Finite Group Databasebeta

← #34111574

Subgroups — #34111574

Order 20096.

370 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#23757879C211yesmaximal, characteristic, complemented
2#23757874C211yesmaximal, characteristic, complemented
3#23757576C211yesmaximal, characteristic, complemented
4#23757572C211yesmaximal, characteristic, complemented
5#23757570C211yesmaximal, characteristic, complemented
6#23757527C211yesmaximal, characteristic, complemented
7#23757525C211yesmaximal, characteristic, complemented
8#23757510C211yesmaximal, characteristic, complemented
9#23757508C211yesmaximal, characteristic, complemented
10#23757469C211yesmaximal, characteristic, complemented
11#23757468C211yesmaximal, characteristic, complemented
12#23757467C211yesmaximal, characteristic, complemented
13#23757467C211yesmaximal, characteristic, complemented
14#23757298C211yesmaximal, characteristic, complemented
15#478×C157C211yesmaximal, characteristic, complemented
16C2×D1256C2211yescharacteristic
17C2×D1256C2211yescharacteristic
18C2×#14578939C2211yescharacteristic
19C2×#14578939C2211yescharacteristic
20C2×#14578937C2211yescharacteristic
21C2×C8×D157C2211yescharacteristic
22#19097768C2211yescharacteristic
23#19097767C2211yescharacteristic
24#19097762C2211yescharacteristic
25#19097756—21no—
26#19097756—21no—
27#19097754—21no—
28#19097753—21no—
29#19097746—21no—
30#19097746—21no—
31#19097746C2211yescharacteristic
32#19097746C2211yescharacteristic
33#19097746C2211yescharacteristic
34#19097745—21no—
35#19097744—21no—
36#19097742C2211yescharacteristic
37C4×D628C2211yescharacteristic
38#19097733C2211yescharacteristic
39#19097733C2211yescharacteristic
40#19097728C2211yescharacteristic
41#19097704C2211yescharacteristic
42#19097702C2211yescharacteristic
43C4⋊#11929434C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097700C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097691C2211yescharacteristic
49#19097691C2211yescharacteristic
50#19097691C2211yescharacteristic
51#19097691C2211yescharacteristic
52#125×C157C2211yescharacteristic
53C4×D4×C157C2211yescharacteristic
54#107×C157C2211yescharacteristic
55#106×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59C2×D628—21no—
60C2×D628—21no—
61C2×D628—21no—
62C2×D628—21no—
63C2×D628—21no—
64C2×D628C2311yescharacteristic
65C2×D628C2311yescharacteristic
66C2×D628C2311yescharacteristic
67C2×C22⋊D157—21no—
68C2×C22⋊D157—21no—
69C2×C22⋊D157—21no—
70C2×C4×D157—21no—
71C2×C4×D157—21no—
72C2×C4×D157—21no—
73C2×C4×D157C2311yescharacteristic
74D1256—41no—
75D1256—41no—
76#14578939—41no—
77#14578939—41no—
78#14578937—41no—
79C2×#11929434C2311yescharacteristic
80C2×#11929434C2311yescharacteristic
81C8×D157—41no—
82C4⋊Dic157—21no—
83C4⋊Dic157C2311yescharacteristic
84#14578933—21no—
85#14578933D411yescharacteristic
86#14578933D411yescharacteristic
87C22⋊Dic157—21no—
88#14578931—21no—
89#14578931—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931—21no—
93#14578931—21no—
94#14578931D411yescharacteristic
95#14578931D411yescharacteristic
96C4×Dic157C2311yescharacteristic
97C2×D4×C157C2311yescharacteristic
98C22×C4×C157—21no—
99C2×C8×C157C2311yescharacteristic
100C2×C8×C157C2311yescharacteristic
101C4⋊C4×C157—21no—
102C4⋊C4×C157—21no—
103C4⋊C4×C157C2311yescharacteristic
104C4⋊C4×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157—21no—
110C22×D157—21no—
111C22×D157C2×D411yescharacteristic
112D628—21no—
113D628—21no—
114D628—21no—
115D628—21no—
116D628—21no—
117D628—21no—
118D628—81no—
119D628—81no—
120D628—81no—
121D628—81no—
122D628—81no—
123C22⋊D157—81no—
124C22⋊D157—81no—
125C22⋊D157—81no—
126C2×Dic157—21no—
127C2×Dic157C2×D411yescharacteristic
128C2×Dic157C2×D411yescharacteristic
129C2×Dic157C2×D411yescharacteristic
130C4×D157—21no—
131C4×D157—21no—
132C4×D157—81no—
133C4×D157—81no—
134C4×D157—81no—
135#11929434—21no—
136#11929434—21no—
137C23×C157—21no—
138D4×C157—21no—
139D4×C157—21no—
140C2×C4×C157—21no—
141C2×C4×C157—21no—
142C2×C4×C157—21no—
143C2×C4×C157—81no—
144C2×C4×C157C2×D411yescharacteristic
145C2×C4×C157C2×D411yescharacteristic
146C2×C4×C157C2411yescharacteristic
147C8×C157—21no—
148C8×C157—21no—
149C22×C157—41no—
150C22×C157—41no—
151C22×C157—41no—
152C22×C157C22×D411yescharacteristic
153C2×D157—21no—
154C2×D157—21no—
155C2×D157—21no—
156C2×D157—41no—
157C2×D157—41no—
158C2×D157—41no—
159C2×D157—41no—
160C2×D157—41no—
161C2×D157—41no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—41no—
168C4×C157—41no—
169C4×C157—41no—
170C4×C157H(5,𝔽2)11yescharacteristic
