Finite Group Databasebeta

← #24985902

Subgroups — #24985902

Order 11008.

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

normal subgroups only

This group has 494 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#19136133C211yesmaximal, characteristic, complemented
2#19136128C212yesmaximal, complemented
3#19132421C211yesmaximal, characteristic, complemented
4#19132416C212yesmaximal, complemented
5C43×#2733C211yesmaximal, characteristic
6C2×#13063258—21no—
7C2×#13063256—22no—
8C2×#13063249—21no—
9C2×#13063246—22no—
10#14582769C2211yescharacteristic
11#14582654C2211yescharacteristic
12#14582654C2212yes—
13C2×#124×C43—21no—
14C43×#394—21no—
15C43×#392—22no—
16C43×#391C2211yescharacteristic
17C43×#390C2212yes—
18C43×#388—22no—
19C22×C43⋊C8—22no—
20C22×C43⋊C8—21no—
21C2×C4⋊Dic43—22no—
22C2×C4⋊Dic43—21no—
23#13063258—42no—
24#13063256—44no—
25#13063249—42no—
26#13063246—44no—
27C22×Q8×C43D411yescharacteristic
28C22×D4×C43—21no—
29C22×D4×C43—21no—
30C22×D4×C43D412yes—
31#124×C43—42no—
32#124×C43—42no—
33C2×C4⋊C4×C43D412yes—
34C2×C4⋊C4×C43D411yescharacteristic
35C2×C22⋊C4×C43—22no—
36C2×C22⋊C4×C43—22no—
37C2×C22⋊C4×C43—22no—
38C2×C22⋊C4×C43—22no—
39C2×C42×C43—21no—
40C2×C42×C43C2311yescharacteristic
41#95×C43—21no—
42#95×C43—22no—
43C24×C43—22no—
44C2×Q8×C43—21no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43SD1612yes—
48C2×D4×C43—22no—
49C2×D4×C43—22no—
50C2×D4×C43—42no—
51C2×D4×C43—42no—
52C2×D4×C43—42no—
53C2×D4×C43—82no—
54C2×D4×C43—81no—
55C2×D4×C43—81no—
56C2×D4×C43—81no—
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43—22no—
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43C2×D412yes—
62C22×Dic43—41no—
63C4⋊C4×C43—42no—
64C4⋊C4×C43—41no—
65C22⋊C4×C43—44no—
66C22⋊C4×C43—42no—
67C22⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C22⋊C4×C43—42no—
70C22⋊C4×C43—82no—
71C42×C43—41no—
72C42×C43—42no—
73C4⋊Dic43—42no—
74C4⋊Dic43—41no—
75C4⋊Dic43—42no—
76C4⋊Dic43—41no—
77C2×C43⋊C8—24no—
78C2×C43⋊C8—22no—
79C2×C43⋊C8—42no—
80C2×C43⋊C8—41no—
81C2×C43⋊C8—42no—
82C2×C43⋊C8—41no—
83C23×C43—42no—
84C23×C43—42no—
85C23×C43—42no—
86C23×C43—42no—
87C23×C43—42no—
88C23×C43—42no—
89C23×C43—42no—
90C23×C43#12011yescharacteristic
91Q8×C43—42no—
92Q8×C43—81no—
93D4×C43—44no—
94D4×C43—82no—
95D4×C43—84no—
96D4×C43—84no—
97C2×C4×C43—22no—
98C2×C4×C43—21no—
99C2×C4×C43—22no—
100C2×C4×C43—21no—
101C2×C4×C43—22no—
102C2×C4×C43—41no—
103C2×C4×C43—41no—
104C2×C4×C43—42no—
105C2×C4×C43—42no—
106C2×C4×C43—42no—
107C2×C4×C43—42no—
108C2×C4×C43—41no—
109C2×C4×C43C2×SD1611yescharacteristic
110C2×C4×C43#13512yes—
111C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C43#13712yes—
113C2×Dic43—81no—
114C2×Dic43—82no—
115C43⋊C8—42no—
116C43⋊C8—44no—
117#7830—431nomaximal, Sylow
118C22×C43—82no—
119C22×C43—82no—
120C22×C43—82no—
121C22×C43—82no—
122C22×C43—82no—
123C22×C43—82no—
124C22×C43—82no—
125C22×C43#45011yescharacteristic
126C22×C43#45212yes—
127C22×C43#45311yescharacteristic
128C22×C43#45312yes—
129C22×C43#45811yescharacteristic
130C4×C43—21no—
131C4×C43—21no—
132C4×C43—22no—
133C4×C43—22no—
134C4×C43—42no—
135C4×C43—82no—
136C4×C43—81no—
137Dic43—161no—
138#2733D4311yescharacteristic
139#2095—431no—
140#2094—432no—
141#1272—431no—
