Finite Group Databasebeta

← #34112157

Subgroups — #34112157

Order 20096.

450 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757963C211yesmaximal, characteristic, complemented
2#23757637C211yesmaximal, characteristic, complemented
3#23757594C211yesmaximal, characteristic, complemented
4#23757584C211yesmaximal, characteristic, complemented
5#23757573C211yesmaximal, characteristic, complemented
6#23757517C211yesmaximal, characteristic, complemented
7#23757500C211yesmaximal, characteristic, complemented
8#23757470C211yesmaximal, characteristic, complemented
9#23757424C211yesmaximal, characteristic, complemented
10#23757424C211yesmaximal, characteristic, complemented
11#23757373C211yesmaximal, characteristic, complemented
12#23757345C211yesmaximal, characteristic, complemented
13#23757278C211yesmaximal, characteristic, complemented
14C2×#19097692C211yesmaximal, characteristic, complemented
15D42×C157C211yesmaximal, characteristic
16C2×#14578942C2211yescharacteristic
17C2×#14578942C2211yescharacteristic, complemented
18C2×#14578942C2211yescharacteristic, complemented
19C2×#14578938C2211yescharacteristic, complemented
20C22×#11929434C2211yescharacteristic, complemented
21#19097764—21no—
22#19097763C2211yescharacteristic, complemented
23#19097761—21no—
24#19097752—21no—
25#19097750C2211yescharacteristic, complemented
26#19097750C2211yescharacteristic, complemented
27C4×Dic314C2211yescharacteristic, complemented
28#19097730C2211yescharacteristic, complemented
29#19097727—21no—
30C2×C4⋊Dic157C2211yescharacteristic, complemented
31#19097704C2211yescharacteristic, complemented
32#19097704C2211yescharacteristic, complemented
33#19097702C2211yescharacteristic, complemented
34C4⋊#11929434C2211yescharacteristic, complemented
35#19097694C2211yescharacteristic, complemented
36#19097692C2211yescharacteristic
37#19097692C2211yescharacteristic
38#19097692C2211yescharacteristic
39#19097692C2211yescharacteristic, complemented
40#19097692C2211yescharacteristic, complemented
41#19097692C2211yescharacteristic, complemented
42#19097692C2211yescharacteristic, complemented
43#19097692C2211yescharacteristic, complemented
44#19097692C2211yescharacteristic, complemented
45C22⋊#11929434C2211yescharacteristic, complemented
46C22⋊#11929434C2211yescharacteristic, complemented
47#19097682C2211yescharacteristic, complemented
48C22×D4×C157—21no—
49C22×D4×C157C2211yescharacteristic
50C22×D4×C157C2211yescharacteristic
51#127×C157C2211yescharacteristic
52#121×C157—21no—
53#121×C157C2211yescharacteristic
54#121×C157C2211yescharacteristic
55#120×C157—21no—
56#120×C157—21no—
57C4×D4×C157C2211yescharacteristic
58C4×D4×C157C2211yescharacteristic
59C2×Dic314C2311yescharacteristic
60C22×Dic157—21no—
61#14578942—22no—
62#14578942—41no—
63#14578942—41no—
64#14578938—41no—
65C2×#11929434—41no—
66C2×#11929434C2311yescharacteristic
67C2×#11929434C2311yescharacteristic
68C2×#11929434C2311yescharacteristic
69C2×#11929434C2311yescharacteristic
70C4⋊Dic157—21no—
71C4⋊Dic157C2311yescharacteristic
72C4⋊Dic157C2311yescharacteristic
73C4⋊Dic157C2311yescharacteristic
74#14578933—21no—
75#14578933—21no—
76#14578933—21no—
77#14578933—21no—
78#14578933—21no—
79C22⋊Dic157—21no—
80C22⋊Dic157—21no—
81C22⋊Dic157—21no—
82C4×Dic157—21no—
83C4×Dic157—21no—
84C24×C157—21no—
85C24×C157—21no—
86C2×D4×C157—22no—
87C2×D4×C157—22no—
88C2×D4×C157—21no—
89C2×D4×C157—21no—
90C2×D4×C157—21no—
91C2×D4×C157—21no—
92C2×D4×C157—21no—
93C2×D4×C157—21no—
94C2×D4×C157—41no—
95C2×D4×C157—41no—
96C2×D4×C157—44no—
97C2×D4×C157D411yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C2×D4×C157C2311yescharacteristic
100C2×D4×C157C2311yescharacteristic
101C22×C4×C157—21no—
102C22×C4×C157C2311yescharacteristic
103C22×C4×C157C2311yescharacteristic
104C4⋊C4×C157D411yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C22⋊C4×C157—21no—
108C22⋊C4×C157—21no—
109C22⋊C4×C157D411yescharacteristic
110C22⋊C4×C157D411yescharacteristic
111C42×C157C2311yescharacteristic
112Dic314—21no—
113Dic314—21no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C2×Dic157—21no—
118C2×Dic157—42no—
119#11929434—21no—
120#11929434—21no—
121#11929434—21no—
122#11929434—21no—
123C23×C157—21no—
124C23×C157—21no—
125C23×C157—21no—
126C23×C157—42no—
127C23×C157—42no—
128C23×C157—42no—
129C23×C157—42no—
130C23×C157—81no—
131C23×C157—81no—
132C23×C157C2×D411yescharacteristic
133C23×C157C2×D411yescharacteristic
134D4×C157—22no—
135D4×C157—21no—
136D4×C157—21no—
137D4×C157—21no—
138D4×C157—21no—
139D4×C157—21no—
140D4×C157—42no—
141D4×C157—42no—
142D4×C157—42no—
143D4×C157—42no—
144D4×C157—42no—
145D4×C157—81no—
146D4×C157#4112yes—
147C2×C4×C157—21no—
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—21no—
151C2×C4×C157—21no—
152C2×C4×C157—42no—
153C2×C4×C157C2×D411yescharacteristic
