Finite Group Databasebeta

← #24985898

Subgroups — #24985898

Order 11008.

394 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 87 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#19141627C211yesmaximal, characteristic
2#19136159C212yesmaximal
3#19136133C211yesmaximal, characteristic
4#19132417C212yesmaximal
5C43×#1272C211yesmaximal, characteristic
6C2×#13063323—21no—
7C2×#13063258—21no—
8C2×#13063249—21no—
9#14582829—21no—
10#14582820—22no—
11#14582797C2212yes—
12#14582784—22no—
13#14582769C2211yescharacteristic
14#14582662—22no—
15#14582662—22no—
16#14582654C2211yescharacteristic
17C43×#391C2211yescharacteristic
18C43×#336C2212yes—
19C22×Dic86—21no—
20C22×C43⋊C8—21no—
21#13063323—42no—
22#13063323—42no—
23C2×C4⋊Dic43—21no—
24C2×C4⋊Dic43—22no—
25C2×C4⋊Dic43—21no—
26C2×C4⋊Dic43D412yes—
27C2×C4⋊Dic43D412yes—
28C2×Dic43⋊C4—22no—
29C2×Dic43⋊C4—22no—
30C2×C4×Dic43—21no—
31#13063258—42no—
32#13063249—42no—
33C43⋊#95—21no—
34C43⋊#95—22no—
35C43⋊#95—22no—
36C22×Q8×C43D411yescharacteristic
37C22×C8×C43—22no—
38C2×C4⋊C4×C43D411yescharacteristic
39C2×C42×C43C2311yescharacteristic
40#95×C43—22no—
41C2×Q8×C43—21no—
42C2×Q8×C43—41no—
43C2×Q8×C43—41no—
44C2×Q8×C43SD1612yes—
45C22×C4×C43—21no—
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—22no—
50C22×Dic43—22no—
51C22×Dic43—41no—
52C2×Dic86—42no—
53C2×Dic86—81no—
54C2×Dic86—81no—
55C2×C8×C43—42no—
56C2×C8×C43—42no—
57C2×C8×C43—42no—
58C4⋊C4×C43—41no—
59C42×C43—41no—
60C4⋊Dic43—22no—
61C4⋊Dic43—42no—
62C4⋊Dic43—41no—
63C4⋊Dic43—41no—
64C4⋊Dic43—44no—
65C4⋊Dic43—81no—
66C4⋊Dic43Q1614yes—
67Dic43⋊C4—44no—
68Dic43⋊C4—42no—
69Dic43⋊C4—42no—
70C4×Dic43—42no—
71C2×C43⋊C8—22no—
72C2×C43⋊C8—41no—
73C2×C43⋊C8—41no—
74C23×C43#12011yescharacteristic
75Q8×C43—42no—
76Q8×C43—81no—
77C2×C4×C43—21no—
78C2×C4×C43—22no—
79C2×C4×C43—21no—
80C2×C4×C43—22no—
81C2×C4×C43—22no—
82C2×C4×C43—41no—
83C2×C4×C43—41no—
84C2×C4×C43—41no—
85C2×C4×C43—42no—
86C2×C4×C43C2×SD1611yescharacteristic
87C2×C4×C43C2×Q1612yes—
88C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
89C2×C4×C43#13712yes—
90C2×Dic43—24no—
91C2×Dic43—42no—
92C2×Dic43—42no—
93C2×Dic43—42no—
94C2×Dic43—42no—
95C2×Dic43—42no—
96C2×Dic43—81no—
97C2×Dic43—82no—
98Dic86—84no—
99C8×C43—82no—
100C43⋊C8—42no—
101#7829—431nomaximal, Sylow
102C22×C43#45011yescharacteristic
103C22×C43#45112yes—
104C22×C43#45311yescharacteristic
105C22×C43#45412yes—
106C22×C43#45811yescharacteristic
107C4×C43—21no—
108C4×C43—21no—
109C4×C43—22no—
110C4×C43—22no—
111C4×C43—42no—
112C4×C43—81no—
113Dic43—44no—
114Dic43—82no—
115Dic43—161no—
116#2734—431no—
117#2100—432no—
118#2095—431no—
119#1272D4311yescharacteristic
120#1271—432no—
121C2×C43#161311yescharacteristic
