
9#14583247C412yes—
10#14583030—22no—
11Q8×C43⋊C8—22no—
12#14582960—22no—
13#14582952C2212yes—
14#14582893—22no—
15C2×C4×C43⋊C8C2211yescharacteristic
16#14582628—22no—
17#14582628—22no—
18C43×#533C2211yescharacteristic
19C4×M16×C43C2212yes—
20C43×#330—22no—
21C2×#10621898—21no—
22C22×C43⋊C8—21no—
23#13063325C2×C411yescharacteristic
24#13063322C2×C411yescharacteristic
25#13063313—21no—
26#13063299—22no—
27C4×D172—22no—
28C4⋊(C43⋊C8)—24no—
29C4⋊(C43⋊C8)D412yes—
30C4⋊(C43⋊C8)D412yes—
31#13063248—24no—
32#13063245—24no—
33C22⋊(C43⋊C8)—22no—
34#13063236—22no—
35C4×C43⋊C8—22no—
36C4×C43⋊C8—21no—
37C4×C43⋊C8—22no—
38C4×C43⋊C8C2×C412yes—
39C2×M16×C43—22no—
40C4⋊Q8×C43C2×C412yes—
41#125×C43D412yes—
42C22⋊Q8×C43—22no—
43C4×Q8×C43—22no—
44#117×C43D412yes—
45C2×C42×C43C2311yescharacteristic
46#97×C43—22no—
47C4×C8×C43—22no—
48C2×Q8×C43—22no—
49C22×C4×C43C2×D411yescharacteristic
50C22×C4×C43#4112yes—
51C2×C22⋊D43—41no—
52#10621898—44no—
53C2×D172—21no—
54C2×D172—22no—
55C2×C4×D43—41no—
56C2×Dic86—21no—
57M16×C43—24no—
58M16×C43—42no—
59C2×C8×C43—42no—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—24no—
62C4⋊C4×C43C22⋊C414yes—
63C22⋊C4×C43—22no—
64C42×C43—22no—
65C42×C43C22×C411yescharacteristic
66C42×C43C2×D412yes—
67C42×C43C2×D411yescharacteristic
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—22no—
70C2×C43⋊C8—22no—
71C2×C43⋊C8—22no—
72C2×C43⋊C8—22no—
73C2×C43⋊C8—42no—
74C23×C43#12311yescharacteristic
75C22×D43—41no—
76Q8×C43—42no—
77Q8×C43—42no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—22no—
81C2×C4×C43—24no—
82C2×C4×C43C2×C22⋊C411yescharacteristic
83C2×C4×C43C4×D412yes—
84C2×C4×C43#12011yescharacteristic
85C2×C4×C43#12112yes—
86C22⋊D43—82no—
87C2×Dic43—41no—
88D172—42no—
89D172—42no—
90D172—42no—
91C4×D43—82no—
92Dic86—42no—
93C8×C43—44no—
94C43⋊C8—42no—
95C43⋊C8—42no—
96C43⋊C8—42no—
97#9070—431nomaximal, Sylow
98C22×C43—22no—
99C22×C43—21no—
100C22×C43#38611yescharacteristic
101C2×D43—82no—
102C2×D43—81no—
103C4×C43—22no—
104C4×C43—21no—
105C4×C43—44no—
106C4×C43#44312yes—
107C4×C43#44412yes—
108C4×C43#45412yes—
109Dic43—81no—
110#3131—431no—
111#2986—431no—
112#1526D4311yescharacteristic, complemented
113#1484—432no—
114#1278—432no—
115C2×C43—41no—
116C2×C43#187612yes—
117C2×C43#188811yescharacteristic
118D43—161no—
119#533C2×D4311yescharacteristic
120#532—431no—
121#488—862no—
122#487—432no—
123#486—432no—
124#446—862no—
125C8×Q8—862no—
126#433—862no—
127#431—432no—
128#416—862no—
129C4×M16C2×D4312yes—
130C2×C4×C8—431no—
131#330—22no—
132D4⋊C8—862no—
133D4⋊C8—862no—
134C43#907011yescharacteristic, complemented, Sylow
135C2×#41—861no—
136C2×M16—22no—
137C22×C8—861no—
138C4⋊Q8—431no—
139C4⋊Q8C4×D4312yes—
140#127—431no—
141#125C22⋊D4312yes—
142#124—861no—
143C22⋊Q8—22no—
144#121—862no—
145C4×Q8—22no—
146C4×D4—862no—
147#117D17212yes—
148C2×C42C22×D4311yescharacteristic
149C4⋊C8—432no—
150C4⋊C8—432no—
151C4⋊C8—864no—
152#103—864no—
153#102—864no—
154C22⋊C8—862no—
155#97—22no—
156#97—862no—
157C4×C8—22no—
158C4×C8—432no—
159C4×C8—862no—
160C4×C8—862no—
161C4×C8—861no—
162#41—1724no—
163C2×Q8—22no—
164C2×Q8—861no—
165C2×D4—861no—
166C2×D4—862no—
167C2×D4—1721no—
168C22×C4—1721no—
169C22×C4C2×D17211yescharacteristic
170C22×C4#1062190012yes—
171M16—24no—
172M16—42no—
173C2×C8—42no—
174C2×C8—862no—
175C2×C8—862no—
176C2×C8—862no—
177C2×C8—1722no—
178C4⋊C4—22no—
179C4⋊C4—24no—
180C4⋊C4—862no—
181C4⋊C4(C2×D43)⋊C414yes—
182C22⋊C4—22no—
183C22⋊C4—1722no—
184C42—22no—
185C42C2×C4×D4311yescharacteristic
186C42D4×D4312yes—
187C42C2×C22⋊D4311yescharacteristic
188C23—1721no—
189C23#1306330911yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—1722no—
193D4—3442no—
194D4—1722no—
195D4—1722no—
196D4—1722no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—3442no—
202C2×C4—1721no—
203C2×C4C2×(C2×D43)⋊C411yescharacteristic
204C2×C4(C22⋊D43)⋊C412yes—
205C2×C4#1306329511yescharacteristic
206C2×C4#1306329712yes—
207C8—44no—
208C8—1722no—
209C8—1722no—
210C8—1722no—
211C22—21no—
212C22—22no—
213C22—3441no—
214C22—3442no—
215C22#1458277611yescharacteristic
216C4—21no—
217C4—22no—
218C4—44no—
219C4—3441no—
220C4#1458301312yes—
221C4#1458301812yes—
222C4#1458307412yes—
223C2—41no—
224C2—6881no—
225C2#1913492012yes—
226C2#1913499611yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1526C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1526D43
hypocenterC43#9070
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1526

Complements

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

NH ≅ G/Ntype
2. #19143697C2semidirect
4. #19132433C2semidirect
5. C43×#1526C2semidirect
112. #1526D43semidirect
134. C43#9070semidirect

Maximal subgroups

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

subgroupindex
#191449202
#191436972
#191330132
#191324332
C43×#15262
#907043