Finite Group Databasebeta

← #19138125

Subgroups — #19138125

Order 5504.

922 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063299C211yesmaximal, characteristic, complemented
2C2×#13063297C211yesmaximal, characteristic, complemented
3C2×#13063295C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5C22×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
6#14582821C211yesmaximal, characteristic, complemented
7#14582816C211yesmaximal, characteristic, complemented
8#14582815C211yesmaximal, characteristic, complemented
9#14582808C211yesmaximal, characteristic, complemented
10#14582801C211yesmaximal, characteristic, complemented
11#14582790C211yesmaximal, characteristic, complemented
12#14582778C211yesmaximal, characteristic, complemented
13#14582778C211yesmaximal, characteristic, complemented
14#14582774C211yesmaximal, characteristic, complemented
15C2×C4×D4×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23C23×Dic43C2211yescharacteristic
24#13063299—24no—
25#13063297—24no—
26#13063295—24no—
27#13063293—24no—
28C2×C4⋊Dic43C2211yescharacteristic, complemented
29C2×C4⋊Dic43C2211yescharacteristic, complemented
30C2×Dic43⋊C4C2211yescharacteristic, complemented
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic, complemented
33C2×(C2×D43)⋊C4—24no—
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C43⋊#95C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C43⋊#95C2211yescharacteristic, complemented
49C22×D4×C43C2211yescharacteristic
50C23×C4×C43C2211yescharacteristic
51C23×C4×C43C2211yescharacteristic, complemented
52C4×D4×C43—24no—
53C2×C4⋊C4×C43C2211yescharacteristic, complemented
54C2×C22⋊C4×C43C2211yescharacteristic
55C2×C22⋊C4×C43C2211yescharacteristic, complemented
56C2×C42×C43C2211yescharacteristic, complemented
57C24×C43C2311yescharacteristic
58C24×C43C2311yescharacteristic
59C23×D43—22no—
60C23×D43—22no—
61C23×D43—22no—
62C23×D43—22no—
63C23×D43—22no—
64C23×D43—41no—
65C23×D43—41no—
66C23×D43C2311yescharacteristic
67C23×D43C2311yescharacteristic
68C23×D43C2311yescharacteristic
69C2×D4×C43—22no—
70C2×D4×C43—22no—
71C2×D4×C43D414yescomplemented
72C22×C4×C43—22no—
73C22×C4×C43—22no—
74C22×C4×C43—22no—
75C22×C4×C43—22no—
76C22×C4×C43—41no—
77C22×C4×C43—41no—
78C22×C4×C43C2311yescharacteristic
79C22×C4×C43C2311yescharacteristic
80C22×C4×C43C2311yescharacteristic
81C22×C4×C43C2311yescharacteristic
82C22×C4×C43C2311yescharacteristic
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—41no—
93C2×C22⋊D43—41no—
94C2×C22⋊D43—41no—
95C22×Dic43—22no—
96C22×Dic43—22no—
97C22×Dic43—41no—
98C22×Dic43C2311yescharacteristic
99C22×Dic43C2311yescharacteristic
100C22×Dic43C2311yescharacteristic
101C22×Dic43C2311yescharacteristic
102C22×Dic43C2311yescharacteristic
103C2×D172—22no—
104C2×D172—22no—
105C2×D172—22no—
106C2×D172—22no—
107C2×D172—41no—
108C2×D172—41no—
109C4⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43D414yescomplemented
112C42×C43—22no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115(C2×D43)⋊C4—22no—
