Finite Group Databasebeta

← #34113203

Subgroups — #34113203

Order 20096.

368 conjugacy classes of subgroups.

The subgroup lattice has 356 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23758008C211yesmaximal, characteristic, complemented
2#23757995C211yesmaximal, characteristic, complemented
3#23757666C211yesmaximal, characteristic, complemented
4#23757662C211yesmaximal, characteristic
5#23757658C211yesmaximal, characteristic, complemented
6#23757498C211yesmaximal, characteristic, complemented
7#23757495C211yesmaximal, characteristic, complemented
8#23757491C211yesmaximal, characteristic, complemented
9#23757491C211yesmaximal, characteristic, complemented
10#23757477C211yesmaximal, characteristic, complemented
11#23757473C211yesmaximal, characteristic, complemented
12#23757401C211yesmaximal, characteristic, complemented
13#23757384C211yesmaximal, characteristic, complemented
14#23757360C211yesmaximal, characteristic, complemented
15#441×C157C211yesmaximal, characteristic, complemented
16C2×#14578944C2211yescharacteristic
17C2×#14578943C2211yescharacteristic
18C2×#14578943C2211yescharacteristic
19C2×#14578941C2211yescharacteristic
20C2×#14578941C2211yescharacteristic
21C2×#14578941C2211yescharacteristic
22C2×D1256C2211yescharacteristic
23C2×D1256C2211yescharacteristic
24#19097769C2211yescharacteristic
25#19097768C2211yescharacteristic
26#19097766—21no—
27#19097765—21no—
28#19097760C2211yescharacteristic
29#19097760C2211yescharacteristic
30#19097760C2211yescharacteristic
31#19097759—21no—
32#19097759C2211yescharacteristic
33#19097756—21no—
34#19097756—21no—
35#19097749—21no—
36C4×Dic314C2211yescharacteristic
37#19097736C2211yescharacteristic
38C4×D628—21no—
39#19097733C2211yescharacteristic
40#19097733C2211yescharacteristic
41#19097733C2211yescharacteristic
42#19097728—21no—
43C4⋊#11929434C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097700C2211yescharacteristic
46#19097694C2211yescharacteristic
47#19097691C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×Q16×C157C2211yescharacteristic
53C4×Q8×C157C2211yescharacteristic
54C4×Q8×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56#103×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#97×C157C2211yescharacteristic
59C2×Dic314D411yescharacteristic
60C2×Dic314C2311yescharacteristic
61C2×D628—21no—
62C2×D628—21no—
63C2×D628C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×C4×D157—21no—
67C2×C4×D157—21no—
68C2×C4×D157—21no—
69#14578944—41no—
70#14578943—22no—
71#14578943—41no—
72#14578941—41no—
73#14578941—41no—
74#14578941—41no—
75D1256—22no—
76D1256—41no—
77C2×#11929434C2311yescharacteristic
78C2×#11929434C2311yescharacteristic
79C4⋊Dic157D411yescharacteristic
80#14578933—21no—
81#14578933—21no—
82#14578933—21no—
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85#14578931—21no—
86#14578931—21no—
87#14578931—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931—21no—
95#14578931—21no—
96C4×Dic157—21no—
97C4×Dic157C2311yescharacteristic
98C4×Dic157C2311yescharacteristic
99C2×Q8×C157C2311yescharacteristic
100C2×Q8×C157C2311yescharacteristic
101Q16×C157—22no—
102C2×C8×C157C2311yescharacteristic
103C2×C8×C157C2311yescharacteristic
104C4⋊C4×C157—21no—
105C4⋊C4×C157—21no—
106C4⋊C4×C157C2311yescharacteristic
107C4⋊C4×C157C2311yescharacteristic
108C42×C157—21no—
109C42×C157—21no—
110C42×C157C2311yescharacteristic
111C22×D157—21no—
112C22×D157—21no—
113C22×D157—21no—
114Dic314—21no—
115Dic314—21no—
116Dic314—41no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—21no—
121D628—21no—
122D628—21no—
123D628—42no—
124D628—81no—
125C2×Dic157—21no—
126C2×Dic157C2×D411yescharacteristic
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C4×D157—42no—
131C4×D157—81no—
132C4×D157—81no—
133#11929434—21no—
134#11929434—21no—
135Q8×C157—21no—
136Q8×C157—21no—
137Q8×C157—21no—
138Q8×C157—21no—
139C2×C4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157C2×D411yescharacteristic
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2411yescharacteristic
146C8×C157—21no—
147C8×C157#4112yes—
148C22×C157C22×D411yescharacteristic
149C2×D157—41no—
150C2×D157—41no—
151C2×D157—41no—
152C2×D157—41no—
153C2×D157—41no—
154C2×D157—41no—
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
158C4×C157—21no—
159C4×C157—21no—
160C4×C157—41no—
161C4×C157—41no—
162C4×C157—41no—
163C4×C157—41no—
164C4×C157C2×#4111yescharacteristic
165C4×C157H(5,𝔽2)11yescharacteristic
