Finite Group Databasebeta

← #19140816

Subgroups — #19140816

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×#13063314C211yesmaximal, characteristic, complemented
2C2×#13063295C211yesmaximal, characteristic, complemented
3C2×#13063293C211yesmaximal, characteristic, complemented
4#14582815C211yesmaximal, characteristic, complemented
5#14582814C211yesmaximal, characteristic, complemented
6#14582810C211yesmaximal, characteristic, complemented
7#14582808C211yesmaximal, characteristic, complemented
8#14582808C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582801C211yesmaximal, characteristic, complemented
11#14582799C211yesmaximal, characteristic, complemented
12#14582792C211yesmaximal, characteristic, complemented
13#14582790C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C2×#124×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23#13063314—24no—
24#13063295—24no—
25#13063293—24no—
26C2×C4⋊Dic43C2211yescharacteristic, complemented
27C2×Dic43⋊C4C2211yescharacteristic, complemented
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic, complemented
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×C4×Dic43C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C43⋊#95C2211yescharacteristic, complemented
47C22×Q8×C43C2211yescharacteristic, complemented
48C22×D4×C43C2211yescharacteristic
49#124×C43—24no—
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic, complemented
53C2×C22⋊C4×C43C2211yescharacteristic, complemented
54C2×C42×C43C2211yescharacteristic, complemented
55C24×C43C2311yescharacteristic
56C24×C43C2311yescharacteristic
57C23×D43—22no—
58C23×D43—22no—
59C23×D43—22no—
60C23×D43—41no—
61C23×D43—41no—
62C23×D43—41no—
63C23×D43—41no—
64C23×D43C2311yescharacteristic
65C23×D43C2311yescharacteristic
66C23×D43C2311yescharacteristic
67C2×Q8×C43—22no—
68C2×Q8×C43—22no—
69C2×Q8×C43—41no—
70C2×D4×C43—22no—
71C2×D4×C43—22no—
72C2×D4×C43—41no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C22×C4×C43C2311yescharacteristic
77C22×C4×C43C2311yescharacteristic
78C2×C22⋊D43—22no—
79C2×C22⋊D43—22no—
80C2×C22⋊D43—22no—
81C2×C22⋊D43—22no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C2×C22⋊D43—41no—
86C2×C22⋊D43—41no—
87C2×C22⋊D43—41no—
88C2×C22⋊D43—41no—
89C2×C22⋊D43—41no—
90C22×Dic43C2311yescharacteristic
91C22×Dic43C2311yescharacteristic
92C22×Dic43C2311yescharacteristic
93C22×Dic43C2311yescharacteristic
94C22×Dic43C2311yescharacteristic
95C2×D172—22no—
96C2×D172—22no—
97C2×D172—22no—
98C2×D172—22no—
99C2×D172—41no—
100C2×D172—41no—
101C22⋊C4×C43—22no—
102C22⋊C4×C43—22no—
103C22⋊C4×C43—22no—
104C22⋊C4×C43D414yescomplemented
105C42×C43—22no—
106C22⋊Dic43—22no—
107C22⋊Dic43—41no—
108C22⋊Dic43—41no—
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)⋊C4D414yescomplemented
120C4⋊Dic43—41no—
121Dic43⋊C4—41no—
122C4×Dic43—22no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43C2×D412yes—
137C23×C43C2411yescharacteristic
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—
166Q8×C43—44no—
167D4×C43—44no—
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×C43C2×D412yes—
181C2×C4×C43C2×D412yes—
182C2×C4×C43C2×D412yes—
183C22⋊D43—44no—
184C22⋊D43—44no—
185C22⋊D43—44no—
186C22⋊D43—44no—
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×Dic43—21no—
198C2×Dic43—21no—
199C2×Dic43—21no—
200C2×Dic43—21no—
201C2×Dic43C2×D412yes—
202D172—44no—
203D172—44no—
204C22×C43—22no—
205C22×C43—22no—
206C22×C43—22no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43—41no—
213C22×C43—41no—
214C22×C43—41no—
215C22×C43—41no—
216C22×C43—41no—
217C22×C43—41no—
218C22×C43C22×D411yescharacteristic
219C22×C43C22×D411yescharacteristic
220C22×C43C2×#4111yescharacteristic
221C22×C43H(5,𝔽2)11yescharacteristic
222C22×C43H(5,𝔽2)11yescharacteristic
223C22×C43H(5,𝔽2)11yescharacteristic
224C22×C43H(5,𝔽2)11yescharacteristic
225C2×D43—22no—
226C2×D43—22no—
227C2×D43—22no—
228C2×D43—22no—
229C2×D43—22no—
230C2×D43—22no—
231C2×D43—416no—
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—
