Finite Group Databasebeta

← #34112736

Subgroups — #34112736

Order 20096.

360 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757969C211yesmaximal, characteristic, complemented
2#23757672C211yesmaximal, characteristic, complemented
3#23757597C211yesmaximal, characteristic, complemented
4#23757594C211yesmaximal, characteristic, complemented
5#23757586C211yesmaximal, characteristic, complemented
6#23757584C211yesmaximal, characteristic, complemented
7#23757573C211yesmaximal, characteristic, complemented
8#23757570C211yesmaximal, characteristic, complemented
9#23757524C211yesmaximal, characteristic, complemented
10#23757524C211yesmaximal, characteristic, complemented
11C4×#14578939C211yesmaximal, characteristic, complemented
12#23757351C211yesmaximal, characteristic, complemented
13#23757316C211yesmaximal, characteristic, complemented
14#23757313C211yesmaximal, characteristic, complemented
15#553×C157C211yesmaximal, characteristic, complemented
16C2×#14578939C2211yescharacteristic
17C2×#14578938C2211yescharacteristic
18C2×#14578938C2211yescharacteristic
19#19097766—21no—
20#19097763C2211yescharacteristic
21#19097753—21no—
22#19097745C2211yescharacteristic
23#19097745C2211yescharacteristic
24#19097743—21no—
25C4×D628C2211yescharacteristic
26#19097731—21no—
27#19097730C2211yescharacteristic
28C2×C4⋊Dic157C2211yescharacteristic
29#19097704C2211yescharacteristic
30#19097704C2211yescharacteristic
31#19097704C2211yescharacteristic
32#19097704C2211yescharacteristic
33#19097704C2211yescharacteristic
34#19097702C2211yescharacteristic
35#19097702C2211yescharacteristic
36#19097702C2211yescharacteristic
37#19097702C2211yescharacteristic
38C4⋊#11929434C2211yescharacteristic
39#19097692C2211yescharacteristic
40#19097692C2211yescharacteristic
41#19097692C2211yescharacteristic
42#19097691C2211yescharacteristic
43#19097691C2211yescharacteristic
44#19097691C2211yescharacteristic
45C22⋊#11929434C2211yescharacteristic
46C22⋊#11929434C2211yescharacteristic
47C4×#11929434C2211yescharacteristic
48#126×C157—21no—
49#125×C157C2211yescharacteristic
50#123×C157—21no—
51#121×C157—21no—
52#121×C157C2211yescharacteristic
53#121×C157C2211yescharacteristic
54C4×D4×C157—21no—
55C4×D4×C157C2211yescharacteristic
56C4×D4×C157C2211yescharacteristic
57#117×C157C2211yescharacteristic
58C2×C4⋊C4×C157C2211yescharacteristic
59C2×D628C2311yescharacteristic
60C2×C22⋊D157—21no—
61C2×C22⋊D157—21no—
62C22×Dic157—21no—
63C2×C4×D157—21no—
64#14578939—22no—
65#14578938—22no—
66#14578938—22no—
67C2×#11929434C2311yescharacteristic
68C2×#11929434C2311yescharacteristic
69C2×#11929434C2311yescharacteristic
70C2×#11929434C2311yescharacteristic
71C4⋊Dic157—21no—
72C4⋊Dic157C2311yescharacteristic
73C4⋊Dic157C2311yescharacteristic
74C4⋊Dic157C2311yescharacteristic
75#14578933—21no—
76#14578933—21no—
77C22⋊Dic157—21no—
78#14578931—21no—
79#14578931—21no—
80#14578931—21no—
81C4×Dic157—21no—
82C2×D4×C157—21no—
83C2×D4×C157—21no—
84C2×D4×C157D411yescharacteristic
85C2×D4×C157C2311yescharacteristic
86C22×C4×C157—21no—
