Finite Group Databasebeta

← #19137917

Subgroups — #19137917

Order 5504.

1116 conjugacy classes of subgroups.

The subgroup lattice has 568 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×D43C211yesmaximal, characteristic
2C2×#13063310C211yesmaximal, characteristic, complemented
3C2×#13063307C211yesmaximal, characteristic, complemented
4C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
5#14582815C211yesmaximal, characteristic, complemented
6#14582814C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582777C211yesmaximal, characteristic, complemented
9#14582775C211yesmaximal, characteristic, complemented
10#14582773C211yesmaximal, characteristic, complemented
11#14582770C211yesmaximal, characteristic, complemented
12#14582754C211yesmaximal, characteristic, complemented
13#14582754C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#394C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C24×D43C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C2×D4×D43—24no—
22C2×D4×D43—24no—
23C2×D4×D43—24no—
24C22×C4×D43C2211yescharacteristic
25C22×C4×D43C2211yescharacteristic, complemented
26C22×C4×D43C2211yescharacteristic, complemented
27#13063310—24no—
28#13063307—24no—
29C2×C4⋊Dic43C2211yescharacteristic, complemented
30C2×Dic43⋊C4C2211yescharacteristic, complemented
31C2×Dic43⋊C4C2211yescharacteristic, complemented
32C2×C22⋊Dic43C2211yescharacteristic, complemented
33C2×C22⋊Dic43C2211yescharacteristic, complemented
34C2×C22⋊Dic43C2211yescharacteristic, complemented
35C2×C22⋊Dic43C2211yescharacteristic, complemented
36C2×(C2×D43)⋊C4C2211yescharacteristic
37C2×(C2×D43)⋊C4C2211yescharacteristic
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
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×(C2×D43)⋊C4C2211yescharacteristic, complemented
46C22⋊C4×D43—24no—
47C43⋊#95C2211yescharacteristic, complemented
48C43⋊#95C2211yescharacteristic, complemented
49C43⋊#95C2211yescharacteristic, complemented
50C22×D4×C43C2211yescharacteristic
51C2×C4⋊C4×C43C2211yescharacteristic, complemented
52C2×C22⋊C4×C43C2211yescharacteristic, complemented
53C2×C22⋊C4×C43C2211yescharacteristic, complemented
54C2×C22⋊C4×C43C2211yescharacteristic, complemented
55C2×C22⋊C4×C43C2211yescharacteristic, complemented
56#95×C43C2211yescharacteristic, complemented
57C24×C43C2311yescharacteristic
58C24×C43C2311yescharacteristic
59C23×D43—22no—
60C23×D43—22no—
61C23×D43—22no—
62C23×D43—22no—
63C23×D43—22no—
64C23×D43—22no—
65C23×D43—22no—
66C23×D43—22no—
67C23×D43—22no—
68C23×D43—41no—
69C23×D43—41no—
70C23×D43—41no—
71C23×D43—41no—
72C23×D43D414yes—
73C23×D43C2311yescharacteristic
74C23×D43C2311yescharacteristic
75C23×D43C2311yescharacteristic
76C2×D4×C43—22no—
77C2×D4×C43—22no—
78C2×D4×C43—22no—
79C22×C4×C43C2311yescharacteristic
80C22×C4×C43C2311yescharacteristic
81C22×C4×C43C2311yescharacteristic
82C22×C4×C43C2311yescharacteristic
83C22×C4×C43C2311yescharacteristic
84C2×C22⋊D43—22no—
85C2×C22⋊D43—22no—
86C2×C22⋊D43—22no—
87C2×C22⋊D43—22no—
