Finite Group Databasebeta

← #19138128

Subgroups — #19138128

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×#13063296C211yesmaximal, characteristic, complemented
2C2×#13063293C211yesmaximal, characteristic, complemented
3C2×#13063293C211yesmaximal, characteristic, complemented
4C2×C4×C22⋊D43C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
6#14582821C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582813C211yesmaximal, characteristic, complemented
9#14582807C211yesmaximal, characteristic, complemented
10#14582799C211yesmaximal, characteristic, complemented
11#14582792C211yesmaximal, characteristic, complemented
12#14582778C211yesmaximal, characteristic, complemented
13#14582775C211yesmaximal, characteristic, complemented
14#14582770C211yesmaximal, characteristic, complemented
15C2×#121×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C4×D43C2211yescharacteristic
22C22×C4×D43C2211yescharacteristic
23#13063296—24no—
24#13063293—24no—
25#13063293—24no—
26C4×C22⋊D43—24no—
27C2×C4⋊Dic43C2211yescharacteristic, complemented
28C2×Dic43⋊C4C2211yescharacteristic, complemented
29C2×Dic43⋊C4C2211yescharacteristic, complemented
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic, complemented
34C2×C22⋊Dic43C2211yescharacteristic, complemented
35C2×C22⋊Dic43C2211yescharacteristic, complemented
36C2×C22⋊Dic43C2211yescharacteristic, complemented
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C22⋊C4×D43—24no—
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—22no—
64C23×D43—22no—
65C23×D43—41no—
66C23×D43—41no—
67C23×D43C2311yescharacteristic
68C23×D43C2311yescharacteristic
69C2×D4×C43—22no—
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—
78C22×C4×C43—22no—
79C22×C4×C43—22no—
80C22×C4×C43—41no—
81C22×C4×C43C2311yescharacteristic
82C22×C4×C43C2311yescharacteristic
83C22×C4×C43C2311yescharacteristic
84C22×C4×C43C2311yescharacteristic
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⋊D43D414yescomplemented
97C22×Dic43C2311yescharacteristic
98C22×Dic43C2311yescharacteristic
99C22×Dic43C2311yescharacteristic
100C22×Dic43C2311yescharacteristic
101C22×Dic43C2311yescharacteristic
102C22×Dic43C2311yescharacteristic
103C2×C4×D43—22no—
104C2×C4×D43—22no—
105C2×C4×D43—22no—
106C2×C4×D43—22no—
107C2×C4×D43—41no—
108C2×C4×D43—41no—
109C4⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43D414yescomplemented
112C22⋊Dic43—22no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—22no—
116C22⋊Dic43—22no—
117C22⋊Dic43—22no—
118C22⋊Dic43—41no—
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)⋊C4D414yescomplemented
125C4⋊Dic43—22no—
126Dic43⋊C4—22no—
127Dic43⋊C4—41no—
128C4×Dic43—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×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×C43C2×D412yes—
149C23×C43C2×D412yes—
150C23×C43C2411yescharacteristic
151C22×D43—21no—
152C22×D43—21no—
153C22×D43—21no—
154C22×D43—21no—
155C22×D43—28no—
156C22×D43—21no—
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—21no—
161C22×D43—21no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43—44no—
165C22×D43—44no—
166C22×D43—44no—
167C22×D43—44no—
168C22×D43C2×D412yes—
169C22×D43C2×D412yes—
170C22×D43#4112yes—
171C22×D43#4112yes—
172D4×C43—44no—
173D4×C43—44no—
174D4×C43—44no—
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×C43C2×D412yes—
186C2×C4×C43C2×D412yes—
187C2×C4×C43C2×D412yes—
188C22⋊D43—28no—
189C22⋊D43—44no—
190C22⋊D43—44no—
191C22⋊D43—44no—
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×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—21no—
207C2×Dic43—21no—
208C2×Dic43C2×D412yes—
209C2×Dic43C2×D412yes—
210C4×D43—44no—
211C4×D43—44no—
212C22×C43—22no—
213C22×C43—22no—
214C22×C43—22no—
215C22×C43—22no—
216C22×C43—22no—
217C22×C43—22no—
218C22×C43—41no—
219C22×C43—41no—
220C22×C43—41no—
221C22×C43—41no—
222C22×C43—41no—
223C22×C43—41no—
224C22×C43—41no—
225C22×C43—41no—
226C22×C43—41no—
227C22×C43—41no—
228C22×C43—41no—
229C22×C43—41no—
230C22×C43—41no—
231C22×C43—41no—
232C22×C43—41no—
233C22×C43C22×D411yescharacteristic
234C22×C43C22×D411yescharacteristic
235C22×C43C22×D411yescharacteristic
236C22×C43C2×#4111yescharacteristic
237C22×C43C2×#4111yescharacteristic
238C22×C43H(5,𝔽2)11yescharacteristic
239C22×C43H(5,𝔽2)11yescharacteristic
240C2×D43—22no—
241C2×D43—22no—
242C2×D43—22no—
243C2×D43—22no—
244C2×D43—22no—
245C2×D43—22no—
