Finite Group Databasebeta

← #24992535

Subgroups — #24992535

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#19144055C211yesmaximal, characteristic
2#19137506C211yesmaximal, characteristic, complemented
3#19133155C211yesmaximal, characteristic, complemented
4#19132985C211yesmaximal, characteristic, complemented
5#19132498C211yesmaximal, characteristic, complemented
6#19132454C211yesmaximal, characteristic, complemented
7C43×#1502C211yesmaximal, characteristic, complemented
8C2×#13063350—21no—
9C2×C4×D172—21no—
10C2×C4×D172C2211yescharacteristic
11#14583111—22no—
12#14583101C412yescomplemented
13#14583091C412yescomplemented
14#14582952C2211yescharacteristic
15#14582923C2211yescharacteristic
16#14582900—21no—
17#14582797—21no—
18#14582770—22no—
19#14582765C2211yescharacteristic
20#14582758—21no—
21#95×D43—21no—
22#14582633—22no—
23#14582626—22no—
24C43×#532C2211yescharacteristic
25C43×#431C2211yescharacteristic
26C4×C4⋊C4×C43C2211yescharacteristic
27C43×#327—21no—
28C43×#327—21no—
29C22×D172D411yescharacteristic
30C22×C4×D43—21no—
31C22×C4×D43—22no—
32#13063350—42no—
33#13063350—42no—
34C2×#10621884—22no—
35C2×#10621882—22no—
36C2×#10621877—21no—
37C4×D172—21no—
38C4×D172—21no—
39C4×D172—42no—
40C4×D172—42no—
41C4×D172C2×C412yes—
42C4×D172D412yes—
43C2×C4⋊Dic43—21no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—22no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—22no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)—21no—
50C4⋊(C43⋊C8)C2×C412yescomplemented
51#13063249—22no—
52#13063246—22no—
53C22⋊(C43⋊C8)—21no—
54C4×C43⋊C8—21no—
55C43⋊#95—22no—
56C43⋊#95—21no—
57C43⋊#95D412yes—
58C2×#41×C43—21no—
59C4⋊Q8×C43C2×C411yescharacteristic, complemented
60#127×C43C2×C411yescharacteristic, complemented
61#124×C43—21no—
62#121×C43—21no—
63#121×C43—21no—
64C4×D4×C43—21no—
65C4×D4×C43—21no—
66C2×C4⋊C4×C43—21no—
67C2×C42×C43—21no—
68C2×C42×C43C2311yescharacteristic
69C4⋊C8×C43—21no—
70C22⋊C8×C43—21no—
71C4×C8×C43—21no—
72#95×C43D411yescharacteristic
73#95×C43D411yescharacteristic
74C23×D43—21no—
75#41×C43—41no—
76#41×C43—41no—
77#41×C43—41no—
78#41×C43—41no—
79C2×Q8×C43—21no—
80C2×D4×C43—21no—
81C2×D4×C43—21no—
82C2×D4×C43—21no—
83C2×D4×C43—41no—
84C22×C4×C43—21no—
85C22×C4×C43—21no—
86C22×C4×C43—41no—
87C22×C4×C43C2×D411yescharacteristic
88C22×C4×C43C2×D411yescharacteristic
89C22×C4×C43C2×D411yescharacteristic
90C22×Dic43—21no—
91C22×Dic43—22no—
92C2×D172—21no—
93C2×D172—21no—
94C2×D172—21no—
95C2×D172C22⋊C412yes—
96C2×D172D812yes—
97C2×D172SD1612yes—
98C2×C4×D43—22no—
99C2×C4×D43—22no—
100C2×C4×D43—44no—
101C2×C4×D43—44no—
102C2×C4×D43—82no—
103C2×C4×D43—82no—
104C2×C8×C43—41no—
105C4⋊C4×C43—21no—
106C4⋊C4×C43—21no—
107C4⋊C4×C43—42no—
108C22⋊C4×C43—41no—
109C22⋊C4×C43—41no—
110C42×C43—41no—
111C42×C43—41no—
112C42×C43C22×C411yescharacteristic
113C42×C43C2×D411yescharacteristic
114C42×C43#4111yescharacteristic
115C42×C43#4111yescharacteristic
116#10621884—44no—
117#10621882—44no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—44no—
121C4⋊Dic43—21no—
122C4⋊Dic43—41no—
123C4⋊Dic43—41no—
124C4⋊Dic43C22⋊C412yes—
125Dic43⋊C4—82no—
126#10621877—41no—
127#10621877—41no—
128C2×C43⋊C8—22no—
129C2×C43⋊C8—41no—
130C23×C43—41no—
131C23×C43#12011yescharacteristic
132C22×D43—22no—
133C22×D43—22no—
