Finite Group Databasebeta

← #24992918

Subgroups — #24992918

Order 11008.

712 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583044C211yesmaximal, characteristic
2#19134539C211yesmaximal, characteristic, complemented
3#19133112C211yesmaximal, characteristic, complemented
4#19132954C211yesmaximal, characteristic, complemented
5#19132471C211yesmaximal, characteristic, complemented
6#19132441C211yesmaximal, characteristic, complemented
7C43×#2880C211yesmaximal, characteristic, complemented
8C22×#10621884C411yescharacteristic, complemented
9C22×#10621882C411yescharacteristic, complemented
10C2×#13063299C2211yescharacteristic
11#14583044—21no—
12#14583044—21no—
13#14583044—21no—
14#14583044—21no—
15C2×#13063252—21no—
16C2×#13063252—21no—
17C2×#13063249C411yescharacteristic, complemented
18C2×#13063246C411yescharacteristic, complemented
19#14582863C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21C4×C22⋊Dic43C2211yescharacteristic
22#14582634—22no—
23#14582622—21no—
24#14582622—21no—
25C22×#41×C43C2211yescharacteristic
26C2×#131×C43—21no—
27C43×#408—21no—
28C43×#408—22no—
29C43×#407—21no—
30C43×#407C2211yescharacteristic
31C2×C22⋊C8×C43—21no—
32C2×C22⋊C8×C43C2211yescharacteristic
33C22×D172C2×C411yescharacteristic
34C22×C22⋊D43—21no—
35C2×#10621884—21no—
36C2×#10621884—21no—
37C2×#10621884—42no—
38C2×#10621882—21no—
39C2×#10621882—21no—
40C2×#10621882—42no—
41C2×#10621877—21no—
42C22×C43⋊C8C2×C411yescharacteristic
43C22×C43⋊C8C2×C411yescharacteristic
44#13063299—21no—
45#13063299—21no—
46#13063299—21no—
47#13063299—21no—
48C2×C4⋊Dic43C2×C411yescharacteristic
49C2×C22⋊Dic43—21no—
50C2×(C2×D43)⋊C4—21no—
51C2×C4×Dic43—21no—
52#13063252—42no—
53#13063252—42no—
54#13063249—21no—
55#13063249—21no—
56#13063246—21no—
57#13063246—21no—
58C22⋊(C43⋊C8)—21no—
59C22⋊(C43⋊C8)—21no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62C43⋊#95—21no—
63C2×#41×C43—21no—
64C2×#41×C43—21no—
65C2×#41×C43—42no—
66C2×#41×C43—42no—
67C2×#41×C43D411yescharacteristic
68C2×#41×C43D411yescharacteristic
69C2×#41×C43D411yescharacteristic
70C2×#41×C43D411yescharacteristic
71C22×Q8×C43C2×C411yescharacteristic
72C22×D4×C43—21no—
73C22×D4×C43C2×C411yescharacteristic
74C23×C4×C43—21no—
75C23×C4×C43C2311yescharacteristic
76#131×C43—42no—
77#131×C43—42no—
78C2×M16×C43—22no—
79C2×M16×C43—21no—
80C22×C8×C43—22no—
81C22×C8×C43—21no—
82C22⋊C8×C43—22no—
83C22⋊C8×C43—22no—
84C22⋊C8×C43—21no—
85C22⋊C8×C43—21no—
86C22⋊C8×C43D411yescharacteristic
87C22⋊C8×C43D411yescharacteristic
88C22⋊C8×C43D412yes—
89C24×C43—21no—
90C24×C43#4111yescharacteristic
91C23×D43—21no—
92#41×C43—22no—
93#41×C43—22no—
94#41×C43—22no—
95#41×C43—22no—
96#41×C43—41no—
97#41×C43—41no—
98#41×C43—41no—
99#41×C43—41no—
100#41×C43—44no—
101#41×C43—44no—
102C2×Q8×C43—21no—
103C2×Q8×C43—22no—
104C2×Q8×C43—41no—
105C2×Q8×C43C22⋊C411yescharacteristic
106C2×Q8×C43C22⋊C411yescharacteristic
107C2×D4×C43—21no—
108C2×D4×C43—21no—
109C2×D4×C43—21no—
110C2×D4×C43—21no—
111C2×D4×C43—21no—
112C2×D4×C43—22no—
