Finite Group Databasebeta

← #37584005

Subgroups — #37584005

Order 24448.

568 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#20259350C211yesmaximal, characteristic, complemented
2C22×D1528C211yesmaximal, characteristic, complemented
3#27133309C211yesmaximal, characteristic, complemented
4D4×D764C211yesmaximal, characteristic, complemented
5#27133052C211yesmaximal, characteristic, complemented
6#27132916C211yesmaximal, characteristic, complemented
7#27132892C211yesmaximal, characteristic, complemented
8#27132879C211yesmaximal, characteristic, complemented
9#27132859C211yesmaximal, characteristic, complemented
10#27132816C211yesmaximal, characteristic, complemented
11#27132810C211yesmaximal, characteristic, complemented
12#27132799C211yesmaximal, characteristic, complemented
13#27132799C211yesmaximal, characteristic, complemented
14#27132776C211yesmaximal, characteristic, complemented
15#435×C191C211yesmaximal, characteristic, complemented
16C2×#15690287C2211yescharacteristic, complemented
17C22×D764C2211yescharacteristic
18C22×D764C2211yescharacteristic, complemented
19C22×D764C2211yescharacteristic, complemented
20C2×D4×D191—21no—
21#20259350—24no—
22C2×#15690276C2211yescharacteristic, complemented
23C2×#15690276C2211yescharacteristic, complemented
24C2×#15690276C2211yescharacteristic, complemented
25C2×D1528—24no—
26C2×D1528C2211yescharacteristic
27C2×D1528C2211yescharacteristic
28C2×D1528C2211yescharacteristic, complemented
29C2×D1528C2211yescharacteristic, complemented
30C2×D1528C2211yescharacteristic, complemented
31C2×D1528C2211yescharacteristic, complemented
32#20259319C2211yescharacteristic, complemented
33#20259310C2211yescharacteristic, complemented
34#20259307—21no—
35#20259301C2211yescharacteristic, complemented
36#20259297—21no—
37#20259296C2211yescharacteristic
38#20259296C2211yescharacteristic, complemented
39#20259296C2211yescharacteristic, complemented
40#20259295—21no—
41#20259292—21no—
42#20259292—21no—
43#20259290—21no—
44C4×D764C2211yescharacteristic, complemented
45C4×D764C2211yescharacteristic, complemented
46C22⋊C4×D191—21no—
47#20259254C2211yescharacteristic, complemented
48#20259247C2211yescharacteristic, complemented
49#20259244C2211yescharacteristic, complemented
50#20259244C2211yescharacteristic, complemented
51#20259244C2211yescharacteristic, complemented
52#20259244C2211yescharacteristic, complemented
53#20259244C2211yescharacteristic, complemented
54C2×M16×C191C2211yescharacteristic, complemented
55C22×C8×C191C2211yescharacteristic, complemented
56C4×D4×C191C2211yescharacteristic
57C4⋊C8×C191C2211yescharacteristic, complemented
58C22⋊C8×C191C2211yescharacteristic, complemented
59C22⋊C8×C191C2211yescharacteristic, complemented
60#97×C191C2211yescharacteristic, complemented
61C23×D191—21no—
62C23×D191—21no—
63C23×D191—21no—
64#15690287—22no—
65#15690287—41no—
66C2×Dic382C2311yescharacteristic
67C2×D764—22no—
68C2×D764—22no—
69C2×D764—22no—
70C2×D764—21no—
71C2×D764—21no—
72C2×D764—21no—
73C2×D764—21no—
74C2×D764—21no—
75C2×D764—41no—
76C2×D764—41no—
77C2×D764—41no—
78C2×D764C2311yescharacteristic
79C2×D764C2311yescharacteristic
80C2×D764C2311yescharacteristic
