Finite Group Databasebeta

← #19140982

Subgroups — #19140982

Order 5504.

666 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063318C211yesmaximal, characteristic, complemented
2#14582835C211yesmaximal, characteristic, complemented
3#14582822C211yesmaximal, characteristic, complemented
4#14582813C211yesmaximal, characteristic, complemented
5#14582813C211yesmaximal, characteristic, complemented
6#14582813C211yesmaximal, characteristic, complemented
7#14582813C211yesmaximal, characteristic, complemented
8#14582802C211yesmaximal, characteristic, complemented
9#14582802C211yesmaximal, characteristic, complemented
10#14582793C211yesmaximal, characteristic, complemented
11#14582792C211yesmaximal, characteristic, complemented
12#14582787C211yesmaximal, characteristic, complemented
13#14582755C211yesmaximal, characteristic, complemented
14#14582755C211yesmaximal, characteristic, complemented
15C2×#120×C43C211yesmaximal, characteristic
16#13063318—24no—
17C2×C4⋊Dic43C2211yescharacteristic, complemented
18C2×C4⋊Dic43C2211yescharacteristic, complemented
19C2×Dic43⋊C4C2211yescharacteristic, complemented
20C2×Dic43⋊C4C2211yescharacteristic, complemented
21C2×Dic43⋊C4C2211yescharacteristic, complemented
22C2×Dic43⋊C4C2211yescharacteristic, complemented
23C2×C22⋊Dic43C2211yescharacteristic
24C2×C22⋊Dic43C2211yescharacteristic
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×C22⋊Dic43C2211yescharacteristic
35C2×C22⋊Dic43C2211yescharacteristic, complemented
36C2×C22⋊Dic43C2211yescharacteristic, complemented
37C2×C22⋊Dic43C2211yescharacteristic, complemented
38C2×C22⋊Dic43C2211yescharacteristic, complemented
39C2×C4×Dic43C2211yescharacteristic, complemented
40C2×C4×Dic43C2211yescharacteristic, complemented
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C25×C43C2211yescharacteristic
46C22×D4×C43C2211yescharacteristic
47C22×D4×C43C2211yescharacteristic
48C22×D4×C43C2211yescharacteristic
49#120×C43—24no—
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
63C24×C43C2311yescharacteristic
64C2×D4×C43—22no—
65C2×D4×C43—22no—
66C2×D4×C43—22no—
67C2×D4×C43—22no—
68C2×D4×C43—22no—
69C2×D4×C43—41no—
70C2×D4×C43—41no—
71C2×D4×C43—41no—
72C2×D4×C43—41no—
73C22×C4×C43C2311yescharacteristic
74C22×C4×C43C2311yescharacteristic
75C22×C4×C43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22×Dic43C2311yescharacteristic
82C22×Dic43C2311yescharacteristic
83C22×Dic43C2311yescharacteristic
84C22⋊C4×C43—22no—
85C22⋊C4×C43—22no—
86C22⋊C4×C43D414yes—
87C22⋊Dic43—22no—
88C22⋊Dic43—22no—
89C22⋊Dic43—22no—
90C22⋊Dic43—22no—
91C22⋊Dic43—41no—
92C22⋊Dic43—41no—
93C22⋊Dic43—41no—
94C22⋊Dic43—41no—
95C22⋊Dic43—41no—
96C22⋊Dic43—41no—
97C22⋊Dic43—41no—
98C22⋊Dic43—41no—
99C22⋊Dic43—41no—
100C22⋊Dic43—41no—
101C22⋊Dic43—41no—
102C22⋊Dic43—41no—
103C4⋊Dic43—22no—
104C4⋊Dic43—41no—
105Dic43⋊C4—22no—
106Dic43⋊C4—22no—
107Dic43⋊C4—41no—
108Dic43⋊C4—41no—
109C4×Dic43—22no—
110C4×Dic43—41no—
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—21no—
130C23×C43—21no—
131C23×C43—21no—
132C23×C43—21no—
133C23×C43—21no—
