Finite Group Databasebeta

← #34110282

Subgroups — #34110282

Order 20096.

430 conjugacy classes of subgroups.

The subgroup lattice has 368 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757818C211yesmaximal, characteristic, complemented
2#23757741C211yesmaximal, characteristic, complemented
3#23757597C211yesmaximal, characteristic, complemented
4#23757557C211yesmaximal, characteristic, complemented
5#23757552C211yesmaximal, characteristic, complemented
6#23757472C211yesmaximal, characteristic, complemented
7#23757467C211yesmaximal, characteristic, complemented
8#23757420C211yesmaximal, characteristic, complemented
9#23757416C211yesmaximal, characteristic, complemented
10#23757384C211yesmaximal, characteristic, complemented
11#23757382C211yesmaximal, characteristic, complemented
12#23757372C211yesmaximal, characteristic, complemented
13#23757370C211yesmaximal, characteristic, complemented
14#23757327C211yesmaximal, characteristic, complemented
15#482×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578953—21no—
18C2×#14578943C2211yescharacteristic
19C2×#14578942C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22#19097770C2211yescharacteristic
23#19097767C2211yescharacteristic
24#19097757—21no—
25#19097745C2211yescharacteristic
26#19097743—21no—
27#19097736C2211yescharacteristic
28#19097736C2211yescharacteristic
29D4×Dic157C2211yescharacteristic
30#19097733C2211yescharacteristic
31#19097733C2211yescharacteristic
32#19097733C2211yescharacteristic
33#19097731—21no—
34#19097731—21no—
35#19097731—21no—
36#19097728—21no—
37C2×C4×Dic157C2211yescharacteristic
38C42×D157—21no—
39#19097704C2211yescharacteristic
40#19097702C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097700C2211yescharacteristic
43#19097696C2211yescharacteristic
44#19097694C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097691C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49C22⋊#11929434C2211yescharacteristic
50#19097681C2211yescharacteristic
51#19097681C2211yescharacteristic
52#121×C157C2211yescharacteristic
53#117×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#102×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58C22⋊C8×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61#14578953—44no—
62C2×Dic314—21no—
63C2×Dic314C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C22×Dic157—21no—
71C22×Dic157D411yescharacteristic
72C22×Dic157D411yescharacteristic
73C2×C4×D157—21no—
74C2×C4×D157—21no—
75C2×C4×D157—21no—
76C2×C4×D157—21no—
77#14578943—22no—
78#14578942—22no—
79D1256—22no—
80#14578939—22no—
81C2×#11929434C2311yescharacteristic
82C2×#11929434C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933—21no—
86#14578933—21no—
87C22⋊Dic157—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92C4×Dic157—21no—
93C4×Dic157—21no—
94C4×Dic157D411yescharacteristic
95C4×Dic157D411yescharacteristic
96C4×Dic157C2311yescharacteristic
97C4×Dic157C2311yescharacteristic
98C2×D4×C157—21no—
99C2×D4×C157C2311yescharacteristic
100C22×C4×C157C2311yescharacteristic
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C22⋊C4×C157—21no—
108C42×C157—21no—
109C22×D157—21no—
110C22×D157—21no—
111Dic314—21no—
112Dic314—42no—
113Dic314#4112yescomplemented
114D628—21no—
115D628—21no—
116D628—21no—
117D628#4112yescomplemented
118C22⋊D157—24no—
119C22⋊D157—42no—
120C22⋊D157—42no—
121C22⋊D157—42no—
122C2×Dic157—21no—
123C2×Dic157—22no—
124C2×Dic157—21no—
125C2×Dic157—41no—
126C2×Dic157—42no—
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C4×D157—24no—
132C4×D157—42no—
133C4×D157—42no—
134C4×D157—42no—
135#11929434—21no—
136#11929434—21no—
137C23×C157—21no—
138C23×C157C2×D411yescharacteristic
139D4×C157—21no—
140D4×C157—21no—
141D4×C157—42no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157—21no—
151C22×C157—21no—
152C22×C157—21no—
153C22×C157—21no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157C22×D411yescharacteristic
158C2×D157—22no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C4×C157—21no—
165C4×C157—41no—
166C4×C157—41no—
167C4×C157—41no—
168C4×C157C2×#4111yescharacteristic
169C4×C157C2×#4111yescharacteristic
170Dic157—22no—
171Dic157—21no—
172Dic157—21no—
173Dic157—21no—
174Dic157—41no—
175Dic157AGL(1,ℤ/8)12yes—
176C2×C157—41no—
177C2×C157—81no—
178C2×C157#52511yescharacteristic
