Finite Group Databasebeta

← #34078626

Subgroups — #34078626

Order 19328.

490 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#18012768C211yesmaximal, characteristic, complemented
2C2×SD16×D151C211yesmaximal, characteristic, complemented
3#23752775C211yesmaximal, characteristic
4#23752688C211yesmaximal, characteristic, complemented
5#23752435C211yesmaximal, characteristic, complemented
6#23752434C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752432C211yesmaximal, characteristic, complemented
9#23752411C211yesmaximal, characteristic, complemented
10#23752410C211yesmaximal, characteristic, complemented
11#23752409C211yesmaximal, characteristic, complemented
12#23752237C211yesmaximal, characteristic, complemented
13#23752215C211yesmaximal, characteristic, complemented
14#23752205C211yesmaximal, characteristic, complemented
15#460×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012768—24no—
20C2×Dic604C2211yescharacteristic, complemented
21C2×#14558994C2211yescharacteristic, complemented
22C2×#14558993C2211yescharacteristic
23C2×#14558992C2211yescharacteristic
24C2×#14558992C2211yescharacteristic, complemented
25C2×#14558991C2211yescharacteristic
26SD16×D151—24no—
27C2×#14558987C2211yescharacteristic
28C2×C8×D151C2211yescharacteristic
29#18012735C2211yescharacteristic
30#18012727C2211yescharacteristic
31#18012726C2211yescharacteristic
32#18012711—21no—
33#18012711—21no—
34#18012707—21no—
35#18012707—21no—
36Q8×Dic151C2211yescharacteristic, complemented
37C4×Dic302—21no—
38C4×Dic302C2211yescharacteristic, complemented
39#18012704—21no—
40#18012704C2211yescharacteristic, complemented
41#18012697—21no—
42#18012697C2211yescharacteristic
43#18012696—21no—
44#18012696C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012662C2211yescharacteristic, complemented
50#18012661C2211yescharacteristic
51#18012660C2211yescharacteristic
52#18012660C2211yescharacteristic, complemented
53#18012659C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic
55C2×SD16×C151C2211yescharacteristic, complemented
56#127×C151C2211yescharacteristic
57C4×Q8×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#102×C151C2211yescharacteristic
60#102×C151C2211yescharacteristic, complemented
61C23×D151—21no—
62#14559003—22no—
63#14559003—22no—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151D414yescomplemented
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72C2×C22⋊D151—21no—
73C2×C22⋊D151—21no—
74D4×D151—22no—
75D4×D151—22no—
76C22×Dic151—21no—
77C2×C4×D151—21no—
78C2×C4×D151C2311yescharacteristic
79Dic604—22no—
80#14558994—22no—
81#14558993—22no—
82#14558992—22no—
83#14558992—22no—
84#14558991—22no—
85#14558987—22no—
86C2×C151⋊C8C2311yescharacteristic
87C2×C151⋊C8C2311yescharacteristic
88C8×D151—22no—
89C4⋊Dic151—21no—
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93Dic151⋊C4D411yescharacteristic
94Dic151⋊C4D411yescharacteristic
95C22⋊Dic151—21no—
96C22⋊Dic151—21no—
97(C2×D151)⋊C4—21no—
98(C2×D151)⋊C4—21no—
99(C2×D151)⋊C4—21no—
100(C2×D151)⋊C4D411yescharacteristic
101(C2×D151)⋊C4D411yescharacteristic
102C4×Dic151—21no—
103C4×Dic151—21no—
104C4×Dic151—21no—
105C4×Dic151—21no—
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151—21no—
109C2×D4×C151—21no—
110C2×D4×C151C2311yescharacteristic
111C2×D4×C151C2311yescharacteristic
112SD16×C151—22no—
113SD16×C151—22no—
