Finite Group Databasebeta

← #25000384

Subgroups — #25000384

Order 11008.

574 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19135402C211yesmaximal, characteristic, complemented
2#19135390C211yesmaximal, characteristic, complemented
3#19134595C211yesmaximal, characteristic, complemented
4C2×#14582651C211yesmaximal, characteristic, complemented
5C2×#14582643C211yesmaximal, characteristic, complemented
6#19132479C211yesmaximal, characteristic, complemented
7C2×C43×#459C211yesmaximal, characteristic
8C2×C4⋊(C43⋊C8)C2211yescharacteristic
9C2×C4⋊(C43⋊C8)C2211yescharacteristic
10C2×#13063246—21no—
11C2×#13063246—21no—
12C2×#13063246—21no—
13C2×C22⋊(C43⋊C8)—21no—
14C2×C22⋊(C43⋊C8)—21no—
15C2×C4×C43⋊C8C2211yescharacteristic
16#14582769C2211yescharacteristic
17#14582661—21no—
18#14582651—22no—
19#14582643—22no—
20C22×D8×C43—21no—
21C2×#127×C43C2211yescharacteristic
22C2×C4×D4×C43C2211yescharacteristic
23C43×#459—22no—
24C43×#459—22no—
25C2×C4⋊C8×C43C2211yescharacteristic
26C2×#102×C43—21no—
27C22×C43⋊C8—21no—
28C22×C43⋊C8—21no—
29C22×C43⋊C8D411yescharacteristic
30C22×C43⋊C8D411yescharacteristic
31C2×C4⋊Dic43—21no—
32C2×C4⋊Dic43—21no—
33C2×C4⋊Dic43—21no—
34C4⋊(C43⋊C8)—21no—
35C4⋊(C43⋊C8)—21no—
36C4⋊(C43⋊C8)—21no—
37C4⋊(C43⋊C8)—21no—
38#13063246—42no—
39#13063246—42no—
40#13063246—42no—
41C22⋊(C43⋊C8)—42no—
42C22⋊(C43⋊C8)—42no—
43C4×C43⋊C8—21no—
44C4×C43⋊C8—21no—
45C22×D4×C43—21no—
46C22×D4×C43—21no—
47C22×D4×C43—21no—
48C22×D4×C43D411yescharacteristic
49C23×C4×C43—21no—
50C2×D8×C43—24no—
51C2×D8×C43—42no—
52C2×D8×C43—42no—
53C22×C8×C43—21no—
54#127×C43—21no—
55#127×C43—21no—
56#127×C43—21no—
57#127×C43D412yes—
58C4×D4×C43—21no—
59C4×D4×C43—21no—
60C4×D4×C43—21no—
61C4×D4×C43—21no—
62C2×C4⋊C4×C43D411yescharacteristic
63C2×C22⋊C4×C43—21no—
64C2×C42×C43C2311yescharacteristic
65C4⋊C8×C43—21no—
66C4⋊C8×C43D412yes—
67#102×C43—24no—
68C24×C43—21no—
69C24×C43—41no—
70C2×D4×C43—21no—
71C2×D4×C43—21no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—21no—
75C2×D4×C43—22no—
76C2×D4×C43—21no—
77C2×D4×C43—21no—
78C2×D4×C43—41no—
79C2×D4×C43—41no—
80C2×D4×C43—41no—
81C2×D4×C43—41no—
82C2×D4×C43—41no—
83C2×D4×C43—41no—
84C2×D4×C43—41no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43—81no—
90C2×D4×C43—81no—
91C2×D4×C43D812yes—
92C22×C4×C43—21no—
93C22×C4×C43—41no—
94C22×C4×C43—41no—
95C22×C4×C43—41no—
96C22×C4×C43—41no—
97C22×C4×C43—41no—
98C22×C4×C43—41no—
99C22×C4×C43C2×D411yescharacteristic
100C22×C4×C43C2×D411yescharacteristic
101C22×C4×C43#4111yescharacteristic
102C22×Dic43—41no—
103D8×C43—48no—
104C2×C8×C43—22no—
105C2×C8×C43—41no—
106C2×C8×C43—41no—
107C4⋊C4×C43—21no—
108C4⋊C4×C43—21no—
109C22⋊C4×C43—41no—
110C22⋊C4×C43—41no—
111C42×C43C2×D411yescharacteristic
