Finite Group Databasebeta

← #24992173

Subgroups — #24992173

Order 11008.

952 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582863C211yesmaximal, characteristic
2C2×#14582636C212yesmaximal, complemented
3#19132818C211yesmaximal, characteristic
4#19132473C212yesmaximal, complemented
5C43×#2848C211yesmaximal, characteristic
6C22×#10621877—21no—
7C22×C22⋊Dic43—21no—
8#14582863—24no—
9C2×C22⋊(C43⋊C8)—21no—
10C2×C22⋊(C43⋊C8)C2212yes—
11C2×C43⋊#95—21no—
12C2×C43⋊#95C2212yes—
13#14582636—24no—
14C24×C4×C43C2211yescharacteristic
15C2×C22⋊Q8×C43C411yescharacteristic, complemented
16C2×C22⋊Q8×C43C411yescharacteristic, complemented
17C2×C22⋊Q8×C43C2211yescharacteristic
18C43×#385—21no—
19C43×#385—21no—
20C43×#385—21no—
21C43×#380C411yescharacteristic, complemented
22C43×#380C411yescharacteristic, complemented
23C43×#380C2211yescharacteristic
24C43×#379—21no—
25C23×Dic43—22no—
26C2×#10621877—24no—
27C2×#10621877—42no—
28C2×#10621877—42no—
29C22×C43⋊C8—22no—
30C2×C22⋊Dic43—24no—
31C2×C22⋊Dic43—42no—
32C2×C22⋊Dic43—42no—
33C22⋊(C43⋊C8)—24no—
34C22⋊(C43⋊C8)—22no—
35C22⋊(C43⋊C8)D414yes—
36C43⋊#95—22no—
37C43⋊#95—22no—
38C43⋊#95—42no—
39C25×C43D411yescharacteristic
40C22×Q8×C43C2×C411yescharacteristic
41C23×C4×C43—22no—
42C23×C4×C43—22no—
43C23×C4×C43—42no—
44C23×C4×C43—42no—
45C23×C4×C43C2×C411yescharacteristic
46C23×C4×C43C2×C411yescharacteristic
47C23×C4×C43D411yescharacteristic
48C23×C4×C43D411yescharacteristic
49C23×C4×C43D411yescharacteristic
50C23×C4×C43C2311yescharacteristic
51C22⋊Q8×C43—22no—
52C22⋊Q8×C43—22no—
53C22⋊Q8×C43—42no—
54C22⋊Q8×C43—42no—
55C2×C4⋊C4×C43—21no—
56C2×C4⋊C4×C43—21no—
57C2×C4⋊C4×C43—21no—
58C2×C4⋊C4×C43C2×C411yescharacteristic
59C2×C4⋊C4×C43C2×C411yescharacteristic
60C2×C4⋊C4×C43C2×C411yescharacteristic
61C2×C22⋊C4×C43—21no—
62C2×C22⋊C4×C43—21no—
63C2×C22⋊C4×C43—21no—
64C2×C22⋊C4×C43—21no—
65C2×C22⋊C4×C43—21no—
66C2×C22⋊C4×C43—21no—
67#95×C43—21no—
68#95×C43—21no—
69#95×C43—21no—
70C24×C43—22no—
71C24×C43—22no—
72C24×C43—21no—
73C24×C43—21no—
74C24×C43—22no—
75C24×C43—22no—
76C24×C43—41no—
77C24×C43—41no—
78C24×C43C22⋊C411yescharacteristic
79C24×C43C22⋊C411yescharacteristic
80C24×C43C2×D411yescharacteristic
81C2×Q8×C43—22no—
82C2×Q8×C43—41no—
83C2×Q8×C43—41no—
84C22×C4×C43—22no—
85C22×C4×C43—21no—
86C22×C4×C43—21no—
87C22×C4×C43—22no—
88C22×C4×C43—22no—
89C22×C4×C43—22no—
90C22×C4×C43—22no—
91C22×C4×C43—21no—
92C22×C4×C43—21no—
93C22×C4×C43—22no—
94C22×C4×C43—22no—
95C22×C4×C43—21no—
96C22×C4×C43—21no—
97C22×C4×C43—21no—
98C22×C4×C43—21no—
99C22×C4×C43—22no—
100C22×C4×C43—41no—
101C22×C4×C43—41no—
102C22×C4×C43—41no—
103C22×C4×C43—41no—
104C22×C4×C43—41no—
105C22×C4×C43—41no—
106C22×C4×C43—41no—
107C22×C4×C43—48no—
108C22×C4×C43—48no—
109C22×C4×C43C22⋊C411yescharacteristic
110C22×C4×C43C22⋊C411yescharacteristic
111C22×C4×C43C22×C411yescharacteristic
112C22×C4×C43C2×D411yescharacteristic
113C22×C4×C43C2×D412yes—