179C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
180C2×C157#57511yescharacteristic
181D157—42no—
182D157—81no—
183C157#311511yescharacteristic, complemented, Sylow
184#3115—1571nomaximal, Sylow
185#532—1571no—
186C4×#41—1571no—
187#482—1571no—
188#482D15711yescharacteristic, complemented
189#475—1571no—
190#474—1571no—
191#460—1571no—
192#459—1571no—
193#449—1571no—
194#449—1571no—
195#442—1571no—
196#442—1571no—
197#440—1571no—
198#440—1571no—
199#432—1571no—
200C2×#41—3141no—
201C2×#41—1571no—
202C2×SD16—1571no—
203C2×SD16—1571no—
204C2×D8—1571no—
205C2×D8—1571no—
206C4⋊Q8—1571no—
207#127—1571no—
208#124—3141no—
209#121—3141no—
210#121—1571no—
211#121C2×D15711yescharacteristic
212C4×Q8—1571no—
213C4×Q8—1571no—
214C4×D4—3141no—
215C4×D4—3141no—
216C4×D4—3141no—
217C4×D4—1571no—
218C4×D4—1571no—
219C4×D4—1571no—
220C4×D4—1571no—
221#117—3141no—
222#117C2×D15711yescharacteristic
223C2×C42—3141no—
224C2×C42—1571no—
225#107—1571no—
226#107C2×D15711yescharacteristic
227#106—1571no—
228#106C2×D15711yescharacteristic
229C4⋊C8—1571no—
230C4⋊C8—1571no—
231#103—1571no—
232#103—1571no—
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102C2×D15711yescharacteristic
238#102C2×D15711yescharacteristic
239C22⋊C8—1571no—
240C22⋊C8C2×D15711yescharacteristic
241#97—1571no—
242#97—1571no—
243#41—3142no—
244#41—3142no—
245#41—6284no—
246C2×Q8—3141no—
247C2×Q8—1571no—
248C2×D4—21no—
249C2×D4—3141no—
250C2×D4—3141no—
251C2×D4—3141no—
252C2×D4—3141no—
253C2×D4—1571no—
254C2×D4—1571no—
255C2×D4C22×D15711yescharacteristic
256C22×C4—3141no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—3141no—
260C22×C4—3141no—
261C22×C4—1571no—
262C22×C4—1571no—
263C22×C4C22×D15711yescharacteristic
264SD16—3142no—
265SD16—3142no—
266D8—3142no—
267D8—3142no—
268C2×C8—1571no—
269C2×C8—1571no—
270C2×C8C22×D15711yescharacteristic
271C2×C8C22×D15711yescharacteristic
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—1571no—
276C4⋊C4C22×D15711yescharacteristic
277C4⋊C4C22×D15711yescharacteristic
278C4⋊C4C22×D15711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C42—21no—
287C42—3141no—
288C42—3141no—
289C42—1571no—
290C42—1571no—
291C42—1571no—
292C42—1571no—
293C23—21no—
294C23—3141no—
295C23—3141no—
296C23D4×D15711yescharacteristic
297Q8—3141no—
298Q8—6282no—
299Q8—1572no—
300D4—21no—
301D4—21no—
302D4—42no—
303D4—3144no—
304D4—3141no—
305D4—3141no—
306D4—3141no—
307D4—6282no—
308D4—6282no—
309D4—6282no—
310D4—1572no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—3144no—
317C2×C4—3141no—
318C2×C4—3142no—
319C2×C4—3141no—
320C2×C4—6282no—
321C2×C4—6282no—
322C2×C4—6282no—
323C2×C4—6281no—
324C2×C4—6282no—
325C2×C4—1571no—
326C2×C4—1571no—
327C2×C4—1571no—
328C2×C4—1571no—
329C2×C4D4×D15711yescharacteristic
330C2×C4C23×D15711yescharacteristic
331C8—21no—
332C8—21no—
333C8—3141no—
334C8—3141no—
335C22—21no—
336C22—21no—
337C22—21no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—3142no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—6281no—
346C22—6281no—
347C22C2×D4×D15711yescharacteristic
348C4—21no—
349C4—41no—
350C4—41no—
351C4—41no—
352C4—3142no—
353C4—3141no—
354C4—3141no—
355C4—3141no—
356C4—6281no—
357C4—1572no—
358C4#41×D15711yescharacteristic
359C4#41×D15711yescharacteristic
360C2—41no—
361C2—81no—
362C2—6282no—
363C2—12561no—
364C2#2375778111yescharacteristic
365C2AGL(1,ℤ/8)×D15711yescharacteristic
366C2#2375807011yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#482×C157C2
socleC22×C157C22×D4
hypercenter#482D157
hypocenterC157#3115
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #23757818C2semidirect
2. #23757741C2semidirect
3. #23757597C2semidirect
4. #23757557C2semidirect
5. #23757552C2semidirect
6. #23757472C2semidirect
7. #23757467C2semidirect
8. #23757420C2semidirect
9. #23757416C2semidirect
10. #23757384C2semidirect
11. #23757382C2semidirect
12. #23757372C2semidirect
13. #23757370C2semidirect
14. #23757327C2semidirect
15. #482×C157C2semidirect
113. Dic314#41semidirect
117. D628#41semidirect
183. C157#3115semidirect
188. #482D157semidirect

Maximal subgroups

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

subgroupindex
#237578182
#237577412
#237575972
#237575572
#237575522
#237574722
#237574672
#237574202
#237574162
#237573842
#237573822
#237573722
#237573702
#237573272
#482×C1572
#3115157