171C4×C1572−1+411yescharacteristic
172Dic157—21no—
173Dic157—21no—
174Dic157—21no—
175Dic157—41no—
176C2×C157—81no—
177C2×C157#53711yescharacteristic
178C2×C157#57611yescharacteristic
179C2×C157#57611yescharacteristic
180D157—41no—
181D157—81no—
182D157—81no—
183D157—81no—
184C157#325911yescharacteristic, complemented, Sylow
185#3259—1571nomaximal, Sylow
186#540—1571no—
187#540—1571no—
188#478—1571no—
189#478—1571no—
190#478—1571no—
191#478D15711yescharacteristic, complemented
192#469—1571no—
193#469—1571no—
194#466—1571no—
195#466—1571no—
196#459—1571no—
197#459—1571no—
198#459—1571no—
199#459—1571no—
200#424—1571no—
201C2×D8—1571no—
202C2×D8—1571no—
203C2×D8—1571no—
204C2×D8—1571no—
205C2×M16—1571no—
206C22×C8—1571no—
207#127—1571no—
208#127—1571no—
209#125—1571no—
210#125C2×D15711yescharacteristic
211#123—3141no—
212#123—3141no—
213#123—3141no—
214#123—3141no—
215#121—3141no—
216#121—3141no—
217#121—3141no—
218#121—3141no—
219#121—1571no—
220#121—1571no—
221#121—1571no—
222#121—1571no—
223C4×D4—1571no—
224C4×D4—1571no—
225C4×D4—1571no—
226C4×D4C2×D15711yescharacteristic
227#117—1571no—
228#107—1571no—
229#107C2×D15711yescharacteristic
230#106—1571no—
231#106C2×D15711yescharacteristic
232C4⋊C8—1571no—
233C4⋊C8—1571no—
234C4⋊C8—1571no—
235C4⋊C8C2×D15711yescharacteristic
236#102—1571no—
237#102—1571no—
238#102—1571no—
239#102—1571no—
240#102—1571no—
241#102—1571no—
242#102C2×D15711yescharacteristic
243#102C2×D15711yescharacteristic
244C2×D4—3141no—
245C2×D4—3141no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—3141no—
251C2×D4—3141no—
252C2×D4—1571no—
253C2×D4—1571no—
254C2×D4—1571no—
255C2×D4C22×D15711yescharacteristic
256C22×C4—21no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—3141no—
260C22×C4—1571no—
261D8—6281no—
262D8—6281no—
263D8—6281no—
264D8—6281no—
265M16—6281no—
266C2×C8—6281no—
267C2×C8—1571no—
268C2×C8—1571no—
269C2×C8C22×D15711yescharacteristic
270C2×C8C22×D15711yescharacteristic
271C4⋊C4—21no—
272C4⋊C4—21no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—1571no—
276C4⋊C4—1571no—
277C4⋊C4—1571no—
278C4⋊C4C22×D15711yescharacteristic
279C4⋊C4C22×D15711yescharacteristic
280C4⋊C4C22×D15711yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—3141no—
283C22⋊C4—3141no—
284C22⋊C4—3141no—
285C22⋊C4—3141no—
286C22⋊C4—3141no—
287C22⋊C4—3141no—
288C22⋊C4—3141no—
289C22⋊C4—1571no—
290C22⋊C4—1571no—
291C42—1571no—
292C42C22×D15711yescharacteristic
293C23—21no—
294C23—3141no—
295C23—3141no—
296C23—3141no—
297C23—1571no—
298D4—21no—
299D4—21no—
300D4—3141no—
301D4—3141no—
302D4—3141no—
303D4—3141no—
304D4—3141no—
305D4—3141no—
306D4—12561no—
307D4—12561no—
308D4—12561no—
309D4—12561no—
310D4—12561no—
311D4—12561no—
312D4—12561no—
313D4—12561no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—81no—
318C2×C4—3141no—
319C2×C4—3141no—
320C2×C4—3141no—
321C2×C4—1571no—
322C2×C4—1571no—
323C2×C4—1571no—
324C2×C4—12561no—
325C2×C4—12561no—
326C2×C4—12561no—
327C2×C4D4×D15711yescharacteristic
328C2×C4D4×D15711yescharacteristic
329C2×C4C23×D15711yescharacteristic
330C8—21no—
331C8—21no—
332C8—3141no—
333C8—3141no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—3141no—
338C22—3141no—
339C22—3141no—
340C22—6281no—
341C22—6281no—
342C22—6281no—
343C22—6281no—
344C22—6281no—
345C22—6281no—
346C22—6281no—
347C22—6281no—
348C22—6281no—
349C22C2×D4×D15711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—41no—
354C4—41no—
355C4—3141no—
356C4—3141no—
357C4—3141no—
358C4—6281no—
359C4#1909781711yescharacteristic
360C4#1909781911yescharacteristic
361C2—81no—
362C2—6281no—
363C2—12561no—
364C2—12561no—
365C2—12561no—
366C2#2375785311yescharacteristic
367C2#2375807511yescharacteristic
368C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#478×C157C2
socleC22×C157C22×D4
hypercenter#478D157
hypocenterC157#3259
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #23757879C2semidirect
2. #23757874C2semidirect
3. #23757576C2semidirect
4. #23757572C2semidirect
5. #23757570C2semidirect
6. #23757527C2semidirect
7. #23757525C2semidirect
8. #23757510C2semidirect
9. #23757508C2semidirect
10. #23757469C2semidirect
11. #23757468C2semidirect
12. #23757467C2semidirect
13. #23757467C2semidirect
14. #23757298C2semidirect
15. #478×C157C2semidirect
184. C157#3259semidirect
191. #478D157semidirect

Maximal subgroups

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

subgroupindex
#237578792
#237578742
#237575762
#237575722
#237575702
#237575272
#237575252
#237575102
#237575082
#237574692
#237574682
#237574672
#237572982
#478×C1572
#3259157