87C22×C4×C157—21no—
88C22×C4×C157C2311yescharacteristic
89C22×C4×C157C2311yescharacteristic
90C4⋊C4×C157—21no—
91C4⋊C4×C157—21no—
92C4⋊C4×C157—21no—
93C4⋊C4×C157D411yescharacteristic
94C4⋊C4×C157C2311yescharacteristic
95C4⋊C4×C157C2311yescharacteristic
96C4⋊C4×C157C2311yescharacteristic
97C22⋊C4×C157—21no—
98C22⋊C4×C157—21no—
99C22⋊C4×C157—21no—
100C22⋊C4×C157—21no—
101C22⋊C4×C157D411yescharacteristic
102C22⋊C4×C157D411yescharacteristic
103C42×C157—21no—
104C42×C157C2311yescharacteristic
105C22×D157—21no—
106D628—21no—
107D628—21no—
108C22⋊D157—42no—
109C22⋊D157—81no—
110C2×Dic157—21no—
111C2×Dic157—21no—
112C2×Dic157—21no—
113C2×Dic157—81no—
114C4×D157—81no—
115#11929434—21no—
116#11929434—21no—
117#11929434—21no—
118#11929434#4112yes—
119C23×C157—21no—
120C23×C157C2×D411yescharacteristic
121C23×C157C2×D411yescharacteristic
122D4×C157—21no—
123D4×C157—21no—
124D4×C157—41no—
125D4×C157—42no—
126D4×C157—81no—
127C2×C4×C157—21no—
128C2×C4×C157—21no—
129C2×C4×C157—21no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157—81no—
135C2×C4×C157—81no—
136C2×C4×C157C2×D411yescharacteristic
137C2×C4×C157C2×D411yescharacteristic
138C2×C4×C157C2×D411yescharacteristic
139C2×C4×C157C2×D411yescharacteristic
140C2×C4×C157C2411yescharacteristic
141C22×C157—21no—
142C22×C157—21no—
143C22×C157—21no—
144C22×C157—21no—
145C22×C157—21no—
146C22×C157—21no—
147C22×C157—41no—
148C22×C157—41no—
149C22×C157—41no—
150C22×C157C22×D411yescharacteristic
151C2×D157—41no—
152C2×D157—41no—
153C2×D157—41no—
154C4×C157—21no—
155C4×C157—21no—
156C4×C157—21no—
157C4×C157—21no—
158C4×C157—41no—
159C4×C157—41no—
160C4×C157—41no—
161C4×C157C2×#4111yescharacteristic
162C4×C1572−1+411yescharacteristic
163Dic157—41no—
164Dic157—41no—
165Dic157—41no—
166C2×C157—41no—
167C2×C157—41no—
168C2×C157—81no—
169C2×C157#54711yescharacteristic
170C2×C157#57511yescharacteristic
171C2×C157#57611yescharacteristic
172D157—81no—
173C157#335511yescharacteristic, complemented, Sylow
174#3355—1571nomaximal, Sylow
175#553—1571no—
176#553D15711yescharacteristic, complemented
177#499—1571no—
178#482—1571no—
179#482—1571no—
180#480—1571no—
181#480—1571no—
182#478—1571no—
183#478—1571no—
184#469—1571no—
185#469—1571no—
186C4×D8—1571no—
187#436—1571no—
188#428—1571no—
189#428—1571no—
190C2×D8—1571no—
191C2×M16—1571no—
192C2×M16—1571no—
193#126—21no—
194#126—3141no—
195#125—1571no—
196#125C2×D15711yescharacteristic
197#123—21no—
198#123—3141no—
199#121—21no—
200#121—3141no—
201#121—1571no—
202#121—1571no—
203#121C2×D15711yescharacteristic
204#121C2×D15711yescharacteristic
205C4×D4—21no—
206C4×D4—3141no—
207C4×D4—1571no—
208C4×D4C2×D15711yescharacteristic
209C4×D4C2×D15711yescharacteristic
210#117—1571no—
211#117C2×D15711yescharacteristic
212C2×C4⋊C4—1571no—
213C2×C4⋊C4C2×D15711yescharacteristic
214#107—1571no—
215#107—1571no—
216#107—1571no—
217#107—1571no—
218#107—1571no—
219#106—1571no—
220#106—1571no—
221#106—1571no—
222#106—1571no—
223C4⋊C8—1571no—
224#102—1571no—
225#102—1571no—
226#102—1571no—
227#102—1571no—
228#102—1571no—
229#102—1571no—
