Finite Group Databasebeta

← #24997214

Subgroups — #24997214

Order 11008.

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

normal subgroups only

This group has 544 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#19145346C211yesmaximal, characteristic
2#19144535C212yesmaximal, complemented
3#19132954C212yesmaximal, complemented
4#19132472C211yesmaximal, characteristic, complemented
5C43×#1818C211yesmaximal, characteristic, complemented
6C2×#13063299C2212yes—
7#14583223—24no—
8#14583217—22no—
9#14583213—22no—
10#14583212—22no—
11#14583135—22no—
12#14583035—22no—
13#14582942—22no—
14#14582903—22no—
15#14582863C2212yes—
16#14582622—24no—
17C2×#117×C43C2211yescharacteristic
18C2×C22⋊C8×C43C2211yescharacteristic
19C2×C22⋊C8×C43C2211yescharacteristic
20C43×#336—22no—
21C22×D172D412yes—
22C22×C22⋊D43—22no—
23C2×D344—22no—
24C2×#10621877—22no—
25#13063299—22no—
26#13063299—22no—
27#13063299—22no—
28#13063299—22no—
29C2×C4⋊Dic43D412yes—
30C2×(C2×D43)⋊C4—22no—
31#13063259—22no—
32#13063258—24no—
33#13063256—24no—
34#13063247—24no—
35#13063245—24no—
36#13063245—24no—
37C22⋊(C43⋊C8)—22no—
38C22⋊(C43⋊C8)D414yes—
39C23×C4×C43C2311yescharacteristic
40C22×C8×C43—21no—
41C22×C8×C43D412yes—
42#117×C43—22no—
43#117×C43—22no—
44C2×C4⋊C4×C43D411yescharacteristic
45C2×C4⋊C4×C43D411yescharacteristic
46C2×C22⋊C4×C43—21no—
47C2×C42×C43—21no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C24×C43#4111yescharacteristic
51C23×D43—22no—
52C22×C4×C43—21no—
53C22×C4×C43—21no—
54C22×C4×C43—42no—
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×D412yes—
57C22×C4×C43C2×D412yes—
58C22×C4×C43C2×D411yescharacteristic
59C2×C22⋊D43—42no—
60C2×C22⋊D43—42no—
61C2×C22⋊D43—84no—
62C22×Dic43—22no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172—44no—
66C2×C8×C43—22no—
67C2×C8×C43—42no—
68C2×C8×C43—42no—
69C2×C8×C43—41no—
70C4⋊C4×C43—22no—
71C4⋊C4×C43—22no—
72C22⋊C4×C43—42no—
73C42×C43—41no—
74C42×C43—41no—
75(C2×D43)⋊C4—42no—
76(C2×D43)⋊C4—42no—
77C4⋊Dic43—22no—
78C4⋊Dic43—22no—
79#10621877—44no—
80C2×C43⋊C8—24no—
81D344—82no—
82C23×C43—22no—
83C23×C43—41no—
84C23×C43—41no—
85C23×C43#12112yes—
86C23×C43#12111yescharacteristic
87C22×D43—42no—
88C22×D43—44no—
89C22×D43—82no—
90C22×D43—82no—
91C2×C4×C43—24no—
92C2×C4×C43—22no—
93C2×C4×C43—41no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—41no—
97C2×C4×C43—41no—
98C2×C4×C43—42no—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43#12012yes—
101C2×C4×C43#12711yescharacteristic
102C22⋊D43—84no—
103C22⋊D43—84no—
104C2×Dic43—42no—
105C2×Dic43—82no—
106D172—44no—
107D172—44no—
108C8×C43—42no—
109C8×C43—81no—
110C43⋊C8—44no—
111#9977—431nomaximal, Sylow
112C22×C43—21no—
113C22×C43—21no—
114C22×C43—22no—
115C22×C43—22no—
116C22×C43—22no—
117C22×C43—82no—
118C22×C43#39211yescharacteristic
119C22×C43#47212yes—
120C2×D43—82no—
121C2×D43—82no—
122C2×D43—82no—
123C2×D43—164no—
124C4×C43—22no—
125C4×C43—21no—
126C4×C43—81no—
127C4×C43—81no—
128C4×C43#45812yes—
129Dic43—82no—
130#3186—431no—
131#3094—432no—
132#1818D4311yescharacteristic, complemented
133#1471—432no—
134#1293—431no—
135C2×C43—22no—
136C2×C43—42no—
