Finite Group Databasebeta

← #34109646

Subgroups — #34109646

Order 20096.

494 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×#19097795C211yesmaximal, characteristic
2C2×SD16×D157C211yesmaximal, characteristic, complemented
3#23757843C211yesmaximal, characteristic, complemented
4#23757745C211yesmaximal, characteristic, complemented
5#23757487C211yesmaximal, characteristic, complemented
6#23757486C211yesmaximal, characteristic, complemented
7#23757485C211yesmaximal, characteristic, complemented
8#23757479C211yesmaximal, characteristic, complemented
9#23757478C211yesmaximal, characteristic, complemented
10#23757477C211yesmaximal, characteristic, complemented
11#23757476C211yesmaximal, characteristic, complemented
12#23757298C211yesmaximal, characteristic, complemented
13#23757280C211yesmaximal, characteristic, complemented
14#23757266C211yesmaximal, characteristic, complemented
15#463×C157C211yesmaximal, characteristic, complemented
16C2×#14578953C2211yescharacteristic
17C2×Q8×D157C2211yescharacteristic
18C2×D4×D157C2211yescharacteristic
19#19097795—24no—
20C2×#14578943C2211yescharacteristic
21C2×#14578943C2211yescharacteristic
22C2×#14578942C2211yescharacteristic
23C2×#14578942C2211yescharacteristic
24C2×#14578941C2211yescharacteristic
25SD16×D157—24no—
26C2×#14578939C2211yescharacteristic
27C2×#14578937C2211yescharacteristic
28C2×C8×D157C2211yescharacteristic
29#19097771C2211yescharacteristic, complemented
30#19097769C2211yescharacteristic, complemented
31#19097758C2211yescharacteristic, complemented
32#19097753—21no—
33#19097753—21no—
34#19097748—21no—
35#19097748—21no—
36C4×D628C2211yescharacteristic
37D4×Dic157C2211yescharacteristic
38#19097733C2211yescharacteristic
39C4×C22⋊D157—21no—
40#19097731—21no—
41#19097729C2211yescharacteristic
42#19097728C2211yescharacteristic
43C2×#14578931—21no—
44C22⋊C4×D157—21no—
45C4⋊#11929434C2211yescharacteristic, complemented
46#19097700C2211yescharacteristic, complemented
47#19097700C2211yescharacteristic, complemented
48#19097696C2211yescharacteristic, complemented
49#19097696C2211yescharacteristic, complemented
50#19097695C2211yescharacteristic, complemented
51#19097694C2211yescharacteristic, complemented
52#19097694C2211yescharacteristic, complemented
53#19097692C2211yescharacteristic, complemented
54C2×SD16×C157C2211yescharacteristic
55C2×D8×C157C2211yescharacteristic
56#124×C157C2211yescharacteristic, complemented
57C4×D4×C157C2211yescharacteristic
58C4⋊C8×C157C2211yescharacteristic, complemented
59#103×C157C2211yescharacteristic, complemented
60#102×C157C2211yescharacteristic, complemented
61C23×D157—21no—
62#14578953—22no—
63#14578953—22no—
64C2×Dic314—21no—
65C2×Dic314C2311yescharacteristic
66C2×Dic314C2311yescharacteristic
67Q8×D157—22no—
68Q8×D157—22no—
69C2×D628C2311yescharacteristic
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72D4×D157—22no—
73D4×D157D414yes—
74C22×Dic157—21no—
75C22×Dic157—21no—
76C2×C4×D157—21no—
77C2×C4×D157—21no—
78C2×C4×D157—21no—
79C2×C4×D157C2311yescharacteristic
80#14578943—22no—
81#14578943—22no—
82#14578942—22no—
83#14578942—22no—
84#14578941—22no—
85#14578939—22no—
86#14578937—22no—
87C2×#11929434C2311yescharacteristic
88C2×#11929434C2311yescharacteristic
89C8×D157—22no—
90C4⋊Dic157—21no—
91C4⋊Dic157—21no—
92C4⋊Dic157C2311yescharacteristic
93#14578933—21no—
94#14578933—21no—
95#14578933D411yescharacteristic
96#14578933D411yescharacteristic
97C22⋊Dic157—21no—
98C22⋊Dic157—21no—
99C22⋊Dic157—21no—
100#14578931—21no—
101#14578931—21no—
102#14578931—21no—
103#14578931D411yescharacteristic
104#14578931D411yescharacteristic
105C4×Dic157—21no—
106C4×Dic157C2311yescharacteristic
107C2×Q8×C157C2311yescharacteristic
108C2×D4×C157C2311yescharacteristic
109C2×D4×C157C2311yescharacteristic
110C22×C4×C157—21no—
111SD16×C157—22no—
112D8×C157—22no—
113C2×C8×C157C2311yescharacteristic
114C2×C8×C157C2311yescharacteristic
115C4⋊C4×C157C2311yescharacteristic
116C22⋊C4×C157—21no—
117C22⋊C4×C157—21no—
118C22⋊C4×C157—21no—
119C42×C157C2311yescharacteristic
120C22×D157—21no—
121C22×D157—24no—
122C22×D157—81no—
123C22×D157—81no—
124C22×D157C2×D411yescharacteristic
125Dic314—21no—
126Dic314—21no—
127Dic314—21no—
128Dic314—21no—
129Dic314—42no—
130D628—21no—
131D628C2×D412yes—
132C22⋊D157—24no—
133C22⋊D157—42no—
134C2×Dic157—21no—
135C2×Dic157—21no—
136C2×Dic157—21no—
137C2×Dic157—42no—
138C2×Dic157—81no—
139C2×Dic157C2×D411yescharacteristic
140C2×Dic157C2×D411yescharacteristic
141C2×Dic157C2×D411yescharacteristic
142C4×D157—42no—
143C4×D157—81no—
144C4×D157—81no—
145C4×D157C2×D412yes—
146C4×D157#4112yes—
147#11929434—21no—
148#11929434—21no—
149C23×C157—21no—
150C23×C157—21no—
151Q8×C157—21no—
152Q8×C157—21no—
153D4×C157—21no—
154D4×C157—21no—
155D4×C157—21no—
156D4×C157C2×D412yes—
157C2×C4×C157—21no—
158C2×C4×C157—21no—
