Finite Group Databasebeta

← #19138841

Subgroups — #19138841

Order 5504.

664 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#13063319C211yesmaximal, characteristic, complemented
2C22×(C2×D43)⋊C4C211yesmaximal, characteristic
3#14582828C211yesmaximal, characteristic, complemented
4#14582828C211yesmaximal, characteristic, complemented
5#14582828C211yesmaximal, characteristic, complemented
6#14582823C211yesmaximal, characteristic, complemented
7#14582790C211yesmaximal, characteristic, complemented
8#14582790C211yesmaximal, characteristic, complemented
9#14582790C211yesmaximal, characteristic, complemented
10#14582772C211yesmaximal, characteristic, complemented
11#14582771C211yesmaximal, characteristic, complemented
12#14582757C211yesmaximal, characteristic, complemented
13#14582754C211yesmaximal, characteristic
14#14582754C211yesmaximal, characteristic
15C4×C22⋊C4×C43C211yesmaximal, characteristic, complemented
16C24×D43C2211yescharacteristic
17C23×Dic43C2211yescharacteristic
18#13063319—24no—
19C2×Dic43⋊C4C2211yescharacteristic, complemented
20C2×Dic43⋊C4C2211yescharacteristic, complemented
21C2×Dic43⋊C4C2211yescharacteristic, complemented
22C2×Dic43⋊C4C2211yescharacteristic, complemented
23C2×Dic43⋊C4C2211yescharacteristic, complemented
24C2×Dic43⋊C4C2211yescharacteristic, complemented
25C2×C22⋊Dic43C2211yescharacteristic
26C2×C22⋊Dic43C2211yescharacteristic
27C2×(C2×D43)⋊C4—24no—
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
38C2×(C2×D43)⋊C4C2211yescharacteristic
39C2×(C2×D43)⋊C4C2211yescharacteristic
40C43⋊#95C2211yescharacteristic, complemented
41C43⋊#95C2211yescharacteristic, complemented
42C43⋊#95C2211yescharacteristic, complemented
43C43⋊#95C2211yescharacteristic, complemented
44C43⋊#95C2211yescharacteristic, complemented
45C43⋊#95C2211yescharacteristic, complemented
46C23×C4×C43C2211yescharacteristic
47C2×C22⋊C4×C43C2211yescharacteristic
48C2×C22⋊C4×C43C2211yescharacteristic
49C2×C42×C43C2211yescharacteristic, complemented
50C2×C42×C43C2211yescharacteristic, complemented
51#95×C43C2211yescharacteristic, complemented
52#95×C43C2211yescharacteristic, complemented
53C24×C43C2311yescharacteristic
54C23×D43—22no—
55C23×D43—22no—
56C23×D43—22no—
57C23×D43—22no—
58C23×D43—22no—
59C23×D43—41no—
60C23×D43—41no—
61C23×D43C2311yescharacteristic
62C23×D43C2311yescharacteristic
63C22×C4×C43—22no—
64C22×C4×C43—22no—
65C22×C4×C43—41no—
66C22×C4×C43C2311yescharacteristic
67C22×C4×C43C2311yescharacteristic
68C22×C4×C43C2311yescharacteristic
69C22×C4×C43C2311yescharacteristic
70C22×C4×C43C2311yescharacteristic
71C22×C4×C43C2311yescharacteristic
72C22×Dic43—22no—
73C22×Dic43—22no—
74C22×Dic43—41no—
75C22×Dic43C2311yescharacteristic
