Finite Group Databasebeta

← #25016071

Subgroups — #25016071

Order 11008.

444 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 73 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#19141627C211yesmaximal, characteristic
2C2×#14582697C212yesmaximal
3#19134986C212yesmaximal
4#19134809C211yesmaximal, characteristic
5C43×#1394C211yesmaximal, characteristic
6C2×#13063323C2212yes—
7#14583377C2211yescharacteristic
8#14582939—21no—
9#14582909—22no—
10C2×#13063244C2211yescharacteristic
11#14582829—21no—
12#14582820—22no—
13#14582797—21no—
14#14582784—22no—
15#14582697—24no—
16#14582660—22no—
17#14582659—21no—
18C2×#101×C43C2212yes—
19C43×#391C2211yescharacteristic
20C22×Dic86D412yes—
21C2×#10621877—21no—
22#13063323—22no—
23#13063323—22no—
24#13063323—22no—
25#13063323—22no—
26Q8×Dic43—41no—
27Q8×Dic43—41no—
28#13063284—22no—
29#13063284—21no—
30C2×C4⋊Dic43—21no—
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×Dic43⋊C4—22no—
34C2×Dic43⋊C4—22no—
35C2×C4×Dic43D412yes—
36#13063258—41no—
37#13063256—41no—
38#13063250—42no—
39#13063250—42no—
40#13063244—21no—
41#13063244D412yes—
42C43⋊#95—21no—
43C43⋊#95—22no—
44C43⋊#95—22no—
45C22×Q8×C43C2311yescharacteristic
46C2×M16×C43—22no—
47C2×C4⋊C4×C43D411yescharacteristic
48C2×C42×C43D411yescharacteristic
49#101×C43—22no—
50#101×C43—22no—
51#95×C43—22no—
52C2×Q8×C43—41no—
53C2×Q8×C43—41no—
54C2×Q8×C43C2×D411yescharacteristic
55C2×Q8×C43#4112yes—
56C2×Q8×C43#4111yescharacteristic
57C22×C4×C43—21no—
58C22×C4×C43—21no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C22×Dic43—22no—
62C22×Dic43—22no—
63C2×Dic86—22no—
64C2×Dic86—22no—
65C2×Dic86—42no—
66C2×Dic86—42no—
67M16×C43—42no—
68M16×C43—42no—
69C2×C8×C43—42no—
70C4⋊C4×C43—41no—
71C42×C43—41no—
72C22⋊Dic43—41no—
73C4⋊Dic43—24no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—21no—
77C4⋊Dic43—21no—
78C4⋊Dic43—81no—
79C4⋊Dic43—81no—
80Dic43⋊C4—42no—
81Dic43⋊C4—42no—
82Dic43⋊C4—42no—
83Dic43⋊C4—42no—
84C4×Dic43—22no—
85C4×Dic43—22no—
86C4×Dic43—41no—
87C4×Dic43—42no—
88#10621877—22no—
89#10621877—41no—
90C2×C43⋊C8—41no—
91C23×C43#12011yescharacteristic
92Q8×C43—41no—
93Q8×C43—42no—
94Q8×C43—41no—
95C2×C4×C43—21no—
96C2×C4×C43—22no—
97C2×C4×C43—21no—
98C2×C4×C43—22no—
99C2×C4×C43—22no—
100C2×C4×C43—41no—
101C2×C4×C43—41no—
102C2×C4×C43—42no—
103C2×C4×C43—41no—
104C2×C4×C43#12112yes—
105C2×C4×C43#12111yescharacteristic
106C2×C4×C43#12312yes—
107C2×C4×C43#12411yescharacteristic
108C2×Dic43—24no—
109C2×Dic43—42no—
110C2×Dic43—42no—
111C2×Dic43—42no—
112C2×Dic43—41no—
113C2×Dic43—41no—
114C2×Dic43—42no—
115C2×Dic43—42no—
116Dic86—44no—
117Dic86—82no—
118C8×C43—82no—
119C43⋊C8—42no—
120#13428—431nomaximal, Sylow
121C22×C43—21no—
122C22×C43—21no—
123C22×C43#39411yescharacteristic
124C22×C43B(4,𝔽2)11yescharacteristic
125C22×C43#45811yescharacteristic
126C4×C43—21no—
127C4×C43—22no—
128C4×C43—22no—
129C4×C43—21no—
130C4×C43—42no—
131C4×C43—81no—
132Dic43—44no—
133Dic43—81no—
134Dic43—81no—
135Dic43—82no—
136#2734—431no—
137C2×#356—432no—
138#1886—432no—
139#1857—431no—
140#1394D4311yescharacteristic
141C2×C43—21no—
142C2×C43—21no—
