Finite Group Databasebeta

← #19140975

Subgroups — #19140975

Order 5504.

688 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063311C211yesmaximal, characteristic, complemented
2C2×#13063294C211yesmaximal, characteristic
3#14582827C211yesmaximal, characteristic, complemented
4#14582824C211yesmaximal, characteristic, complemented
5#14582815C211yesmaximal, characteristic, complemented
6#14582814C211yesmaximal, characteristic, complemented
7#14582811C211yesmaximal, characteristic, complemented
8#14582811C211yesmaximal, characteristic, complemented
9#14582793C211yesmaximal, characteristic, complemented
10#14582792C211yesmaximal, characteristic, complemented
11#14582775C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582775C211yesmaximal, characteristic, complemented
14#14582755C211yesmaximal, characteristic, complemented
15C43×#379C211yesmaximal, characteristic, complemented
16C22×Dic86C2211yescharacteristic, complemented
17C22×C22⋊D43C2211yescharacteristic
18C22×C22⋊D43C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic, complemented
21#13063311—24no—
22#13063294—24no—
23C2×C4⋊Dic43C2211yescharacteristic, complemented
24C2×Dic43⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×C22⋊Dic43C2211yescharacteristic
28C2×C22⋊Dic43C2211yescharacteristic
29C2×C22⋊Dic43C2211yescharacteristic
30C2×C22⋊Dic43C2211yescharacteristic
31C2×C22⋊Dic43C2211yescharacteristic
32C2×C22⋊Dic43C2211yescharacteristic
33C2×C22⋊Dic43C2211yescharacteristic
34C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
35C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
36C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
37C2×C4×Dic43C2211yescharacteristic, complemented
38C43⋊#95C2211yescharacteristic, complemented
39C43⋊#95C2211yescharacteristic, complemented
40C43⋊#95C2211yescharacteristic, complemented
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C25×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50C2×C22⋊C4×C43C2211yescharacteristic
51C2×C22⋊C4×C43C2211yescharacteristic
52C2×C22⋊C4×C43C2211yescharacteristic
53C24×C43—22no—
54C24×C43—22no—
55C24×C43—22no—
56C24×C43—41no—
57C24×C43—41no—
58C24×C43—41no—
59C24×C43—41no—
60C24×C43C2311yescharacteristic
61C24×C43C2311yescharacteristic
62C24×C43C2311yescharacteristic
63C23×D43C2311yescharacteristic
64C22×C4×C43C2311yescharacteristic
65C22×C4×C43C2311yescharacteristic
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C2×C22⋊D43—22no—
69C2×C22⋊D43—22no—
70C2×C22⋊D43—22no—
71C2×C22⋊D43—22no—
72C2×C22⋊D43—41no—
73C2×C22⋊D43—41no—
74C2×C22⋊D43—41no—
75C2×C22⋊D43—41no—
76C2×C22⋊D43D414yes—
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C2×C4×D43—41no—
85C2×C4×D43—41no—
86C2×C4×D43—41no—
87C2×Dic86—22no—
88C2×Dic86—41no—
89C2×Dic86—41no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—22no—
92C22⋊C4×C43—41no—
93C22⋊C4×C43—41no—
94C22⋊C4×C43—41no—
95C22⋊C4×C43—41no—
96C22⋊Dic43—22no—
97C22⋊Dic43—22no—
98C22⋊Dic43—22no—
99C22⋊Dic43—22no—
100C22⋊Dic43—22no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103C22⋊Dic43—41no—
104C22⋊Dic43—41no—
105(C2×D43)⋊C4—22no—
106(C2×D43)⋊C4—22no—
107(C2×D43)⋊C4—41no—
108C4⋊Dic43—41no—
109Dic43⋊C4—41no—
110C4×Dic43—22no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43—21no—
114C23×C43—21no—
115C23×C43—21no—
116C23×C43—21no—
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—44no—
130C23×C43—44no—
131C23×C43—44no—
132C23×C43—44no—
133C23×C43—44no—
134C23×C43—44no—
135C23×C43—44no—
136C23×C43C2×D412yes—
137C23×C43#4112yes—
138C23×C43#4112yes—
139C23×C43C2411yescharacteristic
140C22×D43—21no—
