Finite Group Databasebeta

← #24990973

Subgroups — #24990973

Order 11008.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#19137781C211yesmaximal, characteristic
2#19135565C211yesmaximal, characteristic
3#19134763C212yesmaximal
4#19132477C212yesmaximal
5C2×C43×#330C211yesmaximal, characteristic
6C2×#13063259—22no—
7C2×#13063257—22no—
8C2×#13063236C2211yescharacteristic
9#14582798—22no—
10#14582785—22no—
11#14582785—22no—
12#14582769C2211yescharacteristic
13#14582765C2212yes—
14#14582661—22no—
15C2×#125×C43C2211yescharacteristic
16C2×#97×C43C2212yes—
17C43×#330C414yescomplemented
18C22×C43⋊C8—21no—
19C2×C4⋊Dic43—21no—
20C2×C4⋊Dic43—22no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43D412yes—
23C2×C4⋊Dic43D412yes—
24C2×C4×Dic43—22no—
25#13063259—44no—
26#13063257—44no—
27#13063236—22no—
28C43⋊#95—22no—
29C43⋊#95—22no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C22×C8×C43—22no—
33#125×C43—22no—
34#125×C43C2×C412yes—
35#125×C43Q812yes—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43D412yes—
38C2×C42×C43C2311yescharacteristic
39#97×C43—22no—
40#97×C43C2×C414yes—
41C22×C4×C43—22no—
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43C2×D412yes—
44C22×Dic43—22no—
45C22×Dic43—22no—
46C22×Dic43—41no—
47C2×C8×C43—24no—
48C2×C8×C43—24no—
49C2×C8×C43—24no—
50C4⋊C4×C43—24no—
51C4⋊C4×C43—24no—
52C4⋊C4×C43—22no—
53C4⋊C4×C43C4⋊C414yes—
54C42×C43C22×C411yescharacteristic
55C42×C43C2×Q811yescharacteristic
56C42×C43#4112yes—
57C4⋊Dic43—42no—
58C4⋊Dic43—42no—
59C4⋊Dic43—42no—
60C4⋊Dic43—42no—
61C4⋊Dic43—42no—
62C4⋊Dic43—82no—
63C4×Dic43—82no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8—41no—
67C23×C43#12011yescharacteristic
68C2×C4×C43—22no—
69C2×C4×C43—21no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—24no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43C2×C4⋊C411yescharacteristic
76C2×C4×C43C4×D412yes—
77C2×C4×C43C22⋊Q812yes—
78C2×C4×C43#12311yescharacteristic
79C2×Dic43—42no—
80C2×Dic43—42no—
81C2×Dic43—42no—
82C2×Dic43—42no—
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—82no—
86C2×Dic43—81no—
87C8×C43—28no—
88C43⋊C8—42no—
89#8913—431nomaximal, Sylow
90C22×C43#38511yescharacteristic
91C22×C43#45312yes—
92C22×C43#45411yescharacteristic
93C22×C43#45612yes—
94C22×C43#45611yescharacteristic
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—22no—
98C4×C43—22no—
99C4×C43—44no—
100Dic43—82no—
101Dic43—82no—
102Dic43—161no—
103#2382—431no—
104#1992—431no—
105#1847—432no—
106C2×#330D4311yescharacteristic
107#1295—432no—
108C2×C43#165611yescharacteristic
109C2×C43#166012yes—
110C2×C43#166311yescharacteristic
111C2×C43#185711yescharacteristic
112C2×C43#185912yes—
113C2×#125C2×D4311yescharacteristic
114C2×#107—862no—
115C2×#106—862no—
116C2×#97—431no—
117C2×#97C2×D4312yes—
118#389—862no—
119#387—862no—
120#387—862no—
121#384—431no—
122#382—432no—
123#340—862no—
124#330Dic4314yescomplemented
125C43#891311yescharacteristic, complemented, Sylow
126C22×C8—22no—
127C22×C8—861no—
128#125—22no—
129#125Dic8612yes—
130#125C2×Dic4312yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—862no—
135C2×C4⋊C4—861no—
136C2×C4⋊C4—862no—
137C2×C4⋊C4D17212yes—
138C2×C42—862no—
139C2×C42C22×D4311yescharacteristic
140#107—1724no—
141#106—1724no—
142#97—22no—
143#97—862no—
144#97C2×Dic4314yes—
145#95—862no—
146#95—862no—
147#95—862no—
148#95—862no—
149C22×C4—22no—
150C22×C4—862no—
151C22×C4—862no—
152C22×C4—1721no—
153C22×C4C2×D17211yescharacteristic
154C22×C4D4×D4312yes—
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—862no—
159C2×C8—1721no—
160C2×C8—1721no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—3442no—
165C4⋊C4—1722no—
166C4⋊C4—1722no—
167C4⋊C4—1722no—
168C4⋊C4—1722no—
169C4⋊C4—1722no—
170C4⋊C4C4⋊Dic4314yes—
171C42—3442no—
172C42C2×Dic8611yescharacteristic
173C42#1062190012yes—
174C42C22×Dic4311yescharacteristic
175C23#1306329511yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—3442no—
184C2×C4—3441no—
185C2×C4—1722no—
186C2×C4—1722no—
187C2×C4—1722no—
188C2×C4—1722no—
189C2×C4—1722no—
190C2×C4—1722no—
191C2×C4C2×C4⋊Dic4311yescharacteristic
192C2×C4D4×Dic4312yes—
193C2×C4#1306330212yes—
194C2×C4#1306330911yescharacteristic
195C8—28no—
196C8—1722no—
197C22#1458277411yescharacteristic
198C22#1458306812yes—
199C22#1458307411yescharacteristic
200C22#1458308312yes—
201C22#1458308411yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—3442no—
208C4—3442no—
209C4—6881no—
210C2#1913389011yescharacteristic
211C2#1913390812yes—
212C2#1913392411yescharacteristic
213C2#1913481211yescharacteristic
214C2#1913482312yes—
subgroupG/H
centerC23#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC2×C43×#330C2
socle, prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenterC2×#330D43
hypocenterC43#8913
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
17. C43×#330C4semidirect
124. #330Dic43semidirect
125. C43#8913semidirect

Maximal subgroups

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

subgroupindex
#191377812
#191355652
#191347632
#191324772
C2×C43×#3302
#891343