116(C2×D43)⋊C4—22no—
117(C2×D43)⋊C4—22no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—22no—
122(C2×D43)⋊C4—22no—
123(C2×D43)⋊C4—22no—
124(C2×D43)⋊C4—41no—
125(C2×D43)⋊C4D414yescomplemented
126C4⋊Dic43—22no—
127C4⋊Dic43—41no—
128Dic43⋊C4—22no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—21no—
137C23×C43—21no—
138C23×C43—21no—
139C23×C43C2×D412yes—
140C23×C43C2×D412yes—
141C23×C43C2×D412yes—
142C23×C43#4112yes—
143C23×C43C2411yescharacteristic
144C22×D43—28no—
145C22×D43—21no—
146C22×D43—21no—
147C22×D43—21no—
148C22×D43—21no—
149C22×D43—21no—
150C22×D43—21no—
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—21no—
162C22×D43—21no—
163C22×D43—21no—
164C22×D43—44no—
165C22×D43—44no—
166C22×D43—44no—
167C22×D43—44no—
168C22×D43—44no—
169C22×D43—44no—
170C22×D43C2×D412yes—
171C22×D43#4112yes—
172D4×C43—28no—
173C2×C4×C43—21no—
174C2×C4×C43—21no—
175C2×C4×C43—21no—
176C2×C4×C43—21no—
177C2×C4×C43—21no—
178C2×C4×C43—21no—
179C2×C4×C43—21no—
180C2×C4×C43—21no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—44no—
185C2×C4×C43—44no—
186C2×C4×C43C2×D412yes—
187C2×C4×C43C2×D412yes—
188C2×C4×C43C2×D412yes—
189C2×C4×C43C2×D412yes—
190C22⋊D43—44no—
191C22⋊D43—44no—
192C22⋊D43—44no—
193C22⋊D43—44no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43—44no—
209C2×Dic43C2×D412yes—
210D172—44no—
211D172—44no—
212C22×C43—22no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—22no—
216C22×C43—22no—
217C22×C43—22no—
218C22×C43—22no—
219C22×C43—22no—
220C22×C43—22no—
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43#12114yescomplemented
226C22×C43C22×D411yescharacteristic
227C22×C43C22×D411yescharacteristic
228C22×C43C22×D411yescharacteristic
229C22×C43C2×#4111yescharacteristic
230C22×C43C2×#4111yescharacteristic
231C22×C43H(5,𝔽2)11yescharacteristic
232C22×C43H(5,𝔽2)11yescharacteristic
233C2×D43—22no—
234C2×D43—22no—
235C2×D43—22no—
236C2×D43—22no—
237C2×D43—22no—
238C2×D43—22no—
239C2×D43—416no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—41no—
246C2×D43—41no—
247C2×D43—41no—
248C2×D43—41no—
249C2×D43—41no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C2×D43—41no—
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—22no—
258C4×C43—22no—
259C4×C43—41no—
260Dic43—22no—
261Dic43—41no—
262Dic43—41no—
263Dic43—41no—
264Dic43—41no—
265#2424—431nomaximal, Sylow
266C2×C43—24no—
267C2×C43—42no—
268C2×C43C2×#12111yescharacteristic
269C2×C43#52511yescharacteristic
270C2×C43#53811yescharacteristic
271C2×C43D4211yescharacteristic
272C2×C43D4211yescharacteristic
273C2×C43#54611yescharacteristic
274C2×C43#54611yescharacteristic
275D43—42no—
276D43—42no—
277D43—81no—
278C2×#121—431no—
279C2×#121—431no—
280C2×#120—431no—
281C2×#120—431no—
282C2×C4×D4D4311yescharacteristic, complemented
283C22×C22⋊C4—431no—
284#396—431no—
285#394—431no—
286#394—431no—
287#392—431no—
288#390—431no—
289#388—431no—
290#386—431no—
291#386—431no—
292#385—431no—
293C43#242411yescharacteristic, complemented, Sylow
