Finite Group Databasebeta

← #24992532

Subgroups — #24992532

Order 11008.

620 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19144059C211yesmaximal, characteristic
2#19133154C211yesmaximal, characteristic, complemented
3#19133089C211yesmaximal, characteristic, complemented
4#19132986C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132453C211yesmaximal, characteristic, complemented
7C43×#2349C211yesmaximal, characteristic, complemented
8C2×#13063351—21no—
9#14583449C2211yescharacteristic
10#14583114—22no—
11#14583104C412yescomplemented
12#14583094C412yescomplemented
13#14582952C2211yescharacteristic
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582898—21no—
17#14582632—21no—
18#14582632—21no—
19#14582632—22no—
20D4⋊(C43⋊C8)—22no—
21C2×C4×D4×C43—21no—
22C2×C4×D4×C43C2211yescharacteristic
23C43×#389—21no—
24C43×#385—22no—
25C43×#382C2211yescharacteristic
26C43×#380—21no—
27C4×C4⋊C4×C43C2211yescharacteristic
28C2×#95×C43—21no—
29C2×#10621898—21no—
30#13063351—42no—
31#13063351—42no—
32C2×#10621883—22no—
33C2×#10621882—22no—
34C2×#10621877—21no—
35#13063325C2×C411yescharacteristic, complemented
36#13063322C2×C411yescharacteristic, complemented
37#13063313—21no—
38#13063299—21no—
39#13063299—21no—
40C4×D172—21no—
41C4×D172—21no—
42C4⋊(C43⋊C8)—21no—
43C4⋊(C43⋊C8)—21no—
44C4⋊(C43⋊C8)—21no—
45C4⋊(C43⋊C8)C2×C412yescomplemented
46#13063248—22no—
47#13063245—22no—
48C22⋊(C43⋊C8)—21no—
49C22⋊(C43⋊C8)—21no—
50C4×C43⋊C8—21no—
51C4×C43⋊C8—21no—
52C22×D4×C43D411yescharacteristic
53C23×C4×C43—21no—
54C23×C4×C43—22no—
55C4×D4×C43—21no—
56C4×D4×C43—21no—
57C4×D4×C43—42no—
58C4×D4×C43—42no—
59C4×D4×C43C2×C412yes—
60C4×D4×C43D412yes—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43—21no—
63C2×C4⋊C4×C43—22no—
64C2×C4⋊C4×C43D411yescharacteristic
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—22no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69#95×C43—22no—
70#95×C43—21no—
71#95×C43D411yescharacteristic
72#95×C43D411yescharacteristic
73#95×C43D412yes—
74C24×C43—21no—
75C2×D4×C43—21no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43C22⋊C412yes—
79C2×D4×C43D812yes—
80C2×D4×C43SD1612yes—
81C22×C4×C43—22no—
82C22×C4×C43—22no—
83C22×C4×C43—21no—
84C22×C4×C43—21no—
85C22×C4×C43—22no—
86C22×C4×C43—21no—
87C22×C4×C43—44no—
88C22×C4×C43—44no—
89C22×C4×C43—82no—
90C22×C4×C43—82no—
91C22×C4×C43C2×D411yescharacteristic
92C22×C4×C43C2×D411yescharacteristic
93C22×C4×C43C2×D411yescharacteristic
94C2×C22⋊D43—41no—
95#10621898—41no—
96#10621898—41no—
97#10621898—41no—
98#10621898—41no—
99C2×D172—21no—
100C2×D172—21no—
101C2×D172—21no—
102C2×C4×D43—41no—
103C2×Dic86—21no—
104C4⋊C4×C43—21no—
105C4⋊C4×C43—42no—
106C4⋊C4×C43—41no—
107C4⋊C4×C43—41no—
108C4⋊C4×C43—82no—
109C4⋊C4×C43C22⋊C412yes—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—22no—
112C22⋊C4×C43—44no—
113C42×C43—41no—
114C42×C43—41no—
115C42×C43C22×C411yescharacteristic
116C42×C43C2×D411yescharacteristic
117C42×C43#4111yescharacteristic
118C42×C43#4111yescharacteristic
119#10621883—44no—
120#10621882—44no—
121(C2×D43)⋊C4—41no—
122(C2×D43)⋊C4—41no—
123C4⋊Dic43—21no—
124C4⋊Dic43—21no—
125#10621877—41no—
126#10621877—41no—
127C2×C43⋊C8—22no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C23×C43—22no—
131C23×C43—22no—
132C23×C43—22no—
133C23×C43—42no—
