Finite Group Databasebeta

← #24993394

Subgroups — #24993394

Order 11008.

518 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144059C211yesmaximal, characteristic
2#19134605C211yesmaximal, characteristic, complemented
3#19133156C211yesmaximal, characteristic, complemented
4#19132995C211yesmaximal, characteristic, complemented
5#19132491C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#2975C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9#14583449C2211yescharacteristic
10#14583114—22no—
11#14583104C412yescomplemented
12#14583094C412yescomplemented
13#14582923C2211yescharacteristic
14C2×C4⋊(C43⋊C8)C2211yescharacteristic
15#14582898—21no—
16C2×#13063246—21no—
17#14582765C2211yescharacteristic
18#14582661—21no—
19#14582634—22no—
20#14582628—22no—
21C2×C4×D4×C43C2211yescharacteristic
22C43×#436—22no—
23C43×#436—22no—
24C43×#431C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C43×#407—22no—
27C2×#10621898—21no—
28#13063351—42no—
29#13063351—42no—
30C2×#10621883—22no—
31C2×#10621882—22no—
32C2×#10621877—21no—
33C22×C43⋊C8—21no—
34#13063325C2×C411yescharacteristic
35#13063322C2×C411yescharacteristic
36#13063313—21no—
37#13063299—21no—
38#13063299—21no—
39C4×D172—21no—
40C4×D172—21no—
41C2×C4⋊Dic43—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yes—
46#13063248—22no—
47#13063246—42no—
48#13063245—22no—
49C43⋊#95—21no—
50C43⋊#95—21no—
51C22×D4×C43D411yescharacteristic
52C23×C4×C43—21no—
53C2×M16×C43—24no—
54C4×D4×C43—21no—
55C4×D4×C43—21no—
56C4×D4×C43C2×C412yes—
57C4×D4×C43D412yes—
58C2×C4⋊C4×C43D411yescharacteristic
59C2×C22⋊C4×C43—21no—
60C2×C42×C43C2311yescharacteristic
61C4⋊C8×C43—21no—
62C4⋊C8×C43—21no—
63C22⋊C8×C43—24no—
64C22⋊C8×C43—21no—
65C22⋊C8×C43D412yes—
66C4×C8×C43—21no—
67C4×C8×C43D412yes—
68C24×C43—21no—
69C2×D4×C43—21no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—21no—
73C2×D4×C43—21no—
74C2×D4×C43C22⋊C412yes—
75C22×C4×C43—22no—
76C22×C4×C43—22no—
77C22×C4×C43—21no—
78C22×C4×C43—82no—
79C22×C4×C43C2×D411yescharacteristic
80C22×C4×C43C2×D411yescharacteristic
81C22×C4×C43#4111yescharacteristic
82C2×C22⋊D43—41no—
83C22×Dic43—41no—
84#10621898—41no—
85#10621898—41no—
86#10621898—41no—
87#10621898—41no—
88C2×D172—21no—
89C2×D172—21no—
90C2×D172—21no—
91C2×C4×D43—41no—
92C2×Dic86—21no—
93M16×C43—84no—
94C2×C8×C43—22no—
95C2×C8×C43—22no—
96C4⋊C4×C43—21no—
97C4⋊C4×C43C22⋊C412yes—
98C22⋊C4×C43—22no—
99C22⋊C4×C43—22no—
100C42×C43C22×C411yescharacteristic
101C42×C43C2×D411yescharacteristic
102C42×C43C2×D411yescharacteristic
103C42×C43#4111yescharacteristic
104#10621883—44no—
105#10621882—44no—
106(C2×D43)⋊C4—41no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—21no—
109C4⋊Dic43—21no—
110C4⋊Dic43—41no—
111C4⋊Dic43—41no—
112#10621877—41no—
113#10621877—41no—
114C2×C43⋊C8—22no—
115C2×C43⋊C8—41no—
116C2×C43⋊C8—41no—
117C2×C43⋊C8—41no—
118C23×C43—22no—
119C23×C43—41no—
120C23×C43—41no—
121C23×C43—81no—
122C23×C43—81no—
123C23×C43#12111yescharacteristic
124C22×D43—41no—
125D4×C43—22no—
126D4×C43—22no—
127D4×C43—41no—
