Finite Group Databasebeta

← #25062481

Subgroups — #25062481

Order 11008.

1646 conjugacy classes of subgroups.

The subgroup lattice has 596 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2#19143224C212yesmaximal, complemented
3#19132934C214yesmaximal, complemented
4#19132922C211yesmaximal, characteristic, complemented
5#19132921C212yesmaximal, complemented
6#19132914C214yesmaximal, complemented
7C43×#1462C211yesmaximal, characteristic, complemented
8C23×C22⋊D43C411yescharacteristic
9C24×Dic43C411yescharacteristic
10C23×C4×D43C411yescharacteristic
11C2×(C22⋊D43)⋊C4—22no—
12C2×(C22⋊D43)⋊C4—22no—
13C2×(C22⋊D43)⋊C4—22no—
14C2×(C22⋊D43)⋊C4—22no—
15C2×(C22⋊D43)⋊C4C412yes—
16C2×(C22⋊D43)⋊C4C412yes—
17C2×(C22⋊D43)⋊C4C2212yes—
18C2×(C22⋊D43)⋊C4C2212yes—
19C22×Dic43⋊C4C411yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×C4×Dic43C2211yescharacteristic
22#14582953—22no—
23#14582953C2214yescomplemented
24#14582949—22no—
25#14582949C2214yescomplemented
26#14582922—22no—
27#14582863C2212yes—
28M16×Dic43—22no—
29#14582623C2214yescomplemented
30#14582622C2218yescomplemented
31C22×C22⋊C4×C43C2211yescharacteristic
32C43×#407C2212yes—
33C43×#323C2214yescomplemented
34C24×D43C2×C411yescharacteristic
35C22×C22⋊D43—28no—
36C22×C22⋊D43—22no—
37C22×C22⋊D43—22no—
38C22×C22⋊D43C2×C412yes—
39C22×C22⋊D43C2×C412yes—
40C23×Dic43—21no—
41C23×Dic43—21no—
42C23×Dic43—21no—
43C23×Dic43—21no—
44C23×Dic43—44no—
45C23×Dic43C2×C411yescharacteristic
46C23×Dic43C2×C411yescharacteristic
47C23×Dic43C2×C411yescharacteristic
48C23×Dic43C2×C412yes—
49C23×Dic43C2×C412yes—
50C22×C4×D43—21no—
51C22×C4×D43—21no—
52C22×C4×D43—21no—
53C22×C4×D43—21no—
54C22×C4×D43—44no—
55C22×C4×D43C2×C412yes—
56C22×C4×D43C2×C412yes—
57C2×#10621877—22no—
58(C22⋊D43)⋊C4—24no—
59(C22⋊D43)⋊C4—24no—
60(C22⋊D43)⋊C4—24no—
61(C22⋊D43)⋊C4—24no—
62(C22⋊D43)⋊C4—24no—
63(C22⋊D43)⋊C4—24no—
64(C22⋊D43)⋊C4—24no—
65(C22⋊D43)⋊C4—24no—
66C2×Dic43⋊C4—22no—
67C2×Dic43⋊C4—22no—
68C2×Dic43⋊C4C2×C412yes—
69C2×Dic43⋊C4C2×C412yes—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—22no—
72C2×(C2×D43)⋊C4C2×C412yes—
73C2×(C2×D43)⋊C4C2312yes—
74C2×C4×Dic43C2×C411yescharacteristic
75C2×C4×Dic43C2×C411yescharacteristic
76C2×C4×Dic43D412yes—
77C2×C4×Dic43D412yes—
78C2×C4×Dic43D412yes—
79C2×C4×Dic43D412yes—
80C2×C4×Dic43C2311yescharacteristic
81C2×C4×Dic43C2311yescharacteristic
82Dic43⋊C8—24no—
83Dic43⋊C8—24no—
84C22⋊(C43⋊C8)—22no—
85C22⋊(C43⋊C8)C2314yes—
86#13063235—24no—
87C8×Dic43—24no—
88C25×C43C2×C411yescharacteristic
89C23×C4×C43C2×C411yescharacteristic
90C23×C4×C43C2311yescharacteristic
91C2×M16×C43—22no—
92C2×C22⋊C4×C43—22no—
93C2×C22⋊C4×C43—22no—
94C2×C22⋊C4×C43C2×C412yes—
95C2×C22⋊C4×C43C2312yes—
96C22⋊C8×C43—22no—
97C22⋊C8×C43C2314yes—
98C24×C43—21no—
99C24×C43—21no—
100C24×C43—24no—
101C24×C43—42no—
102C24×C43—42no—
103C24×C43C22×C411yescharacteristic
104C24×C43C22×C412yes—
105C23×D43—21no—
106C23×D43—21no—
107C23×D43—24no—
108C23×D43—42no—
109C23×D43—42no—
110C23×D43C22×C412yes—
111C22×C4×C43—21no—
112C22×C4×C43—21no—
113C22×C4×C43—42no—
114C22×C4×C43—42no—
115C22×C4×C43C22×C412yes—
116C22×C4×C43C22×C411yescharacteristic
117C22×C4×C43C2×D412yes—
118C22×C4×C43C2×D412yes—
119C22×C4×C43C2411yescharacteristic
120C2×C22⋊D43—216no—
121C2×C22⋊D43—216no—
