Finite Group Databasebeta

← #34080609

Subgroups — #34080609

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×#18012763C211yesmaximal, characteristic, complemented
2C22×#14558992C211yesmaximal, characteristic, complemented
3#23752868C211yesmaximal, characteristic, complemented
4D4×C22⋊D151C211yesmaximal, characteristic, complemented
5#23752600C211yesmaximal, characteristic, complemented
6#23752457C211yesmaximal, characteristic, complemented
7#23752446C211yesmaximal, characteristic, complemented
8#23752425C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752364C211yesmaximal, characteristic, complemented
11#23752354C211yesmaximal, characteristic, complemented
12#23752353C211yesmaximal, characteristic, complemented
13#23752309C211yesmaximal, characteristic, complemented
14#23752280C211yesmaximal, characteristic, complemented
15#447×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C22×Dic302C2211yescharacteristic, complemented
18C22×C22⋊D151—21no—
19C2×D4×D151C2211yescharacteristic
20#18012763—24no—
21C2×#14558993C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558992—24no—
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic
26C2×#14558992C2211yescharacteristic, complemented
27C2×#14558992C2211yescharacteristic, complemented
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558987C2211yescharacteristic, complemented
30C22×C151⋊C8C2211yescharacteristic, complemented
31#18012735C2211yescharacteristic
32#18012726C2211yescharacteristic, complemented
33#18012725—21no—
34#18012719C2211yescharacteristic, complemented
35#18012716—21no—
36#18012713C2211yescharacteristic
37#18012711—21no—
38#18012711—21no—
39#18012710C2211yescharacteristic
40#18012708—21no—
41#18012707—21no—
42#18012704C2211yescharacteristic, complemented
43D4×Dic151—21no—
44D4×Dic151C2211yescharacteristic
45C4×C22⋊D151C2211yescharacteristic
46#18012672C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012664C2211yescharacteristic, complemented
50#18012660C2211yescharacteristic, complemented
51#18012659C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012649C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56C2×D8×C151C2211yescharacteristic, complemented
57#121×C151C2211yescharacteristic, complemented
58#102×C151C2211yescharacteristic
59#102×C151C2211yescharacteristic, complemented
60C22⋊C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559003—22no—
63#14559003—41no—
64C2×Dic302—22no—
65C2×Dic302—21no—
66C2×Dic302—41no—
67C2×Dic302C2311yescharacteristic
68C2×Dic302C2311yescharacteristic
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74C2×C22⋊D151—21no—
75C2×C22⋊D151—21no—
76C2×C22⋊D151—44no—
77C2×C22⋊D151D411yescharacteristic
78D4×D151—22no—
79D4×D151—41no—
80C22×Dic151—21no—
81C22×Dic151—21no—
82C22×Dic151—21no—
83C2×C4×D151C2311yescharacteristic
84#14558993—22no—
85#14558993—41no—
86#14558992—22no—
87#14558992—22no—
88#14558992—22no—
89#14558992D414yescomplemented
90#14558989—22no—
91#14558987—22no—
92C2×C151⋊C8—22no—
93C2×C151⋊C8C2311yescharacteristic
94C2×C151⋊C8C2311yescharacteristic
95C4⋊Dic151—21no—
96C4⋊Dic151C2311yescharacteristic
97Dic151⋊C4—21no—
98Dic151⋊C4D411yescharacteristic
99C22⋊Dic151—21no—
100C22⋊Dic151—21no—
101C22⋊Dic151—21no—
102C22⋊Dic151—21no—
103C22⋊Dic151D411yescharacteristic
104(C2×D151)⋊C4—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4D411yescharacteristic
107C4×Dic151—21no—
108C4×Dic151C2311yescharacteristic
109C24×C151—21no—
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—21no—
113C2×D4×C151—41no—
114C2×D4×C151C2311yescharacteristic
115C2×D4×C151C2311yescharacteristic
116C2×D4×C151C2311yescharacteristic
117C22×C4×C151C2311yescharacteristic
118D8×C151—22no—
119D8×C151—41no—
120C2×C8×C151C2311yescharacteristic