230C22⋊C8—1571no—
231C22⋊C8—1571no—
232C4×C8—1571no—
233C2×D4—21no—
234C2×D4—21no—
235C2×D4—3141no—
236C2×D4—3141no—
237C2×D4—1571no—
238C2×D4C22⋊D15711yescharacteristic
239C2×D4C22×D15711yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4—3141no—
243C22×C4—3141no—
244C22×C4C22×D15711yescharacteristic
245C22×C4C22×D15711yescharacteristic
246D8—3142no—
247M16—3142no—
248M16—3142no—
249C2×C8—1571no—
250C2×C8—1571no—
251C2×C8—1571no—
252C2×C8—1571no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—3141no—
257C4⋊C4—3141no—
258C4⋊C4—3141no—
259C4⋊C4—1571no—
260C4⋊C4—1571no—
261C4⋊C4—1571no—
262C4⋊C4C22⋊D15711yescharacteristic
263C4⋊C4C22×D15711yescharacteristic
264C4⋊C4C22×D15711yescharacteristic
265C4⋊C4C22×D15711yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—21no—
269C22⋊C4—21no—
270C22⋊C4—3141no—
271C22⋊C4—3141no—
272C22⋊C4—3141no—
273C22⋊C4—3141no—
274C22⋊C4C22⋊D15711yescharacteristic
275C22⋊C4C22⋊D15711yescharacteristic
276C42—21no—
277C42—3141no—
278C42C22×D15711yescharacteristic
279C23—21no—
280C23—3141no—
281C23C2×C22⋊D15711yescharacteristic
282C23C2×C22⋊D15711yescharacteristic
283D4—21no—
284D4—21no—
285D4—41no—
286D4—42no—
287D4—81no—
288D4—3141no—
289D4—3141no—
290D4—6282no—
291D4—12561no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—81no—
301C2×C4—3141no—
302C2×C4—3141no—
303C2×C4—3141no—
304C2×C4—12561no—
305C2×C4—12561no—
306C2×C4C2×C22⋊D15711yescharacteristic
307C2×C4C2×C22⋊D15711yescharacteristic
308C2×C4C2×C22⋊D15711yescharacteristic
309C2×C4C2×C22⋊D15711yescharacteristic
310C2×C4C23×D15711yescharacteristic
311C8—3141no—
312C8—3141no—
313C8—3141no—
314C8—1572no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—21no—
319C22—21no—
320C22—21no—
321C22—41no—
322C22—41no—
323C22—41no—
324C22—6281no—
325C22—6281no—
326C22—6281no—
327C22C22×C22⋊D15711yescharacteristic
328C4—21no—
329C4—21no—
330C4—21no—
331C4—21no—
332C4—41no—
333C4—41no—
334C4—41no—
335C4—6281no—
336C4—6281no—
337C4—6281no—
338C4#41×D15711yescharacteristic
339C4#1909781811yescharacteristic
340C2—41no—
341C2—41no—
342C2—81no—
343C2—12561no—
344C2#2375792211yescharacteristic
345C2#2375807111yescharacteristic
346C2#2375807611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#553×C157C2
socleC22×C157C22×D4
hypercenter#553D157
hypocenterC157#3355
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23757969C2semidirect
2. #23757672C2semidirect
3. #23757597C2semidirect
4. #23757594C2semidirect
5. #23757586C2semidirect
6. #23757584C2semidirect
7. #23757573C2semidirect
8. #23757570C2semidirect
9. #23757524C2semidirect
10. #23757524C2semidirect
11. C4×#14578939C2semidirect
12. #23757351C2semidirect
13. #23757316C2semidirect
14. #23757313C2semidirect
15. #553×C157C2semidirect
173. C157#3355semidirect
176. #553D157semidirect

Maximal subgroups

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

subgroupindex
#237579692
#237576722
#237575972
#237575942
#237575862
#237575842
#237575732
#237575702
#237575242
C4×#145789392
#237573512
#237573162
#237573132
#553×C1572
#3355157