Finite Group Databasebeta

← #34111953

Subgroups — #34111953

Order 20096.

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#23757981C211yesmaximal, characteristic, complemented
2D4×C22⋊D157C211yesmaximal, characteristic
3#23757618C211yesmaximal, characteristic, complemented
4#23757592C211yesmaximal, characteristic, complemented
5#23757590C211yesmaximal, characteristic, complemented
6#23757561C211yesmaximal, characteristic, complemented
7#23757504C211yesmaximal, characteristic, complemented
8#23757499C211yesmaximal, characteristic, complemented
9#23757471C211yesmaximal, characteristic, complemented
10#23757422C211yesmaximal, characteristic, complemented
11SD16×Dic157C211yesmaximal, characteristic, complemented
12#23757336C211yesmaximal, characteristic, complemented
13C2×#19097692C211yesmaximal, characteristic, complemented
14#102×D157C211yesmaximal, characteristic, complemented
15#450×C157C211yesmaximal, characteristic, complemented
16C22×C22⋊D157—21no—
17C2×D4×D157C2211yescharacteristic
18C2×#14578941C2211yescharacteristic, complemented
19C22×#11929434C2211yescharacteristic, complemented
20C2×C8×D157C2211yescharacteristic, complemented
21#19097770C2211yescharacteristic, complemented
22#19097767C2211yescharacteristic
23#19097761—21no—
24#19097751—21no—
25#19097748—21no—
26#19097747C2211yescharacteristic, complemented
27#19097745C2211yescharacteristic
28#19097743—21no—
29#19097742C2211yescharacteristic
30#19097740—21no—
31#19097739—21no—
32Q8×Dic157C2211yescharacteristic, complemented
33D4×Dic157C2211yescharacteristic
34C4×C22⋊D157C2211yescharacteristic
35#19097731—21no—
36C2×C4⋊Dic157C2211yescharacteristic, complemented
37C4⋊C4×D157C2211yescharacteristic, complemented
38#19097703C2211yescharacteristic, complemented
39#19097703C2211yescharacteristic, complemented
40#19097702C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097695C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic, complemented
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097692C2211yescharacteristic, complemented
48#19097692C2211yescharacteristic, complemented
49#19097691C2211yescharacteristic, complemented
50#19097683C2211yescharacteristic, complemented
51C8×Dic157C2211yescharacteristic, complemented
52C22×D4×C157C2211yescharacteristic
53C2×SD16×C157C2211yescharacteristic
54C2×SD16×C157C2211yescharacteristic, complemented
55C22⋊Q8×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic, complemented
58C22⋊C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60C2×Dic314—21no—
61C2×D628C2311yescharacteristic
62C2×C22⋊D157—21no—
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—44no—
68C2×C22⋊D157D411yescharacteristic
69D4×D157—22no—
70D4×D157—41no—
71C22×Dic157—21no—
72C22×Dic157—21no—
73C2×C4×D157—21no—
74C2×C4×D157C2311yescharacteristic
75#14578941—41no—
76C2×#11929434—41no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C8×D157—41no—
80C4⋊Dic157—21no—
81C4⋊Dic157—21no—
82C4⋊Dic157C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86#14578933—21no—
87#14578933—21no—
88#14578933D411yescharacteristic
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91C22⋊Dic157D411yescharacteristic
92#14578931—21no—
93#14578931—21no—
94#14578931D411yescharacteristic
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C24×C157—21no—
98C2×Q8×C157C2311yescharacteristic
99C2×D4×C157—22no—
100C2×D4×C157—21no—
101C2×D4×C157—41no—
102C2×D4×C157C2311yescharacteristic
103C2×D4×C157C2311yescharacteristic
104C22×C4×C157C2311yescharacteristic
105SD16×C157—22no—
106SD16×C157—41no—
107C2×C8×C157C2311yescharacteristic
108C2×C8×C157C2311yescharacteristic
