Finite Group Databasebeta

← #34109008

Subgroups — #34109008

Order 20096.

484 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19097792C211yesmaximal, characteristic
2#23757755C211yesmaximal, characteristic, complemented
3#23757752C211yesmaximal, characteristic, complemented
4#23757375C211yesmaximal, characteristic, complemented
5#23757374C211yesmaximal, characteristic, complemented
6#23757372C211yesmaximal, characteristic, complemented
7C4×#14578944C211yesmaximal, characteristic, complemented
8#23757365C211yesmaximal, characteristic, complemented
9C4×#14578939C211yesmaximal, characteristic, complemented
10#23757353C211yesmaximal, characteristic, complemented
11#107×D157C211yesmaximal, characteristic, complemented
12#23757273C211yesmaximal, characteristic, complemented
13#23757271C211yesmaximal, characteristic, complemented
14#23757230C211yesmaximal, characteristic, complemented
15#440×C157C211yesmaximal, characteristic, complemented
16C2×#14578955C2211yescharacteristic
17C2×#14578953C2211yescharacteristic
18#19097792C418yescomplemented
19C2×#14578944C2211yescharacteristic
20C2×#14578943C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22C2×#14578937C2211yescharacteristic
23C2×C8×D157C2211yescharacteristic
24Q8×Dic157C2211yescharacteristic
25C4×Dic314C2211yescharacteristic
26#19097736C2211yescharacteristic
27C4×D628—21no—
28C4×D628C2211yescharacteristic
29D4×Dic157C2211yescharacteristic
30#19097733—21no—
31#19097733C2211yescharacteristic
32C4×C22⋊D157—21no—
33#19097731—21no—
34#19097728—21no—
35#19097728C2211yescharacteristic
36#19097727—21no—
37C2×#14578933—21no—
38C4⋊C4×D157—21no—
39C4⋊C4×D157C2211yescharacteristic
40C4⋊C4×D157C2211yescharacteristic
41#19097705C2211yescharacteristic
42#19097704C2211yescharacteristic
43#19097704C2211yescharacteristic
44#19097696C2211yescharacteristic
45#19097695C2211yescharacteristic
46#19097694C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097692C2211yescharacteristic
49#19097691C2211yescharacteristic
50#19097681C2211yescharacteristic
51C4×#11929434C2211yescharacteristic
52C8×Dic157C2211yescharacteristic
53C2×SD16×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic
55C4×D4×C157C2211yescharacteristic
56#107×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59#97×C157C2211yescharacteristic
60#14578955—22no—
61#14578955C2×C414yescomplemented
62#14578953—22no—
63#14578953C2×C414yescomplemented
64C2×Dic314C2311yescharacteristic
65C2×D628—21no—
66C2×D628C2311yescharacteristic
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—
74C2×C4×D157—21no—
75C2×C4×D157C2311yescharacteristic
76#14578944C2×C414yescomplemented
77#14578943C2×C414yescomplemented
78#14578939C2×C414yescomplemented
79#14578937—22no—
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C8×D157C2×C414yescomplemented
83C4⋊Dic157—21no—
84C4⋊Dic157C2311yescharacteristic
85C4⋊Dic157C2311yescharacteristic
86#14578933—21no—
87#14578933—21no—
88#14578933—21no—
89#14578933—21no—
90#14578933D411yescharacteristic
91#14578933D411yescharacteristic
92C22⋊Dic157—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931D411yescharacteristic
96#14578931D411yescharacteristic
97C4×Dic157—21no—
98C4×Dic157—21no—
