Finite Group Databasebeta

← #25000939

Subgroups — #25000939

Order 11008.

500 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 77 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#19135056C212yesmaximal, complemented
3#19134777C211yesmaximal, characteristic, complemented
4#19133112C212yesmaximal, complemented
5C43×#1293C211yesmaximal, characteristic, complemented
6C22×#10621877C2211yescharacteristic
7C2×#13063299C2212yes—
8#14583213—22no—
9#14583135—21no—
10#14583135—21no—
11#14583035—22no—
12C2×Dic43⋊C8—21no—
13C2×#13063241—22no—
14C4×C22⋊Dic43C2211yescharacteristic
15#14582667—22no—
16#14582653—21no—
17#14582634—22no—
18#14582634—22no—
19C43×#407C2212yes—
20C2×C22⋊C8×C43C2211yescharacteristic
21C22×D172D412yes—
22C22×C22⋊D43—22no—
23C2×D344—21no—
24C2×D344—21no—
25C2×#10621877—22no—
26C2×#10621877—42no—
27C22×C43⋊C8—21no—
28#13063299—22no—
29#13063299—22no—
30#13063299—22no—
31#13063299—22no—
32C2×C4⋊Dic43D412yes—
33C2×C22⋊Dic43—21no—
34C2×(C2×D43)⋊C4—22no—
35C2×C4×Dic43—21no—
36#13063259—21no—
37#13063259—21no—
38Dic43⋊C8—42no—
39#13063247—22no—
40#13063247—22no—
41#13063241—44no—
42C43⋊#95D411yescharacteristic
43C43⋊#95D411yescharacteristic
44C23×C4×C43C2311yescharacteristic
45C2×M16×C43—22no—
46C22×C8×C43D411yescharacteristic
47C22×C8×C43D411yescharacteristic
48C22⋊C8×C43—22no—
49C22⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C24×C43#4111yescharacteristic
52C23×D43—22no—
53C22×C4×C43—41no—
54C22×C4×C43—41no—
55C22×C4×C43C2×D411yescharacteristic
56C22×C4×C43C2×D411yescharacteristic
57C22×C4×C43C2×D412yes—
58C22×C4×C43#4112yes—
59C2×C22⋊D43—42no—
60C2×C22⋊D43—42no—
61C2×C22⋊D43—82no—
62C2×C22⋊D43—82no—
63C22×Dic43—21no—
64C22×Dic43—21no—
65C22×Dic43—22no—
66C2×D172—22no—
67C2×D172—22no—
68C2×D172—42no—
69C2×D172—42no—
70M16×C43—42no—
71M16×C43—42no—
72C2×C8×C43—21no—
73C2×C8×C43—21no—
74C2×C8×C43—41no—
75C2×C8×C43—41no—
76C2×C8×C43—42no—
77C22⋊Dic43—42no—
78(C2×D43)⋊C4—42no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43—22no—
81C4⋊Dic43—22no—
82C4×Dic43—41no—
83C4×Dic43—41no—
84#10621877—24no—
85#10621877—42no—
86C2×C43⋊C8—22no—
87C2×C43⋊C8—41no—
88C2×C43⋊C8—41no—
89D344—81no—
90D344—81no—
91C23×C43—21no—
92C23×C43—21no—
93C23×C43—41no—
94C23×C43—41no—
95C23×C43#12111yescharacteristic
96C23×C43#12312yes—
97C22×D43—42no—
98C22×D43—44no—
99C22×D43—82no—
100C22×D43—82no—
101C2×C4×C43—21no—
102C2×C4×C43—22no—
103C2×C4×C43—21no—
104C2×C4×C43—22no—
105C2×C4×C43—41no—
106C2×C4×C43—42no—
107C2×C4×C43#12011yescharacteristic
108C2×C4×C43#12112yes—
109C2×C4×C43#12411yescharacteristic
110C22⋊D43—84no—
111C22⋊D43—82no—
112C22⋊D43—82no—
113C2×Dic43—22no—
114C2×Dic43—41no—
115C2×Dic43—41no—
116C2×Dic43—41no—
117C2×Dic43—41no—
118C2×Dic43—42no—
119C2×Dic43—41no—
120C2×Dic43—82no—
121D172—42no—
122D172—42no—
123D172—82no—
124C8×C43—41no—
125C8×C43—41no—
126C8×C43—82no—
127C43⋊C8—42no—
128#10557—431nomaximal, Sylow
129C22×C43—21no—
130C22×C43—21no—
131C22×C43—22no—
132C22×C43—22no—
133C22×C43—22no—
134C22×C43—81no—
135C22×C43—81no—
136C22×C43#39411yescharacteristic
137C22×C43#47211yescharacteristic
138C22×C43#47211yescharacteristic
139C2×D43—82no—
140C2×D43—82no—
141C2×D43—82no—
142C2×D43—164no—
143C4×C43—22no—
144C4×C43—21no—
145C4×C43B(4,𝔽2)11yescharacteristic
146C4×C43#45811yescharacteristic
147Dic43—42no—
148Dic43—81no—
149Dic43—82no—
150#3186—431no—
151#1900—432no—
152#1851—431no—
153#1507—432no—
154#1293D4311yescharacteristic, complemented
