Finite Group Databasebeta

← #19140978

Subgroups — #19140978

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×#13063314C211yesmaximal, characteristic, complemented
2C2×#13063295C211yesmaximal, characteristic
3#14582828C211yesmaximal, characteristic, complemented
4#14582826C211yesmaximal, characteristic, complemented
5#14582817C211yesmaximal, characteristic, complemented
6#14582815C211yesmaximal, characteristic, complemented
7#14582810C211yesmaximal, characteristic, complemented
8#14582791C211yesmaximal, characteristic, complemented
9#14582787C211yesmaximal, characteristic, complemented
10#14582777C211yesmaximal, characteristic, complemented
11#14582777C211yesmaximal, characteristic, complemented
12#14582775C211yesmaximal, characteristic, complemented
13#14582754C211yesmaximal, characteristic, complemented
14#14582754C211yesmaximal, characteristic, complemented
15C43×#393C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C22×D172C2211yescharacteristic
18C22×D172C2211yescharacteristic
19C22×C22⋊D43C2211yescharacteristic
20C22×C4×D43C2211yescharacteristic, complemented
21#13063314—24no—
22#13063295—24no—
23C2×C4⋊Dic43C2211yescharacteristic, complemented
24C2×Dic43⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×(C2×D43)⋊C4C2211yescharacteristic
28C2×(C2×D43)⋊C4C2211yescharacteristic
29C2×(C2×D43)⋊C4C2211yescharacteristic
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, complemented
38C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
39C2×(C2×D43)⋊C4C2211yescharacteristic, complemented
40C2×C4×Dic43C2211yescharacteristic, complemented
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C22×Q8×C43C2211yescharacteristic, complemented
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C22⋊C4×C43C2211yescharacteristic
50#95×C43C2211yescharacteristic, complemented
51#95×C43C2211yescharacteristic, complemented
52#95×C43C2211yescharacteristic, complemented
53C24×C43C2311yescharacteristic
54C23×D43—22no—
55C23×D43—22no—
56C23×D43—22no—
57C23×D43—41no—
58C23×D43—41no—
59C23×D43—41no—
60C23×D43—41no—
61C23×D43C2311yescharacteristic
62C23×D43C2311yescharacteristic
63C23×D43C2311yescharacteristic
64C2×Q8×C43—22no—
65C2×Q8×C43—41no—
66C2×Q8×C43—41no—
67C22×C4×C43C2311yescharacteristic
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—41no—
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C2×D172—22no—
82C2×D172—22no—
83C2×D172—41no—
84C2×D172—41no—
85C2×D172—41no—
86C2×D172D414yes—
87C2×C4×D43—41no—
88C2×C4×D43—41no—
89C2×C4×D43—41no—
90C22⋊C4×C43—22no—
91C22⋊C4×C43—41no—
92C22⋊C4×C43—41no—
93C22⋊Dic43—22no—
94C22⋊Dic43—41no—
95(C2×D43)⋊C4—22no—
96(C2×D43)⋊C4—22no—
97(C2×D43)⋊C4—22no—
98(C2×D43)⋊C4—22no—
99(C2×D43)⋊C4—22no—
100(C2×D43)⋊C4—22no—
101(C2×D43)⋊C4—22no—
102(C2×D43)⋊C4—41no—
103(C2×D43)⋊C4—41no—
104(C2×D43)⋊C4—41no—
105(C2×D43)⋊C4—41no—
106(C2×D43)⋊C4—41no—
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#4112yes—
118C23×C43C2411yescharacteristic
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—21no—
127C22×D43—21no—
128C22×D43—21no—
129C22×D43—21no—
130C22×D43—21no—
131C22×D43—21no—