99C4×Dic157—21no—
100C4×Dic157C2311yescharacteristic
101C2×Q8×C157C2311yescharacteristic
102C2×D4×C157C2311yescharacteristic
103C22×C4×C157—21no—
104SD16×C157C2×C414yescomplemented
105C2×C8×C157C2311yescharacteristic
106C2×C8×C157C2311yescharacteristic
107C4⋊C4×C157—21no—
108C4⋊C4×C157C2311yescharacteristic
109C4⋊C4×C157C2311yescharacteristic
110C22⋊C4×C157—21no—
111C42×C157—21no—
112C42×C157C2311yescharacteristic
113C22×D157—21no—
114C22×D157C2×D411yescharacteristic
115Dic314—21no—
116Dic314C22×C412yes—
117D628—24no—
118D628—21no—
119D628C22×C412yes—
120C22⋊D157—24no—
121C2×Dic157—21no—
122C2×Dic157—24no—
123C2×Dic157—21no—
124C2×Dic157—21no—
125C2×Dic157—81no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C4×D157—24no—
130C4×D157—81no—
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157C22×C412yes—
135C4×D157#4112yes—
136#11929434—21no—
137#11929434C22×C412yes—
138C23×C157—21no—
139Q8×C157—21no—
140Q8×C157C22×C412yes—
141D4×C157—21no—
142D4×C157C22×C412yes—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—81no—
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2411yescharacteristic
150C8×C157—21no—
151C8×C157C22×C412yes—
152C22×C157—22no—
153C22×C157—41no—
154C22×C157—41no—
155C22×C157C22×D411yescharacteristic
156C2×D157—21no—
157C2×D157—21no—
158C2×D157—22no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157C4×D412yes—
162C4×C157—22no—
163C4×C157—21no—
164C4×C157—21no—
165C4×C157—41no—
166C4×C157—41no—
167C4×C157C23×C411yescharacteristic
168C4×C157C2×#4111yescharacteristic
169Dic157—22no—
170Dic157—21no—
171Dic157—21no—
172Dic157—41no—
173Dic157—41no—
174Dic157C4×D412yes—
175C2×C157—42no—
176C2×C157C2×C4×D411yescharacteristic
177C2×C157#57611yescharacteristic
178C2×C157#57811yescharacteristic
179D157—22no—
180D157—42no—
181C157#295111yescharacteristic, complemented, Sylow
182#2951—1571nomaximal, Sylow
183C2×#135—1571no—
184#520—1571no—
185#520—1571no—
186#440—1571no—
187#440—1571no—
188#440—1571no—
189#440D15711yescharacteristic, complemented
190C4×Q16—1571no—
191C4×Q16—1571no—
192C4×D8—1571no—
193C4×D8—1571no—
194C2×#107—1571no—
195#417—1571no—
196#417—1571no—
197#405—1571no—
198C2×#41—1571no—
199C2×#41—1571no—
200#135—1578no—
201C2×Q16—1571no—
202C2×SD16—1571no—
203C2×SD16C2×D15711yescharacteristic
204C2×D8—1571no—
205C2×M16—1571no—
206C22×C8—1571no—
207C4×Q8—1571no—
208C4×Q8—1571no—
209C4×Q8—1571no—
210C4×Q8C2×D15711yescharacteristic
211C4×D4—3141no—
212C4×D4—3141no—
213C4×D4—3141no—
214C4×D4—3141no—
215C4×D4—1571no—
216C4×D4—1571no—
217C4×D4—1571no—
218C4×D4C2×D15711yescharacteristic
219#117—3141no—
220#117—3141no—
221#117—1571no—
222C2×C4⋊C4—3141no—
223C2×C4⋊C4—3141no—
224C2×C4⋊C4—1571no—
225C2×C4⋊C4—1571no—
226#107—1571no—
227#107—1571no—
228#107—1571no—
229#107C2×D15711yescharacteristic
230#103—1571no—
231#103—1571no—
232#103—1571no—
233#103C2×D15711yescharacteristic
234#102—1571no—
235#102—1571no—
236#102—1571no—
237#102C2×D15711yescharacteristic
238#97—1571no—
239#97C2×D15711yescharacteristic
240C4×C8—1571no—
241C4×C8—1571no—
242#41—3142no—
243#41—3142no—
244#41—1574no—
245#41—1574no—
246C2×Q8—1571no—
247C2×Q8C22×D15711yescharacteristic
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—1571no—