122C2×C22⋊D43—24no—
123C2×C22⋊D43—24no—
124C2×C22⋊D43—24no—
125C2×C22⋊D43—24no—
126C2×C22⋊D43—24no—
127C2×C22⋊D43M1618yescomplemented
128C22×Dic43—24no—
129C22×Dic43—24no—
130C22×Dic43—22no—
131C22×Dic43—22no—
132C22×Dic43—22no—
133C22×Dic43—22no—
134C22×Dic43—21no—
135C22×Dic43—21no—
136C22×Dic43—42no—
137C22×Dic43—44no—
138C22×Dic43—44no—
139C22×Dic43—44no—
140C22×Dic43—44no—
141C22×Dic43—44no—
142C22×Dic43—44no—
143C22×Dic43C22⋊C412yes—
144C22×Dic43C22⋊C412yes—
145C22×Dic43C22⋊C411yescharacteristic
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C22⋊C411yescharacteristic
148C22×Dic43C22⋊C411yescharacteristic
149C22×Dic43C22×C411yescharacteristic
150C22×Dic43C22×C411yescharacteristic
151C22×Dic43C22×C411yescharacteristic
152C22×Dic43C22×C412yes—
153C22×Dic43C22×C411yescharacteristic
154C2×C4×D43—22no—
155C2×C4×D43—22no—
156C2×C4×D43—22no—
157C2×C4×D43—22no—
158C2×C4×D43—44no—
159C2×C4×D43—44no—
160C2×C4×D43—44no—
161C2×C4×D43—44no—
162C2×C4×D43—44no—
163C2×C4×D43—44no—
164M16×C43—44no—
165C2×C8×C43—24no—
166C22⋊C4×C43—24no—
167C22⋊C4×C43—24no—
168(C2×D43)⋊C4—24no—
169(C2×D43)⋊C4—24no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172C4×Dic43C22⋊C412yes—
173C4×Dic43C22⋊C412yes—
174C4×Dic43C22⋊C412yes—
175C4×Dic43C22⋊C412yes—
176C4×Dic43C2×D412yes—
177C4×Dic43C2×D412yes—
178C4×Dic43C2×D412yes—
179C4×Dic43C2×D412yes—
180#10621877—44no—
181C2×C43⋊C8—24no—
182C23×C43—22no—
183C23×C43—22no—
184C23×C43—22no—
185C23×C43—24no—
186C23×C43—24no—
187C23×C43—22no—
188C23×C43—22no—
189C23×C43—42no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—416no—
193C23×C43—42no—
194C23×C43—42no—
195C23×C43—42no—
196C23×C43C2×C22⋊C411yescharacteristic
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43C2×M1614yes—
199C23×C43C23×C411yescharacteristic
200C22×D43—24no—
201C22×D43—24no—
202C22×D43—22no—
203C22×D43—22no—
204C22×D43—42no—
205C22×D43—416no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43C2×M1614yes—
212C2×C4×C43—24no—
213C2×C4×C43—22no—
214C2×C4×C43—41no—
215C2×C4×C43—42no—
216C2×C4×C43—41no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43C2×C22⋊C412yes—
221C2×C4×C43C22×D412yes—
222C22⋊D43—216no—
223C22⋊D43—216no—
224C2×Dic43—22no—
225C2×Dic43—22no—
226C2×Dic43—24no—
227C2×Dic43—24no—
228C2×Dic43—22no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—22no—
232C2×Dic43—22no—
233C2×Dic43—44no—
234C2×Dic43—44no—
235C2×Dic43—42no—
236C2×Dic43—42no—
237C2×Dic43—44no—
238C2×Dic43—44no—
239C2×Dic43—42no—
240C2×Dic43#10014yes—
241C2×Dic43C2×C22⋊C412yes—
242C2×Dic43C2×C22⋊C411yescharacteristic
243C2×Dic43C2×C22⋊C411yescharacteristic
244C2×Dic43C2×C22⋊C412yes—
245C2×Dic43C2×C22⋊C411yescharacteristic
246C2×Dic43C2×C22⋊C411yescharacteristic
247C2×Dic43C2×M1614yes—
248C4×D43—44no—
249C4×D43—44no—
250C4×D43—44no—
251C4×D43—44no—
252C8×C43—44no—
253C43⋊C8—44no—
254#17364—431nomaximal, Sylow
255C22×C43—28no—
256C22×C43—21no—
257C22×C43—21no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—24no—
263C22×C43—44no—
264C22×C43—44no—
265C22×C43—48no—
266C22×C43—48no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43#41012yes—
270C22×C43C2×#10012yes—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43C22×M1612yes—
273C2×D43—24no—
274C2×D43—44no—
275C2×D43—48no—
