Finite Group Databasebeta

← #34111573

Subgroups — #34111573

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#23757877C211yesmaximal, characteristic, complemented
2#23757874C211yesmaximal, characteristic, complemented
3#23757575C211yesmaximal, characteristic, complemented
4#23757574C211yesmaximal, characteristic, complemented
5#23757573C211yesmaximal, characteristic, complemented
6#23757571C211yesmaximal, characteristic, complemented
7#23757525C211yesmaximal, characteristic, complemented
8#23757523C211yesmaximal, characteristic, complemented
9#23757508C211yesmaximal, characteristic, complemented
10#23757506C211yesmaximal, characteristic, complemented
11#23757466C211yesmaximal, characteristic, complemented
12#23757466C211yesmaximal, characteristic, complemented
13#23757465C211yesmaximal, characteristic, complemented
14#23757298C211yesmaximal, characteristic, complemented
15#459×C157C211yesmaximal, characteristic, complemented
16C2×#14578939C2211yescharacteristic
17C2×#14578939C2211yescharacteristic
18C2×#14578937C2211yescharacteristic
19C2×C8×D157C2211yescharacteristic
20#19097767C2211yescharacteristic
21#19097763C2211yescharacteristic
22#19097762C2211yescharacteristic
23#19097754—21no—
24#19097753—21no—
25#19097752—21no—
26#19097752—21no—
27#19097746C2211yescharacteristic
28#19097745—21no—
29#19097744—21no—
30#19097743—21no—
31#19097743—21no—
32#19097742C2211yescharacteristic
33#19097742C2211yescharacteristic
34#19097742C2211yescharacteristic
35C4×D628C2211yescharacteristic
36D4×Dic157C2211yescharacteristic
37D4×Dic157C2211yescharacteristic
38#19097728C2211yescharacteristic
39#19097705C2211yescharacteristic
40#19097704C2211yescharacteristic
41#19097703C2211yescharacteristic
42#19097702C2211yescharacteristic
43C4⋊#11929434C2211yescharacteristic
44#19097700C2211yescharacteristic
45#19097700C2211yescharacteristic
46#19097693C2211yescharacteristic
47#19097693C2211yescharacteristic
48#19097692C2211yescharacteristic
49#19097692C2211yescharacteristic
50#19097692C2211yescharacteristic
51#19097692C2211yescharacteristic
52C2×D8×C157C2211yescharacteristic
53C2×D8×C157C2211yescharacteristic
54#127×C157C2211yescharacteristic
55C4×D4×C157C2211yescharacteristic
56C4⋊C8×C157C2211yescharacteristic
57#102×C157C2211yescharacteristic
58#102×C157C2211yescharacteristic
59C2×D628—21no—
60C2×D628C2311yescharacteristic
61C2×C22⋊D157—21no—
62C2×C22⋊D157—21no—
63C2×C22⋊D157—21no—
64C2×C22⋊D157—21no—
65C2×C22⋊D157—21no—
66C22×Dic157—21no—
67C22×Dic157—21no—
68C2×C4×D157—21no—
69C2×C4×D157C2311yescharacteristic
70#14578939—41no—
71#14578939—41no—
72#14578937—41no—
73C2×#11929434C2311yescharacteristic
74C2×#11929434C2311yescharacteristic
75C8×D157—41no—
76C4⋊Dic157—21no—
77C4⋊Dic157C2311yescharacteristic
78C4⋊Dic157C2311yescharacteristic
79C4⋊Dic157C2311yescharacteristic
80#14578933—21no—
81#14578933—21no—
82#14578933—21no—
83#14578933D411yescharacteristic
84#14578933D411yescharacteristic
85C22⋊Dic157—21no—
86C22⋊Dic157—21no—
87C22⋊Dic157—21no—
88C22⋊Dic157—21no—
89C22⋊Dic157—21no—
90#14578931—21no—
91#14578931—21no—
92#14578931D411yescharacteristic
93#14578931D411yescharacteristic
94C4×Dic157C2311yescharacteristic
95C2×D4×C157—21no—
96C2×D4×C157—21no—
97C2×D4×C157C2311yescharacteristic
98C2×D4×C157C2311yescharacteristic
99C2×D4×C157C2311yescharacteristic
100C22×C4×C157—21no—
101D8×C157—41no—
102D8×C157—41no—
103C2×C8×C157C2311yescharacteristic
104C2×C8×C157C2311yescharacteristic
105C4⋊C4×C157C2311yescharacteristic
106C22⋊C4×C157—21no—
107C42×C157C2311yescharacteristic
108C22×D157—21no—
109C22×D157C2×D411yescharacteristic
110D628—21no—
111D628—21no—
112D628—81no—
113C22⋊D157—81no—
114C22⋊D157—81no—
115C22⋊D157—81no—
116C22⋊D157—81no—
117C22⋊D157—81no—
118C2×Dic157—21no—
119C2×Dic157—21no—
120C2×Dic157—21no—
121C2×Dic157—81no—
122C2×Dic157—81no—
123C2×Dic157C2×D411yescharacteristic
124C2×Dic157C2×D411yescharacteristic
125C2×Dic157C2×D411yescharacteristic
126C4×D157—21no—
127C4×D157—21no—
128C4×D157—81no—
129#11929434—21no—
130#11929434—21no—
131C23×C157—21no—
132C23×C157—21no—
