Finite Group Databasebeta

← #34080606

Subgroups — #34080606

Order 19328.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012764C211yesmaximal, characteristic, complemented
2C22×#14558991C211yesmaximal, characteristic, complemented
3D4×D604C211yesmaximal, characteristic, complemented
4#23752602C211yesmaximal, characteristic, complemented
5#23752460C211yesmaximal, characteristic, complemented
6#23752446C211yesmaximal, characteristic, complemented
7#23752424C211yesmaximal, characteristic, complemented
8#23752412C211yesmaximal, characteristic, complemented
9#23752362C211yesmaximal, characteristic, complemented
10#23752357C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752345C211yesmaximal, characteristic, complemented
13#23752310C211yesmaximal, characteristic, complemented
14#23752284C211yesmaximal, characteristic, complemented
15#548×C151C211yesmaximal, characteristic, complemented
16C22×D604C2211yescharacteristic
17C22×D604C2211yescharacteristic
18C2×D4×D151—21no—
19#18012764—24no—
20C2×#14558991—24no—
21C2×#14558991C2211yescharacteristic
22C2×#14558991C2211yescharacteristic
23C2×#14558991C2211yescharacteristic, complemented
24C2×#14558991C2211yescharacteristic, complemented
25C2×#14558991C2211yescharacteristic, complemented
26C2×#14558991C2211yescharacteristic, complemented
27C2×#14558989C2211yescharacteristic
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558989C2211yescharacteristic, complemented
30C2×#14558988C2211yescharacteristic, complemented
31C22×C151⋊C8C2211yescharacteristic, complemented
32#18012736C2211yescharacteristic
33#18012714—21no—
34#18012713C2211yescharacteristic
35#18012713C2211yescharacteristic
36#18012709—21no—
37#18012709—21no—
38C4×D604C2211yescharacteristic
39#18012672C2211yescharacteristic, complemented
40C4⋊(C151⋊C8)C2211yescharacteristic, complemented
41#18012663C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012660C2211yescharacteristic, complemented
44#18012659C2211yescharacteristic
45#18012659C2211yescharacteristic, complemented
46#18012659C2211yescharacteristic, complemented
47C22⋊(C151⋊C8)C2211yescharacteristic, complemented
48C22⋊(C151⋊C8)C2211yescharacteristic, complemented
49#18012650C2211yescharacteristic, complemented
50C2×#41×C151C2211yescharacteristic, complemented
51C22×Q8×C151C2211yescharacteristic, complemented
52#124×C151—21no—
53#124×C151C2211yescharacteristic, complemented
54C22⋊Q8×C151—21no—
55C22⋊Q8×C151C2211yescharacteristic, complemented
56#121×C151—21no—
57#121×C151C2211yescharacteristic, complemented
58C4×Q8×C151C2211yescharacteristic, complemented
59C4×D4×C151—21no—
60C4×D4×C151C2211yescharacteristic
61C23×D151—21no—
62C23×D151—21no—
63C2×D604—22no—
64C2×D604—22no—
65C2×D604—21no—
66C2×D604—21no—
67C2×D604—21no—
68C2×D604—21no—
69C2×D604—41no—
70C2×D604—41no—
71C2×D604C2311yescharacteristic
72C2×D604C2311yescharacteristic
73C2×D604C2311yescharacteristic
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76D4×D151—44no—
77C2×C4×D151—21no—
78#14558991—22no—
79#14558991—22no—
80#14558991—22no—
81#14558991—22no—
82#14558991—41no—
83#14558991D414yescomplemented
84#14558989—22no—
85#14558989—22no—
86#14558989—41no—
87#14558988—22no—
88C2×C151⋊C8—22no—
89C2×C151⋊C8C2311yescharacteristic
90C2×C151⋊C8C2311yescharacteristic
91C2×C151⋊C8C2311yescharacteristic
92C2×C151⋊C8C2311yescharacteristic
93C4⋊Dic151C2311yescharacteristic
94(C2×D151)⋊C4—21no—
95(C2×D151)⋊C4—21no—
