Finite Group Databasebeta

← #34078599

Subgroups — #34078599

Order 19328.

500 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×#18012763C211yesmaximal, characteristic
3#124×D151C211yesmaximal, characteristic, complemented
4C4×#14559003C211yesmaximal, characteristic, complemented
5#23752437C211yesmaximal, characteristic, complemented
6#23752435C211yesmaximal, characteristic, complemented
7#23752433C211yesmaximal, characteristic, complemented
8#23752431C211yesmaximal, characteristic, complemented
9#23752429C211yesmaximal, characteristic, complemented
10#23752427C211yesmaximal, characteristic, complemented
11#23752425C211yesmaximal, characteristic, complemented
12#23752234C211yesmaximal, characteristic, complemented
13#23752219C211yesmaximal, characteristic, complemented
14#23752215C211yesmaximal, characteristic, complemented
15#463×C151C211yesmaximal, characteristic, complemented
16C2×#14559003C2211yescharacteristic
17C2×Q8×D151C2211yescharacteristic
18C2×D4×D151C2211yescharacteristic
19#18012768—24no—
20#18012763—24no—
21C2×Dic604C2211yescharacteristic, complemented
22C2×#14558994C2211yescharacteristic, complemented
23C2×#14558993C2211yescharacteristic
24C2×#14558992C2211yescharacteristic
25C2×#14558992C2211yescharacteristic, complemented
26C2×#14558989C2211yescharacteristic
27C2×#14558987C2211yescharacteristic
28C2×#14558987C2211yescharacteristic
29#18012728C2211yescharacteristic
30#18012727C2211yescharacteristic
31#18012726C2211yescharacteristic
32#18012725—21no—
33#18012725—21no—
34C4×Dic302C2211yescharacteristic, complemented
35#18012704C2211yescharacteristic, complemented
36D4×Dic151C2211yescharacteristic, complemented
37C4×C22⋊D151—21no—
38(C22⋊D151)⋊C4—21no—
39#18012697C2211yescharacteristic
40#18012695—21no—
41C22⋊C4×D151—21no—
42C22⋊C4×D151—21no—
43C2×C4×Dic151—21no—
44C42×D151C2211yescharacteristic
45C4⋊(C151⋊C8)C2211yescharacteristic, complemented
46Dic151⋊C8C2211yescharacteristic, complemented
47Dic151⋊C8C2211yescharacteristic, complemented
48#18012664C2211yescharacteristic, complemented
49#18012663C2211yescharacteristic, complemented
50#18012662C2211yescharacteristic, complemented
51#18012661C2211yescharacteristic
52#18012660C2211yescharacteristic
53#18012659C2211yescharacteristic
54C2×SD16×C151C2211yescharacteristic, complemented
55C2×D8×C151C2211yescharacteristic
56#124×C151C2211yescharacteristic
57C4×D4×C151C2211yescharacteristic, complemented
58C4⋊C8×C151C2211yescharacteristic, complemented
59#103×C151C2211yescharacteristic, complemented
60#102×C151C2211yescharacteristic
61C23×D151—21no—
62#14559003—22no—
63#14559003D414yes—
64C2×Dic302—21no—
65C2×Dic302C2311yescharacteristic
66C2×Dic302C2311yescharacteristic
67Q8×D151—22no—
68Q8×D151—22no—
69C2×D604C2311yescharacteristic
70C2×C22⋊D151—21no—
71C2×C22⋊D151—21no—
72D4×D151—22no—
73D4×D151—22no—
74C22×Dic151—21no—
75C22×Dic151—21no—
76C2×C4×D151—21no—
77C2×C4×D151D411yescharacteristic
78C2×C4×D151D411yescharacteristic
79C2×C4×D151C2311yescharacteristic
80Dic604—22no—
81#14558994—22no—
82#14558993—22no—
83#14558992—22no—
84#14558992—22no—
85#14558989—22no—
86#14558987—22no—
87#14558987—22no—
88C2×C151⋊C8C2311yescharacteristic
89C2×C151⋊C8C2311yescharacteristic
90C4⋊Dic151C2311yescharacteristic
91Dic151⋊C4—21no—
92Dic151⋊C4—21no—
93C22⋊Dic151—21no—
94C22⋊Dic151—21no—
95C22⋊Dic151—21no—
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—
101C4×Dic151—21no—
