Finite Group Databasebeta

← #34112701

Subgroups — #34112701

Order 20096.

348 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757973C211yesmaximal, characteristic
2#23757964C211yesmaximal, characteristic, complemented
3#23757675C211yesmaximal, characteristic, complemented
4#23757612C211yesmaximal, characteristic, complemented
5#23757602C211yesmaximal, characteristic, complemented
6#23757596C211yesmaximal, characteristic, complemented
7#23757590C211yesmaximal, characteristic, complemented
8#23757580C211yesmaximal, characteristic, complemented
9#23757573C211yesmaximal, characteristic, complemented
10#23757516C211yesmaximal, characteristic, complemented
11#23757516C211yesmaximal, characteristic, complemented
12#23757352C211yesmaximal, characteristic, complemented
13#23757312C211yesmaximal, characteristic, complemented
14#23757312C211yesmaximal, characteristic, complemented
15C4×SD16×C157C211yesmaximal, characteristic, complemented
16C2×#14578937C2211yescharacteristic
17C2×#14578937C2211yescharacteristic
18#19097765—21no—
19#19097764—21no—
20#19097763C2211yescharacteristic
21#19097763C2211yescharacteristic
22#19097761—21no—
23#19097756—21no—
24#19097754—21no—
25#19097747C2211yescharacteristic
26#19097747C2211yescharacteristic
27#19097744—21no—
28#19097742C2211yescharacteristic
29#19097742C2211yescharacteristic
30C4×D628C2211yescharacteristic
31C4×C22⋊D157—21no—
32#19097729C2211yescharacteristic
33#19097729C2211yescharacteristic
34#19097728—21no—
35C4⋊C4×D157C2211yescharacteristic
36C4⋊C4×D157C2211yescharacteristic
37#19097705C2211yescharacteristic
38#19097705C2211yescharacteristic
39#19097704C2211yescharacteristic
40#19097704C2211yescharacteristic
41#19097703C2211yescharacteristic
42#19097703C2211yescharacteristic
43#19097702C2211yescharacteristic
44#19097702C2211yescharacteristic
45C4⋊#11929434C2211yescharacteristic
46#19097695C2211yescharacteristic
47#19097695C2211yescharacteristic
48#19097692C2211yescharacteristic
49#19097692C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097683C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58C4×C8×C157C2211yescharacteristic
59C2×D628D411yescharacteristic
60C2×C22⋊D157—21no—
61C2×C22⋊D157—21no—
62C2×C4×D157—21no—
63C2×C4×D157—21no—
64C2×C4×D157C2311yescharacteristic
65C2×C4×D157C2311yescharacteristic
66#14578937—22no—
67#14578937—22no—
68C2×#11929434C2311yescharacteristic
69C2×#11929434C2311yescharacteristic
70C4⋊Dic157D411yescharacteristic
71C4⋊Dic157C2311yescharacteristic
72C4⋊Dic157C2311yescharacteristic
73C4⋊Dic157C2311yescharacteristic
74C4⋊Dic157C2311yescharacteristic
75#14578933—21no—
76#14578933—21no—
77#14578933—21no—
78#14578933—21no—
79#14578933—21no—
80#14578933—21no—
81#14578933—21no—
82#14578933—21no—
83C22⋊Dic157—21no—
84C22⋊Dic157—21no—
85#14578931—21no—
86#14578931—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931D411yescharacteristic