96(C2×D151)⋊C4—21no—
97#41×C151—22no—
98#41×C151—41no—
99C2×Q8×C151—21no—
100C2×Q8×C151—22no—
101C2×Q8×C151—41no—
102C2×Q8×C151C2311yescharacteristic
103C2×Q8×C151C2311yescharacteristic
104C2×D4×C151—21no—
105C2×D4×C151—21no—
106C2×D4×C151D411yescharacteristic
107C2×D4×C151C2311yescharacteristic
108C22×C4×C151—21no—
109C22×C4×C151—21no—
110C22×C4×C151C2311yescharacteristic
111C22×C4×C151C2311yescharacteristic
112C4⋊C4×C151—21no—
113C4⋊C4×C151—21no—
114C4⋊C4×C151D411yescharacteristic
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C22⋊C4×C151—21no—
120C22⋊C4×C151D411yescharacteristic
121C22⋊C4×C151D411yescharacteristic
122C42×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—81no—
132C22×D151—81no—
133D604—21no—
134D604—21no—
135D604—21no—
136D604—21no—
137D604—21no—
138D604—42no—
139D604—42no—
140D604—42no—
141D604—81no—
142D604C2×D412yes—
143C22⋊D151—42no—
144C22⋊D151—42no—
145C2×Dic151—21no—
146C4×D151—42no—
147C151⋊C8—21no—
148C151⋊C8—21no—
149C151⋊C8—21no—
150C151⋊C8C2×D412yescomplemented
151C23×C151—21no—
152C23×C151C2×D411yescharacteristic
153C23×C151C2×D411yescharacteristic
154Q8×C151—21no—
155Q8×C151—21no—
156Q8×C151—21no—
157Q8×C151—42no—
158Q8×C151C2×D412yescomplemented
159D4×C151—22no—
160D4×C151—21no—
161D4×C151—21no—
162D4×C151—42no—
163D4×C151—42no—
164C2×C4×C151—21no—
165C2×C4×C151—21no—
166C2×C4×C151—21no—
167C2×C4×C151—21no—
168C2×C4×C151—21no—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—42no—
172C2×C4×C151—42no—
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2×D411yescharacteristic
176C2×C4×C151C2×D411yescharacteristic
177C2×C4×C151C2411yescharacteristic
178C22×C151—21no—
179C22×C151—21no—
180C22×C151—21no—
181C22×C151—21no—
182C22×C151—21no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151AGL(1,ℤ/8)12yescomplemented
187C22×C151C22×D411yescharacteristic
188C2×D151—22no—
189C2×D151—41no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C2×D151—41no—
197C2×D151—84no—
198C2×D151—84no—
199C4×C151—21no—
200C4×C151—21no—
201C4×C151—22no—
202C4×C151—21no—
203C4×C151—21no—
204C4×C151—41no—
205C4×C151—41no—
206C4×C151C22×D411yescharacteristic
207C4×C151H(5,𝔽2)11yescharacteristic
208Dic151—41no—
209C2×C151—22no—
210C2×C151—41no—
211C2×C151—81no—
212C2×C151D4211yescharacteristic
213C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C151#57711yescharacteristic
215D151—42no—
216D151—81no—
217D151—81no—
218C151#326511yescharacteristic, complemented, Sylow
219#3265—1511nomaximal, Sylow
220C2×AGL(1,ℤ/8)—1511no—
221C22×SD16—1511no—
222#548D15111yescharacteristic, complemented
223D42—1511no—
224#496—1511no—
225#468—1511no—
226#466—1511no—
227#463—1511no—
228#460—1511no—
229#450—1511no—
230#449—1511no—
231#448—1511no—
232#447—1511no—
233#440—1511no—
234#435—1511no—
235C2×#41C2×D15111yescharacteristic, complemented
236C22×Q8C2×D15111yescharacteristic, complemented
237C22×D4—3021no—
238C22×D4—1511no—
239C22×D4—1511no—
240AGL(1,ℤ/8)—3024no—
241C2×SD16—3024no—
242C2×SD16—1511no—
243C2×SD16—1511no—
244C2×SD16—1511no—
245C2×SD16—1511no—
246C2×SD16—1511no—
247C2×SD16—1511no—
248C2×D8—1511no—
249C2×D8—1511no—
250C2×D8—1511no—
251C2×M16—1511no—
252C22×C8—1511no—
253#127—1511no—
254#124—21no—
255#124C2×D15111yescharacteristic, complemented
256C22⋊Q8—21no—
257C22⋊Q8C2×D15111yescharacteristic, complemented
258#121—21no—
259#121—3021no—
260#121—1511no—
261#121—1511no—
262#121C2×D15111yescharacteristic, complemented