134C23×C43—21no—
135C23×C43—21no—
136C23×C43—44no—
137C23×C43—44no—
138C23×C43—44no—
139C23×C43—44no—
140C23×C43—44no—
141C23×C43—44no—
142C23×C43—44no—
143C23×C43C2×D412yes—
144C23×C43#4112yes—
145C23×C43#4112yes—
146C23×C43C2411yescharacteristic
147D4×C43—44no—
148D4×C43—44no—
149D4×C43—44no—
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×C43C2×D412yes—
158C2×C4×C43C2×D412yes—
159C2×Dic43—21no—
160C2×Dic43—21no—
161C2×Dic43—21no—
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×Dic43—21no—
183C22×C43—22no—
184C22×C43—22no—
185C22×C43—22no—
186C22×C43—22no—
187C22×C43—22no—
188C22×C43—22no—
189C22×C43—22no—
190C22×C43—22no—
191C22×C43—22no—
192C22×C43—416no—
193C22×C43—41no—
194C22×C43—41no—
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×C43—41no—
208C22×C43—41no—
209C22×C43—41no—
210C22×C43—41no—
211C22×C43—41no—
212C22×C43C22×D411yescharacteristic
213C22×C43C2×#4111yescharacteristic
214C22×C43C2×#4111yescharacteristic
215C22×C43H(5,𝔽2)11yescharacteristic
216C22×C43H(5,𝔽2)11yescharacteristic
217C22×C43H(5,𝔽2)11yescharacteristic
218C22×C43H(5,𝔽2)11yescharacteristic
219C4×C43—22no—
220C4×C43—22no—
221C4×C43—41no—
222Dic43—41no—
223Dic43—41no—
224Dic43—41no—
225Dic43—41no—
226Dic43—41no—
227Dic43—41no—
228Dic43—41no—
229Dic43—41no—
230#2685—431nomaximal, Sylow
231C2×C43—42no—
232C2×C43—42no—
233C2×C43—42no—
234C2×C43—81no—
235C2×C43#53511yescharacteristic
236C2×C43#53811yescharacteristic
237C2×C43#53811yescharacteristic
238C2×C43#54611yescharacteristic
239C2×C43#54611yescharacteristic
240C2×C43#55111yescharacteristic
241C2×C43#56011yescharacteristic
242C2×#126—431no—
243C2×#120D4311yescharacteristic
244#399—431no—
245#396—431no—
246#394—431no—
247#394—431no—
248#394—431no—
249#394—431no—
250#390—431no—
251#390—431no—
252#388—431no—
253#388—431no—
254#388—431no—
255#379—431no—
256#379—431no—
257C43#268511yescharacteristic, complemented, Sylow
258C25C2×D4311yescharacteristic
259C22×D4C2×D4311yescharacteristic
260C22×D4C2×D4311yescharacteristic
261C22×D4C2×D4311yescharacteristic
262#126—864no—
263#120—24no—
264C2×C4⋊C4—431no—
265C2×C4⋊C4—431no—
266C2×C4⋊C4—431no—
267C2×C4⋊C4—431no—
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⋊C4—431no—
286C2×C22⋊C4C2×D4311yescharacteristic
287C2×C22⋊C4C2×D4311yescharacteristic
288C2×C22⋊C4C2×D4311yescharacteristic
289C2×C42—431no—
290C2×C42—431no—
291#95—431no—
292#95—431no—
293#95—431no—
294#95—431no—
295C24—22no—
296C24—22no—
297C24—22no—
298C24—41no—
299C24—41no—
300C24—41no—
301C24—41no—
302C24C22×D4311yescharacteristic
303C24C22×D4311yescharacteristic
304C24C22×D4311yescharacteristic
305C24C22×D4311yescharacteristic
306C2×D4—22no—
307C2×D4—22no—
308C2×D4—22no—
309C2×D4—22no—
310C2×D4—22no—
311C2×D4—41no—
312C2×D4—41no—
313C2×D4—41no—
314C2×D4—41no—
315C22×C4—431no—
316C22×C4—431no—
317C22×C4—431no—
318C22×C4—431no—
319C22×C4—431no—
320C22×C4—431no—
321C22×C4—431no—
322C22×C4—431no—
323C22×C4C22×D4311yescharacteristic
324C22×C4C22×D4311yescharacteristic
325C22×C4C22×D4311yescharacteristic
326C4⋊C4—862no—
327C4⋊C4—862no—