112C42×C43C2×D411yescharacteristic
113C42×C43#4111yescharacteristic
114C42×C43#4111yescharacteristic
115C4⋊Dic43—41no—
116C4⋊Dic43—41no—
117C4⋊Dic43—41no—
118C4⋊Dic43—41no—
119C4⋊Dic43—81no—
120C2×C43⋊C8—21no—
121C2×C43⋊C8—21no—
122C2×C43⋊C8—21no—
123C2×C43⋊C8—21no—
124C2×C43⋊C8—21no—
125C2×C43⋊C8—41no—
126C2×C43⋊C8—41no—
127C2×C43⋊C8—41no—
128C2×C43⋊C8—41no—
129C2×C43⋊C8—41no—
130C2×C43⋊C8—41no—
131C2×C43⋊C8D812yescomplemented
132C23×C43—22no—
133C23×C43—41no—
134C23×C43—41no—
135C23×C43—41no—
136C23×C43—41no—
137C23×C43—41no—
138C23×C43—41no—
139C23×C43—42no—
140C23×C43—81no—
141C23×C43—81no—
142C23×C43—81no—
143C23×C43—81no—
144C23×C43—81no—
145C23×C43—81no—
146C23×C43#12111yescharacteristic
147D4×C43—22no—
148D4×C43—22no—
149D4×C43—42no—
150D4×C43—41no—
151D4×C43—42no—
152D4×C43—42no—
153D4×C43—42no—
154D4×C43—41no—
155D4×C43—82no—
156D4×C43—82no—
157D4×C43—81no—
158D4×C43—81no—
159D4×C43—81no—
160D4×C43—81no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—41no—
164C2×C4×C43—41no—
165C2×C4×C43—41no—
166C2×C4×C43—81no—
167C2×C4×C43—81no—
168C2×C4×C43—81no—
169C2×C4×C43—81no—
170C2×C4×C43#12011yescharacteristic
171C2×C4×C43#12111yescharacteristic
172C2×C4×C43#12111yescharacteristic
173C2×C4×C43#12311yescharacteristic
174C2×C4×C43#12311yescharacteristic
175C2×C4×C43#12411yescharacteristic
176C2×C4×C43C2×D811yescharacteristic
177C2×C4×C43C2×D811yescharacteristic
178C2×C4×C43#13511yescharacteristic
179C2×C4×C43#13511yescharacteristic
180C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
181C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
182C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
183C2×C4×C43#13711yescharacteristic
184C2×Dic43—81no—
185C2×Dic43—81no—
186C2×Dic43—81no—
187C8×C43—42no—
188C43⋊C8—22no—
189C43⋊C8—41no—
190C43⋊C8—81no—
191C43⋊C8—81no—
192#10472—431nomaximal, Sylow
193C22×C43—42no—
194C22×C43—42no—
195C22×C43—42no—
196C22×C43—81no—
197C22×C43—81no—
198C22×C43—81no—
199C22×C43—81no—
200C22×C43—82no—
201C22×C43—82no—
202C22×C43—82no—
203C22×C43—161no—
204C22×C43—161no—
205C22×C43—161no—
206C22×C43—161no—
207C22×C43#39411yescharacteristic
208C22×C43#45911yescharacteristic
209C22×C43#46311yescharacteristic
210C22×C43#46611yescharacteristic
211C22×C43#46811yescharacteristic
212C22×C43#47111yescharacteristic
213C22×C43#47211yescharacteristic
214C4×C43—21no—
215C4×C43—21no—
216C4×C43—81no—
217C4×C43#44711yescharacteristic
218C4×C43#45211yescharacteristic
219C4×C43#45911yescharacteristic
220C4×C43#46311yescharacteristic
221C4×C43#46611yescharacteristic
222C4×C43#46911yescharacteristic
223C4×C43#48011yescharacteristic
224C4×C43#48211yescharacteristic
225Dic43—161no—
226C2×#459D4311yescharacteristic
