Finite Group Databasebeta

← #34113220

Subgroups — #34113220

Order 20096.

380 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#23758008C211yesmaximal, characteristic, complemented
2#23757663C211yesmaximal, characteristic, complemented
3#23757660C211yesmaximal, characteristic, complemented
4#23757655C211yesmaximal, characteristic, complemented
5#23757495C211yesmaximal, characteristic, complemented
6#23757492C211yesmaximal, characteristic, complemented
7#23757488C211yesmaximal, characteristic, complemented
8#23757485C211yesmaximal, characteristic, complemented
9#23757468C211yesmaximal, characteristic, complemented
10#23757465C211yesmaximal, characteristic, complemented
11#23757404C211yesmaximal, characteristic, complemented
12#23757373C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14C4×#14578939C211yesmaximal, characteristic, complemented
15#559×C157C211yesmaximal, characteristic, complemented
16C2×#14578944C2211yescharacteristic
17C2×#14578942C2211yescharacteristic
18C2×#14578942C2211yescharacteristic
19C2×#14578941C2211yescharacteristic
20C2×#14578941C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23C2×#14578939C2211yescharacteristic
24C2×#14578939C2211yescharacteristic
25#19097768C2211yescharacteristic
26#19097760—21no—
27#19097759C2211yescharacteristic
28#19097759C2211yescharacteristic
29#19097756—21no—
30#19097756—21no—
31C4×Dic314C2211yescharacteristic
32C4×D628C2211yescharacteristic
33C4×D628C2211yescharacteristic
34#19097733—21no—
35#19097704C2211yescharacteristic
36C4⋊#11929434C2211yescharacteristic
37C4⋊#11929434C2211yescharacteristic
38C4⋊#11929434C2211yescharacteristic
39#19097695C2211yescharacteristic
40#19097694C2211yescharacteristic
41#19097692C2211yescharacteristic
42#19097692C2211yescharacteristic
43#19097691C2211yescharacteristic
44#19097691C2211yescharacteristic
45#19097682C2211yescharacteristic
46#19097682C2211yescharacteristic
47C4×#11929434C2211yescharacteristic
48#127×C157C2211yescharacteristic
49#124×C157—21no—
50#124×C157C2211yescharacteristic
51#124×C157C2211yescharacteristic
52#123×C157—21no—
53#123×C157—21no—
54C4×Q8×C157C2211yescharacteristic
55C4×Q8×C157C2211yescharacteristic
56C4×D4×C157—21no—
57C4×D4×C157C2211yescharacteristic
58C4×D4×C157C2211yescharacteristic
59C2×Dic314C2311yescharacteristic
60C2×D628—21no—
61C2×D628—21no—
62C2×D628C2311yescharacteristic
63C2×D628C2311yescharacteristic
64C2×C4×D157—21no—
65C2×C4×D157—21no—
66#14578944—41no—
67#14578942—22no—
68#14578942—41no—
69#14578941—22no—
70#14578941—41no—
71#14578939—22no—
72#14578939—41no—
73#14578939—41no—
74#14578939—41no—
75C2×#11929434C2311yescharacteristic
76C2×#11929434C2311yescharacteristic
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C4⋊Dic157C2311yescharacteristic
80#14578933—21no—
81#14578931—21no—
82#14578931—21no—
83#14578931—21no—
84#14578931—21no—
85#14578931—21no—
86#14578931—21no—
87C4×Dic157—21no—
88C2×Q8×C157D411yescharacteristic
89C2×Q8×C157C2311yescharacteristic
90C2×D4×C157—21no—
91C2×D4×C157—21no—
92C2×D4×C157C2311yescharacteristic
93C2×D4×C157C2311yescharacteristic
94C22×C4×C157—21no—
95C22×C4×C157—21no—
96C4⋊C4×C157—21no—
97C4⋊C4×C157D411yescharacteristic
98C4⋊C4×C157D411yescharacteristic
99C4⋊C4×C157D411yescharacteristic
100C4⋊C4×C157C2311yescharacteristic
101C22⋊C4×C157—21no—
102C22⋊C4×C157—21no—
103C22⋊C4×C157—21no—
104C22⋊C4×C157—21no—
105C22⋊C4×C157—21no—
106C22⋊C4×C157—21no—
107C42×C157—21no—
108C42×C157C2311yescharacteristic
109C42×C157C2311yescharacteristic
110C42×C157C2311yescharacteristic
111C22×D157—21no—
112C22×D157—21no—
113Dic314—21no—
114Dic314—21no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—42no—
120D628—81no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C4×D157—81no—
124C4×D157—81no—
125#11929434—21no—
126#11929434—21no—
127#11929434—21no—
128#11929434#4112yes—
129C23×C157—21no—
130C23×C157—21no—
131Q8×C157—21no—
132Q8×C157—21no—
133Q8×C157—41no—
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×C157—81no—
143C2×C4×C157—81no—
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2411yescharacteristic
151C22×C157—41no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157C22×D411yescharacteristic
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C4×C157—21no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—21no—
168C4×C157—21no—
169C4×C157—21no—
170C4×C157—41no—
171C4×C157—41no—
172C4×C157C2×#4111yescharacteristic
173C4×C157H(5,𝔽2)11yescharacteristic
174Dic157—41no—
175Dic157—41no—
176C2×C157—81no—
177C2×C157—81no—