155C2×C43—21no—
156C2×C43—21no—
157C2×C43—42no—
158C2×C43#204411yescharacteristic
159C2×C43#204511yescharacteristic
160C2×C43#205011yescharacteristic
161D43—162no—
162C22×M16—431no—
163C2×#121—432no—
164#480—862no—
165#466—861no—
166#466—861no—
167#447—862no—
168C2×C4⋊C8—861no—
169C2×#100—862no—
170#407C2×D4312yes—
171C2×C22⋊C8C2×D4311yescharacteristic
172C4×C22⋊C4—431no—
173#343—862no—
174#336—861no—
175#327—862no—
176#327—862no—
177C43#1055711yescharacteristic, complemented, Sylow
178C22×D4—432no—
179C22×D4—862no—
180C23×C4C22×D4311yescharacteristic
181C2×D8—861no—
182C2×D8—861no—
183C2×M16—22no—
184C2×M16—862no—
185C2×M16—1722no—
186C22×C8—861no—
187C22×C8D17211yescharacteristic
188C22×C8D17211yescharacteristic
189#121—862no—
190#121—862no—
191#121—862no—
192#121—862no—
193C2×C4⋊C4—432no—
194C2×C22⋊C4—861no—
195C2×C22⋊C4—862no—
196C2×C42—861no—
197#107—861no—
198#107—861no—
199C4⋊C8—1722no—
200#102—862no—
201#102—862no—
202#100—1724no—
203C22⋊C8—22no—
204C22⋊C8—22no—
205C22⋊C8—22no—
206#95—431no—
207#95—431no—
208C24—862no—
209C24#1062190211yescharacteristic
210C2×D4—862no—
211C2×D4—862no—
212C2×D4—3442no—
213C2×D4—3442no—
214C2×D4—1722no—
215C2×D4—1722no—
216C2×D4—1722no—
217C2×D4—1722no—
218C22×C4—41no—
219C22×C4—41no—
220C22×C4—861no—
221C22×C4—862no—
222C22×C4—861no—
223C22×C4C2×D17211yescharacteristic
224C22×C4#1062189812yes—
225C22×C4D4×D4312yes—
226C22×C4D4×D4311yescharacteristic
227D8—3441no—
228D8—3441no—
229M16—42no—
230M16—42no—
231M16—864no—
232M16—1722no—
233C2×C8—21no—
234C2×C8—21no—
235C2×C8—41no—
236C2×C8—41no—
237C2×C8—42no—
238C2×C8—862no—
239C2×C8—1721no—
240C2×C8—1721no—
241C4⋊C4—862no—
242C4⋊C4—862no—
243C22⋊C4—1722no—
244C22⋊C4—1722no—
245C22⋊C4—1722no—
246C42—1721no—
247C42—1721no—
248C23—21no—
249C23—21no—
250C23—41no—
251C23—41no—
252C23—3442no—
253C23—3442no—
254C23—1724no—
255C23—1722no—
256C23#1306330011yescharacteristic
257C23#1306331012yes—
258D4—3442no—
259D4—3444no—
260D4—3442no—
261D4—3442no—
262D4—1722no—
263D4—1722no—
264C2×C4—21no—
265C2×C4—22no—
266C2×C4—21no—
267C2×C4—22no—
268C2×C4—42no—
269C2×C4—41no—
270C2×C4—862no—
271C2×C4—3442no—
272C2×C4—1721no—
273C2×C4—1721no—
274C2×C4—1722no—
275C2×C4—1721no—
276C2×C4—1721no—
277C2×C4—1721no—
278C2×C4#1306329511yescharacteristic
279C2×C4#1306329812yes—
280C2×C4#1306331311yescharacteristic
281C8—41no—
282C8—41no—
283C8—82no—
284C8—1722no—
285C22—21no—
286C22—21no—
287C22—22no—
288C22—22no—
289C22—22no—
290C22—81no—
291C22—81no—
292C22—3442no—
293C22—3442no—
294C22—3442no—
295C22—6884no—
296C22#1458281711yescharacteristic
297C22#1458317011yescharacteristic
298C22#1458317011yescharacteristic
299C4—22no—
300C4—21no—
301C4—3441no—
302C4—3442no—
303C4—1722no—
304C4#1458308711yescharacteristic
305C4#1458309011yescharacteristic
306C2—21no—
307C2—21no—
308C2—42no—
309C2—6882no—
310C2#1913584711yescharacteristic
311C2#1913585211yescharacteristic
312C2#1913588311yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC23×C4×C43C23
FrattiniC23×C4C22×D43
FittingC43×#1293C2
socleC22×C43#394
prime radical#19145346C2
hypercenter#1293D43
hypocenterC43#10557
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. #19135056C2semidirect
3. #19134777C2semidirect
4. #19133112C2semidirect
5. C43×#1293C2semidirect
154. #1293D43semidirect
177. C43#10557semidirect

Maximal subgroups

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

subgroupindex
#191453462
#191350562
#191347772
#191331122
C43×#12932
#1055743