159C2×C4×C157—81no—
160C2×C4×C157C2×D411yescharacteristic
161C2×C4×C157C2×D411yescharacteristic
162C2×C4×C157C2411yescharacteristic
163C8×C157—21no—
164C8×C157—21no—
165C22×C157—22no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157C22×D411yescharacteristic
172C2×D157—21no—
173C2×D157—21no—
174C2×D157—22no—
175C2×D157—41no—
176C2×D157—41no—
177C2×D157—84no—
178C2×D157#12112yes—
179C4×C157—21no—
180C4×C157—21no—
181C4×C157—41no—
182C4×C157—41no—
183C4×C157C22×D411yescharacteristic
184C4×C157C2×#4111yescharacteristic
185Dic157—21no—
186Dic157—21no—
187Dic157—41no—
188Dic157—41no—
189Dic157—41no—
190Dic157#12112yes—
191C2×C157—42no—
192C2×C157—81no—
193C2×C157C2×#12111yescharacteristic
194C2×C157#57711yescharacteristic
195C2×C157#57711yescharacteristic
196D157—22no—
197D157—42no—
198C157#304211yescharacteristic, complemented, Sylow
199#3042—1571nomaximal, Sylow
200C2×AGL(1,ℤ/8)—1571no—
201C22×SD16—1571no—
202#536—1571no—
203#518—1571no—
204#463—1571no—
205#463—1571no—
206#463—1571no—
207#463D15711yescharacteristic, complemented
208#461—1571no—
209#461—1571no—
210#461—1571no—
211#461—1571no—
212#424—1571no—
213#419—1571no—
214#416—1571no—
215C2×#41—1571no—
216C22×Q8—1571no—
217C22×D4—1571no—
218AGL(1,ℤ/8)—3144no—
219C2×SD16—3144no—
220C2×SD16—1571no—
221C2×SD16—1571no—
222C2×SD16—1571no—
223C2×SD16—1571no—
224C2×SD16—1571no—
225C2×SD16C2×D15711yescharacteristic
226C2×D8—1571no—
227C2×D8C2×D15711yescharacteristic
228C2×M16—1571no—
229C22×C8—1571no—
230C4⋊Q8—1571no—
231C4⋊Q8—1571no—
232#124—1571no—
233#124C2×D15711yescharacteristic, complemented
234#123—3141no—
235#123—3141no—
236C22⋊Q8—3141no—
237C22⋊Q8—3141no—
238C4×D4—3141no—
239C4×D4—3141no—
240C4×D4—1571no—
241C4×D4—1571no—
242C4×D4—1571no—
243C4×D4C2×D15711yescharacteristic
244#117—1571no—
245#117—1571no—
246C2×C22⋊C4—3141no—
247C2×C22⋊C4—3141no—
248C4⋊C8—1571no—
249C4⋊C8—1571no—
250C4⋊C8—1571no—
251C4⋊C8C2×D15711yescharacteristic, complemented
252#103—1571no—
253#103—1571no—
254#103—1571no—
255#103—1571no—
256#103—1571no—
257#103C2×D15711yescharacteristic, complemented
258#102—1571no—
259#102C2×D15711yescharacteristic, complemented
260C24—3141no—
261#41—3142no—
262#41—3142no—
263C2×Q8—3141no—
264C2×Q8—3142no—
265C2×Q8—3142no—
266C2×Q8—1571no—
267C2×Q8—1571no—
268C2×Q8C22×D15711yescharacteristic
269C2×D4—3141no—
270C2×D4—3142no—
271C2×D4—3141no—
272C2×D4—1574no—
273C2×D4—1571no—
274C2×D4C22×D15711yescharacteristic
275C2×D4C22×D15711yescharacteristic
276C22×C4—21no—
277C22×C4—3141no—
278C22×C4—3141no—
279C22×C4—3141no—
280C22×C4—3141no—
281C22×C4—3141no—
282C22×C4—1571no—
283SD16—22no—
284SD16—3142no—
285SD16—3142no—
286SD16—3142no—
287SD16—3142no—
288SD16—3142no—
289D8—22no—
290D8—3142no—
291M16—3142no—
292C2×C8—3142no—
293C2×C8—1571no—
294C2×C8—1571no—
295C2×C8C22×D15711yescharacteristic
296C2×C8C22×D15711yescharacteristic
297C4⋊C4—3141no—
298C4⋊C4—3141no—
299C4⋊C4—3141no—
300C4⋊C4—3141no—
301C4⋊C4—1571no—
302C4⋊C4—1571no—
303C4⋊C4—1571no—
304C4⋊C4C22×D15711yescharacteristic
305C22⋊C4—21no—
306C22⋊C4—21no—
307C22⋊C4—21no—
308C22⋊C4—3141no—
309C22⋊C4—3141no—
310C22⋊C4—3141no—
311C22⋊C4—3141no—
312C22⋊C4—3141no—
313C22⋊C4—3141no—
314C22⋊C4—1571no—
315C22⋊C4—1571no—
316C42—3141no—
317C42—1571no—
318C42C22×D15711yescharacteristic
319C23—21no—
320C23—21no—
321C23—3144no—
322C23—3141no—
323C23—1571no—
324C23—12561no—
325C23—12561no—
326Q8—21no—
327Q8—21no—
328Q8—3141no—
329Q8—3141no—
330Q8—3141no—
331Q8—3141no—
332Q8—6282no—
333D4—21no—
334D4—21no—
335D4—21no—
336D4—3144no—
337D4—3141no—
338D4—6282no—
339D4—1572no—
340D4D4×D15712yes—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—81no—
344C2×C4—3141no—
345C2×C4—3141no—
346C2×C4—3141no—
347C2×C4—6282no—
348C2×C4—6282no—
349C2×C4—1571no—
350C2×C4—1571no—
351C2×C4—1571no—
352C2×C4—1572no—
353C2×C4—1572no—
354C2×C4—12561no—
355C2×C4—12561no—
356C2×C4—12561no—
357C2×C4D4×D15711yescharacteristic
358C2×C4D4×D15711yescharacteristic
359C2×C4C23×D15711yescharacteristic
360C8—21no—
361C8—21no—
362C8—3141no—
363C8—3141no—
364C22—22no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—41no—
369C22—41no—
370C22—3141no—
371C22—3141no—
372C22—3142no—
373C22—6281no—
374C22—6281no—
375C22—1572no—
376C22—12564no—
377C22C2×D4×D15711yescharacteristic
378C4—21no—
379C4—21no—
380C4—41no—
381C4—41no—
382C4—3141no—
383C4—3141no—
384C4—6281no—
385C4—6281no—
386C4—6281no—
387C4—1572no—
388C4C2×D4×D15711yescharacteristic
389C4#41×D15711yescharacteristic
390C2—42no—
391C2—81no—
392C2—3142no—
393C2—6282no—
394C2#121×D15711yescharacteristic
395C2#2375808011yescharacteristic
396C2#2375808311yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#463×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097795C2
hypercenter#463D157
hypocenterC157#3042
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #463

