Finite Group Databasebeta

← #34112840

Subgroups — #34112840

Order 20096.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757979C211yesmaximal, characteristic, complemented
2#23757943C211yesmaximal, characteristic, complemented
3#23757636C211yesmaximal, characteristic, complemented
4#23757618C211yesmaximal, characteristic, complemented
5#23757575C211yesmaximal, characteristic, complemented
6#23757570C211yesmaximal, characteristic, complemented
7#23757561C211yesmaximal, characteristic, complemented
8#23757467C211yesmaximal, characteristic, complemented
9#23757467C211yesmaximal, characteristic, complemented
10#23757465C211yesmaximal, characteristic, complemented
11#23757401C211yesmaximal, characteristic, complemented
12#23757386C211yesmaximal, characteristic, complemented
13#23757382C211yesmaximal, characteristic, complemented
14#23757353C211yesmaximal, characteristic, complemented
15#490×C157C211yesmaximal, characteristic, complemented
16C2×#14578953—21no—
17C2×D1256C2211yescharacteristic
18C2×#14578939C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20#19097770C2211yescharacteristic
21#19097767C2211yescharacteristic
22#19097767C2211yescharacteristic
23#19097762C2211yescharacteristic
24#19097751—21no—
25#19097749—21no—
26#19097749—21no—
27#19097743—21no—
28#19097743—21no—
29#19097742—21no—
30C4×Dic314C2211yescharacteristic
31C4×D628C2211yescharacteristic
32C4×D628C2211yescharacteristic
33D4×Dic157C2211yescharacteristic
34D4×Dic157C2211yescharacteristic
35#19097733C2211yescharacteristic
36#19097733C2211yescharacteristic
37C4⋊C4×D157—21no—
38#19097704C2211yescharacteristic
39#19097703C2211yescharacteristic
40#19097702C2211yescharacteristic
41C4⋊#11929434C2211yescharacteristic
42#19097700C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097692C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52#127×C157C2211yescharacteristic
53#125×C157C2211yescharacteristic
54#102×C157C2211yescharacteristic
55#102×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578953—44no—
60C2×Dic314—21no—
61C2×Dic314D411yescharacteristic
62C2×D628C2311yescharacteristic
63C2×D628C2311yescharacteristic
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C22×Dic157—21no—
69C22×Dic157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74D1256—22no—
75#14578939—22no—
76#14578939—22no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C4⋊Dic157—21no—
80C4⋊Dic157D411yescharacteristic
81C4⋊Dic157C2311yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85#14578933D411yescharacteristic
86#14578933D411yescharacteristic
87C22⋊Dic157—21no—
88C22⋊Dic157—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93C4×Dic157C2311yescharacteristic
94C4×Dic157C2311yescharacteristic
95C2×D4×C157—21no—
96C2×D4×C157—21no—
97C2×D4×C157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C4⋊C4×C157—21no—
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C42×C157C2311yescharacteristic
106C22×D157—21no—
107C22×D157—21no—
108Dic314—22no—
109Dic314—81no—
110D628—21no—
111D628—21no—
112D628—21no—
113D628#4112yescomplemented
114C22⋊D157—42no—
115C22⋊D157—42no—
116C22⋊D157—81no—
117C22⋊D157—81no—
118C2×Dic157—21no—
119C2×Dic157—21no—
120C2×Dic157—42no—
121C2×Dic157—42no—
122C2×Dic157C2×D411yescharacteristic
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C4×D157—42no—
127C4×D157—42no—
128C4×D157—81no—
129C4×D157—81no—
130#11929434—21no—
131#11929434—21no—
132C23×C157—21no—
133C23×C157—21no—
134D4×C157—21no—
135D4×C157—21no—
136D4×C157—21no—
137D4×C157—21no—
138D4×C157—42no—
139D4×C157—81no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157C2×D411yescharacteristic
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2411yescharacteristic
145C8×C157—21no—
146C8×C157—21no—
147C22×C157—41no—
148C22×C157—41no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157—41no—
152C22×C157—41no—
153C22×C157C22×D411yescharacteristic
154C2×D157—22no—
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C4×C157—21no—
161C4×C157—21no—
162C4×C157—41no—
163C4×C157—41no—
164C4×C157C2×#4111yescharacteristic
165C4×C1572−1+411yescharacteristic
166Dic157—21no—
167Dic157—21no—
168Dic157—21no—
169Dic157—41no—
170Dic157—41no—
171Dic157AGL(1,ℤ/8)12yes—