263#120—3021no—
264#120—3021no—
265C4×Q8C2×D15111yescharacteristic, complemented
266C4×D4—21no—
267C4×D4—1511no—
268C4×D4C2×D15111yescharacteristic
269#107—1511no—
270C4⋊C8—1511no—
271#103—1511no—
272#103—1511no—
273#102—1511no—
274#102—1511no—
275#102—1511no—
276#102—1511no—
277C22⋊C8—1511no—
278C22⋊C8—1511no—
279#97—1511no—
280C24—3021no—
281C24—3021no—
282#41—22no—
283#41—41no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D15111yescharacteristic
288C2×Q8C22×D15111yescharacteristic
289C2×D4—21no—
290C2×D4—21no—
291C2×D4—3022no—
292C2×D4—3022no—
293C2×D4—3021no—
294C2×D4—3021no—
295C2×D4—3021no—
296C2×D4—3021no—
297C2×D4—3021no—
298C2×D4—3021no—
299C2×D4—6041no—
300C2×D4—6041no—
301C2×D4—6044no—
302C2×D4—1511no—
303C2×D4—1511no—
304C2×D4—1511no—
305C2×D4C22⋊D15111yescharacteristic
306C2×D4C22×D15111yescharacteristic
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—3021no—
310C22×C4C22×D15111yescharacteristic
311C22×C4C22×D15111yescharacteristic
312SD16—3022no—
313SD16—3022no—
314SD16—3022no—
315SD16—3022no—
316SD16—6041no—
317SD16—1514no—
318D8—3022no—
319D8—3022no—
320D8—6041no—
321M16—3022no—
322C2×C8—3022no—
323C2×C8—1511no—
324C2×C8—1511no—
325C2×C8—1511no—
326C2×C8—1511no—
327C4⋊C4—21no—
328C4⋊C4—21no—
329C4⋊C4—1511no—
330C4⋊C4C22⋊D15111yescharacteristic
331C4⋊C4C22×D15111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—21no—
334C22⋊C4—21no—
335C22⋊C4—21no—
336C22⋊C4—3021no—
337C22⋊C4—3021no—
338C22⋊C4—3021no—
339C22⋊C4C22⋊D15111yescharacteristic
340C22⋊C4C22⋊D15111yescharacteristic
341C42—21no—
342C42C22×D15111yescharacteristic
343C23—21no—
344C23—3021no—
345C23—3021no—
346C23—3021no—
347C23—6042no—
348C23—6042no—
349C23—6042no—
350C23—6042no—
351C23—12081no—
352C23—12081no—
353C23C2×C22⋊D15111yescharacteristic
354C23C2×C22⋊D15111yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8D4×D15112yescomplemented
360D4—22no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—42no—
365D4—3021no—
366D4—3021no—
367D4—3021no—
368D4—3021no—
369D4—3021no—
370D4—6042no—
371D4—6042no—
372D4—6042no—
373D4—6042no—
374D4—6042no—
375D4—1512no—
376D4—12081no—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—21no—
384C2×C4—42no—
385C2×C4—42no—
386C2×C4—3021no—
387C2×C4—6042no—
388C2×C4C2×C22⋊D15111yescharacteristic
389C2×C4C2×C22⋊D15111yescharacteristic
390C2×C4C2×C22⋊D15111yescharacteristic
391C2×C4C2×C22⋊D15111yescharacteristic
392C2×C4C23×D15111yescharacteristic
393C8—3021no—
394C8—3021no—
395C8—3021no—
396C8—1512no—
397C22—21no—
398C22—21no—
399C22—21no—
400C22—21no—
401C22—21no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—3022no—
406C22—6041no—
407C22—6041no—
408C22—6041no—
409C22—6041no—
410C22—6041no—
411C22—6041no—
412C22—6041no—
413C22—6041no—
414C22—12084no—
415C22—12084no—
416C22#1801276412yescomplemented
417C22C22×C22⋊D15111yescharacteristic
418C4—21no—
419C4—21no—
420C4—21no—
421C4—21no—
422C4—22no—
423C4—41no—
424C4—41no—
425C4—6041no—
426C4C2×D4×D15111yescharacteristic
427C4#1801278411yescharacteristic
428C2—22no—
429C2—41no—
430C2—81no—
431C2—6042no—
432C2—12081no—
433C2—12081no—
434C2D4×C22⋊D15111yescharacteristic
435C2C2×#1801276411yescharacteristic
436C2#2375302011yescharacteristic
subgroupG/H
centerC22C22×C22⋊D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#548×C151C2
socleC22×C151C22×D4
hypercenter#548D151
hypocenterC151#3265
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C4×D4 ◁ #548