128D4×C43—41no—
129C2×C4×C43—22no—
130C2×C4×C43—41no—
131C2×C4×C43—41no—
132C2×C4×C43—44no—
133C2×C4×C43—82no—
134C2×C4×C43—81no—
135C2×C4×C43C2×C22⋊C411yescharacteristic
136C2×C4×C43C4×D411yescharacteristic
137C2×C4×C43C4×D411yescharacteristic
138C2×C4×C43#12011yescharacteristic
139C2×C4×C43#12111yescharacteristic
140C2×C4×C43#12311yescharacteristic
141C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
142C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
143C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C43#13711yescharacteristic
145C22⋊D43—81no—
146C22⋊D43—81no—
147C2×Dic43—41no—
148C2×Dic43—81no—
149C2×Dic43—81no—
150C2×Dic43—81no—
151D172—42no—
152D172—41no—
153D172—41no—
154D172—81no—
155C4×D43—81no—
156C4×D43—81no—
157Dic86—41no—
158Dic86—41no—
159C8×C43—42no—
160C8×C43—42no—
161C43⋊C8—42no—
162C43⋊C8—81no—
163#9309—431nomaximal, Sylow
164C22×C43—21no—
165C22×C43—21no—
166C22×C43—42no—
167C22×C43—42no—
168C22×C43—42no—
169C22×C43—82no—
170C22×C43—82no—
171C22×C43#38611yescharacteristic
172C22×C43#46811yescharacteristic
173C22×C43#46911yescharacteristic
174C2×D43—81no—
175C2×D43—81no—
176C2×D43—81no—
177C4×C43—21no—
178C4×C43—21no—
179C4×C43—21no—
180C4×C43—21no—
181C4×C43—42no—
182C4×C43#41711yescharacteristic
183C4×C43#41811yescharacteristic
184C4×C43#46811yescharacteristic
185C4×C43#46911yescharacteristic
186Dic43—81no—
187Dic43—161no—
188#3036—431no—
189#2975D4311yescharacteristic, complemented
190#1804—431no—
191#1517—431no—
192#1480—431no—
193#1301—431no—
194#1286—431no—
195C2×C43—21no—
196C2×C43—21no—
197C2×C43—82no—
198C2×C43#188111yescharacteristic
199C2×C43#189511yescharacteristic
200C2×C43#190411yescharacteristic
201D43—161no—
202C2×AGL(1,ℤ/8)—861no—
203#532—431no—
204C2×C4×D4C2×D4311yescharacteristic
205#463—862no—
206#461—432no—
207#459—432no—
208#436—22no—
209#436—22no—
210#431C2×D4311yescharacteristic
211#431C2×D4311yescharacteristic
212#423—431no—
213C2×C4⋊C8—431no—
214#417—861no—
215C2×#102—861no—
216#407—22no—
217#382—431no—
218#340—861no—
219#327—862no—
220D4⋊C8—862no—
221C43#930911yescharacteristic, complemented, Sylow
222C2×#41—861no—
223C22×D4D17211yescharacteristic
224C23×C4—21no—
225AGL(1,ℤ/8)—1722no—
226AGL(1,ℤ/8)—1722no—
227C2×SD16—862no—
228C2×D8—862no—
229C2×M16—24no—
230C2×M16—861no—
231C22×C8—861no—
232C4⋊Q8—431no—
233#127—431no—
234#124—861no—
235#121—861no—
236#121—861no—
237C4×D4—21no—
238C4×D4—21no—
239C4×D4—861no—
240C4×D4—861no—
241C4×D4C4×D4312yes—
242C4×D4C22⋊D4312yes—
243C2×C4⋊C4—861no—
244C2×C4⋊C4D17211yescharacteristic
245C2×C22⋊C4—21no—
246C2×C42C22×D4311yescharacteristic
247C4⋊C8—21no—
248C4⋊C8—21no—
249C4⋊C8—432no—
250C4⋊C8—861no—
251C4⋊C8—861no—
252C4⋊C8—861no—
253#103—862no—
254#102—862no—
255#102—1722no—
256C22⋊C8—24no—
257C22⋊C8—21no—
258C22⋊C8C22⋊D4312yes—
259C4×C8—21no—
260C4×C8C22⋊D4312yes—
261#95—861no—
262#95—861no—
263C24—21no—
264#41—1721no—
265#41—1721no—
266#41—1721no—
267#41—1721no—
268C2×Q8—861no—
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—21no—
272C2×D4—21no—