227#1957—431no—
228#1954—431no—
229#1802—431no—
230C2×#335—431no—
231C2×#331—431no—
232#1296—431no—
233C2×C43—82no—
234C2×C43—162no—
235C2×C43#166711yescharacteristic
236C2×C43#168111yescharacteristic
237C2×C43#168511yescharacteristic
238C2×C43#169711yescharacteristic
239C2×C43#203311yescharacteristic
240C2×C43#205111yescharacteristic
241C2×C43#205411yescharacteristic
242C22×D8—21no—
243C2×#127C2×D4311yescharacteristic
244C2×C4×D4C2×D4311yescharacteristic
245#459—22no—
246#459—22no—
247C2×C4⋊C8—431no—
248C2×C4⋊C8—431no—
249C2×C4⋊C8C2×D4311yescharacteristic
250C2×#102—21no—
251C2×#102—861no—
252C2×#102—861no—
253C2×#102—861no—
254C2×C22⋊C8—861no—
255C2×C22⋊C8—861no—
256C2×C4×C8—431no—
257#384—431no—
258#340—861no—
259#335—862no—
260#331—862no—
261C43#1047211yescharacteristic, complemented, Sylow
262C22×D4—21no—
263C22×D4—21no—
264C22×D4—21no—
265C22×D4C22⋊D4311yescharacteristic
266C23×C4—21no—
267C2×D8—24no—
268C2×D8—42no—
269C2×D8—42no—
270C22×C8—21no—
271C22×C8—431no—
272C22×C8—431no—
273C22×C8—861no—
274C22×C8—861no—
275#127—21no—
276#127—21no—
277#127—21no—
278#127C22⋊D4312yes—
279C4×D4—21no—
280C4×D4—21no—
281C4×D4—21no—
282C4×D4—21no—
283C2×C4⋊C4—861no—
284C2×C4⋊C4—861no—
285C2×C4⋊C4—861no—
286C2×C4⋊C4C22⋊D4311yescharacteristic
287C2×C22⋊C4—21no—
288C2×C42C22×D4311yescharacteristic
289C4⋊C8—21no—
290C4⋊C8—861no—
291C4⋊C8—861no—
292C4⋊C8—861no—
293C4⋊C8—861no—
294C4⋊C8C22⋊D4312yes—
295#102—24no—
296#102—1722no—
297#102—1722no—
298#102—1722no—
299C22⋊C8—1722no—
300C22⋊C8—1722no—
301C4×C8—861no—
302C4×C8—861no—
303C24—21no—
304C24—41no—
305C2×D4—21no—
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—21no—
309C2×D4—22no—
310C2×D4—21no—
311C2×D4—21no—
312C2×D4—21no—
313C2×D4—41no—
314C2×D4—41no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—81no—
325C2×D4—81no—
326C2×D4#1062188212yes—
327C22×C4—21no—
328C22×C4—41no—
329C22×C4—41no—
330C22×C4—41no—
331C22×C4—41no—
332C22×C4—41no—
333C22×C4—41no—
334C22×C4—1721no—
335C22×C4D4×D4311yescharacteristic
336C22×C4#1062190011yescharacteristic
337C22×C4C2×C22⋊D4311yescharacteristic
338D8—48no—
339C2×C8—22no—
340C2×C8—41no—
341C2×C8—41no—
342C2×C8—432no—
343C2×C8—861no—
344C2×C8—861no—
345C2×C8—861no—
346C2×C8—861no—
347C2×C8—861no—
348C2×C8—1721no—
349C2×C8—1721no—
350C2×C8—1721no—
351C2×C8—1721no—
352C2×C8—1721no—
353C2×C8—1721no—
354C4⋊C4—21no—
355C4⋊C4—21no—
356C4⋊C4—3441no—
357C4⋊C4—1721no—
358C4⋊C4—1721no—
359C4⋊C4—1721no—
360C4⋊C4—1721no—
361C22⋊C4—41no—
362C22⋊C4—41no—
363C42#1062190011yescharacteristic
364C42#1062190011yescharacteristic
365C42C2×C22⋊D4311yescharacteristic
366C42C2×C22⋊D4311yescharacteristic
367C23—22no—
368C23—41no—
369C23—41no—
370C23—41no—
371C23—41no—
372C23—41no—