114C22×C4×C43#4112yes—
115C22×Dic43—24no—
116C22×Dic43—42no—
117C22×Dic43—42no—
118C22×Dic43—42no—
119C22×Dic43—42no—
120C22×Dic43—42no—
121C22×Dic43—42no—
122C4⋊C4×C43—22no—
123C4⋊C4×C43—41no—
124C4⋊C4×C43—41no—
125C4⋊C4×C43—42no—
126C4⋊C4×C43—42no—
127C4⋊C4×C43—41no—
128C4⋊C4×C43—41no—
129C22⋊C4×C43—42no—
130C22⋊C4×C43—42no—
131C22⋊C4×C43—42no—
132C22⋊C4×C43—42no—
133C22⋊C4×C43—42no—
134C22⋊C4×C43—41no—
135C22⋊C4×C43—41no—
136C22⋊Dic43—48no—
137#10621877—48no—
138C2×C43⋊C8—24no—
139C2×C43⋊C8—42no—
140C2×C43⋊C8—42no—
141C23×C43—21no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—24no—
146C23×C43—24no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—44no—
160C23×C43—44no—
161C23×C43—44no—
162C23×C43—44no—
163C23×C43—42no—
164C23×C43—42no—
165C23×C43—42no—
166C23×C43—42no—
167C23×C43#9912yes—
168C23×C43#10412yes—
169C23×C43C2×C22⋊C411yescharacteristic
170C23×C43#12112yes—
171C23×C43AGL(1,ℤ/8)11yescharacteristic
172C23×C43#13711yescharacteristic
173C23×C43#13712yes—
174Q8×C43—82no—
175C2×C4×C43—24no—
176C2×C4×C43—24no—
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—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—42no—
187C2×C4×C43—42no—
188C2×C4×C43—44no—
189C2×C4×C43—44no—
190C2×C4×C43—44no—
191C2×C4×C43—42no—
192C2×C4×C43—42no—
193C2×C4×C43—41no—
194C2×C4×C43—41no—
195C2×C4×C43—41no—
196C2×C4×C43—41no—
197C2×C4×C43—41no—
198C2×C4×C43—41no—
199C2×C4×C43—41no—
200C2×C4×C43—41no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43#9912yes—
206C2×C4×C43C4×D412yes—
207C2×C4×C43#12011yescharacteristic
208C2×C4×C43#12311yescharacteristic
209C2×Dic43—44no—
210C2×Dic43—44no—
211C2×Dic43—44no—
212C2×Dic43—82no—
213C2×Dic43—82no—
214C2×Dic43—82no—
215C2×Dic43—82no—
216C43⋊C8—44no—
217#9115—431nomaximal, Sylow
218C22×C43—22no—
219C22×C43—22no—
220C22×C43—21no—
221C22×C43—21no—
222C22×C43—22no—
223C22×C43—22no—
224C22×C43—21no—
225C22×C43—21no—
226C22×C43—22no—
227C22×C43—22no—
228C22×C43—22no—
229C22×C43—22no—
230C22×C43—22no—
231C22×C43—22no—
232C22×C43—48no—
233C22×C43—48no—
234C22×C43—41no—
235C22×C43—41no—
236C22×C43—41no—
237C22×C43—41no—
238C22×C43—41no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43#38611yescharacteristic
243C22×C43C2×#9911yescharacteristic
244C22×C43C2×#9911yescharacteristic
245C22×C43#41711yescharacteristic
246C22×C43#41911yescharacteristic
247C22×C43C2×#10411yescharacteristic
248C22×C43#42111yescharacteristic
249C22×C43#46812yes—
250C22×C43#47012yes—
251C4×C43—21no—
252C4×C43—22no—
253C4×C43—21no—
254C4×C43—22no—
255C4×C43—41no—
256C4×C43—81no—
257C4×C43—81no—
258C4×C43—81no—
259C4×C43—81no—
260Dic43—84no—
261C2×#407—431no—
262#2848D4311yescharacteristic
263C2×#328—432no—
264C22⋊#95—431no—
265#1294—432no—
266C2×C43—22no—
267C2×C43—22no—
268C2×C43—42no—
269C2×C43—42no—
270C2×C43#150411yescharacteristic
271C2×C43#150811yescharacteristic
272C2×C43#151111yescharacteristic
273C2×C43#151311yescharacteristic
