Finite Group Databasebeta

← #24991815

Subgroups — #24991815

Order 11008.

538 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145170C211yesmaximal, characteristic
2#19143341C211yesmaximal, characteristic, complemented
3#19133089C211yesmaximal, characteristic, complemented
4#19132994C211yesmaximal, characteristic, complemented
5#19132436C211yesmaximal, characteristic, complemented
6#19132433C211yesmaximal, characteristic, complemented
7C43×#1980C211yesmaximal, characteristic, complemented
8C2×#13063333—21no—
9#14583449C2211yescharacteristic
10#14583302C411yescharacteristic, complemented
11#14583275C411yescharacteristic, complemented
12#14583247C411yescharacteristic, complemented
13#14583245C411yescharacteristic, complemented
14#14583133—22no—
15C4×#10621882—22no—
16#14582978—21no—
17#14582972—22no—
18C8×D172—21no—
19#14582952C2211yescharacteristic
20C2×C4⋊(C43⋊C8)C2211yescharacteristic
21#14582867—21no—
22C2×C4×C43⋊C8C2211yescharacteristic
23#14582632—22no—
24D4⋊(C43⋊C8)—21no—
25D4⋊(C43⋊C8)—21no—
26C43×#532C2211yescharacteristic
27C2×#104×C43—21no—
28C2×#104×C43—21no—
29C4×M16×C43C2211yescharacteristic
30C4×C4⋊C4×C43C2211yescharacteristic
31C2×#10621898—21no—
32C2×#10621882—22no—
33#13063333—42no—
34#13063333—42no—
35C2×#10621872—22no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38C2×C8×D43—22no—
39#13063325C2×C411yescharacteristic
40#13063322C2×C411yescharacteristic
41#13063313—21no—
42#13063299—21no—
43#13063299D412yes—
44C4×D172—21no—
45C4×D172D412yes—
46#13063258—22no—
47C4⋊(C43⋊C8)—21no—
48C4⋊(C43⋊C8)—21no—
49C4⋊(C43⋊C8)D411yescharacteristic
50C4⋊(C43⋊C8)D411yescharacteristic
51#13063246—22no—
52#13063245—22no—
53C22⋊(C43⋊C8)—21no—
54(C2×D43)⋊C8—22no—
55(C2×D43)⋊C8—22no—
56C4×C43⋊C8—21no—
57C4×C43⋊C8—21no—
58C4×C43⋊C8C2×C411yescharacteristic
59C4×C43⋊C8C2×C411yescharacteristic
60C2×#41×C43—21no—
61C2×M16×C43D411yescharacteristic
62C2×M16×C43D411yescharacteristic
63C4⋊Q8×C43C2×C411yescharacteristic
64#127×C43C2×C411yescharacteristic
65#124×C43—21no—
66#121×C43—21no—
67#121×C43—21no—
68C4×D4×C43—21no—
69C4×D4×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C42×C43—21no—
72C2×C42×C43C2311yescharacteristic
73#104×C43—42no—
74#104×C43—42no—
75#97×C43—21no—
76C4×C8×C43—21no—
77#95×C43—21no—
78#41×C43—41no—
79#41×C43—41no—
80#41×C43—41no—
81#41×C43—41no—
82C2×Q8×C43—21no—
83C2×D4×C43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C22×C4×C43—41no—
88C22×C4×C43—41no—
89C22×C4×C43C2×D411yescharacteristic
90C22×C4×C43C2×D411yescharacteristic
91C22×C4×C43#4111yescharacteristic
92C2×C22⋊D43—22no—
93#10621898—41no—
94#10621898—41no—
95#10621898—41no—
96#10621898—41no—
97C2×D172—21no—
98C2×D172—21no—
99C2×D172C22⋊C412yes—
100C2×C4×D43—22no—
101C2×Dic86—21no—
102M16×C43—21no—
103M16×C43—21no—
104M16×C43—21no—
105M16×C43D812yescomplemented
106C2×C8×C43—21no—
107C2×C8×C43—21no—
108C4⋊C4×C43—22no—
109C4⋊C4×C43—21no—
110C4⋊C4×C43—21no—
111C4⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊C4×C43—41no—
114C42×C43—41no—
115C42×C43—41no—
116C42×C43C22×C411yescharacteristic
117C42×C43C2×D411yescharacteristic
118C42×C43C2×D411yescharacteristic
119C42×C43#4111yescharacteristic
120#10621882—44no—
121(C2×D43)⋊C4—22no—
122(C2×D43)⋊C4—22no—
123C4⋊Dic43—21no—
124C4⋊Dic43C22⋊C412yes—
125C2×C43⋊C8—21no—
126C2×C43⋊C8—21no—
127C2×C43⋊C8—21no—
128C2×C43⋊C8—21no—
129C2×C43⋊C8—42no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8—41no—
