Finite Group Databasebeta

← #24998821

Subgroups — #24998821

Order 11008.

468 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 81 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#19145793C212yesmaximal
2#19135426C211yesmaximal, characteristic
3#19133107C212yesmaximal, complemented
4#19132506C211yesmaximal, characteristic, complemented
5C43×#3255C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14583309—22no—
8#14583265—22no—
9#14583223—24no—
10#14583186—22no—
11#14583176—22no—
12#14582956C2212yes—
13C2×#13063251—22no—
14#14582745C2211yescharacteristic
15#14582636—24no—
16C43×#533C2212yes—
17C43×#475—22no—
18C43×#470—22no—
19C43×#462—22no—
20C43×#423C2211yescharacteristic
21C2×#10621898—21no—
22#13063325D411yescharacteristic
23#13063322D411yescharacteristic
24#13063313—21no—
25#13063299—22no—
26C4×D172—22no—
27C2×C4×Dic43—21no—
28#13063258—24no—
29#13063256—24no—
30C4⋊(C43⋊C8)—22no—
31#13063251—44no—
32#13063245—24no—
33#13063245—24no—
34C22⋊(C43⋊C8)D414yes—
35#13063236—22no—
36C43⋊#95—22no—
37C2×Q16×C43—22no—
38C2×M16×C43D412yes—
39C4⋊Q8×C43D412yes—
40C4⋊Q8×C43D412yes—
41#125×C43—22no—
42C22⋊Q8×C43—22no—
43C22⋊Q8×C43—22no—
44C4×Q8×C43—22no—
45C4×Q8×C43—22no—
46#117×C43—22no—
47C2×C42×C43C2311yescharacteristic
48#106×C43—22no—
49C4⋊C8×C43—22no—
50#103×C43—24no—
51C2×Q8×C43—22no—
52C2×Q8×C43—22no—
53C22×C4×C43C2×D412yes—
54C22×C4×C43C2×D411yescharacteristic
55C2×C22⋊D43—41no—
56C22×Dic43—41no—
57#10621898—42no—
58#10621898—42no—
59C2×D172—22no—
60C2×D172—21no—
61C2×C4×D43—41no—
62C2×Dic86—21no—
63Q16×C43—82no—
64M16×C43—42no—
65C2×C8×C43—22no—
66C4⋊C4×C43—22no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—22no—
69C4⋊C4×C43—22no—
70C4⋊C4×C43—42no—
71C4⋊C4×C43—42no—
72C22⋊C4×C43—42no—
73C42×C43—42no—
74C42×C43C2×D411yescharacteristic
75C42×C43C2×D412yes—
76C42×C43#4111yescharacteristic
77(C2×D43)⋊C4—42no—
78C4⋊Dic43—22no—
79C4×Dic43—22no—
80C4×Dic43—41no—
81C2×C43⋊C8—24no—
82C23×C43#12711yescharacteristic
83C22×D43—41no—
84Q8×C43—42no—
85Q8×C43—42no—
86Q8×C43—82no—
87C2×C4×C43—21no—
88C2×C4×C43—21no—
89C2×C4×C43—42no—
90C2×C4×C43—42no—
91C2×C4×C43—42no—
92C2×C4×C43#12012yes—
93C2×C4×C43#12011yescharacteristic
94C2×C4×C43#12111yescharacteristic
95C2×C4×C43#12112yes—
96C22⋊D43—82no—
97C2×Dic43—42no—
98C2×Dic43—41no—
99C2×Dic43—82no—
100D172—44no—
101D172—42no—
102C4×D43—81no—
103C4×D43—81no—
104Dic86—42no—
105C8×C43—42no—
106C43⋊C8—44no—
107#10216—431nomaximal, Sylow
108C22×C43—21no—
109C22×C43—22no—
110C22×C43#39211yescharacteristic
111C2×D43—81no—
112C2×D43—82no—
113C4×C43—21no—
114C4×C43—22no—
115C4×C43—22no—
116C4×C43—82no—
117C4×C43—82no—
118C4×C43#45311yescharacteristic
119C4×C43#45411yescharacteristic
120Dic43—82no—
121Dic43—81no—
122#3255D4311yescharacteristic, complemented
123#3235—432no—
124#1963—431no—
125#1506—432no—