154C2×C4×C157C2×D411yescharacteristic
155C2×C4×C157C2×D411yescharacteristic
156C2×C4×C157C2×D411yescharacteristic
157C2×C4×C157C2411yescharacteristic
158C22×C157—21no—
159C22×C157—21no—
160C22×C157—21no—
161C22×C157—22no—
162C22×C157—21no—
163C22×C157—21no—
164C22×C157—41no—
165C22×C157—41no—
166C22×C157—41no—
167C22×C157—41no—
168C22×C157—41no—
169C22×C157—41no—
170C22×C157—41no—
171C22×C157—41no—
172C22×C157—84no—
173C22×C157—84no—
174C22×C157AGL(1,ℤ/8)12yes—
175C22×C157C22×D411yescharacteristic
176C4×C157—21no—
177C4×C157—21no—
178C4×C157—21no—
179C4×C157—21no—
180C4×C157—41no—
181C4×C157C2×#4111yescharacteristic
182C4×C157H(5,𝔽2)11yescharacteristic
183Dic157—41no—
184Dic157—41no—
185Dic157—41no—
186Dic157—41no—
187C2×C157—22no—
188C2×C157—41no—
189C2×C157—42no—
190C2×C157—81no—
191C2×C157—81no—
192C2×C157#54611yescharacteristic
193C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
194C2×C157#57711yescharacteristic
195C157#331011yescharacteristic, complemented, Sylow
196#3310—1571nomaximal, Sylow
197#552—1571no—
198D42D15711yescharacteristic
199#490—1571no—
200#482—1571no—
201#480—1571no—
202#478—1571no—
203#468—1571no—
204#465—1571no—
205#460—1571no—
206#450—1571no—
207#450—1571no—
208#440—1571no—
209#435—1571no—
210#418—1571no—
211C2×#102—1571no—
212C22×D4—21no—
213C22×D4C2×D15711yescharacteristic
214C22×D4C2×D15711yescharacteristic
215C2×SD16—1571no—
216C2×SD16—1571no—
217C2×SD16—1571no—
218C2×M16—1571no—
219C22×C8—1571no—
220#127C2×D15711yescharacteristic
221#126—3141no—
222#125—3141no—
223#125—1571no—
224#123—3141no—
225C22⋊Q8—1571no—
226C22⋊Q8—1571no—
227#121—21no—
228#121C2×D15711yescharacteristic
229#121C2×D15711yescharacteristic
230#120—21no—
231#120—21no—
232C4×Q8—1571no—
233C4×D4C2×D15711yescharacteristic
234C4×D4C2×D15711yescharacteristic
235#117—3141no—
236#117—1571no—
237C2×C4⋊C4—1571no—
238#107—1571no—
239#107—1571no—
240#106—1571no—
241C4⋊C8—1571no—
242#103—1571no—
243#102—1571no—
244#102—1571no—
245#102—1571no—
246#102—1571no—
247#102—1571no—
248#102—1571no—
249#102—1571no—
250#102—1571no—
251#102—1571no—
252C22⋊C8—1571no—
253C22⋊C8—1571no—
254#97—1571no—
255C24—21no—
256C24—21no—
257C2×Q8—1571no—
258C2×D4—22no—
259C2×D4—22no—
260C2×D4—21no—
261C2×D4—21no—
262C2×D4—21no—
263C2×D4—21no—
264C2×D4—21no—
265C2×D4—21no—
266C2×D4—41no—
267C2×D4—41no—
268C2×D4—44no—
269C2×D4C22⋊D15711yescharacteristic
270C2×D4C22×D15711yescharacteristic
271C2×D4C22×D15711yescharacteristic
272C2×D4C22×D15711yescharacteristic
273C22×C4—21no—
274C22×C4—3141no—
275C22×C4C22×D15711yescharacteristic
276C22×C4C22×D15711yescharacteristic
277SD16—3142no—
278SD16—6281no—
279SD16—6281no—
280M16—6281no—
281C2×C8—6281no—
282C2×C8—1571no—
283C2×C8—1571no—
284C2×C8—1571no—
285C2×C8—1571no—
286C4⋊C4—3141no—
287C4⋊C4—3141no—
288C4⋊C4—3141no—
289C4⋊C4—3141no—
290C4⋊C4—3141no—
291C4⋊C4—3141no—
292C4⋊C4—1571no—
293C4⋊C4—1571no—
294C4⋊C4—1571no—
295C4⋊C4C22⋊D15711yescharacteristic
296C4⋊C4C22×D15711yescharacteristic
297C22⋊C4—21no—
298C22⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—3141no—
301C22⋊C4—3141no—
302C22⋊C4—3141no—
303C22⋊C4C22⋊D15711yescharacteristic
304C22⋊C4C22⋊D15711yescharacteristic
305C42—3141no—
306C42—3141no—
307C42C22×D15711yescharacteristic
308C23—21no—
309C23—21no—
310C23—21no—
311C23—42no—
312C23—42no—
313C23—42no—
314C23—42no—
315C23—81no—
316C23—81no—
317C23C2×C22⋊D15711yescharacteristic
318C23C2×C22⋊D15711yescharacteristic
319Q8—3141no—
320Q8—3141no—
321D4—22no—
322D4—21no—
323D4—21no—
324D4—21no—
325D4—21no—
326D4—21no—
327D4—42no—
328D4—42no—
329D4—42no—
330D4—42no—
331D4—42no—
332D4—81no—
333D4#1457895312yes—
334C2×C4—21no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—42no—
340C2×C4—3141no—
341C2×C4—3141no—
342C2×C4—3141no—
343C2×C4—3141no—
344C2×C4—6282no—
345C2×C4C2×C22⋊D15711yescharacteristic
346C2×C4C2×C22⋊D15711yescharacteristic
347C2×C4C2×C22⋊D15711yescharacteristic
348C2×C4C2×C22⋊D15711yescharacteristic
349C2×C4C23×D15711yescharacteristic
350C8—3141no—
351C8—3141no—
352C8—3141no—
353C8—3141no—
354C22—21no—
355C22—21no—
356C22—21no—
357C22—21no—
358C22—22no—
359C22—21no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—41no—
367C22—41no—
368C22—84no—
369C22—84no—
370C22#1909779712yes—
371C22C22×C22⋊D15711yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—41no—
377C4—6281no—
378C4—6281no—
379C4—6281no—
380C4—6281no—
381C4C2×#1457895311yescharacteristic
382C4#1909781611yescharacteristic
383C2—22no—
384C2—41no—
385C2—42no—
386C2—81no—
387C2—81no—
388C2#2375791711yescharacteristic
389C2C2×#1909779711yescharacteristic
390C2#2375808411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting, prime radicalD42×C157C2
socleC22×C157C22×D4
hypercenterD42D157
hypocenterC157#3310
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ D42

