Finite Group Databasebeta

← #34110134

Subgroups — #34110134

Order 20096.

492 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757820C211yesmaximal, characteristic, complemented
2C4×D4×D157C211yesmaximal, characteristic, complemented
3#23757588C211yesmaximal, characteristic, complemented
4#23757585C211yesmaximal, characteristic, complemented
5#23757552C211yesmaximal, characteristic, complemented
6#23757551C211yesmaximal, characteristic, complemented
7#23757467C211yesmaximal, characteristic, complemented
8#23757466C211yesmaximal, characteristic, complemented
9#23757408C211yesmaximal, characteristic, complemented
10#23757405C211yesmaximal, characteristic, complemented
11C4×D1256C211yesmaximal, characteristic, complemented
12C4×#14578939C211yesmaximal, characteristic, complemented
13C4×#14578939C211yesmaximal, characteristic, complemented
14#23757324C211yesmaximal, characteristic, complemented
15C4×D8×C157C211yesmaximal, characteristic, complemented
16C2×#14578954—21no—
17C2×D4×D157C2211yescharacteristic
18C22×C4×D157—21no—
19C2×D1256C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22#19097770C2211yescharacteristic, complemented
23#19097767C2211yescharacteristic, complemented
24#19097757—21no—
25#19097746C2211yescharacteristic
26#19097744—21no—
27#19097742C2211yescharacteristic
28C4×D628C2211yescharacteristic
29C4×D628C2211yescharacteristic, complemented
30D4×Dic157C2211yescharacteristic
31#19097733C2211yescharacteristic
32C4×C22⋊D157—21no—
33C4×C22⋊D157—21no—
34#19097731—21no—
35C4⋊C4×D157C2211yescharacteristic
36C22⋊C4×D157—21no—
37C42×D157C2211yescharacteristic
38#19097705C2211yescharacteristic, complemented
39#19097704C2211yescharacteristic, complemented
40#19097704C2211yescharacteristic, complemented
41#19097700C2211yescharacteristic, complemented
42#19097700C2211yescharacteristic, complemented
43#19097693C2211yescharacteristic
44#19097693C2211yescharacteristic, complemented
45#19097692C2211yescharacteristic
46#19097692C2211yescharacteristic, complemented
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic, complemented
49#19097683C2211yescharacteristic
50#19097683C2211yescharacteristic
51C4×#11929434C2211yescharacteristic, complemented
52C2×D8×C157C2211yescharacteristic
53C4×D4×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic, complemented
55#107×C157C2211yescharacteristic, complemented
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic, complemented
58C4×C8×C157C2211yescharacteristic, complemented
59C23×D157—21no—
60#14578954—44no—
61C2×Dic314—21no—
62C2×D628—21no—
63C2×D628C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69D4×D157—22no—
70D4×D157—22no—
71C22×Dic157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76C2×C4×D157—44no—
77C2×C4×D157D411yescharacteristic
78C2×C4×D157D411yescharacteristic
79C2×C4×D157C2311yescharacteristic
80D1256—22no—
81#14578939—22no—
82#14578939—22no—
83C2×#11929434C2311yescharacteristic
84C2×#11929434C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86C4⋊Dic157C2311yescharacteristic
87#14578933—21no—
88#14578933—21no—
89C22⋊Dic157—21no—
90C22⋊Dic157—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95C4×Dic157D411yescharacteristic
96C4×Dic157D411yescharacteristic
97C4×Dic157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C2×D4×C157C2311yescharacteristic
100C22×C4×C157—21no—
101C22×C4×C157—21no—
102D8×C157—22no—
103C2×C8×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C4⋊C4×C157C2311yescharacteristic
107C22⋊C4×C157—21no—