143C2×C43#204411yescharacteristic
144C2×C43#220311yescharacteristic
145C2×C43#220511yescharacteristic
146C2×C4⋊Q8—432no—
147#519—431no—
148#428—861no—
149#419—862no—
150C2×#101—431no—
151C2×#101C2×D4312yes—
152#398—861no—
153#395—862no—
154#391C2×D4311yescharacteristic
155#389—861no—
156#387—862no—
157#356—864no—
158#339—862no—
159#339—861no—
160C43#1342811yescharacteristic, complemented, Sylow
161C22×Q8—432no—
162C22×Q8C22×D4311yescharacteristic
163C2×M16—22no—
164C2×M16—861no—
165C4⋊Q8—862no—
166C4⋊Q8—862no—
167C4⋊Q8—862no—
168C4⋊Q8—862no—
169C4×Q8—1721no—
170C4×Q8—1721no—
171#117—861no—
172#117—862no—
173C2×C4⋊C4—861no—
174C2×C4⋊C4—861no—
175C2×C4⋊C4—861no—
176C2×C4⋊C4—862no—
177C2×C4⋊C4—862no—
178C2×C4⋊C4D17211yescharacteristic
179C2×C42—432no—
180C2×C42D17211yescharacteristic
181#107—1721no—
182#106—1721no—
183#103—1722no—
184#103—1722no—
185#101—22no—
186#101—22no—
187#101—432no—
188#101—861no—
189#95—22no—
190#95—861no—
191#95—862no—
192#95—862no—
193C2×Q8—41no—
194C2×Q8—41no—
195C2×Q8—862no—
196C2×Q8—862no—
197C2×Q8—1722no—
198C2×Q8—1722no—
199C2×Q8#1062189812yes—
200C2×Q8D4×D4311yescharacteristic
201C2×Q8#1062190211yescharacteristic
202C22×C4—21no—
203C22×C4—21no—
204C22×C4—862no—
205C22×C4—862no—
206C22×C4C2×D17211yescharacteristic
207C22×C4D4×D4312yes—
208M16—42no—
209M16—42no—
210M16—862no—
211M16—1721no—
212C2×C8—42no—
213C2×C8—1721no—
214C4⋊C4—41no—
215C4⋊C4—864no—
216C4⋊C4—862no—
217C4⋊C4—862no—
218C4⋊C4—861no—
219C4⋊C4—861no—
220C4⋊C4—3441no—
221C4⋊C4—3441no—
222C4⋊C4—1722no—
223C4⋊C4—1722no—
224C4⋊C4—1722no—
225C4⋊C4—1722no—
226C22⋊C4—1721no—
227C42—41no—
228C42—862no—
229C42—862no—
230C42—1721no—
231C42—1722no—
232C23#1306329511yescharacteristic
233Q8—42no—
234Q8—41no—
235Q8—41no—
236Q8—3442no—
237Q8—1724no—
238C2×C4—21no—
239C2×C4—22no—
240C2×C4—21no—
241C2×C4—22no—
242C2×C4—22no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—41no—
247C2×C4—864no—
248C2×C4—1722no—
249C2×C4—1721no—
250C2×C4—1721no—
251C2×C4—1722no—
252C2×C4—1722no—
253C2×C4—1722no—
254C2×C4—1722no—
255C2×C4#1306329812yes—
256C2×C4#1306330011yescharacteristic
257C2×C4#1306331012yes—
258C2×C4#1306331311yescharacteristic
259C8—82no—
260C8—1722no—
261C22—21no—
262C22—21no—
263C22#1458281711yescharacteristic
264C22#1458308711yescharacteristic
265C22#1458309011yescharacteristic
266C4—22no—
267C4—21no—
268C4—22no—
269C4—21no—
270C4—42no—
271C4—81no—
272C4—3442no—
273C4—3441no—
274C4—3441no—
275C4—1724no—
276C2—21no—
277C2—21no—
278C2#1913584711yescharacteristic
279C2#1913661811yescharacteristic
280C2#1913662611yescharacteristic
subgroupG/H
centerC22#14583087
commutator, cosocleC22×Q8×C43C23
FrattiniC22×Q8C22×D43
FittingC43×#1394C2
socleC22×C43B(4,𝔽2)
prime radicalC23×C43#120
hypercenter#1394D43
hypocenterC43#13428
LCSG ▷ C22×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23 ◁ C22×Q8 ◁ #1394

Complements

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

NH ≅ G/Ntype
160. C43#13428semidirect

Maximal subgroups

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

subgroupindex
#191416272
C2×#145826972
#191349862
#191348092
C43×#13942
#1342843