Finite Group Databasebeta

← #34110285

Subgroups — #34110285

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#23757820C211yesmaximal, characteristic, complemented
2C4×#14578955C211yesmaximal, characteristic, complemented
3#23757600C211yesmaximal, characteristic, complemented
4#23757596C211yesmaximal, characteristic, complemented
5#23757556C211yesmaximal, characteristic, complemented
6#23757552C211yesmaximal, characteristic, complemented
7#23757471C211yesmaximal, characteristic, complemented
8#23757467C211yesmaximal, characteristic, complemented
9#23757421C211yesmaximal, characteristic, complemented
10#23757417C211yesmaximal, characteristic, complemented
11#23757386C211yesmaximal, characteristic, complemented
12#23757383C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14#23757328C211yesmaximal, characteristic, complemented
15#440×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578954—21no—
18C2×#14578941C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21#19097770C2211yescharacteristic
22#19097767C2211yescharacteristic
23#19097757—21no—
24#19097746C2211yescharacteristic
25#19097744—21no—
26#19097742C2211yescharacteristic
27Q8×Dic157C2211yescharacteristic
28C4×D628—21no—
29C4×D628C2211yescharacteristic
30C4×D628C2211yescharacteristic
31#19097733—21no—
32#19097733C2211yescharacteristic
33C4×C22⋊D157—21no—
34#19097729—21no—
35#19097729C2211yescharacteristic
36C42×D157—21no—
37C42×D157C2211yescharacteristic
38#19097704C2211yescharacteristic
39#19097703C2211yescharacteristic
40#19097702C2211yescharacteristic
41#19097700C2211yescharacteristic
42#19097700C2211yescharacteristic
43#19097695C2211yescharacteristic
44#19097693C2211yescharacteristic
45#19097693C2211yescharacteristic
46#19097692C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097683C2211yescharacteristic
50#19097683C2211yescharacteristic
51#19097682C2211yescharacteristic
52C2×SD16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54C4×D4×C157C2211yescharacteristic
55#107×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59#14578955—22no—
60#14578955—22no—
61#14578954—44no—
62C2×Dic314—21no—
63C2×D628—21no—
64C2×D628—21no—
65C2×D628C2311yescharacteristic
66C2×D628C2311yescharacteristic
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74C2×C4×D157D411yescharacteristic
75C2×C4×D157D411yescharacteristic
76C2×C4×D157C2311yescharacteristic
77#14578941—22no—
78D1256—22no—
79#14578939—22no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C4⋊Dic157—21no—
83C4⋊Dic157C2311yescharacteristic
84C4⋊Dic157C2311yescharacteristic
85#14578933—21no—
86C22⋊Dic157—21no—
87#14578931—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
97C2×Q8×C157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C22×C4×C157—21no—
100SD16×C157—22no—
101C2×C8×C157C2311yescharacteristic
102C2×C8×C157C2311yescharacteristic
103C4⋊C4×C157—21no—
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C42×C157—21no—
108C42×C157C2311yescharacteristic
109C22×D157—21no—
110C22×D157—21no—
111C22×D157C2×D411yescharacteristic
112Dic314—42no—
113D628—24no—
114D628—21no—
115D628—21no—
116D628—21no—
117D628—42no—
118D628#4112yescomplemented
119C22⋊D157—42no—
120C22⋊D157—42no—
121C22⋊D157—42no—
122C2×Dic157—21no—
123C2×Dic157—21no—
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C2×Dic157C2×D411yescharacteristic
127C4×D157—24no—
128C4×D157—21no—
129C4×D157—21no—
130C4×D157—22no—
131C4×D157—41no—
132C4×D157—42no—
133C4×D157—42no—
134C4×D157—42no—
135#11929434—21no—
136#11929434—21no—
137C23×C157—21no—
138Q8×C157—21no—
139Q8×C157#4112yescomplemented
140D4×C157—21no—
141D4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—42no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157—21no—
151C22×C157—41no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157C22×D411yescharacteristic
155C2×D157—21no—
156C2×D157—22no—
157C2×D157—21no—
158C2×D157—21no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C4×C157—22no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157C2×#4111yescharacteristic
170C4×C157C2×#4111yescharacteristic
171Dic157—21no—
172Dic157—21no—
173Dic157—41no—
174Dic157—41no—
175Dic157AGL(1,ℤ/8)12yes—
176C2×C157—81no—
177C2×C157#52511yescharacteristic
178C2×C157C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C157#57511yescharacteristic