108C22⋊C4×C157—21no—
109C42×C157C2311yescharacteristic
110C22×D157—24no—
111C22×D157—21no—
112C22×D157—21no—
113C22×D157—42no—
114C22×D157—42no—
115C22×D157C2×D411yescharacteristic
116Dic314—42no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—42no—
121D628#4112yescomplemented
122C22⋊D157—24no—
123C22⋊D157—42no—
124C22⋊D157—42no—
125C22⋊D157—42no—
126C2×Dic157—21no—
127C2×Dic157—21no—
128C2×Dic157—42no—
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C2×Dic157C2×D411yescharacteristic
132C4×D157—21no—
133C4×D157—21no—
134C4×D157—41no—
135C4×D157—42no—
136C4×D157—42no—
137C4×D157—42no—
138C4×D157—42no—
139C4×D157D814yescomplemented
140#11929434—21no—
141#11929434—21no—
142C23×C157—21no—
143C23×C157—21no—
144D4×C157—21no—
145D4×C157—21no—
146D4×C157—21no—
147D4×C157#4112yescomplemented
148C2×C4×C157—21no—
149C2×C4×C157—21no—
150C2×C4×C157—42no—
151C2×C4×C157—42no—
152C2×C4×C157C2×D411yescharacteristic
153C2×C4×C157C2×D411yescharacteristic
154C2×C4×C157C2411yescharacteristic
155C8×C157—21no—
156C8×C157—21no—
157C22×C157—22no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157—41no—
162C22×C157—41no—
163C22×C157C22×D411yescharacteristic
164C2×D157—21no—
165C2×D157—21no—
166C2×D157—22no—
167C2×D157—48no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C2×D157—41no—
172C2×D157—41no—
173C2×D157C2×D812yes—
174C4×C157—21no—
175C4×C157—41no—
176C4×C157—41no—
177C4×C157C2×D812yes—
178C4×C157C2×#4111yescharacteristic
179C4×C157C2×#4111yescharacteristic
180Dic157—21no—
181Dic157—21no—
182Dic157—41no—
183Dic157—41no—
184Dic157C2×D812yes—
185C2×C157—42no—
186C2×C157—81no—
187C2×C157#52511yescharacteristic
188C2×C157C22×D811yescharacteristic
189C2×C157#57511yescharacteristic
190D157—22no—
191D157—42no—
192D157—81no—
193C157#310011yescharacteristic, complemented, Sylow
194#3100—1571nomaximal, Sylow
195#532—1571no—
196C2×C4×D4—1571no—
197#480—1571no—
198#480—1571no—
199#474—1571no—
200#474—1571no—
201#459—1571no—
202#459—1571no—
203#447—1571no—
204#447—1571no—
205C4×D8—1571no—
206C4×D8—1571no—
207C4×D8—1571no—
208C4×D8D15711yescharacteristic, complemented
209#431—1571no—
210C2×#41—3141no—
211C22×D4—1571no—
212C23×C4—3141no—
213C2×D8—1571no—
214C2×D8—1571no—
215C2×D8—1571no—
216C2×D8C2×D15711yescharacteristic
217C4⋊Q8—1571no—
218#127—1571no—
219#124—3141no—
220#121—3141no—
221#121—1571no—
222#121—1571no—
223C4×D4—3141no—
224C4×D4—3141no—
225C4×D4—3141no—
226C4×D4—1571no—
227C4×D4—1571no—
228C4×D4—1571no—
229C4×D4—1571no—
230C4×D4C2×D15711yescharacteristic
231C4×D4C2×D15711yescharacteristic, complemented
232C2×C4⋊C4—1571no—
233C2×C22⋊C4—3141no—
234C2×C42—1571no—
235#107—1571no—
236#107—1571no—
237#107—1571no—
238#107C2×D15711yescharacteristic, complemented
239C4⋊C8—1571no—
240C4⋊C8—1571no—
241#102—1571no—
242#102—1571no—
243#102—1571no—
244#102—1571no—
245#102—1571no—
246#102—1571no—
247#102C2×D15711yescharacteristic
248#102C2×D15711yescharacteristic, complemented
249C22⋊C8—1571no—
250C22⋊C8—1571no—
251C4×C8—1571no—
252C4×C8C2×D15711yescharacteristic, complemented
253C24—3141no—
254#41—6284no—
255C2×Q8—3141no—
256C2×D4—3141no—
257C2×D4—3142no—
258C2×D4—3142no—
259C2×D4—3141no—
260C2×D4—3141no—
261C2×D4—3141no—
262C2×D4—3141no—
263C2×D4—1571no—
264C2×D4—1571no—
265C2×D4C22×D15711yescharacteristic
266C2×D4C22×D15711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4—3141no—
272C22×C4—3141no—
273C22×C4—3141no—
274C22×C4—6284no—
275C22×C4—1571no—
276C22×C4—1571no—
277C22×C4—1571no—
278D8—22no—
279D8—3142no—
280D8—3142no—
