Finite Group Databasebeta

← #19142591

Subgroups — #19142591

Order 5504.

712 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063295C211yesmaximal, characteristic, complemented
2C2×#13063293C211yesmaximal, characteristic, complemented
3#14582827C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582825C211yesmaximal, characteristic, complemented
6#14582817C211yesmaximal, characteristic, complemented
7#14582816C211yesmaximal, characteristic, complemented
8#14582815C211yesmaximal, characteristic, complemented
9#14582815C211yesmaximal, characteristic, complemented
10#14582814C211yesmaximal, characteristic, complemented
11#14582808C211yesmaximal, characteristic, complemented
12#14582808C211yesmaximal, characteristic, complemented
13#14582807C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#394C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C22⋊D43C2211yescharacteristic
21C22×C22⋊D43C2211yescharacteristic
22C22×C22⋊D43C2211yescharacteristic, complemented
23#13063295—24no—
24#13063293—24no—
25C2×C4⋊Dic43C2211yescharacteristic, complemented
26C2×Dic43⋊C4C2211yescharacteristic, complemented
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic, complemented
30C2×(C2×D43)⋊C4C2211yescharacteristic
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, complemented
39C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
40C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C22×D4×C43C2211yescharacteristic
47C2×C4⋊C4×C43C2211yescharacteristic, complemented
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic, complemented
51C2×C22⋊C4×C43C2211yescharacteristic, complemented
52#95×C43C2211yescharacteristic, complemented
53C24×C43C2311yescharacteristic
54C24×C43C2311yescharacteristic
55C23×D43—41no—
56C23×D43—41no—
57C23×D43—41no—
58C23×D43—41no—
59C23×D43—41no—
60C23×D43—41no—
61C23×D43D414yescomplemented
62C23×D43C2311yescharacteristic
63C23×D43C2311yescharacteristic
64C23×D43C2311yescharacteristic
65C2×D4×C43—22no—
66C2×D4×C43—41no—
67C2×D4×C43—41no—
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—
79C2×C22⋊D43—41no—
80C2×C22⋊D43—41no—
81C2×C22⋊D43—41no—
82C2×C22⋊D43—41no—
83C2×C22⋊D43—41no—
84C2×C22⋊D43—41no—
85C22×Dic43C2311yescharacteristic
86C22×Dic43C2311yescharacteristic
87C22×Dic43C2311yescharacteristic
88C22×Dic43C2311yescharacteristic
89C22×Dic43C2311yescharacteristic
90C2×D172—22no—
91C2×D172—22no—
92C2×D172—41no—
93C2×D172—41no—
94C2×D172—41no—
95C2×D172—41no—
96C4⋊C4×C43—41no—
97C22⋊C4×C43—22no—
98C22⋊C4×C43—41no—
99C22⋊C4×C43—41no—
100C22⋊C4×C43—41no—
101C22⋊Dic43—22no—
102C22⋊Dic43—41no—
103C22⋊Dic43—41no—
104(C2×D43)⋊C4—22no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—22no—
108(C2×D43)⋊C4—41no—
109(C2×D43)⋊C4—41no—
110(C2×D43)⋊C4—41no—
111(C2×D43)⋊C4—41no—
112(C2×D43)⋊C4—41no—
113(C2×D43)⋊C4—41no—
114(C2×D43)⋊C4—41no—
115C4⋊Dic43—41no—
116Dic43⋊C4—41no—
117C23×C43—21no—
118C23×C43—21no—
119C23×C43—21no—
120C23×C43—21no—
121C23×C43—21no—
122C23×C43—21no—
123C23×C43—21no—
124C23×C43—21no—
125C23×C43—21no—
126C23×C43—21no—
127C23×C43—21no—
128C23×C43—21no—
129C23×C43—21no—
130C23×C43C2×D412yes—
131C23×C43C2411yescharacteristic
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—44no—
152C22×D43—44no—
153C22×D43—44no—
154C22×D43—44no—
155C22×D43—44no—
156C22×D43—44no—
157C22×D43—44no—
158C22×D43C2×D412yes—
159C22×D43C2×D412yes—
160D4×C43—44no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43—21no—
