Finite Group Databasebeta

← #34080595

Subgroups — #34080595

Order 19328.

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×#18012767C211yesmaximal, characteristic, complemented
2C22×D1208C211yesmaximal, characteristic, complemented
3#23752858C211yesmaximal, characteristic, complemented
4D4×D604C211yesmaximal, characteristic, complemented
5#23752601C211yesmaximal, characteristic, complemented
6#23752465C211yesmaximal, characteristic, complemented
7#23752441C211yesmaximal, characteristic, complemented
8#23752428C211yesmaximal, characteristic, complemented
9#23752408C211yesmaximal, characteristic, complemented
10#23752365C211yesmaximal, characteristic, complemented
11#23752359C211yesmaximal, characteristic, complemented
12#23752348C211yesmaximal, characteristic, complemented
13#23752348C211yesmaximal, characteristic, complemented
14#23752325C211yesmaximal, characteristic, complemented
15#435×C151C211yesmaximal, characteristic, complemented
16C2×#14559004C2211yescharacteristic, complemented
17C22×D604C2211yescharacteristic
18C22×D604C2211yescharacteristic, complemented
19C22×D604C2211yescharacteristic, complemented
20C2×D4×D151—21no—
21#18012767—24no—
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic, complemented
24C2×#14558993C2211yescharacteristic, complemented
25C2×D1208—24no—
26C2×D1208C2211yescharacteristic
27C2×D1208C2211yescharacteristic
28C2×D1208C2211yescharacteristic, complemented
29C2×D1208C2211yescharacteristic, complemented
30C2×D1208C2211yescharacteristic, complemented
31C2×D1208C2211yescharacteristic, complemented
32#18012736C2211yescharacteristic, complemented
33#18012727C2211yescharacteristic, complemented
34#18012724—21no—
35#18012718C2211yescharacteristic, complemented
36#18012714—21no—
37#18012713C2211yescharacteristic
38#18012713C2211yescharacteristic, complemented
39#18012713C2211yescharacteristic, complemented
40#18012712—21no—
41#18012709—21no—
42#18012709—21no—
43#18012707—21no—
44C4×D604C2211yescharacteristic, complemented
45C4×D604C2211yescharacteristic, complemented
46C22⋊C4×D151—21no—
47#18012671C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic, complemented
52#18012661C2211yescharacteristic, complemented
53#18012661C2211yescharacteristic, complemented
54C2×M16×C151C2211yescharacteristic, complemented
55C22×C8×C151C2211yescharacteristic, complemented
56C4×D4×C151C2211yescharacteristic
57C4⋊C8×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C22⋊C8×C151C2211yescharacteristic, complemented
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63C23×D151—21no—
64#14559004—22no—
65#14559004—41no—
66C2×Dic302C2311yescharacteristic
67C2×D604—22no—
68C2×D604—22no—
69C2×D604—22no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—21no—
74C2×D604—21no—
75C2×D604—41no—
76C2×D604—41no—
77C2×D604—41no—
78C2×D604C2311yescharacteristic
79C2×D604C2311yescharacteristic
80C2×D604C2311yescharacteristic
81C2×D604C2311yescharacteristic
82C2×D604C2311yescharacteristic
83C2×C22⋊D151—21no—
84C2×C22⋊D151—21no—
85C2×C22⋊D151—21no—
86C2×C22⋊D151—21no—
87D4×D151—44no—
88C2×C4×D151—21no—
89C2×C4×D151—21no—
90C2×C4×D151—21no—
91#14558993—22no—
92#14558993—22no—
93#14558993—41no—
94D1208—22no—
95D1208—22no—
96D1208—22no—
97D1208—22no—
98D1208—41no—
99D1208D414yescomplemented
100C4⋊Dic151C2311yescharacteristic
101C4⋊Dic151C2311yescharacteristic
102Dic151⋊C4—21no—
103C22⋊Dic151—21no—
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4—21no—
