Finite Group Databasebeta

← #24985694

Subgroups — #24985694

Order 11008.

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

normal subgroups only

This group has 478 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#19140967C211yesmaximal, characteristic
2#19136067C212yesmaximal, complemented
3#19132417C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic
5C43×#2093C211yesmaximal, characteristic
6C2×#13063302—22no—
7C2×#13063258—22no—
8#14582822—22no—
9#14582819—21no—
10#14582797C2212yes—
11#14582779—21no—
12#14582661—22no—
13#14582654C2212yes—
14C2×#107×C43—21no—
15C2×#102×C43—21no—
16C43×#390C2211yescharacteristic
17C43×#384C2211yescharacteristic
18C43×#336C2211yescharacteristic
19C22×Dic86—21no—
20C23×Dic43—21no—
21C22×C43⋊C8—22no—
22#13063302—44no—
23#13063302—44no—
24C2×C4⋊Dic43D412yes—
25C2×C4⋊Dic43D412yes—
26C2×Dic43⋊C4—22no—
27C2×Dic43⋊C4—22no—
28C2×C22⋊Dic43—22no—
29C2×C22⋊Dic43—21no—
30#13063258—44no—
31C43⋊#95—21no—
32C43⋊#95—22no—
33C22×D4×C43D411yescharacteristic
34C22×C8×C43—21no—
35C2×C4⋊C4×C43—22no—
36C2×C4⋊C4×C43—21no—
37C2×C4⋊C4×C43D411yescharacteristic
38C2×C22⋊C4×C43—22no—
39C2×C42×C43C2311yescharacteristic
40#107×C43—42no—
41#102×C43—42no—
42C24×C43—21no—
43C2×D4×C43—21no—
44C2×D4×C43—41no—
45C2×D4×C43—41no—
46C2×D4×C43Q1612yes—
47C22×C4×C43—21no—
48C22×C4×C43—41no—
49C22×C4×C43C2×D412yes—
50C22×C4×C43C2×D411yescharacteristic
51C22×Dic43—22no—
52C22×Dic43—22no—
53C22×Dic43—44no—
54C22×Dic43—81no—
55C2×Dic86—44no—
56C2×Dic86—81no—
57C2×C8×C43—22no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—41no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—42no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C42×C43—41no—
68C22⋊Dic43—44no—
69C22⋊Dic43—81no—
70C4⋊Dic43—22no—
71C4⋊Dic43—42no—
72C4⋊Dic43D814yes—
73Dic43⋊C4—44no—
74Dic43⋊C4—42no—
75Dic43⋊C4—42no—
76C2×C43⋊C8—24no—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—42no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43—41no—
82C23×C43—42no—
83C23×C43—41no—
84C23×C43#12011yescharacteristic
85D4×C43—42no—
86D4×C43—81no—
87C2×C4×C43—21no—
88C2×C4×C43—22no—
89C2×C4×C43—22no—
90C2×C4×C43—21no—
91C2×C4×C43—42no—
92C2×C4×C43—41no—
93C2×C4×C43—82no—
94C2×C4×C43—81no—
95C2×C4×C43C2×D812yes—
96C2×C4×C43C2×Q1611yescharacteristic
97C2×C4×C43AGL(1,ℤ/8)12yes—
98C2×C4×C43#13711yescharacteristic
99C2×Dic43—24no—
100C2×Dic43—42no—
101C2×Dic43—42no—
102C2×Dic43—42no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—84no—
106Dic86—84no—
107C8×C43—42no—
108C43⋊C8—44no—
109#7797—431nomaximal, Sylow
110C22×C43—42no—
111C22×C43—44no—
112C22×C43—82no—
113C22×C43—81no—
114C22×C43—81no—
115C22×C43#44712yes—
116C22×C43#45111yescharacteristic
117C22×C43#45311yescharacteristic
118C22×C43#45612yes—
119C22×C43#45811yescharacteristic
120C4×C43—22no—
121C4×C43—22no—
122C4×C43—21no—
123C4×C43—21no—
124C4×C43—81no—
125C4×C43—161no—
126Dic43—44no—
127Dic43—82no—
128#2683—431no—
129#2093D4311yescharacteristic
130#2083—432no—