281D8—3142no—
282C2×C8—1571no—
283C2×C8—1571no—
284C2×C8C22×D15711yescharacteristic
285C2×C8C22×D15711yescharacteristic
286C4⋊C4—3141no—
287C4⋊C4—3141no—
288C4⋊C4—1571no—
289C4⋊C4—1571no—
290C4⋊C4C22×D15711yescharacteristic
291C4⋊C4C22×D15711yescharacteristic
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—3141no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4—3141no—
298C22⋊C4—3141no—
299C22⋊C4—3141no—
300C42—1571no—
301C42—1571no—
302C42—1571no—
303C42C22×D15711yescharacteristic
304C23—21no—
305C23—21no—
306C23—3144no—
307C23—3141no—
308C23—3141no—
309C23—6282no—
310C23—6282no—
311C23—1571no—
312Q8—6282no—
313D4—21no—
314D4—21no—
315D4—21no—
316D4—3144no—
317D4—3141no—
318D4—3141no—
319D4—3141no—
320D4—6282no—
321D4—6282no—
322D4—6282no—
323D4—6282no—
324D4—1572no—
325D4#1457895412yescomplemented
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—42no—
329C2×C4—42no—
330C2×C4—3141no—
331C2×C4—3141no—
332C2×C4—3141no—
333C2×C4—3141no—
334C2×C4—6281no—
335C2×C4—6282no—
336C2×C4—6282no—
337C2×C4—6282no—
338C2×C4—6282no—
339C2×C4—6282no—
340C2×C4—1571no—
341C2×C4—1571no—
342C2×C4—1571no—
343C2×C4—1574no—
344C2×C4D4×D15711yescharacteristic
345C2×C4D4×D15711yescharacteristic
346C2×C4C23×D15711yescharacteristic
347C8—21no—
348C8—21no—
349C8—3141no—
350C8—3141no—
351C22—22no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—41no—
356C22—41no—
357C22—3141no—
358C22—3141no—
359C22—3142no—
360C22—6288no—
361C22—6281no—
362C22—6281no—
363C22—6281no—
364C22—6281no—
365C22—6281no—
366C22—1572no—
367C22C2×D4×D15711yescharacteristic
368C4—21no—
369C4—41no—
370C4—41no—
371C4—3141no—
372C4—3141no—
373C4—6281no—
374C4—6281no—
375C4—1572no—
376C4D8×D15712yes—
377C4#41×D15711yescharacteristic
378C4C2×#1457895411yescharacteristic
379C2—42no—
380C2—81no—
381C2—3142no—
382C2—6282no—
383C2—12561no—
384C2#2375778211yescharacteristic
385C2C2×D8×D15711yescharacteristic
386C2#2375807011yescharacteristic
subgroupG/H
centerC2×C4D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×D8×C157C2
socleC22×C157C22×D4
hypercenterC4×D8D157
hypocenterC157#3100
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #23757820C2semidirect
2. C4×D4×D157C2semidirect
3. #23757588C2semidirect
4. #23757585C2semidirect
5. #23757552C2semidirect
6. #23757551C2semidirect
7. #23757467C2semidirect
8. #23757466C2semidirect
9. #23757408C2semidirect
10. #23757405C2semidirect
11. C4×D1256C2semidirect
12. C4×#14578939C2semidirect
13. C4×#14578939C2semidirect
14. #23757324C2semidirect
15. C4×D8×C157C2semidirect
22. #19097770C22semidirect
23. #19097767C22semidirect
29. C4×D628C22semidirect
38. #19097705C22semidirect
39. #19097704C22semidirect
40. #19097704C22semidirect
41. #19097700C22semidirect
42. #19097700C22semidirect
44. #19097693C22semidirect
46. #19097692C22semidirect
48. #19097691C22semidirect
51. C4×#11929434C22semidirect
54. C4×D4×C157C22semidirect
55. #107×C157C22semidirect
57. #102×C157C22semidirect
58. C4×C8×C157C22semidirect
121. D628#41semidirect
139. C4×D157D8semidirect
147. D4×C157#41semidirect
193. C157#3100semidirect
208. C4×D8D157semidirect
231. C4×D4C2×D157semidirect
238. #107C2×D157semidirect
248. #102C2×D157semidirect
252. C4×C8C2×D157semidirect
325. D4#14578954semidirect

Maximal subgroups

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

subgroupindex
#237578202
C4×D4×D1572
#237575882
#237575852
#237575522
#237575512
#237574672
#237574662
#237574082
#237574052
C4×D12562
C4×#145789392
#237573242
C4×D8×C1572
#3100157