Finite Group Databasebeta

← #34112136

Subgroups — #34112136

Order 20096.

404 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757944C211yesmaximal, characteristic, complemented
2#23757639C211yesmaximal, characteristic, complemented
3#23757597C211yesmaximal, characteristic, complemented
4#23757586C211yesmaximal, characteristic, complemented
5#23757577C211yesmaximal, characteristic, complemented
6#23757524C211yesmaximal, characteristic, complemented
7#23757507C211yesmaximal, characteristic, complemented
8#23757468C211yesmaximal, characteristic, complemented
9#23757416C211yesmaximal, characteristic, complemented
10#23757416C211yesmaximal, characteristic, complemented
11#23757373C211yesmaximal, characteristic, complemented
12#23757345C211yesmaximal, characteristic, complemented
13#23757272C211yesmaximal, characteristic, complemented
14#23757267C211yesmaximal, characteristic, complemented
15#553×C157C211yesmaximal, characteristic, complemented
16C2×#14578954C2211yescharacteristic
17C2×#14578954C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578938C2211yescharacteristic
22C22×#11929434C2211yescharacteristic
23#19097768C2211yescharacteristic
24#19097767—21no—
25#19097745C2211yescharacteristic
26#19097745C2211yescharacteristic
27#19097744—21no—
28#19097744—21no—
29C4×Dic314C2211yescharacteristic
30#19097733—21no—
31#19097704C2211yescharacteristic
32#19097704C2211yescharacteristic
33#19097702C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35#19097694C2211yescharacteristic
36#19097694C2211yescharacteristic
37#19097694C2211yescharacteristic
38#19097692C2211yescharacteristic
39#19097691C2211yescharacteristic
40#19097691C2211yescharacteristic
41#19097691C2211yescharacteristic
42#19097691C2211yescharacteristic
43#19097691C2211yescharacteristic
44#19097691C2211yescharacteristic
45C22⋊#11929434C2211yescharacteristic
46C22⋊#11929434C2211yescharacteristic
47#19097682C2211yescharacteristic
48#126×C157—21no—
49#125×C157C2211yescharacteristic
50#123×C157—21no—
51#121×C157—21no—
52#121×C157C2211yescharacteristic
53#121×C157C2211yescharacteristic
54C4×D4×C157—21no—
55C4×D4×C157C2211yescharacteristic
56C4×D4×C157C2211yescharacteristic
57#117×C157C2211yescharacteristic
58C2×C4⋊C4×C157C2211yescharacteristic
59#14578954—22no—
60#14578954—22no—
61#14578954—41no—
62#14578954—41no—
63C2×Dic314C2311yescharacteristic
64C2×D628—21no—
65C2×D628—21no—
66C2×D628C2311yescharacteristic
67C2×D628C2311yescharacteristic
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C22⋊D157—21no—
71C2×C22⋊D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157—21no—
74#14578942—22no—
75#14578939—41no—
76#14578939—41no—
77#14578938—41no—
78C2×#11929434—41no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C2×#11929434C2311yescharacteristic
82C2×#11929434C2311yescharacteristic
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578931—21no—
86#14578931—21no—
87C4×Dic157—21no—
88C2×D4×C157—21no—
89C2×D4×C157—21no—
90C2×D4×C157D411yescharacteristic
91C2×D4×C157C2311yescharacteristic
92C22×C4×C157—21no—
93C22×C4×C157—21no—
94C22×C4×C157C2311yescharacteristic
95C22×C4×C157C2311yescharacteristic
96C4⋊C4×C157—21no—
97C4⋊C4×C157—21no—
98C4⋊C4×C157—21no—
99C4⋊C4×C157D411yescharacteristic