134C23×C43—42no—
135C23×C43#12011yescharacteristic
136C22×D43—41no—
137D4×C43—22no—
138D4×C43—22no—
139D4×C43—22no—
140D4×C43#10214yes—
141C2×C4×C43—22no—
142C2×C4×C43—22no—
143C2×C4×C43—41no—
144C2×C4×C43—41no—
145C2×C4×C43—42no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—42no—
152C2×C4×C43—41no—
153C2×C4×C43—42no—
154C2×C4×C43—82no—
155C2×C4×C43—82no—
156C2×C4×C43—88no—
157C2×C4×C43C2×C22⋊C411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43C4×D411yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12111yescharacteristic
162C2×C4×C43#12311yescharacteristic
163C2×C4×C43C2×D811yescharacteristic
164C2×C4×C43C2×SD1611yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C43#13711yescharacteristic
167C22⋊D43—81no—
168C22⋊D43—81no—
169C2×Dic43—41no—
170D172—41no—
171D172—41no—
172D172—81no—
173D172—81no—
174C4×D43—81no—
175C4×D43—81no—
176Dic86—41no—
177Dic86—41no—
178C43⋊C8—42no—
179C43⋊C8—81no—
180C43⋊C8—81no—
181#9179—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—24no—
185C22×C43—44no—
186C22×C43—44no—
187C22×C43—42no—
188C22×C43—42no—
189C22×C43#38611yescharacteristic
190C22×C43#44711yescharacteristic
191C22×C43#44811yescharacteristic
192C2×D43—81no—
193C2×D43—81no—
194C2×D43—81no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—42no—
200C4×C43—42no—
201C4×C43—81no—
202C4×C43—82no—
203C4×C43C2×#10211yescharacteristic
204C4×C43#41711yescharacteristic
205C4×C43#48011yescharacteristic
206C4×C43#48111yescharacteristic
207Dic43—81no—
208#3036—431no—
209#2349D4311yescharacteristic, complemented
210#1517—431no—
211#1502—431no—
212#1478—431no—
213#1303—431no—
214#1286—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—44no—
218C2×C43#187411yescharacteristic
219C2×C43#190411yescharacteristic
220C2×C43#190611yescharacteristic
221D43—161no—
222C2×AGL(1,ℤ/8)—861no—
223#532—431no—
224C2×C4×D4—21no—
225C2×C4×D4C2×D4311yescharacteristic
226#463—862no—
227#461—432no—
228#459—432no—
229#431—431no—
230#431—431no—
231#423—431no—
232#417—861no—
233#389—21no—
234#385—22no—
235#382C2×D4311yescharacteristic
236#380—21no—
237C4×C4⋊C4C2×D4311yescharacteristic
238C2×#95—21no—
239#327—861no—
240#327—861no—
241#327—862no—
242D4⋊C8—862no—
243C43#917911yescharacteristic, complemented, Sylow
244C2×#41—861no—
245C22×D4C22⋊D4311yescharacteristic
246C23×C4—21no—
247C23×C4—22no—
248AGL(1,ℤ/8)—1722no—
249AGL(1,ℤ/8)—1722no—
250C2×SD16—862no—
251C2×D8—862no—
252C2×M16—861no—
253C4⋊Q8—431no—
254#127—431no—
255#124—861no—
256#121—861no—
257#121—861no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—42no—
261C4×D4—42no—
262C4×D4—861no—
263C4×D4—861no—
264C4×D4C4×D4312yes—
265C4×D4D17212yes—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—22no—
269C2×C4⋊C4C22⋊D4311yescharacteristic
270C2×C22⋊C4—21no—
271C2×C22⋊C4—22no—
272C2×C42—21no—
273C2×C42C22×D4311yescharacteristic
274C4⋊C8—432no—
275C4⋊C8—861no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278#103—862no—
279#102—862no—
280C22⋊C8—861no—
281C22⋊C8—861no—
282C4×C8—861no—
283C4×C8—861no—
284#95—22no—
285#95—21no—
286#95C22⋊D4311yescharacteristic
287#95C22⋊D4311yescharacteristic
288#95C22⋊D4312yes—
289C24—21no—
290#41—1721no—
291#41—1721no—
292#41—1721no—
293#41—1721no—
294C2×Q8—861no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—861no—
299C2×D4—861no—