274C2×C43#187111yescharacteristic
275C2×C43#189411yescharacteristic
276C2×C43#189811yescharacteristic
277C24×C4C2×D4311yescharacteristic
278C22×M16—861no—
279C2×C22⋊Q8Dic4311yescharacteristic, complemented
280C2×C22⋊Q8Dic4311yescharacteristic, complemented
281C2×C22⋊Q8C2×D4311yescharacteristic
282C22×C22⋊C4—861no—
283#407—864no—
284C2×C22⋊C8—432no—
285C2×C22⋊C8—861no—
286#385—21no—
287#385—21no—
288#385—21no—
289#380Dic4311yescharacteristic, complemented
290#380Dic4311yescharacteristic, complemented
291#380C2×D4311yescharacteristic
292#379—21no—
293C2×#95—432no—
294C2×#95—861no—
295#328—864no—
296C43#911511yescharacteristic, complemented, Sylow
297C25C22⋊D4311yescharacteristic
298C22×Q8C2×Dic4311yescharacteristic
299C23×C4—22no—
300C23×C4—22no—
301C23×C4—42no—
302C23×C4—42no—
303C23×C4—862no—
304C23×C4C2×Dic4311yescharacteristic
305C23×C4C2×Dic4311yescharacteristic
306C23×C4C22⋊D4311yescharacteristic
307C23×C4C22⋊D4311yescharacteristic
308C23×C4C22⋊D4311yescharacteristic
309C23×C4C22×D4311yescharacteristic
310C2×M16—864no—
311C2×M16—1722no—
312C2×M16—1722no—
313C22×C8—862no—
314C22⋊Q8—22no—
315C22⋊Q8—22no—
316C22⋊Q8—42no—
317C22⋊Q8—42no—
318C2×C4⋊C4—21no—
319C2×C4⋊C4—21no—
320C2×C4⋊C4—21no—
321C2×C4⋊C4C2×Dic4311yescharacteristic
322C2×C4⋊C4C2×Dic4311yescharacteristic
323C2×C4⋊C4C2×Dic4311yescharacteristic
324C2×C22⋊C4—21no—
325C2×C22⋊C4—21no—
326C2×C22⋊C4—21no—
327C2×C22⋊C4—21no—
328C2×C22⋊C4—21no—
329C2×C22⋊C4—21no—
330C2×C22⋊C4—864no—
331C2×C22⋊C4—1722no—
332C2×C22⋊C4—1722no—
333C22⋊C8—434no—
334C22⋊C8—864no—
335C22⋊C8—862no—
336#95—21no—
337#95—21no—
338#95—21no—
339#95—862no—
340#95—862no—
341#95—1722no—
342C24—22no—
343C24—22no—
344C24—21no—
345C24—21no—
346C24—22no—
347C24—22no—
348C24—41no—
349C24—41no—
350C24C22⋊Dic4311yescharacteristic
351C24C22⋊Dic4311yescharacteristic
352C24C2×C22⋊D4311yescharacteristic
353C2×Q8—22no—
354C2×Q8—41no—
355C2×Q8—41no—
356C22×C4—22no—
357C22×C4—22no—
358C22×C4—21no—
359C22×C4—21no—
360C22×C4—22no—
361C22×C4—22no—
362C22×C4—22no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—22no—
366C22×C4—21no—
367C22×C4—21no—
368C22×C4—21no—
369C22×C4—21no—
370C22×C4—21no—
371C22×C4—21no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—41no—
375C22×C4—41no—
376C22×C4—41no—
377C22×C4—41no—
378C22×C4—41no—
379C22×C4—48no—
380C22×C4—48no—
381C22×C4—864no—
382C22×C4—1722no—
383C22×C4—1722no—
384C22×C4—1722no—
385C22×C4—1722no—
386C22×C4—1722no—
387C22×C4—1722no—
388C22×C4C22⋊Dic4311yescharacteristic
389C22×C4C22⋊Dic4311yescharacteristic
390C22×C4D4×D4312yes—
391C22×C4#1062190012yes—
392C22×C4C22×Dic4311yescharacteristic
393C22×C4C2×C22⋊D4311yescharacteristic
394M16—1728no—
395C2×C8—864no—
396C2×C8—1722no—
397C2×C8—1722no—
398C4⋊C4—22no—
399C4⋊C4—41no—
400C4⋊C4—41no—
401C4⋊C4—42no—
402C4⋊C4—42no—
403C4⋊C4—41no—
404C4⋊C4—41no—
405C22⋊C4—42no—
406C22⋊C4—42no—
407C22⋊C4—42no—
408C22⋊C4—42no—
409C22⋊C4—42no—