76C22×Dic43C2311yescharacteristic
77C22×Dic43C2311yescharacteristic
78C22×Dic43C2311yescharacteristic
79C22×Dic43C2311yescharacteristic
80C22×Dic43C2311yescharacteristic
81C22⋊C4×C43—22no—
82C22⋊C4×C43—22no—
83C42×C43—22no—
84C42×C43—41no—
85C22⋊Dic43—22no—
86C22⋊Dic43—22no—
87(C2×D43)⋊C4—22no—
88(C2×D43)⋊C4—22no—
89(C2×D43)⋊C4—22no—
90(C2×D43)⋊C4—22no—
91(C2×D43)⋊C4—22no—
92(C2×D43)⋊C4—22no—
93(C2×D43)⋊C4—22no—
94(C2×D43)⋊C4—41no—
95(C2×D43)⋊C4—41no—
96(C2×D43)⋊C4—41no—
97(C2×D43)⋊C4—41no—
98(C2×D43)⋊C4D414yes—
99Dic43⋊C4—22no—
100Dic43⋊C4—22no—
101Dic43⋊C4—22no—
102Dic43⋊C4—41no—
103Dic43⋊C4—41no—
104Dic43⋊C4—41no—
105C23×C43—21no—
106C23×C43—21no—
107C23×C43—21no—
108C23×C43—21no—
109C23×C43#4112yes—
110C23×C43#4112yes—
111C23×C43#4112yes—
112C23×C43C2411yescharacteristic
113C22×D43—28no—
114C22×D43—21no—
115C22×D43—21no—
116C22×D43—21no—
117C22×D43—21no—
118C22×D43—21no—
119C22×D43—21no—
120C22×D43—21no—
121C22×D43—21no—
122C22×D43—21no—
123C22×D43—21no—
124C22×D43—21no—
125C22×D43—21no—
126C22×D43—44no—
127C22×D43—44no—
128C22×D43—44no—
129C22×D43—44no—
130C22×D43—44no—
131C22×D43—44no—
132C22×D43C2×D412yes—
133C22×D43#4112yes—
134C2×C4×C43—21no—
135C2×C4×C43—21no—
136C2×C4×C43—21no—
137C2×C4×C43—21no—
138C2×C4×C43—21no—
139C2×C4×C43—21no—
140C2×C4×C43—21no—
141C2×C4×C43—21no—
142C2×C4×C43—21no—
143C2×C4×C43—21no—
144C2×C4×C43—21no—
145C2×C4×C43—21no—
146C2×C4×C43—21no—
147C2×C4×C43—21no—
148C2×C4×C43—21no—
149C2×C4×C43—21no—
150C2×C4×C43—21no—
151C2×C4×C43—44no—
152C2×C4×C43C2×D412yes—
153C2×Dic43—21no—
154C2×Dic43—21no—
155C2×Dic43—21no—
156C2×Dic43—21no—
157C2×Dic43—21no—
158C2×Dic43—21no—
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—44no—
171C2×Dic43C2×D412yes—
172C22×C43—22no—
173C22×C43—22no—
174C22×C43—22no—
175C22×C43—22no—
176C22×C43—22no—
177C22×C43—22no—
178C22×C43#12614yescomplemented
179C22×C43C22×D411yescharacteristic
180C22×C43C2×#4111yescharacteristic
181C22×C43C2×#4111yescharacteristic
182C22×C43C2×#4111yescharacteristic
183C22×C43C2×#4111yescharacteristic
184C22×C43H(5,𝔽2)11yescharacteristic
185C22×C43H(5,𝔽2)11yescharacteristic
186C2×D43—22no—
187C2×D43—22no—
188C2×D43—22no—
189C2×D43—22no—
190C2×D43—22no—
191C2×D43—22no—
192C2×D43—416no—
193C2×D43—41no—
194C2×D43—41no—
195C2×D43—41no—
196C2×D43—41no—
197C2×D43—41no—
198C2×D43—41no—
199C2×D43—41no—
200C2×D43—41no—
201C4×C43—22no—
202C4×C43—41no—
203C4×C43—41no—
204C4×C43—41no—
205C4×C43—41no—
206C4×C43—41no—
207Dic43—22no—
208Dic43—41no—
209Dic43—41no—
210Dic43—41no—
211Dic43—41no—
212Dic43—41no—
213#2480—431nomaximal, Sylow
214C2×C43—24no—
215C2×C43#52511yescharacteristic
216C2×C43C2×#12611yescharacteristic
217C2×C43#53811yescharacteristic
