Finite Group Databasebeta

← #34080605

Subgroups — #34080605

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×#18012766C211yesmaximal, characteristic, complemented
2#23752873C211yesmaximal, characteristic, complemented
3D4×C22⋊D151C211yesmaximal, characteristic, complemented
4#23752598C211yesmaximal, characteristic, complemented
5#23752455C211yesmaximal, characteristic, complemented
6#23752448C211yesmaximal, characteristic, complemented
7#23752429C211yesmaximal, characteristic, complemented
8#23752410C211yesmaximal, characteristic, complemented
9#23752361C211yesmaximal, characteristic, complemented
10#23752356C211yesmaximal, characteristic, complemented
11#23752351C211yesmaximal, characteristic, complemented
12#23752346C211yesmaximal, characteristic, complemented
13#23752313C211yesmaximal, characteristic, complemented
14#23752283C211yesmaximal, characteristic, complemented
15C22×SD16×C151C211yesmaximal, characteristic, complemented
16C2×#14559005C2211yescharacteristic, complemented
17C22×C22⋊D151—21no—
18C2×D4×D151C2211yescharacteristic
19#18012766—24no—
20C2×#14558991C2211yescharacteristic, complemented
21C2×#14558991C2211yescharacteristic, complemented
22C2×D1208C2211yescharacteristic, complemented
23C2×#14558989C2211yescharacteristic
24C2×#14558989C2211yescharacteristic, complemented
25C2×#14558987C2211yescharacteristic, complemented
26#18012735C2211yescharacteristic
27#18012728—21no—
28#18012728C2211yescharacteristic, complemented
29#18012715—21no—
30#18012715C2211yescharacteristic, complemented
31#18012713—21no—
32#18012713C2211yescharacteristic
33#18012713C2211yescharacteristic, complemented
34#18012711—21no—
35#18012710C2211yescharacteristic
36#18012708—21no—
37#18012707—21no—
38Q8×Dic151C2211yescharacteristic, complemented
39D4×Dic151C2211yescharacteristic
40C4×C22⋊D151—21no—
41C4×C22⋊D151C2211yescharacteristic
42#18012673C2211yescharacteristic, complemented
43Dic151⋊C8C2211yescharacteristic, complemented
44#18012663C2211yescharacteristic, complemented
45#18012663C2211yescharacteristic, complemented
46#18012661C2211yescharacteristic, complemented
47#18012661C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic
49#18012660C2211yescharacteristic, complemented
50C22⋊(C151⋊C8)C2211yescharacteristic, complemented
51(C2×D151)⋊C8C2211yescharacteristic, complemented
52#18012649C2211yescharacteristic, complemented
53C22×Q8×C151C2211yescharacteristic, complemented
54C22×D4×C151C2211yescharacteristic
55C2×SD16×C151—24no—
56C2×SD16×C151C2211yescharacteristic
57C2×SD16×C151C2211yescharacteristic
58C2×SD16×C151C2211yescharacteristic, complemented
59C2×SD16×C151C2211yescharacteristic, complemented
60C22×C8×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559005—22no—
63#14559005—41no—
64C2×D604—21no—
65C2×D604C2311yescharacteristic
66C2×D604C2311yescharacteristic
67C2×C22⋊D151—21no—
68C2×C22⋊D151—21no—
69C2×C22⋊D151—21no—
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—44no—
74C2×C22⋊D151D411yescharacteristic
75D4×D151—22no—
76D4×D151—41no—
77C22×Dic151—21no—
78C2×C4×D151—21no—
79C2×C4×D151C2311yescharacteristic
80#14558991—22no—
81#14558991—41no—
82D1208—22no—
83#14558989—22no—
84#14558989—41no—
85#14558987—22no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C4⋊Dic151—21no—
89C4⋊Dic151C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4D411yescharacteristic
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151D411yescharacteristic
96(C2×D151)⋊C4—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4—21no—
101(C2×D151)⋊C4D411yescharacteristic
102C4×Dic151—21no—
103C4×Dic151C2311yescharacteristic
104C24×C151—21no—
105C2×Q8×C151—21no—
106C2×Q8×C151—22no—
107C2×Q8×C151—41no—
108C2×Q8×C151C2311yescharacteristic
