Finite Group Databasebeta

← #19140819

Subgroups — #19140819

Order 5504.

796 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063313C211yesmaximal, characteristic, complemented
2C2×#13063311C211yesmaximal, characteristic, complemented
3C2×#13063295C211yesmaximal, characteristic, complemented
4C2×#13063295C211yesmaximal, characteristic, complemented
5#14582816C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582812C211yesmaximal, characteristic, complemented
8#14582809C211yesmaximal, characteristic, complemented
9#14582809C211yesmaximal, characteristic, complemented
10#14582808C211yesmaximal, characteristic, complemented
11#14582801C211yesmaximal, characteristic, complemented
12#14582800C211yesmaximal, characteristic, complemented
13#14582791C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#388C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×Dic86C2211yescharacteristic, complemented
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic
20C22×D172C2211yescharacteristic
21C22×D172C2211yescharacteristic
22C22×D172C2211yescharacteristic, complemented
23C22×C22⋊D43C2211yescharacteristic
24C22×C22⋊D43C2211yescharacteristic
25#13063313—24no—
26#13063311—24no—
27#13063295—24no—
28#13063295—24no—
29C2×C4⋊Dic43C2211yescharacteristic, complemented
30C2×C22⋊Dic43C2211yescharacteristic
31C2×(C2×D43)⋊C4C2211yescharacteristic
32C2×(C2×D43)⋊C4C2211yescharacteristic
33C2×(C2×D43)⋊C4C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic
35C2×(C2×D43)⋊C4C2211yescharacteristic
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
41C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
42C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
43C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
45C2×C4×Dic43C2211yescharacteristic, complemented
46C43⋊#95C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C2×C4⋊C4×C43C2211yescharacteristic, complemented
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C42×C43C2211yescharacteristic, complemented
53#95×C43C2211yescharacteristic, complemented
54#95×C43C2211yescharacteristic, complemented
55C24×C43C2311yescharacteristic
56C23×D43—22no—
57C23×D43—22no—
58C23×D43—22no—
59C23×D43—41no—
60C23×D43—41no—
61C23×D43—41no—
62C23×D43—41no—
63C23×D43C2311yescharacteristic
64C23×D43C2311yescharacteristic
65C23×D43C2311yescharacteristic
66C23×D43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C22×C4×C43C2311yescharacteristic
72C22×C4×C43C2311yescharacteristic
73C2×C22⋊D43—22no—
74C2×C22⋊D43—22no—
75C2×C22⋊D43—22no—
76C2×C22⋊D43—41no—
77C2×C22⋊D43—41no—
78C2×C22⋊D43—41no—
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C2×D172—22no—
84C2×D172—22no—
85C2×D172—22no—
86C2×D172—22no—
87C2×D172—22no—
88C2×D172—22no—
89C2×D172—22no—
90C2×D172—41no—
91C2×D172—41no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C2×D172—41no—
97C2×D172—41no—
98C2×Dic86—22no—
99C2×Dic86—22no—
100C2×Dic86—41no—
101C4⋊C4×C43—41no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—41no—
104C22⋊C4×C43D414yescomplemented
105C42×C43—22no—
106C22⋊Dic43—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—22no—
109(C2×D43)⋊C4—22no—
110(C2×D43)⋊C4—22no—
111(C2×D43)⋊C4—22no—
112(C2×D43)⋊C4—22no—
113(C2×D43)⋊C4—22no—
114(C2×D43)⋊C4—22no—
115(C2×D43)⋊C4—41no—
116(C2×D43)⋊C4—41no—
117(C2×D43)⋊C4—41no—
118(C2×D43)⋊C4—41no—
119(C2×D43)⋊C4—41no—
120(C2×D43)⋊C4D414yescomplemented
121C4⋊Dic43—41no—
122C4×Dic43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43C2×D412yes—
130C23×C43C2411yescharacteristic
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—21no—
138C22×D43—21no—
139C22×D43—21no—
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
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—44no—
158C22×D43—44no—
159C22×D43—44no—
160C22×D43—44no—
161C22×D43—44no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43C2×D412yes—
165C22×D43#4112yes—
166C2×C4×C43—21no—
167C2×C4×C43—21no—
