Finite Group Databasebeta

← #19140809

Subgroups — #19140809

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×#13063298C211yesmaximal, characteristic, complemented
3C2×#13063296C211yesmaximal, characteristic, complemented
4C2×#13063294C211yesmaximal, characteristic, complemented
5C2×#13063294C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582807C211yesmaximal, characteristic, complemented
11#14582807C211yesmaximal, characteristic, complemented
12#14582793C211yesmaximal, characteristic, complemented
13#14582792C211yesmaximal, characteristic, complemented
14#14582775C211yesmaximal, characteristic, complemented
15C2×#120×C43C211yesmaximal, characteristic, complemented
16C22×D172C2211yescharacteristic, complemented
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic
23C22×C22⋊D43C2211yescharacteristic, complemented
24C22×C22⋊D43C2211yescharacteristic, complemented
25C22×C4×D43C2211yescharacteristic, complemented
26#13063321—24no—
27#13063298—24no—
28#13063296—24no—
29#13063294—24no—
30#13063294—24no—
31C2×C4⋊Dic43C2211yescharacteristic, complemented
32C2×Dic43⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C22⋊Dic43C2211yescharacteristic
35C2×C22⋊Dic43C2211yescharacteristic
36C2×C22⋊Dic43C2211yescharacteristic
37C2×C22⋊Dic43C2211yescharacteristic
38C2×C22⋊Dic43C2211yescharacteristic
39C2×C22⋊Dic43C2211yescharacteristic, complemented
40C2×C22⋊Dic43C2211yescharacteristic, complemented
41C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
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
49C25×C43C2211yescharacteristic
50C22×D4×C43C2211yescharacteristic
51C22×D4×C43C2211yescharacteristic
52C22×D4×C43C2211yescharacteristic
53#120×C43—24no—
54C2×C22⋊C4×C43C2211yescharacteristic
55C2×C22⋊C4×C43C2211yescharacteristic
56C2×C22⋊C4×C43C2211yescharacteristic
57C24×C43—22no—
58C24×C43—22no—
59C24×C43—22no—
60C24×C43—41no—
61C24×C43—41no—
62C24×C43—41no—
63C24×C43—41no—
64C24×C43C2311yescharacteristic
65C24×C43C2311yescharacteristic
66C24×C43C2311yescharacteristic
67C24×C43C2311yescharacteristic
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—41no—
76C2×D4×C43—41no—
77C2×D4×C43—41no—
78C2×D4×C43—41no—
79C22×C4×C43C2311yescharacteristic
80C22×C4×C43C2311yescharacteristic
81C22×C4×C43C2311yescharacteristic
82C2×C22⋊D43—22no—
83C2×C22⋊D43—22no—
84C2×C22⋊D43—22no—
85C2×C22⋊D43—22no—
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—41no—
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⋊D43D414yescomplemented
106C22×Dic43C2311yescharacteristic
107C22×Dic43C2311yescharacteristic
108C22×Dic43C2311yescharacteristic
109C22×Dic43C2311yescharacteristic
110C22×Dic43C2311yescharacteristic
111C22×Dic43C2311yescharacteristic
112C2×D172—22no—
113C2×D172—22no—
114C2×D172—41no—
115C2×C4×D43—22no—
116C2×C4×D43—22no—
117C2×C4×D43—41no—
118C22⋊C4×C43—22no—
119C22⋊C4×C43—22no—
120C22⋊C4×C43D414yescomplemented
121C22⋊Dic43—22no—
122C22⋊Dic43—22no—
123C22⋊Dic43—22no—
124C22⋊Dic43—22no—
125C22⋊Dic43—22no—
126C22⋊Dic43—22no—
127C22⋊Dic43—41no—
128C22⋊Dic43D414yescomplemented
129(C2×D43)⋊C4—22no—
130(C2×D43)⋊C4—41no—
131(C2×D43)⋊C4—41no—
