Finite Group Databasebeta

← #24992916

Subgroups — #24992916

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#19143044C211yesmaximal, characteristic, complemented
3#19133110C211yesmaximal, characteristic, complemented
4#19132956C211yesmaximal, characteristic, complemented
5#19132471C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7C43×#1789C211yesmaximal, characteristic, complemented
8C22×#10621884C411yescharacteristic, complemented
9C22×#10621882C411yescharacteristic, complemented
10C2×#13063332—21no—
11C2×#13063299C2211yescharacteristic
12#14583044—21no—
13#14583044—21no—
14#14583044—21no—
15#14583044—21no—
16C2×#13063249C411yescharacteristic, complemented
17C2×#13063246C411yescharacteristic, complemented
18#14582866—22no—
19#14582866—21no—
20#14582863—21no—
21#14582863C2211yescharacteristic
22C2×C22⋊(C43⋊C8)—21no—
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×C22⋊(C43⋊C8)C2211yescharacteristic
25#14582632—22no—
26#14582622—21no—
27#14582622—21no—
28C22×#41×C43C2211yescharacteristic
29C2×#104×C43—21no—
30C2×#104×C43—21no—
31C43×#407C2211yescharacteristic
32C4×C22⋊C4×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—
41#13063332—42no—
42#13063332—42no—
43C2×#10621877—22no—
44C2×#10621877—21no—
45C22×C43⋊C8—22no—
46C22×C43⋊C8—21no—
47C22×C43⋊C8C2×C411yescharacteristic
48C22×C43⋊C8C2×C411yescharacteristic
49#13063299—21no—
50#13063299—21no—
51#13063299—21no—
52#13063299—21no—
53C2×C4⋊Dic43C2×C411yescharacteristic
54C2×(C2×D43)⋊C4—21no—
55#13063249—21no—
56#13063249—21no—
57#13063246—21no—
58#13063246—21no—
59C22⋊(C43⋊C8)—22no—
60C22⋊(C43⋊C8)—22no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)—21no—
63C22⋊(C43⋊C8)—21no—
64C22⋊(C43⋊C8)—21no—
65C22⋊(C43⋊C8)D411yescharacteristic
66C22⋊(C43⋊C8)D411yescharacteristic
67C22⋊(C43⋊C8)D412yes—
68C2×#41×C43—21no—
69C2×#41×C43—21no—
70C2×#41×C43—42no—
71C2×#41×C43—42no—
72C2×#41×C43D411yescharacteristic
73C2×#41×C43D411yescharacteristic
74C2×#41×C43D411yescharacteristic
75C2×#41×C43D411yescharacteristic
76C22×Q8×C43C2×C411yescharacteristic
77C22×D4×C43—21no—
78C22×D4×C43C2×C411yescharacteristic
79C23×C4×C43—21no—
80C23×C4×C43C2311yescharacteristic
81C2×M16×C43—21no—
82C2×C22⋊C4×C43—21no—
83C2×C42×C43—21no—
84#104×C43—42no—
85#104×C43—42no—
86C22⋊C8×C43—21no—
87C22⋊C8×C43—21no—
88#95×C43—21no—
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×C43—41no—
126C22×C4×C43C22×C411yescharacteristic
127C22×C4×C43C2×D411yescharacteristic
128C22×C4×C43C2×D411yescharacteristic
129C22×C4×C43C2×D411yescharacteristic
130C22×C4×C43C2×D411yescharacteristic
131C22×C4×C43#4111yescharacteristic
132C2×C22⋊D43—41no—
133C2×C22⋊D43—41no—
134C2×C22⋊D43—82no—
135C22×Dic43—21no—
136C2×D172—21no—
137C2×D172—21no—
138C2×D172—41no—
139C2×D172—41no—
140M16×C43—41no—
141M16×C43—41no—
142C2×C8×C43—41no—
143C22⋊C4×C43—22no—
144C22⋊C4×C43—41no—
145C42×C43—41no—
146C42×C43—41no—
147#10621884—42no—
148#10621884—42no—
149#10621882—42no—
150#10621882—42no—
151(C2×D43)⋊C4—41no—
152(C2×D43)⋊C4—41no—
153C4⋊Dic43—21no—
154C4⋊Dic43—21no—
155#10621877—44no—
156#10621877—41no—
157#10621877—41no—
158C2×C43⋊C8—21no—
159C2×C43⋊C8—21no—
160C2×C43⋊C8—21no—
161C2×C43⋊C8—22no—
162C2×C43⋊C8—21no—
163C2×C43⋊C8—44no—
164C2×C43⋊C8—41no—
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×C43—42no—
217C2×C4×C43—81no—
218C2×C4×C43—81no—
219C2×C4×C43C2×C22⋊C411yescharacteristic
220C2×C4×C43C4×D411yescharacteristic
221C2×C4×C43#12011yescharacteristic
222C2×C4×C43#12111yescharacteristic
223C22⋊D43—82no—
224C22⋊D43—82no—
225C2×Dic43—41no—
226C2×Dic43—81no—
227D172—41no—
228D172—41no—
229D172—81no—
230C8×C43—81no—
231C43⋊C8—41no—
232C43⋊C8—42no—
233C43⋊C8—41no—
234C43⋊C8—41no—
235C43⋊C8—41no—
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×C43—82no—