252Dic43—22no—
253Dic43—41no—
254Dic43—41no—
255Dic43—41no—
256Dic43—41no—
257#2670—431nomaximal, Sylow
258C2×C43—42no—
259C2×C43—81no—
260C2×C43#53511yescharacteristic
261C2×C43#53511yescharacteristic
262C2×C43#53811yescharacteristic
263C2×C43D4211yescharacteristic
264C2×C43#54611yescharacteristic
265C2×C43#54611yescharacteristic
266C2×C43H(3,𝔽4)11yescharacteristic
267D43—42no—
268D43—42no—
269D43—81no—
270C2×#124—431no—
271C2×#124D4311yescharacteristic, complemented
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#388—431no—
284#379—431no—
285C43#267011yescharacteristic, complemented, Sylow
286C25—431no—
287C22×Q8C2×D4311yescharacteristic, complemented
288C22×D4—431no—
289C22×D4—431no—
290C22×D4—431no—
291C22×D4—431no—
292C22×D4—431no—
293C22×D4—431no—
294C22×D4C2×D4311yescharacteristic
295#124—24no—
296#124—864no—
297#120—864no—
298#120—864no—
299C2×C4⋊C4—431no—
300C2×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
316C2×C22⋊C4C2×D4311yescharacteristic
317C2×C22⋊C4C2×D4311yescharacteristic, complemented
318C2×C22⋊C4C2×D4311yescharacteristic, complemented
319C2×C42—431no—
320C2×C42C2×D4311yescharacteristic, complemented
321#95—431no—
322#95—431no—
323#95—431no—
324#95—431no—
325C24—431no—
326C24—431no—
327C24—431no—
328C24—862no—
329C24—862no—
330C24—862no—
331C24—1721no—
332C24—1721no—
333C24—1721no—
334C24—1721no—
335C24C22×D4311yescharacteristic
336C24C22×D4311yescharacteristic
337C2×Q8—22no—
338C2×Q8—22no—
339C2×Q8—41no—
340C2×D4—22no—
341C2×D4—22no—
342C2×D4—41no—
343C2×D4—862no—
344C2×D4—862no—
345C2×D4—862no—
346C2×D4—862no—
347C2×D4—862no—
348C2×D4—862no—
349C2×D4—862no—
350C2×D4—862no—
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×C4—431no—
366C22×C4C22×D4311yescharacteristic
367C22×C4C22×D4311yescharacteristic
368C22×C4C22×D4311yescharacteristic
369C22×C4C22×D4311yescharacteristic
370C22×C4C22×D4311yescharacteristic
371C4⋊C4—1721no—
372C4⋊C4—1721no—
373C22⋊C4—22no—
374C22⋊C4—22no—
375C22⋊C4—22no—
376C22⋊C4—434no—
377C22⋊C4—862no—
378C22⋊C4—862no—
379C22⋊C4—862no—
380C22⋊C4—862no—
381C22⋊C4—862no—
382C22⋊C4—862no—
383C22⋊C4—862no—
384C22⋊C4—1721no—
385C22⋊C4—1721no—
386C22⋊C4—1721no—
387C22⋊C4—1721no—
388C22⋊C4—1721no—
389C22⋊C4—1721no—
390C22⋊C4C22⋊D4314yescomplemented
391C42—22no—
392C42—862no—
393C23—21no—
394C23—21no—
395C23—21no—
396C23—21no—
397C23—21no—
398C23—21no—
399C23—21no—
400C23—21no—
401C23—21no—
402C23—21no—
403C23—21no—
404C23—21no—
405C23—21no—
406C23—432no—
407C23—432no—
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×C22⋊D4312yes—
435C23C23×D4311yescharacteristic
436Q8—44no—
437D4—44no—
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—432no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—861no—
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×C4D4×D4312yes—
472C2×C4C2×C22⋊D4312yes—
473C2×C4C2×C22⋊D4312yes—
474C22—22no—
475C22—22no—
476C22—22no—
477C22—41no—
478C22—41no—
479C22—41no—
480C22—41no—
481C22—41no—
482C22—41no—
483C22—41no—
484C22—41no—
485C22—41no—
486C22—41no—
487C22—41no—
488C22—862no—
489C22—862no—
490C22—862no—
491C22—862no—
492C22—862no—
493C22—862no—
494C22—17216no—
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×C22⋊D4311yescharacteristic
512C22#41×D4311yescharacteristic
513C22#1306337011yescharacteristic
514C22#1306337111yescharacteristic
515C22#1306337111yescharacteristic
516C22#1306337111yescharacteristic
517C4—22no—
518C4—22no—
519C4—22no—
520C4—41no—
521C4—41no—
522C4—862no—
523C4—1721no—
524C4—1721no—
525C4—1721no—
526C4—1721no—
527C2—42no—
528C2—81no—
529C2—3441no—
530C2—1722no—
531C2—1722no—
532C2#1458346311yescharacteristic
533C2#1458346711yescharacteristic
534C2#1458348311yescharacteristic
535C2D4×C22⋊D4311yescharacteristic
536C2#1458353711yescharacteristic
537C2#1458354211yescharacteristic
538C2#1458364111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#124×C43C2
hypercenterC2×#124D43
hypocenterC43#2670
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#124