109(C2×D151)⋊C4—21no—
110(C2×D151)⋊C4—21no—
111C2×D4×C151D411yescharacteristic
112C22×C4×C151C2311yescharacteristic
113C22×C4×C151C2311yescharacteristic
114M16×C151—22no—
115C2×C8×C151—22no—
116C2×C8×C151C2311yescharacteristic
117C2×C8×C151C2311yescharacteristic
118C2×C8×C151C2311yescharacteristic
119C2×C8×C151C2311yescharacteristic
120C4⋊C4×C151D411yescharacteristic
121C22⋊C4×C151D411yescharacteristic
122C22⋊C4×C151D411yescharacteristic
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—21no—
127C22×D151—21no—
128C22×D151—21no—
129C22×D151—42no—
130C22×D151—42no—
131C22×D151—42no—
132C22×D151—42no—
133C22×D151—42no—
134C22×D151—42no—
135C22×D151—81no—
136C22×D151—81no—
137C22×D151—81no—
138Dic302—21no—
139Dic302—21no—
140D604—21no—
141D604—21no—
142D604—21no—
143D604—21no—
144D604—21no—
145D604—21no—
146D604—21no—
147D604—21no—
148D604—42no—
149D604—42no—
150D604—42no—
151D604—42no—
152D604—81no—
153D604C2×D412yes—
154D604C2×D412yescomplemented
155C22⋊D151—42no—
156C22⋊D151—42no—
157C22⋊D151—42no—
158C22⋊D151—81no—
159C2×Dic151—21no—
160C2×Dic151—21no—
161C2×Dic151—21no—
162C4×D151—42no—
163C4×D151—42no—
164C4×D151—81no—
165C23×C151C2×D411yescharacteristic
166C23×C151C2×D411yescharacteristic
167D4×C151—22no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151C2×D411yescharacteristic
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2×D411yescharacteristic
176C2×C4×C151C2411yescharacteristic
177C8×C151—21no—
178C8×C151—21no—
179C8×C151—21no—
180C8×C151C2×D412yescomplemented
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—21no—
184C22×C151—21no—
185C22×C151—21no—
186C22×C151AGL(1,ℤ/8)12yescomplemented
187C22×C151C22×D411yescharacteristic
188C2×D151—22no—
189C2×D151—22no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C2×D151—41no—
197C2×D151—41no—
198C2×D151—41no—
199C2×D151—41no—
200C2×D151—41no—
201C2×D151—41no—
202C2×D151—41no—
203C2×D151—84no—
204C2×D151—84no—
205C2×D151—84no—
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—21no—
209C4×C151—21no—
210C4×C151C22×D411yescharacteristic
211C4×C151H(5,𝔽2)11yescharacteristic
212Dic151—41no—
213Dic151—41no—
214Dic151—41no—
215C2×C151—22no—
216C2×C151—41no—
217C2×C151D4211yescharacteristic
218C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C151#57611yescharacteristic
220D151—42no—
221D151—42no—
222D151—81no—
223D151—81no—
224D151—81no—
225C151#326411yescharacteristic, complemented, Sylow
226#3264—1511nomaximal, Sylow
227C2×AGL(1,ℤ/8)—1511no—
228C22×D8—1511no—
229#546—1511no—
230D42—1511no—
231#496—1511no—
232#469—1511no—
233#465—1511no—
234#463—1511no—
235#459—1511no—
236#450—1511no—
237#449—1511no—
238#447—1511no—
239#447—1511no—
240#442—1511no—
241#435D15111yescharacteristic, complemented
242C2×#41—1511no—
243C22×D4—3021no—
244C22×D4—1511no—
245C22×D4—1511no—
246C22×D4—1511no—
247AGL(1,ℤ/8)—3024no—
248C2×SD16—1511no—
249C2×SD16—1511no—
250C2×SD16—1511no—
251C2×D8—3024no—
252C2×D8—1511no—
253C2×D8—1511no—
254C2×D8—1511no—
255C2×D8—1511no—
256C2×D8—1511no—
257C2×D8—1511no—
258C2×M16C2×D15111yescharacteristic, complemented
259C22×C8C2×D15111yescharacteristic, complemented
260#127—1511no—
261#124—1511no—
262#123—3021no—
263C22⋊Q8—1511no—
264#121—3021no—
265#121—3021no—
266#121—1511no—
267#121—1511no—
268#121—1511no—
269#120—3021no—
270#120—3021no—
271#120—3021no—
272C4×D4—1511no—
273C4×D4—1511no—
274C4×D4C2×D15111yescharacteristic
275C2×C22⋊C4—3021no—
276#106—1511no—
277C4⋊C8C2×D15111yescharacteristic, complemented
