Finite Group Databasebeta

← #34080611

Subgroups — #34080611

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
2C2×SD16×D151C211yesmaximal, characteristic, complemented
3#23752870C211yesmaximal, characteristic, complemented
4D4×D604C211yesmaximal, characteristic, complemented
5#23752602C211yesmaximal, characteristic, complemented
6#23752461C211yesmaximal, characteristic, complemented
7#23752447C211yesmaximal, characteristic, complemented
8#23752413C211yesmaximal, characteristic, complemented
9#23752361C211yesmaximal, characteristic, complemented
10#23752358C211yesmaximal, characteristic, complemented
11#23752352C211yesmaximal, characteristic, complemented
12#23752344C211yesmaximal, characteristic, complemented
13#23752312C211yesmaximal, characteristic, complemented
14#23752282C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic, complemented
17C2×Q8×D151C2211yescharacteristic, complemented
18C22×D604—21no—
19C2×D4×D151C2211yescharacteristic
20C2×D4×D151C2211yescharacteristic
21#18012763—24no—
22C2×#14558993C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic, complemented
24C2×#14558992C2211yescharacteristic
25C2×#14558991C2211yescharacteristic, complemented
26C2×#14558991C2211yescharacteristic, complemented
27SD16×D151—24no—
28C2×#14558989C2211yescharacteristic, complemented
29C2×#14558989C2211yescharacteristic, complemented
30C2×#14558987C2211yescharacteristic, complemented
31C2×C8×D151C2211yescharacteristic, complemented
32#18012736C2211yescharacteristic
33#18012725—21no—
34#18012716—21no—
35#18012715C2211yescharacteristic, complemented
36#18012714C2211yescharacteristic
37#18012714C2211yescharacteristic
38#18012713—21no—
39#18012712—21no—
40#18012710C2211yescharacteristic, complemented
41#18012709—21no—
42#18012709—21no—
43C4×Dic302C2211yescharacteristic, complemented
44C4×D604C2211yescharacteristic
45(C22⋊D151)⋊C4—21no—
46#18012672C2211yescharacteristic, complemented
47#18012662C2211yescharacteristic, complemented
48#18012661C2211yescharacteristic, complemented
49#18012661C2211yescharacteristic, complemented
50#18012660C2211yescharacteristic
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52(C2×D151)⋊C8C2211yescharacteristic, complemented
53#18012650C2211yescharacteristic, complemented
54C2×SD16×C151C2211yescharacteristic
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic, complemented
57C4×D4×C151C2211yescharacteristic
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62C23×D151—21no—
63#14559003—22no—
64#14559003—41no—
65C2×Dic302—21no—
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—41no—
69C2×D604—21no—
70C2×D604—21no—
71C2×D604—21no—
72C2×D604—21no—
73C2×D604—44no—
74C2×D604D411yescharacteristic
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—41no—
84D4×D151—41no—
85C22×Dic151—21no—
86C2×C4×D151—21no—
87C2×C4×D151C2311yescharacteristic
88C2×C4×D151C2311yescharacteristic
89#14558993—22no—
90#14558993—22no—
91#14558992D414yescomplemented
92#14558991—22no—
93#14558991—41no—
94#14558989—22no—
95#14558989—41no—
96#14558987—22no—
97C2×C151⋊C8C2311yescharacteristic
98C2×C151⋊C8C2311yescharacteristic
99C8×D151—22no—
100C4⋊Dic151D411yescharacteristic
101C4⋊Dic151C2311yescharacteristic
102Dic151⋊C4—21no—
103Dic151⋊C4—21no—
104C22⋊Dic151—21no—
105(C2×D151)⋊C4—21no—
106(C2×D151)⋊C4—21no—
107(C2×D151)⋊C4—21no—
108(C2×D151)⋊C4D411yescharacteristic
109(C2×D151)⋊C4D411yescharacteristic
110C4×Dic151—21no—
111C2×Q8×C151C2311yescharacteristic
112C2×D4×C151C2311yescharacteristic
113C2×D4×C151C2311yescharacteristic
114C22×C4×C151—21no—
115SD16×C151—22no—
116D8×C151—22no—