Complements

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

NH ≅ G/Ntype
1. C2×#18012764C2semidirect
2. C22×#14558991C2semidirect
3. D4×D604C2semidirect
4. #23752602C2semidirect
5. #23752460C2semidirect
6. #23752446C2semidirect
7. #23752424C2semidirect
8. #23752412C2semidirect
9. #23752362C2semidirect
10. #23752357C2semidirect
11. #23752351C2semidirect
12. #23752345C2semidirect
13. #23752310C2semidirect
14. #23752284C2semidirect
15. #548×C151C2semidirect
23. C2×#14558991C22semidirect
24. C2×#14558991C22semidirect
25. C2×#14558991C22semidirect
26. C2×#14558991C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558989C22semidirect
30. C2×#14558988C22semidirect
31. C22×C151⋊C8C22semidirect
39. #18012672C22semidirect
40. C4⋊(C151⋊C8)C22semidirect
41. #18012663C22semidirect
42. #18012663C22semidirect
43. #18012660C22semidirect
45. #18012659C22semidirect
46. #18012659C22semidirect
47. C22⋊(C151⋊C8)C22semidirect
48. C22⋊(C151⋊C8)C22semidirect
49. #18012650C22semidirect
50. C2×#41×C151C22semidirect
51. C22×Q8×C151C22semidirect
53. #124×C151C22semidirect
55. C22⋊Q8×C151C22semidirect
57. #121×C151C22semidirect
58. C4×Q8×C151C22semidirect
83. #14558991D4semidirect
150. C151⋊C8C2×D4semidirect
158. Q8×C151C2×D4semidirect
186. C22×C151AGL(1,ℤ/8)semidirect
218. C151#3265semidirect
222. #548D151semidirect
235. C2×#41C2×D151semidirect
236. C22×Q8C2×D151semidirect
255. #124C2×D151semidirect
257. C22⋊Q8C2×D151semidirect
262. #121C2×D151semidirect
265. C4×Q8C2×D151semidirect
359. Q8D4×D151semidirect
416. C22#18012764semidirect

Maximal subgroups

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

subgroupindex
C2×#180127642
C22×#145589912
D4×D6042
#237526022
#237524602
#237524462
#237524242
#237524122
#237523622
#237523572
#237523512
#237523452
#237523102
#237522842
#548×C1512
#3265151