Finite Group Databasebeta

← #24997553

Subgroups — #24997553

Order 11008.

520 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 520 conjugacy classes of subgroups — too many to draw. Only its 83 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#19145940C211yesmaximal, characteristic, complemented
2#19144694C212yesmaximal
3#19133209C212yesmaximal, complemented
4#19132465C211yesmaximal, characteristic, complemented
5C43×#1955C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583234—22no—
8#14583195—22no—
9#14583179—22no—
10#14583140—22no—
11#14583110—22no—
12#14583104—22no—
13#14583050—22no—
14#14582999—24no—
15#14582956C2212yes—
16#14582640—24no—
17C2×C4×D4×C43C2211yescharacteristic
18C2×C4⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43—22no—
20C2×#97×C43C2211yescharacteristic
21C2×Dic172—22no—
22C2×#10621883—24no—
23#13063325D412yes—
24#13063325D412yes—
25#13063317—22no—
26#13063304—22no—
27#13063304—22no—
28C4×Dic86—22no—
29C4×Dic86—22no—
30#13063284—22no—
31#13063259—22no—
32#13063258—24no—
33C4⋊(C43⋊C8)—22no—
34#13063250—24no—
35#13063248—24no—
36#13063246—24no—
37C22⋊(C43⋊C8)—22no—
38#13063236D414yes—
39C22×D4×C43D411yescharacteristic
40C23×C4×C43—21no—
41C22×C8×C43—21no—
42C22×C8×C43D412yes—
43C4×D4×C43—22no—
44C4×D4×C43—22no—
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43C2311yescharacteristic
48C4⋊C8×C43—22no—
49C22⋊C8×C43—44no—
50#97×C43—22no—
51C24×C43—21no—
52C2×D4×C43—22no—
53C2×D4×C43—42no—
54C22×C4×C43—21no—
55C22×C4×C43—42no—
56C22×C4×C43—42no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D411yescharacteristic
61C22×C4×C43#4111yescharacteristic
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×C8×C43—22no—
65C2×C8×C43—22no—
66C2×C8×C43—41no—
67C2×C8×C43—41no—
68C2×C8×C43—42no—
69C4⋊C4×C43—22no—
70C22⋊C4×C43—42no—
71C42×C43C2×D412yes—
72C42×C43C2×D412yes—
73C22⋊Dic43—42no—
74#10621883—48no—
75C4⋊Dic43—22no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—22no—
79Dic43⋊C4—42no—
80Dic43⋊C4—42no—
81C4×Dic43—42no—
82C2×C43⋊C8—24no—
83Dic172—82no—
84C23×C43—22no—
85C23×C43—42no—
86C23×C43—41no—
87C23×C43—41no—
88C23×C43—42no—
89C23×C43#12111yescharacteristic
90D4×C43—24no—
91D4×C43—42no—
92C2×C4×C43—22no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—41no—
96C2×C4×C43—42no—
97C2×C4×C43—41no—
98C2×C4×C43—82no—
99C2×C4×C43—81no—
100C2×C4×C43—81no—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12012yes—
103C2×C4×C43#12112yes—
104C2×C4×C43#12711yescharacteristic
105C2×Dic43—42no—
106C2×Dic43—42no—
107Dic86—44no—
108Dic86—42no—
109Dic86—42no—
110C8×C43—42no—
111C8×C43—42no—
112C43⋊C8—44no—
113#10030—431nomaximal, Sylow
114C22×C43—21no—
115C22×C43—21no—
116C22×C43—44no—
117C22×C43—42no—
118C22×C43—82no—
119C22×C43—81no—
120C22×C43—81no—
121C22×C43#39211yescharacteristic
122C22×C43#47312yes—
123C4×C43—21no—
124C4×C43—22no—
125C4×C43—22no—
126C4×C43—81no—
127C4×C43#45311yescharacteristic
128C4×C43#45411yescharacteristic
129Dic43—82no—
130Dic43—82no—
131#3249—431no—
132#3110—432no—
133#1955D4311yescharacteristic