278#103—1511no—
279#102—1511no—
280#102—1511no—
281#102—1511no—
282#102—1511no—
283#102—1511no—
284C22⋊C8C2×D15111yescharacteristic, complemented
285C22⋊C8C2×D15111yescharacteristic, complemented
286#97C2×D15111yescharacteristic, complemented
287C24—3021no—
288C24—3021no—
289C24—3021no—
290#41—3022no—
291#41—6041no—
292C2×Q8—1511no—
293C2×D4—3022no—
294C2×D4—3022no—
295C2×D4—3022no—
296C2×D4—3021no—
297C2×D4—3021no—
298C2×D4—3021no—
299C2×D4—3021no—
300C2×D4—3021no—
301C2×D4—3021no—
302C2×D4—3021no—
303C2×D4—3021no—
304C2×D4—3021no—
305C2×D4—6041no—
306C2×D4—6041no—
307C2×D4—6041no—
308C2×D4—6044no—
309C2×D4—1511no—
310C2×D4—1511no—
311C2×D4—1511no—
312C2×D4—1511no—
313C2×D4—1511no—
314C2×D4D60411yescharacteristic
315C22×C4—3021no—
316C22×C4—3021no—
317C22×C4—3021no—
318C22×C4C22×D15111yescharacteristic
319C22×C4C22×D15111yescharacteristic
320SD16—3022no—
321SD16—3022no—
322SD16—6041no—
323D8—3022no—
324D8—3022no—
325D8—3022no—
326D8—3022no—
327D8—6041no—
328D8—1514no—
329M16—22no—
330C2×C8—22no—
331C2×C8C22×D15111yescharacteristic
332C2×C8C22×D15111yescharacteristic
333C2×C8C22×D15111yescharacteristic
334C2×C8C22×D15111yescharacteristic
335C4⋊C4—3021no—
336C4⋊C4—1511no—
337C4⋊C4—1511no—
338C4⋊C4D60411yescharacteristic
339C22⋊C4—3021no—
340C22⋊C4—3021no—
341C22⋊C4—3021no—
342C22⋊C4—3021no—
343C22⋊C4—3021no—
344C22⋊C4—3021no—
345C22⋊C4—3021no—
346C22⋊C4—3021no—
347C22⋊C4D60411yescharacteristic
348C22⋊C4D60411yescharacteristic
349C42C22×D15111yescharacteristic
350C23—3021no—
351C23—3021no—
352C23—3021no—
353C23—3021no—
354C23—3021no—
355C23—6042no—
356C23—6042no—
357C23—6042no—
358C23—6042no—
359C23—6042no—
360C23—6042no—
361C23—12081no—
362C23—12081no—
363C23—12081no—
364C23C2×D60411yescharacteristic
365C23C2×D60411yescharacteristic
366Q8—3021no—
367Q8—3021no—
368D4—22no—
369D4—3021no—
370D4—3021no—
371D4—3021no—
372D4—3021no—
373D4—3021no—
374D4—3021no—
375D4—3021no—
376D4—3021no—
377D4—6042no—
378D4—6042no—
379D4—6042no—
380D4—6042no—
381D4—6042no—
382D4—6042no—
383D4—6042no—
384D4—1512no—
385D4—1512no—
386D4—12081no—
387D4—12081no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—3021no—
395C2×C4—6042no—
396C2×C4—6042no—
397C2×C4—12081no—
398C2×C4C2×D60411yescharacteristic
399C2×C4C2×D60411yescharacteristic
400C2×C4C2×D60411yescharacteristic
401C2×C4C2×D60411yescharacteristic
402C2×C4C23×D15111yescharacteristic
403C8—21no—
404C8—21no—
405C8—21no—
406C8D4×D15112yescomplemented
407C22—21no—
408C22—21no—
409C22—21no—
410C22—21no—
411C22—21no—
412C22—3022no—
413C22—3022no—
414C22—6041no—
415C22—6041no—
416C22—6041no—
417C22—6041no—
418C22—6041no—
419C22—6041no—
420C22—6041no—
421C22—6041no—
422C22—6041no—
423C22—6041no—
424C22—6041no—
425C22—6041no—
426C22—6041no—
427C22—12084no—
428C22—12084no—
429C22—12084no—
430C22#1801276712yescomplemented
431C22C22×D60411yescharacteristic
432C4—21no—
433C4—21no—
434C4—21no—
435C4—21no—
436C4—6041no—
437C4—6041no—
438C4—6041no—
439C4C2×D4×D15111yescharacteristic
440C4#1801278511yescharacteristic
441C2—22no—
442C2—41no—
443C2—6042no—
444C2—6042no—
445C2—12081no—
446C2—12081no—
447C2—12081no—
448C2D4×D60411yescharacteristic
449C2C2×#1801276711yescharacteristic
450C2#2375301711yescharacteristic
subgroupG/H
centerC22C22×D604
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#435×C151C2
socleC22×C151C22×D4
hypercenter#435D151
hypocenterC151#3264
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #435