100C4⋊C4×C157C2311yescharacteristic
101C4⋊C4×C157C2311yescharacteristic
102C4⋊C4×C157C2311yescharacteristic
103C22⋊C4×C157—21no—
104C22⋊C4×C157—21no—
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C22⋊C4×C157D411yescharacteristic
108C22⋊C4×C157D411yescharacteristic
109C42×C157—21no—
110C42×C157C2311yescharacteristic
111C22×D157—21no—
112C22×D157—21no—
113Dic314—21no—
114Dic314#4112yes—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—42no—
120D628—81no—
121C22⋊D157—42no—
122C22⋊D157—42no—
123C22⋊D157—81no—
124C22⋊D157—81no—
125C2×Dic157—21no—
126C2×Dic157—21no—
127C4×D157—42no—
128C4×D157—42no—
129#11929434—21no—
130#11929434—21no—
131#11929434—21no—
132#11929434—21no—
133C23×C157—21no—
134C23×C157C2×D411yescharacteristic
135C23×C157C2×D411yescharacteristic
136D4×C157—21no—
137D4×C157—21no—
138D4×C157—41no—
139D4×C157—42no—
140D4×C157—81no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157—21no—
147C2×C4×C157—21no—
148C2×C4×C157—81no—
149C2×C4×C157—81no—
150C2×C4×C157C2×D411yescharacteristic
151C2×C4×C157C2×D411yescharacteristic
152C2×C4×C157C2×D411yescharacteristic
153C2×C4×C157C2×D411yescharacteristic
154C2×C4×C157C2411yescharacteristic
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—21no—
159C22×C157—21no—
160C22×C157—21no—
161C22×C157—41no—
162C22×C157—41no—
163C22×C157—41no—
164C22×C157C22×D411yescharacteristic
165C2×D157—41no—
166C2×D157—41no—
167C2×D157—41no—
168C2×D157—41no—
169C2×D157—41no—
170C2×D157—41no—
171C4×C157—21no—
172C4×C157—21no—
173C4×C157—21no—
174C4×C157—21no—
175C4×C157—41no—
176C4×C157—41no—
177C4×C157—41no—
178C4×C157C2×#4111yescharacteristic
179C4×C157H(5,𝔽2)11yescharacteristic
180Dic157—22no—
181Dic157—41no—
182C2×C157—41no—
183C2×C157—41no—
184C2×C157—81no—
185C2×C157#54611yescharacteristic
186C2×C157#57511yescharacteristic
187C2×C157#57611yescharacteristic
188D157—81no—
189D157—81no—
190C157#330911yescharacteristic, complemented, Sylow
191#3309—1571nomaximal, Sylow
192#553D15711yescharacteristic, complemented
193#550—1571no—
194#490—1571no—
195#482—1571no—
196#480—1571no—
197#479—1571no—
198#469—1571no—
199#466—1571no—
200#459—1571no—
201#449—1571no—
202#449—1571no—
203#440—1571no—
204#435—1571no—
205#417—1571no—
206#416—1571no—
207C2×#41—1571no—
208C2×#41—1571no—
209C2×SD16—1571no—
210C2×D8—1571no—
211C2×D8—1571no—
212C2×M16—1571no—
213C22×C8—1571no—
214#127—3141no—
215#127—1571no—
216#126—21no—
217#125C2×D15711yescharacteristic
218#123—21no—
219#121—21no—
220#121—3141no—
221#121—3141no—
222#121—1571no—
223#121—1571no—
224#121C2×D15711yescharacteristic
225#121C2×D15711yescharacteristic
226C4×Q8—1571no—
227C4×D4—21no—
228C4×D4—3141no—
229C4×D4C2×D15711yescharacteristic
230C4×D4C2×D15711yescharacteristic
231#117C2×D15711yescharacteristic
232C2×C4⋊C4C2×D15711yescharacteristic
233#107—1571no—
234#107—1571no—
235#106—1571no—
236C4⋊C8—1571no—
237#103—1571no—
238#103—1571no—
239#103—1571no—
240#102—1571no—
241#102—1571no—
242#102—1571no—
243#102—1571no—
244#102—1571no—
245#102—1571no—
246#102—1571no—
247C22⋊C8—1571no—
248C22⋊C8—1571no—
249#97—1571no—
250#41—3142no—
251#41—3142no—
252#41—6281no—
253#41—6281no—
254C2×Q8—1571no—
255C2×D4—21no—
256C2×D4—21no—
257C2×D4—3141no—
258C2×D4—3141no—
259C2×D4—3141no—
260C2×D4—3141no—
261C2×D4—3141no—