218C2×C43#54611yescharacteristic
219C2×C43#54611yescharacteristic
220C2×C43#55111yescharacteristic
221C2×C43#55111yescharacteristic
222D43—42no—
223D43—42no—
224C2×#126—431no—
225C22×C22⋊C4—431no—
226#397—431no—
227#397—431no—
228#397—431no—
229#396—431no—
230#388—431no—
231#388—431no—
232#388—431no—
233#385—431no—
234#385—431no—
235#380—431no—
236#379—431no—
237#379—431no—
238C4×C22⋊C4D4311yescharacteristic, complemented
239C43#248011yescharacteristic, complemented, Sylow
240C25—431no—
241C23×C4—431no—
242C23×C4C2×D4311yescharacteristic
243#126—864no—
244C2×C4⋊C4—431no—
245C2×C4⋊C4—431no—
246C2×C4⋊C4—431no—
247C2×C4⋊C4—431no—
248C2×C4⋊C4—431no—
249C2×C4⋊C4—431no—
250C2×C22⋊C4—431no—
251C2×C22⋊C4—431no—
252C2×C22⋊C4—431no—
253C2×C22⋊C4—431no—
254C2×C22⋊C4—431no—
255C2×C22⋊C4—431no—
256C2×C22⋊C4—431no—
257C2×C22⋊C4—431no—
258C2×C22⋊C4—431no—
259C2×C22⋊C4—431no—
260C2×C22⋊C4—431no—
261C2×C22⋊C4—431no—
262C2×C22⋊C4—431no—
263C2×C22⋊C4—431no—
264C2×C22⋊C4—864no—
265C2×C22⋊C4C2×D4311yescharacteristic
266C2×C22⋊C4C2×D4311yescharacteristic
267C2×C42C2×D4311yescharacteristic, complemented
268C2×C42C2×D4311yescharacteristic, complemented
269#95—431no—
270#95—431no—
271#95—431no—
272#95—431no—
273#95—431no—
274#95—431no—
275#95C2×D4311yescharacteristic, complemented
276#95C2×D4311yescharacteristic, complemented
277C24—431no—
278C24—431no—
279C24—862no—
280C24—862no—
281C24—862no—
282C24—862no—
283C24—862no—
284C24—1721no—
285C24—1721no—
286C24C22×D4311yescharacteristic
287C22×C4—22no—
288C22×C4—22no—
289C22×C4—41no—
290C22×C4—431no—
291C22×C4—431no—
292C22×C4—431no—
293C22×C4—431no—
294C22×C4—431no—
295C22×C4—431no—
296C22×C4—862no—
297C22×C4—862no—
298C22×C4—1721no—
299C22×C4C22×D4311yescharacteristic
300C22×C4C22×D4311yescharacteristic
301C22×C4C22×D4311yescharacteristic
302C22×C4C22×D4311yescharacteristic
303C22×C4C22×D4311yescharacteristic
304C22×C4C22×D4311yescharacteristic
305C4⋊C4—862no—
306C4⋊C4—862no—
307C4⋊C4—862no—
308C4⋊C4—1721no—
309C4⋊C4—1721no—
310C4⋊C4—1721no—
311C22⋊C4—22no—
312C22⋊C4—22no—
313C22⋊C4—434no—
314C22⋊C4—862no—
315C22⋊C4—862no—
316C22⋊C4—862no—
317C22⋊C4—862no—
318C22⋊C4—862no—
319C22⋊C4—862no—
320C22⋊C4—862no—
321C22⋊C4—862no—
322C22⋊C4—862no—
323C22⋊C4—1721no—
324C22⋊C4—1721no—
325C22⋊C4—1721no—
326C22⋊C4—1721no—
327C42—22no—
328C42—41no—
329C23—21no—
330C23—21no—
331C23—21no—
332C23—21no—
333C23—432no—
334C23—432no—
335C23—868no—
336C23—861no—
337C23—861no—
338C23—861no—
339C23—861no—
340C23—861no—
341C23—861no—
342C23—861no—
343C23—861no—
344C23—861no—
345C23—861no—
346C23—861no—
347C23—861no—
348C23—1724no—
349C23—1724no—
350C23—1724no—
351C23—1724no—
352C23—1724no—
353C23—1724no—
354C23#1062189812yes—
