Finite Group Databasebeta

← #24993173

Subgroups — #24993173

Order 11008.

648 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19145343C211yesmaximal, characteristic
2#19137645C211yesmaximal, characteristic, complemented
3#19133162C211yesmaximal, characteristic, complemented
4C2×#14582633C211yesmaximal, characteristic, complemented
5#19132473C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#1964C211yesmaximal, characteristic, complemented
8C2×#13063299C2211yescharacteristic
9C2×(C22⋊D43)⋊C4—21no—
10#14583212C412yescomplemented
11#14583210—21no—
12#14583133—22no—
13#14583033C412yescomplemented
14#14583032—21no—
15C2×C22⋊(C43⋊C8)C2211yescharacteristic
16C2×C22⋊(C43⋊C8)C2211yescharacteristic
17#14582790—21no—
18#14582784—21no—
19#14582777—21no—
20#14582776—21no—
21C4×(C2×D43)⋊C4—21no—
22C2×C43⋊#95C2211yescharacteristic
23#14582633—21no—
24#14582633—21no—
25#14582632—22no—
26C2×#121×C43C2211yescharacteristic
27C2×#99×C43—21no—
28C2×#99×C43—21no—
29C43×#380C2211yescharacteristic
30C4×C22⋊C4×C43C2211yescharacteristic
31C22×D172D411yescharacteristic
32C22×C22⋊D43—21no—
33C23×Dic43—21no—
34C22×C4×D43—21no—
35C2×#10621882—22no—
36C22×C43⋊C8—21no—
37C22×C43⋊C8—21no—
38#13063299—21no—
39#13063299—21no—
40#13063299C2×C412yes—
41#13063299D412yes—
42(C22⋊D43)⋊C4—42no—
43(C22⋊D43)⋊C4—42no—
44C2×C4⋊Dic43D411yescharacteristic
45C2×Dic43⋊C4—21no—
46C2×(C2×D43)⋊C4—21no—
47C2×(C2×D43)⋊C4—21no—
48C2×(C2×D43)⋊C4—21no—
49C2×(C2×D43)⋊C4—21no—
50C2×C4×Dic43—21no—
51#13063258—22no—
52#13063246—22no—
53#13063245—22no—
54C22⋊(C43⋊C8)—21no—
55C22⋊(C43⋊C8)—21no—
56C22⋊(C43⋊C8)—21no—
57C22⋊(C43⋊C8)C2×C412yescomplemented
58C43⋊#95—21no—
59C43⋊#95—21no—
60C43⋊#95—21no—
61C43⋊#95D411yescharacteristic
62C43⋊#95D411yescharacteristic
63C22×D4×C43—21no—
64C22×D4×C43C2×C411yescharacteristic, complemented
65C23×C4×C43C2311yescharacteristic
66#121×C43—21no—
67#121×C43—21no—
68#121×C43—21no—
69#121×C43—21no—
70C2×C4⋊C4×C43—21no—
71C2×C4⋊C4×C43C2×C411yescharacteristic, complemented
72C2×C22⋊C4×C43—21no—
73C2×C22⋊C4×C43—21no—
74C2×C22⋊C4×C43D411yescharacteristic
75C2×C22⋊C4×C43D411yescharacteristic
76C2×C42×C43—21no—
77#99×C43—42no—
78#99×C43—42no—
79#95×C43—21no—
80#95×C43—21no—
81C24×C43—21no—
82C24×C43C2×D411yescharacteristic
83C23×D43—21no—
84C2×D4×C43—21no—
85C2×D4×C43—21no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—41no—
90C2×D4×C43—41no—
91C2×D4×C43—41no—
92C2×D4×C43—81no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—21no—
96C22×C4×C43—41no—
97C22×C4×C43—81no—
98C22×C4×C43C22×C411yescharacteristic
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43C2×D411yescharacteristic
102C22×C4×C43#4111yescharacteristic
103C22×C4×C43#4111yescharacteristic
104C2×C22⋊D43—22no—
105C2×C22⋊D43—22no—
106C2×C22⋊D43—41no—
107C2×C22⋊D43—41no—
108C2×C22⋊D43—41no—
109C2×C22⋊D43—41no—
110C22×Dic43—21no—
111C22×Dic43—21no—
112C22×Dic43—21no—
113C22×Dic43—42no—
114C22×Dic43—41no—
115C22×Dic43—41no—
116C22×Dic43—81no—
117C2×D172—21no—
118C2×D172—81no—
