Finite Group Databasebeta

← #24993044

Subgroups — #24993044

Order 11008.

966 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583033C211yesmaximal, characteristic
2#19135431C211yesmaximal, characteristic, complemented
3#19134526C211yesmaximal, characteristic, complemented
4#19133162C211yesmaximal, characteristic, complemented
5#19132462C211yesmaximal, characteristic, complemented
6#19132443C211yesmaximal, characteristic, complemented
7D4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
8C22×#10621882C412yescomplemented
9C2×#13063299C2211yescharacteristic
10#14583033—22no—
11#14583033—21no—
12#14583033—21no—
13C2×#13063246—22no—
14C2×#13063246C412yescomplemented
15C2×#13063239—21no—
16C2×#13063239—21no—
17C2×C22⋊(C43⋊C8)C2211yescharacteristic
18C2×C22⋊(C43⋊C8)C2211yescharacteristic
19#14582759C2211yescharacteristic
20#14582632—22no—
21C23×D4×C43C2211yescharacteristic
22C2×C4×D4×C43—21no—
23C22×C22⋊C4×C43—21no—
24C43×#390—21no—
25C43×#386—22no—
26C43×#380C2211yescharacteristic
27C43×#379—21no—
28C4×C22⋊C4×C43C2211yescharacteristic
29C22×D172C2×C411yescharacteristic, complemented
30C22×C22⋊D43—21no—
31C2×#10621882—22no—
32C2×#10621882—22no—
33C2×#10621882—44no—
34C22×C43⋊C8—21no—
35C22×C43⋊C8C2×C412yescomplemented
36#13063299—21no—
37#13063299—21no—
38#13063299—21no—
39#13063299—21no—
40C2×C4⋊Dic43—21no—
41C2×C4⋊Dic43C2×C411yescharacteristic, complemented
42C2×C22⋊Dic43—21no—
43C2×(C2×D43)⋊C4—21no—
44#13063246—22no—
45#13063246—22no—
46#13063246—44no—
47#13063239—42no—
48#13063239—42no—
49C22⋊(C43⋊C8)—21no—
50C22⋊(C43⋊C8)—21no—
51C22⋊(C43⋊C8)—21no—
52C22⋊(C43⋊C8)—21no—
53C43⋊#95—21no—
54C25×C43—21no—
55C22×D4×C43—21no—
56C22×D4×C43—21no—
57C22×D4×C43—21no—
58C22×D4×C43—44no—
59C22×D4×C43C2×C412yes—
60C22×D4×C43D412yes—
61C22×D4×C43D411yescharacteristic
62C22×D4×C43D411yescharacteristic
63C23×C4×C43—22no—
64C23×C4×C43C2311yescharacteristic
65C4×D4×C43—44no—
66C2×C4⋊C4×C43—21no—
67C2×C22⋊C4×C43—22no—
68C2×C22⋊C4×C43—22no—
69C2×C22⋊C4×C43—21no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—42no—
72C2×C22⋊C4×C43—42no—
73C2×C22⋊C4×C43D411yescharacteristic
74C2×C22⋊C4×C43D411yescharacteristic
75C2×C42×C43—21no—
76#95×C43—21no—
77#95×C43D412yes—
78C24×C43—21no—
79C24×C43—21no—
80C24×C43—22no—
81C24×C43—22no—
82C24×C43—44no—
83C24×C43—41no—
84C24×C43—41no—
85C24×C43—41no—
86C24×C43—41no—
87C24×C43—82no—
88C24×C43C2×D411yescharacteristic
89C23×D43—21no—
90C2×D4×C43—24no—
91C2×D4×C43—22no—
92C2×D4×C43—22no—
93C2×D4×C43—21no—
94C2×D4×C43—21no—
95C2×D4×C43—24no—
96C2×D4×C43—24no—
97C2×D4×C43—44no—
98C2×D4×C43—42no—
99C2×D4×C43—42no—
100C2×D4×C43—42no—
101C2×D4×C43—44no—
102C2×D4×C43—44no—
103C2×D4×C43C22⋊C412yes—
104C2×D4×C43C22⋊C412yes—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—22no—
108C22×C4×C43—44no—
109C22×C4×C43—42no—
110C22×C4×C43—44no—
111C22×C4×C43—82no—
112C22×C4×C43C22×C411yescharacteristic
113C22×C4×C43C2×D411yescharacteristic
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2×D411yescharacteristic
116C22×C4×C43#4111yescharacteristic
117C22×C4×C43#4111yescharacteristic
118C2×C22⋊D43—41no—
119C2×C22⋊D43—41no—
120C2×C22⋊D43—41no—
121C2×C22⋊D43—41no—