141C22×D43—21no—
142C22×D43—21no—
143C22×D43—21no—
144C22×D43—21no—
145C22×D43—21no—
146C22×D43C2×D412yes—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—21no—
152C2×C4×C43—21no—
153C2×C4×C43—21no—
154C2×C4×C43—21no—
155C2×C4×C43—21no—
156C2×C4×C43—21no—
157C2×C4×C43—21no—
158C2×C4×C43—21no—
159C22⋊D43—44no—
160C22⋊D43—44no—
161C22⋊D43—44no—
162C2×Dic43—21no—
163C2×Dic43—21no—
164C2×Dic43—21no—
165C2×Dic43—21no—
166C2×Dic43—21no—
167C2×Dic43—21no—
168C2×Dic43—21no—
169C2×Dic43—21no—
170C2×Dic43—21no—
171C2×Dic43—21no—
172C2×Dic43—21no—
173C2×Dic43—21no—
174C2×Dic43—21no—
175C2×Dic43—21no—
176C2×Dic43—21no—
177C2×Dic43—21no—
178C2×Dic43—21no—
179C2×Dic43—21no—
180C2×Dic43—21no—
181C2×Dic43—21no—
182C2×Dic43C2×D412yes—
183C4×D43—44no—
184Dic86—44no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—22no—
193C22×C43—22no—
194C22×C43—416no—
195C22×C43—41no—
196C22×C43—41no—
197C22×C43—41no—
198C22×C43—41no—
199C22×C43—41no—
200C22×C43—41no—
201C22×C43—41no—
202C22×C43—41no—
203C22×C43—41no—
204C22×C43—41no—
205C22×C43—41no—
206C22×C43—41no—
207C22×C43C22×D411yescharacteristic
208C22×C43C2×#4111yescharacteristic
209C22×C43C2×#4111yescharacteristic
210C22×C43H(5,𝔽2)11yescharacteristic
211C22×C43H(5,𝔽2)11yescharacteristic
212C22×C43H(5,𝔽2)11yescharacteristic
213C22×C43H(5,𝔽2)11yescharacteristic
214C2×D43—22no—
215C2×D43—22no—
216C2×D43—22no—
217C2×D43—41no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C4×C43—41no—
222C4×C43—41no—
223C4×C43—41no—
224C4×C43—41no—
225Dic43—22no—
226Dic43—41no—
227Dic43—41no—
228Dic43—41no—
229Dic43—41no—
230Dic43—41no—
231Dic43—41no—
232#2684—431nomaximal, Sylow
233C2×C43—42no—
234C2×C43—42no—
235C2×C43—42no—
236C2×C43#53411yescharacteristic
237C2×C43#53811yescharacteristic
238C2×C43#53811yescharacteristic
239C2×C43#54611yescharacteristic
240C2×C43#54611yescharacteristic
241C2×C43#55111yescharacteristic
242C2×C43H(3,𝔽4)11yescharacteristic
243D43—42no—
244C2×#124—431no—
245C2×#120—431no—
246#397—431no—
247#397—431no—
248#394—431no—
249#394—431no—
250#393—431no—
251#393—431no—
252#388—431no—
253#388—431no—
254#386—431no—
255#386—431no—
256#386—431no—
257#379—431no—
258#379D4311yescharacteristic, complemented
259C43#268411yescharacteristic, complemented, Sylow
260C25C2×D4311yescharacteristic
261C22×Q8—431no—
262C22×D4—431no—
263C22×D4—431no—
264C22×D4—431no—
265C23×C4—431no—
266#124—864no—
267#120—864no—
268C2×C4⋊C4—431no—
269C2×C4⋊C4—431no—
270C2×C22⋊C4—431no—
271C2×C22⋊C4—431no—
272C2×C22⋊C4—431no—
273C2×C22⋊C4—431no—
274C2×C22⋊C4—431no—
275C2×C22⋊C4—431no—
276C2×C22⋊C4—431no—
277C2×C22⋊C4—431no—
278C2×C22⋊C4—431no—
279C2×C22⋊C4—431no—
280C2×C22⋊C4—431no—
281C2×C22⋊C4—431no—
282C2×C22⋊C4C2×D4311yescharacteristic
283C2×C22⋊C4C2×D4311yescharacteristic
284C2×C22⋊C4C2×D4311yescharacteristic
285C2×C22⋊C4C2×D4311yescharacteristic
286C2×C22⋊C4C2×D4311yescharacteristic
287C2×C22⋊C4C2×D4311yescharacteristic
288C2×C42—431no—
289#95—431no—
290#95—431no—
291#95—431no—
292#95—431no—
293#95—431no—
294#95—431no—
295#95—431no—
296#95—431no—
297C24—22no—
298C24—22no—
299C24—22no—
300C24—41no—
301C24—41no—
302C24—41no—
303C24—41no—
304C24—431no—
305C24C22×D4311yescharacteristic
306C24C22×D4311yescharacteristic
307C24C22×D4311yescharacteristic
308C2×Q8—862no—
309C2×Q8—1721no—
310C2×Q8—1721no—
311C2×D4—434no—
312C2×D4—862no—
313C2×D4—862no—
314C2×D4—862no—
315C2×D4—862no—
316C2×D4—1721no—
317C2×D4—1721no—
318C2×D4—1721no—
319C2×D4—1721no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4—431no—
324C22×C4—431no—
325C22×C4—431no—
326C22×C4—431no—
327C22×C4—1721no—
328C22×C4—1721no—