113C2×D4×C43—41no—
114C2×D4×C43—44no—
115C2×D4×C43C22⋊C411yescharacteristic
116C2×D4×C43C22⋊C411yescharacteristic
117C22×C4×C43—21no—
118C22×C4×C43—21no—
119C22×C4×C43—21no—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—41no—
123C22×C4×C43—41no—
124C22×C4×C43—44no—
125C22×C4×C43C22×C411yescharacteristic
126C22×C4×C43C2×D411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43#4111yescharacteristic
131C2×C22⋊D43—41no—
132C2×C22⋊D43—41no—
133C2×C22⋊D43—82no—
134C22×Dic43—21no—
135C22×Dic43—41no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—41no—
139C2×D172—41no—
140M16×C43—44no—
141M16×C43—41no—
142M16×C43—41no—
143C2×C8×C43—21no—
144C2×C8×C43—22no—
145C2×C8×C43—21no—
146C2×C8×C43—44no—
147C2×C8×C43—41no—
148C2×C8×C43—41no—
149C22⋊Dic43—22no—
150C22⋊Dic43—41no—
151#10621884—42no—
152#10621884—42no—
153#10621882—42no—
154#10621882—42no—
155(C2×D43)⋊C4—41no—
156(C2×D43)⋊C4—41no—
157C4⋊Dic43—21no—
158C4⋊Dic43—21no—
159C4×Dic43—41no—
160C4×Dic43—41no—
161#10621877—41no—
162#10621877—41no—
163C2×C43⋊C8—21no—
164C2×C43⋊C8—21no—
165C2×C43⋊C8—41no—
166C2×C43⋊C8—41no—
167C2×C43⋊C8—41no—
168C23×C43—21no—
169C23×C43—21no—
170C23×C43—21no—
171C23×C43—21no—
172C23×C43—41no—
173C23×C43—41no—
174C23×C43—42no—
175C23×C43—41no—
176C23×C43—41no—
177C23×C43—81no—
178C23×C43C4×D411yescharacteristic
179C23×C43#12111yescharacteristic
180C23×C43#12311yescharacteristic
181C22×D43—41no—
182C22×D43—41no—
183C22×D43—41no—
184C22×D43—81no—
185C22×D43—81no—
186Q8×C43—21no—
187Q8×C43—21no—
188Q8×C43—21no—
189Q8×C43—42no—
190Q8×C43#9912yes—
191D4×C43—24no—
192D4×C43—21no—
193D4×C43—21no—
194D4×C43—21no—
195D4×C43—42no—
196D4×C43—42no—
197D4×C43—42no—
198D4×C43—42no—
199D4×C43#9912yes—
200C2×C4×C43—24no—
201C2×C4×C43—21no—
202C2×C4×C43—21no—
203C2×C4×C43—21no—
204C2×C4×C43—21no—
205C2×C4×C43—21no—
206C2×C4×C43—21no—
207C2×C4×C43—21no—
208C2×C4×C43—21no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—41no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43C2×C22⋊C411yescharacteristic
217C2×C4×C43C4×D411yescharacteristic
218C2×C4×C43#12011yescharacteristic
219C2×C4×C43#12111yescharacteristic
220C22⋊D43—82no—
221C22⋊D43—82no—
222C2×Dic43—42no—
223C2×Dic43—41no—
224C2×Dic43—81no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227D172—41no—
228D172—41no—
229D172—81no—
230C8×C43—41no—
231C8×C43—42no—
232C8×C43—41no—
233C43⋊C8—41no—
234C43⋊C8—41no—
235C43⋊C8—81no—
236#9241—431nomaximal, Sylow
237C22×C43—21no—
238C22×C43—21no—
239C22×C43—21no—
240C22×C43—21no—
241C22×C43—22no—
242C22×C43—21no—
243C22×C43—21no—
244C22×C43—21no—
245C22×C43—21no—
246C22×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—81no—
252C22×C43—81no—
253C22×C43—82no—
254C22×C43—82no—
255C22×C43#38611yescharacteristic
256C22×C43#44311yescharacteristic
257C22×C43#44411yescharacteristic
258C2×D43—81no—
259C2×D43—81no—
260C2×D43—81no—
261C2×D43—161no—
262C2×D43—161no—
263C4×C43—21no—
264C4×C43—21no—
265C4×C43—21no—
266C4×C43—22no—
267C4×C43—41no—
268C4×C43C2×#9911yescharacteristic
