Finite Group Databasebeta

← #34080927

Subgroups — #34080927

Order 19328.

462 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23752920C211yesmaximal, characteristic, complemented
2D4×C22⋊D151C211yesmaximal, characteristic
3#23752557C211yesmaximal, characteristic, complemented
4#23752531C211yesmaximal, characteristic, complemented
5#23752529C211yesmaximal, characteristic, complemented
6#23752500C211yesmaximal, characteristic, complemented
7#23752443C211yesmaximal, characteristic, complemented
8#23752438C211yesmaximal, characteristic, complemented
9#23752410C211yesmaximal, characteristic, complemented
10#23752361C211yesmaximal, characteristic, complemented
11SD16×Dic151C211yesmaximal, characteristic, complemented
12(C22⋊D151)⋊C8C211yesmaximal, characteristic, complemented
13C2×#18012660C211yesmaximal, characteristic, complemented
14#102×D151C211yesmaximal, characteristic, complemented
15#450×C151C211yesmaximal, characteristic, complemented
16C22×C22⋊D151—21no—
17C2×D4×D151C2211yescharacteristic
18C2×#14558991C2211yescharacteristic, complemented
19C22×C151⋊C8C2211yescharacteristic, complemented
20C2×C8×D151C2211yescharacteristic, complemented
21#18012738C2211yescharacteristic, complemented
22#18012735C2211yescharacteristic
23#18012729—21no—
24#18012719—21no—
25#18012716—21no—
26#18012715C2211yescharacteristic, complemented
27#18012713C2211yescharacteristic
28#18012711—21no—
29#18012710C2211yescharacteristic
30#18012708—21no—
31#18012707—21no—
32Q8×Dic151C2211yescharacteristic, complemented
33D4×Dic151C2211yescharacteristic
34C4×C22⋊D151C2211yescharacteristic
35(C22⋊D151)⋊C4—21no—
36C2×C4⋊Dic151C2211yescharacteristic, complemented
37C4⋊C4×D151C2211yescharacteristic, complemented
38#18012671C2211yescharacteristic, complemented
39#18012671C2211yescharacteristic, complemented
40#18012670C2211yescharacteristic, complemented
41Dic151⋊C8C2211yescharacteristic, complemented
42#18012663C2211yescharacteristic, complemented
43#18012661C2211yescharacteristic, complemented
44#18012661C2211yescharacteristic, complemented
45#18012660C2211yescharacteristic
46#18012660C2211yescharacteristic
47#18012660C2211yescharacteristic, complemented
48#18012660C2211yescharacteristic, complemented
49#18012659C2211yescharacteristic, complemented
50(C2×D151)⋊C8C2211yescharacteristic, complemented
51C8×Dic151C2211yescharacteristic, complemented
52C22×D4×C151C2211yescharacteristic
53C2×SD16×C151C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic, complemented
55C22⋊Q8×C151C2211yescharacteristic, complemented
56#102×C151C2211yescharacteristic
57#102×C151C2211yescharacteristic, complemented
58C22⋊C8×C151C2211yescharacteristic, complemented
59C23×D151—21no—
60C2×Dic302—21no—
61C2×D604C2311yescharacteristic
62C2×C22⋊D151—21no—
63C2×C22⋊D151—21no—
64C2×C22⋊D151—21no—
65C2×C22⋊D151—21no—
66C2×C22⋊D151—21no—
67C2×C22⋊D151—44no—
68C2×C22⋊D151D411yescharacteristic
69D4×D151—22no—
70D4×D151—41no—
71C22×Dic151—21no—
72C22×Dic151—21no—
73C2×C4×D151—21no—
74C2×C4×D151C2311yescharacteristic
75#14558991—41no—
76C2×C151⋊C8—41no—
77C2×C151⋊C8C2311yescharacteristic
78C2×C151⋊C8C2311yescharacteristic
79C8×D151—41no—
80C4⋊Dic151—21no—
81C4⋊Dic151—21no—
82C4⋊Dic151C2311yescharacteristic
83C4⋊Dic151C2311yescharacteristic
84C4⋊Dic151C2311yescharacteristic
85Dic151⋊C4—21no—
86Dic151⋊C4—21no—
87Dic151⋊C4—21no—
88Dic151⋊C4D411yescharacteristic
89C22⋊Dic151—21no—
90C22⋊Dic151—21no—
91C22⋊Dic151D411yescharacteristic
92(C2×D151)⋊C4—21no—
93(C2×D151)⋊C4—21no—
94(C2×D151)⋊C4D411yescharacteristic
95C4×Dic151—21no—
96C4×Dic151C2311yescharacteristic
97C24×C151—21no—
98C2×Q8×C151C2311yescharacteristic
99C2×D4×C151—22no—
100C2×D4×C151—21no—
101C2×D4×C151—41no—
