Finite Group Databasebeta

← #34113223

Subgroups — #34113223

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#23758005C211yesmaximal, characteristic, complemented
3#23757663C211yesmaximal, characteristic, complemented
4#23757659C211yesmaximal, characteristic, complemented
5#23757658C211yesmaximal, characteristic, complemented
6#23757497C211yesmaximal, characteristic, complemented
7#23757491C211yesmaximal, characteristic, complemented
8#23757490C211yesmaximal, characteristic, complemented
9#23757469C211yesmaximal, characteristic, complemented
10#23757467C211yesmaximal, characteristic, complemented
11#23757402C211yesmaximal, characteristic, complemented
12#23757376C211yesmaximal, characteristic, complemented
13#23757371C211yesmaximal, characteristic, complemented
14#23757353C211yesmaximal, characteristic, complemented
15#464×C157C211yesmaximal, characteristic, complemented
16C2×#14578941C2211yescharacteristic
17C2×#14578941C2211yescharacteristic
18C2×#14578941C2211yescharacteristic
19C2×D1256C2211yescharacteristic
20C2×D1256C2211yescharacteristic
21C2×#14578939C2211yescharacteristic
22C2×#14578939C2211yescharacteristic
23#19097768C2211yescharacteristic
24#19097767C2211yescharacteristic
25#19097760C2211yescharacteristic
26#19097760C2211yescharacteristic
27#19097760C2211yescharacteristic
28#19097759—21no—
29#19097757—21no—
30#19097756—21no—
31#19097756—21no—
32#19097755—21no—
33#19097753—21no—
34Q8×Dic157C2211yescharacteristic
35C4×Dic314C2211yescharacteristic
36C4×D628—21no—
37C4×D628C2211yescharacteristic
38D4×Dic157C2211yescharacteristic
39#19097733C2211yescharacteristic
40#19097733C2211yescharacteristic
41#19097731—21no—
42#19097704C2211yescharacteristic
43#19097700C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097695C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097682C2211yescharacteristic
50#19097681C2211yescharacteristic
51C8×Dic157C2211yescharacteristic
52C2×Q16×C157C2211yescharacteristic
53C2×SD16×C157C2211yescharacteristic
54#124×C157C2211yescharacteristic
55C4×Q8×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#103×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59C2×Dic314D411yescharacteristic
60C2×D628—21no—
61C2×D628—21no—
62C2×D628C2311yescharacteristic
63C2×D628C2311yescharacteristic
64C2×D628C2311yescharacteristic
65C2×C22⋊D157—21no—
66C2×C22⋊D157—21no—
67C22×Dic157—21no—
68C2×C4×D157—21no—
69C2×C4×D157—21no—
70C2×C4×D157—21no—
71#14578941—22no—
72#14578941—22no—
73#14578941—41no—
74D1256—41no—
75D1256—41no—
76#14578939—22no—
77#14578939—41no—
78C2×#11929434C2311yescharacteristic
79C2×#11929434C2311yescharacteristic
80C4⋊Dic157—21no—
81C4⋊Dic157D411yescharacteristic
82C4⋊Dic157C2311yescharacteristic
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85C22⋊Dic157—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—
95C4×Dic157—21no—
96C4×Dic157C2311yescharacteristic
97C4×Dic157C2311yescharacteristic
98C2×Q8×C157C2311yescharacteristic
99C2×Q8×C157C2311yescharacteristic
100C2×D4×C157C2311yescharacteristic
101Q16×C157—41no—
102SD16×C157—41no—
103C2×C8×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C4⋊C4×C157—21no—
106C4⋊C4×C157C2311yescharacteristic
107C22⋊C4×C157—21no—
108C22⋊C4×C157—21no—
109C42×C157—21no—
110C42×C157C2311yescharacteristic
111C22×D157—21no—
112C22×D157—21no—
113C22×D157—21no—
114Dic314—41no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—21no—
119D628—21no—
120D628—21no—
121D628—42no—
122D628—81no—
123C22⋊D157—42no—
124C22⋊D157—81no—
125C2×Dic157—21no—
126C2×Dic157—81no—
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C2×Dic157C2×D411yescharacteristic
131C4×D157—81no—
132C4×D157—81no—
133C4×D157—81no—
134#11929434—21no—
135#11929434#4112yes—
136C23×C157—21no—
137Q8×C157—21no—
138Q8×C157—21no—
139Q8×C157—21no—
140Q8×C157—21no—
141D4×C157—21no—
142D4×C157—21no—
143C2×C4×C157—21no—
144C2×C4×C157—21no—
145C2×C4×C157—21no—
146C2×C4×C157C2×D411yescharacteristic
147C2×C4×C157C2×D411yescharacteristic
148C2×C4×C157C2411yescharacteristic
149C8×C157—21no—
150C8×C157—21no—
151C22×C157—41no—
152C22×C157—41no—
153C22×C157—41no—
154C22×C157C22×D411yescharacteristic
155C2×D157—41no—
156C2×D157—41no—
157C2×D157—41no—
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—41no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157C2×#4111yescharacteristic
170C4×C157H(5,𝔽2)11yescharacteristic
171Dic157—21no—
172Dic157—21no—