117C2×C8×C151C2311yescharacteristic
118C2×C8×C151C2311yescharacteristic
119C4⋊C4×C151C2311yescharacteristic
120C22⋊C4×C151—21no—
121C22⋊C4×C151—21no—
122C22⋊C4×C151—21no—
123C42×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—42no—
129C22×D151—42no—
130C22×D151—81no—
131C22×D151—81no—
132C22×D151C2×D411yescharacteristic
133C22×D151C2×D411yescharacteristic
134Dic302—21no—
135Dic302—42no—
136Dic302C2×D412yescomplemented
137D604—22no—
138D604—21no—
139D604—21no—
140D604—21no—
141D604—21no—
142D604—42no—
143D604—42no—
144D604—42no—
145D604—81no—
146C22⋊D151—42no—
147C22⋊D151—42no—
148C22⋊D151—42no—
149C22⋊D151—42no—
150C2×Dic151—21no—
151C2×Dic151—21no—
152C2×Dic151—42no—
153C2×Dic151C2×D411yescharacteristic
154C2×Dic151C2×D411yescharacteristic
155C4×D151—21no—
156C4×D151—21no—
157C4×D151—21no—
158C4×D151—21no—
159C4×D151—42no—
160C151⋊C8—21no—
161C151⋊C8C2×D412yescomplemented
162C23×C151—21no—
163C23×C151—21no—
164Q8×C151—21no—
165Q8×C151—21no—
166D4×C151—21no—
167D4×C151—21no—
168D4×C151—21no—
169D4×C151C2×D412yes—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—42no—
173C2×C4×C151C2×D411yescharacteristic
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2411yescharacteristic
176C8×C151—21no—
177C8×C151—21no—
178C22×C151—22no—
179C22×C151—41no—
180C22×C151—41no—
181C22×C151—41no—
182C22×C151—41no—
183C22×C151—41no—
184C22×C151C22×D411yescharacteristic
185C2×D151—21no—
186C2×D151—21no—
187C2×D151—21no—
188C2×D151—21no—
189C2×D151—21no—
190C2×D151—41no—
191C2×D151—41no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C2×D151—84no—
197C2×D151—84no—
198C2×D151AGL(1,ℤ/8)12yescomplemented
199C4×C151—21no—
200C4×C151—21no—
201C4×C151—41no—
202C4×C151—41no—
203C4×C151C22×D411yescharacteristic
204C4×C151H(5,𝔽2)11yescharacteristic
205Dic151—21no—
206Dic151—21no—
207Dic151—22no—
208Dic151—41no—
209C2×C151—42no—
210C2×C151—81no—
211C2×C151D4211yescharacteristic
212C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
213C2×C151#57711yescharacteristic
214D151—22no—
215D151—41no—
216D151—81no—
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#463D15111yescharacteristic, complemented
228#460—1511no—
229#450—1511no—
230#449—1511no—
231#448—1511no—
232#447—1511no—
233#440—1511no—
234#435—1511no—
235C2×#41—1511no—
236C22×Q8—1511no—
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×SD16C2×D15111yescharacteristic
248C2×D8—1511no—
249C2×D8—1511no—
250C2×D8C2×D15111yescharacteristic
251C2×M16—1511no—
252C22×C8—1511no—
253#127—1511no—
254#124—3021no—
255#124C2×D15111yescharacteristic, complemented
256C22⋊Q8—3021no—
257C22⋊Q8—1511no—
258#121—3021no—
259#121—3021no—
260#121—1511no—
261#121—1511no—
262#121—1511no—
263#120—3021no—
264#120—3021no—
265C4×Q8—1511no—
266C4×D4—3021no—
267C4×D4—1511no—
268C4×D4C2×D15111yescharacteristic
269#107—1511no—
270C4⋊C8C2×D15111yescharacteristic, complemented
271#103—1511no—
272#103C2×D15111yescharacteristic, complemented
273#102—1511no—
274#102—1511no—
275#102—1511no—
276#102C2×D15111yescharacteristic, complemented
277C22⋊C8—1511no—
278C22⋊C8—1511no—
279#97—1511no—
280C24—3021no—
281C24—3021no—
282#41—3022no—
283#41—6041no—
284C2×Q8—3021no—
285C2×Q8—3022no—
286C2×Q8—6041no—
287C2×Q8—1511no—
288C2×Q8C22×D15111yescharacteristic
289C2×D4—3021no—
290C2×D4—3021no—
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—6044no—
300C2×D4—6041no—
301C2×D4—6041no—
302C2×D4—1511no—
303C2×D4—1511no—
304C2×D4—1511no—
305C2×D4C22×D15111yescharacteristic
306C2×D4C22×D15111yescharacteristic
307C22×C4—21no—
308C22×C4—3021no—
309C22×C4—3021no—
310C22×C4—1511no—
311C22×C4—1511no—
312SD16—22no—