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—
176C22⋊D43—44no—
177C22⋊D43—44no—
178C22⋊D43—44no—
179C22⋊D43—44no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43—21no—
183C2×Dic43—21no—
184C2×Dic43—21no—
185C2×Dic43—21no—
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—
195D172—44no—
196D172—44no—
197C22×C43—22no—
198C22×C43—22no—
199C22×C43—22no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43C22×D411yescharacteristic
212C22×C43H(5,𝔽2)11yescharacteristic
213C22×C43H(5,𝔽2)11yescharacteristic
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—
240C4×C43—41no—
241C4×C43—41no—
242C4×C43—41no—
243C4×C43—41no—
244C4×C43—41no—
245Dic43—41no—
246Dic43—41no—
247Dic43—41no—
248Dic43—41no—
249Dic43—41no—
250#2812—431nomaximal, Sylow
251C2×C43—42no—
252C2×C43—81no—
253C2×C43#53411yescharacteristic
254C2×C43#53411yescharacteristic
255C2×C43#53411yescharacteristic
256C2×C43#56011yescharacteristic
257C2×C43#56011yescharacteristic
258C2×C43#56011yescharacteristic
259C2×C43H(3,𝔽4)11yescharacteristic
260D43—42no—
261D43—42no—
262D43—81no—
263C2×#120—431no—
264C2×#120—431no—
265#397—431no—
266#397—431no—
267#397—431no—
268#394—431no—
269#394—431no—
270#394—431no—
271#394—431no—
272#394—431no—
273#394D4311yescharacteristic, complemented
274#392—431no—
275#392—431no—
276#392—431no—
277#379—431no—
278C43#281211yescharacteristic, complemented, Sylow
279C25—431no—
280C22×D4—431no—
281C22×D4—431no—
282C22×D4—431no—
283C22×D4—431no—
284C22×D4—431no—
285C22×D4—431no—
286C22×D4C2×D4311yescharacteristic
287#120—864no—
288#120—864no—
289C2×C4⋊C4—431no—
290C2×C4⋊C4—431no—
291C2×C4⋊C4C2×D4311yescharacteristic, complemented
292C2×C22⋊C4—431no—
293C2×C22⋊C4—431no—
294C2×C22⋊C4—431no—
295C2×C22⋊C4—431no—
296C2×C22⋊C4—431no—
297C2×C22⋊C4—431no—
298C2×C22⋊C4—431no—
299C2×C22⋊C4—431no—
300C2×C22⋊C4—431no—
301C2×C22⋊C4—431no—
302C2×C22⋊C4—431no—
303C2×C22⋊C4—431no—
304C2×C22⋊C4—431no—
305C2×C22⋊C4—431no—
306C2×C22⋊C4C2×D4311yescharacteristic
307C2×C22⋊C4C2×D4311yescharacteristic
308C2×C22⋊C4C2×D4311yescharacteristic, complemented
309C2×C22⋊C4C2×D4311yescharacteristic, complemented
310#95—431no—
311#95—431no—
312#95—431no—
313#95—431no—
314#95—431no—
315#95C2×D4311yescharacteristic, complemented
316C24—431no—
317C24—431no—
318C24—434no—
319C24—431no—
320C24—1721no—
321C24—1721no—
322C24—1721no—
323C24—1721no—
324C24—1721no—
325C24—1721no—
326C24C22×D4311yescharacteristic
327C24C22×D4311yescharacteristic
328C2×D4—22no—
329C2×D4—41no—
330C2×D4—41no—
331C2×D4—862no—
332C2×D4—862no—
333C2×D4—862no—
334C2×D4—862no—
335C2×D4—862no—
336C2×D4—1721no—
337C2×D4—1721no—
338C2×D4—1721no—
339C2×D4—1721no—
340C2×D4—1721no—
341C2×D4—1721no—
342C2×D4—1721no—
343C2×D4—1721no—
344C2×D4—1721no—
345C2×D4—1721no—
346C2×D4—1721no—
347C2×D4—1721no—
348C2×D4—1721no—
349C22×C4—431no—
350C22×C4—431no—
351C22×C4—431no—
352C22×C4—431no—
353C22×C4—431no—
354C22×C4C22×D4311yescharacteristic
355C22×C4C22×D4311yescharacteristic
356C22×C4C22×D4311yescharacteristic
357C22×C4C22×D4311yescharacteristic
358C22×C4C22×D4311yescharacteristic
359C4⋊C4—41no—
360C4⋊C4—1721no—
361C4⋊C4—1721no—
362C22⋊C4—22no—
363C22⋊C4—41no—
364C22⋊C4—41no—
365C22⋊C4—41no—
366C22⋊C4—862no—
367C22⋊C4—862no—
368C22⋊C4—862no—
369C22⋊C4—862no—
370C22⋊C4—862no—
371C22⋊C4—1721no—
372C22⋊C4—1721no—
373C22⋊C4—1721no—
374C22⋊C4—1721no—
375C22⋊C4—1721no—
376C22⋊C4—1721no—
