Finite Group Databasebeta

← #24988047

Subgroups — #24988047

Order 11008.

908 conjugacy classes of subgroups.

The subgroup lattice has 506 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19134663C211yesmaximal, characteristic, complemented
2C2×#14582636C212yesmaximal, complemented
3C2×#14582633C212yesmaximal
4#19132822C211yesmaximal, characteristic, complemented
5C2×C43×#529C211yesmaximal, characteristic
6C2×C22⋊(C43⋊C8)C2212yes—
7C2×C43⋊#95—21no—
8C2×C43⋊#95—21no—
9C2×C43⋊#95C2212yes—
10#14582654—21no—
11#14582654—21no—
12#14582636—24no—
13#14582633—24no—
14C43×#529—24no—
15C43×#529—24no—
16C2×#126×C43—21no—
17C2×#125×C43C411yescharacteristic, complemented
18C2×#124×C43C411yescharacteristic, complemented
19C2×#123×C43—21no—
20C2×C22⋊Q8×C43C2211yescharacteristic
21C2×#121×C43C2211yescharacteristic
22C2×C4×Q8×C43C411yescharacteristic, complemented
23C2×C4×D4×C43—21no—
24C2×C4×D4×C43C411yescharacteristic, complemented
25C2×#117×C43—21no—
26C22×C42×C43C2211yescharacteristic
27C23×Dic43—22no—
28C22×C43⋊C8—22no—
29C22⋊(C43⋊C8)—22no—
30C22⋊(C43⋊C8)—22no—
31C43⋊#95—24no—
32C43⋊#95—22no—
33C43⋊#95—22no—
34C43⋊#95—42no—
35C22×Q8×C43C2×C411yescharacteristic
36C22×D4×C43—21no—
37C22×D4×C43C2×C411yescharacteristic
38C23×C4×C43—21no—
39C23×C4×C43D411yescharacteristic
40C23×C4×C43D411yescharacteristic
41C23×C4×C43C2311yescharacteristic
42#126×C43—28no—
43#125×C43—22no—
44#125×C43—22no—
45#124×C43—22no—
46#124×C43—22no—
47#123×C43—28no—
48C22⋊Q8×C43—22no—
49C22⋊Q8×C43D414yes—
50#121×C43—22no—
51#121×C43D414yes—
52C4×Q8×C43—22no—
53C4×Q8×C43—22no—
54C4×D4×C43—28no—
55C4×D4×C43—22no—
56C4×D4×C43—22no—
57#117×C43—28no—
58C2×C4⋊C4×C43—21no—
59C2×C4⋊C4×C43—21no—
60C2×C4⋊C4×C43—21no—
61C2×C4⋊C4×C43—21no—
62C2×C4⋊C4×C43C2×C411yescharacteristic
63C2×C4⋊C4×C43C2×C411yescharacteristic
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67C2×C22⋊C4×C43—21no—
68C2×C22⋊C4×C43—21no—
69C2×C42×C43—21no—
70C2×C42×C43—22no—
71C2×C42×C43—22no—
72C2×C42×C43C2×C411yescharacteristic
73C2×C42×C43C2×C411yescharacteristic
74C2×C42×C43D411yescharacteristic
75C2×C42×C43D411yescharacteristic
76C24×C43—21no—
77C24×C43C2×D411yescharacteristic
78C2×Q8×C43—21no—
79C2×Q8×C43—41no—
80C2×Q8×C43—41no—
81C2×Q8×C43C22⋊C412yes—
82C2×D4×C43—21no—
83C2×D4×C43—24no—
84C2×D4×C43—42no—
85C2×D4×C43—41no—
86C2×D4×C43—41no—
87C2×D4×C43—41no—
88C2×D4×C43—41no—
89C2×D4×C43C22⋊C412yes—
90C22×C4×C43—24no—
91C22×C4×C43—22no—
92C22×C4×C43—21no—
93C22×C4×C43—21no—
94C22×C4×C43—21no—
95C22×C4×C43—22no—
96C22×C4×C43—22no—
97C22×C4×C43—22no—
98C22×C4×C43—21no—
99C22×C4×C43—21no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
105C22×C4×C43C22⋊C411yescharacteristic
106C22×C4×C43C22⋊C411yescharacteristic
107C22×C4×C43C22⋊C411yescharacteristic
108C22×C4×C43C22⋊C411yescharacteristic