180D157—41no—
181D157—42no—
182D157—81no—
183C157#311511yescharacteristic, complemented, Sylow
184#3115—1571nomaximal, Sylow
185#532—1571no—
186C4×#41—1571no—
187#482—1571no—
188#482—1571no—
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#440D15711yescharacteristic, complemented
199#432—1571no—
200C2×#41—3141no—
201C2×#41—1571no—
202C2×SD16—1571no—
203C2×SD16C2×D15711yescharacteristic
204C2×D8—1571no—
205C2×D8—1571no—
206C4⋊Q8—1571no—
207#127—1571no—
208#124—3141no—
209#121—3141no—
210#121—1571no—
211#121—1571no—
212C4×Q8—1571no—
213C4×Q8C2×D15711yescharacteristic
214C4×D4—3141no—
215C4×D4—3141no—
216C4×D4—3141no—
217C4×D4—1571no—
218C4×D4—1571no—
219C4×D4—1571no—
220C4×D4C2×D15711yescharacteristic
221#117—3141no—
222#117—1571no—
223C2×C42—3141no—
224C2×C42—1571no—
225#107—1571no—
226#107C2×D15711yescharacteristic
227#106—1571no—
228#106—1571no—
229C4⋊C8—1571no—
230C4⋊C8—1571no—
231#103—1571no—
232#103C2×D15711yescharacteristic
233#102—1571no—
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102—1571no—
238#102C2×D15711yescharacteristic
239C22⋊C8—1571no—
240C22⋊C8—1571no—
241#97—1571no—
242#97C2×D15711yescharacteristic
243#41—3142no—
244#41—3142no—
245#41—6284no—
246C2×Q8—3141no—
247C2×Q8C22×D15711yescharacteristic
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—3141no—
251C2×D4—3141no—
252C2×D4—3141no—
253C2×D4—1571no—
254C2×D4—1571no—
255C2×D4C22×D15711yescharacteristic
256C22×C4—21no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—3141no—
260C22×C4—3141no—
261C22×C4—1571no—
262C22×C4—1571no—
263C22×C4—1571no—
264SD16—22no—
265SD16—3142no—
266D8—3142no—
267D8—3142no—
268C2×C8—1571no—
269C2×C8—1571no—
270C2×C8C22×D15711yescharacteristic
271C2×C8C22×D15711yescharacteristic
272C4⋊C4—21no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—1571no—
276C4⋊C4—1571no—
277C4⋊C4C22×D15711yescharacteristic
278C4⋊C4C22×D15711yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—3141no—
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—
292C42C22×D15711yescharacteristic
293C23—21no—
294C23—3141no—
295C23—3141no—
296C23—1571no—
297Q8—21no—
298Q8—6282no—
299Q8#1457895412yescomplemented
300D4—21no—
301D4—21no—
302D4—3144no—
303D4—3141no—
304D4—3141no—
305D4—3141no—
306D4—6282no—
307D4—6282no—
308D4—6282no—
309D4—6282no—
310D4—1572no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—42no—
315C2×C4—3144no—
316C2×C4—3142no—
317C2×C4—3141no—
318C2×C4—3141no—
319C2×C4—3141no—
320C2×C4—3141no—
321C2×C4—6281no—
322C2×C4—6282no—
323C2×C4—6282no—
324C2×C4—6282no—
325C2×C4—1571no—
326C2×C4—1571no—
327C2×C4—1571no—
328C2×C4D4×D15711yescharacteristic
329C2×C4D4×D15711yescharacteristic
330C2×C4C23×D15711yescharacteristic
331C8—21no—
332C8—21no—
333C8—3141no—
334C8—3141no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—3141no—
339C22—3142no—
340C22—3141no—
341C22—3141no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—6281no—
346C22—6281no—
347C22C2×D4×D15711yescharacteristic
348C4—22no—
349C4—21no—
350C4—21no—
351C4—41no—
352C4—41no—
353C4—3141no—
354C4—3141no—
355C4—6281no—
356C4—6281no—
357C4—1572no—
358C4#41×D15711yescharacteristic
359C4C2×#1457895411yescharacteristic
360C2—81no—
361C2—6281no—
362C2—6282no—
363C2—12561no—
364C2#2375778211yescharacteristic
365C2AGL(1,ℤ/8)×D15711yescharacteristic
366C2#2375807211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#440×C157C2
socleC22×C157C22×D4
hypercenter#440D157
hypocenterC157#3115
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #23757820C2semidirect
2. C4×#14578955C2semidirect
3. #23757600C2semidirect
4. #23757596C2semidirect
5. #23757556C2semidirect
6. #23757552C2semidirect
7. #23757471C2semidirect
8. #23757467C2semidirect
9. #23757421C2semidirect
10. #23757417C2semidirect
11. #23757386C2semidirect
12. #23757383C2semidirect
13. #23757371C2semidirect
14. #23757328C2semidirect
15. #440×C157C2semidirect
118. D628#41semidirect
139. Q8×C157#41semidirect
183. C157#3115semidirect
198. #440D157semidirect
299. Q8#14578954semidirect

Maximal subgroups

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

subgroupindex
#237578202
C4×#145789552
#237576002
#237575962
#237575562
#237575522
#237574712
#237574672
#237574212
#237574172
#237573862
#237573832
#237573712
#237573282
#440×C1572
#3115157