Finite Group Databasebeta

← #24997215

Subgroups — #24997215

Order 11008.

544 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 544 conjugacy classes of subgroups — too many to draw. Only its 85 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#19144536C212yesmaximal, complemented
3#19134664C211yesmaximal, characteristic, complemented
4#19132956C212yesmaximal, complemented
5C43×#1293C211yesmaximal, characteristic, complemented
6C2×#13063299C2212yes—
7C2×#13063284C2211yescharacteristic
8#14583224—24no—
9#14583218—22no—
10#14583213—22no—
11#14583213—22no—
12#14583135—22no—
13#14583035—22no—
14#14582941—22no—
15#14582905—22no—
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582653—22no—
18#14582622—24no—
19C43×#407C2212yes—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×D172D412yes—
22C22×C22⋊D43—22no—
23C2×D344—22no—
24C22×C43⋊C8—21no—
25#13063299—22no—
26#13063299—22no—
27#13063299—22no—
28#13063299—22no—
29#13063284—22no—
30#13063284—22no—
31C2×C4⋊Dic43D411yescharacteristic
32C2×C4⋊Dic43D411yescharacteristic
33C2×C4⋊Dic43D412yes—
34C2×C22⋊Dic43—21no—
35C2×(C2×D43)⋊C4—22no—
36C2×C4×Dic43—21no—
37#13063259—22no—
38#13063259—24no—
39#13063257—24no—
40#13063247—24no—
41#13063247—24no—
42#13063247—24no—
43C22⋊(C43⋊C8)—22no—
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C22×C8×C43D412yes—
47C22⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C22⋊C8×C43D414yes—
50C24×C43#4111yescharacteristic
51C23×D43—22no—
52C22×C4×C43—42no—
53C22×C4×C43C2×D411yescharacteristic
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D412yes—
56C22×C4×C43C2×D411yescharacteristic
57C2×C22⋊D43—42no—
58C2×C22⋊D43—42no—
59C2×C22⋊D43—84no—
60C22×Dic43—21no—
61C22×Dic43—21no—
62C22×Dic43—22no—
63C2×D172—22no—
64C2×D172—22no—
65C2×D172—44no—
66M16×C43—44no—
67C2×C8×C43—22no—
68C2×C8×C43—24no—
69C2×C8×C43—42no—
70C22⋊Dic43—42no—
71(C2×D43)⋊C4—42no—
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—22no—
77C4×Dic43—41no—
78C4×Dic43—41no—
79C2×C43⋊C8—42no—
80C2×C43⋊C8—41no—
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—22no—
92C2×C4×C43—24no—
93C2×C4×C43—42no—
94C2×C4×C43—41no—
95C2×C4×C43#12012yes—
96C2×C4×C43#12011yescharacteristic
97C2×C4×C43#12711yescharacteristic
98C22⋊D43—84no—
99C22⋊D43—84no—
100C2×Dic43—42no—
101C2×Dic43—41no—
102C2×Dic43—41no—
103C2×Dic43—42no—
104C2×Dic43—42no—
105C2×Dic43—82no—
106D172—44no—
107D172—44no—
108C8×C43—44no—
109C8×C43—42no—
110C43⋊C8—81no—
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—21no—
125C4×C43—22no—
126C4×C43#45812yes—
127Dic43—81no—
128Dic43—81no—
129Dic43—82no—
130#3186—431no—
131#3094—432no—
132#1818—431no—
133#1471—432no—
134#1293D4311yescharacteristic, complemented
135C2×C43—22no—
136C2×C43—42no—
137C2×C43#201711yescharacteristic
138C2×C43#201811yescharacteristic
139C2×C43#202211yescharacteristic
140D43—162no—
141C2×#121—432no—
142C2×#117—431no—
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#407C2×D4312yes—
152C2×C22⋊C8—431no—
153C2×C22⋊C8C2×D4311yescharacteristic
154#336—862no—
155#323—864no—
156C43#997711yescharacteristic, complemented, Sylow
157C22×D4—432no—
158C22×D4—862no—
159C23×C4C22×D4311yescharacteristic
160C2×D8—862no—
161C2×M16—22no—
162C22×C8—861no—
163C22×C8D17212yes—
164#121—862no—
165#121—862no—
166#121—862no—
167#121—862no—
168#117—862no—
169#117—862no—
170C2×C4⋊C4—431no—
171C2×C4⋊C4—431no—
172C2×C4⋊C4—432no—
173C2×C22⋊C4—861no—
174C2×C22⋊C4—862no—
175C2×C42—861no—
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—862no—
185C22⋊C8D17214yes—
186C24—862no—
187C24#1062190211yescharacteristic
188C2×D4—862no—
189C2×D4—862no—
190C2×D4—3444no—
191C2×D4—1724no—
192C2×D4—1722no—
193C2×D4—1722no—
194C22×C4—42no—
195C22×C4—862no—
196C22×C4—861no—
197C22×C4—861no—
198C22×C4C2×D17211yescharacteristic
199C22×C4C2×D17212yes—
200C22×C4D4×D4312yes—
201C22×C4D4×D4311yescharacteristic
202D8—3442no—
203M16—44no—
204C2×C8—22no—
205C2×C8—24no—
206C2×C8—42no—
207C2×C8—1722no—
208C2×C8—1721no—
209C4⋊C4—862no—
210C4⋊C4—862no—
211C4⋊C4—862no—
212C4⋊C4—862no—
213C22⋊C4—1722no—
214C22⋊C4—1722no—
215C22⋊C4—1722no—
216C42—1721no—
217C42—1721no—
218C23—22no—
219C23—41no—
220C23—41no—
221C23—3442no—
222C23—3442no—
223C23—1724no—
224C23—1722no—
225C23#1306330012yes—
226C23#1306330011yescharacteristic
227D4—3444no—
228D4—3444no—
229D4—1724no—
230D4—1724no—
231C2×C4—22no—
232C2×C4—24no—
233C2×C4—42no—
234C2×C4—41no—
235C2×C4—3442no—
236C2×C4—1722no—
237C2×C4—1721no—
238C2×C4—1721no—
239C2×C4—1722no—
240C2×C4—1722no—
241C2×C4#1306329512yes—
242C2×C4#1306329511yescharacteristic
243C2×C4#1306332211yescharacteristic
244C8—44no—
245C8—42no—
246C8—3441no—
247C22—21no—
248C22—21no—
249C22—22no—
250C22—22no—
251C22—22no—
252C22—82no—
253C22—3442no—
254C22—3442no—
255C22—3442no—
256C22—6884no—
257C22#1458280911yescharacteristic
258C22#1458317012yes—
259C4—22no—
260C4—21no—
261C4—3441no—
262C4—3442no—
263C4—3441no—
264C4#1458309012yes—
265C2—22no—
266C2—42no—
267C2—6882no—
268C2#1913570011yescharacteristic
269C2#1913570511yescharacteristic
270C2#1913572711yescharacteristic
subgroupG/H
centerC22#14582809
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1293C2
socleC22×C43#392
prime radical#19145346C2
hypercenter#1293D43
hypocenterC43#9977
LCSG ▷ C23×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1293

Complements

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

NH ≅ G/Ntype
2. #19144536C2semidirect
3. #19134664C2semidirect
4. #19132956C2semidirect
5. C43×#1293C2semidirect
134. #1293D43semidirect
156. C43#9977semidirect

Maximal subgroups

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

subgroupindex
#191453462
#191445362
#191346642
#191329562
C43×#12932
#997743