Finite Group Databasebeta

← #34111671

Subgroups — #34111671

Order 20096.

510 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097798C211yesmaximal, characteristic, complemented
2C2×#19097794C211yesmaximal, characteristic, complemented
3#23757945C211yesmaximal, characteristic, complemented
4#23757916C211yesmaximal, characteristic, complemented
5#23757663C211yesmaximal, characteristic, complemented
6#23757522C211yesmaximal, characteristic, complemented
7#23757508C211yesmaximal, characteristic, complemented
8#23757469C211yesmaximal, characteristic, complemented
9#23757434C211yesmaximal, characteristic, complemented
10#23757421C211yesmaximal, characteristic, complemented
11#23757417C211yesmaximal, characteristic, complemented
12#23757408C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14#23757343C211yesmaximal, characteristic, complemented
15#464×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578955C2211yescharacteristic
18C2×#14578955C2211yescharacteristic, complemented
19C2×D4×D157C2211yescharacteristic
20#19097798—24no—
21#19097794—24no—
22C2×#14578941C2211yescharacteristic
23C2×#14578941C2211yescharacteristic, complemented
24C2×#14578941C2211yescharacteristic, complemented
25C2×D1256C2211yescharacteristic
26C2×D1256C2211yescharacteristic
27C2×#14578939C2211yescharacteristic
28C2×#14578939C2211yescharacteristic
29C2×#14578937C2211yescharacteristic
30C2×C8×D157C2211yescharacteristic, complemented
31#19097768—21no—
32#19097768C2211yescharacteristic, complemented
33#19097753—21no—
34#19097747C2211yescharacteristic
35#19097746—21no—
36#19097746—21no—
37#19097746C2211yescharacteristic
38#19097746C2211yescharacteristic, complemented
39#19097744—21no—
40#19097742C2211yescharacteristic
41#19097741—21no—
42C4×D628—21no—
43C4×D628C2211yescharacteristic
44C4×D628C2211yescharacteristic
45C22⋊C4×D157—21no—
46#19097704C2211yescharacteristic, complemented
47#19097695C2211yescharacteristic, complemented
48#19097693C2211yescharacteristic, complemented
49#19097693C2211yescharacteristic, complemented
50#19097691C2211yescharacteristic
51#19097683C2211yescharacteristic
52#19097683C2211yescharacteristic, complemented
53#19097682C2211yescharacteristic, complemented
54C2×Q16×C157C2211yescharacteristic, complemented
55C2×SD16×C157C2211yescharacteristic
56#124×C157C2211yescharacteristic
57C4×Q8×C157C2211yescharacteristic, complemented
58C4⋊C8×C157C2211yescharacteristic, complemented
59#103×C157C2211yescharacteristic, complemented
60#102×C157C2211yescharacteristic
61C23×D157—21no—
62#14578955—22no—
63#14578955—22no—
64#14578955—22no—
65#14578955—41no—
66#14578955—41no—
67#14578955—41no—
68C2×D628—21no—
69C2×D628—21no—
70C2×D628—21no—
71C2×D628—21no—
72C2×D628—21no—
73C2×D628—21no—
74C2×D628—21no—
75C2×D628D411yescharacteristic
76C2×D628C2311yescharacteristic
77C2×D628C2311yescharacteristic
78C2×D628C2311yescharacteristic
79C2×C22⋊D157—21no—
80C2×C22⋊D157—21no—
81D4×D157—22no—
82D4×D157—41no—
83C2×C4×D157—21no—
84C2×C4×D157—21no—
85C2×C4×D157—21no—
86C2×C4×D157—21no—
87C2×C4×D157C2311yescharacteristic
88C2×C4×D157C2311yescharacteristic
89#14578941—22no—
90#14578941—41no—
91#14578941D414yescomplemented
92D1256—22no—
93D1256—22no—
94#14578939—22no—
95#14578939—41no—
96#14578937—22no—
97C2×#11929434C2311yescharacteristic
98C2×#11929434C2311yescharacteristic
99C8×D157—22no—
100C4⋊Dic157D411yescharacteristic
101C4⋊Dic157C2311yescharacteristic
102#14578933—21no—
103C22⋊Dic157—21no—
104#14578931—21no—
105#14578931—21no—
106#14578931—21no—
107#14578931—21no—
108#14578931D411yescharacteristic
109#14578931D411yescharacteristic
110C2×Q8×C157C2311yescharacteristic
111C2×Q8×C157C2311yescharacteristic
112C2×D4×C157C2311yescharacteristic
113Q16×C157—22no—