300C2×D4—861no—
301C2×D4—1721no—
302C2×D4(C2×D43)⋊C412yes—
303C2×D4#1062188212yes—
304C2×D4#1062188412yes—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—22no—
308C22×C4—22no—
309C22×C4—22no—
310C22×C4—21no—
311C22×C4—44no—
312C22×C4—44no—
313C22×C4—82no—
314C22×C4—82no—
315C22×C4—1721no—
316C22×C4C2×C22⋊D4311yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319SD16—1724no—
320D8—1724no—
321M16—1721no—
322M16—1721no—
323C2×C8—862no—
324C2×C8—1721no—
325C2×C8—1721no—
326C4⋊C4—21no—
327C4⋊C4—42no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—82no—
331C4⋊C4—861no—
332C4⋊C4—861no—
333C4⋊C4(C2×D43)⋊C412yes—
334C22⋊C4—22no—
335C22⋊C4—22no—
336C22⋊C4—44no—
337C22⋊C4—1721no—
338C22⋊C4—1721no—
339C42—41no—
340C42—41no—
341C42C2×C4×D4311yescharacteristic
342C42C2×D17211yescharacteristic
343C42#1062189811yescharacteristic
344C42#1062189811yescharacteristic
345C23—22no—
346C23—22no—
347C23—22no—
348C23—42no—
349C23—42no—
350C23—1721no—
351C23#1306329411yescharacteristic
352Q8—1721no—
353Q8—1721no—
354D4—22no—
355D4—22no—
356D4—22no—
357D4—3441no—
358D4—3441no—
359D4—3441no—
360D4—3441no—
361D4—1721no—
362D4—1721no—
363D4#1306324514yes—
364C2×C4—22no—
365C2×C4—22no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—42no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—42no—
374C2×C4—42no—
375C2×C4—41no—
376C2×C4—42no—
377C2×C4—82no—
378C2×C4—82no—
379C2×C4—88no—
380C2×C4—3441no—
381C2×C4—3441no—
382C2×C4—1721no—
383C2×C4C2×(C2×D43)⋊C411yescharacteristic
384C2×C4C4×C22⋊D4311yescharacteristic
385C2×C4C4×C22⋊D4311yescharacteristic
386C2×C4#1306329911yescharacteristic
387C2×C4#1306329911yescharacteristic
388C2×C4#1306330811yescharacteristic
389C2×C4C2×#1062188211yescharacteristic
390C2×C4C2×#1062188411yescharacteristic
391C2×C4#1306335111yescharacteristic
392C2×C4#1306335611yescharacteristic
393C8—3441no—
394C8—3441no—
395C8—1722no—
396C22—21no—
397C22—21no—
398C22—24no—
399C22—44no—
400C22—44no—
401C22—42no—
402C22—42no—
403C22—3441no—
404C22—3441no—
405C22—3441no—
406C22#1458277811yescharacteristic
407C22#1458303311yescharacteristic
408C22#1458303811yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—42no—
415C4—82no—
416C4—81no—
417C4—3441no—
418C4C2×#1306324511yescharacteristic
419C4#1458289811yescharacteristic
420C4#1458321211yescharacteristic
421C4#1458321711yescharacteristic
422C2—21no—
423C2—21no—
424C2—44no—
425C2—6881no—
426C2#1913491211yescharacteristic
427C2#1913508211yescharacteristic
428C2#1913509611yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2349C2
socleC22×C43#386
prime radical#19144059C2
cosocleC2×C42×C43C23
hypercenter#2349D43
hypocenterC43#9179
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2349

Complements

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

NH ≅ G/Ntype
2. #19133154C2semidirect
3. #19133089C2semidirect
4. #19132986C2semidirect
5. #19132498C2semidirect
6. #19132453C2semidirect
7. C43×#2349C2semidirect
11. #14583104C4semidirect
12. #14583094C4semidirect
35. #13063325C2×C4semidirect
36. #13063322C2×C4semidirect
45. C4⋊(C43⋊C8)C2×C4semidirect
209. #2349D43semidirect
243. C43#9179semidirect

Maximal subgroups

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

subgroupindex
#191440592
#191331542
#191330892
#191329862
#191324982
#191324532
C43×#23492
#917943