81C2×D764C2311yescharacteristic
82C2×D764C2311yescharacteristic
83C2×C22⋊D191—21no—
84C2×C22⋊D191—21no—
85C2×C22⋊D191—21no—
86C2×C22⋊D191—21no—
87D4×D191—44no—
88C2×C4×D191—21no—
89C2×C4×D191—21no—
90C2×C4×D191—21no—
91#15690276—22no—
92#15690276—22no—
93#15690276—41no—
94D1528—22no—
95D1528—22no—
96D1528—22no—
97D1528—22no—
98D1528—41no—
99D1528D414yescomplemented
100C4⋊Dic191C2311yescharacteristic
101C4⋊Dic191C2311yescharacteristic
102Dic191⋊C4—21no—
103C22⋊Dic191—21no—
104(C2×D191)⋊C4—21no—
105(C2×D191)⋊C4—21no—
106(C2×D191)⋊C4—21no—
107(C2×D191)⋊C4—21no—
108(C2×D191)⋊C4—21no—
109(C2×D191)⋊C4—21no—
110(C2×D191)⋊C4—21no—
111C2×D4×C191D411yescharacteristic
112C22×C4×C191C2311yescharacteristic
113C22×C4×C191C2311yescharacteristic
114M16×C191—22no—
115C2×C8×C191—22no—
116C2×C8×C191C2311yescharacteristic
117C2×C8×C191C2311yescharacteristic
118C2×C8×C191C2311yescharacteristic
119C2×C8×C191C2311yescharacteristic
120C4⋊C4×C191D411yescharacteristic
121C22⋊C4×C191D411yescharacteristic
122C22⋊C4×C191D411yescharacteristic
123C42×C191C2311yescharacteristic
124C22×D191—21no—
125C22×D191—21no—
126C22×D191—21no—
127C22×D191—21no—
128C22×D191—21no—
129C22×D191—42no—
130C22×D191—42no—
131C22×D191—42no—
132C22×D191—42no—
133C22×D191—42no—
134C22×D191—42no—
135C22×D191—81no—
136C22×D191—81no—
137C22×D191—81no—
138Dic382—21no—
139Dic382—21no—
140D764—21no—
141D764—21no—
142D764—21no—
143D764—21no—
144D764—21no—
145D764—21no—
146D764—21no—
147D764—21no—
148D764—42no—
149D764—42no—
150D764—42no—
151D764—42no—
152D764—81no—
153D764C2×D412yes—
154D764C2×D412yescomplemented
155C22⋊D191—42no—
156C22⋊D191—42no—
157C22⋊D191—42no—
158C22⋊D191—81no—
159C2×Dic191—21no—
160C2×Dic191—21no—
161C2×Dic191—21no—
162C4×D191—42no—
163C4×D191—42no—
164C4×D191—81no—
165C23×C191C2×D411yescharacteristic
166C23×C191C2×D411yescharacteristic
167D4×C191—22no—
168C2×C4×C191—21no—
169C2×C4×C191—21no—
170C2×C4×C191—21no—
171C2×C4×C191—21no—
172C2×C4×C191C2×D411yescharacteristic
173C2×C4×C191C2×D411yescharacteristic
174C2×C4×C191C2×D411yescharacteristic
175C2×C4×C191C2×D411yescharacteristic
176C2×C4×C191C2411yescharacteristic
177C8×C191—21no—
178C8×C191—21no—
179C8×C191—21no—
180C8×C191C2×D412yescomplemented
181C22×C191—21no—
182C22×C191—21no—
183C22×C191—21no—
184C22×C191—21no—
185C22×C191—21no—
186C22×C191AGL(1,ℤ/8)12yescomplemented
187C22×C191C22×D411yescharacteristic
188C2×D191—22no—
189C2×D191—22no—
190C2×D191—41no—
191C2×D191—41no—
192C2×D191—41no—
193C2×D191—41no—
194C2×D191—41no—
195C2×D191—41no—
196C2×D191—41no—
197C2×D191—41no—
198C2×D191—41no—
199C2×D191—41no—
200C2×D191—41no—
201C2×D191—41no—
202C2×D191—41no—
203C2×D191—84no—
204C2×D191—84no—
205C2×D191—84no—
206C4×C191—21no—
207C4×C191—21no—
208C4×C191—21no—
209C4×C191—21no—
210C4×C191C22×D411yescharacteristic
211C4×C191H(5,𝔽2)11yescharacteristic
212Dic191—41no—
213Dic191—41no—
214Dic191—41no—
215C2×C191—22no—
216C2×C191—41no—
217C2×C191D4211yescharacteristic
218C2×C191C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C191#57611yescharacteristic
220D191—42no—
221D191—42no—
222D191—81no—
223D191—81no—
224D191—81no—
225C191#326411yescharacteristic, complemented, Sylow