119C2×D172C22⋊C412yes—
120C2×C4×D43—42no—
121C2×C4×D43—42no—
122C2×C4×D43—81no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—81no—
126C22⋊C4×C43—21no—
127C22⋊C4×C43—21no—
128C22⋊C4×C43—21no—
129C22⋊C4×C43—41no—
130C22⋊C4×C43—41no—
131C22⋊C4×C43—41no—
132C22⋊C4×C43—41no—
133C22⋊C4×C43D812yescomplemented
134C42×C43—81no—
135#10621882—82no—
136(C2×D43)⋊C4—22no—
137(C2×D43)⋊C4—22no—
138(C2×D43)⋊C4—42no—
139(C2×D43)⋊C4—42no—
140(C2×D43)⋊C4—81no—
141C4⋊Dic43—21no—
142C4⋊Dic43C22⋊C412yes—
143Dic43⋊C4—42no—
144C4×Dic43—42no—
145C2×C43⋊C8—22no—
146C2×C43⋊C8—41no—
147C2×C43⋊C8—81no—
148C2×C43⋊C8—81no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43—81no—
155C23×C43—81no—
156C23×C43C4×D411yescharacteristic
157C23×C43#12011yescharacteristic
158C23×C43#12111yescharacteristic
159C23×C43C2×D811yescharacteristic
160C23×C43#13511yescharacteristic
161C23×C43AGL(1,ℤ/8)11yescharacteristic
162C23×C43AGL(1,ℤ/8)11yescharacteristic
163C22×D43—22no—
164C22×D43—41no—
165C22×D43—41no—
166C22×D43—41no—
167C22×D43—41no—
168C22×D43—41no—
169C22×D43—41no—
170D4×C43—42no—
171D4×C43—81no—
172D4×C43—81no—
173D4×C43—81no—
174D4×C43—81no—
175D4×C43—81no—
176C2×C4×C43—22no—
177C2×C4×C43—41no—
178C2×C4×C43—41no—
179C2×C4×C43—41no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—41no—
183C2×C4×C43—41no—
184C2×C4×C43—41no—
185C2×C4×C43—41no—
186C2×C4×C43—41no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—81no—
192C2×C4×C43—81no—
193C2×C4×C43—81no—
194C2×C4×C43C2×C22⋊C411yescharacteristic
195C2×C4×C43C4×D411yescharacteristic
196C2×C4×C43#12111yescharacteristic
197C2×C4×C43#12311yescharacteristic
198C22⋊D43—42no—
199C22⋊D43—42no—
200C22⋊D43—42no—
201C22⋊D43—42no—
202C2×Dic43—22no—
203C2×Dic43—22no—
204C2×Dic43—41no—
205C2×Dic43—41no—
206C2×Dic43—41no—
207C2×Dic43—41no—
208C2×Dic43—41no—
209C2×Dic43—41no—
210C2×Dic43—41no—
211C2×Dic43—82no—
212C2×Dic43—82no—
213D172—42no—
214D172—81no—
215C4×D43—84no—
216C43⋊C8—42no—
217C43⋊C8—81no—
218#9277—431nomaximal, Sylow
219C22×C43—21no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—21no—
223C22×C43—21no—
224C22×C43—21no—
225C22×C43—41no—
226C22×C43—41no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—81no—
230C22×C43—81no—
231C22×C43—81no—
232C22×C43—161no—
233C22×C43—161no—
234C22×C43#38611yescharacteristic
235C22×C43C4×D811yescharacteristic
236C22×C43#44211yescharacteristic
237C22×C43#44711yescharacteristic
238C22×C43#44911yescharacteristic
239C22×C43#45911yescharacteristic
240C22×C43#46311yescharacteristic
241C2×D43—42no—
242C2×D43—42no—
243C2×D43—42no—
244C2×D43—81no—
245C2×D43—81no—
246C2×D43—81no—
247C2×D43—81no—
248C4×C43—21no—
249C4×C43—21no—
250C4×C43—21no—
251C4×C43—21no—
252C4×C43—42no—
253C4×C43—81no—
254C4×C43—81no—
255C4×C43—161no—
256Dic43—42no—
257Dic43—42no—
258Dic43—81no—
259#3186—431no—
260#2364—431no—
261#1964D4311yescharacteristic, complemented
262#1519—431no—
263C2×#327—431no—
264#1294—431no—
265#1282—431no—
266C2×C43—21no—
267C2×C43—21no—
268C2×C43—21no—
269C2×C43—21no—
270C2×C43—21no—