132C4⋊Dic43—22no—
133Dic43⋊C4—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×C43—21no—
155C23×C43—21no—
156C23×C43—21no—
157C23×C43—21no—
158C23×C43—21no—
159C23×C43—21no—
160C23×C43—44no—
161C23×C43—44no—
162C23×C43—44no—
163C23×C43—44no—
164C23×C43—44no—
165C23×C43—44no—
166C23×C43—44no—
167C23×C43C2×D412yes—
168C23×C43C2×D412yes—
169C23×C43C2×D412yes—
170C23×C43C2411yescharacteristic
171C22×D43—21no—
172C22×D43—21no—
173C22×D43—21no—
174C22×D43—21no—
175C22×D43—21no—
176C22×D43—21no—
177C22×D43—21no—
178C22×D43—21no—
179C22×D43—21no—
180C22×D43—21no—
181C22×D43—21no—
182C22×D43—21no—
183C22×D43—21no—
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×C43C2×D412yes—
196C2×C4×C43C2×D412yes—
197C22⋊D43—44no—
198C22⋊D43—44no—
199C22⋊D43—44no—
200C22⋊D43—44no—
201C22⋊D43—44no—
202C22⋊D43—44no—
203C22⋊D43—44no—
204C22⋊D43—44no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
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×Dic43C2×D412yes—
221C2×Dic43C2×D412yes—
222C2×Dic43C2×D412yes—
223D172—44no—
224C4×D43—44no—
225C22×C43—22no—
226C22×C43—22no—
227C22×C43—22no—
228C22×C43—22no—
229C22×C43—22no—
230C22×C43—22no—
231C22×C43—22no—
232C22×C43—22no—
233C22×C43—22no—
234C22×C43—416no—
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×C43—41no—
247C22×C43—41no—
248C22×C43—41no—
249C22×C43—41no—
250C22×C43—41no—
251C22×C43—41no—
252C22×C43—41no—
253C22×C43—41no—
254C22×C43C22×D411yescharacteristic
255C22×C43C22×D411yescharacteristic
256C22×C43C22×D411yescharacteristic
257C22×C43H(5,𝔽2)11yescharacteristic
258C22×C43H(5,𝔽2)11yescharacteristic
259C22×C43H(5,𝔽2)11yescharacteristic
260C22×C43H(5,𝔽2)11yescharacteristic
261C2×D43—22no—
262C2×D43—22no—
263C2×D43—22no—
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—41no—
278Dic43—22no—
279Dic43—22no—
280Dic43—22no—
281Dic43—41no—
282Dic43—41no—
283Dic43—41no—
284#2669—431nomaximal, Sylow
285C2×C43—42no—
286C2×C43—42no—
287C2×C43—42no—
288C2×C43—81no—
289C2×C43#53411yescharacteristic
290C2×C43#53511yescharacteristic
291C2×C43#53511yescharacteristic
292C2×C43D4211yescharacteristic
293C2×C43D4211yescharacteristic
294C2×C43D4211yescharacteristic
295C2×C43#56011yescharacteristic
296D43—42no—
297D43—81no—
298C2×#127—431no—
299C2×#121—431no—
300C2×#121—431no—
301C2×#120—431no—
302C2×#120—431no—
303C2×#120D4311yescharacteristic, complemented
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
314C25C2×D4311yescharacteristic
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
327C23×C4—431no—
328#127—864no—
329#121—864no—
330#121—864no—
331#120—24no—
332#120—864no—
333#120—864no—
334C2×C4⋊C4—431no—
335C2×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
348C2×C22⋊C4C2×D4311yescharacteristic
349C2×C22⋊C4C2×D4311yescharacteristic
350C2×C42—431no—
351#95—431no—
352#95—431no—
353#95—431no—
354#95—431no—
355C24—22no—
356C24—22no—
357C24—22no—
358C24—41no—
359C24—41no—
360C24—41no—
361C24—41no—
362C24—431no—
363C24—431no—
364C24C22×D4311yescharacteristic
365C24C22×D4311yescharacteristic
366C24C22×D4311yescharacteristic
367C24C22×D4311yescharacteristic
368C2×D4—22no—
369C2×D4—22no—
