Finite Group Databasebeta

← #34110700

Subgroups — #34110700

Order 20096.

380 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757807C211yesmaximal, characteristic, complemented
2#23757672C211yesmaximal, characteristic, complemented
3#23757655C211yesmaximal, characteristic, complemented
4#23757630C211yesmaximal, characteristic, complemented
5#23757627C211yesmaximal, characteristic, complemented
6#23757512C211yesmaximal, characteristic, complemented
7#23757507C211yesmaximal, characteristic
8#23757504C211yesmaximal, characteristic, complemented
9#23757500C211yesmaximal, characteristic, complemented
10C4×#14578944C211yesmaximal, characteristic, complemented
11C4×#14578941C211yesmaximal, characteristic, complemented
12C4×#14578942C211yesmaximal, characteristic, complemented
13C4×#14578939C211yesmaximal, characteristic, complemented
14C2×C4×#11929434C211yesmaximal, characteristic, complemented
15#529×C157C211yesmaximal, characteristic, complemented
16C2×#14578944C2211yescharacteristic
17C2×#14578942C2211yescharacteristic
18C2×#14578941C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C22×#11929434C2211yescharacteristic
21C22×#11929434C2211yescharacteristic
22#19097765—21no—
23#19097763C2211yescharacteristic
24#19097759C2211yescharacteristic
25#19097754—21no—
26#19097750C2211yescharacteristic
27#19097745C2211yescharacteristic
28C4×Dic314C2211yescharacteristic
29C4×D628C2211yescharacteristic
30C4×C22⋊D157—21no—
31#19097728—21no—
32#19097704C2211yescharacteristic
33#19097704C2211yescharacteristic
34#19097702C2211yescharacteristic
35#19097702C2211yescharacteristic
36#19097695C2211yescharacteristic
37#19097695C2211yescharacteristic
38#19097694C2211yescharacteristic
39#19097694C2211yescharacteristic
40#19097692C2211yescharacteristic
41#19097692C2211yescharacteristic
42#19097691C2211yescharacteristic
43#19097691C2211yescharacteristic
44C4×#11929434C2211yescharacteristic
45C4×#11929434C2211yescharacteristic
46C4×#11929434C2211yescharacteristic
47C4×#11929434C2211yescharacteristic
48#126×C157—21no—
49#125×C157C2211yescharacteristic
50#124×C157C2211yescharacteristic
51#123×C157—21no—
52C22⋊Q8×C157C2211yescharacteristic
53#121×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic
55C4×D4×C157—21no—
56C4×D4×C157C2211yescharacteristic
57#117×C157—21no—
58C2×C42×C157C2211yescharacteristic
59C2×Dic314C2311yescharacteristic
60C2×D628C2311yescharacteristic
61C2×C22⋊D157—21no—
62C2×C4×D157—21no—
63#14578944—22no—
64#14578942—22no—
65#14578941—22no—
66#14578939—22no—
67C2×#11929434—22no—
68C2×#11929434—22no—
69C2×#11929434C2311yescharacteristic
70C2×#11929434C2311yescharacteristic
71C2×#11929434C2311yescharacteristic
72C2×#11929434C2311yescharacteristic
73C4⋊Dic157C2311yescharacteristic
74C4⋊Dic157C2311yescharacteristic
75#14578933—21no—
76#14578933—21no—
77#14578933—21no—
78#14578933—21no—
79C22⋊Dic157—21no—
80#14578931—21no—
81#14578931—21no—
82#14578931—21no—
83#14578931—21no—
84C4×Dic157—21no—
85C2×Q8×C157C2311yescharacteristic
86C2×D4×C157—21no—
87C2×D4×C157C2311yescharacteristic
88C22×C4×C157—21no—
89C22×C4×C157D411yescharacteristic