114C2×C8×C151C2311yescharacteristic
115C2×C8×C151C2311yescharacteristic
116C4⋊C4×C151—21no—
117C4⋊C4×C151C2311yescharacteristic
118C42×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—42no—
122C22×D151—81no—
123C22×D151—81no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—24no—
127Dic302—21no—
128Dic302—21no—
129Dic302C2×D412yes—
130D604—21no—
131D604—21no—
132C22⋊D151—42no—
133C22⋊D151—42no—
134C22⋊D151—81no—
135C22⋊D151—81no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—21no—
139C2×Dic151—42no—
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C2×Dic151C2×D411yescharacteristic
143C4×D151—24no—
144C4×D151C2×D412yes—
145C4×D151#4112yes—
146C151⋊C8—21no—
147C151⋊C8—21no—
148C23×C151—21no—
149C23×C151—21no—
150Q8×C151—21no—
151Q8×C151C2×D412yes—
152D4×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151—81no—
157D4×C151—81no—
158C2×C4×C151—21no—
159C2×C4×C151—21no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2×D411yescharacteristic
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—41no—
166C22×C151—41no—
167C22×C151—41no—
168C22×C151—41no—
169C22×C151—41no—
170C22×C151—41no—
171C22×C151C22×D411yescharacteristic
172C2×D151—21no—
173C2×D151—21no—
174C2×D151—41no—
175C2×D151—41no—
176C2×D151—41no—
177C2×D151—84no—
178C2×D151#12112yes—
179C4×C151—22no—
180C4×C151—21no—
181C4×C151—21no—
182C4×C151—41no—
183C4×C151C22×D411yescharacteristic
184C4×C151C2×#4111yescharacteristic
185Dic151—22no—
186Dic151—21no—
187Dic151—21no—
188Dic151—41no—
189Dic151—41no—
190Dic151#12112yes—
191C2×C151—81no—
192C2×C151—81no—
193C2×C151C2×#12111yescharacteristic
194C2×C151#57711yescharacteristic
195C2×C151#57711yescharacteristic
196D151—22no—
197D151—81no—
198C151#304311yescharacteristic, complemented, Sylow
199#3043—1511nomaximal, Sylow
200C2×#137—1511no—
201C22×SD16—1511no—
202#535—1511no—
203#519—1511no—
204#464—1511no—
205#464—1511no—
206#464—1511no—
207#464—1511no—
208#460—1511no—
209#460—1511no—
210#460—1511no—
211#460D15111yescharacteristic, complemented
212#424—1511no—
213#418—1511no—
214#416—1511no—
215C2×#41—1511no—
216C22×Q8—1511no—
217C22×D4—1511no—
218#137—3024no—
219C2×Q16—1511no—
220C2×Q16—1511no—
221C2×SD16—3024no—
222C2×SD16—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×SD16—1511no—
226C2×SD16C2×D15111yescharacteristic
227C2×SD16C2×D15111yescharacteristic, complemented
228C2×M16—1511no—
229C22×C8—1511no—
230#127—1511no—
231#127C2×D15111yescharacteristic
232#124—1511no—
233#124—1511no—
234#121—3021no—
235#121—3021no—
236#120—3021no—
237#120—3021no—
238C4×Q8—3021no—
239C4×Q8—3021no—
240C4×Q8—1511no—
241C4×Q8—1511no—
242C4×Q8—1511no—
243C4×Q8C2×D15111yescharacteristic, complemented
244#117—3021no—
245#117—3021no—
246#117—1511no—
247#117—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8—1511no—
251C4⋊C8C2×D15111yescharacteristic, complemented
252#103—1511no—
253#103—1511no—
254#102—1511no—
255#102—1511no—
256#102—1511no—
257#102—1511no—
258#102C2×D15111yescharacteristic
259#102C2×D15111yescharacteristic, complemented
260C24—3021no—
261#41—3022no—
262#41—3022no—
263C2×Q8—3021no—
264C2×Q8—3022no—
265C2×Q8—1514no—
266C2×Q8—1511no—
267C2×Q8—1511no—
268C2×Q8C22×D15111yescharacteristic
269C2×D4—21no—
270C2×D4—21no—
271C2×D4—3021no—
272C2×D4—3022no—
273C2×D4—3022no—
274C2×D4—3021no—
275C2×D4—3021no—
276C2×D4—3021no—
277C2×D4—1511no—
278C2×D4C22×D15111yescharacteristic