294C25—431no—
295C22×D4—431no—
296C22×D4—431no—
297C22×D4—431no—
298C22×D4—431no—
299C22×D4—431no—
300C22×D4—431no—
301C22×D4C2×D4311yescharacteristic
302C23×C4—431no—
303C23×C4C2×D4311yescharacteristic
304C23×C4C2×D4311yescharacteristic, complemented
305#121—864no—
306#121—864no—
307#120—864no—
308#120—864no—
309C4×D4—24no—
310C2×C4⋊C4—431no—
311C2×C4⋊C4—431no—
312C2×C4⋊C4—431no—
313C2×C4⋊C4C2×D4311yescharacteristic, complemented
314C2×C22⋊C4—431no—
315C2×C22⋊C4—431no—
316C2×C22⋊C4—431no—
317C2×C22⋊C4—431no—
318C2×C22⋊C4—431no—
319C2×C22⋊C4—431no—
320C2×C22⋊C4—431no—
321C2×C22⋊C4—431no—
322C2×C22⋊C4—431no—
323C2×C22⋊C4—431no—
324C2×C22⋊C4—431no—
325C2×C22⋊C4—431no—
326C2×C22⋊C4—431no—
327C2×C22⋊C4—864no—
328C2×C22⋊C4C2×D4311yescharacteristic
329C2×C22⋊C4C2×D4311yescharacteristic, complemented
330C2×C42C2×D4311yescharacteristic, complemented
331#95—431no—
332#95—431no—
333#95—431no—
334#95—431no—
335C24—431no—
336C24—431no—
337C24—431no—
338C24—862no—
339C24—862no—
340C24—862no—
341C24—862no—
342C24—862no—
343C24—1721no—
344C24—1721no—
345C24C22×D4311yescharacteristic
346C24C22×D4311yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—862no—
350C2×D4—862no—
351C2×D4—862no—
352C2×D4—862no—
353C2×D4—862no—
354C2×D4—862no—
355C2×D4—862no—
356C2×D4—862no—
357C2×D4—862no—
358C2×D4—862no—
359C2×D4—862no—
360C2×D4—862no—
361C2×D4—862no—
362C2×D4—1721no—
363C2×D4—1721no—
364C2×D4—1721no—
365C2×D4—1721no—
366C2×D4—1721no—
367C2×D4D17214yescomplemented
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—22no—
371C22×C4—22no—
372C22×C4—41no—
373C22×C4—41no—
374C22×C4—431no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—431no—
378C22×C4—431no—
379C22×C4—862no—
380C22×C4—862no—
381C22×C4—1721no—
382C22×C4C22×D4311yescharacteristic
383C22×C4C22×D4311yescharacteristic
384C22×C4C22×D4311yescharacteristic
385C22×C4C22×D4311yescharacteristic
386C22×C4C22×D4311yescharacteristic
387C4⋊C4—22no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—1721no—
391C22⋊C4—22no—
392C22⋊C4—434no—
393C22⋊C4—862no—
394C22⋊C4—862no—
395C22⋊C4—862no—
396C22⋊C4—862no—
397C22⋊C4—862no—
398C22⋊C4—862no—
399C22⋊C4—862no—
400C22⋊C4—862no—
401C22⋊C4—862no—
402C22⋊C4—862no—
403C22⋊C4—862no—
404C22⋊C4—1721no—
405C22⋊C4C22⋊D4314yescomplemented
406C42—22no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—432no—
418C23—432no—
419C23—868no—
420C23—861no—
421C23—861no—
422C23—861no—
423C23—861no—
424C23—861no—
425C23—861no—
426C23—861no—
427C23—861no—
428C23—861no—
429C23—861no—
430C23—861no—
431C23—861no—
432C23—861no—
433C23—861no—
434C23—861no—
435C23—861no—
436C23—861no—
437C23—861no—
438C23—861no—
439C23—1724no—
440C23—1724no—
441C23—1724no—
442C23—1724no—
443C23—1724no—
444C23—1724no—
445C23C2×D17212yes—
446C23C2×D17212yes—
447C23#1062189812yes—
448C23C2×C22⋊D4312yes—
449C23C23×D4311yescharacteristic
450D4—28no—
451D4—1724no—
452D4—1724no—
453D4—1724no—
454D4—1724no—
455D4—1724no—
456D4—1724no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—21no—