88C2×C22⋊D43—22no—
89C2×C22⋊D43D414yes—
90C22×Dic43C2311yescharacteristic
91C22×Dic43C2311yescharacteristic
92C22×Dic43C2311yescharacteristic
93C22×Dic43C2311yescharacteristic
94C22×Dic43C2311yescharacteristic
95D4×D43—232no—
96C2×D172—22no—
97C2×D172—22no—
98C2×D172D414yes—
99C2×C4×D43—22no—
100C2×C4×D43—22no—
101C2×C4×D43—22no—
102C2×C4×D43—22no—
103C2×C4×D43—22no—
104C2×C4×D43—22no—
105C2×C4×D43—22no—
106C2×C4×D43—41no—
107C2×C4×D43—41no—
108C4⋊C4×C43—22no—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—41no—
112C22⋊C4×C43—41no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—41no—
116C22⋊Dic43—41no—
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—22no—
125(C2×D43)⋊C4—41no—
126(C2×D43)⋊C4—41no—
127C4⋊Dic43—22no—
128Dic43⋊C4—22no—
129Dic43⋊C4—22no—
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×C43C2×D412yes—
143C23×C43C2×D412yes—
144C23×C43C2411yescharacteristic
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—28no—
154C22×D43—21no—
155C22×D43—21no—
156C22×D43—21no—
157C22×D43—21no—
158C22×D43—21no—
159C22×D43—21no—
160C22×D43—28no—
161C22×D43—28no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43—44no—
165C22×D43—44no—
166C22×D43—44no—
167C22×D43—44no—
168C22×D43—44no—
169C22×D43—44no—
170C22×D43—44no—
171C22×D43—44no—
172C22×D43—44no—
173C22×D43C2×D412yes—
174C22×D43C2×D412yes—
175C22×D43C2×D412yes—
176C22×D43C2×D412yes—
177C22×D43C2×D412yes—
178C22×D43#4112yes—
179C22×D43#4112yes—
180D4×C43—28no—
181C2×C4×C43—21no—
182C2×C4×C43—21no—
183C2×C4×C43—21no—
184C2×C4×C43—21no—
185C2×C4×C43—21no—
186C2×C4×C43—21no—
187C2×C4×C43—21no—
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—
196C22⋊D43—28no—
197C22⋊D43—28no—
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—21no—
209C2×Dic43—21no—
210C2×Dic43—21no—
211C2×Dic43—21no—
212C2×Dic43C2×D412yes—
213D172—28no—
214C4×D43—28no—
215C4×D43—44no—
216C4×D43—44no—
217C22×C43—22no—
218C22×C43—22no—
219C22×C43—22no—
220C22×C43—22no—
221C22×C43—22no—
222C22×C43—22no—
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×C43C22×D411yescharacteristic
232C22×C43C22×D411yescharacteristic
233C22×C43C22×D411yescharacteristic
234C22×C43C2×#4111yescharacteristic
235C22×C43C2×#4111yescharacteristic
236C22×C43H(5,𝔽2)11yescharacteristic
237C22×C43H(5,𝔽2)11yescharacteristic
238C2×D43—22no—
239C2×D43—22no—
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—22no—
250C2×D43—22no—
251C2×D43—22no—
252C2×D43—22no—
253C2×D43—416no—
254C2×D43—416no—
255C2×D43—41no—
256C2×D43—41no—
257C2×D43—41no—
258C2×D43—41no—
259C2×D43#12014yes—
260C2×D43#12314yescomplemented
261C4×C43—22no—
262C4×C43—41no—
263C4×C43—41no—
264C4×C43—41no—
265C4×C43—41no—
266Dic43—22no—
267Dic43—41no—
268Dic43—41no—
269Dic43—41no—
270Dic43—41no—
271#2405—431nomaximal, Sylow
272C2×C43—42no—
273C2×C43—42no—
274C2×C43C2×#12011yescharacteristic
275C2×C43C2×#12311yescharacteristic
276C2×C43#53411yescharacteristic
277C2×C43#54611yescharacteristic
278C2×C43#54611yescharacteristic