109C22×C4×C43C22×C411yescharacteristic
110C22×C4×C43C2×D411yescharacteristic
111C22×C4×C43C2×D412yes—
112C22×C4×C43C2×D412yes—
113C22×Dic43—24no—
114C22×Dic43—42no—
115C22×Dic43—42no—
116C22×Dic43—42no—
117C22×Dic43—42no—
118C22×Dic43—42no—
119C22×Dic43—42no—
120C4⋊C4×C43—24no—
121C4⋊C4×C43—24no—
122C4⋊C4×C43—24no—
123C4⋊C4×C43—21no—
124C4⋊C4×C43—21no—
125C4⋊C4×C43—24no—
126C4⋊C4×C43C22⋊C412yes—
127C4⋊C4×C43C22⋊C412yes—
128C22⋊C4×C43—24no—
129C22⋊C4×C43—24no—
130C22⋊C4×C43—24no—
131C22⋊C4×C43—24no—
132C22⋊C4×C43—24no—
133C42×C43—24no—
134C42×C43—21no—
135C42×C43—21no—
136C42×C43—21no—
137C42×C43—21no—
138C42×C43—22no—
139C42×C43—22no—
140C2×C43⋊C8—42no—
141C2×C43⋊C8—42no—
142C2×C43⋊C8—42no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—22no—
148C23×C43—41no—
149C23×C43—41no—
150C23×C43—41no—
151C23×C43—41no—
152C23×C43—41no—
153C23×C43—41no—
154C23×C43C2×C22⋊C411yescharacteristic
155C23×C43#12012yes—
156C23×C43#13512yes—
157C23×C43AGL(1,ℤ/8)11yescharacteristic
158C23×C43#13711yescharacteristic
159Q8×C43—42no—
160Q8×C43—42no—
161D4×C43—42no—
162D4×C43—42no—
163D4×C43—44no—
164D4×C43—44no—
165C2×C4×C43—21no—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
173C2×C4×C43—21no—
174C2×C4×C43—22no—
175C2×C4×C43—22no—
176C2×C4×C43—22no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—42no—
184C2×C4×C43—42no—
185C2×C4×C43—44no—
186C2×C4×C43—48no—
187C2×C4×C43—41no—
188C2×C4×C43—41no—
189C2×C4×C43—41no—
190C2×C4×C43—41no—
191C2×C4×C43—41no—
192C2×C4×C43—41no—
193C2×C4×C43—42no—
194C2×C4×C43—42no—
195C2×C4×C43#10412yes—
196C2×C4×C43C2×C22⋊C411yescharacteristic
197C2×C4×C43C2×C22⋊C411yescharacteristic
198C2×C4×C43#12012yes—
199C2×Dic43—44no—
200C2×Dic43—44no—
201C2×Dic43—44no—
202C2×Dic43—82no—
203C2×Dic43—82no—
204C2×Dic43—82no—
205C2×Dic43—82no—
206C43⋊C8—82no—
207#8330—431nomaximal, Sylow
208C22×C43—22no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—22no—
216C22×C43—42no—
217C22×C43—42no—
218C22×C43—42no—
219C22×C43—81no—
220C22×C43—81no—
221C22×C43—81no—
222C22×C43—81no—
223C22×C43#37911yescharacteristic
224C22×C43#41011yescharacteristic
225C22×C43#41011yescharacteristic
226C22×C43#41611yescharacteristic
227C22×C43#41711yescharacteristic
228C22×C43C2×#10411yescharacteristic
229C22×C43#42111yescharacteristic
230C22×C43#44912yes—
231C22×C43#45212yes—
232C4×C43—22no—
233C4×C43—21no—
234C4×C43—21no—
235C4×C43—22no—
236C4×C43—42no—
237C4×C43—41no—
238C4×C43—41no—
239C4×C43—42no—
240C4×C43—41no—
241C4×C43—42no—
242Dic43—84no—
243C2×#529D4311yescharacteristic
244#1817—431no—
245C2×#328—432no—
246C2×#327—432no—
247#1434—431no—
248C2×C43—22no—
249C2×C43—22no—
250C2×C43—82no—
251C2×C43#150011yescharacteristic
252C2×C43#150911yescharacteristic
253C2×C43#151211yescharacteristic
254C2×C43#152111yescharacteristic
255C2×C43#178211yescharacteristic