Complements

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

NH ≅ G/Ntype
2. C2×SD16×D157C2semidirect
3. #23757843C2semidirect
4. #23757745C2semidirect
5. #23757487C2semidirect
6. #23757486C2semidirect
7. #23757485C2semidirect
8. #23757479C2semidirect
9. #23757478C2semidirect
10. #23757477C2semidirect
11. #23757476C2semidirect
12. #23757298C2semidirect
13. #23757280C2semidirect
14. #23757266C2semidirect
15. #463×C157C2semidirect
29. #19097771C22semidirect
30. #19097769C22semidirect
31. #19097758C22semidirect
45. C4⋊#11929434C22semidirect
46. #19097700C22semidirect
47. #19097700C22semidirect
48. #19097696C22semidirect
49. #19097696C22semidirect
50. #19097695C22semidirect
51. #19097694C22semidirect
52. #19097694C22semidirect
53. #19097692C22semidirect
56. #124×C157C22semidirect
58. C4⋊C8×C157C22semidirect
59. #103×C157C22semidirect
60. #102×C157C22semidirect
198. C157#3042semidirect
207. #463D157semidirect
233. #124C2×D157semidirect
251. C4⋊C8C2×D157semidirect
257. #103C2×D157semidirect
259. #102C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977952
C2×SD16×D1572
#237578432
#237577452
#237574872
#237574862
#237574852
#237574792
#237574782
#237574772
#237574762
#237572982
#237572802
#237572662
#463×C1572
#3042157