Finite Group Databasebeta

← #19140807

Subgroups — #19140807

Order 5504.

932 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
1C2×#13063321C211yesmaximal, characteristic, complemented
2C2×#13063299C211yesmaximal, characteristic, complemented
3C2×#13063295C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5C2×#13063293C211yesmaximal, characteristic, complemented
6#14582816C211yesmaximal, characteristic, complemented
7#14582815C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582807C211yesmaximal, characteristic, complemented
11#14582807C211yesmaximal, characteristic, complemented
12#14582792C211yesmaximal, characteristic, complemented
13#14582789C211yesmaximal, characteristic, complemented
14#14582778C211yesmaximal, characteristic, complemented
15C2×#121×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic
24C22×C22⋊D43C2211yescharacteristic, complemented
25C22×C22⋊D43C2211yescharacteristic, complemented
26#13063321—24no—
27#13063299—24no—
28#13063295—24no—
29#13063293—24no—
30#13063293—24no—
31C2×C4⋊Dic43C2211yescharacteristic, complemented
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C22⋊Dic43C2211yescharacteristic, complemented
35C2×C22⋊Dic43C2211yescharacteristic, complemented
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C2×C4×Dic43C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C43⋊#95C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C43⋊#95C2211yescharacteristic, complemented
49C22×D4×C43C2211yescharacteristic
50C22×D4×C43C2211yescharacteristic
51C22×D4×C43C2211yescharacteristic, complemented
52C23×C4×C43C2211yescharacteristic, complemented
53#121×C43—24no—
54C2×C4⋊C4×C43C2211yescharacteristic, complemented
55C2×C22⋊C4×C43C2211yescharacteristic
56C2×C22⋊C4×C43C2211yescharacteristic, complemented
57C24×C43C2311yescharacteristic
58C24×C43C2311yescharacteristic
59C24×C43C2311yescharacteristic
60C23×D43—22no—
61C23×D43—22no—
62C23×D43—22no—
63C23×D43—41no—
64C23×D43—41no—
65C23×D43—41no—
66C23×D43—41no—
67C23×D43C2311yescharacteristic
68C23×D43C2311yescharacteristic
69C23×D43C2311yescharacteristic
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—22no—
73C2×D4×C43—22no—
74C2×D4×C43—22no—
75C2×D4×C43—22no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C22×C4×C43—22no—
80C22×C4×C43—22no—
81C22×C4×C43—41no—
82C22×C4×C43C2311yescharacteristic
83C22×C4×C43C2311yescharacteristic
84C22×C4×C43C2311yescharacteristic
85C22×C4×C43C2311yescharacteristic
86C2×C22⋊D43—22no—
87C2×C22⋊D43—22no—
88C2×C22⋊D43—22no—
89C2×C22⋊D43—22no—
90C2×C22⋊D43—22no—
91C2×C22⋊D43—22no—
92C2×C22⋊D43—22no—
93C2×C22⋊D43—22no—
94C2×C22⋊D43—22no—
95C2×C22⋊D43—41no—
96C2×C22⋊D43—41no—
97C2×C22⋊D43—41no—
98C2×C22⋊D43—41no—
99C2×C22⋊D43—41no—
100C2×C22⋊D43—41no—
101C2×C22⋊D43—41no—
102C2×C22⋊D43—41no—
103C2×C22⋊D43—41no—
104C2×C22⋊D43—41no—
105C2×C22⋊D43—41no—
106C2×C22⋊D43D414yescomplemented
107C22×Dic43C2311yescharacteristic
108C22×Dic43C2311yescharacteristic
109C22×Dic43C2311yescharacteristic
110C22×Dic43C2311yescharacteristic
111C22×Dic43C2311yescharacteristic
112C2×D172—22no—
113C2×D172—22no—
114C2×D172—22no—
115C2×D172—22no—
116C2×D172—41no—