132C22×D43—21no—
133C22×D43—21no—
134C22×D43—21no—
135C22×D43—21no—
136C22×D43—21no—
137C22×D43—44no—
138C22×D43—44no—
139C22×D43—44no—
140C22×D43—44no—
141C22×D43—44no—
142C22×D43—44no—
143C22×D43—44no—
144C22×D43C2×D412yes—
145C22×D43C2×D412yes—
146C22×D43#4112yes—
147Q8×C43—44no—
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—
159C2×C4×C43—21no—
160C2×C4×C43—21no—
161C2×C4×C43—21no—
162C2×C4×C43—21no—
163C2×C4×C43—21no—
164C2×C4×C43—21no—
165C2×C4×C43C2×D412yes—
166C22⋊D43—44no—
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—
182D172—44no—
183D172—44no—
184C4×D43—44no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—41no—
189C22×C43—41no—
190C22×C43—41no—
191C22×C43—41no—
192C22×C43C22×D411yescharacteristic
193C22×C43C2×#4111yescharacteristic
194C22×C43C2×#4111yescharacteristic
195C22×C43H(5,𝔽2)11yescharacteristic
196C22×C43H(5,𝔽2)11yescharacteristic
197C22×C43H(5,𝔽2)11yescharacteristic
198C22×C43H(5,𝔽2)11yescharacteristic
199C2×D43—22no—
200C2×D43—22no—
201C2×D43—22no—
202C2×D43—22no—
203C2×D43—22no—
204C2×D43—22no—
205C2×D43—22no—
206C2×D43—22no—
207C2×D43—22no—
208C2×D43—416no—
209C2×D43—41no—
210C2×D43—41no—
211C2×D43—41no—
212C2×D43—41no—
213C2×D43—41no—
214C2×D43—41no—
215C2×D43—41no—
216C2×D43—41no—
217C2×D43—41no—
218C2×D43—41no—
219C2×D43—41no—
220C2×D43—41no—
221C4×C43—22no—
222C4×C43—41no—
223C4×C43—41no—
224C4×C43—41no—
225C4×C43—41no—
226C4×C43—41no—
227Dic43—41no—
228Dic43—41no—
229Dic43—41no—
230Dic43—41no—
231Dic43—41no—
232#2684—431nomaximal, Sylow
233C2×C43—42no—
234C2×C43#53411yescharacteristic
235C2×C43#53811yescharacteristic
236C2×C43#53811yescharacteristic
237C2×C43#54611yescharacteristic
238C2×C43#54611yescharacteristic
239C2×C43#55111yescharacteristic
240C2×C43H(3,𝔽4)11yescharacteristic
241D43—42no—
242D43—42no—
243D43—42no—
244C2×#124—431no—
245C2×#120—431no—
246#397—431no—
247#397—431no—
248#394—431no—
249#394—431no—
250#393—431no—
251#393D4311yescharacteristic, complemented
252#388—431no—
253#388—431no—
254#386—431no—
255#386—431no—
256#386—431no—
257#379—431no—
258#379—431no—
259C43#268411yescharacteristic, complemented, Sylow
260C25—431no—
261C22×Q8C2×D4311yescharacteristic, complemented
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⋊C4—431no—
283C2×C22⋊C4—431no—
284C2×C22⋊C4—431no—
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#95C2×D4311yescharacteristic, complemented
295#95C2×D4311yescharacteristic, complemented
296#95C2×D4311yescharacteristic, complemented
297C24—431no—
298C24—431no—
299C24—431no—
300C24—862no—
301C24—862no—
302C24—862no—
303C24—1721no—
304C24—1721no—
305C24—1721no—
306C24—1721no—
307C24C22×D4311yescharacteristic
308C2×Q8—22no—
309C2×Q8—41no—
310C2×Q8—41no—
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—1721no—
326C22×C4—1721no—
327C22×C4—1721no—
328C22×C4C22×D4311yescharacteristic
329C22×C4C22×D4311yescharacteristic
330C22×C4C22×D4311yescharacteristic
331C22×C4C22×D4311yescharacteristic
332C22×C4C22×D4311yescharacteristic
333C22×C4C22×D4311yescharacteristic
334C4⋊C4—1721no—
335C4⋊C4—1721no—
336C22⋊C4—22no—
337C22⋊C4—41no—
338C22⋊C4—41no—