134C22×D43—22no—
135C22×D43—42no—
136C22×D43—42no—
137Q8×C43—41no—
138Q8×C43—41no—
139D4×C43—41no—
140D4×C43—41no—
141D4×C43—81no—
142D4×C43—81no—
143D4×C43—81no—
144D4×C43—81no—
145C2×C4×C43—22no—
146C2×C4×C43—41no—
147C2×C4×C43—41no—
148C2×C4×C43—41no—
149C2×C4×C43—41no—
150C2×C4×C43—41no—
151C2×C4×C43—41no—
152C2×C4×C43—41no—
153C2×C4×C43—41no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12111yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43C2×SD1611yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43#13711yescharacteristic
166C2×Dic43—22no—
167C2×Dic43—42no—
168C2×Dic43—42no—
169C2×Dic43—42no—
170C2×Dic43—42no—
171D172—22no—
172D172—22no—
173D172—22no—
174D172#10214yes—
175C4×D43—82no—
176C4×D43—82no—
177C4×D43—88no—
178C8×C43—81no—
179C43⋊C8—42no—
180C43⋊C8—81no—
181#9179—431nomaximal, Sylow
182C22×C43—21no—
183C22×C43—21no—
184C22×C43—81no—
185C22×C43—81no—
186C22×C43—81no—
187C22×C43#38611yescharacteristic
188C22×C43#44711yescharacteristic
189C22×C43#44811yescharacteristic
190C2×D43—24no—
191C2×D43—44no—
192C2×D43—44no—
193C2×D43—42no—
194C2×D43—42no—
195C4×C43—21no—
196C4×C43—21no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—42no—
200C4×C43—81no—
201C4×C43—81no—
202C4×C43C2×#10211yescharacteristic
203C4×C43#41711yescharacteristic
204C4×C43#48011yescharacteristic
205C4×C43#48111yescharacteristic
206Dic43—42no—
207Dic43—82no—
208#3036—431no—
209#2349—431no—
210#1517—431no—
211#1502D4311yescharacteristic, complemented
212#1478—431no—
213#1303—431no—
214#1286—431no—
215C2×C43—21no—
216C2×C43—21no—
217C2×C43—161no—
218C2×C43#187411yescharacteristic
219C2×C43#190411yescharacteristic
220C2×C43#190611yescharacteristic
221D43—44no—
222C2×AGL(1,ℤ/8)—861no—
223#532C2×D4311yescharacteristic
224C2×C4×D4—431no—
225C2×C4×D4—861no—
226#463—862no—
227#461—432no—
228#459—432no—
229#431—431no—
230#431C2×D4311yescharacteristic
231#423—431no—
232#417—861no—
233#389—861no—
234#385—862no—
235#382—431no—
236#380—861no—
237C4×C4⋊C4C2×D4311yescharacteristic
238C2×#95—861no—
239#327—21no—
240#327—21no—
241#327—862no—
242D4⋊C8—862no—
243C43#917911yescharacteristic, complemented, Sylow
244C2×#41—21no—
245C22×D4—431no—
246C23×C4—862no—
247C23×C4—861no—
248AGL(1,ℤ/8)—1722no—
249AGL(1,ℤ/8)—1722no—
250C2×SD16—862no—
251C2×D8—862no—
252C2×M16—861no—
253C4⋊Q8C4×D4311yescharacteristic, complemented
254#127C4×D4311yescharacteristic, complemented
255#124—21no—
256#121—21no—
257#121—21no—
258C4×D4—21no—
259C4×D4—21no—
260C4×D4—432no—
261C4×D4—432no—
262C4×D4—861no—
263C4×D4—861no—
264C4×D4—1722no—
265C4×D4—1722no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—431no—
268C2×C4⋊C4—862no—
269C2×C4⋊C4—861no—
270C2×C22⋊C4—861no—
271C2×C22⋊C4—862no—
272C2×C42—21no—
273C2×C42C22×D4311yescharacteristic
274C4⋊C8—21no—
275C4⋊C8—432no—
276C4⋊C8—861no—
277C4⋊C8—861no—
278#103—862no—
279#102—862no—
280C22⋊C8—21no—
281C22⋊C8—861no—
282C4×C8—21no—
283C4×C8—861no—
284#95—432no—
285#95—862no—
286#95—861no—
287#95C22⋊D4311yescharacteristic
288#95C22⋊D4311yescharacteristic
289C24—861no—
290#41—41no—
291#41—41no—
292#41—41no—
293#41—41no—
294C2×Q8—21no—
295C2×D4—21no—
296C2×D4—21no—
297C2×D4—21no—
298C2×D4—41no—
299C2×D4—432no—
300C2×D4—432no—
301C2×D4—432no—
302C2×D4—861no—
303C2×D4—861no—
304C2×D4—861no—
305C22×C4—21no—