142#1270—432no—
143C2×C43—162no—
144C2×C43#161311yescharacteristic
145C2×C43#161812yes—
146C2×C43#163112yes—
147C2×C43#163411yescharacteristic
148C2×C43#165511yescharacteristic
149C2×#124—21no—
150C2×#107—861no—
151C2×#106—862no—
152C2×#103—861no—
153C2×#102—862no—
154#394—21no—
155#392—22no—
156#391C2×D4311yescharacteristic
157#390C2×D4312yes—
158#388—22no—
159#384—431no—
160#336—432no—
161#336—431no—
162C43#783011yescharacteristic, complemented, Sylow
163C22×Q8C22⋊D4311yescharacteristic
164C22×D4—21no—
165C22×D4—21no—
166C22×D4C22⋊D4312yes—
167C22×C8—862no—
168C22×C8—861no—
169#124—42no—
170#124—42no—
171C2×C4⋊C4—862no—
172C2×C4⋊C4—861no—
173C2×C4⋊C4C22⋊D4312yes—
174C2×C4⋊C4C22⋊D4311yescharacteristic
175C2×C22⋊C4—22no—
176C2×C22⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—22no—
179C2×C42—21no—
180C2×C42C22×D4311yescharacteristic
181#107—1722no—
182#106—1724no—
183#103—1722no—
184#102—1724no—
185#95—21no—
186#95—22no—
187C24—22no—
188C2×Q8—21no—
189C2×Q8—41no—
190C2×Q8—41no—
191C2×Q8#1062188312yes—
192C2×D4—22no—
193C2×D4—22no—
194C2×D4—42no—
195C2×D4—42no—
196C2×D4—42no—
197C2×D4—81no—
198C2×D4—81no—
199C2×D4—82no—
200C2×D4—81no—
201C22×C4—21no—
202C22×C4—21no—
203C22×C4—22no—
204C22×C4—1721no—
205C22×C4C2×C22⋊D4311yescharacteristic
206C22×C4C2×C22⋊D4312yes—
207C2×C8—864no—
208C2×C8—862no—
209C2×C8—1722no—
210C2×C8—1721no—
211C2×C8—1722no—
212C2×C8—1721no—
213C4⋊C4—42no—
214C4⋊C4—41no—
215C4⋊C4—1722no—
216C4⋊C4—1721no—
217C4⋊C4—1722no—
218C4⋊C4—1721no—
219C22⋊C4—44no—
220C22⋊C4—42no—
221C22⋊C4—42no—
222C22⋊C4—42no—
223C22⋊C4—42no—
224C22⋊C4—82no—
225C42—41no—
226C42—42no—
227C23—42no—
228C23—42no—
229C23—42no—
230C23—42no—
231C23—42no—
232C23—42no—
233C23—42no—
234C23#1306329411yescharacteristic
235Q8—42no—
236Q8—81no—
237D4—44no—
238D4—82no—
239D4—84no—
240D4—84no—
241C2×C4—22no—
242C2×C4—21no—
243C2×C4—22no—
244C2×C4—21no—
245C2×C4—22no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—42no—
249C2×C4—42no—
250C2×C4—42no—
251C2×C4—42no—
252C2×C4—41no—
253C2×C4—3442no—
254C2×C4—3441no—
255C2×C4C2×#1062188311yescharacteristic
256C2×C4#1306334512yes—
257C2×C4#1306335111yescharacteristic
258C2×C4#1306335512yes—
259C8—1722no—
260C8—1724no—
261C22—82no—
262C22—82no—
263C22—82no—
264C22—82no—
265C22—82no—
266C22—82no—
267C22—82no—
268C22#1458305011yescharacteristic
269C22#1458306112yes—
270C22#1458306712yes—
271C22#1458306711yescharacteristic
272C22#1458308911yescharacteristic
273C4—21no—
274C4—21no—
275C4—22no—
276C4—22no—
277C4—42no—
278C4—82no—
279C4—81no—
280C4—6881no—
281C2—162no—
282C2#1913361511yescharacteristic
283C2#1913364312yes—
284C2#1913372212yes—
285C2#1913374011yescharacteristic
286C2#1913388411yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#2733C2
socleC23×C43#120
hypercenter#2733D43
hypocenterC43#7830
LCSG ▷ C2×C42×C43 ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2733

Complements

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

NH ≅ G/Ntype
1. #19136133C2semidirect
2. #19136128C2semidirect
3. #19132421C2semidirect
4. #19132416C2semidirect
162. C43#7830semidirect

Maximal subgroups

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

subgroupindex
#191361332
#191361282
#191324212
#191324162
C43×#27332
#783043