132C2×C43⋊C8—41no—
133#10621872—44no—
134C8×D43—44no—
135C23×C43—41no—
136C23×C43#12111yescharacteristic
137C22×D43—22no—
138Q8×C43—41no—
139Q8×C43—41no—
140D4×C43—42no—
141D4×C43—41no—
142D4×C43—41no—
143D4×C43—41no—
144D4×C43—41no—
145D4×C43—81no—
146D4×C43—81no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—41no—
150C2×C4×C43—42no—
151C2×C4×C43—41no—
152C2×C4×C43—81no—
153C2×C4×C43—81no—
154C2×C4×C43—81no—
155C2×C4×C43—81no—
156C2×C4×C43C2×C22⋊C411yescharacteristic
157C2×C4×C43C4×D411yescharacteristic
158C2×C4×C43C4×D411yescharacteristic
159C2×C4×C43#12011yescharacteristic
160C2×C4×C43#12111yescharacteristic
161C2×C4×C43#12311yescharacteristic
162C2×C4×C43C2×D811yescharacteristic
163C2×C4×C43#13511yescharacteristic
164C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
165C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
166C22⋊D43—42no—
167C22⋊D43—42no—
168C2×Dic43—22no—
169D172—42no—
170D172—41no—
171D172—41no—
172D172—41no—
173D172—41no—
174C4×D43—42no—
175C4×D43—42no—
176Dic86—41no—
177Dic86—41no—
178C8×C43—22no—
179C8×C43—41no—
180C43⋊C8—22no—
181C43⋊C8—41no—
182C43⋊C8—41no—
183C43⋊C8—41no—
184C43⋊C8—81no—
185#9053—431nomaximal, Sylow
186C22×C43—21no—
187C22×C43—21no—
188C22×C43—81no—
189C22×C43—81no—
190C22×C43—81no—
191C22×C43#38611yescharacteristic
192C22×C43#45911yescharacteristic
193C22×C43#46311yescharacteristic
194C2×D43—42no—
195C2×D43—42no—
196C2×D43—42no—
197C4×C43—21no—
198C4×C43—21no—
199C4×C43—21no—
200C4×C43—82no—
201C4×C43—81no—
202C4×C43C4×D811yescharacteristic
203C4×C43#44211yescharacteristic
204C4×C43#44311yescharacteristic
205C4×C43#44411yescharacteristic
206C4×C43#44711yescharacteristic
207C4×C43#44911yescharacteristic
208Dic43—42no—
209#3169—431no—
210#2935—431no—
211#1980D4311yescharacteristic, complemented
212#1502—431no—
213#1480—431no—
214#1279—431no—
215#1278—431no—
216C2×C43—21no—
217C2×C43—21no—
218C2×C43—161no—
219C2×C43#187611yescharacteristic
220C2×C43#187911yescharacteristic
221C2×C43#188411yescharacteristic
222D43—82no—
223C2×#131—861no—
224#532—431no—
225#532C2×D4311yescharacteristic
226#500—431no—
227#493—431no—
228#486—431no—
229#486—431no—
230#466—862no—
231C4×D8—862no—
232#436—861no—
233#435—862no—
234C8×D4—861no—
235#431—431no—
236C2×C4⋊C8—431no—
237C2×#104—21no—
238C2×#104—21no—
239#408—861no—
240C4×M16C2×D4311yescharacteristic
241C2×C4×C8—431no—
242C4×C4⋊C4C2×D4311yescharacteristic
243#327—862no—
244D4⋊C8—861no—
245D4⋊C8—861no—
246C43#905311yescharacteristic, complemented, Sylow
247C2×#41—21no—
248C2×#41—861no—
249C2×D8—862no—
250#131—1722no—
251#131—1722no—
252C2×M16—862no—
253C2×M16C22⋊D4311yescharacteristic
254C2×M16C22⋊D4311yescharacteristic
255C22×C8—862no—
256C22×C8—861no—
257C22×C8—861no—
258C4⋊Q8—431no—
259C4⋊Q8C4×D4311yescharacteristic
260#127—431no—
261#127C4×D4311yescharacteristic
262#124—21no—
263#124—861no—
264#121—21no—
265#121—21no—
266#121—432no—
267#121—861no—
268C4×D4—21no—
269C4×D4—21no—
270C4×D4—432no—
271C4×D4—861no—
272C2×C4⋊C4—21no—
273C2×C42—21no—
274C2×C42C22×D4311yescharacteristic
275#107—862no—
276C4⋊C8—431no—
277C4⋊C8—431no—
278C4⋊C8—861no—
279C4⋊C8—861no—
280#104—42no—
281#104—42no—
282#102—862no—
283#102—862no—
284C22⋊C8—862no—
285C22⋊C8—862no—
286C22⋊C8—861no—
287#97—21no—
288C4×C8—21no—
289C4×C8—431no—
290C4×C8—431no—
291C4×C8—861no—
292C4×C8—861no—
293#95—21no—
294#41—41no—
295#41—41no—
296#41—41no—
297#41—41no—
298#41—1721no—
299#41—1721no—
300#41—1721no—