279C2×C43#54611yescharacteristic
280C2×C43#54611yescharacteristic
281D43—24no—
282D43—24no—
283D43—42no—
284C23×D4—431no—
285C2×#123—431no—
286C2×#123—431no—
287C22×C22⋊C4—431no—
288#394—431no—
289#394—431no—
290#394—431no—
291#394D4311yescharacteristic, complemented
292#386—431no—
293#386—431no—
294#385—431no—
295#385—431no—
296#379—431no—
297#379—431no—
298#379—431no—
299C43#240511yescharacteristic, complemented, Sylow
300C25—431no—
301C25—431no—
302C22×D4—431no—
303C22×D4—431no—
304C22×D4—431no—
305C22×D4—864no—
306C22×D4—864no—
307C22×D4—864no—
308C22×D4C2×D4311yescharacteristic
309C23×C4—431no—
310C23×C4—431no—
311C23×C4—431no—
312#123—864no—
313#123—864no—
314C2×C4⋊C4—431no—
315C2×C4⋊C4—431no—
316C2×C4⋊C4—431no—
317C2×C4⋊C4C2×D4311yescharacteristic, complemented
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—431no—
328C2×C22⋊C4—431no—
329C2×C22⋊C4—431no—
330C2×C22⋊C4—431no—
331C2×C22⋊C4—431no—
332C2×C22⋊C4—864no—
333C2×C22⋊C4C2×D4311yescharacteristic, complemented
334C2×C22⋊C4C2×D4311yescharacteristic, complemented
335C2×C22⋊C4C2×D4311yescharacteristic, complemented
336C2×C22⋊C4C2×D4311yescharacteristic, complemented
337#95—431no—
338#95—431no—
339#95—431no—
340#95C2×D4311yescharacteristic, complemented
341C24—431no—
342C24—431no—
343C24—431no—
344C24—434no—
345C24—862no—
346C24—862no—
347C24—862no—
348C24—862no—
349C24—862no—
350C24—862no—
351C24—862no—
352C24—862no—
353C24—862no—
354C24—1721no—
355C24—1721no—
356C24—1721no—
357C24—1721no—
358C24C22×D4311yescharacteristic
359C24C22×D4311yescharacteristic
360C2×D4—22no—
361C2×D4—22no—
362C2×D4—22no—
363C2×D4—434no—
364C2×D4—434no—
365C2×D4—862no—
366C2×D4—862no—
367C2×D4—862no—
368C2×D4—8632no—
369C2×D4—862no—
370C2×D4—862no—
371C2×D4—862no—
372C2×D4—862no—
373C22×C4—431no—
374C22×C4—431no—
375C22×C4—431no—
376C22×C4—431no—
377C22×C4—431no—
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×C4C22×D4311yescharacteristic
388C22×C4C22×D4311yescharacteristic
389C22×C4C22×D4311yescharacteristic
390C22×C4C22×D4311yescharacteristic
391C22×C4C22×D4311yescharacteristic
392C4⋊C4—22no—
393C4⋊C4—862no—
394C4⋊C4—862no—
395C4⋊C4—862no—
396C22⋊C4—22no—
397C22⋊C4—22no—
398C22⋊C4—41no—
399C22⋊C4—41no—
400C22⋊C4—862no—
401C22⋊C4—862no—
402C22⋊C4—862no—
403C22⋊C4—862no—
404C22⋊C4—862no—
405C22⋊C4—862no—
406C22⋊C4—862no—
407C22⋊C4—862no—
408C22⋊C4—862no—
409C22⋊C4—862no—
410C22⋊C4—1721no—
411C22⋊C4—1721no—
412C22⋊C4—1721no—
413C22⋊C4—1721no—
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—432no—
431C23—432no—
432C23—432no—
433C23—868no—
434C23—868no—
435C23—868no—
436C23—861no—
437C23—861no—
438C23—861no—
439C23—861no—
440C23—861no—
441C23—861no—
442C23—861no—
443C23—861no—
444C23—861no—
445C23—861no—
446C23—861no—
447C23—861no—
448C23—861no—
449C23—861no—
450C23—1724no—
451C23—1724no—
452C23—1724no—
453C23—1724no—
454C23—1724no—
455C23—1724no—
456C23—1724no—
457C23—1724no—
458C23—1724no—
459C23—1724no—
460C23—1724no—
461C23D4×D4312yes—
462C23D4×D4312yes—
463C23C23×D4311yescharacteristic