173Dic157—21no—
174Dic157—21no—
175Dic157—41no—
176C2×C157—81no—
177C2×C157#55011yescharacteristic
178C2×C157#57511yescharacteristic
179C2×C157#57611yescharacteristic
180D157—81no—
181D157—81no—
182D157—81no—
183C157#340311yescharacteristic, complemented, Sylow
184#3403—1571nomaximal, Sylow
185#559—1571no—
186#559—1571no—
187#496—1571no—
188#496—1571no—
189#495—1571no—
190#464—1571no—
191#464D15711yescharacteristic, complemented
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×Q16C2×D15711yescharacteristic
201C2×SD16—1571no—
202C2×SD16—1571no—
203C2×SD16—1571no—
204C2×SD16C2×D15711yescharacteristic
205C2×D8—1571no—
206C2×D8—1571no—
207C2×D8—1571no—
208C2×D8—1571no—
209#127—1571no—
210#127—1571no—
211#124—3141no—
212#124—3141no—
213#124—1571no—
214#124—1571no—
215#124—1571no—
216#124C2×D15711yescharacteristic
217#123—3141no—
218#123—3141no—
219#123—3141no—
220#123—3141no—
221C4×Q8—1571no—
222C4×Q8—1571no—
223C4×Q8C2×D15711yescharacteristic
224C4×D4—3141no—
225C4×D4—3141no—
226C4×D4—1571no—
227C4×D4—1571no—
228C4×D4—1571no—
229C4×D4—1571no—
230#107—1571no—
231C4⋊C8—1571no—
232C4⋊C8—1571no—
233C4⋊C8C2×D15711yescharacteristic
234#103—1571no—
235#103C2×D15711yescharacteristic
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102C2×D15711yescharacteristic
240#97—1571no—
241#97—1571no—
242C4×C8—1571no—
243C2×Q8—1571no—
244C2×Q8C22×D15711yescharacteristic
245C2×Q8C22×D15711yescharacteristic
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—1571no—
251C2×D4—1571no—
252C2×D4—1571no—
253C2×D4C22×D15711yescharacteristic
254C22×C4—3141no—
255C22×C4—3141no—
256C22×C4—3141no—
257C22×C4—3141no—
258Q16—41no—
259SD16—41no—
260SD16—3142no—
261SD16—3142no—
262SD16—6281no—
263D8—3142no—
264D8—6281no—
265D8—6281no—
266D8—6281no—
267C2×C8—1571no—
268C2×C8—1571no—
269C2×C8C22×D15711yescharacteristic
270C2×C8C22×D15711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—3141no—
273C4⋊C4—1571no—
274C4⋊C4—1571no—
275C4⋊C4—1571no—
276C4⋊C4—1571no—
277C4⋊C4C22×D15711yescharacteristic
278C22⋊C4—21no—
279C22⋊C4—21no—
280C22⋊C4—3141no—
281C22⋊C4—3141no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C22⋊C4—3141no—
290C42—21no—
291C42—3141no—
292C42—1571no—
293C42—1571no—
294C42C22×D15711yescharacteristic
295C23—21no—
296C23—3141no—
297C23—3141no—
298C23—3141no—
299Q8—21no—
300Q8—21no—
301Q8—21no—
302Q8—21no—
303Q8—6281no—
304D4—21no—
305D4—21no—
306D4—3141no—
307D4—3141no—
308D4—3141no—
309D4—3141no—
310D4—3141no—
311D4—3141no—
312D4—6282no—
313D4—6282no—
314D4—12561no—
315D4—12561no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—3141no—
320C2×C4—1571no—
321C2×C4—1571no—
322C2×C4—1571no—
323C2×C4—1571no—
324C2×C4—12561no—
325C2×C4—12561no—
326C2×C4—12561no—
327C2×C4—12561no—
328C2×C4D4×D15711yescharacteristic
329C2×C4D4×D15711yescharacteristic
330C2×C4C23×D15711yescharacteristic
331C8—21no—
332C8—21no—
333C8—3141no—
334C8—1572no—
335C22—41no—
336C22—41no—
337C22—41no—
338C22—6281no—
339C22—6281no—
340C22—6281no—
341C22—6281no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—6281no—
346C22—6281no—
347C22C2×D4×D15711yescharacteristic
348C4—21no—
349C4—21no—
350C4—41no—
351C4—41no—
352C4—41no—
353C4—3141no—
354C4—3141no—
355C4—3141no—
356C4—3141no—
357C4—6281no—
358C4#41×D15711yescharacteristic
359C4#1909781611yescharacteristic
360C2—81no—
361C2—12561no—
362C2—12561no—
363C2—12561no—
364C2#2375794111yescharacteristic
365C2#2375807211yescharacteristic
366C2#2375807511yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#464×C157C2
socleC22×C157C22×D4
hypercenter#464D157
hypocenterC157#3403
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #464

Complements

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

NH ≅ G/Ntype
1. #23758008C2semidirect
2. #23758005C2semidirect
3. #23757663C2semidirect
4. #23757659C2semidirect
5. #23757658C2semidirect
6. #23757497C2semidirect
7. #23757491C2semidirect
8. #23757490C2semidirect
9. #23757469C2semidirect
10. #23757467C2semidirect
11. #23757402C2semidirect
12. #23757376C2semidirect
13. #23757371C2semidirect
14. #23757353C2semidirect
15. #464×C157C2semidirect
183. C157#3403semidirect
191. #464D157semidirect

Maximal subgroups

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

subgroupindex
#237580082
#237580052
#237576632
#237576592
#237576582
#237574972
#237574912
#237574902
#237574692
#237574672
#237574022
#237573762
#237573712
#237573532
#464×C1572
#3403157