Finite Group Databasebeta

← #34080592

Subgroups — #34080592

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×#18012763C211yesmaximal, characteristic, complemented
2C2×D8×D151C211yesmaximal, characteristic, complemented
3#23752857C211yesmaximal, characteristic, complemented
4D4×D604C211yesmaximal, characteristic, complemented
5#23752601C211yesmaximal, characteristic, complemented
6#23752466C211yesmaximal, characteristic, complemented
7#23752442C211yesmaximal, characteristic, complemented
8#23752427C211yesmaximal, characteristic, complemented
9#23752407C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752358C211yesmaximal, characteristic, complemented
12#23752347C211yesmaximal, characteristic, complemented
13#23752347C211yesmaximal, characteristic, complemented
14#23752285C211yesmaximal, characteristic, complemented
15#442×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C22×D604—21no—
18C2×D4×D151C2211yescharacteristic
19C2×D4×D151C2211yescharacteristic, complemented
20C2×D4×D151C2211yescharacteristic, complemented
21#18012763—24no—
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic, complemented
24C2×#14558992C2211yescharacteristic, complemented
25C2×D1208C2211yescharacteristic, complemented
26C2×D1208C2211yescharacteristic, complemented
27C2×#14558989C2211yescharacteristic
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558989C2211yescharacteristic, complemented
30D8×D151—24no—
31C2×#14558987C2211yescharacteristic, complemented
32C2×C8×D151C2211yescharacteristic, complemented
33#18012736C2211yescharacteristic, complemented
34#18012727C2211yescharacteristic, complemented
35#18012723—21no—
36#18012719C2211yescharacteristic, complemented
37#18012714C2211yescharacteristic
38#18012714C2211yescharacteristic, complemented
39#18012714C2211yescharacteristic, complemented
40#18012713—21no—
41#18012713—21no—
42#18012709—21no—
43#18012709—21no—
44#18012709—21no—
45C4×D604C2211yescharacteristic
46C2×(C2×D151)⋊C4—21no—
47C4⋊(C151⋊C8)C2211yescharacteristic, complemented
48#18012662C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic, complemented
50#18012659C2211yescharacteristic, complemented
51#18012659C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53(C2×D151)⋊C8C2211yescharacteristic, complemented
54C2×D8×C151C2211yescharacteristic
55C4×D4×C151C2211yescharacteristic, complemented
56C4×D4×C151C2211yescharacteristic, complemented
57#106×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic, complemented
60#97×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63C23×D151—21no—
64#14559003—22no—
65#14559003—41no—
66C2×Dic302C2311yescharacteristic
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—44no—
73C2×D604D411yescharacteristic
74C2×D604C2311yescharacteristic
75C2×D604C2311yescharacteristic
76C2×D604C2311yescharacteristic
77C2×C22⋊D151—21no—
78C2×C22⋊D151—21no—
79C2×C22⋊D151—21no—
80C2×C22⋊D151—21no—
81D4×D151—22no—
82D4×D151—22no—
83D4×D151—22no—
84D4×D151—41no—
85D4×D151—41no—
86D4×D151—41no—
87C22×Dic151—21no—
88C2×C4×D151C2311yescharacteristic
89C2×C4×D151C2311yescharacteristic
90#14558993—22no—
91#14558993—41no—
92#14558992—22no—
93D1208—22no—
94D1208—41no—
95#14558989—22no—
96#14558989—22no—
97#14558989—22no—
98#14558987—22no—
99C2×C151⋊C8C2311yescharacteristic
100C2×C151⋊C8C2311yescharacteristic
101C8×D151—22no—
102C4⋊Dic151—21no—
103C4⋊Dic151D411yescharacteristic
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)⋊C4D411yescharacteristic
111(C2×D151)⋊C4D411yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114C22×C4×C151—21no—
115C22×C4×C151—21no—
116D8×C151D414yescomplemented
117C2×C8×C151C2311yescharacteristic
118C2×C8×C151C2311yescharacteristic