122C2×C22⋊D43—41no—
123C2×C22⋊D43—41no—
124C22×Dic43—21no—
125C22×Dic43—41no—
126C2×D172—21no—
127C2×D172—21no—
128C2×D172—42no—
129C4⋊C4×C43—42no—
130C22⋊C4×C43—21no—
131C22⋊C4×C43—21no—
132C22⋊C4×C43—21no—
133C22⋊C4×C43—44no—
134C22⋊C4×C43—44no—
135C22⋊C4×C43—41no—
136C22⋊C4×C43—41no—
137C22⋊C4×C43—82no—
138C22⋊C4×C43D812yescomplemented
139C42×C43—42no—
140C22⋊Dic43—41no—
141C22⋊Dic43—41no—
142#10621882—44no—
143#10621882—44no—
144(C2×D43)⋊C4—41no—
145(C2×D43)⋊C4—41no—
146C4⋊Dic43—21no—
147C4⋊Dic43—21no—
148C4⋊Dic43—42no—
149C2×C43⋊C8—22no—
150C2×C43⋊C8—42no—
151C2×C43⋊C8—42no—
152C2×C43⋊C8—41no—
153C23×C43—24no—
154C23×C43—22no—
155C23×C43—22no—
156C23×C43—41no—
157C23×C43—41no—
158C23×C43—44no—
159C23×C43—44no—
160C23×C43—42no—
161C23×C43—42no—
162C23×C43—42no—
163C23×C43—41no—
164C23×C43—41no—
165C23×C43—42no—
166C23×C43—42no—
167C23×C43—41no—
168C23×C43—41no—
169C23×C43—42no—
170C23×C43—42no—
171C23×C43—82no—
172C23×C43—82no—
173C23×C43—84no—
174C23×C43—84no—
175C23×C43—84no—
176C23×C43—84no—
177C23×C43C4×D411yescharacteristic
178C23×C43#12011yescharacteristic
179C23×C43#12111yescharacteristic
180C23×C43C2×D811yescharacteristic
181C23×C43#13511yescharacteristic
182C23×C43AGL(1,ℤ/8)11yescharacteristic
183C23×C43AGL(1,ℤ/8)11yescharacteristic
184C22×D43—41no—
185C22×D43—41no—
186C22×D43—41no—
187C22×D43—81no—
188C22×D43—81no—
189D4×C43—24no—
190D4×C43—22no—
191D4×C43—22no—
192D4×C43—22no—
193D4×C43—44no—
194D4×C43—44no—
195D4×C43—42no—
196D4×C43#9914yescomplemented
197C2×C4×C43—22no—
198C2×C4×C43—22no—
199C2×C4×C43—22no—
200C2×C4×C43—22no—
201C2×C4×C43—41no—
202C2×C4×C43—41no—
203C2×C4×C43—41no—
204C2×C4×C43—41no—
205C2×C4×C43—41no—
206C2×C4×C43—41no—
207C2×C4×C43—42no—
208C2×C4×C43—41no—
209C2×C4×C43—42no—
210C2×C4×C43—42no—
211C2×C4×C43—41no—
212C2×C4×C43—88no—
213C2×C4×C43C2×C22⋊C411yescharacteristic
214C2×C4×C43C4×D411yescharacteristic
215C2×C4×C43#12111yescharacteristic
216C2×C4×C43#12311yescharacteristic
217C22⋊D43—81no—
218C22⋊D43—81no—
219C22⋊D43—81no—
220C22⋊D43—81no—
221C2×Dic43—41no—
222C2×Dic43—41no—
223C2×Dic43—41no—
224C2×Dic43—81no—
225C2×Dic43—81no—
226C2×Dic43—81no—
227D172—42no—
228D172—81no—
229C43⋊C8—42no—
230C43⋊C8—81no—
231#9259—431nomaximal, Sylow
232C22×C43—21no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—21no—
238C22×C43—24no—
239C22×C43—41no—
240C22×C43—41no—
241C22×C43—41no—
242C22×C43—41no—
243C22×C43—44no—
244C22×C43—44no—
245C22×C43—42no—
246C22×C43—42no—
247C22×C43—42no—
248C22×C43—42no—
249C22×C43—42no—
250C22×C43—84no—
251C22×C43—84no—
252C22×C43—84no—
253C22×C43—84no—
254C22×C43—82no—
255C22×C43—82no—
256C22×C43#38611yescharacteristic
257C22×C43C4×D811yescharacteristic
258C22×C43#44211yescharacteristic
259C22×C43#44711yescharacteristic
260C22×C43#44911yescharacteristic
261C22×C43#45911yescharacteristic
262C22×C43#46311yescharacteristic
263C2×D43—81no—
264C2×D43—81no—
265C2×D43—81no—
266C2×D43—161no—
267C2×D43—161no—
268C4×C43—21no—
269C4×C43—21no—
270C4×C43—21no—
271C4×C43—42no—
272C4×C43—81no—
273C4×C43—82no—
274C4×C43C2×#9912yes—
275Dic43—81no—
276Dic43—161no—
277C2×#447—431no—
278D4×C22⋊C4D4311yescharacteristic, complemented
279#1964—431no—