126#1307—431no—
127C2×C43—41no—
128C2×C43#200611yescharacteristic
129C2×C43#200912yes—
130D43—161no—
131#533C2×D4312yes—
132#532—431no—
133#501—862no—
134#490—862no—
135#482—864no—
136#476—862no—
137#475—22no—
138#474—862no—
139#470—22no—
140#462—22no—
141#432—432no—
142#423C2×D4311yescharacteristic
143C2×#104—862no—
144#376—431no—
145#328—864no—
146C43#1021611yescharacteristic, complemented, Sylow
147C2×#41—861no—
148C2×Q16—22no—
149C2×M16C22⋊D4312yes—
150C4⋊Q8—431no—
151C4⋊Q8C22⋊D4312yes—
152C4⋊Q8C22⋊D4312yes—
153#127—431no—
154#125—22no—
155#124—861no—
156C22⋊Q8—22no—
157C22⋊Q8—22no—
158#121—862no—
159C4×Q8—22no—
160C4×Q8—22no—
161C4×D4—862no—
162#117—22no—
163C2×C42—861no—
164C2×C42C22×D4311yescharacteristic
165#107—864no—
166#106—22no—
167#106—864no—
168C4⋊C8—22no—
169C4⋊C8—862no—
170#104—1724no—
171#103—24no—
172#102—864no—
173#102—864no—
174C22⋊C8—434no—
175#97—862no—
176#95—862no—
177#41—1722no—
178#41—1722no—
179C2×Q8—22no—
180C2×Q8—22no—
181C2×Q8—861no—
182C2×D4—862no—
183C2×D4—861no—
184C2×D4—1721no—
185C22×C4—1721no—
186C22×C4—1721no—
187C22×C4D4×D4312yes—
188C22×C4C2×C22⋊D4311yescharacteristic
189Q16—82no—
190M16—42no—
191C2×C8—22no—
192C2×C8—864no—
193C4⋊C4—22no—
194C4⋊C4—22no—
195C4⋊C4—22no—
196C4⋊C4—22no—
197C4⋊C4—42no—
198C4⋊C4—42no—
199C4⋊C4—862no—
200C22⋊C4—42no—
201C22⋊C4—1722no—
202C42—42no—
203C42—862no—
204C42—1721no—
205C42D4×D4311yescharacteristic
206C42#1062190011yescharacteristic
207C42C2×C22⋊D4312yes—
208C23—1721no—
209C23#1306332111yescharacteristic
210Q8—42no—
211Q8—42no—
212Q8—82no—
213Q8—1722no—
214D4—3442no—
215D4—1722no—
216D4—1724no—
217C2×C4—21no—
218C2×C4—21no—
219C2×C4—42no—
220C2×C4—42no—
221C2×C4—42no—
222C2×C4—3442no—
223C2×C4—3441no—
224C2×C4—3441no—
225C2×C4—1722no—
226C2×C4—1721no—
227C2×C4#1306329312yes—
228C2×C4#1306329411yescharacteristic
229C2×C4#1306329611yescharacteristic
230C2×C4#1306329712yes—
231C8—42no—
232C8—1724no—
233C22—21no—
234C22—22no—
235C22—3441no—
236C22—3442no—
237C22#1458280711yescharacteristic
238C4—21no—
239C4—22no—
240C4—22no—
241C4—82no—
242C4—82no—
243C4—3442no—
244C4—3441no—
245C4#1458306711yescharacteristic
246C4#1458307211yescharacteristic
247C2—41no—
248C2—6881no—
249C2#1913563711yescharacteristic
250C2#1913565312yes—
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#3255C2
socleC22×C43#392
prime radical#14583449C22
hypercenter#3255D43
hypocenterC43#10216
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3255

Complements

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

NH ≅ G/Ntype
3. #19133107C2semidirect
4. #19132506C2semidirect
5. C43×#3255C2semidirect
122. #3255D43semidirect
146. C43#10216semidirect

Maximal subgroups

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

subgroupindex
#191457932
#191354262
#191331072
#191325062
C43×#32552
#1021643