256C2×C43#178811yescharacteristic
257C2×C43#178911yescharacteristic
258#529—24no—
259#529—24no—
260C2×#126—21no—
261C2×#125Dic4311yescharacteristic, complemented
262C2×#124Dic4311yescharacteristic, complemented
263C2×#123—21no—
264C2×C22⋊Q8C2×D4311yescharacteristic
265C2×#121C2×D4311yescharacteristic
266C2×C4×Q8Dic4311yescharacteristic, complemented
267C2×C4×D4—21no—
268C2×C4×D4Dic4311yescharacteristic, complemented
269C2×#117—21no—
270C22×C42C2×D4311yescharacteristic
271C2×C22⋊C8—432no—
272C2×#95—432no—
273C2×#95—861no—
274C2×#95—861no—
275#336—861no—
276#336—861no—
277#328—864no—
278#327—864no—
279C43#833011yescharacteristic, complemented, Sylow
280C22×Q8C2×Dic4311yescharacteristic
281C22×D4—21no—
282C22×D4C2×Dic4311yescharacteristic
283C23×C4—21no—
284C23×C4—862no—
285C23×C4C22⋊D4311yescharacteristic
286C23×C4C22⋊D4311yescharacteristic
287C23×C4C22×D4311yescharacteristic
288C22×C8—862no—
289#126—28no—
290#125—22no—
291#125—22no—
292#124—22no—
293#124—22no—
294#123—28no—
295C22⋊Q8—22no—
296C22⋊Q8C22⋊D4314yes—
297#121—22no—
298#121C22⋊D4314yes—
299C4×Q8—22no—
300C4×Q8—22no—
301C4×D4—28no—
302C4×D4—22no—
303C4×D4—22no—
304#117—28no—
305C2×C4⋊C4—21no—
306C2×C4⋊C4—21no—
307C2×C4⋊C4—21no—
308C2×C4⋊C4—21no—
309C2×C4⋊C4C2×Dic4311yescharacteristic
310C2×C4⋊C4C2×Dic4311yescharacteristic
311C2×C22⋊C4—21no—
312C2×C22⋊C4—21no—
313C2×C22⋊C4—21no—
314C2×C22⋊C4—21no—
315C2×C22⋊C4—21no—
316C2×C42—21no—
317C2×C42—22no—
318C2×C42—22no—
319C2×C42C2×Dic4311yescharacteristic
320C2×C42C2×Dic4311yescharacteristic
321C2×C42C22⋊D4311yescharacteristic
322C2×C42C22⋊D4311yescharacteristic
323C22⋊C8—862no—
324C22⋊C8—862no—
325#95—864no—
326#95—862no—
327#95—862no—
328#95—1722no—
329C24—21no—
330C24C2×C22⋊D4311yescharacteristic
331C2×Q8—21no—
332C2×Q8—41no—
333C2×Q8—41no—
334C2×Q8C22⋊Dic4312yes—
335C2×D4—24no—
336C2×D4—21no—
337C2×D4—41no—
338C2×D4—41no—
339C2×D4—42no—
340C2×D4—41no—
341C2×D4—41no—
342C2×D4C22⋊Dic4312yes—
343C22×C4—24no—
344C22×C4—21no—
345C22×C4—21no—
346C22×C4—21no—
347C22×C4—22no—
348C22×C4—22no—
349C22×C4—22no—
350C22×C4—21no—
351C22×C4—21no—
352C22×C4—22no—
353C22×C4—41no—
354C22×C4—41no—
355C22×C4—41no—
356C22×C4—42no—
357C22×C4—42no—
358C22×C4—864no—
359C22×C4—1722no—
360C22×C4—1722no—
361C22×C4—1722no—
362C22×C4—1722no—
363C22×C4—1722no—
364C22×C4—1722no—
365C22×C4C22⋊Dic4311yescharacteristic
366C22×C4C22⋊Dic4311yescharacteristic
367C22×C4C22⋊Dic4311yescharacteristic
368C22×C4C22⋊Dic4311yescharacteristic
369C22×C4C22×Dic4311yescharacteristic
370C22×C4C2×C22⋊D4311yescharacteristic
371C22×C4C2×C22⋊D4312yes—
372C22×C4C2×C22⋊D4312yes—
373C2×C8—1722no—
374C2×C8—1722no—
375C2×C8—1722no—
376C4⋊C4—24no—
377C4⋊C4—24no—
378C4⋊C4—24no—
379C4⋊C4—21no—
380C4⋊C4—21no—
381C4⋊C4—24no—
382C4⋊C4C22⋊Dic4312yes—
383C4⋊C4C22⋊Dic4312yes—
384C22⋊C4—24no—