166Dic157—21no—
167Dic157—21no—
168Dic157—21no—
169Dic157—21no—
170Dic157—41no—
171C2×C157#55011yescharacteristic
172C2×C157#57511yescharacteristic
173C2×C157#57711yescharacteristic
174D157—81no—
175D157—81no—
176D157—81no—
177C157#340111yescharacteristic, complemented, Sylow
178#3401—1571nomaximal, Sylow
179#559—1571no—
180#556—1571no—
181#497—1571no—
182#496—1571no—
183#495—1571no—
184#464—1571no—
185#464—1571no—
186#463—1571no—
187#463—1571no—
188#461—1571no—
189#460—1571no—
190#446—1571no—
191#442—1571no—
192#441D15711yescharacteristic, complemented
193C4×SD16—1571no—
194C2×Q16—1571no—
195C2×Q16C2×D15711yescharacteristic
196C2×SD16—1571no—
197C2×SD16—1571no—
198C2×SD16—1571no—
199C2×SD16—1571no—
200C2×SD16—1571no—
201C2×D8—1571no—
202C2×D8—1571no—
203C4⋊Q8—1571no—
204#127—1571no—
205#126—3141no—
206#126—3141no—
207#124—3141no—
208#124—1571no—
209#124—1571no—
210#124—1571no—
211#124—1571no—
212#123—3141no—
213#123—3141no—
214C22⋊Q8—3141no—
215C4×Q8—1571no—
216C4×Q8—1571no—
217C4×Q8C2×D15711yescharacteristic
218C4×Q8C2×D15711yescharacteristic
219C4×D4—3141no—
220C4×D4—1571no—
221C4×D4—1571no—
222C4×D4—1571no—
223#117—3141no—
224#106C2×D15711yescharacteristic
225C4⋊C8—1571no—
226C4⋊C8—1571no—
227C4⋊C8—1571no—
228#103—1571no—
229#103C2×D15711yescharacteristic
230#103C2×D15711yescharacteristic
231#102—1571no—
232#102—1571no—
233#102—1571no—
234#97—1571no—
235#97C2×D15711yescharacteristic
236C4×C8—1571no—
237C2×Q8—1571no—
238C2×Q8—1571no—
239C2×Q8C22×D15711yescharacteristic
240C2×Q8C22×D15711yescharacteristic
241C2×D4—3141no—
242C2×D4—3141no—
243C2×D4—1571no—
244C2×D4—1571no—
245C2×D4—1571no—
246C22×C4—3141no—
247C22×C4—3141no—
248C22×C4—3141no—
249Q16—22no—
250Q16—6281no—
251SD16—3142no—
252SD16—6281no—
253SD16—6281no—
254SD16—6281no—
255SD16—6281no—
256D8—3142no—
257D8—6281no—
258C2×C8—1571no—
259C2×C8—1571no—
260C2×C8C22×D15711yescharacteristic
261C2×C8C22×D15711yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—21no—
264C4⋊C4—3141no—
265C4⋊C4—3141no—
266C4⋊C4—3141no—
267C4⋊C4—1571no—
268C4⋊C4—1571no—
269C4⋊C4—1571no—
270C4⋊C4C22×D15711yescharacteristic
271C4⋊C4C22×D15711yescharacteristic
272C22⋊C4—3141no—
273C22⋊C4—3141no—
274C22⋊C4—3141no—
275C22⋊C4—3141no—
276C22⋊C4—3141no—
277C22⋊C4—3141no—
278C22⋊C4—3141no—
279C22⋊C4—3141no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C42—21no—
284C42—21no—
285C42—3141no—
286C42—1571no—
287C42—1571no—
288C42C22×D15711yescharacteristic
289C23—3141no—
290C23—3141no—
291C23—3141no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—3141no—
297Q8—3141no—
298Q8—6281no—
299D4—3141no—
300D4—3141no—
301D4—3141no—
302D4—3141no—
303D4—3141no—
304D4—3141no—
305D4—6282no—
306D4—12561no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—3141no—
312C2×C4—6282no—
313C2×C4—1571no—
314C2×C4—1571no—
315C2×C4—1571no—
316C2×C4—1571no—
317C2×C4—12561no—
318C2×C4—12561no—
319C2×C4D4×D15711yescharacteristic
320C2×C4D4×D15711yescharacteristic
321C2×C4C23×D15711yescharacteristic
322C8—21no—
323C8—3141no—
324C8—3141no—
325C8#1457895412yes—
326C22—6281no—
327C22—6281no—
328C22—6281no—
329C22—6281no—
330C22—6281no—
331C22—6281no—
332C22—6281no—
333C22—6281no—
334C22—6281no—
335C22C2×D4×D15711yescharacteristic
336C4—21no—
337C4—21no—
338C4—41no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—3141no—
343C4—3141no—
344C4—3141no—
345C4—3141no—
346C4—6281no—
347C4C2×#1457895411yescharacteristic
348C4#1909781711yescharacteristic
349C2—12561no—
350C2—12561no—
351C2—12561no—
352C2#2375794411yescharacteristic
353C2#2375807211yescharacteristic
354C2#2375808211yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#441×C157C2
socleC22×C157C22×D4
prime radical#23757662C2
hypercenter#441D157
hypocenterC157#3401
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #23758008C2semidirect
2. #23757995C2semidirect
3. #23757666C2semidirect
5. #23757658C2semidirect
6. #23757498C2semidirect
7. #23757495C2semidirect
8. #23757491C2semidirect
9. #23757491C2semidirect
10. #23757477C2semidirect
11. #23757473C2semidirect
12. #23757401C2semidirect
13. #23757384C2semidirect
14. #23757360C2semidirect
15. #441×C157C2semidirect
177. C157#3401semidirect
192. #441D157semidirect

Maximal subgroups

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

subgroupindex
#237580082
#237579952
#237576662
#237576622
#237576582
#237574982
#237574952
#237574912
#237574772
#237574732
#237574012
#237573842
#237573602
#441×C1572
#3401157