121C2×C8×C151C2311yescharacteristic
122C4⋊C4×C151C2311yescharacteristic
123C22⋊C4×C151—21no—
124C22×D151—21no—
125C22×D151—42no—
126C22×D151—42no—
127C22×D151—81no—
128C22×D151C2×D411yescharacteristic
129Dic302—21no—
130Dic302—21no—
131Dic302—21no—
132Dic302—42no—
133Dic302C2×D412yescomplemented
134D604—21no—
135D604—21no—
136C22⋊D151—22no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—42no—
140C22⋊D151—42no—
141C22⋊D151—42no—
142C22⋊D151—81no—
143C2×Dic151—21no—
144C2×Dic151—21no—
145C2×Dic151—21no—
146C2×Dic151—42no—
147C2×Dic151—42no—
148C2×Dic151—42no—
149C2×Dic151C2×D411yescharacteristic
150C2×Dic151C2×D411yescharacteristic
151C2×Dic151C2×D411yescharacteristic
152C4×D151—21no—
153C4×D151—21no—
154C151⋊C8—21no—
155C151⋊C8C2×D412yescomplemented
156C23×C151—21no—
157C23×C151—21no—
158C23×C151—21no—
159C23×C151—42no—
160C23×C151—42no—
161C23×C151—81no—
162C23×C151C2×D411yescharacteristic
163D4×C151—21no—
164D4×C151—21no—
165D4×C151—21no—
166D4×C151—21no—
167D4×C151—21no—
168D4×C151—42no—
169D4×C151—42no—
170D4×C151C2×D412yes—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—21no—
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2411yescharacteristic
176C8×C151—21no—
177C8×C151—21no—
178C22×C151—21no—
179C22×C151—21no—
180C22×C151—22no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151—41no—
185C22×C151—41no—
186C22×C151—41no—
187C22×C151—41no—
188C22×C151—41no—
189C22×C151—84no—
190C22×C151AGL(1,ℤ/8)12yescomplemented
191C22×C151C22×D411yescharacteristic
192C2×D151—21no—
193C2×D151—21no—
194C2×D151—21no—
195C2×D151—41no—
196C2×D151—41no—
197C2×D151—41no—
198C2×D151—84no—
199C4×C151—21no—
200C4×C151—41no—
201C4×C151C22×D411yescharacteristic
202C4×C151H(5,𝔽2)11yescharacteristic
203Dic151—21no—
204Dic151—22no—
205Dic151—21no—
206Dic151—21no—
207Dic151—41no—
208Dic151—41no—
209C2×C151—22no—
210C2×C151—42no—
211C2×C151—81no—
212C2×C151—81no—
213C2×C151D4211yescharacteristic
214C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
215C2×C151#57711yescharacteristic
216D151—41no—
217D151—81no—
218C151#326511yescharacteristic, complemented, Sylow
219#3265—1511nomaximal, Sylow
220C2×AGL(1,ℤ/8)—1511no—
221C22×SD16—1511no—
222#548—1511no—
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#447D15111yescharacteristic, complemented
233#440—1511no—
234#435—1511no—
235C2×#41—1511no—
236C22×Q8—1511no—
237C22×D4—3021no—
238C22×D4—1511no—
239C22×D4C2×D15111yescharacteristic
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×D8C2×D15111yescharacteristic
250C2×D8C2×D15111yescharacteristic, complemented
251C2×M16—1511no—
252C22×C8—1511no—
253#127—1511no—
254#124—3021no—
255#124—1511no—
256C22⋊Q8—3021no—
257C22⋊Q8—1511no—
258#121—3021no—
259#121—3021no—
260#121—1511no—
261#121—1511no—
262#121C2×D15111yescharacteristic, complemented
263#120—3021no—
264#120—3021no—
265C4×Q8—1511no—
266C4×D4—3021no—
267C4×D4—1511no—
268C4×D4—1511no—
269#107—1511no—
270C4⋊C8—1511no—
271#103—1511no—
272#103—1511no—
273#102—1511no—
274#102—1511no—
275#102C2×D15111yescharacteristic
276#102C2×D15111yescharacteristic, complemented
277C22⋊C8—1511no—
278C22⋊C8C2×D15111yescharacteristic, complemented
279#97—1511no—
280C24—21no—
281C24—3021no—
282#41—3022no—
283#41—6041no—
284C2×Q8—3022no—
285C2×Q8—3021no—
286C2×Q8—6041no—
287C2×Q8—1511no—
288C2×Q8—1511no—
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—21no—
292C2×D4—41no—
293C2×D4—3022no—
294C2×D4—3021no—
295C2×D4—3021no—
296C2×D4—3021no—
297C2×D4—3021no—
298C2×D4—3021no—
299C2×D4—3021no—
300C2×D4—6041no—
301C2×D4—6044no—
302C2×D4—1511no—
303C2×D4—1511no—
304C2×D4C22×D15111yescharacteristic
305C2×D4C22×D15111yescharacteristic
306C2×D4C22×D15111yescharacteristic
307C22×C4—3021no—
308C22×C4—3021no—
309C22×C4—3021no—
310C22×C4—1511no—