102C4×Dic151—21no—
103C4×Dic151—21no—
104C4×Dic151D411yescharacteristic
105C4×Dic151D411yescharacteristic
106C4×Dic151C2311yescharacteristic
107C2×Q8×C151C2311yescharacteristic
108C2×D4×C151C2311yescharacteristic
109C2×D4×C151C2311yescharacteristic
110C22×C4×C151—21no—
111SD16×C151—22no—
112D8×C151—22no—
113C2×C8×C151C2311yescharacteristic
114C2×C8×C151C2311yescharacteristic
115C4⋊C4×C151C2311yescharacteristic
116C22⋊C4×C151—21no—
117C22⋊C4×C151—21no—
118C22⋊C4×C151—21no—
119C42×C151C2311yescharacteristic
120C22×D151—21no—
121C22×D151—42no—
122C22×D151—42no—
123C22×D151—42no—
124C22×D151C2×D411yescharacteristic
125Dic302—21no—
126Dic302—21no—
127Dic302—21no—
128Dic302—42no—
129Dic302C2×D412yes—
130D604—21no—
131D604—21no—
132C22⋊D151—24no—
133C22⋊D151—42no—
134C2×Dic151—21no—
135C2×Dic151—24no—
136C2×Dic151—21no—
137C2×Dic151—21no—
138C2×Dic151—42no—
139C2×Dic151C2×D411yescharacteristic
140C2×Dic151C2×D411yescharacteristic
141C2×Dic151C2×D411yescharacteristic
142C4×D151—41no—
143C4×D151—41no—
144C4×D151—42no—
145C4×D151C2×D412yes—
146C4×D151#4112yes—
147C151⋊C8—21no—
148C151⋊C8—21no—
149C23×C151—21no—
150C23×C151—21no—
151Q8×C151—21no—
152Q8×C151—21no—
153D4×C151—21no—
154D4×C151—21no—
155D4×C151—21no—
156D4×C151C2×D412yes—
157C2×C4×C151—21no—
158C2×C4×C151—21no—
159C2×C4×C151—42no—
160C2×C4×C151C2×D411yescharacteristic
161C2×C4×C151C2×D411yescharacteristic
162C2×C4×C151C2411yescharacteristic
163C8×C151—21no—
164C8×C151—21no—
165C22×C151—22no—
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—21no—
180C4×C151—21no—
181C4×C151—41no—
182C4×C151—41no—
183C4×C151C22×D411yescharacteristic
184C4×C151C2×#4111yescharacteristic
185Dic151—22no—
186Dic151—21no—
187Dic151—21no—
188Dic151—41no—
189Dic151—41no—
190Dic151#12112yes—
191C2×C151—42no—
192C2×C151—81no—
193C2×C151C2×#12111yescharacteristic
194C2×C151#57511yescharacteristic
195C2×C151#57511yescharacteristic
196D151—22no—
197D151—81no—
198C151#304011yescharacteristic, complemented, Sylow
199#3040—1511nomaximal, Sylow
200C2×#137—1511no—
201C2×AGL(1,ℤ/8)—1511no—
202C2×#124—1511no—
203C4×#41—1511no—
204#464—1511no—
205#464—1511no—
206#464—1511no—
207#464—1511no—
208#463—1511no—
209#463—1511no—
210#463—1511no—
211#463D15111yescharacteristic, complemented
212#423—1511no—
213#419—1511no—
214#418—1511no—
215C2×#41—1511no—
216C22×Q8—1511no—
217C22×D4—1511no—
218#137—3024no—
219AGL(1,ℤ/8)—3024no—
220C2×Q16—1511no—
221C2×Q16—1511no—
222C2×SD16—1511no—
223C2×SD16—1511no—
224C2×SD16—1511no—
225C2×SD16C2×D15111yescharacteristic, complemented
226C2×D8—1511no—
227C2×D8C2×D15111yescharacteristic
228C2×M16—1511no—
229C2×M16—1511no—
230#124—3021no—
231#124—3021no—
232#124—1511no—
233#124—1511no—
234#124—1511no—
235#124C2×D15111yescharacteristic
236C4×Q8—1511no—
237C4×Q8—1511no—
238C4×D4—3021no—
239C4×D4—3021no—
240C4×D4—1511no—
241C4×D4C2×D15111yescharacteristic, complemented
242#117—3021no—
243#117—1511no—
244C2×C22⋊C4—3021no—
245C2×C22⋊C4—3021no—
246C2×C42—3021no—
247C2×C42—1511no—
248C4⋊C8—1511no—
249C4⋊C8—1511no—
250C4⋊C8—1511no—
251C4⋊C8C2×D15111yescharacteristic, complemented
252#103—1511no—
253#103—1511no—
254#103—1511no—
255#103C2×D15111yescharacteristic, complemented
256#102—1511no—
257#102—1511no—
258#102—1511no—
259#102C2×D15111yescharacteristic
260C24—3021no—
261#41—3022no—
262#41—1514no—
263C2×Q8—3021no—
264C2×Q8—3022no—
265C2×Q8—3022no—
266C2×Q8—1511no—
267C2×Q8—1511no—