102C2×D4×C151C2311yescharacteristic
103C2×D4×C151C2311yescharacteristic
104C22×C4×C151C2311yescharacteristic
105SD16×C151—22no—
106SD16×C151—41no—
107C2×C8×C151C2311yescharacteristic
108C2×C8×C151C2311yescharacteristic
109C4⋊C4×C151—21no—
110C4⋊C4×C151C2311yescharacteristic
111C22⋊C4×C151—21no—
112C22×D151—21no—
113C22×D151—42no—
114C22×D151—42no—
115C22×D151—81no—
116C22×D151C2×D411yescharacteristic
117Dic302—81no—
118D604—21no—
119D604—21no—
120C22⋊D151—42no—
121C22⋊D151—42no—
122C22⋊D151—42no—
123C22⋊D151—42no—
124C22⋊D151—81no—
125C22⋊D151SD1614yescomplemented
126C2×Dic151—21no—
127C2×Dic151—21no—
128C2×Dic151—21no—
129C2×Dic151—42no—
130C2×Dic151—81no—
131C2×Dic151C2×D411yescharacteristic
132C2×Dic151C2×D411yescharacteristic
133C2×Dic151C2×D411yescharacteristic
134C4×D151—21no—
135C4×D151—21no—
136C4×D151—81no—
137C151⋊C8—21no—
138C151⋊C8—21no—
139C23×C151—21no—
140C23×C151—21no—
141C23×C151—42no—
142C23×C151—42no—
143C23×C151—81no—
144C23×C151C2×D411yescharacteristic
145Q8×C151—21no—
146Q8×C151—21no—
147D4×C151—21no—
148D4×C151—21no—
149D4×C151—21no—
150D4×C151—42no—
151D4×C151#4112yes—
152C2×C4×C151—21no—
153C2×C4×C151—21no—
154C2×C4×C151—21no—
155C2×C4×C151—21no—
156C2×C4×C151C2×D411yescharacteristic
157C2×C4×C151C2411yescharacteristic
158C8×C151—21no—
159C8×C151—21no—
160C22×C151—21no—
161C22×C151—21no—
162C22×C151—22no—
163C22×C151—41no—
164C22×C151—41no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—84no—
169C22×C151C2×SD1612yes—
170C22×C151C22×D411yescharacteristic
171C2×D151—21no—
172C2×D151—21no—
173C2×D151—41no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—84no—
177C2×D151C2×SD1612yes—
178C4×C151—21no—
179C4×C151—41no—
180C4×C151—41no—
181C4×C151C2×#4111yescharacteristic
182C4×C151H(5,𝔽2)11yescharacteristic
183Dic151—21no—
184Dic151—21no—
185Dic151—41no—
186Dic151—41no—
187Dic151—41no—
188Dic151C2×SD1612yes—
189C2×C151—22no—
190C2×C151—42no—
191C2×C151—81no—
192C2×C151#54611yescharacteristic
193C2×C151C22×SD1611yescharacteristic
194C2×C151#57611yescharacteristic
195D151—22no—
196D151—81no—
197C151#329511yescharacteristic, complemented, Sylow
198#3295—1511nomaximal, Sylow
199#554—1511no—
200D42—1511no—
201#486—1511no—
202#481—1511no—
203#481—1511no—
204#476—1511no—
205#465—1511no—
206#465—1511no—
207#460—1511no—
208#450—1511no—
209#450D15111yescharacteristic, complemented
210C4×SD16—1511no—
211C8×D4—1511no—
212C2×#102—1511no—
213C2×#102—1511no—
214C22×D4—3021no—
215C22×D4—1511no—
216C22×D4C2×D15111yescharacteristic
217C2×SD16—1511no—
218C2×SD16C2×D15111yescharacteristic
219C2×SD16C2×D15111yescharacteristic, complemented
220C22×C8—1511no—
221C22×C8—1511no—
222C4⋊Q8—1511no—
223#127—1511no—
224#125—3021no—
225C22⋊Q8—3021no—
226C22⋊Q8—3021no—
227C22⋊Q8—1511no—
228C22⋊Q8C2×D15111yescharacteristic, complemented
229#121—3021no—
230#121—1511no—
231#121—1511no—
232#120—3021no—
233#120—3021no—
234C4×Q8—1511no—
235C4×D4—3021no—
236C4×D4—1511no—
237C4×D4—1511no—
238C2×C4⋊C4—1511no—
239C2×C4⋊C4—1511no—
240#106—1511no—
241#106—1511no—
242#106—1511no—
243C4⋊C8—1511no—
244#103—1511no—
245#102—1511no—
246#102—1511no—
247#102—1511no—
248#102—1511no—
249#102—1511no—
250#102—1511no—
251#102—1511no—
252#102C2×D15111yescharacteristic
253#102C2×D15111yescharacteristic, complemented
254C22⋊C8—1511no—
255C22⋊C8C2×D15111yescharacteristic, complemented
256C4×C8—1511no—
257C24—21no—
258C24—3021no—
259C2×Q8—3021no—
260C2×Q8C22×D15111yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—3022no—
265C2×D4—3021no—
266C2×D4—3021no—
267C2×D4—3021no—
268C2×D4—3021no—
269C2×D4—3021no—
270C2×D4—6041no—
271C2×D4—6044no—
272C2×D4—1511no—
273C2×D4—1511no—
274C2×D4C22×D15111yescharacteristic
275C2×D4C22×D15111yescharacteristic
