Finite Group Databasebeta

← #34112106

Subgroups — #34112106

Order 20096.

394 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23757928C211yesmaximal, characteristic, complemented
2#23757643C211yesmaximal, characteristic, complemented
3#23757614C211yesmaximal, characteristic, complemented
4#23757603C211yesmaximal, characteristic, complemented
5#23757570C211yesmaximal, characteristic, complemented
6#23757517C211yesmaximal, characteristic, complemented
7#23757500C211yesmaximal, characteristic, complemented
8#23757478C211yesmaximal, characteristic, complemented
9#23757416C211yesmaximal, characteristic, complemented
10#23757416C211yesmaximal, characteristic, complemented
11#23757383C211yesmaximal, 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×#14578942C2211yescharacteristic
20C2×#14578939C2211yescharacteristic
21C2×#14578938C2211yescharacteristic
22C22×#11929434C2211yescharacteristic
23#19097771C2211yescharacteristic
24#19097753—21no—
25#19097753—21no—
26#19097750C2211yescharacteristic
27#19097750C2211yescharacteristic
28#19097742—21no—
29C4×D628C2211yescharacteristic
30C4⋊C4×D157—21no—
31#19097704C2211yescharacteristic
32#19097702C2211yescharacteristic
33#19097702C2211yescharacteristic
34C4⋊#11929434C2211yescharacteristic
35#19097694C2211yescharacteristic
36#19097694C2211yescharacteristic
37#19097694C2211yescharacteristic
38#19097694C2211yescharacteristic
39#19097694C2211yescharacteristic
40#19097694C2211yescharacteristic
41#19097692C2211yescharacteristic
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×Dic314C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C22⋊D157—21no—
67C2×C22⋊D157—21no—
68C2×C4×D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71#14578942—41no—
72#14578942—41no—
73#14578939—22no—
74#14578938—41no—
75C2×#11929434—41no—
76C2×#11929434C2311yescharacteristic
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C4⋊Dic157—21no—
81C4⋊Dic157—21no—
82C4⋊Dic157C2311yescharacteristic
83#14578933—21no—
84#14578933—21no—
85C22⋊Dic157—21no—
86C22⋊Dic157—21no—
87#14578931—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—
112Dic314—21no—
113Dic314—21no—
114Dic314—21no—
115Dic314—21no—
116D628—21no—
117D628#4112yes—
118C22⋊D157—42no—
119C22⋊D157—42no—
120C2×Dic157—21no—
121C2×Dic157—21no—
122C2×Dic157—21no—
123C4×D157—42no—
124C4×D157—42no—
125C4×D157—42no—
126#11929434—21no—
127#11929434—21no—
128#11929434—21no—
129#11929434—21no—
130C23×C157—21no—
131C23×C157C2×D411yescharacteristic
132C23×C157C2×D411yescharacteristic
133D4×C157—21no—
134D4×C157—21no—
135D4×C157—41no—
136D4×C157—42no—
137D4×C157—81no—
138C2×C4×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—81no—
146C2×C4×C157—81no—
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2×D411yescharacteristic
149C2×C4×C157C2×D411yescharacteristic
150C2×C4×C157C2×D411yescharacteristic
151C2×C4×C157C2411yescharacteristic
152C22×C157—21no—
153C22×C157—21no—
154C22×C157—21no—
155C22×C157—21no—
156C22×C157—21no—
157C22×C157—21no—
158C22×C157—41no—
159C22×C157—41no—
160C22×C157—41no—
161C22×C157C22×D411yescharacteristic
162C2×D157—22no—
163C2×D157—41no—
164C2×D157—41no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—21no—
168C4×C157—21no—
169C4×C157—41no—
170C4×C157—41no—
171C4×C157—41no—
172C4×C157C2×#4111yescharacteristic
173C4×C157H(5,𝔽2)11yescharacteristic
174Dic157—41no—
175Dic157—41no—
176Dic157—41no—
177C2×C157—41no—
178C2×C157—41no—
179C2×C157—81no—
180C2×C157#54611yescharacteristic
181C2×C157#57511yescharacteristic
182C2×C157#57711yescharacteristic
183D157—42no—
184C157#330711yescharacteristic, complemented, Sylow
185#3307—1571nomaximal, Sylow
186#553D15711yescharacteristic, complemented
187#547—1571no—
188#491—1571no—
189#485—1571no—
190#483—1571no—
191#478—1571no—
192#468—1571no—
193#465—1571no—
194#461—1571no—
195#449—1571no—
196#449—1571no—
197#442—1571no—
198#435—1571no—
199#417—1571no—
200#416—1571no—
201C2×#41—1571no—
