Finite Group Databasebeta

← #19138134

Subgroups — #19138134

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×#13063297C211yesmaximal, characteristic, complemented
2C2×#13063296C211yesmaximal, characteristic, complemented
3C2×#13063293C211yesmaximal, characteristic, complemented
4C2×#13063293C211yesmaximal, characteristic, complemented
5C2×(C22⋊D43)⋊C4C211yesmaximal, characteristic, complemented
6C2×C22⋊C4×D43C211yesmaximal, characteristic, complemented
7#14582822C211yesmaximal, characteristic, complemented
8#14582815C211yesmaximal, characteristic, complemented
9#14582814C211yesmaximal, characteristic, complemented
10#14582802C211yesmaximal, characteristic, complemented
11#14582791C211yesmaximal, characteristic, complemented
12#14582779C211yesmaximal, characteristic, complemented
13#14582775C211yesmaximal, characteristic, complemented
14#14582773C211yesmaximal, characteristic, complemented
15C43×#392C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C23×Dic43C2211yescharacteristic, complemented
22C22×C4×D43C2211yescharacteristic
23C22×C4×D43C2211yescharacteristic
24#13063297—24no—
25#13063296—24no—
26#13063293—24no—
27#13063293—24no—
28(C22⋊D43)⋊C4—24no—
29C2×C4⋊Dic43C2211yescharacteristic, complemented
30C2×C4⋊Dic43C2211yescharacteristic, complemented
31C2×Dic43⋊C4C2211yescharacteristic, complemented
32C2×Dic43⋊C4C2211yescharacteristic, complemented
33C2×C22⋊Dic43C2211yescharacteristic
34C2×C22⋊Dic43C2211yescharacteristic
35C2×C22⋊Dic43C2211yescharacteristic
36C2×C22⋊Dic43C2211yescharacteristic, complemented
37C2×C22⋊Dic43C2211yescharacteristic, complemented
38C2×C22⋊Dic43C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C2×(C2×D43)⋊C4C2211yescharacteristic
41C2×(C2×D43)⋊C4C2211yescharacteristic
42C2×(C2×D43)⋊C4C2211yescharacteristic
43C2×(C2×D43)⋊C4C2211yescharacteristic
44C2×(C2×D43)⋊C4C2211yescharacteristic
45C22⋊C4×D43—24no—
46C2×C4×Dic43C2211yescharacteristic, complemented
47C43⋊#95C2211yescharacteristic, complemented
48C43⋊#95C2211yescharacteristic, complemented
49C43⋊#95C2211yescharacteristic, complemented
50C22×D4×C43C2211yescharacteristic
51C22×D4×C43C2211yescharacteristic
52C22×D4×C43C2211yescharacteristic, complemented
53C2×C22⋊C4×C43C2211yescharacteristic
54C2×C22⋊C4×C43C2211yescharacteristic, complemented
55C2×C22⋊C4×C43C2211yescharacteristic, complemented
56#95×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×C43C2311yescharacteristic
79C22×C4×C43C2311yescharacteristic
80C22×C4×C43C2311yescharacteristic
81C22×C4×C43C2311yescharacteristic
82C2×C22⋊D43—22no—
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—41no—
92C2×C22⋊D43—41no—
93C2×C22⋊D43D414yescomplemented
94C22×Dic43—22no—
95C22×Dic43—22no—
96C22×Dic43—41no—
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—
109C22⋊C4×C43—22no—
110C22⋊C4×C43—22no—
111C22⋊C4×C43—41no—
112C22⋊Dic43—22no—
113C22⋊Dic43—22no—
114C22⋊Dic43—22no—
115C22⋊Dic43—22no—
116C22⋊Dic43—22no—
117C22⋊Dic43—22no—
118(C2×D43)⋊C4—22no—
119(C2×D43)⋊C4—22no—
120(C2×D43)⋊C4—22no—
121(C2×D43)⋊C4—22no—
122(C2×D43)⋊C4D414yescomplemented
123(C2×D43)⋊C4D414yescomplemented
124C4⋊Dic43—22no—
125C4⋊Dic43—41no—
126Dic43⋊C4—22no—
127Dic43⋊C4—22no—
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×C43#4112yes—
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×D43C2×D412yes—
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—21no—
185C2×C4×C43C2×D412yes—
186C2×C4×C43C2×D412yes—
187C22⋊D43—28no—
188C22⋊D43—44no—
189C22⋊D43—44no—
190C22⋊D43—44no—
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×Dic43—21no—
202C2×Dic43—21no—
203C2×Dic43—21no—
204C2×Dic43—21no—
205C2×Dic43—21no—
206C2×Dic43—44no—
207C2×Dic43C2×D412yes—
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—41no—
258C4×C43—41no—
259Dic43—22no—
260Dic43—22no—
261Dic43—22no—
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×#121—431no—
280C2×#120—431no—
281C2×#120—431no—
282C2×C4×D4—431no—
283C22×C22⋊C4—431no—
284#396—431no—
285#394—431no—
286#394—431no—
287#392D4311yescharacteristic, complemented
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×C4—431no—
305#121—864no—
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⋊C4—431no—
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—864no—
327C2×C22⋊C4C2×D4311yescharacteristic
328C2×C22⋊C4C2×D4311yescharacteristic, complemented
329C2×C22⋊C4C2×D4311yescharacteristic, complemented
330C2×C42—431no—
331#95—431no—
332#95—431no—
333#95—431no—
334#95C2×D4311yescharacteristic, complemented
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—431no—
369C22×C4—431no—
370C22×C4—431no—
371C22×C4—431no—
372C22×C4—431no—
373C22×C4—431no—
374C22×C4—862no—
375C22×C4—862no—
376C22×C4—862no—
377C22×C4—862no—
378C22×C4—862no—
379C22×C4—862no—
380C22×C4—1721no—
381C22×C4—1721no—
382C22×C4—1721no—
383C22×C4C22×D4311yescharacteristic
384C22×C4C22×D4311yescharacteristic
385C22×C4C22×D4311yescharacteristic
386C22×C4C22×D4311yescharacteristic
387C4⋊C4—862no—
388C4⋊C4—862no—
389C4⋊C4—862no—
390C4⋊C4—1721no—
391C22⋊C4—22no—
392C22⋊C4—22no—
393C22⋊C4—41no—
394C22⋊C4—434no—
395C22⋊C4—434no—
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—862no—
405C22⋊C4—862no—
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—
448C23#1062190012yes—
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—21no—
467C2×C4—432no—
468C2×C4—432no—
469C2×C4—432no—
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×C4—1724no—
488C2×C4D4×D4312yes—
489C2×C4D4×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
528C22C2×D4×D4311yescharacteristic
529C22#41×D4311yescharacteristic
530C22C2×#1062190011yescharacteristic
531C22#1306337011yescharacteristic
532C22#1306337011yescharacteristic
533C4—22no—
534C4—22no—
535C4—41no—
536C4—41no—
537C4—862no—
538C4—862no—
539C4—862no—
540C4—1721no—
541C4—1721no—
542C4—1721no—
543C2—42no—
544C2—42no—
545C2—81no—
546C2—864no—
547C2—1722no—
548C2#121×D4311yescharacteristic
549C2#1458340911yescharacteristic
550C2#1458348111yescharacteristic
551C2#1458353111yescharacteristic
552C2#1458353411yescharacteristic
553C2#1458353611yescharacteristic
554C2#1458353611yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#392C2
hypercenter#392D43
hypocenterC43#2424
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #392