355C23#1062189812yes—
356C23#1062189812yes—
357C23C23×D4311yescharacteristic
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—44no—
376C2×C4—432no—
377C2×C4—861no—
378C2×C4—861no—
379C2×C4—861no—
380C2×C4—861no—
381C2×C4—861no—
382C2×C4—861no—
383C2×C4—861no—
384C2×C4—861no—
385C2×C4—861no—
386C2×C4—861no—
387C2×C4—861no—
388C2×C4—861no—
389C2×C4—861no—
390C2×C4—861no—
391C2×C4—861no—
392C2×C4—861no—
393C2×C4—861no—
394C2×C4—1724no—
395C2×C4D4×D4312yes—
396C22—22no—
397C22—22no—
398C22—22no—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—862no—
403C22—862no—
404C22—862no—
405C22—862no—
406C22—862no—
407C22—862no—
408C22—17216no—
409C22—1721no—
410C22—1721no—
411C22—1721no—
412C22—1721no—
413C22—1721no—
414C22—1721no—
415C22—1721no—
416C22—1721no—
417C22#1306331914yescomplemented
418C22C2×D4×D4311yescharacteristic
419C22#41×D4311yescharacteristic
420C22C2×#1062189811yescharacteristic
421C22C2×#1062189811yescharacteristic
422C22C2×#1062189811yescharacteristic
423C22#1306337011yescharacteristic
424C22#1306337111yescharacteristic
425C4—22no—
426C4—41no—
427C4—41no—
428C4—41no—
429C4—41no—
430C4—41no—
431C4—862no—
432C4—1721no—
433C4—1721no—
434C4—1721no—
435C4—1721no—
436C4—1721no—
437C2—24no—
438C2—1722no—
439C2—1722no—
440C2#1458340811yescharacteristic
441C2C2×#1306331911yescharacteristic
442C2#1458348211yescharacteristic
443C2#1458353911yescharacteristic
444C2#1458354511yescharacteristic
445C2#1458357311yescharacteristic
446C2#1458357811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D43
commutator, socleC23×C43C24
FittingC4×C22⋊C4×C43C2
hypercenterC4×C22⋊C4D43
hypocenterC43#2480
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C23 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#13063319C2semidirect
3. #14582828C2semidirect
4. #14582828C2semidirect
5. #14582828C2semidirect
6. #14582823C2semidirect
7. #14582790C2semidirect
8. #14582790C2semidirect
9. #14582790C2semidirect
10. #14582772C2semidirect
11. #14582771C2semidirect
12. #14582757C2semidirect
15. C4×C22⋊C4×C43C2semidirect
19. C2×Dic43⋊C4C22semidirect
20. C2×Dic43⋊C4C22semidirect
21. C2×Dic43⋊C4C22semidirect
22. C2×Dic43⋊C4C22semidirect
23. C2×Dic43⋊C4C22semidirect
24. C2×Dic43⋊C4C22semidirect
40. C43⋊#95C22semidirect
41. C43⋊#95C22semidirect
42. C43⋊#95C22semidirect
43. C43⋊#95C22semidirect
44. C43⋊#95C22semidirect
45. C43⋊#95C22semidirect
49. C2×C42×C43C22semidirect
50. C2×C42×C43C22semidirect
51. #95×C43C22semidirect
52. #95×C43C22semidirect
178. C22×C43#126semidirect
238. C4×C22⋊C4D43semidirect
239. C43#2480semidirect
267. C2×C42C2×D43semidirect
268. C2×C42C2×D43semidirect
275. #95C2×D43semidirect
276. #95C2×D43semidirect
417. C22#13063319semidirect