328C4⋊C4—862no—
329C4⋊C4—1721no—
330C4⋊C4—1721no—
331C4⋊C4—1721no—
332C22⋊C4—22no—
333C22⋊C4—22no—
334C22⋊C4—862no—
335C22⋊C4—862no—
336C22⋊C4—862no—
337C22⋊C4—862no—
338C22⋊C4—1721no—
339C22⋊C4—1721no—
340C22⋊C4—1721no—
341C22⋊C4—1721no—
342C22⋊C4—1721no—
343C22⋊C4—1721no—
344C22⋊C4—1721no—
345C22⋊C4—1721no—
346C22⋊C4—1721no—
347C22⋊C4—1721no—
348C22⋊C4—1721no—
349C22⋊C4—1721no—
350C22⋊C4C22⋊D4314yes—
351C42—862no—
352C42—1721no—
353C23—21no—
354C23—21no—
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—21no—
374C23—21no—
375C23—21no—
376C23—21no—
377C23—21no—
378C23—44no—
379C23—44no—
380C23—44no—
381C23—44no—
382C23—44no—
383C23—44no—
384C23—44no—
385C23#1062190012yes—
386C23#1062190012yes—
387C23C2×C22⋊D4312yes—
388C23C23×D4311yescharacteristic
389D4—44no—
390D4—44no—
391D4—44no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—861no—
400C2×C4—861no—
401C2×C4—861no—
402C2×C4—861no—
403C2×C4—861no—
404C2×C4—861no—
405C2×C4—861no—
406C2×C4—861no—
407C2×C4—861no—
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×C4C2×C22⋊D4312yes—
424C2×C4C2×C22⋊D4312yes—
425C22—22no—
426C22—22no—
427C22—22no—
428C22—22no—
429C22—22no—
430C22—22no—
431C22—22no—
432C22—22no—
433C22—22no—
434C22—416no—
435C22—41no—
436C22—41no—
437C22—41no—
438C22—41no—
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—41no—
452C22—41no—
453C22—41no—
454C22C22×C22⋊D4311yescharacteristic
455C22C2×#1062190011yescharacteristic
456C22C2×#1062190011yescharacteristic
457C22#1306337011yescharacteristic
458C22#1306337011yescharacteristic
459C22#1306337011yescharacteristic
460C22#1306337011yescharacteristic
461C4—22no—
462C4—22no—
463C4—41no—
464C4—1721no—
465C4—1721no—
466C4—1721no—
467C4—1721no—
468C4—1721no—
469C4—1721no—
470C4—1721no—
471C4—1721no—
472C2—42no—
473C2—42no—
474C2—42no—
475C2—81no—
476C2#1458346611yescharacteristic
477C2#1458348411yescharacteristic
478C2#1458348411yescharacteristic
479C2#1458354311yescharacteristic
480C2#1458354311yescharacteristic
481C2#1458358011yescharacteristic
482C2#1458363811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC2×#120×C43C2
hypercenterC2×#120D43
hypocenterC43#2685
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×#120

Complements

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

NH ≅ G/Ntype
1. C2×#13063318C2semidirect
2. #14582835C2semidirect
3. #14582822C2semidirect
4. #14582813C2semidirect
5. #14582813C2semidirect
6. #14582813C2semidirect
7. #14582813C2semidirect
8. #14582802C2semidirect
9. #14582802C2semidirect
10. #14582793C2semidirect
11. #14582792C2semidirect
12. #14582787C2semidirect
13. #14582755C2semidirect
14. #14582755C2semidirect
17. C2×C4⋊Dic43C22semidirect
18. C2×C4⋊Dic43C22semidirect
19. C2×Dic43⋊C4C22semidirect
20. C2×Dic43⋊C4C22semidirect
21. C2×Dic43⋊C4C22semidirect
22. C2×Dic43⋊C4C22semidirect
35. C2×C22⋊Dic43C22semidirect
36. C2×C22⋊Dic43C22semidirect
37. C2×C22⋊Dic43C22semidirect
38. C2×C22⋊Dic43C22semidirect
39. C2×C4×Dic43C22semidirect
40. C2×C4×Dic43C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
257. C43#2685semidirect