464D4—28no—
465D4—868no—
466D4—868no—
467D4—868no—
468C2×C4—21no—
469C2×C4—21no—
470C2×C4—21no—
471C2×C4—21no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—432no—
483C2×C4—868no—
484C2×C4—861no—
485C2×C4—861no—
486C2×C4—861no—
487C2×C4—861no—
488C2×C4—861no—
489C2×C4—861no—
490C2×C4—861no—
491C2×C4—861no—
492C2×C4—861no—
493C2×C4—861no—
494C2×C4—861no—
495C2×C4—861no—
496C2×C4—861no—
497C2×C4—861no—
498C2×C4—1724no—
499C2×C4—1724no—
500C2×C4D4×D4312yes—
501C22—22no—
502C22—22no—
503C22—22no—
504C22—22no—
505C22—22no—
506C22—22no—
507C22—41no—
508C22—41no—
509C22—41no—
510C22—41no—
511C22—41no—
512C22—41no—
513C22—41no—
514C22—41no—
515C22—434no—
516C22—434no—
517C22—862no—
518C22—862no—
519C22—862no—
520C22—862no—
521C22—862no—
522C22—862no—
523C22—862no—
524C22—862no—
525C22—862no—
526C22—862no—
527C22—862no—
528C22—862no—
529C22—862no—
530C22—862no—
531C22—862no—
532C22—17216no—
533C22—17216no—
534C22—1721no—
535C22—1721no—
536C22—1721no—
537C22—1721no—
538C22C2×D4×D4311yescharacteristic
539C22C2×D4×D4311yescharacteristic
540C22C2×D4×D4311yescharacteristic
541C22#41×D4311yescharacteristic
542C22#41×D4311yescharacteristic
543C22#1306337011yescharacteristic
544C22#1306337111yescharacteristic
545C4—22no—
546C4—41no—
547C4—41no—
548C4—41no—
549C4—41no—
550C4—862no—
551C4—1721no—
552C4—1721no—
553C4—1721no—
554C4—1721no—
555C2—42no—
556C2—42no—
557C2—864no—
558C2—864no—
559C2—1722no—
560C2#120×D4311yescharacteristic
561C2#123×D4311yescharacteristic
562C2#1458345711yescharacteristic
563C2#1458353811yescharacteristic
564C2#1458354111yescharacteristic
565C2#1458354211yescharacteristic
566C2#1458354611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2405
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
2. C2×#13063310C2semidirect
3. C2×#13063307C2semidirect
4. C2×C22⋊C4×D43C2semidirect
5. #14582815C2semidirect
6. #14582814C2semidirect
7. #14582813C2semidirect
8. #14582777C2semidirect
9. #14582775C2semidirect
10. #14582773C2semidirect
11. #14582770C2semidirect
12. #14582754C2semidirect
13. #14582754C2semidirect
14. #14582754C2semidirect
15. C43×#394C2semidirect
25. C22×C4×D43C22semidirect
26. C22×C4×D43C22semidirect
29. C2×C4⋊Dic43C22semidirect
30. C2×Dic43⋊C4C22semidirect
31. C2×Dic43⋊C4C22semidirect
32. C2×C22⋊Dic43C22semidirect
33. C2×C22⋊Dic43C22semidirect
34. C2×C22⋊Dic43C22semidirect
35. C2×C22⋊Dic43C22semidirect
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×(C2×D43)⋊C4C22semidirect
47. C43⋊#95C22semidirect
48. C43⋊#95C22semidirect
49. C43⋊#95C22semidirect
51. C2×C4⋊C4×C43C22semidirect
52. C2×C22⋊C4×C43C22semidirect
53. C2×C22⋊C4×C43C22semidirect
54. C2×C22⋊C4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. #95×C43C22semidirect
260. C2×D43#123semidirect
291. #394D43semidirect
299. C43#2405semidirect
317. C2×C4⋊C4C2×D43semidirect
333. C2×C22⋊C4C2×D43semidirect
334. C2×C22⋊C4C2×D43semidirect
335. C2×C22⋊C4C2×D43semidirect
336. C2×C22⋊C4C2×D43semidirect
340. #95C2×D43semidirect