Complements

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

NH ≅ G/Ntype
1. C2×#13063314C2semidirect
2. C2×#13063295C2semidirect
3. C2×#13063293C2semidirect
4. #14582815C2semidirect
5. #14582814C2semidirect
6. #14582810C2semidirect
7. #14582808C2semidirect
8. #14582808C2semidirect
9. #14582807C2semidirect
10. #14582801C2semidirect
11. #14582799C2semidirect
12. #14582792C2semidirect
13. #14582790C2semidirect
14. #14582754C2semidirect
15. C2×#124×C43C2semidirect
22. C22×C22⋊D43C22semidirect
26. C2×C4⋊Dic43C22semidirect
27. C2×Dic43⋊C4C22semidirect
30. C2×C22⋊Dic43C22semidirect
39. C2×(C2×D43)⋊C4C22semidirect
40. C2×(C2×D43)⋊C4C22semidirect
41. C2×(C2×D43)⋊C4C22semidirect
42. C2×C4×Dic43C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
46. C43⋊#95C22semidirect
47. C22×Q8×C43C22semidirect
52. C2×C22⋊C4×C43C22semidirect
53. C2×C22⋊C4×C43C22semidirect
54. C2×C42×C43C22semidirect
104. C22⋊C4×C43D4semidirect
119. (C2×D43)⋊C4D4semidirect
271. C2×#124D43semidirect
285. C43#2670semidirect
287. C22×Q8C2×D43semidirect
317. C2×C22⋊C4C2×D43semidirect
318. C2×C22⋊C4C2×D43semidirect
320. C2×C42C2×D43semidirect
390. C22⋊C4C22⋊D43semidirect