276C2×D43—48no—
277C2×D43—42no—
278C2×D43—42no—
279C2×D43—44no—
280C4×C43—22no—
281C4×C43—22no—
282C4×C43—42no—
283Dic43—22no—
284Dic43—21no—
285Dic43—21no—
286Dic43—42no—
287Dic43#40714yes—
288Dic43C2×#10012yes—
289Dic43C2×#10012yes—
290C22×C4×D4—431no—
291#2920—432no—
292#1466—434no—
293#1462—432no—
294#1462—431no—
295#1462D4311yescharacteristic, complemented
296#1460—434no—
297C2×C43—22no—
298C2×C43—22no—
299C2×C43—22no—
300C2×C43—44no—
301C2×C43C2×#40711yescharacteristic
302C2×C43C2×#41011yescharacteristic
303C2×C43C22×#10011yescharacteristic
304D43—44no—
305C23×D4—431no—
306C24×C4—431no—
307C24×C4—431no—
308C2×C4×D4—432no—
309C2×C4×D4—432no—
310C2×C4×D4—432no—
311C2×C4×D4—432no—
312C2×C4×D4—862no—
313C2×C4×D4—862no—
314C2×C4×D4—862no—
315C2×C4×D4—862no—
316C22×C4⋊C4—431no—
317C22×C22⋊C4—431no—
318C22×C22⋊C4C2×D4311yescharacteristic
319C22×C42—431no—
320#432—434no—
321#432—862no—
322#431—434no—
323#431—862no—
324#423—862no—
325#407—432no—
326#407C2×D4312yes—
327C4×M16—862no—
328#323—434no—
329#323—438no—
330#323C2×D4314yescomplemented
331C43#1736411yescharacteristic, complemented, Sylow
332C25—431no—
333C25C4×D4311yescharacteristic
334C22×D4—432no—
335C22×D4—432no—
336C22×D4—862no—
337C22×D4—862no—
338C22×D4—868no—
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—431no—
342C23×C4—432no—
343C23×C4—432no—
344C23×C4—432no—
345C23×C4—432no—
346C23×C4—861no—
347C23×C4—861no—
348C23×C4—861no—
349C23×C4—861no—
350C23×C4—861no—
351C23×C4—861no—
352C23×C4—861no—
353C23×C4—861no—
354C23×C4—1724no—
355C23×C4—1724no—
356C23×C4C4×D4311yescharacteristic
357C23×C4C22×D4311yescharacteristic
358C2×M16—22no—
359C2×M16—862no—
360C4×D4—864no—
361C4×D4—864no—
362C4×D4—864no—
363C4×D4—864no—
364C4×D4—864no—
365C4×D4—864no—
366C4×D4—864no—
367C4×D4—864no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—432no—
370C2×C4⋊C4—862no—
371C2×C4⋊C4—862no—
372C2×C22⋊C4—22no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—432no—
375C2×C22⋊C4—432no—
376C2×C22⋊C4—862no—
377C2×C22⋊C4—862no—
378C2×C22⋊C4C4×D4312yes—
379C2×C22⋊C4C22×D4312yes—
380C2×C42—431no—
381C2×C42—431no—
382C2×C42—432no—
383C2×C42—432no—
384C2×C42—432no—
385C2×C42—432no—
386C2×C42—431no—
387C2×C42—431no—
388C4⋊C8—864no—
389C4⋊C8—864no—
390C22⋊C8—22no—
391C22⋊C8—434no—
392C22⋊C8—862no—
393C22⋊C8C22×D4314yes—
394#97—864no—
395C4×C8—864no—
396C24—21no—
397C24—21no—
398C24—24no—
399C24—42no—
400C24—42no—
401C24—432no—
402C24—864no—
403C24—861no—
404C24—861no—
405C24—1722no—
406C24—1722no—
407C24C2×C4×D4311yescharacteristic
408C24C2×C4×D4312yes—
409C2×D4—438no—
410C2×D4—864no—
411C2×D4—864no—
412C2×D4—864no—
413C2×D4—864no—
414C2×D4—8616no—
415C2×D4—8616no—
416C2×D4—864no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—42no—
420C22×C4—42no—
421C22×C4—431no—
422C22×C4—431no—
423C22×C4—432no—
424C22×C4—432no—
425C22×C4—431no—
426C22×C4—431no—
427C22×C4—431no—
428C22×C4—431no—
429C22×C4—431no—
430C22×C4—431no—
431C22×C4—432no—
432C22×C4—862no—
433C22×C4—862no—
434C22×C4—862no—
435C22×C4—862no—
436C22×C4—864no—
437C22×C4—864no—
438C22×C4—862no—
439C22×C4—862no—
440C22×C4—862no—
441C22×C4—862no—
442C22×C4—861no—
443C22×C4—861no—
444C22×C4—1724no—
445C22×C4—1724no—
446C22×C4—1724no—
447C22×C4—1724no—
448C22×C4—1724no—