109C4⋊C4×C157—21no—
110C4⋊C4×C157C2311yescharacteristic
111C22⋊C4×C157—21no—
112C22×D157—21no—
113C22×D157—42no—
114C22×D157—42no—
115C22×D157—81no—
116C22×D157C2×D411yescharacteristic
117Dic314—81no—
118D628—21no—
119D628—21no—
120C22⋊D157—42no—
121C22⋊D157—42no—
122C22⋊D157—42no—
123C22⋊D157—42no—
124C22⋊D157—81no—
125C22⋊D157SD1614yescomplemented
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—21no—
129C2×Dic157—42no—
130C2×Dic157—81no—
131C2×Dic157C2×D411yescharacteristic
132C2×Dic157C2×D411yescharacteristic
133C2×Dic157C2×D411yescharacteristic
134C4×D157—21no—
135C4×D157—21no—
136C4×D157—81no—
137#11929434—21no—
138#11929434—21no—
139C23×C157—21no—
140C23×C157—21no—
141C23×C157—42no—
142C23×C157—42no—
143C23×C157—81no—
144C23×C157C2×D411yescharacteristic
145Q8×C157—21no—
146Q8×C157—21no—
147D4×C157—21no—
148D4×C157—21no—
149D4×C157—21no—
150D4×C157—42no—
151D4×C157#4112yes—
152C2×C4×C157—21no—
153C2×C4×C157—21no—
154C2×C4×C157—21no—
155C2×C4×C157—21no—
156C2×C4×C157C2×D411yescharacteristic
157C2×C4×C157C2411yescharacteristic
158C8×C157—21no—
159C8×C157—21no—
160C22×C157—21no—
161C22×C157—21no—
162C22×C157—22no—
163C22×C157—41no—
164C22×C157—41no—
165C22×C157—41no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—84no—
169C22×C157C2×SD1612yes—
170C22×C157C22×D411yescharacteristic
171C2×D157—21no—
172C2×D157—21no—
173C2×D157—41no—
174C2×D157—41no—
175C2×D157—41no—
176C2×D157—84no—
177C2×D157C2×SD1612yes—
178C4×C157—21no—
179C4×C157—41no—
180C4×C157—41no—
181C4×C157C2×#4111yescharacteristic
182C4×C157H(5,𝔽2)11yescharacteristic
183Dic157—21no—
184Dic157—21no—
185Dic157—41no—
186Dic157—41no—
187Dic157—41no—
188Dic157C2×SD1612yes—
189C2×C157—22no—
190C2×C157—42no—
191C2×C157—81no—
192C2×C157#54611yescharacteristic
193C2×C157C22×SD1611yescharacteristic
194C2×C157#57611yescharacteristic
195D157—22no—
196D157—81no—
197C157#329511yescharacteristic, complemented, Sylow
198#3295—1571nomaximal, Sylow
199#554—1571no—
200D42—1571no—
201#486—1571no—
202#481—1571no—
203#481—1571no—
204#476—1571no—
205#465—1571no—
206#465—1571no—
207#460—1571no—
208#450—1571no—
209#450D15711yescharacteristic, complemented
210C4×SD16—1571no—
211C8×D4—1571no—
212C2×#102—1571no—
213C2×#102—1571no—
214C22×D4—3141no—
215C22×D4—1571no—
216C22×D4C2×D15711yescharacteristic
217C2×SD16—1571no—
218C2×SD16C2×D15711yescharacteristic
219C2×SD16C2×D15711yescharacteristic, complemented
220C22×C8—1571no—
221C22×C8—1571no—
222C4⋊Q8—1571no—
223#127—1571no—
224#125—3141no—
225C22⋊Q8—3141no—
226C22⋊Q8—3141no—
227C22⋊Q8—1571no—
228C22⋊Q8C2×D15711yescharacteristic, complemented
229#121—3141no—
230#121—1571no—
231#121—1571no—
232#120—3141no—
233#120—3141no—
234C4×Q8—1571no—
235C4×D4—3141no—
236C4×D4—1571no—
237C4×D4—1571no—
238C2×C4⋊C4—1571no—
239C2×C4⋊C4—1571no—
240#106—1571no—
241#106—1571no—
242#106—1571no—
243C4⋊C8—1571no—
244#103—1571no—
245#102—1571no—
246#102—1571no—
247#102—1571no—
248#102—1571no—
249#102—1571no—
250#102—1571no—
251#102—1571no—
252#102C2×D15711yescharacteristic
253#102C2×D15711yescharacteristic, complemented
254C22⋊C8—1571no—
255C22⋊C8C2×D15711yescharacteristic, complemented
256C4×C8—1571no—
257C24—21no—
258C24—3141no—
259C2×Q8—3141no—
260C2×Q8C22×D15711yescharacteristic
261C2×D4—22no—
262C2×D4—21no—
263C2×D4—41no—
264C2×D4—3142no—
265C2×D4—3141no—
266C2×D4—3141no—
267C2×D4—3141no—
268C2×D4—3141no—
269C2×D4—3141no—
270C2×D4—6281no—
271C2×D4—6284no—
272C2×D4—1571no—
273C2×D4—1571no—
274C2×D4C22×D15711yescharacteristic
275C2×D4C22×D15711yescharacteristic
276C22×C4—3141no—
277C22×C4—3141no—
278C22×C4—3141no—
279C22×C4—1571no—
280C22×C4C22×D15711yescharacteristic