114SD16×C157—22no—
115C2×C8×C157C2311yescharacteristic
116C2×C8×C157C2311yescharacteristic
117C4⋊C4×C157—21no—
118C4⋊C4×C157C2311yescharacteristic
119C22⋊C4×C157—21no—
120C22⋊C4×C157—21no—
121C42×C157—21no—
122C42×C157C2311yescharacteristic
123C22×D157—21no—
124C22×D157—21no—
125C22×D157—21no—
126C22×D157—42no—
127C22×D157—42no—
128C22×D157—81no—
129C22×D157C2×D411yescharacteristic
130C22×D157C2×D411yescharacteristic
131D628—21no—
132D628—21no—
133D628—21no—
134D628—21no—
135D628—21no—
136D628—41no—
137D628—42no—
138D628—42no—
139D628—42no—
140D628—42no—
141D628—81no—
142D628—81no—
143D628—81no—
144D628C2×D412yes—
145C22⋊D157—42no—
146C22⋊D157—81no—
147C2×Dic157—21no—
148C2×Dic157C2×D411yescharacteristic
149C2×Dic157C2×D411yescharacteristic
150C4×D157—21no—
151C4×D157—21no—
152C4×D157—21no—
153C4×D157—21no—
154C4×D157—42no—
155C4×D157—42no—
156C4×D157—42no—
157C4×D157—81no—
158#11929434—21no—
159#11929434C2×D412yes—
160C23×C157—21no—
161Q8×C157—21no—
162Q8×C157—21no—
163Q8×C157—21no—
164Q8×C157C2×D412yes—
165D4×C157—21no—
166D4×C157—21no—
167C2×C4×C157—21no—
168C2×C4×C157—21no—
169C2×C4×C157—21no—
170C2×C4×C157C2×D411yescharacteristic
171C2×C4×C157C2×D411yescharacteristic
172C2×C4×C157C2411yescharacteristic
173C8×C157—21no—
174C8×C157—21no—
175C22×C157—41no—
176C22×C157—41no—
177C22×C157—41no—
178C22×C157C22×D411yescharacteristic
179C2×D157—21no—
180C2×D157—21no—
181C2×D157—22no—
182C2×D157—21no—
183C2×D157—21no—
184C2×D157—21no—
185C2×D157—21no—
186C2×D157—41no—
187C2×D157—41no—
188C2×D157—41no—
189C2×D157—41no—
190C2×D157—41no—
191C2×D157—41no—
192C2×D157—41no—
193C2×D157—41no—
194C2×D157—84no—
195C4×C157—22no—
196C4×C157—21no—
197C4×C157—21no—
198C4×C157—41no—
199C4×C157—41no—
200C4×C157C22×D411yescharacteristic
201C4×C157H(5,𝔽2)11yescharacteristic
202Dic157—21no—
203Dic157—21no—
204Dic157—41no—
205C2×C157—81no—
206C2×C157D4211yescharacteristic
207C2×C157#57511yescharacteristic
208C2×C157#57611yescharacteristic
209D157—41no—
210D157—41no—
211D157—42no—
212D157—81no—
213D157—81no—
214C157#326811yescharacteristic, complemented, Sylow
215#3268—1571nomaximal, Sylow
216C2×AGL(1,ℤ/8)—1571no—
217C2×#135—1571no—
218#550—1571no—
219#546—1571no—
220#496—1571no—
221#468—1571no—
222#466—1571no—
223#464D15711yescharacteristic, complemented
224#459—1571no—
225#452—1571no—
226#449—1571no—
227#449—1571no—
228#447—1571no—
229#440—1571no—
230#435—1571no—
231C2×#41—1571no—
232C2×#41—1571no—
233C2×#41—1571no—
234C22×D4—1571no—
235AGL(1,ℤ/8)—3144no—
236#135—3144no—
237C2×Q16C2×D15711yescharacteristic, complemented
238C2×SD16—1571no—
239C2×SD16—1571no—
240C2×SD16—1571no—
241C2×SD16C2×D15711yescharacteristic
242C2×D8—1571no—
243C2×D8—1571no—
244C2×D8—1571no—
245C2×D8—1571no—
246C2×M16—1571no—
247C22×C8—1571no—
248#127—3141no—
249#127—1571no—
250#124C2×D15711yescharacteristic
251#123—3141no—
252C22⋊Q8—1571no—
253#121—3141no—
254#121—3141no—
255#121—3141no—
256#121—1571no—
257#121—1571no—
258#121—1571no—
259#120—3141no—
260C4×Q8C2×D15711yescharacteristic, complemented
261C4×D4—3141no—
262C4×D4—1571no—
263C4×D4—1571no—
264C2×C22⋊C4—3141no—
265#107—1571no—
266C4⋊C8C2×D15711yescharacteristic, complemented
267#103—1571no—
268#103C2×D15711yescharacteristic, complemented
269#102—1571no—
270#102—1571no—
271#102—1571no—
272#102C2×D15711yescharacteristic
273C22⋊C8—1571no—
274C22⋊C8—1571no—
275#97—1571no—
276C24—3141no—
277#41—3142no—
278#41—3142no—
279#41—3142no—
280#41—6281no—
281#41—6281no—
282#41—6281no—
283C2×Q8C22×D15711yescharacteristic
284C2×Q8C22×D15711yescharacteristic
285C2×D4—3141no—
286C2×D4—3141no—
287C2×D4—3141no—
288C2×D4—3141no—
289C2×D4—3141no—
290C2×D4—3142no—
291C2×D4—3141no—
292C2×D4—3141no—
293C2×D4—3141no—
294C2×D4—3141no—
295C2×D4—6281no—