90#14578931D411yescharacteristic
91C4×Dic157—21no—
92C4×Dic157—21no—
93C2×Q8×C157C2311yescharacteristic
94C2×D4×C157C2311yescharacteristic
95C22×C4×C157—21no—
96SD16×C157—22no—
97C2×C8×C157C2311yescharacteristic
98C2×C8×C157C2311yescharacteristic
99C4⋊C4×C157—21no—
100C4⋊C4×C157C2311yescharacteristic
101C4⋊C4×C157C2311yescharacteristic
102C22⋊C4×C157—21no—
103C42×C157—21no—
104C42×C157C2311yescharacteristic
105C22×D157C2×D411yescharacteristic
106C22×D157C2×D411yescharacteristic
107D628—41no—
108C22⋊D157—42no—
109C22⋊D157—81no—
110C2×Dic157—21no—
111C2×Dic157—21no—
112C2×Dic157—21no—
113C2×Dic157—21no—
114C2×Dic157C2×D411yescharacteristic
115C2×Dic157C2×D411yescharacteristic
116C4×D157—21no—
117C4×D157—21no—
118C4×D157—21no—
119C4×D157—21no—
120C4×D157—42no—
121C4×D157—81no—
122#11929434—21no—
123#11929434—21no—
124C23×C157—21no—
125Q8×C157—21no—
126Q8×C157—21no—
127D4×C157—21no—
128D4×C157—21no—
129C2×C4×C157—21no—
130C2×C4×C157—21no—
131C2×C4×C157—21no—
132C2×C4×C157—81no—
133C2×C4×C157C2×D411yescharacteristic
134C2×C4×C157C2×D411yescharacteristic
135C2×C4×C157C2411yescharacteristic
136C8×C157—21no—
137C8×C157#4112yes—
138C22×C157—41no—
139C22×C157—41no—
140C22×C157—41no—
141C22×C157C22×D411yescharacteristic
142C2×D157—21no—
143C2×D157—21no—
144C2×D157—21no—
145C2×D157—21no—
146C2×D157—21no—
147C2×D157—21no—
148C4×C157—21no—
149C4×C157—21no—
150C4×C157—41no—
151C4×C157—41no—
152C4×C157—41no—
153C4×C157C2×#4111yescharacteristic
154C4×C1572−1+411yescharacteristic
155Dic157—21no—
156Dic157—21no—
157Dic157—41no—
158Dic157—41no—
159Dic157—41no—
160Dic157—41no—
161C2×C157—81no—
162C2×C157#54711yescharacteristic
163C2×C157#57511yescharacteristic
164C2×C157#57711yescharacteristic
165D157—41no—
166D157—41no—
167C157#335111yescharacteristic, complemented, Sylow
168#3351—1571nomaximal, Sylow
169#553—1571no—
170#552—1571no—
171#499—1571no—
172#485—1571no—
173#483—1571no—
174#482—1571no—
175#481—1571no—
176#479—1571no—
177#478—1571no—
178#468—1571no—
179#468—1571no—
180C4×SD16D15711yescharacteristic, complemented
181#436—1571no—
182#428—1571no—
183#428—1571no—
184C2×SD16C2×D15711yescharacteristic
185C2×M16—1571no—
186C2×M16—1571no—
187#126—3141no—
188#126—3141no—
189#125—3141no—
190#125—1571no—
191#125—1571no—
192#123—3141no—
193#123—3141no—
194C22⋊Q8—1571no—
195C22⋊Q8—1571no—
196#121—3141no—
197#121—1571no—
198#121—1571no—
199C4×Q8C2×D15711yescharacteristic
200C4×D4—3141no—
201C4×D4—1571no—
202C4×D4C2×D15711yescharacteristic
203#117—3141no—
204#117—1571no—
205#117—1571no—
206C2×C4⋊C4—1571no—
207C2×C4⋊C4—1571no—
208#107—1571no—
209#107—1571no—
210#107—1571no—
211#107—1571no—
212#106—1571no—
213#106—1571no—
214#106—1571no—
215#106—1571no—
216#106C2×D15711yescharacteristic
217C4⋊C8—1571no—
218#103—1571no—
219#103—1571no—
220#103C2×D15711yescharacteristic
221#102—1571no—
222#102—1571no—
223#102C2×D15711yescharacteristic
224C22⋊C8—1571no—
225C22⋊C8—1571no—