122C2×C43#161712yes—
123C2×C43#163311yescharacteristic
124C2×C43#163712yes—
125C2×C43#165711yescharacteristic
126C2×C4⋊Q8—861no—
127C2×#107—861no—
128C2×#103—861no—
129#398—861no—
130#395—862no—
131#391C2×D4311yescharacteristic
132#389—432no—
133#387—862no—
134#384—431no—
135#340—862no—
136#340—862no—
137#336—431no—
138#336C2×D4312yes—
139C43#782911yescharacteristic, complemented, Sylow
140C22×Q8—861no—
141C22×Q8D17211yescharacteristic
142C22×C8—22no—
143C22×C8—861no—
144C4⋊Q8—1722no—
145C4⋊Q8—1722no—
146C2×C4⋊C4—432no—
147C2×C4⋊C4—432no—
148C2×C4⋊C4—861no—
149C2×C4⋊C4—862no—
150C2×C4⋊C4—862no—
151C2×C4⋊C4—861no—
152C2×C4⋊C4—862no—
153C2×C4⋊C4D17211yescharacteristic
154C2×C42—861no—
155C2×C42C22×D4311yescharacteristic
156#107—1722no—
157#103—1722no—
158#95—22no—
159#95—861no—
160#95—862no—
161#95—862no—
162C2×Q8—21no—
163C2×Q8—41no—
164C2×Q8—41no—
165C2×Q8—3441no—
166C2×Q8—3441no—
167C2×Q8—1722no—
168C2×Q8#1062187312yes—
169C22×C4—21no—
170C22×C4—21no—
171C22×C4—862no—
172C22×C4—862no—
173C22×C4—1721no—
174C22×C4C2×D17211yescharacteristic
175C22×C4D4×D4312yes—
176C2×C8—42no—
177C2×C8—42no—
178C2×C8—42no—
179C2×C8—862no—
180C2×C8—1721no—
181C2×C8—1721no—
182C4⋊C4—41no—
183C4⋊C4—434no—
184C4⋊C4—862no—
185C4⋊C4—3441no—
186C4⋊C4—1721no—
187C4⋊C4—1721no—
188C4⋊C4—1724no—
189C4⋊C4—1722no—
190C4⋊C4—1724no—
191C4⋊C4—1722no—
192C4⋊C4—1722no—
193C42—41no—
194C42—1722no—
195C23#1306329511yescharacteristic
196Q8—42no—
197Q8—81no—
198Q8—3444no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—41no—
205C2×C4—41no—
206C2×C4—41no—
207C2×C4—42no—
208C2×C4—864no—
209C2×C4—3441no—
210C2×C4—3442no—
211C2×C4—1722no—
212C2×C4—1722no—
213C2×C4—1722no—
214C2×C4—1722no—
215C2×C4—1722no—
216C2×C4C2×#1062187311yescharacteristic
217C2×C4Q16×D4312yes—
218C2×C4#1306335311yescharacteristic
219C2×C4#1306335412yes—
220C8—82no—
221C8—1722no—
222C22#1458305211yescharacteristic
223C22#1458305612yes—
224C22#1458306911yescharacteristic
225C22#1458307312yes—
226C22#1458309011yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—22no—
231C4—42no—
232C4—81no—
233C4—3442no—
234C4—1724no—
235C4—6881no—
236C2#1913361711yescharacteristic
237C2#1913363812yes—
238C2#1913373611yescharacteristic
239C2#1913376212yes—
240C2#1913389411yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1272C2
socle, prime radicalC23×C43#120
hypercenter#1272D43
hypocenterC43#7829
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1272

Complements

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

NH ≅ G/Ntype
139. C43#7829semidirect

Maximal subgroups

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

subgroupindex
#191416272
#191361592
#191361332
#191324172
C43×#12722
#782943