137C2×C43#201711yescharacteristic
138C2×C43#201811yescharacteristic
139C2×C43#202211yescharacteristic
140D43—162no—
141C2×#121—432no—
142C2×#117C2×D4311yescharacteristic
143#482—864no—
144#481—862no—
145#480—862no—
146#480—862no—
147#466—862no—
148#447—862no—
149#428—862no—
150#418—862no—
151#407—432no—
152C2×C22⋊C8C2×D4311yescharacteristic
153C2×C22⋊C8C2×D4311yescharacteristic
154#336—22no—
155#323—864no—
156C43#997711yescharacteristic, complemented, Sylow
157C22×D4—432no—
158C22×D4—862no—
159C23×C4C22×D4311yescharacteristic
160C2×D8—862no—
161C2×M16—862no—
162C22×C8—21no—
163C22×C8C22⋊D4312yes—
164#121—862no—
165#121—862no—
166#121—862no—
167#121—862no—
168#117—22no—
169#117—22no—
170C2×C4⋊C4—432no—
171C2×C4⋊C4D17211yescharacteristic
172C2×C4⋊C4D17211yescharacteristic
173C2×C22⋊C4—21no—
174C2×C22⋊C4—862no—
175C2×C42—21no—
176#107—864no—
177#107—862no—
178#106—864no—
179#102—864no—
180#102—864no—
181#102—864no—
182C22⋊C8—22no—
183C22⋊C8—22no—
184C22⋊C8—434no—
185C22⋊C8—862no—
186C24—862no—
187C24#1062189811yescharacteristic
188C2×D4—862no—
189C2×D4—862no—
190C2×D4—3444no—
191C2×D4—1724no—
192C2×D4—1722no—
193C2×D4—1722no—
194C22×C4—21no—
195C22×C4—21no—
196C22×C4—42no—
197C22×C4—862no—
198C22×C4C2×D17211yescharacteristic
199C22×C4D4×D4312yes—
200C22×C4D4×D4312yes—
201C22×C4C2×C22⋊D4311yescharacteristic
202D8—3442no—
203M16—1724no—
204C2×C8—22no—
205C2×C8—42no—
206C2×C8—42no—
207C2×C8—41no—
208C2×C8—864no—
209C4⋊C4—22no—
210C4⋊C4—22no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C22⋊C4—42no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—41no—
217C42—41no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—3442no—
222C23—3442no—
223C23—1724no—
224C23—1722no—
225C23#1306329812yes—
226C23#1306329911yescharacteristic
227D4—3444no—
228D4—3444no—
229D4—1724no—
230D4—1724no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—41no—
234C2×C4—42no—
235C2×C4—42no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—3442no—
240C2×C4—1722no—
241C2×C4#1306329311yescharacteristic
242C2×C4#1306329512yes—
243C2×C4#1306332111yescharacteristic
244C8—42no—
245C8—81no—
246C8—1724no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—3442no—
254C22—3442no—
255C22—3442no—
256C22—6884no—
257C22#1458280811yescharacteristic
258C22#1458316912yes—
259C4—21no—
260C4—22no—
261C4—81no—
262C4—81no—
263C4—3442no—
264C4#1458308812yes—
265C2—22no—
266C2—42no—
267C2—6882no—
268C2#1913569911yescharacteristic
269C2#1913570411yescharacteristic
270C2#1913572611yescharacteristic
subgroupG/H
centerC22#14582808
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1818C2
socleC22×C43#392
prime radical#19145346C2
hypercenter#1818D43
hypocenterC43#9977
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1818

Complements

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

NH ≅ G/Ntype
2. #19144535C2semidirect
3. #19132954C2semidirect
4. #19132472C2semidirect
5. C43×#1818C2semidirect
132. #1818D43semidirect
156. C43#9977semidirect

Maximal subgroups

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

subgroupindex
#191453462
#191445352
#191329542
#191324722
C43×#18182
#997743