262C2×D4—3141no—
263C2×D4—1571no—
264C2×D4—1571no—
265C2×D4C22⋊D15711yescharacteristic
266C2×D4C22×D15711yescharacteristic
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—3141no—
270C22×C4—3141no—
271C22×C4C22×D15711yescharacteristic
272C22×C4C22×D15711yescharacteristic
273SD16—3142no—
274D8—6281no—
275D8—6281no—
276M16—6281no—
277C2×C8—6281no—
278C2×C8—1571no—
279C2×C8—1571no—
280C2×C8—1571no—
281C2×C8—1571no—
282C4⋊C4—21no—
283C4⋊C4—21no—
284C4⋊C4—21no—
285C4⋊C4—3141no—
286C4⋊C4—1571no—
287C4⋊C4C22⋊D15711yescharacteristic
288C4⋊C4C22×D15711yescharacteristic
289C4⋊C4C22×D15711yescharacteristic
290C4⋊C4C22×D15711yescharacteristic
291C22⋊C4—21no—
292C22⋊C4—21no—
293C22⋊C4—21no—
294C22⋊C4—21no—
295C22⋊C4—3141no—
296C22⋊C4—3141no—
297C22⋊C4C22⋊D15711yescharacteristic
298C22⋊C4C22⋊D15711yescharacteristic
299C42—21no—
300C42—3141no—
301C42C22×D15711yescharacteristic
302C23—21no—
303C23—3141no—
304C23—3141no—
305C23C2×C22⋊D15711yescharacteristic
306C23C2×C22⋊D15711yescharacteristic
307Q8—3141no—
308Q8—1572no—
309D4—21no—
310D4—21no—
311D4—41no—
312D4—42no—
313D4—81no—
314D4—3141no—
315D4—3141no—
316D4—3141no—
317D4—3141no—
318D4—6282no—
319D4—6282no—
320D4—6282no—
321D4—12561no—
322D4—12561no—
323D4—12561no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—21no—
327C2×C4—21no—
328C2×C4—21no—
329C2×C4—21no—
330C2×C4—21no—
331C2×C4—81no—
332C2×C4—81no—
333C2×C4—3141no—
334C2×C4—3141no—
335C2×C4—6282no—
336C2×C4—6282no—
337C2×C4C2×C22⋊D15711yescharacteristic
338C2×C4C2×C22⋊D15711yescharacteristic
339C2×C4C2×C22⋊D15711yescharacteristic
340C2×C4C2×C22⋊D15711yescharacteristic
341C2×C4C23×D15711yescharacteristic
342C8—3141no—
343C8—3141no—
344C8—3141no—
345C8—3141no—
346C22—21no—
347C22—21no—
348C22—21no—
349C22—21no—
350C22—21no—
351C22—21no—
352C22—41no—
353C22—41no—
354C22—41no—
355C22—6281no—
356C22—6281no—
357C22—6281no—
358C22—6281no—
359C22—6281no—
360C22—6281no—
361C22C22×C22⋊D15711yescharacteristic
362C4—21no—
363C4—21no—
364C4—21no—
365C4—21no—
366C4—41no—
367C4—41no—
368C4—41no—
369C4—3142no—
370C4—6281no—
371C4#41×D15711yescharacteristic
372C4#1909781711yescharacteristic
373C2—41no—
374C2—41no—
375C2—81no—
376C2—12561no—
377C2—12561no—
378C2#2375791111yescharacteristic
379C2#2375807111yescharacteristic
380C2#2375807611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#553×C157C2
socleC22×C157C22×D4
hypercenter#553D157
hypocenterC157#3309
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×D4 ◁ #553

Complements

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

NH ≅ G/Ntype
1. #23757944C2semidirect
2. #23757639C2semidirect
3. #23757597C2semidirect
4. #23757586C2semidirect
5. #23757577C2semidirect
6. #23757524C2semidirect
7. #23757507C2semidirect
8. #23757468C2semidirect
9. #23757416C2semidirect
10. #23757416C2semidirect
11. #23757373C2semidirect
12. #23757345C2semidirect
13. #23757272C2semidirect
14. #23757267C2semidirect
15. #553×C157C2semidirect
190. C157#3309semidirect
192. #553D157semidirect

Maximal subgroups

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

subgroupindex
#237579442
#237576392
#237575972
#237575862
#237575772
#237575242
#237575072
#237574682
#237574162
#237573732
#237573452
#237572722
#237572672
#553×C1572
#3309157