90C22×C4×C157D411yescharacteristic
91C22×C4×C157C2311yescharacteristic
92C4⋊C4×C157—21no—
93C4⋊C4×C157—21no—
94C4⋊C4×C157—21no—
95C4⋊C4×C157—21no—
96C4⋊C4×C157C2311yescharacteristic
97C4⋊C4×C157C2311yescharacteristic
98C22⋊C4×C157—21no—
99C22⋊C4×C157—21no—
100C22⋊C4×C157—21no—
101C22⋊C4×C157—21no—
102C22⋊C4×C157—21no—
103C42×C157—21no—
104C42×C157D411yescharacteristic
105C42×C157D411yescharacteristic
106C42×C157C2311yescharacteristic
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109Dic314—21no—
110Dic314—21no—
111D628—21no—
112D628—21no—
113C22⋊D157—42no—
114C2×Dic157—21no—
115C2×Dic157—21no—
116C2×Dic157—21no—
117C4×D157—42no—
118#11929434—21no—
119#11929434—21no—
120#11929434#4112yes—
121#11929434#4112yes—
122C23×C157—21no—
123C23×C157C2×D411yescharacteristic
124Q8×C157—21no—
125Q8×C157—21no—
126D4×C157—21no—
127D4×C157—21no—
128D4×C157—42no—
129C2×C4×C157—22no—
130C2×C4×C157—22no—
131C2×C4×C157—21no—
132C2×C4×C157—21no—
133C2×C4×C157—21no—
134C2×C4×C157—21no—
135C2×C4×C157—21no—
136C2×C4×C157—42no—
137C2×C4×C157C2×D411yescharacteristic
138C2×C4×C157C2×D411yescharacteristic
139C2×C4×C157C2×D411yescharacteristic
140C2×C4×C157C2×D411yescharacteristic
141C2×C4×C157C2×D411yescharacteristic
142C2×C4×C157C2411yescharacteristic
143C22×C157—21no—
144C22×C157—21no—
145C22×C157—41no—
146C22×C157—41no—
147C22×C157—41no—
148C22×C157#13512yes—
149C22×C157C22×D411yescharacteristic
150C2×D157—41no—
151C2×D157—41no—
152C2×D157—41no—
153C4×C157—21no—
154C4×C157—21no—
155C4×C157—21no—
156C4×C157—21no—
157C4×C157—41no—
158C4×C157—41no—
159C4×C157—41no—
160C4×C157#13512yes—
161C4×C157C2×#4111yescharacteristic
162C4×C157C2×#4111yescharacteristic
163Dic157—41no—
164Dic157—41no—
165Dic157—41no—
166C2×C157—22no—
167C2×C157—81no—
168C2×C157#53211yescharacteristic
169C2×C157C2×#13511yescharacteristic
170C2×C157C2×#13511yescharacteristic
171D157—81no—
172C157#316811yescharacteristic, complemented, Sylow
173#3168—1571nomaximal, Sylow
174#529—1571no—
175#529D15711yescharacteristic, complemented
176#499—1571no—
177#495—1571no—
178#488—1571no—
179#488—1571no—
180#467—1571no—
181#466—1571no—
182#465—1571no—
183#465—1571no—
184C4×Q16—1571no—
185C4×SD16—1571no—
186C4×SD16—1571no—
187C4×D8—1571no—
188C2×C4×C8—1571no—
189C2×Q16—1571no—
190C2×SD16—1571no—
191C2×SD16—1571no—
192C2×D8—1571no—
193C22×C8—1571no—
194C22×C8—1571no—
195#126—21no—
196#126—3141no—
197#125—1571no—
198#125C2×D15711yescharacteristic
199#124—1571no—
200#124C2×D15711yescharacteristic
201#123—21no—
202#123—3141no—
203C22⋊Q8—1571no—
204C22⋊Q8C2×D15711yescharacteristic
205#121—1571no—
206#121C2×D15711yescharacteristic
207C4×Q8—1571no—
208C4×Q8C2×D15711yescharacteristic
209C4×D4—21no—
210C4×D4—3141no—
211C4×D4—1571no—
212C4×D4C2×D15711yescharacteristic
213#117—21no—
214#117—3141no—
215C2×C42C2×D15711yescharacteristic
216#107—1571no—
217#107—1571no—
218#106—1571no—
219#106—1571no—
220#103—1571no—
221#103—1571no—
222#103—1571no—
223#103—1571no—
224#102—1571no—
225#102—1571no—
226#102—1571no—
227#102—1571no—
228C4×C8—1571no—
229C4×C8—1571no—
230C4×C8—1571no—