109C2×Q8×C151C2311yescharacteristic
110C2×D4×C151—22no—
111C2×D4×C151—21no—
112C2×D4×C151—41no—
113C2×D4×C151C2311yescharacteristic
114C2×D4×C151C2311yescharacteristic
115C22×C4×C151—21no—
116C22×C4×C151C2311yescharacteristic
117SD16×C151—22no—
118SD16×C151—22no—
119SD16×C151—22no—
120SD16×C151D414yescomplemented
121C2×C8×C151—22no—
122C2×C8×C151C2311yescharacteristic
123C2×C8×C151C2311yescharacteristic
124C22×D151—21no—
125C22×D151—21no—
126C22×D151—42no—
127C22×D151—42no—
128C22×D151—81no—
129C22×D151C2×D411yescharacteristic
130D604—21no—
131D604—21no—
132D604—21no—
133D604—21no—
134D604—42no—
135C22⋊D151—22no—
136C22⋊D151—42no—
137C22⋊D151—42no—
138C22⋊D151—42no—
139C22⋊D151—42no—
140C22⋊D151—42no—
141C22⋊D151—81no—
142C2×Dic151—21no—
143C2×Dic151—21no—
144C2×Dic151—42no—
145C2×Dic151C2×D411yescharacteristic
146C2×Dic151C2×D411yescharacteristic
147C2×Dic151C2×D411yescharacteristic
148C4×D151—21no—
149C4×D151—21no—
150C4×D151—42no—
151C151⋊C8—21no—
152C151⋊C8—21no—
153C23×C151—21no—
154C23×C151—21no—
155C23×C151—42no—
156C23×C151—42no—
157C23×C151—81no—
158C23×C151C2×D411yescharacteristic
159Q8×C151—21no—
160Q8×C151—21no—
161Q8×C151—21no—
162Q8×C151—42no—
163Q8×C151C2×D412yescomplemented
164D4×C151—21no—
165D4×C151—21no—
166D4×C151—21no—
167D4×C151—42no—
168D4×C151C2×D412yes—
169C2×C4×C151—21no—
170C2×C4×C151—21no—
171C2×C4×C151—21no—
172C2×C4×C151—21no—
173C2×C4×C151—42no—
174C2×C4×C151C2×D411yescharacteristic
175C2×C4×C151C2411yescharacteristic
176C8×C151—21no—
177C8×C151C2×D412yescomplemented
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—84no—
187C22×C151AGL(1,ℤ/8)12yescomplemented
188C22×C151C22×D411yescharacteristic
189C2×D151—21no—
190C2×D151—21no—
191C2×D151—21no—
192C2×D151—41no—
193C2×D151—41no—
194C2×D151—41no—
195C2×D151—41no—
196C2×D151—41no—
197C2×D151—41no—
198C2×D151—84no—
199C4×C151—21no—
200C4×C151—22no—
201C4×C151—41no—
202C4×C151C22×D411yescharacteristic
203C4×C151H(5,𝔽2)11yescharacteristic
204Dic151—21no—
205Dic151—21no—
206Dic151—21no—
207Dic151—41no—
208Dic151—41no—
209C2×C151—22no—
210C2×C151—42no—
211C2×C151—81no—
212C2×C151D4211yescharacteristic
213C2×C151C2×AGL(1,ℤ/8)11yescharacteristic
214C2×C151#57711yescharacteristic
215D151—41no—
216D151—81no—
217D151—81no—
218C151#326511yescharacteristic, complemented, Sylow
219#3265—1511nomaximal, Sylow
220C2×AGL(1,ℤ/8)—1511no—
221C22×SD16D15111yescharacteristic, complemented
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#447—1511no—
233#440—1511no—
234#435—1511no—
235C2×#41—1511no—
236C22×Q8C2×D15111yescharacteristic, complemented
237C22×D4—3021no—
238C22×D4—1511no—
239C22×D4C2×D15111yescharacteristic
240AGL(1,ℤ/8)—3024no—
241C2×SD16—24no—
242C2×SD16—1511no—
243C2×SD16—1511no—
244C2×SD16C2×D15111yescharacteristic
245C2×SD16C2×D15111yescharacteristic
246C2×SD16C2×D15111yescharacteristic, complemented
247C2×SD16C2×D15111yescharacteristic, complemented
248C2×D8—1511no—
249C2×D8—1511no—
250C2×D8—1511no—
251C2×M16—1511no—
252C22×C8C2×D15111yescharacteristic, complemented
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#121—1511no—
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#102—1511no—
276#102—1511no—
277C22⋊C8—1511no—
278C22⋊C8—1511no—
279#97—1511no—
280C24—21no—
281C24—3021no—
282#41—3022no—
283#41—6041no—
284C2×Q8—21no—
285C2×Q8—22no—
286C2×Q8—41no—
287C2×Q8C22×D15111yescharacteristic
288C2×Q8C22×D15111yescharacteristic
289C2×D4—22no—
290C2×D4—21no—
291C2×D4—41no—
292C2×D4—3021no—
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×D4—1511no—
305C2×D4C22×D15111yescharacteristic
306C2×D4C22×D15111yescharacteristic
307C22×C4—21no—
308C22×C4—3021no—
309C22×C4—3021no—
310C22×C4—1511no—
311C22×C4C22×D15111yescharacteristic