268C2×Q8C22×D15111yescharacteristic
269C2×D4—3021no—
270C2×D4—3022no—
271C2×D4—3022no—
272C2×D4—3021no—
273C2×D4—1511no—
274C2×D4C22×D15111yescharacteristic
275C2×D4C22×D15111yescharacteristic
276C22×C4—21no—
277C22×C4—3021no—
278C22×C4—3021no—
279C22×C4—3021no—
280C22×C4—1511no—
281C22×C4—1511no—
282C22×C4—1511no—
283Q16—3022no—
284Q16—3022no—
285SD16—22no—
286SD16—3022no—
287SD16—3022no—
288SD16—3022no—
289D8—22no—
290D8—3022no—
291M16—3022no—
292M16—3022no—
293C2×C8—1511no—
294C2×C8—1511no—
295C2×C8C22×D15111yescharacteristic
296C2×C8C22×D15111yescharacteristic
297C4⋊C4—3021no—
298C4⋊C4—3021no—
299C4⋊C4—1511no—
300C4⋊C4C22×D15111yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—21no—
303C22⋊C4—21no—
304C22⋊C4—3021no—
305C22⋊C4—3021no—
306C22⋊C4—3021no—
307C22⋊C4—3021no—
308C22⋊C4—3021no—
309C22⋊C4—3021no—
310C22⋊C4—3021no—
311C22⋊C4—3021no—
312C42—3021no—
313C42—3021no—
314C42—3021no—
315C42—1511no—
316C42—1511no—
317C42—1511no—
318C42C22×D15111yescharacteristic
319C23—21no—
320C23—21no—
321C23—3021no—
322C23—6042no—
323C23—6042no—
324C23—6042no—
325C23—1511no—
326Q8—21no—
327Q8—21no—
328Q8—3021no—
329Q8—3021no—
330Q8—3021no—
331Q8—6042no—
332Q8—1512no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—3024no—
337D4—3021no—
338D4—3021no—
339D4—6042no—
340D4D4×D15112yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—42no—
344C2×C4—3021no—
345C2×C4—3024no—
346C2×C4—3021no—
347C2×C4—3021no—
348C2×C4—6041no—
349C2×C4—6041no—
350C2×C4—6042no—
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—22no—
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—41no—
381C4—41no—
382C4—3021no—
383C4—3021no—
384C4—3022no—
385C4—6041no—
386C4—6041no—
387C4—1512no—
388C4C2×D4×D15111yescharacteristic
389C4#41×D15111yescharacteristic
390C2—42no—
391C2—81no—
392C2—3022no—
393C2—12081no—
394C2#121×D15111yescharacteristic
395C2#2375300811yescharacteristic
396C2#2375300911yescharacteristic
subgroupG/H
centerC22C2×D4×D151
commutator, cosocleC2×C4×C151C24
FrattiniC2×C4C23×D151
Fitting#463×C151C2
socleC22×C151C22×D4
prime radicalC2×#18012763C2
hypercenter#463D151
hypocenterC151#3040
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×#18012768C2semidirect
3. #124×D151C2semidirect
4. C4×#14559003C2semidirect
5. #23752437C2semidirect
6. #23752435C2semidirect
7. #23752433C2semidirect
8. #23752431C2semidirect
9. #23752429C2semidirect
10. #23752427C2semidirect
11. #23752425C2semidirect
12. #23752234C2semidirect
13. #23752219C2semidirect
14. #23752215C2semidirect
15. #463×C151C2semidirect
21. C2×Dic604C22semidirect
22. C2×#14558994C22semidirect
25. C2×#14558992C22semidirect
34. C4×Dic302C22semidirect
35. #18012704C22semidirect
36. D4×Dic151C22semidirect
45. C4⋊(C151⋊C8)C22semidirect
46. Dic151⋊C8C22semidirect
47. Dic151⋊C8C22semidirect
48. #18012664C22semidirect
49. #18012663C22semidirect
50. #18012662C22semidirect
54. C2×SD16×C151C22semidirect
57. C4×D4×C151C22semidirect
58. C4⋊C8×C151C22semidirect
59. #103×C151C22semidirect
198. C151#3040semidirect
211. #463D151semidirect
225. C2×SD16C2×D151semidirect
241. C4×D4C2×D151semidirect
251. C4⋊C8C2×D151semidirect
255. #103C2×D151semidirect

Maximal subgroups

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

subgroupindex
C2×#180127682
C2×#180127632
#124×D1512
C4×#145590032
#237524372
#237524352
#237524332
#237524312
#237524292
#237524272
#237524252
#237522342
#237522192
#237522152
#463×C1512
#3040151