168C2×C4×C43—21no—
169C2×C4×C43—21no—
170C2×C4×C43—21no—
171C2×C4×C43—21no—
172C2×C4×C43—21no—
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×C43C2×D412yes—
182C2×C4×C43C2×D412yes—
183C2×C4×C43C2×D412yes—
184C22⋊D43—44no—
185C22⋊D43—44no—
186C2×Dic43—21no—
187C2×Dic43—21no—
188C2×Dic43—21no—
189C2×Dic43—21no—
190C2×Dic43—21no—
191C2×Dic43—21no—
192C2×Dic43—21no—
193C2×Dic43—21no—
194C2×Dic43—21no—
195C2×Dic43—21no—
196C2×Dic43—21no—
197C2×Dic43C2×D412yes—
198D172—44no—
199D172—44no—
200D172—44no—
201D172—44no—
202D172—44no—
203Dic86—44no—
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43C22×D411yescharacteristic
212C22×C43C22×D411yescharacteristic
213C22×C43C2×#4111yescharacteristic
214C22×C43H(5,𝔽2)11yescharacteristic
215C22×C43H(5,𝔽2)11yescharacteristic
216C22×C43H(5,𝔽2)11yescharacteristic
217C22×C43H(5,𝔽2)11yescharacteristic
218C2×D43—22no—
219C2×D43—22no—
220C2×D43—22no—
221C2×D43—22no—
222C2×D43—22no—
223C2×D43—22no—
224C2×D43—416no—
225C2×D43—41no—
226C2×D43—41no—
227C2×D43—41no—
228C2×D43—41no—
229C2×D43—41no—
230C2×D43—41no—
231C2×D43—41no—
232C2×D43—41no—
233C2×D43—41no—
234C2×D43—41no—
235C2×D43—41no—
236C2×D43—41no—
237C2×D43—41no—
238C2×D43—41no—
239C2×D43—41no—
240C2×D43—41no—
241C2×D43—41no—
242C2×D43—41no—
243C2×D43—41no—
244C2×D43—41no—
245C2×D43—41no—
246C2×D43—41no—
247C4×C43—22no—
248C4×C43—22no—
249C4×C43—22no—
250C4×C43—41no—
251C4×C43—41no—
252C4×C43—41no—
253Dic43—22no—
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257#2670—431nomaximal, Sylow
258C2×C43—42no—
259C2×C43#53511yescharacteristic
260C2×C43#53511yescharacteristic
261C2×C43#53811yescharacteristic
262C2×C43D4211yescharacteristic
263C2×C43#54611yescharacteristic
264C2×C43#54611yescharacteristic
265C2×C43H(3,𝔽4)11yescharacteristic
266D43—42no—
267D43—42no—
268D43—81no—
269D43—81no—
270C2×#124—431no—
271C2×#124—431no—
272C2×#120—431no—
273C2×#120—431no—
274#394—431no—
275#394—431no—
276#393—431no—
277#392—431no—
278#392—431no—
279#392—431no—
280#390—431no—
281#390—431no—
282#388—431no—
283#388D4311yescharacteristic, complemented
284#379—431no—
285C43#267011yescharacteristic, complemented, Sylow
286C25—431no—
287C22×Q8—431no—
288C22×D4—431no—
289C22×D4—431no—
290C22×D4—431no—
291C22×D4—431no—
292C22×D4—431no—
293C22×D4—431no—
294C22×D4—431no—
295#124—864no—
296#124—864no—
297#120—864no—
298#120—864no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4C2×D4311yescharacteristic, complemented
301C2×C22⋊C4—431no—
302C2×C22⋊C4—431no—
303C2×C22⋊C4—431no—
304C2×C22⋊C4—431no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4—431no—
307C2×C22⋊C4—431no—
308C2×C22⋊C4—431no—
309C2×C22⋊C4—431no—
310C2×C22⋊C4—431no—
311C2×C22⋊C4—431no—
312C2×C22⋊C4—431no—
313C2×C22⋊C4—431no—
314C2×C22⋊C4—431no—
315C2×C22⋊C4—431no—
316C2×C22⋊C4C2×D4311yescharacteristic
317C2×C22⋊C4C2×D4311yescharacteristic
318C2×C22⋊C4C2×D4311yescharacteristic
319C2×C42—431no—
320C2×C42C2×D4311yescharacteristic, complemented
321#95—431no—
322#95—431no—
323#95C2×D4311yescharacteristic, complemented
324#95C2×D4311yescharacteristic, complemented
325C24—431no—
326C24—431no—
327C24—431no—
328C24—431no—
329C24—862no—
330C24—862no—
331C24—862no—
332C24—1721no—
333C24—1721no—
334C24—1721no—
335C24—1721no—
336C24C22×D4311yescharacteristic
337C2×Q8—862no—
338C2×Q8—862no—
339C2×Q8—1721no—
340C2×D4—862no—
341C2×D4—862no—
342C2×D4—862no—
343C2×D4—862no—
344C2×D4—862no—
345C2×D4—862no—
346C2×D4—862no—
347C2×D4—862no—
348C2×D4—862no—
349C2×D4—862no—
350C2×D4—1721no—
351C2×D4—1721no—
352C2×D4—1721no—
353C2×D4—1721no—
354C2×D4—1721no—
355C2×D4—1721no—
356C2×D4—1721no—
357C2×D4—1721no—
358C2×D4—1721no—
359C2×D4—1721no—
360C2×D4—1721no—
361C22×C4—431no—
362C22×C4—431no—
363C22×C4—431no—
364C22×C4—431no—
365C22×C4C22×D4311yescharacteristic
366C22×C4C22×D4311yescharacteristic
367C22×C4C22×D4311yescharacteristic
368C22×C4C22×D4311yescharacteristic
369C22×C4C22×D4311yescharacteristic