119C4⋊C4×C151C2311yescharacteristic
120C4⋊C4×C151C2311yescharacteristic
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—21no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151—42no—
130C22×D151—42no—
131C22×D151—42no—
132C22×D151—42no—
133C22×D151—81no—
134C22×D151—81no—
135C22×D151—81no—
136C22×D151C2×D411yescharacteristic
137C22×D151C2×D411yescharacteristic
138Dic302—21no—
139Dic302—21no—
140D604—22no—
141D604—21no—
142D604—21no—
143D604—21no—
144D604—21no—
145D604—21no—
146D604—21no—
147D604—42no—
148D604—42no—
149D604—42no—
150D604—81no—
151D604—81no—
152C22⋊D151—42no—
153C22⋊D151—42no—
154C22⋊D151—42no—
155C22⋊D151—42no—
156C2×Dic151—21no—
157C2×Dic151—42no—
158C2×Dic151C2×D411yescharacteristic
159C2×Dic151C2×D411yescharacteristic
160C4×D151—21no—
161C4×D151—21no—
162C4×D151—21no—
163C4×D151—21no—
164C151⋊C8—21no—
165C151⋊C8—21no—
166C23×C151—21no—
167C23×C151—21no—
168D4×C151—21no—
169D4×C151—21no—
170D4×C151C2×D412yes—
171D4×C151C2×D412yescomplemented
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151—42no—
175C2×C4×C151—81no—
176C2×C4×C151C2×D411yescharacteristic
177C2×C4×C151C2×D411yescharacteristic
178C2×C4×C151C2411yescharacteristic
179C8×C151—21no—
180C8×C151C2×D412yescomplemented
181C22×C151—22no—
182C22×C151—22no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151C22×D411yescharacteristic
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—21no—
191C2×D151—21no—
192C2×D151—21no—
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—84no—
203C2×D151—84no—
204C2×D151—84no—
205C2×D151AGL(1,ℤ/8)12yescomplemented
206C4×C151—21no—
207C4×C151—21no—
208C4×C151—41no—
209C4×C151—41no—
210C4×C151C22×D411yescharacteristic
211C4×C151H(5,𝔽2)11yescharacteristic
212Dic151—21no—
213Dic151—21no—
214Dic151—41no—
215C2×C151—42no—
216C2×C151—42no—
217C2×C151D4211yescharacteristic
218C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
219C2×C151#57611yescharacteristic
220D151—22no—
221D151—41no—
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#442D15111yescharacteristic, complemented
241#435—1511no—
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×D8C2×D15111yescharacteristic
258C2×M16—1511no—
259C22×C8—1511no—
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×D4C2×D15111yescharacteristic, complemented
274C4×D4C2×D15111yescharacteristic, complemented
275C2×C22⋊C4—3021no—
276#106C2×D15111yescharacteristic, complemented
277C4⋊C8—1511no—
278#103—1511no—
279#102—1511no—
280#102—1511no—
281#102—1511no—
282#102C2×D15111yescharacteristic, complemented
283#102C2×D15111yescharacteristic, complemented
284C22⋊C8—1511no—
285C22⋊C8—1511no—
286#97C2×D15111yescharacteristic, complemented
287C24—3021no—
288C24—3021no—
289C24—3021no—
290#41—3022no—
291#41—6041no—
292C2×Q8—1511no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—3021no—
296C2×D4—3022no—
297C2×D4—3022no—
298C2×D4—3022no—
299C2×D4—3021no—
300C2×D4—3021no—
301C2×D4—3021no—
302C2×D4—3021no—
303C2×D4—3021no—
304C2×D4—3021no—
305C2×D4—6044no—
306C2×D4—6041no—
307C2×D4—6041no—
308C2×D4—6041no—
309C2×D4—1511no—
310C2×D4—1511no—
311C2×D4—1511no—
312C2×D4—1511no—
313C2×D4C22×D15111yescharacteristic
314C2×D4C22×D15111yescharacteristic
315C22×C4—21no—
316C22×C4—21no—
317C22×C4—3021no—
318C22×C4—1511no—
319C22×C4—1511no—
320SD16—3022no—
321SD16—3022no—
322SD16—6041no—
323D8—3022no—
324D8—3022no—
325D8—3022no—
326D8—3022no—
327D8—6041no—
328D8D60414yescomplemented
329M16—3022no—
330C2×C8—3022no—
331C2×C8—1511no—
332C2×C8—1511no—
333C2×C8C22×D15111yescharacteristic
334C2×C8C22×D15111yescharacteristic
335C4⋊C4—3021no—
336C4⋊C4—1511no—
337C4⋊C4C22×D15111yescharacteristic
338C4⋊C4C22×D15111yescharacteristic
339C22⋊C4—21no—
340C22⋊C4—21no—