246C2×D43—22no—
247C2×D43—22no—
248C2×D43—22no—
249C2×D43—416no—
250C2×D43—41no—
251C2×D43—41no—
252C2×D43—41no—
253C2×D43—41no—
254C2×D43#12114yescomplemented
255C4×C43—22no—
256C4×C43—22no—
257C4×C43—22no—
258C4×C43—41no—
259Dic43—22no—
260Dic43—22no—
261Dic43—41no—
262Dic43—41no—
263Dic43—41no—
264Dic43—41no—
265#2424—431nomaximal, Sylow
266C2×C43—42no—
267C2×C43—42no—
268C2×C43—81no—
269C2×C43C2×#12111yescharacteristic
270C2×C43#52511yescharacteristic
271C2×C43#53811yescharacteristic
272C2×C43D4211yescharacteristic
273C2×C43D4211yescharacteristic
274C2×C43#54611yescharacteristic
275C2×C43#54611yescharacteristic
276D43—24no—
277D43—42no—
278C2×#121—431no—
279C2×#121D4311yescharacteristic, complemented
280C2×#120—431no—
281C2×#120—431no—
282C2×C4×D4—431no—
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×D4C2×D4311yescharacteristic
300C22×D4C2×D4311yescharacteristic
301C22×D4C2×D4311yescharacteristic, complemented
302C23×C4—431no—
303C23×C4—431no—
304C23×C4C2×D4311yescharacteristic, complemented
305#121—24no—
306#121—864no—
307#120—864no—
308#120—864no—
309C4×D4—864no—
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×C42—431no—
331#95—431no—
332#95—431no—
333#95—431no—
334#95—431no—
335C24—431no—
336C24—431no—
337C24—862no—
338C24—862no—
339C24—862no—
340C24—862no—
341C24—862no—
342C24—1721no—
343C24—1721no—
344C24C22×D4311yescharacteristic
345C24C22×D4311yescharacteristic
346C24C22×D4311yescharacteristic
347C2×D4—22no—
348C2×D4—22no—
349C2×D4—22no—
350C2×D4—22no—
351C2×D4—22no—
352C2×D4—22no—
353C2×D4—41no—
354C2×D4—41no—
355C2×D4—41no—
356C2×D4—434no—
357C2×D4—862no—
358C2×D4—862no—
359C2×D4—862no—
360C2×D4—862no—
361C2×D4—862no—
362C2×D4—862no—
363C2×D4—862no—
364C2×D4—862no—
365C2×D4—862no—
366C2×D4—1721no—
367C2×D4—1721no—
368C22×C4—22no—
369C22×C4—22no—
370C22×C4—41no—
371C22×C4—431no—
372C22×C4—431no—
373C22×C4—431no—
374C22×C4—431no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—862no—
378C22×C4—862no—
379C22×C4—862no—
380C22×C4—862no—
381C22×C4—1721no—
382C22×C4—1721no—
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—862no—
407C23—21no—
408C23—21no—
409C23—21no—
410C23—21no—
411C23—21no—
412C23—21no—
413C23—21no—
414C23—21no—
415C23—21no—
416C23—21no—
417C23—21no—
418C23—21no—
419C23—21no—
420C23—21no—
421C23—21no—
422C23—21no—
423C23—21no—
424C23—21no—
425C23—21no—
426C23—432no—
427C23—432no—
428C23—432no—
429C23—432no—
430C23—868no—
431C23—861no—
432C23—861no—
433C23—861no—
434C23—861no—
435C23—861no—
436C23—861no—
437C23—861no—
438C23—861no—
439C23—861no—
440C23—861no—
441C23—1724no—
442C23—1724no—
443C23—1724no—
444C23—1724no—
445C23—1724no—
446C23—1724no—
447C23D4×D4312yes—
448C23C2×C22⋊D4312yes—
449C23C23×D4311yescharacteristic
450D4—44no—
451D4—44no—
452D4—44no—
453D4—868no—
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—44no—
467C2×C4—432no—
468C2×C4—432no—
469C2×C4—861no—
470C2×C4—861no—
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×C4—1724no—
487C2×C4D4×D4312yes—
488C2×C4C2×C22⋊D4312yes—
489C2×C4C2×C22⋊D4312yes—
490C22—22no—
491C22—22no—
492C22—22no—
493C22—22no—
494C22—22no—
495C22—22no—
496C22—41no—
497C22—41no—
498C22—41no—
499C22—41no—
500C22—41no—
501C22—41no—
502C22—41no—
503C22—41no—
504C22—41no—
505C22—41no—
506C22—41no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—434no—
512C22—862no—
513C22—862no—
514C22—862no—
515C22—862no—
516C22—862no—
517C22—862no—
518C22—862no—
519C22—862no—
520C22—862no—
521C22—17216no—
522C22—1721no—
523C22—1721no—
524C22—1721no—
525C22—1721no—
526C22C2×D4×D4311yescharacteristic
527C22C2×D4×D4311yescharacteristic
528C22C22×C22⋊D4311yescharacteristic
529C22#41×D4311yescharacteristic
530C22#41×D4311yescharacteristic
531C22#1306337011yescharacteristic
532C22#1306337011yescharacteristic
533C4—22no—
534C4—22no—
535C4—22no—
536C4—41no—
537C4—862no—
538C4—862no—
539C4—1721no—
540C4—1721no—
541C4—1721no—
542C4—1721no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—864no—
547C2—1722no—
548C2#121×D4311yescharacteristic
549C2#1458340611yescharacteristic
550C2#1458348111yescharacteristic
551C2D4×C22⋊D4311yescharacteristic
552C2D4×C22⋊D4311yescharacteristic
553C2#1458353811yescharacteristic
554C2#1458354611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#121×C43C2
hypercenterC2×#121D43
hypocenterC43#2424
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#121