276C22×C4—3021no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—1511no—
280C22×C4C22×D15111yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—6041no—
284C2×C8—6041no—
285C2×C8—6041no—
286C2×C8—1511no—
287C2×C8—1511no—
288C2×C8C22×D15111yescharacteristic
289C2×C8C22×D15111yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3021no—
292C4⋊C4—3021no—
293C4⋊C4—3021no—
294C4⋊C4—3021no—
295C4⋊C4—3021no—
296C4⋊C4—1511no—
297C4⋊C4—1511no—
298C4⋊C4—1511no—
299C4⋊C4—1511no—
300C4⋊C4C22×D15111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—3021no—
303C22⋊C4—3021no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—1511no—
307C22⋊C4—1511no—
308C42—3021no—
309C42—1511no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—3021no—
316C23—6042no—
317C23—6042no—
318C23—1511no—
319C23—12081no—
320C23D4×D15111yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—12081no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—3021no—
329D4—3021no—
330D4—6042no—
331D4—6042no—
332D4—6042no—
333D4—6042no—
334D4—1514no—
335D4—12081no—
336D4#1455900312yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3021no—
342C2×C4—3021no—
343C2×C4—3021no—
344C2×C4—3021no—
345C2×C4—3021no—
346C2×C4—6042no—
347C2×C4—1511no—
348C2×C4—1511no—
349C2×C4—1511no—
350C2×C4—12081no—
351C2×C4—12081no—
352C2×C4D4×D15111yescharacteristic
353C2×C4C23×D15111yescharacteristic
354C8—21no—
355C8—21no—
356C8—3021no—
357C8—3021no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—3021no—
368C22—3021no—
369C22—6041no—
370C22—6041no—
371C22—6041no—
372C22—1512no—
373C22—12084no—
374C22SD16×D15112yes—
375C22C2×D4×D15111yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3021no—
380C4—3021no—
381C4—6041no—
382C4—6041no—
383C4—6041no—
384C4—1512no—
385C4C2×#1455900311yescharacteristic
386C4#1801278411yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—3022no—
391C2—12081no—
392C2#2375284911yescharacteristic
393C2C2×SD16×D15111yescharacteristic
394C2#2375301611yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#450×C151C2
socleC22×C151C22×D4
prime radicalD4×C22⋊D151C2
hypercenter#450D151
hypocenterC151#3295
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23752920C2semidirect
3. #23752557C2semidirect
4. #23752531C2semidirect
5. #23752529C2semidirect
6. #23752500C2semidirect
7. #23752443C2semidirect
8. #23752438C2semidirect
9. #23752410C2semidirect
10. #23752361C2semidirect
11. SD16×Dic151C2semidirect
12. (C22⋊D151)⋊C8C2semidirect
13. C2×#18012660C2semidirect
14. #102×D151C2semidirect
15. #450×C151C2semidirect
18. C2×#14558991C22semidirect
19. C22×C151⋊C8C22semidirect
20. C2×C8×D151C22semidirect
21. #18012738C22semidirect
26. #18012715C22semidirect
32. Q8×Dic151C22semidirect
36. C2×C4⋊Dic151C22semidirect
37. C4⋊C4×D151C22semidirect
38. #18012671C22semidirect
39. #18012671C22semidirect
40. #18012670C22semidirect
41. Dic151⋊C8C22semidirect
42. #18012663C22semidirect
43. #18012661C22semidirect
44. #18012661C22semidirect
47. #18012660C22semidirect
48. #18012660C22semidirect
49. #18012659C22semidirect
50. (C2×D151)⋊C8C22semidirect
51. C8×Dic151C22semidirect
54. C2×SD16×C151C22semidirect
55. C22⋊Q8×C151C22semidirect
57. #102×C151C22semidirect
58. C22⋊C8×C151C22semidirect
125. C22⋊D151SD16semidirect
197. C151#3295semidirect
209. #450D151semidirect
219. C2×SD16C2×D151semidirect
228. C22⋊Q8C2×D151semidirect
253. #102C2×D151semidirect
255. C22⋊C8C2×D151semidirect

Maximal subgroups

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

subgroupindex
#237529202
D4×C22⋊D1512
#237525572
#237525312
#237525292
#237525002
#237524432
#237524382
#237524102
#237523612
SD16×Dic1512
(C22⋊D151)⋊C82
C2×#180126602
#102×D1512
#450×C1512
#3295151