269C4×C43C2×#9911yescharacteristic
270Dic43—82no—
271Dic43—81no—
272C2×#449—431no—
273#2880D4311yescharacteristic, complemented
274#1789—431no—
275#1507—431no—
276#1471—431no—
277#1293—431no—
278#1282—431no—
279C2×C43—21no—
280C2×C43—21no—
281C2×C43—41no—
282C2×C43—41no—
283C2×C43—42no—
284C2×C43—81no—
285C2×C43#187611yescharacteristic
286C2×C43#189811yescharacteristic
287C2×C43#190311yescharacteristic
288D43—161no—
289C22×#41C2×D4311yescharacteristic
290C22×SD16—431no—
291C22×D8—431no—
292C2×#131—21no—
293C2×#121—431no—
294#449—861no—
295#449—861no—
296#449—861no—
297#449—861no—
298C2×#104—861no—
299C2×#104—861no—
300C2×#103—431no—
301C2×#102—431no—
302#408—21no—
303#408—22no—
304#407—21no—
305#407—431no—
306#407C2×D4311yescharacteristic
307C2×C22⋊C8—21no—
308C2×C22⋊C8—431no—
309C2×C22⋊C8C2×D4311yescharacteristic
310C4×C22⋊C4—431no—
311#327—862no—
312#323—861no—
313#323—861no—
314C43#924111yescharacteristic, complemented, Sylow
315C2×#41—21no—
316C2×#41—21no—
317C2×#41—42no—
318C2×#41—42no—
319C2×#41D17211yescharacteristic
320C2×#41D17211yescharacteristic
321C2×#41C22⋊D4311yescharacteristic
322C2×#41C22⋊D4311yescharacteristic
323C22×Q8C4×D4311yescharacteristic
324C22×D4—21no—
325C22×D4—431no—
326C22×D4—861no—
327C22×D4C4×D4311yescharacteristic
328C23×C4—21no—
329C23×C4C22×D4311yescharacteristic
330C2×SD16—861no—
331C2×SD16—861no—
332C2×SD16—1722no—
333C2×D8—861no—
334C2×D8—861no—
335C2×D8—1722no—
336#131—42no—
337#131—42no—
338C2×M16—22no—
339C2×M16—21no—
340C2×M16—861no—
341C22×C8—22no—
342C22×C8—21no—
343C22×C8—431no—
344C22×C8—431no—
345#121—861no—
346#121—861no—
347#121—861no—
348#121—861no—
349C2×C4⋊C4—431no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C42—861no—
353#104—1722no—
354#104—1722no—
355#103—861no—
356#103—861no—
357#102—861no—
358#102—861no—
359C22⋊C8—22no—
360C22⋊C8—22no—
361C22⋊C8—21no—
362C22⋊C8—21no—
363C22⋊C8—861no—
364C22⋊C8—861no—
365C22⋊C8—861no—
366C22⋊C8—861no—
367C22⋊C8C22⋊D4311yescharacteristic
368C22⋊C8C22⋊D4311yescharacteristic
369C22⋊C8C22⋊D4312yes—
370#95—861no—
371C24—21no—
372C24—861no—
373C24#1062189811yescharacteristic
374#41—22no—
375#41—22no—
376#41—22no—
377#41—22no—
378#41—41no—
379#41—41no—
380#41—41no—
381#41—41no—
382#41—44no—
383#41—44no—
384C2×Q8—21no—
385C2×Q8—22no—
386C2×Q8—41no—
387C2×Q8(C2×D43)⋊C411yescharacteristic
388C2×Q8(C2×D43)⋊C411yescharacteristic
389C2×D4—21no—
390C2×D4—22no—
391C2×D4—21no—
392C2×D4—21no—
393C2×D4—21no—
394C2×D4—21no—
395C2×D4—41no—
396C2×D4—44no—
397C2×D4—861no—
398C2×D4—861no—
399C2×D4—3442no—
400C2×D4—1721no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C2×D4(C2×D43)⋊C411yescharacteristic
405C2×D4(C2×D43)⋊C411yescharacteristic
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—41no—
412C22×C4—41no—
413C22×C4—44no—
414C22×C4—861no—
415C22×C4—1721no—
416C22×C4C2×C4×D4311yescharacteristic
417C22×C4C2×D17211yescharacteristic
418C22×C4#1062189811yescharacteristic
419C22×C4C2×C22⋊D4311yescharacteristic
420C22×C4C2×C22⋊D4311yescharacteristic