280#1786—431no—
281#1519—431no—
282#1289—431no—
283#1282—431no—
284C2×C43—21no—
285C2×C43—21no—
286C2×C43—21no—
287C2×C43—21no—
288C2×C43—21no—
289C2×C43—21no—
290C2×C43—44no—
291C2×C43—82no—
292C2×C43#187911yescharacteristic
293C2×C43#189811yescharacteristic
294C2×C43#190411yescharacteristic
295D43—161no—
296C23×D4C2×D4311yescharacteristic
297C22×D8—432no—
298C2×#121—431no—
299C2×C4×D4—21no—
300C22×C22⋊C4—21no—
301#447—862no—
302#447—861no—
303#447—861no—
304C2×#102—432no—
305C2×#102—862no—
306C2×#99—861no—
307C2×#99—861no—
308C2×C22⋊C8—431no—
309C2×C22⋊C8—431no—
310#390—21no—
311#386—22no—
312#380—431no—
313#380C2×D4311yescharacteristic
314#379—21no—
315C4×C22⋊C4C2×D4311yescharacteristic
316#327—862no—
317C43#925911yescharacteristic, complemented, Sylow
318C25—21no—
319C22×D4—21no—
320C22×D4—21no—
321C22×D4—21no—
322C22×D4—44no—
323C22×D4—431no—
324C22×D4—861no—
325C22×D4C4×D4312yes—
326C22×D4D17212yes—
327C22×D4C22⋊D4311yescharacteristic
328C22×D4C22⋊D4311yescharacteristic
329C23×C4—22no—
330C23×C4C22×D4311yescharacteristic
331C2×D8—862no—
332C2×D8—862no—
333C2×D8—1724no—
334C22×C8—432no—
335C22×C8—861no—
336#121—861no—
337#121—861no—
338#121—861no—
339#121—861no—
340C4×D4—44no—
341C2×C4⋊C4—21no—
342C2×C4⋊C4—431no—
343C2×C4⋊C4—861no—
344C2×C22⋊C4—22no—
345C2×C22⋊C4—22no—
346C2×C22⋊C4—21no—
347C2×C22⋊C4—22no—
348C2×C22⋊C4—42no—
349C2×C22⋊C4—42no—
350C2×C22⋊C4—861no—
351C2×C22⋊C4—861no—
352C2×C22⋊C4C22⋊D4311yescharacteristic
353C2×C22⋊C4C22⋊D4311yescharacteristic
354C2×C42—21no—
355#102—862no—
356#102—862no—
357#102—1724no—
358#99—1722no—
359#99—1722no—
360C22⋊C8—861no—
361C22⋊C8—861no—
362C22⋊C8—861no—
363C22⋊C8—861no—
364#95—21no—
365#95—861no—
366#95C22⋊D4312yes—
367C24—21no—
368C24—21no—
369C24—22no—
370C24—22no—
371C24—44no—
372C24—41no—
373C24—41no—
374C24—41no—
375C24—41no—
376C24—82no—
377C24—861no—
378C24C2×C22⋊D4311yescharacteristic
379C2×D4—24no—
380C2×D4—24no—
381C2×D4—24no—
382C2×D4—22no—
383C2×D4—22no—
384C2×D4—21no—
385C2×D4—21no—
386C2×D4—42no—
387C2×D4—42no—
388C2×D4—42no—
389C2×D4—44no—
390C2×D4—44no—
391C2×D4—44no—
392C2×D4—861no—
393C2×D4—861no—
394C2×D4—1722no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4—1721no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4—1721no—
401C2×D4(C2×D43)⋊C412yes—
402C2×D4(C2×D43)⋊C412yes—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—22no—
406C22×C4—42no—
407C22×C4—44no—
408C22×C4—44no—
409C22×C4—82no—
410C22×C4—861no—
411C22×C4—1721no—
412C22×C4C2×C4×D4311yescharacteristic
413C22×C4C2×D17211yescharacteristic
414C22×C4#1062189811yescharacteristic
415C22×C4#1062189811yescharacteristic
416C22×C4C2×C22⋊D4311yescharacteristic
417C22×C4C2×C22⋊D4311yescharacteristic
418D8—1724no—
419D8—1724no—
420C2×C8—862no—
421C2×C8—1722no—
422C2×C8—1721no—
423C2×C8—1722no—
424C4⋊C4—42no—
425C4⋊C4—861no—
426C4⋊C4—861no—
427C4⋊C4—1722no—
428C22⋊C4—21no—
429C22⋊C4—21no—
430C22⋊C4—21no—
431C22⋊C4—44no—
432C22⋊C4—44no—
433C22⋊C4—41no—
434C22⋊C4—41no—
435C22⋊C4—82no—
436C22⋊C4—1721no—
437C22⋊C4—1721no—
438C22⋊C4—1721no—
439C22⋊C4—1721no—
440C22⋊C4#1062188212yescomplemented
441C42—42no—
442C23—24no—
443C23—22no—
444C23—22no—
445C23—41no—