370C22×C4C22×D4311yescharacteristic
371C4⋊C4—41no—
372C4⋊C4—1721no—
373C22⋊C4—22no—
374C22⋊C4—41no—
375C22⋊C4—434no—
376C22⋊C4—862no—
377C22⋊C4—862no—
378C22⋊C4—862no—
379C22⋊C4—862no—
380C22⋊C4—862no—
381C22⋊C4—862no—
382C22⋊C4—862no—
383C22⋊C4—862no—
384C22⋊C4—862no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4D17214yescomplemented
391C42—22no—
392C42—862no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—432no—
400C23—432no—
401C23—861no—
402C23—861no—
403C23—861no—
404C23—861no—
405C23—861no—
406C23—861no—
407C23—861no—
408C23—861no—
409C23—861no—
410C23—861no—
411C23—861no—
412C23—861no—
413C23—861no—
414C23—861no—
415C23—861no—
416C23—861no—
417C23—861no—
418C23—861no—
419C23—861no—
420C23—861no—
421C23—861no—
422C23—861no—
423C23—861no—
424C23—861no—
425C23—861no—
426C23—861no—
427C23—1724no—
428C23—1724no—
429C23—1724no—
430C23—1724no—
431C23—1724no—
432C23—1724no—
433C23—1724no—
434C23C2×D17212yes—
435C23C23×D4311yescharacteristic
436Q8—1724no—
437D4—1724no—
438D4—1724no—
439D4—1724no—
440D4—1724no—
441D4—1724no—
442D4—1724no—
443D4—1724no—
444C2×C4—21no—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—21no—
451C2×C4—21no—
452C2×C4—21no—
453C2×C4—21no—
454C2×C4—21no—
455C2×C4—21no—
456C2×C4—21no—
457C2×C4—21no—
458C2×C4—21no—
459C2×C4—432no—
460C2×C4—861no—
461C2×C4—861no—
462C2×C4—861no—
463C2×C4—861no—
464C2×C4—861no—
465C2×C4—861no—
466C2×C4—861no—
467C2×C4—861no—
468C2×C4—861no—
469C2×C4—861no—
470C2×C4—861no—
471C2×C4C2×D17212yes—
472C2×C4C2×D17212yes—
473C2×C4D4×D4312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—862no—
482C22—862no—
483C22—862no—
484C22—862no—
485C22—862no—
486C22—862no—
487C22—17216no—
488C22—1721no—
489C22—1721no—
490C22—1721no—
491C22—1721no—
492C22—1721no—
493C22—1721no—
494C22—1721no—
495C22—1721no—
496C22—1721no—
497C22—1721no—
498C22—1721no—
499C22—1721no—
500C22—1721no—
501C22—1721no—
502C22—1721no—
503C22—1721no—
504C22—1721no—
505C22—1721no—
506C22—1721no—
507C22—1721no—
508C22—1721no—
509C22—1721no—
510C22C2×D4×D4311yescharacteristic
511C22C22×D17211yescharacteristic
512C22#41×D4311yescharacteristic
513C22#1306337011yescharacteristic
514C22#1306337111yescharacteristic
515C22#1306337111yescharacteristic
516C22#1306337111yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—41no—
523C4—862no—
524C4—1721no—
525C4—1721no—
526C4—1721no—
527C2—42no—
528C2—3441no—
529C2—3441no—
530C2—1722no—
531C2—1722no—
532C2#1458346511yescharacteristic
533C2#1458346811yescharacteristic
534C2#1458348811yescharacteristic
535C2D4×D17211yescharacteristic
536C2#1458354111yescharacteristic
537C2#1458354411yescharacteristic
538C2#1458364111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#388C2
hypercenter#388D43
hypocenterC43#2670
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
1. C2×#13063313C2semidirect
2. C2×#13063311C2semidirect
3. C2×#13063295C2semidirect
4. C2×#13063295C2semidirect
5. #14582816C2semidirect
6. #14582815C2semidirect
7. #14582812C2semidirect
8. #14582809C2semidirect
9. #14582809C2semidirect
10. #14582808C2semidirect
11. #14582801C2semidirect
12. #14582800C2semidirect
13. #14582791C2semidirect
14. #14582754C2semidirect
15. C43×#388C2semidirect
17. C22×Dic86C22semidirect
22. C22×D172C22semidirect
29. C2×C4⋊Dic43C22semidirect
39. C2×(C2×D43)⋊C4C22semidirect
40. C2×(C2×D43)⋊C4C22semidirect
41. C2×(C2×D43)⋊C4C22semidirect
42. C2×(C2×D43)⋊C4C22semidirect
43. C2×(C2×D43)⋊C4C22semidirect
44. C2×(C2×D43)⋊C4C22semidirect
45. C2×C4×Dic43C22semidirect
46. C43⋊#95C22semidirect
47. C43⋊#95C22semidirect
48. C2×C4⋊C4×C43C22semidirect
52. C2×C42×C43C22semidirect
53. #95×C43C22semidirect
54. #95×C43C22semidirect
104. C22⋊C4×C43D4semidirect
120. (C2×D43)⋊C4D4semidirect
283. #388D43semidirect
285. C43#2670semidirect
300. C2×C4⋊C4C2×D43semidirect
320. C2×C42C2×D43semidirect
323. #95C2×D43semidirect
324. #95C2×D43semidirect
390. C22⋊C4D172semidirect