226#3264—1911nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1911no—
228C22×D8—1911no—
229#546—1911no—
230D42—1911no—
231#496—1911no—
232#469—1911no—
233#465—1911no—
234#463—1911no—
235#459—1911no—
236#450—1911no—
237#449—1911no—
238#447—1911no—
239#447—1911no—
240#442—1911no—
241#435D19111yescharacteristic, complemented
242C2×#41—1911no—
243C22×D4—3821no—
244C22×D4—1911no—
245C22×D4—1911no—
246C22×D4—1911no—
247AGL(1,ℤ/8)—3824no—
248C2×SD16—1911no—
249C2×SD16—1911no—
250C2×SD16—1911no—
251C2×D8—3824no—
252C2×D8—1911no—
253C2×D8—1911no—
254C2×D8—1911no—
255C2×D8—1911no—
256C2×D8—1911no—
257C2×D8—1911no—
258C2×M16C2×D19111yescharacteristic, complemented
259C22×C8C2×D19111yescharacteristic, complemented
260#127—1911no—
261#124—1911no—
262#123—3821no—
263C22⋊Q8—1911no—
264#121—3821no—
265#121—3821no—
266#121—1911no—
267#121—1911no—
268#121—1911no—
269#120—3821no—
270#120—3821no—
271#120—3821no—
272C4×D4—1911no—
273C4×D4—1911no—
274C4×D4C2×D19111yescharacteristic
275C2×C22⋊C4—3821no—
276#106—1911no—
277C4⋊C8C2×D19111yescharacteristic, complemented
278#103—1911no—
279#102—1911no—
280#102—1911no—
281#102—1911no—
282#102—1911no—
283#102—1911no—
284C22⋊C8C2×D19111yescharacteristic, complemented
285C22⋊C8C2×D19111yescharacteristic, complemented
286#97C2×D19111yescharacteristic, complemented
287C24—3821no—
288C24—3821no—
289C24—3821no—
290#41—3822no—
291#41—7641no—
292C2×Q8—1911no—
293C2×D4—3822no—
294C2×D4—3822no—
295C2×D4—3822no—
296C2×D4—3821no—
297C2×D4—3821no—
298C2×D4—3821no—
299C2×D4—3821no—
300C2×D4—3821no—
301C2×D4—3821no—
302C2×D4—3821no—
303C2×D4—3821no—
304C2×D4—3821no—
305C2×D4—1911no—
306C2×D4—1911no—
307C2×D4—1911no—
308C2×D4—1911no—
309C2×D4—1911no—
310C2×D4—7641no—
311C2×D4—7641no—
312C2×D4—7641no—
313C2×D4—7644no—
314C2×D4D76411yescharacteristic
315C22×C4—3821no—
316C22×C4—3821no—
317C22×C4—3821no—
318C22×C4C22×D19111yescharacteristic
319C22×C4C22×D19111yescharacteristic
320SD16—3822no—
321SD16—3822no—
322SD16—7641no—
323D8—3822no—
324D8—3822no—
325D8—3822no—
326D8—3822no—
327D8—1914no—
328D8—7641no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D19111yescharacteristic
332C2×C8C22×D19111yescharacteristic
333C2×C8C22×D19111yescharacteristic
334C2×C8C22×D19111yescharacteristic
335C4⋊C4—3821no—
336C4⋊C4—1911no—
337C4⋊C4—1911no—
338C4⋊C4D76411yescharacteristic
339C22⋊C4—3821no—
340C22⋊C4—3821no—
341C22⋊C4—3821no—
342C22⋊C4—3821no—
343C22⋊C4—3821no—
344C22⋊C4—3821no—
345C22⋊C4—3821no—
346C22⋊C4—3821no—
347C22⋊C4D76411yescharacteristic
348C22⋊C4D76411yescharacteristic
349C42C22×D19111yescharacteristic
350C23—3821no—
351C23—3821no—
352C23—3821no—
353C23—3821no—
354C23—3821no—
355C23—15281no—
356C23—15281no—
357C23—15281no—
358C23—7642no—
359C23—7642no—
360C23—7642no—
361C23—7642no—
362C23—7642no—
363C23—7642no—
364C23C2×D76411yescharacteristic
365C23C2×D76411yescharacteristic
366Q8—3821no—
367Q8—3821no—
368D4—22no—
369D4—3821no—
370D4—3821no—
371D4—3821no—
372D4—3821no—
373D4—3821no—
374D4—3821no—
375D4—3821no—
376D4—3821no—
377D4—1912no—
378D4—1912no—
379D4—15281no—
380D4—15281no—
381D4—7642no—
382D4—7642no—
383D4—7642no—
384D4—7642no—
385D4—7642no—
386D4—7642no—