377C22⋊C4—1721no—
378C22⋊C4—1721no—
379C22⋊C4—1721no—
380C23—21no—
381C23—21no—
382C23—21no—
383C23—21no—
384C23—21no—
385C23—21no—
386C23—21no—
387C23—21no—
388C23—21no—
389C23—21no—
390C23—21no—
391C23—21no—
392C23—21no—
393C23—432no—
394C23—432no—
395C23—861no—
396C23—861no—
397C23—861no—
398C23—861no—
399C23—861no—
400C23—861no—
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—1724no—
415C23—1724no—
416C23—1724no—
417C23—1724no—
418C23—1724no—
419C23—1724no—
420C23—1724no—
421C23D4×D4312yes—
422C23C23×D4311yescharacteristic
423D4—44no—
424D4—1724no—
425D4—1724no—
426D4—1724no—
427D4—1724no—
428D4—1724no—
429D4—1724no—
430C2×C4—21no—
431C2×C4—21no—
432C2×C4—21no—
433C2×C4—21no—
434C2×C4—21no—
435C2×C4—21no—
436C2×C4—21no—
437C2×C4—21no—
438C2×C4—21no—
439C2×C4—21no—
440C2×C4—21no—
441C2×C4—21no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—21no—
445C2×C4—861no—
446C2×C4—861no—
447C2×C4—861no—
448C2×C4—861no—
449C2×C4—861no—
450C2×C4—861no—
451C2×C4—861no—
452C2×C4—861no—
453C2×C4—861no—
454C2×C4—861no—
455C2×C4—861no—
456C2×C4—861no—
457C2×C4—861no—
458C2×C4—861no—
459C2×C4—861no—
460C22—22no—
461C22—22no—
462C22—22no—
463C22—41no—
464C22—41no—
465C22—41no—
466C22—41no—
467C22—41no—
468C22—41no—
469C22—41no—
470C22—41no—
471C22—41no—
472C22—41no—
473C22—41no—
474C22—862no—
475C22—862no—
476C22—862no—
477C22—862no—
478C22—862no—
479C22—862no—
480C22—17216no—
481C22—1721no—
482C22—1721no—
483C22—1721no—
484C22—1721no—
485C22—1721no—
486C22—1721no—
487C22—1721no—
488C22—1721no—
489C22—1721no—
490C22—1721no—
491C22—1721no—
492C22—1721no—
493C22—1721no—
494C22—1721no—
495C22—1721no—
496C22C2×D4×D4311yescharacteristic
497C22#1306337011yescharacteristic
498C22#1306337011yescharacteristic
499C22#1306337011yescharacteristic
500C22#1306337111yescharacteristic
501C22#1306337111yescharacteristic
502C22#1306337111yescharacteristic
503C4—41no—
504C4—41no—
505C4—41no—
506C4—41no—
507C4—41no—
508C4—1721no—
509C4—1721no—
510C4—1721no—
511C4—1721no—
512C4—1721no—
513C2—42no—
514C2—81no—
515C2—3441no—
516C2—1722no—
517C2—1722no—
518C2#1458345711yescharacteristic
519C2#1458345911yescharacteristic
520C2#1458346011yescharacteristic
521C2#1458363711yescharacteristic
522C2#1458363711yescharacteristic
523C2#1458363911yescharacteristic
524C2#1458364111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#394C2
hypercenter#394D43
hypocenterC43#2812
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#13063295C2semidirect
2. C2×#13063293C2semidirect
3. #14582827C2semidirect
4. #14582826C2semidirect
5. #14582825C2semidirect
6. #14582817C2semidirect
7. #14582816C2semidirect
8. #14582815C2semidirect
9. #14582815C2semidirect
10. #14582814C2semidirect
11. #14582808C2semidirect
12. #14582808C2semidirect
13. #14582807C2semidirect
14. #14582754C2semidirect
15. C43×#394C2semidirect
22. C22×C22⋊D43C22semidirect
25. C2×C4⋊Dic43C22semidirect
26. C2×Dic43⋊C4C22semidirect
29. C2×C22⋊Dic43C22semidirect
38. C2×(C2×D43)⋊C4C22semidirect
39. C2×(C2×D43)⋊C4C22semidirect
40. C2×(C2×D43)⋊C4C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
47. C2×C4⋊C4×C43C22semidirect
50. C2×C22⋊C4×C43C22semidirect
51. C2×C22⋊C4×C43C22semidirect
52. #95×C43C22semidirect
61. C23×D43D4semidirect
273. #394D43semidirect
278. C43#2812semidirect
291. C2×C4⋊C4C2×D43semidirect
308. C2×C22⋊C4C2×D43semidirect
309. C2×C22⋊C4C2×D43semidirect
315. #95C2×D43semidirect