281SD16—22no—
282SD16—41no—
283SD16—6281no—
284C2×C8—6281no—
285C2×C8—6281no—
286C2×C8—1571no—
287C2×C8—1571no—
288C2×C8C22×D15711yescharacteristic
289C2×C8C22×D15711yescharacteristic
290C4⋊C4—21no—
291C4⋊C4—3141no—
292C4⋊C4—3141no—
293C4⋊C4—3141no—
294C4⋊C4—3141no—
295C4⋊C4—3141no—
296C4⋊C4—1571no—
297C4⋊C4—1571no—
298C4⋊C4—1571no—
299C4⋊C4—1571no—
300C4⋊C4C22×D15711yescharacteristic
301C22⋊C4—21no—
302C22⋊C4—3141no—
303C22⋊C4—3141no—
304C22⋊C4—3141no—
305C22⋊C4—3141no—
306C22⋊C4—1571no—
307C22⋊C4—1571no—
308C42—3141no—
309C42—1571no—
310C23—21no—
311C23—21no—
312C23—42no—
313C23—42no—
314C23—81no—
315C23—3141no—
316C23—6282no—
317C23—6282no—
318C23—1571no—
319C23—12561no—
320C23D4×D15711yescharacteristic
321Q8—21no—
322Q8—21no—
323Q8—12561no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—3141no—
329D4—3141no—
330D4—6282no—
331D4—6282no—
332D4—6282no—
333D4—6282no—
334D4—1574no—
335D4—12561no—
336D4#1457895312yes—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—3141no—
342C2×C4—3141no—
343C2×C4—3141no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—6282no—
347C2×C4—1571no—
348C2×C4—1571no—
349C2×C4—1571no—
350C2×C4—12561no—
351C2×C4—12561no—
352C2×C4D4×D15711yescharacteristic
353C2×C4C23×D15711yescharacteristic
354C8—21no—
355C8—21no—
356C8—3141no—
357C8—3141no—
358C22—21no—
359C22—21no—
360C22—22no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—84no—
367C22—3141no—
368C22—3141no—
369C22—6281no—
370C22—6281no—
371C22—6281no—
372C22—1572no—
373C22—12564no—
374C22SD16×D15712yes—
375C22C2×D4×D15711yescharacteristic
376C4—21no—
377C4—41no—
378C4—41no—
379C4—3141no—
380C4—3141no—
381C4—6281no—
382C4—6281no—
383C4—6281no—
384C4—1572no—
385C4C2×#1457895311yescharacteristic
386C4#1909781611yescharacteristic
387C2—22no—
388C2—42no—
389C2—81no—
390C2—3142no—
391C2—12561no—
392C2#2375791011yescharacteristic
393C2C2×SD16×D15711yescharacteristic
394C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#450×C157C2
socleC22×C157C22×D4
prime radicalD4×C22⋊D157C2
hypercenter#450D157
hypocenterC157#3295
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. #23757981C2semidirect
3. #23757618C2semidirect
4. #23757592C2semidirect
5. #23757590C2semidirect
6. #23757561C2semidirect
7. #23757504C2semidirect
8. #23757499C2semidirect
9. #23757471C2semidirect
10. #23757422C2semidirect
11. SD16×Dic157C2semidirect
12. #23757336C2semidirect
13. C2×#19097692C2semidirect
14. #102×D157C2semidirect
15. #450×C157C2semidirect
18. C2×#14578941C22semidirect
19. C22×#11929434C22semidirect
20. C2×C8×D157C22semidirect
21. #19097770C22semidirect
26. #19097747C22semidirect
32. Q8×Dic157C22semidirect
36. C2×C4⋊Dic157C22semidirect
37. C4⋊C4×D157C22semidirect
38. #19097703C22semidirect
39. #19097703C22semidirect
40. #19097702C22semidirect
41. #19097700C22semidirect
42. #19097695C22semidirect
43. #19097693C22semidirect
44. #19097693C22semidirect
47. #19097692C22semidirect
48. #19097692C22semidirect
49. #19097691C22semidirect
50. #19097683C22semidirect
51. C8×Dic157C22semidirect
54. C2×SD16×C157C22semidirect
55. C22⋊Q8×C157C22semidirect
57. #102×C157C22semidirect
58. C22⋊C8×C157C22semidirect
125. C22⋊D157SD16semidirect
197. C157#3295semidirect
209. #450D157semidirect
219. C2×SD16C2×D157semidirect
228. C22⋊Q8C2×D157semidirect
253. #102C2×D157semidirect
255. C22⋊C8C2×D157semidirect

Maximal subgroups

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

subgroupindex
#237579812
D4×C22⋊D1572
#237576182
#237575922
#237575902
#237575612
#237575042
#237574992
#237574712
#237574222
SD16×Dic1572
#237573362
C2×#190976922
#102×D1572
#450×C1572
#3295157