370C2×D4—22no—
371C2×D4—22no—
372C2×D4—22no—
373C2×D4—41no—
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—862no—
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—431no—
405C22×C4—431no—
406C22×C4—431no—
407C22×C4—431no—
408C22×C4—431no—
409C22×C4—431no—
410C22×C4—862no—
411C22×C4—862no—
412C22×C4—1721no—
413C22×C4C22×D4311yescharacteristic
414C22×C4C22×D4311yescharacteristic
415C22×C4C22×D4311yescharacteristic
416C4⋊C4—862no—
417C4⋊C4—862no—
418C22⋊C4—22no—
419C22⋊C4—22no—
420C22⋊C4—434no—
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—21no—
453C23—21no—
454C23—21no—
455C23—21no—
456C23—21no—
457C23—21no—
458C23—44no—
459C23—44no—
460C23—44no—
461C23—44no—
462C23—44no—
463C23—44no—
464C23—44no—
465C23—432no—
466C23—861no—
467C23—861no—
468C23—861no—
469C23—861no—
470C23—861no—
471C23—861no—
472C23—861no—
473C23—861no—
474C23—861no—
475C23—861no—
476C23—861no—
477C23—861no—
478C23—861no—
479C23D4×D4312yes—
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—432no—
503C2×C4—432no—
504C2×C4—432no—
505C2×C4—861no—
506C2×C4—861no—
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×C4—1724no—
521C2×C4C2×C22⋊D4312yes—
522C2×C4C2×C22⋊D4312yes—
523C22—22no—
524C22—22no—
525C22—22no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—22no—
530C22—22no—
531C22—22no—
532C22—416no—
533C22—41no—
534C22—41no—
535C22—41no—
536C22—41no—
537C22—41no—
538C22—41no—
539C22—41no—
540C22—41no—
541C22—41no—
542C22—41no—
543C22—41no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22—862no—
553C22—862no—
554C22—862no—
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#1306337011yescharacteristic
572C22#1306337011yescharacteristic
573C4—22no—
574C4—22no—
575C4—41no—
576C4—862no—
577C4—862no—
578C4—862no—
579C4—1721no—
580C4—1721no—
581C4—1721no—
582C2—42no—
583C2—42no—
584C2—42no—
585C2—81no—
586C2—3441no—
587C2—1722no—
588C2#1458345911yescharacteristic
589C2#1458346411yescharacteristic
590C2#1458346611yescharacteristic
591C2#1458353111yescharacteristic
592C2D4×C22⋊D4311yescharacteristic
593C2D4×C22⋊D4311yescharacteristic
594C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#120×C43C2
hypercenterC2×#120D43
hypocenterC43#2669
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13063321C2semidirect
2. C2×#13063298C2semidirect
3. C2×#13063296C2semidirect
4. C2×#13063294C2semidirect
5. C2×#13063294C2semidirect
6. #14582815C2semidirect
7. #14582813C2semidirect
8. #14582808C2semidirect
9. #14582807C2semidirect
10. #14582807C2semidirect
11. #14582807C2semidirect
12. #14582793C2semidirect
13. #14582792C2semidirect
14. #14582775C2semidirect
15. C2×#120×C43C2semidirect
16. C22×D172C22semidirect
23. C22×C22⋊D43C22semidirect
24. C22×C22⋊D43C22semidirect
25. C22×C4×D43C22semidirect
31. C2×C4⋊Dic43C22semidirect
32. C2×Dic43⋊C4C22semidirect
39. C2×C22⋊Dic43C22semidirect
40. C2×C22⋊Dic43C22semidirect
41. C2×(C2×D43)⋊C4C22semidirect
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
105. C2×C22⋊D43D4semidirect
120. C22⋊C4×C43D4semidirect
128. C22⋊Dic43D4semidirect
303. C2×#120D43semidirect
313. C43#2669semidirect
431. C22⋊C4C22⋊D43semidirect