387D4—7642no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—3821no—
393C2×C4—3821no—
394C2×C4—3821no—
395C2×C4—15281no—
396C2×C4—7642no—
397C2×C4—7642no—
398C2×C4C2×D76411yescharacteristic
399C2×C4C2×D76411yescharacteristic
400C2×C4C2×D76411yescharacteristic
401C2×C4C2×D76411yescharacteristic
402C2×C4C23×D19111yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D19112yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—3822no—
413C22—3822no—
414C22—15284no—
415C22—15284no—
416C22—15284no—
417C22—7641no—
418C22—7641no—
419C22—7641no—
420C22—7641no—
421C22—7641no—
422C22—7641no—
423C22—7641no—
424C22—7641no—
425C22—7641no—
426C22—7641no—
427C22—7641no—
428C22—7641no—
429C22—7641no—
430C22#2025935012yescomplemented
431C22C22×D76411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—7641no—
437C4—7641no—
438C4—7641no—
439C4C2×D4×D19111yescharacteristic
440C4#2025936811yescharacteristic
441C2—22no—
442C2—41no—
443C2—15281no—
444C2—15281no—
445C2—15281no—
446C2—7642no—
447C2—7642no—
448C2D4×D76411yescharacteristic
449C2C2×#2025935011yescharacteristic
450C2#2713346811yescharacteristic
subgroupG/H
centerC22C22×D764
commutator, cosocleC2×C4×C191C24
FrattiniC2×C4C23×D191
Fitting#435×C191C2
socleC22×C191C22×D4
hypercenter#435D191
hypocenterC191#3264
LCSG ▷ C2×C4×C191 ▷ C2×C191 ▷ C191
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#20259350C2semidirect
2. C22×D1528C2semidirect
3. #27133309C2semidirect
4. D4×D764C2semidirect
5. #27133052C2semidirect
6. #27132916C2semidirect
7. #27132892C2semidirect
8. #27132879C2semidirect
9. #27132859C2semidirect
10. #27132816C2semidirect
11. #27132810C2semidirect
12. #27132799C2semidirect
13. #27132799C2semidirect
14. #27132776C2semidirect
15. #435×C191C2semidirect
16. C2×#15690287C22semidirect
18. C22×D764C22semidirect
19. C22×D764C22semidirect
22. C2×#15690276C22semidirect
23. C2×#15690276C22semidirect
24. C2×#15690276C22semidirect
28. C2×D1528C22semidirect
29. C2×D1528C22semidirect
30. C2×D1528C22semidirect
31. C2×D1528C22semidirect
32. #20259319C22semidirect
33. #20259310C22semidirect
35. #20259301C22semidirect
38. #20259296C22semidirect
39. #20259296C22semidirect
44. C4×D764C22semidirect
45. C4×D764C22semidirect
47. #20259254C22semidirect
48. #20259247C22semidirect
49. #20259244C22semidirect
50. #20259244C22semidirect
51. #20259244C22semidirect
52. #20259244C22semidirect
53. #20259244C22semidirect
54. C2×M16×C191C22semidirect
55. C22×C8×C191C22semidirect
57. C4⋊C8×C191C22semidirect
58. C22⋊C8×C191C22semidirect
59. C22⋊C8×C191C22semidirect
60. #97×C191C22semidirect
99. D1528D4semidirect
154. D764C2×D4semidirect
180. C8×C191C2×D4semidirect
186. C22×C191AGL(1,ℤ/8)semidirect
225. C191#3264semidirect
241. #435D191semidirect
258. C2×M16C2×D191semidirect
259. C22×C8C2×D191semidirect
277. C4⋊C8C2×D191semidirect
284. C22⋊C8C2×D191semidirect
285. C22⋊C8C2×D191semidirect
286. #97C2×D191semidirect
406. C8D4×D191semidirect
430. C22#20259350semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#202593502
C22×D15282
#271333092
D4×D7642
#271330522
#271329162
#271328922
#271328792
#271328592
#271328162
#271328102
#271327992
#271327762
#435×C1912
#3264191