279C2×D4C22×D15111yescharacteristic
280C22×C4—3021no—
281C22×C4—3021no—
282C22×C4—1511no—
283Q16—3022no—
284Q16—3022no—
285SD16—22no—
286SD16—22no—
287SD16—3022no—
288SD16—3022no—
289SD16—3022no—
290SD16—3022no—
291M16—3022no—
292C2×C8—3022no—
293C2×C8—1511no—
294C2×C8—1511no—
295C2×C8C22×D15111yescharacteristic
296C2×C8C22×D15111yescharacteristic
297C4⋊C4—21no—
298C4⋊C4—3021no—
299C4⋊C4—3021no—
300C4⋊C4—3021no—
301C4⋊C4—1511no—
302C4⋊C4—1511no—
303C4⋊C4—1511no—
304C4⋊C4C22×D15111yescharacteristic
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—1511no—
311C22⋊C4—1511no—
312C42—21no—
313C42—3021no—
314C42—3021no—
315C42—3021no—
316C42—3021no—
317C42—1511no—
318C42C22×D15111yescharacteristic
319C23—21no—
320C23—21no—
321C23—3021no—
322C23—6042no—
323C23—1511no—
324C23—12081no—
325C23—12081no—
326Q8—21no—
327Q8—3024no—
328Q8—3021no—
329Q8—3021no—
330Q8—3021no—
331Q8—1512no—
332Q8D4×D15112yes—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—21no—
337D4—81no—
338D4—81no—
339D4—3021no—
340D4—3021no—
341D4—6042no—
342D4—6042no—
343D4—12081no—
344D4—12081no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—3024no—
348C2×C4—3021no—
349C2×C4—3021no—
350C2×C4—3021no—
351C2×C4—6042no—
352C2×C4—1511no—
353C2×C4—1511no—
354C2×C4—1511no—
355C2×C4—1512no—
356C2×C4—1512no—
357C2×C4D4×D15111yescharacteristic
358C2×C4D4×D15111yescharacteristic
359C2×C4C23×D15111yescharacteristic
360C8—21no—
361C8—21no—
362C8—3021no—
363C8—3021no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—3021no—
371C22—3021no—
372C22—6041no—
373C22—6041no—
374C22—6041no—
375C22—1512no—
376C22—12084no—
377C22C2×D4×D15111yescharacteristic
378C4—21no—
379C4—21no—
380C4—22no—
381C4—41no—
382C4—3021no—
383C4—3021no—
384C4—3022no—
385C4—6041no—
386C4—6041no—
387C4—1512no—
388C4C2×D4×D15111yescharacteristic
389C4#41×D15111yescharacteristic
390C2—81no—
391C2—81no—
392C2—3022no—
393C2—12081no—
394C2#121×D15111yescharacteristic
395C2#2375301811yescharacteristic
396C2#2375302211yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#460×C151C2
socleC22×C151C22×D4
prime radical#23752775C2
hypercenter#460D151
hypocenterC151#3043
LCSG ▷ C2×C4×C151 ▷ C2×C151 ▷ C151
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. C2×#18012768C2semidirect
2. C2×SD16×D151C2semidirect
4. #23752688C2semidirect
5. #23752435C2semidirect
6. #23752434C2semidirect
7. #23752433C2semidirect
8. #23752432C2semidirect
9. #23752411C2semidirect
10. #23752410C2semidirect
11. #23752409C2semidirect
12. #23752237C2semidirect
13. #23752215C2semidirect
14. #23752205C2semidirect
15. #460×C151C2semidirect
20. C2×Dic604C22semidirect
21. C2×#14558994C22semidirect
24. C2×#14558992C22semidirect
36. Q8×Dic151C22semidirect
38. C4×Dic302C22semidirect
40. #18012704C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012662C22semidirect
52. #18012660C22semidirect
55. C2×SD16×C151C22semidirect
57. C4×Q8×C151C22semidirect
58. C4⋊C8×C151C22semidirect
60. #102×C151C22semidirect
68. Q8×D151D4semidirect
198. C151#3043semidirect
211. #460D151semidirect
227. C2×SD16C2×D151semidirect
243. C4×Q8C2×D151semidirect
251. C4⋊C8C2×D151semidirect
259. #102C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C2×SD16×D1512
#237527752
#237526882
#237524352
#237524342
#237524332
#237524322
#237524112
#237524102
#237524092
#237522372
#237522152
#237522052
#460×C1512
#3043151