202C2×#41—1571no—
203C2×SD16—1571no—
204C2×SD16—1571no—
205C2×D8—1571no—
206C2×M16—1571no—
207C22×C8—1571no—
208C4⋊Q8—1571no—
209#126—21no—
210#125C2×D15711yescharacteristic
211#123—21no—
212#123—3141no—
213#123—3141no—
214C22⋊Q8—1571no—
215C22⋊Q8—1571no—
216#121—21no—
217#121—3141no—
218#121C2×D15711yescharacteristic
219#121C2×D15711yescharacteristic
220C4×D4—21no—
221C4×D4—1571no—
222C4×D4C2×D15711yescharacteristic
223C4×D4C2×D15711yescharacteristic
224#117C2×D15711yescharacteristic
225C2×C4⋊C4—3141no—
226C2×C4⋊C4C2×D15711yescharacteristic
227#107—1571no—
228#106—1571no—
229#106—1571no—
230C4⋊C8—1571no—
231#103—1571no—
232#103—1571no—
233#103—1571no—
234#103—1571no—
235#103—1571no—
236#103—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241C22⋊C8—1571no—
242C22⋊C8—1571no—
243#97—1571no—
244#41—3142no—
245#41—3142no—
246#41—6281no—
247#41—6281no—
248C2×Q8—1571no—
249C2×Q8—1571no—
250C2×D4—21no—
251C2×D4—21no—
252C2×D4—3141no—
253C2×D4—3141no—
254C2×D4—1571no—
255C2×D4C22⋊D15711yescharacteristic
256C2×D4C22×D15711yescharacteristic
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—3141no—
260C22×C4—3141no—
261C22×C4—3141no—
262C22×C4C22×D15711yescharacteristic
263C22×C4C22×D15711yescharacteristic
264SD16—6281no—
265SD16—6281no—
266D8—3142no—
267M16—6281no—
268C2×C8—6281no—
269C2×C8—1571no—
270C2×C8—1571no—
271C2×C8—1571no—
272C2×C8—1571no—
273C4⋊C4—21no—
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—3141no—
277C4⋊C4—3141no—
278C4⋊C4—3141no—
279C4⋊C4—3141no—
280C4⋊C4—1571no—
281C4⋊C4C22⋊D15711yescharacteristic
282C4⋊C4C22×D15711yescharacteristic
283C4⋊C4C22×D15711yescharacteristic
284C4⋊C4C22×D15711yescharacteristic
285C22⋊C4—21no—
286C22⋊C4—21no—
287C22⋊C4—21no—
288C22⋊C4—21no—
289C22⋊C4—3141no—
290C22⋊C4—3141no—
291C22⋊C4—3141no—
292C22⋊C4C22⋊D15711yescharacteristic
293C22⋊C4C22⋊D15711yescharacteristic
294C42—21no—
295C42C22×D15711yescharacteristic
296C23—21no—
297C23—3141no—
298C23C2×C22⋊D15711yescharacteristic
299C23C2×C22⋊D15711yescharacteristic
300Q8—3141no—
301Q8—3141no—
302Q8—3141no—
303Q8—3141no—
304D4—21no—
305D4—21no—
306D4—41no—
307D4—42no—
308D4—81no—
309D4—3141no—
310D4—6282no—
311D4—6282no—
312D4—1572no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—81no—
322C2×C4—3141no—
323C2×C4—3141no—
324C2×C4—3141no—
325C2×C4—6282no—
326C2×C4—6282no—
327C2×C4—6282no—
328C2×C4C2×C22⋊D15711yescharacteristic
329C2×C4C2×C22⋊D15711yescharacteristic
330C2×C4C2×C22⋊D15711yescharacteristic
331C2×C4C2×C22⋊D15711yescharacteristic
332C2×C4C23×D15711yescharacteristic
333C8—3141no—
334C8—3141no—
335C8—3141no—
336C8—3141no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—3142no—
347C22—6281no—
348C22—6281no—
349C22C22×C22⋊D15711yescharacteristic
350C4—21no—
351C4—21no—
352C4—21no—
353C4—21no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—6281no—
358C4—6281no—
359C4—6281no—
360C4#41×D15711yescharacteristic
361C4#1909781711yescharacteristic
362C2—41no—
363C2—41no—
364C2—81no—
365C2—6282no—
366C2#2375791111yescharacteristic
367C2#2375807111yescharacteristic
368C2#2375808411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#553×C157C2
socleC22×C157C22×D4
hypercenter#553D157
hypocenterC157#3307
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. #23757928C2semidirect
2. #23757643C2semidirect
3. #23757614C2semidirect
4. #23757603C2semidirect
5. #23757570C2semidirect
6. #23757517C2semidirect
7. #23757500C2semidirect
8. #23757478C2semidirect
9. #23757416C2semidirect
10. #23757416C2semidirect
11. #23757383C2semidirect
12. #23757345C2semidirect
13. #23757272C2semidirect
14. #23757267C2semidirect
15. #553×C157C2semidirect
184. C157#3307semidirect
186. #553D157semidirect

Maximal subgroups

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

subgroupindex
#237579282
#237576432
#237576142
#237576032
#237575702
#237575172
#237575002
#237574782
#237574162
#237573832
#237573452
#237572722
#237572672
#553×C1572
#3307157