306C22×C4—21no—
307C22×C4—41no—
308C22×C4—861no—
309C22×C4—862no—
310C22×C4—862no—
311C22×C4—862no—
312C22×C4—3442no—
313C22×C4—3442no—
314C22×C4—1724no—
315C22×C4—1724no—
316C22×C4D4×D4311yescharacteristic
317C22×C4D4×D4311yescharacteristic
318C22×C4C2×C22⋊D4311yescharacteristic
319SD16—1724no—
320D8—1724no—
321M16—1721no—
322M16—1721no—
323C2×C8—41no—
324C2×C8—862no—
325C2×C8—1721no—
326C4⋊C4—21no—
327C4⋊C4—21no—
328C4⋊C4—42no—
329C4⋊C4—432no—
330C4⋊C4—861no—
331C4⋊C4—3442no—
332C4⋊C4—1721no—
333C4⋊C4—1721no—
334C22⋊C4—41no—
335C22⋊C4—41no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C22⋊C4—1724no—
339C42—41no—
340C42—41no—
341C42C2×C4×D4311yescharacteristic
342C42#1062189811yescharacteristic
343C42D4×D4311yescharacteristic
344C42#1062190011yescharacteristic
345C23—41no—
346C23—862no—
347C23—862no—
348C23—862no—
349C23—1722no—
350C23—1722no—
351C23#1306329311yescharacteristic
352Q8—41no—
353Q8—41no—
354D4—41no—
355D4—41no—
356D4—81no—
357D4—81no—
358D4—81no—
359D4—81no—
360D4—434no—
361D4—862no—
362D4—862no—
363D4—862no—
364C2×C4—22no—
365C2×C4—41no—
366C2×C4—41no—
367C2×C4—41no—
368C2×C4—41no—
369C2×C4—41no—
370C2×C4—41no—
371C2×C4—41no—
372C2×C4—41no—
373C2×C4—81no—
374C2×C4—81no—
375C2×C4—862no—
376C2×C4—3442no—
377C2×C4—3442no—
378C2×C4—3448no—
379C2×C4—1722no—
380C2×C4—1722no—
381C2×C4—1722no—
382C2×C4—1722no—
383C2×C4C22⋊C4×D4311yescharacteristic
384C2×C4(C22⋊D43)⋊C411yescharacteristic
385C2×C4C4×C22⋊D4311yescharacteristic
386C2×C4#1306329611yescharacteristic
387C2×C4#1306329811yescharacteristic
388C2×C4#1306330711yescharacteristic
389C2×C4D8×D4311yescharacteristic
390C2×C4SD16×D4311yescharacteristic
391C2×C4#1306334911yescharacteristic
392C2×C4#1306335411yescharacteristic
393C8—81no—
394C8—3441no—
395C8—1722no—
396C22—21no—
397C22—21no—
398C22—81no—
399C22—81no—
400C22—81no—
401C22—864no—
402C22—1724no—
403C22—1724no—
404C22—1722no—
405C22—1722no—
406C22#1458277511yescharacteristic
407C22#1458303111yescharacteristic
408C22#1458303611yescharacteristic
409C4—21no—
410C4—21no—
411C4—21no—
412C4—21no—
413C4—42no—
414C4—81no—
415C4—81no—
416C4—3442no—
417C4—1722no—
418C4#102×D4311yescharacteristic
419C4#1458289711yescharacteristic
420C4#1458321111yescharacteristic
421C4#1458321611yescharacteristic
422C2—21no—
423C2—21no—
424C2—161no—
425C2—1724no—
426C2#1913490911yescharacteristic
427C2#1913508511yescharacteristic
428C2#1913509911yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1502C2
socleC22×C43#386
prime radical#19144055C2
cosocleC2×C42×C43C23
hypercenter#1502D43
hypocenterC43#9179
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1502

Complements

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

NH ≅ G/Ntype
2. #19137506C2semidirect
3. #19133155C2semidirect
4. #19132985C2semidirect
5. #19132498C2semidirect
6. #19132454C2semidirect
7. C43×#1502C2semidirect
12. #14583101C4semidirect
13. #14583091C4semidirect
50. C4⋊(C43⋊C8)C2×C4semidirect
59. C4⋊Q8×C43C2×C4semidirect
60. #127×C43C2×C4semidirect
211. #1502D43semidirect
243. C43#9179semidirect
253. C4⋊Q8C4×D43semidirect
254. #127C4×D43semidirect

Maximal subgroups

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

subgroupindex
#191440552
#191375062
#191331552
#191329852
#191324982
#191324542
C43×#15022
#917943