178C2×C157#55011yescharacteristic
179C2×C157#57511yescharacteristic
180C2×C157#57611yescharacteristic
181D157—81no—
182D157—81no—
183C157#340311yescharacteristic, complemented, Sylow
184#3403—1571nomaximal, Sylow
185#559—1571no—
186#559D15711yescharacteristic, complemented
187#496—1571no—
188#496—1571no—
189#495—1571no—
190#464—1571no—
191#464—1571no—
192#463—1571no—
193#463—1571no—
194#459—1571no—
195#459—1571no—
196#446—1571no—
197#440—1571no—
198#440—1571no—
199C4×D8—1571no—
200C2×Q16—1571no—
201C2×SD16—1571no—
202C2×SD16—1571no—
203C2×SD16—1571no—
204C2×SD16—1571no—
205C2×D8—1571no—
206C2×D8—1571no—
207C2×D8—1571no—
208C2×D8—1571no—
209#127—1571no—
210#127C2×D15711yescharacteristic
211#124—21no—
212#124—3141no—
213#124—1571no—
214#124—1571no—
215#124C2×D15711yescharacteristic
216#124C2×D15711yescharacteristic
217#123—21no—
218#123—21no—
219#123—3141no—
220#123—3141no—
221C4×Q8—1571no—
222C4×Q8C2×D15711yescharacteristic
223C4×Q8C2×D15711yescharacteristic
224C4×D4—21no—
225C4×D4—3141no—
226C4×D4—1571no—
227C4×D4—1571no—
228C4×D4C2×D15711yescharacteristic
229C4×D4C2×D15711yescharacteristic
230#107—1571no—
231C4⋊C8—1571no—
232C4⋊C8—1571no—
233C4⋊C8—1571no—
234#103—1571no—
235#103—1571no—
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#97—1571no—
241#97—1571no—
242C4×C8—1571no—
243C2×Q8—1571no—
244C2×Q8C22⋊D15711yescharacteristic
245C2×Q8C22×D15711yescharacteristic
246C2×D4—21no—
247C2×D4—21no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—1571no—
251C2×D4—1571no—
252C2×D4C22×D15711yescharacteristic
253C2×D4C22×D15711yescharacteristic
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—3141no—
257C22×C4—3141no—
258Q16—6281no—
259SD16—3142no—
260SD16—3142no—
261SD16—6281no—
262SD16—6281no—
263D8—3142no—
264D8—6281no—
265D8—6281no—
266D8—6281no—
267C2×C8—1571no—
268C2×C8—1571no—
269C2×C8—1571no—
270C2×C8—1571no—
271C4⋊C4—21no—
272C4⋊C4—3141no—
273C4⋊C4—1571no—
274C4⋊C4C22⋊D15711yescharacteristic
275C4⋊C4C22⋊D15711yescharacteristic
276C4⋊C4C22⋊D15711yescharacteristic
277C4⋊C4C22×D15711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—21no—
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—21no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C22⋊C4—3141no—
290C42—21no—
291C42—3141no—
292C42C22×D15711yescharacteristic
293C42C22×D15711yescharacteristic
294C42C22×D15711yescharacteristic
295C23—21no—
296C23—21no—
297C23—3141no—
298C23—3141no—
299Q8—21no—
300Q8—21no—
301Q8—41no—
302Q8—3141no—
303Q8—3141no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—42no—
309D4—81no—
310D4—3141no—
311D4—3141no—
312D4—3141no—
313D4—3141no—
314D4—6282no—
315D4—12561no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—3141no—
321C2×C4—3141no—
322C2×C4—12561no—
323C2×C4—12561no—
324C2×C4C2×C22⋊D15711yescharacteristic
325C2×C4C2×C22⋊D15711yescharacteristic
326C2×C4C2×C22⋊D15711yescharacteristic
327C2×C4C2×C22⋊D15711yescharacteristic
328C2×C4C2×C22⋊D15711yescharacteristic
329C2×C4C2×C22⋊D15711yescharacteristic
330C2×C4C23×D15711yescharacteristic
331C8—3141no—
332C8—3141no—
333C8—3141no—
334C8—1572no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—6281no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—6281no—
346C22—6281no—
347C22C22×C22⋊D15711yescharacteristic
348C4—21no—
349C4—21no—
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—6281no—
357C4—6281no—
358C4#41×D15711yescharacteristic
359C4#1909781711yescharacteristic
360C2—81no—
361C2—81no—
362C2—12561no—
363C2—12561no—
364C2#2375794211yescharacteristic
365C2#2375807111yescharacteristic
366C2#2375807611yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#559×C157C2
socleC22×C157C22×D4
hypercenter#559D157
hypocenterC157#3403
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C4×Q8 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #23758008C2semidirect
2. #23757663C2semidirect
3. #23757660C2semidirect
4. #23757655C2semidirect
5. #23757495C2semidirect
6. #23757492C2semidirect
7. #23757488C2semidirect
8. #23757485C2semidirect
9. #23757468C2semidirect
10. #23757465C2semidirect
11. #23757404C2semidirect
12. #23757373C2semidirect
13. #23757371C2semidirect
14. C4×#14578939C2semidirect
15. #559×C157C2semidirect
183. C157#3403semidirect
186. #559D157semidirect

Maximal subgroups

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

subgroupindex
#237580082
#237576632
#237576602
#237576552
#237574952
#237574922
#237574882
#237574852
#237574682
#237574652
#237574042
#237573732
#237573712
C4×#145789392
#559×C1572
#3403157