446C23—41no—
447C23—44no—
448C23—44no—
449C23—42no—
450C23—42no—
451C23—42no—
452C23—41no—
453C23—41no—
454C23—41no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—42no—
459C23—41no—
460C23—82no—
461C23—82no—
462C23—84no—
463C23—84no—
464C23—84no—
465C23—84no—
466C23—3441no—
467C23—3441no—
468C23—1721no—
469C23—1721no—
470C23—1721no—
471C23C4×C22⋊D4311yescharacteristic
472C23#1306329411yescharacteristic
473C23#1306329911yescharacteristic
474C23C2×#1062188211yescharacteristic
475C23#1306334511yescharacteristic
476C23#1306335011yescharacteristic
477C23#1306335111yescharacteristic
478D4—24no—
479D4—22no—
480D4—22no—
481D4—22no—
482D4—44no—
483D4—44no—
484D4—42no—
485D4—3441no—
486D4—3441no—
487D4—3441no—
488D4—3441no—
489D4—3441no—
490D4—1722no—
491D4#1306323914yescomplemented
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—22no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—42no—
503C2×C4—41no—
504C2×C4—42no—
505C2×C4—41no—
506C2×C4—42no—
507C2×C4—88no—
508C2×C4—3441no—
509C2×C4—3441no—
510C2×C4—3441no—
511C2×C4—1721no—
512C2×C4—1721no—
513C2×C4—1721no—
514C2×C4C2×(C2×D43)⋊C411yescharacteristic
515C2×C4C4×C22⋊D4311yescharacteristic
516C2×C4#1306329911yescharacteristic
517C2×C4#1306330811yescharacteristic
518C8—3441no—
519C8—1722no—
520C22—21no—
521C22—21no—
522C22—21no—
523C22—21no—
524C22—21no—
525C22—21no—
526C22—24no—
527C22—41no—
528C22—41no—
529C22—41no—
530C22—41no—
531C22—44no—
532C22—44no—
533C22—42no—
534C22—42no—
535C22—42no—
536C22—42no—
537C22—42no—
538C22—84no—
539C22—84no—
540C22—84no—
541C22—84no—
542C22—82no—
543C22—82no—
544C22—3441no—
545C22—3441no—
546C22—3441no—
547C22—6881no—
548C22—6881no—
549C22#1458277811yescharacteristic
550C22C4×#1062188211yescharacteristic
551C22#1458300911yescharacteristic
552C22#1458303311yescharacteristic
553C22#1458304411yescharacteristic
554C22#1458309411yescharacteristic
555C22#1458311411yescharacteristic
556C4—21no—
557C4—21no—
558C4—21no—
559C4—42no—
560C4—82no—
561C4—81no—
562C4—3441no—
563C4—6881no—
564C4C2×#1306323912yes—
565C2—21no—
566C2—21no—
567C2—21no—
568C2—21no—
569C2—21no—
570C2—21no—
571C2—44no—
572C2—82no—
573C2—6881no—
574C2#1913494311yescharacteristic
575C2#1913504811yescharacteristic
576C2#1913508211yescharacteristic
subgroupG/H
centerC22#14582778
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingD4×C22⋊C4×C43C2
socleC22×C43#386
prime radicalC2×#14583033C2
cosocleC23×C4×C43C23
hypercenterD4×C22⋊C4D43
hypocenterC43#9259
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #19135431C2semidirect
3. #19134526C2semidirect
4. #19133162C2semidirect
5. #19132462C2semidirect
6. #19132443C2semidirect
7. D4×C22⋊C4×C43C2semidirect
8. C22×#10621882C4semidirect
14. C2×#13063246C4semidirect
29. C22×D172C2×C4semidirect
35. C22×C43⋊C8C2×C4semidirect
41. C2×C4⋊Dic43C2×C4semidirect
138. C22⋊C4×C43D8semidirect
196. D4×C43#99semidirect
278. D4×C22⋊C4D43semidirect
317. C43#9259semidirect
440. C22⋊C4#10621882semidirect
491. D4#13063239semidirect

Maximal subgroups

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

subgroupindex
C2×#145830332
#191354312
#191345262
#191331622
#191324622
#191324432
D4×C22⋊C4×C432
#925943