460C2×C4—21no—
461C2×C4—21no—
462C2×C4—21no—
463C2×C4—21no—
464C2×C4—21no—
465C2×C4—21no—
466C2×C4—21no—
467C2×C4—21no—
468C2×C4—44no—
469C2×C4—44no—
470C2×C4—432no—
471C2×C4—861no—
472C2×C4—861no—
473C2×C4—861no—
474C2×C4—861no—
475C2×C4—861no—
476C2×C4—861no—
477C2×C4—861no—
478C2×C4—861no—
479C2×C4—861no—
480C2×C4—861no—
481C2×C4—861no—
482C2×C4—861no—
483C2×C4—861no—
484C2×C4—861no—
485C2×C4—1724no—
486C2×C4C2×D17212yes—
487C2×C4D4×D4312yes—
488C2×C4C2×C22⋊D4312yes—
489C2×C4C2×C22⋊D4312yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—22no—
497C22—22no—
498C22—22no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—862no—
504C22—862no—
505C22—862no—
506C22—862no—
507C22—862no—
508C22—862no—
509C22—17216no—
510C22—1721no—
511C22—1721no—
512C22—1721no—
513C22—1721no—
514C22—1721no—
515C22—1721no—
516C22—1721no—
517C22—1721no—
518C22—1721no—
519C22—1721no—
520C22—1721no—
521C22—1721no—
522C22—1721no—
523C22—1721no—
524C22—1721no—
525C22#1306329914yescomplemented
526C22C2×D4×D4311yescharacteristic
527C22C22×C22⋊D4311yescharacteristic
528C22C22×D17211yescharacteristic
529C22#41×D4311yescharacteristic
530C22C2×#1062189811yescharacteristic
531C22#1306337011yescharacteristic
532C22#1306337111yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—22no—
537C4—41no—
538C4—862no—
539C4—1721no—
540C4—1721no—
541C4—1721no—
542C4—1721no—
543C2—24no—
544C2—42no—
545C2—3441no—
546C2—1722no—
547C2—1722no—
548C2C2×#1306329911yescharacteristic
549C2#1458340811yescharacteristic
550C2#1458348211yescharacteristic
551C2D4×C22⋊D4311yescharacteristic
552C2D4×D17211yescharacteristic
553C2#1458353711yescharacteristic
554C2#1458354411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×C4×D4×C43C2
hypercenterC2×C4×D4D43
hypocenterC43#2424
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13063299C2semidirect
2. C2×#13063297C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063293C2semidirect
5. C22×(C2×D43)⋊C4C2semidirect
6. #14582821C2semidirect
7. #14582816C2semidirect
8. #14582815C2semidirect
9. #14582808C2semidirect
10. #14582801C2semidirect
11. #14582790C2semidirect
12. #14582778C2semidirect
13. #14582778C2semidirect
14. #14582774C2semidirect
15. C2×C4×D4×C43C2semidirect
22. C22×C22⋊D43C22semidirect
28. C2×C4⋊Dic43C22semidirect
29. C2×C4⋊Dic43C22semidirect
30. C2×Dic43⋊C4C22semidirect
32. C2×C22⋊Dic43C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C43⋊#95C22semidirect
46. C43⋊#95C22semidirect
47. C43⋊#95C22semidirect
48. C43⋊#95C22semidirect
51. C23×C4×C43C22semidirect
53. C2×C4⋊C4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. C2×C42×C43C22semidirect
71. C2×D4×C43D4semidirect
111. C22⋊C4×C43D4semidirect
125. (C2×D43)⋊C4D4semidirect
225. C22×C43#121semidirect
282. C2×C4×D4D43semidirect
293. C43#2424semidirect
304. C23×C4C2×D43semidirect
313. C2×C4⋊C4C2×D43semidirect
329. C2×C22⋊C4C2×D43semidirect
330. C2×C42C2×D43semidirect
367. C2×D4D172semidirect
405. C22⋊C4C22⋊D43semidirect
525. C22#13063299semidirect