311C22×C4C22×D15111yescharacteristic
312SD16—3022no—
313SD16—3022no—
314SD16—3022no—
315SD16—3022no—
316SD16—6041no—
317SD16—1514no—
318D8—22no—
319D8—41no—
320D8—3022no—
321M16—3022no—
322C2×C8—3022no—
323C2×C8—1511no—
324C2×C8—1511no—
325C2×C8C22×D15111yescharacteristic
326C2×C8C22×D15111yescharacteristic
327C4⋊C4—3021no—
328C4⋊C4—3021no—
329C4⋊C4—1511no—
330C4⋊C4—1511no—
331C4⋊C4C22×D15111yescharacteristic
332C22⋊C4—21no—
333C22⋊C4—3021no—
334C22⋊C4—3021no—
335C22⋊C4—3021no—
336C22⋊C4—3021no—
337C22⋊C4—3021no—
338C22⋊C4—3021no—
339C22⋊C4—1511no—
340C22⋊C4—1511no—
341C42—3021no—
342C42—1511no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—42no—
347C23—42no—
348C23—81no—
349C23—3021no—
350C23—6042no—
351C23—6042no—
352C23—1511no—
353C23—12081no—
354C23D4×D15111yescharacteristic
355Q8—3021no—
356Q8—3021no—
357Q8—3021no—
358Q8—6042no—
359Q8—1512no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—21no—
364D4—21no—
365D4—42no—
366D4—42no—
367D4—3022no—
368D4—3021no—
369D4—3021no—
370D4—6042no—
371D4—6042no—
372D4—6042no—
373D4—6042no—
374D4—6042no—
375D4—12081no—
376D4D4×D15112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—3021no—
381C2×C4—3021no—
382C2×C4—3021no—
383C2×C4—3021no—
384C2×C4—3021no—
385C2×C4—6042no—
386C2×C4—6042no—
387C2×C4—6042no—
388C2×C4—1511no—
389C2×C4—1511no—
390C2×C4—1511no—
391C2×C4D4×D15111yescharacteristic
392C2×C4C23×D15111yescharacteristic
393C8—21no—
394C8—21no—
395C8—3021no—
396C8—1512no—
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—84no—
409C22—3021no—
410C22—3021no—
411C22—3021no—
412C22—6041no—
413C22—6041no—
414C22—6041no—
415C22—12084no—
416C22#1801276312yescomplemented
417C22C2×D4×D15111yescharacteristic
418C4—21no—
419C4—41no—
420C4—3021no—
421C4—3021no—
422C4—3021no—
423C4—3022no—
424C4—6041no—
425C4—6041no—
426C4C2×D4×D15111yescharacteristic
427C4#1801278411yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—81no—
432C2—6041no—
433C2—12081no—
434C2#2375284411yescharacteristic
435C2C2×#1801276311yescharacteristic
436C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#447×C151C2
socleC22×C151C22×D4
hypercenter#447D151
hypocenterC151#3265
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C22×#14558992C2semidirect
3. #23752868C2semidirect
4. D4×C22⋊D151C2semidirect
5. #23752600C2semidirect
6. #23752457C2semidirect
7. #23752446C2semidirect
8. #23752425C2semidirect
9. #23752411C2semidirect
10. #23752364C2semidirect
11. #23752354C2semidirect
12. #23752353C2semidirect
13. #23752309C2semidirect
14. #23752280C2semidirect
15. #447×C151C2semidirect
16. C2×#14559003C22semidirect
17. C22×Dic302C22semidirect
21. C2×#14558993C22semidirect
22. C2×#14558993C22semidirect
26. C2×#14558992C22semidirect
27. C2×#14558992C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558987C22semidirect
30. C22×C151⋊C8C22semidirect
32. #18012726C22semidirect
34. #18012719C22semidirect
42. #18012704C22semidirect
46. #18012672C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012664C22semidirect
50. #18012660C22semidirect
51. #18012659C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012649C22semidirect
56. C2×D8×C151C22semidirect
57. #121×C151C22semidirect
59. #102×C151C22semidirect
60. C22⋊C8×C151C22semidirect
89. #14558992D4semidirect
133. Dic302C2×D4semidirect
155. C151⋊C8C2×D4semidirect
190. C22×C151AGL(1,ℤ/8)semidirect
218. C151#3265semidirect
232. #447D151semidirect
250. C2×D8C2×D151semidirect
262. #121C2×D151semidirect
276. #102C2×D151semidirect
278. C22⋊C8C2×D151semidirect
416. C22#18012763semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C22×#145589922
#237528682
D4×C22⋊D1512
#237526002
#237524572
#237524462
#237524252
#237524112
#237523642
#237523542
#237523532
#237523092
#237522802
#447×C1512
#3265151