Finite Group Databasebeta

← #25000092

Subgroups — #25000092

Order 11008.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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#19142663C211yesmaximal, characteristic
2#19135564C212yesmaximal
3#19134728C211yesmaximal, characteristic
4C2×#14582640C212yesmaximal
5C43×#1295C211yesmaximal, characteristic
6C2×#13063317C2212yes—
7C2×#13063236C2211yescharacteristic
8#14582839—22no—
9#14582831—22no—
10#14582829—22no—
11#14582769C2211yescharacteristic
12#14582662—22no—
13#14582662—22no—
14#14582661—22no—
15#14582640—24no—
16C2×#97×C43C2212yes—
17C43×#382C2211yescharacteristic
18C22×C43⋊C8—21no—
19#13063317—22no—
20#13063317—22no—
21#13063317—22no—
22#13063317—22no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—22no—
26C2×C4⋊Dic43D412yes—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30#13063236—21no—
31#13063236D412yes—
32C43⋊#95—24no—
33C43⋊#95—22no—
34C22×C8×C43—22no—
35C2×C4⋊C4×C43D412yes—
36C2×C42×C43C2311yescharacteristic
37#97×C43—22no—
38#97×C43—22no—
39#95×C43—22no—
40C22×C4×C43—22no—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43C2×D412yes—
43C22×Dic43—22no—
44C22×Dic43—22no—
45C22×Dic43—41no—
46C2×C8×C43—24no—
47C2×C8×C43—42no—
48C2×C8×C43—42no—
49C4⋊C4×C43—42no—
50C42×C43C2×D411yescharacteristic
51C42×C43#4112yes—
52C42×C43#4111yescharacteristic
53C4⋊Dic43—22no—
54C4⋊Dic43—22no—
55C4⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4⋊Dic43—42no—
58C4⋊Dic43—44no—
59C4⋊Dic43—82no—
60Dic43⋊C4—42no—
61Dic43⋊C4—42no—
62Dic43⋊C4—42no—
63Dic43⋊C4—42no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8—41no—
66C2×C43⋊C8—41no—
67C23×C43#12011yescharacteristic
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—21no—
71C2×C4×C43—22no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43#12112yes—
76C2×C4×C43#12111yescharacteristic
77C2×C4×C43#12312yes—
78C2×C4×C43#12411yescharacteristic
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—44no—
88C43⋊C8—42no—
89#10428—431nomaximal, Sylow
90C22×C43#39411yescharacteristic
91C22×C43#45412yes—
92C22×C43#45411yescharacteristic
93C22×C43#45511yescharacteristic
94C22×C43#45612yes—
95C4×C43—22no—
96C4×C43—22no—
97C4×C43—21no—
98C4×C43—21no—
99C4×C43—82no—
100Dic43—82no—
101Dic43—82no—
102Dic43—161no—
103#2822—431no—
104#1992—432no—
105#1836—431no—
106C2×#330—432no—
107#1295D4311yescharacteristic
108C2×C43#165811yescharacteristic
109C2×C43#166311yescharacteristic
110C2×C43#166412yes—
111C2×C43#203812yes—
112C2×C43#204011yescharacteristic
113C2×#125—432no—
114C2×#97—431no—
115C2×#97C2×D4312yes—
116#400—862no—
117#398—862no—
118#398—862no—
119#384—431no—
120#382C2×D4311yescharacteristic
121#340—862no—
122#340—862no—
123#340—862no—
124#330—864no—
125C43#1042811yescharacteristic, complemented, Sylow
126C22×C8—22no—
127C22×C8—861no—
128#125—862no—
129#125—862no—
130#125—862no—
131#125—862no—
132C2×C4⋊C4—432no—
133C2×C4⋊C4—432no—
134C2×C4⋊C4—862no—
135C2×C4⋊C4—862no—
136C2×C4⋊C4—862no—
137C2×C4⋊C4—861no—
138C2×C4⋊C4—862no—
139C2×C4⋊C4D17212yes—
140C2×C42C22×D4311yescharacteristic
141#97—22no—
142#97—22no—
143#97—432no—
144#97—861no—
145#95—22no—
146#95—864no—
147#95—862no—
148C22×C4—22no—
149C22×C4—862no—
150C22×C4—862no—
151C22×C4—1721no—
152C22×C4C2×D17211yescharacteristic
153C22×C4D4×D4312yes—
154C2×C8—24no—
155C2×C8—42no—
156C2×C8—42no—
157C2×C8—862no—
158C2×C8—1721no—
159C2×C8—1721no—
160C4⋊C4—42no—
161C4⋊C4—862no—
162C4⋊C4—862no—
163C4⋊C4—862no—
164C4⋊C4—862no—
165C4⋊C4—3442no—
166C4⋊C4—1724no—
167C4⋊C4—1722no—
168C4⋊C4—1722no—
169C4⋊C4—1722no—
170C4⋊C4—1722no—
171C4⋊C4—1722no—
172C42#1062189812yes—
173C42D4×D4311yescharacteristic
174C42#1062190211yescharacteristic
175C23#1306329511yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
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×C4#1306329812yes—
192C2×C4#1306330011yescharacteristic
193C2×C4#1306331012yes—
194C2×C4#1306331311yescharacteristic
195C8—44no—
196C8—1722no—
197C22#1458281711yescharacteristic
198C22#1458307312yes—
199C22#1458307411yescharacteristic
200C22#1458307911yescharacteristic
201C22#1458308312yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—3442no—
208C4—3442no—
209C4—6881no—
210C2#1913389811yescharacteristic
211C2#1913392411yescharacteristic
212C2#1913393212yes—
213C2#1913581512yes—
214C2#1913582511yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1295C2
socle, prime radicalC23×C43#120
hypercenter#1295D43
hypocenterC43#10428
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
125. C43#10428semidirect

Maximal subgroups

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

subgroupindex
#191426632
#191355642
#191347282
C2×#145826402
C43×#12952
#1042843