373C23—41no—
374C23—42no—
375C23—81no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23#1306329711yescharacteristic
382D4—22no—
383D4—22no—
384D4—41no—
385D4—42no—
386D4—42no—
387D4—42no—
388D4—41no—
389D4—42no—
390D4—82no—
391D4—82no—
392D4—81no—
393D4—81no—
394D4—81no—
395D4—81no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—41no—
399C2×C4—41no—
400C2×C4—41no—
401C2×C4—81no—
402C2×C4—81no—
403C2×C4—81no—
404C2×C4—81no—
405C2×C4—3441no—
406C2×C4—3441no—
407C2×C4—3441no—
408C2×C4#1306329411yescharacteristic
409C2×C4#1306329611yescharacteristic
410C2×C4#1306329711yescharacteristic
411C2×C4#1306330611yescharacteristic
412C2×C4#1306330611yescharacteristic
413C2×C4#1306331211yescharacteristic
414C2×C4D8×D4311yescharacteristic
415C2×C4C2×#1062188211yescharacteristic
416C2×C4#1306334411yescharacteristic
417C2×C4#1306334511yescharacteristic
418C2×C4#1306334911yescharacteristic
419C2×C4#1306334911yescharacteristic
420C2×C4#1306335111yescharacteristic
421C2×C4#1306335511yescharacteristic
422C8—42no—
423C8—862no—
424C8—3441no—
425C8—3441no—
426C8—1721no—
427C22—42no—
428C22—42no—
429C22—42no—
430C22—81no—
431C22—81no—
432C22—81no—
433C22—81no—
434C22—82no—
435C22—82no—
436C22—82no—
437C22—161no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22#1458281311yescharacteristic
442C22#1458309211yescharacteristic
443C22#1458311211yescharacteristic
444C22#1458313311yescharacteristic
445C22#1458314311yescharacteristic
446C22#1458316011yescharacteristic
447C22#1458316711yescharacteristic
448C4—21no—
449C4—21no—
450C4—81no—
451C4—6881no—
452C4#1458303311yescharacteristic
453C4#1458306111yescharacteristic
454C4#1458309211yescharacteristic
455C4#1458311211yescharacteristic
456C4#1458313211yescharacteristic
457C4#1458314911yescharacteristic
458C4#1458321011yescharacteristic
459C4#1458322011yescharacteristic
460C2—82no—
461C2—162no—
462C2#1913394811yescharacteristic
463C2#1913403011yescharacteristic
464C2#1913405811yescharacteristic
465C2#1913412611yescharacteristic
466C2#1913577411yescharacteristic
467C2#1913588411yescharacteristic
468C2#1913590311yescharacteristic
subgroupG/H
centerC23#13063297
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC2×C43×#459C2
socleC23×C43#121
hypercenterC2×#459D43
hypocenterC43#10472
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. #19135402C2semidirect
2. #19135390C2semidirect
3. #19134595C2semidirect
4. C2×#14582651C2semidirect
5. C2×#14582643C2semidirect
6. #19132479C2semidirect
131. C2×C43⋊C8D8semidirect
261. C43#10472semidirect

Maximal subgroups

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

subgroupindex
#191354022
#191353902
#191345952
C2×#145826512
C2×#145826432
#191324792
C2×C43×#4592
#1047243