Complements

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

NH ≅ G/Ntype
1. #23757963C2semidirect
2. #23757637C2semidirect
3. #23757594C2semidirect
4. #23757584C2semidirect
5. #23757573C2semidirect
6. #23757517C2semidirect
7. #23757500C2semidirect
8. #23757470C2semidirect
9. #23757424C2semidirect
10. #23757424C2semidirect
11. #23757373C2semidirect
12. #23757345C2semidirect
13. #23757278C2semidirect
14. C2×#19097692C2semidirect
17. C2×#14578942C22semidirect
18. C2×#14578942C22semidirect
19. C2×#14578938C22semidirect
20. C22×#11929434C22semidirect
22. #19097763C22semidirect
25. #19097750C22semidirect
26. #19097750C22semidirect
27. C4×Dic314C22semidirect
28. #19097730C22semidirect
30. C2×C4⋊Dic157C22semidirect
31. #19097704C22semidirect
32. #19097704C22semidirect
33. #19097702C22semidirect
34. C4⋊#11929434C22semidirect
35. #19097694C22semidirect
39. #19097692C22semidirect
40. #19097692C22semidirect
41. #19097692C22semidirect
42. #19097692C22semidirect
43. #19097692C22semidirect
44. #19097692C22semidirect
45. C22⋊#11929434C22semidirect
46. C22⋊#11929434C22semidirect
47. #19097682C22semidirect
195. C157#3310semidirect

Maximal subgroups

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

subgroupindex
#237579632
#237576372
#237575942
#237575842
#237575732
#237575172
#237575002
#237574702
#237574242
#237573732
#237573452
#237572782
C2×#190976922
D42×C1572
#3310157