296C2×D4—1571no—
297C2×D4—1571no—
298C2×D4—1571no—
299C2×D4—1571no—
300C2×D4C22×D15711yescharacteristic
301C22×C4—3141no—
302C22×C4—3141no—
303C22×C4—3141no—
304C22×C4—3141no—
305C22×C4—1571no—
306C22×C4—1571no—
307Q16—22no—
308SD16—22no—
309SD16—3142no—
310SD16—6281no—
311SD16—1574no—
312D8—3142no—
313D8—3142no—
314D8—3142no—
315D8—6281no—
316M16—3142no—
317C2×C8—3142no—
318C2×C8—1571no—
319C2×C8—1571no—
320C2×C8C22×D15711yescharacteristic
321C2×C8C22×D15711yescharacteristic
322C4⋊C4—21no—
323C4⋊C4—3141no—
324C4⋊C4—1571no—
325C4⋊C4—1571no—
326C4⋊C4C22×D15711yescharacteristic
327C22⋊C4—21no—
328C22⋊C4—21no—
329C22⋊C4—3141no—
330C22⋊C4—3141no—
331C22⋊C4—3141no—
332C22⋊C4—3141no—
333C22⋊C4—3141no—
334C22⋊C4—1571no—
335C22⋊C4—1571no—
336C42—21no—
337C42C22×D15711yescharacteristic
338C23—21no—
339C23—3141no—
340C23—3141no—
341C23—3141no—
342C23—6282no—
343C23—6282no—
344C23—1571no—
345C23—1571no—
346C23—12561no—
347Q8—21no—
348Q8—21no—
349Q8—21no—
350Q8D4×D15712yes—
351D4—21no—
352D4—21no—
353D4—3141no—
354D4—3141no—
355D4—3141no—
356D4—3141no—
357D4—3141no—
358D4—6281no—
359D4—6282no—
360D4—6282no—
361D4—6282no—
362D4—6282no—
363D4—6282no—
364D4—1572no—
365D4—12561no—
366D4—12561no—
367D4—12561no—
368D4—12561no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—3141no—
373C2×C4—3141no—
374C2×C4—3141no—
375C2×C4—3141no—
376C2×C4—3141no—
377C2×C4—6282no—
378C2×C4—6282no—
379C2×C4—6282no—
380C2×C4—1571no—
381C2×C4—1571no—
382C2×C4—12561no—
383C2×C4D4×D15711yescharacteristic
384C2×C4D4×D15711yescharacteristic
385C2×C4C23×D15711yescharacteristic
386C8—21no—
387C8—21no—
388C8—3141no—
389C8—1572no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—3141no—
394C22—3141no—
395C22—3142no—
396C22—3141no—
397C22—3141no—
398C22—3141no—
399C22—3141no—
400C22—6281no—
401C22—6281no—
402C22—6281no—
403C22—6281no—
404C22—6281no—
405C22—6281no—
406C22—6281no—
407C22—6281no—
408C22—12564no—
409C22C2×D4×D15711yescharacteristic
410C4—22no—
411C4—21no—
412C4—21no—
413C4—41no—
414C4—41no—
415C4—3141no—
416C4—3141no—
417C4—6281no—
418C4C2×D4×D15711yescharacteristic
419C4#1909781711yescharacteristic
420C2—81no—
421C2—6281no—
422C2—6281no—
423C2—6282no—
424C2—12561no—
425C2—12561no—
426C2#2375790711yescharacteristic
427C2#2375807211yescharacteristic
428C2#2375807511yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#464×C157C2
socleC22×C157C22×D4
hypercenter#464D157
hypocenterC157#3268
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. C2×#19097798C2semidirect
2. C2×#19097794C2semidirect
3. #23757945C2semidirect
4. #23757916C2semidirect
5. #23757663C2semidirect
6. #23757522C2semidirect
7. #23757508C2semidirect
8. #23757469C2semidirect
9. #23757434C2semidirect
10. #23757421C2semidirect
11. #23757417C2semidirect
12. #23757408C2semidirect
13. #23757371C2semidirect
14. #23757343C2semidirect
15. #464×C157C2semidirect
18. C2×#14578955C22semidirect
23. C2×#14578941C22semidirect
24. C2×#14578941C22semidirect
30. C2×C8×D157C22semidirect
32. #19097768C22semidirect
38. #19097746C22semidirect
46. #19097704C22semidirect
47. #19097695C22semidirect
48. #19097693C22semidirect
49. #19097693C22semidirect
52. #19097683C22semidirect
53. #19097682C22semidirect
54. C2×Q16×C157C22semidirect
57. C4×Q8×C157C22semidirect
58. C4⋊C8×C157C22semidirect
59. #103×C157C22semidirect
91. #14578941D4semidirect
214. C157#3268semidirect
223. #464D157semidirect
237. C2×Q16C2×D157semidirect
260. C4×Q8C2×D157semidirect
266. C4⋊C8C2×D157semidirect
268. #103C2×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977982
C2×#190977942
#237579452
#237579162
#237576632
#237575222
#237575082
#237574692
#237574342
#237574212
#237574172
#237574082
#237573712
#237573432
#464×C1572
#3268157