117C2×D172—41no—
118C4⋊C4×C43—22no—
119C22⋊C4×C43—22no—
120C22⋊C4×C43D414yescomplemented
121C22⋊Dic43—22no—
122C22⋊Dic43—22no—
123C22⋊Dic43—41no—
124C22⋊Dic43—41no—
125(C2×D43)⋊C4—22no—
126(C2×D43)⋊C4—22no—
127(C2×D43)⋊C4—22no—
128(C2×D43)⋊C4—22no—
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—22no—
131(C2×D43)⋊C4—41no—
132(C2×D43)⋊C4D414yescomplemented
133C4⋊Dic43—22no—
134C4×Dic43—22no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43—21no—
140C23×C43—21no—
141C23×C43—21no—
142C23×C43—21no—
143C23×C43—21no—
144C23×C43—21no—
145C23×C43—21no—
146C23×C43—21no—
147C23×C43—21no—
148C23×C43—21no—
149C23×C43—21no—
150C23×C43—21no—
151C23×C43—21no—
152C23×C43—21no—
153C23×C43—21no—
154C23×C43C2×D412yes—
155C23×C43C2×D412yes—
156C23×C43C2411yescharacteristic
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—21no—
162C22×D43—21no—
163C22×D43—21no—
164C22×D43—21no—
165C22×D43—21no—
166C22×D43—21no—
167C22×D43—21no—
168C22×D43—21no—
169C22×D43—21no—
170C22×D43—21no—
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—44no—
177C22×D43—44no—
178C22×D43—44no—
179C22×D43—44no—
180C22×D43—44no—
181C22×D43—44no—
182C22×D43—44no—
183C22×D43C2×D412yes—
184C22×D43C2×D412yes—
185D4×C43—44no—
186D4×C43—44no—
187D4×C43—44no—
188C2×C4×C43—21no—
189C2×C4×C43—21no—
190C2×C4×C43—21no—
191C2×C4×C43—21no—
192C2×C4×C43—21no—
193C2×C4×C43—21no—
194C2×C4×C43—21no—
195C2×C4×C43—21no—
196C2×C4×C43—21no—
197C2×C4×C43—44no—
198C2×C4×C43C2×D412yes—
199C2×C4×C43C2×D412yes—
200C2×C4×C43C2×D412yes—
201C22⋊D43—44no—
202C22⋊D43—44no—
203C22⋊D43—44no—
204C22⋊D43—44no—
205C22⋊D43—44no—
206C22⋊D43—44no—
207C22⋊D43—44no—
208C2×Dic43—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43—21no—
213C2×Dic43—21no—
214C2×Dic43—21no—
215C2×Dic43—21no—
216C2×Dic43—21no—
217C2×Dic43—21no—
218C2×Dic43—21no—
219C2×Dic43—21no—
220C2×Dic43—21no—
221C2×Dic43C2×D412yes—
222C2×Dic43C2×D412yes—
223D172—44no—
224D172—44no—
225C22×C43—22no—
226C22×C43—22no—
227C22×C43—22no—
228C22×C43—22no—
229C22×C43—22no—
230C22×C43—22no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43—41no—
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—41no—
243C22×C43—41no—
244C22×C43—41no—
245C22×C43—41no—
246C22×C43C22×D411yescharacteristic
247C22×C43C22×D411yescharacteristic
248C22×C43C22×D411yescharacteristic
249C22×C43H(5,𝔽2)11yescharacteristic
250C22×C43H(5,𝔽2)11yescharacteristic
251C22×C43H(5,𝔽2)11yescharacteristic
252C22×C43H(5,𝔽2)11yescharacteristic
253C2×D43—22no—
254C2×D43—22no—
255C2×D43—22no—
256C2×D43—22no—
257C2×D43—22no—
258C2×D43—22no—
259C2×D43—416no—
260C2×D43—41no—
261C2×D43—41no—
262C2×D43—41no—
263C2×D43—41no—
264C2×D43—41no—
265C2×D43—41no—
266C2×D43—41no—
267C2×D43—41no—
268C2×D43—41no—
269C2×D43—41no—
270C2×D43—41no—
271C2×D43—41no—
272C2×D43—41no—
273C2×D43—41no—
274C2×D43—41no—
275C4×C43—22no—
276C4×C43—22no—
277C4×C43—22no—
278C4×C43—41no—
279Dic43—22no—
280Dic43—22no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#2669—431nomaximal, Sylow
285C2×C43—42no—
286C2×C43—42no—
287C2×C43—81no—
288C2×C43#53411yescharacteristic
289C2×C43#53511yescharacteristic
290C2×C43#53511yescharacteristic