Complements

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

NH ≅ G/Ntype
1. C2×#13063296C2semidirect
2. C2×#13063293C2semidirect
3. C2×#13063293C2semidirect
4. C2×C4×C22⋊D43C2semidirect
5. C2×C22⋊C4×D43C2semidirect
6. #14582821C2semidirect
7. #14582813C2semidirect
8. #14582813C2semidirect
9. #14582807C2semidirect
10. #14582799C2semidirect
11. #14582792C2semidirect
12. #14582778C2semidirect
13. #14582775C2semidirect
14. #14582770C2semidirect
15. C2×#121×C43C2semidirect
27. C2×C4⋊Dic43C22semidirect
28. C2×Dic43⋊C4C22semidirect
29. C2×Dic43⋊C4C22semidirect
33. C2×C22⋊Dic43C22semidirect
34. C2×C22⋊Dic43C22semidirect
35. C2×C22⋊Dic43C22semidirect
36. C2×C22⋊Dic43C22semidirect
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
96. C2×C22⋊D43D4semidirect
111. C22⋊C4×C43D4semidirect
124. (C2×D43)⋊C4D4semidirect
254. C2×D43#121semidirect
279. C2×#121D43semidirect
293. C43#2424semidirect
301. C22×D4C2×D43semidirect
304. C23×C4C2×D43semidirect
313. C2×C4⋊C4C2×D43semidirect
329. C2×C22⋊C4C2×D43semidirect
405. C22⋊C4C22⋊D43semidirect