226C4×C8C2×D15711yescharacteristic
227C2×Q8C22×D15711yescharacteristic
228C2×D4—3141no—
229C2×D4—3141no—
230C2×D4—1571no—
231C2×D4C22×D15711yescharacteristic
232C22×C4—21no—
233C22×C4—3141no—
234C22×C4—3141no—
235C22×C4—1571no—
236C22×C4—1571no—
237SD16—22no—
238M16—3142no—
239M16—3142no—
240C2×C8—1571no—
241C2×C8—1571no—
242C2×C8C22×D15711yescharacteristic
243C2×C8C22×D15711yescharacteristic
244C4⋊C4—21no—
245C4⋊C4—3141no—
246C4⋊C4—3141no—
247C4⋊C4—3141no—
248C4⋊C4—3141no—
249C4⋊C4—3141no—
250C4⋊C4—3141no—
251C4⋊C4—3141no—
252C4⋊C4—3141no—
253C4⋊C4—1571no—
254C4⋊C4—1571no—
255C4⋊C4—1571no—
256C4⋊C4—1571no—
257C4⋊C4—1571no—
258C4⋊C4C22×D15711yescharacteristic
259C4⋊C4C22×D15711yescharacteristic
260C22⋊C4—21no—
261C22⋊C4—3141no—
262C22⋊C4—3141no—
263C22⋊C4—3141no—
264C22⋊C4—3141no—
265C22⋊C4—3141no—
266C22⋊C4—3141no—
267C22⋊C4—1571no—
268C22⋊C4—1571no—
269C42—21no—
270C42—3141no—
271C42—3141no—
272C42C22×D15711yescharacteristic
273C23—21no—
274C23—1571no—
275C23—1571no—
276Q8—21no—
277Q8—21no—
278D4—21no—
279D4—21no—
280D4—6281no—
281D4—6282no—
282D4—12561no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—81no—
287C2×C4—3141no—
288C2×C4—3141no—
289C2×C4—3141no—
290C2×C4—3141no—
291C2×C4—3141no—
292C2×C4—3141no—
293C2×C4—3141no—
294C2×C4—3141no—
295C2×C4—6282no—
296C2×C4—1571no—
297C2×C4—1571no—
298C2×C4—12561no—
299C2×C4D4×D15711yescharacteristic
300C2×C4D4×D15711yescharacteristic
301C2×C4C23×D15711yescharacteristic
302C8—21no—
303C8—3141no—
304C8—3141no—
305C8#1457895412yes—
306C22—41no—
307C22—41no—
308C22—41no—
309C22—3141no—
310C22—3141no—
311C22—3141no—
312C22—3141no—
313C22—3141no—
314C22—3141no—
315C22C2×D4×D15711yescharacteristic
316C4—21no—
317C4—21no—
318C4—41no—
319C4—41no—
320C4—41no—
321C4—3141no—
322C4—3141no—
323C4—6281no—
324C4—6281no—
325C4—6281no—
326C4—6281no—
327C4C2×#1457895411yescharacteristic
328C4#1909781811yescharacteristic
329C2—81no—
330C2—6281no—
331C2—6281no—
332C2#2375792811yescharacteristic
333C2#2375807011yescharacteristic
334C2#2375807911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
FittingC4×SD16×C157C2
socleC22×C157C22×D4
prime radical#23757973C2
hypercenterC4×SD16D157
hypocenterC157#3351
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. #23757964C2semidirect
3. #23757675C2semidirect
4. #23757612C2semidirect
5. #23757602C2semidirect
6. #23757596C2semidirect
7. #23757590C2semidirect
8. #23757580C2semidirect
9. #23757573C2semidirect
10. #23757516C2semidirect
11. #23757516C2semidirect
12. #23757352C2semidirect
13. #23757312C2semidirect
14. #23757312C2semidirect
15. C4×SD16×C157C2semidirect
167. C157#3351semidirect
180. C4×SD16D157semidirect

Maximal subgroups

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

subgroupindex
#237579732
#237579642
#237576752
#237576122
#237576022
#237575962
#237575902
#237575802
#237575732
#237575162
#237573522
#237573122
C4×SD16×C1572
#3351157