251C2×D4C22×D15711yescharacteristic
252C22×C4—21no—
253C22×C4—3141no—
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—3141no—
260C22×C4—1571no—
261Q16—1574no—
262SD16—1574no—
263SD16C4×D15714yescomplemented
264D8—1574no—
265M16—3142no—
266C2×C8—1571no—
267C2×C8—1571no—
268C2×C8—1574no—
269C2×C8C22×D15711yescharacteristic
270C2×C8C22×D15711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—3141no—
276C4⋊C4—3141no—
277C4⋊C4—1571no—
278C4⋊C4—1571no—
279C4⋊C4—1571no—
280C4⋊C4—1571no—
281C4⋊C4C22×D15711yescharacteristic
282C4⋊C4C22×D15711yescharacteristic
283C22⋊C4—21no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—1571no—
288C22⋊C4—1571no—
289C42—21no—
290C42—3141no—
291C42—3141no—
292C42—3141no—
293C42—1571no—
294C42C22×D15711yescharacteristic
295C23—21no—
296C23—3141no—
297C23—1571no—
298Q8—21no—
299Q8—3141no—
300Q8—1572no—
301Q8C2×C4×D15712yes—
302D4—21no—
303D4—3144no—
304D4—3144no—
305D4—3141no—
306D4—1572no—
307D4C2×C4×D15712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—3144no—
313C2×C4—3141no—
314C2×C4—3144no—
315C2×C4—3141no—
316C2×C4—3141no—
317C2×C4—1571no—
318C2×C4—1571no—
319C2×C4—1571no—
320C2×C4—1572no—
321C2×C4—1572no—
322C2×C4—12561no—
323C2×C4—12561no—
324C2×C4—12561no—
325C2×C4—12561no—
326C2×C4—12561no—
327C2×C4D4×D15711yescharacteristic
328C2×C4D4×D15711yescharacteristic
329C2×C4C23×D15711yescharacteristic
330C8—21no—
331C8—3141no—
332C8—1572no—
333C8C2×C4×D15712yes—
334C22—22no—
335C22—41no—
336C22—41no—
337C22—3141no—
338C22—3141no—
339C22—3142no—
340C22—6281no—
341C22—6281no—
342C22—1572no—
343C22C2×D4×D15711yescharacteristic
344C4—21no—
345C4—22no—
346C4—21no—
347C4—41no—
348C4—41no—
349C4—3141no—
350C4—3142no—
351C4—3141no—
352C4—6281no—
353C4—6281no—
354C4—1572no—
355C4C22×C4×D15711yescharacteristic
356C4#41×D15711yescharacteristic
357C2—42no—
358C2—3142no—
359C2—6282no—
360C2C4×D4×D15711yescharacteristic
361C2#2375807711yescharacteristic
362C2#2375808911yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutatorC4×C157C23×C4
FrattiniC2×C4C23×D157
Fitting#440×C157C2
socleC22×C157C22×D4
prime radicalC2×#19097792C2
cosocleC2×C4×C157C24
hypercenter#440D157
hypocenterC157#2951
LCSG ▷ C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
2. #23757755C2semidirect
3. #23757752C2semidirect
4. #23757375C2semidirect
5. #23757374C2semidirect
6. #23757372C2semidirect
7. C4×#14578944C2semidirect
8. #23757365C2semidirect
9. C4×#14578939C2semidirect
10. #23757353C2semidirect
11. #107×D157C2semidirect
12. #23757273C2semidirect
13. #23757271C2semidirect
14. #23757230C2semidirect
15. #440×C157C2semidirect
18. #19097792C4semidirect
61. #14578955C2×C4semidirect
63. #14578953C2×C4semidirect
76. #14578944C2×C4semidirect
77. #14578943C2×C4semidirect
78. #14578939C2×C4semidirect
82. C8×D157C2×C4semidirect
104. SD16×C157C2×C4semidirect
181. C157#2951semidirect
189. #440D157semidirect
263. SD16C4×D157semidirect

Maximal subgroups

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

subgroupindex
C2×#190977922
#237577552
#237577522
#237573752
#237573742
#237573722
C4×#145789442
#237573652
C4×#145789392
#237573532
#107×D1572
#237572732
#237572712
#237572302
#440×C1572
#2951157