329C22×C4—1721no—
330C22×C4C22×D4311yescharacteristic
331C22×C4C22×D4311yescharacteristic
332C22×C4C22×D4311yescharacteristic
333C22×C4C22×D4311yescharacteristic
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C22⋊C4—22no—
337C22⋊C4—22no—
338C22⋊C4—41no—
339C22⋊C4—41no—
340C22⋊C4—41no—
341C22⋊C4—41no—
342C22⋊C4—862no—
343C22⋊C4—862no—
344C22⋊C4—862no—
345C22⋊C4—862no—
346C22⋊C4—862no—
347C22⋊C4—862no—
348C22⋊C4—862no—
349C22⋊C4—1721no—
350C22⋊C4—1721no—
351C22⋊C4—1721no—
352C22⋊C4—1721no—
353C22⋊C4—1721no—
354C42—862no—
355C23—21no—
356C23—21no—
357C23—21no—
358C23—21no—
359C23—21no—
360C23—21no—
361C23—21no—
362C23—21no—
363C23—21no—
364C23—21no—
365C23—21no—
366C23—21no—
367C23—21no—
368C23—21no—
369C23—21no—
370C23—21no—
371C23—21no—
372C23—21no—
373C23—44no—
374C23—44no—
375C23—44no—
376C23—44no—
377C23—44no—
378C23—44no—
379C23—44no—
380C23—432no—
381C23—861no—
382C23—861no—
383C23—861no—
384C23—861no—
385C23—861no—
386C23—861no—
387C23#1062189812yes—
388C23D4×D4312yes—
389C23#1062190012yes—
390C23C23×D4311yescharacteristic
391Q8—1724no—
392D4—1724no—
393D4—1724no—
394D4—1724no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—21no—
402C2×C4—21no—
403C2×C4—21no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—21no—
407C2×C4—432no—
408C2×C4—861no—
409C2×C4—861no—
410C2×C4—861no—
411C2×C4—861no—
412C2×C4—861no—
413C2×C4—861no—
414C2×C4—861no—
415C2×C4—861no—
416C2×C4—861no—
417C2×C4—861no—
418C2×C4—861no—
419C2×C4—861no—
420C2×C4—861no—
421C2×C4—861no—
422C2×C4—861no—
423C2×C4—861no—
424C2×C4—861no—
425C2×C4—861no—
426C2×C4—861no—
427C2×C4—861no—
428C2×C4—1724no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—22no—
435C22—22no—
436C22—22no—
437C22—22no—
438C22—416no—
439C22—41no—
440C22—41no—
441C22—41no—
442C22—41no—
443C22—41no—
444C22—41no—
445C22—41no—
446C22—41no—
447C22—41no—
448C22—41no—
449C22—41no—
450C22—41no—
451C22—862no—
452C22—862no—
453C22—862no—
454C22—1721no—
455C22—1721no—
456C22—1721no—
457C22—1721no—
458C22C2×D4×D4311yescharacteristic
459C22C2×#1062190011yescharacteristic
460C22C2×#1062189811yescharacteristic
461C22#1306337011yescharacteristic
462C22#1306337011yescharacteristic
463C22#1306337011yescharacteristic
464C22#1306337011yescharacteristic
465C4—41no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—862no—
470C4—1721no—
471C4—1721no—
472C4—1721no—
473C4—1721no—
474C4—1721no—
475C4—1721no—
476C2—42no—
477C2—42no—
478C2—42no—
479C2—1722no—
480C2#1458345911yescharacteristic
481C2#1458348411yescharacteristic
482C2#1458348711yescharacteristic
483C2#1458353611yescharacteristic
484C2#1458353911yescharacteristic
485C2#1458357511yescharacteristic
486C2#1458364211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#379C2
hypercenter#379D43
hypocenterC43#2684
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C2×#13063311C2semidirect
3. #14582827C2semidirect
4. #14582824C2semidirect
5. #14582815C2semidirect
6. #14582814C2semidirect
7. #14582811C2semidirect
8. #14582811C2semidirect
9. #14582793C2semidirect
10. #14582792C2semidirect
11. #14582775C2semidirect
12. #14582775C2semidirect
13. #14582775C2semidirect
14. #14582755C2semidirect
15. C43×#379C2semidirect
16. C22×Dic86C22semidirect
20. C22×C4×D43C22semidirect
23. C2×C4⋊Dic43C22semidirect
24. C2×Dic43⋊C4C22semidirect
34. C2×(C2×D43)⋊C4C22semidirect
35. C2×(C2×D43)⋊C4C22semidirect
36. C2×(C2×D43)⋊C4C22semidirect
37. C2×C4×Dic43C22semidirect
38. C43⋊#95C22semidirect
39. C43⋊#95C22semidirect
40. C43⋊#95C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
258. #379D43semidirect
259. C43#2684semidirect