231C4×C8—1571no—
232C2×Q8—1571no—
233C2×Q8C22×D15711yescharacteristic
234C2×D4—21no—
235C2×D4—3141no—
236C2×D4—1571no—
237C2×D4C22×D15711yescharacteristic
238C22×C4—21no—
239C22×C4—3141no—
240C22×C4C22⋊D15711yescharacteristic
241C22×C4C22⋊D15711yescharacteristic
242C22×C4C22×D15711yescharacteristic
243Q16—3142no—
244SD16—3142no—
245SD16—3142no—
246D8—3142no—
247C2×C8—3142no—
248C2×C8—3142no—
249C2×C8—1571no—
250C2×C8—1571no—
251C2×C8—1571no—
252C2×C8—1571no—
253C4⋊C4—21no—
254C4⋊C4—21no—
255C4⋊C4—21no—
256C4⋊C4—21no—
257C4⋊C4—3141no—
258C4⋊C4—3141no—
259C4⋊C4—3141no—
260C4⋊C4—3141no—
261C4⋊C4—1571no—
262C4⋊C4—1571no—
263C4⋊C4C22×D15711yescharacteristic
264C4⋊C4C22×D15711yescharacteristic
265C22⋊C4—21no—
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⋊C4—3141no—
275C42—21no—
276C42—3141no—
277C42C22⋊D15711yescharacteristic
278C42C22⋊D15711yescharacteristic
279C42C22×D15711yescharacteristic
280C42C22×D15711yescharacteristic
281C23—21no—
282C23—3141no—
283C23C2×C22⋊D15711yescharacteristic
284Q8—21no—
285Q8—21no—
286Q8—3141no—
287Q8—3141no—
288D4—21no—
289D4—21no—
290D4—42no—
291D4—3141no—
292D4—3141no—
293D4—6282no—
294C2×C4—22no—
295C2×C4—22no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—42no—
302C2×C4—3141no—
303C2×C4—3141no—
304C2×C4—3141no—
305C2×C4—6282no—
306C2×C4C2×C22⋊D15711yescharacteristic
307C2×C4C2×C22⋊D15711yescharacteristic
308C2×C4C2×C22⋊D15711yescharacteristic
309C2×C4C2×C22⋊D15711yescharacteristic
310C2×C4C2×C22⋊D15711yescharacteristic
311C2×C4C23×D15711yescharacteristic
312C8—3141no—
313C8—3141no—
314C8—1572no—
315C8—1572no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—6281no—
322C22—6281no—
323C22—6281no—
324C22#1909779112yes—
325C22C22×C22⋊D15711yescharacteristic
326C4—21no—
327C4—21no—
328C4—21no—
329C4—21no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—6281no—
334C4—6281no—
335C4—6281no—
336C4#1909779112yes—
337C4#41×D15711yescharacteristic
338C4#41×D15711yescharacteristic
339C2—22no—
340C2—81no—
341C2—12561no—
342C2#2375781911yescharacteristic
343C2C2×#1909779111yescharacteristic
344C2C2×#1909779111yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#529×C157C2
socleC22×C157C22×D4
prime radical#23757507C2
hypercenter#529D157
hypocenterC157#3168
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #529

Complements

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

NH ≅ G/Ntype
1. #23757807C2semidirect
2. #23757672C2semidirect
3. #23757655C2semidirect
4. #23757630C2semidirect
5. #23757627C2semidirect
6. #23757512C2semidirect
8. #23757504C2semidirect
9. #23757500C2semidirect
10. C4×#14578944C2semidirect
11. C4×#14578941C2semidirect
12. C4×#14578942C2semidirect
13. C4×#14578939C2semidirect
14. C2×C4×#11929434C2semidirect
15. #529×C157C2semidirect
172. C157#3168semidirect
175. #529D157semidirect

Maximal subgroups

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

subgroupindex
#237578072
#237576722
#237576552
#237576302
#237576272
#237575122
#237575072
#237575042
#237575002
C4×#145789442
C4×#145789412
C4×#145789422
C4×#145789392
C2×C4×#119294342
#529×C1572
#3168157