410C22⋊C4—41no—
411C22⋊C4—41no—
412C22⋊C4—1728no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—24no—
418C23—24no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—21no—
427C23—21no—
428C23—21no—
429C23—21no—
430C23—21no—
431C23—44no—
432C23—44no—
433C23—44no—
434C23—44no—
435C23—42no—
436C23—42no—
437C23—42no—
438C23—42no—
439C23#1306324012yes—
440C23#1306325212yes—
441C23C2×C22⋊Dic4311yescharacteristic
442C23#1306329712yes—
443C23#1306335011yescharacteristic
444C23#1306335511yescharacteristic
445C23#1306335612yes—
446Q8—82no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—42no—
459C2×C4—42no—
460C2×C4—44no—
461C2×C4—44no—
462C2×C4—44no—
463C2×C4—42no—
464C2×C4—42no—
465C2×C4—41no—
466C2×C4—41no—
467C2×C4—41no—
468C2×C4—41no—
469C2×C4—41no—
470C2×C4—41no—
471C2×C4—41no—
472C2×C4—41no—
473C2×C4—41no—
474C2×C4—41no—
475C2×C4—41no—
476C2×C4—41no—
477C2×C4—3442no—
478C2×C4—3442no—
479C2×C4—3442no—
480C2×C4—3442no—
481C2×C4—1724no—
482C2×C4—1724no—
483C2×C4—1724no—
484C2×C4#1306324012yes—
485C2×C4D4×Dic4312yes—
486C2×C4#1306329311yescharacteristic
487C2×C4#1306330611yescharacteristic
488C8—1724no—
489C22—22no—
490C22—21no—
491C22—21no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—21no—
496C22—21no—
497C22—22no—
498C22—22no—
499C22—22no—
500C22—22no—
501C22—22no—
502C22—22no—
503C22—48no—
504C22—48no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22#1458277911yescharacteristic
514C22C2×#1306324011yescharacteristic
515C22C2×#1306324011yescharacteristic
516C22#1458290011yescharacteristic
517C22#1458290811yescharacteristic
518C22C2×#1306325211yescharacteristic
519C22#1458291611yescharacteristic
520C22#1458314712yes—
521C22#1458315512yes—
522C4—21no—
523C4—22no—
524C4—21no—
525C4—22no—
526C4—41no—
527C4—81no—
528C4—81no—
529C4—81no—
530C4—81no—
531C4—3444no—
532C2—22no—
533C2—22no—
534C2—42no—
535C2—42no—
536C2#1913309911yescharacteristic
537C2#1913311511yescharacteristic
538C2#1913312811yescharacteristic
539C2#1913313811yescharacteristic
540C2#1913489811yescharacteristic
541C2#1913502911yescharacteristic
542C2#1913504911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic43
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2848C2
socleC23×C43C2×C22⋊C4
prime radicalC25×C43D4
cosocleC23×C4×C43C23
hypercenter#2848D43
hypocenterC43#9115
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ #2848

Complements

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

NH ≅ G/Ntype
2. C2×#14582636C2semidirect
4. #19132473C2semidirect
15. C2×C22⋊Q8×C43C4semidirect
16. C2×C22⋊Q8×C43C4semidirect
21. C43×#380C4semidirect
22. C43×#380C4semidirect
279. C2×C22⋊Q8Dic43semidirect
280. C2×C22⋊Q8Dic43semidirect
289. #380Dic43semidirect
290. #380Dic43semidirect
296. C43#9115semidirect

Maximal subgroups

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

subgroupindex
C2×#145828632
C2×#145826362
#191328182
#191324732
C43×#28482
#911543