131#1271—432no—
132#1270—431no—
133C2×C43—82no—
134C2×C43#161012yes—
135C2×C43#161411yescharacteristic
136C2×C43#161911yescharacteristic
137C2×C43#164912yes—
138C2×C43#166011yescharacteristic
139C2×C22⋊Q8—862no—
140C2×#107—21no—
141C2×#107—862no—
142C2×#102—21no—
143#396—862no—
144#395—861no—
145#390C2×D4311yescharacteristic
146#389—432no—
147#386—861no—
148#384C2×D4311yescharacteristic
149#340—862no—
150#336—432no—
151#336C2×D4311yescharacteristic
152C43#779711yescharacteristic, complemented, Sylow
153C22×Q8—861no—
154C22×D4C22⋊D4311yescharacteristic
155C23×C4—861no—
156C22×C8—21no—
157C22×C8—862no—
158C22⋊Q8—1724no—
159C22⋊Q8—1724no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—21no—
162C2×C4⋊C4—432no—
163C2×C4⋊C4—432no—
164C2×C4⋊C4—862no—
165C2×C4⋊C4—862no—
166C2×C4⋊C4C22⋊D4311yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—861no—
169C2×C22⋊C4—862no—
170C2×C42C22×D4311yescharacteristic
171#107—42no—
172#107—1724no—
173#102—42no—
174#95—861no—
175#95—862no—
176C24—21no—
177C2×Q8—3441no—
178C2×Q8—1724no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#1062188512yes—
183C22×C4—21no—
184C22×C4—41no—
185C22×C4—862no—
186C22×C4—862no—
187C22×C4—3441no—
188C22×C4—1724no—
189C22×C4D4×D4312yes—
190C22×C4C2×C22⋊D4311yescharacteristic
191C2×C8—22no—
192C2×C8—41no—
193C2×C8—41no—
194C2×C8—864no—
195C2×C8—1722no—
196C2×C8—1722no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—434no—
203C4⋊C4—862no—
204C4⋊C4—1722no—
205C4⋊C4—1724no—
206C4⋊C4—1722no—
207C4⋊C4—1722no—
208C22⋊C4—42no—
209C22⋊C4—42no—
210C22⋊C4—3441no—
211C22⋊C4—1724no—
212C42—41no—
213C23—22no—
214C23—41no—
215C23—42no—
216C23—41no—
217C23—42no—
218C23#1306329311yescharacteristic
219Q8—3444no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—81no—
229C2×C4—82no—
230C2×C4—864no—
231C2×C4—3444no—
232C2×C4—1722no—
233C2×C4—1722no—
234C2×C4—1722no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4D8×D4312yes—
238C2×C4C2×#1062188511yescharacteristic
239C2×C4#1306334912yes—
240C2×C4#1306335511yescharacteristic
241C8—42no—
242C8—1724no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1458303112yes—
249C22#1458305411yescharacteristic
250C22#1458306611yescharacteristic
251C22#1458308012yes—
252C22#1458308811yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—81no—
258C4—161no—
259C4—3442no—
260C4—1724no—
261C2—82no—
262C2#1913359612yes—
263C2#1913361911yescharacteristic
264C2#1913364711yescharacteristic
265C2#1913384312yes—
266C2#1913390411yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2093C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#2093D43
hypocenterC43#7797
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2093

Complements

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

NH ≅ G/Ntype
2. #19136067C2semidirect
3. #19132417C2semidirect
152. C43#7797semidirect

Maximal subgroups

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

subgroupindex
#191409672
#191360672
#191324172
#191324162
C43×#20932
#779743