Complements

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

NH ≅ G/Ntype
1. C2×#18012767C2semidirect
2. C22×D1208C2semidirect
3. #23752858C2semidirect
4. D4×D604C2semidirect
5. #23752601C2semidirect
6. #23752465C2semidirect
7. #23752441C2semidirect
8. #23752428C2semidirect
9. #23752408C2semidirect
10. #23752365C2semidirect
11. #23752359C2semidirect
12. #23752348C2semidirect
13. #23752348C2semidirect
14. #23752325C2semidirect
15. #435×C151C2semidirect
16. C2×#14559004C22semidirect
18. C22×D604C22semidirect
19. C22×D604C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558993C22semidirect
24. C2×#14558993C22semidirect
28. C2×D1208C22semidirect
29. C2×D1208C22semidirect
30. C2×D1208C22semidirect
31. C2×D1208C22semidirect
32. #18012736C22semidirect
33. #18012727C22semidirect
35. #18012718C22semidirect
38. #18012713C22semidirect
39. #18012713C22semidirect
44. C4×D604C22semidirect
45. C4×D604C22semidirect
47. #18012671C22semidirect
48. #18012664C22semidirect
49. #18012661C22semidirect
50. #18012661C22semidirect
51. #18012661C22semidirect
52. #18012661C22semidirect
53. #18012661C22semidirect
54. C2×M16×C151C22semidirect
55. C22×C8×C151C22semidirect
57. C4⋊C8×C151C22semidirect
58. C22⋊C8×C151C22semidirect
59. C22⋊C8×C151C22semidirect
60. #97×C151C22semidirect
99. D1208D4semidirect
154. D604C2×D4semidirect
180. C8×C151C2×D4semidirect
186. C22×C151AGL(1,ℤ/8)semidirect
225. C151#3264semidirect
241. #435D151semidirect
258. C2×M16C2×D151semidirect
259. C22×C8C2×D151semidirect
277. C4⋊C8C2×D151semidirect
284. C22⋊C8C2×D151semidirect
285. C22⋊C8C2×D151semidirect
286. #97C2×D151semidirect
406. C8D4×D151semidirect
430. C22#18012767semidirect

Maximal subgroups

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

subgroupindex
C2×#180127672
C22×D12082
#237528582
D4×D6042
#237526012
#237524652
#237524412
#237524282
#237524082
#237523652
#237523592
#237523482
#237523252
#435×C1512
#3264151