421C22×C4C2×C22⋊D4311yescharacteristic
422SD16—1722no—
423SD16—1722no—
424D8—1722no—
425D8—1722no—
426M16—44no—
427M16—41no—
428M16—41no—
429M16—1721no—
430M16—1721no—
431C2×C8—21no—
432C2×C8—22no—
433C2×C8—21no—
434C2×C8—44no—
435C2×C8—41no—
436C2×C8—41no—
437C2×C8—861no—
438C2×C8—861no—
439C2×C8—1721no—
440C2×C8—1721no—
441C2×C8—1721no—
442C4⋊C4—861no—
443C4⋊C4—861no—
444C22⋊C4—862no—
445C22⋊C4—1721no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C42—1721no—
449C42—1721no—
450C23—21no—
451C23—21no—
452C23—21no—
453C23—21no—
454C23—41no—
455C23—41no—
456C23—42no—
457C23—41no—
458C23—41no—
459C23—81no—
460C23—3441no—
461C23—3441no—
462C23—1721no—
463C23—1721no—
464C23—1721no—
465C23C4×C22⋊D4311yescharacteristic
466C23#1306329911yescharacteristic
467C23#1306330811yescharacteristic
468Q8—21no—
469Q8—21no—
470Q8—21no—
471Q8—42no—
472Q8#1306323912yes—
473D4—24no—
474D4—21no—
475D4—21no—
476D4—21no—
477D4—42no—
478D4—42no—
479D4—42no—
480D4—42no—
481D4—3441no—
482D4—3442no—
483D4—3442no—
484D4—1721no—
485D4—1721no—
486D4#1306323912yes—
487C2×C4—24no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—21no—
493C2×C4—21no—
494C2×C4—21no—
495C2×C4—21no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—42no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—3441no—
504C2×C4—3441no—
505C2×C4—3441no—
506C2×C4—1722no—
507C2×C4—1721no—
508C2×C4C2×(C2×D43)⋊C411yescharacteristic
509C2×C4C4×C22⋊D4311yescharacteristic
510C2×C4#1306329411yescharacteristic
511C2×C4#1306329911yescharacteristic
512C8—41no—
513C8—42no—
514C8—41no—
515C8—3441no—
516C8—1721no—
517C8—1721no—
518C22—21no—
519C22—21no—
520C22—21no—
521C22—21no—
522C22—22no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—21no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—81no—
533C22—81no—
534C22—82no—
535C22—82no—
536C22—3441no—
537C22—3441no—
538C22—3441no—
539C22—6881no—
540C22—6881no—
541C22#1458277811yescharacteristic
542C22#1458301411yescharacteristic
543C22#1458301911yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—3442no—
550C4—3441no—
551C4C2×#1306323911yescharacteristic
552C4C2×#1306323911yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—6881no—
560C2#1913492211yescharacteristic
561C2#1913504811yescharacteristic
562C2#1913507511yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#2880C2
socleC22×C43#386
prime radicalC2×#14583044C2
cosocleC23×C4×C43C23
hypercenter#2880D43
hypocenterC43#9241
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. #19134539C2semidirect
3. #19133112C2semidirect
4. #19132954C2semidirect
5. #19132471C2semidirect
6. #19132441C2semidirect
7. C43×#2880C2semidirect
8. C22×#10621884C4semidirect
9. C22×#10621882C4semidirect
17. C2×#13063249C4semidirect
18. C2×#13063246C4semidirect
273. #2880D43semidirect
314. C43#9241semidirect

Maximal subgroups

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

subgroupindex
C2×#145830442
#191345392
#191331122
#191329542
#191324712
#191324412
C43×#28802
#924143