341C22⋊C4—3021no—
342C22⋊C4—3021no—
343C22⋊C4—3021no—
344C22⋊C4—3021no—
345C22⋊C4—3021no—
346C22⋊C4—3021no—
347C22⋊C4—1511no—
348C22⋊C4—1511no—
349C42C22×D15111yescharacteristic
350C23—21no—
351C23—21no—
352C23—3021no—
353C23—3021no—
354C23—3021no—
355C23—6042no—
356C23—6042no—
357C23—6042no—
358C23—6042no—
359C23—6042no—
360C23—6042no—
361C23—1511no—
362C23—1511no—
363C23—12081no—
364C23—12081no—
365C23—12081no—
366Q8—3021no—
367Q8—3021no—
368D4—21no—
369D4—21no—
370D4—3022no—
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—12081no—
385D4—12081no—
386D4C2×D60412yes—
387D4C2×D60412yescomplemented
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—42no—
391C2×C4—81no—
392C2×C4—3021no—
393C2×C4—3021no—
394C2×C4—3021no—
395C2×C4—3021no—
396C2×C4—3021no—
397C2×C4—6042no—
398C2×C4—1511no—
399C2×C4—1511no—
400C2×C4D4×D15111yescharacteristic
401C2×C4D4×D15111yescharacteristic
402C2×C4C23×D15111yescharacteristic
403C8—21no—
404C8—3021no—
405C8—3021no—
406C8C2×D60412yescomplemented
407C22—22no—
408C22—22no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—3021no—
414C22—3021no—
415C22—3021no—
416C22—3021no—
417C22—3021no—
418C22—6041no—
419C22—6041no—
420C22—6041no—
421C22—6041no—
422C22—6041no—
423C22—6041no—
424C22—6041no—
425C22—6041no—
426C22—6041no—
427C22—1512no—
428C22—12084no—
429C22—12084no—
430C22—12084no—
431C22C2×D4×D15111yescharacteristic
432C4—21no—
433C4—21no—
434C4—41no—
435C4—41no—
436C4—3021no—
437C4—3021no—
438C4—6041no—
439C4C22×D60411yescharacteristic
440C4#1801278511yescharacteristic
441C2—42no—
442C2—42no—
443C2—3022no—
444C2—6041no—
445C2—12081no—
446C2—12081no—
447C2—12081no—
448C2D4×D60411yescharacteristic
449C2AGL(1,ℤ/8)×D15111yescharacteristic
450C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#442×C151C2
socleC22×C151C22×D4
hypercenter#442D151
hypocenterC151#3264
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×D8×D151C2semidirect
3. #23752857C2semidirect
4. D4×D604C2semidirect
5. #23752601C2semidirect
6. #23752466C2semidirect
7. #23752442C2semidirect
8. #23752427C2semidirect
9. #23752407C2semidirect
10. #23752364C2semidirect
11. #23752358C2semidirect
12. #23752347C2semidirect
13. #23752347C2semidirect
14. #23752285C2semidirect
15. #442×C151C2semidirect
16. C2×#14559003C22semidirect
19. C2×D4×D151C22semidirect
20. C2×D4×D151C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558993C22semidirect
24. C2×#14558992C22semidirect
25. C2×D1208C22semidirect
26. C2×D1208C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558989C22semidirect
31. C2×#14558987C22semidirect
32. C2×C8×D151C22semidirect
33. #18012736C22semidirect
34. #18012727C22semidirect
36. #18012719C22semidirect
38. #18012714C22semidirect
39. #18012714C22semidirect
47. C4⋊(C151⋊C8)C22semidirect
48. #18012662C22semidirect
49. #18012659C22semidirect
50. #18012659C22semidirect
51. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. (C2×D151)⋊C8C22semidirect
55. C4×D4×C151C22semidirect
56. C4×D4×C151C22semidirect
57. #106×C151C22semidirect
58. #102×C151C22semidirect
59. #102×C151C22semidirect
60. #97×C151C22semidirect
116. D8×C151D4semidirect
171. D4×C151C2×D4semidirect
180. C8×C151C2×D4semidirect
205. C2×D151AGL(1,ℤ/8)semidirect
225. C151#3264semidirect
240. #442D151semidirect
273. C4×D4C2×D151semidirect
274. C4×D4C2×D151semidirect
276. #106C2×D151semidirect
282. #102C2×D151semidirect
283. #102C2×D151semidirect
286. #97C2×D151semidirect
328. D8D604semidirect
387. D4C2×D604semidirect
406. C8C2×D604semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×D8×D1512
#237528572
D4×D6042
#237526012
#237524662
#237524422
#237524272
#237524072
#237523642
#237523582
#237523472
#237522852
#442×C1512
#3264151