291C2×C43D4211yescharacteristic
292C2×C43D4211yescharacteristic
293C2×C43D4211yescharacteristic
294C2×C43#56011yescharacteristic
295D43—42no—
296D43—42no—
297D43—81no—
298C2×#127—431no—
299C2×#121—431no—
300C2×#121D4311yescharacteristic, complemented
301C2×#120—431no—
302C2×#120—431no—
303C2×#120—431no—
304#394—431no—
305#394—431no—
306#392—431no—
307#392—431no—
308#392—431no—
309#392—431no—
310#388—431no—
311#388—431no—
312#386—431no—
313C43#266911yescharacteristic, complemented, Sylow
314C25—431no—
315C22×D4—431no—
316C22×D4—431no—
317C22×D4—431no—
318C22×D4—431no—
319C22×D4—431no—
320C22×D4—431no—
321C22×D4—431no—
322C22×D4—431no—
323C22×D4—431no—
324C22×D4C2×D4311yescharacteristic
325C22×D4C2×D4311yescharacteristic
326C22×D4C2×D4311yescharacteristic, complemented
327C23×C4C2×D4311yescharacteristic, complemented
328#127—864no—
329#121—24no—
330#121—864no—
331#120—864no—
332#120—864no—
333#120—864no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4C2×D4311yescharacteristic, complemented
336C2×C22⋊C4—431no—
337C2×C22⋊C4—431no—
338C2×C22⋊C4—431no—
339C2×C22⋊C4—431no—
340C2×C22⋊C4—431no—
341C2×C22⋊C4—431no—
342C2×C22⋊C4—431no—
343C2×C22⋊C4—431no—
344C2×C22⋊C4—431no—
345C2×C22⋊C4—431no—
346C2×C22⋊C4—431no—
347C2×C22⋊C4—431no—
348C2×C22⋊C4C2×D4311yescharacteristic
349C2×C22⋊C4C2×D4311yescharacteristic, complemented
350C2×C42—431no—
351#95—431no—
352#95—431no—
353#95—431no—
354#95—431no—
355C24—431no—
356C24—431no—
357C24—431no—
358C24—862no—
359C24—862no—
360C24—862no—
361C24—1721no—
362C24—1721no—
363C24—1721no—
364C24—1721no—
365C24C22×D4311yescharacteristic
366C24C22×D4311yescharacteristic
367C24C22×D4311yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—22no—
374C2×D4—41no—
375C2×D4—41no—
376C2×D4—41no—
377C2×D4—434no—
378C2×D4—862no—
379C2×D4—862no—
380C2×D4—862no—
381C2×D4—862no—
382C2×D4—862no—
383C2×D4—862no—
384C2×D4—862no—
385C2×D4—862no—
386C2×D4—862no—
387C2×D4—862no—
388C2×D4—862no—
389C2×D4—862no—
390C2×D4—862no—
391C2×D4—1721no—
392C2×D4—1721no—
393C2×D4—1721no—
394C2×D4—1721no—
395C2×D4—1721no—
396C2×D4—1721no—
397C2×D4—1721no—
398C2×D4—1721no—
399C2×D4—1721no—
400C2×D4—1721no—
401C2×D4—1721no—
402C2×D4—1721no—
403C2×D4—1721no—
404C22×C4—22no—
405C22×C4—22no—
406C22×C4—41no—
407C22×C4—431no—
408C22×C4—431no—
409C22×C4—431no—
410C22×C4—431no—
411C22×C4—431no—
412C22×C4C22×D4311yescharacteristic
413C22×C4C22×D4311yescharacteristic
414C22×C4C22×D4311yescharacteristic
415C22×C4C22×D4311yescharacteristic
416C4⋊C4—22no—
417C4⋊C4—862no—
418C22⋊C4—22no—
419C22⋊C4—434no—
420C22⋊C4—862no—
421C22⋊C4—862no—
422C22⋊C4—862no—
423C22⋊C4—862no—
424C22⋊C4—862no—
425C22⋊C4—862no—
426C22⋊C4—862no—
427C22⋊C4—862no—
428C22⋊C4—1721no—
429C22⋊C4—1721no—
430C22⋊C4—1721no—
431C22⋊C4C22⋊D4314yescomplemented
432C42—862no—
433C23—21no—
434C23—21no—
435C23—21no—
436C23—21no—
437C23—21no—
438C23—21no—
439C23—21no—
440C23—21no—
441C23—21no—
442C23—21no—
443C23—21no—
444C23—21no—
445C23—21no—
446C23—21no—
447C23—21no—
448C23—21no—
449C23—21no—
450C23—21no—
451C23—21no—
452C23—432no—
453C23—432no—
454C23—861no—
455C23—861no—
456C23—861no—
457C23—861no—
458C23—861no—
459C23—861no—
460C23—861no—