312SD16—22no—
313SD16—22no—
314SD16—22no—
315SD16—3022no—
316SD16—6041no—
317SD16C22⋊D15114yescomplemented
318D8—3022no—
319D8—3022no—
320D8—6041no—
321M16—3022no—
322C2×C8—22no—
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⋊C4—1511no—
332C22⋊C4—3021no—
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—42no—
346C23—42no—
347C23—81no—
348C23—3021no—
349C23—3021no—
350C23—6042no—
351C23—6042no—
352C23—1511no—
353C23—12081no—
354C23D4×D15111yescharacteristic
355Q8—21no—
356Q8—21no—
357Q8—21no—
358Q8—42no—
359Q8C2×C22⋊D15112yescomplemented
360D4—21no—
361D4—21no—
362D4—21no—
363D4—42no—
364D4—3022no—
365D4—3021no—
366D4—3021no—
367D4—3021no—
368D4—3021no—
369D4—6042no—
370D4—6042no—
371D4—6042no—
372D4—6042no—
373D4—6042no—
374D4—6042no—
375D4—12081no—
376D4C2×C22⋊D15112yes—
377C2×C4—21no—
378C2×C4—21no—
379C2×C4—21no—
380C2×C4—21no—
381C2×C4—42no—
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×C4—1511no—
391C2×C4D4×D15111yescharacteristic
392C2×C4C23×D15111yescharacteristic
393C8—21no—
394C8—3021no—
395C8—3021no—
396C8C2×C22⋊D15112yescomplemented
397C22—21no—
398C22—21no—
399C22—22no—
400C22—41no—
401C22—41no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—84no—
406C22—3021no—
407C22—3021no—
408C22—3021no—
409C22—6041no—
410C22—6041no—
411C22—6041no—
412C22—6041no—
413C22—6041no—
414C22—6041no—
415C22—12084no—
416C22#1801276612yescomplemented
417C22C2×D4×D15111yescharacteristic
418C4—21no—
419C4—22no—
420C4—41no—
421C4—3021no—
422C4—3021no—
423C4—3021no—
424C4—6041no—
425C4—6041no—
426C4C22×C22⋊D15111yescharacteristic
427C4#1801278411yescharacteristic
428C2—22no—
429C2—42no—
430C2—81no—
431C2—6041no—
432C2—12081no—
433C2—12081no—
434C2D4×C22⋊D15111yescharacteristic
435C2C2×#1801276611yescharacteristic
436C2#2375301811yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
FittingC22×SD16×C151C2
socleC22×C151C22×D4
hypercenterC22×SD16D151
hypocenterC151#3265
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#18012766C2semidirect
2. #23752873C2semidirect
3. D4×C22⋊D151C2semidirect
4. #23752598C2semidirect
5. #23752455C2semidirect
6. #23752448C2semidirect
7. #23752429C2semidirect
8. #23752410C2semidirect
9. #23752361C2semidirect
10. #23752356C2semidirect
11. #23752351C2semidirect
12. #23752346C2semidirect
13. #23752313C2semidirect
14. #23752283C2semidirect
15. C22×SD16×C151C2semidirect
16. C2×#14559005C22semidirect
20. C2×#14558991C22semidirect
21. C2×#14558991C22semidirect
22. C2×D1208C22semidirect
24. C2×#14558989C22semidirect
25. C2×#14558987C22semidirect
28. #18012728C22semidirect
30. #18012715C22semidirect
33. #18012713C22semidirect
38. Q8×Dic151C22semidirect
42. #18012673C22semidirect
43. Dic151⋊C8C22semidirect
44. #18012663C22semidirect
45. #18012663C22semidirect
46. #18012661C22semidirect
47. #18012661C22semidirect
49. #18012660C22semidirect
50. C22⋊(C151⋊C8)C22semidirect
51. (C2×D151)⋊C8C22semidirect
52. #18012649C22semidirect
53. C22×Q8×C151C22semidirect
58. C2×SD16×C151C22semidirect
59. C2×SD16×C151C22semidirect
60. C22×C8×C151C22semidirect
120. SD16×C151D4semidirect
163. Q8×C151C2×D4semidirect
177. C8×C151C2×D4semidirect
187. C22×C151AGL(1,ℤ/8)semidirect
218. C151#3265semidirect
221. C22×SD16D151semidirect
236. C22×Q8C2×D151semidirect
246. C2×SD16C2×D151semidirect
247. C2×SD16C2×D151semidirect
252. C22×C8C2×D151semidirect
317. SD16C22⋊D151semidirect
359. Q8C2×C22⋊D151semidirect
396. C8C2×C22⋊D151semidirect
416. C22#18012766semidirect

Maximal subgroups

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

subgroupindex
C2×#180127662
#237528732
D4×C22⋊D1512
#237525982
#237524552
#237524482
#237524292
#237524102
#237523612
#237523562
#237523512
#237523462
#237523132
#237522832
C22×SD16×C1512
#3265151