Complements

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

NH ≅ G/Ntype
1. C2×#13063297C2semidirect
2. C2×#13063296C2semidirect
3. C2×#13063293C2semidirect
4. C2×#13063293C2semidirect
5. C2×(C22⋊D43)⋊C4C2semidirect
6. C2×C22⋊C4×D43C2semidirect
7. #14582822C2semidirect
8. #14582815C2semidirect
9. #14582814C2semidirect
10. #14582802C2semidirect
11. #14582791C2semidirect
12. #14582779C2semidirect
13. #14582775C2semidirect
14. #14582773C2semidirect
15. C43×#392C2semidirect
21. C23×Dic43C22semidirect
29. C2×C4⋊Dic43C22semidirect
30. C2×C4⋊Dic43C22semidirect
31. C2×Dic43⋊C4C22semidirect
32. C2×Dic43⋊C4C22semidirect
36. C2×C22⋊Dic43C22semidirect
37. C2×C22⋊Dic43C22semidirect
38. C2×C22⋊Dic43C22semidirect
46. C2×C4×Dic43C22semidirect
47. C43⋊#95C22semidirect
48. C43⋊#95C22semidirect
49. C43⋊#95C22semidirect
52. C22×D4×C43C22semidirect
54. C2×C22⋊C4×C43C22semidirect
55. C2×C22⋊C4×C43C22semidirect
56. #95×C43C22semidirect
93. C2×C22⋊D43D4semidirect
122. (C2×D43)⋊C4D4semidirect
123. (C2×D43)⋊C4D4semidirect
254. C2×D43#121semidirect
287. #392D43semidirect
293. C43#2424semidirect
301. C22×D4C2×D43semidirect
328. C2×C22⋊C4C2×D43semidirect
329. C2×C22⋊C4C2×D43semidirect
334. #95C2×D43semidirect