271C2×C43—21no—
272C2×C43—161no—
273C2×C43#187911yescharacteristic
274C2×C43#190611yescharacteristic
275C2×C43#191311yescharacteristic
276D43—82no—
277C2×#121—431no—
278C2×#121C2×D4311yescharacteristic
279C2×C4×D4—861no—
280#480—432no—
281#480—861no—
282#466—862no—
283#447—432no—
284#447—861no—
285C2×#99—21no—
286C2×#99—21no—
287C2×C22⋊C8—431no—
288C2×C22⋊C8—431no—
289#388—861no—
290#387—861no—
291#386—861no—
292#386—861no—
293#380C2×D4311yescharacteristic
294C4×C22⋊C4—861no—
295C4×C22⋊C4C2×D4311yescharacteristic
296C2×#95—431no—
297#327—862no—
298#327—861no—
299#327—861no—
300C43#927711yescharacteristic, complemented, Sylow
301C22×D4—21no—
302C22×D4—431no—
303C22×D4—861no—
304C22×D4C4×D4311yescharacteristic, complemented
305C23×C4—861no—
306C23×C4—861no—
307C23×C4C22×D4311yescharacteristic
308C2×D8—862no—
309C22×C8—861no—
310C22×C8—861no—
311#121—21no—
312#121—21no—
313#121—21no—
314#121—21no—
315#121—432no—
316#121—432no—
317#121—861no—
318#121—861no—
319C4×D4—1722no—
320C4×D4—1722no—
321C2×C4⋊C4—21no—
322C2×C4⋊C4—431no—
323C2×C4⋊C4—861no—
324C2×C4⋊C4C4×D4311yescharacteristic, complemented
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—861no—
328C2×C22⋊C4—861no—
329C2×C22⋊C4—861no—
330C2×C22⋊C4—861no—
331C2×C22⋊C4C22⋊D4311yescharacteristic
332C2×C22⋊C4C22⋊D4311yescharacteristic
333C2×C42—21no—
334C2×C42—861no—
335#107—862no—
336#102—862no—
337#102—862no—
338#99—42no—
339#99—42no—
340C22⋊C8—432no—
341C22⋊C8—861no—
342C22⋊C8—861no—
343C22⋊C8—861no—
344#95—21no—
345#95—21no—
346#95—431no—
347#95—431no—
348#95—861no—
349#95—861no—
350#95—861no—
351C24—21no—
352C24—861no—
353C24C2×C22⋊D4311yescharacteristic
354C2×D4—21no—
355C2×D4—21no—
356C2×D4—41no—
357C2×D4—41no—
358C2×D4—41no—
359C2×D4—41no—
360C2×D4—41no—
361C2×D4—41no—
362C2×D4—81no—
363C2×D4—432no—
364C2×D4—862no—
365C2×D4—862no—
366C2×D4—861no—
367C2×D4—3441no—
368C2×D4—1721no—
369C2×D4—1721no—
370C2×D4—1721no—
371C2×D4—1721no—
372C22×C4—21no—
373C22×C4—21no—
374C22×C4—21no—
375C22×C4—41no—
376C22×C4—81no—
377C22×C4—861no—
378C22×C4—861no—
379C22×C4—861no—
380C22×C4—3441no—
381C22×C4—3441no—
382C22×C4—1722no—
383C22×C4—1722no—
384C22×C4—1722no—
385C22×C4—1721no—
386C22×C4—1721no—
387C22×C4C2×C4×D4311yescharacteristic
388C22×C4#1062189811yescharacteristic
389C22×C4D4×D4311yescharacteristic
390C22×C4D4×D4311yescharacteristic
391C22×C4D4×D4311yescharacteristic
392C22×C4#1062190011yescharacteristic
393D8—3442no—
394C2×C8—862no—
395C2×C8—3441no—
396C2×C8—3441no—
397C2×C8—1721no—
398C4⋊C4—21no—
399C4⋊C4—21no—
400C4⋊C4—81no—
401C4⋊C4—432no—
402C4⋊C4—861no—
403C4⋊C4—1722no—
404C22⋊C4—21no—
405C22⋊C4—21no—
406C22⋊C4—21no—
407C22⋊C4—41no—
408C22⋊C4—41no—
409C22⋊C4—41no—
410C22⋊C4—41no—
411C22⋊C4—862no—
412C22⋊C4—862no—
413C22⋊C4—3441no—
414C22⋊C4—1722no—
415C22⋊C4—1722no—
416C22⋊C4#1062188212yescomplemented
417C42—81no—
418C42—1722no—
419C23—41no—
420C23—41no—
421C23—41no—
422C23—41no—
423C23—41no—
424C23—81no—
425C23—81no—
426C23—862no—
427C23—1721no—
428C23—1721no—
429C23—1721no—