301#41—1721no—
302C2×Q8—21no—
303C2×Q8—861no—
304C2×D4—21no—
305C2×D4—21no—
306C2×D4—21no—
307C2×D4—41no—
308C2×D4—432no—
309C2×D4—862no—
310C2×D4—861no—
311C2×D4—861no—
312C22×C4—41no—
313C22×C4—41no—
314C22×C4—862no—
315C22×C4D4×D4311yescharacteristic
316C22×C4#1062190011yescharacteristic
317C22×C4C2×C22⋊D4311yescharacteristic
318D8—1724no—
319M16—21no—
320M16—21no—
321M16—21no—
322M16—1724no—
323M16#1062188212yescomplemented
324C2×C8—21no—
325C2×C8—21no—
326C2×C8—861no—
327C2×C8—861no—
328C2×C8—861no—
329C2×C8—861no—
330C2×C8—1724no—
331C2×C8—1722no—
332C2×C8—1721no—
333C2×C8—1721no—
334C2×C8—1721no—
335C4⋊C4—22no—
336C4⋊C4—21no—
337C4⋊C4—21no—
338C4⋊C4—41no—
339C4⋊C4—432no—
340C4⋊C4—861no—
341C22⋊C4—41no—
342C22⋊C4—41no—
343C22⋊C4—862no—
344C22⋊C4—862no—
345C42—41no—
346C42—41no—
347C42C2×C4×D4311yescharacteristic
348C42#1062189811yescharacteristic
349C42D4×D4311yescharacteristic
350C42D4×D4311yescharacteristic
351C23—41no—
352C23—862no—
353C23#1306329611yescharacteristic
354Q8—41no—
355Q8—41no—
356Q8—1721no—
357Q8—1721no—
358D4—42no—
359D4—41no—
360D4—41no—
361D4—41no—
362D4—41no—
363D4—81no—
364D4—81no—
365D4—1722no—
366D4—1722no—
367D4—1722no—
368D4—1721no—
369D4—1721no—
370D4—1721no—
371D4—1721no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—41no—
375C2×C4—42no—
376C2×C4—41no—
377C2×C4—81no—
378C2×C4—81no—
379C2×C4—81no—
380C2×C4—81no—
381C2×C4—862no—
382C2×C4—1722no—
383C2×C4—1722no—
384C2×C4C22⋊C4×D4311yescharacteristic
385C2×C4(C22⋊D43)⋊C411yescharacteristic
386C2×C4C4×C22⋊D4311yescharacteristic
387C2×C4#1306329311yescharacteristic
388C2×C4#1306329811yescharacteristic
389C2×C4#1306330711yescharacteristic
390C2×C4C2×#1062188211yescharacteristic
391C2×C4#1306334511yescharacteristic
392C2×C4#1306335011yescharacteristic
393C2×C4#1306335111yescharacteristic
394C8—22no—
395C8—41no—
396C8—862no—
397C8—3441no—
398C8—1721no—
399C8—1721no—
400C8—1721no—
401C22—21no—
402C22—21no—
403C22—81no—
404C22—81no—
405C22—81no—
406C22—1722no—
407C22—1722no—
408C22—1722no—
409C22#1458277511yescharacteristic
410C22#1458309111yescharacteristic
411C22#1458311111yescharacteristic
412C4—21no—
413C4—21no—
414C4—21no—
415C4—82no—
416C4—81no—
417C4—1722no—
418C4C4×#1062188211yescharacteristic
419C4#1458300911yescharacteristic
420C4#1458301311yescharacteristic
421C4#1458301811yescharacteristic
422C4#1458303211yescharacteristic
423C4#1458304211yescharacteristic
424C2—21no—
425C2—21no—
426C2—161no—
427C2—3442no—
428C2#1913491911yescharacteristic
429C2#1913494611yescharacteristic
430C2#1913497511yescharacteristic
subgroupG/H
centerC2×C4#13063293
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1980C2
socleC22×C43#386
prime radical#19145170C2
cosocleC2×C42×C43C23
hypercenter#1980D43
hypocenterC43#9053
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1980

Complements

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

NH ≅ G/Ntype
2. #19143341C2semidirect
3. #19133089C2semidirect
4. #19132994C2semidirect
5. #19132436C2semidirect
6. #19132433C2semidirect
7. C43×#1980C2semidirect
10. #14583302C4semidirect
11. #14583275C4semidirect
12. #14583247C4semidirect
13. #14583245C4semidirect
105. M16×C43D8semidirect
211. #1980D43semidirect
246. C43#9053semidirect
323. M16#10621882semidirect

Maximal subgroups

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

subgroupindex
#191451702
#191433412
#191330892
#191329942
#191324362
#191324332
C43×#19802
#905343