385C22⋊C4—24no—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—24no—
389C42—24no—
390C42—21no—
391C42—21no—
392C42—21no—
393C42—21no—
394C42—22no—
395C42—22no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—22no—
401C23—41no—
402C23—41no—
403C23—41no—
404C23—41no—
405C23—41no—
406C23—41no—
407C23C2×C22⋊Dic4311yescharacteristic
408C23#1306329412yes—
409C23#1306334512yes—
410C23#1306335011yescharacteristic
411C23#1306335511yescharacteristic
412Q8—42no—
413Q8—42no—
414D4—42no—
415D4—42no—
416D4—44no—
417D4—44no—
418C2×C4—21no—
419C2×C4—21no—
420C2×C4—21no—
421C2×C4—21no—
422C2×C4—21no—
423C2×C4—21no—
424C2×C4—21no—
425C2×C4—21no—
426C2×C4—21no—
427C2×C4—21no—
428C2×C4—21no—
429C2×C4—21no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—22no—
436C2×C4—42no—
437C2×C4—42no—
438C2×C4—44no—
439C2×C4—48no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—41no—
443C2×C4—41no—
444C2×C4—41no—
445C2×C4—41no—
446C2×C4—41no—
447C2×C4—41no—
448C2×C4—3442no—
449C2×C4—3442no—
450C2×C4—3442no—
451C2×C4—3442no—
452C2×C4—1724no—
453C2×C4—1724no—
454C2×C4—1724no—
455C2×C4#1306325212yes—
456C2×C4C2×C22⋊Dic4311yescharacteristic
457C2×C4C2×C22⋊Dic4311yescharacteristic
458C2×C4#1306329412yes—
459C8—3442no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—21no—
464C22—21no—
465C22—21no—
466C22—21no—
467C22—22no—
468C22—42no—
469C22—42no—
470C22—42no—
471C22—81no—
472C22—81no—
473C22—81no—
474C22—81no—
475C22#1458275511yescharacteristic
476C22#1458287311yescharacteristic
477C22#1458287311yescharacteristic
478C22#1458289511yescharacteristic
479C22#1458290011yescharacteristic
480C22C2×#1306325211yescharacteristic
481C22#1458291611yescharacteristic
482C22#1458304412yes—
483C22#1458306112yes—
484C4—22no—
485C4—21no—
486C4—21no—
487C4—22no—
488C4—42no—
489C4—41no—
490C4—41no—
491C4—42no—
492C4—41no—
493C4—42no—
494C4—3444no—
495C2—22no—
496C2—22no—
497C2—82no—
498C2#1913308111yescharacteristic
499C2#1913312011yescharacteristic
500C2#1913313311yescharacteristic
501C2#1913317211yescharacteristic
502C2#1913451311yescharacteristic
503C2#1913453511yescharacteristic
504C2#1913453911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC2×C43×#529C2
socleC23×C43C2×C22⋊C4
prime radicalC2×#121×C43C22
cosocleC23×C4×C43C23
hypercenterC2×#529D43
hypocenterC43#8330
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #19134663C2semidirect
2. C2×#14582636C2semidirect
4. #19132822C2semidirect
17. C2×#125×C43C4semidirect
18. C2×#124×C43C4semidirect
22. C2×C4×Q8×C43C4semidirect
24. C2×C4×D4×C43C4semidirect
261. C2×#125Dic43semidirect
262. C2×#124Dic43semidirect
266. C2×C4×Q8Dic43semidirect
268. C2×C4×D4Dic43semidirect
279. C43#8330semidirect

Maximal subgroups

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

subgroupindex
#191346632
C2×#145826362
C2×#145826332
#191328222
C2×C43×#5292
#833043