449C22×C4—1724no—
450C22×C4—1724no—
451C22×C4—1724no—
452C22×C4—1724no—
453C22×C4—1724no—
454C22×C4—1724no—
455C22×C4—1724no—
456C22×C4—1722no—
457C22×C4C2×C4×D4312yes—
458C22×C4C2×C4×D4311yescharacteristic
459C22×C4D4×D4312yes—
460C22×C4D4×D4312yes—
461C22×C4C23×D4311yescharacteristic
462M16—44no—
463M16—1724no—
464C2×C8—24no—
465C2×C8—864no—
466C4⋊C4—864no—
467C4⋊C4—864no—
468C22⋊C4—24no—
469C22⋊C4—24no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C42—432no—
473C42—432no—
474C42—432no—
475C42—432no—
476C42—432no—
477C42—432no—
478C42—432no—
479C42—432no—
480C23—22no—
481C23—22no—
482C23—22no—
483C23—24no—
484C23—24no—
485C23—22no—
486C23—22no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—416no—
491C23—42no—
492C23—42no—
493C23—42no—
494C23—434no—
495C23—864no—
496C23—864no—
497C23—862no—
498C23—862no—
499C23—1722no—
500C23—1722no—
501C23—1722no—
502C23—17216no—
503C23—1722no—
504C23—1722no—
505C23—1722no—
506C23C22⋊C4×D4311yescharacteristic
507C23C22⋊C4×D4311yescharacteristic
508C23M16×D4314yes—
509C23C22×C4×D4311yescharacteristic
510D4—8616no—
511D4—8616no—
512C2×C4—24no—
513C2×C4—22no—
514C2×C4—41no—
515C2×C4—42no—
516C2×C4—41no—
517C2×C4—42no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—432no—
521C2×C4—431no—
522C2×C4—431no—
523C2×C4—434no—
524C2×C4—434no—
525C2×C4—432no—
526C2×C4—431no—
527C2×C4—431no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—862no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—862no—
535C2×C4—862no—
536C2×C4—862no—
537C2×C4—1724no—
538C2×C4—1724no—
539C2×C4—1724no—
540C2×C4—1724no—
541C2×C4—1724no—
542C2×C4—1724no—
543C2×C4—1724no—
544C2×C4—1724no—
545C2×C4—1722no—
546C2×C4—1722no—
547C2×C4—1722no—
548C2×C4C22⋊C4×D4312yes—
549C2×C4C2×D4×D4312yes—
550C8—44no—
551C8—1724no—
552C22—28no—
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—24no—
560C22—44no—
561C22—48no—
562C22—48no—
563C22—44no—
564C22—42no—
565C22—42no—
566C22—864no—
567C22—1724no—
568C22—1728no—
569C22—1728no—
570C22—1724no—
571C22—1722no—
572C22—1722no—
573C22#1458287112yes—
574C22#100×D4312yes—
575C22C2×C22⋊C4×D4311yescharacteristic
576C22C2×M16×D4312yes—
577C4—22no—
578C4—22no—
579C4—42no—
580C4—434no—
581C4—432no—
582C4—432no—
583C4—862no—
584C4—861no—
585C4—861no—
586C4—1722no—
587C2—22no—
588C2—22no—
589C2—22no—
590C2—44no—
591C2—1724no—
592C2#407×D4311yescharacteristic
593C2C2×#1458287111yescharacteristic
594C2C2×#100×D4311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC43×#1462C2
socleC22×C43C22×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC22×C4×C43C24
hypercenter#1462D43
hypocenterC43#17364
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1462

Complements

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

NH ≅ G/Ntype
2. #19143224C2semidirect
3. #19132934C2semidirect
4. #19132922C2semidirect
5. #19132921C2semidirect
6. #19132914C2semidirect
7. C43×#1462C2semidirect
23. #14582953C22semidirect
25. #14582949C22semidirect
29. #14582623C22semidirect
30. #14582622C22semidirect
33. C43×#323C22semidirect
127. C2×C22⋊D43M16semidirect
295. #1462D43semidirect
330. #323C2×D43semidirect
331. C43#17364semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
#191432242
#191329342
#191329222
#191329212
#191329142
C43×#14622
#1736443