134#1531—432no—
135#1290—431no—
136C2×C43—22no—
137C2×C43—82no—
138C2×C43#200611yescharacteristic
139C2×C43#201011yescharacteristic
140C2×C43#202011yescharacteristic
141#533—432no—
142C2×C4×D4C2×D4311yescharacteristic
143#484—862no—
144#477—862no—
145#474—862no—
146#467—862no—
147#462—862no—
148#461—862no—
149#450—862no—
150#440—864no—
151#432—432no—
152C2×C4⋊C8C2×D4311yescharacteristic
153C2×C22⋊C8—22no—
154C2×#97C2×D4311yescharacteristic
155#330—864no—
156C43#1003011yescharacteristic, complemented, Sylow
157C22×D4D17211yescharacteristic
158C23×C4—21no—
159C2×Q16—862no—
160C2×SD16—864no—
161C22×C8—21no—
162C22×C8C22⋊D4312yes—
163C4⋊Q8—432no—
164C4⋊Q8—432no—
165#125—862no—
166C22⋊Q8—862no—
167C22⋊Q8—862no—
168C4×Q8—862no—
169C4×Q8—862no—
170C4×D4—22no—
171C4×D4—22no—
172#117—862no—
173C2×C4⋊C4D17211yescharacteristic
174C2×C22⋊C4—21no—
175C2×C42C22×D4311yescharacteristic
176#107—864no—
177#107—862no—
178C4⋊C8—22no—
179C4⋊C8—862no—
180#103—864no—
181#103—864no—
182#102—864no—
183C22⋊C8—44no—
184C22⋊C8—862no—
185#97—22no—
186#97—434no—
187C24—21no—
188C2×Q8—862no—
189C2×Q8—862no—
190C2×D4—22no—
191C2×D4—42no—
192C22×C4—21no—
193C22×C4—42no—
194C22×C4—42no—
195C22×C4—41no—
196C22×C4—41no—
197C22×C4C2×D17211yescharacteristic
198C22×C4#1062189811yescharacteristic
199C22×C4C2×C22⋊D4311yescharacteristic
200Q16—3442no—
201SD16—1728no—
202C2×C8—22no—
203C2×C8—22no—
204C2×C8—41no—
205C2×C8—41no—
206C2×C8—42no—
207C2×C8—864no—
208C4⋊C4—22no—
209C4⋊C4—862no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C4⋊C4—1722no—
214C4⋊C4—1722no—
215C22⋊C4—42no—
216C22⋊C4—1722no—
217C42—1722no—
218C42D4×D4312yes—
219C42D4×D4312yes—
220C23—22no—
221C23—42no—
222C23—41no—
223C23—41no—
224C23—42no—
225C23#1306329911yescharacteristic
226Q8—1724no—
227Q8—1722no—
228Q8—1722no—
229D4—24no—
230D4—42no—
231C2×C4—22no—
232C2×C4—21no—
233C2×C4—21no—
234C2×C4—41no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—82no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4#1306329311yescharacteristic
243C2×C4#1306329512yes—
244C2×C4#1306329812yes—
245C2×C4#1306332111yescharacteristic
246C8—42no—
247C8—42no—
248C8—1724no—
249C22—21no—
250C22—21no—
251C22—44no—
252C22—42no—
253C22—82no—
254C22—81no—
255C22—81no—
256C22#1458280811yescharacteristic
257C22#1458317412yes—
258C4—21no—
259C4—22no—
260C4—22no—
261C4—81no—
262C4—3442no—
263C4—3442no—
264C4#1458306611yescharacteristic
265C4#1458307111yescharacteristic
266C2—22no—
267C2—82no—
268C2#1913563611yescharacteristic
269C2#1913566211yescharacteristic
270C2#1913571611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1955C2
socleC22×C43#392
prime radicalC22×D4×C43D4
hypercenter#1955D43
hypocenterC43#10030
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1955

Complements

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

NH ≅ G/Ntype
1. #19145940C2semidirect
3. #19133209C2semidirect
4. #19132465C2semidirect
156. C43#10030semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191446942
#191332092
#191324652
C43×#19552
#1003043