430C23—1721no—
431C23—1721no—
432C23—1721no—
433C23C4×C22⋊D4311yescharacteristic
434C23#1306329311yescharacteristic
435C23#1306329611yescharacteristic
436C23C2×#1062188211yescharacteristic
437C23#1306334511yescharacteristic
438C23#1306335011yescharacteristic
439C23#1306335111yescharacteristic
440D4—42no—
441D4—81no—
442D4—81no—
443D4—81no—
444D4—81no—
445D4—81no—
446D4—3441no—
447D4—1722no—
448D4—1722no—
449D4—1722no—
450D4—1722no—
451D4—1722no—
452C2×C4—22no—
453C2×C4—41no—
454C2×C4—41no—
455C2×C4—41no—
456C2×C4—41no—
457C2×C4—41no—
458C2×C4—41no—
459C2×C4—41no—
460C2×C4—41no—
461C2×C4—41no—
462C2×C4—41no—
463C2×C4—41no—
464C2×C4—41no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—81no—
468C2×C4—81no—
469C2×C4—81no—
470C2×C4—862no—
471C2×C4—862no—
472C2×C4—3444no—
473C2×C4—3442no—
474C2×C4—3442no—
475C2×C4—1721no—
476C2×C4—1721no—
477C2×C4—1721no—
478C2×C4—1721no—
479C2×C4—1721no—
480C2×C4—1721no—
481C2×C4—1721no—
482C2×C4C22⋊C4×D4311yescharacteristic
483C2×C4(C22⋊D43)⋊C411yescharacteristic
484C2×C4#1306329811yescharacteristic
485C2×C4#1306330711yescharacteristic
486C8—3441no—
487C8—1722no—
488C22—21no—
489C22—21no—
490C22—21no—
491C22—21no—
492C22—21no—
493C22—21no—
494C22—41no—
495C22—41no—
496C22—41no—
497C22—41no—
498C22—81no—
499C22—81no—
500C22—81no—
501C22—161no—
502C22—161no—
503C22—3441no—
504C22—3441no—
505C22—3441no—
506C22—3441no—
507C22—1722no—
508C22—1722no—
509C22—1722no—
510C22#1458277511yescharacteristic
511C22C4×#1062188211yescharacteristic
512C22#1458300911yescharacteristic
513C22#1458303211yescharacteristic
514C22#1458304211yescharacteristic
515C22#1458309111yescharacteristic
516C22#1458311111yescharacteristic
517C4—21no—
518C4—21no—
519C4—21no—
520C4—21no—
521C4—42no—
522C4—81no—
523C4—81no—
524C4—161no—
525C4—3441no—
526C4—1722no—
527C4—1722no—
528C2—21no—
529C2—21no—
530C2—21no—
531C2—21no—
532C2—21no—
533C2—21no—
534C2—161no—
535C2—3442no—
536C2#1913494611yescharacteristic
537C2#1913509311yescharacteristic
538C2#1913513411yescharacteristic
subgroupG/H
centerC22#14582775
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1964C2
socleC22×C43#386
prime radical#19145343C2
cosocleC23×C4×C43C23
hypercenter#1964D43
hypocenterC43#9277
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1964

Complements

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

NH ≅ G/Ntype
2. #19137645C2semidirect
3. #19133162C2semidirect
4. C2×#14582633C2semidirect
5. #19132473C2semidirect
6. #19132443C2semidirect
7. C43×#1964C2semidirect
10. #14583212C4semidirect
13. #14583033C4semidirect
57. C22⋊(C43⋊C8)C2×C4semidirect
64. C22×D4×C43C2×C4semidirect
71. C2×C4⋊C4×C43C2×C4semidirect
133. C22⋊C4×C43D8semidirect
261. #1964D43semidirect
300. C43#9277semidirect
304. C22×D4C4×D43semidirect
324. C2×C4⋊C4C4×D43semidirect
416. C22⋊C4#10621882semidirect

Maximal subgroups

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

subgroupindex
#191453432
#191376452
#191331622
C2×#145826332
#191324732
#191324432
C43×#19642
#927743