339C22⋊C4—862no—
340C22⋊C4—862no—
341C22⋊C4—862no—
342C22⋊C4—862no—
343C22⋊C4—862no—
344C22⋊C4—862no—
345C22⋊C4—862no—
346C22⋊C4—862no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
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—432no—
362C23—432no—
363C23—432no—
364C23—861no—
365C23—861no—
366C23—861no—
367C23—861no—
368C23—861no—
369C23—861no—
370C23—861no—
371C23—861no—
372C23—861no—
373C23—861no—
374C23—861no—
375C23—861no—
376C23—861no—
377C23—861no—
378C23—861no—
379C23—861no—
380C23—861no—
381C23—861no—
382C23—1724no—
383C23—1724no—
384C23—1724no—
385C23—1724no—
386C23—1724no—
387C23—1724no—
388C23—1724no—
389C23#1062190212yes—
390C23C23×D4311yescharacteristic
391Q8—44no—
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—21no—
408C2×C4—21no—
409C2×C4—21no—
410C2×C4—21no—
411C2×C4—21no—
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—1724no—
428C2×C4D4×D4312yes—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—41no—
433C22—41no—
434C22—41no—
435C22—41no—
436C22—862no—
437C22—862no—
438C22—862no—
439C22—862no—
440C22—862no—
441C22—862no—
442C22—862no—
443C22—862no—
444C22—862no—
445C22—17216no—
446C22—1721no—
447C22—1721no—
448C22—1721no—
449C22—1721no—
450C22—1721no—
451C22—1721no—
452C22—1721no—
453C22—1721no—
454C22—1721no—
455C22—1721no—
456C22—1721no—
457C22—1721no—
458C22C2×D4×D4311yescharacteristic
459C22#41×D4311yescharacteristic
460C22C2×#1062190211yescharacteristic
461C22#1306337011yescharacteristic
462C22#1306337011yescharacteristic
463C22#1306337111yescharacteristic
464C22#1306337111yescharacteristic
465C4—22no—
466C4—41no—
467C4—41no—
468C4—41no—
469C4—41no—
470C4—41no—
471C4—1721no—
472C4—1721no—
473C4—1721no—
474C4—1721no—
475C4—1721no—
476C2—42no—
477C2—1722no—
478C2—1722no—
479C2—1722no—
480C2#1458345911yescharacteristic
481C2#1458348311yescharacteristic
482C2#1458348911yescharacteristic
483C2#1458354011yescharacteristic
484C2#1458354211yescharacteristic
485C2#1458357611yescharacteristic
486C2#1458364111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC43×#393C2
hypercenter#393D43
hypocenterC43#2684
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ #393

Complements

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

NH ≅ G/Ntype
1. C2×#13063314C2semidirect
3. #14582828C2semidirect
4. #14582826C2semidirect
5. #14582817C2semidirect
6. #14582815C2semidirect
7. #14582810C2semidirect
8. #14582791C2semidirect
9. #14582787C2semidirect
10. #14582777C2semidirect
11. #14582777C2semidirect
12. #14582775C2semidirect
13. #14582754C2semidirect
14. #14582754C2semidirect
15. C43×#393C2semidirect
20. C22×C4×D43C22semidirect
23. C2×C4⋊Dic43C22semidirect
24. C2×Dic43⋊C4C22semidirect
37. C2×(C2×D43)⋊C4C22semidirect
38. C2×(C2×D43)⋊C4C22semidirect
39. C2×(C2×D43)⋊C4C22semidirect
40. C2×C4×Dic43C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
46. C22×Q8×C43C22semidirect
50. #95×C43C22semidirect
51. #95×C43C22semidirect
52. #95×C43C22semidirect
251. #393D43semidirect
259. C43#2684semidirect
261. C22×Q8C2×D43semidirect
294. #95C2×D43semidirect
295. #95C2×D43semidirect
296. #95C2×D43semidirect