269C4×C43C2×#9911yescharacteristic
270C4×C43C2×#9911yescharacteristic
271Dic43—81no—
272C2×#449—431no—
273#2880—431no—
274#1789D4311yescharacteristic, complemented
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—861no—
293C2×#121—431no—
294#449—861no—
295#449—861no—
296#449—861no—
297#449—861no—
298C2×#104—21no—
299C2×#104—21no—
300C2×#103—431no—
301C2×#102—431no—
302#408—862no—
303#408—861no—
304#407—431no—
305#407—861no—
306#407C2×D4311yescharacteristic
307C2×C22⋊C8—431no—
308C2×C22⋊C8—431no—
309C2×C22⋊C8—861no—
310C4×C22⋊C4C2×D4311yescharacteristic
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—1722no—
337#131—1722no—
338C2×M16—21no—
339C2×M16—862no—
340C2×M16—861no—
341C22×C8—431no—
342C22×C8—431no—
343C22×C8—862no—
344C22×C8—861no—
345#121—861no—
346#121—861no—
347#121—861no—
348#121—861no—
349C2×C4⋊C4—431no—
350C2×C22⋊C4—21no—
351C2×C22⋊C4—861no—
352C2×C42—21no—
353#104—42no—
354#104—42no—
355#103—861no—
356#103—861no—
357#102—861no—
358#102—861no—
359C22⋊C8—21no—
360C22⋊C8—21no—
361C22⋊C8—431no—
362C22⋊C8—431no—
363C22⋊C8—432no—
364C22⋊C8—862no—
365C22⋊C8—862no—
366C22⋊C8—861no—
367C22⋊C8—861no—
368C22⋊C8—861no—
369C22⋊C8—861no—
370#95—21no—
371C24—21no—
372C24—861no—
373C24#1062190011yescharacteristic
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—41no—
415C22×C4—861no—
416C22×C4C2×C4×D4311yescharacteristic
417C22×C4C2×D17211yescharacteristic
418C22×C4D4×D4311yescharacteristic
419C22×C4D4×D4311yescharacteristic
420C22×C4#1062190011yescharacteristic
421C22×C4C2×C22⋊D4311yescharacteristic
422SD16—1722no—
423SD16—1722no—
424D8—1722no—
425D8—1722no—
426M16—41no—
427M16—41no—
428M16—1724no—
429M16—1721no—
430M16—1721no—
431C2×C8—41no—
432C2×C8—861no—
433C2×C8—861no—
434C2×C8—861no—
435C2×C8—861no—
436C2×C8—862no—
437C2×C8—1724no—
438C2×C8—1721no—
439C2×C8—1721no—
440C2×C8—1721no—
441C2×C8—1721no—
442C4⋊C4—861no—
443C4⋊C4—861no—
444C22⋊C4—22no—
445C22⋊C4—41no—
446C22⋊C4—1721no—
447C22⋊C4—1721no—
448C42—41no—
449C42—41no—
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—
465C23(C22⋊D43)⋊C411yescharacteristic
466C23#1306329711yescharacteristic
467C23#1306330911yescharacteristic
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—42no—
504C2×C4—81no—
505C2×C4—81no—
506C2×C4—3441no—
507C2×C4—1721no—
508C2×C4C2×(C2×D43)⋊C411yescharacteristic
509C2×C4(C22⋊D43)⋊C411yescharacteristic
510C2×C4#1306329511yescharacteristic
511C2×C4#1306329711yescharacteristic
512C8—81no—
513C8—1721no—
514C8—1721no—
515C8—1722no—
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#1458277611yescharacteristic
542C22#1458301311yescharacteristic
543C22#1458301811yescharacteristic
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—82no—
550C4—3441no—
551C4C2×#1306323911yescharacteristic
552C4C2×#1306323911yescharacteristic
553C2—21no—
554C2—21no—
555C2—41no—
556C2—41no—
557C2—42no—
558C2—81no—
559C2—6881no—
560C2#1913492011yescharacteristic
561C2#1913504611yescharacteristic
562C2#1913507311yescharacteristic
subgroupG/H
centerC22#14582776
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1789C2
socleC22×C43#386
prime radicalC2×#14583044C2
cosocleC23×C4×C43C23
hypercenter#1789D43
hypocenterC43#9241
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1789

Complements

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

NH ≅ G/Ntype
2. #19143044C2semidirect
3. #19133110C2semidirect
4. #19132956C2semidirect
5. #19132471C2semidirect
6. #19132443C2semidirect
7. C43×#1789C2semidirect
8. C22×#10621884C4semidirect
9. C22×#10621882C4semidirect
16. C2×#13063249C4semidirect
17. C2×#13063246C4semidirect
274. #1789D43semidirect
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
#191430442
#191331102
#191329562
#191324712
#191324432
C43×#17892
#924143