172C2×C157—81no—
173C2×C157—81no—
174C2×C157#54811yescharacteristic
175C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C157#57611yescharacteristic
177D157—42no—
178D157—81no—
179C157#336611yescharacteristic, complemented, Sylow
180#3366—1571nomaximal, Sylow
181#554—1571no—
182#550—1571no—
183#490—1571no—
184#490D15711yescharacteristic, complemented
185#486—1571no—
186#478—1571no—
187#478—1571no—
188#476—1571no—
189#459—1571no—
190#459—1571no—
191#459—1571no—
192#446—1571no—
193#442—1571no—
194#442—1571no—
195C4×D8—1571no—
196C2×#41—3141no—
197C2×D8—1571no—
198C2×D8—1571no—
199C2×D8—1571no—
200C4⋊Q8—1571no—
201#127—1571no—
202#127—1571no—
203#127C2×D15711yescharacteristic
204#125—1571no—
205#125C2×D15711yescharacteristic
206C22⋊Q8—3141no—
207C22⋊Q8—3141no—
208C22⋊Q8—3141no—
209#121—3141no—
210#121—3141no—
211#121—3141no—
212C4×Q8—1571no—
213C4×D4—1571no—
214C4×D4—1571no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4—1571no—
218C4×D4—1571no—
219C2×C4⋊C4—3141no—
220#107—1571no—
221#106—1571no—
222#106—1571no—
223C4⋊C8—1571no—
224C4⋊C8—1571no—
225C4⋊C8—1571no—
226#102—1571no—
227#102—1571no—
228#102—1571no—
229#102—1571no—
230#102—1571no—
231#102—1571no—
232#102C2×D15711yescharacteristic
233#102C2×D15711yescharacteristic
234#102C2×D15711yescharacteristic
235#102C2×D15711yescharacteristic
236#97—1571no—
237#97C2×D15711yescharacteristic
238C4×C8—1571no—
239#41—6284no—
240C2×Q8—3141no—
241C2×Q8—1571no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—1571no—
249C2×D4—1571no—
250C2×D4C22×D15711yescharacteristic
251C2×D4C22×D15711yescharacteristic
252C22×C4—3141no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—3141no—
258D8—3142no—
259D8—3142no—
260D8—3142no—
261C2×C8—1571no—
262C2×C8—1571no—
263C2×C8C22×D15711yescharacteristic
264C2×C8C22×D15711yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—3141no—
268C4⋊C4—3141no—
269C4⋊C4—3141no—
270C4⋊C4—1571no—
271C4⋊C4—1571no—
272C4⋊C4—1571no—
273C4⋊C4—1571no—
274C4⋊C4—1571no—
275C4⋊C4C22×D15711yescharacteristic
276C4⋊C4C22×D15711yescharacteristic
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C42—1571no—
284C42—1571no—
285C42C22×D15711yescharacteristic
286C23—21no—
287C23—21no—
288C23—3141no—
289C23—3141no—
290Q8—3142no—
291Q8—12561no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—3141no—
299D4—3141no—
300D4—3141no—
301D4—6282no—
302D4—6282no—
303D4—1572no—
304D4—12561no—
305D4—12561no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—3141no—
309C2×C4—3141no—
310C2×C4—6282no—
311C2×C4—6282no—
312C2×C4—6282no—
313C2×C4—6282no—
314C2×C4—1571no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—1571no—
318C2×C4—12561no—
319C2×C4—12561no—
320C2×C4D4×D15711yescharacteristic
321C2×C4D4×D15711yescharacteristic
322C2×C4C23×D15711yescharacteristic
323C8—21no—
324C8—21no—
325C8—3141no—
326C8—3141no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—3142no—
334C22—6281no—
335C22—6281no—
336C22—6281no—
337C22—6281no—
338C22—6281no—
339C22C2×D4×D15711yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—3141no—
345C4—3141no—
346C4—3141no—
347C4—6281no—
348C4—6281no—
349C4—1572no—
350C4#41×D15711yescharacteristic
351C4#1909781811yescharacteristic
352C2—81no—
353C2—81no—
354C2—6282no—
355C2—12561no—
356C2#2375793111yescharacteristic
357C2AGL(1,ℤ/8)×D15711yescharacteristic
358C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#490×C157C2
socleC22×C157C22×D4
hypercenter#490D157
hypocenterC157#3366
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #23757979C2semidirect
2. #23757943C2semidirect
3. #23757636C2semidirect
4. #23757618C2semidirect
5. #23757575C2semidirect
6. #23757570C2semidirect
7. #23757561C2semidirect
8. #23757467C2semidirect
9. #23757467C2semidirect
10. #23757465C2semidirect
11. #23757401C2semidirect
12. #23757386C2semidirect
13. #23757382C2semidirect
14. #23757353C2semidirect
15. #490×C157C2semidirect
113. D628#41semidirect
179. C157#3366semidirect
184. #490D157semidirect

Maximal subgroups

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

subgroupindex
#237579792
#237579432
#237576362
#237576182
#237575752
#237575702
#237575612
#237574672
#237574652
#237574012
#237573862
#237573822
#237573532
#490×C1572
#3366157