461C23—861no—
462C23—861no—
463C23—861no—
464C23—861no—
465C23—861no—
466C23—861no—
467C23—861no—
468C23—861no—
469C23—861no—
470C23—861no—
471C23—861no—
472C23—861no—
473C23—1724no—
474C23—1724no—
475C23—1724no—
476C23—1724no—
477C23—1724no—
478C23—1724no—
479C23—1724no—
480C23D4×D4312yes—
481C23C2×C22⋊D4312yes—
482C23C23×D4311yescharacteristic
483D4—44no—
484D4—44no—
485D4—44no—
486D4—1724no—
487D4—1724no—
488D4—1724no—
489D4—1724no—
490D4—1724no—
491D4—1724no—
492D4—1724no—
493D4—1724no—
494D4—1724no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—44no—
505C2×C4—432no—
506C2×C4—432no—
507C2×C4—861no—
508C2×C4—861no—
509C2×C4—861no—
510C2×C4—861no—
511C2×C4—861no—
512C2×C4—861no—
513C2×C4—861no—
514C2×C4—861no—
515C2×C4—861no—
516C2×C4—861no—
517C2×C4—861no—
518C2×C4—861no—
519C2×C4—861no—
520C2×C4D4×D4312yes—
521C2×C4C2×C22⋊D4312yes—
522C2×C4C2×C22⋊D4312yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—862no—
545C22—862no—
546C22—862no—
547C22—862no—
548C22—862no—
549C22—862no—
550C22—17216no—
551C22—1721no—
552C22—1721no—
553C22—1721no—
554C22—1721no—
555C22—1721no—
556C22—1721no—
557C22—1721no—
558C22—1721no—
559C22—1721no—
560C22—1721no—
561C22—1721no—
562C22—1721no—
563C22—1721no—
564C22—1721no—
565C22—1721no—
566C22C2×D4×D4311yescharacteristic
567C22C2×D4×D4311yescharacteristic
568C22C22×C22⋊D4311yescharacteristic
569C22#1306337011yescharacteristic
570C22#1306337011yescharacteristic
571C22#1306337111yescharacteristic
572C22#1306337111yescharacteristic
573C4—22no—
574C4—22no—
575C4—22no—
576C4—41no—
577C4—862no—
578C4—862no—
579C4—1721no—
580C4—1721no—
581C4—1721no—
582C2—42no—
583C2—42no—
584C2—81no—
585C2—3441no—
586C2—1722no—
587C2—1722no—
588C2#1458345711yescharacteristic
589C2#1458346311yescharacteristic
590C2#1458346511yescharacteristic
591C2D4×C22⋊D4311yescharacteristic
592C2D4×C22⋊D4311yescharacteristic
593C2#1458353311yescharacteristic
594C2#1458363711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2669
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13063321C2semidirect
2. C2×#13063299C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063293C2semidirect
5. C2×#13063293C2semidirect
6. #14582816C2semidirect
7. #14582815C2semidirect
8. #14582808C2semidirect
9. #14582807C2semidirect
10. #14582807C2semidirect
11. #14582807C2semidirect
12. #14582792C2semidirect
13. #14582789C2semidirect
14. #14582778C2semidirect
15. C2×#121×C43C2semidirect
24. C22×C22⋊D43C22semidirect
25. C22×C22⋊D43C22semidirect
31. C2×C4⋊Dic43C22semidirect
34. C2×C22⋊Dic43C22semidirect
35. C2×C22⋊Dic43C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×C4×Dic43C22semidirect
45. C43⋊#95C22semidirect
46. C43⋊#95C22semidirect
47. C43⋊#95C22semidirect
48. C43⋊#95C22semidirect
51. C22×D4×C43C22semidirect
52. C23×C4×C43C22semidirect
54. C2×C4⋊C4×C43C22semidirect
56. C2×C22⋊C4×C43C22semidirect
106. C2×C22⋊D43D4semidirect
120. C22⋊C4×C43D4semidirect
132. (C2×D43)⋊C4D4semidirect
300. C2×#121D43semidirect
313. C43#2669semidirect
326. C22×D4C2×D43semidirect
327. C23×C4C2×D43semidirect
335. C2×C4⋊C4C2×D43semidirect
349. C2×C22⋊C4C2×D43semidirect
431. C22⋊C4C22⋊D43semidirect