133C23×C157—21no—
134D4×C157—21no—
135D4×C157—21no—
136D4×C157—21no—
137D4×C157—21no—
138D4×C157—21no—
139D4×C157—21no—
140D4×C157—81no—
141D4×C157—81no—
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×C157—41no—
153C22×C157—41no—
154C22×C157—41no—
155C22×C157—41no—
156C22×C157—41no—
157C22×C157—41no—
158C22×C157C22×D411yescharacteristic
159C2×D157—21no—
160C2×D157—21no—
161C2×D157—21no—
162C2×D157—41no—
163C2×D157—41no—
164C2×D157—41no—
165C4×C157—21no—
166C4×C157—21no—
167C4×C157—41no—
168C4×C157H(5,𝔽2)11yescharacteristic
169C4×C1572−1+411yescharacteristic
170Dic157—21no—
171Dic157—21no—
172Dic157—21no—
173Dic157—41no—
174Dic157—41no—
175Dic157—41no—
176C2×C157—81no—
177C2×C157—81no—
178C2×C157—81no—
179C2×C157#53711yescharacteristic
180C2×C157#57611yescharacteristic
181C2×C157#57611yescharacteristic
182D157—41no—
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#478—1571no—
192#469—1571no—
193#469—1571no—
194#466—1571no—
195#466—1571no—
196#459—1571no—
197#459—1571no—
198#459—1571no—
199#459D15711yescharacteristic, complemented
200#424—1571no—
201C2×D8—1571no—
202C2×D8—1571no—
203C2×D8C2×D15711yescharacteristic
204C2×D8C2×D15711yescharacteristic
205C2×M16—1571no—
206C22×C8—1571no—
207#127—1571no—
208#127C2×D15711yescharacteristic
209#125—1571no—
210#125—1571no—
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#107—1571no—
230#106—1571no—
231#106—1571no—
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—21no—
245C2×D4—21no—
246C2×D4—3141no—
247C2×D4—3141no—
248C2×D4—3141no—
249C2×D4—3141no—
250C2×D4—3141no—
251C2×D4—3141no—
252C2×D4—1571no—
253C2×D4C22×D15711yescharacteristic
254C2×D4C22×D15711yescharacteristic
255C2×D4C22×D15711yescharacteristic
256C22×C4—21no—
257C22×C4—3141no—
258C22×C4—3141no—
259C22×C4—3141no—
260C22×C4—1571no—
261D8—41no—
262D8—41no—
263D8—6281no—
264D8—6281no—
265M16—6281no—
266C2×C8—6281no—
267C2×C8—1571no—
268C2×C8—1571no—
269C2×C8C22×D15711yescharacteristic
270C2×C8C22×D15711yescharacteristic
271C4⋊C4—3141no—
272C4⋊C4—3141no—
273C4⋊C4—3141no—
274C4⋊C4—3141no—
275C4⋊C4—1571no—
276C4⋊C4—1571no—
277C4⋊C4—1571no—
278C4⋊C4—1571no—
279C4⋊C4—1571no—
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—21no—
295C23—21no—
296C23—3141no—
297C23—1571no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—21no—
303D4—21no—
304D4—81no—
305D4—81no—
306D4—3141no—
307D4—3141no—
308D4—12561no—
309D4—12561no—
310D4—12561no—
311D4—12561no—
312D4—12561no—
313D4—12561no—
314C2×C4—21no—
315C2×C4—81no—
316C2×C4—3141no—
317C2×C4—3141no—
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—41no—
338C22—41no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—3141no—
344C22—3141no—
345C22—3141no—
346C22—6281no—
347C22—6281no—
348C22—6281no—
349C22C2×D4×D15711yescharacteristic
350C4—21no—
351C4—21no—
352C4—41no—
353C4—3141no—
354C4—3141no—
355C4—3141no—
356C4—6281no—
357C4—6281no—
358C4—6281no—
359C4#1909781611yescharacteristic
360C4#1909781811yescharacteristic
361C2—81no—
362C2—81no—
363C2—81no—
364C2—6281no—
365C2—12561no—
366C2#2375785211yescharacteristic
367C2#2375807411yescharacteristic
368C2#2375807711yescharacteristic
subgroupG/H
centerC22C2×D4×D157
commutator, cosocleC2×C4×C157C24
FrattiniC2×C4C23×D157
Fitting#459×C157C2
socleC22×C157C22×D4
hypercenter#459D157
hypocenterC157#3259
LCSG ▷ C2×C4×C157 ▷ C2×C157 ▷ C157
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #23757877C2semidirect
2. #23757874C2semidirect
3. #23757575C2semidirect
4. #23757574C2semidirect
5. #23757573C2semidirect
6. #23757571C2semidirect
7. #23757525C2semidirect
8. #23757523C2semidirect
9. #23757508C2semidirect
10. #23757506C2semidirect
11. #23757466C2semidirect
12. #23757466C2semidirect
13. #23757465C2semidirect
14. #23757298C2semidirect
15. #459×C157C2semidirect
184. C157#3259semidirect
199. #459D157semidirect

Maximal subgroups

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

subgroupindex
#237578772
#237578742
#237575752
#237575742
#237575732
#237575712
#237575252
#237575232
#237575082
#237575062
#237574662
#237574652
#237572982
#459×C1572
#3259157