Finite Group Databasebeta

← #24985695

Subgroups — #24985695

Order 11008.

478 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 95 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#19136123C211yesmaximal, characteristic
2#19136066C212yesmaximal, complemented
3#19132418C212yesmaximal, complemented
4#19132416C211yesmaximal, characteristic
5C43×#2683C211yesmaximal, characteristic
6C2×#13063258—22no—
7C2×#13063258—21no—
8C2×#13063246—21no—
9#14582769C2211yescharacteristic
10#14582661—22no—
11#14582654C2212yes—
12#14582654C2211yescharacteristic
13C2×C22⋊Q8×C43—22no—
14C43×#396—22no—
15C43×#395—21no—
16C43×#390C2211yescharacteristic
17C43×#389C2212yes—
18C43×#386—21no—
19C22×C43⋊C8—21no—
20C22×C43⋊C8—22no—
21C2×C4⋊Dic43—21no—
22C2×C4⋊Dic43—22no—
23#13063258—42no—
24#13063258—44no—
25#13063246—42no—
26C22×Q8×C43—21no—
27C22×D4×C43D411yescharacteristic
28C23×C4×C43—21no—
29C22⋊Q8×C43—44no—
30C22⋊Q8×C43—44no—
31C2×C4⋊C4×C43—22no—
32C2×C4⋊C4×C43—22no—
33C2×C4⋊C4×C43D412yes—
34C2×C4⋊C4×C43D412yes—
35C2×C4⋊C4×C43D411yescharacteristic
36C2×C22⋊C4×C43—22no—
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—21no—
39C2×C42×C43C2311yescharacteristic
40#95×C43—21no—
41#95×C43—22no—
42C24×C43—21no—
43C2×Q8×C43—44no—
44C2×Q8×C43—81no—
45C2×D4×C43—21no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43Q1612yes—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—21no—
52C22×C4×C43—44no—
53C22×C4×C43—81no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—41no—
57C4⋊C4×C43—22no—
58C4⋊C4×C43—42no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—44no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43D814yes—
64C22⋊C4×C43—44no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C22⋊C4×C43—81no—
68C42×C43—41no—
69C4⋊Dic43—41no—
70C4⋊Dic43—41no—
71C4⋊Dic43—42no—
72C4⋊Dic43—42no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—24no—
75C2×C43⋊C8—42no—
76C2×C43⋊C8—41no—
77C2×C43⋊C8—42no—
78C2×C43⋊C8—41no—
79C23×C43—22no—
80C23×C43—42no—
81C23×C43—41no—
82C23×C43—42no—
83C23×C43—41no—
84C23×C43#12011yescharacteristic
85Q8×C43—84no—
86D4×C43—42no—
87D4×C43—81no—
88C2×C4×C43—21no—
89C2×C4×C43—22no—
90C2×C4×C43—22no—
91C2×C4×C43—21no—
92C2×C4×C43—24no—
93C2×C4×C43—42no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43—42no—
100C2×C4×C43—84no—
101C2×C4×C43C2×D812yes—
102C2×C4×C43C2×Q1611yescharacteristic
103C2×C4×C43AGL(1,ℤ/8)12yes—
104C2×C4×C43#13711yescharacteristic
105C2×Dic43—82no—
106C2×Dic43—81no—
107C43⋊C8—44no—
108C43⋊C8—42no—
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—44no—
125C4×C43—82no—
126C4×C43—81no—
127Dic43—161no—
128#2683D4311yescharacteristic
129#2093—431no—
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—22no—
140C2×#107—862no—
141C2×#107—861no—
142C2×#102—861no—
143#396—22no—
144#395—21no—
145#390C2×D4311yescharacteristic
146#389C2×D4312yes—
147#386—21no—
148#384—431no—
149#340—862no—
150#336—432no—
151#336—431no—
152C43#779711yescharacteristic, complemented, Sylow
153C22×Q8—21no—
154C22×D4C22⋊D4311yescharacteristic
155C23×C4—21no—
156C22×C8—862no—
157C22×C8—861no—
158C22⋊Q8—44no—
159C22⋊Q8—44no—
160C2×C4⋊C4—22no—
161C2×C4⋊C4—22no—
162C2×C4⋊C4—862no—
163C2×C4⋊C4—861no—
164C2×C4⋊C4C22⋊D4312yes—
165C2×C4⋊C4C22⋊D4312yes—
166C2×C4⋊C4C22⋊D4311yescharacteristic
167C2×C22⋊C4—22no—
168C2×C22⋊C4—22no—
169C2×C22⋊C4—21no—
170C2×C42C22×D4311yescharacteristic
171#107—1722no—
172#107—1724no—
173#102—1722no—
174#95—21no—
175#95—22no—
176C24—21no—
177C2×Q8—44no—
178C2×Q8—81no—
179C2×D4—21no—
180C2×D4—41no—
181C2×D4—41no—
182C2×D4#1062188512yes—
183C22×C4—22no—
184C22×C4—22no—
185C22×C4—21no—
186C22×C4—44no—
187C22×C4—81no—
188C22×C4—1721no—
189C22×C4C2×C22⋊D4312yes—
190C22×C4C2×C22⋊D4311yescharacteristic
191C2×C8—862no—
192C2×C8—864no—
193C2×C8—1722no—
194C2×C8—1721no—
195C2×C8—1722no—
196C2×C8—1721no—
197C4⋊C4—22no—
198C4⋊C4—41no—
199C4⋊C4—42no—
200C4⋊C4—44no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C4⋊C4—1721no—
204C4⋊C4—1721no—
205C4⋊C4—1722no—
206C4⋊C4—1722no—
207C4⋊C4#1062188214yes—
208C22⋊C4—44no—
209C22⋊C4—42no—
210C22⋊C4—42no—
211C22⋊C4—81no—
212C42—41no—
213C23—22no—
214C23—41no—
215C23—42no—
216C23—41no—
217C23—42no—
218C23#1306329411yescharacteristic
219Q8—84no—
220D4—42no—
221D4—81no—
222C2×C4—21no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—21no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—41no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4—42no—
234C2×C4—84no—
235C2×C4—3441no—
236C2×C4—3442no—
237C2×C4C2×#1062188212yes—
238C2×C4C2×#1062188511yescharacteristic
239C2×C4#1306335112yes—
240C2×C4#1306335611yescharacteristic
241C8—1724no—
242C8—1722no—
243C22—44no—
244C22—42no—
245C22—82no—
246C22—81no—
247C22—81no—
248C22#1458303312yes—
249C22#1458305511yescharacteristic
250C22#1458306711yescharacteristic
251C22#1458308212yes—
252C22#1458308911yescharacteristic
253C4—22no—
254C4—22no—
255C4—21no—
256C4—21no—
257C4—44no—
258C4—82no—
259C4—81no—
260C4—6881no—
261C2—82no—
262C2#1913359812yes—
263C2#1913362011yescharacteristic
264C2#1913364911yescharacteristic
265C2#1913384412yes—
266C2#1913390611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2683C2
socleC23×C43#120
prime radicalC22×D4×C43D4
hypercenter#2683D43
hypocenterC43#7797
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2683

Complements

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

NH ≅ G/Ntype
2. #19136066C2semidirect
3. #19132418C2semidirect
152. C43#7797semidirect

Maximal subgroups

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

subgroupindex
#191361232
#191360662
#191324182
#191324162
C43×#26832
#779743