273C2×D4—21no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—1721no—
278C2×D4(C2×D43)⋊C412yes—
279C22×C4—21no—
280C22×C4—22no—
281C22×C4—22no—
282C22×C4—82no—
283C22×C4—1721no—
284C22×C4—1721no—
285C22×C4C2×D17211yescharacteristic
286C22×C4#1062189811yescharacteristic
287C22×C4C2×C22⋊D4311yescharacteristic
288SD16—1724no—
289D8—1724no—
290M16—84no—
291M16—1721no—
292M16—1721no—
293C2×C8—22no—
294C2×C8—22no—
295C2×C8—862no—
296C2×C8—1721no—
297C2×C8—1721no—
298C2×C8—1721no—
299C4⋊C4—21no—
300C4⋊C4—861no—
301C4⋊C4—861no—
302C4⋊C4—1721no—
303C4⋊C4—1721no—
304C4⋊C4(C2×D43)⋊C412yes—
305C22⋊C4—22no—
306C22⋊C4—22no—
307C22⋊C4—1721no—
308C22⋊C4—1721no—
309C42C2×C4×D4311yescharacteristic
310C42#1062189811yescharacteristic
311C42C2×C22⋊D4311yescharacteristic
312C42C2×C22⋊D4311yescharacteristic
313C23—22no—
314C23—41no—
315C23—41no—
316C23—81no—
317C23—81no—
318C23—1721no—
319C23#1306329911yescharacteristic
320Q8—1721no—
321Q8—1721no—
322D4—22no—
323D4—22no—
324D4—41no—
325D4—41no—
326D4—3441no—
327D4—3441no—
328D4—3441no—
329D4—1722no—
330D4—1721no—
331D4—1721no—
332C2×C4—22no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—44no—
336C2×C4—82no—
337C2×C4—81no—
338C2×C4—3441no—
339C2×C4—3441no—
340C2×C4—3441no—
341C2×C4—3441no—
342C2×C4—3441no—
343C2×C4—1721no—
344C2×C4C2×(C2×D43)⋊C411yescharacteristic
345C2×C4C4×C22⋊D4311yescharacteristic
346C2×C4C4×C22⋊D4311yescharacteristic
347C2×C4#1306329411yescharacteristic
348C2×C4#1306329911yescharacteristic
349C2×C4#1306330811yescharacteristic
350C2×C4#1306335311yescharacteristic
351C2×C4#1306335311yescharacteristic
352C2×C4#1306335311yescharacteristic
353C2×C4#1306335811yescharacteristic
354C8—42no—
355C8—42no—
356C8—3441no—
357C8—1722no—
358C22—21no—
359C22—21no—
360C22—42no—
361C22—42no—
362C22—42no—
363C22—82no—
364C22—82no—
365C22—3441no—
366C22—3441no—
367C22—3441no—
368C22#1458277811yescharacteristic
369C22#1458314511yescharacteristic
370C22#1458315211yescharacteristic
371C4—21no—
372C4—21no—
373C4—21no—
374C4—21no—
375C4—42no—
376C4—3441no—
377C4—6881no—
378C4#1458290111yescharacteristic
379C4#1458290511yescharacteristic
380C4#1458314511yescharacteristic
381C4#1458315211yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—6881no—
386C2#1913495711yescharacteristic
387C2#1913503311yescharacteristic
388C2#1913508211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2975C2
socleC22×C43#386
prime radical#19144059C2
cosocleC2×C42×C43C23
hypercenter#2975D43
hypocenterC43#9309
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2975

Complements

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

NH ≅ G/Ntype
2. #19134605C2semidirect
3. #19133156C2semidirect
4. #19132995C2semidirect
5. #19132491C2semidirect
6. #19132454C2semidirect
7. C43×#2975C2semidirect
11. #14583104C4semidirect
12. #14583094C4semidirect
189. #2975D43semidirect
221. C43#9309semidirect

Maximal subgroups

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

subgroupindex
#191440592
#191346052
#191331562
#191329952
#191324912
#191324542
C43×#29752
#930943