313SD16—3022no—
314SD16—3022no—
315SD16—3022no—
316SD16—6041no—
317SD16—1514no—
318D8—22no—
319D8—3022no—
320D8—6041no—
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—21no—
334C22⋊C4—21no—
335C22⋊C4—3021no—
336C22⋊C4—3021no—
337C22⋊C4—3021no—
338C22⋊C4—3021no—
339C22⋊C4—1511no—
340C22⋊C4—1511no—
341C42—3021no—
342C42C22×D15111yescharacteristic
343C23—21no—
344C23—21no—
345C23—3021no—
346C23—3021no—
347C23—6042no—
348C23—6042no—
349C23—6042no—
350C23—6042no—
351C23—1511no—
352C23—1511no—
353C23—12081no—
354C23—12081no—
355Q8—21no—
356Q8—21no—
357Q8—3021no—
358Q8—6042no—
359Q8—1512no—
360D4—21no—
361D4—21no—
362D4—21no—
363D4—3022no—
364D4—3021no—
365D4—3021no—
366D4—3021no—
367D4—3021no—
368D4—6042no—
369D4—6042no—
370D4—6042no—
371D4—6042no—
372D4—6042no—
373D4—6042no—
374D4—6042no—
375D4—12081no—
376D4D4×D15112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—42no—
380C2×C4—3021no—
381C2×C4—3021no—
382C2×C4—3021no—
383C2×C4—3021no—
384C2×C4—3021no—
385C2×C4—3021no—
386C2×C4—6042no—
387C2×C4—6042no—
388C2×C4—1511no—
389C2×C4—1511no—
390C2×C4D4×D15111yescharacteristic
391C2×C4D4×D15111yescharacteristic
392C2×C4C23×D15111yescharacteristic
393C8—21no—
394C8—21no—
395C8—3021no—
396C8—1512no—
397C22—22no—
398C22—41no—
399C22—41no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—3021no—
404C22—3021no—
405C22—3021no—
406C22—3021no—
407C22—3021no—
408C22—6041no—
409C22—6041no—
410C22—6041no—
411C22—6041no—
412C22—6041no—
413C22—6041no—
414C22—1512no—
415C22—12084no—
416C22—12084no—
417C22C2×D4×D15111yescharacteristic
418C4—21no—
419C4—21no—
420C4—41no—
421C4—41no—
422C4—3021no—
423C4—3021no—
424C4—3022no—
425C4—6041no—
426C4C2×D4×D15111yescharacteristic
427C4#1801278511yescharacteristic
428C2—42no—
429C2—81no—
430C2—3022no—
431C2—6041no—
432C2—12081no—
433C2—12081no—
434C2#2375284611yescharacteristic
435C2AGL(1,ℤ/8)×D15111yescharacteristic
436C2#2375301911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
hypercenter#463D151
hypocenterC151#3265
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
1. C2×#18012763C2semidirect
2. C2×SD16×D151C2semidirect
3. #23752870C2semidirect
4. D4×D604C2semidirect
5. #23752602C2semidirect
6. #23752461C2semidirect
7. #23752447C2semidirect
8. #23752413C2semidirect
9. #23752361C2semidirect
10. #23752358C2semidirect
11. #23752352C2semidirect
12. #23752344C2semidirect
13. #23752312C2semidirect
14. #23752282C2semidirect
15. #463×C151C2semidirect
16. C2×#14559003C22semidirect
17. C2×Q8×D151C22semidirect
22. C2×#14558993C22semidirect
23. C2×#14558993C22semidirect
25. C2×#14558991C22semidirect
26. C2×#14558991C22semidirect
28. C2×#14558989C22semidirect
29. C2×#14558989C22semidirect
30. C2×#14558987C22semidirect
31. C2×C8×D151C22semidirect
35. #18012715C22semidirect
40. #18012710C22semidirect
43. C4×Dic302C22semidirect
46. #18012672C22semidirect
47. #18012662C22semidirect
48. #18012661C22semidirect
49. #18012661C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. (C2×D151)⋊C8C22semidirect
53. #18012650C22semidirect
56. #124×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
60. #102×C151C22semidirect
91. #14558992D4semidirect
136. Dic302C2×D4semidirect
161. C151⋊C8C2×D4semidirect
198. C2×D151AGL(1,ℤ/8)semidirect
218. C151#3265semidirect
227. #463D151semidirect
255. #124C2×D151semidirect
270. C4⋊C8C2×D151semidirect
272. #103C2×D151semidirect
276. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127632
C2×SD16×D1512
#237528702
D4×D6042
#237526022
#237524612
#237524472
#237524132
#237523612
#237523582
#237523522
#237523442
#237523122
#237522822
#463×C1512
#3265151